diff --git a/navipy/forecasting/src/ESNs/ESN.m b/navipy/forecasting/src/ESNs/ESN.m
new file mode 100644
index 0000000000000000000000000000000000000000..da899bd6e73ad78d6738be1eda2c4bc9bf191dce
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/ESN.m
@@ -0,0 +1,409 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%          Copyright (c) 2013 R. F. Reinhart, CoR-Lab                 %%%
+%%%          Bielefeld University, Germany, http://cor-lab.de           %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Modified by Alexander Schulz and Benjamin Paaßen in 2017
+% ( {aschulz,bpaassen}@techfak.uni-bielefeld.de)
+
+
+classdef ESN < Learner
+%ESN Summary of this class goes here
+%   Detailed explanation goes here
+%
+%
+    
+    properties
+    
+        hidDim = 10;        % number of neurons in the hidden layer
+        wInp = [];          % weights from input layer to hidden layer
+        wRes = [];          % weights from hidden layer to hidden layer
+        wOut = [];          % weights from hidden layer to output layer
+        bias = [];          % bias parameters for activation function
+        a = [];             % activation of the hidden layer
+        %aNew = [];          % temporal activation, weighted with dt and added to old activation
+        h = [];             % set by the act function
+        h_old = [];
+        y = [];             % is this really needed?
+        
+        h_init = [];        % initial hidden state. used if use_init_h == 1
+        use_init_h = 0;     % variable indicating whether after each 
+                            % subsequence the initial state should be
+                            % resumed
+        
+        collectH = 0;       % specifies if the hidden states should be saved
+        Hcoll    = [];      % memory for saving hidden states
+                            
+        % statistics for incremental learning
+        HTH = [];           % statistic to store H' * H
+        HTY = [];           % statistic to store H' * Y
+        
+        universRes = 1;     % use Tino's 'Cycle Reservoir with Jumps' (CRJ)
+                            % or a standard random reservoir
+        universResPars =... % params for the CRJ reservoir: the absolute 
+          0.1 * [1 1 1 50]; % magnitude of input weights, the circular and 
+                            % jump connection strengths r_c and r_j and the
+                            % jump distance between neurons
+                            
+        linearESN = 0;      % use a linear ESN, i.e. no sigmoid functions
+        useReLU   = 0;      % use tanh or a ReLU activation function
+        psdRes    = 0;      % use a psd reservoir. good with RelUs?
+
+        dt = 1;             % factor for weighting the contribution of the new reservoir activation
+        inpScale = 1;       % scaling for input weights
+        biasScale = 0;      % scaling for bias
+        inpDensity = 1;     % density of input weights matrix
+        resDensity = 0.2;   % density of reservoir weights matrix
+        reg = 1e-6;         % regularization parameter for ridge regression
+        specRad = 0.95;     % spectral radius for the reservoir weights matrix
+        woSteps = 200;      % washout steps applied to the beginning of each sequence
+        convergeSteps = 0;  % if >0 the net is fed with the first data vector convergeSteps times before train/apply
+        %batchSize = 1000;  % number of samples used for a minibatch
+        
+    end
+    
+    methods
+        function l = ESN(inpDim, outDim, spec)
+            l = l@Learner(inpDim, outDim, spec);
+        end
+
+        function updateFromJSON(l, json)
+            fields = fieldnames(json.esn);
+            for f=1:numel(fields)
+                l.(fields{f}) = json.esn.(fields{f});
+            end
+        end
+        
+        function init(l, X)  
+           if l.universRes == 0
+               % use a random reservoir
+               if l.inpDensity == 1
+                   l.wInp = l.inpScale * (2 * rand(l.hidDim,l.inpDim) - ones(l.hidDim,l.inpDim));
+               else
+                   l.wInp = createSparseMatrix(l.hidDim, l.inpDim, l.inpDensity, l.inpScale);
+               end
+               %l.wRes = 2 * rand(l.hidDim,l.hidDim) - ones(l.hidDim,l.hidDim);
+               if (l.resDensity > 0)
+                   if ~l.psdRes
+                       l.wRes = createSparseMatrix(l.hidDim, l.hidDim, l.resDensity, 1);
+                   
+                   else
+                       useVariant = 3;
+                       
+                       if useVariant == 1
+                           % variant 1: compute a scalar product.
+                           % It is not sparse
+                           l.wRes = createSparseMatrix(l.hidDim, l.hidDim, l.resDensity, 1);
+                           % use psd matrices with ReLU activations
+                           l.wRes = l.wRes * l.wRes' + eye(l.hidDim);
+                       elseif useVariant == 2
+                           % variant 2: use sprandsym. Quote from the doc:
+                           % It has a great deal of topological and 
+                           % algebraic structure.
+                           l.wRes = sprandsym(l.hidDim, l.resDensity, (1+rand(l.hidDim,1))/2);
+                       elseif useVariant == 3
+                           % variant 3: set symmetric random values
+                           % there are l.hidDim*(l.hidDim-1)/2 elements in the
+                           % upper triangle of a matrix.
+                           % set random values for off diagonal elements
+                           randPos   = randperm(round(l.hidDim*(l.hidDim-1)/2));
+                           nonZeroE  = round(l.resDensity*l.hidDim*(l.hidDim-1)/2);
+                           randVals1 = zeros(round(l.hidDim*(l.hidDim-1)/2),1);
+                           randVals1(randPos(1:nonZeroE)) = randu(nonZeroE,1);
+                           % set random values for off diagonal elements
+                           randPos   = randperm(l.hidDim);
+                           nonZeroE  = round(l.resDensity*l.hidDim);
+                           randVals2 = zeros(l.hidDim,1);
+                           randVals2(randPos(1:nonZeroE)) = randu(nonZeroE,1);
+                               
+                           l.wRes = sparse(squareform(randVals1) + diag(randVals2));
+                           l.wRes(1:l.hidDim+1:end) = l.wRes(1:l.hidDim+1:end) ...
+                               - eigs(l.wRes, 1,'sa');
+                       end
+                   end
+                   
+                   % old scaling
+                   %sr     = max(abs(eigs(l.wRes)));
+                   %l.wRes = (l.specRad / sr) .* l.wRes;
+                   
+                   % use the effective spectral radius for leaky integrator
+                   sr = max(abs(eigs(l.dt*l.wRes  + (1-l.dt)*eye(l.hidDim))));
+                   l.wRes = ((l.specRad -(1-l.dt)) / (sr-(1-l.dt))) .* l.wRes;
+               else
+                   l.wRes = zeros(l.hidDim);
+               end    
+           else
+               % use Peter Tino's CRJ
+               % set the input weights
+               currPath   = mfilename('fullpath');
+               currPath   = currPath(1:end-3);
+               piDecExpan = loadjson([currPath 'pi_8000.json']);
+               piDecExpan = piDecExpan.pi8000(1:l.hidDim*l.inpDim);
+               
+               tmpInp = (-1) * l.universResPars(1) * (piDecExpan < 4.5);
+               tmpInp = tmpInp + l.universResPars(1) * (piDecExpan > 4.5);
+               l.wInp = reshape(tmpInp, l.hidDim, l.inpDim);
+               clear tmpInp piDecExpan;
+               
+               % set the reservoir weights
+               l.wRes = spalloc(l.hidDim, l.hidDim, ...
+                   l.hidDim + 2*floor(l.hidDim/l.universResPars(4)));
+               % set the circular connection weights
+               circ_idx = 2:l.hidDim+1:l.hidDim^2;
+               l.wRes(circ_idx) = l.universResPars(2);
+               l.wRes(1, l.hidDim) = l.universResPars(2);
+               % set the jump weights
+               nextToLast = (lower(l.hidDim/l.universResPars(4))-2)*l.universResPars(4) + 1;
+               jump_idx   = (1:l.universResPars(4):nextToLast)';
+               jump_idx   = [jump_idx+l.universResPars(4) jump_idx];
+               if mod(l.hidDim, l.universResPars(4)) == 0
+                   jump_idx(end+1, :) = [1 jump_idx(end,1)];
+               else
+                   jump_idx(end+1, :) = [jump_idx(end,1)+l.universResPars(4) jump_idx(end,1)];
+               end
+               
+               jump_idx1  = (jump_idx(:,2)-1)*l.hidDim + jump_idx(:,1);
+               jump_idx2  = (jump_idx(:,1)-1)*l.hidDim + jump_idx(:,2);
+               l.wRes(jump_idx1) = l.universResPars(3);
+               l.wRes(jump_idx2) = l.universResPars(3);
+               clear circ_idx jump_idx jump_idx1 jump_idx2 nextToLast
+           end
+           
+           l.wOut  = zeros(l.hidDim, l.outDim);
+           l.bias  = l.biasScale * (2 * rand(l.hidDim,1) - ones(l.hidDim,1));
+           l.h     = zeros(l.hidDim,1);
+           l.h_old = zeros(l.hidDim,1);
+           l.a     = zeros(size(l.h));
+           %l.aNew = zeros(size(l.h));
+           l.y     = zeros(1,l.outDim);
+           
+           %not required
+           %if nargin > 1
+           %     l.normalizeIO(X);
+           %end
+        end
+        
+        function train(l, X, Y)
+            if iscell(X)
+                % check if the input normalization is already set
+                if isempty(l.inpOffset)
+                    l.normalizeIO(cell2mat(X), cell2mat(Y));
+                end
+                l.HTH = zeros(l.hidDim, l.hidDim);
+                l.HTY = zeros(l.hidDim, l.outDim);                
+                numSequences = length(X);
+                for i=1:numSequences
+                    X{i} = range2norm(X{i}, l.inpRange, l.inpOffset);
+                    Y{i} = range2norm(Y{i}, l.outRange, l.outOffset);
+                    
+                    if l.convergeSteps > 0
+                        convergenceInput = repmat(X{i}(1,:), l.convergeSteps, 1);
+                        l.calcHiddenStates(convergenceInput);
+                    end
+                    
+                    if l.use_init_h
+                        l.h = l.h_init;
+                    end
+                    H = l.calcHiddenStates(X{i});
+                    if l.woSteps > size(X{i},1)
+                        warning(['washout longer than sequence ' num2str(i)]);
+                        return;
+                    end
+                    H = H(l.woSteps+1:end,:);
+                    l.HTH = l.HTH + H' * H;
+                    l.HTY = l.HTY + H' * Y{i}(l.woSteps+1:end,:);
+                end
+                HTH = l.HTH + diag(repmat(l.reg, 1, l.hidDim));
+                l.wOut = HTH\l.HTY;
+            else
+                % check if the input normalization is already set
+                if isempty(l.inpOffset)
+                    [X, Y] = l.normalizeIO(X, Y);
+                else
+                    if l.inpNormalization
+                        X = range2norm(X, l.inpRange, l.inpOffset);
+                    end
+                    if l.outNormalization
+                        Y = range2norm(Y, l.outRange, l.outOffset);
+                    end
+                end
+                
+                if l.convergeSteps > 0
+                    convergenceInput = repmat(X(1,:), l.convergeSteps, 1);
+                    l.calcHiddenStates(convergenceInput);
+                end
+                
+                if l.use_init_h
+                    l.h = l.h_init;
+                end
+                numSamples = size(X,1);
+                H = l.calcHiddenStates(X);
+                
+                if l.woSteps > numSamples
+                    warning('washout longer than sequence');
+                    return;
+                end
+                Y = Y(l.woSteps+1:end,:);
+                H = H(l.woSteps+1:end,:);
+                l.HTH  = H' * H;
+                l.HTY  = H' * Y;
+                l.wOut = (l.HTH + l.reg * eye(l.hidDim))\(l.HTY);
+            end
+        end
+        
+        % This function implements an online least squares method. 
+        % Before the first run, a manual washout should be performed by
+        % executing
+        %   l.calcHiddenStates(X);
+        % for woSteps number of samples.
+        % No forgetting rate is currently implemented.
+        function train_online(l, X, Y)
+            if isempty(l.HTH) || isempty(l.HTY)
+                % if no prior training has been performed (either batch or
+                % online): initialize statistics with zeros
+                l.HTH = zeros(l.hidDim, l.hidDim);
+                l.HTY = zeros(l.hidDim, l.outDim);
+            end
+            
+            if l.inpNormalization
+                X = range2norm(X, l.inpRange, l.inpOffset);
+            end
+            if l.outNormalization
+                Y = range2norm(Y, l.outRange, l.outOffset);
+            end
+            
+            
+            if l.convergeSteps > 0
+                convergenceInput = repmat(X(1,:), l.convergeSteps, 1);
+                l.calcHiddenStates(convergenceInput);
+            end
+            
+            % update the statistics
+            H = l.calcHiddenStates(X);
+            l.HTH = l.HTH + H' * H;
+            l.HTY = l.HTY + H' * Y;
+            
+            % compute the new weights
+            l.wOut = (l.HTH + l.reg * eye(l.hidDim))\(l.HTY);
+            %l.wOut = l.HTH\(l.HTY);
+        end
+        
+        function [Y] = apply(l, X)
+            if iscell(X)
+                Y = cell(length(X),1);
+                for i=1:length(X)
+                    Y{i} = l.apply(X{i});
+                end
+            else
+                if (l.inpNormalization)
+                    X = range2norm(X, l.inpRange, l.inpOffset);
+                end
+                %l.calcHiddenStates(repmat(X(1,:), l.woSteps, 1)); %washout transients
+                
+                if l.convergeSteps > 0
+                    convergenceInput = repmat(X(1,:), l.convergeSteps, 1);
+                    l.calcHiddenStates(convergenceInput);
+                end
+                
+                if l.use_init_h
+                    l.h = l.h_init;
+                end
+                H = l.calcHiddenStates(X);
+                if l.collectH
+                    l.Hcoll = H;
+                end
+                
+                Y = H * l.wOut;
+                if (l.outNormalization)
+                    Y = norm2range(Y, l.outRange, l.outOffset);
+                end
+                l.out = Y(end,:);
+            end
+        end
+
+        % input to calcHiddenStates is always one sequence (steps x dim)
+        function [H] = calcHiddenStates(l, X)
+            numSamples = size(X,1);
+            H = zeros(numSamples, l.hidDim);
+            for k=1:numSamples
+                l.act(X(k,:));
+                H(k,:) = l.h;
+            end
+        end
+
+        function act(l, x)
+            l.a = l.wInp * x' + l.wRes * l.h + l.bias;
+            % Hx1 = HxI * (1xI)' + HxH * Hx1 + Hx1
+            if l.linearESN
+                l.h = l.a;
+            else
+                % nonlinear activation function
+                if l.useReLU
+                    l.h = l.a;
+                    l.h(l.h<0) = 0;
+                else
+                    l.h = tanh(l.a);
+                end
+            end
+            
+            if l.dt ~= 1
+                l.h     = (1-l.dt) * l.h_old + l.dt * l.h;
+                l.h_old = l.h;
+            end
+        end
+        
+        % If this method is used, the data normalization constants should 
+        % be set in advance. Use
+        %   l.normalizeIO(X, Y); 
+        % for this purpose.
+        function set_initState(l, X)
+            if l.inpNormalization
+                X = range2norm(X, l.inpRange, l.inpOffset);
+            end
+            H = l.calcHiddenStates(X);
+            l.h_init = H(end,:)';
+        end
+        
+        % new function performing a json export of a trained reservoir.
+        % str specifies the name of the output
+        % if mode == 1, the method will export only the output weights,
+        % if mode == 2, everything is exported
+        function export(l, str, mode)
+            if nargin < 3
+                mode = 1;
+            end
+            
+            if mode == 1
+                savejson('esn', l.wOut', str);
+            elseif mode == 2
+                % select the properties to be stored
+                res.inpDim     = l.inpDim;
+                res.hidDim     = l.hidDim;
+                res.outDim     = l.outDim;
+
+                res.wInp       = l.wInp;
+                res.inpOffset  = l.inpOffset;
+                res.inpRange   = l.inpRange;
+
+                res.bias       = l.bias;
+                res.dt         = l.dt;
+                res.universRes = l.universRes;
+                res.wRes       = l.wRes;
+
+                res.outOffset  = l.outOffset;
+                res.outRange   = l.outRange;
+
+                savejson('esn', res, str);
+            end
+        end
+
+        function reset(l)
+           l.h     = zeros(l.hidDim,1);
+           l.h_old = zeros(l.hidDim,1);
+           l.a     = zeros(size(l.h));
+           %l.aNew = zeros(size(l.h));
+           l.y     = zeros(1,l.outDim);
+        end
+    end
+    
+end
+
diff --git a/navipy/forecasting/src/ESNs/Learner.m b/navipy/forecasting/src/ESNs/Learner.m
new file mode 100644
index 0000000000000000000000000000000000000000..1f6c4cb10c1b53cb527f66119d1e3d4c8fd26031
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/Learner.m
@@ -0,0 +1,84 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%          Copyright (c) 2013 R. F. Reinhart, CoR-Lab                 %%%
+%%%          Bielefeld University, Germany, http://cor-lab.de           %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+classdef Learner < handle
+    %LEARNER Interface class for function approximator models.
+    %   Detailed explanation goes here
+    
+    properties
+        inpDim = 0; %dimension of input
+        outDim = 0; %dimension of output
+        out = [];
+        
+        inpNormalization = 1;   % (de)activates normalization of the input
+        outNormalization = 1;   % (de)activates normalization of the output
+        inpOffset = [];
+        inpRange = [];
+        outOffset = [];
+        outRange = [];
+    end
+    
+    methods
+        function l = Learner(inpDim, outDim, spec)
+            l.inpDim = inpDim;
+            l.outDim = outDim;
+            l.out = zeros(1,l.outDim);
+            
+            if nargin > 2
+                for s=1:size(spec,1)
+                    if ~strcmp(spec{s,1}, 'class')
+                        try
+                            l.(spec{s,1}) = spec{s,2};
+                        catch me
+                            disp(me.message);
+                        end
+                    end
+                end
+            end
+        end
+        
+        function [X Y] = normalizeIO(l, X, Y)
+            % default values for already normalized data
+            l.inpOffset = zeros(1, l.inpDim);
+            l.outOffset = zeros(1, l.outDim);
+            l.inpRange = repmat([-1; 1], 1, l.inpDim);
+            l.outRange = repmat([-1; 1], 1, l.outDim);
+            
+            if l.inpNormalization && nargin > 1
+                [X l.inpOffset l.inpRange] = normalize(X);
+            end
+            
+            if l.outNormalization && nargin > 2
+                [Y l.outOffset l.outRange] = normalize(Y);
+            end
+        end
+        
+        function init(l, X, Y)
+        end
+        
+        % expect X and Y to be either matrices or cell-arrays of matrices
+        function train(l, X, Y)
+        end
+        
+        function Y = apply(l, X)
+        end
+        
+        function new = copy(this)
+            new = feval(class(this));
+            p = properties(this);
+            for i = 1:length(p)
+                if( isa(this.(p{i}), 'handle'))
+                    new.(p{i}) = this.(p{i}).copy();
+                elseif isa(this.(p{i}),'cell')
+                    new.(p{i}) = deepCopyCellArray(numel(this.(p{i})));
+                else
+                    new.(p{i}) = this.(p{i});
+                end
+            end
+        end
+    end
+    
+end
+
diff --git a/navipy/forecasting/src/ESNs/chud_pi.m b/navipy/forecasting/src/ESNs/chud_pi.m
new file mode 100644
index 0000000000000000000000000000000000000000..b623a1daf35716d1832478b352ea2d3c06486974
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/chud_pi.m
@@ -0,0 +1,19 @@
+function P = chud_pi(d) 
+ % CHUD_PI Chudnovsky algorithm for pi. 
+ % chud_pi(d) produces d decimal digits. 
+ %
+ % From Mathworks:
+ % https://de.mathworks.com/company/newsletters/articles/computing-pi.html
+ 
+ k = sym(0); 
+ s = sym(0); 
+ sig = sym(1); 
+ n = ceil(d/14); 
+ for j = 1:n 
+     s = s + sig * prod(3*k+1:6*k)/prod(1:k)^3 * ... 
+     (13591409+545140134*k) / 640320^(3*k+3/2); 
+     k = k+1; 
+     sig = -sig; 
+ end 
+ S = 1/(12*s); 
+ P = vpa(S,d); 
\ No newline at end of file
diff --git a/navipy/forecasting/src/ESNs/compute_write_pi.m b/navipy/forecasting/src/ESNs/compute_write_pi.m
new file mode 100644
index 0000000000000000000000000000000000000000..c3954b76e32339e48b483b78add494440b48e3d1
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/compute_write_pi.m
@@ -0,0 +1,20 @@
+% create pi to a certain precision and write it to a file
+
+% compute Pi for a reservoir of size 1000 with 8 inputs
+num_digits = 8*1000;
+p = chud_pi(num_digits);
+
+% convert the sym number to a string
+piStr    = char(p);
+% represent each digit as an entry in a vector
+piVec    = zeros(numel(piStr)-1,1);
+piVec(1) = 3;
+for i = 3:numel(piStr)
+    piVec(i-1) = str2double(piStr(i));
+end
+
+% write it to a file
+savejson('pi8000', piVec,'pi_8000.json');
+
+% --- don't use the csv format for strings. they do not load
+% csvwrite(sprintf('pi_%i.csv', num_digits), piStr);
\ No newline at end of file
diff --git a/navipy/forecasting/src/ESNs/createSparseMatrix.m b/navipy/forecasting/src/ESNs/createSparseMatrix.m
new file mode 100644
index 0000000000000000000000000000000000000000..2f0cc5fa02cd8285dd822442f59e9e74ddde11ab
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/createSparseMatrix.m
@@ -0,0 +1,24 @@
+function [ M ] = createSparseMatrix(rows, cols, density, range)
+%CREATESPARSEMATRIX Summary of this function goes here
+%   Detailed explanation goes here
+
+if density == 1.0
+    M = randu(rows,cols,range);
+    return;
+end
+
+nonzero = max(0, min(round(density * rows * cols), rows * cols));
+
+M = zeros(rows, cols);
+p = randperm(rows * cols);
+
+for i=1:nonzero
+    row = ceil(p(i)/cols);
+    col = mod(p(i), cols) + 1;
+    M(row, col) = randu(1,1,range);
+end
+
+M = sparse(M);
+
+end
+
diff --git a/navipy/forecasting/src/ESNs/demo_addingProblem.m b/navipy/forecasting/src/ESNs/demo_addingProblem.m
new file mode 100644
index 0000000000000000000000000000000000000000..c222a099c1e802ff7a7868f41deb60bea7b143f2
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/demo_addingProblem.m
@@ -0,0 +1,62 @@
+% test ESN on the adding problem ... ESNs do not work well here
+% generate the data
+seqL    = 40;
+numS_tr = 10000;
+numS_te = 1000;
+
+X = cell(numS_tr+numS_te,1);
+Y = cell(numS_tr+numS_te,1);
+for s = 1:(numS_tr+numS_te)
+    X{s} = rand(seqL,1);
+    X{s} = [X{s}, zeros(seqL,1)];
+    % select two random entries
+    randIdx = randperm(seqL);
+    randIdx = randIdx(1:2);
+    X{s}(randIdx,2) = 1;
+    
+    Y{s} = repmat(sum(X{s}(randIdx,1)), seqL, 1);
+end
+
+X_tr = X(1:numS_tr);
+X_te = X(numS_tr+1:numS_tr+numS_te);
+Y_tr = Y(1:numS_tr);
+Y_te = Y(numS_tr+1:numS_tr+numS_te);
+
+%% apply the ESN model
+resS    = 200;
+reg     = 0.01;
+woSteps = 1; % dont do washout since the inportant position can be anywhere
+dimIn   = 2;
+dimOut  = 1;
+dtCons  = 0.4;
+specRad = 0.9;
+univRes = 0;
+linESN  = 0;
+useRelu = 0;
+lspecs  = {'class','ESN'; 'hidDim',resS; 'reg',reg; ...
+        'woSteps',woSteps; 'inpDim',dimIn; 'outDim',dimOut; ...
+        'dt', dtCons; 'specRad', specRad; 'universRes', univRes; ...
+        'linearESN', linESN; 'useReLU',useRelu; 'use_init_h', 1}; %; ...
+        %'universResPars', [v,rc,rj,jumps]; };
+                
+esn = ESN(dimIn, dimOut, lspecs);
+esn.init();
+% set the normalization constants
+esn.normalizeIO(cell2mat(X_tr), cell2mat(Y_tr));
+esn.set_initState([rand(seqL,1) zeros(seqL,1)]);
+esn.train(X_tr, Y_tr);
+
+preds_te = esn.apply(X_te);
+
+result_vals = zeros(numS_te,2);
+for i=1:numel(X_te)
+    result_vals(i,:) = [preds_te{i}(end) Y_te{i}(end)];
+end
+
+constMSE = mean((result_vals(:,2) - 1).^2)
+esnMSE   = mean((result_vals(:,2) - result_vals(:,1)).^2)
+
+
+
+
+
diff --git a/navipy/forecasting/src/ESNs/demo_memoryCapacity.m b/navipy/forecasting/src/ESNs/demo_memoryCapacity.m
new file mode 100644
index 0000000000000000000000000000000000000000..cfdf4272d5a06b347beddd5c665bf5332ed6bd20
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/demo_memoryCapacity.m
@@ -0,0 +1,104 @@
+% demo memory capacity
+% compute the memory capacity on a 1D signal as in
+% Jaeger: Short term memory in echo state networks, 2002
+
+%% generate the input
+seqL_tr = 200;
+seqL_te = 200;
+seqL    = seqL_tr + seqL_te;
+nRep    = 10;
+
+Xtmp = 2*rand(round(seqL/nRep), 1) -1;
+% copy each value 10 times to reproduce jaergers scenario
+X = zeros(seqL,1);
+count = 0;
+for i=1:nRep:seqL
+    count = count+1;
+    X(i:i+nRep-1) = repmat(Xtmp(count), nRep, 1);
+end
+
+X_tr = X(1:seqL_tr);
+X_te = X(seqL_tr+1:seqL_tr+seqL_te);
+
+%% generate the target, i.e. delay the input
+K = 40;
+Y = zeros(seqL,K);
+for k=1:K
+    Y(1:k,k)     = 2*rand(k, 1) -1;
+    Y(k+1:end,k) = X(1:end-k);
+end
+
+Y_tr = Y(1:seqL_tr, :);
+Y_te = Y(seqL_tr+1:seqL_tr+seqL_te, :);
+
+
+%% apply the ESN model
+resS    = 20;
+reg     = 0.00000;
+woSteps = 100;
+dimIn   = 1;
+dimOut  = K;
+dtCons  = 1; % no leaky rate as in jaegers paper
+specRad = 0.90;
+univRes = 0;
+linESN  = 0;
+psdRes  = 1;
+useRelu = 0;
+lspecs  = {'class','ESN'; 'hidDim',resS; 'reg',reg; 'inpScale', 1; ...
+        'woSteps',woSteps; 'inpDim',dimIn; 'outDim',dimOut; 'psdRes', psdRes; ...
+        'dt', dtCons; 'specRad', specRad; 'universRes', univRes; ...
+        'linearESN', linESN; 'useReLU',useRelu; 'use_init_h', 0}; %; ...
+        %'universResPars', [v,rc,rj,jumps]; };
+
+esn = ESN(dimIn, dimOut, lspecs);
+esn.init();
+esn.train(X_tr, Y_tr);
+
+
+preds_te = esn.apply(X_te);
+preds_te = preds_te(woSteps+1:end,:);
+Y_teEval = Y_te(woSteps+1:end,:);
+
+preds_tr = esn.apply(X_tr);
+preds_tr = preds_tr(woSteps+1:end,:);
+Y_trEval = Y_tr(woSteps+1:end,:);
+
+corrSq_tr = zeros(K,1);
+for k=1:K
+    corrSq_tr(k) = ...
+        mean((preds_tr(:,k) - mean(preds_tr(:,k))) .* (Y_trEval(:,k) - mean(Y_trEval(:,k))))/ ...
+        (std(preds_tr(:,k)) * std(Y_trEval(:,k)));
+    corrSq_tr(k) = corrSq_tr(k)^2;
+end
+
+corrSq = zeros(K,1);
+for k=1:K
+    corrSq(k) = ...
+        mean((preds_te(:,k) - mean(preds_te(:,k))) .* (Y_teEval(:,k) - mean(Y_teEval(:,k))))/ ...
+        (std(preds_te(:,k)) * std(Y_teEval(:,k)));
+    corrSq(k) = corrSq(k)^2;
+end
+MC = sum(corrSq);
+
+figure
+%myFigure; 
+subplot(1,2,1);
+plot(corrSq_tr); 
+title(['trainingm MC: ' num2str(sum(corrSq_tr))]); axis([0 K 0 1]);
+subplot(1,2,2); plot(corrSq); 
+title(['testing, MC: ' num2str(MC)]); axis([0 K 0 1]);
+
+% % plot example predictions
+% k = 7;
+% myFigure; hold on;
+% plot(1:size(Y_teEval,1), Y_teEval(:,k), 'b');
+% plot(1:size(preds_te,1), preds_te(:,k), 'g');
+% 
+% myFigure; hold on;
+% plot(1:size(Y_trEval,1), Y_trEval(:,k), 'b');
+% plot(1:size(preds_tr,1), preds_tr(:,k), 'g');
+
+
+
+
+
diff --git a/navipy/forecasting/src/ESNs/eval_contin_fun_pred.m b/navipy/forecasting/src/ESNs/eval_contin_fun_pred.m
new file mode 100644
index 0000000000000000000000000000000000000000..2dd54bcdd1352cf2be071e74dae39552cac2372d
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/eval_contin_fun_pred.m
@@ -0,0 +1,124 @@
+function [acc,classwiseAcc] = eval_contin_fun_pred(targets, preds, woSteps, showResults, colors, col_dofs, model)
+% This function receives a target signal and a prediction of a model.
+% It excepts the targets to be scaled from -1 to 1, with a three class
+% encoding consisting of classes -1, 0 and +1. The function removes all the
+% values in between this 
+
+if nargin < 4
+    showResults = 0;
+end
+if nargin < 7
+    model = '';
+end
+
+if ~iscell(targets)
+    targets = {targets};
+    preds   = {preds};
+end
+
+% compe an accuracy for each class in each Dof
+dofs    = size(targets{1},2);
+% there are 3 classes per degree of freedom: -1,0,1
+classes = [-1 0 1];
+
+numSeq        = numel(targets);
+accs          = zeros(numSeq, dofs);
+classwiseAccs = zeros(numel(classes), dofs, numSeq);
+for seq = 1:numSeq
+    % remove the first woSteps instances
+    predsS      = preds{seq}(woSteps:end,:);
+    targetsS    = targets{seq}(woSteps:end,:);
+    % remove the intermediate segments
+    addr_vec    = (abs(targetsS) <= 0.001) + (abs(targetsS) >= 0.99);
+    addr_vec    = logical(min(addr_vec, [], 2));
+    preds_cut   = round(predsS(addr_vec, :));
+    targets_cut = round(targetsS(addr_vec, :));
+
+    % compute the overall accuracy
+    accs(seq,:) = sum(preds_cut == targets_cut)/size(preds_cut,1);
+
+    for dof = 1:dofs
+        for cl = 1:numel(classes)
+            curr_class_idx = classes(cl) == targets_cut(:, dof);
+            curr_pred      = preds_cut(curr_class_idx, dof);
+            % compute the accuracy of class cl in degree of freedom dof
+            classwiseAccs(cl, dof, seq) = sum(curr_pred == classes(cl))/sum(curr_class_idx);
+        end
+    end
+end
+acc          = sum(accs,1)/numSeq;
+classwiseAcc = sum(classwiseAccs,3)/numSeq;
+
+
+% print the accuracy?
+if showResults > 0
+    if dofs == 1
+        disp(['=========' model '=Performance=========']);
+        fprintf('               DoF1     \n');
+        fprintf(' overall acc: %6.2f%%   \n', 100*acc(1));
+        disp(' -------------------------------');
+        fprintf(' cl ''-1'' acc: %6.2f%%    \n', 100*classwiseAcc(1,1));
+        fprintf(' cl  ''0'' acc: %6.2f%%    \n', 100*classwiseAcc(2,1));
+        fprintf(' cl ''+1'' acc: %6.2f%%    \n', 100*classwiseAcc(3,1));
+        disp('=================================');
+    elseif dofs == 2
+        disp(['=========' model '=Performance=========']);
+        fprintf('               DoF1      DoF2\n');
+        fprintf(' overall acc: %6.2f%%    %6.2f%%\n', 100*acc(1), 100*acc(2));
+        disp(' -------------------------------');
+        fprintf(' cl ''-1'' acc: %6.2f%%    %6.2f%%\n', 100*classwiseAcc(1,1), 100*classwiseAcc(1,2));
+        fprintf(' cl  ''0'' acc: %6.2f%%    %6.2f%%\n', 100*classwiseAcc(2,1), 100*classwiseAcc(2,2));
+        fprintf(' cl ''+1'' acc: %6.2f%%    %6.2f%%\n', 100*classwiseAcc(3,1), 100*classwiseAcc(3,2));
+        disp('=================================');
+    elseif dofs == 3
+        fprintf('The accuracy amounts to %5.2f%% %5.2f%% %5.2f%% \n', ...
+            100*acc(1), 100*acc(2), 100*acc(3));
+        % TODO: add the detailed accuracies
+    end
+end
+
+% do visualizations?
+if showResults > 1
+    myFigure; hold on;
+    nSamples = size(targets_cut,1);
+    hTar  = zeros(dofs,1);
+    hPred = zeros(dofs,1);
+    if showResults == 2
+        prettyShift = [0.005 -0.005];
+    elseif showResults == 3
+        prettyShift = [0 0];
+    end
+
+    % plot the target curve and the predictions
+    for dof=1:dofs
+        if showResults == 3
+            subplot(dofs,1,dof); hold on;
+        end
+
+        hTar(dof)  = plot(1:nSamples, targets_cut(:, dof)+prettyShift(dof), '-', 'Color', squeeze(colors(col_dofs(dof), 1, :)));
+        hPred(dof) = plot(1:nSamples, preds_cut(:, dof), 'o', 'Color', squeeze(colors(col_dofs(dof), 3, :)));
+        
+        currAx = axis;
+        axis([0 currAx(2) -1.1 1.1])
+    end
+
+    % add a legend and the accuracy
+    if showResults == 2
+        % use a brief accuracy description
+        legend([hTar; hPred], {'DoF1 gt', 'DoF2 gt', 'DoF1 pred', 'DoF2 pred'});
+        title(sprintf('%s Accuracy: DoF1: %5.2f%%, DoF2: %5.2f%%', model, 100*acc(1), 100*acc(2)));
+    elseif showResults == 3
+        % provide a detailed accuracy description
+        for dof=1:dofs
+            subplot(dofs,1,dof);
+            currDof = sprintf('DoF%i', dof);
+            legend([hTar(dof); hPred(dof)], {[currDof ' gt'], [currDof ' pred']});
+
+            title(sprintf('%s accs in DoF%i: %2.0f%%, %2.0f%%, %2.0f%%', ...
+                model, dof, 100*classwiseAcc(1,dof), ...
+                100*classwiseAcc(2,dof), 100*classwiseAcc(3,dof)));
+        end
+
+    end
+
+end
\ No newline at end of file
diff --git a/navipy/forecasting/src/ESNs/msl_example.m b/navipy/forecasting/src/ESNs/msl_example.m
new file mode 100644
index 0000000000000000000000000000000000000000..8ef6959347a7bf55d5a3d9a43fd6d8b0a35f0fb1
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/msl_example.m
@@ -0,0 +1,85 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%          Copyright (c) 2013 R. F. Reinhart, CoR-Lab                 %%%
+%%%          Bielefeld University, Germany, http://cor-lab.de           %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%Example for learning in the model space
+%The goal is to differentiate between two noisy sine waves
+
+length = 10000;
+sample_length = 100;
+noise_std = 0.1;
+n_samples = 2*length/sample_length
+N = 30;
+
+rng(42);
+t=[0:length]';
+sin1=sin(0.2*t)+noise_std*randn(length+1,1);
+sin2=sin(0.311*t)+noise_std*randn(length+1,1);
+
+X_mat = zeros(n_samples,sample_length);
+X = cell(n_samples,1);
+Y = cell(n_samples,1);
+ind = 1;
+for i=1:sample_length:length
+    X{ind} = sin1(i:i+sample_length-1);
+    X_mat(ind,:) = X{ind};
+    Y{ind} = sin1(i+1:i+sample_length);
+    ind = ind + 1;
+    X{ind} = sin2(i:i+sample_length-1);
+    X_mat(ind,:) = X{ind};
+    Y{ind} = sin2(i+1:i+sample_length);
+    ind = ind + 1;
+end
+sine1_ind = 1:2:n_samples;
+sine2_ind = 2:2:n_samples;
+
+
+% figure
+% plot(X{1})
+% figure;
+% plot(Y{1})
+
+lspecs = {'class','ESN'; 'hidDim',N; 'reg',1; 'woSteps',5; 'inpDim',1; 'outDim',1};
+%% create learner
+rng(42);
+learner = ESN(1, 1, lspecs);
+%cmd = ['learner = ' lspecs{1,2} '(inpDim, outDim, lspecs);'];
+%eval(cmd);
+learner.init(X(1:2));
+
+%% create models
+models = zeros(n_samples,N);
+for i=1:n_samples
+    learner.h = zeros(N,1);
+    learner.train(X(i), Y(i));
+    models(i,:) = reshape(learner.wOut, 1, numel(learner.wOut));
+end
+
+figure('position', [300, 150, 1000, 800])
+subplot(2,2,1:2)
+plot(sin1(1:500), 'b');
+hold on;
+plot(sin2(1:500), 'g');
+title('Signals');
+legend('sin(0.2)', 'sin(0.311)');
+
+subplot(2,2,3)
+[eigvalues eigvectors repr mX]= pca(X_mat, 2); 
+hold on;
+plot(repr(sine1_ind,1), repr(sine1_ind,2), 'bo')
+plot(repr(sine2_ind,1), repr(sine2_ind,2), 'go')
+legend('sin(0.2)', 'sin(0.311)');
+title('Signal Space')
+xlabel('pc1'); ylabel('pc2');
+
+subplot(2,2,4)
+[eigvalues eigvectors repr mX]= pca(models, 2); 
+plot(repr(sine1_ind,1), repr(sine1_ind,2), 'bo')
+hold on;
+plot(repr(sine2_ind,1), repr(sine2_ind,2), 'go')
+legend('sin(0.2)', 'sin(0.311)');
+title('Model Space')
+xlabel('pc1'); ylabel('pc2');
+hold off;
diff --git a/navipy/forecasting/src/ESNs/norm2range.m b/navipy/forecasting/src/ESNs/norm2range.m
new file mode 100644
index 0000000000000000000000000000000000000000..d96f6373e7084704942e3c783dff1639f8361daa
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/norm2range.m
@@ -0,0 +1,35 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%          Copyright (c) 2013 R. F. Reinhart, CoR-Lab                 %%%
+%%%          Bielefeld University, Germany, http://cor-lab.de           %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+function [y] = norm2range(x, ra, offset, minmax)
+%NORM2RANGE y = norm2range(x, ra, minmax)
+%   ra is a dim x 2 matrix holding min and max values per dimension
+%   minmax is repmat([-1 1], dim, 1) by default
+
+if nargin < 3
+    offset = zeros(1, size(x,2));
+end
+
+if nargin < 4
+    minmax = repmat([-1 1]', 1, size(x,2));
+end
+
+%cut exceeding dimensions
+ra = ra(:,1:min(size(ra,2), size(x,2)));
+x = x(:,1:min(size(ra,2), size(x,2)));
+
+tmp = minmax(2,:) - minmax(1,:);
+tmp(tmp==0) = 1;
+scale = 1./(tmp);
+range = (ra(2,:) - ra(1,:));
+
+%y = zeros(size(x));
+%for i=1:size(x,1)
+%    y(i,:) = (scale .* (x(i,:) - minmax(1,:))) .* range + ra(1,:);
+%    y(i,:) = y(i,:) + offset;
+%end
+
+y = repmat(scale .* range, size(x,1), 1) .* (x - repmat(minmax(1,:), size(x,1), 1)) + repmat(ra(1,:) + offset, size(x,1), 1);
diff --git a/navipy/forecasting/src/ESNs/normalize.m b/navipy/forecasting/src/ESNs/normalize.m
new file mode 100644
index 0000000000000000000000000000000000000000..5d4dcaf39ead0a58b66757739212ee3f9d45ed50
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/normalize.m
@@ -0,0 +1,18 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%          Copyright (c) 2013 R. F. Reinhart, CoR-Lab                 %%%
+%%%          Bielefeld University, Germany, http://cor-lab.de           %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+function [data offset range] = normalize(data)
+%NORMALIZE Summary of this function goes here
+%   Detailed explanation goes here
+
+offset = mean(data, 1);
+%data = data - repmat(offset, size(data,1), 1);
+data = bsxfun(@minus, data, offset);
+
+range = [min(data, [], 1); max(data, [], 1)];
+data = range2norm(data, range);
+
+end
diff --git a/navipy/forecasting/src/ESNs/pca.m b/navipy/forecasting/src/ESNs/pca.m
new file mode 100644
index 0000000000000000000000000000000000000000..419bda689c01852d250a8e293fc051787f13f78a
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/pca.m
@@ -0,0 +1,33 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%          Copyright (c) 2013 R. F. Reinhart, CoR-Lab                 %%%
+%%%          Bielefeld University, Germany, http://cor-lab.de           %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+function [eigvalues eigvectors coeffs mX] = pca(X, dim)
+%PCA Summary of this function goes here
+%   [eigvalues eigvectors coeffs mX] = pca(X, dim)
+
+numSamples = size(X,1);
+
+%remove mean
+mX = mean(X,1);
+X = X - repmat(mX, numSamples, 1);
+
+%calc covariance matrix
+C = X'*X;
+
+%calc eigenvectors and values
+[v, e] = eig(C);
+
+%sort eigenvalues and vectors
+% [eigvalues, indices] = sort(diag(e), 'descend');
+% eigvectors = v(:,indices);
+eigvalues = flipdim(diag(e),1); % eig returns everything in ascending order
+eigvectors = flipdim(v,2);
+
+%conduct transformation into pca-space using dim components
+coeffs = X * eigvectors(:,1:dim);
+
+end
+
diff --git a/navipy/forecasting/src/ESNs/pi_8000.json b/navipy/forecasting/src/ESNs/pi_8000.json
new file mode 100644
index 0000000000000000000000000000000000000000..d2e6f12d311c0ed6613b9a10aeff928588fe8746
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/pi_8000.json
@@ -0,0 +1,8004 @@
+{
+	"pi8000": [
+		[3],
+		[1],
+		[4],
+		[1],
+		[5],
+		[9],
+		[2],
+		[6],
+		[5],
+		[3],
+		[5],
+		[8],
+		[9],
+		[7],
+		[9],
+		[3],
+		[2],
+		[3],
+		[8],
+		[4],
+		[6],
+		[2],
+		[6],
+		[4],
+		[3],
+		[3],
+		[8],
+		[3],
+		[2],
+		[7],
+		[9],
+		[5],
+		[0],
+		[2],
+		[8],
+		[8],
+		[4],
+		[1],
+		[9],
+		[7],
+		[1],
+		[6],
+		[9],
+		[3],
+		[9],
+		[9],
+		[3],
+		[7],
+		[5],
+		[1],
+		[0],
+		[5],
+		[8],
+		[2],
+		[0],
+		[9],
+		[7],
+		[4],
+		[9],
+		[4],
+		[4],
+		[5],
+		[9],
+		[2],
+		[3],
+		[0],
+		[7],
+		[8],
+		[1],
+		[6],
+		[4],
+		[0],
+		[6],
+		[2],
+		[8],
+		[6],
+		[2],
+		[0],
+		[8],
+		[9],
+		[9],
+		[8],
+		[6],
+		[2],
+		[8],
+		[0],
+		[3],
+		[4],
+		[8],
+		[2],
+		[5],
+		[3],
+		[4],
+		[2],
+		[1],
+		[1],
+		[7],
+		[0],
+		[6],
+		[7],
+		[9],
+		[8],
+		[2],
+		[1],
+		[4],
+		[8],
+		[0],
+		[8],
+		[6],
+		[5],
+		[1],
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+}
diff --git a/navipy/forecasting/src/ESNs/randu.m b/navipy/forecasting/src/ESNs/randu.m
new file mode 100644
index 0000000000000000000000000000000000000000..b494499895b9f10b05fc3749487fd633170b8413
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/randu.m
@@ -0,0 +1,18 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%          Copyright (c) 2013 R. F. Reinhart, CoR-Lab                 %%%
+%%%          Bielefeld University, Germany, http://cor-lab.de           %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+function [ R ] = randu(rows, cols, range)
+%RANDU Summary of this function goes here
+%   Detailed explanation goes here
+
+if nargin < 3
+    range = 1;
+end
+
+R = range * 2.0 * (rand(rows, cols) - 0.5);
+
+end
+
diff --git a/navipy/forecasting/src/ESNs/range2norm.m b/navipy/forecasting/src/ESNs/range2norm.m
new file mode 100644
index 0000000000000000000000000000000000000000..168908d6b16c619660f7243b94f52cf8845c7f60
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/range2norm.m
@@ -0,0 +1,37 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%          Copyright (c) 2013 R. F. Reinhart, CoR-Lab                 %%%
+%%%          Bielefeld University, Germany, http://cor-lab.de           %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+function [y] = range2norm(x, ra, offset, minmax)
+%RANGE2NORM y = range2norm(x, ra, minmax)
+%   ra is a dim x 2 matrix holding min and max values per dimension
+%   minmax is repmat([-1 1], dim, 1) by default
+
+if nargin < 3
+    offset = zeros(1, size(x,2));
+end
+
+if nargin < 4
+    minmax = repmat([-1 1]', 1, size(x,2));
+end
+
+%cut exceeding dimensions
+ra = ra(:,1:min(size(ra,2), size(x,2)));
+x = x(:,1:min(size(ra,2), size(x,2)));
+
+tmp = ra(2,:) - ra(1,:);
+tmp(tmp==0) = 1;
+scale = 1 ./ (tmp);
+
+%y = zeros(size(x));
+%for i=1:size(x,1)
+    %y(i,:) = x(i,:) - offset;
+    %%y(i,:) = 2 * (((y(i,:) - ra(1,:)) .* scale) - 0.5);
+    %y(i,:) = ((minmax(2,:) - minmax(1,:)) .* ((y(i,:) - ra(1,:)) .* scale)) + minmax(1,:);
+%end
+
+y = repmat(minmax(2,:) - minmax(1,:), size(x,1), 1) .* (x - repmat(offset, size(x,1), 1) - repmat(ra(1,:), size(x,1), 1)) .* repmat(scale, size(x,1), 1) + repmat(minmax(1,:), size(x,1), 1);
+
+%y = bsxfun(@plus, bsxfun(@times, bsxfun(@times, minmax(2,:) - minmax(1,:), bsxfun(@minus, x, offset-ra(1,:))), scale), minmax(1,:));
diff --git a/navipy/forecasting/src/ESNs/raw.json b/navipy/forecasting/src/ESNs/raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..cde01cefd1fc7f6497688d6b6e6168c4a2286403
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/raw.json
@@ -0,0 +1,1004 @@
+{
+	"raw": [
+		[0.6675255606,0.4335105612,0.4530937042,0.7517335869,0.8036162693,0.7554009555,0.8591274931,0.7330609113],
+		[0.6213475916,0.7669851458,0.8400577404,1.303517896,1.544369158,1.510866374,1.30063414,1.246418467],
+		[1.084723501,1.053437089,1.072648373,1.406871407,1.455313074,1.485179537,1.461928248,1.561047426],
+		[0.9320144176,0.8422990524,0.9023250495,1.30835312,1.573236948,1.278878852,1.581632849,1.407851445],
+		[0.4459522295,0.5185789065,0.6675687766,0.7601044399,0.8579613134,0.7490120325,1.214213297,0.965949233],
+		[0.06575573297,0.2360384623,0.007431303128,0.0351024658,0.1909114892,0.1600933277,0.1546187636,0.3844660648],
+		[-0.3515091833,-0.3488957712,-0.3739876709,-0.6800535787,-0.3385566323,-0.4078141142,-0.7263498912,-0.3464784448],
+		[-0.426369557,-0.6845875742,-0.7820263782,-1.217911816,-0.835348606,-0.9749794161,-1.252782375,-1.297462968],
+		[-0.7096385849,-0.9982605985,-0.8542924106,-0.8991087019,-1.128951831,-1.115388624,-1.795249064,-1.638358521],
+		[-1.077283009,-0.94879044,-1.056918958,-0.8816949564,-1.262571864,-0.9374705043,-1.918894261,-1.693396412],
+		[-0.3589256708,-1.012187791,-0.6156191848,-0.6567496518,-0.8905202957,-0.6987951492,-1.198770996,-1.364512392],
+		[-0.1443864279,-0.3089415424,-0.1464262482,-0.110380366,-0.4566511414,-0.08730852762,-0.5312373278,-0.5955662829],
+		[0.2764939365,0.3148216729,0.1167142704,0.4418583263,0.06863205053,0.3100762882,0.361551229,0.2117735042],
+		[0.7832957071,0.6875158895,0.8887765116,0.8025036724,0.4969006855,0.9526183161,1.250216858,0.9154138384],
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+}
diff --git a/navipy/forecasting/src/ESNs/reservoir.json b/navipy/forecasting/src/ESNs/reservoir.json
new file mode 100644
index 0000000000000000000000000000000000000000..362012ee4822629702fcfe045b4e795cf4bb420c
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/reservoir.json
@@ -0,0 +1,18630 @@
+{
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+}
diff --git a/navipy/forecasting/src/ESNs/test.esn b/navipy/forecasting/src/ESNs/test.esn
new file mode 100644
index 0000000000000000000000000000000000000000..6aa179f807eb4aed915010be33515751c9c3a2de
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/test.esn
@@ -0,0 +1,19845 @@
+{
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+		"h": [
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+		],
+		"y": 0,
+		"HTH": null,
+		"HTY": null,
+		"dt": 0.7,
+		"inpScale": 1,
+		"biasScale": 0,
+		"inpDensity": 1,
+		"resDensity": 0.2,
+		"reg": 1e-05,
+		"specRad": 0.9,
+		"woSteps": 20,
+		"convergeSteps": 0,
+		"inpDim": 8,
+		"outDim": 1,
+		"out": 0,
+		"inpNormalization": 0,
+		"outNormalization": 0,
+		"inpOffset": null,
+		"inpRange": null,
+		"outOffset": null,
+		"outRange": null
+	}
+}
diff --git a/navipy/forecasting/src/ESNs/toy_example.m b/navipy/forecasting/src/ESNs/toy_example.m
new file mode 100644
index 0000000000000000000000000000000000000000..8b7a5b4a384fc6fdd6aa9abd090900c18ff00d15
--- /dev/null
+++ b/navipy/forecasting/src/ESNs/toy_example.m
@@ -0,0 +1,78 @@
+%% Some initial settings 
+clear all; close all; clc;
+%% generate the data
+
+nSamples = 1000;
+nChan    = 8;
+nOuts    = 3;
+X = zeros(nSamples , nChan);
+Y = zeros(nSamples , nOuts);
+
+for n = 1:nOuts
+    freq    = 0.02*pi;
+    Y(:, n) = sin(freq * (1:nSamples) + (2*n)/(3*freq));
+    Y(Y(:,n) < 0, n) = 0;
+end
+
+for n = 1:nChan
+    freq   = 0.5 + randn*0.01;
+    
+    if n <=3 
+        ampl = Y(:,1) + 1;
+    elseif n <=6
+        ampl = Y(:,2) + 1;
+    else
+        ampl = Y(:,3) + 1;
+    end
+    
+    X(:,n) = ampl.*sin(freq * (1:nSamples)') + randn(nSamples, 1) * 0.1;
+end
+
+figure; hold on;
+plot(1:nSamples, X(:,1), 'b');
+plot(1:nSamples, Y(:,1), 'g'); 
+hold off;
+
+%% initialize an ESN
+woSteps = 20;
+N = 300;
+
+lspecs = {'class','ESN'; 'hidDim',N; 'reg',1e-7; 'woSteps',woSteps; 'inpDim',8; 'outDim',3; 'dt', 0.25; 'specRad', 0.9; 'universRes', 0; 'linearESN', 0; 'useReLU', 0; 'psdRes', 0};
+esn = ESN(8, 3, lspecs);
+esn.init();
+
+esn.train(X, Y);
+
+%% apply the ESN
+
+esn.reset();
+Y_esn = esn.apply(X);
+
+%% Compare with linear regression
+
+W    = (X' * X + 1E-16 * eye(nChan)) \ X' * Y;
+
+Y_lr = X * W;
+
+%% plot the results
+
+addpath ../plotting/;
+
+colors = tango_color_scheme();
+
+figure;
+hold on;
+for dof=1:3
+    plot(1:nSamples, Y(:, dof),     '-',  'Color', squeeze(colors(dof, 1, :)));
+    plot(1:nSamples, Y_esn(:, dof), '-', 'Color', squeeze(colors(dof, 3, :)));
+    plot(1:nSamples, Y_lr(:, dof),  '--',  'Color', squeeze(colors(dof, 3, :)));
+end
+hold off;
+
+%% export results to JSON
+
+addpath ../jsonlab/;
+
+savejson('raw', X, 'raw.json');
+esn.export('reservoir.json', 2);
+esn.export('out.json', 1);
diff --git a/navipy/forecasting/src/Python/acf_pacf_lag_finder_script.py b/navipy/forecasting/src/Python/acf_pacf_lag_finder_script.py
new file mode 100644
index 0000000000000000000000000000000000000000..c26872205c1a6db96bae8dc248720c24a85bf19c
--- /dev/null
+++ b/navipy/forecasting/src/Python/acf_pacf_lag_finder_script.py
@@ -0,0 +1,76 @@
+from pandas import Series
+from matplotlib import pyplot
+from statsmodels.graphics.tsaplots import plot_acf
+from statsmodels.graphics.tsaplots import plot_pacf
+from statsmodels.tsa.stattools import acf
+from statsmodels.tsa.stattools import pacf
+import pdb
+
+def difference(dataset, interval=1):
+	diff = list()
+	for i in range(interval, len(dataset)):
+		value = dataset[i] - dataset[i - interval]
+		diff.append(value)
+	return Series(diff)
+
+	
+def find_lag(singe_dim_acf_val, corresponding_conf_val):
+	t = 0;
+	is_in_interv = False;
+	while (is_in_interv is False and t<len(singe_dim_acf_val)):
+		if(t<len(singe_dim_acf_val)):
+			upper_margin =  corresponding_conf_val[t, 1] - singe_dim_acf_val[t]
+			lower_margin =  corresponding_conf_val[t, 0] - singe_dim_acf_val[t]
+			if (singe_dim_acf_val[t] < upper_margin):
+				is_in_interv = True
+			if (singe_dim_acf_val[t] < 0 and singe_dim_acf_val[t] > lower_margin):
+				is_in_interv = True
+		else:
+			t=-1
+		t = t+1
+			
+	return (t-1)		
+
+lag_values = []
+trial = 1
+#for trial in range(0,len(tr)):
+traj = tr[trial]
+traj_lags = []
+series = []
+for dim in traj.keys():
+	h = []
+	series = traj[dim]
+	series = difference(series)
+	ac_val, conf_ac_val = acf(series,nlags=40, alpha=0.05)
+	pac_val, conf_pac_val = pacf(series,nlags=40, alpha=0.05)
+	ac_lags = find_lag(ac_val,conf_ac_val)
+	pac_lags = find_lag(pac_val,conf_pac_val)
+	h.append(ac_lags)
+	h.append(pac_lags)
+	traj_lags.append(h)
+	print('Done with dim:'+ dim)	
+print('Done with trial:'+ str(trial))	
+lag_values.append(traj_lags)	
+		
+plot_acf(series)
+pyplot.show(block=False)
+pdb.set_trace()
+plot_pacf(series)
+pyplot.show(block=False)
+
+		
+		
+'''
+pyplot.figure()
+pyplot.plot(ac_val,'*')
+pyplot.figure()
+pyplot.plot(conf_ac_val, '*')
+pyplot.figure()
+pyplot.plot(conf_ac_val[:, 0] - ac_val, '*')
+pyplot.figure()
+pyplot.plot(confs[:, 1] - ac_val, '*')
+
+plot_acf(series)
+pyplot.show(block=False)
+
+'''
diff --git a/navipy/forecasting/src/Python/analysis_script.py b/navipy/forecasting/src/Python/analysis_script.py
new file mode 100644
index 0000000000000000000000000000000000000000..e6835dcd4000078ab23a0bf8f09b774cba6e3895
--- /dev/null
+++ b/navipy/forecasting/src/Python/analysis_script.py
@@ -0,0 +1,134 @@
+import cozybank as cbank
+from matplotlib import pyplot as plt
+import pdb
+import pandas as pd
+import os
+import glob
+import datetime
+from pick import pick
+
+'''Specify Script options'''
+SINGLE = 0
+MULTIPLE = 1
+CHECK_STAB = 0
+				
+FIT_ARIMA = 1
+SAVE_PICKLES = 1	
+WITH_TRUE_PR_STEP = 1	
+NUM_OF_PREDS = 100
+DROP_SPEED = 1
+folders = glob.glob('data_mat\\charlotts\\*')
+
+#Specify ARIMA Parameters 
+LAG = 2#Autoregressive Part
+DIFF = 1	#Integrated Part
+ORDER = 0	#Moving Average Part 
+
+
+
+#load data
+if SINGLE ==1: 
+	title = 'Choose data set to summon!'
+	options = folders
+	foldername, index = pick(options,title)
+	train, test, esn_res, ids_res, spcs, foldernm = cbank.summon_data(foldername)
+	
+	if DROP_SPEED == 1:
+		for i in range(0,len(train)):
+			if spcs['target_type'][0][1] =='1': 
+				b = train[i].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+			else:
+				b = train[i].drop(['df_Cos','df_Sin'], axis=1) 
+			train[i] = b
+			del b
+		
+			if spcs['target_type'][0][5] =='1':
+				b = test[i].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+			else:
+				b = test[i].drop(['df_Cos','df_Sin'], axis=1) 
+			test[i] = b
+			del b 
+	PR_STEP = spcs['pr_step'][0]
+	#Get Results from ARIMA model
+	if FIT_ARIMA == 1:
+		#arima just casts 1-step ahead
+		result = cbank.execute(train,test,LAG,DIFF,ORDER, PR_STEP,NUM_OF_PREDS)
+		print('I am here')
+	
+	#Name of the files saved as results from arima
+	PICKLE_SAVE_NAME = 'L'+str(LAG)+'_D'+str(DIFF)+'_O'+str(ORDER)+'_ForecastWidth'+str(PR_STEP)
+	PICKLE_PATH_NAME = foldernm+'\\pickles\\'+PICKLE_SAVE_NAME+'\\'
+
+	if SAVE_PICKLES == 1:
+		if not os.path.exists(PICKLE_PATH_NAME):
+			os.makedirs(PICKLE_PATH_NAME)
+		for i in range(0,len(result)):
+			d = result[i]
+			nm = PICKLE_PATH_NAME+'pckl_' + '{0:03}'.format(i)
+			d.to_pickle(nm)
+	
+###################################################################################################
+###################################################################################################
+elif MULTIPLE ==1:
+	#mass summoning
+	#for fn in range(int(len(folders)/2),len(folders)):
+	#for fn in range(0,int(len(folders)/2)):
+	
+	for fn in range(0,len(folders)):
+		arima_res = []
+		folder = folders[fn]
+		print(folder)
+		#pdb.set_trace()
+		tr, te, esn_r, ids_r, spc, fldernm = cbank.summon_data(folder)
+		
+		if DROP_SPEED == 1:
+			for i in range(0,len(tr)):
+				if spc['target_type'][0][1] =='1': 
+					b = tr[i].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+				else:
+					if spc['is_charlotts'][0] == 0:
+						b = tr[i].drop(['df_Cos','df_Sin'], axis=1) 
+					else:
+						b = tr[i].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+				tr[i] = b
+				del b
+		
+				if spc['target_type'][0][5] =='1':
+					b = te[i].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+				else:
+					if spc['is_charlotts'][0] == 0:
+						b = te[i].drop(['df_Cos','df_Sin'], axis=1) 
+					else:
+						b = te[i].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+				
+				te[i] = b
+				del b
+	
+		#How far to cast into the future
+		PR_STEP = spc['pr_step'][0]
+		
+		if FIT_ARIMA == 1:
+			#arima just casts 1-step ahead
+			arima_res = cbank.execute(tr,te,LAG,DIFF,ORDER, PR_STEP,NUM_OF_PREDS)
+		
+		
+		PICKLE_SAVE_NAME = 'L'+str(LAG)+'_D'+str(DIFF)+'_O'+str(ORDER)+'_ForecastWidth'+str(PR_STEP)
+		PICKLE_PATH_NAME = fldernm+'\\pickles\\'+PICKLE_SAVE_NAME+'\\'
+
+		if SAVE_PICKLES == 1:
+			if not os.path.exists(PICKLE_PATH_NAME):
+				os.makedirs(PICKLE_PATH_NAME)
+			for j in range(0,len(arima_res)):
+				
+				d = arima_res[j]
+				nm = PICKLE_PATH_NAME+'pckl_' + '{0:03}'.format(j)
+				d.to_pickle(nm)
+
+		print('Dataset: '+str(fn)+'/'+str(len(folders)))
+if CHECK_STAB == 1:
+	stab_mat_train = cbank.check_stability(train,0.1)
+	stab_mat_test = cbank.check_stability(test,0.1)
+	
+	
+
+			
diff --git a/navipy/forecasting/src/Python/cozybank.py b/navipy/forecasting/src/Python/cozybank.py
new file mode 100644
index 0000000000000000000000000000000000000000..86fc98b9014c6afe01c9468081df56b9cda06cbf
--- /dev/null
+++ b/navipy/forecasting/src/Python/cozybank.py
@@ -0,0 +1,241 @@
+from statsmodels.tsa.arima_model import ARIMA
+from matplotlib import pyplot
+import scipy.io as spio
+import pandas as pd
+from pandas.plotting import autocorrelation_plot
+#from pandas import datetime
+#from pandas import DataFrame
+import pdb as pdb
+import inv_stat
+from sklearn.metrics import mean_squared_error
+import pyflux as pf
+import math
+import time
+import os
+from pick import pick
+from fastdtw import fastdtw as dtw
+import glob 
+
+def summon_data(foldername):
+	
+	pos_needed = 0
+	ori_needed = 0
+	
+	''' gather data information '''
+	set_splitting, source, data_id, pr_step, with_spd = __extract_information__(foldername)
+	
+	#Get what spatial info is needed 
+	if len(data_id) == 7:
+		if data_id[1] == '1' or data_id[5] == '1':
+			pos_needed = 1
+		if data_id[2] == '1' or data_id[6] == '1':
+			ori_needed = 1
+			
+	# convert to numbers
+	pr_step=int(pr_step)
+	with_spd = int(with_spd)
+	
+	''' gather experimental information '''
+	specs = __load_specification__(foldername)
+	
+	''' gather data'''
+	train = __load_data__(foldername,source, 'train',pos_needed,ori_needed, with_spd)
+	test = __load_data__(foldername,source, 'test',pos_needed,ori_needed, with_spd)
+	
+	''' gather results'''
+	esn_res = __load_results__(foldername,'esn', source, pos_needed,ori_needed, with_spd)
+	ids_res = __load_results__(foldername, 'ids', source, pos_needed,ori_needed, with_spd)
+	
+	return train, test, esn_res, ids_res, specs, foldername
+
+def execute	(train, test, lag,diff,order,forcasting_horizon,global_num_of_predictions):
+	res = []
+	for tr in range(0,len(train)):
+		
+		dim_prediction_df = pd.DataFrame()
+		
+		local_num_of_predictions = global_num_of_predictions
+		fitting_data = train[tr]
+		if local_num_of_predictions>len(test[tr]):
+			local_num_of_predictions = len(test[tr])
+			
+		future_data = test[tr].head(local_num_of_predictions)
+		for dim in range(0,len(fitting_data.columns)):
+			dim_key = fitting_data.keys()[dim]
+			ser = fitting_data[dim_key]
+			ser_future = future_data[dim_key] 
+			history = [x for x in ser]
+			predictions = list()
+			for t in range(0,local_num_of_predictions):
+				try:
+					model = ARIMA(history, order=(lag,diff,order))
+					model_fit = model.fit(disp=0)
+					output = model_fit.forecast(forcasting_horizon)
+					yhat = output[0][-1]
+					predictions.append(yhat)
+					obs = ser_future.iloc[t]
+					history.append(obs)
+				except:
+					print ('Entered except at t='+t+' dim='+dim+' trial='+tr)
+			predictions = pd.DataFrame({dim_key:predictions})
+			dim_prediction_df = pd.concat([dim_prediction_df, predictions],axis=1)
+			
+			
+		res.append(dim_prediction_df)
+	return res
+	
+
+def check_stability(data, sig_level):
+	
+	stat_mat = inv_stat.check_stationary(data, sig_level)
+	print(stat_mat)
+	return stat_mat
+
+def do_autocorrelation(series):
+	pyplot.figure()
+	autocorrelation_plot(series)
+
+	
+def calc_cost(A,B, norm):
+	dst = dtw(A,B)
+	dst = dst[0]
+	if (norm == 1) and len(B) != 0:
+		dst = dst/len(B)
+	return dst	
+	
+def __load_specification__(foldername):
+		
+		filename = glob.glob(foldername+'\\*taskspcs*')
+		
+		data = spio.loadmat(filename[0])
+		tsk_spc = data['task_specs']
+		i1 = {'min_l': tsk_spc[0][0][0][0][0]}
+		i2 = {'learn_type': tsk_spc[0][0][1][0]}
+		i3 = {'target_type': tsk_spc[0][0][2][0]}
+		i4 = {'pr_step': tsk_spc[0][0][4][0][0]}
+		i5 = {'tr_l' : tsk_spc[0][0][5][0][0]}
+		i6 = {'te_l' : tsk_spc[0][0][5][0][1]}
+		i7 = {'with_spd': tsk_spc[0][0][9][0][0]}
+		i8 = {'is_charlotts': tsk_spc[0][0][8][0][0]}
+		
+		tsk_spc = dict(i1, **i2,**i3,**i4,**i5,**i6, **i7, **i8)
+		tsk_spc = pd.DataFrame(tsk_spc, index = [0])
+		
+		return tsk_spc
+
+def __load_data__(foldername,source, purpose,pos_needed,ori_needed, with_spd):
+
+	trial_df = pd.DataFrame()
+	dataframe = []
+	filename = glob.glob(foldername+'\\*'+purpose+'*')
+	data = spio.loadmat(filename[0])
+	if purpose == 'train':
+		data = data['tr_TA']
+	elif purpose == 'test':
+		data = data['te_IN']
+	
+	for t in range(0,len(data)):
+			
+		trial = data[t][0]
+		
+		if pos_needed == 1 and with_spd ==0:
+			trial = __transform2dict__(trial,'pos')
+		elif pos_needed == 1 and with_spd ==1:
+			trial = __transform2dict__(trial,'pos+spd')
+		trial_df = pd.DataFrame(trial)
+		
+		if ori_needed == 1 and with_spd == 0:
+			if source == 'Char':
+				trial = __transform2dict__(trial,'ori_char')
+			else:
+				trial = __transform2dict__(trial,'ori_anne')
+		elif ori_needed == 1 and with_spd == 1:
+			if source == 'Char':
+				trial = __transform2dict__(trial,'ori_char+spd')
+			else:
+				trial = __transform2dict__(trial,'ori_anne+spd')
+		trial_df = pd.DataFrame(trial)
+		dataframe.append(trial_df)
+		
+	return dataframe
+
+def __load_results__(foldername,model, source, p,o, with_spd):
+	
+	filename = glob.glob(foldername+'\\*'+model+'*'+'*res*')
+	data = spio.loadmat(filename[0])
+	dataframe = []
+	if model == 'esn':
+		data = data['pred']
+	elif model == 'ids':
+		data = data['bench_results']
+	
+	for t in range(0,len(data)):
+		trial = data[t][0]
+		if p == 1 and with_spd ==0:
+			trial = __transform2dict__(trial,'pos')
+		elif p == 1 and with_spd ==1:
+			trial = __transform2dict__(trial,'pos+spd')
+		elif o == 1 and source == 'Char' and with_spd ==0:
+			trial = __transform2dict__(trial,'ori_char')
+		elif o == 1 and source == 'Char' and with_spd ==1:
+			trial = __transform2dict__(trial,'ori_char+spd')
+		elif o == 1 and source == 'Anne' and with_spd ==0:
+			trial = __transform2dict__(trial,'ori_anne')
+		elif o == 1 and source == 'Anne' and with_spd ==1:
+			trial = __transform2dict__(trial,'ori_anne+spd')
+		
+		trial_df = pd.DataFrame(trial)
+		dataframe.append(trial_df)
+		
+	return dataframe
+	
+def __transform2dict__ (trial,mode):
+	
+	
+	if mode == 'pos':
+		trial_dict = {'xPos':trial[:,0], 'yPos':trial[:,1], 'zPos':trial[:,2]}
+	elif mode == 'pos+spd':
+		trial_dict = {'xPos':trial[:,0], 'xPos_spd':trial[:,1], 'yPos':trial[:,2],'yPos_spd':trial[:,3],
+			'zPos':trial[:,4], 'zPos_spd':trial[:,5]}
+	elif mode == 'ori_char':
+		trial_dict = {'yaw_sin':trial[:,0],'yaw_cos':trial[:,1], 'pitch_sin':trial[:,2], 'pitch_cos':trial[:,3], 'roll_sin':trial[:,4], 'roll_cos':trial[:,5]}
+	elif mode == 'ori_char+spd':
+		trial_dict = {'yaw_sin':trial[:,0],'df_yaw_sin':trial[:,1],'yaw_cos':trial[:,2],'df_yaw_cos':trial[:,3],
+		'pitch_sin':trial[:,4],'df_pitch_sin':trial[:,5], 'pitch_cos':trial[:,6],'df_pitch_cos':trial[:,7],
+		'roll_sin':trial[:,8],'df_roll_sin':trial[:,9], 'roll_cos':trial[:,10], 'df_roll_cos':trial[:,11]}
+	elif mode == 'ori_anne':
+		trial_dict = {'Sin':trial[:,0], 'Cos':trial[:,1]}
+	elif mode == 'ori_anne+spd':
+		trial_dict = {'Sin':trial[:,0], 'df_Sin':trial[:,1], 'Cos':trial[:,2], 'df_Cos':trial[:,3]}
+			
+	return trial_dict
+
+def __extract_information__ (foldername):
+	
+	# cut path
+	k = foldername.find('\\')
+	fn = foldername[k+1:]
+	while fn.find('\\') !=-1:
+		fn = fn[k+1:]
+	# discard name modification if there is one
+	if fn[0] != 'i': 
+		k = fn.find('_')
+		fn = fn[k+1:]
+	# TODO create a name file for refferencing files (MatLab)
+	# read information from filename
+	k = fn.find('_')
+	set_splitting = fn[:k]
+	fn = fn[k+1:]
+	k = fn.find('_')
+	source = fn[:k]
+	fn = fn[k+1:]
+	k = fn.find('_')
+	data_id = fn[:k]
+	fn = fn[k+1:]
+	k = fn.find('_')
+	pr_step = fn[6:k]
+	fn = fn[k+1:]
+	k = fn.find('_')
+	with_spd = fn[len(fn)-1]
+	
+	return set_splitting, source, data_id, pr_step, with_spd	
\ No newline at end of file
diff --git a/navipy/forecasting/src/Python/evaluation_script.py b/navipy/forecasting/src/Python/evaluation_script.py
new file mode 100644
index 0000000000000000000000000000000000000000..e6179a89ca2c3636ecf82f7f90e7110b080969bc
--- /dev/null
+++ b/navipy/forecasting/src/Python/evaluation_script.py
@@ -0,0 +1,347 @@
+import cozybank as cbank
+from matplotlib import pyplot as plt
+import pdb
+import pandas as pd
+import os
+import glob
+import datetime
+from pick import pick
+import statistics 
+import numpy as np
+
+LOAD_PICKLES = 0
+SINGLE = 0
+MULTIPLE = 1-SINGLE
+CREATE_SCORE_PLOT = 0
+folders = glob.glob('data_mat/*b102b10*')
+
+#Single set summoning
+if SINGLE ==1: 
+	title = 'Choose data set to summon!'
+	options = folders
+	foldername, index = pick(options,title)
+	tr, te, esn_r, ids_r, spc, fldrnm = cbank.summon_data(foldername)
+	ari_res = {}
+	if os.path.exists(fldrnm+'\\pickles'):
+		pckl_folders = os.listdir(fldrnm+'\\pickles')
+		for p in range(0,len(pckl_folders)):
+			folder = pckl_folders[p]
+			folder_path = fldrnm+'\\pickles\\'+folder+'\\*'
+			PICKLE_LOAD_NAME = 'pckl_'
+			pckls = glob.glob(folder_path)
+			pres = []
+			for f in range(0,len(pckls)):
+				pres.append(pd.read_pickle(pckls[f]))
+			ari_res[folder[0:8]] = pres
+	else:
+		print('No pickle dir found.')
+	
+	
+	for t in range(0,len(tr)):
+			#Drop dim
+			
+			if  int(spc['with_spd']) == 1:
+				if spc['target_type'][0][1] =='1': 
+					b = tr[t].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+					c = esn_r[t].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+					d = ids_r[t].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+				else:
+					if spc['is_charlotts'][0] == 0:
+						b = tr[t].drop(['df_Cos','df_Sin'], axis=1)
+						c = esn_r[t].drop(['df_Cos','df_Sin'], axis=1)
+						d = ids_r[t].drop(['df_Cos','df_Sin'], axis=1)
+					else:
+						b = tr[t].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+						c = esn_r[t].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+						d = ids_r[t].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+					
+				tr[t]=b
+				esn_r[t]=c
+				ids_r[t] =d
+				del b
+				del c 
+				del d
+				
+				if spc['target_type'][0][5] =='1':
+					b = te[t].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+				else:
+					if spc['is_charlotts'][0] == 0:
+						b = te[t].drop(['df_Cos','df_Sin'], axis=1) 
+					else:
+						b = te[t].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+				te[t] = b
+				del b
+	
+	cost_esn = {}
+	cost_ids = {}
+	cost_esn_mean = {}
+	cost_ids_mean = {}
+	arima_costs = {}
+	
+	for mokey in ari_res.keys():
+			arima_costs[mokey] = {}
+			for dim_key in te[0].keys():
+				arima_costs[mokey][dim_key] = []
+				
+		
+	for dim_key in te[0].keys():
+		cost_esn[dim_key] = []
+		cost_ids[dim_key] = []
+							
+	for t in range(0,len(tr)):
+		#For each dimension and each arima model calculate the score for this trial
+		try:
+			for dim_key in te[t].keys():
+				te_mlab = te[t].shift(-int(spc['pr_step'][0]))
+				te_mlab = te_mlab[np.isfinite(te_mlab[dim_key])]
+				te_mlab = te_mlab[dim_key]
+				if len(te_mlab) != 0:
+					for mokey in ari_res.keys():
+						model_pr =ari_res[mokey][t][dim_key]
+						model_pr = model_pr.dropna(axis=0)
+						if len(te_mlab) >= len(model_pr):
+							te_mlab = te_mlab[0:len(model_pr)]
+						else:
+							model_pr = model_pr[0:len(te_mlab)]
+						if (len(model_pr) > 0):
+							arima_costs[mokey][dim_key].append(cbank.calc_cost(model_pr,te_mlab,1))
+						else:
+							arima_costs[mokey][dim_key].append(np.NaN)
+							print(mokey)
+						
+				
+					cost_esn[dim_key].append(cbank.calc_cost(esn_r[t][dim_key][0:len(model_pr)],te_mlab,1))
+					cost_ids[dim_key].append(cbank.calc_cost(ids_r[t][dim_key][0:len(model_pr)],te_mlab,1))
+		except: 
+			pdb.set_trace()
+
+elif MULTIPLE ==1:
+	#mass summoning
+	
+	#Extract strcuture data to create variables	
+	folder = folders[0]
+	tr,_,_,_,spc,fldrnm = cbank.summon_data(folder)
+	
+	arima_costs_final = {}
+	esn_costs_final = {}
+	ids_costs_final = {}
+	
+	if os.path.exists(fldrnm+'\\pickles'):
+			pckl_folders = os.listdir(fldrnm+'\\pickles')
+	
+	if  int(spc['with_spd']) == 1:
+		if spc['target_type'][0][1] =='1': 
+			b = tr[0].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+		else:
+			if spc['is_charlotts'][0] == 0:
+				b = tr[0].drop(['df_Cos','df_Sin'], axis=1) 
+			else:
+				b = tr[0].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+			
+		tr[0]=b
+		del b
+					
+	for momo in pckl_folders:
+		momo = momo[0:8]
+		arima_costs_final[momo] = {}
+		for dd in tr[0].keys():
+			arima_costs_final[momo][dd] = []
+			esn_costs_final[dd] = []
+			ids_costs_final[dd] = []
+	
+	
+	#For all set_ups
+	for d_set in range(0,len(folders)):
+		#Load all data and esn and ids results 
+		folder = folders[d_set]
+		tr, te, esn_r, ids_r, spc, fldrnm = cbank.summon_data(folder)
+		
+		#Load pickles from all arima models
+		ari_res = {}
+		if os.path.exists(fldrnm+'\\pickles'):
+			pckl_folders = os.listdir(fldrnm+'\\pickles')
+			for p in range(0,len(pckl_folders)):
+				folder = pckl_folders[p]
+				folder_path = fldrnm+'\\pickles\\'+folder+'\\*'
+				PICKLE_LOAD_NAME = 'pckl_'
+				pckls = glob.glob(folder_path)
+				pres = []
+				for f in range(0,len(pckls)):
+					pres.append(pd.read_pickle(pckls[f]))
+				ari_res[folder[0:8]] = pres
+				
+		else:
+			print('No pickle dir found.')
+		
+		
+		
+	
+		
+		#For each trial calculate dtw	
+		for t in range(0,len(tr)):
+			#Drop dim
+			if  int(spc['with_spd']) == 1:
+				if spc['target_type'][0][1] =='1': 
+					b = tr[t].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+					c = esn_r[t].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+					d = ids_r[t].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+				else:
+					if spc['is_charlotts'][0] == 0:
+						b = tr[t].drop(['df_Cos','df_Sin'], axis=1)
+						c = esn_r[t].drop(['df_Cos','df_Sin'], axis=1)
+						d = ids_r[t].drop(['df_Cos','df_Sin'], axis=1)
+					else:
+						b = tr[t].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+						c = esn_r[t].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+						d = ids_r[t].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+					
+					
+				tr[t]=b
+				esn_r[t]=c
+				ids_r[t] =d
+				del b
+				del c 
+				del d
+				
+				if spc['target_type'][0][5] =='1':
+					b = te[t].drop(['xPos_spd','yPos_spd','zPos_spd'], axis=1)
+				else:
+					if spc['is_charlotts'][0] == 0:
+						b = te[t].drop(['df_Cos','df_Sin'], axis=1) 
+					else:
+						b = te[t].drop(['df_yaw_cos','df_yaw_sin','df_pitch_cos','df_pitch_sin', 'df_roll_cos','df_roll_sin'], axis=1)
+				te[t] = b
+				del b
+		
+		cost_esn = {}
+		cost_ids = {}
+		cost_esn_mean = {}
+		cost_ids_mean = {}
+		arima_costs = {}
+		
+		for mokey in ari_res.keys():
+			arima_costs[mokey] = {}
+			for dim_key in te[0].keys():
+				arima_costs[mokey][dim_key] = []
+				
+		
+		for dim_key in te[0].keys():
+			cost_esn[dim_key] = []
+			cost_ids[dim_key] = []
+							
+		for t in range(0,len(tr)):
+			#For each dimension and each arima model calculate the score for this trial
+			try:
+				for dim_key in te[t].keys():
+					te_mlab = te[t].shift(-int(spc['pr_step'][0]))
+					te_mlab = te_mlab[np.isfinite(te_mlab[dim_key])]
+					te_mlab = te_mlab[dim_key]
+					if len(te_mlab) != 0:
+						for mokey in ari_res.keys():
+							model_pr =ari_res[mokey][t][dim_key]
+							model_pr = model_pr.dropna(axis=0)
+							if len(te_mlab) >= len(model_pr):
+								te_mlab = te_mlab[0:len(model_pr)]
+							else:
+								model_pr = model_pr[0:len(te_mlab)]
+							if (len(model_pr) > 0):
+								arima_costs[mokey][dim_key].append(cbank.calc_cost(model_pr,te_mlab,1))
+							else:
+								arima_costs[mokey][dim_key].append(np.NaN)
+								print(mokey)
+						cost_esn[dim_key].append(cbank.calc_cost(esn_r[t][dim_key][0:len(model_pr)],te_mlab,1))
+						cost_ids[dim_key].append(cbank.calc_cost(ids_r[t][dim_key][0:len(model_pr)],te_mlab,1))
+			except: 
+				pdb.set_trace()
+		#After all trials are through, call the mean score for this set up
+		
+		for mokey in arima_costs.keys():
+			for dim_key in arima_costs[mokey].keys():
+				if len(te_mlab) != 0:
+					arima_costs_final[mokey][dim_key].append(statistics.mean(arima_costs[mokey][dim_key]))
+				else:
+					arima_costs_final[mokey][dim_key].append(np.NaN)
+		
+		for dim_key in cost_esn.keys():
+			if len(te_mlab) != 0:
+				esn_costs_final[dim_key].append(statistics.mean(cost_esn[dim_key]))
+				ids_costs_final[dim_key].append(statistics.mean(cost_ids[dim_key]))
+			else:	
+				esn_costs_final[dim_key].append(np.NaN)
+				ids_costs_final[dim_key].append(np.NaN)
+
+			#new_row = pd.DataFrame(cost_esn_mean[dim_key],cost_ids_mean])
+		
+		print('Set prepared! Remaining: '+str(len(folders)-1-d_set))	
+		'''
+		pdb.set_trace()
+		
+		cost_arimas = cozybank(arima_model_1,test)
+		
+		'''
+		
+	
+	
+	
+##########################################################################
+#####################Plot Stuff###########################################
+##########################################################################
+		
+		
+		
+	
+	print('''train,test,esn_res,ids_res all have the structure:
+	int-datasetupnr][int-trialnr][str-featuredim][int-singlepoint]
+	
+	arima_res has the structure:
+	[int-datasetupnr][str-arimamodelname][int_trialnr]
+	[str-featuredim][int-nthobservation][int-predictionintofuture]
+	'''
+	)
+		
+
+
+	
+	'''
+	esn_df = pd.DataFrame(esn_costs_final)
+	ids_df = pd.DataFrame(ids_costs_final)
+	arima_110 = pd.DataFrame(arima_costs_final['L1_D1_O0'])
+	arima_120 = pd.DataFrame(arima_costs_final['L1_D2_O0'])
+	arima_220 = pd.DataFrame(arima_costs_final['L2_D2_O0'])
+	arima_320 = pd.DataFrame(arima_costs_final['L3_D2_O0'])
+
+	for dim in esn_df.keys():
+		plt.figure()
+		plt_arima_110, = plt.plot(arima_110[dim], color='#ACA6FF', label= 'ARIMA_110')
+		plt_arima_120, = plt.plot(arima_120[dim], color='#737DFF', label= 'ARIMA_120')
+		plt_arima_220, = plt.plot(arima_220[dim], color='#3A2CFF', label= 'ARIMA_220')
+		plt_arima_320, = plt.plot(arima_320[dim], color='#1100FF', label= 'ARIMA_320')
+		plt_esn, = plt.plot(esn_df[dim], 'r', label= 'ESN')
+		plt_ids, = plt.plot(ids_df[dim], 'g', label= 'IDS')
+		plt.legend(handles=[plt_arima_110,plt_arima_120,plt_arima_220,
+			plt_arima_320,plt_esn,plt_ids])
+		plt.show(block=False)
+	'''
+		
+
+if LOAD_PICKLES == 1:
+	ari_res ={}
+	if os.path.exists(foldernm+'\\pickles'):
+		pckl_folders = os.listdir(foldernm+'\\pickles')
+		for p in range(0,len(pckl_folders)):
+			folder = pckl_folders[p]
+			folder_path = foldernm+'\\pickles\\'+folder+'\\*'
+			PICKLE_LOAD_NAME = 'pckl_'
+			pckls = glob.glob(folder_path)
+			pres = []
+			for f in range(0,len(pckls)):
+				pres.append(pd.read_pickle(pckls[f]))
+			ari_res[folder[0:8]] = pres	
+	else:
+		print('No pickle dir found.')
+		
+print('''Results have the following structure:
+ari_res[str-arimamodelname][int-trialnr][str-featuredim]\n[int-timeofobservation][int-predictionintofuture]''')
+
+	
+	
\ No newline at end of file
diff --git a/navipy/forecasting/src/Python/inv_stat.py b/navipy/forecasting/src/Python/inv_stat.py
new file mode 100644
index 0000000000000000000000000000000000000000..f7db1f8063d8fb58b3afcd8638cabab7ee903f92
--- /dev/null
+++ b/navipy/forecasting/src/Python/inv_stat.py
@@ -0,0 +1,39 @@
+from statsmodels.tsa.stattools import adfuller as df_test
+import pdb
+
+def check_stationary (data, sig_level):
+	"""
+	This function investigates if given data is stationary or not.
+	INPUT:
+
+	data = pandas dataframe with N-trials, each having r_i rows and p-columns
+	
+	sig_level = p-value that must be surpased in order to be considered stationary.
+
+	OUPUT:
+
+	stat_mat = [[s_1,s_2,...s_m],[s_1,s_2,...s_m],...k]
+	where s_i is 0 of the feature can not be considered stationary, or 1 otherwise. 
+	"""
+	stat_mat = []
+	n_trials = len(data)
+	print(n_trials)
+	for trial in range(0,n_trials):
+			trial_stat = []
+			this_trial = data[trial]
+			num_of_col = int(this_trial.size/len(this_trial))
+		
+			for dim in range(0,len(data[0].columns)):
+				dim_key = this_trial.keys()[dim]
+				feat_is_stat = 1 
+				this_series = this_trial[dim_key] 
+				df_res = df_test(this_series)
+				if df_res[1] > sig_level:
+					print('Trial number: ' + str(trial) +  ' is not stationary in feature: ' + dim_key)
+					feat_is_stat = 0
+				else:
+					print('Trial number: ' + str(trial) +  ' is stationary in feature: ' + dim_key)
+				trial_stat.append(feat_is_stat)
+		
+			stat_mat.append(trial_stat)
+	return stat_mat
\ No newline at end of file
diff --git a/navipy/forecasting/src/Python/misc_script.py b/navipy/forecasting/src/Python/misc_script.py
new file mode 100644
index 0000000000000000000000000000000000000000..b8edd2855178aaabb7acfa05e68c4043bb1a8e09
--- /dev/null
+++ b/navipy/forecasting/src/Python/misc_script.py
@@ -0,0 +1,34 @@
+import seaborn as sns
+from matplotlib import pyplot as plt
+ 
+TRIAL = 39
+
+trialplt = plt.figure()
+a = df_te[TRIAL]['xPos']
+b = df_te[TRIAL]['xPos_TA']
+c = df_pred[TRIAL]['xPos_Pred']
+d = df_pred_bch[TRIAL]['xPos_Pred_BCH']
+
+observed, = plt.plot(a,'--b', label='Observed')
+future, = plt.plot(b,'b', label='Corresponding Future Value')
+prediction, = plt.plot(c,'--g', label='Corresponding ESN Prediction')
+benchmark, = plt.plot(d,'--r', label='Corresponding BENCH Prediction')
+plt.legend(handles=[observed,future, prediction, benchmark])
+
+sns.set_style('whitegrid')
+
+plt.show(block=False)
+
+##########################
+
+scoresplt = plt.figure()
+
+sc_esn = ESNscores['Sin']
+sc_bch = BCHscores['Sin']
+sc_esn_plt, = plt.plot(sc_esn,'--g', label='ESN')
+sc_bch_plt, = plt.plot(sc_bch,'--r', label='BCH')
+plt.legend(handles=[sc_esn_plt,sc_bch_plt])
+
+sns.set_style('whitegrid')
+
+plt.show(block=False)
diff --git a/navipy/forecasting/src/Python/reworked/Showcase.ipynb b/navipy/forecasting/src/Python/reworked/Showcase.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..75fcdd7c6b379dd21c737cf35a24433e98b0600b
--- /dev/null
+++ b/navipy/forecasting/src/Python/reworked/Showcase.ipynb
@@ -0,0 +1,12316 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Showcase For Predictorbox"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from test_predictor_box import GeneralProvider\n",
+    "from predictor_box import Investigator\n",
+    "from predictor_box import Modelmaker\n",
+    "import pandas\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Generate Artificial Data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "TOTAL_NUM_TRIALS = 40\n",
+    "\n",
+    "gp = GeneralProvider()\n",
+    "data_stationary = []\n",
+    "data_not_stationary = []\n",
+    "data_ar1 = []\n",
+    "data_ar3 = []\n",
+    "for t in range(0, TOTAL_NUM_TRIALS):\n",
+    "    data_stationary.append(gp._generate_random_data_(is_stationary=True))\n",
+    "    data_not_stationary.append(gp._generate_random_data_(is_stationary=False))\n",
+    "    data_ar1.append(gp._generate_ar1_data_())\n",
+    "    data_ar3.append(gp._generate_ar3_data_())\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[     position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.713394  0.558804  0.952301  0.621651  0.303503  0.950869\n",
+       " 1    0.693921  0.341748  0.688553  0.273584  0.194699  0.489226\n",
+       " 2    0.485258  0.749679  0.239443  0.578324  0.192139  0.811631\n",
+       " 3    0.527538  0.812442  0.936462  0.823429  0.187038  0.085112\n",
+       " 4    0.980802  0.751555  0.204525  0.913367  0.863582  0.391901\n",
+       " 5    0.501384  0.768070  0.583533  0.238801  0.938927  0.001697\n",
+       " 6    0.884653  0.711280  0.643619  0.727751  0.254669  0.724542\n",
+       " 7    0.824409  0.252376  0.442818  0.917564  0.062139  0.437003\n",
+       " 8    0.194396  0.784972  0.559187  0.561501  0.966510  0.077899\n",
+       " 9    0.572441  0.970402  0.914694  0.394568  0.325566  0.489678\n",
+       " 10   0.135500  0.649933  0.338452  0.496569  0.104072  0.813459\n",
+       " 11   0.190201  0.596502  0.660666  0.957509  0.066421  0.680215\n",
+       " 12   0.893663  0.498590  0.737613  0.887587  0.177015  0.862661\n",
+       " 13   0.697618  0.475454  0.792464  0.958830  0.772566  0.609292\n",
+       " 14   0.365387  0.631366  0.670369  0.970978  0.704623  0.516423\n",
+       " 15   0.627459  0.657467  0.554767  0.704645  0.103863  0.536292\n",
+       " 16   0.405692  0.517918  0.400499  0.876686  0.247595  0.860154\n",
+       " 17   0.249390  0.262713  0.964648  0.497568  0.055632  0.163468\n",
+       " 18   0.143209  0.678832  0.741095  0.984783  0.888094  0.450872\n",
+       " 19   0.273066  0.984683  0.566629  0.170315  0.992120  0.329564\n",
+       " 20   0.177715  0.287379  0.859619  0.966348  0.881137  0.779843\n",
+       " 21   0.017014  0.491508  0.025132  0.602554  0.354306  0.450568\n",
+       " 22   0.390776  0.246614  0.261370  0.181476  0.645498  0.985779\n",
+       " 23   0.996268  0.847721  0.697756  0.855199  0.140554  0.583185\n",
+       " 24   0.705986  0.032736  0.695038  0.826817  0.335105  0.130661\n",
+       " 25   0.528716  0.673525  0.408862  0.059376  0.787330  0.175889\n",
+       " 26   0.279086  0.818187  0.875709  0.799302  0.885274  0.421946\n",
+       " 27   0.829997  0.307805  0.666966  0.059069  0.651914  0.689628\n",
+       " 28   0.449230  0.756868  0.443049  0.263764  0.175750  0.406234\n",
+       " 29   0.647267  0.320314  0.576268  0.909005  0.221654  0.093164\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.768164  0.464613  0.979449  0.468147  0.122883  0.921458\n",
+       " 971  0.688389  0.235740  0.791231  0.498372  0.108111  0.002166\n",
+       " 972  0.162460  0.782338  0.074359  0.944090  0.406326  0.142624\n",
+       " 973  0.581483  0.850834  0.207017  0.033808  0.138556  0.264641\n",
+       " 974  0.098203  0.108250  0.555721  0.523537  0.677515  0.496823\n",
+       " 975  0.348477  0.560011  0.246918  0.712585  0.869328  0.172561\n",
+       " 976  0.184610  0.474887  0.707533  0.219217  0.756445  0.058116\n",
+       " 977  0.107121  0.114278  0.328057  0.557602  0.186852  0.333781\n",
+       " 978  0.051943  0.800307  0.964606  0.125327  0.075177  0.171888\n",
+       " 979  0.246495  0.501191  0.128893  0.170918  0.119197  0.527956\n",
+       " 980  0.858319  0.142160  0.902074  0.923743  0.272024  0.110320\n",
+       " 981  0.593179  0.098855  0.993251  0.804272  0.677915  0.211419\n",
+       " 982  0.341133  0.526625  0.820062  0.555413  0.342558  0.171840\n",
+       " 983  0.716745  0.080159  0.851671  0.428264  0.275323  0.575494\n",
+       " 984  0.338232  0.022727  0.899510  0.130999  0.452276  0.771269\n",
+       " 985  0.847094  0.885428  0.736573  0.314234  0.864004  0.539775\n",
+       " 986  0.170861  0.161908  0.395312  0.399315  0.798736  0.633492\n",
+       " 987  0.496934  0.410562  0.434563  0.235151  0.605872  0.805379\n",
+       " 988  0.998896  0.641061  0.071799  0.410506  0.152709  0.472354\n",
+       " 989  0.164651  0.722294  0.570799  0.989525  0.665813  0.328031\n",
+       " 990  0.735852  0.368556  0.218096  0.690836  0.184288  0.498047\n",
+       " 991  0.368312  0.466259  0.449191  0.530664  0.891784  0.216411\n",
+       " 992  0.026815  0.598293  0.221538  0.099410  0.904817  0.695313\n",
+       " 993  0.958085  0.335577  0.483649  0.021776  0.585446  0.326760\n",
+       " 994  0.545093  0.230290  0.520875  0.042310  0.046816  0.381087\n",
+       " 995  0.483144  0.531245  0.336097  0.640824  0.499570  0.310572\n",
+       " 996  0.385118  0.724749  0.021050  0.321376  0.620818  0.102242\n",
+       " 997  0.062822  0.126599  0.310931  0.442431  0.386567  0.315585\n",
+       " 998  0.069833  0.886394  0.342162  0.339282  0.607422  0.231841\n",
+       " 999  0.523620  0.467092  0.330192  0.853122  0.323126  0.658714\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.641896  0.884144  0.878570  0.435294  0.878440  0.582637\n",
+       " 1    0.077099  0.629845  0.019224  0.020226  0.533341  0.265213\n",
+       " 2    0.267025  0.752046  0.025762  0.733100  0.632403  0.183982\n",
+       " 3    0.882693  0.858452  0.778071  0.224143  0.971754  0.892726\n",
+       " 4    0.000167  0.136837  0.636594  0.169290  0.573504  0.010120\n",
+       " 5    0.377165  0.072300  0.976427  0.853311  0.181661  0.007513\n",
+       " 6    0.408183  0.470504  0.974963  0.364965  0.400485  0.558171\n",
+       " 7    0.563825  0.395460  0.884457  0.926095  0.548083  0.203705\n",
+       " 8    0.875507  0.879009  0.915613  0.955559  0.099502  0.455109\n",
+       " 9    0.800304  0.279660  0.383542  0.009464  0.671718  0.065054\n",
+       " 10   0.419128  0.666091  0.583377  0.764721  0.681252  0.767606\n",
+       " 11   0.391033  0.576569  0.549494  0.542033  0.203251  0.932645\n",
+       " 12   0.113917  0.152628  0.957382  0.334273  0.637350  0.542086\n",
+       " 13   0.717823  0.556110  0.862354  0.077628  0.918476  0.052399\n",
+       " 14   0.735001  0.099806  0.515014  0.389561  0.906197  0.921534\n",
+       " 15   0.075810  0.229152  0.726110  0.265446  0.792900  0.747002\n",
+       " 16   0.772204  0.451776  0.755313  0.960795  0.790915  0.432904\n",
+       " 17   0.107243  0.889800  0.205310  0.780349  0.505097  0.537241\n",
+       " 18   0.537517  0.071133  0.618491  0.651440  0.600280  0.375804\n",
+       " 19   0.111205  0.974951  0.865642  0.227150  0.807965  0.041430\n",
+       " 20   0.721077  0.329328  0.026609  0.956697  0.376889  0.599494\n",
+       " 21   0.809937  0.827721  0.491483  0.730751  0.817490  0.061372\n",
+       " 22   0.967883  0.300450  0.621577  0.090459  0.342692  0.794300\n",
+       " 23   0.799067  0.698810  0.291534  0.742199  0.352417  0.048347\n",
+       " 24   0.479084  0.921024  0.311813  0.992547  0.273440  0.819227\n",
+       " 25   0.428257  0.994253  0.111437  0.635913  0.463021  0.468426\n",
+       " 26   0.000502  0.780724  0.065317  0.679625  0.139817  0.065218\n",
+       " 27   0.625302  0.237873  0.386001  0.999508  0.045834  0.799030\n",
+       " 28   0.153017  0.224854  0.646539  0.608570  0.065885  0.049780\n",
+       " 29   0.682977  0.432788  0.728313  0.136140  0.712237  0.722628\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.683782  0.706650  0.055460  0.238991  0.566080  0.308280\n",
+       " 971  0.192788  0.282566  0.324487  0.052589  0.342136  0.950318\n",
+       " 972  0.943388  0.885851  0.660811  0.120741  0.596234  0.468158\n",
+       " 973  0.484952  0.134798  0.530632  0.413354  0.330924  0.718097\n",
+       " 974  0.362981  0.340146  0.404325  0.314849  0.353725  0.707279\n",
+       " 975  0.513709  0.170644  0.915834  0.391640  0.385848  0.936556\n",
+       " 976  0.628535  0.706580  0.514156  0.999332  0.361439  0.260350\n",
+       " 977  0.975739  0.036707  0.641509  0.158992  0.808219  0.734380\n",
+       " 978  0.802700  0.946187  0.635331  0.895974  0.351794  0.237468\n",
+       " 979  0.926676  0.957317  0.770409  0.598628  0.728745  0.993515\n",
+       " 980  0.439282  0.346969  0.209351  0.382463  0.624093  0.061866\n",
+       " 981  0.963816  0.857687  0.770094  0.302339  0.871689  0.667098\n",
+       " 982  0.507303  0.924858  0.886785  0.789679  0.827283  0.336195\n",
+       " 983  0.862546  0.824444  0.242083  0.544098  0.465870  0.642925\n",
+       " 984  0.018319  0.007979  0.035404  0.271808  0.208737  0.150822\n",
+       " 985  0.781167  0.958340  0.794564  0.938363  0.376942  0.234230\n",
+       " 986  0.710490  0.943633  0.431633  0.772833  0.000610  0.922117\n",
+       " 987  0.642413  0.384966  0.667943  0.244367  0.969903  0.614410\n",
+       " 988  0.840043  0.225708  0.775010  0.467936  0.250582  0.993996\n",
+       " 989  0.173548  0.505326  0.556465  0.015354  0.359656  0.579296\n",
+       " 990  0.261619  0.823184  0.393896  0.299433  0.315171  0.610224\n",
+       " 991  0.444931  0.748044  0.410461  0.821882  0.270119  0.383746\n",
+       " 992  0.217216  0.532472  0.889403  0.990191  0.860141  0.465265\n",
+       " 993  0.574833  0.383687  0.476907  0.858794  0.419740  0.008999\n",
+       " 994  0.615652  0.495235  0.307835  0.907743  0.622642  0.542864\n",
+       " 995  0.727641  0.773546  0.130884  0.231748  0.651179  0.432261\n",
+       " 996  0.611518  0.444654  0.826139  0.608418  0.859568  0.238394\n",
+       " 997  0.453415  0.349752  0.723044  0.781235  0.688030  0.369733\n",
+       " 998  0.294744  0.742334  0.437708  0.749533  0.352956  0.998703\n",
+       " 999  0.885904  0.515625  0.414375  0.531478  0.265375  0.609467\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.462406  0.299954  0.522248  0.502932  0.771007  0.454146\n",
+       " 1    0.123347  0.334319  0.173801  0.006220  0.504185  0.672602\n",
+       " 2    0.274871  0.612056  0.279535  0.049685  0.670247  0.417058\n",
+       " 3    0.474096  0.680385  0.801104  0.709759  0.375829  0.628904\n",
+       " 4    0.948815  0.777025  0.966692  0.706826  0.947886  0.282955\n",
+       " 5    0.322897  0.260276  0.368204  0.919270  0.992768  0.987925\n",
+       " 6    0.455035  0.492292  0.290689  0.779812  0.834969  0.706141\n",
+       " 7    0.838890  0.822446  0.847734  0.028510  0.661951  0.054735\n",
+       " 8    0.297533  0.831039  0.985031  0.246350  0.301537  0.861984\n",
+       " 9    0.740183  0.153037  0.688562  0.536296  0.642558  0.089725\n",
+       " 10   0.174682  0.493777  0.131303  0.184759  0.109779  0.146988\n",
+       " 11   0.098814  0.916897  0.591895  0.062727  0.427857  0.844514\n",
+       " 12   0.401763  0.136964  0.934817  0.368134  0.249122  0.026933\n",
+       " 13   0.133039  0.892515  0.922300  0.175539  0.970085  0.907268\n",
+       " 14   0.402067  0.043471  0.133373  0.329464  0.248330  0.170718\n",
+       " 15   0.182963  0.230787  0.706754  0.498516  0.730355  0.137536\n",
+       " 16   0.022819  0.444002  0.566926  0.862916  0.258175  0.530613\n",
+       " 17   0.124754  0.979261  0.009230  0.688299  0.221964  0.186997\n",
+       " 18   0.271855  0.745158  0.501928  0.339048  0.280570  0.198892\n",
+       " 19   0.453179  0.660212  0.255376  0.374834  0.032309  0.295105\n",
+       " 20   0.187893  0.383533  0.127664  0.848504  0.503968  0.265007\n",
+       " 21   0.973090  0.305108  0.425305  0.045245  0.395479  0.381628\n",
+       " 22   0.979458  0.486925  0.630467  0.582653  0.168855  0.492560\n",
+       " 23   0.347689  0.769111  0.337205  0.209073  0.415087  0.552377\n",
+       " 24   0.776009  0.805991  0.890296  0.800313  0.159008  0.447734\n",
+       " 25   0.824241  0.326022  0.396208  0.097644  0.330938  0.609962\n",
+       " 26   0.618830  0.926060  0.572984  0.149691  0.923896  0.304471\n",
+       " 27   0.378310  0.384591  0.800913  0.920595  0.555008  0.805355\n",
+       " 28   0.123604  0.422756  0.099137  0.254637  0.529323  0.142207\n",
+       " 29   0.078431  0.338264  0.197050  0.513600  0.504582  0.280049\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.701497  0.026884  0.618022  0.826822  0.382220  0.310812\n",
+       " 971  0.380793  0.767459  0.872616  0.148645  0.043092  0.292844\n",
+       " 972  0.929193  0.282082  0.059581  0.203002  0.350503  0.347948\n",
+       " 973  0.356206  0.557489  0.211222  0.984639  0.080836  0.346224\n",
+       " 974  0.128444  0.850308  0.172271  0.010475  0.639609  0.469133\n",
+       " 975  0.640117  0.614256  0.914666  0.310723  0.865187  0.320291\n",
+       " 976  0.660883  0.220825  0.558958  0.706236  0.717936  0.260147\n",
+       " 977  0.423867  0.854960  0.009215  0.836226  0.667726  0.712488\n",
+       " 978  0.815226  0.533553  0.372100  0.022122  0.740660  0.321651\n",
+       " 979  0.209884  0.608489  0.428565  0.823312  0.692199  0.118263\n",
+       " 980  0.035735  0.615121  0.413167  0.666253  0.053333  0.257689\n",
+       " 981  0.208569  0.127228  0.691316  0.270366  0.520378  0.592441\n",
+       " 982  0.904912  0.664221  0.222642  0.940864  0.867395  0.520449\n",
+       " 983  0.076269  0.754294  0.222364  0.621370  0.031210  0.713662\n",
+       " 984  0.948145  0.874087  0.038621  0.244513  0.121738  0.559730\n",
+       " 985  0.663211  0.672810  0.182778  0.341684  0.931923  0.552768\n",
+       " 986  0.541149  0.919294  0.680051  0.184290  0.959884  0.923975\n",
+       " 987  0.976761  0.693029  0.104929  0.002000  0.355270  0.359571\n",
+       " 988  0.285926  0.494800  0.039261  0.442875  0.734163  0.293335\n",
+       " 989  0.409443  0.597139  0.705692  0.714731  0.214206  0.065389\n",
+       " 990  0.047352  0.008660  0.249929  0.303890  0.174482  0.958471\n",
+       " 991  0.504558  0.627062  0.742851  0.341348  0.361642  0.097341\n",
+       " 992  0.272264  0.215173  0.532933  0.874058  0.056270  0.288893\n",
+       " 993  0.484625  0.630598  0.411580  0.498009  0.157677  0.861071\n",
+       " 994  0.522140  0.341403  0.549379  0.573651  0.847338  0.876372\n",
+       " 995  0.210074  0.208964  0.625038  0.374349  0.660135  0.477257\n",
+       " 996  0.701587  0.317576  0.418409  0.647291  0.897521  0.569607\n",
+       " 997  0.054573  0.324595  0.883702  0.271894  0.936211  0.087675\n",
+       " 998  0.679132  0.837807  0.682855  0.486546  0.177065  0.524187\n",
+       " 999  0.407368  0.245940  0.021591  0.027388  0.916734  0.320332\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.023314  0.622396  0.776736  0.282696  0.158916  0.468390\n",
+       " 1    0.714464  0.517275  0.186138  0.349082  0.117360  0.273258\n",
+       " 2    0.580707  0.521138  0.536873  0.998040  0.274017  0.448821\n",
+       " 3    0.441410  0.439454  0.303648  0.508279  0.444107  0.587336\n",
+       " 4    0.581006  0.223336  0.033450  0.822624  0.354971  0.001316\n",
+       " 5    0.391188  0.013769  0.559418  0.889890  0.966634  0.300994\n",
+       " 6    0.537122  0.133341  0.779518  0.387964  0.830273  0.091514\n",
+       " 7    0.648040  0.879617  0.235150  0.923383  0.814551  0.868091\n",
+       " 8    0.590850  0.072268  0.342327  0.063800  0.173880  0.835571\n",
+       " 9    0.524408  0.470054  0.250539  0.379431  0.458728  0.136789\n",
+       " 10   0.112301  0.257497  0.897550  0.284598  0.803992  0.836898\n",
+       " 11   0.223720  0.058963  0.263088  0.595249  0.998473  0.238054\n",
+       " 12   0.880439  0.557219  0.610293  0.966711  0.453616  0.654911\n",
+       " 13   0.250301  0.470718  0.361120  0.324368  0.537672  0.801676\n",
+       " 14   0.628647  0.034128  0.576828  0.522687  0.809665  0.048352\n",
+       " 15   0.619457  0.412077  0.280563  0.955415  0.590776  0.732167\n",
+       " 16   0.422373  0.865259  0.456268  0.629455  0.174722  0.377207\n",
+       " 17   0.371340  0.689175  0.664594  0.803101  0.440049  0.165373\n",
+       " 18   0.974948  0.253902  0.464185  0.748278  0.850140  0.071700\n",
+       " 19   0.396875  0.979513  0.831365  0.016888  0.225834  0.626775\n",
+       " 20   0.534464  0.102983  0.104711  0.183380  0.077426  0.034833\n",
+       " 21   0.465761  0.236340  0.824295  0.348332  0.511554  0.766968\n",
+       " 22   0.543108  0.529897  0.468439  0.443461  0.685455  0.138886\n",
+       " 23   0.807068  0.874168  0.321116  0.846054  0.908136  0.567418\n",
+       " 24   0.185136  0.141308  0.317983  0.185506  0.026541  0.165818\n",
+       " 25   0.905401  0.547785  0.572942  0.308246  0.435554  0.131252\n",
+       " 26   0.648860  0.683526  0.707055  0.923240  0.100584  0.966376\n",
+       " 27   0.766478  0.965951  0.692280  0.392671  0.108544  0.453739\n",
+       " 28   0.432077  0.037395  0.222951  0.732920  0.075211  0.323235\n",
+       " 29   0.599632  0.205590  0.061629  0.123956  0.816066  0.534283\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.835832  0.045906  0.899239  0.617273  0.695513  0.567672\n",
+       " 971  0.933925  0.567483  0.710795  0.582361  0.407503  0.691055\n",
+       " 972  0.929455  0.227050  0.812183  0.745548  0.672713  0.305145\n",
+       " 973  0.816469  0.729507  0.343271  0.168080  0.871184  0.855009\n",
+       " 974  0.015829  0.702298  0.276442  0.773527  0.699961  0.305481\n",
+       " 975  0.153922  0.153596  0.807956  0.041715  0.787402  0.565508\n",
+       " 976  0.618518  0.832589  0.390882  0.657369  0.301980  0.765965\n",
+       " 977  0.178780  0.469036  0.325109  0.842022  0.317609  0.911264\n",
+       " 978  0.329379  0.330775  0.873620  0.499473  0.864696  0.241581\n",
+       " 979  0.099819  0.118279  0.629525  0.603163  0.379673  0.679054\n",
+       " 980  0.190873  0.074092  0.739977  0.735049  0.861896  0.184297\n",
+       " 981  0.155098  0.856268  0.283114  0.164757  0.071871  0.800319\n",
+       " 982  0.009049  0.199840  0.852559  0.036889  0.263030  0.993500\n",
+       " 983  0.525804  0.477940  0.060626  0.689617  0.010398  0.336966\n",
+       " 984  0.853736  0.897404  0.603134  0.420159  0.445343  0.335924\n",
+       " 985  0.917706  0.551856  0.620740  0.547179  0.685823  0.726578\n",
+       " 986  0.703030  0.939650  0.622826  0.429029  0.017975  0.270246\n",
+       " 987  0.237589  0.578465  0.194060  0.780308  0.378401  0.182564\n",
+       " 988  0.536854  0.866731  0.938962  0.743979  0.889779  0.704164\n",
+       " 989  0.287678  0.812606  0.072448  0.626344  0.936438  0.494606\n",
+       " 990  0.408212  0.778908  0.384347  0.542023  0.267435  0.373205\n",
+       " 991  0.340323  0.713303  0.449007  0.964388  0.018529  0.443711\n",
+       " 992  0.208270  0.026534  0.573845  0.062757  0.043960  0.150571\n",
+       " 993  0.227432  0.748393  0.824013  0.905079  0.176831  0.198270\n",
+       " 994  0.938700  0.482343  0.614761  0.757120  0.882448  0.840835\n",
+       " 995  0.844851  0.365643  0.677389  0.644715  0.516050  0.625118\n",
+       " 996  0.113506  0.375668  0.002162  0.158851  0.279009  0.549904\n",
+       " 997  0.835069  0.822344  0.612098  0.505003  0.913569  0.018575\n",
+       " 998  0.075833  0.040266  0.184215  0.332886  0.338792  0.043347\n",
+       " 999  0.890310  0.920305  0.699096  0.591553  0.921918  0.733942\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.980263  0.989884  0.735042  0.815737  0.327329  0.929585\n",
+       " 1    0.997090  0.255186  0.237411  0.670323  0.773064  0.902918\n",
+       " 2    0.164058  0.263719  0.448491  0.961527  0.086087  0.820516\n",
+       " 3    0.882246  0.941095  0.916982  0.336376  0.107455  0.860499\n",
+       " 4    0.154021  0.293395  0.006708  0.312336  0.817114  0.560859\n",
+       " 5    0.675539  0.949208  0.504225  0.903881  0.053120  0.527188\n",
+       " 6    0.884550  0.727771  0.557071  0.843354  0.942122  0.816035\n",
+       " 7    0.556671  0.078016  0.385211  0.098198  0.114586  0.882467\n",
+       " 8    0.724390  0.809352  0.058206  0.613807  0.139974  0.740942\n",
+       " 9    0.707930  0.108352  0.257022  0.283041  0.689556  0.273980\n",
+       " 10   0.656950  0.601689  0.221907  0.349473  0.435997  0.251094\n",
+       " 11   0.650032  0.875834  0.976480  0.077574  0.264529  0.792794\n",
+       " 12   0.068365  0.839491  0.187344  0.342310  0.798890  0.465983\n",
+       " 13   0.132298  0.544732  0.125782  0.208673  0.583251  0.617260\n",
+       " 14   0.446351  0.798982  0.725335  0.822669  0.514302  0.032730\n",
+       " 15   0.514498  0.072236  0.171108  0.121550  0.048000  0.347785\n",
+       " 16   0.473442  0.752704  0.248771  0.937420  0.441048  0.881453\n",
+       " 17   0.837182  0.044463  0.733534  0.183351  0.247528  0.243379\n",
+       " 18   0.572847  0.660174  0.921666  0.872119  0.492503  0.621822\n",
+       " 19   0.415559  0.747606  0.139852  0.659460  0.191917  0.708282\n",
+       " 20   0.386698  0.557081  0.453154  0.236612  0.415273  0.736572\n",
+       " 21   0.994067  0.456376  0.561793  0.178692  0.592519  0.963881\n",
+       " 22   0.692291  0.519793  0.909649  0.052473  0.481257  0.690889\n",
+       " 23   0.735224  0.735130  0.016669  0.313371  0.727120  0.151537\n",
+       " 24   0.769410  0.010337  0.375932  0.854318  0.572007  0.919143\n",
+       " 25   0.392760  0.888385  0.960416  0.626058  0.501553  0.938640\n",
+       " 26   0.108670  0.421158  0.906134  0.642890  0.036753  0.459832\n",
+       " 27   0.849932  0.469373  0.441795  0.665158  0.482355  0.554422\n",
+       " 28   0.688805  0.482521  0.025257  0.189806  0.719154  0.335935\n",
+       " 29   0.101962  0.597128  0.735077  0.073068  0.520190  0.426316\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.135533  0.343922  0.130001  0.248677  0.003845  0.909065\n",
+       " 971  0.608385  0.530615  0.837220  0.544993  0.086455  0.731928\n",
+       " 972  0.649363  0.602815  0.821194  0.740652  0.570890  0.169858\n",
+       " 973  0.629702  0.336924  0.198850  0.935768  0.923677  0.971001\n",
+       " 974  0.597451  0.305094  0.625084  0.336109  0.334403  0.503384\n",
+       " 975  0.290778  0.655689  0.000803  0.314399  0.359403  0.568629\n",
+       " 976  0.345697  0.618142  0.358242  0.285831  0.311798  0.828133\n",
+       " 977  0.752618  0.965807  0.378855  0.044352  0.214204  0.480585\n",
+       " 978  0.467096  0.604320  0.281016  0.842181  0.241721  0.183549\n",
+       " 979  0.177212  0.363512  0.576848  0.152779  0.724065  0.055645\n",
+       " 980  0.902429  0.991582  0.339112  0.548114  0.682384  0.206682\n",
+       " 981  0.140826  0.499412  0.017603  0.044706  0.910720  0.990576\n",
+       " 982  0.309749  0.933615  0.482857  0.543398  0.551414  0.582369\n",
+       " 983  0.642888  0.983657  0.448480  0.850522  0.374042  0.407357\n",
+       " 984  0.643820  0.243926  0.143259  0.428097  0.645812  0.016433\n",
+       " 985  0.676087  0.695937  0.486923  0.965195  0.697605  0.685252\n",
+       " 986  0.262084  0.028545  0.069521  0.323403  0.996325  0.784255\n",
+       " 987  0.336469  0.759317  0.709387  0.343922  0.835027  0.091230\n",
+       " 988  0.992903  0.463370  0.142903  0.815769  0.493452  0.278277\n",
+       " 989  0.543890  0.780679  0.511587  0.431601  0.852696  0.200866\n",
+       " 990  0.185453  0.934606  0.709740  0.431302  0.522169  0.675742\n",
+       " 991  0.955181  0.827704  0.077096  0.292449  0.539352  0.880414\n",
+       " 992  0.468673  0.530440  0.019585  0.523655  0.180078  0.505780\n",
+       " 993  0.577236  0.831636  0.373320  0.499315  0.259452  0.446084\n",
+       " 994  0.135368  0.565424  0.667364  0.275212  0.097441  0.051657\n",
+       " 995  0.696560  0.702908  0.877178  0.901495  0.809911  0.593186\n",
+       " 996  0.027727  0.295573  0.773535  0.186403  0.163704  0.294675\n",
+       " 997  0.459361  0.813192  0.938124  0.802879  0.763226  0.067246\n",
+       " 998  0.043423  0.092924  0.736871  0.261262  0.445059  0.449782\n",
+       " 999  0.662436  0.085790  0.353124  0.872053  0.614638  0.163459\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.267958  0.698618  0.665330  0.317844  0.771205  0.576259\n",
+       " 1    0.547938  0.917377  0.548285  0.292636  0.977602  0.449334\n",
+       " 2    0.275141  0.832086  0.886917  0.720097  0.855644  0.913819\n",
+       " 3    0.640576  0.239222  0.766712  0.633881  0.379981  0.087065\n",
+       " 4    0.429211  0.725544  0.088688  0.736561  0.308895  0.587597\n",
+       " 5    0.509918  0.759499  0.267401  0.262312  0.451113  0.879349\n",
+       " 6    0.247515  0.236049  0.426369  0.185725  0.089598  0.661523\n",
+       " 7    0.892015  0.931195  0.915188  0.866485  0.373889  0.616618\n",
+       " 8    0.599594  0.119469  0.734967  0.527619  0.042595  0.355188\n",
+       " 9    0.595791  0.231404  0.509475  0.317853  0.695696  0.391856\n",
+       " 10   0.768650  0.505798  0.005782  0.861094  0.399621  0.631862\n",
+       " 11   0.507091  0.322167  0.093027  0.495444  0.616223  0.246288\n",
+       " 12   0.066582  0.364669  0.179277  0.135241  0.229008  0.825414\n",
+       " 13   0.131766  0.818143  0.694173  0.844204  0.103890  0.352178\n",
+       " 14   0.093944  0.527329  0.803281  0.270990  0.888874  0.586818\n",
+       " 15   0.286545  0.660014  0.234053  0.186014  0.312790  0.697305\n",
+       " 16   0.717157  0.034285  0.592423  0.047973  0.872783  0.736814\n",
+       " 17   0.042196  0.882196  0.067823  0.586948  0.951836  0.608989\n",
+       " 18   0.518239  0.104311  0.508533  0.724223  0.119167  0.730389\n",
+       " 19   0.986796  0.891264  0.966262  0.678208  0.430742  0.734666\n",
+       " 20   0.796833  0.262309  0.329688  0.967192  0.421998  0.954126\n",
+       " 21   0.933879  0.990668  0.043144  0.328681  0.154111  0.857774\n",
+       " 22   0.497099  0.507964  0.960878  0.446226  0.081889  0.297692\n",
+       " 23   0.159878  0.864630  0.430169  0.990265  0.835935  0.828699\n",
+       " 24   0.198283  0.604709  0.929665  0.115298  0.387656  0.155764\n",
+       " 25   0.749567  0.477814  0.412702  0.236050  0.264423  0.405876\n",
+       " 26   0.096779  0.757443  0.225502  0.438685  0.103831  0.120365\n",
+       " 27   0.897591  0.047779  0.739691  0.785371  0.411004  0.223539\n",
+       " 28   0.230450  0.010111  0.474795  0.269839  0.902153  0.951013\n",
+       " 29   0.544430  0.196269  0.480405  0.934339  0.996375  0.749060\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.842101  0.475870  0.633514  0.912683  0.483200  0.045196\n",
+       " 971  0.370009  0.159488  0.163306  0.822024  0.962514  0.486097\n",
+       " 972  0.361836  0.442339  0.768811  0.356060  0.003440  0.150248\n",
+       " 973  0.581086  0.208147  0.506774  0.689220  0.876858  0.849197\n",
+       " 974  0.232627  0.550994  0.587327  0.860071  0.858776  0.697134\n",
+       " 975  0.372509  0.486239  0.377352  0.242347  0.656832  0.287349\n",
+       " 976  0.781667  0.627652  0.896232  0.430916  0.281080  0.267239\n",
+       " 977  0.155639  0.486341  0.912885  0.354097  0.855613  0.638041\n",
+       " 978  0.552366  0.966335  0.632348  0.377992  0.317095  0.716476\n",
+       " 979  0.513220  0.246853  0.892870  0.514703  0.721343  0.200347\n",
+       " 980  0.949462  0.674228  0.069774  0.851652  0.901264  0.691269\n",
+       " 981  0.070363  0.438324  0.698191  0.125508  0.902514  0.969116\n",
+       " 982  0.822096  0.912662  0.442715  0.310631  0.962148  0.501065\n",
+       " 983  0.448722  0.012436  0.226950  0.305104  0.101573  0.814760\n",
+       " 984  0.557068  0.339082  0.580206  0.645566  0.280516  0.330802\n",
+       " 985  0.499726  0.546768  0.702819  0.334359  0.851048  0.536956\n",
+       " 986  0.142680  0.582204  0.510869  0.335582  0.590276  0.617613\n",
+       " 987  0.911754  0.222542  0.357010  0.761558  0.822578  0.207305\n",
+       " 988  0.050124  0.067555  0.469987  0.899778  0.573436  0.554093\n",
+       " 989  0.807347  0.826874  0.112402  0.341714  0.375424  0.056479\n",
+       " 990  0.658961  0.729744  0.940443  0.780564  0.876453  0.649595\n",
+       " 991  0.569943  0.580990  0.487481  0.306588  0.681527  0.404413\n",
+       " 992  0.308607  0.712303  0.085453  0.546427  0.432232  0.915009\n",
+       " 993  0.159399  0.695747  0.313057  0.007194  0.194272  0.535019\n",
+       " 994  0.235392  0.525493  0.052514  0.813972  0.722838  0.118881\n",
+       " 995  0.178242  0.202426  0.227241  0.274003  0.709299  0.524072\n",
+       " 996  0.866427  0.903231  0.350669  0.848440  0.233883  0.712707\n",
+       " 997  0.373128  0.583720  0.998265  0.363972  0.380928  0.235167\n",
+       " 998  0.561731  0.128895  0.254809  0.816076  0.115532  0.451042\n",
+       " 999  0.224303  0.621777  0.172618  0.750277  0.548677  0.406697\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.881953  0.513945  0.192514  0.068325  0.293174  0.093807\n",
+       " 1    0.913475  0.551795  0.905220  0.419075  0.454190  0.897827\n",
+       " 2    0.967425  0.280991  0.935663  0.346968  0.643665  0.926115\n",
+       " 3    0.237016  0.536713  0.680378  0.284476  0.205511  0.779276\n",
+       " 4    0.418468  0.115906  0.509024  0.825602  0.354341  0.584280\n",
+       " 5    0.811739  0.176051  0.892065  0.185842  0.636800  0.413514\n",
+       " 6    0.985074  0.181567  0.238207  0.017114  0.043655  0.546580\n",
+       " 7    0.965074  0.712326  0.687320  0.535717  0.277397  0.762965\n",
+       " 8    0.784717  0.083299  0.807822  0.406839  0.983267  0.386104\n",
+       " 9    0.896291  0.830857  0.184620  0.613933  0.600820  0.899570\n",
+       " 10   0.037810  0.131950  0.637722  0.674442  0.823018  0.990649\n",
+       " 11   0.777078  0.018779  0.507573  0.493348  0.629957  0.909245\n",
+       " 12   0.887639  0.148170  0.332928  0.343507  0.923335  0.483031\n",
+       " 13   0.994399  0.288948  0.909972  0.637442  0.054031  0.759437\n",
+       " 14   0.454807  0.617804  0.145941  0.799253  0.353502  0.389329\n",
+       " 15   0.294840  0.632134  0.801355  0.679804  0.968031  0.967143\n",
+       " 16   0.373391  0.836809  0.425175  0.494840  0.311135  0.593671\n",
+       " 17   0.767568  0.418538  0.218794  0.352131  0.087823  0.421681\n",
+       " 18   0.851605  0.827791  0.996291  0.144968  0.775840  0.896336\n",
+       " 19   0.472419  0.226732  0.803017  0.851164  0.020157  0.990262\n",
+       " 20   0.315618  0.141045  0.707092  0.162457  0.932380  0.285277\n",
+       " 21   0.671847  0.672157  0.568870  0.167385  0.356765  0.090358\n",
+       " 22   0.915517  0.071713  0.816107  0.884915  0.623119  0.312802\n",
+       " 23   0.670827  0.610175  0.778585  0.244197  0.348264  0.686716\n",
+       " 24   0.067847  0.267519  0.819051  0.958414  0.795525  0.853288\n",
+       " 25   0.546630  0.361106  0.743197  0.399086  0.709785  0.770268\n",
+       " 26   0.292981  0.971732  0.249393  0.759369  0.644626  0.330580\n",
+       " 27   0.089117  0.216187  0.294251  0.169504  0.794472  0.345737\n",
+       " 28   0.932659  0.952496  0.275799  0.846025  0.883779  0.086520\n",
+       " 29   0.490891  0.808362  0.504310  0.241311  0.005646  0.858170\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.809921  0.368087  0.713626  0.113342  0.560158  0.084672\n",
+       " 971  0.525162  0.504881  0.465628  0.808615  0.453489  0.373091\n",
+       " 972  0.676382  0.645550  0.671983  0.913422  0.664282  0.347353\n",
+       " 973  0.713073  0.923332  0.746013  0.013083  0.039949  0.100860\n",
+       " 974  0.214313  0.007883  0.776071  0.876206  0.527668  0.858220\n",
+       " 975  0.037509  0.442129  0.028929  0.062103  0.756837  0.448203\n",
+       " 976  0.728229  0.437320  0.222238  0.835939  0.412124  0.405416\n",
+       " 977  0.205991  0.618233  0.783198  0.125398  0.964376  0.267423\n",
+       " 978  0.812616  0.498232  0.766115  0.483788  0.417386  0.234837\n",
+       " 979  0.841736  0.490284  0.805372  0.072218  0.430678  0.571435\n",
+       " 980  0.770370  0.168123  0.153955  0.977543  0.865299  0.226809\n",
+       " 981  0.691724  0.973077  0.174034  0.279618  0.970552  0.980061\n",
+       " 982  0.003911  0.438800  0.103387  0.609708  0.376913  0.989122\n",
+       " 983  0.334919  0.906339  0.177426  0.575354  0.711036  0.280104\n",
+       " 984  0.767575  0.358197  0.452996  0.689525  0.065221  0.420539\n",
+       " 985  0.538935  0.977334  0.421618  0.849886  0.584884  0.891881\n",
+       " 986  0.773389  0.670171  0.566665  0.679823  0.683929  0.860379\n",
+       " 987  0.396501  0.482188  0.752680  0.990607  0.786845  0.141149\n",
+       " 988  0.832795  0.874664  0.656403  0.527317  0.929661  0.151589\n",
+       " 989  0.025786  0.913799  0.708875  0.436000  0.022063  0.031272\n",
+       " 990  0.493400  0.799202  0.471641  0.539356  0.943894  0.773648\n",
+       " 991  0.994402  0.170098  0.383391  0.984276  0.795962  0.532762\n",
+       " 992  0.998108  0.043315  0.001836  0.746556  0.078224  0.573625\n",
+       " 993  0.149103  0.877707  0.028449  0.413526  0.652007  0.324016\n",
+       " 994  0.179667  0.800248  0.486022  0.470908  0.382104  0.176743\n",
+       " 995  0.908356  0.096450  0.510874  0.983861  0.496384  0.893833\n",
+       " 996  0.947614  0.342024  0.151211  0.309558  0.521926  0.672963\n",
+       " 997  0.312691  0.809579  0.943238  0.489684  0.133664  0.086646\n",
+       " 998  0.929212  0.794486  0.441326  0.997824  0.333187  0.587295\n",
+       " 999  0.586605  0.395430  0.111076  0.881858  0.035311  0.047890\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.277444  0.615042  0.255637  0.487139  0.237314  0.341917\n",
+       " 1    0.261385  0.832273  0.440559  0.125432  0.764301  0.788645\n",
+       " 2    0.325224  0.693914  0.250955  0.653258  0.324317  0.894848\n",
+       " 3    0.777049  0.586955  0.299053  0.627191  0.306704  0.586204\n",
+       " 4    0.983402  0.578100  0.254331  0.091124  0.731817  0.929353\n",
+       " 5    0.374038  0.920485  0.964885  0.989446  0.551998  0.983359\n",
+       " 6    0.396330  0.979452  0.506591  0.697706  0.256837  0.363439\n",
+       " 7    0.543661  0.867354  0.138616  0.702216  0.127949  0.473381\n",
+       " 8    0.249482  0.250446  0.903223  0.591410  0.349121  0.665649\n",
+       " 9    0.849935  0.540143  0.449373  0.763728  0.646094  0.301732\n",
+       " 10   0.796591  0.013651  0.867999  0.942210  0.786961  0.403474\n",
+       " 11   0.635981  0.862126  0.307807  0.930464  0.145792  0.914296\n",
+       " 12   0.028280  0.087063  0.231319  0.786209  0.392334  0.574838\n",
+       " 13   0.513638  0.870512  0.534831  0.192910  0.292276  0.314974\n",
+       " 14   0.606176  0.776067  0.809882  0.651995  0.479567  0.370779\n",
+       " 15   0.473116  0.209659  0.057325  0.030062  0.894157  0.282725\n",
+       " 16   0.970870  0.388495  0.647908  0.859205  0.715453  0.558738\n",
+       " 17   0.953116  0.693587  0.234033  0.981531  0.151752  0.474695\n",
+       " 18   0.891714  0.860184  0.020129  0.927014  0.960595  0.391829\n",
+       " 19   0.757435  0.336525  0.210436  0.931647  0.786862  0.548045\n",
+       " 20   0.145441  0.942668  0.721915  0.414717  0.116976  0.311132\n",
+       " 21   0.882112  0.143851  0.025301  0.561266  0.323558  0.650134\n",
+       " 22   0.319798  0.768974  0.785300  0.150737  0.990832  0.097639\n",
+       " 23   0.812141  0.983987  0.824487  0.848753  0.123085  0.634502\n",
+       " 24   0.712547  0.920170  0.384405  0.479217  0.065775  0.471590\n",
+       " 25   0.514299  0.553016  0.268128  0.267109  0.500267  0.702987\n",
+       " 26   0.397420  0.071691  0.036989  0.735759  0.167556  0.440420\n",
+       " 27   0.981763  0.366942  0.498531  0.451265  0.506677  0.757794\n",
+       " 28   0.516154  0.980443  0.543992  0.842650  0.956078  0.625919\n",
+       " 29   0.671073  0.915081  0.537021  0.633496  0.948508  0.092730\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.571857  0.308051  0.690601  0.561479  0.504038  0.545426\n",
+       " 971  0.565505  0.553079  0.622279  0.135657  0.746452  0.846087\n",
+       " 972  0.204373  0.045933  0.401751  0.866421  0.875568  0.766613\n",
+       " 973  0.240367  0.540028  0.495720  0.391829  0.220025  0.209121\n",
+       " 974  0.163618  0.781618  0.887715  0.275834  0.495351  0.468062\n",
+       " 975  0.160404  0.461576  0.281928  0.218879  0.584019  0.895733\n",
+       " 976  0.779304  0.217971  0.497115  0.076194  0.189475  0.290340\n",
+       " 977  0.986011  0.168859  0.481843  0.657630  0.748181  0.190604\n",
+       " 978  0.017733  0.899483  0.681731  0.624646  0.708947  0.434166\n",
+       " 979  0.195220  0.126137  0.476853  0.905161  0.148423  0.870986\n",
+       " 980  0.545246  0.506572  0.744008  0.975316  0.938504  0.012573\n",
+       " 981  0.279151  0.748906  0.529089  0.683443  0.400910  0.673085\n",
+       " 982  0.298023  0.350553  0.065625  0.127980  0.068108  0.561225\n",
+       " 983  0.058474  0.599851  0.934202  0.894723  0.003897  0.156983\n",
+       " 984  0.822848  0.660120  0.362478  0.221483  0.491531  0.662235\n",
+       " 985  0.938543  0.313133  0.396201  0.259469  0.240792  0.357198\n",
+       " 986  0.068744  0.715190  0.143723  0.301528  0.620198  0.539901\n",
+       " 987  0.484563  0.820137  0.277380  0.322314  0.777374  0.998620\n",
+       " 988  0.647812  0.585988  0.232052  0.236875  0.931418  0.553610\n",
+       " 989  0.257592  0.840896  0.164540  0.872499  0.622544  0.072581\n",
+       " 990  0.748070  0.618911  0.412672  0.026361  0.530184  0.617698\n",
+       " 991  0.545924  0.048283  0.096062  0.644142  0.626620  0.200587\n",
+       " 992  0.207574  0.823187  0.958167  0.781985  0.494207  0.232603\n",
+       " 993  0.055342  0.362492  0.026215  0.584555  0.708083  0.631631\n",
+       " 994  0.147030  0.272046  0.069279  0.694533  0.732758  0.957620\n",
+       " 995  0.640884  0.084588  0.310294  0.641319  0.348980  0.725725\n",
+       " 996  0.816641  0.268617  0.671199  0.473767  0.722822  0.031387\n",
+       " 997  0.080201  0.431074  0.473730  0.438974  0.563830  0.061984\n",
+       " 998  0.589597  0.546571  0.760354  0.615697  0.843517  0.396563\n",
+       " 999  0.394219  0.912863  0.490504  0.427741  0.711510  0.903142\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.406756  0.794916  0.947748  0.528506  0.545643  0.706005\n",
+       " 1    0.916933  0.391026  0.423463  0.906465  0.665306  0.546926\n",
+       " 2    0.773975  0.123724  0.768249  0.994153  0.882860  0.654344\n",
+       " 3    0.107335  0.524048  0.075400  0.188507  0.036014  0.712509\n",
+       " 4    0.118985  0.071993  0.782322  0.892715  0.290495  0.288819\n",
+       " 5    0.183175  0.707724  0.485182  0.678045  0.452889  0.190101\n",
+       " 6    0.301880  0.296820  0.639328  0.780162  0.622696  0.247965\n",
+       " 7    0.533903  0.286218  0.632845  0.693699  0.986336  0.438528\n",
+       " 8    0.424741  0.077594  0.669935  0.323507  0.538696  0.804542\n",
+       " 9    0.815334  0.768520  0.426230  0.675076  0.720806  0.599076\n",
+       " 10   0.765175  0.404193  0.132272  0.015418  0.002131  0.103913\n",
+       " 11   0.436694  0.463001  0.808603  0.693652  0.987546  0.587942\n",
+       " 12   0.480143  0.148308  0.456334  0.606236  0.657454  0.168150\n",
+       " 13   0.994042  0.988291  0.449704  0.694261  0.415134  0.053041\n",
+       " 14   0.269637  0.002096  0.296859  0.739142  0.737208  0.049799\n",
+       " 15   0.262998  0.582152  0.164061  0.016142  0.463286  0.970942\n",
+       " 16   0.069148  0.121461  0.100175  0.289643  0.112648  0.688100\n",
+       " 17   0.102095  0.838867  0.924472  0.702057  0.427097  0.285565\n",
+       " 18   0.032402  0.401319  0.058750  0.189548  0.738136  0.714988\n",
+       " 19   0.847390  0.003721  0.296601  0.528522  0.173592  0.217763\n",
+       " 20   0.786362  0.450862  0.071399  0.181372  0.916123  0.793091\n",
+       " 21   0.425064  0.756702  0.446833  0.645308  0.680022  0.621535\n",
+       " 22   0.956673  0.658782  0.564982  0.684199  0.085832  0.866625\n",
+       " 23   0.086515  0.404230  0.262266  0.822325  0.013176  0.221921\n",
+       " 24   0.026932  0.522433  0.960282  0.383225  0.172677  0.756605\n",
+       " 25   0.198384  0.353890  0.359232  0.895627  0.763765  0.521400\n",
+       " 26   0.306019  0.311452  0.642558  0.003865  0.722194  0.077565\n",
+       " 27   0.696823  0.975858  0.251512  0.364745  0.404383  0.197439\n",
+       " 28   0.659256  0.501092  0.664517  0.471084  0.091080  0.784632\n",
+       " 29   0.953192  0.466488  0.670856  0.399815  0.483956  0.508145\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.358961  0.072787  0.710999  0.704437  0.851901  0.063446\n",
+       " 971  0.939316  0.642038  0.120853  0.145497  0.435136  0.784840\n",
+       " 972  0.448587  0.258330  0.386836  0.511717  0.221598  0.554280\n",
+       " 973  0.172516  0.403833  0.865428  0.464702  0.688198  0.041285\n",
+       " 974  0.051972  0.045566  0.521386  0.220229  0.497515  0.170989\n",
+       " 975  0.354053  0.382087  0.941822  0.737324  0.897885  0.600691\n",
+       " 976  0.341101  0.031672  0.645025  0.047714  0.910851  0.695942\n",
+       " 977  0.339515  0.954300  0.539037  0.626228  0.337909  0.038357\n",
+       " 978  0.565519  0.894263  0.853559  0.748639  0.823762  0.588703\n",
+       " 979  0.246898  0.401992  0.512493  0.023515  0.189595  0.954172\n",
+       " 980  0.574695  0.376323  0.270936  0.999780  0.223254  0.885879\n",
+       " 981  0.893391  0.570189  0.942578  0.272301  0.005066  0.796102\n",
+       " 982  0.641254  0.410475  0.936308  0.138125  0.169802  0.760013\n",
+       " 983  0.264843  0.896752  0.362217  0.777314  0.974496  0.724129\n",
+       " 984  0.965033  0.378385  0.982344  0.095794  0.479302  0.919390\n",
+       " 985  0.893925  0.060998  0.018978  0.458415  0.686720  0.121469\n",
+       " 986  0.608454  0.390522  0.529878  0.734067  0.822267  0.619513\n",
+       " 987  0.520784  0.657236  0.929091  0.550108  0.169860  0.329250\n",
+       " 988  0.420282  0.784163  0.616174  0.613967  0.792751  0.073226\n",
+       " 989  0.255002  0.372010  0.487345  0.378266  0.375970  0.577356\n",
+       " 990  0.021494  0.110736  0.823523  0.087171  0.019338  0.694684\n",
+       " 991  0.026556  0.544336  0.594698  0.851570  0.866105  0.742064\n",
+       " 992  0.829669  0.233105  0.349409  0.202948  0.982687  0.104709\n",
+       " 993  0.928436  0.475137  0.527999  0.342303  0.401130  0.456777\n",
+       " 994  0.078682  0.866147  0.622667  0.574582  0.541337  0.620093\n",
+       " 995  0.474660  0.773749  0.576200  0.799920  0.245390  0.859838\n",
+       " 996  0.929583  0.343986  0.769676  0.266969  0.975543  0.551582\n",
+       " 997  0.951001  0.173043  0.564255  0.617431  0.760863  0.055343\n",
+       " 998  0.250420  0.550022  0.685472  0.360968  0.361109  0.355148\n",
+       " 999  0.802059  0.341142  0.017195  0.592720  0.982926  0.145614\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.943149  0.882240  0.202633  0.454768  0.462976  0.262732\n",
+       " 1    0.961499  0.578208  0.592122  0.897121  0.710514  0.492831\n",
+       " 2    0.168382  0.756670  0.507605  0.647847  0.709014  0.300398\n",
+       " 3    0.061583  0.640962  0.785671  0.384496  0.072647  0.147033\n",
+       " 4    0.077325  0.116601  0.538354  0.901575  0.630491  0.076573\n",
+       " 5    0.799837  0.117008  0.394405  0.585774  0.914169  0.544146\n",
+       " 6    0.456191  0.643741  0.248645  0.125755  0.078089  0.503904\n",
+       " 7    0.129560  0.127810  0.790861  0.186342  0.636004  0.343031\n",
+       " 8    0.875495  0.511093  0.731399  0.384033  0.301337  0.754910\n",
+       " 9    0.729409  0.984015  0.688588  0.242418  0.773371  0.579236\n",
+       " 10   0.451571  0.371788  0.388791  0.793808  0.277907  0.288524\n",
+       " 11   0.974624  0.214825  0.728365  0.447424  0.663359  0.914587\n",
+       " 12   0.790380  0.724336  0.531750  0.903218  0.624703  0.330063\n",
+       " 13   0.282419  0.642079  0.791053  0.031053  0.393131  0.001920\n",
+       " 14   0.641933  0.266952  0.926055  0.496418  0.892439  0.218440\n",
+       " 15   0.463538  0.873369  0.021533  0.524375  0.407200  0.109120\n",
+       " 16   0.605308  0.046631  0.453776  0.485006  0.293410  0.950837\n",
+       " 17   0.812287  0.673899  0.292750  0.544201  0.683097  0.187571\n",
+       " 18   0.104686  0.037015  0.894388  0.500205  0.994103  0.445520\n",
+       " 19   0.611431  0.373156  0.294012  0.251531  0.171827  0.731384\n",
+       " 20   0.976293  0.800073  0.631849  0.313311  0.652068  0.709466\n",
+       " 21   0.954159  0.890491  0.788002  0.123086  0.316699  0.354159\n",
+       " 22   0.763863  0.374312  0.764065  0.678861  0.027458  0.906980\n",
+       " 23   0.583834  0.526703  0.390876  0.641769  0.741289  0.216546\n",
+       " 24   0.154444  0.348931  0.419867  0.896993  0.026021  0.923626\n",
+       " 25   0.966275  0.745523  0.400751  0.021676  0.528947  0.519239\n",
+       " 26   0.058939  0.922156  0.650922  0.864506  0.512387  0.714131\n",
+       " 27   0.261762  0.130447  0.111518  0.154985  0.958736  0.191165\n",
+       " 28   0.907267  0.161245  0.004870  0.632410  0.350508  0.178059\n",
+       " 29   0.018407  0.833899  0.959481  0.081389  0.206934  0.134484\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.726075  0.973867  0.390420  0.797064  0.949560  0.200749\n",
+       " 971  0.712555  0.783491  0.453170  0.414601  0.116020  0.456265\n",
+       " 972  0.954848  0.380663  0.448770  0.825769  0.421305  0.394716\n",
+       " 973  0.535237  0.070235  0.373194  0.624277  0.606830  0.182017\n",
+       " 974  0.950129  0.362701  0.488771  0.741210  0.366874  0.922112\n",
+       " 975  0.316406  0.480512  0.801408  0.430294  0.123425  0.898310\n",
+       " 976  0.385635  0.047306  0.999290  0.142800  0.781115  0.234565\n",
+       " 977  0.820718  0.535836  0.095393  0.330569  0.140403  0.904174\n",
+       " 978  0.354874  0.231145  0.180291  0.565520  0.849219  0.410115\n",
+       " 979  0.547325  0.609036  0.545542  0.393331  0.306681  0.431230\n",
+       " 980  0.799819  0.014912  0.237044  0.118375  0.548431  0.231973\n",
+       " 981  0.016650  0.662991  0.813858  0.811468  0.166233  0.342053\n",
+       " 982  0.166447  0.830782  0.906563  0.260633  0.348919  0.054307\n",
+       " 983  0.217625  0.157896  0.802373  0.820843  0.441487  0.382899\n",
+       " 984  0.059224  0.765193  0.040137  0.798114  0.356674  0.732559\n",
+       " 985  0.922791  0.664306  0.615567  0.005805  0.107895  0.446402\n",
+       " 986  0.099568  0.167623  0.547082  0.224852  0.477213  0.068022\n",
+       " 987  0.659953  0.680708  0.713760  0.927194  0.932789  0.049402\n",
+       " 988  0.317328  0.843798  0.417159  0.036399  0.407277  0.410187\n",
+       " 989  0.228983  0.637302  0.101374  0.915189  0.034049  0.266731\n",
+       " 990  0.401948  0.811850  0.320627  0.646442  0.072118  0.043440\n",
+       " 991  0.754121  0.706233  0.080076  0.382122  0.646245  0.926333\n",
+       " 992  0.380233  0.244616  0.602998  0.410171  0.205609  0.645042\n",
+       " 993  0.866955  0.236635  0.707823  0.973694  0.708959  0.235252\n",
+       " 994  0.046428  0.859272  0.212579  0.008115  0.428249  0.702237\n",
+       " 995  0.074237  0.818771  0.400074  0.380012  0.584879  0.161210\n",
+       " 996  0.012125  0.495110  0.717546  0.556402  0.477387  0.168312\n",
+       " 997  0.753107  0.618335  0.498168  0.926332  0.005192  0.350558\n",
+       " 998  0.479527  0.252214  0.981867  0.502935  0.961366  0.123307\n",
+       " 999  0.722388  0.387156  0.496268  0.078186  0.184037  0.820686\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.894865  0.845435  0.447153  0.618032  0.280480  0.463773\n",
+       " 1    0.859958  0.667510  0.489510  0.751639  0.018888  0.028758\n",
+       " 2    0.590820  0.812319  0.559377  0.446572  0.385140  0.835683\n",
+       " 3    0.381812  0.360184  0.012529  0.376454  0.213341  0.631718\n",
+       " 4    0.186700  0.661060  0.289767  0.179970  0.701080  0.615986\n",
+       " 5    0.605075  0.228509  0.532877  0.384867  0.460415  0.353077\n",
+       " 6    0.400777  0.062889  0.581020  0.926911  0.355027  0.375373\n",
+       " 7    0.796633  0.725543  0.002962  0.862183  0.823589  0.879699\n",
+       " 8    0.793345  0.115230  0.648968  0.513047  0.732811  0.967850\n",
+       " 9    0.280831  0.715494  0.652296  0.455703  0.037052  0.282457\n",
+       " 10   0.814145  0.946510  0.877867  0.508738  0.093610  0.737955\n",
+       " 11   0.845683  0.478186  0.148612  0.007671  0.166239  0.413162\n",
+       " 12   0.546084  0.365864  0.136875  0.407430  0.390146  0.829501\n",
+       " 13   0.113292  0.873401  0.736204  0.507921  0.326934  0.084815\n",
+       " 14   0.058515  0.030275  0.732392  0.293407  0.569487  0.520329\n",
+       " 15   0.880271  0.326219  0.998067  0.508320  0.266270  0.961161\n",
+       " 16   0.778625  0.062360  0.067279  0.200781  0.976415  0.962383\n",
+       " 17   0.349369  0.596094  0.346105  0.621427  0.423634  0.275536\n",
+       " 18   0.212151  0.910746  0.976516  0.065543  0.447644  0.292088\n",
+       " 19   0.205227  0.543029  0.030124  0.497807  0.070609  0.357776\n",
+       " 20   0.711558  0.053366  0.046774  0.289391  0.514737  0.942192\n",
+       " 21   0.868829  0.752777  0.973418  0.750665  0.429058  0.082491\n",
+       " 22   0.256441  0.093162  0.426997  0.472953  0.383236  0.929469\n",
+       " 23   0.083202  0.045347  0.418119  0.608508  0.815902  0.560734\n",
+       " 24   0.599661  0.377009  0.824798  0.521251  0.433435  0.734291\n",
+       " 25   0.373807  0.927618  0.324324  0.998949  0.232538  0.104774\n",
+       " 26   0.535426  0.494361  0.666379  0.757954  0.135622  0.394044\n",
+       " 27   0.217414  0.980922  0.157009  0.644338  0.151923  0.226244\n",
+       " 28   0.356687  0.071096  0.750094  0.625629  0.608566  0.485404\n",
+       " 29   0.494148  0.001131  0.347593  0.857148  0.623298  0.590560\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.678085  0.208731  0.587879  0.078450  0.880020  0.637998\n",
+       " 971  0.442257  0.034220  0.583180  0.618921  0.597905  0.040869\n",
+       " 972  0.301460  0.270614  0.521581  0.144976  0.434862  0.388474\n",
+       " 973  0.816318  0.369484  0.112964  0.533128  0.322479  0.096712\n",
+       " 974  0.447329  0.182397  0.868252  0.945172  0.366191  0.185265\n",
+       " 975  0.500155  0.080791  0.732337  0.936846  0.832349  0.248383\n",
+       " 976  0.568622  0.222448  0.922352  0.735285  0.872919  0.061709\n",
+       " 977  0.753251  0.851021  0.863288  0.909052  0.787276  0.454755\n",
+       " 978  0.881948  0.172069  0.495175  0.505540  0.942135  0.581309\n",
+       " 979  0.742753  0.889862  0.951893  0.989953  0.903218  0.492521\n",
+       " 980  0.128016  0.079924  0.857422  0.100699  0.149460  0.823998\n",
+       " 981  0.539354  0.226435  0.138153  0.608950  0.950129  0.069476\n",
+       " 982  0.088636  0.464036  0.758584  0.600241  0.017130  0.602419\n",
+       " 983  0.205582  0.575540  0.119515  0.199019  0.324386  0.345010\n",
+       " 984  0.532220  0.176673  0.404811  0.352150  0.764086  0.838804\n",
+       " 985  0.396228  0.520307  0.402517  0.786700  0.915980  0.313885\n",
+       " 986  0.401544  0.191088  0.472935  0.178296  0.250866  0.031765\n",
+       " 987  0.482226  0.503173  0.745445  0.399883  0.832963  0.128819\n",
+       " 988  0.654311  0.401617  0.107747  0.297164  0.328964  0.315267\n",
+       " 989  0.867781  0.885117  0.524942  0.747628  0.473007  0.552497\n",
+       " 990  0.702540  0.820126  0.459799  0.689409  0.107547  0.755110\n",
+       " 991  0.400797  0.393350  0.638252  0.419203  0.641170  0.812821\n",
+       " 992  0.607353  0.057315  0.516829  0.338593  0.298516  0.314161\n",
+       " 993  0.322630  0.452808  0.951361  0.917627  0.656915  0.758449\n",
+       " 994  0.129071  0.890707  0.733957  0.546344  0.570210  0.082942\n",
+       " 995  0.848031  0.982842  0.192159  0.226111  0.439956  0.984376\n",
+       " 996  0.229673  0.190158  0.912002  0.080190  0.934278  0.615795\n",
+       " 997  0.518770  0.170442  0.706007  0.555146  0.548127  0.824273\n",
+       " 998  0.402955  0.561338  0.004056  0.069887  0.488912  0.529403\n",
+       " 999  0.691895  0.595905  0.482049  0.220959  0.445104  0.434486\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.418672  0.908553  0.636963  0.669003  0.838342  0.488370\n",
+       " 1    0.728460  0.589162  0.028098  0.073679  0.599221  0.296658\n",
+       " 2    0.627307  0.383228  0.781694  0.999293  0.743718  0.327371\n",
+       " 3    0.614012  0.583399  0.499179  0.224104  0.959207  0.310518\n",
+       " 4    0.385602  0.782300  0.021883  0.917770  0.169792  0.346052\n",
+       " 5    0.721417  0.263544  0.473077  0.387703  0.519108  0.172538\n",
+       " 6    0.774912  0.875061  0.680768  0.691415  0.870930  0.691635\n",
+       " 7    0.805767  0.973019  0.848423  0.063198  0.823762  0.206122\n",
+       " 8    0.252068  0.684906  0.355742  0.545675  0.062109  0.453388\n",
+       " 9    0.646771  0.621573  0.250018  0.404698  0.723873  0.083827\n",
+       " 10   0.999656  0.460915  0.440131  0.381114  0.467807  0.712204\n",
+       " 11   0.706230  0.578804  0.186888  0.797006  0.360963  0.967009\n",
+       " 12   0.272038  0.728557  0.185375  0.663341  0.387472  0.233399\n",
+       " 13   0.423689  0.822920  0.505914  0.418393  0.199068  0.144452\n",
+       " 14   0.386774  0.655080  0.216416  0.506225  0.222239  0.897422\n",
+       " 15   0.890127  0.750997  0.068728  0.707187  0.553979  0.746152\n",
+       " 16   0.517941  0.244287  0.521593  0.045270  0.417384  0.119994\n",
+       " 17   0.819692  0.125918  0.080898  0.480686  0.091851  0.721878\n",
+       " 18   0.876576  0.410702  0.030117  0.838892  0.228094  0.182395\n",
+       " 19   0.498311  0.124457  0.572348  0.836888  0.787842  0.581370\n",
+       " 20   0.473656  0.855989  0.002020  0.792967  0.033755  0.492897\n",
+       " 21   0.131715  0.999930  0.673240  0.136291  0.698472  0.343762\n",
+       " 22   0.641965  0.694454  0.377496  0.205537  0.959949  0.980644\n",
+       " 23   0.720274  0.112269  0.801416  0.632874  0.092277  0.564042\n",
+       " 24   0.211686  0.319885  0.367158  0.203840  0.999065  0.405761\n",
+       " 25   0.152132  0.199151  0.350081  0.899187  0.958816  0.209275\n",
+       " 26   0.329258  0.355894  0.376400  0.234881  0.190672  0.372162\n",
+       " 27   0.629014  0.562974  0.170557  0.756691  0.135540  0.157132\n",
+       " 28   0.093377  0.976403  0.627395  0.930563  0.894231  0.395402\n",
+       " 29   0.878634  0.584711  0.963688  0.520500  0.980013  0.731207\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.985248  0.513643  0.769566  0.366302  0.927945  0.201698\n",
+       " 971  0.504953  0.494903  0.890689  0.979947  0.674850  0.925287\n",
+       " 972  0.231492  0.279449  0.623576  0.115622  0.125955  0.302851\n",
+       " 973  0.009458  0.003588  0.209556  0.343495  0.726314  0.331654\n",
+       " 974  0.273821  0.890460  0.560552  0.333001  0.667618  0.316965\n",
+       " 975  0.140161  0.057209  0.791980  0.936270  0.293613  0.342706\n",
+       " 976  0.252045  0.588963  0.922393  0.435663  0.110299  0.336759\n",
+       " 977  0.900362  0.018770  0.532583  0.619061  0.743762  0.649103\n",
+       " 978  0.348259  0.390397  0.113982  0.406965  0.734314  0.882940\n",
+       " 979  0.443311  0.411925  0.913496  0.109272  0.491821  0.100065\n",
+       " 980  0.387342  0.726508  0.402301  0.072580  0.926860  0.347904\n",
+       " 981  0.815091  0.778437  0.715678  0.390441  0.632177  0.759985\n",
+       " 982  0.730501  0.487126  0.347007  0.714217  0.594194  0.245515\n",
+       " 983  0.279153  0.628261  0.240250  0.351947  0.702418  0.215890\n",
+       " 984  0.566799  0.473759  0.622344  0.394514  0.639734  0.229104\n",
+       " 985  0.452549  0.787065  0.487364  0.365469  0.457726  0.602495\n",
+       " 986  0.435322  0.150431  0.412403  0.836961  0.015661  0.339511\n",
+       " 987  0.312830  0.542599  0.027677  0.138894  0.896995  0.837013\n",
+       " 988  0.343122  0.131761  0.954082  0.381128  0.011351  0.019603\n",
+       " 989  0.062267  0.640067  0.999560  0.847306  0.369991  0.672379\n",
+       " 990  0.769946  0.854196  0.554823  0.059307  0.957843  0.739270\n",
+       " 991  0.663227  0.100857  0.967172  0.830363  0.809268  0.495267\n",
+       " 992  0.249396  0.964461  0.650218  0.730055  0.446322  0.486781\n",
+       " 993  0.025704  0.171104  0.365395  0.497593  0.081010  0.083953\n",
+       " 994  0.660740  0.333125  0.470041  0.347483  0.130103  0.918416\n",
+       " 995  0.966401  0.277296  0.647625  0.934649  0.132571  0.637454\n",
+       " 996  0.390605  0.578731  0.769177  0.405258  0.389708  0.805684\n",
+       " 997  0.216127  0.366903  0.587961  0.673586  0.219139  0.210984\n",
+       " 998  0.758142  0.524066  0.711657  0.770902  0.321266  0.994946\n",
+       " 999  0.931040  0.352282  0.626260  0.082823  0.250101  0.831662\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.040169  0.216491  0.954747  0.170718  0.606037  0.858656\n",
+       " 1    0.202760  0.572392  0.156700  0.546342  0.579545  0.192599\n",
+       " 2    0.735014  0.263027  0.274152  0.674748  0.591107  0.713823\n",
+       " 3    0.759868  0.006826  0.493026  0.493726  0.543831  0.520540\n",
+       " 4    0.729844  0.093692  0.021483  0.421264  0.362270  0.929177\n",
+       " 5    0.516762  0.267518  0.529371  0.814879  0.692495  0.945478\n",
+       " 6    0.702354  0.058741  0.247165  0.249586  0.635682  0.263631\n",
+       " 7    0.410551  0.889912  0.664969  0.800145  0.737878  0.502720\n",
+       " 8    0.867440  0.450101  0.071909  0.261862  0.180909  0.085694\n",
+       " 9    0.009502  0.048957  0.943207  0.430755  0.597792  0.356567\n",
+       " 10   0.713628  0.421409  0.445139  0.360717  0.750766  0.277948\n",
+       " 11   0.247709  0.901607  0.027461  0.689412  0.931421  0.186628\n",
+       " 12   0.300827  0.180914  0.297064  0.276323  0.150176  0.652923\n",
+       " 13   0.048441  0.188747  0.896046  0.393984  0.709672  0.355850\n",
+       " 14   0.125854  0.961024  0.585095  0.623300  0.578446  0.241159\n",
+       " 15   0.354382  0.499554  0.921651  0.378361  0.210737  0.546485\n",
+       " 16   0.976861  0.918723  0.693703  0.085490  0.249060  0.981153\n",
+       " 17   0.893920  0.071422  0.566040  0.144595  0.431410  0.212562\n",
+       " 18   0.990073  0.777788  0.585678  0.432590  0.034406  0.002017\n",
+       " 19   0.866560  0.538227  0.607619  0.627291  0.954379  0.602818\n",
+       " 20   0.845518  0.442575  0.120325  0.395336  0.945587  0.098898\n",
+       " 21   0.375568  0.010732  0.588202  0.290779  0.496200  0.874933\n",
+       " 22   0.561279  0.105009  0.278147  0.110587  0.181558  0.053786\n",
+       " 23   0.463722  0.847818  0.079190  0.309017  0.561585  0.568903\n",
+       " 24   0.875713  0.843130  0.798014  0.576723  0.522616  0.747159\n",
+       " 25   0.720111  0.722854  0.709845  0.157867  0.586807  0.270623\n",
+       " 26   0.858183  0.225381  0.311496  0.329904  0.607484  0.498099\n",
+       " 27   0.255319  0.738539  0.471676  0.239655  0.218404  0.154255\n",
+       " 28   0.389523  0.043627  0.067185  0.633756  0.062269  0.631460\n",
+       " 29   0.954624  0.824432  0.376089  0.022529  0.089867  0.964630\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.405670  0.438127  0.050085  0.577644  0.162022  0.964400\n",
+       " 971  0.149395  0.040203  0.689915  0.669714  0.921553  0.103560\n",
+       " 972  0.670861  0.249998  0.104992  0.379855  0.941062  0.982140\n",
+       " 973  0.257039  0.424933  0.962663  0.818568  0.252572  0.121278\n",
+       " 974  0.594154  0.515796  0.041574  0.243557  0.072242  0.585972\n",
+       " 975  0.873108  0.915715  0.686748  0.454253  0.935726  0.166062\n",
+       " 976  0.192209  0.712665  0.669938  0.278146  0.179851  0.084251\n",
+       " 977  0.168158  0.487105  0.259952  0.393563  0.562843  0.786165\n",
+       " 978  0.049372  0.397819  0.483249  0.153252  0.803393  0.383134\n",
+       " 979  0.058768  0.266731  0.609832  0.005647  0.596295  0.111126\n",
+       " 980  0.221060  0.350094  0.188450  0.052978  0.677548  0.302439\n",
+       " 981  0.816086  0.251261  0.462390  0.075279  0.658470  0.987775\n",
+       " 982  0.039434  0.867957  0.717894  0.389375  0.159234  0.323451\n",
+       " 983  0.399111  0.965801  0.820463  0.243713  0.981327  0.063266\n",
+       " 984  0.993761  0.957011  0.550151  0.831102  0.108146  0.448243\n",
+       " 985  0.628141  0.733364  0.648783  0.649709  0.861794  0.937280\n",
+       " 986  0.791256  0.258712  0.028822  0.581428  0.332730  0.896721\n",
+       " 987  0.768980  0.927489  0.074456  0.714434  0.400591  0.263799\n",
+       " 988  0.912433  0.642163  0.920004  0.867979  0.080781  0.625290\n",
+       " 989  0.804425  0.235803  0.713539  0.552100  0.648978  0.361264\n",
+       " 990  0.169118  0.427535  0.543225  0.070836  0.669149  0.856579\n",
+       " 991  0.537837  0.986767  0.739353  0.112920  0.021081  0.502078\n",
+       " 992  0.575135  0.247189  0.277068  0.530775  0.319884  0.347143\n",
+       " 993  0.348559  0.115755  0.347240  0.550011  0.897941  0.997410\n",
+       " 994  0.795969  0.043303  0.581648  0.536013  0.364785  0.234344\n",
+       " 995  0.864207  0.587414  0.037019  0.364566  0.784323  0.359659\n",
+       " 996  0.550756  0.498006  0.222787  0.404534  0.328658  0.284598\n",
+       " 997  0.979965  0.924258  0.463334  0.363823  0.297809  0.547051\n",
+       " 998  0.038946  0.823418  0.695161  0.352784  0.738407  0.549628\n",
+       " 999  0.368054  0.383856  0.223546  0.719063  0.341393  0.040027\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.231065  0.998301  0.175820  0.254528  0.334822  0.732503\n",
+       " 1    0.093209  0.782860  0.206966  0.798759  0.195272  0.300762\n",
+       " 2    0.286457  0.227397  0.054973  0.449952  0.907355  0.529249\n",
+       " 3    0.408577  0.376444  0.028440  0.249666  0.598351  0.146085\n",
+       " 4    0.389191  0.520526  0.418943  0.836412  0.781064  0.860446\n",
+       " 5    0.103937  0.052367  0.145557  0.263030  0.995110  0.511219\n",
+       " 6    0.545137  0.683309  0.715528  0.032294  0.769510  0.546503\n",
+       " 7    0.072527  0.551281  0.955553  0.125460  0.688854  0.867377\n",
+       " 8    0.135854  0.893313  0.655831  0.932163  0.147189  0.278437\n",
+       " 9    0.391401  0.709665  0.457762  0.475204  0.117618  0.329137\n",
+       " 10   0.597197  0.571541  0.816109  0.429274  0.909508  0.142283\n",
+       " 11   0.292043  0.549959  0.451093  0.281203  0.983974  0.075226\n",
+       " 12   0.739969  0.582758  0.181941  0.903866  0.161941  0.607735\n",
+       " 13   0.232743  0.729276  0.525740  0.973430  0.296667  0.687229\n",
+       " 14   0.379884  0.024747  0.265777  0.694113  0.168106  0.246897\n",
+       " 15   0.924857  0.188305  0.499682  0.705600  0.079622  0.826701\n",
+       " 16   0.494173  0.257765  0.624520  0.120024  0.019527  0.677937\n",
+       " 17   0.349720  0.113712  0.575377  0.780206  0.236805  0.284219\n",
+       " 18   0.742240  0.774198  0.788718  0.265223  0.757192  0.712750\n",
+       " 19   0.799571  0.094474  0.475025  0.191154  0.100504  0.438025\n",
+       " 20   0.148610  0.694025  0.976229  0.539088  0.439940  0.021577\n",
+       " 21   0.697792  0.608599  0.600401  0.308094  0.638212  0.735886\n",
+       " 22   0.354647  0.662974  0.274360  0.053191  0.037997  0.016258\n",
+       " 23   0.900254  0.774539  0.943158  0.166360  0.367680  0.107693\n",
+       " 24   0.263790  0.818962  0.975768  0.342621  0.269924  0.280824\n",
+       " 25   0.117736  0.566932  0.729511  0.538204  0.759001  0.342539\n",
+       " 26   0.318656  0.867719  0.625098  0.042219  0.795998  0.235242\n",
+       " 27   0.982713  0.341575  0.941048  0.206548  0.785324  0.172674\n",
+       " 28   0.805466  0.302095  0.974218  0.560977  0.696464  0.907714\n",
+       " 29   0.123128  0.988558  0.039269  0.148007  0.473596  0.365447\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.823081  0.223601  0.488485  0.469881  0.035381  0.137225\n",
+       " 971  0.851683  0.783267  0.065632  0.579480  0.613251  0.265654\n",
+       " 972  0.431460  0.690491  0.428801  0.625228  0.173447  0.845016\n",
+       " 973  0.593264  0.613334  0.549836  0.170128  0.770186  0.543084\n",
+       " 974  0.473312  0.772954  0.692541  0.403748  0.432499  0.412654\n",
+       " 975  0.987228  0.411138  0.047414  0.225299  0.203423  0.653881\n",
+       " 976  0.256525  0.322047  0.138024  0.444207  0.034844  0.304967\n",
+       " 977  0.184551  0.742319  0.383981  0.923800  0.969326  0.864566\n",
+       " 978  0.071879  0.744814  0.355711  0.225796  0.891195  0.349080\n",
+       " 979  0.326033  0.115550  0.815813  0.322643  0.552509  0.696345\n",
+       " 980  0.571304  0.953700  0.488962  0.946387  0.100622  0.226928\n",
+       " 981  0.267815  0.965493  0.638240  0.798401  0.826116  0.259130\n",
+       " 982  0.568257  0.646134  0.798737  0.171650  0.428100  0.204375\n",
+       " 983  0.102442  0.103869  0.035123  0.206784  0.762709  0.891475\n",
+       " 984  0.596792  0.170766  0.154419  0.927627  0.941746  0.065867\n",
+       " 985  0.129921  0.957153  0.281408  0.926568  0.109659  0.902665\n",
+       " 986  0.248583  0.619841  0.185323  0.644463  0.663153  0.687696\n",
+       " 987  0.465215  0.273423  0.829406  0.987479  0.241578  0.397528\n",
+       " 988  0.253651  0.706957  0.961009  0.243783  0.716838  0.671018\n",
+       " 989  0.625348  0.286775  0.448946  0.994326  0.845259  0.534825\n",
+       " 990  0.249246  0.104864  0.607909  0.037879  0.248274  0.842083\n",
+       " 991  0.642737  0.878566  0.747508  0.455112  0.916797  0.387085\n",
+       " 992  0.638944  0.315385  0.844029  0.717600  0.158610  0.895777\n",
+       " 993  0.674470  0.446259  0.619206  0.669377  0.954592  0.639037\n",
+       " 994  0.835495  0.717028  0.368227  0.785031  0.731392  0.013838\n",
+       " 995  0.642161  0.575921  0.982204  0.011889  0.967767  0.706246\n",
+       " 996  0.408521  0.462822  0.646463  0.189758  0.785337  0.827377\n",
+       " 997  0.671252  0.717262  0.281616  0.365817  0.290541  0.381708\n",
+       " 998  0.086600  0.368946  0.270171  0.918587  0.489853  0.366266\n",
+       " 999  0.574339  0.485240  0.476435  0.207713  0.288673  0.831037\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.315964  0.777513  0.824680  0.972548  0.727166  0.723548\n",
+       " 1    0.459007  0.107897  0.659560  0.980714  0.762292  0.228397\n",
+       " 2    0.833455  0.806631  0.888121  0.496738  0.478373  0.214438\n",
+       " 3    0.267093  0.492161  0.953283  0.636041  0.534274  0.476051\n",
+       " 4    0.922326  0.544349  0.078265  0.094107  0.830886  0.781895\n",
+       " 5    0.383064  0.980319  0.688233  0.285758  0.299924  0.180810\n",
+       " 6    0.369825  0.287564  0.654350  0.669727  0.834953  0.583026\n",
+       " 7    0.599665  0.779461  0.556204  0.218212  0.663463  0.644639\n",
+       " 8    0.162052  0.328286  0.479231  0.030576  0.124010  0.692022\n",
+       " 9    0.191874  0.808783  0.538364  0.170171  0.004110  0.978462\n",
+       " 10   0.843773  0.191693  0.977434  0.858372  0.582540  0.777828\n",
+       " 11   0.537897  0.917147  0.059730  0.288959  0.893890  0.654628\n",
+       " 12   0.361384  0.124828  0.691486  0.400595  0.102606  0.187401\n",
+       " 13   0.407774  0.209602  0.507897  0.769352  0.589829  0.380805\n",
+       " 14   0.232722  0.768443  0.328507  0.482490  0.986651  0.051274\n",
+       " 15   0.480096  0.668099  0.647441  0.890463  0.087213  0.546632\n",
+       " 16   0.325211  0.840268  0.395227  0.841751  0.440175  0.972535\n",
+       " 17   0.748625  0.118980  0.785746  0.573471  0.030012  0.922668\n",
+       " 18   0.665881  0.317609  0.216891  0.911741  0.882585  0.949767\n",
+       " 19   0.646059  0.297945  0.807317  0.246421  0.579017  0.834828\n",
+       " 20   0.066991  0.659414  0.526293  0.621277  0.836270  0.429406\n",
+       " 21   0.492013  0.928355  0.599472  0.447742  0.662101  0.103247\n",
+       " 22   0.467191  0.417517  0.012079  0.733820  0.123275  0.205138\n",
+       " 23   0.802781  0.588992  0.657041  0.034899  0.286801  0.271700\n",
+       " 24   0.376849  0.338083  0.546155  0.753292  0.663348  0.203256\n",
+       " 25   0.441739  0.811412  0.742247  0.859738  0.983709  0.525757\n",
+       " 26   0.803006  0.836723  0.129142  0.476476  0.453831  0.087806\n",
+       " 27   0.682232  0.714030  0.635992  0.945135  0.718346  0.891474\n",
+       " 28   0.641120  0.420933  0.350910  0.655947  0.956588  0.217342\n",
+       " 29   0.816790  0.659873  0.914224  0.378565  0.021410  0.197129\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.081479  0.463252  0.056658  0.764544  0.281891  0.941903\n",
+       " 971  0.352059  0.337241  0.925898  0.073955  0.946109  0.050535\n",
+       " 972  0.056996  0.492837  0.822637  0.123482  0.361834  0.447015\n",
+       " 973  0.842447  0.271768  0.343425  0.988468  0.041660  0.483521\n",
+       " 974  0.093548  0.369551  0.081943  0.156546  0.749623  0.086618\n",
+       " 975  0.989713  0.834600  0.104289  0.533765  0.857150  0.292396\n",
+       " 976  0.649099  0.512176  0.676500  0.949705  0.485610  0.530439\n",
+       " 977  0.976091  0.427205  0.034736  0.204356  0.325643  0.170417\n",
+       " 978  0.503143  0.057637  0.937230  0.561760  0.110932  0.764911\n",
+       " 979  0.709134  0.957918  0.485298  0.000635  0.135974  0.231190\n",
+       " 980  0.359174  0.503781  0.038727  0.573889  0.347550  0.711585\n",
+       " 981  0.128470  0.374766  0.522623  0.408565  0.351088  0.881569\n",
+       " 982  0.379666  0.791171  0.139774  0.125294  0.096028  0.806762\n",
+       " 983  0.151670  0.777660  0.678224  0.549970  0.443540  0.738556\n",
+       " 984  0.255376  0.105862  0.573079  0.072144  0.092528  0.818829\n",
+       " 985  0.785542  0.356803  0.176411  0.576486  0.799148  0.343188\n",
+       " 986  0.745657  0.569956  0.172899  0.125631  0.248869  0.679814\n",
+       " 987  0.313409  0.063553  0.954654  0.191022  0.260076  0.012351\n",
+       " 988  0.608221  0.806465  0.189551  0.829994  0.203929  0.647875\n",
+       " 989  0.541129  0.805945  0.223192  0.439952  0.444381  0.169289\n",
+       " 990  0.126839  0.605544  0.785510  0.143927  0.023193  0.079271\n",
+       " 991  0.960404  0.036342  0.668100  0.477766  0.715867  0.820188\n",
+       " 992  0.090662  0.947601  0.372680  0.294796  0.121551  0.546870\n",
+       " 993  0.429167  0.849665  0.779001  0.334039  0.091055  0.786011\n",
+       " 994  0.390918  0.726471  0.023754  0.273068  0.452360  0.652221\n",
+       " 995  0.307482  0.377721  0.985484  0.108932  0.859894  0.715454\n",
+       " 996  0.391913  0.544009  0.140223  0.276796  0.967076  0.738273\n",
+       " 997  0.681006  0.591511  0.913642  0.418754  0.654240  0.294397\n",
+       " 998  0.901405  0.579369  0.467151  0.094599  0.769924  0.746383\n",
+       " 999  0.794829  0.796598  0.225015  0.969429  0.791202  0.060532\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.694926  0.530543  0.384409  0.081958  0.302253  0.878869\n",
+       " 1    0.572226  0.344497  0.690602  0.684890  0.341873  0.999669\n",
+       " 2    0.240450  0.765281  0.873237  0.247931  0.055660  0.581173\n",
+       " 3    0.455850  0.667183  0.612941  0.163633  0.601216  0.140470\n",
+       " 4    0.503994  0.127783  0.694964  0.921011  0.871221  0.022127\n",
+       " 5    0.697148  0.810242  0.537743  0.894806  0.939765  0.829196\n",
+       " 6    0.603845  0.140098  0.421466  0.387896  0.139686  0.394187\n",
+       " 7    0.280877  0.011429  0.501354  0.176146  0.417805  0.195721\n",
+       " 8    0.804420  0.327873  0.902698  0.971073  0.902306  0.444040\n",
+       " 9    0.788354  0.876455  0.656847  0.287691  0.933507  0.948225\n",
+       " 10   0.274364  0.211889  0.552461  0.351794  0.527967  0.431713\n",
+       " 11   0.609878  0.922425  0.092498  0.695152  0.192717  0.468482\n",
+       " 12   0.486077  0.202150  0.803138  0.919800  0.282207  0.021008\n",
+       " 13   0.456278  0.075045  0.041235  0.411774  0.232774  0.655602\n",
+       " 14   0.060000  0.830492  0.744969  0.907124  0.438068  0.253589\n",
+       " 15   0.943242  0.270016  0.819451  0.605278  0.318102  0.025055\n",
+       " 16   0.122804  0.488173  0.093604  0.644172  0.995815  0.769515\n",
+       " 17   0.449846  0.790660  0.051594  0.038315  0.532893  0.960053\n",
+       " 18   0.539361  0.922693  0.654557  0.876687  0.255519  0.634139\n",
+       " 19   0.113999  0.335781  0.543071  0.445411  0.242912  0.695200\n",
+       " 20   0.852416  0.620707  0.850602  0.220839  0.978177  0.678281\n",
+       " 21   0.880728  0.674992  0.494803  0.801466  0.491485  0.594824\n",
+       " 22   0.059765  0.609427  0.328219  0.674721  0.120203  0.625210\n",
+       " 23   0.317752  0.463894  0.859108  0.744630  0.216944  0.720897\n",
+       " 24   0.105315  0.983202  0.047788  0.370749  0.652417  0.600432\n",
+       " 25   0.659560  0.494521  0.291267  0.430728  0.626659  0.830118\n",
+       " 26   0.012882  0.431758  0.403995  0.777634  0.172775  0.422799\n",
+       " 27   0.294198  0.138645  0.719989  0.733473  0.409031  0.352080\n",
+       " 28   0.882565  0.760558  0.399849  0.101655  0.698774  0.106437\n",
+       " 29   0.895639  0.338373  0.068789  0.492603  0.131101  0.895606\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.055619  0.337984  0.358412  0.894199  0.119834  0.461897\n",
+       " 971  0.368052  0.659773  0.769795  0.673069  0.843779  0.216678\n",
+       " 972  0.787959  0.952173  0.306412  0.669783  0.125268  0.461703\n",
+       " 973  0.634350  0.818087  0.130060  0.051196  0.008870  0.040733\n",
+       " 974  0.592798  0.098068  0.907778  0.234517  0.780747  0.917456\n",
+       " 975  0.158464  0.056362  0.204288  0.361693  0.420664  0.767359\n",
+       " 976  0.869998  0.603216  0.964396  0.715295  0.147977  0.924002\n",
+       " 977  0.361224  0.452606  0.032256  0.674127  0.677849  0.159769\n",
+       " 978  0.174385  0.218372  0.479313  0.097185  0.001350  0.758071\n",
+       " 979  0.720753  0.104683  0.980346  0.274241  0.627343  0.492555\n",
+       " 980  0.854452  0.012744  0.598556  0.247598  0.120902  0.166320\n",
+       " 981  0.470906  0.749942  0.257828  0.816769  0.139699  0.146081\n",
+       " 982  0.881303  0.579319  0.387497  0.256325  0.251053  0.361646\n",
+       " 983  0.876181  0.396150  0.128635  0.438454  0.124004  0.421006\n",
+       " 984  0.225684  0.025290  0.866532  0.417451  0.643887  0.940200\n",
+       " 985  0.076809  0.401807  0.626113  0.055437  0.597843  0.775521\n",
+       " 986  0.614098  0.543643  0.163772  0.360434  0.700880  0.051538\n",
+       " 987  0.069542  0.892477  0.720776  0.675573  0.195002  0.269457\n",
+       " 988  0.765681  0.099542  0.068610  0.254725  0.923857  0.230101\n",
+       " 989  0.873229  0.295532  0.636100  0.695478  0.292220  0.418360\n",
+       " 990  0.158905  0.701138  0.539888  0.430824  0.068264  0.574442\n",
+       " 991  0.431523  0.450354  0.792982  0.456355  0.123314  0.724563\n",
+       " 992  0.391881  0.280753  0.481997  0.280761  0.676948  0.883848\n",
+       " 993  0.910873  0.876480  0.295110  0.594947  0.986844  0.479879\n",
+       " 994  0.405610  0.841446  0.384052  0.437318  0.211921  0.751025\n",
+       " 995  0.423926  0.894281  0.459375  0.425617  0.237780  0.231735\n",
+       " 996  0.317512  0.963571  0.082325  0.641108  0.093726  0.373670\n",
+       " 997  0.011902  0.121561  0.568207  0.490349  0.596265  0.725275\n",
+       " 998  0.061698  0.065848  0.766027  0.641835  0.093363  0.848945\n",
+       " 999  0.326151  0.772513  0.765875  0.498704  0.260161  0.379217\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.261278  0.465314  0.400828  0.517966  0.990572  0.040784\n",
+       " 1    0.335324  0.179184  0.552598  0.010332  0.417525  0.175196\n",
+       " 2    0.351877  0.906976  0.432610  0.373943  0.766336  0.416376\n",
+       " 3    0.152331  0.282187  0.102945  0.019034  0.515848  0.879528\n",
+       " 4    0.574768  0.536352  0.972390  0.267322  0.597034  0.702062\n",
+       " 5    0.272473  0.871075  0.766627  0.733660  0.767660  0.599399\n",
+       " 6    0.141533  0.505485  0.774614  0.454717  0.374602  0.270436\n",
+       " 7    0.229717  0.412230  0.367272  0.012474  0.808864  0.722385\n",
+       " 8    0.969192  0.510523  0.273357  0.643571  0.922633  0.406040\n",
+       " 9    0.814261  0.502974  0.886657  0.957990  0.401317  0.624108\n",
+       " 10   0.911404  0.888833  0.909709  0.642696  0.437210  0.271811\n",
+       " 11   0.142408  0.195244  0.454553  0.038489  0.570134  0.827420\n",
+       " 12   0.537380  0.820255  0.300860  0.325629  0.652399  0.705484\n",
+       " 13   0.568753  0.254806  0.662743  0.526436  0.517939  0.063693\n",
+       " 14   0.631069  0.381474  0.356064  0.053059  0.503323  0.459324\n",
+       " 15   0.612521  0.618474  0.419055  0.333207  0.592310  0.547445\n",
+       " 16   0.970412  0.998023  0.463839  0.777752  0.054674  0.802940\n",
+       " 17   0.728837  0.288041  0.198012  0.011904  0.842944  0.885687\n",
+       " 18   0.698092  0.541397  0.492125  0.468365  0.145437  0.294057\n",
+       " 19   0.276047  0.774858  0.596277  0.427619  0.336070  0.198968\n",
+       " 20   0.200967  0.038731  0.815073  0.436701  0.888574  0.465891\n",
+       " 21   0.510348  0.762698  0.751951  0.377782  0.226993  0.755335\n",
+       " 22   0.499877  0.594303  0.342330  0.137975  0.627535  0.941463\n",
+       " 23   0.366515  0.050146  0.444808  0.203670  0.306867  0.406803\n",
+       " 24   0.928982  0.362797  0.370035  0.789415  0.081659  0.734599\n",
+       " 25   0.376159  0.054727  0.632046  0.334400  0.183395  0.145365\n",
+       " 26   0.969154  0.190022  0.056743  0.039023  0.836491  0.679397\n",
+       " 27   0.933434  0.227214  0.402764  0.529741  0.552043  0.749141\n",
+       " 28   0.395505  0.271322  0.961973  0.742141  0.370217  0.030013\n",
+       " 29   0.840108  0.533754  0.329244  0.874861  0.363690  0.596349\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.316837  0.131103  0.103840  0.322929  0.036081  0.910607\n",
+       " 971  0.110560  0.615157  0.875872  0.997654  0.188233  0.441798\n",
+       " 972  0.916172  0.929578  0.043823  0.064840  0.114662  0.695731\n",
+       " 973  0.286954  0.597926  0.076156  0.475330  0.974151  0.697133\n",
+       " 974  0.642776  0.757725  0.997080  0.805252  0.778094  0.235681\n",
+       " 975  0.114351  0.753168  0.680671  0.002353  0.615300  0.094691\n",
+       " 976  0.082974  0.715380  0.937789  0.567397  0.140587  0.015723\n",
+       " 977  0.696884  0.886139  0.584411  0.090009  0.051424  0.424574\n",
+       " 978  0.854420  0.207999  0.559615  0.747012  0.317026  0.246715\n",
+       " 979  0.928461  0.442180  0.030333  0.073060  0.847760  0.398741\n",
+       " 980  0.637206  0.386465  0.544316  0.331816  0.354975  0.171978\n",
+       " 981  0.062959  0.851370  0.926813  0.661122  0.656684  0.777785\n",
+       " 982  0.227003  0.726542  0.785127  0.857733  0.239338  0.036989\n",
+       " 983  0.538933  0.751829  0.293724  0.781534  0.345330  0.360917\n",
+       " 984  0.697970  0.369161  0.365895  0.497031  0.983326  0.730337\n",
+       " 985  0.575037  0.762107  0.517507  0.320078  0.349990  0.552460\n",
+       " 986  0.893525  0.782871  0.584623  0.794117  0.984025  0.043585\n",
+       " 987  0.137883  0.227458  0.229507  0.822509  0.418650  0.516144\n",
+       " 988  0.947960  0.161903  0.581424  0.963967  0.479324  0.865024\n",
+       " 989  0.907195  0.622373  0.553678  0.989484  0.388279  0.867975\n",
+       " 990  0.910340  0.712716  0.280775  0.513433  0.467181  0.997330\n",
+       " 991  0.848973  0.815572  0.716104  0.971868  0.588530  0.694854\n",
+       " 992  0.283849  0.081417  0.881938  0.983092  0.038804  0.210290\n",
+       " 993  0.266794  0.007842  0.701541  0.857481  0.751825  0.778118\n",
+       " 994  0.248763  0.898068  0.211742  0.035217  0.792043  0.291930\n",
+       " 995  0.992562  0.588720  0.649252  0.236627  0.875069  0.678754\n",
+       " 996  0.010572  0.646652  0.560649  0.681801  0.206260  0.153936\n",
+       " 997  0.441307  0.517259  0.040842  0.596592  0.163509  0.414037\n",
+       " 998  0.080587  0.955398  0.381982  0.884193  0.891258  0.827153\n",
+       " 999  0.084929  0.609863  0.055960  0.140573  0.213114  0.465136\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.167235  0.178982  0.563043  0.556035  0.585386  0.498973\n",
+       " 1    0.152274  0.537567  0.704396  0.287205  0.696318  0.410778\n",
+       " 2    0.287907  0.646479  0.474539  0.608896  0.588490  0.504834\n",
+       " 3    0.182328  0.132573  0.521910  0.983460  0.417389  0.900517\n",
+       " 4    0.622377  0.946464  0.258888  0.611899  0.267183  0.578765\n",
+       " 5    0.569674  0.287922  0.004934  0.053450  0.907762  0.655201\n",
+       " 6    0.252566  0.911741  0.812713  0.701096  0.292910  0.112909\n",
+       " 7    0.093898  0.294340  0.815533  0.208441  0.643731  0.997631\n",
+       " 8    0.519815  0.608399  0.386125  0.871700  0.010559  0.176855\n",
+       " 9    0.140288  0.622056  0.843048  0.295406  0.984800  0.700116\n",
+       " 10   0.221548  0.497804  0.527453  0.671500  0.906846  0.955540\n",
+       " 11   0.089347  0.407191  0.801420  0.322815  0.038931  0.778506\n",
+       " 12   0.099334  0.021510  0.157070  0.920351  0.013006  0.104289\n",
+       " 13   0.736806  0.738283  0.123599  0.234588  0.455882  0.865469\n",
+       " 14   0.913919  0.867767  0.099454  0.926903  0.767324  0.953525\n",
+       " 15   0.780096  0.517705  0.087875  0.447439  0.021850  0.905797\n",
+       " 16   0.846297  0.262289  0.513611  0.354181  0.010564  0.079838\n",
+       " 17   0.234322  0.570679  0.308188  0.961388  0.392490  0.960770\n",
+       " 18   0.103637  0.769317  0.914269  0.955097  0.932905  0.339013\n",
+       " 19   0.414449  0.393612  0.705240  0.252470  0.771794  0.703898\n",
+       " 20   0.184379  0.603857  0.979468  0.680110  0.739566  0.096910\n",
+       " 21   0.650446  0.945871  0.734541  0.446183  0.475283  0.771679\n",
+       " 22   0.710939  0.408806  0.130526  0.582964  0.844897  0.085744\n",
+       " 23   0.546331  0.826681  0.839121  0.664907  0.871425  0.858963\n",
+       " 24   0.289531  0.490239  0.260165  0.130362  0.167866  0.317244\n",
+       " 25   0.405640  0.061423  0.985928  0.845341  0.776645  0.465084\n",
+       " 26   0.964318  0.219833  0.545381  0.584778  0.735394  0.459683\n",
+       " 27   0.756258  0.583083  0.421986  0.578346  0.804059  0.183015\n",
+       " 28   0.023005  0.073464  0.814167  0.868322  0.865428  0.570278\n",
+       " 29   0.715160  0.295217  0.232177  0.038497  0.147053  0.456111\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.591660  0.595296  0.248297  0.575880  0.995160  0.773171\n",
+       " 971  0.468130  0.354109  0.463711  0.250503  0.977750  0.467303\n",
+       " 972  0.253871  0.326022  0.579721  0.223542  0.497423  0.275735\n",
+       " 973  0.162142  0.650560  0.312481  0.218786  0.629463  0.559332\n",
+       " 974  0.992846  0.942952  0.275307  0.696024  0.762688  0.614394\n",
+       " 975  0.449747  0.422200  0.294275  0.316434  0.666879  0.188175\n",
+       " 976  0.437093  0.934206  0.334801  0.538072  0.832500  0.306400\n",
+       " 977  0.207529  0.047176  0.338703  0.844276  0.170684  0.502766\n",
+       " 978  0.651174  0.533455  0.977507  0.822136  0.212726  0.013904\n",
+       " 979  0.221855  0.736891  0.978711  0.179720  0.848085  0.292505\n",
+       " 980  0.539421  0.211670  0.174298  0.463432  0.801430  0.948067\n",
+       " 981  0.640096  0.016810  0.824671  0.651005  0.314414  0.376422\n",
+       " 982  0.543493  0.004907  0.770541  0.924225  0.560850  0.972318\n",
+       " 983  0.297749  0.444769  0.927657  0.229064  0.121479  0.675474\n",
+       " 984  0.504752  0.484626  0.787650  0.083993  0.016102  0.513614\n",
+       " 985  0.369193  0.934375  0.371740  0.020558  0.273410  0.183798\n",
+       " 986  0.078286  0.846188  0.930554  0.277345  0.408954  0.696575\n",
+       " 987  0.590207  0.720166  0.839714  0.822311  0.084172  0.367421\n",
+       " 988  0.195542  0.480138  0.619418  0.566354  0.418575  0.809692\n",
+       " 989  0.654187  0.952503  0.415597  0.759860  0.446167  0.855994\n",
+       " 990  0.262354  0.962387  0.390442  0.100706  0.207539  0.441065\n",
+       " 991  0.406673  0.212819  0.220631  0.143345  0.127460  0.472942\n",
+       " 992  0.254248  0.018273  0.576073  0.823603  0.793142  0.638318\n",
+       " 993  0.503806  0.440656  0.211959  0.089855  0.704599  0.322483\n",
+       " 994  0.977936  0.327230  0.972620  0.778379  0.251469  0.432575\n",
+       " 995  0.078640  0.635896  0.036029  0.890043  0.035665  0.614422\n",
+       " 996  0.762650  0.817362  0.780714  0.915229  0.919458  0.944153\n",
+       " 997  0.880912  0.717752  0.486444  0.999540  0.209019  0.588906\n",
+       " 998  0.635399  0.671044  0.448398  0.027119  0.035909  0.377248\n",
+       " 999  0.662807  0.741339  0.145598  0.244617  0.462341  0.194006\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.774690  0.028188  0.722235  0.880092  0.317861  0.946794\n",
+       " 1    0.088306  0.062192  0.964802  0.493911  0.377204  0.863994\n",
+       " 2    0.612168  0.945618  0.032971  0.959310  0.953033  0.819522\n",
+       " 3    0.834236  0.796167  0.058418  0.686401  0.734841  0.936308\n",
+       " 4    0.676778  0.295727  0.332377  0.004027  0.964012  0.530574\n",
+       " 5    0.450122  0.802851  0.915585  0.542858  0.356462  0.805125\n",
+       " 6    0.651969  0.329703  0.436959  0.314402  0.251748  0.105866\n",
+       " 7    0.571205  0.844307  0.115235  0.438071  0.441990  0.441890\n",
+       " 8    0.587868  0.302394  0.622627  0.576271  0.358754  0.797042\n",
+       " 9    0.275232  0.582128  0.269014  0.349070  0.158424  0.868575\n",
+       " 10   0.318543  0.514955  0.492956  0.886439  0.157603  0.653435\n",
+       " 11   0.666577  0.896995  0.992434  0.368320  0.640190  0.071362\n",
+       " 12   0.058863  0.889288  0.156748  0.664757  0.004565  0.606883\n",
+       " 13   0.149931  0.618473  0.491997  0.806704  0.042298  0.979662\n",
+       " 14   0.745786  0.674465  0.069741  0.678271  0.438752  0.102099\n",
+       " 15   0.848919  0.568431  0.814969  0.138439  0.403766  0.471333\n",
+       " 16   0.901856  0.893888  0.764401  0.203499  0.023534  0.298712\n",
+       " 17   0.516525  0.992791  0.293834  0.085057  0.199024  0.662759\n",
+       " 18   0.392020  0.083909  0.788489  0.383907  0.599560  0.008250\n",
+       " 19   0.583170  0.378253  0.581009  0.853209  0.436299  0.063395\n",
+       " 20   0.760719  0.927041  0.934163  0.263356  0.706653  0.281658\n",
+       " 21   0.388406  0.615243  0.977957  0.790793  0.649391  0.168030\n",
+       " 22   0.751343  0.730264  0.380280  0.916997  0.942686  0.149685\n",
+       " 23   0.354234  0.475022  0.498149  0.205728  0.192772  0.351700\n",
+       " 24   0.970907  0.228946  0.095653  0.713750  0.357829  0.530255\n",
+       " 25   0.046015  0.577599  0.874152  0.881380  0.571538  0.604302\n",
+       " 26   0.046147  0.733832  0.934948  0.740733  0.713957  0.191170\n",
+       " 27   0.208420  0.572023  0.339682  0.486292  0.753956  0.196231\n",
+       " 28   0.432397  0.387514  0.248892  0.758243  0.115110  0.231223\n",
+       " 29   0.469616  0.657124  0.420890  0.515952  0.751109  0.788960\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.537208  0.730178  0.822959  0.933546  0.813256  0.778478\n",
+       " 971  0.399588  0.601525  0.891440  0.110189  0.364656  0.440830\n",
+       " 972  0.751073  0.514663  0.865388  0.999198  0.775620  0.655896\n",
+       " 973  0.164631  0.983795  0.621379  0.555796  0.310953  0.479820\n",
+       " 974  0.156793  0.575718  0.752350  0.967983  0.722102  0.424195\n",
+       " 975  0.283924  0.511404  0.662576  0.467447  0.520372  0.008004\n",
+       " 976  0.782616  0.878593  0.423332  0.977835  0.667416  0.347352\n",
+       " 977  0.597731  0.368970  0.322350  0.144251  0.430592  0.422152\n",
+       " 978  0.756162  0.158143  0.304340  0.527339  0.889881  0.007850\n",
+       " 979  0.039216  0.761387  0.101624  0.423553  0.687612  0.320981\n",
+       " 980  0.447942  0.227432  0.684721  0.295098  0.059046  0.193623\n",
+       " 981  0.899619  0.239661  0.467212  0.562933  0.156985  0.482291\n",
+       " 982  0.466063  0.115344  0.909629  0.238139  0.550260  0.933350\n",
+       " 983  0.977948  0.565110  0.454474  0.719961  0.121102  0.026353\n",
+       " 984  0.511254  0.918843  0.251731  0.234057  0.605386  0.233348\n",
+       " 985  0.706782  0.694411  0.685419  0.942972  0.626979  0.937922\n",
+       " 986  0.201769  0.327521  0.363327  0.678235  0.725557  0.813044\n",
+       " 987  0.020886  0.464514  0.680396  0.350629  0.398516  0.198407\n",
+       " 988  0.561075  0.596666  0.402397  0.982607  0.487909  0.053414\n",
+       " 989  0.714616  0.696613  0.517337  0.572418  0.775346  0.449634\n",
+       " 990  0.710054  0.307431  0.486547  0.079790  0.934158  0.751145\n",
+       " 991  0.130568  0.609951  0.583508  0.226887  0.638481  0.119528\n",
+       " 992  0.231211  0.745002  0.060783  0.395352  0.107278  0.275772\n",
+       " 993  0.399652  0.880249  0.145734  0.691450  0.198669  0.657325\n",
+       " 994  0.236052  0.611517  0.118391  0.140749  0.331245  0.543989\n",
+       " 995  0.136033  0.252954  0.330541  0.246882  0.297272  0.212922\n",
+       " 996  0.847481  0.742644  0.080108  0.166267  0.509060  0.977554\n",
+       " 997  0.410394  0.930843  0.650748  0.427661  0.711962  0.214474\n",
+       " 998  0.386753  0.674037  0.552340  0.204775  0.953608  0.136318\n",
+       " 999  0.764080  0.852498  0.577726  0.918169  0.735937  0.160771\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.544884  0.384323  0.624904  0.906514  0.461540  0.771168\n",
+       " 1    0.988191  0.918771  0.041672  0.025083  0.888178  0.933918\n",
+       " 2    0.045850  0.137215  0.366365  0.402554  0.864050  0.691804\n",
+       " 3    0.692017  0.790893  0.780982  0.733193  0.291715  0.381709\n",
+       " 4    0.650471  0.450103  0.783842  0.064019  0.104524  0.271375\n",
+       " 5    0.440801  0.237053  0.524266  0.779131  0.807854  0.481662\n",
+       " 6    0.571013  0.281101  0.228443  0.293195  0.109246  0.024171\n",
+       " 7    0.292103  0.570168  0.144226  0.541874  0.098524  0.208127\n",
+       " 8    0.609192  0.334427  0.051570  0.238272  0.880120  0.319047\n",
+       " 9    0.393454  0.345687  0.862281  0.538372  0.635357  0.333790\n",
+       " 10   0.177697  0.679839  0.233362  0.823405  0.075213  0.389938\n",
+       " 11   0.463278  0.450428  0.268530  0.372733  0.511461  0.959446\n",
+       " 12   0.851689  0.601085  0.991990  0.992014  0.542559  0.884758\n",
+       " 13   0.381540  0.174224  0.898856  0.909063  0.697299  0.467083\n",
+       " 14   0.010932  0.174878  0.005368  0.170812  0.749135  0.815702\n",
+       " 15   0.877683  0.725239  0.777277  0.577029  0.410672  0.367918\n",
+       " 16   0.964475  0.718299  0.880009  0.391848  0.515206  0.136583\n",
+       " 17   0.143544  0.775791  0.656291  0.208369  0.511935  0.507947\n",
+       " 18   0.826626  0.680359  0.301331  0.434865  0.538051  0.589680\n",
+       " 19   0.728246  0.978725  0.843819  0.519966  0.880854  0.433005\n",
+       " 20   0.895707  0.726237  0.163259  0.340541  0.122437  0.491184\n",
+       " 21   0.827382  0.762358  0.289081  0.516369  0.432074  0.276951\n",
+       " 22   0.231432  0.015119  0.858905  0.328768  0.549867  0.792600\n",
+       " 23   0.194303  0.524437  0.061540  0.401889  0.452389  0.614210\n",
+       " 24   0.868638  0.038466  0.699142  0.265453  0.635687  0.953207\n",
+       " 25   0.440723  0.836509  0.900608  0.697457  0.577141  0.819207\n",
+       " 26   0.730908  0.135273  0.473479  0.991664  0.122668  0.068136\n",
+       " 27   0.943644  0.591693  0.609421  0.216590  0.543899  0.011345\n",
+       " 28   0.800817  0.308474  0.691618  0.280228  0.734991  0.061772\n",
+       " 29   0.132672  0.867414  0.486770  0.865219  0.590693  0.151182\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.166598  0.317932  0.207918  0.445271  0.741880  0.511356\n",
+       " 971  0.982881  0.014916  0.934249  0.307666  0.575285  0.071063\n",
+       " 972  0.247427  0.893228  0.164105  0.176164  0.440474  0.873547\n",
+       " 973  0.218001  0.774776  0.229973  0.646491  0.760460  0.742781\n",
+       " 974  0.615022  0.124289  0.049756  0.541809  0.398730  0.699712\n",
+       " 975  0.348974  0.411188  0.175857  0.749020  0.555435  0.196943\n",
+       " 976  0.735137  0.177921  0.776572  0.960611  0.008190  0.440344\n",
+       " 977  0.902110  0.868966  0.525482  0.130586  0.529898  0.619917\n",
+       " 978  0.749067  0.948357  0.182140  0.622420  0.902359  0.541833\n",
+       " 979  0.956856  0.905178  0.629774  0.386093  0.165294  0.696686\n",
+       " 980  0.917719  0.519381  0.846494  0.239391  0.891321  0.959992\n",
+       " 981  0.407592  0.583603  0.340308  0.712131  0.652517  0.627635\n",
+       " 982  0.112017  0.609647  0.462730  0.219417  0.521557  0.481335\n",
+       " 983  0.801672  0.626181  0.848253  0.109303  0.866026  0.210663\n",
+       " 984  0.136681  0.568864  0.036660  0.389550  0.345385  0.176998\n",
+       " 985  0.914611  0.714074  0.279669  0.064237  0.821687  0.794929\n",
+       " 986  0.074390  0.108381  0.898729  0.098480  0.139352  0.653586\n",
+       " 987  0.032378  0.166219  0.835435  0.860532  0.729408  0.975526\n",
+       " 988  0.954035  0.871893  0.074992  0.829526  0.412343  0.360296\n",
+       " 989  0.294536  0.648514  0.910774  0.173360  0.295314  0.356720\n",
+       " 990  0.985924  0.230864  0.474140  0.927075  0.644124  0.946368\n",
+       " 991  0.616295  0.257221  0.132290  0.260958  0.895757  0.905391\n",
+       " 992  0.593862  0.381349  0.550372  0.511697  0.204836  0.182564\n",
+       " 993  0.057067  0.704948  0.155406  0.995069  0.836201  0.008478\n",
+       " 994  0.220411  0.386331  0.712919  0.952611  0.549574  0.906709\n",
+       " 995  0.414698  0.015175  0.161252  0.298408  0.422824  0.786796\n",
+       " 996  0.795812  0.167611  0.769704  0.603974  0.046627  0.413629\n",
+       " 997  0.442186  0.720052  0.124958  0.819415  0.372013  0.556995\n",
+       " 998  0.056169  0.578027  0.610934  0.736933  0.304216  0.455448\n",
+       " 999  0.849211  0.545201  0.930792  0.279170  0.730153  0.673767\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.494103  0.678217  0.284331  0.457069  0.432385  0.257691\n",
+       " 1    0.355742  0.885890  0.063652  0.283103  0.324213  0.330324\n",
+       " 2    0.223412  0.386791  0.952464  0.811633  0.893195  0.783638\n",
+       " 3    0.805550  0.526472  0.813104  0.426990  0.038240  0.117107\n",
+       " 4    0.062564  0.538280  0.646672  0.200590  0.837206  0.537537\n",
+       " 5    0.140631  0.477325  0.797785  0.993039  0.518536  0.300631\n",
+       " 6    0.297740  0.222186  0.779634  0.142373  0.092207  0.505278\n",
+       " 7    0.568733  0.648744  0.754470  0.672387  0.215639  0.349483\n",
+       " 8    0.151967  0.341680  0.566779  0.242748  0.487326  0.825071\n",
+       " 9    0.134840  0.357224  0.923620  0.817089  0.758692  0.951886\n",
+       " 10   0.473305  0.712162  0.716418  0.583041  0.536569  0.333629\n",
+       " 11   0.926303  0.111040  0.093100  0.839442  0.971607  0.909453\n",
+       " 12   0.663711  0.795404  0.968748  0.124330  0.102676  0.836088\n",
+       " 13   0.092875  0.062168  0.007095  0.456378  0.310057  0.801451\n",
+       " 14   0.184998  0.261866  0.936869  0.834685  0.058953  0.540019\n",
+       " 15   0.049406  0.927619  0.441500  0.152473  0.639159  0.667833\n",
+       " 16   0.975950  0.233581  0.550534  0.610128  0.794651  0.514964\n",
+       " 17   0.122247  0.831821  0.650477  0.038763  0.216237  0.333018\n",
+       " 18   0.259183  0.129989  0.711975  0.028465  0.397055  0.258543\n",
+       " 19   0.245084  0.259161  0.753107  0.634555  0.170274  0.663176\n",
+       " 20   0.698158  0.644446  0.623118  0.546795  0.434697  0.136532\n",
+       " 21   0.594406  0.692405  0.318254  0.735022  0.885542  0.762259\n",
+       " 22   0.673353  0.134452  0.987220  0.733379  0.746861  0.118539\n",
+       " 23   0.441339  0.777012  0.726376  0.368438  0.534193  0.865119\n",
+       " 24   0.448221  0.894229  0.749210  0.611181  0.206095  0.578702\n",
+       " 25   0.359631  0.558852  0.274748  0.008616  0.689618  0.796125\n",
+       " 26   0.313304  0.043260  0.336585  0.275763  0.584324  0.060408\n",
+       " 27   0.825883  0.731964  0.655568  0.146806  0.797812  0.344891\n",
+       " 28   0.377739  0.114272  0.315524  0.502791  0.904174  0.672358\n",
+       " 29   0.194711  0.161537  0.985706  0.320355  0.544724  0.474829\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.468191  0.501542  0.262867  0.004542  0.292347  0.324096\n",
+       " 971  0.381613  0.804636  0.290245  0.721241  0.344380  0.874513\n",
+       " 972  0.684689  0.105513  0.273858  0.130837  0.807134  0.871484\n",
+       " 973  0.592675  0.415528  0.658948  0.535662  0.313459  0.550583\n",
+       " 974  0.790488  0.184103  0.979686  0.638310  0.991226  0.721278\n",
+       " 975  0.465510  0.991883  0.698232  0.293003  0.539556  0.487438\n",
+       " 976  0.071822  0.952519  0.900035  0.755628  0.905142  0.096805\n",
+       " 977  0.329453  0.629941  0.896416  0.067565  0.839108  0.827193\n",
+       " 978  0.581514  0.377570  0.656413  0.903105  0.305771  0.378268\n",
+       " 979  0.985763  0.740223  0.017026  0.120202  0.422634  0.724635\n",
+       " 980  0.356828  0.687453  0.036893  0.777047  0.836793  0.544022\n",
+       " 981  0.371537  0.976490  0.092427  0.264030  0.478742  0.285514\n",
+       " 982  0.773775  0.885131  0.807815  0.076592  0.820678  0.591206\n",
+       " 983  0.304351  0.418230  0.498950  0.519451  0.705130  0.976697\n",
+       " 984  0.840271  0.057871  0.195178  0.785842  0.423410  0.494787\n",
+       " 985  0.129293  0.159664  0.118711  0.382884  0.606806  0.653366\n",
+       " 986  0.231529  0.050369  0.406021  0.152800  0.576785  0.611584\n",
+       " 987  0.454119  0.886696  0.542978  0.016005  0.900313  0.163641\n",
+       " 988  0.787138  0.620682  0.924237  0.596001  0.385057  0.067252\n",
+       " 989  0.664055  0.259385  0.499129  0.949064  0.561737  0.224585\n",
+       " 990  0.485633  0.268603  0.742027  0.449065  0.354824  0.491527\n",
+       " 991  0.019646  0.413575  0.982778  0.582464  0.418985  0.572098\n",
+       " 992  0.674725  0.219834  0.391535  0.271233  0.005506  0.630368\n",
+       " 993  0.427657  0.314735  0.182471  0.245848  0.189860  0.225223\n",
+       " 994  0.522064  0.922081  0.124260  0.413123  0.323055  0.170807\n",
+       " 995  0.695240  0.370750  0.120867  0.646522  0.490560  0.979367\n",
+       " 996  0.246372  0.228099  0.917852  0.381222  0.572385  0.886085\n",
+       " 997  0.554238  0.209724  0.316180  0.591117  0.113784  0.841597\n",
+       " 998  0.700021  0.029454  0.295785  0.184832  0.777929  0.380473\n",
+       " 999  0.715173  0.012011  0.412440  0.527088  0.318298  0.048390\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.604408  0.561588  0.426379  0.977692  0.046037  0.112797\n",
+       " 1    0.807949  0.014684  0.453555  0.747640  0.297731  0.978299\n",
+       " 2    0.621877  0.208288  0.981275  0.885547  0.730642  0.739295\n",
+       " 3    0.735708  0.536950  0.053895  0.591126  0.063080  0.517068\n",
+       " 4    0.624867  0.146076  0.271266  0.643334  0.081075  0.323593\n",
+       " 5    0.729281  0.838595  0.703800  0.646913  0.880345  0.748116\n",
+       " 6    0.688777  0.200996  0.835660  0.209399  0.213295  0.711397\n",
+       " 7    0.921793  0.065885  0.736379  0.136363  0.053132  0.166699\n",
+       " 8    0.854910  0.571697  0.532979  0.683278  0.377173  0.715497\n",
+       " 9    0.609710  0.900220  0.558978  0.551673  0.160193  0.175916\n",
+       " 10   0.766687  0.131400  0.434726  0.278079  0.692842  0.126396\n",
+       " 11   0.082060  0.597453  0.361208  0.651587  0.744397  0.182103\n",
+       " 12   0.616970  0.827861  0.186546  0.324324  0.720120  0.881519\n",
+       " 13   0.232108  0.661403  0.215665  0.033151  0.664627  0.428771\n",
+       " 14   0.141285  0.842048  0.201885  0.908184  0.353243  0.123316\n",
+       " 15   0.159946  0.038681  0.276244  0.053946  0.092736  0.229676\n",
+       " 16   0.221103  0.580514  0.162896  0.153750  0.321616  0.414459\n",
+       " 17   0.075526  0.922980  0.817894  0.208337  0.152884  0.317747\n",
+       " 18   0.455387  0.724267  0.275009  0.434443  0.203859  0.169959\n",
+       " 19   0.369078  0.217885  0.866164  0.535912  0.520067  0.926163\n",
+       " 20   0.211995  0.071661  0.739672  0.916381  0.483050  0.388665\n",
+       " 21   0.358657  0.901189  0.198188  0.424096  0.529312  0.275074\n",
+       " 22   0.401587  0.647709  0.003492  0.629839  0.886548  0.038697\n",
+       " 23   0.003022  0.297849  0.027125  0.836826  0.936955  0.604951\n",
+       " 24   0.436622  0.516774  0.075852  0.917943  0.956395  0.332417\n",
+       " 25   0.115765  0.905587  0.284503  0.369706  0.346735  0.074101\n",
+       " 26   0.800482  0.597716  0.549763  0.498719  0.475988  0.621701\n",
+       " 27   0.258462  0.248751  0.859107  0.355028  0.849823  0.468301\n",
+       " 28   0.451104  0.059992  0.901995  0.692754  0.755402  0.323501\n",
+       " 29   0.531502  0.374402  0.706627  0.216714  0.788390  0.744020\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.259981  0.785244  0.100160  0.223234  0.670497  0.222170\n",
+       " 971  0.273847  0.995823  0.085190  0.600037  0.568080  0.151049\n",
+       " 972  0.994754  0.627622  0.999316  0.560880  0.513907  0.336929\n",
+       " 973  0.173831  0.944327  0.455642  0.598398  0.112906  0.914231\n",
+       " 974  0.096599  0.717707  0.151816  0.881368  0.999598  0.446419\n",
+       " 975  0.534492  0.827099  0.372920  0.702278  0.542165  0.536115\n",
+       " 976  0.472260  0.565529  0.725686  0.981907  0.931373  0.052978\n",
+       " 977  0.674337  0.494038  0.287117  0.945603  0.394140  0.504363\n",
+       " 978  0.473819  0.965412  0.860370  0.408615  0.541006  0.287295\n",
+       " 979  0.670283  0.064614  0.427084  0.773644  0.740821  0.212650\n",
+       " 980  0.825453  0.519008  0.259802  0.481604  0.714243  0.325751\n",
+       " 981  0.324004  0.568975  0.025521  0.066257  0.510789  0.073366\n",
+       " 982  0.079991  0.271552  0.041924  0.582569  0.158176  0.413628\n",
+       " 983  0.553128  0.552512  0.061679  0.741659  0.231772  0.787460\n",
+       " 984  0.244124  0.197214  0.476882  0.221482  0.178165  0.246998\n",
+       " 985  0.186742  0.858254  0.486742  0.398468  0.626843  0.127888\n",
+       " 986  0.435559  0.171265  0.639184  0.865229  0.242855  0.571279\n",
+       " 987  0.986567  0.728239  0.906259  0.102583  0.930709  0.531835\n",
+       " 988  0.101967  0.764948  0.190000  0.694628  0.894339  0.914928\n",
+       " 989  0.630132  0.861962  0.244676  0.349357  0.934795  0.026913\n",
+       " 990  0.699582  0.315623  0.551093  0.094694  0.127600  0.226653\n",
+       " 991  0.326832  0.174566  0.893029  0.609088  0.573020  0.326978\n",
+       " 992  0.928103  0.150889  0.372174  0.289067  0.361611  0.034487\n",
+       " 993  0.778207  0.793823  0.475421  0.681355  0.381929  0.900694\n",
+       " 994  0.797259  0.471506  0.012171  0.910351  0.679429  0.704963\n",
+       " 995  0.990030  0.352449  0.667623  0.054339  0.254552  0.509395\n",
+       " 996  0.548202  0.440487  0.771569  0.058563  0.717421  0.407700\n",
+       " 997  0.609063  0.805412  0.796043  0.789574  0.862882  0.578646\n",
+       " 998  0.138654  0.376635  0.264356  0.174285  0.046926  0.461945\n",
+       " 999  0.189224  0.032019  0.231765  0.462251  0.552935  0.565676\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.420894  0.120218  0.270295  0.005222  0.046221  0.031319\n",
+       " 1    0.493708  0.658754  0.470938  0.597282  0.849529  0.823128\n",
+       " 2    0.192900  0.021293  0.311890  0.144889  0.281072  0.474001\n",
+       " 3    0.816348  0.378167  0.208579  0.488630  0.358491  0.915063\n",
+       " 4    0.334848  0.579239  0.452945  0.506877  0.694942  0.698479\n",
+       " 5    0.964248  0.118671  0.987676  0.798463  0.958648  0.736654\n",
+       " 6    0.691329  0.856666  0.734358  0.372973  0.950616  0.590886\n",
+       " 7    0.607181  0.381220  0.345096  0.629840  0.784953  0.847244\n",
+       " 8    0.401920  0.866841  0.512828  0.834463  0.894238  0.698786\n",
+       " 9    0.827816  0.515464  0.768217  0.925938  0.148376  0.168172\n",
+       " 10   0.506917  0.722928  0.293351  0.798496  0.111844  0.483562\n",
+       " 11   0.281889  0.001155  0.844442  0.998439  0.324613  0.759921\n",
+       " 12   0.273133  0.057848  0.864736  0.737628  0.638913  0.078696\n",
+       " 13   0.561096  0.689817  0.809341  0.028150  0.665832  0.880699\n",
+       " 14   0.930849  0.869572  0.736521  0.113850  0.141150  0.175929\n",
+       " 15   0.521311  0.734827  0.586170  0.479517  0.744266  0.366425\n",
+       " 16   0.893428  0.048810  0.288757  0.419290  0.283470  0.869581\n",
+       " 17   0.554674  0.823621  0.963585  0.460154  0.735268  0.511692\n",
+       " 18   0.939219  0.007495  0.170653  0.301599  0.662144  0.187289\n",
+       " 19   0.571363  0.319552  0.556969  0.383473  0.167444  0.822128\n",
+       " 20   0.155217  0.412670  0.905098  0.110986  0.478290  0.149622\n",
+       " 21   0.756405  0.434465  0.891560  0.111529  0.526677  0.531484\n",
+       " 22   0.799001  0.018988  0.885405  0.692452  0.591091  0.146646\n",
+       " 23   0.495032  0.881761  0.580308  0.514148  0.791928  0.372100\n",
+       " 24   0.519627  0.591300  0.199516  0.350734  0.913472  0.748747\n",
+       " 25   0.811829  0.448703  0.431388  0.699675  0.256722  0.119235\n",
+       " 26   0.888223  0.809705  0.574737  0.116030  0.124540  0.004695\n",
+       " 27   0.041716  0.603263  0.412020  0.456034  0.022932  0.270833\n",
+       " 28   0.394513  0.910903  0.141091  0.279967  0.706042  0.533848\n",
+       " 29   0.553099  0.327429  0.963789  0.323404  0.598743  0.543922\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.174760  0.670702  0.343417  0.455691  0.264818  0.507012\n",
+       " 971  0.830293  0.062464  0.421531  0.654379  0.190180  0.776293\n",
+       " 972  0.496956  0.467394  0.295215  0.193972  0.580816  0.743906\n",
+       " 973  0.563332  0.707592  0.670691  0.857334  0.099873  0.029672\n",
+       " 974  0.185146  0.929061  0.801180  0.296459  0.247143  0.099223\n",
+       " 975  0.775468  0.204825  0.824039  0.215193  0.937828  0.311914\n",
+       " 976  0.437211  0.377581  0.059533  0.213652  0.401313  0.238237\n",
+       " 977  0.981660  0.826460  0.905328  0.673959  0.059727  0.107676\n",
+       " 978  0.148970  0.333597  0.792749  0.814329  0.861960  0.766065\n",
+       " 979  0.313100  0.380867  0.658731  0.419963  0.766767  0.347959\n",
+       " 980  0.235951  0.701151  0.689458  0.541559  0.172303  0.234974\n",
+       " 981  0.204432  0.255091  0.143535  0.780129  0.310162  0.874601\n",
+       " 982  0.881433  0.761367  0.003686  0.674642  0.806604  0.300910\n",
+       " 983  0.154404  0.431766  0.473909  0.076380  0.129765  0.919174\n",
+       " 984  0.498274  0.879379  0.500334  0.561462  0.300051  0.818463\n",
+       " 985  0.459443  0.481806  0.216333  0.483964  0.596843  0.539607\n",
+       " 986  0.658363  0.772146  0.384956  0.305148  0.926917  0.386833\n",
+       " 987  0.038515  0.837358  0.191355  0.926664  0.645890  0.420876\n",
+       " 988  0.934517  0.122086  0.895846  0.163804  0.298315  0.863459\n",
+       " 989  0.154025  0.277621  0.925847  0.349378  0.935985  0.202365\n",
+       " 990  0.380605  0.228588  0.712246  0.421955  0.199936  0.682693\n",
+       " 991  0.567046  0.909436  0.557669  0.423666  0.641032  0.602783\n",
+       " 992  0.677809  0.220483  0.622385  0.310431  0.387469  0.516632\n",
+       " 993  0.297818  0.747379  0.398618  0.134300  0.132825  0.055313\n",
+       " 994  0.189678  0.255729  0.596682  0.620903  0.927538  0.758739\n",
+       " 995  0.311207  0.588242  0.461871  0.469284  0.800849  0.977913\n",
+       " 996  0.527535  0.363224  0.851812  0.682089  0.583174  0.787949\n",
+       " 997  0.399928  0.375584  0.812789  0.704492  0.561406  0.004730\n",
+       " 998  0.360612  0.930175  0.248492  0.442569  0.517047  0.262805\n",
+       " 999  0.805432  0.698873  0.196362  0.509182  0.914987  0.082929\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.628493  0.657643  0.453289  0.581917  0.058397  0.645990\n",
+       " 1    0.068597  0.711522  0.880247  0.949038  0.147071  0.698430\n",
+       " 2    0.787702  0.242052  0.504442  0.007064  0.221261  0.040699\n",
+       " 3    0.211362  0.163984  0.130771  0.653734  0.531342  0.335344\n",
+       " 4    0.104802  0.439913  0.577457  0.037782  0.076293  0.257602\n",
+       " 5    0.605445  0.490530  0.848565  0.282610  0.359115  0.459545\n",
+       " 6    0.086818  0.304544  0.702073  0.088639  0.603697  0.179191\n",
+       " 7    0.041201  0.096143  0.648962  0.282954  0.210454  0.536021\n",
+       " 8    0.851179  0.017166  0.705906  0.667174  0.452824  0.129151\n",
+       " 9    0.749913  0.281261  0.257286  0.914656  0.711675  0.352132\n",
+       " 10   0.707660  0.063651  0.952015  0.929548  0.412551  0.744047\n",
+       " 11   0.666131  0.901434  0.436014  0.436250  0.639734  0.090305\n",
+       " 12   0.712616  0.946473  0.846557  0.554256  0.452921  0.885472\n",
+       " 13   0.226994  0.553556  0.692510  0.182607  0.546208  0.285324\n",
+       " 14   0.756624  0.653141  0.066419  0.368175  0.801782  0.969328\n",
+       " 15   0.494278  0.501097  0.169841  0.121035  0.725284  0.167612\n",
+       " 16   0.513050  0.679429  0.837076  0.119278  0.634324  0.721826\n",
+       " 17   0.353355  0.631980  0.333394  0.689710  0.420572  0.936041\n",
+       " 18   0.687872  0.750129  0.965507  0.160600  0.415504  0.872902\n",
+       " 19   0.111875  0.785050  0.548580  0.264817  0.306278  0.892150\n",
+       " 20   0.265866  0.886119  0.395099  0.045107  0.806716  0.370083\n",
+       " 21   0.550889  0.154146  0.237952  0.398972  0.864280  0.723264\n",
+       " 22   0.416565  0.201211  0.730360  0.725692  0.229093  0.020886\n",
+       " 23   0.687330  0.033446  0.956050  0.504375  0.049070  0.634936\n",
+       " 24   0.963005  0.264902  0.734464  0.979861  0.567316  0.528478\n",
+       " 25   0.363586  0.047541  0.193967  0.709198  0.917238  0.764629\n",
+       " 26   0.469375  0.663019  0.398204  0.815743  0.983154  0.283473\n",
+       " 27   0.883598  0.237731  0.063106  0.977998  0.548084  0.651419\n",
+       " 28   0.083808  0.853188  0.913357  0.139900  0.460110  0.781041\n",
+       " 29   0.202391  0.377433  0.068444  0.373381  0.307059  0.851521\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.239652  0.753370  0.945455  0.483785  0.450089  0.395930\n",
+       " 971  0.332290  0.432488  0.765919  0.052243  0.136278  0.870896\n",
+       " 972  0.259566  0.031650  0.969486  0.605923  0.548991  0.953174\n",
+       " 973  0.280838  0.887564  0.068731  0.229849  0.037054  0.871406\n",
+       " 974  0.715122  0.232897  0.398055  0.179346  0.845635  0.166357\n",
+       " 975  0.456902  0.925059  0.491388  0.000611  0.874488  0.248193\n",
+       " 976  0.360481  0.268095  0.249532  0.704149  0.139360  0.118299\n",
+       " 977  0.212796  0.061663  0.864661  0.443535  0.956635  0.174401\n",
+       " 978  0.042792  0.843744  0.951001  0.616460  0.023649  0.011333\n",
+       " 979  0.351356  0.379164  0.873533  0.512622  0.996368  0.080854\n",
+       " 980  0.603509  0.249022  0.583165  0.178830  0.500018  0.765483\n",
+       " 981  0.670169  0.851951  0.383019  0.272425  0.292866  0.127196\n",
+       " 982  0.013324  0.114839  0.439285  0.149327  0.070703  0.027472\n",
+       " 983  0.673156  0.035185  0.825215  0.037248  0.813291  0.743104\n",
+       " 984  0.655985  0.777591  0.160606  0.366498  0.504258  0.989248\n",
+       " 985  0.529044  0.943389  0.586589  0.350131  0.089517  0.960795\n",
+       " 986  0.287829  0.587361  0.103674  0.736337  0.629268  0.806945\n",
+       " 987  0.962533  0.694610  0.001455  0.416236  0.695169  0.199680\n",
+       " 988  0.674503  0.427097  0.442742  0.123042  0.740228  0.533033\n",
+       " 989  0.228420  0.514447  0.103125  0.450407  0.350447  0.484984\n",
+       " 990  0.810795  0.592272  0.232825  0.517790  0.044658  0.565103\n",
+       " 991  0.716032  0.628221  0.164341  0.347033  0.793937  0.113619\n",
+       " 992  0.548067  0.330316  0.809099  0.822879  0.643093  0.119057\n",
+       " 993  0.267651  0.070499  0.121000  0.623423  0.894274  0.349711\n",
+       " 994  0.811701  0.544413  0.642940  0.782559  0.457153  0.266041\n",
+       " 995  0.846107  0.482429  0.560402  0.657780  0.062803  0.992971\n",
+       " 996  0.629761  0.236316  0.593983  0.251268  0.370581  0.177335\n",
+       " 997  0.309400  0.515841  0.712342  0.574818  0.538283  0.020231\n",
+       " 998  0.197813  0.140253  0.454320  0.955685  0.436990  0.173566\n",
+       " 999  0.206639  0.939605  0.323364  0.149614  0.354833  0.512671\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.281598  0.320963  0.105812  0.201677  0.976234  0.276237\n",
+       " 1    0.326993  0.863804  0.481756  0.719264  0.767585  0.844376\n",
+       " 2    0.084236  0.435560  0.377233  0.546597  0.088124  0.073094\n",
+       " 3    0.719720  0.063991  0.040908  0.802726  0.113659  0.405346\n",
+       " 4    0.597404  0.284845  0.173930  0.819399  0.172422  0.446094\n",
+       " 5    0.213564  0.118976  0.854183  0.778308  0.122617  0.807581\n",
+       " 6    0.591242  0.237898  0.699395  0.201910  0.418387  0.327032\n",
+       " 7    0.276084  0.605730  0.386469  0.516123  0.901192  0.668678\n",
+       " 8    0.173735  0.243804  0.308132  0.947153  0.585635  0.326699\n",
+       " 9    0.853631  0.710604  0.492036  0.265059  0.496530  0.012927\n",
+       " 10   0.516587  0.192661  0.214295  0.304543  0.988395  0.685542\n",
+       " 11   0.832037  0.020141  0.019408  0.304639  0.612657  0.053499\n",
+       " 12   0.299508  0.382172  0.538847  0.746119  0.721442  0.616406\n",
+       " 13   0.367767  0.628347  0.655744  0.370941  0.583543  0.334816\n",
+       " 14   0.316307  0.498488  0.126704  0.111241  0.976652  0.675822\n",
+       " 15   0.938822  0.932402  0.927172  0.809630  0.806288  0.978265\n",
+       " 16   0.080284  0.821703  0.914855  0.797344  0.156269  0.795174\n",
+       " 17   0.412707  0.189119  0.716008  0.881310  0.413286  0.345130\n",
+       " 18   0.056970  0.832491  0.136043  0.325740  0.385471  0.220519\n",
+       " 19   0.910127  0.028287  0.798808  0.004656  0.417969  0.508497\n",
+       " 20   0.100447  0.501243  0.463940  0.379455  0.561850  0.772524\n",
+       " 21   0.597666  0.975223  0.264673  0.805929  0.727020  0.102480\n",
+       " 22   0.386912  0.259283  0.252092  0.409704  0.185772  0.360578\n",
+       " 23   0.972404  0.493359  0.474904  0.799007  0.022092  0.438783\n",
+       " 24   0.232483  0.706034  0.887015  0.649628  0.349412  0.701494\n",
+       " 25   0.971492  0.882092  0.538880  0.869304  0.889353  0.246930\n",
+       " 26   0.439777  0.462393  0.001246  0.016219  0.372467  0.443117\n",
+       " 27   0.486266  0.745299  0.211596  0.723901  0.864318  0.920193\n",
+       " 28   0.776142  0.124804  0.610466  0.791255  0.295723  0.945936\n",
+       " 29   0.711474  0.067254  0.622690  0.445799  0.575352  0.241428\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.735240  0.393119  0.141618  0.637437  0.014078  0.832257\n",
+       " 971  0.270939  0.352430  0.973297  0.623573  0.502955  0.321176\n",
+       " 972  0.241678  0.205156  0.632997  0.450263  0.873330  0.013568\n",
+       " 973  0.521584  0.928318  0.163010  0.304433  0.795046  0.805415\n",
+       " 974  0.081584  0.334938  0.730708  0.907888  0.921871  0.590513\n",
+       " 975  0.356924  0.255429  0.521138  0.103039  0.610584  0.297144\n",
+       " 976  0.969210  0.021516  0.983152  0.676534  0.632840  0.159233\n",
+       " 977  0.280155  0.332457  0.668084  0.303670  0.641616  0.033887\n",
+       " 978  0.432926  0.763575  0.344850  0.434758  0.825070  0.533455\n",
+       " 979  0.964233  0.047139  0.158419  0.328665  0.075380  0.667335\n",
+       " 980  0.221763  0.670299  0.789042  0.822905  0.871565  0.066435\n",
+       " 981  0.329618  0.770890  0.830709  0.794046  0.379937  0.575315\n",
+       " 982  0.525515  0.298137  0.662047  0.294173  0.793875  0.450641\n",
+       " 983  0.420449  0.414809  0.493457  0.951897  0.361026  0.229338\n",
+       " 984  0.360689  0.069636  0.177957  0.795900  0.902462  0.687851\n",
+       " 985  0.856095  0.211931  0.949224  0.588984  0.015651  0.243448\n",
+       " 986  0.525875  0.234652  0.176588  0.063854  0.424334  0.071123\n",
+       " 987  0.083148  0.483046  0.058567  0.670803  0.035654  0.387525\n",
+       " 988  0.218959  0.590882  0.494964  0.825367  0.887043  0.757884\n",
+       " 989  0.969122  0.662544  0.054046  0.595199  0.100341  0.125680\n",
+       " 990  0.171590  0.525711  0.290286  0.774858  0.510220  0.270967\n",
+       " 991  0.090142  0.033386  0.242598  0.281131  0.169844  0.787807\n",
+       " 992  0.330807  0.044325  0.974902  0.323406  0.758795  0.812334\n",
+       " 993  0.668874  0.246898  0.763098  0.343357  0.864728  0.074984\n",
+       " 994  0.459855  0.742720  0.459793  0.815694  0.651976  0.917259\n",
+       " 995  0.535858  0.809476  0.352404  0.740414  0.337597  0.064252\n",
+       " 996  0.168143  0.817523  0.416103  0.743936  0.812288  0.850861\n",
+       " 997  0.959395  0.273643  0.933575  0.361050  0.472213  0.176566\n",
+       " 998  0.009732  0.010788  0.097274  0.765099  0.087013  0.375842\n",
+       " 999  0.057581  0.640913  0.496854  0.981280  0.147583  0.276298\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.705158  0.384434  0.687367  0.340494  0.797965  0.806789\n",
+       " 1    0.450407  0.828351  0.833352  0.283533  0.736250  0.718370\n",
+       " 2    0.055122  0.407623  0.397486  0.924425  0.115671  0.043383\n",
+       " 3    0.311757  0.205788  0.895124  0.812817  0.924614  0.050886\n",
+       " 4    0.495904  0.073778  0.915008  0.107621  0.779138  0.817353\n",
+       " 5    0.149338  0.058675  0.735369  0.911524  0.653887  0.117371\n",
+       " 6    0.313522  0.682492  0.042998  0.284405  0.800140  0.759105\n",
+       " 7    0.137420  0.871595  0.542244  0.828467  0.838431  0.298128\n",
+       " 8    0.389298  0.924765  0.879387  0.989405  0.363555  0.107104\n",
+       " 9    0.596920  0.108735  0.770118  0.463007  0.912127  0.346846\n",
+       " 10   0.118107  0.108277  0.785890  0.109704  0.503645  0.444186\n",
+       " 11   0.151612  0.538132  0.915884  0.931333  0.501121  0.771716\n",
+       " 12   0.928644  0.195156  0.304074  0.635429  0.218175  0.080276\n",
+       " 13   0.152565  0.418293  0.406149  0.053983  0.578548  0.425613\n",
+       " 14   0.788852  0.496349  0.914797  0.429915  0.269266  0.518056\n",
+       " 15   0.625567  0.699632  0.961646  0.870850  0.813573  0.877803\n",
+       " 16   0.721854  0.622525  0.041195  0.732354  0.196179  0.970775\n",
+       " 17   0.208823  0.727552  0.444256  0.967178  0.897290  0.530092\n",
+       " 18   0.635332  0.541648  0.338065  0.331454  0.414569  0.704931\n",
+       " 19   0.694959  0.695945  0.698727  0.511172  0.468524  0.021534\n",
+       " 20   0.684734  0.437319  0.694900  0.407975  0.310437  0.101614\n",
+       " 21   0.900070  0.617774  0.768901  0.212121  0.571546  0.324729\n",
+       " 22   0.522571  0.507616  0.792466  0.637867  0.912570  0.602436\n",
+       " 23   0.716421  0.855375  0.255989  0.348480  0.982067  0.065516\n",
+       " 24   0.196344  0.356946  0.262523  0.844495  0.325739  0.363292\n",
+       " 25   0.434030  0.025598  0.469266  0.149817  0.849139  0.857984\n",
+       " 26   0.693566  0.167121  0.424241  0.907481  0.728857  0.020744\n",
+       " 27   0.087271  0.594890  0.155356  0.245496  0.962884  0.493270\n",
+       " 28   0.036137  0.732567  0.898897  0.863567  0.357661  0.831779\n",
+       " 29   0.095019  0.712235  0.543450  0.027361  0.012610  0.217426\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.456900  0.059672  0.194702  0.051900  0.113929  0.457171\n",
+       " 971  0.610102  0.368420  0.572197  0.522889  0.743680  0.239326\n",
+       " 972  0.008030  0.933340  0.716431  0.608020  0.027095  0.458727\n",
+       " 973  0.673636  0.621933  0.553995  0.337839  0.078951  0.832551\n",
+       " 974  0.706831  0.020294  0.301685  0.152777  0.304625  0.048171\n",
+       " 975  0.458340  0.254315  0.098257  0.849172  0.402148  0.478583\n",
+       " 976  0.749612  0.494188  0.178243  0.256834  0.393393  0.351174\n",
+       " 977  0.270632  0.566382  0.240672  0.021622  0.850065  0.196081\n",
+       " 978  0.640812  0.320525  0.795734  0.946995  0.475229  0.365739\n",
+       " 979  0.349797  0.753505  0.470378  0.003623  0.012563  0.687516\n",
+       " 980  0.026454  0.402979  0.587108  0.608333  0.525331  0.875757\n",
+       " 981  0.536937  0.707826  0.167127  0.934590  0.614088  0.538514\n",
+       " 982  0.445460  0.187527  0.003383  0.765794  0.079643  0.780517\n",
+       " 983  0.029964  0.413612  0.893019  0.445029  0.728586  0.454588\n",
+       " 984  0.425326  0.213682  0.432560  0.659516  0.370513  0.037192\n",
+       " 985  0.755889  0.597565  0.617281  0.065035  0.220401  0.829433\n",
+       " 986  0.908644  0.061250  0.879375  0.073606  0.083732  0.449098\n",
+       " 987  0.470178  0.772245  0.278451  0.993121  0.296427  0.212779\n",
+       " 988  0.200941  0.187035  0.338004  0.379157  0.206626  0.531277\n",
+       " 989  0.674717  0.830915  0.022763  0.058959  0.281767  0.294134\n",
+       " 990  0.110021  0.798606  0.608469  0.852031  0.917922  0.883335\n",
+       " 991  0.351631  0.028837  0.109119  0.497667  0.252681  0.218074\n",
+       " 992  0.839792  0.680444  0.490317  0.344930  0.305722  0.333163\n",
+       " 993  0.895906  0.126008  0.285955  0.458102  0.436569  0.852860\n",
+       " 994  0.935148  0.807407  0.573720  0.838697  0.695600  0.284947\n",
+       " 995  0.111714  0.254324  0.134129  0.275925  0.759361  0.207273\n",
+       " 996  0.816867  0.335600  0.786389  0.479054  0.304108  0.631818\n",
+       " 997  0.262502  0.063675  0.677955  0.534524  0.458557  0.020795\n",
+       " 998  0.522343  0.688785  0.174211  0.775297  0.455164  0.306633\n",
+       " 999  0.096395  0.649405  0.812813  0.335164  0.603458  0.993684\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.992932  0.239063  0.308656  0.682711  0.046799  0.931831\n",
+       " 1    0.359384  0.956743  0.272838  0.434878  0.193489  0.523973\n",
+       " 2    0.396211  0.557217  0.104515  0.687250  0.126142  0.271354\n",
+       " 3    0.399561  0.147689  0.180103  0.861062  0.585651  0.207662\n",
+       " 4    0.223504  0.365266  0.864568  0.696569  0.617931  0.962496\n",
+       " 5    0.656033  0.136533  0.608348  0.959530  0.521623  0.566696\n",
+       " 6    0.126996  0.538745  0.855432  0.408919  0.233092  0.278636\n",
+       " 7    0.941326  0.082331  0.361254  0.383483  0.219149  0.085147\n",
+       " 8    0.403104  0.540327  0.983538  0.221010  0.500938  0.498951\n",
+       " 9    0.116369  0.408540  0.510156  0.185282  0.692299  0.526745\n",
+       " 10   0.500053  0.541390  0.396831  0.284374  0.052813  0.643656\n",
+       " 11   0.948173  0.726460  0.257288  0.553286  0.239737  0.912669\n",
+       " 12   0.680210  0.089122  0.713873  0.340422  0.861800  0.527693\n",
+       " 13   0.419510  0.845701  0.917715  0.621145  0.668975  0.686282\n",
+       " 14   0.293936  0.776256  0.104084  0.559459  0.978328  0.589751\n",
+       " 15   0.234708  0.140889  0.000218  0.545172  0.398949  0.079045\n",
+       " 16   0.305394  0.775540  0.999637  0.435009  0.762319  0.340838\n",
+       " 17   0.691751  0.912814  0.960301  0.853060  0.263208  0.035634\n",
+       " 18   0.386600  0.673727  0.803331  0.911695  0.143015  0.932234\n",
+       " 19   0.396513  0.758615  0.708619  0.331021  0.474967  0.963536\n",
+       " 20   0.021829  0.183031  0.938193  0.043405  0.239002  0.826735\n",
+       " 21   0.210677  0.129799  0.021736  0.032491  0.939604  0.946760\n",
+       " 22   0.488475  0.224452  0.703720  0.359384  0.235658  0.744760\n",
+       " 23   0.560784  0.737773  0.334992  0.023098  0.047923  0.342515\n",
+       " 24   0.420672  0.686916  0.101993  0.807416  0.168614  0.210449\n",
+       " 25   0.118240  0.781987  0.787012  0.554590  0.956857  0.465154\n",
+       " 26   0.779833  0.774868  0.417565  0.105075  0.106239  0.843896\n",
+       " 27   0.870091  0.209580  0.504126  0.908552  0.471102  0.170502\n",
+       " 28   0.391638  0.325485  0.700531  0.499233  0.251272  0.626606\n",
+       " 29   0.120530  0.949320  0.775209  0.367970  0.410549  0.051534\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.756065  0.836023  0.839531  0.016985  0.495972  0.712460\n",
+       " 971  0.807409  0.769435  0.338556  0.139054  0.218098  0.940997\n",
+       " 972  0.854677  0.958031  0.146366  0.048198  0.780710  0.219126\n",
+       " 973  0.049424  0.925804  0.658230  0.146343  0.856388  0.392906\n",
+       " 974  0.398805  0.492642  0.638415  0.236943  0.169300  0.183198\n",
+       " 975  0.060639  0.724964  0.520734  0.406892  0.738264  0.646435\n",
+       " 976  0.525469  0.289711  0.970781  0.096797  0.476008  0.483375\n",
+       " 977  0.573544  0.155747  0.945062  0.398608  0.493097  0.126392\n",
+       " 978  0.104419  0.591657  0.441944  0.884375  0.157270  0.654896\n",
+       " 979  0.488185  0.910787  0.884050  0.833351  0.006580  0.059606\n",
+       " 980  0.313255  0.084898  0.294740  0.563527  0.222545  0.643287\n",
+       " 981  0.547759  0.355509  0.300539  0.386753  0.009299  0.598470\n",
+       " 982  0.652214  0.975181  0.459421  0.092191  0.919266  0.182563\n",
+       " 983  0.173780  0.252693  0.163412  0.545513  0.813241  0.006074\n",
+       " 984  0.508630  0.324472  0.069259  0.402391  0.349676  0.853361\n",
+       " 985  0.580336  0.243184  0.652008  0.536090  0.169731  0.489563\n",
+       " 986  0.951471  0.711780  0.157640  0.124874  0.626129  0.276331\n",
+       " 987  0.148534  0.592504  0.242041  0.463590  0.215743  0.385774\n",
+       " 988  0.448703  0.517830  0.708326  0.559387  0.653218  0.446416\n",
+       " 989  0.168555  0.867761  0.113596  0.981860  0.821576  0.002342\n",
+       " 990  0.079834  0.200507  0.932119  0.035653  0.368589  0.864821\n",
+       " 991  0.893146  0.593431  0.887426  0.731140  0.141140  0.535149\n",
+       " 992  0.436502  0.450548  0.621186  0.000826  0.875195  0.403210\n",
+       " 993  0.359299  0.453082  0.381295  0.172484  0.994534  0.613228\n",
+       " 994  0.696173  0.078473  0.811656  0.079523  0.511239  0.376841\n",
+       " 995  0.552661  0.097480  0.693793  0.870239  0.807461  0.015932\n",
+       " 996  0.028801  0.757703  0.665663  0.002492  0.388100  0.267612\n",
+       " 997  0.683442  0.983104  0.879676  0.490874  0.425258  0.818542\n",
+       " 998  0.733677  0.217140  0.859408  0.314590  0.084750  0.905069\n",
+       " 999  0.330758  0.784648  0.708591  0.720162  0.987960  0.788195\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.575308  0.444444  0.418967  0.197519  0.447354  0.129103\n",
+       " 1    0.446771  0.744671  0.800997  0.181244  0.209742  0.377514\n",
+       " 2    0.060380  0.378406  0.673595  0.560305  0.203591  0.471526\n",
+       " 3    0.853943  0.737898  0.813298  0.400444  0.543652  0.732261\n",
+       " 4    0.599743  0.602936  0.109978  0.032373  0.912224  0.631602\n",
+       " 5    0.828262  0.925449  0.424325  0.336165  0.942563  0.998221\n",
+       " 6    0.628487  0.810576  0.319512  0.575550  0.392595  0.946882\n",
+       " 7    0.804163  0.273292  0.256723  0.892207  0.938761  0.891956\n",
+       " 8    0.323357  0.588426  0.837523  0.142282  0.083687  0.342899\n",
+       " 9    0.963956  0.062129  0.836329  0.938527  0.413196  0.548728\n",
+       " 10   0.549563  0.371804  0.524762  0.236001  0.602233  0.860693\n",
+       " 11   0.700121  0.661282  0.146398  0.574233  0.651322  0.623361\n",
+       " 12   0.658623  0.504664  0.667072  0.381689  0.198424  0.938280\n",
+       " 13   0.717757  0.480709  0.734979  0.749520  0.790499  0.782130\n",
+       " 14   0.629510  0.060980  0.422200  0.263578  0.660654  0.867866\n",
+       " 15   0.527041  0.242369  0.625623  0.766871  0.365086  0.135308\n",
+       " 16   0.246332  0.050966  0.572979  0.736212  0.760126  0.426165\n",
+       " 17   0.046978  0.501784  0.584747  0.254950  0.816849  0.044175\n",
+       " 18   0.459476  0.436979  0.522653  0.193652  0.866955  0.016421\n",
+       " 19   0.912489  0.156384  0.551282  0.792031  0.963390  0.767689\n",
+       " 20   0.654711  0.027561  0.487254  0.367675  0.157167  0.775502\n",
+       " 21   0.246906  0.145294  0.026153  0.200164  0.379856  0.659291\n",
+       " 22   0.478895  0.475090  0.430118  0.101268  0.026014  0.566665\n",
+       " 23   0.404704  0.121168  0.034458  0.533156  0.416163  0.458534\n",
+       " 24   0.878665  0.023463  0.781051  0.037035  0.469752  0.040225\n",
+       " 25   0.982700  0.353413  0.099626  0.244461  0.678222  0.980338\n",
+       " 26   0.101858  0.158114  0.656764  0.592105  0.541831  0.820622\n",
+       " 27   0.280271  0.957217  0.042715  0.933873  0.419717  0.362913\n",
+       " 28   0.814469  0.042324  0.480052  0.920695  0.010677  0.307211\n",
+       " 29   0.014625  0.688544  0.478255  0.151999  0.614359  0.624658\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.447214  0.906012  0.568223  0.366994  0.511821  0.228052\n",
+       " 971  0.226189  0.580903  0.645478  0.014308  0.781205  0.394658\n",
+       " 972  0.145478  0.814071  0.894190  0.253511  0.861651  0.154860\n",
+       " 973  0.395346  0.815706  0.590567  0.559839  0.544087  0.644652\n",
+       " 974  0.558841  0.380080  0.612881  0.544473  0.895035  0.326694\n",
+       " 975  0.484362  0.273542  0.054005  0.246772  0.215611  0.905340\n",
+       " 976  0.892265  0.449092  0.337743  0.691458  0.049043  0.849059\n",
+       " 977  0.315025  0.236663  0.719869  0.601316  0.849653  0.310367\n",
+       " 978  0.499375  0.773483  0.118849  0.059460  0.682631  0.145579\n",
+       " 979  0.452868  0.847622  0.364794  0.561808  0.197437  0.946571\n",
+       " 980  0.096820  0.838391  0.417557  0.812736  0.829302  0.171946\n",
+       " 981  0.637294  0.031322  0.284304  0.865382  0.384122  0.491036\n",
+       " 982  0.251692  0.514349  0.833935  0.835764  0.890979  0.718895\n",
+       " 983  0.314823  0.215150  0.517485  0.755573  0.875637  0.280298\n",
+       " 984  0.186288  0.836659  0.913586  0.901163  0.330936  0.156044\n",
+       " 985  0.524572  0.716747  0.642778  0.458601  0.881704  0.304695\n",
+       " 986  0.398653  0.149473  0.180805  0.714043  0.491643  0.891281\n",
+       " 987  0.020267  0.088676  0.312557  0.034946  0.270757  0.214545\n",
+       " 988  0.464548  0.345558  0.041549  0.896599  0.740744  0.149108\n",
+       " 989  0.986718  0.996314  0.981373  0.617739  0.457206  0.581901\n",
+       " 990  0.882173  0.675879  0.280461  0.245433  0.727020  0.022323\n",
+       " 991  0.769191  0.878408  0.000454  0.752120  0.990620  0.725296\n",
+       " 992  0.336016  0.271288  0.138622  0.215410  0.294312  0.152747\n",
+       " 993  0.159273  0.024294  0.228266  0.726618  0.554165  0.182530\n",
+       " 994  0.628481  0.765898  0.985919  0.930543  0.090752  0.669239\n",
+       " 995  0.941916  0.540228  0.416669  0.239330  0.539755  0.620251\n",
+       " 996  0.912692  0.631699  0.983217  0.559523  0.513620  0.576367\n",
+       " 997  0.714825  0.781060  0.883985  0.698819  0.448008  0.114146\n",
+       " 998  0.806841  0.172358  0.751658  0.564025  0.135651  0.397173\n",
+       " 999  0.585119  0.274213  0.633312  0.786576  0.083056  0.481986\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.142928  0.112233  0.115148  0.110296  0.180020  0.683587\n",
+       " 1    0.918304  0.482610  0.796965  0.738359  0.929168  0.303592\n",
+       " 2    0.301540  0.723825  0.093500  0.078681  0.719822  0.219850\n",
+       " 3    0.864311  0.766329  0.988518  0.790730  0.886800  0.510344\n",
+       " 4    0.403423  0.814646  0.375899  0.390414  0.613015  0.881143\n",
+       " 5    0.166826  0.034896  0.912287  0.441320  0.284936  0.314398\n",
+       " 6    0.054600  0.715396  0.928779  0.900918  0.425096  0.870381\n",
+       " 7    0.032155  0.097087  0.030197  0.787137  0.164462  0.109030\n",
+       " 8    0.759311  0.789498  0.346222  0.898256  0.292086  0.239229\n",
+       " 9    0.838616  0.564843  0.537237  0.085678  0.379794  0.996737\n",
+       " 10   0.364656  0.143315  0.245064  0.236650  0.798983  0.793211\n",
+       " 11   0.265455  0.656980  0.721087  0.686081  0.964491  0.868393\n",
+       " 12   0.111388  0.578365  0.506807  0.367830  0.340415  0.391109\n",
+       " 13   0.947225  0.906918  0.330280  0.580539  0.815358  0.250820\n",
+       " 14   0.041645  0.359435  0.494145  0.046246  0.883132  0.116185\n",
+       " 15   0.286223  0.141051  0.363422  0.469730  0.199595  0.024677\n",
+       " 16   0.785135  0.834124  0.283602  0.741643  0.069796  0.797698\n",
+       " 17   0.256685  0.752995  0.325015  0.782609  0.047763  0.129172\n",
+       " 18   0.305054  0.179297  0.420267  0.216249  0.232996  0.695724\n",
+       " 19   0.250427  0.224892  0.685413  0.449471  0.399583  0.294677\n",
+       " 20   0.958855  0.587331  0.805977  0.020372  0.700544  0.290285\n",
+       " 21   0.776203  0.087395  0.856297  0.505077  0.798219  0.808204\n",
+       " 22   0.511131  0.957367  0.290867  0.288532  0.275546  0.291838\n",
+       " 23   0.782298  0.556458  0.973749  0.720737  0.751231  0.266129\n",
+       " 24   0.944751  0.972747  0.255733  0.176529  0.676532  0.047018\n",
+       " 25   0.773033  0.005422  0.391408  0.884840  0.913451  0.834940\n",
+       " 26   0.235788  0.205767  0.579820  0.077527  0.758384  0.577984\n",
+       " 27   0.064696  0.176887  0.969545  0.399594  0.851725  0.987435\n",
+       " 28   0.283848  0.518756  0.069672  0.363907  0.202779  0.104140\n",
+       " 29   0.874364  0.063555  0.081189  0.616980  0.726144  0.510021\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.753120  0.125414  0.899344  0.578395  0.416536  0.084785\n",
+       " 971  0.638679  0.113601  0.684097  0.514063  0.659892  0.807408\n",
+       " 972  0.500598  0.201493  0.507802  0.336715  0.131935  0.738245\n",
+       " 973  0.937666  0.998885  0.072046  0.819522  0.356954  0.517077\n",
+       " 974  0.719111  0.193881  0.572503  0.461413  0.587209  0.164410\n",
+       " 975  0.021102  0.995944  0.049760  0.346525  0.240307  0.235386\n",
+       " 976  0.951745  0.538690  0.805106  0.597866  0.308443  0.238085\n",
+       " 977  0.196228  0.855292  0.172475  0.602964  0.231001  0.508947\n",
+       " 978  0.232565  0.478559  0.625534  0.075866  0.448658  0.180272\n",
+       " 979  0.330514  0.926545  0.845226  0.596437  0.525280  0.256019\n",
+       " 980  0.928248  0.244323  0.764190  0.256060  0.543505  0.983989\n",
+       " 981  0.895317  0.023081  0.347256  0.426536  0.352631  0.752342\n",
+       " 982  0.243286  0.712329  0.917295  0.758881  0.708198  0.639136\n",
+       " 983  0.663278  0.561370  0.401718  0.959440  0.072363  0.867747\n",
+       " 984  0.084271  0.593258  0.831396  0.644340  0.936607  0.100627\n",
+       " 985  0.392881  0.857527  0.532434  0.480016  0.768496  0.719784\n",
+       " 986  0.232886  0.729696  0.428502  0.706553  0.796428  0.090372\n",
+       " 987  0.181175  0.949810  0.529805  0.029277  0.598028  0.820913\n",
+       " 988  0.678209  0.438174  0.031568  0.044025  0.783879  0.962949\n",
+       " 989  0.390336  0.822790  0.374011  0.467669  0.556343  0.372540\n",
+       " 990  0.954765  0.965793  0.475176  0.910099  0.935356  0.761190\n",
+       " 991  0.264246  0.404175  0.424718  0.701723  0.163064  0.484622\n",
+       " 992  0.639907  0.995852  0.681860  0.564438  0.910259  0.580027\n",
+       " 993  0.212050  0.888697  0.508874  0.468341  0.894735  0.992838\n",
+       " 994  0.543668  0.121146  0.204181  0.702745  0.762334  0.244662\n",
+       " 995  0.850483  0.103596  0.886443  0.369157  0.424228  0.234821\n",
+       " 996  0.630823  0.127207  0.743587  0.398604  0.068989  0.885270\n",
+       " 997  0.860759  0.585008  0.021639  0.663581  0.996175  0.312877\n",
+       " 998  0.152096  0.532149  0.242905  0.044370  0.256093  0.266716\n",
+       " 999  0.635362  0.709204  0.798100  0.295470  0.581965  0.300551\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.432380  0.492211  0.468788  0.388435  0.740196  0.762209\n",
+       " 1    0.795759  0.241430  0.564067  0.654280  0.456590  0.522346\n",
+       " 2    0.358067  0.906476  0.208553  0.639748  0.455456  0.016669\n",
+       " 3    0.706910  0.419662  0.874147  0.347885  0.410849  0.553179\n",
+       " 4    0.597871  0.385290  0.064695  0.660901  0.559091  0.964370\n",
+       " 5    0.286864  0.610012  0.159321  0.126973  0.554888  0.804067\n",
+       " 6    0.329688  0.206073  0.801841  0.145509  0.959709  0.910369\n",
+       " 7    0.247126  0.985071  0.140506  0.819431  0.730531  0.879158\n",
+       " 8    0.933988  0.425610  0.792199  0.748701  0.272415  0.164458\n",
+       " 9    0.801511  0.708690  0.228745  0.705455  0.783366  0.494745\n",
+       " 10   0.757539  0.624752  0.807773  0.688599  0.547840  0.768420\n",
+       " 11   0.004671  0.557325  0.297772  0.552535  0.052892  0.761929\n",
+       " 12   0.556786  0.768106  0.854104  0.669149  0.045467  0.522316\n",
+       " 13   0.611421  0.664794  0.314056  0.921852  0.517940  0.527655\n",
+       " 14   0.273610  0.499935  0.542431  0.578280  0.403140  0.928682\n",
+       " 15   0.557085  0.086650  0.145330  0.892434  0.972967  0.246522\n",
+       " 16   0.393247  0.833060  0.407915  0.827573  0.487064  0.085282\n",
+       " 17   0.274179  0.526733  0.282337  0.114940  0.287635  0.517596\n",
+       " 18   0.787852  0.274589  0.018411  0.146337  0.898374  0.957847\n",
+       " 19   0.036870  0.771355  0.750732  0.326392  0.361944  0.575594\n",
+       " 20   0.591089  0.167905  0.223625  0.790564  0.786536  0.522766\n",
+       " 21   0.925338  0.174899  0.567651  0.798475  0.318240  0.749570\n",
+       " 22   0.535400  0.520883  0.215602  0.088785  0.137627  0.842137\n",
+       " 23   0.321435  0.285634  0.786117  0.979448  0.611659  0.385334\n",
+       " 24   0.869772  0.270412  0.099929  0.796017  0.604944  0.122344\n",
+       " 25   0.825372  0.927675  0.286375  0.680212  0.592885  0.461722\n",
+       " 26   0.123198  0.171861  0.079445  0.265123  0.554868  0.473138\n",
+       " 27   0.001862  0.116363  0.215775  0.953028  0.994578  0.584456\n",
+       " 28   0.511877  0.563199  0.693129  0.811859  0.222948  0.722887\n",
+       " 29   0.137320  0.688724  0.672503  0.286401  0.855307  0.723681\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.488677  0.747973  0.873523  0.694236  0.506524  0.554982\n",
+       " 971  0.681423  0.036165  0.389038  0.339681  0.803985  0.273071\n",
+       " 972  0.337100  0.694343  0.349230  0.169845  0.879951  0.266336\n",
+       " 973  0.843476  0.597913  0.920552  0.181300  0.910493  0.544349\n",
+       " 974  0.821561  0.833997  0.404104  0.820522  0.861419  0.408767\n",
+       " 975  0.718691  0.780278  0.148979  0.808839  0.232224  0.636907\n",
+       " 976  0.628559  0.813825  0.906901  0.067263  0.426504  0.547431\n",
+       " 977  0.102627  0.995215  0.075532  0.168637  0.743015  0.635645\n",
+       " 978  0.254919  0.800733  0.728594  0.225207  0.196782  0.763086\n",
+       " 979  0.597069  0.874547  0.045486  0.226253  0.406591  0.984955\n",
+       " 980  0.748210  0.482505  0.622166  0.012898  0.780749  0.992005\n",
+       " 981  0.350642  0.183005  0.518014  0.218945  0.753589  0.204834\n",
+       " 982  0.492115  0.614199  0.769136  0.115295  0.244271  0.829390\n",
+       " 983  0.281420  0.442474  0.675958  0.204633  0.416445  0.813029\n",
+       " 984  0.479356  0.765986  0.562175  0.737577  0.953967  0.873422\n",
+       " 985  0.131019  0.301326  0.302405  0.096363  0.681822  0.697560\n",
+       " 986  0.061503  0.871920  0.862027  0.602023  0.478691  0.325931\n",
+       " 987  0.870794  0.248638  0.539782  0.405356  0.896504  0.750754\n",
+       " 988  0.384830  0.741311  0.242947  0.850599  0.695178  0.086108\n",
+       " 989  0.544696  0.337923  0.348691  0.969291  0.918132  0.495689\n",
+       " 990  0.605458  0.497922  0.593082  0.235873  0.980138  0.192215\n",
+       " 991  0.791409  0.429035  0.746016  0.725613  0.594880  0.808463\n",
+       " 992  0.647087  0.219863  0.938483  0.542188  0.830093  0.156196\n",
+       " 993  0.101385  0.137914  0.564872  0.609254  0.432792  0.369962\n",
+       " 994  0.037099  0.418899  0.050615  0.855941  0.017930  0.826339\n",
+       " 995  0.799777  0.343225  0.248269  0.950401  0.838808  0.807685\n",
+       " 996  0.185686  0.223366  0.516837  0.745190  0.390359  0.180655\n",
+       " 997  0.200429  0.027331  0.470948  0.446358  0.797157  0.934671\n",
+       " 998  0.089471  0.900589  0.364505  0.685383  0.394753  0.286676\n",
+       " 999  0.166242  0.430873  0.182224  0.608708  0.678557  0.896074\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.547073  0.234786  0.130264  0.266232  0.190714  0.722669\n",
+       " 1    0.578049  0.294414  0.796304  0.259309  0.012884  0.102295\n",
+       " 2    0.525380  0.444379  0.820553  0.940814  0.621844  0.790401\n",
+       " 3    0.933722  0.455495  0.810153  0.702981  0.158845  0.577412\n",
+       " 4    0.253574  0.388311  0.074335  0.566093  0.337223  0.175309\n",
+       " 5    0.352796  0.681447  0.242028  0.692558  0.431139  0.555310\n",
+       " 6    0.525787  0.267629  0.623084  0.668004  0.776684  0.981749\n",
+       " 7    0.434313  0.778824  0.705401  0.158585  0.849418  0.185319\n",
+       " 8    0.342190  0.756614  0.035576  0.332401  0.655306  0.508675\n",
+       " 9    0.432024  0.557383  0.925559  0.308368  0.760790  0.383760\n",
+       " 10   0.477241  0.635753  0.272820  0.334481  0.070738  0.292609\n",
+       " 11   0.338907  0.726218  0.635873  0.493461  0.943351  0.808784\n",
+       " 12   0.476212  0.152441  0.563286  0.763423  0.717598  0.661442\n",
+       " 13   0.163080  0.368852  0.002350  0.562086  0.243232  0.498945\n",
+       " 14   0.750637  0.444242  0.643666  0.866835  0.606250  0.153532\n",
+       " 15   0.075121  0.955467  0.028893  0.854312  0.588933  0.653653\n",
+       " 16   0.537925  0.363137  0.693995  0.408050  0.617088  0.221440\n",
+       " 17   0.657983  0.646492  0.082756  0.874353  0.773366  0.427477\n",
+       " 18   0.988835  0.915392  0.542597  0.251320  0.024626  0.080235\n",
+       " 19   0.454182  0.536827  0.362133  0.572744  0.347604  0.424788\n",
+       " 20   0.838627  0.503802  0.261465  0.124769  0.683858  0.999057\n",
+       " 21   0.004829  0.455191  0.950377  0.558705  0.201675  0.554006\n",
+       " 22   0.931087  0.079876  0.452324  0.409153  0.719838  0.312651\n",
+       " 23   0.993659  0.574544  0.864647  0.848430  0.908398  0.435828\n",
+       " 24   0.010627  0.937715  0.249148  0.002703  0.360044  0.952059\n",
+       " 25   0.423630  0.627263  0.404361  0.439359  0.676681  0.329665\n",
+       " 26   0.459405  0.188443  0.424802  0.583677  0.947789  0.498662\n",
+       " 27   0.520434  0.992145  0.943463  0.008719  0.984217  0.588134\n",
+       " 28   0.926324  0.611365  0.743898  0.980664  0.378810  0.600427\n",
+       " 29   0.834672  0.876859  0.302836  0.649555  0.653437  0.963721\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.092076  0.285872  0.856234  0.225674  0.414886  0.738988\n",
+       " 971  0.400450  0.228136  0.111029  0.833442  0.967305  0.576530\n",
+       " 972  0.087278  0.916357  0.627653  0.752740  0.477008  0.674393\n",
+       " 973  0.873960  0.421997  0.131590  0.220078  0.630376  0.747216\n",
+       " 974  0.368680  0.001222  0.247344  0.196374  0.626479  0.637629\n",
+       " 975  0.779081  0.897755  0.345031  0.804810  0.536401  0.181638\n",
+       " 976  0.481568  0.503710  0.509867  0.957528  0.230678  0.527573\n",
+       " 977  0.889702  0.073755  0.160435  0.437505  0.223385  0.511816\n",
+       " 978  0.740743  0.774159  0.234349  0.033180  0.966897  0.053300\n",
+       " 979  0.599502  0.358029  0.727679  0.017434  0.280126  0.154146\n",
+       " 980  0.812074  0.277753  0.762224  0.605444  0.521820  0.695638\n",
+       " 981  0.438931  0.963522  0.982681  0.691297  0.557665  0.162190\n",
+       " 982  0.002262  0.411525  0.730924  0.474271  0.509191  0.199034\n",
+       " 983  0.787864  0.141578  0.054392  0.193255  0.808121  0.608936\n",
+       " 984  0.072631  0.154886  0.684360  0.974801  0.567635  0.897625\n",
+       " 985  0.667617  0.033660  0.605645  0.105473  0.314403  0.687435\n",
+       " 986  0.332794  0.314826  0.119495  0.861507  0.675091  0.393378\n",
+       " 987  0.433918  0.341166  0.528335  0.709448  0.737054  0.589256\n",
+       " 988  0.071572  0.812093  0.865259  0.778037  0.105749  0.156589\n",
+       " 989  0.353584  0.769948  0.852785  0.316094  0.144001  0.742290\n",
+       " 990  0.985487  0.328845  0.552085  0.816902  0.902655  0.345883\n",
+       " 991  0.993592  0.186755  0.007620  0.444519  0.440477  0.026645\n",
+       " 992  0.465878  0.300702  0.995103  0.588871  0.051413  0.607207\n",
+       " 993  0.208514  0.222802  0.211509  0.078932  0.252039  0.238934\n",
+       " 994  0.818538  0.051437  0.595126  0.337181  0.910518  0.057106\n",
+       " 995  0.689489  0.244098  0.910018  0.143863  0.810607  0.685337\n",
+       " 996  0.008817  0.022008  0.570845  0.383373  0.491022  0.714620\n",
+       " 997  0.911011  0.922827  0.859213  0.400226  0.969783  0.463579\n",
+       " 998  0.286413  0.105374  0.464300  0.870343  0.674377  0.385227\n",
+       " 999  0.539555  0.672306  0.947826  0.424564  0.862153  0.922253\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.910449  0.353732  0.815932  0.928061  0.881256  0.234206\n",
+       " 1    0.254000  0.016406  0.994220  0.365470  0.877596  0.076062\n",
+       " 2    0.670636  0.972386  0.497348  0.374388  0.304058  0.606787\n",
+       " 3    0.575062  0.787722  0.383289  0.720894  0.672545  0.917051\n",
+       " 4    0.892700  0.998779  0.536533  0.106587  0.943271  0.449890\n",
+       " 5    0.536972  0.816346  0.566520  0.890459  0.619058  0.643380\n",
+       " 6    0.923028  0.489065  0.903364  0.172921  0.830199  0.622332\n",
+       " 7    0.561286  0.276079  0.898048  0.687958  0.488218  0.495688\n",
+       " 8    0.801066  0.581625  0.117235  0.403992  0.462589  0.535103\n",
+       " 9    0.423995  0.809008  0.891258  0.828010  0.812167  0.960923\n",
+       " 10   0.573006  0.189412  0.952220  0.859139  0.114309  0.716836\n",
+       " 11   0.143035  0.872372  0.792886  0.878778  0.321370  0.027678\n",
+       " 12   0.120221  0.158039  0.099443  0.061155  0.613247  0.349457\n",
+       " 13   0.362861  0.870955  0.569376  0.776359  0.499042  0.057082\n",
+       " 14   0.523408  0.471606  0.699577  0.119678  0.845395  0.627424\n",
+       " 15   0.724208  0.575510  0.658442  0.923626  0.734902  0.084632\n",
+       " 16   0.983777  0.461436  0.921213  0.048423  0.174533  0.292592\n",
+       " 17   0.527329  0.330612  0.561744  0.961844  0.240631  0.513279\n",
+       " 18   0.974383  0.723000  0.304853  0.061214  0.947784  0.283013\n",
+       " 19   0.951220  0.050992  0.831702  0.714250  0.391205  0.642644\n",
+       " 20   0.076829  0.602059  0.936252  0.117149  0.095831  0.414457\n",
+       " 21   0.815972  0.232741  0.706499  0.662975  0.926001  0.645929\n",
+       " 22   0.110263  0.463312  0.614998  0.637533  0.433742  0.177730\n",
+       " 23   0.790496  0.330807  0.435487  0.861627  0.053641  0.886372\n",
+       " 24   0.681260  0.165443  0.799418  0.061726  0.770996  0.592100\n",
+       " 25   0.348970  0.825677  0.303333  0.244385  0.812283  0.715958\n",
+       " 26   0.213037  0.598022  0.531544  0.718733  0.230811  0.787755\n",
+       " 27   0.254549  0.133611  0.928430  0.035240  0.709085  0.919652\n",
+       " 28   0.593841  0.476377  0.628625  0.912065  0.547416  0.670259\n",
+       " 29   0.010717  0.987612  0.933119  0.073568  0.729715  0.577774\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.578673  0.981279  0.168237  0.859811  0.409522  0.108525\n",
+       " 971  0.347689  0.516022  0.615911  0.449876  0.554641  0.128161\n",
+       " 972  0.645589  0.941767  0.290109  0.602814  0.809785  0.604996\n",
+       " 973  0.856329  0.577387  0.492601  0.056311  0.467819  0.801695\n",
+       " 974  0.602000  0.050737  0.140791  0.099364  0.921043  0.948542\n",
+       " 975  0.157094  0.345595  0.032651  0.271012  0.548032  0.467741\n",
+       " 976  0.187062  0.932510  0.723005  0.100498  0.984587  0.248230\n",
+       " 977  0.620355  0.580639  0.929880  0.275923  0.087513  0.223805\n",
+       " 978  0.463243  0.334304  0.614460  0.101545  0.682355  0.015869\n",
+       " 979  0.831530  0.597446  0.029121  0.029320  0.248965  0.734360\n",
+       " 980  0.592709  0.614729  0.458623  0.095952  0.893599  0.487483\n",
+       " 981  0.339012  0.456912  0.687135  0.455179  0.823512  0.052763\n",
+       " 982  0.806673  0.805953  0.642643  0.826170  0.411262  0.163992\n",
+       " 983  0.658313  0.868823  0.058835  0.019498  0.612201  0.264716\n",
+       " 984  0.827209  0.688132  0.465616  0.053114  0.222944  0.404556\n",
+       " 985  0.085695  0.799983  0.750875  0.877668  0.960272  0.832196\n",
+       " 986  0.731236  0.072419  0.167504  0.158479  0.116377  0.572464\n",
+       " 987  0.345305  0.949670  0.173283  0.219794  0.813858  0.688043\n",
+       " 988  0.375778  0.487097  0.713665  0.731385  0.430438  0.005370\n",
+       " 989  0.329607  0.923605  0.871138  0.503893  0.032738  0.379596\n",
+       " 990  0.217946  0.738356  0.361329  0.004750  0.025290  0.886736\n",
+       " 991  0.720058  0.267721  0.917918  0.779602  0.256519  0.426352\n",
+       " 992  0.401926  0.862420  0.455125  0.872781  0.209549  0.864696\n",
+       " 993  0.105531  0.259596  0.145944  0.224063  0.213120  0.956616\n",
+       " 994  0.205527  0.058397  0.861669  0.049129  0.262312  0.455817\n",
+       " 995  0.628008  0.169015  0.572849  0.213886  0.766886  0.924960\n",
+       " 996  0.978584  0.406700  0.482774  0.381777  0.227452  0.443722\n",
+       " 997  0.400205  0.094942  0.153964  0.048338  0.611053  0.889536\n",
+       " 998  0.888753  0.037132  0.534523  0.985150  0.792060  0.008386\n",
+       " 999  0.941298  0.775473  0.432018  0.399156  0.477331  0.942971\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.581456  0.291078  0.619042  0.191945  0.891947  0.263280\n",
+       " 1    0.605316  0.105112  0.589345  0.191992  0.223193  0.634518\n",
+       " 2    0.111497  0.821555  0.125319  0.446820  0.140184  0.711505\n",
+       " 3    0.485465  0.950882  0.552583  0.693039  0.445181  0.588219\n",
+       " 4    0.744627  0.208496  0.000250  0.804481  0.634813  0.072163\n",
+       " 5    0.818302  0.698531  0.173002  0.474911  0.240432  0.994600\n",
+       " 6    0.230059  0.954662  0.646078  0.953632  0.252926  0.574529\n",
+       " 7    0.452779  0.271989  0.165391  0.528969  0.081116  0.716434\n",
+       " 8    0.296937  0.084818  0.835293  0.863623  0.139534  0.189066\n",
+       " 9    0.601852  0.714622  0.226600  0.738981  0.916342  0.428811\n",
+       " 10   0.246875  0.253137  0.319939  0.930746  0.196087  0.246533\n",
+       " 11   0.397453  0.579838  0.859854  0.402264  0.808282  0.598897\n",
+       " 12   0.577278  0.545581  0.992159  0.267971  0.853552  0.565285\n",
+       " 13   0.539216  0.257653  0.225664  0.518042  0.520551  0.282306\n",
+       " 14   0.536579  0.178789  0.011388  0.589832  0.934510  0.160212\n",
+       " 15   0.107914  0.297240  0.335649  0.332105  0.025240  0.470940\n",
+       " 16   0.452954  0.083682  0.455736  0.858200  0.787168  0.473961\n",
+       " 17   0.957735  0.751907  0.379316  0.198798  0.272582  0.280742\n",
+       " 18   0.898054  0.157599  0.023580  0.194216  0.055107  0.459582\n",
+       " 19   0.114752  0.133432  0.164244  0.973291  0.939621  0.289290\n",
+       " 20   0.616126  0.632019  0.372898  0.607893  0.636241  0.215832\n",
+       " 21   0.597196  0.450665  0.133538  0.187384  0.959362  0.038270\n",
+       " 22   0.460699  0.646516  0.907813  0.807063  0.694308  0.659913\n",
+       " 23   0.044041  0.425213  0.042664  0.145597  0.088588  0.096884\n",
+       " 24   0.877930  0.729778  0.694752  0.949893  0.172036  0.380275\n",
+       " 25   0.795804  0.741853  0.962138  0.028219  0.517596  0.564085\n",
+       " 26   0.011049  0.119963  0.125836  0.781170  0.459621  0.197321\n",
+       " 27   0.152360  0.994069  0.662009  0.050648  0.134808  0.291642\n",
+       " 28   0.409547  0.727245  0.635754  0.636413  0.683949  0.952846\n",
+       " 29   0.308002  0.157225  0.709481  0.510872  0.063799  0.525758\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.434317  0.008555  0.617061  0.769907  0.511312  0.745739\n",
+       " 971  0.620472  0.355022  0.467726  0.102930  0.157289  0.801989\n",
+       " 972  0.394640  0.471140  0.361898  0.475957  0.096438  0.431039\n",
+       " 973  0.489293  0.971039  0.102558  0.545566  0.997437  0.842933\n",
+       " 974  0.283266  0.393203  0.946786  0.396986  0.161669  0.249852\n",
+       " 975  0.997521  0.199232  0.555790  0.008524  0.179713  0.019109\n",
+       " 976  0.283816  0.510172  0.089531  0.448148  0.066805  0.531864\n",
+       " 977  0.137637  0.506725  0.465712  0.814497  0.602121  0.783359\n",
+       " 978  0.685519  0.586661  0.541771  0.858037  0.973155  0.346895\n",
+       " 979  0.520991  0.149919  0.741363  0.694569  0.297505  0.044200\n",
+       " 980  0.305054  0.915269  0.437353  0.991105  0.169514  0.708162\n",
+       " 981  0.891666  0.473014  0.908541  0.448810  0.952460  0.266853\n",
+       " 982  0.639965  0.747545  0.933367  0.651365  0.072504  0.299521\n",
+       " 983  0.447699  0.488181  0.620307  0.273976  0.289784  0.983860\n",
+       " 984  0.308128  0.926367  0.115576  0.428141  0.208062  0.176832\n",
+       " 985  0.875511  0.775330  0.988226  0.856244  0.068528  0.746878\n",
+       " 986  0.725006  0.408336  0.102261  0.957366  0.068739  0.804297\n",
+       " 987  0.607900  0.296514  0.390833  0.949648  0.902304  0.631563\n",
+       " 988  0.000906  0.368591  0.845075  0.697710  0.253298  0.590040\n",
+       " 989  0.556324  0.149222  0.616023  0.157251  0.645315  0.185428\n",
+       " 990  0.513753  0.718023  0.633352  0.364770  0.897377  0.525662\n",
+       " 991  0.562041  0.722507  0.554040  0.348118  0.487281  0.482342\n",
+       " 992  0.812900  0.583875  0.523891  0.643126  0.385352  0.246555\n",
+       " 993  0.848530  0.789559  0.025877  0.306653  0.354149  0.881371\n",
+       " 994  0.783929  0.216737  0.537433  0.551527  0.667906  0.934502\n",
+       " 995  0.372843  0.813830  0.776255  0.134556  0.601108  0.310864\n",
+       " 996  0.686899  0.449399  0.362465  0.868907  0.849811  0.170066\n",
+       " 997  0.199422  0.530434  0.987127  0.047522  0.382159  0.356641\n",
+       " 998  0.883582  0.529655  0.547235  0.491492  0.386427  0.273724\n",
+       " 999  0.555474  0.369129  0.389315  0.663595  0.332997  0.854864\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.627708  0.537528  0.283913  0.847787  0.982045  0.050907\n",
+       " 1    0.499350  0.173662  0.710269  0.991402  0.677016  0.470022\n",
+       " 2    0.463568  0.714303  0.164058  0.877593  0.368604  0.167215\n",
+       " 3    0.135000  0.292289  0.109291  0.135250  0.107133  0.653763\n",
+       " 4    0.418096  0.014933  0.223053  0.343243  0.270118  0.993893\n",
+       " 5    0.496509  0.496926  0.968780  0.965309  0.968106  0.394535\n",
+       " 6    0.726897  0.425201  0.616798  0.269655  0.782616  0.650223\n",
+       " 7    0.798114  0.230521  0.427166  0.253705  0.855016  0.923612\n",
+       " 8    0.532732  0.618889  0.053593  0.283236  0.246363  0.533418\n",
+       " 9    0.629272  0.926261  0.010814  0.309613  0.411238  0.082680\n",
+       " 10   0.891939  0.798239  0.001302  0.253849  0.788333  0.071875\n",
+       " 11   0.707895  0.609581  0.764900  0.332349  0.793842  0.937668\n",
+       " 12   0.724915  0.375811  0.319391  0.105548  0.688429  0.773849\n",
+       " 13   0.107241  0.908889  0.242401  0.625874  0.610947  0.481290\n",
+       " 14   0.195429  0.835217  0.200322  0.323639  0.644978  0.664033\n",
+       " 15   0.431298  0.183131  0.903854  0.691939  0.617125  0.529115\n",
+       " 16   0.139529  0.262494  0.382699  0.473713  0.906923  0.215624\n",
+       " 17   0.075933  0.478698  0.005905  0.653054  0.793167  0.790469\n",
+       " 18   0.280112  0.381425  0.869975  0.824125  0.836196  0.070806\n",
+       " 19   0.197999  0.615657  0.298885  0.074567  0.170795  0.839185\n",
+       " 20   0.189364  0.051162  0.138502  0.481285  0.226456  0.708316\n",
+       " 21   0.065938  0.766515  0.402243  0.397832  0.838855  0.087489\n",
+       " 22   0.417260  0.869815  0.135235  0.257124  0.432937  0.124071\n",
+       " 23   0.608502  0.695773  0.051761  0.586769  0.762982  0.257496\n",
+       " 24   0.952272  0.525969  0.050848  0.826498  0.482538  0.374591\n",
+       " 25   0.677734  0.601361  0.799229  0.352296  0.720557  0.355359\n",
+       " 26   0.701488  0.022187  0.310177  0.568824  0.004158  0.898768\n",
+       " 27   0.450073  0.649188  0.669079  0.097961  0.754027  0.685896\n",
+       " 28   0.843223  0.039097  0.212211  0.467596  0.847249  0.272875\n",
+       " 29   0.026714  0.153441  0.493751  0.709982  0.024617  0.720757\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.357867  0.350961  0.460982  0.093857  0.993110  0.139424\n",
+       " 971  0.185923  0.992495  0.176331  0.934890  0.748948  0.786348\n",
+       " 972  0.730106  0.572602  0.896955  0.900467  0.453129  0.815370\n",
+       " 973  0.165244  0.346074  0.597441  0.615633  0.425716  0.565757\n",
+       " 974  0.194995  0.868415  0.189710  0.333569  0.464476  0.738050\n",
+       " 975  0.261282  0.399891  0.246747  0.722163  0.755340  0.574068\n",
+       " 976  0.787748  0.419409  0.670469  0.161002  0.255743  0.931816\n",
+       " 977  0.037491  0.313106  0.755705  0.939913  0.946340  0.837173\n",
+       " 978  0.839962  0.821496  0.866492  0.047827  0.525493  0.076263\n",
+       " 979  0.096276  0.567823  0.454376  0.900347  0.971886  0.654696\n",
+       " 980  0.261977  0.181686  0.042426  0.484398  0.079037  0.806161\n",
+       " 981  0.622640  0.567058  0.639682  0.410740  0.753717  0.062077\n",
+       " 982  0.358660  0.572169  0.637872  0.596450  0.763362  0.107850\n",
+       " 983  0.386078  0.990625  0.125526  0.459195  0.611566  0.943060\n",
+       " 984  0.393483  0.537234  0.487964  0.954896  0.309123  0.041018\n",
+       " 985  0.844576  0.503604  0.524689  0.553407  0.635825  0.426958\n",
+       " 986  0.680967  0.002449  0.866934  0.116355  0.518069  0.376050\n",
+       " 987  0.339765  0.655318  0.947240  0.322954  0.693819  0.017761\n",
+       " 988  0.039533  0.803887  0.547643  0.329774  0.447289  0.680143\n",
+       " 989  0.614278  0.963894  0.232209  0.355117  0.877798  0.843044\n",
+       " 990  0.216540  0.601534  0.781843  0.260061  0.406748  0.195881\n",
+       " 991  0.915409  0.471824  0.157851  0.028521  0.259022  0.746169\n",
+       " 992  0.419946  0.728676  0.765122  0.159336  0.976043  0.490913\n",
+       " 993  0.295304  0.750041  0.243192  0.859350  0.339832  0.048799\n",
+       " 994  0.854051  0.078411  0.690015  0.491021  0.523440  0.957038\n",
+       " 995  0.738347  0.859221  0.718854  0.644937  0.341380  0.977161\n",
+       " 996  0.414806  0.883558  0.013217  0.555560  0.393767  0.329545\n",
+       " 997  0.968237  0.897598  0.789131  0.031294  0.350399  0.589341\n",
+       " 998  0.196003  0.053757  0.975420  0.593202  0.304883  0.395052\n",
+       " 999  0.033164  0.549623  0.614589  0.437801  0.263186  0.825849\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.815075  0.488519  0.261270  0.250061  0.877282  0.734487\n",
+       " 1    0.552144  0.266140  0.053490  0.279741  0.807316  0.444078\n",
+       " 2    0.003024  0.266205  0.851313  0.860177  0.278485  0.284180\n",
+       " 3    0.482607  0.666170  0.109148  0.730416  0.215544  0.599507\n",
+       " 4    0.315629  0.341381  0.852669  0.451056  0.675253  0.854056\n",
+       " 5    0.292483  0.312331  0.660839  0.404739  0.484794  0.576125\n",
+       " 6    0.995025  0.477877  0.862878  0.503902  0.861796  0.056572\n",
+       " 7    0.074974  0.320936  0.587268  0.441972  0.137542  0.790519\n",
+       " 8    0.471062  0.168282  0.066682  0.322079  0.737690  0.959165\n",
+       " 9    0.854720  0.508603  0.474592  0.178730  0.241608  0.475435\n",
+       " 10   0.691742  0.580048  0.217784  0.751317  0.484818  0.539074\n",
+       " 11   0.273184  0.951108  0.600366  0.148005  0.824164  0.225139\n",
+       " 12   0.615746  0.228719  0.126817  0.618064  0.288179  0.348155\n",
+       " 13   0.934273  0.257990  0.417766  0.391031  0.317533  0.091479\n",
+       " 14   0.707853  0.379833  0.710853  0.366224  0.235477  0.460438\n",
+       " 15   0.039808  0.807347  0.190474  0.820575  0.202156  0.963385\n",
+       " 16   0.400963  0.892482  0.991047  0.891854  0.801822  0.344869\n",
+       " 17   0.108881  0.977567  0.904952  0.884267  0.900197  0.680669\n",
+       " 18   0.230882  0.802865  0.908986  0.817590  0.544997  0.372990\n",
+       " 19   0.708474  0.331003  0.271168  0.662871  0.972727  0.997215\n",
+       " 20   0.916074  0.263934  0.981950  0.416157  0.865920  0.709364\n",
+       " 21   0.761547  0.814435  0.651405  0.202146  0.181391  0.935012\n",
+       " 22   0.658896  0.090203  0.450909  0.970814  0.125611  0.888766\n",
+       " 23   0.063984  0.480109  0.912275  0.391802  0.673471  0.793377\n",
+       " 24   0.919232  0.734077  0.887855  0.719844  0.684300  0.198095\n",
+       " 25   0.451867  0.845980  0.239931  0.394705  0.510595  0.257238\n",
+       " 26   0.377523  0.490857  0.036165  0.429909  0.337905  0.645207\n",
+       " 27   0.724883  0.525490  0.807577  0.543226  0.397595  0.829515\n",
+       " 28   0.331438  0.925556  0.217382  0.515741  0.557046  0.876918\n",
+       " 29   0.311600  0.516347  0.734082  0.290214  0.179366  0.681460\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.651748  0.028022  0.623583  0.925984  0.011654  0.112892\n",
+       " 971  0.454645  0.390786  0.831055  0.112807  0.402713  0.749274\n",
+       " 972  0.733423  0.750965  0.531976  0.946479  0.290350  0.681326\n",
+       " 973  0.357744  0.864301  0.422687  0.151861  0.032857  0.278960\n",
+       " 974  0.687521  0.037996  0.906278  0.260426  0.089677  0.390887\n",
+       " 975  0.250061  0.540411  0.760292  0.913843  0.247943  0.897086\n",
+       " 976  0.123223  0.984265  0.398352  0.156474  0.320389  0.033480\n",
+       " 977  0.503936  0.350437  0.971377  0.677102  0.450573  0.345232\n",
+       " 978  0.060867  0.359374  0.194800  0.406698  0.896633  0.278379\n",
+       " 979  0.855909  0.878705  0.087030  0.262301  0.106841  0.540309\n",
+       " 980  0.369468  0.962369  0.592250  0.978234  0.420448  0.707226\n",
+       " 981  0.749210  0.705269  0.376000  0.104462  0.076379  0.395568\n",
+       " 982  0.816736  0.941247  0.696216  0.557726  0.021823  0.569084\n",
+       " 983  0.645431  0.086716  0.523276  0.457966  0.990895  0.051557\n",
+       " 984  0.522883  0.404067  0.137705  0.436183  0.674911  0.022694\n",
+       " 985  0.506432  0.315454  0.343641  0.347437  0.042147  0.042719\n",
+       " 986  0.401639  0.883530  0.952641  0.383275  0.546273  0.994898\n",
+       " 987  0.540708  0.397210  0.882191  0.090763  0.196273  0.278600\n",
+       " 988  0.886393  0.301648  0.618093  0.862737  0.564031  0.165432\n",
+       " 989  0.274822  0.413023  0.012761  0.629582  0.699212  0.450761\n",
+       " 990  0.024357  0.506516  0.810325  0.725633  0.642509  0.210293\n",
+       " 991  0.951018  0.867198  0.400399  0.389059  0.051136  0.732173\n",
+       " 992  0.174819  0.227343  0.672559  0.296078  0.171447  0.052644\n",
+       " 993  0.240869  0.530582  0.614925  0.539578  0.648053  0.939249\n",
+       " 994  0.218546  0.129713  0.754695  0.952646  0.935237  0.254552\n",
+       " 995  0.628217  0.178823  0.079779  0.079898  0.210532  0.206290\n",
+       " 996  0.088548  0.793026  0.671756  0.172528  0.621823  0.086637\n",
+       " 997  0.178640  0.493469  0.475165  0.383162  0.922717  0.418610\n",
+       " 998  0.091681  0.082174  0.621614  0.600814  0.880618  0.602452\n",
+       " 999  0.773642  0.663284  0.639317  0.754271  0.460677  0.612926\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.319010  0.079541  0.834849  0.291873  0.555684  0.126063\n",
+       " 1    0.823878  0.073295  0.367776  0.572961  0.718065  0.217394\n",
+       " 2    0.230319  0.437047  0.335279  0.510431  0.603903  0.417357\n",
+       " 3    0.266232  0.114018  0.370908  0.137080  0.580193  0.055995\n",
+       " 4    0.733006  0.163193  0.689686  0.178835  0.548272  0.677408\n",
+       " 5    0.333307  0.831685  0.806289  0.884843  0.990683  0.516538\n",
+       " 6    0.339222  0.266691  0.274908  0.672036  0.471657  0.624373\n",
+       " 7    0.806537  0.176810  0.920873  0.810930  0.201054  0.558544\n",
+       " 8    0.522824  0.904881  0.251781  0.658343  0.814791  0.268150\n",
+       " 9    0.449171  0.610798  0.406176  0.391143  0.798277  0.926350\n",
+       " 10   0.127550  0.177128  0.506874  0.771626  0.604078  0.355615\n",
+       " 11   0.205326  0.038215  0.697224  0.289774  0.258452  0.355940\n",
+       " 12   0.831782  0.960431  0.479401  0.699849  0.747175  0.875499\n",
+       " 13   0.377338  0.911561  0.589315  0.014406  0.819067  0.179597\n",
+       " 14   0.282226  0.953091  0.226978  0.087557  0.999019  0.903749\n",
+       " 15   0.149783  0.836659  0.569022  0.425509  0.048256  0.007747\n",
+       " 16   0.534935  0.588501  0.675434  0.459183  0.345690  0.001573\n",
+       " 17   0.955025  0.558857  0.476806  0.964203  0.479147  0.967291\n",
+       " 18   0.756993  0.788525  0.776298  0.225551  0.366617  0.699263\n",
+       " 19   0.392479  0.837898  0.702013  0.042269  0.575934  0.643131\n",
+       " 20   0.240380  0.255173  0.152347  0.894583  0.418224  0.400398\n",
+       " 21   0.349608  0.105063  0.040259  0.263219  0.514978  0.944609\n",
+       " 22   0.977683  0.654060  0.059765  0.007543  0.695152  0.735419\n",
+       " 23   0.070476  0.706936  0.858101  0.090613  0.569669  0.568897\n",
+       " 24   0.844206  0.342128  0.571471  0.685936  0.181698  0.596346\n",
+       " 25   0.662922  0.000595  0.710049  0.748918  0.989352  0.841359\n",
+       " 26   0.012534  0.680441  0.310498  0.471536  0.539659  0.190240\n",
+       " 27   0.561141  0.265144  0.859130  0.723166  0.668178  0.332867\n",
+       " 28   0.327478  0.232366  0.667941  0.620573  0.527616  0.904449\n",
+       " 29   0.199431  0.260630  0.796772  0.507862  0.339819  0.088713\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.084592  0.002757  0.475428  0.215689  0.385313  0.071607\n",
+       " 971  0.028930  0.342627  0.010770  0.137327  0.951992  0.808740\n",
+       " 972  0.758590  0.800042  0.856398  0.463675  0.416433  0.621909\n",
+       " 973  0.472394  0.444152  0.017647  0.764548  0.134468  0.026231\n",
+       " 974  0.241233  0.671473  0.221422  0.032526  0.040140  0.284118\n",
+       " 975  0.698005  0.868026  0.417422  0.091420  0.516900  0.040083\n",
+       " 976  0.407160  0.045084  0.468174  0.128202  0.732825  0.310388\n",
+       " 977  0.311998  0.303104  0.471411  0.464810  0.692032  0.813104\n",
+       " 978  0.078705  0.653529  0.117951  0.596879  0.619713  0.600871\n",
+       " 979  0.557117  0.801916  0.327767  0.174508  0.551483  0.590042\n",
+       " 980  0.881993  0.250553  0.498257  0.097090  0.035590  0.807725\n",
+       " 981  0.252596  0.422693  0.818125  0.490952  0.946017  0.614212\n",
+       " 982  0.479460  0.905817  0.419322  0.742912  0.038184  0.826064\n",
+       " 983  0.333335  0.343558  0.421134  0.701848  0.046915  0.820039\n",
+       " 984  0.109692  0.166441  0.443088  0.163946  0.134935  0.859088\n",
+       " 985  0.313608  0.995814  0.176061  0.825788  0.711276  0.710056\n",
+       " 986  0.445838  0.623024  0.776717  0.192213  0.163982  0.685679\n",
+       " 987  0.101788  0.566595  0.680074  0.073581  0.277119  0.918944\n",
+       " 988  0.771143  0.820136  0.637289  0.579434  0.822128  0.632670\n",
+       " 989  0.175275  0.947043  0.127348  0.980208  0.082268  0.567326\n",
+       " 990  0.063462  0.956176  0.777562  0.631523  0.545932  0.592767\n",
+       " 991  0.293535  0.135381  0.424689  0.974643  0.352436  0.006657\n",
+       " 992  0.675756  0.354801  0.991114  0.293141  0.463153  0.288586\n",
+       " 993  0.805756  0.558366  0.825443  0.699815  0.358356  0.733805\n",
+       " 994  0.136633  0.523439  0.349194  0.487622  0.967764  0.314406\n",
+       " 995  0.330244  0.876792  0.200931  0.228766  0.711824  0.400869\n",
+       " 996  0.020915  0.707875  0.651711  0.211319  0.750436  0.613333\n",
+       " 997  0.559592  0.840330  0.849206  0.191647  0.195375  0.403629\n",
+       " 998  0.077472  0.098974  0.479598  0.482582  0.062665  0.919598\n",
+       " 999  0.042749  0.237977  0.502496  0.606459  0.429510  0.361890\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.316545  0.866216  0.851158  0.881728  0.614212  0.217804\n",
+       " 1    0.938738  0.912532  0.415975  0.350650  0.032255  0.709436\n",
+       " 2    0.526507  0.998712  0.906947  0.552167  0.829434  0.489297\n",
+       " 3    0.469717  0.064703  0.958363  0.867824  0.303387  0.554153\n",
+       " 4    0.842056  0.001237  0.624385  0.359545  0.485075  0.900788\n",
+       " 5    0.653600  0.769250  0.069031  0.865063  0.786889  0.131051\n",
+       " 6    0.894899  0.649787  0.411010  0.948140  0.944974  0.445183\n",
+       " 7    0.853100  0.401513  0.176967  0.539026  0.506812  0.930225\n",
+       " 8    0.043068  0.804079  0.555328  0.849736  0.974248  0.078851\n",
+       " 9    0.871452  0.196760  0.620036  0.668806  0.031320  0.973392\n",
+       " 10   0.613273  0.639621  0.366861  0.257904  0.445338  0.680787\n",
+       " 11   0.650715  0.282425  0.651765  0.885428  0.974492  0.545692\n",
+       " 12   0.138826  0.998769  0.074061  0.178554  0.429951  0.051023\n",
+       " 13   0.102603  0.471636  0.766104  0.412954  0.519611  0.463641\n",
+       " 14   0.122762  0.621002  0.056172  0.170274  0.739887  0.766028\n",
+       " 15   0.886769  0.606035  0.810466  0.320985  0.926195  0.395556\n",
+       " 16   0.199486  0.524135  0.706366  0.731619  0.383539  0.772230\n",
+       " 17   0.525244  0.358626  0.310177  0.729691  0.484750  0.957276\n",
+       " 18   0.749451  0.234627  0.885238  0.149593  0.385103  0.603685\n",
+       " 19   0.188411  0.663693  0.234674  0.932024  0.381991  0.297120\n",
+       " 20   0.021725  0.344282  0.875396  0.432774  0.309059  0.710350\n",
+       " 21   0.621438  0.884457  0.089933  0.555466  0.583000  0.734210\n",
+       " 22   0.171655  0.713978  0.031372  0.672589  0.139588  0.900246\n",
+       " 23   0.608628  0.226784  0.542272  0.142383  0.358316  0.635505\n",
+       " 24   0.550189  0.905842  0.116501  0.504861  0.292785  0.570017\n",
+       " 25   0.102401  0.292232  0.322921  0.254221  0.585459  0.578396\n",
+       " 26   0.101505  0.301711  0.941333  0.085644  0.424033  0.921265\n",
+       " 27   0.435135  0.566862  0.982194  0.016434  0.640693  0.751928\n",
+       " 28   0.685939  0.996480  0.964209  0.351642  0.085508  0.209979\n",
+       " 29   0.886045  0.654960  0.703528  0.402004  0.433488  0.405528\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.199784  0.564519  0.834532  0.357498  0.470955  0.661544\n",
+       " 971  0.072451  0.917081  0.355943  0.050679  0.121779  0.367240\n",
+       " 972  0.391957  0.195413  0.123718  0.639714  0.821228  0.181564\n",
+       " 973  0.037769  0.573656  0.263573  0.220274  0.069552  0.555076\n",
+       " 974  0.242690  0.347374  0.637216  0.617772  0.870922  0.697070\n",
+       " 975  0.143435  0.123512  0.335582  0.921038  0.267226  0.716318\n",
+       " 976  0.702581  0.021914  0.384356  0.795503  0.859109  0.587857\n",
+       " 977  0.336917  0.035569  0.902358  0.194458  0.202751  0.786312\n",
+       " 978  0.012398  0.416433  0.661122  0.635333  0.473715  0.449108\n",
+       " 979  0.644338  0.193378  0.958097  0.417143  0.587210  0.014700\n",
+       " 980  0.746086  0.976542  0.170830  0.872244  0.577610  0.559561\n",
+       " 981  0.396134  0.321668  0.831738  0.040101  0.213146  0.901478\n",
+       " 982  0.238186  0.612973  0.627245  0.895502  0.434530  0.829379\n",
+       " 983  0.418616  0.230882  0.227087  0.681469  0.958512  0.915477\n",
+       " 984  0.587630  0.357674  0.196675  0.208442  0.936227  0.598198\n",
+       " 985  0.388748  0.607182  0.770996  0.135977  0.154043  0.866367\n",
+       " 986  0.782324  0.476685  0.476860  0.904856  0.468023  0.295243\n",
+       " 987  0.502848  0.391119  0.880286  0.141569  0.600588  0.844762\n",
+       " 988  0.024857  0.008766  0.785989  0.670424  0.446298  0.458229\n",
+       " 989  0.927726  0.109649  0.488678  0.469206  0.158633  0.010499\n",
+       " 990  0.794797  0.924582  0.487010  0.476290  0.153185  0.085422\n",
+       " 991  0.334244  0.903936  0.876815  0.121556  0.121346  0.994163\n",
+       " 992  0.301544  0.187787  0.827463  0.147934  0.454074  0.214798\n",
+       " 993  0.764274  0.395686  0.119199  0.653385  0.960820  0.064074\n",
+       " 994  0.708947  0.498953  0.078334  0.142168  0.577399  0.484276\n",
+       " 995  0.895655  0.614203  0.233454  0.982022  0.497486  0.104169\n",
+       " 996  0.797090  0.250844  0.360796  0.727291  0.198673  0.124661\n",
+       " 997  0.773640  0.324830  0.149302  0.518035  0.710678  0.830760\n",
+       " 998  0.464890  0.057418  0.839886  0.019700  0.472734  0.717501\n",
+       " 999  0.718079  0.813571  0.272179  0.892133  0.399858  0.508644\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.897949  0.436821  0.334158  0.910948  0.390674  0.951386\n",
+       " 1    0.117646  0.004848  0.145750  0.883618  0.988716  0.400071\n",
+       " 2    0.952221  0.679926  0.685714  0.541707  0.354324  0.191253\n",
+       " 3    0.951158  0.671586  0.460024  0.930337  0.825738  0.845561\n",
+       " 4    0.316897  0.177463  0.698781  0.450096  0.664735  0.346028\n",
+       " 5    0.980384  0.914951  0.950949  0.963511  0.512342  0.735342\n",
+       " 6    0.431554  0.004218  0.721848  0.356822  0.611823  0.209144\n",
+       " 7    0.059458  0.874118  0.691093  0.664041  0.860349  0.870071\n",
+       " 8    0.682526  0.237373  0.986660  0.719636  0.404041  0.162857\n",
+       " 9    0.163821  0.939638  0.124197  0.008617  0.980309  0.330785\n",
+       " 10   0.501494  0.216273  0.020130  0.144248  0.494656  0.940896\n",
+       " 11   0.919186  0.215112  0.057693  0.651383  0.194383  0.974702\n",
+       " 12   0.555781  0.759217  0.228808  0.022520  0.847383  0.841217\n",
+       " 13   0.599143  0.094610  0.885606  0.686725  0.435789  0.551800\n",
+       " 14   0.613192  0.202781  0.190791  0.924408  0.656332  0.891009\n",
+       " 15   0.260539  0.491180  0.094093  0.546118  0.840043  0.191597\n",
+       " 16   0.354369  0.618842  0.261125  0.209292  0.343408  0.070024\n",
+       " 17   0.123692  0.551990  0.029779  0.266198  0.120930  0.374307\n",
+       " 18   0.712904  0.880080  0.383013  0.292187  0.274894  0.494717\n",
+       " 19   0.001216  0.016321  0.643887  0.637831  0.135602  0.967494\n",
+       " 20   0.320565  0.577042  0.985852  0.680155  0.374422  0.576326\n",
+       " 21   0.333310  0.343173  0.392281  0.907745  0.100688  0.046281\n",
+       " 22   0.762303  0.102936  0.477211  0.519117  0.361561  0.007092\n",
+       " 23   0.824414  0.276226  0.939292  0.269527  0.109327  0.650856\n",
+       " 24   0.914457  0.137213  0.050881  0.143600  0.464871  0.744002\n",
+       " 25   0.204411  0.778559  0.166961  0.502051  0.106770  0.923723\n",
+       " 26   0.587179  0.599280  0.313415  0.779855  0.392135  0.729841\n",
+       " 27   0.889788  0.343553  0.193590  0.613965  0.164877  0.631403\n",
+       " 28   0.800483  0.379858  0.523480  0.607730  0.976958  0.083362\n",
+       " 29   0.304272  0.508641  0.976497  0.860727  0.653566  0.660917\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.678135  0.505868  0.840510  0.699798  0.788723  0.908087\n",
+       " 971  0.830909  0.069008  0.721579  0.469757  0.483532  0.880381\n",
+       " 972  0.639689  0.416281  0.005632  0.928100  0.178794  0.589411\n",
+       " 973  0.151768  0.697832  0.511029  0.688094  0.671389  0.234511\n",
+       " 974  0.035276  0.841267  0.321623  0.203678  0.446535  0.819491\n",
+       " 975  0.115546  0.116783  0.336075  0.668120  0.423806  0.361942\n",
+       " 976  0.555437  0.337489  0.014528  0.764202  0.320265  0.244884\n",
+       " 977  0.257841  0.658981  0.187260  0.863040  0.989517  0.572176\n",
+       " 978  0.782615  0.817973  0.799037  0.411113  0.352863  0.100925\n",
+       " 979  0.626868  0.209438  0.134052  0.660275  0.341523  0.539145\n",
+       " 980  0.065569  0.224795  0.162688  0.340475  0.406459  0.191578\n",
+       " 981  0.372426  0.617229  0.401295  0.957295  0.617407  0.613829\n",
+       " 982  0.348876  0.085725  0.244612  0.169822  0.011382  0.967583\n",
+       " 983  0.982503  0.437502  0.342052  0.233192  0.600657  0.897353\n",
+       " 984  0.506320  0.306398  0.702741  0.754280  0.804226  0.641031\n",
+       " 985  0.038395  0.320677  0.630383  0.223745  0.092748  0.003422\n",
+       " 986  0.816780  0.274860  0.167410  0.240676  0.178732  0.297183\n",
+       " 987  0.847608  0.336192  0.555042  0.997418  0.332401  0.535487\n",
+       " 988  0.639704  0.295153  0.549238  0.386104  0.079553  0.594370\n",
+       " 989  0.356944  0.414819  0.032667  0.846247  0.109512  0.590233\n",
+       " 990  0.226674  0.494712  0.416005  0.596886  0.480664  0.943340\n",
+       " 991  0.537169  0.061863  0.442147  0.104381  0.294116  0.628377\n",
+       " 992  0.936810  0.640603  0.836501  0.282983  0.485562  0.626397\n",
+       " 993  0.263516  0.554194  0.455274  0.730868  0.496592  0.534790\n",
+       " 994  0.852218  0.039252  0.066472  0.743481  0.123496  0.369085\n",
+       " 995  0.471342  0.012622  0.839009  0.074654  0.746211  0.938946\n",
+       " 996  0.914077  0.404842  0.816569  0.752329  0.443962  0.648024\n",
+       " 997  0.659877  0.547854  0.546185  0.397348  0.487445  0.782776\n",
+       " 998  0.305352  0.847927  0.293624  0.081849  0.718861  0.136441\n",
+       " 999  0.686076  0.586199  0.120656  0.309898  0.366429  0.888506\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.333033  0.046392  0.849756  0.844117  0.756731  0.693090\n",
+       " 1    0.176014  0.548675  0.062138  0.355843  0.765326  0.090539\n",
+       " 2    0.155095  0.926941  0.466353  0.707147  0.641214  0.236875\n",
+       " 3    0.080573  0.319689  0.621399  0.056529  0.933024  0.323453\n",
+       " 4    0.524282  0.843187  0.058885  0.590389  0.039876  0.875888\n",
+       " 5    0.076150  0.159493  0.084964  0.268625  0.188988  0.546757\n",
+       " 6    0.255839  0.501668  0.330847  0.875273  0.091523  0.284668\n",
+       " 7    0.763676  0.779210  0.099260  0.283702  0.729965  0.674880\n",
+       " 8    0.098352  0.772512  0.262127  0.577933  0.985104  0.970264\n",
+       " 9    0.779158  0.524204  0.349665  0.351574  0.581054  0.797407\n",
+       " 10   0.188364  0.319668  0.282698  0.550779  0.213311  0.983472\n",
+       " 11   0.218999  0.029959  0.039223  0.827230  0.675509  0.866124\n",
+       " 12   0.659943  0.593038  0.165672  0.650606  0.069984  0.188579\n",
+       " 13   0.760098  0.778193  0.225531  0.001218  0.847675  0.280088\n",
+       " 14   0.419712  0.145912  0.369096  0.578534  0.999339  0.639145\n",
+       " 15   0.550643  0.821984  0.259689  0.287845  0.516814  0.434135\n",
+       " 16   0.621985  0.796302  0.358906  0.955230  0.728937  0.905711\n",
+       " 17   0.841507  0.575636  0.641070  0.190838  0.291923  0.251294\n",
+       " 18   0.763887  0.212244  0.495873  0.109540  0.947110  0.941853\n",
+       " 19   0.318809  0.671112  0.683044  0.525916  0.228495  0.959248\n",
+       " 20   0.903243  0.432014  0.542585  0.611370  0.102751  0.295038\n",
+       " 21   0.362091  0.258232  0.272556  0.515442  0.687616  0.062301\n",
+       " 22   0.575162  0.509906  0.561070  0.051773  0.007823  0.788010\n",
+       " 23   0.311129  0.856446  0.640549  0.353196  0.478431  0.744857\n",
+       " 24   0.470477  0.624492  0.406674  0.604497  0.785328  0.724493\n",
+       " 25   0.052195  0.799106  0.588394  0.498300  0.051709  0.864125\n",
+       " 26   0.554905  0.041283  0.959438  0.790567  0.571955  0.802866\n",
+       " 27   0.293754  0.740901  0.368729  0.437794  0.809327  0.678296\n",
+       " 28   0.566555  0.003529  0.893885  0.652843  0.141045  0.875486\n",
+       " 29   0.994207  0.207632  0.636159  0.006780  0.177908  0.785081\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.616464  0.740990  0.690231  0.792671  0.373085  0.934581\n",
+       " 971  0.535568  0.742944  0.295992  0.693701  0.507212  0.581756\n",
+       " 972  0.762322  0.982274  0.193161  0.765673  0.942356  0.427242\n",
+       " 973  0.173670  0.945937  0.975711  0.055580  0.255240  0.543428\n",
+       " 974  0.366309  0.060043  0.015526  0.003428  0.063633  0.999114\n",
+       " 975  0.824485  0.474008  0.743921  0.208575  0.053265  0.143940\n",
+       " 976  0.462687  0.493482  0.696330  0.028084  0.742533  0.419741\n",
+       " 977  0.018798  0.393638  0.263414  0.876904  0.856346  0.179497\n",
+       " 978  0.842100  0.318424  0.020449  0.429973  0.395938  0.208205\n",
+       " 979  0.807972  0.578555  0.520832  0.145670  0.708217  0.816327\n",
+       " 980  0.359016  0.454054  0.836526  0.128322  0.986882  0.640663\n",
+       " 981  0.920399  0.757826  0.655774  0.883243  0.851351  0.407500\n",
+       " 982  0.029872  0.670318  0.891641  0.962455  0.357869  0.014809\n",
+       " 983  0.190562  0.360151  0.139951  0.937782  0.832054  0.241879\n",
+       " 984  0.609395  0.095868  0.584615  0.786539  0.443377  0.841252\n",
+       " 985  0.517280  0.874434  0.549003  0.112511  0.052653  0.671694\n",
+       " 986  0.330642  0.576341  0.321928  0.978113  0.437359  0.276229\n",
+       " 987  0.226446  0.148315  0.819679  0.865955  0.380242  0.177109\n",
+       " 988  0.523197  0.604839  0.458060  0.775881  0.204327  0.232029\n",
+       " 989  0.197421  0.707517  0.449101  0.317221  0.248816  0.076272\n",
+       " 990  0.087002  0.500083  0.640721  0.867064  0.881646  0.173928\n",
+       " 991  0.143997  0.650857  0.537886  0.690487  0.046321  0.086674\n",
+       " 992  0.199210  0.193037  0.523348  0.511345  0.605872  0.257110\n",
+       " 993  0.514812  0.942335  0.704875  0.424562  0.741218  0.842322\n",
+       " 994  0.008269  0.911926  0.003568  0.076844  0.246726  0.443958\n",
+       " 995  0.198463  0.893883  0.532660  0.262119  0.642313  0.687954\n",
+       " 996  0.770815  0.459404  0.703055  0.732800  0.389722  0.655059\n",
+       " 997  0.302371  0.532000  0.064153  0.299964  0.545305  0.117152\n",
+       " 998  0.010846  0.812327  0.843239  0.306763  0.644027  0.618594\n",
+       " 999  0.580345  0.476859  0.988876  0.231913  0.033464  0.669132\n",
+       " \n",
+       " [1000 rows x 6 columns],\n",
+       "      position                         r-xyz                    \n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2\n",
+       " 0    0.132944  0.956304  0.833149  0.549216  0.690046  0.566770\n",
+       " 1    0.220414  0.956259  0.592039  0.195486  0.901958  0.522270\n",
+       " 2    0.668032  0.179027  0.297226  0.927352  0.306206  0.019481\n",
+       " 3    0.113978  0.832474  0.815118  0.964817  0.147111  0.879627\n",
+       " 4    0.063025  0.685158  0.708261  0.988719  0.475819  0.679357\n",
+       " 5    0.122603  0.050275  0.178128  0.648590  0.074787  0.436381\n",
+       " 6    0.285898  0.148586  0.136640  0.272759  0.038183  0.559743\n",
+       " 7    0.828761  0.537722  0.311465  0.565836  0.681658  0.395757\n",
+       " 8    0.972371  0.030288  0.050300  0.413820  0.003550  0.543379\n",
+       " 9    0.206760  0.522595  0.912604  0.473295  0.731249  0.460707\n",
+       " 10   0.988445  0.756264  0.006794  0.244567  0.406938  0.701223\n",
+       " 11   0.120944  0.983590  0.785065  0.315098  0.428533  0.136569\n",
+       " 12   0.654552  0.431042  0.887687  0.904558  0.810851  0.212032\n",
+       " 13   0.787523  0.621298  0.084506  0.876051  0.857776  0.821420\n",
+       " 14   0.362512  0.118958  0.945656  0.117961  0.148084  0.292765\n",
+       " 15   0.531068  0.698085  0.770898  0.298503  0.726505  0.272444\n",
+       " 16   0.025158  0.929358  0.322068  0.033540  0.812672  0.421281\n",
+       " 17   0.270447  0.543843  0.870861  0.974038  0.536998  0.807655\n",
+       " 18   0.528107  0.832056  0.291667  0.498647  0.014001  0.077398\n",
+       " 19   0.384942  0.377744  0.831789  0.781069  0.921614  0.421941\n",
+       " 20   0.617073  0.797459  0.310775  0.932069  0.066848  0.729254\n",
+       " 21   0.937862  0.926329  0.434252  0.134158  0.473562  0.701661\n",
+       " 22   0.170728  0.224822  0.659037  0.467627  0.969962  0.257221\n",
+       " 23   0.578044  0.327925  0.781170  0.098882  0.550434  0.827660\n",
+       " 24   0.659016  0.836791  0.445487  0.678376  0.873683  0.423183\n",
+       " 25   0.258834  0.312115  0.084403  0.168902  0.628195  0.796976\n",
+       " 26   0.754756  0.588085  0.939852  0.401381  0.833260  0.201205\n",
+       " 27   0.211013  0.323312  0.893854  0.893972  0.534390  0.425508\n",
+       " 28   0.764016  0.933121  0.487342  0.858824  0.497056  0.723343\n",
+       " 29   0.313932  0.527734  0.754901  0.812594  0.973529  0.481254\n",
+       " ..        ...       ...       ...       ...       ...       ...\n",
+       " 970  0.870000  0.877744  0.133704  0.513539  0.666621  0.564714\n",
+       " 971  0.499018  0.274353  0.736660  0.830019  0.491201  0.451893\n",
+       " 972  0.750874  0.769365  0.083992  0.218780  0.761929  0.793199\n",
+       " 973  0.713476  0.393839  0.237411  0.476521  0.600149  0.453182\n",
+       " 974  0.745033  0.873177  0.270454  0.493940  0.433444  0.390541\n",
+       " 975  0.153189  0.767793  0.343223  0.244022  0.169986  0.614239\n",
+       " 976  0.852508  0.264026  0.332159  0.666647  0.642824  0.564611\n",
+       " 977  0.173108  0.191677  0.759217  0.034953  0.914400  0.460453\n",
+       " 978  0.254409  0.738450  0.509990  0.080427  0.616239  0.000965\n",
+       " 979  0.638512  0.781548  0.887692  0.954444  0.949442  0.129483\n",
+       " 980  0.954968  0.009181  0.534708  0.743827  0.068192  0.673499\n",
+       " 981  0.586043  0.853359  0.927984  0.063555  0.118149  0.275798\n",
+       " 982  0.566880  0.412768  0.568313  0.865864  0.557034  0.732554\n",
+       " 983  0.001795  0.774738  0.549257  0.397866  0.392590  0.247907\n",
+       " 984  0.329392  0.322411  0.751285  0.639416  0.039985  0.519509\n",
+       " 985  0.716027  0.423020  0.279140  0.942273  0.496716  0.684701\n",
+       " 986  0.436532  0.908938  0.553185  0.456237  0.677512  0.983449\n",
+       " 987  0.811382  0.552620  0.632298  0.074343  0.370701  0.504376\n",
+       " 988  0.117925  0.087259  0.311347  0.690308  0.067740  0.637832\n",
+       " 989  0.258071  0.099449  0.799456  0.694128  0.907442  0.300405\n",
+       " 990  0.284239  0.957305  0.747812  0.413767  0.347265  0.340289\n",
+       " 991  0.824210  0.860996  0.833149  0.622665  0.218785  0.522948\n",
+       " 992  0.565616  0.514524  0.102584  0.685392  0.581374  0.865684\n",
+       " 993  0.184010  0.639498  0.923305  0.401373  0.938501  0.658912\n",
+       " 994  0.053389  0.271161  0.316990  0.516743  0.563797  0.659869\n",
+       " 995  0.766754  0.423027  0.569732  0.317902  0.586919  0.591215\n",
+       " 996  0.142093  0.896484  0.983356  0.703119  0.263204  0.294038\n",
+       " 997  0.565694  0.521118  0.484091  0.635578  0.173175  0.630106\n",
+       " 998  0.409339  0.177391  0.790018  0.698171  0.101989  0.499348\n",
+       " 999  0.617710  0.525864  0.686019  0.423778  0.744281  0.539085\n",
+       " \n",
+       " [1000 rows x 6 columns]]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "data_stationary"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Investigator Class"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This class provides means for investigating data in the context of time-series prediction. In particular it provides the following features:\n",
+    "\n",
+    "* Check if series is stationary (non changing mean/ no trend)\n",
+    "* Find significant lags (minimum lag that still shows correlation, when series is shifted against itself)\n",
+    "* plot auto correlation function (ACF) and partial ACF (PACF)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Initialize"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Help on class Investigator in module predictor_box:\n",
+      "\n",
+      "class Investigator(builtins.object)\n",
+      " |  This class provides methods for time series analysis like\n",
+      " |  ACF and PACF, as well as stability checks. Invoking an instance of this\n",
+      " |  class requires the data which is wished to be investigated. The expected\n",
+      " |  data structure is equal to the one used in navipy, which is given by \n",
+      " |  \n",
+      " |  pd.MultiIndex.from_tuples([('position', 'x'),\n",
+      " |                                           ('position', 'y'),\n",
+      " |                                           ('position', 'z'),\n",
+      " |                                           ('r-xyz', 'alpha_0'),\n",
+      " |                                           ('r-xyz', 'alpha_1'),\n",
+      " |                                           ('r-xyz', 'alpha_2')])\n",
+      " |  \n",
+      " |  You can provide a single MultiIndex or a list of MultiIndex.\n",
+      " |  \n",
+      " |  Methods defined here:\n",
+      " |  \n",
+      " |  __init__(self, data)\n",
+      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
+      " |  \n",
+      " |  check_stationary(self, trial_id=-1, sig_level=None, print_res=False, diff_order=0)\n",
+      " |      Checks selected data for stationarity.\n",
+      " |      \n",
+      " |      This function checks selected data for stationarity in a time-series\n",
+      " |      context with a dickey-fuller test. It returns a pandas dataframe of\n",
+      " |      booleans, where each row is one trial and each column one feature dim-\n",
+      " |      emnsion.\n",
+      " |      \n",
+      " |      Keyword arguments:\n",
+      " |      trial_id -- int or [int] containing the id of the trials to be investi\n",
+      " |                  gated. If trial_id = -1, all trials are checked.\n",
+      " |                  Default = -1\n",
+      " |      sig_level -- float level of significance.\n",
+      " |                  Default = 0.05\n",
+      " |      print_res -- boolean value, if true, results are printed.\n",
+      " |                  Default = False\n",
+      " |      diff_order -- int in [0,3]. Number of times the time-series is\n",
+      " |                  differenced befor it is checked for stability.\n",
+      " |                  Default = 0\n",
+      " |          \n",
+      " |      Returns:\n",
+      " |      stationarity_df -- pandas dataframe of booleans.\n",
+      " |  \n",
+      " |  get_significant_lags(self, trial_id=-1, function_type='acf', n_lags=40, sig_level=0.05, diff_order=0)\n",
+      " |      This function analysis the data for the number of significant\n",
+      " |      legs with respect to either autocorrelation fucntion (acf) or\n",
+      " |      partial acf (pacf). It returns the last significant lag.\n",
+      " |  \n",
+      " |  plot_cf_function(self, function_type='acf', trial_id=0, dim=('position', 'x'))\n",
+      " |      Plots results of either ACF or PACF for a single dimension.\n",
+      " |      \n",
+      " |      This function plots the results of an auto-correlation-function (ACF)\n",
+      " |      or partial ACF (PACF), depending on the selected funtion_type, for a \n",
+      " |      single dimension. \n",
+      " |      It is basically acting as a tunnel-implementation of plot_acf/_pacf\n",
+      " |      of the statsmodels.graphics.tsaplots module. \n",
+      " |      \n",
+      " |       Keyword arguments:\n",
+      " |      trial_id -- int or [int] containing the id of the trials to be investi\n",
+      " |                  gated. If trial_id = -1, all trials are checked.\n",
+      " |                  Default = -1\n",
+      " |      dim -- tuple of features like ('position','x'). This column in data\n",
+      " |              is used as a time series and plotted \n",
+      " |      \n",
+      " |      Returns:\n",
+      " |      figs -- list of pyplot figures [fig].\n",
+      " |  \n",
+      " |  ----------------------------------------------------------------------\n",
+      " |  Data descriptors defined here:\n",
+      " |  \n",
+      " |  __dict__\n",
+      " |      dictionary for instance variables (if defined)\n",
+      " |  \n",
+      " |  __weakref__\n",
+      " |      list of weak references to the object (if defined)\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "help(Investigator)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "# with stationary data set\n",
+    "Inv_stat = Investigator(data_stationary)\n",
+    "# with non-stationary data set\n",
+    "Inv_not_stat = Investigator(data_not_stationary)\n",
+    "# with data from an AR1 process \n",
+    "Inv_ar1 = Investigator(data_ar1)\n",
+    "# with data from an AR3 process\n",
+    "Inv_ar3 = Investigator(data_ar3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "__Stability and Lags investigation__"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "statdf = Inv_stat.check_stationary()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead tr th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr>\n",
+       "      <th></th>\n",
+       "      <th colspan=\"3\" halign=\"left\">position</th>\n",
+       "      <th colspan=\"3\" halign=\"left\">r-xyz</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th></th>\n",
+       "      <th>x</th>\n",
+       "      <th>y</th>\n",
+       "      <th>z</th>\n",
+       "      <th>alpha_0</th>\n",
+       "      <th>alpha_1</th>\n",
+       "      <th>alpha_2</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  position               r-xyz                \n",
+       "         x     y     z alpha_0 alpha_1 alpha_2\n",
+       "0     True  True  True    True    True    True\n",
+       "1     True  True  True    True    True    True\n",
+       "2     True  True  True    True    True    True\n",
+       "3     True  True  True    True    True    True\n",
+       "4     True  True  True    True    True    True"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "statdf.head(5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "statdf = Inv_not_stat.check_stationary()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead tr th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr>\n",
+       "      <th></th>\n",
+       "      <th colspan=\"3\" halign=\"left\">position</th>\n",
+       "      <th colspan=\"3\" halign=\"left\">r-xyz</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th></th>\n",
+       "      <th>x</th>\n",
+       "      <th>y</th>\n",
+       "      <th>z</th>\n",
+       "      <th>alpha_0</th>\n",
+       "      <th>alpha_1</th>\n",
+       "      <th>alpha_2</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  position                 r-xyz                \n",
+       "         x      y      z alpha_0 alpha_1 alpha_2\n",
+       "0    False  False  False   False   False   False\n",
+       "1    False  False  False   False   False   False\n",
+       "2    False  False  False   False   False   False\n",
+       "3    False  False  False   False   False   False\n",
+       "4    False  False  False   False   False   False"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "statdf.head(5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sig_lags = Inv_ar1.get_significant_lags()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead tr th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr>\n",
+       "      <th></th>\n",
+       "      <th colspan=\"3\" halign=\"left\">position</th>\n",
+       "      <th colspan=\"3\" halign=\"left\">r-xyz</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th></th>\n",
+       "      <th>x</th>\n",
+       "      <th>y</th>\n",
+       "      <th>z</th>\n",
+       "      <th>alpha_0</th>\n",
+       "      <th>alpha_1</th>\n",
+       "      <th>alpha_2</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  position         r-xyz                \n",
+       "         x  y  z alpha_0 alpha_1 alpha_2\n",
+       "0        1  1  1       1       1       1\n",
+       "1        1  1  1       1       1       1\n",
+       "2        1  1  1       1       1       1\n",
+       "3        1  1  1       1       1       1\n",
+       "4        1  1  1       1       1       1"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sig_lags.head(5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sig_lags = Inv_ar3.get_significant_lags()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead tr th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr>\n",
+       "      <th></th>\n",
+       "      <th colspan=\"3\" halign=\"left\">position</th>\n",
+       "      <th colspan=\"3\" halign=\"left\">r-xyz</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th></th>\n",
+       "      <th>x</th>\n",
+       "      <th>y</th>\n",
+       "      <th>z</th>\n",
+       "      <th>alpha_0</th>\n",
+       "      <th>alpha_1</th>\n",
+       "      <th>alpha_2</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  position         r-xyz                \n",
+       "         x  y  z alpha_0 alpha_1 alpha_2\n",
+       "0        2  2  2       2       2       2\n",
+       "1        2  2  2       2       2       2\n",
+       "2        2  2  2       2       2       2\n",
+       "3        2  2  2       2       2       2\n",
+       "4        2  2  2       2       2       2"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sig_lags.head(5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "__Plotting ACF and PACF__"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<Figure size 432x288 with 1 Axes>]"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "Inv_ar3.plot_cf_function(trial_id=0, dim=('position', 'y'), function_type='acf')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "c:\\users\\stefan(local)\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\statsmodels\\regression\\linear_model.py:1283: RuntimeWarning: invalid value encountered in sqrt\n",
+      "  return rho, np.sqrt(sigmasq)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<Figure size 432x288 with 1 Axes>]"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# This one makes problems I did not dig into yet.\n",
+    "Inv_ar1.plot_cf_function(trial_id=0, dim=('position', 'z'), function_type='pacf')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Modelmaker Class "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This class provides the means to create time series forecasting ARIMA models. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Help on class Modelmaker in module predictor_box:\n",
+      "\n",
+      "class Modelmaker(builtins.object)\n",
+      " |  Methods defined here:\n",
+      " |  \n",
+      " |  __init__(self, data)\n",
+      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
+      " |  \n",
+      " |  apply_arima_models(self, p=1, d=0, q=0, pred_step=1, dim=('position', 'x'), trial_id=-1, n_preds=40, rolling=True, override=True, metric=<function mean_squared_error at 0x000001C3CA47D950>)\n",
+      " |      This function applies ARIMA models to data and saves results internally\n",
+      " |      \n",
+      " |      This function applies an ARIMA(p,d,q) model to all trials selected with trial_id.\n",
+      " |      The results are internally saved in Modelmaker.results, where you can see predictions\n",
+      " |      or directly access the model instance. \n",
+      " |      \n",
+      " |      Keyword arguments:\n",
+      " |      p -- int > 0, number of lag observations\n",
+      " |          Default = 1\n",
+      " |      d -- int > 0, order of differentiation\n",
+      " |          Default = 0\n",
+      " |      q -- int > 0, size of MA window\n",
+      " |          Default = 0\n",
+      " |      pred_step -- int > 0, forecasting horizon\n",
+      " |      dim -- str tuple matching any feature in data, determining which feature values are used in \n",
+      " |              this model.\n",
+      " |              Default = ('position','x')\n",
+      " |      trial_id -- [int >0] or int >= -1, If list of int, all trials which ID matches any element of\n",
+      " |              said list will be fitted by an ARIMA model. If int  is -1, all trials will be fitted by\n",
+      " |              and ARIMA model\n",
+      " |              Default = -1\n",
+      " |      n_preds -- int > 0, number of predictions that shall be made. If this number is largere than the\n",
+      " |              number of observations estimates can be compared to, it will throw a warning and will only\n",
+      " |              produce len(observation) estimates.\n",
+      " |              Default = 40\n",
+      " |      rolling -- bool, if True, after each estimate, the actual observation is added to the history,\n",
+      " |                 and the model parameters are fitted to the updated history, befor making the next \n",
+      " |                 estimate\n",
+      " |                 Default = True\n",
+      " |      override -- bool, if True, if the trial_id has already been fitted by an ARIMA, these results will \n",
+      " |                  be deleted and the new results will be shown for this row in results. If False,\n",
+      " |                  a new row is added (MIND that TrialID is not unique anymore in this case)\n",
+      " |                  Default = True\n",
+      " |      metric -- function(list,list), user defined metric funtcion that handles two list arguments of the \n",
+      " |                  same length as inputs. Takes EXACTLY two list inputs, so modify before passing as argument.\n",
+      " |                  Note: Pass without brackets e.g. metric = my_metric BUT NOT LIKE metric = my_metric()\n",
+      " |                  Default = sklearn.metrics.mean_squared_error\n",
+      " |      Returns:\n",
+      " |      self.results -- Pandas dataframe, where each row contains informations about the fitted model \n",
+      " |                         to the respective trial id\n",
+      " |  \n",
+      " |  setup_data(self, random_split=True, tr_size=0.6, te_size=0.3, ev_size=0.1, pred_size=-1, split_type='inter')\n",
+      " |      This function put data into train, test and eval set\n",
+      " |      \n",
+      " |      This function splits all trials in data into training, test \n",
+      " |      and evaluation set and creates targets from a given shift.\n",
+      " |      The number of trials in each set depends on \n",
+      " |      the user specified allocation. \n",
+      " |      Furthermore, the user has to select pred_size, which determines\n",
+      " |      how far into the future the prediction shall take place\n",
+      " |      \n",
+      " |      Keyword arguments:\n",
+      " |      random_split -- bool determining if data is allocated randomly to each set\n",
+      " |                      Default = True\n",
+      " |      tr_size -- float determining the percentage of over all data allocated to \n",
+      " |                  training set.\n",
+      " |                  Default = .6\n",
+      " |      te_size -- float determining the percentage of over all data allocated to \n",
+      " |                  test set.\n",
+      " |                  Default = .3                \n",
+      " |      ev_size -- float determining the percentage of over all data allocated to \n",
+      " |                  evaluation set.\n",
+      " |                  Default = .1\n",
+      " |              MIND THAT tr_size + te_size + ev_size = 1 HAS TO BE TRUE\n",
+      " |      \n",
+      " |      pred_size -- int <= 0 determining the shift of target to input data. Number\n",
+      " |                  has to be negative to be consistent with numpy shift method.\n",
+      " |                  Default = -1\n",
+      " |      split_type -- string 'inter' or 'intra' determining how the sets are created.\n",
+      " |                  When 'inter', each set consists of complete, independent trajectories\n",
+      " |                      - Use this for neural networks\n",
+      " |                  When 'intra', each trajectory is cut into a training and a test part\n",
+      " |                      - Use this for ARIMA models\n",
+      " |                  Default = 'intra' \n",
+      " |                  \n",
+      " |      Returns:\n",
+      " |      ls_df_tr -- list of pandas.DataFrames, one entry per trajectory in training set\n",
+      " |      ls_df_te -- list of pandas.DataFrames, one entry per trajectory in test set\n",
+      " |      ls_df_ev -- list of pandas.DataFrames, one entry per trajectory in evaluation set\n",
+      " |  \n",
+      " |  ----------------------------------------------------------------------\n",
+      " |  Data descriptors defined here:\n",
+      " |  \n",
+      " |  __dict__\n",
+      " |      dictionary for instance variables (if defined)\n",
+      " |  \n",
+      " |  __weakref__\n",
+      " |      list of weak references to the object (if defined)\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "help(Modelmaker)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Mom_ar1 = Modelmaker(data_ar1)\n",
+    "Mom_ar3 = Modelmaker(data_ar3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Data Splitting"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "([    position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -1.744240   \n",
+       "  3  -1.744240  1.228898  0.809295  2.914220  1.251183 -0.446121 -1.921393   \n",
+       "  4  -1.921393  2.032020 -0.757841  2.481291  1.061665 -0.720897 -1.407941   \n",
+       "  5  -1.407941 -0.480671 -2.112934  1.436692  1.113866 -0.533631 -1.344827   \n",
+       "  6  -1.344827  0.431634 -2.353882 -0.283165 -1.663704  0.083051  0.427435   \n",
+       "  7   0.427435 -2.404765 -1.785370 -1.517594 -2.263802  1.187547  2.265210   \n",
+       "  8   2.265210 -1.701558 -0.908770 -3.246183 -2.732020  1.278594  0.997496   \n",
+       "  9   0.997496  1.135113  0.846938 -3.811131 -1.962079  0.090256  0.315674   \n",
+       "  10  0.315674  2.752873  2.230618 -1.688955  1.110582 -2.051597 -1.823367   \n",
+       "  11 -1.823367  2.487168  2.505903  0.719245  1.105423 -1.998565 -0.882475   \n",
+       "  12 -0.882475  1.137694  0.352369  3.074586  1.561490 -1.981527 -1.194490   \n",
+       "  13 -1.194490 -0.545080  0.170560  3.980628  0.196529  0.182747  0.098864   \n",
+       "  14  0.098864 -2.005421 -0.381956  1.957991 -1.323987  2.041334  0.048647   \n",
+       "  15  0.048647 -1.551038  0.865690  0.650338 -3.438464  2.322486  0.946489   \n",
+       "  16  0.946489 -0.756231 -0.704060 -2.226902 -3.062890  0.987046  0.340657   \n",
+       "  17  0.340657 -1.104541  0.120287 -4.500092 -0.118761 -0.222539  0.667615   \n",
+       "  18  0.667615  0.483095 -1.320007 -4.111491  0.813397 -0.922173 -0.560804   \n",
+       "  19 -0.560804  0.336268 -0.648774  0.239329  1.991543 -0.924966 -1.684131   \n",
+       "  20 -1.684131  1.951121  1.443834  5.190550  1.705568 -2.466884 -2.747811   \n",
+       "  21 -2.747811  1.375362  3.554259  4.597036  0.344731 -0.557874 -0.502713   \n",
+       "  22 -0.502713 -0.674163  2.002393  2.354066 -1.139776  0.771171 -0.058053   \n",
+       "  23 -0.058053 -1.959510  0.565586 -0.698477 -3.540839  0.465691  0.326641   \n",
+       "  24  0.326641 -2.368123 -0.254322 -2.247901 -1.848817  0.235249  1.210514   \n",
+       "  25  1.210514 -0.476281 -1.816677 -2.584184  0.671943 -1.486245 -1.251921   \n",
+       "  26 -1.251921  1.513415 -2.518059  0.197278  2.970736 -2.169113 -3.691956   \n",
+       "  27 -3.691956  1.488689 -1.357890  2.354118  2.373551 -0.169923 -2.061642   \n",
+       "  28 -2.061642 -0.761768 -1.039491  3.761669  0.075456  1.240698 -0.164424   \n",
+       "  29 -0.164424 -0.963620 -0.143660  4.180956  0.775145  0.221612  2.078956   \n",
+       "  30  2.078956 -1.606119  1.594503 -0.093073 -1.280650 -0.838107  2.173016   \n",
+       "  31  2.173016 -1.776196  3.002580 -1.585050 -1.326680 -0.984627  1.617967   \n",
+       "  32  1.617967 -0.069657  1.003372 -1.464292 -2.537261 -0.300181  0.351987   \n",
+       "  33  0.351987  2.310903 -0.803151 -0.439890 -0.799398 -0.397638 -0.962931   \n",
+       "  34 -0.962931  2.196184 -2.703686  1.405508 -1.534419  0.627291 -1.169513   \n",
+       "  35 -1.169513  0.700846 -2.085808  2.749838  1.472912 -0.555535 -0.517220   \n",
+       "  36 -0.517220 -2.098504  0.173063  2.248060  2.280103 -1.517237  1.622213   \n",
+       "  37  1.622213 -4.252582  1.209729  0.775217  0.564671 -2.573873  1.451846   \n",
+       "  38  1.451846 -1.779297  2.200273 -1.917085 -0.375297  0.090014  1.515698   \n",
+       "  39  1.515698  1.988354  2.501336  0.006340 -3.795914  2.961847 -0.831004   \n",
+       "  40 -0.831004  4.924174 -0.075625  1.190934 -3.448300  3.072060 -0.448419   \n",
+       "  41 -0.448419  3.513246 -3.660039  1.334119  0.183009  1.564466 -0.735075   \n",
+       "  42 -0.735075  1.054362 -2.615633  0.878387  2.471791 -2.244138  0.443930   \n",
+       "  43  0.443930 -2.310438  0.493542 -1.130766  3.097810 -3.220894  0.291975   \n",
+       "  44  0.291975 -4.201588  3.258515 -0.617337  2.196061 -2.174451  0.524926   \n",
+       "  45  0.524926 -1.910970  3.413091 -2.178605  0.024091  0.137740 -0.465506   \n",
+       "  46 -0.465506  1.373613  0.793212 -0.396716 -1.738105  1.625695 -1.134138   \n",
+       "  47 -1.134138  4.307870 -3.151712  1.453002 -2.032503  2.234171 -2.045541   \n",
+       "  48 -2.045541  3.556081 -5.500059  1.047938 -1.433129  1.503650 -1.272189   \n",
+       "  49 -1.272189 -0.831744 -1.520325  2.114841  0.168384 -0.634652  2.110553   \n",
+       "  50  2.110553 -4.853836  3.801293 -0.854057  0.872098 -0.203789  4.253020   \n",
+       "  51  4.253020 -3.369076  4.932908 -2.196828  1.051284 -1.043276  3.478043   \n",
+       "  52  3.478043 -0.085829  4.191190 -3.232815 -0.202653 -1.794674  1.186498   \n",
+       "  53  1.186498  2.045900  1.504774  1.038618 -1.267746 -1.544647  0.135967   \n",
+       "  54  0.135967  2.342222 -1.903823  2.168939 -0.116845  0.141361 -2.728233   \n",
+       "  55 -2.728233  0.236471 -1.792883  4.001782  0.630038  1.301725 -2.951259   \n",
+       "  56 -2.951259 -1.257151 -1.328745  2.116946  1.084168  1.284163 -2.105207   \n",
+       "  57 -2.105207 -2.833330  1.256223 -0.187060  0.736395 -1.193363 -1.789597   \n",
+       "  58 -1.789597 -2.496292  1.247981 -2.222462  0.060721 -2.485366 -0.948538   \n",
+       "  59 -0.948538 -1.333909 -0.974388 -2.908412 -1.009430 -2.473623 -0.276321   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.228898  0.809295    2.914220    1.251183   -0.446121  \n",
+       "  3   2.032020 -0.757841    2.481291    1.061665   -0.720897  \n",
+       "  4  -0.480671 -2.112934    1.436692    1.113866   -0.533631  \n",
+       "  5   0.431634 -2.353882   -0.283165   -1.663704    0.083051  \n",
+       "  6  -2.404765 -1.785370   -1.517594   -2.263802    1.187547  \n",
+       "  7  -1.701558 -0.908770   -3.246183   -2.732020    1.278594  \n",
+       "  8   1.135113  0.846938   -3.811131   -1.962079    0.090256  \n",
+       "  9   2.752873  2.230618   -1.688955    1.110582   -2.051597  \n",
+       "  10  2.487168  2.505903    0.719245    1.105423   -1.998565  \n",
+       "  11  1.137694  0.352369    3.074586    1.561490   -1.981527  \n",
+       "  12 -0.545080  0.170560    3.980628    0.196529    0.182747  \n",
+       "  13 -2.005421 -0.381956    1.957991   -1.323987    2.041334  \n",
+       "  14 -1.551038  0.865690    0.650338   -3.438464    2.322486  \n",
+       "  15 -0.756231 -0.704060   -2.226902   -3.062890    0.987046  \n",
+       "  16 -1.104541  0.120287   -4.500092   -0.118761   -0.222539  \n",
+       "  17  0.483095 -1.320007   -4.111491    0.813397   -0.922173  \n",
+       "  18  0.336268 -0.648774    0.239329    1.991543   -0.924966  \n",
+       "  19  1.951121  1.443834    5.190550    1.705568   -2.466884  \n",
+       "  20  1.375362  3.554259    4.597036    0.344731   -0.557874  \n",
+       "  21 -0.674163  2.002393    2.354066   -1.139776    0.771171  \n",
+       "  22 -1.959510  0.565586   -0.698477   -3.540839    0.465691  \n",
+       "  23 -2.368123 -0.254322   -2.247901   -1.848817    0.235249  \n",
+       "  24 -0.476281 -1.816677   -2.584184    0.671943   -1.486245  \n",
+       "  25  1.513415 -2.518059    0.197278    2.970736   -2.169113  \n",
+       "  26  1.488689 -1.357890    2.354118    2.373551   -0.169923  \n",
+       "  27 -0.761768 -1.039491    3.761669    0.075456    1.240698  \n",
+       "  28 -0.963620 -0.143660    4.180956    0.775145    0.221612  \n",
+       "  29 -1.606119  1.594503   -0.093073   -1.280650   -0.838107  \n",
+       "  30 -1.776196  3.002580   -1.585050   -1.326680   -0.984627  \n",
+       "  31 -0.069657  1.003372   -1.464292   -2.537261   -0.300181  \n",
+       "  32  2.310903 -0.803151   -0.439890   -0.799398   -0.397638  \n",
+       "  33  2.196184 -2.703686    1.405508   -1.534419    0.627291  \n",
+       "  34  0.700846 -2.085808    2.749838    1.472912   -0.555535  \n",
+       "  35 -2.098504  0.173063    2.248060    2.280103   -1.517237  \n",
+       "  36 -4.252582  1.209729    0.775217    0.564671   -2.573873  \n",
+       "  37 -1.779297  2.200273   -1.917085   -0.375297    0.090014  \n",
+       "  38  1.988354  2.501336    0.006340   -3.795914    2.961847  \n",
+       "  39  4.924174 -0.075625    1.190934   -3.448300    3.072060  \n",
+       "  40  3.513246 -3.660039    1.334119    0.183009    1.564466  \n",
+       "  41  1.054362 -2.615633    0.878387    2.471791   -2.244138  \n",
+       "  42 -2.310438  0.493542   -1.130766    3.097810   -3.220894  \n",
+       "  43 -4.201588  3.258515   -0.617337    2.196061   -2.174451  \n",
+       "  44 -1.910970  3.413091   -2.178605    0.024091    0.137740  \n",
+       "  45  1.373613  0.793212   -0.396716   -1.738105    1.625695  \n",
+       "  46  4.307870 -3.151712    1.453002   -2.032503    2.234171  \n",
+       "  47  3.556081 -5.500059    1.047938   -1.433129    1.503650  \n",
+       "  48 -0.831744 -1.520325    2.114841    0.168384   -0.634652  \n",
+       "  49 -4.853836  3.801293   -0.854057    0.872098   -0.203789  \n",
+       "  50 -3.369076  4.932908   -2.196828    1.051284   -1.043276  \n",
+       "  51 -0.085829  4.191190   -3.232815   -0.202653   -1.794674  \n",
+       "  52  2.045900  1.504774    1.038618   -1.267746   -1.544647  \n",
+       "  53  2.342222 -1.903823    2.168939   -0.116845    0.141361  \n",
+       "  54  0.236471 -1.792883    4.001782    0.630038    1.301725  \n",
+       "  55 -1.257151 -1.328745    2.116946    1.084168    1.284163  \n",
+       "  56 -2.833330  1.256223   -0.187060    0.736395   -1.193363  \n",
+       "  57 -2.496292  1.247981   -2.222462    0.060721   -2.485366  \n",
+       "  58 -1.333909 -0.974388   -2.908412   -1.009430   -2.473623  \n",
+       "  59  1.175908 -0.046573   -0.701116   -2.762168   -0.184531  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -0.136976   \n",
+       "  3  -0.136976  0.169535 -0.167234  1.820554  1.243867  0.483561 -2.791354   \n",
+       "  4  -2.791354  0.510436 -0.312877  1.192658  0.984949 -2.332386 -2.874428   \n",
+       "  5  -2.874428  2.167704 -1.563790 -0.200315 -0.933489 -1.063442 -3.334640   \n",
+       "  6  -3.334640  2.037827 -3.000256 -1.346699 -2.474281 -0.035192 -0.026759   \n",
+       "  7  -0.026759  0.789896 -1.245784 -2.958124 -2.967843  2.323630  2.367162   \n",
+       "  8   2.367162 -0.907434  0.312766 -0.402987 -0.469602 -0.138266  4.445028   \n",
+       "  9   4.445028 -1.820006  3.492131 -1.252073  2.155221 -0.746289  2.479106   \n",
+       "  10  2.479106 -2.026215  2.838512  1.762089  2.399370 -0.340089 -1.369667   \n",
+       "  11 -1.369667 -1.357677 -1.213046  1.563106  1.507531  0.580107 -2.064100   \n",
+       "  12 -2.064100  1.771866 -2.606669  0.450228 -2.397419  1.196333 -2.159874   \n",
+       "  13 -2.159874  2.506719 -3.336156  0.621837 -2.934824 -0.253424 -0.774652   \n",
+       "  14 -0.774652  1.525554 -1.458013  0.941694 -1.579011 -1.493030  2.236525   \n",
+       "  15  2.236525  0.517298  0.250545 -0.905767  1.849315 -1.426801  3.309127   \n",
+       "  16  3.309127 -1.415682  0.621018  0.107009  3.822939 -0.330407  1.585050   \n",
+       "  17  1.585050 -0.011243 -1.559915 -0.011949  3.620777  1.173570 -2.532073   \n",
+       "  18 -2.532073 -0.174861 -2.674552 -0.277392 -1.095771  1.806712 -2.451805   \n",
+       "  19 -2.451805  0.900539 -2.918828  1.847249 -3.032000  2.473510 -2.625352   \n",
+       "  20 -2.625352  0.075977  0.933779  2.913903 -4.336392  0.994904 -1.642030   \n",
+       "  21 -1.642030 -2.644082  1.816727  2.094737 -3.457106 -1.533139  2.131071   \n",
+       "  22  2.131071 -2.221054  3.561492  1.205971 -0.569255 -1.547320  4.562305   \n",
+       "  23  4.562305  1.149597  1.955219 -1.105265  1.961821 -1.553824  2.945799   \n",
+       "  24  2.945799  3.077599  0.740475 -2.212612  3.602185 -0.845427 -0.284106   \n",
+       "  25 -0.284106  3.043777 -1.507068  0.065724  1.787608  0.594827 -0.669199   \n",
+       "  26 -0.669199  2.569452 -2.230038  1.980950 -0.170681  1.181455 -0.588685   \n",
+       "  27 -0.588685  0.703083 -0.251208  2.227583 -1.517610 -2.458289 -0.442671   \n",
+       "  28 -0.442671 -1.630201  0.133017  1.550302 -0.844372 -2.372612  1.432679   \n",
+       "  29  1.432679 -2.033587  1.114533  0.654841  1.241295 -2.890783  2.301631   \n",
+       "  30  2.301631 -1.751470 -0.253533 -0.591388  1.523619 -1.482465  0.730189   \n",
+       "  31  0.730189  1.431999 -0.920938 -2.941508  1.236018  2.329418 -1.229187   \n",
+       "  32 -1.229187  1.274976 -0.759853 -2.995458  1.122720  2.636417 -0.997234   \n",
+       "  33 -0.997234  1.213212 -0.071331 -2.010444  0.898060  1.343742  0.048191   \n",
+       "  34  0.048191 -1.164744  0.522574  0.578546 -0.196999  1.534728  0.506296   \n",
+       "  35  0.506296 -4.514941  1.833245  3.762009 -0.341640  0.133153  2.136748   \n",
+       "  36  2.136748 -1.080238 -0.681902  2.738695 -0.897404 -1.519585  2.196679   \n",
+       "  37  2.196679  1.188594 -0.937350  0.100027 -0.576238 -1.903214  2.727297   \n",
+       "  38  2.727297  4.143169 -0.682946 -2.590976 -1.347214 -1.397702  1.627790   \n",
+       "  39  1.627790  2.781045 -0.493974 -3.366258 -0.055739 -0.136695 -1.526930   \n",
+       "  40 -1.526930  0.421500  0.405981 -1.779374 -0.211722  2.582277 -2.103959   \n",
+       "  41 -2.103959 -2.091425  0.513163  0.367312  1.533712  1.330853 -1.841643   \n",
+       "  42 -1.841643 -3.159631  2.114616  1.045207  2.039339  0.543324  0.443261   \n",
+       "  43  0.443261 -3.923499  0.636723  1.701834  1.190742 -1.022250  2.024557   \n",
+       "  44  2.024557  0.649032  1.340127  0.803442 -0.613205  0.268388 -0.103283   \n",
+       "  45 -0.103283  3.114742 -0.543707 -0.813909 -1.807418 -0.044613 -1.408039   \n",
+       "  46 -1.408039  4.744205 -2.171075 -0.850103 -1.623114 -1.732633 -0.418849   \n",
+       "  47 -0.418849  0.539332 -3.432679 -2.624554  0.546654 -2.374571 -1.456723   \n",
+       "  48 -1.456723 -0.937030  0.539128 -3.270855  1.807075 -0.004178  0.140531   \n",
+       "  49  0.140531 -3.824385  3.353668 -2.256291  2.049140  0.792891 -0.467285   \n",
+       "  50 -0.467285 -4.396166  3.259791  0.850917  1.563336  1.456098  0.413488   \n",
+       "  51  0.413488 -1.904467  2.196588  2.620744 -0.814350  0.950693  1.019815   \n",
+       "  52  1.019815  3.025832  0.733139  3.531684 -2.470152  0.318217  1.679805   \n",
+       "  53  1.679805  2.248438 -2.076623  0.767921 -3.327069  0.440793  0.143060   \n",
+       "  54  0.143060  2.399569 -1.702345 -3.447291 -1.466930 -0.183127 -2.007235   \n",
+       "  55 -2.007235  0.497393 -2.765455 -4.315283  0.058723 -0.630622 -2.410771   \n",
+       "  56 -2.410771 -0.618555 -0.900115 -1.943442  1.844041  0.835385 -0.645030   \n",
+       "  57 -0.645030 -1.229009  0.517632  2.277377  1.959033  0.110742  1.597426   \n",
+       "  58  1.597426  0.050658  0.101252  4.067144  1.276119  1.254552  2.043885   \n",
+       "  59  2.043885  0.738504  0.968405  1.666112 -0.286331 -0.935965 -0.469514   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.169535 -0.167234    1.820554    1.243867    0.483561  \n",
+       "  3   0.510436 -0.312877    1.192658    0.984949   -2.332386  \n",
+       "  4   2.167704 -1.563790   -0.200315   -0.933489   -1.063442  \n",
+       "  5   2.037827 -3.000256   -1.346699   -2.474281   -0.035192  \n",
+       "  6   0.789896 -1.245784   -2.958124   -2.967843    2.323630  \n",
+       "  7  -0.907434  0.312766   -0.402987   -0.469602   -0.138266  \n",
+       "  8  -1.820006  3.492131   -1.252073    2.155221   -0.746289  \n",
+       "  9  -2.026215  2.838512    1.762089    2.399370   -0.340089  \n",
+       "  10 -1.357677 -1.213046    1.563106    1.507531    0.580107  \n",
+       "  11  1.771866 -2.606669    0.450228   -2.397419    1.196333  \n",
+       "  12  2.506719 -3.336156    0.621837   -2.934824   -0.253424  \n",
+       "  13  1.525554 -1.458013    0.941694   -1.579011   -1.493030  \n",
+       "  14  0.517298  0.250545   -0.905767    1.849315   -1.426801  \n",
+       "  15 -1.415682  0.621018    0.107009    3.822939   -0.330407  \n",
+       "  16 -0.011243 -1.559915   -0.011949    3.620777    1.173570  \n",
+       "  17 -0.174861 -2.674552   -0.277392   -1.095771    1.806712  \n",
+       "  18  0.900539 -2.918828    1.847249   -3.032000    2.473510  \n",
+       "  19  0.075977  0.933779    2.913903   -4.336392    0.994904  \n",
+       "  20 -2.644082  1.816727    2.094737   -3.457106   -1.533139  \n",
+       "  21 -2.221054  3.561492    1.205971   -0.569255   -1.547320  \n",
+       "  22  1.149597  1.955219   -1.105265    1.961821   -1.553824  \n",
+       "  23  3.077599  0.740475   -2.212612    3.602185   -0.845427  \n",
+       "  24  3.043777 -1.507068    0.065724    1.787608    0.594827  \n",
+       "  25  2.569452 -2.230038    1.980950   -0.170681    1.181455  \n",
+       "  26  0.703083 -0.251208    2.227583   -1.517610   -2.458289  \n",
+       "  27 -1.630201  0.133017    1.550302   -0.844372   -2.372612  \n",
+       "  28 -2.033587  1.114533    0.654841    1.241295   -2.890783  \n",
+       "  29 -1.751470 -0.253533   -0.591388    1.523619   -1.482465  \n",
+       "  30  1.431999 -0.920938   -2.941508    1.236018    2.329418  \n",
+       "  31  1.274976 -0.759853   -2.995458    1.122720    2.636417  \n",
+       "  32  1.213212 -0.071331   -2.010444    0.898060    1.343742  \n",
+       "  33 -1.164744  0.522574    0.578546   -0.196999    1.534728  \n",
+       "  34 -4.514941  1.833245    3.762009   -0.341640    0.133153  \n",
+       "  35 -1.080238 -0.681902    2.738695   -0.897404   -1.519585  \n",
+       "  36  1.188594 -0.937350    0.100027   -0.576238   -1.903214  \n",
+       "  37  4.143169 -0.682946   -2.590976   -1.347214   -1.397702  \n",
+       "  38  2.781045 -0.493974   -3.366258   -0.055739   -0.136695  \n",
+       "  39  0.421500  0.405981   -1.779374   -0.211722    2.582277  \n",
+       "  40 -2.091425  0.513163    0.367312    1.533712    1.330853  \n",
+       "  41 -3.159631  2.114616    1.045207    2.039339    0.543324  \n",
+       "  42 -3.923499  0.636723    1.701834    1.190742   -1.022250  \n",
+       "  43  0.649032  1.340127    0.803442   -0.613205    0.268388  \n",
+       "  44  3.114742 -0.543707   -0.813909   -1.807418   -0.044613  \n",
+       "  45  4.744205 -2.171075   -0.850103   -1.623114   -1.732633  \n",
+       "  46  0.539332 -3.432679   -2.624554    0.546654   -2.374571  \n",
+       "  47 -0.937030  0.539128   -3.270855    1.807075   -0.004178  \n",
+       "  48 -3.824385  3.353668   -2.256291    2.049140    0.792891  \n",
+       "  49 -4.396166  3.259791    0.850917    1.563336    1.456098  \n",
+       "  50 -1.904467  2.196588    2.620744   -0.814350    0.950693  \n",
+       "  51  3.025832  0.733139    3.531684   -2.470152    0.318217  \n",
+       "  52  2.248438 -2.076623    0.767921   -3.327069    0.440793  \n",
+       "  53  2.399569 -1.702345   -3.447291   -1.466930   -0.183127  \n",
+       "  54  0.497393 -2.765455   -4.315283    0.058723   -0.630622  \n",
+       "  55 -0.618555 -0.900115   -1.943442    1.844041    0.835385  \n",
+       "  56 -1.229009  0.517632    2.277377    1.959033    0.110742  \n",
+       "  57  0.050658  0.101252    4.067144    1.276119    1.254552  \n",
+       "  58  0.738504  0.968405    1.666112   -0.286331   -0.935965  \n",
+       "  59  0.103457 -0.802459   -2.725664   -1.994039    0.407783  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.895841   \n",
+       "  3   0.895841  0.508701 -0.893944  0.355988  0.628985  0.236117 -0.360323   \n",
+       "  4  -0.360323  0.127981 -1.263108 -1.077391 -0.750686 -1.076984  0.740892   \n",
+       "  5   0.740892 -0.738062 -0.104229 -1.944208 -3.537495 -1.091518 -0.736378   \n",
+       "  6  -0.736378 -0.243751  1.893374 -2.150719 -3.562060  0.259886 -1.387877   \n",
+       "  7  -1.387877 -0.405179  0.404415 -2.222590 -1.198933  0.266637 -0.536830   \n",
+       "  8  -0.536830 -0.006396  0.854866 -0.806788  1.960796  1.246698 -1.137163   \n",
+       "  9  -1.137163  0.927161  0.456963 -0.579748  0.841613  1.326939 -0.454393   \n",
+       "  10 -0.454393  1.849599 -0.769404 -0.420741  0.176354  1.452577  0.501748   \n",
+       "  11  0.501748  1.274157 -1.143936  1.508543 -0.922262  0.197210  2.374510   \n",
+       "  12  2.374510 -0.615998 -1.914260  2.155526 -0.264526  0.840377  3.256293   \n",
+       "  13  3.256293 -1.814476  0.502293  0.927124  1.450840 -0.402807  2.338238   \n",
+       "  14  2.338238 -2.841411  1.824410  1.413577 -0.701954  1.121792  0.194049   \n",
+       "  15  0.194049 -2.132490  1.082684  1.557233  0.807041 -1.414795 -2.725659   \n",
+       "  16 -2.725659 -0.453253 -1.669782  0.588088 -0.283590 -1.380294 -1.431663   \n",
+       "  17 -1.431663  2.273236 -1.284572 -0.646138  0.944577 -0.357522 -0.861380   \n",
+       "  18 -0.861380  3.759362 -2.194158 -2.471559 -0.401709  0.471806 -0.657506   \n",
+       "  19 -0.657506  1.877004 -2.230400 -1.044678 -0.074214 -0.362863  0.157130   \n",
+       "  20  0.157130  0.276619 -0.303760  1.220672 -0.065399  0.174058 -0.737300   \n",
+       "  21 -0.737300 -0.746679  0.315782  3.746944  1.472605  0.855112 -1.393870   \n",
+       "  22 -1.393870 -1.228319  1.625162  2.007528  0.564494  1.388150 -2.241409   \n",
+       "  23 -2.241409 -0.572897 -0.029086 -0.451118 -2.954668 -0.388366 -0.081915   \n",
+       "  24 -0.081915 -0.796172 -2.005429 -3.148151 -1.998100 -0.656000  0.513823   \n",
+       "  25  0.513823 -0.435109 -2.307173 -3.072056 -0.947881 -0.868710  2.153878   \n",
+       "  26  2.153878 -1.079462  0.447172 -0.714506 -0.266717 -0.416152  1.046552   \n",
+       "  27  1.046552  1.096921  2.068994  1.104010  2.136101  0.914198 -0.473614   \n",
+       "  28 -0.473614  2.207755  2.500973  2.302944  2.957255  1.187356 -0.664989   \n",
+       "  29 -0.664989  1.285954  3.130623  2.165401  3.184077  0.469497 -1.289526   \n",
+       "  30 -1.289526  0.362876  0.553690 -1.961598  0.790970  1.015679  0.590794   \n",
+       "  31  0.590794 -2.255570 -2.534010 -4.188143 -2.506270  0.951098  1.227505   \n",
+       "  32  1.227505 -1.593698 -3.075393 -2.643829 -4.226707 -1.277455  0.249739   \n",
+       "  33  0.249739 -0.548759  0.078493 -1.263646 -2.898904 -1.736998 -0.084245   \n",
+       "  34 -0.084245  0.620133  0.623671  0.591161  0.390427 -2.945627 -2.223556   \n",
+       "  35 -2.223556  1.310231  1.064197  2.943777  2.999562 -0.237244 -1.424389   \n",
+       "  36 -1.424389  1.190637 -0.076852  3.220444  3.575221  1.431932 -0.417076   \n",
+       "  37 -0.417076  0.228281 -0.276202  0.376402  4.328132  2.893848  3.164514   \n",
+       "  38  3.164514 -0.859328 -0.456566 -3.594740  0.198735  0.983158  2.343577   \n",
+       "  39  2.343577 -0.951350  1.585643 -4.164832 -2.288563  0.277251  2.597913   \n",
+       "  40  2.597913 -1.395871  1.080715 -4.526313 -4.248303 -1.624725 -0.179397   \n",
+       "  41 -0.179397 -0.185294 -0.526255  0.104716 -3.684406 -2.173040 -0.715679   \n",
+       "  42 -0.715679 -0.314139 -2.264514  3.304640 -1.284019 -2.404289 -0.484608   \n",
+       "  43 -0.484608  0.650403 -2.987171  5.356563  0.843409  0.168977  1.380031   \n",
+       "  44  1.380031  0.393947 -0.956007  3.690160  2.965167  1.778012 -0.213344   \n",
+       "  45 -0.213344  0.328462  0.641448  0.161533  3.188270  3.278157 -0.645677   \n",
+       "  46 -0.645677 -0.938095  2.696492 -3.163444  2.393935  1.846714 -1.819813   \n",
+       "  47 -1.819813  1.069063  2.640593 -4.059076 -0.934045 -0.555106 -0.060650   \n",
+       "  48 -0.060650  2.832344  0.419341 -1.762832 -2.011250 -2.730722  1.574337   \n",
+       "  49  1.574337  0.296034 -2.449723  1.427821 -2.617912 -0.891377  1.648484   \n",
+       "  50  1.648484 -2.577897 -4.456872  5.383484 -1.122133 -0.291147  0.470128   \n",
+       "  51  0.470128 -2.092748  0.054405  4.194663  0.431307  1.054826  0.418704   \n",
+       "  52  0.418704 -0.104815 -0.155819  1.869624  1.715551  1.828606  0.212312   \n",
+       "  53  0.212312  2.136892  0.565776 -2.449772  0.455328  0.465133 -2.493116   \n",
+       "  54 -2.493116  1.482777  1.831065 -3.415001 -1.384483 -1.134266 -2.932764   \n",
+       "  55 -2.932764  0.646100  2.946157 -1.666874 -0.775951 -2.164853 -2.901539   \n",
+       "  56 -2.901539 -0.606953  0.832042  2.166167  0.534006  0.644717 -0.491919   \n",
+       "  57 -0.491919 -0.622643 -1.842031  2.978643  0.110604  0.488744  0.293133   \n",
+       "  58  0.293133  1.290826 -2.043039  0.396222  0.000410  0.589532  0.647176   \n",
+       "  59  0.647176  0.610055 -0.074264 -2.500920 -0.465789  0.556178  1.917445   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.508701 -0.893944    0.355988    0.628985    0.236117  \n",
+       "  3   0.127981 -1.263108   -1.077391   -0.750686   -1.076984  \n",
+       "  4  -0.738062 -0.104229   -1.944208   -3.537495   -1.091518  \n",
+       "  5  -0.243751  1.893374   -2.150719   -3.562060    0.259886  \n",
+       "  6  -0.405179  0.404415   -2.222590   -1.198933    0.266637  \n",
+       "  7  -0.006396  0.854866   -0.806788    1.960796    1.246698  \n",
+       "  8   0.927161  0.456963   -0.579748    0.841613    1.326939  \n",
+       "  9   1.849599 -0.769404   -0.420741    0.176354    1.452577  \n",
+       "  10  1.274157 -1.143936    1.508543   -0.922262    0.197210  \n",
+       "  11 -0.615998 -1.914260    2.155526   -0.264526    0.840377  \n",
+       "  12 -1.814476  0.502293    0.927124    1.450840   -0.402807  \n",
+       "  13 -2.841411  1.824410    1.413577   -0.701954    1.121792  \n",
+       "  14 -2.132490  1.082684    1.557233    0.807041   -1.414795  \n",
+       "  15 -0.453253 -1.669782    0.588088   -0.283590   -1.380294  \n",
+       "  16  2.273236 -1.284572   -0.646138    0.944577   -0.357522  \n",
+       "  17  3.759362 -2.194158   -2.471559   -0.401709    0.471806  \n",
+       "  18  1.877004 -2.230400   -1.044678   -0.074214   -0.362863  \n",
+       "  19  0.276619 -0.303760    1.220672   -0.065399    0.174058  \n",
+       "  20 -0.746679  0.315782    3.746944    1.472605    0.855112  \n",
+       "  21 -1.228319  1.625162    2.007528    0.564494    1.388150  \n",
+       "  22 -0.572897 -0.029086   -0.451118   -2.954668   -0.388366  \n",
+       "  23 -0.796172 -2.005429   -3.148151   -1.998100   -0.656000  \n",
+       "  24 -0.435109 -2.307173   -3.072056   -0.947881   -0.868710  \n",
+       "  25 -1.079462  0.447172   -0.714506   -0.266717   -0.416152  \n",
+       "  26  1.096921  2.068994    1.104010    2.136101    0.914198  \n",
+       "  27  2.207755  2.500973    2.302944    2.957255    1.187356  \n",
+       "  28  1.285954  3.130623    2.165401    3.184077    0.469497  \n",
+       "  29  0.362876  0.553690   -1.961598    0.790970    1.015679  \n",
+       "  30 -2.255570 -2.534010   -4.188143   -2.506270    0.951098  \n",
+       "  31 -1.593698 -3.075393   -2.643829   -4.226707   -1.277455  \n",
+       "  32 -0.548759  0.078493   -1.263646   -2.898904   -1.736998  \n",
+       "  33  0.620133  0.623671    0.591161    0.390427   -2.945627  \n",
+       "  34  1.310231  1.064197    2.943777    2.999562   -0.237244  \n",
+       "  35  1.190637 -0.076852    3.220444    3.575221    1.431932  \n",
+       "  36  0.228281 -0.276202    0.376402    4.328132    2.893848  \n",
+       "  37 -0.859328 -0.456566   -3.594740    0.198735    0.983158  \n",
+       "  38 -0.951350  1.585643   -4.164832   -2.288563    0.277251  \n",
+       "  39 -1.395871  1.080715   -4.526313   -4.248303   -1.624725  \n",
+       "  40 -0.185294 -0.526255    0.104716   -3.684406   -2.173040  \n",
+       "  41 -0.314139 -2.264514    3.304640   -1.284019   -2.404289  \n",
+       "  42  0.650403 -2.987171    5.356563    0.843409    0.168977  \n",
+       "  43  0.393947 -0.956007    3.690160    2.965167    1.778012  \n",
+       "  44  0.328462  0.641448    0.161533    3.188270    3.278157  \n",
+       "  45 -0.938095  2.696492   -3.163444    2.393935    1.846714  \n",
+       "  46  1.069063  2.640593   -4.059076   -0.934045   -0.555106  \n",
+       "  47  2.832344  0.419341   -1.762832   -2.011250   -2.730722  \n",
+       "  48  0.296034 -2.449723    1.427821   -2.617912   -0.891377  \n",
+       "  49 -2.577897 -4.456872    5.383484   -1.122133   -0.291147  \n",
+       "  50 -2.092748  0.054405    4.194663    0.431307    1.054826  \n",
+       "  51 -0.104815 -0.155819    1.869624    1.715551    1.828606  \n",
+       "  52  2.136892  0.565776   -2.449772    0.455328    0.465133  \n",
+       "  53  1.482777  1.831065   -3.415001   -1.384483   -1.134266  \n",
+       "  54  0.646100  2.946157   -1.666874   -0.775951   -2.164853  \n",
+       "  55 -0.606953  0.832042    2.166167    0.534006    0.644717  \n",
+       "  56 -0.622643 -1.842031    2.978643    0.110604    0.488744  \n",
+       "  57  1.290826 -2.043039    0.396222    0.000410    0.589532  \n",
+       "  58  0.610055 -0.074264   -2.500920   -0.465789    0.556178  \n",
+       "  59  0.424083  1.814160   -2.762027   -0.682391    0.843818  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.335460   \n",
+       "  3   0.335460  0.655162  0.670093  0.389612  0.004659  0.598505 -0.208547   \n",
+       "  4  -0.208547 -0.890658 -1.612670  0.376960 -1.802568 -1.252062  0.404304   \n",
+       "  5   0.404304 -2.675789 -2.718366 -0.170598 -2.470702 -2.858259  2.055651   \n",
+       "  6   2.055651 -1.815587 -0.604856 -2.417181 -1.743743 -2.999192 -0.220935   \n",
+       "  7  -0.220935  0.267567  0.943556 -2.867000  0.010486 -2.238655 -0.511906   \n",
+       "  8  -0.511906  1.017433  3.256458 -2.488174  3.396665  0.846595 -0.041042   \n",
+       "  9  -0.041042  1.203074  1.291150 -1.251536  2.262240  2.521921 -0.941694   \n",
+       "  10 -0.941694 -1.213438 -0.061213  1.615200  0.676420  0.633186 -0.233857   \n",
+       "  11 -0.233857 -0.921131 -1.102887  2.549480 -2.514193 -0.780633  0.165066   \n",
+       "  12  0.165066 -2.438291 -0.844134  0.963100 -2.825777 -1.822103  1.129537   \n",
+       "  13  1.129537 -0.162070 -0.516229 -0.670428 -1.043052 -1.052848  2.161762   \n",
+       "  14  2.161762  0.918260  1.352535 -2.323096 -0.399578 -1.378945  1.442923   \n",
+       "  15  1.442923  1.629839  2.225494 -2.270462  1.129031 -1.417942  0.347769   \n",
+       "  16  0.347769  3.413448 -0.191074 -1.808550  1.973937  1.106743 -0.574102   \n",
+       "  17 -0.574102  1.638654 -1.320441 -0.147742  1.135646  2.739340 -1.299385   \n",
+       "  18 -1.299385 -0.613843 -0.411610  0.850235 -0.301220  4.015155 -1.523066   \n",
+       "  19 -1.523066 -2.574435  1.211386  0.413553 -2.113989  1.660017 -1.892813   \n",
+       "  20 -1.892813 -2.804607  0.059938 -0.257098 -0.758289 -2.467536 -1.089078   \n",
+       "  21 -1.089078  0.590464 -2.427556 -1.448122  0.390327 -2.953615  1.226063   \n",
+       "  22  1.226063  3.764462 -2.637002 -0.503448  1.361878 -3.021622  3.509015   \n",
+       "  23  3.509015  3.751618 -1.730019  0.087818  1.276690 -0.093709  2.818303   \n",
+       "  24  2.818303  0.158158 -0.199380 -0.143180  0.120962  1.805356  0.229331   \n",
+       "  25  0.229331 -0.591048  2.670172 -0.357351 -0.826568  1.387230 -2.464145   \n",
+       "  26 -2.464145 -0.044925  2.747674 -0.253695  0.723745  0.114984 -3.345175   \n",
+       "  27 -3.345175 -1.764404  0.158404 -0.544685  0.220944 -1.443938 -1.145725   \n",
+       "  28 -1.145725  0.088009 -2.731045  0.561418  0.067424 -2.603352  1.310971   \n",
+       "  29  1.310971  1.156000 -1.794040  1.691130 -1.591638 -1.407345  2.223143   \n",
+       "  30  2.223143  4.824818  0.878699  1.189443 -1.754989  3.061639  1.414679   \n",
+       "  31  1.414679  2.640800  1.674868  2.068266 -0.563996  3.398923  0.989823   \n",
+       "  32  0.989823 -0.039458  2.260515  2.326047  0.600151  2.172148 -0.735382   \n",
+       "  33 -0.735382 -3.096089  1.261165  0.509975  1.248398 -1.525461 -0.047531   \n",
+       "  34 -0.047531 -3.231603  1.657593 -1.922735  2.184441 -3.716679 -0.359053   \n",
+       "  35 -0.359053 -2.610354 -0.679358 -2.046545 -0.165774 -2.917921 -0.949985   \n",
+       "  36 -0.949985  0.392372 -1.520801 -0.479727 -0.365007 -1.873181 -2.092549   \n",
+       "  37 -2.092549  3.029674 -2.883829  2.580641  0.382171  1.777564 -1.337893   \n",
+       "  38 -1.337893  5.118429 -1.277671  3.423585 -0.475706  2.364838  0.296578   \n",
+       "  39  0.296578  2.266558  0.847617  2.624259 -0.462602  1.482921  0.303848   \n",
+       "  40  0.303848 -1.410757  1.350369  0.283178 -0.807884 -0.596860 -0.931483   \n",
+       "  41 -0.931483 -2.713135  2.216366 -3.137491 -0.852208 -1.838674 -0.975211   \n",
+       "  42 -0.975211 -2.498506 -1.500245 -2.589947  0.724829 -0.411845  0.843411   \n",
+       "  43  0.843411 -0.786873 -1.134872 -2.289547  2.097922  1.835627  1.920358   \n",
+       "  44  1.920358 -0.877096 -1.809103  0.142405  2.038431  3.066529  2.251817   \n",
+       "  45  2.251817  0.864103  0.089954  1.141480 -0.633200 -1.301880  2.806659   \n",
+       "  46  2.806659  0.322746  2.999028  2.384193 -0.728005 -1.152484 -0.432737   \n",
+       "  47 -0.432737 -0.680141  2.065455  0.683194 -0.755575 -0.809104 -0.194410   \n",
+       "  48 -0.194410  1.242534  0.293164  0.075415  1.146329  0.296959 -1.482473   \n",
+       "  49 -1.482473 -0.421868  0.086281 -0.017071  3.256341  0.994896 -0.863906   \n",
+       "  50 -0.863906 -0.472445 -0.532720 -1.093271  1.861063  0.001726 -0.168904   \n",
+       "  51 -0.168904  1.414452 -1.856463  0.263074  0.115330 -1.489293 -0.780541   \n",
+       "  52 -0.780541  0.299929 -1.697547  1.454566 -1.896505 -2.053233  0.876243   \n",
+       "  53  0.876243  0.572516 -0.725803  0.673569 -1.648956 -0.737723  0.602638   \n",
+       "  54  0.602638  1.342478 -1.167023  0.039504 -0.912043  1.047737 -0.007609   \n",
+       "  55 -0.007609 -0.650921  0.299647 -1.460090  2.442997  1.049209 -0.679776   \n",
+       "  56 -0.679776 -0.733743  1.708542 -0.874956  2.631051  0.003174 -1.012600   \n",
+       "  57 -1.012600  0.201594  2.098921 -0.063446  2.086554  0.236624 -0.726567   \n",
+       "  58 -0.726567  1.752496  1.826904  0.304219 -0.637870  1.188979 -0.851441   \n",
+       "  59 -0.851441  2.443209  0.404109  0.265671 -0.864321  0.198650 -0.713908   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.655162  0.670093    0.389612    0.004659    0.598505  \n",
+       "  3  -0.890658 -1.612670    0.376960   -1.802568   -1.252062  \n",
+       "  4  -2.675789 -2.718366   -0.170598   -2.470702   -2.858259  \n",
+       "  5  -1.815587 -0.604856   -2.417181   -1.743743   -2.999192  \n",
+       "  6   0.267567  0.943556   -2.867000    0.010486   -2.238655  \n",
+       "  7   1.017433  3.256458   -2.488174    3.396665    0.846595  \n",
+       "  8   1.203074  1.291150   -1.251536    2.262240    2.521921  \n",
+       "  9  -1.213438 -0.061213    1.615200    0.676420    0.633186  \n",
+       "  10 -0.921131 -1.102887    2.549480   -2.514193   -0.780633  \n",
+       "  11 -2.438291 -0.844134    0.963100   -2.825777   -1.822103  \n",
+       "  12 -0.162070 -0.516229   -0.670428   -1.043052   -1.052848  \n",
+       "  13  0.918260  1.352535   -2.323096   -0.399578   -1.378945  \n",
+       "  14  1.629839  2.225494   -2.270462    1.129031   -1.417942  \n",
+       "  15  3.413448 -0.191074   -1.808550    1.973937    1.106743  \n",
+       "  16  1.638654 -1.320441   -0.147742    1.135646    2.739340  \n",
+       "  17 -0.613843 -0.411610    0.850235   -0.301220    4.015155  \n",
+       "  18 -2.574435  1.211386    0.413553   -2.113989    1.660017  \n",
+       "  19 -2.804607  0.059938   -0.257098   -0.758289   -2.467536  \n",
+       "  20  0.590464 -2.427556   -1.448122    0.390327   -2.953615  \n",
+       "  21  3.764462 -2.637002   -0.503448    1.361878   -3.021622  \n",
+       "  22  3.751618 -1.730019    0.087818    1.276690   -0.093709  \n",
+       "  23  0.158158 -0.199380   -0.143180    0.120962    1.805356  \n",
+       "  24 -0.591048  2.670172   -0.357351   -0.826568    1.387230  \n",
+       "  25 -0.044925  2.747674   -0.253695    0.723745    0.114984  \n",
+       "  26 -1.764404  0.158404   -0.544685    0.220944   -1.443938  \n",
+       "  27  0.088009 -2.731045    0.561418    0.067424   -2.603352  \n",
+       "  28  1.156000 -1.794040    1.691130   -1.591638   -1.407345  \n",
+       "  29  4.824818  0.878699    1.189443   -1.754989    3.061639  \n",
+       "  30  2.640800  1.674868    2.068266   -0.563996    3.398923  \n",
+       "  31 -0.039458  2.260515    2.326047    0.600151    2.172148  \n",
+       "  32 -3.096089  1.261165    0.509975    1.248398   -1.525461  \n",
+       "  33 -3.231603  1.657593   -1.922735    2.184441   -3.716679  \n",
+       "  34 -2.610354 -0.679358   -2.046545   -0.165774   -2.917921  \n",
+       "  35  0.392372 -1.520801   -0.479727   -0.365007   -1.873181  \n",
+       "  36  3.029674 -2.883829    2.580641    0.382171    1.777564  \n",
+       "  37  5.118429 -1.277671    3.423585   -0.475706    2.364838  \n",
+       "  38  2.266558  0.847617    2.624259   -0.462602    1.482921  \n",
+       "  39 -1.410757  1.350369    0.283178   -0.807884   -0.596860  \n",
+       "  40 -2.713135  2.216366   -3.137491   -0.852208   -1.838674  \n",
+       "  41 -2.498506 -1.500245   -2.589947    0.724829   -0.411845  \n",
+       "  42 -0.786873 -1.134872   -2.289547    2.097922    1.835627  \n",
+       "  43 -0.877096 -1.809103    0.142405    2.038431    3.066529  \n",
+       "  44  0.864103  0.089954    1.141480   -0.633200   -1.301880  \n",
+       "  45  0.322746  2.999028    2.384193   -0.728005   -1.152484  \n",
+       "  46 -0.680141  2.065455    0.683194   -0.755575   -0.809104  \n",
+       "  47  1.242534  0.293164    0.075415    1.146329    0.296959  \n",
+       "  48 -0.421868  0.086281   -0.017071    3.256341    0.994896  \n",
+       "  49 -0.472445 -0.532720   -1.093271    1.861063    0.001726  \n",
+       "  50  1.414452 -1.856463    0.263074    0.115330   -1.489293  \n",
+       "  51  0.299929 -1.697547    1.454566   -1.896505   -2.053233  \n",
+       "  52  0.572516 -0.725803    0.673569   -1.648956   -0.737723  \n",
+       "  53  1.342478 -1.167023    0.039504   -0.912043    1.047737  \n",
+       "  54 -0.650921  0.299647   -1.460090    2.442997    1.049209  \n",
+       "  55 -0.733743  1.708542   -0.874956    2.631051    0.003174  \n",
+       "  56  0.201594  2.098921   -0.063446    2.086554    0.236624  \n",
+       "  57  1.752496  1.826904    0.304219   -0.637870    1.188979  \n",
+       "  58  2.443209  0.404109    0.265671   -0.864321    0.198650  \n",
+       "  59  0.320904 -0.782775   -0.722663    0.071847    1.164273  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.282104   \n",
+       "  3   0.282104  2.527072  0.053751 -0.747270  1.024441 -0.308084 -0.176100   \n",
+       "  4  -0.176100  2.774437 -1.417617 -2.388603  0.792882 -0.005661 -0.362647   \n",
+       "  5  -0.362647  1.514889 -0.693398 -1.809003  0.833227 -0.568688  0.957764   \n",
+       "  6   0.957764 -1.160846 -0.058331 -1.922642  0.743373 -0.265602  1.338473   \n",
+       "  7   1.338473 -1.967087 -0.120655 -0.104962 -1.718009  1.391402  0.553285   \n",
+       "  8   0.553285 -0.104141  1.145635  2.358642 -3.899148  0.792603 -0.678316   \n",
+       "  9  -0.678316 -1.062196  0.286197  1.387253 -2.968791 -0.655180 -1.023560   \n",
+       "  10 -1.023560  0.070290 -0.601704  0.081933 -0.296993 -2.802071 -1.052147   \n",
+       "  11 -1.052147 -0.865385 -0.627210 -2.013738  2.784223 -2.851043 -1.110459   \n",
+       "  12 -1.110459  0.741748  0.383432  0.422551  2.655531 -0.533976 -0.090489   \n",
+       "  13 -0.090489  0.182364  2.693943  1.580954  1.182287  1.611254  2.120551   \n",
+       "  14  2.120551  2.273338  2.467618 -0.254572 -0.270416  1.709722  1.738960   \n",
+       "  15  1.738960  2.080701 -0.742729 -0.059489 -1.225876 -0.117220  0.570438   \n",
+       "  16  0.570438  1.984019 -2.306678 -1.286392 -1.737922 -2.791504 -0.802916   \n",
+       "  17 -0.802916 -0.347147 -2.086733  0.064133  0.415610 -3.966435 -1.155271   \n",
+       "  18 -1.155271 -0.859487 -0.447376  1.367782  2.113830 -2.161248 -2.299598   \n",
+       "  19 -2.299598 -2.780202  1.881964  1.186347  1.757235 -0.837007 -1.141388   \n",
+       "  20 -1.141388 -1.640727  2.919352 -0.231114  0.607976 -0.260294  0.161895   \n",
+       "  21  0.161895 -0.311408  1.090522 -1.996058 -1.495137 -1.211999  0.977533   \n",
+       "  22  0.977533  2.682223 -0.486868 -1.591319 -0.717460  2.030335  2.276005   \n",
+       "  23  2.276005  3.180912 -0.825177  1.745693 -0.582786  0.580919  0.976614   \n",
+       "  24  0.976614  1.026754 -1.835023  2.948012  0.355221  1.070721 -0.170970   \n",
+       "  25 -0.170970 -2.650657 -0.600131  2.631935  1.283404  0.859911 -2.301919   \n",
+       "  26 -2.301919 -2.591763  0.666658 -0.815957  0.709718  0.575041 -2.162117   \n",
+       "  27 -2.162117 -3.144118  1.978704 -3.179458 -0.327112  0.444054 -0.142863   \n",
+       "  28 -0.142863  1.171749  1.832748 -3.959632 -0.593044 -0.562229 -0.210030   \n",
+       "  29 -0.210030  1.768602  0.620396 -2.747506 -0.207836 -2.844866 -0.323817   \n",
+       "  30 -0.323817  1.252998 -0.126409  0.725120  2.096069 -2.800235  0.692522   \n",
+       "  31  0.692522 -0.287751 -1.876668  1.104504  1.738656 -0.780270  0.314512   \n",
+       "  32  0.314512 -0.609485 -0.810917  0.433018  4.643991  1.886823  0.423391   \n",
+       "  33  0.423391  0.220317 -1.634879  1.863596  2.541357  2.402389 -1.433340   \n",
+       "  34 -1.433340 -0.748816  0.990298 -1.533559 -0.220269 -0.329485 -1.363885   \n",
+       "  35 -1.363885  1.172366  2.919815 -0.785801 -2.879285 -2.947995 -1.939667   \n",
+       "  36 -1.939667  1.017393  2.695288 -0.313108 -1.961810 -2.480942 -1.090117   \n",
+       "  37 -1.090117 -0.704449  1.214843  0.658240 -2.082969 -0.578416  0.511365   \n",
+       "  38  0.511365 -0.276308 -1.183597  1.427139  1.186688 -0.193197  1.800518   \n",
+       "  39  1.800518 -0.464079 -1.075941 -0.035424  0.404930  0.267656  0.724119   \n",
+       "  40  0.724119 -1.230749 -0.105793 -3.371898  2.586482  1.765092  0.751606   \n",
+       "  41  0.751606  0.538642  2.489840 -2.608553  0.442343 -0.941855 -0.847326   \n",
+       "  42 -0.847326  0.775761  3.760244 -2.112103 -1.680635 -1.249386 -1.853155   \n",
+       "  43 -1.853155 -0.452540  1.794177  1.151963 -1.876895 -1.170304 -0.654036   \n",
+       "  44 -0.654036 -2.492525  0.051561  2.105576 -0.170984  0.702284  1.573789   \n",
+       "  45  1.573789 -3.448222 -2.746071  2.795223  0.622504  2.152162  2.814233   \n",
+       "  46  2.814233 -2.027479 -0.839718  0.892700  0.181053  1.795559  0.497675   \n",
+       "  47  0.497675  2.972686 -0.102682 -1.786268 -0.167836  0.476839 -1.778522   \n",
+       "  48 -1.778522  3.261193  0.502008 -1.381174 -1.162240 -1.859938 -3.313097   \n",
+       "  49 -3.313097  2.755658  0.977600 -1.362209 -1.465292 -2.815439 -2.521233   \n",
+       "  50 -2.521233  0.815185  1.297312  0.366652 -1.496349 -1.424725  0.797144   \n",
+       "  51  0.797144 -2.310906  1.183123  2.838157  1.074323  0.850057  4.129593   \n",
+       "  52  4.129593 -2.578172 -0.798237  1.281898  1.179945  2.874887  4.110154   \n",
+       "  53  4.110154 -0.945592 -1.762863  0.315564  1.005154  2.319699 -0.012547   \n",
+       "  54 -0.012547  1.840674 -2.510027 -2.585997  1.054641  0.266067 -3.277374   \n",
+       "  55 -3.277374  3.807379 -1.546171 -1.848162 -2.399580 -1.670707 -3.762632   \n",
+       "  56 -3.762632  1.141575  0.033080 -0.707013 -2.612053 -1.311284 -0.794816   \n",
+       "  57 -0.794816 -0.789798  0.591530  1.716511 -1.229454 -1.466167  2.457440   \n",
+       "  58  2.457440 -4.099479  0.565011 -0.243943  0.213565 -0.062243  2.390794   \n",
+       "  59  2.390794 -2.137371  0.586170 -0.721870  1.484510  0.544669 -0.243095   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   2.527072  0.053751   -0.747270    1.024441   -0.308084  \n",
+       "  3   2.774437 -1.417617   -2.388603    0.792882   -0.005661  \n",
+       "  4   1.514889 -0.693398   -1.809003    0.833227   -0.568688  \n",
+       "  5  -1.160846 -0.058331   -1.922642    0.743373   -0.265602  \n",
+       "  6  -1.967087 -0.120655   -0.104962   -1.718009    1.391402  \n",
+       "  7  -0.104141  1.145635    2.358642   -3.899148    0.792603  \n",
+       "  8  -1.062196  0.286197    1.387253   -2.968791   -0.655180  \n",
+       "  9   0.070290 -0.601704    0.081933   -0.296993   -2.802071  \n",
+       "  10 -0.865385 -0.627210   -2.013738    2.784223   -2.851043  \n",
+       "  11  0.741748  0.383432    0.422551    2.655531   -0.533976  \n",
+       "  12  0.182364  2.693943    1.580954    1.182287    1.611254  \n",
+       "  13  2.273338  2.467618   -0.254572   -0.270416    1.709722  \n",
+       "  14  2.080701 -0.742729   -0.059489   -1.225876   -0.117220  \n",
+       "  15  1.984019 -2.306678   -1.286392   -1.737922   -2.791504  \n",
+       "  16 -0.347147 -2.086733    0.064133    0.415610   -3.966435  \n",
+       "  17 -0.859487 -0.447376    1.367782    2.113830   -2.161248  \n",
+       "  18 -2.780202  1.881964    1.186347    1.757235   -0.837007  \n",
+       "  19 -1.640727  2.919352   -0.231114    0.607976   -0.260294  \n",
+       "  20 -0.311408  1.090522   -1.996058   -1.495137   -1.211999  \n",
+       "  21  2.682223 -0.486868   -1.591319   -0.717460    2.030335  \n",
+       "  22  3.180912 -0.825177    1.745693   -0.582786    0.580919  \n",
+       "  23  1.026754 -1.835023    2.948012    0.355221    1.070721  \n",
+       "  24 -2.650657 -0.600131    2.631935    1.283404    0.859911  \n",
+       "  25 -2.591763  0.666658   -0.815957    0.709718    0.575041  \n",
+       "  26 -3.144118  1.978704   -3.179458   -0.327112    0.444054  \n",
+       "  27  1.171749  1.832748   -3.959632   -0.593044   -0.562229  \n",
+       "  28  1.768602  0.620396   -2.747506   -0.207836   -2.844866  \n",
+       "  29  1.252998 -0.126409    0.725120    2.096069   -2.800235  \n",
+       "  30 -0.287751 -1.876668    1.104504    1.738656   -0.780270  \n",
+       "  31 -0.609485 -0.810917    0.433018    4.643991    1.886823  \n",
+       "  32  0.220317 -1.634879    1.863596    2.541357    2.402389  \n",
+       "  33 -0.748816  0.990298   -1.533559   -0.220269   -0.329485  \n",
+       "  34  1.172366  2.919815   -0.785801   -2.879285   -2.947995  \n",
+       "  35  1.017393  2.695288   -0.313108   -1.961810   -2.480942  \n",
+       "  36 -0.704449  1.214843    0.658240   -2.082969   -0.578416  \n",
+       "  37 -0.276308 -1.183597    1.427139    1.186688   -0.193197  \n",
+       "  38 -0.464079 -1.075941   -0.035424    0.404930    0.267656  \n",
+       "  39 -1.230749 -0.105793   -3.371898    2.586482    1.765092  \n",
+       "  40  0.538642  2.489840   -2.608553    0.442343   -0.941855  \n",
+       "  41  0.775761  3.760244   -2.112103   -1.680635   -1.249386  \n",
+       "  42 -0.452540  1.794177    1.151963   -1.876895   -1.170304  \n",
+       "  43 -2.492525  0.051561    2.105576   -0.170984    0.702284  \n",
+       "  44 -3.448222 -2.746071    2.795223    0.622504    2.152162  \n",
+       "  45 -2.027479 -0.839718    0.892700    0.181053    1.795559  \n",
+       "  46  2.972686 -0.102682   -1.786268   -0.167836    0.476839  \n",
+       "  47  3.261193  0.502008   -1.381174   -1.162240   -1.859938  \n",
+       "  48  2.755658  0.977600   -1.362209   -1.465292   -2.815439  \n",
+       "  49  0.815185  1.297312    0.366652   -1.496349   -1.424725  \n",
+       "  50 -2.310906  1.183123    2.838157    1.074323    0.850057  \n",
+       "  51 -2.578172 -0.798237    1.281898    1.179945    2.874887  \n",
+       "  52 -0.945592 -1.762863    0.315564    1.005154    2.319699  \n",
+       "  53  1.840674 -2.510027   -2.585997    1.054641    0.266067  \n",
+       "  54  3.807379 -1.546171   -1.848162   -2.399580   -1.670707  \n",
+       "  55  1.141575  0.033080   -0.707013   -2.612053   -1.311284  \n",
+       "  56 -0.789798  0.591530    1.716511   -1.229454   -1.466167  \n",
+       "  57 -4.099479  0.565011   -0.243943    0.213565   -0.062243  \n",
+       "  58 -2.137371  0.586170   -0.721870    1.484510    0.544669  \n",
+       "  59  1.506121  1.096045   -0.004722    0.324182    0.155714  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.378455   \n",
+       "  3   0.378455  0.776508  0.213522  0.275094  1.475377  0.364476  1.037866   \n",
+       "  4   1.037866 -0.072874  0.488741 -0.794264  0.693952 -1.109638 -0.965873   \n",
+       "  5  -0.965873 -2.954792  0.371759 -1.957637  0.901472 -1.204365 -1.844634   \n",
+       "  6  -1.844634 -2.488432  1.690841 -0.243125 -1.092026  0.240313 -2.420104   \n",
+       "  7  -2.420104 -1.823961  0.966756  0.550093 -1.716824  0.581879 -1.266796   \n",
+       "  8  -1.266796  0.542935 -1.202578  1.115746 -1.474920 -0.627377  1.273326   \n",
+       "  9   1.273326  1.736443 -2.683670  1.966648  0.660967  0.084064  2.703130   \n",
+       "  10  2.703130  1.607021 -2.067175  1.442297  1.255416 -0.262734  2.699483   \n",
+       "  11  2.699483  1.206374 -1.524551  0.061082  1.457719  0.398994  0.734178   \n",
+       "  12  0.734178  0.372624  2.155501 -2.774415  0.342608  0.741186 -0.028405   \n",
+       "  13 -0.028405 -1.013060  3.048330 -3.696410  0.891614  1.021334 -0.016214   \n",
+       "  14 -0.016214 -2.116188  2.431874 -3.511950 -0.058272  2.089617 -0.857499   \n",
+       "  15 -0.857499 -0.421967 -0.511038 -0.416645 -1.421972 -0.284781 -1.012070   \n",
+       "  16 -1.012070  0.299183 -2.804121  0.968201 -1.901654 -1.682502 -1.840285   \n",
+       "  17 -1.840285  2.051892 -4.406471  1.993474 -0.859435 -0.984918 -1.482107   \n",
+       "  18 -1.482107 -0.161555 -1.859687  2.192961  2.585930  0.154996  1.197861   \n",
+       "  19  1.197861 -1.038923  2.178356  0.757758  2.840570  0.034330  1.306196   \n",
+       "  20  1.306196 -2.008332  5.598330 -2.480298  3.903125 -0.034025  1.673864   \n",
+       "  21  1.673864 -0.711806  2.279509 -1.051688  2.268906 -0.269051 -0.768399   \n",
+       "  22 -0.768399  0.335862  0.218177 -1.729386 -1.476073  1.057878 -1.109299   \n",
+       "  23 -1.109299  0.505126 -3.938745  0.855583 -3.922319  1.394151 -0.120216   \n",
+       "  24 -0.120216  0.532879 -3.389386 -1.201590 -2.260341  1.027111  0.453352   \n",
+       "  25  0.453352 -1.293620 -2.974333  0.096551 -0.500409 -1.091079  1.564753   \n",
+       "  26  1.564753  0.357606  1.406405 -1.479762  2.720080 -2.516855  1.145274   \n",
+       "  27  1.145274 -0.399598  3.543833 -0.046988  4.402862 -2.636111 -0.236416   \n",
+       "  28 -0.236416  0.401114  2.493810  0.924911  2.612138 -2.568294 -0.028772   \n",
+       "  29 -0.028772 -0.522318  1.479028  0.429463 -1.462608  0.102740  0.128842   \n",
+       "  30  0.128842  0.969300 -1.379167 -0.817582 -2.252670  1.766374  0.541339   \n",
+       "  31  0.541339 -0.092317 -3.490624  0.406936 -3.297469  3.239574  2.059623   \n",
+       "  32  2.059623 -0.690176 -2.662388  0.630048 -2.928993  1.593206  1.584778   \n",
+       "  33  1.584778 -1.630560  0.176908  0.164934 -0.246025 -0.263072  2.476793   \n",
+       "  34  2.476793 -3.004510  1.684908  0.447151 -0.248457 -3.231017  1.328193   \n",
+       "  35  1.328193 -1.595857  1.046456 -0.695596  0.959798 -2.318286 -1.187795   \n",
+       "  36 -1.187795  2.197959  0.840433  1.421704  0.900844 -0.951817 -2.525590   \n",
+       "  37 -2.525590  3.532254  0.149741  1.940425 -0.914243  1.192757 -2.088411   \n",
+       "  38 -2.088411  2.099292 -0.246678 -2.310950 -1.085594  1.387556  0.073715   \n",
+       "  39  0.073715 -0.883000  0.790003 -1.485170  0.065575  0.022207  3.326604   \n",
+       "  40  3.326604 -1.155933  1.410834  0.324600 -0.018344 -0.383010  3.079776   \n",
+       "  41  3.079776  0.043708  0.894049  1.262497  1.969248 -0.398393 -0.239154   \n",
+       "  42 -0.239154 -0.245836 -0.108141  1.143202  1.458055 -2.135497 -1.502325   \n",
+       "  43 -1.502325 -0.014972 -1.282017 -0.501202 -0.567298 -1.908627 -1.442037   \n",
+       "  44 -1.442037 -1.824234 -0.994224 -0.139724 -0.584988 -1.849846 -0.918801   \n",
+       "  45 -0.918801 -0.352990  0.565151 -0.759315 -0.243491 -0.699568 -0.017823   \n",
+       "  46 -0.017823 -0.765662  1.447845 -1.732452 -2.261699  1.256630  0.785466   \n",
+       "  47  0.785466  0.092144 -0.019249 -1.136951 -1.945732  0.838662  2.405748   \n",
+       "  48  2.405748 -1.051869 -1.590047  0.241121 -0.563075  0.867396  0.235173   \n",
+       "  49  0.235173 -0.351813 -0.694345  3.179260  0.478047 -0.965181 -0.777403   \n",
+       "  50 -0.777403  0.776612 -2.138001  2.634922  0.345560 -2.681070 -1.653753   \n",
+       "  51 -1.653753  0.482743  0.074324  0.797883  1.048900 -0.937570 -3.966789   \n",
+       "  52 -3.966789 -0.172360 -0.105806 -0.972196 -1.254406 -0.310352 -1.183711   \n",
+       "  53 -1.183711 -0.118997  0.467985 -2.885004 -2.417977  1.693067  2.225806   \n",
+       "  54  2.225806 -0.221202  0.034003 -0.238432 -2.236071  1.778877  3.335497   \n",
+       "  55  3.335497  0.501093 -0.922847  0.389756 -0.105427  0.079287  2.053333   \n",
+       "  56  2.053333 -0.558446 -1.483744  1.704437  2.502420 -0.398955  0.506482   \n",
+       "  57  0.506482  1.151281 -1.125418  1.350853  4.376453 -1.124249 -2.172355   \n",
+       "  58 -2.172355  0.715366  0.465498 -0.993527  2.482670 -0.020335 -1.218193   \n",
+       "  59 -1.218193  1.641138  0.160555 -2.059767 -2.222499  0.254544 -1.844121   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.776508  0.213522    0.275094    1.475377    0.364476  \n",
+       "  3  -0.072874  0.488741   -0.794264    0.693952   -1.109638  \n",
+       "  4  -2.954792  0.371759   -1.957637    0.901472   -1.204365  \n",
+       "  5  -2.488432  1.690841   -0.243125   -1.092026    0.240313  \n",
+       "  6  -1.823961  0.966756    0.550093   -1.716824    0.581879  \n",
+       "  7   0.542935 -1.202578    1.115746   -1.474920   -0.627377  \n",
+       "  8   1.736443 -2.683670    1.966648    0.660967    0.084064  \n",
+       "  9   1.607021 -2.067175    1.442297    1.255416   -0.262734  \n",
+       "  10  1.206374 -1.524551    0.061082    1.457719    0.398994  \n",
+       "  11  0.372624  2.155501   -2.774415    0.342608    0.741186  \n",
+       "  12 -1.013060  3.048330   -3.696410    0.891614    1.021334  \n",
+       "  13 -2.116188  2.431874   -3.511950   -0.058272    2.089617  \n",
+       "  14 -0.421967 -0.511038   -0.416645   -1.421972   -0.284781  \n",
+       "  15  0.299183 -2.804121    0.968201   -1.901654   -1.682502  \n",
+       "  16  2.051892 -4.406471    1.993474   -0.859435   -0.984918  \n",
+       "  17 -0.161555 -1.859687    2.192961    2.585930    0.154996  \n",
+       "  18 -1.038923  2.178356    0.757758    2.840570    0.034330  \n",
+       "  19 -2.008332  5.598330   -2.480298    3.903125   -0.034025  \n",
+       "  20 -0.711806  2.279509   -1.051688    2.268906   -0.269051  \n",
+       "  21  0.335862  0.218177   -1.729386   -1.476073    1.057878  \n",
+       "  22  0.505126 -3.938745    0.855583   -3.922319    1.394151  \n",
+       "  23  0.532879 -3.389386   -1.201590   -2.260341    1.027111  \n",
+       "  24 -1.293620 -2.974333    0.096551   -0.500409   -1.091079  \n",
+       "  25  0.357606  1.406405   -1.479762    2.720080   -2.516855  \n",
+       "  26 -0.399598  3.543833   -0.046988    4.402862   -2.636111  \n",
+       "  27  0.401114  2.493810    0.924911    2.612138   -2.568294  \n",
+       "  28 -0.522318  1.479028    0.429463   -1.462608    0.102740  \n",
+       "  29  0.969300 -1.379167   -0.817582   -2.252670    1.766374  \n",
+       "  30 -0.092317 -3.490624    0.406936   -3.297469    3.239574  \n",
+       "  31 -0.690176 -2.662388    0.630048   -2.928993    1.593206  \n",
+       "  32 -1.630560  0.176908    0.164934   -0.246025   -0.263072  \n",
+       "  33 -3.004510  1.684908    0.447151   -0.248457   -3.231017  \n",
+       "  34 -1.595857  1.046456   -0.695596    0.959798   -2.318286  \n",
+       "  35  2.197959  0.840433    1.421704    0.900844   -0.951817  \n",
+       "  36  3.532254  0.149741    1.940425   -0.914243    1.192757  \n",
+       "  37  2.099292 -0.246678   -2.310950   -1.085594    1.387556  \n",
+       "  38 -0.883000  0.790003   -1.485170    0.065575    0.022207  \n",
+       "  39 -1.155933  1.410834    0.324600   -0.018344   -0.383010  \n",
+       "  40  0.043708  0.894049    1.262497    1.969248   -0.398393  \n",
+       "  41 -0.245836 -0.108141    1.143202    1.458055   -2.135497  \n",
+       "  42 -0.014972 -1.282017   -0.501202   -0.567298   -1.908627  \n",
+       "  43 -1.824234 -0.994224   -0.139724   -0.584988   -1.849846  \n",
+       "  44 -0.352990  0.565151   -0.759315   -0.243491   -0.699568  \n",
+       "  45 -0.765662  1.447845   -1.732452   -2.261699    1.256630  \n",
+       "  46  0.092144 -0.019249   -1.136951   -1.945732    0.838662  \n",
+       "  47 -1.051869 -1.590047    0.241121   -0.563075    0.867396  \n",
+       "  48 -0.351813 -0.694345    3.179260    0.478047   -0.965181  \n",
+       "  49  0.776612 -2.138001    2.634922    0.345560   -2.681070  \n",
+       "  50  0.482743  0.074324    0.797883    1.048900   -0.937570  \n",
+       "  51 -0.172360 -0.105806   -0.972196   -1.254406   -0.310352  \n",
+       "  52 -0.118997  0.467985   -2.885004   -2.417977    1.693067  \n",
+       "  53 -0.221202  0.034003   -0.238432   -2.236071    1.778877  \n",
+       "  54  0.501093 -0.922847    0.389756   -0.105427    0.079287  \n",
+       "  55 -0.558446 -1.483744    1.704437    2.502420   -0.398955  \n",
+       "  56  1.151281 -1.125418    1.350853    4.376453   -1.124249  \n",
+       "  57  0.715366  0.465498   -0.993527    2.482670   -0.020335  \n",
+       "  58  1.641138  0.160555   -2.059767   -2.222499    0.254544  \n",
+       "  59  1.404062  0.133012   -2.177573   -4.991557    2.725737  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.914351   \n",
+       "  3   0.914351  0.279692  0.786687 -0.420632  1.119058 -0.940237 -0.386352   \n",
+       "  4  -0.386352  0.592250  0.753954 -1.399072  1.303383 -1.003872 -2.233661   \n",
+       "  5  -2.233661 -0.206589 -1.863412 -1.084334  0.823669 -2.318723 -2.308382   \n",
+       "  6  -2.308382  0.362146 -4.188005  0.218386 -0.160193 -0.493740  0.005241   \n",
+       "  7   0.005241  1.179544 -0.899674 -0.478227 -1.697157 -0.586380  0.245932   \n",
+       "  8   0.245932  0.604156  1.544335 -0.893085 -1.054102  0.482247  0.882581   \n",
+       "  9   0.882581 -0.948512  1.925015 -0.876863 -0.649525 -0.543929  0.931100   \n",
+       "  10  0.931100 -0.435892  0.917200 -0.322423  0.846942 -0.614335 -0.103525   \n",
+       "  11 -0.103525  0.310080 -0.559660 -0.722863  0.870797 -0.421355 -2.437414   \n",
+       "  12 -2.437414  1.666332 -1.952640  0.144167  1.454393  0.620418 -2.799790   \n",
+       "  13 -2.799790  1.712183 -2.017011 -0.462776  0.922048  1.422826 -1.823646   \n",
+       "  14 -1.823646 -1.619299 -0.402705 -0.864877  0.626590  0.573559 -0.634449   \n",
+       "  15 -0.634449 -1.964751  3.215743  0.652286 -0.698703  0.983745  1.724776   \n",
+       "  16  1.724776 -1.043173  3.303242  1.892438 -0.392165  1.959949  3.048332   \n",
+       "  17  3.048332  1.366690  1.806685  0.537361 -0.663663  0.365948  2.728174   \n",
+       "  18  2.728174  3.917896  0.204939 -0.237478 -1.612678 -2.617322  0.588017   \n",
+       "  19  0.588017  2.971521 -1.937362 -1.110111 -0.648242 -5.234922 -2.944768   \n",
+       "  20 -2.944768 -0.878132 -2.592058  1.355370  1.897755 -4.076812 -4.330964   \n",
+       "  21 -4.330964 -1.182677 -1.001999  0.525892  2.325570  0.297279 -2.539485   \n",
+       "  22 -2.539485 -3.252722  1.846660 -1.172722  2.942914  3.624056  0.321653   \n",
+       "  23  0.321653  1.174717  4.379161 -0.345409  2.458086  3.818184  2.588637   \n",
+       "  24  2.588637  2.247795  2.714474 -1.126631 -0.407101  1.266261  3.756483   \n",
+       "  25  3.756483  2.015922 -1.988133  0.070230 -2.895631 -1.260718  2.401574   \n",
+       "  26  2.401574  0.040155 -5.371255  0.999040 -3.743910 -1.328824  1.105973   \n",
+       "  27  1.105973 -4.352793 -6.262370  1.545516 -2.682200 -0.891996 -1.443727   \n",
+       "  28 -1.443727 -5.271961 -2.538321  0.670198 -1.158738 -0.052345 -2.503177   \n",
+       "  29 -2.503177 -3.784723  3.662490  1.211886  2.395341  1.363250 -0.576489   \n",
+       "  30 -0.576489  1.439743  4.610926 -0.211768  0.886343 -0.044033  2.447427   \n",
+       "  31  2.447427  5.850003  3.521308 -2.137057  1.868113  1.550056  2.456059   \n",
+       "  32  2.456059  6.333669 -0.115289 -0.850551  1.202907 -0.006278  1.239744   \n",
+       "  33  1.239744  1.065255 -1.281616  0.093622  1.386926  0.537589 -0.938457   \n",
+       "  34 -0.938457 -5.105597 -2.855645 -0.233438  0.211221 -3.202369 -1.299310   \n",
+       "  35 -1.299310 -6.522691 -4.217502 -0.189525 -1.782493 -3.713565 -0.810934   \n",
+       "  36 -0.810934 -3.385014 -1.535661 -0.473167 -0.709294 -2.407378  0.212972   \n",
+       "  37  0.212972  0.561707 -0.087964  1.648577 -0.337090  0.243640  2.096035   \n",
+       "  38  2.096035  2.443421  3.617485  1.804028  2.529868  3.232696  1.247451   \n",
+       "  39  1.247451  3.248722  4.320485  0.669525  2.204730  3.062716  0.233335   \n",
+       "  40  0.233335 -0.857444  2.990080 -2.292345  0.819584 -1.267134 -0.697278   \n",
+       "  41 -0.697278 -2.459495 -1.869073 -2.895470 -1.621816 -3.870099 -0.555277   \n",
+       "  42 -0.555277 -2.920027 -3.720368 -1.069367 -2.554158 -2.992091 -0.261636   \n",
+       "  43 -0.261636 -1.094934 -3.667740  0.219746 -1.479152 -3.511843 -0.085339   \n",
+       "  44 -0.085339  0.093415 -0.251302  2.640145 -0.103501 -1.054451  0.653216   \n",
+       "  45  0.653216 -1.334311  0.512502  3.176904  0.943866  1.600837  1.156405   \n",
+       "  46  1.156405 -1.726206  2.455302  2.152744  0.655889  1.479804 -0.577448   \n",
+       "  47 -0.577448 -0.356541  3.248353 -0.589589 -0.222225  0.799858  0.110494   \n",
+       "  48  0.110494 -0.224461  1.659231 -1.448271  0.061054 -1.409323 -0.789853   \n",
+       "  49 -0.789853 -0.871551 -1.781328 -1.526381 -3.142034 -2.786962  0.083473   \n",
+       "  50  0.083473 -0.725514 -1.644055 -2.182444 -3.655033 -2.646716 -0.081662   \n",
+       "  51 -0.081662 -0.550598 -1.332974 -2.591792  0.084960  0.656416 -0.705029   \n",
+       "  52 -0.705029  1.780171  1.925241  0.538080  3.522184  2.605465  0.509917   \n",
+       "  53  0.509917  1.430839  3.934221  2.149107  5.812846  3.603049  0.599120   \n",
+       "  54  0.599120 -0.705936  4.352086  3.752831  4.417654  1.356096  0.370853   \n",
+       "  55  0.370853 -2.324843  1.381317  1.188245 -0.464690  0.786167 -1.031053   \n",
+       "  56 -1.031053 -1.689765 -1.325555 -2.195983 -4.002159  0.347821 -0.764412   \n",
+       "  57 -0.764412  0.797326 -4.319571 -3.386548 -4.247981  0.292304 -1.086714   \n",
+       "  58 -1.086714  4.776283 -2.332443 -2.489155 -2.202156 -0.356559 -0.124727   \n",
+       "  59 -0.124727  3.548468  0.525876  1.244570  1.274732 -0.416665  1.670596   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.279692  0.786687   -0.420632    1.119058   -0.940237  \n",
+       "  3   0.592250  0.753954   -1.399072    1.303383   -1.003872  \n",
+       "  4  -0.206589 -1.863412   -1.084334    0.823669   -2.318723  \n",
+       "  5   0.362146 -4.188005    0.218386   -0.160193   -0.493740  \n",
+       "  6   1.179544 -0.899674   -0.478227   -1.697157   -0.586380  \n",
+       "  7   0.604156  1.544335   -0.893085   -1.054102    0.482247  \n",
+       "  8  -0.948512  1.925015   -0.876863   -0.649525   -0.543929  \n",
+       "  9  -0.435892  0.917200   -0.322423    0.846942   -0.614335  \n",
+       "  10  0.310080 -0.559660   -0.722863    0.870797   -0.421355  \n",
+       "  11  1.666332 -1.952640    0.144167    1.454393    0.620418  \n",
+       "  12  1.712183 -2.017011   -0.462776    0.922048    1.422826  \n",
+       "  13 -1.619299 -0.402705   -0.864877    0.626590    0.573559  \n",
+       "  14 -1.964751  3.215743    0.652286   -0.698703    0.983745  \n",
+       "  15 -1.043173  3.303242    1.892438   -0.392165    1.959949  \n",
+       "  16  1.366690  1.806685    0.537361   -0.663663    0.365948  \n",
+       "  17  3.917896  0.204939   -0.237478   -1.612678   -2.617322  \n",
+       "  18  2.971521 -1.937362   -1.110111   -0.648242   -5.234922  \n",
+       "  19 -0.878132 -2.592058    1.355370    1.897755   -4.076812  \n",
+       "  20 -1.182677 -1.001999    0.525892    2.325570    0.297279  \n",
+       "  21 -3.252722  1.846660   -1.172722    2.942914    3.624056  \n",
+       "  22  1.174717  4.379161   -0.345409    2.458086    3.818184  \n",
+       "  23  2.247795  2.714474   -1.126631   -0.407101    1.266261  \n",
+       "  24  2.015922 -1.988133    0.070230   -2.895631   -1.260718  \n",
+       "  25  0.040155 -5.371255    0.999040   -3.743910   -1.328824  \n",
+       "  26 -4.352793 -6.262370    1.545516   -2.682200   -0.891996  \n",
+       "  27 -5.271961 -2.538321    0.670198   -1.158738   -0.052345  \n",
+       "  28 -3.784723  3.662490    1.211886    2.395341    1.363250  \n",
+       "  29  1.439743  4.610926   -0.211768    0.886343   -0.044033  \n",
+       "  30  5.850003  3.521308   -2.137057    1.868113    1.550056  \n",
+       "  31  6.333669 -0.115289   -0.850551    1.202907   -0.006278  \n",
+       "  32  1.065255 -1.281616    0.093622    1.386926    0.537589  \n",
+       "  33 -5.105597 -2.855645   -0.233438    0.211221   -3.202369  \n",
+       "  34 -6.522691 -4.217502   -0.189525   -1.782493   -3.713565  \n",
+       "  35 -3.385014 -1.535661   -0.473167   -0.709294   -2.407378  \n",
+       "  36  0.561707 -0.087964    1.648577   -0.337090    0.243640  \n",
+       "  37  2.443421  3.617485    1.804028    2.529868    3.232696  \n",
+       "  38  3.248722  4.320485    0.669525    2.204730    3.062716  \n",
+       "  39 -0.857444  2.990080   -2.292345    0.819584   -1.267134  \n",
+       "  40 -2.459495 -1.869073   -2.895470   -1.621816   -3.870099  \n",
+       "  41 -2.920027 -3.720368   -1.069367   -2.554158   -2.992091  \n",
+       "  42 -1.094934 -3.667740    0.219746   -1.479152   -3.511843  \n",
+       "  43  0.093415 -0.251302    2.640145   -0.103501   -1.054451  \n",
+       "  44 -1.334311  0.512502    3.176904    0.943866    1.600837  \n",
+       "  45 -1.726206  2.455302    2.152744    0.655889    1.479804  \n",
+       "  46 -0.356541  3.248353   -0.589589   -0.222225    0.799858  \n",
+       "  47 -0.224461  1.659231   -1.448271    0.061054   -1.409323  \n",
+       "  48 -0.871551 -1.781328   -1.526381   -3.142034   -2.786962  \n",
+       "  49 -0.725514 -1.644055   -2.182444   -3.655033   -2.646716  \n",
+       "  50 -0.550598 -1.332974   -2.591792    0.084960    0.656416  \n",
+       "  51  1.780171  1.925241    0.538080    3.522184    2.605465  \n",
+       "  52  1.430839  3.934221    2.149107    5.812846    3.603049  \n",
+       "  53 -0.705936  4.352086    3.752831    4.417654    1.356096  \n",
+       "  54 -2.324843  1.381317    1.188245   -0.464690    0.786167  \n",
+       "  55 -1.689765 -1.325555   -2.195983   -4.002159    0.347821  \n",
+       "  56  0.797326 -4.319571   -3.386548   -4.247981    0.292304  \n",
+       "  57  4.776283 -2.332443   -2.489155   -2.202156   -0.356559  \n",
+       "  58  3.548468  0.525876    1.244570    1.274732   -0.416665  \n",
+       "  59  0.616349  4.417277    3.862959    3.691000   -0.454728  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.868416   \n",
+       "  3   0.868416  1.321093  1.727641 -0.262541  2.105194 -1.067591 -0.155233   \n",
+       "  4  -0.155233  1.482346  0.965927 -0.916428  0.931473  0.842719 -2.393763   \n",
+       "  5  -2.393763  1.067941 -0.048495 -0.010817 -0.143972  0.418030 -2.060748   \n",
+       "  6  -2.060748  2.089087 -0.697960  0.984295 -2.345255  0.468482 -0.632625   \n",
+       "  7  -0.632625  0.227086 -2.162293  0.389671 -1.552563 -1.226870 -0.371507   \n",
+       "  8  -0.371507 -1.098497 -1.151150 -0.700145 -0.539726 -2.238267  1.168264   \n",
+       "  9   1.168264 -1.526555  1.082787 -0.778940  0.394836 -1.785657  0.786246   \n",
+       "  10  0.786246 -0.654213  1.443750 -1.073907  1.844021  0.375883 -0.751830   \n",
+       "  11 -0.751830  0.194191  0.916816  0.450944  1.414008  3.373255 -1.104196   \n",
+       "  12 -1.104196  1.197185  0.603237  0.795686 -1.470411  3.615386 -2.074345   \n",
+       "  13 -2.074345  0.958241 -1.110277  0.881413 -3.997199  2.171350 -0.832631   \n",
+       "  14 -0.832631 -0.003952 -1.256300  0.704125 -2.909593 -1.180725  2.349666   \n",
+       "  15  2.349666  0.155400 -0.018647 -0.149649  0.123290 -4.759832  3.402154   \n",
+       "  16  3.402154  0.143451 -0.127479 -2.522173  2.628852 -4.827338  3.403214   \n",
+       "  17  3.403214  0.139928 -0.528014 -0.112141  2.508572  0.521860  2.127522   \n",
+       "  18  2.127522  1.240379 -0.237082  0.163394  1.190996  3.379988 -2.012624   \n",
+       "  19 -2.012624  1.372927  0.443051  1.741814 -2.159682  2.515637 -3.295713   \n",
+       "  20 -3.295713  1.593682  1.953121 -0.091336 -4.250879 -2.018191 -2.644823   \n",
+       "  21 -2.644823 -0.462299  1.612431 -0.991727 -4.084084 -2.421688 -0.060817   \n",
+       "  22 -0.060817 -2.511828  0.094559  1.421580 -0.839424 -0.911525  2.141486   \n",
+       "  23  2.141486 -2.086096  0.325699  1.204851  0.920848  1.835353  1.503031   \n",
+       "  24  1.503031 -1.582481 -0.719193  1.597221  1.540709  2.795088 -1.843673   \n",
+       "  25 -1.843673 -0.803067  3.239874  0.429574 -0.606268  1.339409 -3.429154   \n",
+       "  26 -3.429154  1.636475  1.361791 -0.768381 -0.289290 -1.133015 -1.912875   \n",
+       "  27 -1.912875  2.102947  2.671617 -0.037192  0.951203 -1.826617 -0.883209   \n",
+       "  28 -0.883209  0.447536 -1.442157  0.736366 -0.071568 -1.045533  0.873867   \n",
+       "  29  0.873867  0.873983 -1.436802  2.761834  1.529954 -0.598560  2.771858   \n",
+       "  30  2.771858  1.904530 -0.824966  2.119248 -1.423261 -0.024394  2.899437   \n",
+       "  31  2.899437  3.012867  2.337418 -0.260336 -1.284845  0.333319  1.818066   \n",
+       "  32  1.818066  2.794222  2.519744 -2.215461 -0.818225 -0.501021 -0.553388   \n",
+       "  33 -0.553388  0.257664  3.140468 -1.129238 -0.195817  0.187708 -0.750108   \n",
+       "  34 -0.750108 -0.830098  0.616830 -0.152958  1.327891 -0.924132 -0.338196   \n",
+       "  35 -0.338196 -1.484782 -0.197615  0.957385  1.569100 -0.902378 -0.151879   \n",
+       "  36 -0.151879 -0.424161 -1.158824  2.058933  0.967919  0.409829  1.430388   \n",
+       "  37  1.430388  0.227661 -2.782146  2.144666 -1.321250  1.921307  1.213964   \n",
+       "  38  1.213964  0.494168 -1.124484  0.832788 -2.013194  1.643368  0.178952   \n",
+       "  39  0.178952  1.799705 -0.447661 -1.492533 -1.780594 -1.367405  0.072707   \n",
+       "  40  0.072707  3.427588  1.056140 -1.309706  0.823535 -1.729318  0.449724   \n",
+       "  41  0.449724  1.668969 -0.824488 -0.601704  1.378308 -1.376493 -0.404913   \n",
+       "  42 -0.404913 -0.722896 -1.644954  1.777326  0.680209 -0.604676  0.609184   \n",
+       "  43  0.609184 -3.529111 -2.169586  2.101842  0.301781  0.440588 -0.454187   \n",
+       "  44 -0.454187 -3.849659  0.114429  0.458982 -0.903334  0.040719 -0.616899   \n",
+       "  45 -0.616899 -0.283020  2.299979 -0.925746 -0.583118 -1.164491  0.235143   \n",
+       "  46  0.235143  2.025275  1.321730 -2.491641 -2.661143 -0.056811  0.347094   \n",
+       "  47  0.347094  2.433562 -0.319701 -0.395380 -1.181889  1.094302  2.178857   \n",
+       "  48  2.178857  0.019538 -2.314808  1.173450  0.430581  2.915304  2.483478   \n",
+       "  49  2.483478 -0.926507 -3.244936  3.410719 -0.230252  2.858202  1.890463   \n",
+       "  50  1.890463 -1.285173 -0.553471  1.317462 -0.179179  0.563778 -1.569718   \n",
+       "  51 -1.569718 -1.786158  0.753662 -0.572367  0.016908  0.141306 -1.352876   \n",
+       "  52 -1.352876 -1.001572  2.707536 -1.557699  2.044801 -1.879017 -0.212683   \n",
+       "  53 -0.212683 -1.478809  3.528430 -0.782040  2.231826 -2.798661  0.395327   \n",
+       "  54  0.395327 -1.220788  1.724532  0.068774  0.708304 -2.006263 -1.163963   \n",
+       "  55 -1.163963 -0.383659 -2.814762  0.462956 -2.526851  0.133583  1.275068   \n",
+       "  56  1.275068  1.649826 -3.204494  1.843917 -2.172719  1.910066  0.436557   \n",
+       "  57  0.436557  1.094148 -3.362474  1.512505 -0.090649  3.049729  0.113467   \n",
+       "  58  0.113467  0.880315 -1.479724  0.352929  2.657158  1.373467 -0.883894   \n",
+       "  59 -0.883894  0.654878  1.293089 -0.796823  3.585384  0.402906 -0.017873   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.321093  1.727641   -0.262541    2.105194   -1.067591  \n",
+       "  3   1.482346  0.965927   -0.916428    0.931473    0.842719  \n",
+       "  4   1.067941 -0.048495   -0.010817   -0.143972    0.418030  \n",
+       "  5   2.089087 -0.697960    0.984295   -2.345255    0.468482  \n",
+       "  6   0.227086 -2.162293    0.389671   -1.552563   -1.226870  \n",
+       "  7  -1.098497 -1.151150   -0.700145   -0.539726   -2.238267  \n",
+       "  8  -1.526555  1.082787   -0.778940    0.394836   -1.785657  \n",
+       "  9  -0.654213  1.443750   -1.073907    1.844021    0.375883  \n",
+       "  10  0.194191  0.916816    0.450944    1.414008    3.373255  \n",
+       "  11  1.197185  0.603237    0.795686   -1.470411    3.615386  \n",
+       "  12  0.958241 -1.110277    0.881413   -3.997199    2.171350  \n",
+       "  13 -0.003952 -1.256300    0.704125   -2.909593   -1.180725  \n",
+       "  14  0.155400 -0.018647   -0.149649    0.123290   -4.759832  \n",
+       "  15  0.143451 -0.127479   -2.522173    2.628852   -4.827338  \n",
+       "  16  0.139928 -0.528014   -0.112141    2.508572    0.521860  \n",
+       "  17  1.240379 -0.237082    0.163394    1.190996    3.379988  \n",
+       "  18  1.372927  0.443051    1.741814   -2.159682    2.515637  \n",
+       "  19  1.593682  1.953121   -0.091336   -4.250879   -2.018191  \n",
+       "  20 -0.462299  1.612431   -0.991727   -4.084084   -2.421688  \n",
+       "  21 -2.511828  0.094559    1.421580   -0.839424   -0.911525  \n",
+       "  22 -2.086096  0.325699    1.204851    0.920848    1.835353  \n",
+       "  23 -1.582481 -0.719193    1.597221    1.540709    2.795088  \n",
+       "  24 -0.803067  3.239874    0.429574   -0.606268    1.339409  \n",
+       "  25  1.636475  1.361791   -0.768381   -0.289290   -1.133015  \n",
+       "  26  2.102947  2.671617   -0.037192    0.951203   -1.826617  \n",
+       "  27  0.447536 -1.442157    0.736366   -0.071568   -1.045533  \n",
+       "  28  0.873983 -1.436802    2.761834    1.529954   -0.598560  \n",
+       "  29  1.904530 -0.824966    2.119248   -1.423261   -0.024394  \n",
+       "  30  3.012867  2.337418   -0.260336   -1.284845    0.333319  \n",
+       "  31  2.794222  2.519744   -2.215461   -0.818225   -0.501021  \n",
+       "  32  0.257664  3.140468   -1.129238   -0.195817    0.187708  \n",
+       "  33 -0.830098  0.616830   -0.152958    1.327891   -0.924132  \n",
+       "  34 -1.484782 -0.197615    0.957385    1.569100   -0.902378  \n",
+       "  35 -0.424161 -1.158824    2.058933    0.967919    0.409829  \n",
+       "  36  0.227661 -2.782146    2.144666   -1.321250    1.921307  \n",
+       "  37  0.494168 -1.124484    0.832788   -2.013194    1.643368  \n",
+       "  38  1.799705 -0.447661   -1.492533   -1.780594   -1.367405  \n",
+       "  39  3.427588  1.056140   -1.309706    0.823535   -1.729318  \n",
+       "  40  1.668969 -0.824488   -0.601704    1.378308   -1.376493  \n",
+       "  41 -0.722896 -1.644954    1.777326    0.680209   -0.604676  \n",
+       "  42 -3.529111 -2.169586    2.101842    0.301781    0.440588  \n",
+       "  43 -3.849659  0.114429    0.458982   -0.903334    0.040719  \n",
+       "  44 -0.283020  2.299979   -0.925746   -0.583118   -1.164491  \n",
+       "  45  2.025275  1.321730   -2.491641   -2.661143   -0.056811  \n",
+       "  46  2.433562 -0.319701   -0.395380   -1.181889    1.094302  \n",
+       "  47  0.019538 -2.314808    1.173450    0.430581    2.915304  \n",
+       "  48 -0.926507 -3.244936    3.410719   -0.230252    2.858202  \n",
+       "  49 -1.285173 -0.553471    1.317462   -0.179179    0.563778  \n",
+       "  50 -1.786158  0.753662   -0.572367    0.016908    0.141306  \n",
+       "  51 -1.001572  2.707536   -1.557699    2.044801   -1.879017  \n",
+       "  52 -1.478809  3.528430   -0.782040    2.231826   -2.798661  \n",
+       "  53 -1.220788  1.724532    0.068774    0.708304   -2.006263  \n",
+       "  54 -0.383659 -2.814762    0.462956   -2.526851    0.133583  \n",
+       "  55  1.649826 -3.204494    1.843917   -2.172719    1.910066  \n",
+       "  56  1.094148 -3.362474    1.512505   -0.090649    3.049729  \n",
+       "  57  0.880315 -1.479724    0.352929    2.657158    1.373467  \n",
+       "  58  0.654878  1.293089   -0.796823    3.585384    0.402906  \n",
+       "  59  0.998343  2.111248   -1.558481    2.200494   -1.872177  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.116205   \n",
+       "  3   1.116205 -0.585625 -0.651541  0.927191  0.351492  1.355950 -0.120295   \n",
+       "  4  -0.120295 -2.466730 -0.413913 -0.309549 -0.063760 -1.066544  0.727889   \n",
+       "  5   0.727889 -2.102417 -1.757160 -1.935884 -0.795233 -0.713505 -0.802338   \n",
+       "  6  -0.802338 -1.286759 -0.190359 -1.637917  0.646708 -1.108992 -2.905418   \n",
+       "  7  -2.905418  0.991350  0.396223 -1.556540 -0.439191  1.007685 -3.178178   \n",
+       "  8  -3.178178  2.263202 -0.606901  0.015538 -0.104431 -0.581372 -1.166735   \n",
+       "  9  -1.166735  1.614967  0.710702  0.048411  0.239028  1.367029  0.381899   \n",
+       "  10  0.381899  0.383630  0.007290  1.361428  1.612603  0.569687  2.260950   \n",
+       "  11  2.260950 -2.165064  1.402680 -0.100576  2.262224  0.759479  3.162103   \n",
+       "  12  3.162103 -2.818846 -0.347506  0.511667  1.192568 -0.764180  0.577693   \n",
+       "  13  0.577693 -1.993171 -1.022234  0.506723 -1.564632  0.282353 -1.151302   \n",
+       "  14 -1.151302  0.589244  1.349701 -0.207062 -3.481754  0.046102  0.282784   \n",
+       "  15  0.282784  4.369572  1.959130 -0.515390 -2.391487 -1.584574 -1.339735   \n",
+       "  16 -1.339735  2.515476  0.854793 -1.722235 -0.636202 -2.029523 -1.266215   \n",
+       "  17 -1.266215 -2.244856 -1.439863 -0.141368  2.304388 -1.103860 -0.463105   \n",
+       "  18 -0.463105 -5.625679 -3.331247 -1.614359  3.239369  0.070085 -0.424107   \n",
+       "  19 -0.424107 -4.617854 -2.463417 -0.592131  2.681225  1.347117  0.931446   \n",
+       "  20  0.931446  0.255947  0.551848  2.622595 -0.412654  1.381318  1.413759   \n",
+       "  21  1.413759  1.975776  5.160218  2.189867 -1.691719  1.245141  1.102276   \n",
+       "  22  1.102276  4.687078  5.010940  1.924222 -1.465098  0.976828  0.419959   \n",
+       "  23  0.419959  1.989310  3.684043 -0.212866 -0.948673 -1.085678 -1.330310   \n",
+       "  24 -1.330310  0.462894 -0.667066 -0.843863 -0.307654 -1.663625 -1.646142   \n",
+       "  25 -1.646142 -1.112266 -2.309587  0.153475  0.822588 -3.152228 -1.389874   \n",
+       "  26 -1.389874 -1.796384 -4.147028  0.496938  0.618613 -1.560787 -0.558672   \n",
+       "  27 -0.558672 -1.245364 -0.465178  1.449101  1.544318 -0.280403  0.460108   \n",
+       "  28  0.460108  1.652548  1.313114  2.192110 -0.390528  2.299420  0.432541   \n",
+       "  29  0.432541  1.842031  5.415393  0.547737 -2.127156  2.310064 -1.204965   \n",
+       "  30 -1.204965  1.879933  3.696211 -1.908744 -2.572626  0.705773  0.462987   \n",
+       "  31  0.462987 -1.577610  0.092693 -2.875769 -2.349430 -1.959106  1.130348   \n",
+       "  32  1.130348 -1.128772 -4.434922 -1.319775 -1.789925 -1.848460 -0.544475   \n",
+       "  33 -0.544475 -1.954904 -4.163133  1.166742  0.242686 -0.050907 -0.065379   \n",
+       "  34 -0.065379  0.290437 -2.382655  1.986740  2.102769  1.439065 -0.330474   \n",
+       "  35 -0.330474  1.592562  0.047350  2.230137  0.770844  3.615939  0.098606   \n",
+       "  36  0.098606  2.443227  3.103779 -0.961233  0.277917  2.404025 -0.570677   \n",
+       "  37 -0.570677  2.011592  3.312563 -1.555856 -2.142779  0.730975  0.142442   \n",
+       "  38  0.142442 -0.678993  0.775157 -0.628137 -0.802319 -2.433800  2.185285   \n",
+       "  39  2.185285 -1.918580 -2.508532 -0.123579 -1.059532 -5.318375  1.651606   \n",
+       "  40  1.651606 -2.134386 -4.283509  2.208554  0.777933 -2.171808  1.560538   \n",
+       "  41  1.560538 -2.016096 -2.339398  1.849733  0.044917  1.233967 -0.956519   \n",
+       "  42 -0.956519  1.163318 -1.103976  1.963738  1.093038  3.140406  0.927841   \n",
+       "  43  0.927841  3.535280  1.025741 -0.646987  0.249802  3.875335  0.500084   \n",
+       "  44  0.500084  2.345230  2.083583 -1.681355  1.090317  2.651768  0.939768   \n",
+       "  45  0.939768 -0.057454  2.450753 -1.921881 -0.765700 -2.910202 -1.126640   \n",
+       "  46 -1.126640 -1.392520  1.311628 -1.148454 -1.182070 -5.829534 -1.132419   \n",
+       "  47 -1.132419 -1.363820 -0.307806  0.121440 -0.007680 -5.180798 -0.981878   \n",
+       "  48 -0.981878 -1.159695 -1.284926  1.607384  1.285612  0.078910  0.015810   \n",
+       "  49  0.015810 -0.361758 -1.092523  1.107645  0.179051  3.510551  0.966716   \n",
+       "  50  0.966716  1.234876  0.184001  0.243490 -1.584633  4.821866  0.855238   \n",
+       "  51  0.855238  3.879302  1.046822 -1.538397 -3.747216  1.909304  1.162877   \n",
+       "  52  1.162877  2.755351  0.729327 -0.620157 -1.698644 -2.625865 -1.583648   \n",
+       "  53 -1.583648  1.637537  0.047079  0.537089 -0.125021 -5.229059 -2.138304   \n",
+       "  54 -2.138304 -2.422000 -0.349468  1.854862  1.038610 -2.052543 -1.457822   \n",
+       "  55 -1.457822 -3.725617 -1.200303  0.705486  1.353693  1.055182 -1.482015   \n",
+       "  56 -1.482015 -1.050080 -1.351674 -1.046671 -0.182755  3.953836 -1.314024   \n",
+       "  57 -1.314024  2.028062  0.452911 -0.872480 -0.535840  2.372050  0.404127   \n",
+       "  58  0.404127  2.726155  0.458115 -0.887347 -0.208348 -0.780662  1.958484   \n",
+       "  59  1.958484  1.738955  1.102767  1.475758  0.020138 -2.697545  2.364563   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.585625 -0.651541    0.927191    0.351492    1.355950  \n",
+       "  3  -2.466730 -0.413913   -0.309549   -0.063760   -1.066544  \n",
+       "  4  -2.102417 -1.757160   -1.935884   -0.795233   -0.713505  \n",
+       "  5  -1.286759 -0.190359   -1.637917    0.646708   -1.108992  \n",
+       "  6   0.991350  0.396223   -1.556540   -0.439191    1.007685  \n",
+       "  7   2.263202 -0.606901    0.015538   -0.104431   -0.581372  \n",
+       "  8   1.614967  0.710702    0.048411    0.239028    1.367029  \n",
+       "  9   0.383630  0.007290    1.361428    1.612603    0.569687  \n",
+       "  10 -2.165064  1.402680   -0.100576    2.262224    0.759479  \n",
+       "  11 -2.818846 -0.347506    0.511667    1.192568   -0.764180  \n",
+       "  12 -1.993171 -1.022234    0.506723   -1.564632    0.282353  \n",
+       "  13  0.589244  1.349701   -0.207062   -3.481754    0.046102  \n",
+       "  14  4.369572  1.959130   -0.515390   -2.391487   -1.584574  \n",
+       "  15  2.515476  0.854793   -1.722235   -0.636202   -2.029523  \n",
+       "  16 -2.244856 -1.439863   -0.141368    2.304388   -1.103860  \n",
+       "  17 -5.625679 -3.331247   -1.614359    3.239369    0.070085  \n",
+       "  18 -4.617854 -2.463417   -0.592131    2.681225    1.347117  \n",
+       "  19  0.255947  0.551848    2.622595   -0.412654    1.381318  \n",
+       "  20  1.975776  5.160218    2.189867   -1.691719    1.245141  \n",
+       "  21  4.687078  5.010940    1.924222   -1.465098    0.976828  \n",
+       "  22  1.989310  3.684043   -0.212866   -0.948673   -1.085678  \n",
+       "  23  0.462894 -0.667066   -0.843863   -0.307654   -1.663625  \n",
+       "  24 -1.112266 -2.309587    0.153475    0.822588   -3.152228  \n",
+       "  25 -1.796384 -4.147028    0.496938    0.618613   -1.560787  \n",
+       "  26 -1.245364 -0.465178    1.449101    1.544318   -0.280403  \n",
+       "  27  1.652548  1.313114    2.192110   -0.390528    2.299420  \n",
+       "  28  1.842031  5.415393    0.547737   -2.127156    2.310064  \n",
+       "  29  1.879933  3.696211   -1.908744   -2.572626    0.705773  \n",
+       "  30 -1.577610  0.092693   -2.875769   -2.349430   -1.959106  \n",
+       "  31 -1.128772 -4.434922   -1.319775   -1.789925   -1.848460  \n",
+       "  32 -1.954904 -4.163133    1.166742    0.242686   -0.050907  \n",
+       "  33  0.290437 -2.382655    1.986740    2.102769    1.439065  \n",
+       "  34  1.592562  0.047350    2.230137    0.770844    3.615939  \n",
+       "  35  2.443227  3.103779   -0.961233    0.277917    2.404025  \n",
+       "  36  2.011592  3.312563   -1.555856   -2.142779    0.730975  \n",
+       "  37 -0.678993  0.775157   -0.628137   -0.802319   -2.433800  \n",
+       "  38 -1.918580 -2.508532   -0.123579   -1.059532   -5.318375  \n",
+       "  39 -2.134386 -4.283509    2.208554    0.777933   -2.171808  \n",
+       "  40 -2.016096 -2.339398    1.849733    0.044917    1.233967  \n",
+       "  41  1.163318 -1.103976    1.963738    1.093038    3.140406  \n",
+       "  42  3.535280  1.025741   -0.646987    0.249802    3.875335  \n",
+       "  43  2.345230  2.083583   -1.681355    1.090317    2.651768  \n",
+       "  44 -0.057454  2.450753   -1.921881   -0.765700   -2.910202  \n",
+       "  45 -1.392520  1.311628   -1.148454   -1.182070   -5.829534  \n",
+       "  46 -1.363820 -0.307806    0.121440   -0.007680   -5.180798  \n",
+       "  47 -1.159695 -1.284926    1.607384    1.285612    0.078910  \n",
+       "  48 -0.361758 -1.092523    1.107645    0.179051    3.510551  \n",
+       "  49  1.234876  0.184001    0.243490   -1.584633    4.821866  \n",
+       "  50  3.879302  1.046822   -1.538397   -3.747216    1.909304  \n",
+       "  51  2.755351  0.729327   -0.620157   -1.698644   -2.625865  \n",
+       "  52  1.637537  0.047079    0.537089   -0.125021   -5.229059  \n",
+       "  53 -2.422000 -0.349468    1.854862    1.038610   -2.052543  \n",
+       "  54 -3.725617 -1.200303    0.705486    1.353693    1.055182  \n",
+       "  55 -1.050080 -1.351674   -1.046671   -0.182755    3.953836  \n",
+       "  56  2.028062  0.452911   -0.872480   -0.535840    2.372050  \n",
+       "  57  2.726155  0.458115   -0.887347   -0.208348   -0.780662  \n",
+       "  58  1.738955  1.102767    1.475758    0.020138   -2.697545  \n",
+       "  59 -0.042790  1.147040    0.660839    0.086087   -3.001265  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.887539   \n",
+       "  3   1.887539  0.828004 -1.211351  0.979353  0.234471  0.396440  0.982264   \n",
+       "  4   0.982264  0.357972 -3.223626  0.270672 -2.217138 -0.061212 -0.480594   \n",
+       "  5  -0.480594  0.837672 -3.193108 -0.666256 -2.486409 -0.356141 -0.419123   \n",
+       "  6  -0.419123  0.619616  0.076935 -0.222990 -1.329024 -0.156050 -0.262813   \n",
+       "  7  -0.262813  0.933983  1.350147 -0.163785  1.146033 -0.499985  0.015912   \n",
+       "  8   0.015912  0.105304 -0.069449  0.350606  1.026978 -0.017482  0.976538   \n",
+       "  9   0.976538 -1.376102 -0.657553 -0.358478  0.612138  0.556489 -0.245117   \n",
+       "  10 -0.245117 -1.912776 -1.398009  2.777055  0.470992 -0.835056  0.068967   \n",
+       "  11  0.068967 -2.667254 -0.623760  1.499518 -0.533611 -0.870066  1.532904   \n",
+       "  12  1.532904 -1.730776  0.258348  0.401152 -1.537462 -0.947702  1.210735   \n",
+       "  13  1.210735  1.957878  3.052908 -2.694918  0.035917  0.536005  0.086846   \n",
+       "  14  0.086846  4.192227  4.485813 -2.923895  0.533290  0.522564 -1.468997   \n",
+       "  15 -1.468997  2.904548  2.708724  0.052018  1.338634  1.293101 -2.580610   \n",
+       "  16 -2.580610  1.095849 -1.253447  2.434344  1.472001  1.369350 -2.342136   \n",
+       "  17 -2.342136 -1.460090 -3.679514  0.307312  0.544483 -2.444222 -0.914291   \n",
+       "  18 -0.914291 -2.543889 -1.692203  0.024610  0.555303 -2.872289  1.293053   \n",
+       "  19  1.293053 -3.612237  2.598470 -1.081511 -2.525992 -2.151999  2.691952   \n",
+       "  20  2.691952 -1.822356  4.789610 -1.057425 -2.492103  1.377938  1.147556   \n",
+       "  21  1.147556  0.616745  3.228515 -0.265247 -0.369796  1.112634 -1.577104   \n",
+       "  22 -1.577104  2.993611 -0.012294  0.879651  2.733481  2.501440 -3.146918   \n",
+       "  23 -3.146918  3.335085 -3.981763  1.075896  3.823840  0.160322 -0.770976   \n",
+       "  24 -0.770976  2.247185 -3.410538  0.290224  0.404196 -1.235817  2.326925   \n",
+       "  25  2.326925 -0.294935 -0.942615 -1.204198 -2.342754 -1.532772  5.450820   \n",
+       "  26  5.450820 -3.493202  0.787396 -1.003759 -3.330566  0.289869  2.403482   \n",
+       "  27  2.403482 -3.284273  1.858601 -0.458022 -1.493170  0.565517  0.883759   \n",
+       "  28  0.883759 -0.734660  0.344543  1.452443 -0.891782  1.373013 -0.084531   \n",
+       "  29 -0.084531  1.709846 -1.100961  2.373892  0.237609 -0.157046 -0.257698   \n",
+       "  30 -0.257698  2.811452 -2.459800  1.826824  1.427396 -0.432697 -0.595984   \n",
+       "  31 -0.595984  1.190729 -2.870284 -1.398411  1.584561 -2.364580 -0.211513   \n",
+       "  32 -0.211513 -1.311356 -2.285681 -1.806526  0.160432 -1.990357  0.351281   \n",
+       "  33  0.351281 -1.358347  0.594933 -1.557698 -0.275963 -0.279830 -0.408940   \n",
+       "  34 -0.408940 -0.825809  3.253288 -1.470560 -0.597146  0.329373 -0.980441   \n",
+       "  35 -0.980441 -0.870141  1.309740  2.241835  0.520294  0.919535  0.559853   \n",
+       "  36  0.559853 -0.610262 -1.023373  3.749274  0.838034  0.901490  2.200834   \n",
+       "  37  2.200834 -0.744703 -2.691433  0.518638  0.795279 -0.798712  0.932971   \n",
+       "  38  0.932971 -0.221151 -2.175975 -3.110737 -2.078318 -0.832937 -0.615586   \n",
+       "  39 -0.615586 -0.910873  1.050625 -3.509187 -0.657294 -2.161540 -1.754324   \n",
+       "  40 -1.754324  1.171308  2.007227 -2.683830 -1.461873 -3.102210 -2.282545   \n",
+       "  41 -2.282545 -0.057196  3.872202 -0.133544 -0.265368 -0.814969  0.239826   \n",
+       "  42  0.239826  1.507615  2.029408  1.215461  0.898728  2.545752  0.546980   \n",
+       "  43  0.546980  1.244836  0.858786  2.846143  0.688299  2.774339  0.790365   \n",
+       "  44  0.790365  2.528271 -1.975276  0.158981 -1.307157 -0.708032  1.122831   \n",
+       "  45  1.122831  0.681326 -1.211016 -0.599276 -1.959789 -3.263615  0.346465   \n",
+       "  46  0.346465  1.192877 -0.366503 -2.748591 -0.560406 -2.071957  0.174470   \n",
+       "  47  0.174470 -1.242134 -0.065756 -0.791349  1.897004 -1.236261  0.857519   \n",
+       "  48  0.857519 -1.515245  0.566508 -0.082597  2.080731  3.355853 -0.008891   \n",
+       "  49 -0.008891 -2.047206  0.149180  2.126017  1.595701  5.013910  0.016847   \n",
+       "  50  0.016847 -0.690617 -0.350005  3.390588  0.618807  2.481275  0.834221   \n",
+       "  51  0.834221  0.169412 -0.296091  0.150605 -2.447624 -2.458940 -1.053420   \n",
+       "  52 -1.053420  0.960765  1.429181  0.420657 -3.540707 -4.364681 -0.437403   \n",
+       "  53 -0.437403 -0.295707  1.281966 -0.854904 -1.587393 -4.272998 -0.020325   \n",
+       "  54 -0.020325 -0.195871  1.113605  0.402654  2.046538 -0.759788 -1.998087   \n",
+       "  55 -1.998087 -0.978876  0.910474  0.594930  3.394784  3.353344 -1.957254   \n",
+       "  56 -1.957254 -2.809278  1.551618 -0.572012  2.520460  4.923684  0.150961   \n",
+       "  57  0.150961 -2.940518  0.876980 -0.636990  0.312410  1.944864  2.406103   \n",
+       "  58  2.406103 -1.032221 -1.363667 -0.967603 -0.657497  0.236358  1.555457   \n",
+       "  59  1.555457  1.202744 -1.154148 -0.756086 -1.044460 -3.335433 -0.872374   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.828004 -1.211351    0.979353    0.234471    0.396440  \n",
+       "  3   0.357972 -3.223626    0.270672   -2.217138   -0.061212  \n",
+       "  4   0.837672 -3.193108   -0.666256   -2.486409   -0.356141  \n",
+       "  5   0.619616  0.076935   -0.222990   -1.329024   -0.156050  \n",
+       "  6   0.933983  1.350147   -0.163785    1.146033   -0.499985  \n",
+       "  7   0.105304 -0.069449    0.350606    1.026978   -0.017482  \n",
+       "  8  -1.376102 -0.657553   -0.358478    0.612138    0.556489  \n",
+       "  9  -1.912776 -1.398009    2.777055    0.470992   -0.835056  \n",
+       "  10 -2.667254 -0.623760    1.499518   -0.533611   -0.870066  \n",
+       "  11 -1.730776  0.258348    0.401152   -1.537462   -0.947702  \n",
+       "  12  1.957878  3.052908   -2.694918    0.035917    0.536005  \n",
+       "  13  4.192227  4.485813   -2.923895    0.533290    0.522564  \n",
+       "  14  2.904548  2.708724    0.052018    1.338634    1.293101  \n",
+       "  15  1.095849 -1.253447    2.434344    1.472001    1.369350  \n",
+       "  16 -1.460090 -3.679514    0.307312    0.544483   -2.444222  \n",
+       "  17 -2.543889 -1.692203    0.024610    0.555303   -2.872289  \n",
+       "  18 -3.612237  2.598470   -1.081511   -2.525992   -2.151999  \n",
+       "  19 -1.822356  4.789610   -1.057425   -2.492103    1.377938  \n",
+       "  20  0.616745  3.228515   -0.265247   -0.369796    1.112634  \n",
+       "  21  2.993611 -0.012294    0.879651    2.733481    2.501440  \n",
+       "  22  3.335085 -3.981763    1.075896    3.823840    0.160322  \n",
+       "  23  2.247185 -3.410538    0.290224    0.404196   -1.235817  \n",
+       "  24 -0.294935 -0.942615   -1.204198   -2.342754   -1.532772  \n",
+       "  25 -3.493202  0.787396   -1.003759   -3.330566    0.289869  \n",
+       "  26 -3.284273  1.858601   -0.458022   -1.493170    0.565517  \n",
+       "  27 -0.734660  0.344543    1.452443   -0.891782    1.373013  \n",
+       "  28  1.709846 -1.100961    2.373892    0.237609   -0.157046  \n",
+       "  29  2.811452 -2.459800    1.826824    1.427396   -0.432697  \n",
+       "  30  1.190729 -2.870284   -1.398411    1.584561   -2.364580  \n",
+       "  31 -1.311356 -2.285681   -1.806526    0.160432   -1.990357  \n",
+       "  32 -1.358347  0.594933   -1.557698   -0.275963   -0.279830  \n",
+       "  33 -0.825809  3.253288   -1.470560   -0.597146    0.329373  \n",
+       "  34 -0.870141  1.309740    2.241835    0.520294    0.919535  \n",
+       "  35 -0.610262 -1.023373    3.749274    0.838034    0.901490  \n",
+       "  36 -0.744703 -2.691433    0.518638    0.795279   -0.798712  \n",
+       "  37 -0.221151 -2.175975   -3.110737   -2.078318   -0.832937  \n",
+       "  38 -0.910873  1.050625   -3.509187   -0.657294   -2.161540  \n",
+       "  39  1.171308  2.007227   -2.683830   -1.461873   -3.102210  \n",
+       "  40 -0.057196  3.872202   -0.133544   -0.265368   -0.814969  \n",
+       "  41  1.507615  2.029408    1.215461    0.898728    2.545752  \n",
+       "  42  1.244836  0.858786    2.846143    0.688299    2.774339  \n",
+       "  43  2.528271 -1.975276    0.158981   -1.307157   -0.708032  \n",
+       "  44  0.681326 -1.211016   -0.599276   -1.959789   -3.263615  \n",
+       "  45  1.192877 -0.366503   -2.748591   -0.560406   -2.071957  \n",
+       "  46 -1.242134 -0.065756   -0.791349    1.897004   -1.236261  \n",
+       "  47 -1.515245  0.566508   -0.082597    2.080731    3.355853  \n",
+       "  48 -2.047206  0.149180    2.126017    1.595701    5.013910  \n",
+       "  49 -0.690617 -0.350005    3.390588    0.618807    2.481275  \n",
+       "  50  0.169412 -0.296091    0.150605   -2.447624   -2.458940  \n",
+       "  51  0.960765  1.429181    0.420657   -3.540707   -4.364681  \n",
+       "  52 -0.295707  1.281966   -0.854904   -1.587393   -4.272998  \n",
+       "  53 -0.195871  1.113605    0.402654    2.046538   -0.759788  \n",
+       "  54 -0.978876  0.910474    0.594930    3.394784    3.353344  \n",
+       "  55 -2.809278  1.551618   -0.572012    2.520460    4.923684  \n",
+       "  56 -2.940518  0.876980   -0.636990    0.312410    1.944864  \n",
+       "  57 -1.032221 -1.363667   -0.967603   -0.657497    0.236358  \n",
+       "  58  1.202744 -1.154148   -0.756086   -1.044460   -3.335433  \n",
+       "  59  1.990135  0.297583   -1.066695    0.091423   -4.943615  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.197009   \n",
+       "  3   1.197009  1.779361  0.021960 -0.044624  0.214835 -1.607493 -0.180980   \n",
+       "  4  -0.180980 -0.620453 -0.813259 -0.680065  0.349371 -0.664669 -1.290166   \n",
+       "  5  -1.290166 -0.609287  1.001839 -3.630840  0.806594 -0.149219 -1.379859   \n",
+       "  6  -1.379859 -1.744891  2.218177 -1.821681 -0.179876  0.568841  0.082561   \n",
+       "  7   0.082561 -1.524624  1.169497 -0.069320 -1.446325  0.225652  1.573722   \n",
+       "  8   1.573722  1.351006  1.163755  1.840492 -2.892866 -0.256759  1.934695   \n",
+       "  9   1.934695  2.857057 -1.011746  0.848750 -2.246643 -1.164241  1.293546   \n",
+       "  10  1.293546  1.140161 -1.349805 -0.470894  1.440248 -0.886689 -0.446658   \n",
+       "  11 -0.446658 -0.978421 -1.181505 -2.257022  1.792813 -0.638492 -2.093984   \n",
+       "  12 -2.093984 -1.477406 -0.826629 -4.409630 -0.029222  2.418531 -1.168244   \n",
+       "  13 -1.168244 -2.560843 -0.947345 -2.653906 -1.109826  3.123519  0.124285   \n",
+       "  14  0.124285 -1.765233 -0.324886  0.387910 -2.446421  0.883685  1.737892   \n",
+       "  15  1.737892  1.501552 -0.487333  3.904343 -0.204878 -0.691241 -0.209979   \n",
+       "  16 -0.209979  1.605504  0.526293  7.031135 -0.210310 -1.708889  1.386761   \n",
+       "  17  1.386761  1.441932  0.495324  2.979709  2.194582 -1.358569  0.317254   \n",
+       "  18  0.317254  1.180005  2.117686 -2.726094  1.194330  0.448802  0.524638   \n",
+       "  19  0.524638  1.289943  0.040562 -5.625667  1.080415  1.942648 -0.474342   \n",
+       "  20 -0.474342 -1.107831  0.140114 -3.786878  0.035459  2.705663 -0.160875   \n",
+       "  21 -0.160875 -3.211338 -0.912856 -0.134637 -2.205062  2.321547 -0.411829   \n",
+       "  22 -0.411829 -2.699141 -0.086881  2.839253 -2.587339 -0.718198 -0.197879   \n",
+       "  23 -0.197879  1.626099 -1.298653  3.928912 -0.267763 -3.392999  0.234968   \n",
+       "  24  0.234968  2.225146 -0.450848  2.925394  1.563572 -2.955163 -1.088147   \n",
+       "  25 -1.088147  3.480901  0.790813 -0.379814  1.257906 -2.370293  0.642400   \n",
+       "  26  0.642400  0.237591  1.887676 -1.518023 -1.000331  1.183291  2.125414   \n",
+       "  27  2.125414 -4.039252  1.611523 -0.581996 -0.266119  1.759310  1.508007   \n",
+       "  28  1.508007 -4.673705 -1.179660  0.040835 -1.937017  1.977368 -0.025956   \n",
+       "  29 -0.025956 -1.504621 -1.620296  1.605568 -0.447837  0.172241 -0.152013   \n",
+       "  30 -0.152013  1.790220 -0.832939  1.099291  1.185291 -0.686784  0.830025   \n",
+       "  31  0.830025  4.280119 -0.021640  0.418814  0.745397 -1.082938  0.863881   \n",
+       "  32  0.863881  2.011199  0.103833 -0.076602 -0.190216  0.394013  2.267288   \n",
+       "  33  2.267288 -0.589109  2.504384  0.188644 -2.019803 -0.371594  1.683347   \n",
+       "  34  1.683347 -4.491737  1.035606 -2.392685 -2.435672 -1.376776 -0.256831   \n",
+       "  35 -0.256831 -4.984564  1.013362  0.068300 -0.367996 -1.519206 -1.991256   \n",
+       "  36 -1.991256 -2.098704 -0.241604  0.380458  2.286739 -1.000093 -3.335087   \n",
+       "  37 -3.335087  3.134711 -1.731882 -1.247300  3.746744  2.098413 -1.164669   \n",
+       "  38 -1.164669  5.600220 -1.161859 -2.215446  0.579363  3.022941  0.758406   \n",
+       "  39  0.758406  3.190993 -0.125954 -1.460756 -2.004477  2.358559  1.507391   \n",
+       "  40  1.507391  0.519929  0.877790  1.367260 -4.394447  0.604920 -0.677905   \n",
+       "  41 -0.677905 -3.297266  0.295210  2.319616 -3.348575 -2.011856 -0.016792   \n",
+       "  42 -0.016792 -4.712518  0.772888  2.716809 -1.862875 -2.655213 -1.370133   \n",
+       "  43 -1.370133 -1.866420  0.816213  2.881788  1.334642 -0.148999 -2.146073   \n",
+       "  44 -2.146073  0.967837  0.083085  1.330721  1.424308  0.685261 -1.480351   \n",
+       "  45 -1.480351  1.937242 -1.900620 -2.243222  1.836357 -0.171811 -1.030237   \n",
+       "  46 -1.030237  2.377607 -0.896493 -0.779666 -1.915065 -2.174003  1.119493   \n",
+       "  47  1.119493 -0.091167  0.362952 -0.263298 -2.520907 -1.837627  2.706213   \n",
+       "  48  2.706213 -1.351743  1.542164 -0.645522 -2.712501 -0.738632  1.602180   \n",
+       "  49  1.602180 -0.823846  1.713202 -0.381370 -0.312287 -0.915901  1.809686   \n",
+       "  50  1.809686 -1.270055  0.283716 -1.443489  1.261499  1.106987 -1.114180   \n",
+       "  51 -1.114180 -0.726763 -0.841199 -1.920196  0.076112  3.065888 -1.877618   \n",
+       "  52 -1.877618  1.500852 -2.622861 -2.722844  0.372366  1.742997  0.128254   \n",
+       "  53  0.128254  2.262112  0.200967 -1.681266 -0.101048  0.402313  1.249110   \n",
+       "  54  1.249110  1.060349  1.715205  1.845918 -0.235781 -3.306168  2.002820   \n",
+       "  55  2.002820 -0.291987  1.696364  3.676648  0.354993 -4.623794  2.140582   \n",
+       "  56  2.140582 -3.251702 -0.015805  2.850392  0.419113 -0.116155  0.055338   \n",
+       "  57  0.055338 -1.260636 -0.962917 -0.006017  0.771567  1.718137 -1.945521   \n",
+       "  58 -1.945521  0.998862 -0.391249 -2.142054 -0.631692  2.655036 -3.186095   \n",
+       "  59 -3.186095  3.198617 -2.015426 -0.209166 -2.748340  0.257170 -3.052695   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.779361  0.021960   -0.044624    0.214835   -1.607493  \n",
+       "  3  -0.620453 -0.813259   -0.680065    0.349371   -0.664669  \n",
+       "  4  -0.609287  1.001839   -3.630840    0.806594   -0.149219  \n",
+       "  5  -1.744891  2.218177   -1.821681   -0.179876    0.568841  \n",
+       "  6  -1.524624  1.169497   -0.069320   -1.446325    0.225652  \n",
+       "  7   1.351006  1.163755    1.840492   -2.892866   -0.256759  \n",
+       "  8   2.857057 -1.011746    0.848750   -2.246643   -1.164241  \n",
+       "  9   1.140161 -1.349805   -0.470894    1.440248   -0.886689  \n",
+       "  10 -0.978421 -1.181505   -2.257022    1.792813   -0.638492  \n",
+       "  11 -1.477406 -0.826629   -4.409630   -0.029222    2.418531  \n",
+       "  12 -2.560843 -0.947345   -2.653906   -1.109826    3.123519  \n",
+       "  13 -1.765233 -0.324886    0.387910   -2.446421    0.883685  \n",
+       "  14  1.501552 -0.487333    3.904343   -0.204878   -0.691241  \n",
+       "  15  1.605504  0.526293    7.031135   -0.210310   -1.708889  \n",
+       "  16  1.441932  0.495324    2.979709    2.194582   -1.358569  \n",
+       "  17  1.180005  2.117686   -2.726094    1.194330    0.448802  \n",
+       "  18  1.289943  0.040562   -5.625667    1.080415    1.942648  \n",
+       "  19 -1.107831  0.140114   -3.786878    0.035459    2.705663  \n",
+       "  20 -3.211338 -0.912856   -0.134637   -2.205062    2.321547  \n",
+       "  21 -2.699141 -0.086881    2.839253   -2.587339   -0.718198  \n",
+       "  22  1.626099 -1.298653    3.928912   -0.267763   -3.392999  \n",
+       "  23  2.225146 -0.450848    2.925394    1.563572   -2.955163  \n",
+       "  24  3.480901  0.790813   -0.379814    1.257906   -2.370293  \n",
+       "  25  0.237591  1.887676   -1.518023   -1.000331    1.183291  \n",
+       "  26 -4.039252  1.611523   -0.581996   -0.266119    1.759310  \n",
+       "  27 -4.673705 -1.179660    0.040835   -1.937017    1.977368  \n",
+       "  28 -1.504621 -1.620296    1.605568   -0.447837    0.172241  \n",
+       "  29  1.790220 -0.832939    1.099291    1.185291   -0.686784  \n",
+       "  30  4.280119 -0.021640    0.418814    0.745397   -1.082938  \n",
+       "  31  2.011199  0.103833   -0.076602   -0.190216    0.394013  \n",
+       "  32 -0.589109  2.504384    0.188644   -2.019803   -0.371594  \n",
+       "  33 -4.491737  1.035606   -2.392685   -2.435672   -1.376776  \n",
+       "  34 -4.984564  1.013362    0.068300   -0.367996   -1.519206  \n",
+       "  35 -2.098704 -0.241604    0.380458    2.286739   -1.000093  \n",
+       "  36  3.134711 -1.731882   -1.247300    3.746744    2.098413  \n",
+       "  37  5.600220 -1.161859   -2.215446    0.579363    3.022941  \n",
+       "  38  3.190993 -0.125954   -1.460756   -2.004477    2.358559  \n",
+       "  39  0.519929  0.877790    1.367260   -4.394447    0.604920  \n",
+       "  40 -3.297266  0.295210    2.319616   -3.348575   -2.011856  \n",
+       "  41 -4.712518  0.772888    2.716809   -1.862875   -2.655213  \n",
+       "  42 -1.866420  0.816213    2.881788    1.334642   -0.148999  \n",
+       "  43  0.967837  0.083085    1.330721    1.424308    0.685261  \n",
+       "  44  1.937242 -1.900620   -2.243222    1.836357   -0.171811  \n",
+       "  45  2.377607 -0.896493   -0.779666   -1.915065   -2.174003  \n",
+       "  46 -0.091167  0.362952   -0.263298   -2.520907   -1.837627  \n",
+       "  47 -1.351743  1.542164   -0.645522   -2.712501   -0.738632  \n",
+       "  48 -0.823846  1.713202   -0.381370   -0.312287   -0.915901  \n",
+       "  49 -1.270055  0.283716   -1.443489    1.261499    1.106987  \n",
+       "  50 -0.726763 -0.841199   -1.920196    0.076112    3.065888  \n",
+       "  51  1.500852 -2.622861   -2.722844    0.372366    1.742997  \n",
+       "  52  2.262112  0.200967   -1.681266   -0.101048    0.402313  \n",
+       "  53  1.060349  1.715205    1.845918   -0.235781   -3.306168  \n",
+       "  54 -0.291987  1.696364    3.676648    0.354993   -4.623794  \n",
+       "  55 -3.251702 -0.015805    2.850392    0.419113   -0.116155  \n",
+       "  56 -1.260636 -0.962917   -0.006017    0.771567    1.718137  \n",
+       "  57  0.998862 -0.391249   -2.142054   -0.631692    2.655036  \n",
+       "  58  3.198617 -2.015426   -0.209166   -2.748340    0.257170  \n",
+       "  59  1.771650 -0.104490   -0.244687   -2.180743   -1.086017  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  2.081573   \n",
+       "  3   2.081573  2.157172  1.082466  1.827453 -0.923204  0.799860  0.081885   \n",
+       "  4   0.081885  0.134497 -0.490639  0.704077 -2.320631 -0.755877 -1.226938   \n",
+       "  5  -1.226938 -2.370257  0.459415 -0.997229 -1.618863 -0.414506 -1.659394   \n",
+       "  6  -1.659394 -1.717504 -2.391174 -2.105346 -1.335523  1.380745  1.101106   \n",
+       "  7   1.101106 -0.866937 -1.550664 -0.841492 -0.743984  0.833207  0.977310   \n",
+       "  8   0.977310  0.049902 -1.187549  0.720046  0.104454 -0.662987  1.890721   \n",
+       "  9   1.890721  2.049720  1.013918  2.408039  1.756857 -1.358669  0.638275   \n",
+       "  10  0.638275  2.330796  2.967666  1.876851 -0.313701  0.218153  2.082017   \n",
+       "  11  2.082017  0.011434  2.524816 -1.259446 -0.883716 -0.386265  0.999264   \n",
+       "  12  0.999264 -0.699490  2.590715 -1.413315 -1.760328  1.362875 -0.553754   \n",
+       "  13 -0.553754 -2.333560  0.527146 -0.449863  0.997240  1.290374 -1.422911   \n",
+       "  14 -1.422911 -1.891223 -2.259207 -0.997521  1.227547  0.368038 -0.061639   \n",
+       "  15 -0.061639 -1.307584 -3.006242  1.095031  2.082675 -2.207648  0.110649   \n",
+       "  16  0.110649  0.513688 -2.692399  2.361554  2.071530 -1.694188  0.608912   \n",
+       "  17  0.608912  1.408806  0.403479  2.040524 -0.295266 -0.482202 -0.299782   \n",
+       "  18 -0.299782  1.535544  3.027189 -1.430073 -0.098439  1.974288  0.744819   \n",
+       "  19  0.744819 -0.981114  3.595581 -1.799051 -0.803619  2.522046 -0.314926   \n",
+       "  20 -0.314926 -1.289086 -1.908998  0.223172 -0.571324  1.757235 -0.568291   \n",
+       "  21 -0.568291 -1.448027 -3.168606  0.505512  0.482341 -0.398487 -0.867070   \n",
+       "  22 -0.867070 -0.809139 -3.540698  1.805388  2.549107 -1.191550 -0.488257   \n",
+       "  23 -0.488257  0.812978 -0.495964  1.440436  1.480647 -3.505810  0.215590   \n",
+       "  24  0.215590 -0.013073  2.044638 -2.260026 -1.166347 -2.799849  1.584320   \n",
+       "  25  1.584320 -0.790195  2.461582 -2.655673 -2.594604 -0.309779  0.954113   \n",
+       "  26  0.954113 -0.527014  0.879421 -2.017056 -2.248945  2.145201  0.005853   \n",
+       "  27  0.005853  1.416025  1.161154 -0.384566  0.352875  3.766059 -2.302996   \n",
+       "  28 -2.302996  2.423035 -1.345011  0.747501  2.059487  2.090043 -2.109288   \n",
+       "  29 -2.109288  2.241558 -2.147407  2.913573  1.742182  0.139681 -0.316774   \n",
+       "  30 -0.316774 -1.049456 -1.418913 -0.542128  0.802717 -2.450994  2.248338   \n",
+       "  31  2.248338 -1.755383  0.202390 -2.452597 -0.600119 -2.380185  4.199424   \n",
+       "  32  4.199424 -1.347008  1.117267 -1.720330 -1.874401 -0.796630  1.132681   \n",
+       "  33  1.132681 -0.899679 -0.973125  0.640783 -3.512650  1.194536 -2.168233   \n",
+       "  34 -2.168233  1.918117  1.102948  3.219103 -2.678196  3.477266 -3.664124   \n",
+       "  35 -3.664124  1.504458 -0.085482  1.365202 -0.755834  2.683182 -0.479357   \n",
+       "  36 -0.479357  1.765521 -0.388709 -0.311314  2.750275 -0.358151  1.985426   \n",
+       "  37  1.985426  0.166715 -2.063929 -2.577913  4.428027 -3.284688  2.454851   \n",
+       "  38  2.454851 -1.676978 -1.045527 -2.266411  1.187470 -2.842842  2.574266   \n",
+       "  39  2.574266 -3.254193 -0.697583  0.321040 -2.237131  1.400952  0.432997   \n",
+       "  40  0.432997 -3.047356  0.788831  0.548895 -2.362273  3.854241 -1.027304   \n",
+       "  41 -1.027304 -1.135431 -0.144724  0.125797  0.033962  3.350270 -1.950277   \n",
+       "  42 -1.950277  0.525775  1.437477 -0.202528  1.836341  3.328651 -0.017703   \n",
+       "  43 -0.017703  1.538319 -0.140644 -1.217405  2.069967  0.792744  0.190962   \n",
+       "  44  0.190962  2.932902  0.554729 -1.907393  2.035209 -2.150061  0.484037   \n",
+       "  45  0.484037  2.333283  1.455170 -1.937977  1.313303 -2.777023  1.774416   \n",
+       "  46  1.774416 -0.001808  1.574599 -1.850736  0.624375 -0.669982  1.147910   \n",
+       "  47  1.147910 -1.692882 -0.089836 -1.195379 -1.914599 -0.116182  1.758373   \n",
+       "  48  1.758373 -1.833849 -1.450620  0.521683 -1.438189 -0.340139  0.837231   \n",
+       "  49  0.837231  0.066339 -2.260149  2.438626  0.104489  0.177975 -0.013505   \n",
+       "  50 -0.013505  1.396474 -2.326273  3.521002  1.032670  2.149567 -0.744147   \n",
+       "  51 -0.744147  1.236931 -1.009779  1.037026  2.439109  0.991710 -0.904646   \n",
+       "  52 -0.904646  1.340458  0.046162 -0.430225  1.906470  1.522304  1.429062   \n",
+       "  53  1.429062 -0.367172  2.296631 -2.843612  1.188817 -0.130212  2.942406   \n",
+       "  54  2.942406 -0.649109  1.277546 -1.972287 -2.234162 -0.217570 -0.023195   \n",
+       "  55 -0.023195  0.482279 -0.304473 -2.252321 -3.297961  0.562628 -0.506097   \n",
+       "  56 -0.506097 -0.524116 -3.123385  1.796879 -3.774879  0.950071 -0.528343   \n",
+       "  57 -0.528343 -1.181191 -3.082972  4.505657 -1.268820  2.213315 -1.071430   \n",
+       "  58 -1.071430 -1.073407 -1.700992  3.826304  1.047155  2.509111 -1.154746   \n",
+       "  59 -1.154746 -1.742202  1.093333  0.315560  2.701085  0.188557  0.100819   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   2.157172  1.082466    1.827453   -0.923204    0.799860  \n",
+       "  3   0.134497 -0.490639    0.704077   -2.320631   -0.755877  \n",
+       "  4  -2.370257  0.459415   -0.997229   -1.618863   -0.414506  \n",
+       "  5  -1.717504 -2.391174   -2.105346   -1.335523    1.380745  \n",
+       "  6  -0.866937 -1.550664   -0.841492   -0.743984    0.833207  \n",
+       "  7   0.049902 -1.187549    0.720046    0.104454   -0.662987  \n",
+       "  8   2.049720  1.013918    2.408039    1.756857   -1.358669  \n",
+       "  9   2.330796  2.967666    1.876851   -0.313701    0.218153  \n",
+       "  10  0.011434  2.524816   -1.259446   -0.883716   -0.386265  \n",
+       "  11 -0.699490  2.590715   -1.413315   -1.760328    1.362875  \n",
+       "  12 -2.333560  0.527146   -0.449863    0.997240    1.290374  \n",
+       "  13 -1.891223 -2.259207   -0.997521    1.227547    0.368038  \n",
+       "  14 -1.307584 -3.006242    1.095031    2.082675   -2.207648  \n",
+       "  15  0.513688 -2.692399    2.361554    2.071530   -1.694188  \n",
+       "  16  1.408806  0.403479    2.040524   -0.295266   -0.482202  \n",
+       "  17  1.535544  3.027189   -1.430073   -0.098439    1.974288  \n",
+       "  18 -0.981114  3.595581   -1.799051   -0.803619    2.522046  \n",
+       "  19 -1.289086 -1.908998    0.223172   -0.571324    1.757235  \n",
+       "  20 -1.448027 -3.168606    0.505512    0.482341   -0.398487  \n",
+       "  21 -0.809139 -3.540698    1.805388    2.549107   -1.191550  \n",
+       "  22  0.812978 -0.495964    1.440436    1.480647   -3.505810  \n",
+       "  23 -0.013073  2.044638   -2.260026   -1.166347   -2.799849  \n",
+       "  24 -0.790195  2.461582   -2.655673   -2.594604   -0.309779  \n",
+       "  25 -0.527014  0.879421   -2.017056   -2.248945    2.145201  \n",
+       "  26  1.416025  1.161154   -0.384566    0.352875    3.766059  \n",
+       "  27  2.423035 -1.345011    0.747501    2.059487    2.090043  \n",
+       "  28  2.241558 -2.147407    2.913573    1.742182    0.139681  \n",
+       "  29 -1.049456 -1.418913   -0.542128    0.802717   -2.450994  \n",
+       "  30 -1.755383  0.202390   -2.452597   -0.600119   -2.380185  \n",
+       "  31 -1.347008  1.117267   -1.720330   -1.874401   -0.796630  \n",
+       "  32 -0.899679 -0.973125    0.640783   -3.512650    1.194536  \n",
+       "  33  1.918117  1.102948    3.219103   -2.678196    3.477266  \n",
+       "  34  1.504458 -0.085482    1.365202   -0.755834    2.683182  \n",
+       "  35  1.765521 -0.388709   -0.311314    2.750275   -0.358151  \n",
+       "  36  0.166715 -2.063929   -2.577913    4.428027   -3.284688  \n",
+       "  37 -1.676978 -1.045527   -2.266411    1.187470   -2.842842  \n",
+       "  38 -3.254193 -0.697583    0.321040   -2.237131    1.400952  \n",
+       "  39 -3.047356  0.788831    0.548895   -2.362273    3.854241  \n",
+       "  40 -1.135431 -0.144724    0.125797    0.033962    3.350270  \n",
+       "  41  0.525775  1.437477   -0.202528    1.836341    3.328651  \n",
+       "  42  1.538319 -0.140644   -1.217405    2.069967    0.792744  \n",
+       "  43  2.932902  0.554729   -1.907393    2.035209   -2.150061  \n",
+       "  44  2.333283  1.455170   -1.937977    1.313303   -2.777023  \n",
+       "  45 -0.001808  1.574599   -1.850736    0.624375   -0.669982  \n",
+       "  46 -1.692882 -0.089836   -1.195379   -1.914599   -0.116182  \n",
+       "  47 -1.833849 -1.450620    0.521683   -1.438189   -0.340139  \n",
+       "  48  0.066339 -2.260149    2.438626    0.104489    0.177975  \n",
+       "  49  1.396474 -2.326273    3.521002    1.032670    2.149567  \n",
+       "  50  1.236931 -1.009779    1.037026    2.439109    0.991710  \n",
+       "  51  1.340458  0.046162   -0.430225    1.906470    1.522304  \n",
+       "  52 -0.367172  2.296631   -2.843612    1.188817   -0.130212  \n",
+       "  53 -0.649109  1.277546   -1.972287   -2.234162   -0.217570  \n",
+       "  54  0.482279 -0.304473   -2.252321   -3.297961    0.562628  \n",
+       "  55 -0.524116 -3.123385    1.796879   -3.774879    0.950071  \n",
+       "  56 -1.181191 -3.082972    4.505657   -1.268820    2.213315  \n",
+       "  57 -1.073407 -1.700992    3.826304    1.047155    2.509111  \n",
+       "  58 -1.742202  1.093333    0.315560    2.701085    0.188557  \n",
+       "  59 -1.442561  2.752056   -3.877231    2.416107   -2.059157  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.506363   \n",
+       "  3   0.506363 -0.416391  0.519294  0.252693  1.298203 -0.166385  0.415436   \n",
+       "  4   0.415436 -1.561911  0.574382  0.401916 -0.871294 -0.161943 -1.509003   \n",
+       "  5  -1.509003 -1.729693  0.128825 -0.737933 -1.652144  0.396225 -1.659152   \n",
+       "  6  -1.659152 -3.299555 -1.384097 -0.759017 -0.973677 -2.377067 -0.934981   \n",
+       "  7  -0.934981 -1.020896 -0.983980 -0.391849  0.798031 -0.583015  2.121147   \n",
+       "  8   2.121147 -0.921241  0.015281 -0.195998  1.642598  1.340034  1.854867   \n",
+       "  9   1.854867  0.307292  1.700150 -1.987675  0.690684  3.354308  1.023804   \n",
+       "  10  1.023804  1.187948  0.773218 -1.416515 -0.338342  3.168177 -2.229072   \n",
+       "  11 -2.229072 -0.470279  0.698640  0.534407  0.725221 -0.857437 -2.491828   \n",
+       "  12 -2.491828 -2.407723 -1.085655  3.592895  0.656306 -5.208937 -0.850445   \n",
+       "  13 -0.850445 -2.329257 -1.204436  2.153713 -0.504950 -3.990626  0.898529   \n",
+       "  14  0.898529 -1.048109 -1.903120 -1.047234  0.475610  0.063038  1.985635   \n",
+       "  15  1.985635 -0.670449 -1.197948 -2.426973  0.201310  2.504772 -1.493573   \n",
+       "  16 -1.493573 -0.745068 -1.008657 -2.977363  1.290570  2.626904 -1.442032   \n",
+       "  17 -1.442032 -0.889574  2.038630 -0.793931  0.421097  1.170693 -1.495913   \n",
+       "  18 -1.495913 -0.731167  3.104410  1.098810  1.615246 -0.554990  0.470722   \n",
+       "  19  0.470722  1.046309  1.712311  3.758919  0.678489 -1.901035 -0.274651   \n",
+       "  20 -0.274651  0.060362  0.418744  2.863469 -1.303635 -1.974320  1.410994   \n",
+       "  21  1.410994  0.208342 -1.343609  0.463382 -0.807962 -1.116455  1.178044   \n",
+       "  22  1.178044 -2.318696 -1.656542 -1.451503 -0.731382  0.446086  0.253097   \n",
+       "  23  0.253097 -2.882078 -2.637322 -2.051079  0.239895  1.816080  0.672301   \n",
+       "  24  0.672301 -2.200459 -0.647355 -0.892703 -0.146656  1.119167 -0.414125   \n",
+       "  25 -0.414125  0.642966  3.138627 -0.088817  0.315958  1.211577 -0.103433   \n",
+       "  26 -0.103433 -0.080010  4.532521  1.242015  2.450826 -0.731180 -0.644010   \n",
+       "  27 -0.644010  0.693372  2.879671  2.833404  1.765009 -2.641698 -0.641130   \n",
+       "  28 -0.641130 -0.750188 -2.562960  0.726191 -0.169567 -2.529428  0.247907   \n",
+       "  29  0.247907 -0.274413 -4.085473  0.076987 -1.546045 -0.859154  0.180840   \n",
+       "  30  0.180840  0.634143 -3.298632  0.342899 -1.327006  0.798797 -0.071152   \n",
+       "  31 -0.071152  0.865464 -0.098859  0.354531 -1.490963  2.430844  0.759709   \n",
+       "  32  0.759709  1.118750  2.072834 -1.376788 -0.421779  2.093022  0.316206   \n",
+       "  33  0.316206  0.708286  3.640291  0.400989  0.045393 -1.065015 -0.090664   \n",
+       "  34 -0.090664  2.017521  2.564498  1.490142  1.206605 -1.959821 -1.160877   \n",
+       "  35 -1.160877  0.226640 -0.064744  0.997490  1.191920 -1.131837  0.713806   \n",
+       "  36  0.713806 -2.024911 -1.640616 -0.992888 -0.361650  0.809326  0.669673   \n",
+       "  37  0.669673 -1.167133 -2.157655 -3.538706 -0.265016  2.837523  1.604908   \n",
+       "  38  1.604908  0.191914 -1.352218 -3.848506  0.559138  2.530879 -0.451953   \n",
+       "  39 -0.451953 -0.304974 -1.607094  0.167834  1.301650  1.620309 -0.837445   \n",
+       "  40 -0.837445  0.356095  0.091208  2.893725  1.236546 -2.110679 -0.565972   \n",
+       "  41 -0.565972 -0.688144  0.720905  3.002074 -0.401916 -1.368092 -0.687414   \n",
+       "  42 -0.687414 -1.796247  2.176086  0.464220 -1.386655  0.298046  2.657197   \n",
+       "  43  2.657197 -1.666727  0.505186 -1.335174 -0.707899  1.234577  2.510606   \n",
+       "  44  2.510606 -0.314143 -0.814567 -0.741256 -0.089580  1.994202  3.460970   \n",
+       "  45  3.460970  1.044810 -1.244719  0.394298  1.613923  0.225526 -0.776378   \n",
+       "  46 -0.776378  1.883075  0.217918  1.415233  2.144880 -1.980448 -3.464235   \n",
+       "  47 -3.464235  0.170027 -0.078014  0.917127  1.379860 -2.437392 -3.519416   \n",
+       "  48 -3.519416 -2.853112 -0.582413 -0.578832  1.008642 -2.024317 -2.978405   \n",
+       "  49 -2.978405 -2.379350 -1.525531 -1.691186 -1.334542 -0.051935  1.250805   \n",
+       "  50  1.250805 -1.688630 -0.795558 -0.160968 -0.373649  2.139144  4.304309   \n",
+       "  51  4.304309  0.054855  0.619522 -0.864931 -0.725347  4.093600  6.618858   \n",
+       "  52  6.618858  2.071472  1.562518  1.377346 -0.274420  2.635857  2.415447   \n",
+       "  53  2.415447  4.409225  2.318643  2.006720 -1.648534  1.053061  0.199549   \n",
+       "  54  0.199549  2.484565  1.825217  0.608954 -1.092834 -1.067879 -3.540117   \n",
+       "  55 -3.540117 -0.872828  0.392292 -1.377312 -0.101963 -0.941830 -2.592341   \n",
+       "  56 -2.592341 -2.743858 -1.728629 -4.675228  2.212385 -0.594946 -0.800231   \n",
+       "  57 -0.800231 -1.658473 -0.459496 -2.811738  0.871613 -2.625279  1.752777   \n",
+       "  58  1.752777  0.654791  0.237954  1.691088 -0.288996 -2.084280  2.737216   \n",
+       "  59  2.737216  2.289079  0.736139  4.404961 -0.609714 -1.842561  2.953675   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.416391  0.519294    0.252693    1.298203   -0.166385  \n",
+       "  3  -1.561911  0.574382    0.401916   -0.871294   -0.161943  \n",
+       "  4  -1.729693  0.128825   -0.737933   -1.652144    0.396225  \n",
+       "  5  -3.299555 -1.384097   -0.759017   -0.973677   -2.377067  \n",
+       "  6  -1.020896 -0.983980   -0.391849    0.798031   -0.583015  \n",
+       "  7  -0.921241  0.015281   -0.195998    1.642598    1.340034  \n",
+       "  8   0.307292  1.700150   -1.987675    0.690684    3.354308  \n",
+       "  9   1.187948  0.773218   -1.416515   -0.338342    3.168177  \n",
+       "  10 -0.470279  0.698640    0.534407    0.725221   -0.857437  \n",
+       "  11 -2.407723 -1.085655    3.592895    0.656306   -5.208937  \n",
+       "  12 -2.329257 -1.204436    2.153713   -0.504950   -3.990626  \n",
+       "  13 -1.048109 -1.903120   -1.047234    0.475610    0.063038  \n",
+       "  14 -0.670449 -1.197948   -2.426973    0.201310    2.504772  \n",
+       "  15 -0.745068 -1.008657   -2.977363    1.290570    2.626904  \n",
+       "  16 -0.889574  2.038630   -0.793931    0.421097    1.170693  \n",
+       "  17 -0.731167  3.104410    1.098810    1.615246   -0.554990  \n",
+       "  18  1.046309  1.712311    3.758919    0.678489   -1.901035  \n",
+       "  19  0.060362  0.418744    2.863469   -1.303635   -1.974320  \n",
+       "  20  0.208342 -1.343609    0.463382   -0.807962   -1.116455  \n",
+       "  21 -2.318696 -1.656542   -1.451503   -0.731382    0.446086  \n",
+       "  22 -2.882078 -2.637322   -2.051079    0.239895    1.816080  \n",
+       "  23 -2.200459 -0.647355   -0.892703   -0.146656    1.119167  \n",
+       "  24  0.642966  3.138627   -0.088817    0.315958    1.211577  \n",
+       "  25 -0.080010  4.532521    1.242015    2.450826   -0.731180  \n",
+       "  26  0.693372  2.879671    2.833404    1.765009   -2.641698  \n",
+       "  27 -0.750188 -2.562960    0.726191   -0.169567   -2.529428  \n",
+       "  28 -0.274413 -4.085473    0.076987   -1.546045   -0.859154  \n",
+       "  29  0.634143 -3.298632    0.342899   -1.327006    0.798797  \n",
+       "  30  0.865464 -0.098859    0.354531   -1.490963    2.430844  \n",
+       "  31  1.118750  2.072834   -1.376788   -0.421779    2.093022  \n",
+       "  32  0.708286  3.640291    0.400989    0.045393   -1.065015  \n",
+       "  33  2.017521  2.564498    1.490142    1.206605   -1.959821  \n",
+       "  34  0.226640 -0.064744    0.997490    1.191920   -1.131837  \n",
+       "  35 -2.024911 -1.640616   -0.992888   -0.361650    0.809326  \n",
+       "  36 -1.167133 -2.157655   -3.538706   -0.265016    2.837523  \n",
+       "  37  0.191914 -1.352218   -3.848506    0.559138    2.530879  \n",
+       "  38 -0.304974 -1.607094    0.167834    1.301650    1.620309  \n",
+       "  39  0.356095  0.091208    2.893725    1.236546   -2.110679  \n",
+       "  40 -0.688144  0.720905    3.002074   -0.401916   -1.368092  \n",
+       "  41 -1.796247  2.176086    0.464220   -1.386655    0.298046  \n",
+       "  42 -1.666727  0.505186   -1.335174   -0.707899    1.234577  \n",
+       "  43 -0.314143 -0.814567   -0.741256   -0.089580    1.994202  \n",
+       "  44  1.044810 -1.244719    0.394298    1.613923    0.225526  \n",
+       "  45  1.883075  0.217918    1.415233    2.144880   -1.980448  \n",
+       "  46  0.170027 -0.078014    0.917127    1.379860   -2.437392  \n",
+       "  47 -2.853112 -0.582413   -0.578832    1.008642   -2.024317  \n",
+       "  48 -2.379350 -1.525531   -1.691186   -1.334542   -0.051935  \n",
+       "  49 -1.688630 -0.795558   -0.160968   -0.373649    2.139144  \n",
+       "  50  0.054855  0.619522   -0.864931   -0.725347    4.093600  \n",
+       "  51  2.071472  1.562518    1.377346   -0.274420    2.635857  \n",
+       "  52  4.409225  2.318643    2.006720   -1.648534    1.053061  \n",
+       "  53  2.484565  1.825217    0.608954   -1.092834   -1.067879  \n",
+       "  54 -0.872828  0.392292   -1.377312   -0.101963   -0.941830  \n",
+       "  55 -2.743858 -1.728629   -4.675228    2.212385   -0.594946  \n",
+       "  56 -1.658473 -0.459496   -2.811738    0.871613   -2.625279  \n",
+       "  57  0.654791  0.237954    1.691088   -0.288996   -2.084280  \n",
+       "  58  2.289079  0.736139    4.404961   -0.609714   -1.842561  \n",
+       "  59 -0.018045  1.151584    2.071645   -0.155312    0.391748  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -1.033971   \n",
+       "  3  -1.033971 -1.036928  1.743280  0.324114 -0.321830  0.215198 -2.402086   \n",
+       "  4  -2.402086 -1.090772  1.123681  0.866205 -2.099479 -1.807045 -1.482336   \n",
+       "  5  -1.482336 -1.310867  0.278924 -0.544468 -2.110080 -2.078683 -0.879108   \n",
+       "  6  -0.879108  0.553838 -1.730547 -0.167848 -0.277493 -0.411524  0.845823   \n",
+       "  7   0.845823  0.933186 -2.817727 -0.355726  1.975941  1.529176  1.362749   \n",
+       "  8   1.362749  2.779835 -2.048026 -0.889540  1.448001  2.906255  0.667971   \n",
+       "  9   0.667971  0.767239  0.778340  0.070017  1.094866  0.460945 -1.074423   \n",
+       "  10 -1.074423 -1.432348  5.543541  0.369470 -0.519694 -1.616690 -2.138198   \n",
+       "  11 -2.138198 -1.239737  3.332462  1.060192 -1.839839 -3.826937 -1.004013   \n",
+       "  12 -1.004013 -0.421295 -0.183658 -0.415507 -0.074031 -1.600722  1.159910   \n",
+       "  13  1.159910 -0.588815 -3.263474 -1.581749  1.780521  1.274503  2.560528   \n",
+       "  14  2.560528 -1.660773 -3.174779 -3.367556  3.685679  3.991161  0.159927   \n",
+       "  15  0.159927 -0.631137 -0.074775 -1.454250  3.697271  1.719603 -0.969571   \n",
+       "  16 -0.969571 -1.771504  0.668395  2.703316  1.927671  0.046695 -1.862471   \n",
+       "  17 -1.862471  0.475051  2.085562  5.058878 -2.015220 -3.060488 -0.355537   \n",
+       "  18 -0.355537  1.210017  0.406390  1.876233 -3.502964 -3.270738 -0.772437   \n",
+       "  19 -0.772437  1.394203 -0.453812 -0.871003 -0.850588  1.473388 -0.740990   \n",
+       "  20 -0.740990  1.592182 -0.627937 -4.889736 -0.475981  3.076949  0.950733   \n",
+       "  21  0.950733  0.601985  0.930683 -3.881586  2.004011  4.172172  0.329449   \n",
+       "  22  0.329449 -2.977816  0.878889  0.925728  0.293455  2.115880 -1.117072   \n",
+       "  23 -1.117072 -2.114078  1.231170  2.710910 -0.117714 -3.230767 -2.169891   \n",
+       "  24 -2.169891 -0.912703  1.173213  1.927552 -2.264963 -3.997902 -0.590621   \n",
+       "  25 -0.590621  0.683153 -0.220398 -0.353655 -3.792756 -2.510844  1.061492   \n",
+       "  26  1.061492  3.107781 -0.761083 -2.514951 -4.957393  1.376960 -0.017070   \n",
+       "  27 -0.017070  3.029493  0.775285 -1.252870 -1.046154  4.459479 -1.371027   \n",
+       "  28 -1.371027  0.039985  2.494282  0.573320  2.993198  3.572649 -3.138694   \n",
+       "  29 -3.138694 -2.256731  2.558225  0.048693  2.915537 -0.981168 -3.305553   \n",
+       "  30 -3.305553 -2.957870 -0.116931  1.661837  2.119342 -2.087648 -1.221080   \n",
+       "  31 -1.221080 -1.184497 -3.156497  2.323460 -0.662745 -2.509665  1.953233   \n",
+       "  32  1.953233  0.263010 -3.801637  3.223165  0.600748 -2.376291  3.399461   \n",
+       "  33  3.399461  1.647142 -1.024647  1.047887 -1.271659  0.778479  3.849145   \n",
+       "  34  3.849145  3.537557  1.479736 -1.213221 -1.090338  2.749885  0.418495   \n",
+       "  35  0.418495  2.595600  3.705031 -4.136876  0.795283  3.043120 -1.018801   \n",
+       "  36 -1.018801  0.146286  3.796340 -4.035630 -1.339834  0.992288 -3.552941   \n",
+       "  37 -3.552941 -2.179729  1.189097 -1.988725  0.165260 -1.256376 -1.533886   \n",
+       "  38 -1.533886 -3.439622 -1.716947  2.632833 -1.225221 -2.361889  1.458307   \n",
+       "  39  1.458307 -1.458096 -3.795834  4.536536 -0.070055 -0.639790  3.706520   \n",
+       "  40  3.706520 -0.609177 -1.297505  2.676816 -0.336977  0.633279  2.524686   \n",
+       "  41  2.524686  1.445347  1.159752 -2.118298  1.382673  0.467340 -0.821947   \n",
+       "  42 -0.821947  2.192899  2.504138 -4.303391  0.454977  1.611849 -1.213457   \n",
+       "  43 -1.213457  0.389356  2.881600 -4.281237  1.137153 -0.655767 -2.476213   \n",
+       "  44 -2.476213 -0.294026 -1.593845  0.886607 -0.079979 -2.426806 -1.678171   \n",
+       "  45 -1.678171 -2.237737 -3.569994  3.207116 -0.097912 -4.054588  1.898293   \n",
+       "  46  1.898293 -0.686797 -2.050984  3.586065 -1.610913 -3.070287  3.739445   \n",
+       "  47  3.739445  1.367299  1.460386  2.587259 -1.931577 -0.728978  2.539366   \n",
+       "  48  2.539366  0.603506  3.360234 -1.096054 -0.414804  4.034559 -0.794720   \n",
+       "  49 -0.794720  2.004157  3.008132 -1.853891 -0.025832  5.136864 -2.164818   \n",
+       "  50 -2.164818  3.207096 -0.122170 -2.922189  3.216425  3.597797 -2.599248   \n",
+       "  51 -2.599248  2.491874 -0.777759 -1.778900  2.242162 -1.541586 -2.297882   \n",
+       "  52 -2.297882 -0.513105 -1.465947 -1.566115 -0.763914 -4.193889 -0.354095   \n",
+       "  53 -0.354095 -2.147848  0.362528 -0.780618 -3.561415 -3.173202  1.293901   \n",
+       "  54  1.293901 -1.931050  0.366544 -0.562651 -3.418581 -0.161159  0.616647   \n",
+       "  55  0.616647 -0.802016 -0.198337  1.004934  1.136431  1.694662 -0.137480   \n",
+       "  56 -0.137480  1.348078  1.420927  2.843317  3.671969  2.265137  1.470643   \n",
+       "  57  1.470643  4.026778 -0.658287  2.770530  2.732431  2.838627 -0.079922   \n",
+       "  58 -0.079922  4.139057 -1.497544  0.598660 -0.047711 -0.042838  0.461036   \n",
+       "  59  0.461036  2.114902 -0.355058 -2.775137 -2.695539 -2.990217  0.912505   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -1.036928  1.743280    0.324114   -0.321830    0.215198  \n",
+       "  3  -1.090772  1.123681    0.866205   -2.099479   -1.807045  \n",
+       "  4  -1.310867  0.278924   -0.544468   -2.110080   -2.078683  \n",
+       "  5   0.553838 -1.730547   -0.167848   -0.277493   -0.411524  \n",
+       "  6   0.933186 -2.817727   -0.355726    1.975941    1.529176  \n",
+       "  7   2.779835 -2.048026   -0.889540    1.448001    2.906255  \n",
+       "  8   0.767239  0.778340    0.070017    1.094866    0.460945  \n",
+       "  9  -1.432348  5.543541    0.369470   -0.519694   -1.616690  \n",
+       "  10 -1.239737  3.332462    1.060192   -1.839839   -3.826937  \n",
+       "  11 -0.421295 -0.183658   -0.415507   -0.074031   -1.600722  \n",
+       "  12 -0.588815 -3.263474   -1.581749    1.780521    1.274503  \n",
+       "  13 -1.660773 -3.174779   -3.367556    3.685679    3.991161  \n",
+       "  14 -0.631137 -0.074775   -1.454250    3.697271    1.719603  \n",
+       "  15 -1.771504  0.668395    2.703316    1.927671    0.046695  \n",
+       "  16  0.475051  2.085562    5.058878   -2.015220   -3.060488  \n",
+       "  17  1.210017  0.406390    1.876233   -3.502964   -3.270738  \n",
+       "  18  1.394203 -0.453812   -0.871003   -0.850588    1.473388  \n",
+       "  19  1.592182 -0.627937   -4.889736   -0.475981    3.076949  \n",
+       "  20  0.601985  0.930683   -3.881586    2.004011    4.172172  \n",
+       "  21 -2.977816  0.878889    0.925728    0.293455    2.115880  \n",
+       "  22 -2.114078  1.231170    2.710910   -0.117714   -3.230767  \n",
+       "  23 -0.912703  1.173213    1.927552   -2.264963   -3.997902  \n",
+       "  24  0.683153 -0.220398   -0.353655   -3.792756   -2.510844  \n",
+       "  25  3.107781 -0.761083   -2.514951   -4.957393    1.376960  \n",
+       "  26  3.029493  0.775285   -1.252870   -1.046154    4.459479  \n",
+       "  27  0.039985  2.494282    0.573320    2.993198    3.572649  \n",
+       "  28 -2.256731  2.558225    0.048693    2.915537   -0.981168  \n",
+       "  29 -2.957870 -0.116931    1.661837    2.119342   -2.087648  \n",
+       "  30 -1.184497 -3.156497    2.323460   -0.662745   -2.509665  \n",
+       "  31  0.263010 -3.801637    3.223165    0.600748   -2.376291  \n",
+       "  32  1.647142 -1.024647    1.047887   -1.271659    0.778479  \n",
+       "  33  3.537557  1.479736   -1.213221   -1.090338    2.749885  \n",
+       "  34  2.595600  3.705031   -4.136876    0.795283    3.043120  \n",
+       "  35  0.146286  3.796340   -4.035630   -1.339834    0.992288  \n",
+       "  36 -2.179729  1.189097   -1.988725    0.165260   -1.256376  \n",
+       "  37 -3.439622 -1.716947    2.632833   -1.225221   -2.361889  \n",
+       "  38 -1.458096 -3.795834    4.536536   -0.070055   -0.639790  \n",
+       "  39 -0.609177 -1.297505    2.676816   -0.336977    0.633279  \n",
+       "  40  1.445347  1.159752   -2.118298    1.382673    0.467340  \n",
+       "  41  2.192899  2.504138   -4.303391    0.454977    1.611849  \n",
+       "  42  0.389356  2.881600   -4.281237    1.137153   -0.655767  \n",
+       "  43 -0.294026 -1.593845    0.886607   -0.079979   -2.426806  \n",
+       "  44 -2.237737 -3.569994    3.207116   -0.097912   -4.054588  \n",
+       "  45 -0.686797 -2.050984    3.586065   -1.610913   -3.070287  \n",
+       "  46  1.367299  1.460386    2.587259   -1.931577   -0.728978  \n",
+       "  47  0.603506  3.360234   -1.096054   -0.414804    4.034559  \n",
+       "  48  2.004157  3.008132   -1.853891   -0.025832    5.136864  \n",
+       "  49  3.207096 -0.122170   -2.922189    3.216425    3.597797  \n",
+       "  50  2.491874 -0.777759   -1.778900    2.242162   -1.541586  \n",
+       "  51 -0.513105 -1.465947   -1.566115   -0.763914   -4.193889  \n",
+       "  52 -2.147848  0.362528   -0.780618   -3.561415   -3.173202  \n",
+       "  53 -1.931050  0.366544   -0.562651   -3.418581   -0.161159  \n",
+       "  54 -0.802016 -0.198337    1.004934    1.136431    1.694662  \n",
+       "  55  1.348078  1.420927    2.843317    3.671969    2.265137  \n",
+       "  56  4.026778 -0.658287    2.770530    2.732431    2.838627  \n",
+       "  57  4.139057 -1.497544    0.598660   -0.047711   -0.042838  \n",
+       "  58  2.114902 -0.355058   -2.775137   -2.695539   -2.990217  \n",
+       "  59 -1.512408  1.835188   -1.239491   -4.682574   -2.325343  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.456139   \n",
+       "  3   0.456139  2.033950 -2.046513 -0.679731  1.135633  0.818384 -1.946087   \n",
+       "  4  -1.946087  0.141335 -3.409339 -2.187148  1.407804 -0.509551 -1.353935   \n",
+       "  5  -1.353935 -1.177802 -2.695117 -2.219436 -0.147177 -3.134879 -0.946563   \n",
+       "  6  -0.946563 -1.657310 -0.525838  0.606351  0.157475 -2.527644  1.276337   \n",
+       "  7   1.276337 -1.362393  1.800790  2.002042 -3.075572 -1.100843  2.200142   \n",
+       "  8   2.200142  2.133039  1.690947  3.034566 -1.833836  3.165127  2.258333   \n",
+       "  9   2.258333  3.706683  1.428262  0.454780 -0.092936  3.910391  2.323043   \n",
+       "  10  2.323043  3.375028 -0.431636 -0.868125  1.126580  1.738411 -1.716722   \n",
+       "  11 -1.716722 -0.433157 -0.825890 -1.502924  0.791846 -0.517542 -2.689213   \n",
+       "  12 -2.689213 -1.829422  0.054082  0.106613  0.290463 -0.789086 -2.975608   \n",
+       "  13 -2.975608 -2.871748  0.894493  0.744721 -2.113682 -1.130676 -1.727847   \n",
+       "  14 -1.727847 -2.711665  1.161757  2.031144 -2.870653  0.071517  0.427228   \n",
+       "  15  0.427228 -0.113340  0.949348  0.316162 -1.385519  3.806739  0.564925   \n",
+       "  16  0.564925  2.057385  1.039775 -0.623176  0.099741  1.271971  2.049510   \n",
+       "  17  2.049510  1.595090 -0.234343  0.105804 -0.001625 -1.393216  2.522457   \n",
+       "  18  2.522457  1.332716 -1.437976  0.373610 -0.482371 -3.437311 -0.380589   \n",
+       "  19 -0.380589 -0.267075 -1.636537  0.157671 -0.924619 -1.520724 -0.699467   \n",
+       "  20 -0.699467 -1.956348  0.225975  0.697267 -0.382217  0.399963 -2.576038   \n",
+       "  21 -2.576038 -2.401017 -0.472728  1.891687 -0.868663  3.292571 -2.428426   \n",
+       "  22 -2.428426 -1.825708 -1.042407  0.917457 -0.006722  1.892131  1.007903   \n",
+       "  23  1.007903  1.154417 -0.453969 -1.185986  0.137176 -0.332798  2.932754   \n",
+       "  24  2.932754  3.449951  1.793620 -2.243633  1.146430 -2.298090  3.845612   \n",
+       "  25  3.845612  3.121728  1.032544 -2.541492  3.111695 -1.798627  2.321308   \n",
+       "  26  2.321308 -0.756534 -0.357808 -1.287982  1.814216 -0.636919 -2.883602   \n",
+       "  27 -2.883602 -3.265791 -1.845157  1.397658  0.416660  1.190803 -4.393371   \n",
+       "  28 -4.393371 -2.826694 -1.578862  3.578787  0.501153  2.248068 -3.939542   \n",
+       "  29 -3.939542 -1.409613  0.346436  2.447079 -0.946258  1.117609 -0.422044   \n",
+       "  30 -0.422044  0.222810  1.621238  1.425877 -2.560335 -1.419810  2.614954   \n",
+       "  31  2.614954  1.836742  1.332091 -1.861679 -2.765314 -2.983803  4.134722   \n",
+       "  32  4.134722  3.046882  2.237327 -3.980240 -2.292201 -0.492999  1.662077   \n",
+       "  33  1.662077  2.598044  0.132894 -2.901868  0.249111  0.241125 -0.993745   \n",
+       "  34 -0.993745  0.887032 -0.892237  1.191983  1.088214  0.235628 -2.845174   \n",
+       "  35 -2.845174 -0.927633  0.470763  3.835530 -0.176758 -0.121987 -2.109499   \n",
+       "  36 -2.109499 -2.032350  0.315970  3.252841  1.036818 -0.253389 -2.352635   \n",
+       "  37 -2.352635 -0.644517  0.361973  0.067051 -0.349566 -2.567000 -0.529544   \n",
+       "  38 -0.529544  1.353728 -1.670419 -1.575184  0.364356 -2.840914  1.395305   \n",
+       "  39  1.395305  1.299287 -2.035795 -2.657987 -0.053606 -1.478779  0.808270   \n",
+       "  40  0.808270  2.091232 -1.181800 -0.647351  1.051276  1.713514  0.294733   \n",
+       "  41  0.294733  0.581939 -0.147558  0.186756  2.093678  4.666600 -0.131687   \n",
+       "  42 -0.131687 -0.833201 -0.255809  2.630118  1.398818  1.763036 -1.816932   \n",
+       "  43 -1.816932 -0.874284  0.318485  1.853190 -1.187142  0.873712 -1.113044   \n",
+       "  44 -1.113044  0.054006  0.758793  0.122549 -2.150998 -3.457439 -0.600464   \n",
+       "  45 -0.600464  1.528695 -0.554282 -1.515371 -2.856742 -3.668877  0.732256   \n",
+       "  46  0.732256  3.040098 -0.347260 -1.878399 -0.434363 -2.546813  0.859703   \n",
+       "  47  0.859703 -0.814783 -0.166684 -1.453819  1.159809  1.287451  0.680245   \n",
+       "  48  0.680245 -2.801990  1.402478  0.601321 -0.101334  3.514397  2.521605   \n",
+       "  49  2.521605 -3.801704  1.284970  1.480576  0.663884  3.214898  2.803914   \n",
+       "  50  2.803914 -1.136448  1.477252  3.388175 -0.444768  1.636546  1.248333   \n",
+       "  51  1.248333  0.167580  1.505305  0.651578 -0.553188 -0.967182 -2.816378   \n",
+       "  52 -2.816378 -0.145367  0.819613  0.520284 -0.554975 -1.975603 -5.156425   \n",
+       "  53 -5.156425  0.429505 -0.421366 -2.099518 -0.313168 -2.777604 -2.130591   \n",
+       "  54 -2.130591  0.236751 -1.253015 -1.289499  0.616925 -1.787170  0.087386   \n",
+       "  55  0.087386 -1.632686  2.010301  1.088886  0.282552  0.358503  2.592892   \n",
+       "  56  2.592892 -2.050683  4.390912  0.876416 -0.545238  2.534935  1.805186   \n",
+       "  57  1.805186 -1.278657  3.442197  1.385136 -1.943744  2.998407 -0.263994   \n",
+       "  58 -0.263994 -2.200526 -0.199455  0.787950 -1.213753  0.455107 -0.220292   \n",
+       "  59 -0.220292 -0.291927 -4.861226  0.098120  0.519958 -1.228191 -0.541825   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   2.033950 -2.046513   -0.679731    1.135633    0.818384  \n",
+       "  3   0.141335 -3.409339   -2.187148    1.407804   -0.509551  \n",
+       "  4  -1.177802 -2.695117   -2.219436   -0.147177   -3.134879  \n",
+       "  5  -1.657310 -0.525838    0.606351    0.157475   -2.527644  \n",
+       "  6  -1.362393  1.800790    2.002042   -3.075572   -1.100843  \n",
+       "  7   2.133039  1.690947    3.034566   -1.833836    3.165127  \n",
+       "  8   3.706683  1.428262    0.454780   -0.092936    3.910391  \n",
+       "  9   3.375028 -0.431636   -0.868125    1.126580    1.738411  \n",
+       "  10 -0.433157 -0.825890   -1.502924    0.791846   -0.517542  \n",
+       "  11 -1.829422  0.054082    0.106613    0.290463   -0.789086  \n",
+       "  12 -2.871748  0.894493    0.744721   -2.113682   -1.130676  \n",
+       "  13 -2.711665  1.161757    2.031144   -2.870653    0.071517  \n",
+       "  14 -0.113340  0.949348    0.316162   -1.385519    3.806739  \n",
+       "  15  2.057385  1.039775   -0.623176    0.099741    1.271971  \n",
+       "  16  1.595090 -0.234343    0.105804   -0.001625   -1.393216  \n",
+       "  17  1.332716 -1.437976    0.373610   -0.482371   -3.437311  \n",
+       "  18 -0.267075 -1.636537    0.157671   -0.924619   -1.520724  \n",
+       "  19 -1.956348  0.225975    0.697267   -0.382217    0.399963  \n",
+       "  20 -2.401017 -0.472728    1.891687   -0.868663    3.292571  \n",
+       "  21 -1.825708 -1.042407    0.917457   -0.006722    1.892131  \n",
+       "  22  1.154417 -0.453969   -1.185986    0.137176   -0.332798  \n",
+       "  23  3.449951  1.793620   -2.243633    1.146430   -2.298090  \n",
+       "  24  3.121728  1.032544   -2.541492    3.111695   -1.798627  \n",
+       "  25 -0.756534 -0.357808   -1.287982    1.814216   -0.636919  \n",
+       "  26 -3.265791 -1.845157    1.397658    0.416660    1.190803  \n",
+       "  27 -2.826694 -1.578862    3.578787    0.501153    2.248068  \n",
+       "  28 -1.409613  0.346436    2.447079   -0.946258    1.117609  \n",
+       "  29  0.222810  1.621238    1.425877   -2.560335   -1.419810  \n",
+       "  30  1.836742  1.332091   -1.861679   -2.765314   -2.983803  \n",
+       "  31  3.046882  2.237327   -3.980240   -2.292201   -0.492999  \n",
+       "  32  2.598044  0.132894   -2.901868    0.249111    0.241125  \n",
+       "  33  0.887032 -0.892237    1.191983    1.088214    0.235628  \n",
+       "  34 -0.927633  0.470763    3.835530   -0.176758   -0.121987  \n",
+       "  35 -2.032350  0.315970    3.252841    1.036818   -0.253389  \n",
+       "  36 -0.644517  0.361973    0.067051   -0.349566   -2.567000  \n",
+       "  37  1.353728 -1.670419   -1.575184    0.364356   -2.840914  \n",
+       "  38  1.299287 -2.035795   -2.657987   -0.053606   -1.478779  \n",
+       "  39  2.091232 -1.181800   -0.647351    1.051276    1.713514  \n",
+       "  40  0.581939 -0.147558    0.186756    2.093678    4.666600  \n",
+       "  41 -0.833201 -0.255809    2.630118    1.398818    1.763036  \n",
+       "  42 -0.874284  0.318485    1.853190   -1.187142    0.873712  \n",
+       "  43  0.054006  0.758793    0.122549   -2.150998   -3.457439  \n",
+       "  44  1.528695 -0.554282   -1.515371   -2.856742   -3.668877  \n",
+       "  45  3.040098 -0.347260   -1.878399   -0.434363   -2.546813  \n",
+       "  46 -0.814783 -0.166684   -1.453819    1.159809    1.287451  \n",
+       "  47 -2.801990  1.402478    0.601321   -0.101334    3.514397  \n",
+       "  48 -3.801704  1.284970    1.480576    0.663884    3.214898  \n",
+       "  49 -1.136448  1.477252    3.388175   -0.444768    1.636546  \n",
+       "  50  0.167580  1.505305    0.651578   -0.553188   -0.967182  \n",
+       "  51 -0.145367  0.819613    0.520284   -0.554975   -1.975603  \n",
+       "  52  0.429505 -0.421366   -2.099518   -0.313168   -2.777604  \n",
+       "  53  0.236751 -1.253015   -1.289499    0.616925   -1.787170  \n",
+       "  54 -1.632686  2.010301    1.088886    0.282552    0.358503  \n",
+       "  55 -2.050683  4.390912    0.876416   -0.545238    2.534935  \n",
+       "  56 -1.278657  3.442197    1.385136   -1.943744    2.998407  \n",
+       "  57 -2.200526 -0.199455    0.787950   -1.213753    0.455107  \n",
+       "  58 -0.291927 -4.861226    0.098120    0.519958   -1.228191  \n",
+       "  59  1.120159 -3.811405    0.083991    0.808471   -2.597957  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -0.084820   \n",
+       "  3  -0.084820  1.586022  0.605605  0.266294 -0.383741  0.977382 -1.122647   \n",
+       "  4  -1.122647  0.854189  1.321422  0.966264 -0.580624  0.470157 -1.578504   \n",
+       "  5  -1.578504 -0.483778  0.127585  0.398470 -0.782551 -2.015103 -0.729908   \n",
+       "  6  -0.729908 -2.014713  0.300770 -2.396751 -1.133319 -0.706511 -1.124894   \n",
+       "  7  -1.124894 -1.497068 -1.017088 -2.272468 -0.411644 -0.838707  0.449314   \n",
+       "  8   0.449314  0.192741 -0.242315 -2.704465  0.274524 -0.582956  2.164719   \n",
+       "  9   2.164719  1.722286 -1.712750  1.064334  0.099301 -0.294971  1.759156   \n",
+       "  10  1.759156  3.350718 -0.407800  3.529570 -1.031592  0.673395  0.626004   \n",
+       "  11  0.626004  2.683280 -0.350502  2.684318 -1.599167  0.278267 -0.042787   \n",
+       "  12 -0.042787 -1.213914  1.346368  2.671296 -0.025971 -0.714944 -1.271391   \n",
+       "  13 -1.271391 -4.750429 -0.867737 -1.104370 -0.676145 -1.473033 -1.898141   \n",
+       "  14 -1.898141 -4.113444  0.039146 -1.824884 -1.025157 -0.990827 -2.470745   \n",
+       "  15 -2.470745  0.155865 -1.314758 -3.929785 -1.143205  1.747313 -1.625384   \n",
+       "  16 -1.625384  3.738643  0.782175 -1.848726  0.185037  1.123780 -0.992252   \n",
+       "  17 -0.992252  3.576748  2.457772 -0.459695  0.942031  0.144657  2.121746   \n",
+       "  18  2.121746  0.742074  1.185347  0.500641  1.455157 -1.719053  1.967729   \n",
+       "  19  1.967729 -1.445566 -0.537791  1.018935  0.172908 -1.774566  0.796749   \n",
+       "  20  0.796749 -1.533939 -1.746528 -0.303217 -0.345989 -1.241447 -0.824379   \n",
+       "  21 -0.824379  1.584073  0.166602 -0.724302 -1.221272  1.843296 -2.490751   \n",
+       "  22 -2.490751  1.548178  2.207851 -0.213150 -1.990179  3.573810 -3.447958   \n",
+       "  23 -3.447958  0.248634  1.611866 -0.168619  0.018314  2.796095 -2.376721   \n",
+       "  24 -2.376721 -2.905335 -1.394413 -1.649029  1.104672  0.973432  0.241673   \n",
+       "  25  0.241673 -1.976924 -3.902723 -0.958416  0.368651 -2.088861  2.396964   \n",
+       "  26  2.396964 -1.694297 -2.846993 -2.840523 -1.596794 -1.148152  2.611684   \n",
+       "  27  2.611684  1.034920  0.438464  0.371758 -3.988250 -1.971076  2.027275   \n",
+       "  28  2.027275  2.689096  2.246530  0.178855 -2.712694  0.433516  0.229773   \n",
+       "  29  0.229773  1.966403 -0.120390  0.382189  0.457964  1.082761 -1.746948   \n",
+       "  30 -1.746948 -0.836597 -1.355823  0.405594  2.401371  0.852301 -0.266894   \n",
+       "  31 -0.266894 -2.005864 -1.616316 -0.369139  3.680096  0.070322 -0.451051   \n",
+       "  32 -0.451051 -2.266540 -1.722786  0.706229  1.626690 -0.174371  2.229006   \n",
+       "  33  2.229006 -0.515268  0.790078  2.419978  1.215247 -0.204551 -0.029719   \n",
+       "  34 -0.029719  0.783265  2.216207  1.879481  1.013456 -1.151288 -0.665298   \n",
+       "  35 -0.665298  0.895737  1.610002 -1.214296  0.146467  0.495561 -1.374256   \n",
+       "  36 -1.374256  0.753339  0.232446 -3.231683 -1.846041  1.022112 -1.045696   \n",
+       "  37 -1.045696  0.435387 -1.377666 -3.978548 -1.780212  0.098675 -0.594690   \n",
+       "  38 -0.594690 -0.019753 -2.145913 -1.900961 -1.285559  0.379561  0.350953   \n",
+       "  39  0.350953 -1.029978 -1.434859  1.851050 -0.424611 -0.144572  0.887719   \n",
+       "  40  0.887719 -1.158975  1.762081  4.906418  1.199193 -0.538814  1.673921   \n",
+       "  41  1.673921 -1.027703  2.291069  4.868507  1.431134 -1.622871 -0.536054   \n",
+       "  42 -0.536054 -0.504327  1.004000 -0.251480  0.086518 -0.495568  0.852497   \n",
+       "  43  0.852497  0.492729 -0.887196 -4.646665 -0.738009  0.817979  0.895605   \n",
+       "  44  0.895605  1.596407 -0.625148 -4.603428 -0.133845  1.215867  0.726852   \n",
+       "  45  0.726852  0.332794 -0.353144 -0.393604 -0.460849  1.779608  0.279485   \n",
+       "  46  0.279485  0.458411 -0.953418  3.087747  1.630595  0.266429 -0.806983   \n",
+       "  47 -0.806983 -0.536016  0.454469  3.240582 -0.876753 -1.649949 -1.204320   \n",
+       "  48 -1.204320 -0.657941 -0.412124  2.182656 -0.572200 -0.251045  0.241529   \n",
+       "  49  0.241529 -0.792420 -0.091084  2.632091 -0.393739  0.270266  0.292226   \n",
+       "  50  0.292226 -0.144824 -0.044069  0.673039 -1.200196  1.787417  2.045153   \n",
+       "  51  2.045153 -0.286386 -0.663354  0.359461 -0.707176  1.923379  0.781152   \n",
+       "  52  0.781152 -0.533652  0.694637  0.039517  0.496595 -0.380660 -0.937949   \n",
+       "  53 -0.937949 -1.331851  0.189305  0.633462  2.311603 -2.243716 -0.222445   \n",
+       "  54 -0.222445 -1.170985  0.648793  2.253939  1.398437 -2.832872  0.263281   \n",
+       "  55  0.263281  0.621854  0.557198  2.334345 -0.234236 -1.208194 -0.548493   \n",
+       "  56 -0.548493  0.812788 -0.048157  0.940038 -2.450450  0.570799 -0.892898   \n",
+       "  57 -0.892898  1.274900 -0.738959 -0.447590 -3.114240  2.639979 -2.377209   \n",
+       "  58 -2.377209  0.338150 -0.731722 -1.035184 -2.863573  0.719601 -2.374284   \n",
+       "  59 -2.374284  0.837755 -1.402413 -0.341035 -1.203239  0.012047 -0.610707   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.586022  0.605605    0.266294   -0.383741    0.977382  \n",
+       "  3   0.854189  1.321422    0.966264   -0.580624    0.470157  \n",
+       "  4  -0.483778  0.127585    0.398470   -0.782551   -2.015103  \n",
+       "  5  -2.014713  0.300770   -2.396751   -1.133319   -0.706511  \n",
+       "  6  -1.497068 -1.017088   -2.272468   -0.411644   -0.838707  \n",
+       "  7   0.192741 -0.242315   -2.704465    0.274524   -0.582956  \n",
+       "  8   1.722286 -1.712750    1.064334    0.099301   -0.294971  \n",
+       "  9   3.350718 -0.407800    3.529570   -1.031592    0.673395  \n",
+       "  10  2.683280 -0.350502    2.684318   -1.599167    0.278267  \n",
+       "  11 -1.213914  1.346368    2.671296   -0.025971   -0.714944  \n",
+       "  12 -4.750429 -0.867737   -1.104370   -0.676145   -1.473033  \n",
+       "  13 -4.113444  0.039146   -1.824884   -1.025157   -0.990827  \n",
+       "  14  0.155865 -1.314758   -3.929785   -1.143205    1.747313  \n",
+       "  15  3.738643  0.782175   -1.848726    0.185037    1.123780  \n",
+       "  16  3.576748  2.457772   -0.459695    0.942031    0.144657  \n",
+       "  17  0.742074  1.185347    0.500641    1.455157   -1.719053  \n",
+       "  18 -1.445566 -0.537791    1.018935    0.172908   -1.774566  \n",
+       "  19 -1.533939 -1.746528   -0.303217   -0.345989   -1.241447  \n",
+       "  20  1.584073  0.166602   -0.724302   -1.221272    1.843296  \n",
+       "  21  1.548178  2.207851   -0.213150   -1.990179    3.573810  \n",
+       "  22  0.248634  1.611866   -0.168619    0.018314    2.796095  \n",
+       "  23 -2.905335 -1.394413   -1.649029    1.104672    0.973432  \n",
+       "  24 -1.976924 -3.902723   -0.958416    0.368651   -2.088861  \n",
+       "  25 -1.694297 -2.846993   -2.840523   -1.596794   -1.148152  \n",
+       "  26  1.034920  0.438464    0.371758   -3.988250   -1.971076  \n",
+       "  27  2.689096  2.246530    0.178855   -2.712694    0.433516  \n",
+       "  28  1.966403 -0.120390    0.382189    0.457964    1.082761  \n",
+       "  29 -0.836597 -1.355823    0.405594    2.401371    0.852301  \n",
+       "  30 -2.005864 -1.616316   -0.369139    3.680096    0.070322  \n",
+       "  31 -2.266540 -1.722786    0.706229    1.626690   -0.174371  \n",
+       "  32 -0.515268  0.790078    2.419978    1.215247   -0.204551  \n",
+       "  33  0.783265  2.216207    1.879481    1.013456   -1.151288  \n",
+       "  34  0.895737  1.610002   -1.214296    0.146467    0.495561  \n",
+       "  35  0.753339  0.232446   -3.231683   -1.846041    1.022112  \n",
+       "  36  0.435387 -1.377666   -3.978548   -1.780212    0.098675  \n",
+       "  37 -0.019753 -2.145913   -1.900961   -1.285559    0.379561  \n",
+       "  38 -1.029978 -1.434859    1.851050   -0.424611   -0.144572  \n",
+       "  39 -1.158975  1.762081    4.906418    1.199193   -0.538814  \n",
+       "  40 -1.027703  2.291069    4.868507    1.431134   -1.622871  \n",
+       "  41 -0.504327  1.004000   -0.251480    0.086518   -0.495568  \n",
+       "  42  0.492729 -0.887196   -4.646665   -0.738009    0.817979  \n",
+       "  43  1.596407 -0.625148   -4.603428   -0.133845    1.215867  \n",
+       "  44  0.332794 -0.353144   -0.393604   -0.460849    1.779608  \n",
+       "  45  0.458411 -0.953418    3.087747    1.630595    0.266429  \n",
+       "  46 -0.536016  0.454469    3.240582   -0.876753   -1.649949  \n",
+       "  47 -0.657941 -0.412124    2.182656   -0.572200   -0.251045  \n",
+       "  48 -0.792420 -0.091084    2.632091   -0.393739    0.270266  \n",
+       "  49 -0.144824 -0.044069    0.673039   -1.200196    1.787417  \n",
+       "  50 -0.286386 -0.663354    0.359461   -0.707176    1.923379  \n",
+       "  51 -0.533652  0.694637    0.039517    0.496595   -0.380660  \n",
+       "  52 -1.331851  0.189305    0.633462    2.311603   -2.243716  \n",
+       "  53 -1.170985  0.648793    2.253939    1.398437   -2.832872  \n",
+       "  54  0.621854  0.557198    2.334345   -0.234236   -1.208194  \n",
+       "  55  0.812788 -0.048157    0.940038   -2.450450    0.570799  \n",
+       "  56  1.274900 -0.738959   -0.447590   -3.114240    2.639979  \n",
+       "  57  0.338150 -0.731722   -1.035184   -2.863573    0.719601  \n",
+       "  58  0.837755 -1.402413   -0.341035   -1.203239    0.012047  \n",
+       "  59  1.371179 -0.034546    0.575024    0.063405   -1.284970  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.179776   \n",
+       "  3   0.179776  0.705151 -0.518827  0.879035 -0.189788  0.927866 -1.492325   \n",
+       "  4  -1.492325 -2.577323 -1.892228 -0.416484  0.421171  0.736460 -2.964365   \n",
+       "  5  -2.964365 -3.081388 -2.412075 -1.262453 -1.037205 -0.948056 -1.431617   \n",
+       "  6  -1.431617 -2.452062  1.375724 -1.434674  0.221634 -1.852556 -0.848849   \n",
+       "  7  -0.848849  0.314977  1.880411  0.383738  0.311149 -2.325431  0.870876   \n",
+       "  8   0.870876  2.202430  1.992699  2.869082 -0.375432  1.082437  1.275354   \n",
+       "  9   1.275354  3.156677  2.062388  3.148418  1.483395  2.220596 -0.532490   \n",
+       "  10 -0.532490  2.256572 -0.072261  0.137735  0.140278  2.676524  0.270377   \n",
+       "  11  0.270377  0.263100 -0.652781 -2.065905 -2.178689  0.815830 -0.061954   \n",
+       "  12 -0.061954 -1.930618 -1.051799 -3.354502 -1.086963 -1.754536 -1.444475   \n",
+       "  13 -1.444475 -1.621953 -0.529378 -1.036039 -0.093420 -2.514132 -1.293760   \n",
+       "  14 -1.293760 -2.289644  0.523625  2.065559 -3.011267 -2.211359  2.165571   \n",
+       "  15  2.165571 -1.484126  1.274895  4.366547 -3.190986  0.150075  1.510455   \n",
+       "  16  1.510455 -0.593127  1.651679  3.927912 -1.378541  1.753736  0.231524   \n",
+       "  17  0.231524  1.699171 -0.251820  1.605640 -0.340194  1.998477 -0.924113   \n",
+       "  18 -0.924113  2.766756 -1.374122  0.295110  1.828252  0.776134 -0.270038   \n",
+       "  19 -0.270038  0.852590 -1.189807 -2.208274  4.512939 -0.743966 -0.861215   \n",
+       "  20 -0.861215 -1.201418 -1.853632 -1.228120  3.014088 -2.107879 -0.348218   \n",
+       "  21 -0.348218 -2.495138  0.655888  0.780979  1.463111 -2.676561 -0.183496   \n",
+       "  22 -0.183496 -1.759072  1.622555  1.765515 -1.388207 -1.502780 -1.040556   \n",
+       "  23 -1.040556  1.193348 -0.410972  2.868149 -3.159439 -0.539446 -0.128326   \n",
+       "  24 -0.128326  1.805969 -1.103303  0.318022 -3.302353 -0.167921 -0.863061   \n",
+       "  25 -0.863061  2.568277 -1.104261 -1.561067 -1.338262  1.281970 -0.789417   \n",
+       "  26 -0.789417  1.842573 -0.369911 -1.696355  1.228386  1.514810 -1.295600   \n",
+       "  27 -1.295600 -0.357279  1.856570 -1.501153  4.189601 -0.342745  0.300928   \n",
+       "  28  0.300928 -0.475003  0.621339  0.667416  4.823011 -2.507629  0.703689   \n",
+       "  29  0.703689 -1.505406  1.063988  2.201674  0.643111 -2.155635 -0.270335   \n",
+       "  30 -0.270335 -0.433709  0.649252  4.665453 -4.279853 -1.259942  0.622664   \n",
+       "  31  0.622664  0.083510 -0.829218  0.613535 -4.141262 -1.247436  1.603203   \n",
+       "  32  1.603203 -0.560951  0.364732 -2.112378 -3.336917 -0.079714  1.753701   \n",
+       "  33  1.753701 -2.109242  0.069809 -3.398111 -0.923915 -0.005241 -0.869920   \n",
+       "  34 -0.869920 -2.243175 -0.355020 -1.514303  1.275736  0.679682 -2.802259   \n",
+       "  35 -2.802259 -0.996961 -0.938299  1.358901  3.117145 -0.305145 -2.293090   \n",
+       "  36 -2.293090  2.028631 -1.337559  2.978076  1.220021  0.077404 -1.040522   \n",
+       "  37 -1.040522  1.492070  0.250023  2.993742  0.287929  1.269523  0.443669   \n",
+       "  38  0.443669  4.362485 -1.751330  0.814180 -2.942071  2.393946  1.253705   \n",
+       "  39  1.253705  2.279419 -1.814336 -2.087991 -3.584247  0.851234  0.481516   \n",
+       "  40  0.481516 -2.392975  1.716857 -3.883288 -1.219103 -0.087862 -0.454231   \n",
+       "  41 -0.454231 -3.679352  2.361437  0.085885  1.371191  1.252936 -0.068389   \n",
+       "  42 -0.068389 -3.876423  2.320082  1.880159  1.580066 -0.356909  2.420130   \n",
+       "  43  2.420130 -2.384647 -1.692760  2.633264  2.330987 -0.123049  1.615196   \n",
+       "  44  1.615196 -0.011118 -1.785611  2.122304 -1.065246 -0.099240  0.051880   \n",
+       "  45  0.051880  2.997491 -1.464458 -0.685756 -2.074299  0.128626 -2.043103   \n",
+       "  46 -2.043103  4.358987 -0.630069 -1.483972 -3.086118  0.295065 -2.508570   \n",
+       "  47 -2.508570  3.640037  1.462057 -2.941436 -0.987880  0.039067 -1.862464   \n",
+       "  48 -1.862464  2.559443  3.316397 -1.665328 -0.636959 -1.434608  1.441738   \n",
+       "  49  1.441738 -1.764077  0.564463  2.528719  1.154578  0.767212  2.900315   \n",
+       "  50  2.900315 -4.244167 -0.084727  4.279994  1.498925  0.749733  1.425515   \n",
+       "  51  1.425515 -4.479165 -0.090961  1.415713  1.647196 -0.032505 -0.835461   \n",
+       "  52 -0.835461  0.062701 -0.808363  0.230143  0.801875  0.133362 -2.316843   \n",
+       "  53 -2.316843  2.431321 -0.166618 -2.779320 -0.382213  0.080216 -2.058988   \n",
+       "  54 -2.058988  3.216666 -1.638899 -2.635943  0.111638  0.578590 -0.056214   \n",
+       "  55 -0.056214  2.129468 -3.641569 -2.598537 -0.769324 -0.773465  1.942006   \n",
+       "  56  1.942006 -1.408140 -2.743891 -0.438017 -2.431456 -0.673214  1.828530   \n",
+       "  57  1.828530 -4.219739 -0.813245  1.595086 -1.792187 -0.909410  0.959731   \n",
+       "  58  0.959731 -2.757245  0.018975  1.184817 -0.393676 -0.393984 -0.462973   \n",
+       "  59 -0.462973 -0.487910  0.186785 -0.779990  1.666252  1.025579 -0.234760   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.705151 -0.518827    0.879035   -0.189788    0.927866  \n",
+       "  3  -2.577323 -1.892228   -0.416484    0.421171    0.736460  \n",
+       "  4  -3.081388 -2.412075   -1.262453   -1.037205   -0.948056  \n",
+       "  5  -2.452062  1.375724   -1.434674    0.221634   -1.852556  \n",
+       "  6   0.314977  1.880411    0.383738    0.311149   -2.325431  \n",
+       "  7   2.202430  1.992699    2.869082   -0.375432    1.082437  \n",
+       "  8   3.156677  2.062388    3.148418    1.483395    2.220596  \n",
+       "  9   2.256572 -0.072261    0.137735    0.140278    2.676524  \n",
+       "  10  0.263100 -0.652781   -2.065905   -2.178689    0.815830  \n",
+       "  11 -1.930618 -1.051799   -3.354502   -1.086963   -1.754536  \n",
+       "  12 -1.621953 -0.529378   -1.036039   -0.093420   -2.514132  \n",
+       "  13 -2.289644  0.523625    2.065559   -3.011267   -2.211359  \n",
+       "  14 -1.484126  1.274895    4.366547   -3.190986    0.150075  \n",
+       "  15 -0.593127  1.651679    3.927912   -1.378541    1.753736  \n",
+       "  16  1.699171 -0.251820    1.605640   -0.340194    1.998477  \n",
+       "  17  2.766756 -1.374122    0.295110    1.828252    0.776134  \n",
+       "  18  0.852590 -1.189807   -2.208274    4.512939   -0.743966  \n",
+       "  19 -1.201418 -1.853632   -1.228120    3.014088   -2.107879  \n",
+       "  20 -2.495138  0.655888    0.780979    1.463111   -2.676561  \n",
+       "  21 -1.759072  1.622555    1.765515   -1.388207   -1.502780  \n",
+       "  22  1.193348 -0.410972    2.868149   -3.159439   -0.539446  \n",
+       "  23  1.805969 -1.103303    0.318022   -3.302353   -0.167921  \n",
+       "  24  2.568277 -1.104261   -1.561067   -1.338262    1.281970  \n",
+       "  25  1.842573 -0.369911   -1.696355    1.228386    1.514810  \n",
+       "  26 -0.357279  1.856570   -1.501153    4.189601   -0.342745  \n",
+       "  27 -0.475003  0.621339    0.667416    4.823011   -2.507629  \n",
+       "  28 -1.505406  1.063988    2.201674    0.643111   -2.155635  \n",
+       "  29 -0.433709  0.649252    4.665453   -4.279853   -1.259942  \n",
+       "  30  0.083510 -0.829218    0.613535   -4.141262   -1.247436  \n",
+       "  31 -0.560951  0.364732   -2.112378   -3.336917   -0.079714  \n",
+       "  32 -2.109242  0.069809   -3.398111   -0.923915   -0.005241  \n",
+       "  33 -2.243175 -0.355020   -1.514303    1.275736    0.679682  \n",
+       "  34 -0.996961 -0.938299    1.358901    3.117145   -0.305145  \n",
+       "  35  2.028631 -1.337559    2.978076    1.220021    0.077404  \n",
+       "  36  1.492070  0.250023    2.993742    0.287929    1.269523  \n",
+       "  37  4.362485 -1.751330    0.814180   -2.942071    2.393946  \n",
+       "  38  2.279419 -1.814336   -2.087991   -3.584247    0.851234  \n",
+       "  39 -2.392975  1.716857   -3.883288   -1.219103   -0.087862  \n",
+       "  40 -3.679352  2.361437    0.085885    1.371191    1.252936  \n",
+       "  41 -3.876423  2.320082    1.880159    1.580066   -0.356909  \n",
+       "  42 -2.384647 -1.692760    2.633264    2.330987   -0.123049  \n",
+       "  43 -0.011118 -1.785611    2.122304   -1.065246   -0.099240  \n",
+       "  44  2.997491 -1.464458   -0.685756   -2.074299    0.128626  \n",
+       "  45  4.358987 -0.630069   -1.483972   -3.086118    0.295065  \n",
+       "  46  3.640037  1.462057   -2.941436   -0.987880    0.039067  \n",
+       "  47  2.559443  3.316397   -1.665328   -0.636959   -1.434608  \n",
+       "  48 -1.764077  0.564463    2.528719    1.154578    0.767212  \n",
+       "  49 -4.244167 -0.084727    4.279994    1.498925    0.749733  \n",
+       "  50 -4.479165 -0.090961    1.415713    1.647196   -0.032505  \n",
+       "  51  0.062701 -0.808363    0.230143    0.801875    0.133362  \n",
+       "  52  2.431321 -0.166618   -2.779320   -0.382213    0.080216  \n",
+       "  53  3.216666 -1.638899   -2.635943    0.111638    0.578590  \n",
+       "  54  2.129468 -3.641569   -2.598537   -0.769324   -0.773465  \n",
+       "  55 -1.408140 -2.743891   -0.438017   -2.431456   -0.673214  \n",
+       "  56 -4.219739 -0.813245    1.595086   -1.792187   -0.909410  \n",
+       "  57 -2.757245  0.018975    1.184817   -0.393676   -0.393984  \n",
+       "  58 -0.487910  0.186785   -0.779990    1.666252    1.025579  \n",
+       "  59  2.989016  0.528748   -1.182286    1.231493    1.072577  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.424350   \n",
+       "  3   0.424350  0.956088 -0.761575 -0.939224  1.296796  2.634255 -1.083348   \n",
+       "  4  -1.083348 -1.081354 -1.531318 -1.628442 -0.554422  2.196957  0.407340   \n",
+       "  5   0.407340 -2.145322 -0.594996 -2.148434 -1.370606  0.320765  1.440382   \n",
+       "  6   1.440382 -1.661126  0.545938 -2.712352 -1.572570 -0.540687  1.781789   \n",
+       "  7   1.781789 -0.507846  1.302075  0.767169 -1.682173 -2.007425  0.201612   \n",
+       "  8   0.201612  2.106086  0.282461  3.011740 -0.484688 -0.652787 -1.666407   \n",
+       "  9  -1.666407  1.275642  0.670996  1.466740 -0.048927  0.393168 -0.819827   \n",
+       "  10 -0.819827  3.513093  1.939247 -0.452607  1.669772  1.324490  1.455546   \n",
+       "  11  1.455546  2.055501 -0.189111 -0.690966  0.570646 -0.768148  1.896357   \n",
+       "  12  1.896357  0.133982 -0.421028 -0.499420  0.019653 -1.914447  1.333868   \n",
+       "  13  1.333868 -2.160803 -3.237057  1.299525 -0.392534 -0.424937 -1.412268   \n",
+       "  14 -1.412268 -1.978902 -1.499785 -0.337831 -0.842922  1.116999 -1.017048   \n",
+       "  15 -1.017048 -0.312841  0.883222 -0.942314 -0.959991  0.870738 -1.165632   \n",
+       "  16 -1.165632  3.278483  4.027276  0.149471  0.412576 -0.574434 -0.949069   \n",
+       "  17 -0.949069  3.096621  3.030893  1.594069  1.426958 -0.734849  0.471157   \n",
+       "  18  0.471157 -0.044960  1.696168  0.672319  1.355167  0.269524  3.047377   \n",
+       "  19  3.047377 -4.332984 -3.369904  0.684087  0.926331  3.178263  2.042673   \n",
+       "  20  2.042673 -4.570997 -5.733741  2.555801  0.702299  2.723559  1.364373   \n",
+       "  21  1.364373 -0.544612 -4.217644  0.595081 -1.365641  0.362090 -1.012501   \n",
+       "  22 -1.012501  1.854695  1.490991 -1.483267 -1.656964 -2.400481 -1.179861   \n",
+       "  23 -1.179861  2.676444  2.071601 -2.983219 -0.518086 -3.225319 -1.557369   \n",
+       "  24 -1.557369  2.474025  2.018259 -2.467946  1.980977 -0.906325 -0.364793   \n",
+       "  25 -0.364793 -0.642392  0.273097  0.547766  1.944582  0.710061  1.826441   \n",
+       "  26  1.826441 -1.471136 -1.419001  2.600179  0.711227  1.299322  1.690758   \n",
+       "  27  1.690758 -1.889723 -0.225101  2.523173 -1.692281 -0.911191  1.541700   \n",
+       "  28  1.541700  0.920057  0.273752  1.338413 -2.435083 -0.720160  0.622175   \n",
+       "  29  0.622175  2.040036  2.047272 -0.741664 -1.852610  0.638658  0.490669   \n",
+       "  30  0.490669  1.717528  1.512629 -2.651486 -0.608257  2.281847 -0.558228   \n",
+       "  31 -0.558228 -0.590616  0.206598 -2.246473  1.470030  3.110706  0.191209   \n",
+       "  32  0.191209 -3.721106 -0.626483  1.430352  1.945858  0.671445 -1.567285   \n",
+       "  33 -1.567285 -5.069285 -0.178183  3.630703  0.495705 -1.572048 -1.658615   \n",
+       "  34 -1.658615 -4.107740  0.346364  2.451009 -1.554815 -2.304405 -0.924014   \n",
+       "  35 -0.924014  0.579072  0.660221  1.675970 -0.529761 -2.555140  0.178140   \n",
+       "  36  0.178140  5.515248  0.954126 -0.443835 -0.102765  1.250488  2.215245   \n",
+       "  37  2.215245  4.968142  0.275553 -1.476863  0.164848  0.920084  2.170515   \n",
+       "  38  2.170515  1.892562  1.039423 -1.402640  0.014443  1.029306  2.730353   \n",
+       "  39  2.730353 -2.249652  1.118946  0.861700 -0.862847  0.669090  1.789601   \n",
+       "  40  1.789601 -4.077954  1.153532  4.165547 -1.963938 -1.666896  0.574793   \n",
+       "  41  0.574793 -2.807941  0.212396  2.931046 -2.209207 -1.558250 -1.821812   \n",
+       "  42 -1.821812  1.198386 -0.678525  0.855782  0.684654 -0.672631 -1.899470   \n",
+       "  43 -1.899470  1.479507 -0.426583 -3.638591  3.205880  0.397426 -0.727435   \n",
+       "  44 -0.727435  3.092997  0.456784 -3.341977  2.586760 -0.248305  1.224512   \n",
+       "  45  1.224512  1.707999 -0.736762 -0.715851 -0.066907 -0.186809  3.516577   \n",
+       "  46  3.516577  0.886342 -0.235142  1.780781 -1.331538 -1.059232  2.564213   \n",
+       "  47  2.564213 -0.616261  0.295170  3.678348 -2.565536 -2.301305  1.075307   \n",
+       "  48  1.075307  0.558052  1.201453  2.598913 -1.468275 -1.211257 -2.650328   \n",
+       "  49 -2.650328 -1.040570  1.286266 -0.721651  0.801336  1.293461 -4.197132   \n",
+       "  50 -4.197132 -0.724733  0.869106 -3.227539  0.545627  1.404740 -0.685578   \n",
+       "  51 -0.685578  0.050018  0.502529 -4.208611  0.771799  2.316312  0.318813   \n",
+       "  52  0.318813  0.146925 -1.549535 -1.361181 -0.395816  0.452552  2.003145   \n",
+       "  53  2.003145 -0.077737 -2.868182  0.955887 -1.866289  0.040094  1.018325   \n",
+       "  54  1.018325 -0.469186 -1.981132  2.340997 -0.189379 -0.703125  1.152451   \n",
+       "  55  1.152451 -1.202034  0.449539  2.615214 -0.595460 -0.892483 -1.351545   \n",
+       "  56 -1.351545 -2.214832  1.056101  2.154469  0.386743  0.440469 -2.042848   \n",
+       "  57 -2.042848  0.157953  1.646505 -0.245354  1.050200  0.443469 -0.844486   \n",
+       "  58 -0.844486  1.254288  1.500325 -2.938544  0.151667  1.281105 -0.094579   \n",
+       "  59 -0.094579 -1.178973 -0.467336 -2.256584 -1.187843  0.893389  3.262865   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.956088 -0.761575   -0.939224    1.296796    2.634255  \n",
+       "  3  -1.081354 -1.531318   -1.628442   -0.554422    2.196957  \n",
+       "  4  -2.145322 -0.594996   -2.148434   -1.370606    0.320765  \n",
+       "  5  -1.661126  0.545938   -2.712352   -1.572570   -0.540687  \n",
+       "  6  -0.507846  1.302075    0.767169   -1.682173   -2.007425  \n",
+       "  7   2.106086  0.282461    3.011740   -0.484688   -0.652787  \n",
+       "  8   1.275642  0.670996    1.466740   -0.048927    0.393168  \n",
+       "  9   3.513093  1.939247   -0.452607    1.669772    1.324490  \n",
+       "  10  2.055501 -0.189111   -0.690966    0.570646   -0.768148  \n",
+       "  11  0.133982 -0.421028   -0.499420    0.019653   -1.914447  \n",
+       "  12 -2.160803 -3.237057    1.299525   -0.392534   -0.424937  \n",
+       "  13 -1.978902 -1.499785   -0.337831   -0.842922    1.116999  \n",
+       "  14 -0.312841  0.883222   -0.942314   -0.959991    0.870738  \n",
+       "  15  3.278483  4.027276    0.149471    0.412576   -0.574434  \n",
+       "  16  3.096621  3.030893    1.594069    1.426958   -0.734849  \n",
+       "  17 -0.044960  1.696168    0.672319    1.355167    0.269524  \n",
+       "  18 -4.332984 -3.369904    0.684087    0.926331    3.178263  \n",
+       "  19 -4.570997 -5.733741    2.555801    0.702299    2.723559  \n",
+       "  20 -0.544612 -4.217644    0.595081   -1.365641    0.362090  \n",
+       "  21  1.854695  1.490991   -1.483267   -1.656964   -2.400481  \n",
+       "  22  2.676444  2.071601   -2.983219   -0.518086   -3.225319  \n",
+       "  23  2.474025  2.018259   -2.467946    1.980977   -0.906325  \n",
+       "  24 -0.642392  0.273097    0.547766    1.944582    0.710061  \n",
+       "  25 -1.471136 -1.419001    2.600179    0.711227    1.299322  \n",
+       "  26 -1.889723 -0.225101    2.523173   -1.692281   -0.911191  \n",
+       "  27  0.920057  0.273752    1.338413   -2.435083   -0.720160  \n",
+       "  28  2.040036  2.047272   -0.741664   -1.852610    0.638658  \n",
+       "  29  1.717528  1.512629   -2.651486   -0.608257    2.281847  \n",
+       "  30 -0.590616  0.206598   -2.246473    1.470030    3.110706  \n",
+       "  31 -3.721106 -0.626483    1.430352    1.945858    0.671445  \n",
+       "  32 -5.069285 -0.178183    3.630703    0.495705   -1.572048  \n",
+       "  33 -4.107740  0.346364    2.451009   -1.554815   -2.304405  \n",
+       "  34  0.579072  0.660221    1.675970   -0.529761   -2.555140  \n",
+       "  35  5.515248  0.954126   -0.443835   -0.102765    1.250488  \n",
+       "  36  4.968142  0.275553   -1.476863    0.164848    0.920084  \n",
+       "  37  1.892562  1.039423   -1.402640    0.014443    1.029306  \n",
+       "  38 -2.249652  1.118946    0.861700   -0.862847    0.669090  \n",
+       "  39 -4.077954  1.153532    4.165547   -1.963938   -1.666896  \n",
+       "  40 -2.807941  0.212396    2.931046   -2.209207   -1.558250  \n",
+       "  41  1.198386 -0.678525    0.855782    0.684654   -0.672631  \n",
+       "  42  1.479507 -0.426583   -3.638591    3.205880    0.397426  \n",
+       "  43  3.092997  0.456784   -3.341977    2.586760   -0.248305  \n",
+       "  44  1.707999 -0.736762   -0.715851   -0.066907   -0.186809  \n",
+       "  45  0.886342 -0.235142    1.780781   -1.331538   -1.059232  \n",
+       "  46 -0.616261  0.295170    3.678348   -2.565536   -2.301305  \n",
+       "  47  0.558052  1.201453    2.598913   -1.468275   -1.211257  \n",
+       "  48 -1.040570  1.286266   -0.721651    0.801336    1.293461  \n",
+       "  49 -0.724733  0.869106   -3.227539    0.545627    1.404740  \n",
+       "  50  0.050018  0.502529   -4.208611    0.771799    2.316312  \n",
+       "  51  0.146925 -1.549535   -1.361181   -0.395816    0.452552  \n",
+       "  52 -0.077737 -2.868182    0.955887   -1.866289    0.040094  \n",
+       "  53 -0.469186 -1.981132    2.340997   -0.189379   -0.703125  \n",
+       "  54 -1.202034  0.449539    2.615214   -0.595460   -0.892483  \n",
+       "  55 -2.214832  1.056101    2.154469    0.386743    0.440469  \n",
+       "  56  0.157953  1.646505   -0.245354    1.050200    0.443469  \n",
+       "  57  1.254288  1.500325   -2.938544    0.151667    1.281105  \n",
+       "  58 -1.178973 -0.467336   -2.256584   -1.187843    0.893389  \n",
+       "  59 -0.998738 -2.225457   -0.270655   -0.335106    1.169663  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -0.316107   \n",
+       "  3  -0.316107  1.214341  3.839702  0.245023  0.483819  1.285498 -1.334948   \n",
+       "  4  -1.334948  0.598287  1.663164  0.043404  0.130488  1.091571 -2.463761   \n",
+       "  5  -2.463761  0.301568  0.743760 -2.015148 -0.178018  0.644699 -1.706010   \n",
+       "  6  -1.706010 -1.616814 -3.295883 -0.456191  1.605155 -0.197745 -1.100025   \n",
+       "  7  -1.100025 -2.492777 -2.406323 -1.511529  0.876954  0.150597  0.894835   \n",
+       "  8   0.894835 -1.127580 -1.153697  2.315525  1.058645 -0.954685  1.995743   \n",
+       "  9   1.995743  1.899979  1.327827  2.386708  0.558307 -1.766021  1.077999   \n",
+       "  10  1.077999  3.704464  2.529162  2.696406  0.136733 -0.880065 -0.167353   \n",
+       "  11 -0.167353  4.324939  1.544024  0.291348 -0.611448  1.213934 -1.374161   \n",
+       "  12 -1.374161  0.431289 -1.111183 -2.266551 -1.426928  1.074038  0.468733   \n",
+       "  13  0.468733 -1.115060 -1.956287 -4.260822 -1.267486  2.016760  0.454055   \n",
+       "  14  0.454055 -3.387199 -1.778889 -2.170282  0.081891  0.606850 -1.523718   \n",
+       "  15 -1.523718 -1.209269 -0.308705 -0.709170  2.007109 -1.389624 -3.289789   \n",
+       "  16 -3.289789  1.130077  0.808776  1.994932  2.902635 -1.180499 -3.441924   \n",
+       "  17 -3.441924  2.938353  1.890290  2.780191  2.056846  1.142419  0.397279   \n",
+       "  18  0.397279  1.913974  0.435311  1.193295 -0.688376  1.777939  2.265060   \n",
+       "  19  2.265060  0.609295  1.108161 -0.807674 -3.457965  1.087383  0.952361   \n",
+       "  20  0.952361 -1.495966  0.184042 -1.477737 -3.966989 -0.412521  1.123536   \n",
+       "  21  1.123536 -2.610458 -0.374777 -1.399604  0.010437 -1.202039 -0.444766   \n",
+       "  22 -0.444766 -2.359445 -1.040537  1.273281  1.521154 -0.754361 -1.587355   \n",
+       "  23 -1.587355 -0.608959 -2.177594  1.604300  1.848678 -0.254748 -0.601230   \n",
+       "  24 -0.601230  1.638107 -2.944441  0.655471  0.390931  1.596041  0.842594   \n",
+       "  25  0.842594  1.421481 -2.595857 -1.776874 -1.016404 -0.223425  0.508369   \n",
+       "  26  0.508369  2.091462 -0.267468 -1.639922 -2.598127 -0.491564  0.921113   \n",
+       "  27  0.921113 -1.743807  2.328981 -2.284590 -1.767763 -0.569561 -1.181614   \n",
+       "  28 -1.181614 -2.761839  3.630907  1.581070 -0.242990 -2.681534 -1.550476   \n",
+       "  29 -1.550476 -2.583282  0.872239  2.534679  1.186285 -1.654315 -0.935981   \n",
+       "  30 -0.935981 -1.801311 -0.837862  2.996298  2.793391 -1.266859  1.900481   \n",
+       "  31  1.900481  0.654695 -2.708025  1.308605  2.106634  1.847521  2.021316   \n",
+       "  32  2.021316  0.744351 -4.383398 -1.093890  2.111322  2.140707 -0.338250   \n",
+       "  33 -0.338250  2.222333 -2.338702 -1.924162 -0.299769 -0.736429 -2.582735   \n",
+       "  34 -2.582735  2.883647  0.664945 -1.164459 -1.336245 -1.483437 -3.473688   \n",
+       "  35 -3.473688  1.829653  0.859814 -0.809594 -1.416553 -1.333011 -1.278305   \n",
+       "  36 -1.278305 -1.561560  1.412198 -0.531631 -0.356150 -0.897755  1.726214   \n",
+       "  37  1.726214 -3.835845 -0.754138 -0.623045  1.239593 -0.428012  3.285392   \n",
+       "  38  3.285392 -4.526674 -0.323198  0.205571  0.560537  0.866173  0.896570   \n",
+       "  39  0.896570 -2.081756 -1.320397  1.800091  0.596321  0.666135 -0.630340   \n",
+       "  40 -0.630340  2.527693 -0.773665  1.259465  0.258471  0.110216 -2.199994   \n",
+       "  41 -2.199994  2.420809  0.414252 -0.846955 -1.136685 -0.703185 -0.165447   \n",
+       "  42 -0.165447  0.668560  0.489117 -1.655766 -0.716744 -0.541209  0.729588   \n",
+       "  43  0.729588  0.111268 -0.002753 -0.504412  1.441115  1.094530  0.554378   \n",
+       "  44  0.554378 -2.281409 -1.017887 -0.815677  2.674016  1.536476 -0.458580   \n",
+       "  45 -0.458580 -2.580971 -1.308005  0.921532  1.581436  1.442079 -1.640960   \n",
+       "  46 -1.640960 -1.443983 -1.347976  2.090920 -0.527042  1.390310 -1.505653   \n",
+       "  47 -1.505653  1.355285  0.055951  1.797499 -1.750935  0.057914 -0.441328   \n",
+       "  48 -0.441328  2.634806  0.992989 -0.661639 -2.019793 -2.886680  0.050270   \n",
+       "  49  0.050270  3.426080  1.063484 -1.174345  0.595511 -3.031627  1.808532   \n",
+       "  50  1.808532  1.144074 -0.332067 -3.704902  2.517470 -1.513734  1.103019   \n",
+       "  51  1.103019 -2.980317  1.472097 -0.500912  3.489792 -0.226661 -0.561164   \n",
+       "  52 -0.561164 -4.001002 -0.128999  0.733835  1.326768  1.389195 -1.197963   \n",
+       "  53 -1.197963 -3.272317 -0.046366  1.844433 -0.622360  1.568182 -2.826245   \n",
+       "  54 -2.826245 -0.841280 -0.213707  0.846918 -1.431196  0.421456 -2.193197   \n",
+       "  55 -2.193197  3.574567  0.058661 -0.059375 -1.684858 -0.089289 -1.995562   \n",
+       "  56 -1.995562  5.322045  0.539129  0.643533 -0.540047 -0.691263  0.181600   \n",
+       "  57  0.181600  4.727063  0.612316 -0.628375 -0.226352 -0.686885  2.266723   \n",
+       "  58  2.266723 -0.544853 -1.012204 -2.311122  0.242220  0.126323  1.365099   \n",
+       "  59  1.365099 -4.308706 -1.432291 -1.814350 -0.224097 -0.079947  0.061899   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.214341  3.839702    0.245023    0.483819    1.285498  \n",
+       "  3   0.598287  1.663164    0.043404    0.130488    1.091571  \n",
+       "  4   0.301568  0.743760   -2.015148   -0.178018    0.644699  \n",
+       "  5  -1.616814 -3.295883   -0.456191    1.605155   -0.197745  \n",
+       "  6  -2.492777 -2.406323   -1.511529    0.876954    0.150597  \n",
+       "  7  -1.127580 -1.153697    2.315525    1.058645   -0.954685  \n",
+       "  8   1.899979  1.327827    2.386708    0.558307   -1.766021  \n",
+       "  9   3.704464  2.529162    2.696406    0.136733   -0.880065  \n",
+       "  10  4.324939  1.544024    0.291348   -0.611448    1.213934  \n",
+       "  11  0.431289 -1.111183   -2.266551   -1.426928    1.074038  \n",
+       "  12 -1.115060 -1.956287   -4.260822   -1.267486    2.016760  \n",
+       "  13 -3.387199 -1.778889   -2.170282    0.081891    0.606850  \n",
+       "  14 -1.209269 -0.308705   -0.709170    2.007109   -1.389624  \n",
+       "  15  1.130077  0.808776    1.994932    2.902635   -1.180499  \n",
+       "  16  2.938353  1.890290    2.780191    2.056846    1.142419  \n",
+       "  17  1.913974  0.435311    1.193295   -0.688376    1.777939  \n",
+       "  18  0.609295  1.108161   -0.807674   -3.457965    1.087383  \n",
+       "  19 -1.495966  0.184042   -1.477737   -3.966989   -0.412521  \n",
+       "  20 -2.610458 -0.374777   -1.399604    0.010437   -1.202039  \n",
+       "  21 -2.359445 -1.040537    1.273281    1.521154   -0.754361  \n",
+       "  22 -0.608959 -2.177594    1.604300    1.848678   -0.254748  \n",
+       "  23  1.638107 -2.944441    0.655471    0.390931    1.596041  \n",
+       "  24  1.421481 -2.595857   -1.776874   -1.016404   -0.223425  \n",
+       "  25  2.091462 -0.267468   -1.639922   -2.598127   -0.491564  \n",
+       "  26 -1.743807  2.328981   -2.284590   -1.767763   -0.569561  \n",
+       "  27 -2.761839  3.630907    1.581070   -0.242990   -2.681534  \n",
+       "  28 -2.583282  0.872239    2.534679    1.186285   -1.654315  \n",
+       "  29 -1.801311 -0.837862    2.996298    2.793391   -1.266859  \n",
+       "  30  0.654695 -2.708025    1.308605    2.106634    1.847521  \n",
+       "  31  0.744351 -4.383398   -1.093890    2.111322    2.140707  \n",
+       "  32  2.222333 -2.338702   -1.924162   -0.299769   -0.736429  \n",
+       "  33  2.883647  0.664945   -1.164459   -1.336245   -1.483437  \n",
+       "  34  1.829653  0.859814   -0.809594   -1.416553   -1.333011  \n",
+       "  35 -1.561560  1.412198   -0.531631   -0.356150   -0.897755  \n",
+       "  36 -3.835845 -0.754138   -0.623045    1.239593   -0.428012  \n",
+       "  37 -4.526674 -0.323198    0.205571    0.560537    0.866173  \n",
+       "  38 -2.081756 -1.320397    1.800091    0.596321    0.666135  \n",
+       "  39  2.527693 -0.773665    1.259465    0.258471    0.110216  \n",
+       "  40  2.420809  0.414252   -0.846955   -1.136685   -0.703185  \n",
+       "  41  0.668560  0.489117   -1.655766   -0.716744   -0.541209  \n",
+       "  42  0.111268 -0.002753   -0.504412    1.441115    1.094530  \n",
+       "  43 -2.281409 -1.017887   -0.815677    2.674016    1.536476  \n",
+       "  44 -2.580971 -1.308005    0.921532    1.581436    1.442079  \n",
+       "  45 -1.443983 -1.347976    2.090920   -0.527042    1.390310  \n",
+       "  46  1.355285  0.055951    1.797499   -1.750935    0.057914  \n",
+       "  47  2.634806  0.992989   -0.661639   -2.019793   -2.886680  \n",
+       "  48  3.426080  1.063484   -1.174345    0.595511   -3.031627  \n",
+       "  49  1.144074 -0.332067   -3.704902    2.517470   -1.513734  \n",
+       "  50 -2.980317  1.472097   -0.500912    3.489792   -0.226661  \n",
+       "  51 -4.001002 -0.128999    0.733835    1.326768    1.389195  \n",
+       "  52 -3.272317 -0.046366    1.844433   -0.622360    1.568182  \n",
+       "  53 -0.841280 -0.213707    0.846918   -1.431196    0.421456  \n",
+       "  54  3.574567  0.058661   -0.059375   -1.684858   -0.089289  \n",
+       "  55  5.322045  0.539129    0.643533   -0.540047   -0.691263  \n",
+       "  56  4.727063  0.612316   -0.628375   -0.226352   -0.686885  \n",
+       "  57 -0.544853 -1.012204   -2.311122    0.242220    0.126323  \n",
+       "  58 -4.308706 -1.432291   -1.814350   -0.224097   -0.079947  \n",
+       "  59 -4.148564 -1.765435   -0.359470   -1.822180   -0.247190  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.291089   \n",
+       "  3   0.291089  0.070271 -1.457955  3.043343 -0.057597  0.183382 -1.616795   \n",
+       "  4  -1.616795  0.691335 -2.305842  1.090708  0.334169 -1.742443 -0.557900   \n",
+       "  5  -0.557900  1.517087 -0.371387 -1.445111 -0.342184 -2.433032  1.397066   \n",
+       "  6   1.397066 -0.759798  1.794305 -1.059496 -1.686209 -1.241856  2.917586   \n",
+       "  7   2.917586 -1.432524  0.743355  0.444488 -1.297188 -0.954642  1.679439   \n",
+       "  8   1.679439 -2.278867  0.028622  1.028822 -2.143458  0.303427 -1.449052   \n",
+       "  9  -1.449052 -0.074816 -0.621512  0.874507  0.797968  1.637945 -3.173502   \n",
+       "  10 -3.173502  1.210779 -0.272552 -0.351248  0.501459  1.999461 -5.174780   \n",
+       "  11 -5.174780  1.497686  0.591535 -1.114559  1.068194  1.242397 -0.806546   \n",
+       "  12 -0.806546  0.710957  3.196615 -1.602635  0.905869 -0.538782  1.946805   \n",
+       "  13  1.946805 -0.974814  2.912785 -0.714970 -0.296018 -2.397951  3.916478   \n",
+       "  14  3.916478  0.523742  0.260425 -1.389950 -0.748006 -3.504202  4.196426   \n",
+       "  15  4.196426  1.600406 -2.538217  0.099811 -0.771177 -2.370021 -0.962846   \n",
+       "  16 -0.962846  0.840663 -2.213033  1.474763 -0.072420 -0.435996 -2.371968   \n",
+       "  17 -2.371968 -0.309758 -1.822954  1.959562 -0.908855  1.476922 -5.283463   \n",
+       "  18 -5.283463  0.344929  0.836884  2.306680 -0.134136  3.205823 -2.097289   \n",
+       "  19 -2.097289 -0.736094  2.285133  1.213124 -0.151514  1.992701  1.245711   \n",
+       "  20  1.245711  0.930267  1.014504 -2.016298  0.114279 -1.462913  4.046560   \n",
+       "  21  4.046560 -1.111417 -0.537106 -0.243647  0.116879 -2.257831  4.279691   \n",
+       "  22  4.279691 -0.588214 -1.030610 -0.250024  0.470417 -1.550243  0.923394   \n",
+       "  23  0.923394 -0.990472 -0.123239  0.087966  0.327165  0.525611 -2.712510   \n",
+       "  24 -2.712510 -1.136264  1.006184  0.959984  0.515699  1.820574 -2.469267   \n",
+       "  25 -2.469267  2.028987  2.019513 -0.740334  0.642680  3.272088 -0.861073   \n",
+       "  26 -0.861073  1.926243  1.338143 -1.554748 -0.233067  2.169379  1.844937   \n",
+       "  27  1.844937  1.110983  1.489499 -0.750176  0.547794 -0.762865  1.123166   \n",
+       "  28  1.123166 -0.476685 -0.400631  0.076226  1.170431 -2.460890  1.836425   \n",
+       "  29  1.836425 -0.040893 -3.416113  2.413514  0.604972 -2.839051 -0.223325   \n",
+       "  30 -0.223325 -2.180878 -3.088324  1.246171 -1.703068 -3.076846  0.252366   \n",
+       "  31  0.252366  1.147674 -2.155712  1.348739 -1.677948  0.109784 -0.695643   \n",
+       "  32 -0.695643  0.747368  2.936340 -1.226452 -2.154278  1.554912 -1.250673   \n",
+       "  33 -1.250673  0.381746  3.871143 -1.983693 -1.005230  1.993496 -1.110085   \n",
+       "  34 -1.110085 -0.752307  1.590456 -1.846060  0.776290  0.084151 -0.941313   \n",
+       "  35 -0.941313 -0.582684 -0.507998 -0.450142 -0.051263 -1.628389  1.685745   \n",
+       "  36  1.685745  0.080133 -1.006836  1.218360  0.481659 -1.123637  1.155669   \n",
+       "  37  1.155669  0.686045 -1.269212  1.669177 -0.123751 -1.800732  0.548302   \n",
+       "  38  0.548302  2.285098  0.139907  1.679640 -1.210473 -0.288874 -1.400370   \n",
+       "  39 -1.400370  1.328185  2.600266  0.358248 -0.962665  0.262894 -1.797245   \n",
+       "  40 -1.797245  0.003186  2.024914 -0.482470  1.876406  0.280767 -0.612520   \n",
+       "  41 -0.612520 -0.546993  0.860350 -0.624962  2.447500  0.629293  1.417100   \n",
+       "  42  1.417100 -0.170471 -1.423548  1.812689  1.492693 -0.208798  2.158954   \n",
+       "  43  2.158954 -0.685053 -1.427956  0.556387 -1.910112  0.112197  2.132639   \n",
+       "  44  2.132639  2.308800  0.382268  0.457290 -3.673103  0.247846 -0.883151   \n",
+       "  45 -0.883151  1.394551  3.473264 -0.450938 -2.741438  0.516665 -1.922159   \n",
+       "  46 -1.922159  0.737694  2.027928  0.574261 -1.593243  0.533612 -0.032848   \n",
+       "  47 -0.032848 -2.564548  0.682581  1.042389 -0.344800 -0.523912  1.510286   \n",
+       "  48  1.510286 -2.237660 -1.183418  1.043566  1.284521 -0.405490  1.940662   \n",
+       "  49  1.940662 -0.221761 -0.171733  0.650754  1.162598  0.273190  1.627797   \n",
+       "  50  1.627797  2.561718  0.522551 -2.639111  0.495199  0.501335 -0.395747   \n",
+       "  51 -0.395747  1.755233  1.702207 -0.664792 -0.801116  0.636942 -0.443986   \n",
+       "  52 -0.443986  0.472024  0.941421  0.463518 -0.928358  0.722259 -0.759732   \n",
+       "  53 -0.759732 -0.582306 -0.298528  3.096604 -0.722355 -0.126547 -1.934346   \n",
+       "  54 -1.934346  0.034727 -0.246464  1.954450 -0.830610  0.056756 -2.074153   \n",
+       "  55 -2.074153  0.168237  0.293518 -0.173643 -0.117700  0.372142 -0.467264   \n",
+       "  56 -0.467264 -0.251833  0.567851 -2.361439  0.029157  0.563227  1.303106   \n",
+       "  57  1.303106 -0.053240  1.657361 -2.931083  0.712323 -0.893820  1.105433   \n",
+       "  58  1.105433 -0.690684  1.045002 -2.554431  0.599155  1.283831  0.470630   \n",
+       "  59  0.470630  1.602367  0.659243 -0.281105  0.546481  1.908947  0.491014   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.070271 -1.457955    3.043343   -0.057597    0.183382  \n",
+       "  3   0.691335 -2.305842    1.090708    0.334169   -1.742443  \n",
+       "  4   1.517087 -0.371387   -1.445111   -0.342184   -2.433032  \n",
+       "  5  -0.759798  1.794305   -1.059496   -1.686209   -1.241856  \n",
+       "  6  -1.432524  0.743355    0.444488   -1.297188   -0.954642  \n",
+       "  7  -2.278867  0.028622    1.028822   -2.143458    0.303427  \n",
+       "  8  -0.074816 -0.621512    0.874507    0.797968    1.637945  \n",
+       "  9   1.210779 -0.272552   -0.351248    0.501459    1.999461  \n",
+       "  10  1.497686  0.591535   -1.114559    1.068194    1.242397  \n",
+       "  11  0.710957  3.196615   -1.602635    0.905869   -0.538782  \n",
+       "  12 -0.974814  2.912785   -0.714970   -0.296018   -2.397951  \n",
+       "  13  0.523742  0.260425   -1.389950   -0.748006   -3.504202  \n",
+       "  14  1.600406 -2.538217    0.099811   -0.771177   -2.370021  \n",
+       "  15  0.840663 -2.213033    1.474763   -0.072420   -0.435996  \n",
+       "  16 -0.309758 -1.822954    1.959562   -0.908855    1.476922  \n",
+       "  17  0.344929  0.836884    2.306680   -0.134136    3.205823  \n",
+       "  18 -0.736094  2.285133    1.213124   -0.151514    1.992701  \n",
+       "  19  0.930267  1.014504   -2.016298    0.114279   -1.462913  \n",
+       "  20 -1.111417 -0.537106   -0.243647    0.116879   -2.257831  \n",
+       "  21 -0.588214 -1.030610   -0.250024    0.470417   -1.550243  \n",
+       "  22 -0.990472 -0.123239    0.087966    0.327165    0.525611  \n",
+       "  23 -1.136264  1.006184    0.959984    0.515699    1.820574  \n",
+       "  24  2.028987  2.019513   -0.740334    0.642680    3.272088  \n",
+       "  25  1.926243  1.338143   -1.554748   -0.233067    2.169379  \n",
+       "  26  1.110983  1.489499   -0.750176    0.547794   -0.762865  \n",
+       "  27 -0.476685 -0.400631    0.076226    1.170431   -2.460890  \n",
+       "  28 -0.040893 -3.416113    2.413514    0.604972   -2.839051  \n",
+       "  29 -2.180878 -3.088324    1.246171   -1.703068   -3.076846  \n",
+       "  30  1.147674 -2.155712    1.348739   -1.677948    0.109784  \n",
+       "  31  0.747368  2.936340   -1.226452   -2.154278    1.554912  \n",
+       "  32  0.381746  3.871143   -1.983693   -1.005230    1.993496  \n",
+       "  33 -0.752307  1.590456   -1.846060    0.776290    0.084151  \n",
+       "  34 -0.582684 -0.507998   -0.450142   -0.051263   -1.628389  \n",
+       "  35  0.080133 -1.006836    1.218360    0.481659   -1.123637  \n",
+       "  36  0.686045 -1.269212    1.669177   -0.123751   -1.800732  \n",
+       "  37  2.285098  0.139907    1.679640   -1.210473   -0.288874  \n",
+       "  38  1.328185  2.600266    0.358248   -0.962665    0.262894  \n",
+       "  39  0.003186  2.024914   -0.482470    1.876406    0.280767  \n",
+       "  40 -0.546993  0.860350   -0.624962    2.447500    0.629293  \n",
+       "  41 -0.170471 -1.423548    1.812689    1.492693   -0.208798  \n",
+       "  42 -0.685053 -1.427956    0.556387   -1.910112    0.112197  \n",
+       "  43  2.308800  0.382268    0.457290   -3.673103    0.247846  \n",
+       "  44  1.394551  3.473264   -0.450938   -2.741438    0.516665  \n",
+       "  45  0.737694  2.027928    0.574261   -1.593243    0.533612  \n",
+       "  46 -2.564548  0.682581    1.042389   -0.344800   -0.523912  \n",
+       "  47 -2.237660 -1.183418    1.043566    1.284521   -0.405490  \n",
+       "  48 -0.221761 -0.171733    0.650754    1.162598    0.273190  \n",
+       "  49  2.561718  0.522551   -2.639111    0.495199    0.501335  \n",
+       "  50  1.755233  1.702207   -0.664792   -0.801116    0.636942  \n",
+       "  51  0.472024  0.941421    0.463518   -0.928358    0.722259  \n",
+       "  52 -0.582306 -0.298528    3.096604   -0.722355   -0.126547  \n",
+       "  53  0.034727 -0.246464    1.954450   -0.830610    0.056756  \n",
+       "  54  0.168237  0.293518   -0.173643   -0.117700    0.372142  \n",
+       "  55 -0.251833  0.567851   -2.361439    0.029157    0.563227  \n",
+       "  56 -0.053240  1.657361   -2.931083    0.712323   -0.893820  \n",
+       "  57 -0.690684  1.045002   -2.554431    0.599155    1.283831  \n",
+       "  58  1.602367  0.659243   -0.281105    0.546481    1.908947  \n",
+       "  59  2.158864 -1.276885    1.538736   -1.786920    1.667961  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -2.102771   \n",
+       "  3  -2.102771 -0.484425 -0.395366  0.763085  0.777490  1.507198 -2.870156   \n",
+       "  4  -2.870156 -1.985838 -0.777650 -0.067848 -0.580827 -0.617870 -2.742157   \n",
+       "  5  -2.742157 -4.157783 -2.128175  0.061123 -1.026630 -3.799678  1.125976   \n",
+       "  6   1.125976 -2.229428 -0.726762 -0.871464 -0.196168 -1.313505  1.197445   \n",
+       "  7   1.197445  0.448202  1.265100 -0.809260 -0.179901 -0.410005  1.168179   \n",
+       "  8   1.168179  2.666371  1.944734  1.312874  1.040026  2.177766 -0.048298   \n",
+       "  9  -0.048298  2.190384  1.978848  2.091674 -0.117044  2.712301  0.079084   \n",
+       "  10  0.079084  1.371502  0.242437 -0.427140  0.219584  0.361854  0.552095   \n",
+       "  11  0.552095 -0.991969 -1.891167 -0.421342  0.595494 -1.843124  0.645862   \n",
+       "  12  0.645862 -1.353280 -2.857390 -0.633668  1.142472 -3.192732 -0.125083   \n",
+       "  13 -0.125083 -1.250254 -2.412463 -2.236898  0.945227 -1.207750 -0.295372   \n",
+       "  14 -0.295372 -1.745698  1.179305  0.569110 -1.421152  2.182766 -0.169639   \n",
+       "  15 -0.169639 -1.691919  2.204652  1.244378 -1.909805  2.527525  0.070854   \n",
+       "  16  0.070854 -0.000570  0.808845  2.329872  0.022811  2.829166 -0.947372   \n",
+       "  17 -0.947372  0.195009 -1.531455 -1.180278  3.627907 -0.085738 -1.882144   \n",
+       "  18 -1.882144  0.228619 -0.915824 -2.754534  1.092351 -1.504908 -0.920547   \n",
+       "  19 -0.920547 -0.726075  0.201670 -2.461847 -1.071884 -1.680359  0.570352   \n",
+       "  20  0.570352 -0.597418  0.986023  0.371175 -1.933435 -2.625966  2.894634   \n",
+       "  21  2.894634 -0.476063  1.963026  3.390041 -2.529934 -0.401308  3.276262   \n",
+       "  22  3.276262 -1.670298  0.869728  3.780176 -0.572795  1.667185  0.392803   \n",
+       "  23  0.392803 -1.453946 -1.528317  1.242873  1.466685  2.165906 -1.628944   \n",
+       "  24 -1.628944 -0.729921 -2.191852 -2.136073  1.651602  1.593948 -2.810726   \n",
+       "  25 -2.810726  0.129533 -1.848690 -3.785222 -0.175042  0.048794 -2.267939   \n",
+       "  26 -2.267939 -1.266209 -0.640418 -2.794655 -0.489764 -2.547034  0.128659   \n",
+       "  27  0.128659  0.475281  0.935044  1.417613 -1.768069 -3.677273  2.270577   \n",
+       "  28  2.270577  0.610552  1.107383  5.589082 -2.090879 -3.525724  1.181699   \n",
+       "  29  1.181699  1.326075 -1.439749  3.128629 -0.743972 -0.691522  0.170775   \n",
+       "  30  0.170775  1.010762 -0.576354  0.835862  0.610718  1.428786 -1.189342   \n",
+       "  31 -1.189342  0.018777 -0.929961 -2.657657  1.015857  1.853754 -0.882253   \n",
+       "  32 -0.882253 -1.062784 -2.301875 -2.616409 -0.832530  2.835640  1.490988   \n",
+       "  33  1.490988 -0.170132  0.494388 -0.690276 -0.300974  0.928231  1.021913   \n",
+       "  34  1.021913  0.887247 -0.343062  1.326695 -2.378048 -0.643028  0.725288   \n",
+       "  35  0.725288  0.567921 -0.063494  1.252241 -1.419537 -2.627408 -1.916971   \n",
+       "  36 -1.916971 -0.782034  0.878784  0.581530  0.185076 -2.327619 -3.089691   \n",
+       "  37 -3.089691 -1.476575  1.671285 -1.585991  0.000175  0.973921 -1.495284   \n",
+       "  38 -1.495284 -1.801041  3.435724 -1.272756  0.870291  2.351215  1.590211   \n",
+       "  39  1.590211 -0.309058  1.758696  0.038290 -0.804205  1.546248  1.257268   \n",
+       "  40  1.257268  0.854543  0.135922  1.090240  0.340069  0.157600  0.387387   \n",
+       "  41  0.387387  3.363617 -1.936134  0.079803 -0.241831 -2.239280 -2.539751   \n",
+       "  42 -2.539751  1.829182 -4.010844 -1.132458 -0.229153 -4.293087 -2.038353   \n",
+       "  43 -2.038353  0.783178 -4.286834 -2.759050 -0.887892 -2.023377 -0.917199   \n",
+       "  44 -0.917199 -0.890527 -0.500856 -0.672374  1.613093  0.509527 -0.022525   \n",
+       "  45 -0.022525 -1.443356  2.145817  1.250964 -0.642858  4.951086  0.663505   \n",
+       "  46  0.663505 -0.066799  4.042502  1.654054 -1.607843  4.747824  0.098866   \n",
+       "  47  0.098866  0.259981  2.272553  1.144856 -0.722474  0.806152 -0.309266   \n",
+       "  48 -0.309266 -0.097499 -2.095192  0.093332  1.125670 -2.162729  0.096343   \n",
+       "  49  0.096343  0.695533 -3.071927 -1.294610  2.050293 -3.098564  0.105536   \n",
+       "  50  0.105536  0.699103 -1.228810 -1.202054  2.976675 -2.842441 -1.189660   \n",
+       "  51 -1.189660  0.915921  0.550504 -1.275250  1.058917 -1.140341 -1.486088   \n",
+       "  52 -1.486088  1.264301  0.634178  1.266707 -1.412149  1.929049 -1.766665   \n",
+       "  53 -1.766665  0.182168  0.399211  2.694791 -3.669298  2.756179  0.848864   \n",
+       "  54  0.848864 -0.830169  1.764793  1.591614 -2.603235  3.963133  3.228689   \n",
+       "  55  3.228689 -0.981718  3.437831 -1.081149  0.791562  0.522306  2.409364   \n",
+       "  56  2.409364 -0.632548  2.853118 -1.717878  3.533403 -1.213717 -0.251203   \n",
+       "  57 -0.251203 -1.061540  0.835800 -3.626316  1.755564 -1.230747 -3.601385   \n",
+       "  58 -3.601385 -1.669315 -2.847411 -1.414901 -0.519834 -1.568356 -4.246960   \n",
+       "  59 -4.246960 -1.314198 -4.081043  1.002938 -0.852046  0.163836 -2.234305   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.484425 -0.395366    0.763085    0.777490    1.507198  \n",
+       "  3  -1.985838 -0.777650   -0.067848   -0.580827   -0.617870  \n",
+       "  4  -4.157783 -2.128175    0.061123   -1.026630   -3.799678  \n",
+       "  5  -2.229428 -0.726762   -0.871464   -0.196168   -1.313505  \n",
+       "  6   0.448202  1.265100   -0.809260   -0.179901   -0.410005  \n",
+       "  7   2.666371  1.944734    1.312874    1.040026    2.177766  \n",
+       "  8   2.190384  1.978848    2.091674   -0.117044    2.712301  \n",
+       "  9   1.371502  0.242437   -0.427140    0.219584    0.361854  \n",
+       "  10 -0.991969 -1.891167   -0.421342    0.595494   -1.843124  \n",
+       "  11 -1.353280 -2.857390   -0.633668    1.142472   -3.192732  \n",
+       "  12 -1.250254 -2.412463   -2.236898    0.945227   -1.207750  \n",
+       "  13 -1.745698  1.179305    0.569110   -1.421152    2.182766  \n",
+       "  14 -1.691919  2.204652    1.244378   -1.909805    2.527525  \n",
+       "  15 -0.000570  0.808845    2.329872    0.022811    2.829166  \n",
+       "  16  0.195009 -1.531455   -1.180278    3.627907   -0.085738  \n",
+       "  17  0.228619 -0.915824   -2.754534    1.092351   -1.504908  \n",
+       "  18 -0.726075  0.201670   -2.461847   -1.071884   -1.680359  \n",
+       "  19 -0.597418  0.986023    0.371175   -1.933435   -2.625966  \n",
+       "  20 -0.476063  1.963026    3.390041   -2.529934   -0.401308  \n",
+       "  21 -1.670298  0.869728    3.780176   -0.572795    1.667185  \n",
+       "  22 -1.453946 -1.528317    1.242873    1.466685    2.165906  \n",
+       "  23 -0.729921 -2.191852   -2.136073    1.651602    1.593948  \n",
+       "  24  0.129533 -1.848690   -3.785222   -0.175042    0.048794  \n",
+       "  25 -1.266209 -0.640418   -2.794655   -0.489764   -2.547034  \n",
+       "  26  0.475281  0.935044    1.417613   -1.768069   -3.677273  \n",
+       "  27  0.610552  1.107383    5.589082   -2.090879   -3.525724  \n",
+       "  28  1.326075 -1.439749    3.128629   -0.743972   -0.691522  \n",
+       "  29  1.010762 -0.576354    0.835862    0.610718    1.428786  \n",
+       "  30  0.018777 -0.929961   -2.657657    1.015857    1.853754  \n",
+       "  31 -1.062784 -2.301875   -2.616409   -0.832530    2.835640  \n",
+       "  32 -0.170132  0.494388   -0.690276   -0.300974    0.928231  \n",
+       "  33  0.887247 -0.343062    1.326695   -2.378048   -0.643028  \n",
+       "  34  0.567921 -0.063494    1.252241   -1.419537   -2.627408  \n",
+       "  35 -0.782034  0.878784    0.581530    0.185076   -2.327619  \n",
+       "  36 -1.476575  1.671285   -1.585991    0.000175    0.973921  \n",
+       "  37 -1.801041  3.435724   -1.272756    0.870291    2.351215  \n",
+       "  38 -0.309058  1.758696    0.038290   -0.804205    1.546248  \n",
+       "  39  0.854543  0.135922    1.090240    0.340069    0.157600  \n",
+       "  40  3.363617 -1.936134    0.079803   -0.241831   -2.239280  \n",
+       "  41  1.829182 -4.010844   -1.132458   -0.229153   -4.293087  \n",
+       "  42  0.783178 -4.286834   -2.759050   -0.887892   -2.023377  \n",
+       "  43 -0.890527 -0.500856   -0.672374    1.613093    0.509527  \n",
+       "  44 -1.443356  2.145817    1.250964   -0.642858    4.951086  \n",
+       "  45 -0.066799  4.042502    1.654054   -1.607843    4.747824  \n",
+       "  46  0.259981  2.272553    1.144856   -0.722474    0.806152  \n",
+       "  47 -0.097499 -2.095192    0.093332    1.125670   -2.162729  \n",
+       "  48  0.695533 -3.071927   -1.294610    2.050293   -3.098564  \n",
+       "  49  0.699103 -1.228810   -1.202054    2.976675   -2.842441  \n",
+       "  50  0.915921  0.550504   -1.275250    1.058917   -1.140341  \n",
+       "  51  1.264301  0.634178    1.266707   -1.412149    1.929049  \n",
+       "  52  0.182168  0.399211    2.694791   -3.669298    2.756179  \n",
+       "  53 -0.830169  1.764793    1.591614   -2.603235    3.963133  \n",
+       "  54 -0.981718  3.437831   -1.081149    0.791562    0.522306  \n",
+       "  55 -0.632548  2.853118   -1.717878    3.533403   -1.213717  \n",
+       "  56 -1.061540  0.835800   -3.626316    1.755564   -1.230747  \n",
+       "  57 -1.669315 -2.847411   -1.414901   -0.519834   -1.568356  \n",
+       "  58 -1.314198 -4.081043    1.002938   -0.852046    0.163836  \n",
+       "  59  1.057904 -2.431879    3.996343   -1.888671   -1.001321  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.142617   \n",
+       "  3   0.142617 -0.323442  2.565708  0.305074  1.325506  1.016467  0.545074   \n",
+       "  4   0.545074 -0.982604  0.192550  1.545256 -0.915800 -1.321822 -1.264905   \n",
+       "  5  -1.264905 -1.241931 -3.897219  1.562111 -2.506812  0.187454 -0.706618   \n",
+       "  6  -0.706618 -1.143774 -3.290733  0.569388 -2.284213  0.239147  0.451858   \n",
+       "  7   0.451858 -2.345250 -1.796750 -1.000238  0.092598  1.262878  1.797588   \n",
+       "  8   1.797588 -0.942237  2.679485 -1.671234  2.195480  1.994052 -0.755802   \n",
+       "  9  -0.755802 -0.059870  3.239422 -2.601845  0.187078  0.746928 -0.112465   \n",
+       "  10 -0.112465  0.972965  2.007660  0.696694 -0.138880 -0.191188 -2.461295   \n",
+       "  11 -2.461295  2.296265 -0.791486  2.641458 -0.324559 -1.339222 -0.536074   \n",
+       "  12 -0.536074  1.758719 -1.393077  2.616588 -0.203612 -1.704433  1.669788   \n",
+       "  13  1.669788 -0.901769 -1.480461  2.131135 -0.420063  0.671639  3.819542   \n",
+       "  14  3.819542 -2.500926 -1.786776 -0.808323  1.471082  0.778659  0.680685   \n",
+       "  15  0.680685 -1.332887 -0.514396 -3.880143  1.391213  1.263191 -0.336340   \n",
+       "  16 -0.336340  0.401912  0.735838 -4.213189 -0.199927  0.309023 -2.097375   \n",
+       "  17 -2.097375  0.833699  1.584561 -3.416808 -1.574807  0.085279 -2.123524   \n",
+       "  18 -2.123524 -0.675329 -0.007744  0.095675 -2.919014 -1.256163 -0.198443   \n",
+       "  19 -0.198443 -0.755567 -1.160889  1.626294 -2.667901 -0.657990  0.684332   \n",
+       "  20  0.684332 -2.519408 -0.544917  0.614612 -0.896976 -0.590168  1.242214   \n",
+       "  21  1.242214 -1.231122  0.129743 -0.917925  0.196320  1.234813 -1.428878   \n",
+       "  22 -1.428878  0.844390  0.393234 -0.586949 -1.470698  2.303720 -3.354700   \n",
+       "  23 -3.354700  1.543427 -0.347853 -0.744336 -1.391239  2.596223 -2.445905   \n",
+       "  24 -2.445905  1.947524 -0.614040 -0.188256 -2.197137  2.601424  0.545567   \n",
+       "  25  0.545567  0.928827  0.741635  1.383189 -1.506548  1.019427  2.027607   \n",
+       "  26  2.027607 -0.813963 -0.655158 -0.879716 -0.043015 -2.214631  2.233184   \n",
+       "  27  2.233184  0.098748  1.843233 -0.052841  1.875372 -3.148324  2.258168   \n",
+       "  28  2.258168 -1.306113  0.605321 -0.599748  3.317009 -1.132736  1.353270   \n",
+       "  29  1.353270 -1.408778  0.257083 -1.115843  1.588887  0.919645 -1.592946   \n",
+       "  30 -1.592946 -2.013014 -0.157297 -0.492031 -0.484244  1.024926 -3.847716   \n",
+       "  31 -3.847716 -1.031891 -1.078981 -0.513890 -2.053115  1.367367 -2.808042   \n",
+       "  32 -2.808042 -0.276607 -2.214011 -1.231379 -0.301815  0.217436  1.012798   \n",
+       "  33  1.012798  2.313524 -1.695805  0.850871 -0.187977  1.458275  3.144095   \n",
+       "  34  3.144095  3.660750 -0.180407  0.987094 -0.413004  1.056403  4.553330   \n",
+       "  35  4.553330  1.676997  1.130125  1.365805  0.963555 -0.802183  0.218277   \n",
+       "  36  0.218277 -1.404458  1.543654 -0.313402  1.122811 -2.720866 -2.718453   \n",
+       "  37 -2.718453 -1.267461  0.105779 -1.056235  0.637005 -1.338637 -3.476551   \n",
+       "  38 -3.476551 -0.149510 -0.376487  0.975093 -1.069871  1.648168 -2.718976   \n",
+       "  39 -2.718976  0.794884 -2.113452  0.380080 -2.575192  1.247775  0.526523   \n",
+       "  40  0.526523 -0.785281 -2.134579 -0.523165 -3.352202  0.735276  2.836591   \n",
+       "  41  2.836591  0.770684 -2.123452 -0.124886  0.281878 -0.269844  3.198033   \n",
+       "  42  3.198033  0.765561  0.005824  0.481559  2.258786 -1.099179  1.929474   \n",
+       "  43  1.929474  0.282287  0.666621  1.757937  2.872848 -1.397891 -1.648201   \n",
+       "  44 -1.648201 -1.184314  3.086510  0.769293  1.151440  0.244199 -2.452752   \n",
+       "  45 -2.452752 -1.325908  1.619392 -0.668283 -0.446156  1.196426 -1.349665   \n",
+       "  46 -1.349665 -3.109811  0.726516 -0.270142 -3.603855  0.133906 -0.013233   \n",
+       "  47 -0.013233 -2.246298 -1.623774 -1.196614 -2.906545 -1.082881 -0.124889   \n",
+       "  48 -0.124889  1.957632 -1.966954 -2.696845 -0.386352 -1.678637 -0.784438   \n",
+       "  49 -0.784438  1.693378 -0.996620 -0.875922  2.420029 -0.416004 -0.770196   \n",
+       "  50 -0.770196  1.930820 -0.054944  0.687373  3.031886  0.329294 -2.990324   \n",
+       "  51 -2.990324  1.898739  1.709189  2.595079  0.180889  2.235265 -2.335608   \n",
+       "  52 -2.335608  0.969703  0.592376  2.453616 -1.310927  0.700665 -0.851460   \n",
+       "  53 -0.851460 -0.779726 -0.275641  0.326885 -2.119427 -0.539300  0.221128   \n",
+       "  54  0.221128  0.068652 -0.307728 -0.329609 -1.714354 -1.626750  3.561600   \n",
+       "  55  3.561600  0.038537 -0.588353 -2.510443  1.205123 -0.891989  0.553047   \n",
+       "  56  0.553047 -1.582724 -0.538350 -0.566537  0.455029 -1.130795 -1.921662   \n",
+       "  57 -1.921662 -0.166098 -0.419401  0.723783  0.243205  0.846877 -3.906287   \n",
+       "  58 -3.906287  1.474206 -1.414226  1.548768 -0.693061  1.908280 -2.119313   \n",
+       "  59 -2.119313  2.708197  0.301592  2.755299 -0.333411  1.834614  1.881652   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.323442  2.565708    0.305074    1.325506    1.016467  \n",
+       "  3  -0.982604  0.192550    1.545256   -0.915800   -1.321822  \n",
+       "  4  -1.241931 -3.897219    1.562111   -2.506812    0.187454  \n",
+       "  5  -1.143774 -3.290733    0.569388   -2.284213    0.239147  \n",
+       "  6  -2.345250 -1.796750   -1.000238    0.092598    1.262878  \n",
+       "  7  -0.942237  2.679485   -1.671234    2.195480    1.994052  \n",
+       "  8  -0.059870  3.239422   -2.601845    0.187078    0.746928  \n",
+       "  9   0.972965  2.007660    0.696694   -0.138880   -0.191188  \n",
+       "  10  2.296265 -0.791486    2.641458   -0.324559   -1.339222  \n",
+       "  11  1.758719 -1.393077    2.616588   -0.203612   -1.704433  \n",
+       "  12 -0.901769 -1.480461    2.131135   -0.420063    0.671639  \n",
+       "  13 -2.500926 -1.786776   -0.808323    1.471082    0.778659  \n",
+       "  14 -1.332887 -0.514396   -3.880143    1.391213    1.263191  \n",
+       "  15  0.401912  0.735838   -4.213189   -0.199927    0.309023  \n",
+       "  16  0.833699  1.584561   -3.416808   -1.574807    0.085279  \n",
+       "  17 -0.675329 -0.007744    0.095675   -2.919014   -1.256163  \n",
+       "  18 -0.755567 -1.160889    1.626294   -2.667901   -0.657990  \n",
+       "  19 -2.519408 -0.544917    0.614612   -0.896976   -0.590168  \n",
+       "  20 -1.231122  0.129743   -0.917925    0.196320    1.234813  \n",
+       "  21  0.844390  0.393234   -0.586949   -1.470698    2.303720  \n",
+       "  22  1.543427 -0.347853   -0.744336   -1.391239    2.596223  \n",
+       "  23  1.947524 -0.614040   -0.188256   -2.197137    2.601424  \n",
+       "  24  0.928827  0.741635    1.383189   -1.506548    1.019427  \n",
+       "  25 -0.813963 -0.655158   -0.879716   -0.043015   -2.214631  \n",
+       "  26  0.098748  1.843233   -0.052841    1.875372   -3.148324  \n",
+       "  27 -1.306113  0.605321   -0.599748    3.317009   -1.132736  \n",
+       "  28 -1.408778  0.257083   -1.115843    1.588887    0.919645  \n",
+       "  29 -2.013014 -0.157297   -0.492031   -0.484244    1.024926  \n",
+       "  30 -1.031891 -1.078981   -0.513890   -2.053115    1.367367  \n",
+       "  31 -0.276607 -2.214011   -1.231379   -0.301815    0.217436  \n",
+       "  32  2.313524 -1.695805    0.850871   -0.187977    1.458275  \n",
+       "  33  3.660750 -0.180407    0.987094   -0.413004    1.056403  \n",
+       "  34  1.676997  1.130125    1.365805    0.963555   -0.802183  \n",
+       "  35 -1.404458  1.543654   -0.313402    1.122811   -2.720866  \n",
+       "  36 -1.267461  0.105779   -1.056235    0.637005   -1.338637  \n",
+       "  37 -0.149510 -0.376487    0.975093   -1.069871    1.648168  \n",
+       "  38  0.794884 -2.113452    0.380080   -2.575192    1.247775  \n",
+       "  39 -0.785281 -2.134579   -0.523165   -3.352202    0.735276  \n",
+       "  40  0.770684 -2.123452   -0.124886    0.281878   -0.269844  \n",
+       "  41  0.765561  0.005824    0.481559    2.258786   -1.099179  \n",
+       "  42  0.282287  0.666621    1.757937    2.872848   -1.397891  \n",
+       "  43 -1.184314  3.086510    0.769293    1.151440    0.244199  \n",
+       "  44 -1.325908  1.619392   -0.668283   -0.446156    1.196426  \n",
+       "  45 -3.109811  0.726516   -0.270142   -3.603855    0.133906  \n",
+       "  46 -2.246298 -1.623774   -1.196614   -2.906545   -1.082881  \n",
+       "  47  1.957632 -1.966954   -2.696845   -0.386352   -1.678637  \n",
+       "  48  1.693378 -0.996620   -0.875922    2.420029   -0.416004  \n",
+       "  49  1.930820 -0.054944    0.687373    3.031886    0.329294  \n",
+       "  50  1.898739  1.709189    2.595079    0.180889    2.235265  \n",
+       "  51  0.969703  0.592376    2.453616   -1.310927    0.700665  \n",
+       "  52 -0.779726 -0.275641    0.326885   -2.119427   -0.539300  \n",
+       "  53  0.068652 -0.307728   -0.329609   -1.714354   -1.626750  \n",
+       "  54  0.038537 -0.588353   -2.510443    1.205123   -0.891989  \n",
+       "  55 -1.582724 -0.538350   -0.566537    0.455029   -1.130795  \n",
+       "  56 -0.166098 -0.419401    0.723783    0.243205    0.846877  \n",
+       "  57  1.474206 -1.414226    1.548768   -0.693061    1.908280  \n",
+       "  58  2.708197  0.301592    2.755299   -0.333411    1.834614  \n",
+       "  59  1.504533  0.310889    0.624089    1.772759    0.824027  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -0.097255   \n",
+       "  3  -0.097255 -0.847436 -0.278273  0.545135  2.106799 -0.794775 -0.933618   \n",
+       "  4  -0.933618 -1.031239  0.100414  0.195353  1.350698 -1.374280 -1.670241   \n",
+       "  5  -1.670241 -3.385119 -0.627125 -1.113922  0.544791  0.201992 -2.492564   \n",
+       "  6  -2.492564 -1.230570 -0.389198 -3.349831 -2.162106 -0.722250 -1.136683   \n",
+       "  7  -1.136683  2.181002  2.638977 -3.359813 -2.142743  1.064337  0.432814   \n",
+       "  8   0.432814  4.141883  2.822959  1.180543 -2.519239  0.986702  2.970108   \n",
+       "  9   2.970108  4.814078  1.987351  2.863999 -1.328904  1.044074  1.393096   \n",
+       "  10  1.393096  1.670988 -0.576043  4.386433 -0.120049 -0.193155 -0.643789   \n",
+       "  11 -0.643789 -1.415907 -1.692248  2.770817  0.473526  1.608907 -0.185830   \n",
+       "  12 -0.185830 -2.554664 -3.202153 -0.847273  0.755138 -0.102615 -1.115304   \n",
+       "  13 -1.115304 -2.481167  0.122136 -2.585281  0.119092 -0.143737 -1.454505   \n",
+       "  14 -1.454505  0.103333 -0.024137 -1.430397 -2.218930  0.031967 -0.264450   \n",
+       "  15 -0.264450  2.007520  0.810233  0.642065 -0.849498 -1.209480  1.189375   \n",
+       "  16  1.189375  2.222372  0.760980  2.910051  0.541912 -1.623434  1.387076   \n",
+       "  17  1.387076  2.574007 -1.919748  2.212229  1.619475 -0.823243  1.275525   \n",
+       "  18  1.275525  2.017601 -0.378706 -1.265757  0.749075  0.685087 -1.128821   \n",
+       "  19 -1.128821 -0.915833 -0.179978 -2.887111 -0.132095  2.580569 -1.327335   \n",
+       "  20 -1.327335 -2.585495  1.560795 -4.241848  0.482019  1.748742 -3.204303   \n",
+       "  21 -3.204303 -1.074174  2.096241 -1.162874 -1.593991  0.613191  0.144563   \n",
+       "  22  0.144563 -0.537143  1.755090  2.378124 -1.368596 -0.599338  1.337847   \n",
+       "  23  1.337847  0.749565  0.781683  3.463998  0.747103 -0.456918  0.717819   \n",
+       "  24  0.717819  1.201451 -0.403008  1.437886  2.016549 -0.223259  0.527150   \n",
+       "  25  0.527150  1.388245 -1.088193  0.655687  2.737307 -1.456805 -0.554375   \n",
+       "  26 -0.554375  0.299451 -2.794297 -0.781788  2.758973 -1.798071 -2.111096   \n",
+       "  27 -2.111096 -0.097511 -1.332310 -2.412892 -0.136097 -1.871870 -2.396500   \n",
+       "  28 -2.396500  0.354146  0.315184 -0.401805 -2.885454 -0.580546  0.208377   \n",
+       "  29  0.208377 -1.447430  1.841678 -0.129261 -3.917415  1.616208  0.088033   \n",
+       "  30  0.088033  0.406108  1.856146  0.919164 -1.827482  2.764949  1.468609   \n",
+       "  31  1.468609 -0.159381  1.803652  1.431928  0.742115  0.700043  0.427356   \n",
+       "  32  0.427356  0.113598  1.836244  0.815918  4.074457  1.589805 -1.461175   \n",
+       "  33 -1.461175  0.018267 -0.345085 -1.265947  2.581785 -1.578019 -2.155088   \n",
+       "  34 -2.155088 -0.277621 -1.940921 -4.149291  0.271913 -2.205629 -1.629825   \n",
+       "  35 -1.629825 -0.547103 -1.950063 -2.710894 -1.951336 -1.110367  0.501202   \n",
+       "  36  0.501202 -0.451766 -1.598980 -0.581118 -3.473710  2.125484  2.551543   \n",
+       "  37  2.551543  0.014490  0.476943  0.998908 -2.728791  4.620958  1.676892   \n",
+       "  38  1.676892 -0.984509  0.362643  1.971051 -0.002594  2.448244  0.612359   \n",
+       "  39  0.612359 -2.563352  0.388249  0.479946  2.647648 -2.239033 -2.421751   \n",
+       "  40 -2.421751 -1.999286  0.543244  0.078520  3.511208 -1.110215 -2.909834   \n",
+       "  41 -2.909834 -0.219773 -1.328260  0.181743  1.786630 -2.506821 -0.884838   \n",
+       "  42 -0.884838 -0.194779 -1.412451 -2.711620 -1.315296 -1.243275  1.463870   \n",
+       "  43  1.463870  0.248179 -1.303141 -2.267129 -3.978581 -0.554190  2.301736   \n",
+       "  44  2.301736 -0.334630 -0.991370 -0.803878 -1.842561  2.501365  2.484099   \n",
+       "  45  2.484099 -1.733933  0.302968  1.034515 -0.767585  3.138789  0.650503   \n",
+       "  46  0.650503 -1.278915 -0.766247  3.401751  1.557667  0.461622 -1.433350   \n",
+       "  47 -1.433350 -0.910172 -0.709736  1.333537  1.954243 -1.972797 -2.387494   \n",
+       "  48 -2.387494 -0.685168 -0.335598 -0.937709  1.028002 -3.557188 -3.000821   \n",
+       "  49 -3.000821 -1.903805  1.159908 -2.613912  0.032428 -2.373573  0.280007   \n",
+       "  50  0.280007  0.270466  0.401362 -0.722948 -1.334111 -0.790978  2.290885   \n",
+       "  51  2.290885 -0.093379 -0.699929  1.259657 -1.032949  1.681134  2.947327   \n",
+       "  52  2.947327  0.020192  0.547928  3.264041 -0.458351  0.920056  1.191154   \n",
+       "  53  1.191154 -0.584221  0.479568  3.227536 -0.239292 -0.036841 -0.600755   \n",
+       "  54 -0.600755  0.040740 -0.235856  0.238024 -1.003765 -1.050830 -1.239057   \n",
+       "  55 -1.239057 -0.341336 -0.548102 -1.241153  0.149521 -0.718782 -1.806394   \n",
+       "  56 -1.806394 -1.271543 -2.176711 -2.499480 -0.647990  0.859021 -2.625144   \n",
+       "  57 -2.625144 -1.181203 -1.585722 -1.714649 -1.823321  1.424358 -0.926857   \n",
+       "  58 -0.926857  1.681572 -1.871301 -0.547958 -1.965112  1.937728  0.958249   \n",
+       "  59  0.958249  1.492376  0.035187  3.253533 -1.403905  0.526225  1.680819   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.847436 -0.278273    0.545135    2.106799   -0.794775  \n",
+       "  3  -1.031239  0.100414    0.195353    1.350698   -1.374280  \n",
+       "  4  -3.385119 -0.627125   -1.113922    0.544791    0.201992  \n",
+       "  5  -1.230570 -0.389198   -3.349831   -2.162106   -0.722250  \n",
+       "  6   2.181002  2.638977   -3.359813   -2.142743    1.064337  \n",
+       "  7   4.141883  2.822959    1.180543   -2.519239    0.986702  \n",
+       "  8   4.814078  1.987351    2.863999   -1.328904    1.044074  \n",
+       "  9   1.670988 -0.576043    4.386433   -0.120049   -0.193155  \n",
+       "  10 -1.415907 -1.692248    2.770817    0.473526    1.608907  \n",
+       "  11 -2.554664 -3.202153   -0.847273    0.755138   -0.102615  \n",
+       "  12 -2.481167  0.122136   -2.585281    0.119092   -0.143737  \n",
+       "  13  0.103333 -0.024137   -1.430397   -2.218930    0.031967  \n",
+       "  14  2.007520  0.810233    0.642065   -0.849498   -1.209480  \n",
+       "  15  2.222372  0.760980    2.910051    0.541912   -1.623434  \n",
+       "  16  2.574007 -1.919748    2.212229    1.619475   -0.823243  \n",
+       "  17  2.017601 -0.378706   -1.265757    0.749075    0.685087  \n",
+       "  18 -0.915833 -0.179978   -2.887111   -0.132095    2.580569  \n",
+       "  19 -2.585495  1.560795   -4.241848    0.482019    1.748742  \n",
+       "  20 -1.074174  2.096241   -1.162874   -1.593991    0.613191  \n",
+       "  21 -0.537143  1.755090    2.378124   -1.368596   -0.599338  \n",
+       "  22  0.749565  0.781683    3.463998    0.747103   -0.456918  \n",
+       "  23  1.201451 -0.403008    1.437886    2.016549   -0.223259  \n",
+       "  24  1.388245 -1.088193    0.655687    2.737307   -1.456805  \n",
+       "  25  0.299451 -2.794297   -0.781788    2.758973   -1.798071  \n",
+       "  26 -0.097511 -1.332310   -2.412892   -0.136097   -1.871870  \n",
+       "  27  0.354146  0.315184   -0.401805   -2.885454   -0.580546  \n",
+       "  28 -1.447430  1.841678   -0.129261   -3.917415    1.616208  \n",
+       "  29  0.406108  1.856146    0.919164   -1.827482    2.764949  \n",
+       "  30 -0.159381  1.803652    1.431928    0.742115    0.700043  \n",
+       "  31  0.113598  1.836244    0.815918    4.074457    1.589805  \n",
+       "  32  0.018267 -0.345085   -1.265947    2.581785   -1.578019  \n",
+       "  33 -0.277621 -1.940921   -4.149291    0.271913   -2.205629  \n",
+       "  34 -0.547103 -1.950063   -2.710894   -1.951336   -1.110367  \n",
+       "  35 -0.451766 -1.598980   -0.581118   -3.473710    2.125484  \n",
+       "  36  0.014490  0.476943    0.998908   -2.728791    4.620958  \n",
+       "  37 -0.984509  0.362643    1.971051   -0.002594    2.448244  \n",
+       "  38 -2.563352  0.388249    0.479946    2.647648   -2.239033  \n",
+       "  39 -1.999286  0.543244    0.078520    3.511208   -1.110215  \n",
+       "  40 -0.219773 -1.328260    0.181743    1.786630   -2.506821  \n",
+       "  41 -0.194779 -1.412451   -2.711620   -1.315296   -1.243275  \n",
+       "  42  0.248179 -1.303141   -2.267129   -3.978581   -0.554190  \n",
+       "  43 -0.334630 -0.991370   -0.803878   -1.842561    2.501365  \n",
+       "  44 -1.733933  0.302968    1.034515   -0.767585    3.138789  \n",
+       "  45 -1.278915 -0.766247    3.401751    1.557667    0.461622  \n",
+       "  46 -0.910172 -0.709736    1.333537    1.954243   -1.972797  \n",
+       "  47 -0.685168 -0.335598   -0.937709    1.028002   -3.557188  \n",
+       "  48 -1.903805  1.159908   -2.613912    0.032428   -2.373573  \n",
+       "  49  0.270466  0.401362   -0.722948   -1.334111   -0.790978  \n",
+       "  50 -0.093379 -0.699929    1.259657   -1.032949    1.681134  \n",
+       "  51  0.020192  0.547928    3.264041   -0.458351    0.920056  \n",
+       "  52 -0.584221  0.479568    3.227536   -0.239292   -0.036841  \n",
+       "  53  0.040740 -0.235856    0.238024   -1.003765   -1.050830  \n",
+       "  54 -0.341336 -0.548102   -1.241153    0.149521   -0.718782  \n",
+       "  55 -1.271543 -2.176711   -2.499480   -0.647990    0.859021  \n",
+       "  56 -1.181203 -1.585722   -1.714649   -1.823321    1.424358  \n",
+       "  57  1.681572 -1.871301   -0.547958   -1.965112    1.937728  \n",
+       "  58  1.492376  0.035187    3.253533   -1.403905    0.526225  \n",
+       "  59 -0.681254  2.627465    3.273730    0.650328   -0.936166  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.793371   \n",
+       "  3   0.793371  0.608335  0.208686  0.942131  2.145063 -0.065746  0.464415   \n",
+       "  4   0.464415 -1.595897  0.381543  0.471252  1.535372  0.554212  0.672581   \n",
+       "  5   0.672581 -1.956747  0.310841 -0.044498 -0.126130 -0.345939 -1.042629   \n",
+       "  6  -1.042629 -1.384134 -0.169805 -1.481318 -1.734152 -0.367946 -3.236271   \n",
+       "  7  -3.236271 -0.407939 -1.673839  0.069372 -1.912075  1.109855 -2.516138   \n",
+       "  8  -2.516138  3.159580 -1.354433 -1.683644 -0.439921  1.860357 -0.399159   \n",
+       "  9  -0.399159  2.030101  1.014626  0.279794  0.851410  1.408939  0.980192   \n",
+       "  10  0.980192 -0.114218  1.813768  1.032230  1.550666  1.399924  0.772359   \n",
+       "  11  0.772359 -3.959822  1.813335 -0.348898  2.213738 -0.162223  0.365926   \n",
+       "  12  0.365926 -4.423380  0.885547  0.440532  1.782477 -0.976892  0.471646   \n",
+       "  13  0.471646 -1.784810 -0.209103  0.207151  0.576965 -2.923816  1.502674   \n",
+       "  14  1.502674 -0.014598 -1.242692 -0.621647 -1.438182 -2.972891  0.849494   \n",
+       "  15  0.849494  1.153701 -1.158876 -1.195763 -3.760800  1.708691 -1.290783   \n",
+       "  16 -1.290783  0.828463 -0.133560 -0.681088 -1.454799  4.202581 -1.937294   \n",
+       "  17 -1.937294 -0.496711 -0.006237  0.549601  1.536175  3.993592 -1.218828   \n",
+       "  18 -1.218828  1.072942  0.070126  1.928189  3.008027  1.116213  1.063524   \n",
+       "  19  1.063524  1.797757  1.851830  2.656858  1.470288 -1.271801  1.418172   \n",
+       "  20  1.418172 -0.357979  2.074578  0.046107 -0.147413 -1.753947  3.032501   \n",
+       "  21  3.032501 -0.716845 -0.173010 -2.771846 -2.368830 -1.137771  2.923799   \n",
+       "  22  2.923799 -3.063422 -0.129454 -0.060246 -3.708240 -0.081059 -0.456545   \n",
+       "  23 -0.456545  0.651754 -1.802367 -0.496343 -1.561712  0.637790 -4.979914   \n",
+       "  24 -4.979914  2.252749 -2.520033  2.513091  1.007096  0.352099 -5.605508   \n",
+       "  25 -5.605508  2.206723 -0.039359  2.241955  2.367193  0.318434 -2.131946   \n",
+       "  26 -2.131946  1.726985  0.297870  0.503604  2.352734 -1.321772  1.892535   \n",
+       "  27  1.892535  1.342429  0.762439 -1.865909  0.601285 -1.730692  5.636019   \n",
+       "  28  5.636019 -1.158710  0.415281 -2.396944 -1.436076 -0.097324  5.308845   \n",
+       "  29  5.308845 -3.089888  1.304803 -1.526540 -2.465528 -0.161738  1.176261   \n",
+       "  30  1.176261 -1.704137  0.677547  0.684592 -1.983843 -0.615182 -3.823867   \n",
+       "  31 -3.823867  1.349050 -0.899190  3.585668  0.820113 -0.235968 -4.622256   \n",
+       "  32 -4.622256  2.534820 -2.409223  4.004888  1.445552  1.723270 -3.296507   \n",
+       "  33 -3.296507  1.524698 -2.603104  1.416038  1.003187  1.214698  0.483016   \n",
+       "  34  0.483016 -1.442745 -0.287117  0.580666 -0.224273 -0.147466  3.307090   \n",
+       "  35  3.307090 -4.259868  1.572156 -0.021053  0.706047 -1.378558  2.752236   \n",
+       "  36  2.752236 -4.832743  1.206406 -1.947347  1.336389 -0.033368  1.550099   \n",
+       "  37  1.550099 -1.680879  1.055807 -0.982311  1.125345  0.814200 -1.632859   \n",
+       "  38 -1.632859  2.707793  0.108402 -1.484506 -0.042804  0.056064 -2.475914   \n",
+       "  39 -2.475914  5.060751 -0.621968  0.045641  1.811857 -0.864321 -1.927172   \n",
+       "  40 -1.927172  4.484835 -1.635428  1.191521 -0.529561 -0.029963 -0.824528   \n",
+       "  41 -0.824528 -2.233544 -1.932808  2.702040 -2.178212  0.027159  0.661268   \n",
+       "  42  0.661268 -6.455648  0.169583  0.056700 -2.163362  1.514827  1.579963   \n",
+       "  43  1.579963 -6.784376 -0.215155 -1.593190 -1.461479  0.996294  2.418780   \n",
+       "  44  2.418780 -1.916516  1.887615 -1.883524  1.426236 -1.037335  1.446377   \n",
+       "  45  1.446377  3.758609  0.568907 -2.628826  3.022537 -2.293202 -0.491753   \n",
+       "  46 -0.491753  5.169153  0.459038  0.905661  2.295063 -2.870374 -1.733002   \n",
+       "  47 -1.733002  4.449033 -0.546867  0.346558 -1.310735 -1.248370 -2.730158   \n",
+       "  48 -2.730158  0.292311 -2.036547  2.170211 -2.061413  1.543632 -0.667074   \n",
+       "  49 -0.667074 -3.647191 -1.843267 -0.243427 -1.246530  3.631967  0.941462   \n",
+       "  50  0.941462 -5.030188  0.442262 -1.215539 -0.504955  0.831587  1.512501   \n",
+       "  51  1.512501 -1.527273  0.900074 -2.271377 -1.096260 -1.360456  2.902767   \n",
+       "  52  2.902767  0.829820 -0.769296 -0.904424 -1.652751 -3.971079  2.151003   \n",
+       "  53  2.151003  3.037088 -1.953894 -0.330578 -0.053917 -2.438828 -0.357144   \n",
+       "  54 -0.357144  3.205364 -2.722246 -0.111124  1.885987 -1.873833 -3.177244   \n",
+       "  55 -3.177244  1.433639 -2.321680 -0.057201  2.525003 -0.398746 -5.282097   \n",
+       "  56 -5.282097  0.240568  1.137409  0.260235  1.267374  2.292521 -2.792515   \n",
+       "  57 -2.792515 -0.469249  1.940198  0.830350  0.256088  0.086278 -1.207954   \n",
+       "  58 -1.207954 -2.076796  1.588942  0.601623 -1.848804 -1.013250  2.067723   \n",
+       "  59  2.067723 -1.938729  0.624910  0.871970 -1.797465 -0.524791  1.823529   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.608335  0.208686    0.942131    2.145063   -0.065746  \n",
+       "  3  -1.595897  0.381543    0.471252    1.535372    0.554212  \n",
+       "  4  -1.956747  0.310841   -0.044498   -0.126130   -0.345939  \n",
+       "  5  -1.384134 -0.169805   -1.481318   -1.734152   -0.367946  \n",
+       "  6  -0.407939 -1.673839    0.069372   -1.912075    1.109855  \n",
+       "  7   3.159580 -1.354433   -1.683644   -0.439921    1.860357  \n",
+       "  8   2.030101  1.014626    0.279794    0.851410    1.408939  \n",
+       "  9  -0.114218  1.813768    1.032230    1.550666    1.399924  \n",
+       "  10 -3.959822  1.813335   -0.348898    2.213738   -0.162223  \n",
+       "  11 -4.423380  0.885547    0.440532    1.782477   -0.976892  \n",
+       "  12 -1.784810 -0.209103    0.207151    0.576965   -2.923816  \n",
+       "  13 -0.014598 -1.242692   -0.621647   -1.438182   -2.972891  \n",
+       "  14  1.153701 -1.158876   -1.195763   -3.760800    1.708691  \n",
+       "  15  0.828463 -0.133560   -0.681088   -1.454799    4.202581  \n",
+       "  16 -0.496711 -0.006237    0.549601    1.536175    3.993592  \n",
+       "  17  1.072942  0.070126    1.928189    3.008027    1.116213  \n",
+       "  18  1.797757  1.851830    2.656858    1.470288   -1.271801  \n",
+       "  19 -0.357979  2.074578    0.046107   -0.147413   -1.753947  \n",
+       "  20 -0.716845 -0.173010   -2.771846   -2.368830   -1.137771  \n",
+       "  21 -3.063422 -0.129454   -0.060246   -3.708240   -0.081059  \n",
+       "  22  0.651754 -1.802367   -0.496343   -1.561712    0.637790  \n",
+       "  23  2.252749 -2.520033    2.513091    1.007096    0.352099  \n",
+       "  24  2.206723 -0.039359    2.241955    2.367193    0.318434  \n",
+       "  25  1.726985  0.297870    0.503604    2.352734   -1.321772  \n",
+       "  26  1.342429  0.762439   -1.865909    0.601285   -1.730692  \n",
+       "  27 -1.158710  0.415281   -2.396944   -1.436076   -0.097324  \n",
+       "  28 -3.089888  1.304803   -1.526540   -2.465528   -0.161738  \n",
+       "  29 -1.704137  0.677547    0.684592   -1.983843   -0.615182  \n",
+       "  30  1.349050 -0.899190    3.585668    0.820113   -0.235968  \n",
+       "  31  2.534820 -2.409223    4.004888    1.445552    1.723270  \n",
+       "  32  1.524698 -2.603104    1.416038    1.003187    1.214698  \n",
+       "  33 -1.442745 -0.287117    0.580666   -0.224273   -0.147466  \n",
+       "  34 -4.259868  1.572156   -0.021053    0.706047   -1.378558  \n",
+       "  35 -4.832743  1.206406   -1.947347    1.336389   -0.033368  \n",
+       "  36 -1.680879  1.055807   -0.982311    1.125345    0.814200  \n",
+       "  37  2.707793  0.108402   -1.484506   -0.042804    0.056064  \n",
+       "  38  5.060751 -0.621968    0.045641    1.811857   -0.864321  \n",
+       "  39  4.484835 -1.635428    1.191521   -0.529561   -0.029963  \n",
+       "  40 -2.233544 -1.932808    2.702040   -2.178212    0.027159  \n",
+       "  41 -6.455648  0.169583    0.056700   -2.163362    1.514827  \n",
+       "  42 -6.784376 -0.215155   -1.593190   -1.461479    0.996294  \n",
+       "  43 -1.916516  1.887615   -1.883524    1.426236   -1.037335  \n",
+       "  44  3.758609  0.568907   -2.628826    3.022537   -2.293202  \n",
+       "  45  5.169153  0.459038    0.905661    2.295063   -2.870374  \n",
+       "  46  4.449033 -0.546867    0.346558   -1.310735   -1.248370  \n",
+       "  47  0.292311 -2.036547    2.170211   -2.061413    1.543632  \n",
+       "  48 -3.647191 -1.843267   -0.243427   -1.246530    3.631967  \n",
+       "  49 -5.030188  0.442262   -1.215539   -0.504955    0.831587  \n",
+       "  50 -1.527273  0.900074   -2.271377   -1.096260   -1.360456  \n",
+       "  51  0.829820 -0.769296   -0.904424   -1.652751   -3.971079  \n",
+       "  52  3.037088 -1.953894   -0.330578   -0.053917   -2.438828  \n",
+       "  53  3.205364 -2.722246   -0.111124    1.885987   -1.873833  \n",
+       "  54  1.433639 -2.321680   -0.057201    2.525003   -0.398746  \n",
+       "  55  0.240568  1.137409    0.260235    1.267374    2.292521  \n",
+       "  56 -0.469249  1.940198    0.830350    0.256088    0.086278  \n",
+       "  57 -2.076796  1.588942    0.601623   -1.848804   -1.013250  \n",
+       "  58 -1.938729  0.624910    0.871970   -1.797465   -0.524791  \n",
+       "  59 -1.293195 -0.172053    1.729222    0.207518    1.370205  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.322532   \n",
+       "  3   1.322532  0.332667  1.678036 -0.689670 -0.192008  0.550002  0.739558   \n",
+       "  4   0.739558 -0.543066  0.838718 -1.631112 -0.679348  1.741413 -2.286368   \n",
+       "  5  -2.286368 -1.039440  0.725835 -0.891652 -0.959269 -1.173897 -2.766633   \n",
+       "  6  -2.766633 -1.037867 -0.412836  1.095332 -2.207265 -1.517434 -1.393229   \n",
+       "  7  -1.393229  0.415098 -1.332202  2.031445 -0.590461  1.127137  1.015543   \n",
+       "  8   1.015543  0.076206 -1.734752  1.132282  2.621008  1.032048  2.043008   \n",
+       "  9   2.043008  1.091994 -1.535310  0.102922  4.768402  1.704083  1.936615   \n",
+       "  10  1.936615 -0.219863  0.644751  0.153977  2.153377 -0.184982  0.714044   \n",
+       "  11  0.714044 -1.505539  3.081999 -0.695149 -0.837263 -2.081460 -1.237133   \n",
+       "  12 -1.237133 -1.293946  4.015182  0.271713 -1.957281 -1.152421 -2.505862   \n",
+       "  13 -2.505862 -2.001422  1.029024  0.905472 -3.316382  1.209011 -1.567601   \n",
+       "  14 -1.567601  0.175075 -2.529015  2.271522 -1.554583  1.431295  0.227771   \n",
+       "  15  0.227771  1.131641 -4.116638  0.579631 -0.717962  2.135219  0.893001   \n",
+       "  16  0.893001  1.058405 -2.798881 -0.419234  0.246218  0.037876 -0.696257   \n",
+       "  17 -0.696257  1.023343  1.078114 -2.275281  1.643902  1.254538 -0.193110   \n",
+       "  18 -0.193110  0.717265  2.232613 -2.733490  2.860697  1.212339  0.095952   \n",
+       "  19  0.095952 -3.335699  2.770085  0.853922  1.106641 -0.401924 -0.390264   \n",
+       "  20 -0.390264 -2.454546  2.397183  1.934993  0.267294 -1.597676 -1.688269   \n",
+       "  21 -1.688269  0.020745  0.494584  3.091440 -0.293332 -2.696207 -0.144838   \n",
+       "  22 -0.144838  1.304572 -0.776458 -0.126885  1.072221 -1.199894 -0.053507   \n",
+       "  23 -0.053507  1.187904 -3.224938 -1.900279  0.149262  2.186241  0.785830   \n",
+       "  24  0.785830 -1.021836 -2.151377 -3.589886  1.673073  4.069043  0.156049   \n",
+       "  25  0.156049 -0.203565 -0.308052 -2.268071  1.205659  3.309197 -1.661289   \n",
+       "  26 -1.661289  0.360800  3.744381 -0.534776  1.495934  1.958348 -0.934161   \n",
+       "  27 -0.934161  0.452210  4.049408  1.590588 -0.477321 -0.468865  0.138018   \n",
+       "  28  0.138018 -0.137893  1.182444  2.644357  0.115757 -2.370508  2.136972   \n",
+       "  29  2.136972 -0.471783 -1.596433  3.729727  1.091953 -0.521513  2.109349   \n",
+       "  30  2.109349 -0.576922 -2.698675  1.682337  3.086079  2.099681  0.662083   \n",
+       "  31  0.662083  1.053891 -2.054332 -1.528828  1.987240  1.201330 -0.651751   \n",
+       "  32 -0.651751  0.945190 -0.990162 -3.829287  0.832601  0.700351 -1.725940   \n",
+       "  33 -1.725940  0.601636  1.622118 -3.035782 -1.894465  0.063061 -0.751267   \n",
+       "  34 -0.751267  1.340555  1.592067  1.711210 -2.464272 -2.279823  0.464628   \n",
+       "  35  0.464628 -0.575278 -0.684803  3.026648 -2.062799 -1.795708  0.206633   \n",
+       "  36  0.206633 -1.763200 -3.405665  3.760908  1.958906 -2.030120 -0.573121   \n",
+       "  37 -0.573121 -2.536734 -3.809633  0.829114  2.233373 -1.272391 -0.393744   \n",
+       "  38 -0.393744 -1.443982 -0.707322 -1.824702  1.346946  0.473275 -0.908075   \n",
+       "  39 -0.908075 -0.316702  3.156568 -3.544777 -1.887190  0.403255 -1.247911   \n",
+       "  40 -1.247911  0.875755  3.715150 -1.139747 -4.217030 -0.168784 -0.487875   \n",
+       "  41 -0.487875  3.080501  1.332463 -0.773349 -3.574228 -2.580160 -0.481708   \n",
+       "  42 -0.481708  2.374871 -1.390789 -0.458968 -1.488437 -0.449280  1.658219   \n",
+       "  43  1.658219  1.252663 -2.857591  0.327432  0.904480 -0.589262 -0.879878   \n",
+       "  44 -0.879878 -2.262663 -3.348756  0.251206  2.558032  0.823673 -1.139168   \n",
+       "  45 -1.139168 -0.856331 -0.388905  0.557088  2.259860  2.696675 -1.943498   \n",
+       "  46 -1.943498 -1.297744  1.759379  0.165125 -0.128898  1.047361 -0.621448   \n",
+       "  47 -0.621448  2.044682  2.078604  1.941375 -1.007169  0.510777  0.081835   \n",
+       "  48  0.081835  0.729727  1.642461 -0.006233 -1.302358 -1.372175  0.975011   \n",
+       "  49  0.975011  1.661138  0.679843 -0.472245 -1.657414 -1.311899  2.075272   \n",
+       "  50  2.075272 -1.145632 -0.134422 -0.903139 -0.018928 -0.589234 -0.317225   \n",
+       "  51 -0.317225 -4.114876 -2.149568  0.563834  2.389864  0.786365 -1.866157   \n",
+       "  52 -1.866157 -4.228543 -2.623100  1.034966  0.468015 -0.125892 -3.034263   \n",
+       "  53 -3.034263 -1.669892 -1.916834 -1.764261 -0.329328  0.011596 -0.018199   \n",
+       "  54 -0.018199  0.687086  0.711771 -3.764756 -1.058475  1.029497  3.060504   \n",
+       "  55  3.060504  1.385899  1.671142 -2.112558 -0.266306  0.715543  2.492517   \n",
+       "  56  2.492517  0.308928  0.424200  0.642294  1.173743 -0.255359  0.056518   \n",
+       "  57  0.056518 -0.657440 -1.200107  0.317737  1.655915 -0.079394 -2.057824   \n",
+       "  58 -2.057824 -1.962698 -0.923343  2.222198  1.185334 -0.024114 -2.821504   \n",
+       "  59 -2.821504 -1.408864 -0.295661  2.542928 -0.359368  0.354744 -1.259116   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.332667  1.678036   -0.689670   -0.192008    0.550002  \n",
+       "  3  -0.543066  0.838718   -1.631112   -0.679348    1.741413  \n",
+       "  4  -1.039440  0.725835   -0.891652   -0.959269   -1.173897  \n",
+       "  5  -1.037867 -0.412836    1.095332   -2.207265   -1.517434  \n",
+       "  6   0.415098 -1.332202    2.031445   -0.590461    1.127137  \n",
+       "  7   0.076206 -1.734752    1.132282    2.621008    1.032048  \n",
+       "  8   1.091994 -1.535310    0.102922    4.768402    1.704083  \n",
+       "  9  -0.219863  0.644751    0.153977    2.153377   -0.184982  \n",
+       "  10 -1.505539  3.081999   -0.695149   -0.837263   -2.081460  \n",
+       "  11 -1.293946  4.015182    0.271713   -1.957281   -1.152421  \n",
+       "  12 -2.001422  1.029024    0.905472   -3.316382    1.209011  \n",
+       "  13  0.175075 -2.529015    2.271522   -1.554583    1.431295  \n",
+       "  14  1.131641 -4.116638    0.579631   -0.717962    2.135219  \n",
+       "  15  1.058405 -2.798881   -0.419234    0.246218    0.037876  \n",
+       "  16  1.023343  1.078114   -2.275281    1.643902    1.254538  \n",
+       "  17  0.717265  2.232613   -2.733490    2.860697    1.212339  \n",
+       "  18 -3.335699  2.770085    0.853922    1.106641   -0.401924  \n",
+       "  19 -2.454546  2.397183    1.934993    0.267294   -1.597676  \n",
+       "  20  0.020745  0.494584    3.091440   -0.293332   -2.696207  \n",
+       "  21  1.304572 -0.776458   -0.126885    1.072221   -1.199894  \n",
+       "  22  1.187904 -3.224938   -1.900279    0.149262    2.186241  \n",
+       "  23 -1.021836 -2.151377   -3.589886    1.673073    4.069043  \n",
+       "  24 -0.203565 -0.308052   -2.268071    1.205659    3.309197  \n",
+       "  25  0.360800  3.744381   -0.534776    1.495934    1.958348  \n",
+       "  26  0.452210  4.049408    1.590588   -0.477321   -0.468865  \n",
+       "  27 -0.137893  1.182444    2.644357    0.115757   -2.370508  \n",
+       "  28 -0.471783 -1.596433    3.729727    1.091953   -0.521513  \n",
+       "  29 -0.576922 -2.698675    1.682337    3.086079    2.099681  \n",
+       "  30  1.053891 -2.054332   -1.528828    1.987240    1.201330  \n",
+       "  31  0.945190 -0.990162   -3.829287    0.832601    0.700351  \n",
+       "  32  0.601636  1.622118   -3.035782   -1.894465    0.063061  \n",
+       "  33  1.340555  1.592067    1.711210   -2.464272   -2.279823  \n",
+       "  34 -0.575278 -0.684803    3.026648   -2.062799   -1.795708  \n",
+       "  35 -1.763200 -3.405665    3.760908    1.958906   -2.030120  \n",
+       "  36 -2.536734 -3.809633    0.829114    2.233373   -1.272391  \n",
+       "  37 -1.443982 -0.707322   -1.824702    1.346946    0.473275  \n",
+       "  38 -0.316702  3.156568   -3.544777   -1.887190    0.403255  \n",
+       "  39  0.875755  3.715150   -1.139747   -4.217030   -0.168784  \n",
+       "  40  3.080501  1.332463   -0.773349   -3.574228   -2.580160  \n",
+       "  41  2.374871 -1.390789   -0.458968   -1.488437   -0.449280  \n",
+       "  42  1.252663 -2.857591    0.327432    0.904480   -0.589262  \n",
+       "  43 -2.262663 -3.348756    0.251206    2.558032    0.823673  \n",
+       "  44 -0.856331 -0.388905    0.557088    2.259860    2.696675  \n",
+       "  45 -1.297744  1.759379    0.165125   -0.128898    1.047361  \n",
+       "  46  2.044682  2.078604    1.941375   -1.007169    0.510777  \n",
+       "  47  0.729727  1.642461   -0.006233   -1.302358   -1.372175  \n",
+       "  48  1.661138  0.679843   -0.472245   -1.657414   -1.311899  \n",
+       "  49 -1.145632 -0.134422   -0.903139   -0.018928   -0.589234  \n",
+       "  50 -4.114876 -2.149568    0.563834    2.389864    0.786365  \n",
+       "  51 -4.228543 -2.623100    1.034966    0.468015   -0.125892  \n",
+       "  52 -1.669892 -1.916834   -1.764261   -0.329328    0.011596  \n",
+       "  53  0.687086  0.711771   -3.764756   -1.058475    1.029497  \n",
+       "  54  1.385899  1.671142   -2.112558   -0.266306    0.715543  \n",
+       "  55  0.308928  0.424200    0.642294    1.173743   -0.255359  \n",
+       "  56 -0.657440 -1.200107    0.317737    1.655915   -0.079394  \n",
+       "  57 -1.962698 -0.923343    2.222198    1.185334   -0.024114  \n",
+       "  58 -1.408864 -0.295661    2.542928   -0.359368    0.354744  \n",
+       "  59 -0.385834  1.429974    0.201847   -2.462000    0.740260  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -0.520293   \n",
+       "  3  -0.520293 -0.109723  1.956390 -0.406698  0.204323  2.158707 -1.477633   \n",
+       "  4  -1.477633 -0.249755  3.145191 -1.872890  0.068890  0.814987 -3.566931   \n",
+       "  5  -3.566931 -0.681099 -0.726035 -0.530626 -0.748546 -2.599318 -0.182526   \n",
+       "  6  -0.182526 -1.187291 -1.923037  0.139579 -0.456426 -2.636434  2.502830   \n",
+       "  7   2.502830 -1.087055 -2.340590  1.704102 -0.723720 -1.568220  3.059286   \n",
+       "  8   3.059286 -0.025931 -1.361574  1.705092 -1.448196  1.192026  1.117809   \n",
+       "  9   1.117809  0.272561  0.297855  2.075133 -1.198339  3.273527 -1.378365   \n",
+       "  10 -1.378365  0.309555  1.039707  0.166827  0.692491  2.756655 -3.206142   \n",
+       "  11 -3.206142  0.031429  1.395998 -2.237233  0.815522  0.646515 -2.295338   \n",
+       "  12 -2.295338  0.673692  0.201508 -3.840153  0.750421 -1.663495  0.050681   \n",
+       "  13  0.050681  1.631110 -2.670788 -1.518462  1.112364 -3.471314  1.494536   \n",
+       "  14  1.494536 -0.359936 -1.289608  1.267056  0.005452 -2.101436  2.187118   \n",
+       "  15  2.187118 -1.741496 -0.116780  3.106709 -1.142208 -0.869615  0.563625   \n",
+       "  16  0.563625 -2.526395  1.614472  1.725591  0.057326  2.666487 -0.160209   \n",
+       "  17 -0.160209 -1.518668  2.154205  0.786935  1.495887  2.240553 -1.899237   \n",
+       "  18 -1.899237  1.355525  1.207416 -1.649485  1.454943  2.266537 -0.772245   \n",
+       "  19 -0.772245  3.884840  0.367314 -0.298820  0.725941 -0.320434 -0.997508   \n",
+       "  20 -0.997508  1.699563 -0.367988  0.274988 -0.677102 -1.985275  0.644183   \n",
+       "  21  0.644183  0.708916  0.552751  0.631237 -2.013854 -3.874495  1.385487   \n",
+       "  22  1.385487 -1.714540 -1.064707 -2.163864 -1.063695 -2.216635 -0.070533   \n",
+       "  23 -0.070533 -2.161338 -1.120923 -1.966759  0.102941  0.930983  1.089012   \n",
+       "  24  1.089012 -1.991172 -0.721443 -1.458312  2.282982  2.813257  0.662479   \n",
+       "  25  0.662479  0.532299 -0.410358  0.824656  2.179484  2.967591  2.336025   \n",
+       "  26  2.336025  1.009821 -0.354782  0.955574  3.099191  0.147491  1.211220   \n",
+       "  27  1.211220  3.628663 -0.130757 -0.631935  1.664723 -1.325695 -0.881373   \n",
+       "  28 -0.881373  1.843229 -0.709342 -0.517911 -1.656955 -2.264833 -1.824950   \n",
+       "  29 -1.824950 -0.616835 -1.119329  0.805693 -3.868187 -2.817207 -2.341656   \n",
+       "  30 -2.341656 -3.554203 -1.570185  1.766644 -4.865877 -0.919582 -0.550597   \n",
+       "  31 -0.550597 -4.257360 -0.418469  2.307599 -2.187351  0.963567  1.692934   \n",
+       "  32  1.692934 -0.119455 -0.281621  0.783234  0.393718  1.545330  3.981884   \n",
+       "  33  3.981884  2.878741  0.150550 -2.180582  3.150340  0.726139  1.934070   \n",
+       "  34  1.934070  4.045855  0.673327 -3.695125  3.024373 -0.248885 -3.015425   \n",
+       "  35 -3.015425  1.820807  1.602962 -2.605067  2.059776 -2.151407 -4.635505   \n",
+       "  36 -4.635505 -0.440143 -0.590595  1.852935 -1.406104 -4.160708 -0.857949   \n",
+       "  37 -0.857949 -3.174812 -0.291751  4.630328 -1.580882 -0.958740  1.879940   \n",
+       "  38  1.879940 -1.563825  0.278739  2.897067 -1.391597  1.994374  4.325618   \n",
+       "  39  4.325618  0.441341  2.033921 -1.264514 -0.685457  2.212074  3.681631   \n",
+       "  40  3.681631  1.801959 -0.441788 -3.471700  1.980183  1.442989  1.268863   \n",
+       "  41  1.268863  1.513950 -2.583184 -2.865498  1.549641 -1.146023 -1.176687   \n",
+       "  42 -1.176687 -2.061701 -1.797754 -0.527448  0.942418 -0.684837 -3.868005   \n",
+       "  43 -3.868005 -2.850175 -1.090027  1.084149 -1.962063 -0.640512 -4.159407   \n",
+       "  44 -4.159407 -2.732292  1.271256  2.408177 -2.242937  1.130697 -1.394308   \n",
+       "  45 -1.394308 -0.905164  2.089798  1.466105 -1.487153  1.213567  1.264785   \n",
+       "  46  1.264785  0.611125  0.261792  0.021143 -0.262568  1.364966  3.446130   \n",
+       "  47  3.446130  1.593971 -1.296559 -0.924616  1.371395 -0.453440  2.403719   \n",
+       "  48  2.403719 -0.529872 -2.281316 -1.807695  1.724627  0.145439  1.810803   \n",
+       "  49  1.810803 -1.965396 -0.649996 -0.475454  0.253547  0.444446 -0.189173   \n",
+       "  50 -0.189173 -0.734198  0.208445  0.788400 -1.853269 -0.377664 -2.762137   \n",
+       "  51 -2.762137  0.836875  0.165788 -0.908795 -2.344198 -0.558292 -1.468809   \n",
+       "  52 -1.468809  1.274295  1.831221 -0.497523  0.297553 -1.065603  0.649195   \n",
+       "  53  0.649195  1.930387  1.782486  0.791763  1.606153  0.399564  1.152579   \n",
+       "  54  1.152579  2.143894  1.350928  1.440569  4.128145  0.637437  1.162106   \n",
+       "  55  1.162106  0.362025  0.496611  0.420047  1.800464 -0.112133 -0.499436   \n",
+       "  56 -0.499436 -0.572182  1.240424 -1.262179 -0.925236 -0.530923 -1.698994   \n",
+       "  57 -1.698994 -2.273523 -0.743831 -0.259603 -2.086590 -0.129749 -0.081222   \n",
+       "  58 -0.081222 -1.685532 -0.216767  1.068656 -2.461740 -0.512549  0.463027   \n",
+       "  59  0.463027 -0.486126 -0.680811  2.539918 -1.339505 -1.449519 -0.019892   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.109723  1.956390   -0.406698    0.204323    2.158707  \n",
+       "  3  -0.249755  3.145191   -1.872890    0.068890    0.814987  \n",
+       "  4  -0.681099 -0.726035   -0.530626   -0.748546   -2.599318  \n",
+       "  5  -1.187291 -1.923037    0.139579   -0.456426   -2.636434  \n",
+       "  6  -1.087055 -2.340590    1.704102   -0.723720   -1.568220  \n",
+       "  7  -0.025931 -1.361574    1.705092   -1.448196    1.192026  \n",
+       "  8   0.272561  0.297855    2.075133   -1.198339    3.273527  \n",
+       "  9   0.309555  1.039707    0.166827    0.692491    2.756655  \n",
+       "  10  0.031429  1.395998   -2.237233    0.815522    0.646515  \n",
+       "  11  0.673692  0.201508   -3.840153    0.750421   -1.663495  \n",
+       "  12  1.631110 -2.670788   -1.518462    1.112364   -3.471314  \n",
+       "  13 -0.359936 -1.289608    1.267056    0.005452   -2.101436  \n",
+       "  14 -1.741496 -0.116780    3.106709   -1.142208   -0.869615  \n",
+       "  15 -2.526395  1.614472    1.725591    0.057326    2.666487  \n",
+       "  16 -1.518668  2.154205    0.786935    1.495887    2.240553  \n",
+       "  17  1.355525  1.207416   -1.649485    1.454943    2.266537  \n",
+       "  18  3.884840  0.367314   -0.298820    0.725941   -0.320434  \n",
+       "  19  1.699563 -0.367988    0.274988   -0.677102   -1.985275  \n",
+       "  20  0.708916  0.552751    0.631237   -2.013854   -3.874495  \n",
+       "  21 -1.714540 -1.064707   -2.163864   -1.063695   -2.216635  \n",
+       "  22 -2.161338 -1.120923   -1.966759    0.102941    0.930983  \n",
+       "  23 -1.991172 -0.721443   -1.458312    2.282982    2.813257  \n",
+       "  24  0.532299 -0.410358    0.824656    2.179484    2.967591  \n",
+       "  25  1.009821 -0.354782    0.955574    3.099191    0.147491  \n",
+       "  26  3.628663 -0.130757   -0.631935    1.664723   -1.325695  \n",
+       "  27  1.843229 -0.709342   -0.517911   -1.656955   -2.264833  \n",
+       "  28 -0.616835 -1.119329    0.805693   -3.868187   -2.817207  \n",
+       "  29 -3.554203 -1.570185    1.766644   -4.865877   -0.919582  \n",
+       "  30 -4.257360 -0.418469    2.307599   -2.187351    0.963567  \n",
+       "  31 -0.119455 -0.281621    0.783234    0.393718    1.545330  \n",
+       "  32  2.878741  0.150550   -2.180582    3.150340    0.726139  \n",
+       "  33  4.045855  0.673327   -3.695125    3.024373   -0.248885  \n",
+       "  34  1.820807  1.602962   -2.605067    2.059776   -2.151407  \n",
+       "  35 -0.440143 -0.590595    1.852935   -1.406104   -4.160708  \n",
+       "  36 -3.174812 -0.291751    4.630328   -1.580882   -0.958740  \n",
+       "  37 -1.563825  0.278739    2.897067   -1.391597    1.994374  \n",
+       "  38  0.441341  2.033921   -1.264514   -0.685457    2.212074  \n",
+       "  39  1.801959 -0.441788   -3.471700    1.980183    1.442989  \n",
+       "  40  1.513950 -2.583184   -2.865498    1.549641   -1.146023  \n",
+       "  41 -2.061701 -1.797754   -0.527448    0.942418   -0.684837  \n",
+       "  42 -2.850175 -1.090027    1.084149   -1.962063   -0.640512  \n",
+       "  43 -2.732292  1.271256    2.408177   -2.242937    1.130697  \n",
+       "  44 -0.905164  2.089798    1.466105   -1.487153    1.213567  \n",
+       "  45  0.611125  0.261792    0.021143   -0.262568    1.364966  \n",
+       "  46  1.593971 -1.296559   -0.924616    1.371395   -0.453440  \n",
+       "  47 -0.529872 -2.281316   -1.807695    1.724627    0.145439  \n",
+       "  48 -1.965396 -0.649996   -0.475454    0.253547    0.444446  \n",
+       "  49 -0.734198  0.208445    0.788400   -1.853269   -0.377664  \n",
+       "  50  0.836875  0.165788   -0.908795   -2.344198   -0.558292  \n",
+       "  51  1.274295  1.831221   -0.497523    0.297553   -1.065603  \n",
+       "  52  1.930387  1.782486    0.791763    1.606153    0.399564  \n",
+       "  53  2.143894  1.350928    1.440569    4.128145    0.637437  \n",
+       "  54  0.362025  0.496611    0.420047    1.800464   -0.112133  \n",
+       "  55 -0.572182  1.240424   -1.262179   -0.925236   -0.530923  \n",
+       "  56 -2.273523 -0.743831   -0.259603   -2.086590   -0.129749  \n",
+       "  57 -1.685532 -0.216767    1.068656   -2.461740   -0.512549  \n",
+       "  58 -0.486126 -0.680811    2.539918   -1.339505   -1.449519  \n",
+       "  59  0.208132 -0.662958    0.811238    1.353678   -0.705613  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  2.281756   \n",
+       "  3   2.281756 -0.104726  0.989979  0.182413  0.685058  0.595518  0.529073   \n",
+       "  4   0.529073 -0.782835 -0.924510 -0.808929 -1.441714 -0.617369 -1.315565   \n",
+       "  5  -1.315565 -1.696619 -0.320573 -0.567488 -2.017620 -0.435067 -1.641931   \n",
+       "  6  -1.641931 -1.792124  0.257259  0.085120 -1.746782  0.160893 -0.676535   \n",
+       "  7  -0.676535 -0.891331  2.489812  0.454530 -1.032013  0.827485  0.276114   \n",
+       "  8   0.276114 -0.841488  3.011731  0.620245  1.670192 -0.004846  0.320733   \n",
+       "  9   0.320733  1.523393  0.480012 -0.780799  2.722037 -0.064361  1.037821   \n",
+       "  10  1.037821  1.747199 -0.561979 -1.919763  3.191223 -0.448447  0.914247   \n",
+       "  11  0.914247  0.839933 -4.056442 -2.777253  1.251910 -0.109725 -0.019356   \n",
+       "  12 -0.019356 -2.250154 -2.272770 -0.719598 -3.494035 -0.079461 -0.517964   \n",
+       "  13 -0.517964 -1.893377  0.263116  1.174733 -4.961369  1.678953 -1.111905   \n",
+       "  14 -1.111905 -1.305854  4.372789  2.143022 -1.995260  0.727185 -3.190983   \n",
+       "  15 -3.190983  1.832002  4.402938  0.520251  3.951194  1.259433  0.850982   \n",
+       "  16  0.850982  3.378119  2.345476  0.144696  4.078912  1.018360 -0.577886   \n",
+       "  17 -0.577886  1.163580 -3.998867  0.900513  1.572441 -0.670036 -1.053111   \n",
+       "  18 -1.053111 -1.294868 -6.459579 -0.984140 -0.742592 -1.666544 -2.066852   \n",
+       "  19 -2.066852 -2.011582 -4.962978 -1.699675 -3.353646 -0.856638  0.124404   \n",
+       "  20  0.124404 -2.084386  2.693622 -1.892679 -3.402275  0.266078  0.721310   \n",
+       "  21  0.721310 -0.692648  4.520943 -0.084357  0.730858 -1.010170  1.005062   \n",
+       "  22  1.005062  1.825490  2.946025  1.362885  5.029830 -3.372031 -0.401515   \n",
+       "  23 -0.401515  2.826239 -0.356012  1.931716  4.564370 -3.539547  0.011817   \n",
+       "  24  0.011817  1.877753 -3.378513 -0.283849 -1.010133  0.385494 -0.192049   \n",
+       "  25 -0.192049 -0.702262 -5.385245  0.095841 -4.214576  3.590180 -0.376886   \n",
+       "  26 -0.376886 -2.710419 -3.168278 -1.796347 -5.814152  3.814368  0.530634   \n",
+       "  27  0.530634 -2.591355  2.089775 -0.411734 -1.913852  1.874913  1.272804   \n",
+       "  28  1.272804  1.628381  3.499556  0.777606  1.175932 -0.028875  1.635186   \n",
+       "  29  1.635186  3.825824  3.595698  2.611568  3.332857 -2.759503 -0.828159   \n",
+       "  30 -0.828159  1.381723  0.973025  3.630879 -0.418111 -0.360515 -0.930423   \n",
+       "  31 -0.930423 -1.646350 -1.027102  2.819585 -0.765748  1.014899 -2.168143   \n",
+       "  32 -2.168143 -4.428064 -1.428197 -0.531788 -1.746798  3.145738 -0.771254   \n",
+       "  33 -0.771254 -1.898376  0.377410 -2.823518 -1.547244  2.207226  0.397565   \n",
+       "  34  0.397565  0.892250  2.085340 -1.446977 -0.710798  1.364985  2.385935   \n",
+       "  35  2.385935  4.984096  0.147903 -0.754425  1.856307 -0.756861  1.248256   \n",
+       "  36  1.248256  3.832764 -0.968160  1.251553  2.390711 -3.324401 -0.796673   \n",
+       "  37 -0.796673 -0.002295 -1.445334  1.672072  1.504757 -3.670904 -1.851139   \n",
+       "  38 -1.851139 -4.401388 -1.374624  2.615130  1.224281 -0.253406 -2.338516   \n",
+       "  39 -2.338516 -4.971035 -0.163798 -0.557883 -0.149866  1.779794 -1.727167   \n",
+       "  40 -1.727167 -4.149742  0.969136 -1.604806 -0.083507  2.563173  0.906981   \n",
+       "  41  0.906981  1.678084  1.206301 -3.467221  2.469091  0.903672  2.632122   \n",
+       "  42  2.632122  5.066601  0.744050 -1.715261  4.219725 -0.167695  2.705780   \n",
+       "  43  2.705780  3.664931 -0.655162  0.658072  1.172909 -1.588681 -0.035474   \n",
+       "  44 -0.035474 -1.244256 -1.779374  1.240049 -0.861999 -2.541918 -2.567140   \n",
+       "  45 -2.567140 -2.688780 -0.978329  1.082621 -3.932257 -0.742091 -4.179312   \n",
+       "  46 -4.179312 -3.300514  0.844656 -0.593382 -1.922872  0.345041 -2.185247   \n",
+       "  47 -2.185247 -0.924125  0.675608 -2.409111  1.955821 -0.451554  2.130057   \n",
+       "  48  2.130057  2.696849  1.521502 -1.168165  4.679710 -0.407939  3.710439   \n",
+       "  49  3.710439  4.615198 -0.997355  0.611524  1.073172 -0.848433  4.361181   \n",
+       "  50  4.361181  2.384417 -2.918789  3.838661 -1.488791 -0.731633  0.586905   \n",
+       "  51  0.586905 -0.507198 -3.471601  1.377895 -4.074080 -0.395263 -1.952877   \n",
+       "  52 -1.952877 -3.485944 -0.659707 -0.154230 -3.225369  0.076521 -2.216809   \n",
+       "  53 -2.216809 -2.126139  2.531549 -2.456302 -1.107862 -0.356736 -1.681330   \n",
+       "  54 -1.681330 -0.564192  3.871429 -2.344982  2.001984  1.001094  1.322811   \n",
+       "  55  1.322811  2.273654  2.694155 -1.255781  5.092055  1.228220  2.649471   \n",
+       "  56  2.649471  3.995451 -1.164373 -0.364397  4.019769  0.402438  1.538526   \n",
+       "  57  1.538526  1.566843 -3.343593  1.047361 -1.405118 -0.604568  2.022173   \n",
+       "  58  2.022173 -0.113094 -2.921378  0.187850 -4.220116 -0.270801 -0.961754   \n",
+       "  59 -0.961754 -1.618235  0.724721  0.188169 -3.541615 -1.983905 -3.187256   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.104726  0.989979    0.182413    0.685058    0.595518  \n",
+       "  3  -0.782835 -0.924510   -0.808929   -1.441714   -0.617369  \n",
+       "  4  -1.696619 -0.320573   -0.567488   -2.017620   -0.435067  \n",
+       "  5  -1.792124  0.257259    0.085120   -1.746782    0.160893  \n",
+       "  6  -0.891331  2.489812    0.454530   -1.032013    0.827485  \n",
+       "  7  -0.841488  3.011731    0.620245    1.670192   -0.004846  \n",
+       "  8   1.523393  0.480012   -0.780799    2.722037   -0.064361  \n",
+       "  9   1.747199 -0.561979   -1.919763    3.191223   -0.448447  \n",
+       "  10  0.839933 -4.056442   -2.777253    1.251910   -0.109725  \n",
+       "  11 -2.250154 -2.272770   -0.719598   -3.494035   -0.079461  \n",
+       "  12 -1.893377  0.263116    1.174733   -4.961369    1.678953  \n",
+       "  13 -1.305854  4.372789    2.143022   -1.995260    0.727185  \n",
+       "  14  1.832002  4.402938    0.520251    3.951194    1.259433  \n",
+       "  15  3.378119  2.345476    0.144696    4.078912    1.018360  \n",
+       "  16  1.163580 -3.998867    0.900513    1.572441   -0.670036  \n",
+       "  17 -1.294868 -6.459579   -0.984140   -0.742592   -1.666544  \n",
+       "  18 -2.011582 -4.962978   -1.699675   -3.353646   -0.856638  \n",
+       "  19 -2.084386  2.693622   -1.892679   -3.402275    0.266078  \n",
+       "  20 -0.692648  4.520943   -0.084357    0.730858   -1.010170  \n",
+       "  21  1.825490  2.946025    1.362885    5.029830   -3.372031  \n",
+       "  22  2.826239 -0.356012    1.931716    4.564370   -3.539547  \n",
+       "  23  1.877753 -3.378513   -0.283849   -1.010133    0.385494  \n",
+       "  24 -0.702262 -5.385245    0.095841   -4.214576    3.590180  \n",
+       "  25 -2.710419 -3.168278   -1.796347   -5.814152    3.814368  \n",
+       "  26 -2.591355  2.089775   -0.411734   -1.913852    1.874913  \n",
+       "  27  1.628381  3.499556    0.777606    1.175932   -0.028875  \n",
+       "  28  3.825824  3.595698    2.611568    3.332857   -2.759503  \n",
+       "  29  1.381723  0.973025    3.630879   -0.418111   -0.360515  \n",
+       "  30 -1.646350 -1.027102    2.819585   -0.765748    1.014899  \n",
+       "  31 -4.428064 -1.428197   -0.531788   -1.746798    3.145738  \n",
+       "  32 -1.898376  0.377410   -2.823518   -1.547244    2.207226  \n",
+       "  33  0.892250  2.085340   -1.446977   -0.710798    1.364985  \n",
+       "  34  4.984096  0.147903   -0.754425    1.856307   -0.756861  \n",
+       "  35  3.832764 -0.968160    1.251553    2.390711   -3.324401  \n",
+       "  36 -0.002295 -1.445334    1.672072    1.504757   -3.670904  \n",
+       "  37 -4.401388 -1.374624    2.615130    1.224281   -0.253406  \n",
+       "  38 -4.971035 -0.163798   -0.557883   -0.149866    1.779794  \n",
+       "  39 -4.149742  0.969136   -1.604806   -0.083507    2.563173  \n",
+       "  40  1.678084  1.206301   -3.467221    2.469091    0.903672  \n",
+       "  41  5.066601  0.744050   -1.715261    4.219725   -0.167695  \n",
+       "  42  3.664931 -0.655162    0.658072    1.172909   -1.588681  \n",
+       "  43 -1.244256 -1.779374    1.240049   -0.861999   -2.541918  \n",
+       "  44 -2.688780 -0.978329    1.082621   -3.932257   -0.742091  \n",
+       "  45 -3.300514  0.844656   -0.593382   -1.922872    0.345041  \n",
+       "  46 -0.924125  0.675608   -2.409111    1.955821   -0.451554  \n",
+       "  47  2.696849  1.521502   -1.168165    4.679710   -0.407939  \n",
+       "  48  4.615198 -0.997355    0.611524    1.073172   -0.848433  \n",
+       "  49  2.384417 -2.918789    3.838661   -1.488791   -0.731633  \n",
+       "  50 -0.507198 -3.471601    1.377895   -4.074080   -0.395263  \n",
+       "  51 -3.485944 -0.659707   -0.154230   -3.225369    0.076521  \n",
+       "  52 -2.126139  2.531549   -2.456302   -1.107862   -0.356736  \n",
+       "  53 -0.564192  3.871429   -2.344982    2.001984    1.001094  \n",
+       "  54  2.273654  2.694155   -1.255781    5.092055    1.228220  \n",
+       "  55  3.995451 -1.164373   -0.364397    4.019769    0.402438  \n",
+       "  56  1.566843 -3.343593    1.047361   -1.405118   -0.604568  \n",
+       "  57 -0.113094 -2.921378    0.187850   -4.220116   -0.270801  \n",
+       "  58 -1.618235  0.724721    0.188169   -3.541615   -1.983905  \n",
+       "  59 -1.845119  1.464419   -1.450202   -0.886686   -0.839873  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.065927   \n",
+       "  3   1.065927 -1.129150 -0.145572  0.262962 -0.333127 -2.298379 -0.226851   \n",
+       "  4  -0.226851  0.039067 -0.734459 -0.496890 -0.447066 -2.119690 -1.703235   \n",
+       "  5  -1.703235 -0.942808 -1.876503 -2.231306 -0.183414  0.119081  0.309589   \n",
+       "  6   0.309589  0.419404 -0.520016 -1.629720 -0.489692  1.848125 -0.009855   \n",
+       "  7  -0.009855  1.967671  1.277976  0.281440 -0.637763  3.351311  0.329823   \n",
+       "  8   0.329823  0.467934  1.098174  2.189956 -0.126737  1.548503 -0.365954   \n",
+       "  9  -0.365954 -0.160305 -0.595541  2.404160 -0.548854 -0.978379 -0.290600   \n",
+       "  10 -0.290600 -1.002873 -1.511836  0.803268 -0.531034 -2.787546 -0.118152   \n",
+       "  11 -0.118152 -1.691241  0.583903 -0.356293 -0.644646 -2.757610 -0.676523   \n",
+       "  12 -0.676523 -0.091345  2.585964 -2.635668 -0.396182 -1.319541 -1.729889   \n",
+       "  13 -1.729889  2.664846  1.598919 -0.846428 -1.069782  1.464651  0.037742   \n",
+       "  14  0.037742  2.248253 -0.516167  1.445559 -0.437369  3.320925  0.683733   \n",
+       "  15  0.683733  2.702155 -0.789709  2.326875  0.027665  2.330363 -0.050299   \n",
+       "  16 -0.050299 -1.341871 -0.308714  1.414489  0.613780 -0.470234 -0.300919   \n",
+       "  17 -0.300919 -1.496329  0.566759 -0.110280  0.199763 -1.717141  0.497801   \n",
+       "  18  0.497801 -2.111006 -1.464912 -0.446591 -0.248647 -1.649565 -0.116621   \n",
+       "  19 -0.116621 -1.195970 -1.396335 -0.200363  0.305998 -0.770562 -1.056323   \n",
+       "  20 -1.056323 -1.415069 -0.984094  0.059064  0.742499  0.004599 -1.074624   \n",
+       "  21 -1.074624  1.703966 -0.843011  0.559678  1.921958  0.861007  0.158421   \n",
+       "  22  0.158421  0.858839 -0.651269  0.653220  0.390958  0.271341 -0.918556   \n",
+       "  23 -0.918556  1.198652  1.089130  0.355491 -0.209138  2.123899 -1.908472   \n",
+       "  24 -1.908472  0.049514  2.177901  2.016543 -1.198717  1.338002 -1.188970   \n",
+       "  25 -1.188970 -2.090522  0.739881  3.396631 -1.399606  0.461501  1.356726   \n",
+       "  26  1.356726 -1.903481 -0.717617  2.999752 -1.455623 -1.213643  1.340549   \n",
+       "  27  1.340549 -1.599983 -0.970947  0.680427  0.075556 -1.528777  2.901138   \n",
+       "  28  2.901138 -0.899781 -0.082482 -0.460627  1.865768 -1.247103  0.723529   \n",
+       "  29  0.723529 -0.709187  0.024777 -1.786763  1.302163  1.576788 -1.812212   \n",
+       "  30 -1.812212  0.690808  0.393223 -2.079249  0.303533  2.197076 -3.818319   \n",
+       "  31 -3.818319 -1.320139  0.206937 -1.293462 -0.727758  1.822007 -3.326641   \n",
+       "  32 -3.326641 -2.285418 -0.813170  0.737026  0.912065 -1.083674 -2.541009   \n",
+       "  33 -2.541009 -1.073619 -0.598448  2.994121  0.477853 -1.798934  0.444245   \n",
+       "  34  0.444245 -0.002146 -1.879892  2.696903 -0.492452  0.109271  2.678899   \n",
+       "  35  2.678899  0.867780 -0.606820 -0.551317 -1.144618  1.439191  1.451247   \n",
+       "  36  1.451247  1.910135  1.129813 -1.863781 -2.512545  2.970050 -0.118638   \n",
+       "  37 -0.118638  1.118620  2.939312 -2.548154 -1.226858  2.056891 -1.314716   \n",
+       "  38 -1.314716  0.677813  2.911524  0.574715  0.578413  0.642414 -1.378568   \n",
+       "  39 -1.378568  0.287397 -0.546889  3.177157  2.765899 -0.044400  0.433200   \n",
+       "  40  0.433200  0.028260 -2.840302  3.614373 -0.210755 -1.844972  0.206637   \n",
+       "  41  0.206637 -0.345655 -3.116212  1.100547 -1.194855 -2.528869  0.811475   \n",
+       "  42  0.811475  0.266766  0.278757 -3.727508 -0.857623 -1.034732 -0.548095   \n",
+       "  43 -0.548095  0.752643  2.288811 -4.567603 -0.327425 -0.541517 -1.516738   \n",
+       "  44 -1.516738 -0.600106  3.042099 -1.519572  1.001279  1.030859 -0.175399   \n",
+       "  45 -0.175399  0.791671  0.900606  2.157675  0.795121  2.319914  1.867724   \n",
+       "  46  1.867724  0.200728 -1.005914  3.188506  0.188760  1.557828  2.223633   \n",
+       "  47  2.223633 -0.759599 -2.244884  1.584389  0.113352  0.180305  1.883487   \n",
+       "  48  1.883487 -0.584700 -1.401662 -2.030065  1.025071 -2.501401 -0.952581   \n",
+       "  49 -0.952581 -0.130841 -0.779520 -1.748360  1.336602 -2.500186 -2.658098   \n",
+       "  50 -2.658098 -0.354624  0.586064 -0.806690 -0.100760 -3.219488 -2.515415   \n",
+       "  51 -2.515415  1.091325  0.062565  0.890478 -0.924576  0.586100 -1.674817   \n",
+       "  52 -1.674817  1.923527 -0.502957  2.468804  0.779004  2.364926 -0.852709   \n",
+       "  53 -0.852709  2.235653 -1.077432  3.112891  1.409035  3.062119  2.311048   \n",
+       "  54  2.311048  0.731929 -0.529696  2.942452  2.854957  0.523222  3.515195   \n",
+       "  55  3.515195 -0.269767 -2.093485  0.197627  1.172970 -2.074681  0.516586   \n",
+       "  56  0.516586 -0.223825 -1.843967 -2.119556  1.634726 -2.707545 -1.875293   \n",
+       "  57 -1.875293 -0.322237 -1.549905 -4.123002 -0.604928 -0.760790 -2.287502   \n",
+       "  58 -2.287502  0.987370 -1.872278 -2.316730 -1.455108  0.751001 -2.327922   \n",
+       "  59 -2.327922  0.338159  0.086244  0.922441 -3.607049  2.415006 -0.407831   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -1.129150 -0.145572    0.262962   -0.333127   -2.298379  \n",
+       "  3   0.039067 -0.734459   -0.496890   -0.447066   -2.119690  \n",
+       "  4  -0.942808 -1.876503   -2.231306   -0.183414    0.119081  \n",
+       "  5   0.419404 -0.520016   -1.629720   -0.489692    1.848125  \n",
+       "  6   1.967671  1.277976    0.281440   -0.637763    3.351311  \n",
+       "  7   0.467934  1.098174    2.189956   -0.126737    1.548503  \n",
+       "  8  -0.160305 -0.595541    2.404160   -0.548854   -0.978379  \n",
+       "  9  -1.002873 -1.511836    0.803268   -0.531034   -2.787546  \n",
+       "  10 -1.691241  0.583903   -0.356293   -0.644646   -2.757610  \n",
+       "  11 -0.091345  2.585964   -2.635668   -0.396182   -1.319541  \n",
+       "  12  2.664846  1.598919   -0.846428   -1.069782    1.464651  \n",
+       "  13  2.248253 -0.516167    1.445559   -0.437369    3.320925  \n",
+       "  14  2.702155 -0.789709    2.326875    0.027665    2.330363  \n",
+       "  15 -1.341871 -0.308714    1.414489    0.613780   -0.470234  \n",
+       "  16 -1.496329  0.566759   -0.110280    0.199763   -1.717141  \n",
+       "  17 -2.111006 -1.464912   -0.446591   -0.248647   -1.649565  \n",
+       "  18 -1.195970 -1.396335   -0.200363    0.305998   -0.770562  \n",
+       "  19 -1.415069 -0.984094    0.059064    0.742499    0.004599  \n",
+       "  20  1.703966 -0.843011    0.559678    1.921958    0.861007  \n",
+       "  21  0.858839 -0.651269    0.653220    0.390958    0.271341  \n",
+       "  22  1.198652  1.089130    0.355491   -0.209138    2.123899  \n",
+       "  23  0.049514  2.177901    2.016543   -1.198717    1.338002  \n",
+       "  24 -2.090522  0.739881    3.396631   -1.399606    0.461501  \n",
+       "  25 -1.903481 -0.717617    2.999752   -1.455623   -1.213643  \n",
+       "  26 -1.599983 -0.970947    0.680427    0.075556   -1.528777  \n",
+       "  27 -0.899781 -0.082482   -0.460627    1.865768   -1.247103  \n",
+       "  28 -0.709187  0.024777   -1.786763    1.302163    1.576788  \n",
+       "  29  0.690808  0.393223   -2.079249    0.303533    2.197076  \n",
+       "  30 -1.320139  0.206937   -1.293462   -0.727758    1.822007  \n",
+       "  31 -2.285418 -0.813170    0.737026    0.912065   -1.083674  \n",
+       "  32 -1.073619 -0.598448    2.994121    0.477853   -1.798934  \n",
+       "  33 -0.002146 -1.879892    2.696903   -0.492452    0.109271  \n",
+       "  34  0.867780 -0.606820   -0.551317   -1.144618    1.439191  \n",
+       "  35  1.910135  1.129813   -1.863781   -2.512545    2.970050  \n",
+       "  36  1.118620  2.939312   -2.548154   -1.226858    2.056891  \n",
+       "  37  0.677813  2.911524    0.574715    0.578413    0.642414  \n",
+       "  38  0.287397 -0.546889    3.177157    2.765899   -0.044400  \n",
+       "  39  0.028260 -2.840302    3.614373   -0.210755   -1.844972  \n",
+       "  40 -0.345655 -3.116212    1.100547   -1.194855   -2.528869  \n",
+       "  41  0.266766  0.278757   -3.727508   -0.857623   -1.034732  \n",
+       "  42  0.752643  2.288811   -4.567603   -0.327425   -0.541517  \n",
+       "  43 -0.600106  3.042099   -1.519572    1.001279    1.030859  \n",
+       "  44  0.791671  0.900606    2.157675    0.795121    2.319914  \n",
+       "  45  0.200728 -1.005914    3.188506    0.188760    1.557828  \n",
+       "  46 -0.759599 -2.244884    1.584389    0.113352    0.180305  \n",
+       "  47 -0.584700 -1.401662   -2.030065    1.025071   -2.501401  \n",
+       "  48 -0.130841 -0.779520   -1.748360    1.336602   -2.500186  \n",
+       "  49 -0.354624  0.586064   -0.806690   -0.100760   -3.219488  \n",
+       "  50  1.091325  0.062565    0.890478   -0.924576    0.586100  \n",
+       "  51  1.923527 -0.502957    2.468804    0.779004    2.364926  \n",
+       "  52  2.235653 -1.077432    3.112891    1.409035    3.062119  \n",
+       "  53  0.731929 -0.529696    2.942452    2.854957    0.523222  \n",
+       "  54 -0.269767 -2.093485    0.197627    1.172970   -2.074681  \n",
+       "  55 -0.223825 -1.843967   -2.119556    1.634726   -2.707545  \n",
+       "  56 -0.322237 -1.549905   -4.123002   -0.604928   -0.760790  \n",
+       "  57  0.987370 -1.872278   -2.316730   -1.455108    0.751001  \n",
+       "  58  0.338159  0.086244    0.922441   -3.607049    2.415006  \n",
+       "  59  0.258702  1.856324    2.974512   -3.065267    1.754975  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.303059   \n",
+       "  3   0.303059  0.508749  0.733305  0.546017  0.194887  1.073301  0.658458   \n",
+       "  4   0.658458 -2.267740 -0.585056 -1.111503 -0.547529  0.291365 -1.453656   \n",
+       "  5  -1.453656 -1.716995 -2.356436 -3.253331 -1.387582 -0.598357 -3.240262   \n",
+       "  6  -3.240262 -1.226992 -2.576672 -1.073448 -1.871488 -0.700121 -2.709873   \n",
+       "  7  -2.709873  1.559477 -0.769423  0.319396  0.530785 -0.353852  0.022122   \n",
+       "  8   0.022122  2.380026  1.270768  4.118615  3.138196  0.197063  1.766674   \n",
+       "  9   1.766674 -0.334372  1.685813  2.511961  3.817816 -1.222586  2.686307   \n",
+       "  10  2.686307 -2.607132  1.208918 -0.893193  1.084161  0.027545  2.300942   \n",
+       "  11  2.300942 -2.671846  1.279609 -4.513671 -1.843386  1.769177 -0.675433   \n",
+       "  12 -0.675433 -1.664796  1.367647 -2.635851 -3.255790  0.924899 -1.393441   \n",
+       "  13 -1.393441  0.615029  2.088077 -0.113654 -2.406610 -2.362381 -2.161451   \n",
+       "  14 -2.161451  0.970976 -0.095354  1.745581 -0.083896 -2.822953 -0.178742   \n",
+       "  15 -0.178742  2.337222 -2.759660  0.563344  2.499992 -3.967942  0.334270   \n",
+       "  16  0.334270  1.112930 -2.432778 -0.369116  2.803239 -1.271597  1.687954   \n",
+       "  17  1.687954 -0.660789 -1.984596 -0.799266  0.554888  1.793544  3.633139   \n",
+       "  18  3.633139 -1.673768 -0.213790 -0.664442 -2.569645  3.520735  2.524112   \n",
+       "  19  2.524112 -1.192207 -0.207984 -0.569605 -2.349831  2.510008 -0.942361   \n",
+       "  20 -0.942361  0.445359  0.226624 -0.696736  1.296513  1.489845 -2.289231   \n",
+       "  21 -2.289231  3.150680 -0.225147  0.730078  3.390333 -1.092259 -2.806781   \n",
+       "  22 -2.806781  3.134423 -2.015270  0.296402  2.783491 -2.512975 -0.969148   \n",
+       "  23 -0.969148  0.968312  1.329630  0.966062 -0.072732 -2.173000  1.714887   \n",
+       "  24  1.714887  0.478157  2.311676  0.686641 -3.548052 -1.304401  1.406199   \n",
+       "  25  1.406199 -1.598989  2.788026  0.141853 -4.071758 -0.467957  1.985095   \n",
+       "  26  1.985095 -3.206372  1.709661 -0.748561 -1.353237  0.975790  0.189843   \n",
+       "  27  0.189843 -2.768109 -1.348263 -1.320079  1.602202 -0.795378 -2.202968   \n",
+       "  28 -2.202968 -0.883460 -3.041986 -1.348746  2.285498 -0.300856 -3.748205   \n",
+       "  29 -3.748205 -0.086427 -1.894720  0.898594  2.102088 -0.092700 -1.369822   \n",
+       "  30 -1.369822  0.208175 -0.708731 -0.997437 -0.920050  1.870832  0.769868   \n",
+       "  31  0.769868  0.905983  0.902815 -1.734688 -2.612131  2.336676  2.997934   \n",
+       "  32  2.997934 -1.215010  2.523512 -1.328917 -3.480561  1.327369  2.645706   \n",
+       "  33  2.645706 -0.804223  1.295382  0.098590  0.142812  0.823260 -2.172717   \n",
+       "  34 -2.172717 -0.853546 -0.288420  1.925963  1.004870  1.440017 -2.793952   \n",
+       "  35 -2.793952  0.593602 -0.399525  0.662138  2.282229  1.274813 -3.255706   \n",
+       "  36 -3.255706 -0.853219 -0.942886  0.146956  3.000077  1.633068 -1.315727   \n",
+       "  37 -1.315727 -1.735199 -0.737668 -1.827157  0.341321  0.197879  2.200470   \n",
+       "  38  2.200470 -2.707124 -0.529547 -2.113975 -1.911842 -1.649084  3.095209   \n",
+       "  39  3.095209 -1.143105 -0.082339 -1.715145 -3.511133 -2.785137  0.500564   \n",
+       "  40  0.500564  0.950763  1.357323 -1.219940 -1.537337 -2.807858 -0.030754   \n",
+       "  41 -0.030754  0.983126  1.827488  0.876016  2.931701 -2.520359 -0.518838   \n",
+       "  42 -0.518838  0.223617  1.103188  2.583420  4.858533  1.805786 -1.730338   \n",
+       "  43 -1.730338 -0.166259 -1.176033  2.982766  2.953948  2.193387 -0.420947   \n",
+       "  44 -0.420947  0.262731 -2.021986  0.374629 -0.159264  1.507455  1.284013   \n",
+       "  45  1.284013  0.889959 -0.602899 -1.199823 -2.668727 -0.267424  2.039556   \n",
+       "  46  2.039556 -1.717274  2.517895 -1.051488 -2.372563 -1.049826  0.385622   \n",
+       "  47  0.385622 -2.085320  2.808822  1.019218 -0.729539 -2.521014 -0.076425   \n",
+       "  48 -0.076425 -0.882166  0.711508  0.589100  1.772971 -0.720909 -0.674243   \n",
+       "  49 -0.674243  1.900014  0.686983  1.337531  2.108643  0.728325  1.361858   \n",
+       "  50  1.361858  2.707370 -0.624093  1.085738  3.607258  3.355115  1.541039   \n",
+       "  51  1.541039  1.144388 -2.097365  0.164257  0.406759  3.620174  1.461780   \n",
+       "  52  1.461780 -1.972621 -0.201806 -0.668393 -1.678727  0.411153  1.101052   \n",
+       "  53  1.101052 -3.201331  0.419886 -2.517425 -2.138583 -1.444822 -1.411419   \n",
+       "  54 -1.411419 -1.901268 -0.938771 -1.916766 -1.284322 -3.427905 -2.435400   \n",
+       "  55 -2.435400  0.924225 -0.057511 -1.104618  0.131425 -1.309411 -3.236666   \n",
+       "  56 -3.236666  1.756614  0.672558  0.841896  1.710659  0.410335 -0.349064   \n",
+       "  57 -0.349064  0.617771  1.745129  3.010612  1.623593 -0.183174  3.073416   \n",
+       "  58  3.073416 -0.147128  1.184319  3.310765  0.395828  0.582789  4.934669   \n",
+       "  59  4.934669 -0.592864  0.844094  2.023586 -0.766702  1.608181  2.275064   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.508749  0.733305    0.546017    0.194887    1.073301  \n",
+       "  3  -2.267740 -0.585056   -1.111503   -0.547529    0.291365  \n",
+       "  4  -1.716995 -2.356436   -3.253331   -1.387582   -0.598357  \n",
+       "  5  -1.226992 -2.576672   -1.073448   -1.871488   -0.700121  \n",
+       "  6   1.559477 -0.769423    0.319396    0.530785   -0.353852  \n",
+       "  7   2.380026  1.270768    4.118615    3.138196    0.197063  \n",
+       "  8  -0.334372  1.685813    2.511961    3.817816   -1.222586  \n",
+       "  9  -2.607132  1.208918   -0.893193    1.084161    0.027545  \n",
+       "  10 -2.671846  1.279609   -4.513671   -1.843386    1.769177  \n",
+       "  11 -1.664796  1.367647   -2.635851   -3.255790    0.924899  \n",
+       "  12  0.615029  2.088077   -0.113654   -2.406610   -2.362381  \n",
+       "  13  0.970976 -0.095354    1.745581   -0.083896   -2.822953  \n",
+       "  14  2.337222 -2.759660    0.563344    2.499992   -3.967942  \n",
+       "  15  1.112930 -2.432778   -0.369116    2.803239   -1.271597  \n",
+       "  16 -0.660789 -1.984596   -0.799266    0.554888    1.793544  \n",
+       "  17 -1.673768 -0.213790   -0.664442   -2.569645    3.520735  \n",
+       "  18 -1.192207 -0.207984   -0.569605   -2.349831    2.510008  \n",
+       "  19  0.445359  0.226624   -0.696736    1.296513    1.489845  \n",
+       "  20  3.150680 -0.225147    0.730078    3.390333   -1.092259  \n",
+       "  21  3.134423 -2.015270    0.296402    2.783491   -2.512975  \n",
+       "  22  0.968312  1.329630    0.966062   -0.072732   -2.173000  \n",
+       "  23  0.478157  2.311676    0.686641   -3.548052   -1.304401  \n",
+       "  24 -1.598989  2.788026    0.141853   -4.071758   -0.467957  \n",
+       "  25 -3.206372  1.709661   -0.748561   -1.353237    0.975790  \n",
+       "  26 -2.768109 -1.348263   -1.320079    1.602202   -0.795378  \n",
+       "  27 -0.883460 -3.041986   -1.348746    2.285498   -0.300856  \n",
+       "  28 -0.086427 -1.894720    0.898594    2.102088   -0.092700  \n",
+       "  29  0.208175 -0.708731   -0.997437   -0.920050    1.870832  \n",
+       "  30  0.905983  0.902815   -1.734688   -2.612131    2.336676  \n",
+       "  31 -1.215010  2.523512   -1.328917   -3.480561    1.327369  \n",
+       "  32 -0.804223  1.295382    0.098590    0.142812    0.823260  \n",
+       "  33 -0.853546 -0.288420    1.925963    1.004870    1.440017  \n",
+       "  34  0.593602 -0.399525    0.662138    2.282229    1.274813  \n",
+       "  35 -0.853219 -0.942886    0.146956    3.000077    1.633068  \n",
+       "  36 -1.735199 -0.737668   -1.827157    0.341321    0.197879  \n",
+       "  37 -2.707124 -0.529547   -2.113975   -1.911842   -1.649084  \n",
+       "  38 -1.143105 -0.082339   -1.715145   -3.511133   -2.785137  \n",
+       "  39  0.950763  1.357323   -1.219940   -1.537337   -2.807858  \n",
+       "  40  0.983126  1.827488    0.876016    2.931701   -2.520359  \n",
+       "  41  0.223617  1.103188    2.583420    4.858533    1.805786  \n",
+       "  42 -0.166259 -1.176033    2.982766    2.953948    2.193387  \n",
+       "  43  0.262731 -2.021986    0.374629   -0.159264    1.507455  \n",
+       "  44  0.889959 -0.602899   -1.199823   -2.668727   -0.267424  \n",
+       "  45 -1.717274  2.517895   -1.051488   -2.372563   -1.049826  \n",
+       "  46 -2.085320  2.808822    1.019218   -0.729539   -2.521014  \n",
+       "  47 -0.882166  0.711508    0.589100    1.772971   -0.720909  \n",
+       "  48  1.900014  0.686983    1.337531    2.108643    0.728325  \n",
+       "  49  2.707370 -0.624093    1.085738    3.607258    3.355115  \n",
+       "  50  1.144388 -2.097365    0.164257    0.406759    3.620174  \n",
+       "  51 -1.972621 -0.201806   -0.668393   -1.678727    0.411153  \n",
+       "  52 -3.201331  0.419886   -2.517425   -2.138583   -1.444822  \n",
+       "  53 -1.901268 -0.938771   -1.916766   -1.284322   -3.427905  \n",
+       "  54  0.924225 -0.057511   -1.104618    0.131425   -1.309411  \n",
+       "  55  1.756614  0.672558    0.841896    1.710659    0.410335  \n",
+       "  56  0.617771  1.745129    3.010612    1.623593   -0.183174  \n",
+       "  57 -0.147128  1.184319    3.310765    0.395828    0.582789  \n",
+       "  58 -0.592864  0.844094    2.023586   -0.766702    1.608181  \n",
+       "  59  1.214050 -1.003962   -1.830210   -1.776676    0.730259  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.318022   \n",
+       "  3   1.318022 -0.705374  0.173057  0.222896 -0.588203 -0.198208  1.960537   \n",
+       "  4   1.960537 -2.559435 -0.501387  0.839672  0.559068 -2.160599  0.017721   \n",
+       "  5   0.017721 -3.060237 -1.361309 -1.013573  0.461948 -1.257565  0.155002   \n",
+       "  6   0.155002 -1.119375 -0.454319 -1.688525  2.104402 -1.841894 -1.085753   \n",
+       "  7  -1.085753  1.293196 -0.190458 -0.237182  1.474107  0.436701 -1.867821   \n",
+       "  8  -1.867821  2.047261 -0.283997 -1.028584  0.261120  2.058711 -2.242755   \n",
+       "  9  -2.242755  2.468857  0.427383  1.216543 -0.271528  3.824052  1.339601   \n",
+       "  10  1.339601  1.068227  0.703297  0.365135 -1.042920  2.005444  1.526051   \n",
+       "  11  1.526051 -2.155562 -0.360139  0.185581 -0.847870 -1.594307 -0.611233   \n",
+       "  12 -0.611233 -3.133265 -0.780853 -0.658007 -2.040833 -2.894661 -2.546642   \n",
+       "  13 -2.546642 -1.325509 -0.012907 -0.318319 -1.310871 -2.754281 -3.480478   \n",
+       "  14 -3.480478  0.454084 -0.148165  0.355603  1.332692  0.860725 -1.038057   \n",
+       "  15 -1.038057  2.914358  1.978749 -0.123975  3.120315  3.974005  2.465136   \n",
+       "  16  2.465136  3.173975  2.048742  1.605967  2.188068  4.735691  2.660454   \n",
+       "  17  2.660454  2.024336 -0.171642  0.708423 -1.491908  3.171533  0.770174   \n",
+       "  18  0.770174 -2.050031 -2.343576 -0.454989 -2.442968 -0.885295 -1.531265   \n",
+       "  19 -1.531265 -3.758613 -2.608809 -0.852550 -3.489255 -2.668525 -2.367284   \n",
+       "  20 -2.367284 -3.678954 -2.498845 -0.478235 -0.074406 -1.569569 -1.295346   \n",
+       "  21 -1.295346  0.379940 -0.242977 -0.107173  1.398080  0.135040  0.457778   \n",
+       "  22  0.457778  1.166403  1.562324  1.242453  3.342446  1.904756  0.128416   \n",
+       "  23  0.128416  1.780939  2.391824  1.238379  2.288168  1.843410 -1.150852   \n",
+       "  24 -1.150852  0.140331  1.828930 -0.271579  0.065280  0.365272  0.277162   \n",
+       "  25  0.277162 -2.886062  1.446352 -1.219588 -2.157151  0.484360 -1.083939   \n",
+       "  26 -1.083939 -2.447352 -0.016858 -2.642850 -3.107516 -0.554896 -0.520372   \n",
+       "  27 -0.520372 -0.775812 -1.155487 -1.524357 -0.093602 -0.467962 -0.508474   \n",
+       "  28 -0.508474  1.095141 -0.513294 -0.513172  2.085372 -1.035271 -0.912492   \n",
+       "  29 -0.912492  2.768243 -0.403796  1.619122  2.648908 -0.697494  0.636176   \n",
+       "  30  0.636176  1.517709 -1.667691  2.744214  2.462068 -0.953704  1.062670   \n",
+       "  31  1.062670 -0.140952 -1.705737  0.961319 -0.712476 -0.473472  1.768852   \n",
+       "  32  1.768852 -1.511539  0.402010 -0.309642 -2.144240  0.044911 -0.189505   \n",
+       "  33 -0.189505 -2.000577  1.590773 -0.552878 -2.725425  1.107479 -1.769739   \n",
+       "  34 -1.769739 -0.889156  1.890450 -0.628286 -2.285866  0.883430 -2.971872   \n",
+       "  35 -2.971872  1.297451  0.527166 -0.738494 -2.882699  0.691040 -0.933044   \n",
+       "  36 -0.933044  2.321809 -1.194989  1.762258  0.335505 -1.054582  1.469474   \n",
+       "  37  1.469474  1.563555 -1.745492  0.500360  2.722294 -0.811021  1.242952   \n",
+       "  38  1.242952  0.180440 -1.885440  1.627013  2.248358 -1.808251 -0.087581   \n",
+       "  39 -0.087581 -2.522624 -0.362086  1.007560  0.964299 -0.870588  1.017785   \n",
+       "  40  1.017785 -2.781342  0.817183  0.663562 -1.820148  0.364139 -0.672004   \n",
+       "  41 -0.672004 -2.167255  2.300983 -1.974942 -1.013245  0.564154 -1.123884   \n",
+       "  42 -1.123884 -0.415798  2.441424 -0.765154 -1.424569  1.052126 -1.351663   \n",
+       "  43 -1.351663  2.568096  0.311051 -1.883462 -1.904852  2.275996  1.319484   \n",
+       "  44  1.319484  4.119006 -0.316418  1.779866 -1.687830  0.635614  1.873206   \n",
+       "  45  1.873206  1.781006 -1.377931  3.125754  0.163320 -0.298813  3.919549   \n",
+       "  46  3.919549  0.970347 -1.745440  3.349795  1.482797 -1.296647 -0.051696   \n",
+       "  47 -0.051696 -3.883912 -0.094620  1.607741  1.473814 -3.055682 -2.292837   \n",
+       "  48 -2.292837 -4.235090  2.039402  2.200827  1.205105 -1.701420 -3.080367   \n",
+       "  49 -3.080367 -3.175750  2.986576 -0.647638 -1.331398  0.562753 -1.689837   \n",
+       "  50 -1.689837  0.058628  1.777165 -1.597174 -2.193882  2.956861 -0.031483   \n",
+       "  51 -0.031483  3.252531  0.269073 -2.598201 -2.134880  4.577757  2.509030   \n",
+       "  52  2.509030  2.199100 -3.040408  0.698478  0.686428 -0.294476  2.140124   \n",
+       "  53  2.140124  2.214427 -3.690875  1.791727  0.474349 -2.945262  0.261119   \n",
+       "  54  0.261119 -0.501058 -2.925490  2.707467  1.220996 -3.550328 -2.244344   \n",
+       "  55 -2.244344 -2.334045 -2.372469  0.899737 -0.123707 -1.919580 -3.475013   \n",
+       "  56 -3.475013 -1.973560  0.941548 -2.434012 -0.167311  1.796609 -0.086095   \n",
+       "  57 -0.086095 -0.194237  3.567802 -3.412758 -1.739348  2.765510  2.507061   \n",
+       "  58  2.507061  0.125911  2.318348 -3.203473 -1.879729  1.693009  3.563416   \n",
+       "  59  3.563416  0.851939  2.366013  0.355511 -1.085278 -0.682373  2.474403   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.705374  0.173057    0.222896   -0.588203   -0.198208  \n",
+       "  3  -2.559435 -0.501387    0.839672    0.559068   -2.160599  \n",
+       "  4  -3.060237 -1.361309   -1.013573    0.461948   -1.257565  \n",
+       "  5  -1.119375 -0.454319   -1.688525    2.104402   -1.841894  \n",
+       "  6   1.293196 -0.190458   -0.237182    1.474107    0.436701  \n",
+       "  7   2.047261 -0.283997   -1.028584    0.261120    2.058711  \n",
+       "  8   2.468857  0.427383    1.216543   -0.271528    3.824052  \n",
+       "  9   1.068227  0.703297    0.365135   -1.042920    2.005444  \n",
+       "  10 -2.155562 -0.360139    0.185581   -0.847870   -1.594307  \n",
+       "  11 -3.133265 -0.780853   -0.658007   -2.040833   -2.894661  \n",
+       "  12 -1.325509 -0.012907   -0.318319   -1.310871   -2.754281  \n",
+       "  13  0.454084 -0.148165    0.355603    1.332692    0.860725  \n",
+       "  14  2.914358  1.978749   -0.123975    3.120315    3.974005  \n",
+       "  15  3.173975  2.048742    1.605967    2.188068    4.735691  \n",
+       "  16  2.024336 -0.171642    0.708423   -1.491908    3.171533  \n",
+       "  17 -2.050031 -2.343576   -0.454989   -2.442968   -0.885295  \n",
+       "  18 -3.758613 -2.608809   -0.852550   -3.489255   -2.668525  \n",
+       "  19 -3.678954 -2.498845   -0.478235   -0.074406   -1.569569  \n",
+       "  20  0.379940 -0.242977   -0.107173    1.398080    0.135040  \n",
+       "  21  1.166403  1.562324    1.242453    3.342446    1.904756  \n",
+       "  22  1.780939  2.391824    1.238379    2.288168    1.843410  \n",
+       "  23  0.140331  1.828930   -0.271579    0.065280    0.365272  \n",
+       "  24 -2.886062  1.446352   -1.219588   -2.157151    0.484360  \n",
+       "  25 -2.447352 -0.016858   -2.642850   -3.107516   -0.554896  \n",
+       "  26 -0.775812 -1.155487   -1.524357   -0.093602   -0.467962  \n",
+       "  27  1.095141 -0.513294   -0.513172    2.085372   -1.035271  \n",
+       "  28  2.768243 -0.403796    1.619122    2.648908   -0.697494  \n",
+       "  29  1.517709 -1.667691    2.744214    2.462068   -0.953704  \n",
+       "  30 -0.140952 -1.705737    0.961319   -0.712476   -0.473472  \n",
+       "  31 -1.511539  0.402010   -0.309642   -2.144240    0.044911  \n",
+       "  32 -2.000577  1.590773   -0.552878   -2.725425    1.107479  \n",
+       "  33 -0.889156  1.890450   -0.628286   -2.285866    0.883430  \n",
+       "  34  1.297451  0.527166   -0.738494   -2.882699    0.691040  \n",
+       "  35  2.321809 -1.194989    1.762258    0.335505   -1.054582  \n",
+       "  36  1.563555 -1.745492    0.500360    2.722294   -0.811021  \n",
+       "  37  0.180440 -1.885440    1.627013    2.248358   -1.808251  \n",
+       "  38 -2.522624 -0.362086    1.007560    0.964299   -0.870588  \n",
+       "  39 -2.781342  0.817183    0.663562   -1.820148    0.364139  \n",
+       "  40 -2.167255  2.300983   -1.974942   -1.013245    0.564154  \n",
+       "  41 -0.415798  2.441424   -0.765154   -1.424569    1.052126  \n",
+       "  42  2.568096  0.311051   -1.883462   -1.904852    2.275996  \n",
+       "  43  4.119006 -0.316418    1.779866   -1.687830    0.635614  \n",
+       "  44  1.781006 -1.377931    3.125754    0.163320   -0.298813  \n",
+       "  45  0.970347 -1.745440    3.349795    1.482797   -1.296647  \n",
+       "  46 -3.883912 -0.094620    1.607741    1.473814   -3.055682  \n",
+       "  47 -4.235090  2.039402    2.200827    1.205105   -1.701420  \n",
+       "  48 -3.175750  2.986576   -0.647638   -1.331398    0.562753  \n",
+       "  49  0.058628  1.777165   -1.597174   -2.193882    2.956861  \n",
+       "  50  3.252531  0.269073   -2.598201   -2.134880    4.577757  \n",
+       "  51  2.199100 -3.040408    0.698478    0.686428   -0.294476  \n",
+       "  52  2.214427 -3.690875    1.791727    0.474349   -2.945262  \n",
+       "  53 -0.501058 -2.925490    2.707467    1.220996   -3.550328  \n",
+       "  54 -2.334045 -2.372469    0.899737   -0.123707   -1.919580  \n",
+       "  55 -1.973560  0.941548   -2.434012   -0.167311    1.796609  \n",
+       "  56 -0.194237  3.567802   -3.412758   -1.739348    2.765510  \n",
+       "  57  0.125911  2.318348   -3.203473   -1.879729    1.693009  \n",
+       "  58  0.851939  2.366013    0.355511   -1.085278   -0.682373  \n",
+       "  59 -1.038674 -0.990974    1.332450   -0.164939   -3.103476  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.081768   \n",
+       "  3   0.081768 -0.309255  1.126272  0.300695 -0.774109  1.041044  0.248471   \n",
+       "  4   0.248471 -1.884035  1.209108 -1.022442 -1.494222  1.397284 -0.024922   \n",
+       "  5  -0.024922 -1.296156 -0.175095 -2.366323 -3.345969  1.168661  0.274848   \n",
+       "  6   0.274848 -1.632979 -0.949400 -0.362497 -0.250223 -0.831824 -0.248998   \n",
+       "  7  -0.248998  1.729775 -0.637159  0.458590  2.560417 -1.507674 -0.637704   \n",
+       "  8  -0.637704  1.317286 -0.498336  0.708780  2.565440 -1.012042 -1.353211   \n",
+       "  9  -1.353211  0.935585 -0.275544 -1.996965  3.428663 -1.561964 -0.372519   \n",
+       "  10 -0.372519 -2.797402  1.206747 -1.834660  1.071987 -0.983100  1.429926   \n",
+       "  11  1.429926 -1.803296  3.133812 -1.103610 -1.178627  0.333679  2.517283   \n",
+       "  12  2.517283 -1.543362  2.749359  0.831846 -2.574442  0.473862  0.314119   \n",
+       "  13  0.314119  0.371672  0.440380  2.124000 -3.141057  1.571531 -0.347549   \n",
+       "  14 -0.347549  1.418557 -2.447773  1.195063 -0.711927  1.043852 -2.022627   \n",
+       "  15 -2.022627 -0.155421 -2.544949 -1.130913  1.243148  0.012349 -2.405155   \n",
+       "  16 -2.405155  0.808931 -1.310737 -1.650604  2.605323 -2.099710  0.262842   \n",
+       "  17  0.262842 -0.096364  1.593772 -1.995327 -1.742330 -0.797968 -0.422769   \n",
+       "  18 -0.422769 -1.332827  2.036699  0.176385 -1.214562 -0.594005  1.373380   \n",
+       "  19  1.373380 -1.871557  0.536830  1.997101 -0.480969 -0.297629  1.026735   \n",
+       "  20  1.026735  0.068824 -0.169869  1.601374  0.510521 -0.419812  0.722494   \n",
+       "  21  0.722494  0.720812 -1.434619  2.179372  0.499635  0.370577 -0.533229   \n",
+       "  22 -0.533229  0.825454 -0.163846  0.924967 -1.198584 -0.937493 -1.233355   \n",
+       "  23 -1.233355  1.056568 -0.068654 -1.008528 -1.310346  1.528837 -0.669107   \n",
+       "  24 -0.669107 -0.266703  1.762183 -3.812549 -0.834219  1.113836 -0.823579   \n",
+       "  25 -0.823579 -1.527048  0.902671 -2.616214  1.045983 -1.040706  0.911095   \n",
+       "  26  0.911095 -1.890050 -0.856264 -0.108414  2.725565 -3.462253  1.437069   \n",
+       "  27  1.437069  0.364677 -1.324388  0.238452  1.028790 -2.186889  1.541537   \n",
+       "  28  1.541537  2.199957  0.422379  2.745858 -2.397578  0.465837 -0.137670   \n",
+       "  29 -0.137670  1.484811  2.810246  1.799101 -3.153385  2.492490 -2.121062   \n",
+       "  30 -2.121062 -0.299536  0.788298 -0.037720 -1.761846  1.978805 -3.023063   \n",
+       "  31 -3.023063 -2.176350 -0.300658 -2.860806  1.663133  1.433532 -1.565698   \n",
+       "  32 -1.565698 -1.911574 -2.779845 -3.743198  1.649741 -1.793289  1.492016   \n",
+       "  33  1.492016 -0.948845 -0.985285 -1.971458  1.135587 -2.500652  2.338310   \n",
+       "  34  2.338310  0.235047 -0.274768 -0.745254 -0.805097  0.194976  2.277998   \n",
+       "  35  2.277998  0.791396  1.082425  3.431903 -3.325516  0.995009  0.663557   \n",
+       "  36  0.663557  0.902697  3.294412  2.325678 -2.452488  1.907496 -1.723371   \n",
+       "  37 -1.723371  2.219608  2.521467  1.135364  0.094458  0.834468 -0.605390   \n",
+       "  38 -0.605390  1.237961 -0.197388 -0.751953  2.124663  0.601094 -0.244006   \n",
+       "  39 -0.244006  1.700947 -2.695462 -1.940800  2.725703 -0.561375  1.565081   \n",
+       "  40  1.565081 -1.355505 -3.806281 -1.068767  1.180426 -0.952366  0.486718   \n",
+       "  41  0.486718 -1.730727 -2.599373  0.266506 -1.332043 -1.253009  1.737847   \n",
+       "  42  1.737847 -2.267713 -0.715381  2.292210 -1.310995 -0.732399  0.064020   \n",
+       "  43  0.064020 -1.508513  2.221588  1.022769 -1.144995  0.997470 -1.250930   \n",
+       "  44 -1.250930  1.512030  3.852600  1.332008  0.319911  1.197615 -1.118992   \n",
+       "  45 -1.118992  2.672619  0.358683  0.075972 -0.391566  1.312896 -0.645879   \n",
+       "  46 -0.645879  1.152481  0.029503  0.846784 -0.110546  2.967769  0.565362   \n",
+       "  47  0.565362 -1.454538 -0.916385 -0.215319 -0.144875 -0.045483  0.992438   \n",
+       "  48  0.992438 -2.480947 -3.107309  0.807933  0.032034 -1.986763  0.808697   \n",
+       "  49  0.808697 -0.387218 -2.134421  1.671067  0.255928 -2.860003  0.498677   \n",
+       "  50  0.498677  0.853966 -0.409776 -0.672581  0.835451 -2.196978 -0.495979   \n",
+       "  51 -0.495979  2.931091  3.900857 -1.661873  1.105591 -0.428771 -1.897236   \n",
+       "  52 -1.897236  2.517726  4.060153 -1.089694 -2.354618  1.709086 -1.593582   \n",
+       "  53 -1.593582 -0.540715  1.354560  0.797942 -1.356914  4.565635 -1.483447   \n",
+       "  54 -1.483447 -1.279792 -1.821573  1.521596  0.712855  1.505385 -1.109965   \n",
+       "  55 -1.109965 -1.529919 -3.318152  0.910326  0.484418 -0.699728  0.571321   \n",
+       "  56  0.571321  0.717046 -2.230853  0.496043  1.676909 -1.846823  1.462930   \n",
+       "  57  1.462930  1.359717  1.439399 -2.566130 -0.019771 -3.029154  2.192884   \n",
+       "  58  2.192884  1.596111  3.011619 -1.660083 -0.949091 -0.187413  0.509781   \n",
+       "  59  0.509781 -0.280356  1.024394 -0.225920 -2.450308  0.015715 -0.492635   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.309255  1.126272    0.300695   -0.774109    1.041044  \n",
+       "  3  -1.884035  1.209108   -1.022442   -1.494222    1.397284  \n",
+       "  4  -1.296156 -0.175095   -2.366323   -3.345969    1.168661  \n",
+       "  5  -1.632979 -0.949400   -0.362497   -0.250223   -0.831824  \n",
+       "  6   1.729775 -0.637159    0.458590    2.560417   -1.507674  \n",
+       "  7   1.317286 -0.498336    0.708780    2.565440   -1.012042  \n",
+       "  8   0.935585 -0.275544   -1.996965    3.428663   -1.561964  \n",
+       "  9  -2.797402  1.206747   -1.834660    1.071987   -0.983100  \n",
+       "  10 -1.803296  3.133812   -1.103610   -1.178627    0.333679  \n",
+       "  11 -1.543362  2.749359    0.831846   -2.574442    0.473862  \n",
+       "  12  0.371672  0.440380    2.124000   -3.141057    1.571531  \n",
+       "  13  1.418557 -2.447773    1.195063   -0.711927    1.043852  \n",
+       "  14 -0.155421 -2.544949   -1.130913    1.243148    0.012349  \n",
+       "  15  0.808931 -1.310737   -1.650604    2.605323   -2.099710  \n",
+       "  16 -0.096364  1.593772   -1.995327   -1.742330   -0.797968  \n",
+       "  17 -1.332827  2.036699    0.176385   -1.214562   -0.594005  \n",
+       "  18 -1.871557  0.536830    1.997101   -0.480969   -0.297629  \n",
+       "  19  0.068824 -0.169869    1.601374    0.510521   -0.419812  \n",
+       "  20  0.720812 -1.434619    2.179372    0.499635    0.370577  \n",
+       "  21  0.825454 -0.163846    0.924967   -1.198584   -0.937493  \n",
+       "  22  1.056568 -0.068654   -1.008528   -1.310346    1.528837  \n",
+       "  23 -0.266703  1.762183   -3.812549   -0.834219    1.113836  \n",
+       "  24 -1.527048  0.902671   -2.616214    1.045983   -1.040706  \n",
+       "  25 -1.890050 -0.856264   -0.108414    2.725565   -3.462253  \n",
+       "  26  0.364677 -1.324388    0.238452    1.028790   -2.186889  \n",
+       "  27  2.199957  0.422379    2.745858   -2.397578    0.465837  \n",
+       "  28  1.484811  2.810246    1.799101   -3.153385    2.492490  \n",
+       "  29 -0.299536  0.788298   -0.037720   -1.761846    1.978805  \n",
+       "  30 -2.176350 -0.300658   -2.860806    1.663133    1.433532  \n",
+       "  31 -1.911574 -2.779845   -3.743198    1.649741   -1.793289  \n",
+       "  32 -0.948845 -0.985285   -1.971458    1.135587   -2.500652  \n",
+       "  33  0.235047 -0.274768   -0.745254   -0.805097    0.194976  \n",
+       "  34  0.791396  1.082425    3.431903   -3.325516    0.995009  \n",
+       "  35  0.902697  3.294412    2.325678   -2.452488    1.907496  \n",
+       "  36  2.219608  2.521467    1.135364    0.094458    0.834468  \n",
+       "  37  1.237961 -0.197388   -0.751953    2.124663    0.601094  \n",
+       "  38  1.700947 -2.695462   -1.940800    2.725703   -0.561375  \n",
+       "  39 -1.355505 -3.806281   -1.068767    1.180426   -0.952366  \n",
+       "  40 -1.730727 -2.599373    0.266506   -1.332043   -1.253009  \n",
+       "  41 -2.267713 -0.715381    2.292210   -1.310995   -0.732399  \n",
+       "  42 -1.508513  2.221588    1.022769   -1.144995    0.997470  \n",
+       "  43  1.512030  3.852600    1.332008    0.319911    1.197615  \n",
+       "  44  2.672619  0.358683    0.075972   -0.391566    1.312896  \n",
+       "  45  1.152481  0.029503    0.846784   -0.110546    2.967769  \n",
+       "  46 -1.454538 -0.916385   -0.215319   -0.144875   -0.045483  \n",
+       "  47 -2.480947 -3.107309    0.807933    0.032034   -1.986763  \n",
+       "  48 -0.387218 -2.134421    1.671067    0.255928   -2.860003  \n",
+       "  49  0.853966 -0.409776   -0.672581    0.835451   -2.196978  \n",
+       "  50  2.931091  3.900857   -1.661873    1.105591   -0.428771  \n",
+       "  51  2.517726  4.060153   -1.089694   -2.354618    1.709086  \n",
+       "  52 -0.540715  1.354560    0.797942   -1.356914    4.565635  \n",
+       "  53 -1.279792 -1.821573    1.521596    0.712855    1.505385  \n",
+       "  54 -1.529919 -3.318152    0.910326    0.484418   -0.699728  \n",
+       "  55  0.717046 -2.230853    0.496043    1.676909   -1.846823  \n",
+       "  56  1.359717  1.439399   -2.566130   -0.019771   -3.029154  \n",
+       "  57  1.596111  3.011619   -1.660083   -0.949091   -0.187413  \n",
+       "  58 -0.280356  1.024394   -0.225920   -2.450308    0.015715  \n",
+       "  59  1.193488 -0.964220    2.831891   -1.269955    0.728819  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -0.643972   \n",
+       "  3  -0.643972  1.016044  0.860585  1.690789  0.347095  0.441232  0.270358   \n",
+       "  4   0.270358  0.292850  0.408954 -0.532039 -0.917640 -1.515721 -0.917613   \n",
+       "  5  -0.917613 -1.453639 -0.468863 -1.530135 -2.148745 -1.195013 -0.299028   \n",
+       "  6  -0.299028 -0.421638 -0.871532 -2.705392 -0.902544  0.489841  1.475557   \n",
+       "  7   1.475557  0.686689  0.565070  0.271965 -1.322997  0.491964  1.626954   \n",
+       "  8   1.626954  0.311933  0.958148  1.998011  0.899208  1.379124  0.375734   \n",
+       "  9   0.375734 -0.186438 -0.281887  4.734218  1.510074  0.399471 -1.060143   \n",
+       "  10 -1.060143 -0.462532  0.961618  2.681320  0.600619 -0.366472 -1.349415   \n",
+       "  11 -1.349415  0.462974 -0.216132  0.549046  0.867915 -0.246938 -1.068125   \n",
+       "  12 -1.068125 -0.397060 -1.184004 -0.571492  0.203142  0.216300  1.262711   \n",
+       "  13  1.262711  0.277158 -1.406155 -1.137737 -1.517478  0.661205  1.814930   \n",
+       "  14  1.814930  0.952481 -0.161583  0.447356 -1.840020  2.166054  1.352311   \n",
+       "  15  1.352311  1.494595  0.762790  1.718627  0.850574  0.792606  0.321743   \n",
+       "  16  0.321743  1.444279  1.584814  2.355088  1.156277 -0.288115 -0.548131   \n",
+       "  17 -0.548131 -0.401352 -0.036676  0.462821  1.680272 -2.122905 -2.559383   \n",
+       "  18 -2.559383 -1.852262 -0.450953  0.146973  0.372541 -2.343924 -2.246130   \n",
+       "  19 -2.246130 -2.258574 -0.458888 -1.410924 -0.015053  0.935806  0.375329   \n",
+       "  20  0.375329 -0.054750  1.241237 -1.829865 -0.371102  2.477738  2.167036   \n",
+       "  21  2.167036  2.858659  1.107583 -0.205370 -0.507606  4.057224  2.200281   \n",
+       "  22  2.200281  4.392800  0.694495 -0.108745  1.837926  1.903355  0.893534   \n",
+       "  23  0.893534  1.724628 -0.357138  0.281513  2.208968 -1.908371 -1.408472   \n",
+       "  24 -1.408472 -2.969761  0.442750  0.254794  1.315696 -3.218839 -2.605048   \n",
+       "  25 -2.605048 -5.223585 -0.133583 -0.540723  0.017402 -2.414250 -0.472386   \n",
+       "  26 -0.472386 -2.084212 -0.357503 -0.675924 -0.848592 -0.130136  1.637826   \n",
+       "  27  1.637826  2.490067 -0.352135 -1.362927 -1.951056  1.346805  3.272116   \n",
+       "  28  3.272116  6.288290 -0.241598  0.148912 -0.303293  3.213017  0.553511   \n",
+       "  29  0.553511  3.834168 -0.694995  1.243681  1.556885  0.061858 -0.531412   \n",
+       "  30 -0.531412  0.793550 -1.347912  1.768690  4.233239 -1.141519 -4.900439   \n",
+       "  31 -4.900439 -1.876697 -1.139176 -0.741347  3.295225 -1.920438 -2.599648   \n",
+       "  32 -2.599648 -1.313427 -1.438920 -2.333064 -0.178499 -2.218393 -1.101837   \n",
+       "  33 -1.101837  1.018079 -1.468476 -0.922997 -4.703448 -0.997394  3.411965   \n",
+       "  34  3.411965  1.519072 -0.063453 -0.239944 -4.337529  0.873874  2.075753   \n",
+       "  35  2.075753  1.990481 -0.261700  1.499861 -0.623942  0.741857  1.366793   \n",
+       "  36  1.366793  0.433189  1.036545  1.317740  2.072523 -1.601171 -2.775116   \n",
+       "  37 -2.775116 -0.949157  0.603150  0.336774  3.350728 -0.817647 -3.448139   \n",
+       "  38 -3.448139 -2.147209  2.320784 -0.527810  2.647932  0.021646 -2.776942   \n",
+       "  39 -2.776942 -1.336186  2.423271 -1.397383  0.343422  0.540131 -0.788578   \n",
+       "  40 -0.788578 -1.615008  2.025902 -0.315033 -2.075345  0.082466  1.549234   \n",
+       "  41  1.549234 -0.033145  0.181944  0.534768 -3.480060  0.869169  1.707547   \n",
+       "  42  1.707547  0.561787 -1.810498  0.318910 -1.735728 -0.198542  1.989905   \n",
+       "  43  1.989905  0.684890 -2.525395  0.743387  1.657490 -0.103849 -1.545587   \n",
+       "  44 -1.545587  0.714318 -1.949665 -0.146570  2.653682 -1.148314 -2.860207   \n",
+       "  45 -2.860207  0.062891 -1.243466  0.000561  0.700438 -2.672666 -2.880770   \n",
+       "  46 -2.880770 -0.476714  0.932961  0.592059  0.344312 -0.412484  0.567828   \n",
+       "  47  0.567828  0.044692  1.307045 -0.597500 -0.831250 -0.027228  3.870292   \n",
+       "  48  3.870292  1.187022  3.655154 -1.241593 -1.827808  0.859834  3.974030   \n",
+       "  49  3.974030  0.396005  2.353946 -0.150551 -0.579054  1.900477  0.874437   \n",
+       "  50  0.874437  0.020611  0.435030  1.023317  0.288274  2.009670 -1.834326   \n",
+       "  51 -1.834326  0.673019 -1.032312  2.858615  1.054685  0.426725 -2.854810   \n",
+       "  52 -2.854810  1.570683 -2.112198  3.458974 -0.098534 -0.410022 -4.465046   \n",
+       "  53 -4.465046 -0.033967  0.172575  2.373823 -1.787407 -1.837527 -0.093941   \n",
+       "  54 -0.093941 -1.172114  1.462985 -1.976136 -1.055172 -0.160746  3.060611   \n",
+       "  55  3.060611 -1.223332  2.508153 -2.815903 -1.397981  2.439258  3.038434   \n",
+       "  56  3.038434  0.015925  0.401730 -2.883968  0.685632  2.633146  1.580653   \n",
+       "  57  1.580653  1.288991 -2.567856 -1.700995  1.505105  2.067163 -0.608830   \n",
+       "  58 -0.608830  1.293379 -2.800881 -0.835620  0.707740 -0.265693 -2.567050   \n",
+       "  59 -2.567050 -0.977234 -2.017081  1.030811  1.263834 -2.516746 -3.464854   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.016044  0.860585    1.690789    0.347095    0.441232  \n",
+       "  3   0.292850  0.408954   -0.532039   -0.917640   -1.515721  \n",
+       "  4  -1.453639 -0.468863   -1.530135   -2.148745   -1.195013  \n",
+       "  5  -0.421638 -0.871532   -2.705392   -0.902544    0.489841  \n",
+       "  6   0.686689  0.565070    0.271965   -1.322997    0.491964  \n",
+       "  7   0.311933  0.958148    1.998011    0.899208    1.379124  \n",
+       "  8  -0.186438 -0.281887    4.734218    1.510074    0.399471  \n",
+       "  9  -0.462532  0.961618    2.681320    0.600619   -0.366472  \n",
+       "  10  0.462974 -0.216132    0.549046    0.867915   -0.246938  \n",
+       "  11 -0.397060 -1.184004   -0.571492    0.203142    0.216300  \n",
+       "  12  0.277158 -1.406155   -1.137737   -1.517478    0.661205  \n",
+       "  13  0.952481 -0.161583    0.447356   -1.840020    2.166054  \n",
+       "  14  1.494595  0.762790    1.718627    0.850574    0.792606  \n",
+       "  15  1.444279  1.584814    2.355088    1.156277   -0.288115  \n",
+       "  16 -0.401352 -0.036676    0.462821    1.680272   -2.122905  \n",
+       "  17 -1.852262 -0.450953    0.146973    0.372541   -2.343924  \n",
+       "  18 -2.258574 -0.458888   -1.410924   -0.015053    0.935806  \n",
+       "  19 -0.054750  1.241237   -1.829865   -0.371102    2.477738  \n",
+       "  20  2.858659  1.107583   -0.205370   -0.507606    4.057224  \n",
+       "  21  4.392800  0.694495   -0.108745    1.837926    1.903355  \n",
+       "  22  1.724628 -0.357138    0.281513    2.208968   -1.908371  \n",
+       "  23 -2.969761  0.442750    0.254794    1.315696   -3.218839  \n",
+       "  24 -5.223585 -0.133583   -0.540723    0.017402   -2.414250  \n",
+       "  25 -2.084212 -0.357503   -0.675924   -0.848592   -0.130136  \n",
+       "  26  2.490067 -0.352135   -1.362927   -1.951056    1.346805  \n",
+       "  27  6.288290 -0.241598    0.148912   -0.303293    3.213017  \n",
+       "  28  3.834168 -0.694995    1.243681    1.556885    0.061858  \n",
+       "  29  0.793550 -1.347912    1.768690    4.233239   -1.141519  \n",
+       "  30 -1.876697 -1.139176   -0.741347    3.295225   -1.920438  \n",
+       "  31 -1.313427 -1.438920   -2.333064   -0.178499   -2.218393  \n",
+       "  32  1.018079 -1.468476   -0.922997   -4.703448   -0.997394  \n",
+       "  33  1.519072 -0.063453   -0.239944   -4.337529    0.873874  \n",
+       "  34  1.990481 -0.261700    1.499861   -0.623942    0.741857  \n",
+       "  35  0.433189  1.036545    1.317740    2.072523   -1.601171  \n",
+       "  36 -0.949157  0.603150    0.336774    3.350728   -0.817647  \n",
+       "  37 -2.147209  2.320784   -0.527810    2.647932    0.021646  \n",
+       "  38 -1.336186  2.423271   -1.397383    0.343422    0.540131  \n",
+       "  39 -1.615008  2.025902   -0.315033   -2.075345    0.082466  \n",
+       "  40 -0.033145  0.181944    0.534768   -3.480060    0.869169  \n",
+       "  41  0.561787 -1.810498    0.318910   -1.735728   -0.198542  \n",
+       "  42  0.684890 -2.525395    0.743387    1.657490   -0.103849  \n",
+       "  43  0.714318 -1.949665   -0.146570    2.653682   -1.148314  \n",
+       "  44  0.062891 -1.243466    0.000561    0.700438   -2.672666  \n",
+       "  45 -0.476714  0.932961    0.592059    0.344312   -0.412484  \n",
+       "  46  0.044692  1.307045   -0.597500   -0.831250   -0.027228  \n",
+       "  47  1.187022  3.655154   -1.241593   -1.827808    0.859834  \n",
+       "  48  0.396005  2.353946   -0.150551   -0.579054    1.900477  \n",
+       "  49  0.020611  0.435030    1.023317    0.288274    2.009670  \n",
+       "  50  0.673019 -1.032312    2.858615    1.054685    0.426725  \n",
+       "  51  1.570683 -2.112198    3.458974   -0.098534   -0.410022  \n",
+       "  52 -0.033967  0.172575    2.373823   -1.787407   -1.837527  \n",
+       "  53 -1.172114  1.462985   -1.976136   -1.055172   -0.160746  \n",
+       "  54 -1.223332  2.508153   -2.815903   -1.397981    2.439258  \n",
+       "  55  0.015925  0.401730   -2.883968    0.685632    2.633146  \n",
+       "  56  1.288991 -2.567856   -1.700995    1.505105    2.067163  \n",
+       "  57  1.293379 -2.800881   -0.835620    0.707740   -0.265693  \n",
+       "  58 -0.977234 -2.017081    1.030811    1.263834   -2.516746  \n",
+       "  59 -1.832816 -0.174653    0.259981   -1.209566   -2.210490  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  0.525356   \n",
+       "  3   0.525356  0.150706  1.023990  0.838804 -0.010592  0.586407 -0.270391   \n",
+       "  4  -0.270391 -1.139578 -1.532726  0.223320  0.299724 -1.021736 -3.081549   \n",
+       "  5  -3.081549 -1.186081 -0.698338  1.286465 -0.637114 -1.615092 -2.030892   \n",
+       "  6  -2.030892 -1.738240 -0.259206 -0.683039 -0.245791  0.141006  0.021378   \n",
+       "  7   0.021378 -0.416208  2.214833  0.100306  0.448711  1.876574 -0.093112   \n",
+       "  8  -0.093112  0.707518  2.620600 -1.315596  2.391797  1.240781  1.208494   \n",
+       "  9   1.208494  0.236948  0.644118 -0.579770  2.567896  0.882039  1.674663   \n",
+       "  10  1.674663  2.072354 -0.728898  0.133870  0.884023 -1.370002  0.867666   \n",
+       "  11  0.867666  0.002527 -0.740377  1.012029 -0.293849 -1.594930 -0.498041   \n",
+       "  12 -0.498041  0.416315 -0.962669 -0.389617  0.932168 -2.278471 -2.759980   \n",
+       "  13 -2.759980 -2.197703 -0.145645  0.626029 -0.106223 -1.702629 -2.857217   \n",
+       "  14 -2.857217 -2.212684  2.237381  1.412170  0.662362 -0.710053 -1.077729   \n",
+       "  15 -1.077729 -1.729690  2.167825  0.397522  0.292082  0.189719  2.099266   \n",
+       "  16  2.099266  0.998634  1.701352 -0.867001 -0.261646 -0.474320  3.704961   \n",
+       "  17  3.704961  0.984963 -0.827683 -1.146583 -0.295395 -1.190023  2.695641   \n",
+       "  18  2.695641  0.768414 -2.121488 -2.271377  0.543346 -1.034926 -1.707484   \n",
+       "  19 -1.707484 -0.390565 -1.273850 -1.764560  1.153660 -0.380127 -2.663180   \n",
+       "  20 -2.663180 -0.688449 -0.628572 -0.888705  1.062088  0.393449 -3.384145   \n",
+       "  21 -3.384145 -1.385545  2.545869  1.606823 -0.010512  0.691957 -1.116576   \n",
+       "  22 -1.116576  1.147236  3.127383  1.432325  0.331965  1.508063  2.550410   \n",
+       "  23  2.550410  2.108592  0.096900  0.383721 -0.047847  0.078688  3.455020   \n",
+       "  24  3.455020  1.625179 -2.601991 -2.221231 -1.859317  0.179329  1.884981   \n",
+       "  25  1.884981  0.997261 -2.749940 -1.458548 -1.304859  1.036737  1.274594   \n",
+       "  26  1.274594 -1.228950 -2.520342 -1.649224  0.841975  2.747964 -2.382495   \n",
+       "  27 -2.382495 -0.860290  1.784162 -0.434462  1.469313  2.288075 -3.648825   \n",
+       "  28 -3.648825  0.282148  4.582715  0.353982  0.342164  1.177590 -3.532859   \n",
+       "  29 -3.532859  1.476537  2.017585  0.580358 -1.346505 -3.650287  0.572969   \n",
+       "  30  0.572969  0.219527 -0.998978 -0.500906 -1.140302 -4.153235  3.817366   \n",
+       "  31  3.817366  0.895729 -2.528189 -0.430383 -0.816297 -2.182528  4.543450   \n",
+       "  32  4.543450 -1.367243 -2.610088 -1.161500 -1.224955  1.635736  2.236106   \n",
+       "  33  2.236106 -1.315273 -0.557953 -1.214123 -0.364534  2.492134 -1.736838   \n",
+       "  34 -1.736838 -1.880770  2.655987  0.530109 -0.309856  2.591791 -3.323971   \n",
+       "  35 -3.323971  0.817543  3.662355 -1.179547  1.050539  1.175171 -3.363013   \n",
+       "  36 -3.363013  1.757719  2.410963  1.066334  1.331334 -0.161223  0.193132   \n",
+       "  37  0.193132  2.119009 -0.121798  1.621492  0.413181 -0.748649  3.777190   \n",
+       "  38  3.777190 -1.741579 -2.571428  0.691499  0.248372 -0.331436  4.386548   \n",
+       "  39  4.386548 -4.124329 -3.185852 -0.084208 -0.301036  0.630740  3.671997   \n",
+       "  40  3.671997 -3.838977 -2.143037  0.631365 -1.277899 -0.034913 -0.286317   \n",
+       "  41 -0.286317 -0.297889  0.134237  1.348023  0.558471 -1.518846 -1.855303   \n",
+       "  42 -1.855303  4.128398  1.357613  0.316227 -0.177983  0.401071 -2.813680   \n",
+       "  43 -2.813680  5.589428  0.803248 -1.296759 -0.325767 -0.361456 -2.006440   \n",
+       "  44 -2.006440  1.816941 -0.039538 -0.550915 -0.078941  0.647042  0.795714   \n",
+       "  45  0.795714 -0.885764 -1.850976 -2.152981 -0.105432 -0.373434  2.403765   \n",
+       "  46  2.403765 -3.262054 -0.837072 -0.414193  0.494617 -0.489327  3.249378   \n",
+       "  47  3.249378 -2.867652  0.227408  2.728379  0.439617  0.124358 -0.320494   \n",
+       "  48 -0.320494 -0.882151 -0.037193  3.643907 -0.137790  0.686670 -2.395280   \n",
+       "  49 -2.395280  1.281197  1.163563  2.081505  0.098275 -1.395180 -2.141438   \n",
+       "  50 -2.141438  3.879466  2.430804 -1.317116  0.520738 -0.838826  0.312816   \n",
+       "  51  0.312816  1.324769  1.894223 -3.890013  0.945676 -0.417828  0.674903   \n",
+       "  52  0.674903  0.153160  0.657871 -3.944050 -0.044106 -0.218740 -0.557986   \n",
+       "  53 -0.557986 -2.234936 -1.654406 -1.715637  1.384225 -0.125641 -0.599378   \n",
+       "  54 -0.599378 -0.251940 -3.238273  1.445975  2.414663 -0.247807 -0.236723   \n",
+       "  55 -0.236723  0.699722 -1.391663  4.767941  0.896943 -0.023807  1.129354   \n",
+       "  56  1.129354  1.537215  1.191862  3.634106  0.295285  0.000760  0.920731   \n",
+       "  57  0.920731  1.976168  1.309128  0.508087 -0.430983  1.086792  0.351496   \n",
+       "  58  0.351496  1.089508 -1.565605 -4.050891 -1.074064 -0.386886 -0.546117   \n",
+       "  59 -0.546117 -2.347537 -2.075327 -4.787632 -2.074342 -0.766505 -0.118219   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.150706  1.023990    0.838804   -0.010592    0.586407  \n",
+       "  3  -1.139578 -1.532726    0.223320    0.299724   -1.021736  \n",
+       "  4  -1.186081 -0.698338    1.286465   -0.637114   -1.615092  \n",
+       "  5  -1.738240 -0.259206   -0.683039   -0.245791    0.141006  \n",
+       "  6  -0.416208  2.214833    0.100306    0.448711    1.876574  \n",
+       "  7   0.707518  2.620600   -1.315596    2.391797    1.240781  \n",
+       "  8   0.236948  0.644118   -0.579770    2.567896    0.882039  \n",
+       "  9   2.072354 -0.728898    0.133870    0.884023   -1.370002  \n",
+       "  10  0.002527 -0.740377    1.012029   -0.293849   -1.594930  \n",
+       "  11  0.416315 -0.962669   -0.389617    0.932168   -2.278471  \n",
+       "  12 -2.197703 -0.145645    0.626029   -0.106223   -1.702629  \n",
+       "  13 -2.212684  2.237381    1.412170    0.662362   -0.710053  \n",
+       "  14 -1.729690  2.167825    0.397522    0.292082    0.189719  \n",
+       "  15  0.998634  1.701352   -0.867001   -0.261646   -0.474320  \n",
+       "  16  0.984963 -0.827683   -1.146583   -0.295395   -1.190023  \n",
+       "  17  0.768414 -2.121488   -2.271377    0.543346   -1.034926  \n",
+       "  18 -0.390565 -1.273850   -1.764560    1.153660   -0.380127  \n",
+       "  19 -0.688449 -0.628572   -0.888705    1.062088    0.393449  \n",
+       "  20 -1.385545  2.545869    1.606823   -0.010512    0.691957  \n",
+       "  21  1.147236  3.127383    1.432325    0.331965    1.508063  \n",
+       "  22  2.108592  0.096900    0.383721   -0.047847    0.078688  \n",
+       "  23  1.625179 -2.601991   -2.221231   -1.859317    0.179329  \n",
+       "  24  0.997261 -2.749940   -1.458548   -1.304859    1.036737  \n",
+       "  25 -1.228950 -2.520342   -1.649224    0.841975    2.747964  \n",
+       "  26 -0.860290  1.784162   -0.434462    1.469313    2.288075  \n",
+       "  27  0.282148  4.582715    0.353982    0.342164    1.177590  \n",
+       "  28  1.476537  2.017585    0.580358   -1.346505   -3.650287  \n",
+       "  29  0.219527 -0.998978   -0.500906   -1.140302   -4.153235  \n",
+       "  30  0.895729 -2.528189   -0.430383   -0.816297   -2.182528  \n",
+       "  31 -1.367243 -2.610088   -1.161500   -1.224955    1.635736  \n",
+       "  32 -1.315273 -0.557953   -1.214123   -0.364534    2.492134  \n",
+       "  33 -1.880770  2.655987    0.530109   -0.309856    2.591791  \n",
+       "  34  0.817543  3.662355   -1.179547    1.050539    1.175171  \n",
+       "  35  1.757719  2.410963    1.066334    1.331334   -0.161223  \n",
+       "  36  2.119009 -0.121798    1.621492    0.413181   -0.748649  \n",
+       "  37 -1.741579 -2.571428    0.691499    0.248372   -0.331436  \n",
+       "  38 -4.124329 -3.185852   -0.084208   -0.301036    0.630740  \n",
+       "  39 -3.838977 -2.143037    0.631365   -1.277899   -0.034913  \n",
+       "  40 -0.297889  0.134237    1.348023    0.558471   -1.518846  \n",
+       "  41  4.128398  1.357613    0.316227   -0.177983    0.401071  \n",
+       "  42  5.589428  0.803248   -1.296759   -0.325767   -0.361456  \n",
+       "  43  1.816941 -0.039538   -0.550915   -0.078941    0.647042  \n",
+       "  44 -0.885764 -1.850976   -2.152981   -0.105432   -0.373434  \n",
+       "  45 -3.262054 -0.837072   -0.414193    0.494617   -0.489327  \n",
+       "  46 -2.867652  0.227408    2.728379    0.439617    0.124358  \n",
+       "  47 -0.882151 -0.037193    3.643907   -0.137790    0.686670  \n",
+       "  48  1.281197  1.163563    2.081505    0.098275   -1.395180  \n",
+       "  49  3.879466  2.430804   -1.317116    0.520738   -0.838826  \n",
+       "  50  1.324769  1.894223   -3.890013    0.945676   -0.417828  \n",
+       "  51  0.153160  0.657871   -3.944050   -0.044106   -0.218740  \n",
+       "  52 -2.234936 -1.654406   -1.715637    1.384225   -0.125641  \n",
+       "  53 -0.251940 -3.238273    1.445975    2.414663   -0.247807  \n",
+       "  54  0.699722 -1.391663    4.767941    0.896943   -0.023807  \n",
+       "  55  1.537215  1.191862    3.634106    0.295285    0.000760  \n",
+       "  56  1.976168  1.309128    0.508087   -0.430983    1.086792  \n",
+       "  57  1.089508 -1.565605   -4.050891   -1.074064   -0.386886  \n",
+       "  58 -2.347537 -2.075327   -4.787632   -2.074342   -0.766505  \n",
+       "  59 -1.343190 -1.671193   -2.355654   -1.460661   -1.251164  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -1.460495   \n",
+       "  3  -1.460495  1.912588  1.132007 -1.088552  1.234200 -0.529343 -1.707992   \n",
+       "  4  -1.707992  2.250237  0.591250 -2.358759  0.207270  0.423530 -2.492645   \n",
+       "  5  -2.492645 -0.789537 -0.386179 -0.655764 -2.013513  0.309844 -1.515533   \n",
+       "  6  -1.515533 -0.121015 -0.785068  0.447709 -2.849748  1.137591  0.057112   \n",
+       "  7   0.057112 -0.806830 -0.281554  1.825643 -0.388970 -0.217128 -0.002410   \n",
+       "  8  -0.002410 -3.147486 -0.548539  1.123142  2.318534 -0.558744  0.568343   \n",
+       "  9   0.568343 -1.980728  0.661786 -0.440109  3.100990 -0.990968 -1.539062   \n",
+       "  10 -1.539062 -0.797550  0.686270 -1.002869  2.181586 -0.799378  0.276449   \n",
+       "  11  0.276449 -1.931986  0.919171 -0.987454  1.046267 -1.739747 -1.788654   \n",
+       "  12 -1.788654  0.165837  1.011427  1.436978 -0.899929 -0.180935 -1.644048   \n",
+       "  13 -1.644048  0.598259 -0.949270  2.875957 -1.204852 -0.435004  0.042728   \n",
+       "  14  0.042728  1.649125 -0.686425  3.588159 -1.840352  1.612414  1.201671   \n",
+       "  15  1.201671 -0.037849 -1.506601  0.471100 -0.326872  1.294434  3.124374   \n",
+       "  16  3.124374 -0.089153 -1.420939 -1.964965 -0.851014 -0.759984  2.063423   \n",
+       "  17  2.063423 -1.549209 -0.811980 -2.830266 -1.722104 -3.614796 -0.174696   \n",
+       "  18 -0.174696 -1.105208 -0.282468 -1.287210 -1.235334 -3.937937 -4.011148   \n",
+       "  19 -4.011148 -2.392127  0.439327  1.127064 -0.911000 -2.644641 -3.702969   \n",
+       "  20 -3.702969 -1.127016 -1.015261  3.192795 -0.299573  1.145644 -2.938757   \n",
+       "  21 -2.938757  0.895690  0.115659  2.013292 -0.310094  2.228893  0.157824   \n",
+       "  22  0.157824  2.704790 -0.493252  0.424773  0.463923  2.623550  0.917914   \n",
+       "  23  0.917914  2.247368  0.132142 -0.741028  0.554166 -0.657474  0.880098   \n",
+       "  24  0.880098  1.343635 -0.368763 -0.669536  1.389996 -3.154617 -1.181609   \n",
+       "  25 -1.181609  0.165352 -0.789107 -0.551387  0.700312 -3.184498 -2.327802   \n",
+       "  26 -2.327802 -2.260102 -0.685598 -1.422916  0.698709 -4.450805 -2.344472   \n",
+       "  27 -2.344472 -0.558562 -1.013589  1.454367  0.118384 -2.358087  0.194285   \n",
+       "  28  0.194285 -0.046651 -0.549615  0.510877  0.929227  0.709943  0.334156   \n",
+       "  29  0.334156  2.310950  0.538490 -0.663987 -0.088956  3.786386 -0.393626   \n",
+       "  30 -0.393626  1.549321  0.074990 -0.489234 -0.191996  3.251549  0.233877   \n",
+       "  31  0.233877  0.093737  1.131744 -0.938207  1.128456  0.587845 -0.373892   \n",
+       "  32 -0.373892 -1.483747 -1.353188  1.329924 -0.106040 -1.231958 -0.567444   \n",
+       "  33 -0.567444 -0.812814 -1.558609  0.436183  0.708508 -0.292147 -0.467688   \n",
+       "  34 -0.467688 -1.369721 -0.930513  0.875286 -0.325485  0.004565  1.348018   \n",
+       "  35  1.348018 -1.579261  2.226588 -0.468676  0.341433 -0.729320  1.794607   \n",
+       "  36  1.794607 -1.872862  2.701893 -1.203517 -0.228876 -0.127534  1.484761   \n",
+       "  37  1.484761  0.583903  2.064279 -0.069616  1.263480  0.283869 -0.798394   \n",
+       "  38 -0.798394 -0.460191 -0.572100  0.977592  0.384907 -0.816781 -2.112386   \n",
+       "  39 -2.112386 -0.452864 -2.232370  0.697524 -0.927819 -1.747061 -2.139242   \n",
+       "  40 -2.139242  0.318614 -0.852449  1.785312 -1.885302 -1.696398 -0.390767   \n",
+       "  41 -0.390767  2.397842  0.986484  2.179010 -1.546244 -0.187375  0.561328   \n",
+       "  42  0.561328  2.984107  4.929667 -1.292861 -0.922941 -0.242964 -0.001379   \n",
+       "  43 -0.001379  1.558408  2.685303 -1.571833 -1.494549  0.386914  0.658134   \n",
+       "  44  0.658134 -0.042072 -0.979140 -2.341987 -1.131584  0.705775  0.380250   \n",
+       "  45  0.380250 -1.251772 -3.553846 -0.054711 -1.087582  0.656942  1.580202   \n",
+       "  46  1.580202 -1.017054 -3.369483  1.986514  2.215111  0.981832  0.472977   \n",
+       "  47  0.472977 -0.969424 -0.281621  3.880643  2.614974 -1.001945 -1.689006   \n",
+       "  48 -1.689006  2.425233  0.611294  2.347300  2.121553 -1.171485 -2.854805   \n",
+       "  49 -2.854805  1.661030  2.166593  1.350424  0.114191  0.775308 -4.145649   \n",
+       "  50 -4.145649  1.257411  3.655464 -0.243798 -0.577041  1.521820 -2.041097   \n",
+       "  51 -2.041097 -1.081919  2.700655 -1.510926 -1.374461  1.589505  2.055735   \n",
+       "  52  2.055735 -2.343130  1.385560 -2.403648 -0.289989  0.359096  3.359527   \n",
+       "  53  3.359527 -1.629940 -1.618998 -2.492705  0.752758 -1.331525  2.692577   \n",
+       "  54  2.692577  0.281078 -2.729513  0.123681  0.408820 -1.863929 -1.854863   \n",
+       "  55 -1.854863  1.836764 -2.078585  0.439369 -0.400040 -2.365017 -4.139077   \n",
+       "  56 -4.139077  2.309770 -0.307652  1.547031 -0.370303 -0.436730 -4.882217   \n",
+       "  57 -4.882217  2.247817  1.206863  2.025263  1.159874  1.244296 -0.582007   \n",
+       "  58 -0.582007 -0.241513  2.061881  0.566504  1.491190  2.019820  2.590785   \n",
+       "  59  2.590785 -2.474260  2.174981  0.384847  1.003561  1.311885  4.569306   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.912588  1.132007   -1.088552    1.234200   -0.529343  \n",
+       "  3   2.250237  0.591250   -2.358759    0.207270    0.423530  \n",
+       "  4  -0.789537 -0.386179   -0.655764   -2.013513    0.309844  \n",
+       "  5  -0.121015 -0.785068    0.447709   -2.849748    1.137591  \n",
+       "  6  -0.806830 -0.281554    1.825643   -0.388970   -0.217128  \n",
+       "  7  -3.147486 -0.548539    1.123142    2.318534   -0.558744  \n",
+       "  8  -1.980728  0.661786   -0.440109    3.100990   -0.990968  \n",
+       "  9  -0.797550  0.686270   -1.002869    2.181586   -0.799378  \n",
+       "  10 -1.931986  0.919171   -0.987454    1.046267   -1.739747  \n",
+       "  11  0.165837  1.011427    1.436978   -0.899929   -0.180935  \n",
+       "  12  0.598259 -0.949270    2.875957   -1.204852   -0.435004  \n",
+       "  13  1.649125 -0.686425    3.588159   -1.840352    1.612414  \n",
+       "  14 -0.037849 -1.506601    0.471100   -0.326872    1.294434  \n",
+       "  15 -0.089153 -1.420939   -1.964965   -0.851014   -0.759984  \n",
+       "  16 -1.549209 -0.811980   -2.830266   -1.722104   -3.614796  \n",
+       "  17 -1.105208 -0.282468   -1.287210   -1.235334   -3.937937  \n",
+       "  18 -2.392127  0.439327    1.127064   -0.911000   -2.644641  \n",
+       "  19 -1.127016 -1.015261    3.192795   -0.299573    1.145644  \n",
+       "  20  0.895690  0.115659    2.013292   -0.310094    2.228893  \n",
+       "  21  2.704790 -0.493252    0.424773    0.463923    2.623550  \n",
+       "  22  2.247368  0.132142   -0.741028    0.554166   -0.657474  \n",
+       "  23  1.343635 -0.368763   -0.669536    1.389996   -3.154617  \n",
+       "  24  0.165352 -0.789107   -0.551387    0.700312   -3.184498  \n",
+       "  25 -2.260102 -0.685598   -1.422916    0.698709   -4.450805  \n",
+       "  26 -0.558562 -1.013589    1.454367    0.118384   -2.358087  \n",
+       "  27 -0.046651 -0.549615    0.510877    0.929227    0.709943  \n",
+       "  28  2.310950  0.538490   -0.663987   -0.088956    3.786386  \n",
+       "  29  1.549321  0.074990   -0.489234   -0.191996    3.251549  \n",
+       "  30  0.093737  1.131744   -0.938207    1.128456    0.587845  \n",
+       "  31 -1.483747 -1.353188    1.329924   -0.106040   -1.231958  \n",
+       "  32 -0.812814 -1.558609    0.436183    0.708508   -0.292147  \n",
+       "  33 -1.369721 -0.930513    0.875286   -0.325485    0.004565  \n",
+       "  34 -1.579261  2.226588   -0.468676    0.341433   -0.729320  \n",
+       "  35 -1.872862  2.701893   -1.203517   -0.228876   -0.127534  \n",
+       "  36  0.583903  2.064279   -0.069616    1.263480    0.283869  \n",
+       "  37 -0.460191 -0.572100    0.977592    0.384907   -0.816781  \n",
+       "  38 -0.452864 -2.232370    0.697524   -0.927819   -1.747061  \n",
+       "  39  0.318614 -0.852449    1.785312   -1.885302   -1.696398  \n",
+       "  40  2.397842  0.986484    2.179010   -1.546244   -0.187375  \n",
+       "  41  2.984107  4.929667   -1.292861   -0.922941   -0.242964  \n",
+       "  42  1.558408  2.685303   -1.571833   -1.494549    0.386914  \n",
+       "  43 -0.042072 -0.979140   -2.341987   -1.131584    0.705775  \n",
+       "  44 -1.251772 -3.553846   -0.054711   -1.087582    0.656942  \n",
+       "  45 -1.017054 -3.369483    1.986514    2.215111    0.981832  \n",
+       "  46 -0.969424 -0.281621    3.880643    2.614974   -1.001945  \n",
+       "  47  2.425233  0.611294    2.347300    2.121553   -1.171485  \n",
+       "  48  1.661030  2.166593    1.350424    0.114191    0.775308  \n",
+       "  49  1.257411  3.655464   -0.243798   -0.577041    1.521820  \n",
+       "  50 -1.081919  2.700655   -1.510926   -1.374461    1.589505  \n",
+       "  51 -2.343130  1.385560   -2.403648   -0.289989    0.359096  \n",
+       "  52 -1.629940 -1.618998   -2.492705    0.752758   -1.331525  \n",
+       "  53  0.281078 -2.729513    0.123681    0.408820   -1.863929  \n",
+       "  54  1.836764 -2.078585    0.439369   -0.400040   -2.365017  \n",
+       "  55  2.309770 -0.307652    1.547031   -0.370303   -0.436730  \n",
+       "  56  2.247817  1.206863    2.025263    1.159874    1.244296  \n",
+       "  57 -0.241513  2.061881    0.566504    1.491190    2.019820  \n",
+       "  58 -2.474260  2.174981    0.384847    1.003561    1.311885  \n",
+       "  59 -0.798498  0.609071   -0.021529   -0.209514    0.621347  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.659328   \n",
+       "  3   1.659328  1.470667 -0.741437 -0.336163  0.697369 -1.222405  1.614508   \n",
+       "  4   1.614508 -1.601666 -0.093242 -0.518866 -0.491904  0.167394  0.889474   \n",
+       "  5   0.889474 -2.487073 -0.806240 -1.237883 -1.798801  0.747153 -0.394569   \n",
+       "  6  -0.394569 -3.232731 -1.687066 -1.451805 -2.000661  0.305531 -0.685301   \n",
+       "  7  -0.685301 -1.872433 -1.592740  1.482346 -3.419769  0.290339 -1.938636   \n",
+       "  8  -1.938636  0.893721  0.585552  2.637165 -1.461614  2.160136 -1.338414   \n",
+       "  9  -1.338414  3.585586  0.845715  1.894563 -1.596093  2.093836 -1.053149   \n",
+       "  10 -1.053149  3.124059  0.100199  0.255197  1.930363 -0.770239  0.247500   \n",
+       "  11  0.247500 -0.729467  0.612066 -2.430697  2.633266 -1.119768  2.682240   \n",
+       "  12  2.682240 -1.336865 -0.130827 -1.945779  1.677666 -1.340388  4.497919   \n",
+       "  13  4.497919 -0.781997 -1.341555 -1.482551 -1.933031 -1.619084  2.010710   \n",
+       "  14  2.010710  1.716197 -1.751154 -0.554176 -2.961931 -1.489941 -1.809545   \n",
+       "  15 -1.809545  0.860415  1.898305  2.825755 -3.994513  0.575439 -2.229082   \n",
+       "  16 -2.229082  0.040595  3.036265  4.197393 -1.181305  1.174163 -2.615558   \n",
+       "  17 -2.615558  1.396794  3.313754  1.966988  2.129637  0.136029  0.550037   \n",
+       "  18  0.550037  0.774057  0.278598 -2.486164  1.162591 -0.844707  1.935800   \n",
+       "  19  1.935800  0.283570 -2.229527 -2.000506  0.320520 -0.760449  2.697813   \n",
+       "  20  2.697813 -0.500932 -1.964312  0.188116 -0.048138 -0.609942 -0.061886   \n",
+       "  21 -0.061886 -3.275756 -0.689190  3.273223 -1.062024  0.474888 -0.337795   \n",
+       "  22 -0.337795 -1.165552  0.993445  4.086172 -0.555453  2.751564 -0.947622   \n",
+       "  23 -0.947622 -0.334818  1.172647  1.598178  0.014954  3.960886 -0.719002   \n",
+       "  24 -0.719002  1.181975 -0.495102 -0.417057 -0.124613  1.381490  0.938888   \n",
+       "  25  0.938888  1.335669 -1.634556 -2.718496 -1.979520 -1.718189  2.569394   \n",
+       "  26  2.569394  1.008273 -1.955619 -2.373011 -2.237384 -4.255728  2.568542   \n",
+       "  27  2.568542 -0.695036 -0.810017  0.033122 -1.751549 -3.602789  1.154394   \n",
+       "  28  1.154394  0.004366  0.537831  3.241161 -0.464849 -1.433231 -1.742539   \n",
+       "  29 -1.742539  0.258824  3.340419  2.990223  1.461432  2.606451  0.516932   \n",
+       "  30  0.516932 -0.692610  1.503620  0.885416  1.959302  2.964980 -0.589130   \n",
+       "  31 -0.589130 -0.869936  0.351590 -1.661038  1.934326  3.271168  0.199998   \n",
+       "  32  0.199998  1.684954 -1.922781 -1.998185 -1.393889  1.161394  0.233120   \n",
+       "  33  0.233120  0.827892 -2.478550  0.541063 -1.880941 -0.473325  2.886855   \n",
+       "  34  2.886855  1.310511 -1.257898  3.653700 -1.601337 -1.579658  2.794826   \n",
+       "  35  2.794826  1.043606  1.986497  1.707818  0.193998 -3.864035 -0.682170   \n",
+       "  36 -0.682170 -2.244414  3.867285 -1.943799  1.997772 -3.171677 -1.462622   \n",
+       "  37 -1.462622 -2.800506  3.488811 -3.948828  1.666375 -0.896916 -2.532484   \n",
+       "  38 -2.532484 -2.503104 -1.977504 -2.094718  0.655704  1.698770 -1.759922   \n",
+       "  39 -1.759922 -1.294041 -2.409426  1.429176 -3.232496  1.734380 -0.296633   \n",
+       "  40 -0.296633 -0.763355 -2.186015  3.539124 -4.529510  1.642566  2.283021   \n",
+       "  41  2.283021 -0.018622 -0.427650  2.271382 -2.400871 -0.269681  2.891792   \n",
+       "  42  2.891792 -0.868895  2.965318 -1.471974 -0.858027 -1.173086  1.717377   \n",
+       "  43  1.717377 -0.082183  4.051197 -3.655486  2.698638 -1.210322 -1.337761   \n",
+       "  44 -1.337761 -0.124379  3.188121 -3.109283  2.016316 -1.944258 -3.349653   \n",
+       "  45 -3.349653  1.687972  2.185182  0.187121  0.570115  0.408683 -1.375816   \n",
+       "  46 -1.375816  0.603155 -0.219874  2.621389 -2.080184  1.258935  0.824551   \n",
+       "  47  0.824551  0.423334 -2.571537  2.803567 -2.228183  3.041480  2.756048   \n",
+       "  48  2.756048 -1.222195 -2.947538  0.541672 -1.997911 -0.401189  1.965489   \n",
+       "  49  1.965489  0.309721 -1.188706 -1.580278 -1.870709 -1.209668  0.961710   \n",
+       "  50  0.961710 -0.229298  3.429724 -3.536907 -0.306651 -1.777669 -0.655247   \n",
+       "  51 -0.655247  2.297931  5.527336 -2.058579 -1.499570 -1.452626 -3.011332   \n",
+       "  52 -3.011332  2.013749  2.728451  0.544547  0.938279  0.007270 -3.412607   \n",
+       "  53 -3.412607  1.747087 -0.868734  4.830233  1.650324  1.475109 -1.508962   \n",
+       "  54 -1.508962  1.729754 -4.414808  5.121964  2.255877  1.072432  1.858061   \n",
+       "  55  1.858061 -1.062626 -4.209477  1.062214  1.069024  1.957370  2.384825   \n",
+       "  56  2.384825 -0.315856 -1.682862 -4.669046 -0.586674 -0.644969  1.441364   \n",
+       "  57  1.441364 -0.632748  1.634388 -6.619816 -0.917644 -3.155102 -0.230273   \n",
+       "  58 -0.230273  1.151223  4.163058 -4.551591 -0.541258 -1.567434  0.273854   \n",
+       "  59  0.273854  2.975799  2.433736  0.232740  0.595110  0.518873  0.154244   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.470667 -0.741437   -0.336163    0.697369   -1.222405  \n",
+       "  3  -1.601666 -0.093242   -0.518866   -0.491904    0.167394  \n",
+       "  4  -2.487073 -0.806240   -1.237883   -1.798801    0.747153  \n",
+       "  5  -3.232731 -1.687066   -1.451805   -2.000661    0.305531  \n",
+       "  6  -1.872433 -1.592740    1.482346   -3.419769    0.290339  \n",
+       "  7   0.893721  0.585552    2.637165   -1.461614    2.160136  \n",
+       "  8   3.585586  0.845715    1.894563   -1.596093    2.093836  \n",
+       "  9   3.124059  0.100199    0.255197    1.930363   -0.770239  \n",
+       "  10 -0.729467  0.612066   -2.430697    2.633266   -1.119768  \n",
+       "  11 -1.336865 -0.130827   -1.945779    1.677666   -1.340388  \n",
+       "  12 -0.781997 -1.341555   -1.482551   -1.933031   -1.619084  \n",
+       "  13  1.716197 -1.751154   -0.554176   -2.961931   -1.489941  \n",
+       "  14  0.860415  1.898305    2.825755   -3.994513    0.575439  \n",
+       "  15  0.040595  3.036265    4.197393   -1.181305    1.174163  \n",
+       "  16  1.396794  3.313754    1.966988    2.129637    0.136029  \n",
+       "  17  0.774057  0.278598   -2.486164    1.162591   -0.844707  \n",
+       "  18  0.283570 -2.229527   -2.000506    0.320520   -0.760449  \n",
+       "  19 -0.500932 -1.964312    0.188116   -0.048138   -0.609942  \n",
+       "  20 -3.275756 -0.689190    3.273223   -1.062024    0.474888  \n",
+       "  21 -1.165552  0.993445    4.086172   -0.555453    2.751564  \n",
+       "  22 -0.334818  1.172647    1.598178    0.014954    3.960886  \n",
+       "  23  1.181975 -0.495102   -0.417057   -0.124613    1.381490  \n",
+       "  24  1.335669 -1.634556   -2.718496   -1.979520   -1.718189  \n",
+       "  25  1.008273 -1.955619   -2.373011   -2.237384   -4.255728  \n",
+       "  26 -0.695036 -0.810017    0.033122   -1.751549   -3.602789  \n",
+       "  27  0.004366  0.537831    3.241161   -0.464849   -1.433231  \n",
+       "  28  0.258824  3.340419    2.990223    1.461432    2.606451  \n",
+       "  29 -0.692610  1.503620    0.885416    1.959302    2.964980  \n",
+       "  30 -0.869936  0.351590   -1.661038    1.934326    3.271168  \n",
+       "  31  1.684954 -1.922781   -1.998185   -1.393889    1.161394  \n",
+       "  32  0.827892 -2.478550    0.541063   -1.880941   -0.473325  \n",
+       "  33  1.310511 -1.257898    3.653700   -1.601337   -1.579658  \n",
+       "  34  1.043606  1.986497    1.707818    0.193998   -3.864035  \n",
+       "  35 -2.244414  3.867285   -1.943799    1.997772   -3.171677  \n",
+       "  36 -2.800506  3.488811   -3.948828    1.666375   -0.896916  \n",
+       "  37 -2.503104 -1.977504   -2.094718    0.655704    1.698770  \n",
+       "  38 -1.294041 -2.409426    1.429176   -3.232496    1.734380  \n",
+       "  39 -0.763355 -2.186015    3.539124   -4.529510    1.642566  \n",
+       "  40 -0.018622 -0.427650    2.271382   -2.400871   -0.269681  \n",
+       "  41 -0.868895  2.965318   -1.471974   -0.858027   -1.173086  \n",
+       "  42 -0.082183  4.051197   -3.655486    2.698638   -1.210322  \n",
+       "  43 -0.124379  3.188121   -3.109283    2.016316   -1.944258  \n",
+       "  44  1.687972  2.185182    0.187121    0.570115    0.408683  \n",
+       "  45  0.603155 -0.219874    2.621389   -2.080184    1.258935  \n",
+       "  46  0.423334 -2.571537    2.803567   -2.228183    3.041480  \n",
+       "  47 -1.222195 -2.947538    0.541672   -1.997911   -0.401189  \n",
+       "  48  0.309721 -1.188706   -1.580278   -1.870709   -1.209668  \n",
+       "  49 -0.229298  3.429724   -3.536907   -0.306651   -1.777669  \n",
+       "  50  2.297931  5.527336   -2.058579   -1.499570   -1.452626  \n",
+       "  51  2.013749  2.728451    0.544547    0.938279    0.007270  \n",
+       "  52  1.747087 -0.868734    4.830233    1.650324    1.475109  \n",
+       "  53  1.729754 -4.414808    5.121964    2.255877    1.072432  \n",
+       "  54 -1.062626 -4.209477    1.062214    1.069024    1.957370  \n",
+       "  55 -0.315856 -1.682862   -4.669046   -0.586674   -0.644969  \n",
+       "  56 -0.632748  1.634388   -6.619816   -0.917644   -3.155102  \n",
+       "  57  1.151223  4.163058   -4.551591   -0.541258   -1.567434  \n",
+       "  58  2.975799  2.433736    0.232740    0.595110    0.518873  \n",
+       "  59  1.363363 -0.600139    4.702588    0.078029    1.259880  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -0.483136   \n",
+       "  3  -0.483136 -1.016130  0.123712  1.397567  1.993879  2.387798 -0.806653   \n",
+       "  4  -0.806653 -1.480816  0.783291 -0.079020 -1.061344  1.509508  0.248225   \n",
+       "  5   0.248225 -1.246917  0.323618 -0.307828 -1.754475 -0.060851 -0.053289   \n",
+       "  6  -0.053289 -0.247399 -1.234108  0.131237 -2.412556 -2.672812 -0.565368   \n",
+       "  7  -0.565368  0.414661  0.128247  1.507392 -0.541879 -2.751994 -0.967385   \n",
+       "  8  -0.967385  0.192018  1.162658  2.202068  1.004240 -0.516736 -0.591575   \n",
+       "  9  -0.591575  1.203435  2.481130  1.293142  2.071861  0.251197  1.109731   \n",
+       "  10  1.109731  0.953726 -1.500364 -1.999257  1.104847  0.715830  1.428707   \n",
+       "  11  1.428707 -0.499999 -0.661098 -3.665048  0.071059  2.197274 -0.675934   \n",
+       "  12 -0.675934 -0.839321  0.420326 -1.684807 -1.106330  0.892470 -0.344980   \n",
+       "  13 -0.344980  0.394663  0.197769 -0.319177 -1.661262  0.249500 -0.946755   \n",
+       "  14 -0.946755  2.537649  0.213144  2.301447 -2.524175 -0.365531 -0.263098   \n",
+       "  15 -0.263098  1.862573  0.234529  3.289206 -2.028426 -0.651430 -1.128441   \n",
+       "  16 -1.128441  0.643342  1.898520 -0.029182  0.494289 -0.633810  0.281188   \n",
+       "  17  0.281188  0.352628  1.618974 -2.549814  2.854040  0.814553 -1.272905   \n",
+       "  18 -1.272905  0.445558  0.062765 -2.157021  3.654785  1.922338 -1.230444   \n",
+       "  19 -1.230444  0.177719 -2.932154 -0.004328  2.078907  1.766309 -1.213069   \n",
+       "  20 -1.213069  0.667311 -3.785785  1.768073 -1.067894  0.076001  1.269897   \n",
+       "  21  1.269897  1.674021 -3.521879  0.633185 -2.119802 -1.131199  2.350213   \n",
+       "  22  2.350213  0.784056  1.866259  0.110397 -2.472648 -3.019276  2.101016   \n",
+       "  23  2.101016 -0.265848  2.268159  0.542420 -0.290041 -1.100556  0.833437   \n",
+       "  24  0.833437 -1.839919  2.226807 -1.151024  1.738645  1.146385 -2.001769   \n",
+       "  25 -2.001769  0.261854  0.612013  0.342027  0.462237  1.157938 -3.980020   \n",
+       "  26 -3.980020  1.720868 -1.266145  0.887330 -0.721642  3.134887 -1.890088   \n",
+       "  27 -1.890088  1.477129 -3.549636 -1.062978 -2.290391  1.564261 -0.206557   \n",
+       "  28 -0.206557  0.335176 -2.605780 -0.179249 -1.712505  0.736078  2.037158   \n",
+       "  29  2.037158 -1.424288  0.569851 -0.756863 -0.399685 -0.611096  1.353765   \n",
+       "  30  1.353765 -0.446885  0.870183  1.976883  0.592939 -2.945294 -0.209269   \n",
+       "  31 -0.209269  1.406868  1.075132  2.420444  1.598271 -2.814461 -1.928499   \n",
+       "  32 -1.928499  2.536585  0.675161  1.016936 -0.685853 -1.732688 -1.847865   \n",
+       "  33 -1.847865  1.918389  0.008633 -2.889541 -2.179121  2.363599 -0.321098   \n",
+       "  34 -0.321098  0.734095  0.160415 -2.849511 -2.729122  3.220361 -0.629774   \n",
+       "  35 -0.629774 -1.841677 -0.125695 -0.980443 -2.412680  2.165415  0.688981   \n",
+       "  36  0.688981 -1.661305 -0.392404  1.105050 -0.486235  0.678172  3.503676   \n",
+       "  37  3.503676 -1.213819 -1.247860  1.396008  1.585002 -0.339738  1.221885   \n",
+       "  38  1.221885  0.983337 -2.115917 -0.250066  3.483086 -1.929323 -2.018374   \n",
+       "  39 -2.018374  3.961485 -1.698926 -2.648977  1.826191 -0.202055 -2.924762   \n",
+       "  40 -2.924762  3.953536  0.524201 -3.149967 -0.850019  0.368045 -2.893424   \n",
+       "  41 -2.893424  0.382813  2.440439 -0.894182 -2.966557  0.766801  0.833771   \n",
+       "  42  0.833771 -2.926936  1.582543  2.429970  0.052981  1.801507  3.045849   \n",
+       "  43  3.045849 -5.050238 -1.452359  4.103517  2.397277  2.163810  2.956606   \n",
+       "  44  2.956606 -4.408079 -2.963083  1.549516  2.612366  0.871761  1.240205   \n",
+       "  45  1.240205  0.079219 -2.118333 -1.560608  0.107381  0.693767 -0.791535   \n",
+       "  46 -0.791535  5.035636 -0.026566 -4.489167 -2.412180 -0.387033 -1.811635   \n",
+       "  47 -1.811635  4.950855  1.323260 -4.429681 -1.429082 -0.675436 -0.214651   \n",
+       "  48 -0.214651  1.794452  1.707497 -1.330874  0.243914 -0.700802  1.447666   \n",
+       "  49  1.447666 -2.272526  0.659760  1.993947  0.753801 -0.358989  1.154842   \n",
+       "  50  1.154842 -4.255563  0.891942  2.539308  1.131369  0.203453  1.022527   \n",
+       "  51  1.022527 -4.277109 -1.316801  1.150570  1.544889  1.338272 -1.636064   \n",
+       "  52 -1.636064 -1.350153 -2.794143 -1.044841  1.499268  0.178643 -3.064337   \n",
+       "  53 -3.064337  0.687897 -2.493813 -0.079861 -2.079237 -0.751305 -1.022172   \n",
+       "  54 -1.022172  1.079728 -1.922713  1.283143 -2.360555 -0.555281  1.896589   \n",
+       "  55  1.896589  0.714300 -0.508558  0.082883 -2.234092 -1.635378  3.210960   \n",
+       "  56  3.210960 -0.302253  2.238311 -0.247316 -0.508331 -2.233015  1.651327   \n",
+       "  57  1.651327 -0.616767  3.414043 -0.562590  1.635745 -0.387113  0.329640   \n",
+       "  58  0.329640 -0.709174  0.562548 -1.388546 -0.100240  1.894068 -0.674014   \n",
+       "  59 -0.674014 -1.549266 -1.570168 -0.946268 -2.116076  1.574281 -0.618623   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -1.016130  0.123712    1.397567    1.993879    2.387798  \n",
+       "  3  -1.480816  0.783291   -0.079020   -1.061344    1.509508  \n",
+       "  4  -1.246917  0.323618   -0.307828   -1.754475   -0.060851  \n",
+       "  5  -0.247399 -1.234108    0.131237   -2.412556   -2.672812  \n",
+       "  6   0.414661  0.128247    1.507392   -0.541879   -2.751994  \n",
+       "  7   0.192018  1.162658    2.202068    1.004240   -0.516736  \n",
+       "  8   1.203435  2.481130    1.293142    2.071861    0.251197  \n",
+       "  9   0.953726 -1.500364   -1.999257    1.104847    0.715830  \n",
+       "  10 -0.499999 -0.661098   -3.665048    0.071059    2.197274  \n",
+       "  11 -0.839321  0.420326   -1.684807   -1.106330    0.892470  \n",
+       "  12  0.394663  0.197769   -0.319177   -1.661262    0.249500  \n",
+       "  13  2.537649  0.213144    2.301447   -2.524175   -0.365531  \n",
+       "  14  1.862573  0.234529    3.289206   -2.028426   -0.651430  \n",
+       "  15  0.643342  1.898520   -0.029182    0.494289   -0.633810  \n",
+       "  16  0.352628  1.618974   -2.549814    2.854040    0.814553  \n",
+       "  17  0.445558  0.062765   -2.157021    3.654785    1.922338  \n",
+       "  18  0.177719 -2.932154   -0.004328    2.078907    1.766309  \n",
+       "  19  0.667311 -3.785785    1.768073   -1.067894    0.076001  \n",
+       "  20  1.674021 -3.521879    0.633185   -2.119802   -1.131199  \n",
+       "  21  0.784056  1.866259    0.110397   -2.472648   -3.019276  \n",
+       "  22 -0.265848  2.268159    0.542420   -0.290041   -1.100556  \n",
+       "  23 -1.839919  2.226807   -1.151024    1.738645    1.146385  \n",
+       "  24  0.261854  0.612013    0.342027    0.462237    1.157938  \n",
+       "  25  1.720868 -1.266145    0.887330   -0.721642    3.134887  \n",
+       "  26  1.477129 -3.549636   -1.062978   -2.290391    1.564261  \n",
+       "  27  0.335176 -2.605780   -0.179249   -1.712505    0.736078  \n",
+       "  28 -1.424288  0.569851   -0.756863   -0.399685   -0.611096  \n",
+       "  29 -0.446885  0.870183    1.976883    0.592939   -2.945294  \n",
+       "  30  1.406868  1.075132    2.420444    1.598271   -2.814461  \n",
+       "  31  2.536585  0.675161    1.016936   -0.685853   -1.732688  \n",
+       "  32  1.918389  0.008633   -2.889541   -2.179121    2.363599  \n",
+       "  33  0.734095  0.160415   -2.849511   -2.729122    3.220361  \n",
+       "  34 -1.841677 -0.125695   -0.980443   -2.412680    2.165415  \n",
+       "  35 -1.661305 -0.392404    1.105050   -0.486235    0.678172  \n",
+       "  36 -1.213819 -1.247860    1.396008    1.585002   -0.339738  \n",
+       "  37  0.983337 -2.115917   -0.250066    3.483086   -1.929323  \n",
+       "  38  3.961485 -1.698926   -2.648977    1.826191   -0.202055  \n",
+       "  39  3.953536  0.524201   -3.149967   -0.850019    0.368045  \n",
+       "  40  0.382813  2.440439   -0.894182   -2.966557    0.766801  \n",
+       "  41 -2.926936  1.582543    2.429970    0.052981    1.801507  \n",
+       "  42 -5.050238 -1.452359    4.103517    2.397277    2.163810  \n",
+       "  43 -4.408079 -2.963083    1.549516    2.612366    0.871761  \n",
+       "  44  0.079219 -2.118333   -1.560608    0.107381    0.693767  \n",
+       "  45  5.035636 -0.026566   -4.489167   -2.412180   -0.387033  \n",
+       "  46  4.950855  1.323260   -4.429681   -1.429082   -0.675436  \n",
+       "  47  1.794452  1.707497   -1.330874    0.243914   -0.700802  \n",
+       "  48 -2.272526  0.659760    1.993947    0.753801   -0.358989  \n",
+       "  49 -4.255563  0.891942    2.539308    1.131369    0.203453  \n",
+       "  50 -4.277109 -1.316801    1.150570    1.544889    1.338272  \n",
+       "  51 -1.350153 -2.794143   -1.044841    1.499268    0.178643  \n",
+       "  52  0.687897 -2.493813   -0.079861   -2.079237   -0.751305  \n",
+       "  53  1.079728 -1.922713    1.283143   -2.360555   -0.555281  \n",
+       "  54  0.714300 -0.508558    0.082883   -2.234092   -1.635378  \n",
+       "  55 -0.302253  2.238311   -0.247316   -0.508331   -2.233015  \n",
+       "  56 -0.616767  3.414043   -0.562590    1.635745   -0.387113  \n",
+       "  57 -0.709174  0.562548   -1.388546   -0.100240    1.894068  \n",
+       "  58 -1.549266 -1.570168   -0.946268   -2.116076    1.574281  \n",
+       "  59 -1.851727 -2.646047    1.723866   -0.569919    0.135567  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000 -0.468967   \n",
+       "  3  -0.468967 -0.920024 -0.159053  0.256930  2.110391  0.458116 -2.372537   \n",
+       "  4  -2.372537 -0.611043 -2.317400 -1.218029  1.431782 -0.242059 -2.684611   \n",
+       "  5  -2.684611 -1.434786 -2.210714 -1.219764  0.893911 -0.121772 -1.301341   \n",
+       "  6  -1.301341 -1.606727 -1.547160  0.662123  0.221133 -1.343160 -1.567380   \n",
+       "  7  -1.567380 -1.791833  1.964278  1.158537 -2.557380  0.870609  0.208160   \n",
+       "  8   0.208160  0.393675  3.125767 -0.182474 -2.884842  1.075517  0.464012   \n",
+       "  9   0.464012  1.314111  3.338855 -1.723452 -2.475417  0.163735 -0.687307   \n",
+       "  10 -0.687307 -0.126506 -0.304072 -1.080390 -0.165269 -2.120427  1.500477   \n",
+       "  11  1.500477 -0.589660 -1.589358  0.054522  1.320494 -1.731676  1.759456   \n",
+       "  12  1.759456 -0.439653 -2.260902  2.150817  4.502522  0.408949 -0.281859   \n",
+       "  13 -0.281859 -1.884301  0.096061  2.275332  3.696523  0.413124 -2.534144   \n",
+       "  14 -2.534144 -1.437523  2.402647  0.022069  0.328177  0.095179 -1.506322   \n",
+       "  15 -1.506322 -0.422480  1.315598  0.471286 -2.528619 -0.118501 -1.600316   \n",
+       "  16 -1.600316  1.483071  0.562769 -2.741966 -4.321392 -0.849710 -0.137703   \n",
+       "  17 -0.137703  0.030773 -1.999666 -2.578347 -2.955452 -1.595629  0.965321   \n",
+       "  18  0.965321 -0.354399 -3.815108 -1.258570 -1.181771 -0.534971  1.063954   \n",
+       "  19  1.063954 -0.810860 -1.698277  1.488997  1.821450  0.076379  1.243783   \n",
+       "  20  1.243783  0.318748  0.915713  2.690975  2.641349  0.298558 -1.875362   \n",
+       "  21 -1.875362  1.136144  1.941644  3.288954  1.999516  0.029160 -1.721965   \n",
+       "  22 -1.721965  2.150095  1.032781  2.893486 -1.188752  1.720047 -1.519442   \n",
+       "  23 -1.519442  0.300206 -0.948415  0.080929 -2.447691  1.132587  1.074767   \n",
+       "  24  1.074767 -0.275567 -0.756403 -2.423822 -1.385422 -0.369970  2.340681   \n",
+       "  25  2.340681 -0.069991 -1.684602 -1.422223 -0.332541 -0.455958  0.517682   \n",
+       "  26  0.517682 -0.827997 -0.173546  1.541719  0.594734 -1.047843 -1.974203   \n",
+       "  27 -1.974203  0.044444  0.269837  2.033869  0.709166 -0.204618 -2.542076   \n",
+       "  28 -2.542076 -0.813472  0.509224  2.856834  1.615872  0.779425 -2.036724   \n",
+       "  29 -2.036724  0.057969 -0.838388  2.063659  1.561048  2.427478  0.375636   \n",
+       "  30  0.375636  0.070295  0.502950 -1.154483  0.617646 -0.305377  1.346683   \n",
+       "  31  1.346683  0.809626  1.675305 -3.587048  0.651321 -3.494130  2.756932   \n",
+       "  32  2.756932  1.273997  2.517239 -1.804703 -1.639884 -1.274187  2.015673   \n",
+       "  33  2.015673  2.358326  0.313586  0.898692 -1.566584  1.030086  0.269615   \n",
+       "  34  0.269615  2.041017 -0.586743  2.351203 -0.328180  4.427819 -1.606558   \n",
+       "  35 -1.606558  0.070948 -1.906662  2.654713  0.315324  3.184621 -3.226813   \n",
+       "  36 -3.226813 -1.574179 -3.635879  2.151927  2.445487 -0.172012 -0.961700   \n",
+       "  37 -0.961700 -2.852157 -2.711067 -0.857046  1.179950 -4.186981  1.642120   \n",
+       "  38  1.642120 -2.461715  1.288544 -3.088338  0.875850 -3.910433  2.539010   \n",
+       "  39  2.539010 -0.709166  3.235944 -1.369513  0.661631 -1.128010  0.348557   \n",
+       "  40  0.348557 -0.384589  3.122051 -0.571546 -1.557811  2.617459 -0.812348   \n",
+       "  41 -0.812348  2.137312  2.062804  1.659367 -0.315966  4.292972 -2.514426   \n",
+       "  42 -2.514426  2.070012 -1.179513  1.586120 -0.075326  3.257577 -0.779382   \n",
+       "  43 -0.779382  0.377734 -2.151585  0.070482 -0.595645  0.796287  1.615420   \n",
+       "  44  1.615420 -1.422277 -0.957225 -2.423993  1.115561 -1.744185  1.317598   \n",
+       "  45  1.317598 -1.544153 -0.074055 -3.063305  0.482239 -4.075752  1.048039   \n",
+       "  46  1.048039 -0.434612  0.322758 -2.165389 -0.399565 -2.864003 -1.561196   \n",
+       "  47 -1.561196  0.070380  0.095496  1.248547 -1.698441 -2.101008 -2.409335   \n",
+       "  48 -2.409335  0.408920 -0.547043  2.378768 -1.136689  0.916014 -0.751516   \n",
+       "  49 -0.751516  0.054102  0.469402  0.016635  0.648463  2.566095  0.811348   \n",
+       "  50  0.811348 -0.806501  1.153292 -1.644839  1.170238  3.014222  1.424033   \n",
+       "  51  1.424033 -1.360642 -0.173699 -1.074997  1.470503  1.139047  0.911114   \n",
+       "  52  0.911114 -1.102078  0.583153 -0.786930  1.258409 -2.302884  0.493287   \n",
+       "  53  0.493287 -1.951115  0.522481  0.307798  0.107521 -3.369843 -1.260900   \n",
+       "  54 -1.260900 -0.810897 -0.102822  0.521714 -0.904735 -3.433811 -0.280492   \n",
+       "  55 -0.280492 -0.309973 -1.123923  2.435872 -1.589979  0.375097  0.953506   \n",
+       "  56  0.953506  1.186361  0.195413  1.667811 -0.747632  1.580533  1.925276   \n",
+       "  57  1.925276  0.760211  2.384379 -0.566870  0.693961  1.393821  2.079172   \n",
+       "  58  2.079172  0.623513  2.492177 -1.829346  2.990455 -0.443746  1.577369   \n",
+       "  59  1.577369 -0.594501 -0.512127 -1.731334  1.405480 -2.101463 -1.167226   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -0.920024 -0.159053    0.256930    2.110391    0.458116  \n",
+       "  3  -0.611043 -2.317400   -1.218029    1.431782   -0.242059  \n",
+       "  4  -1.434786 -2.210714   -1.219764    0.893911   -0.121772  \n",
+       "  5  -1.606727 -1.547160    0.662123    0.221133   -1.343160  \n",
+       "  6  -1.791833  1.964278    1.158537   -2.557380    0.870609  \n",
+       "  7   0.393675  3.125767   -0.182474   -2.884842    1.075517  \n",
+       "  8   1.314111  3.338855   -1.723452   -2.475417    0.163735  \n",
+       "  9  -0.126506 -0.304072   -1.080390   -0.165269   -2.120427  \n",
+       "  10 -0.589660 -1.589358    0.054522    1.320494   -1.731676  \n",
+       "  11 -0.439653 -2.260902    2.150817    4.502522    0.408949  \n",
+       "  12 -1.884301  0.096061    2.275332    3.696523    0.413124  \n",
+       "  13 -1.437523  2.402647    0.022069    0.328177    0.095179  \n",
+       "  14 -0.422480  1.315598    0.471286   -2.528619   -0.118501  \n",
+       "  15  1.483071  0.562769   -2.741966   -4.321392   -0.849710  \n",
+       "  16  0.030773 -1.999666   -2.578347   -2.955452   -1.595629  \n",
+       "  17 -0.354399 -3.815108   -1.258570   -1.181771   -0.534971  \n",
+       "  18 -0.810860 -1.698277    1.488997    1.821450    0.076379  \n",
+       "  19  0.318748  0.915713    2.690975    2.641349    0.298558  \n",
+       "  20  1.136144  1.941644    3.288954    1.999516    0.029160  \n",
+       "  21  2.150095  1.032781    2.893486   -1.188752    1.720047  \n",
+       "  22  0.300206 -0.948415    0.080929   -2.447691    1.132587  \n",
+       "  23 -0.275567 -0.756403   -2.423822   -1.385422   -0.369970  \n",
+       "  24 -0.069991 -1.684602   -1.422223   -0.332541   -0.455958  \n",
+       "  25 -0.827997 -0.173546    1.541719    0.594734   -1.047843  \n",
+       "  26  0.044444  0.269837    2.033869    0.709166   -0.204618  \n",
+       "  27 -0.813472  0.509224    2.856834    1.615872    0.779425  \n",
+       "  28  0.057969 -0.838388    2.063659    1.561048    2.427478  \n",
+       "  29  0.070295  0.502950   -1.154483    0.617646   -0.305377  \n",
+       "  30  0.809626  1.675305   -3.587048    0.651321   -3.494130  \n",
+       "  31  1.273997  2.517239   -1.804703   -1.639884   -1.274187  \n",
+       "  32  2.358326  0.313586    0.898692   -1.566584    1.030086  \n",
+       "  33  2.041017 -0.586743    2.351203   -0.328180    4.427819  \n",
+       "  34  0.070948 -1.906662    2.654713    0.315324    3.184621  \n",
+       "  35 -1.574179 -3.635879    2.151927    2.445487   -0.172012  \n",
+       "  36 -2.852157 -2.711067   -0.857046    1.179950   -4.186981  \n",
+       "  37 -2.461715  1.288544   -3.088338    0.875850   -3.910433  \n",
+       "  38 -0.709166  3.235944   -1.369513    0.661631   -1.128010  \n",
+       "  39 -0.384589  3.122051   -0.571546   -1.557811    2.617459  \n",
+       "  40  2.137312  2.062804    1.659367   -0.315966    4.292972  \n",
+       "  41  2.070012 -1.179513    1.586120   -0.075326    3.257577  \n",
+       "  42  0.377734 -2.151585    0.070482   -0.595645    0.796287  \n",
+       "  43 -1.422277 -0.957225   -2.423993    1.115561   -1.744185  \n",
+       "  44 -1.544153 -0.074055   -3.063305    0.482239   -4.075752  \n",
+       "  45 -0.434612  0.322758   -2.165389   -0.399565   -2.864003  \n",
+       "  46  0.070380  0.095496    1.248547   -1.698441   -2.101008  \n",
+       "  47  0.408920 -0.547043    2.378768   -1.136689    0.916014  \n",
+       "  48  0.054102  0.469402    0.016635    0.648463    2.566095  \n",
+       "  49 -0.806501  1.153292   -1.644839    1.170238    3.014222  \n",
+       "  50 -1.360642 -0.173699   -1.074997    1.470503    1.139047  \n",
+       "  51 -1.102078  0.583153   -0.786930    1.258409   -2.302884  \n",
+       "  52 -1.951115  0.522481    0.307798    0.107521   -3.369843  \n",
+       "  53 -0.810897 -0.102822    0.521714   -0.904735   -3.433811  \n",
+       "  54 -0.309973 -1.123923    2.435872   -1.589979    0.375097  \n",
+       "  55  1.186361  0.195413    1.667811   -0.747632    1.580533  \n",
+       "  56  0.760211  2.384379   -0.566870    0.693961    1.393821  \n",
+       "  57  0.623513  2.492177   -1.829346    2.990455   -0.443746  \n",
+       "  58 -0.594501 -0.512127   -1.731334    1.405480   -2.101463  \n",
+       "  59  0.167392 -1.685509   -1.247271   -1.132011   -1.283324  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.599923   \n",
+       "  3   1.599923  0.463188  0.295068  1.391780  0.888733  1.842918 -0.602419   \n",
+       "  4  -0.602419 -0.288498 -0.655939  0.290847  0.381346 -1.214467 -2.282159   \n",
+       "  5  -2.282159 -1.007393 -2.486894  0.756126 -0.356974 -3.255442 -1.066890   \n",
+       "  6  -1.066890  0.477120 -0.246851  0.382820 -1.498688 -1.924419  1.752225   \n",
+       "  7   1.752225  0.407010  0.354290  0.417042 -0.621352 -0.444468  2.534415   \n",
+       "  8   2.534415  1.202604  1.396925  1.685368 -1.720956  1.906117  2.148828   \n",
+       "  9   2.148828  0.432990  2.871181 -0.070882  0.492893  1.883170 -0.942735   \n",
+       "  10 -0.942735 -0.025503  2.123991 -0.416230  2.990582  0.337979 -0.844561   \n",
+       "  11 -0.844561 -1.364164 -0.099469 -2.065891  3.773668 -0.440612 -2.223436   \n",
+       "  12 -2.223436  0.631329 -3.156521 -1.808519  2.868610 -0.337045 -2.377991   \n",
+       "  13 -2.377991  1.719151 -2.599938  0.473574  0.666395 -2.518770 -1.111118   \n",
+       "  14 -1.111118  0.566929 -0.902477  1.537247 -0.600694 -3.356977 -0.197587   \n",
+       "  15 -0.197587 -1.237303  1.456203  1.144403 -2.987715 -1.647419  2.212634   \n",
+       "  16  2.212634 -1.898185  2.995835 -0.669477 -1.000580  0.239893  5.195009   \n",
+       "  17  5.195009 -1.815375  2.527541 -1.015793  0.154367  3.291657  4.105977   \n",
+       "  18  4.105977 -1.049687  1.371862 -1.812644  2.161448  1.939998 -0.118786   \n",
+       "  19 -0.118786  0.739965 -0.773188 -1.508645  5.496945  0.138573 -2.431349   \n",
+       "  20 -2.431349  4.842349 -0.525989  0.135209  5.119929 -2.810803 -3.064905   \n",
+       "  21 -3.064905  3.851476 -0.510802  2.301158  1.848783 -2.481472 -2.315541   \n",
+       "  22 -2.315541  1.030654  0.944303  1.963079 -2.887162 -0.545432  0.313430   \n",
+       "  23  0.313430 -3.707069  1.082699  0.396458 -4.419831  1.897301  1.566677   \n",
+       "  24  1.566677 -3.929562 -0.445620 -0.210662 -1.221757  3.917533  2.037613   \n",
+       "  25  2.037613 -4.812504 -0.027963 -3.126002  1.650088  0.853944 -0.651285   \n",
+       "  26 -0.651285 -0.297311  0.817168 -1.865550  3.240391 -1.571291 -0.395599   \n",
+       "  27 -0.395599  1.950666 -0.117942 -0.790571  4.405124 -2.681467 -1.024567   \n",
+       "  28 -1.024567  4.114355 -1.897802  0.464307 -0.426686 -2.081695 -0.082008   \n",
+       "  29 -0.082008  1.318334 -1.700213  2.424090 -3.399913  0.230160  1.088593   \n",
+       "  30  1.088593  2.017551 -0.164179  3.029643 -2.757385  2.205298  1.869796   \n",
+       "  31  1.869796 -0.282172  1.165117  1.868237 -1.498327  2.349810  1.168333   \n",
+       "  32  1.168333 -1.727360  1.448872 -0.782421 -0.093837  1.567833 -0.402012   \n",
+       "  33 -0.402012 -1.571446  1.878006 -1.112340  1.751983 -2.600283 -1.580227   \n",
+       "  34 -1.580227  2.801343  0.628870 -1.556495 -0.084421 -1.260991  0.399670   \n",
+       "  35  0.399670  2.968609 -1.148216  0.251186  1.714634  0.038445  2.566588   \n",
+       "  36  2.566588  2.807030 -0.820588  0.105158  1.430865  2.472908  0.894239   \n",
+       "  37  0.894239  0.080385 -0.403254  1.734719  0.014233  2.860383  0.115743   \n",
+       "  38  0.115743 -1.117995 -2.089116 -0.425370 -1.663176  1.299552 -1.827834   \n",
+       "  39 -1.827834 -0.736075 -0.916827 -0.968468 -1.346406 -1.944604  0.296449   \n",
+       "  40  0.296449 -0.023109 -1.030013 -0.778158 -0.315951 -3.785529 -0.150391   \n",
+       "  41 -0.150391  0.275945  0.446047 -0.262747  0.125773 -5.180036 -0.320246   \n",
+       "  42 -0.320246 -0.725305 -0.644304 -1.023806  0.564534 -1.161323 -1.416761   \n",
+       "  43 -1.416761 -1.113370  0.605977 -0.487455  0.491842  1.837437  1.285016   \n",
+       "  44  1.285016  1.009661  1.065025  0.591152  1.635190  3.033140  0.524684   \n",
+       "  45  0.524684  2.124662  0.560943  0.447840  1.000324  4.031579  1.767071   \n",
+       "  46  1.767071  1.263890 -1.226500  0.978280  1.298302  1.173376 -0.650222   \n",
+       "  47 -0.650222 -0.738152 -1.697195  1.666936 -1.666130 -0.368154 -0.389472   \n",
+       "  48 -0.389472 -3.426963 -1.262744  2.183479 -2.446648 -2.517340 -0.994790   \n",
+       "  49 -0.994790 -2.458712  0.749473 -0.083694 -1.648348 -2.610991 -1.376143   \n",
+       "  50 -1.376143 -1.182640  2.960134 -2.105850  1.190874 -0.219839 -0.415481   \n",
+       "  51 -0.415481 -0.538449  0.097761 -1.413581  2.988522  1.216089 -0.178644   \n",
+       "  52 -0.178644  0.420401 -0.894578 -1.156375  3.726649  3.441470  0.315139   \n",
+       "  53  0.315139 -0.300625 -2.936420  1.959329  0.952228  4.280181  1.808834   \n",
+       "  54  1.808834  0.572981 -3.090862  1.230629 -2.507934  1.259297  1.451347   \n",
+       "  55  1.451347  0.391973 -0.832008  1.576380 -3.311948 -1.108771  1.822234   \n",
+       "  56  1.822234 -0.009931  1.451005 -1.887146 -2.934540 -3.689405  1.829904   \n",
+       "  57  1.829904 -0.515970  1.933300 -4.069468  1.675945 -0.964538 -0.124637   \n",
+       "  58 -0.124637 -0.232991  1.787869 -4.110275  1.402369  0.606416  0.167802   \n",
+       "  59  0.167802 -1.996565 -0.252800 -0.539942  2.077366  3.243322 -0.398007   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   0.463188  0.295068    1.391780    0.888733    1.842918  \n",
+       "  3  -0.288498 -0.655939    0.290847    0.381346   -1.214467  \n",
+       "  4  -1.007393 -2.486894    0.756126   -0.356974   -3.255442  \n",
+       "  5   0.477120 -0.246851    0.382820   -1.498688   -1.924419  \n",
+       "  6   0.407010  0.354290    0.417042   -0.621352   -0.444468  \n",
+       "  7   1.202604  1.396925    1.685368   -1.720956    1.906117  \n",
+       "  8   0.432990  2.871181   -0.070882    0.492893    1.883170  \n",
+       "  9  -0.025503  2.123991   -0.416230    2.990582    0.337979  \n",
+       "  10 -1.364164 -0.099469   -2.065891    3.773668   -0.440612  \n",
+       "  11  0.631329 -3.156521   -1.808519    2.868610   -0.337045  \n",
+       "  12  1.719151 -2.599938    0.473574    0.666395   -2.518770  \n",
+       "  13  0.566929 -0.902477    1.537247   -0.600694   -3.356977  \n",
+       "  14 -1.237303  1.456203    1.144403   -2.987715   -1.647419  \n",
+       "  15 -1.898185  2.995835   -0.669477   -1.000580    0.239893  \n",
+       "  16 -1.815375  2.527541   -1.015793    0.154367    3.291657  \n",
+       "  17 -1.049687  1.371862   -1.812644    2.161448    1.939998  \n",
+       "  18  0.739965 -0.773188   -1.508645    5.496945    0.138573  \n",
+       "  19  4.842349 -0.525989    0.135209    5.119929   -2.810803  \n",
+       "  20  3.851476 -0.510802    2.301158    1.848783   -2.481472  \n",
+       "  21  1.030654  0.944303    1.963079   -2.887162   -0.545432  \n",
+       "  22 -3.707069  1.082699    0.396458   -4.419831    1.897301  \n",
+       "  23 -3.929562 -0.445620   -0.210662   -1.221757    3.917533  \n",
+       "  24 -4.812504 -0.027963   -3.126002    1.650088    0.853944  \n",
+       "  25 -0.297311  0.817168   -1.865550    3.240391   -1.571291  \n",
+       "  26  1.950666 -0.117942   -0.790571    4.405124   -2.681467  \n",
+       "  27  4.114355 -1.897802    0.464307   -0.426686   -2.081695  \n",
+       "  28  1.318334 -1.700213    2.424090   -3.399913    0.230160  \n",
+       "  29  2.017551 -0.164179    3.029643   -2.757385    2.205298  \n",
+       "  30 -0.282172  1.165117    1.868237   -1.498327    2.349810  \n",
+       "  31 -1.727360  1.448872   -0.782421   -0.093837    1.567833  \n",
+       "  32 -1.571446  1.878006   -1.112340    1.751983   -2.600283  \n",
+       "  33  2.801343  0.628870   -1.556495   -0.084421   -1.260991  \n",
+       "  34  2.968609 -1.148216    0.251186    1.714634    0.038445  \n",
+       "  35  2.807030 -0.820588    0.105158    1.430865    2.472908  \n",
+       "  36  0.080385 -0.403254    1.734719    0.014233    2.860383  \n",
+       "  37 -1.117995 -2.089116   -0.425370   -1.663176    1.299552  \n",
+       "  38 -0.736075 -0.916827   -0.968468   -1.346406   -1.944604  \n",
+       "  39 -0.023109 -1.030013   -0.778158   -0.315951   -3.785529  \n",
+       "  40  0.275945  0.446047   -0.262747    0.125773   -5.180036  \n",
+       "  41 -0.725305 -0.644304   -1.023806    0.564534   -1.161323  \n",
+       "  42 -1.113370  0.605977   -0.487455    0.491842    1.837437  \n",
+       "  43  1.009661  1.065025    0.591152    1.635190    3.033140  \n",
+       "  44  2.124662  0.560943    0.447840    1.000324    4.031579  \n",
+       "  45  1.263890 -1.226500    0.978280    1.298302    1.173376  \n",
+       "  46 -0.738152 -1.697195    1.666936   -1.666130   -0.368154  \n",
+       "  47 -3.426963 -1.262744    2.183479   -2.446648   -2.517340  \n",
+       "  48 -2.458712  0.749473   -0.083694   -1.648348   -2.610991  \n",
+       "  49 -1.182640  2.960134   -2.105850    1.190874   -0.219839  \n",
+       "  50 -0.538449  0.097761   -1.413581    2.988522    1.216089  \n",
+       "  51  0.420401 -0.894578   -1.156375    3.726649    3.441470  \n",
+       "  52 -0.300625 -2.936420    1.959329    0.952228    4.280181  \n",
+       "  53  0.572981 -3.090862    1.230629   -2.507934    1.259297  \n",
+       "  54  0.391973 -0.832008    1.576380   -3.311948   -1.108771  \n",
+       "  55 -0.009931  1.451005   -1.887146   -2.934540   -3.689405  \n",
+       "  56 -0.515970  1.933300   -4.069468    1.675945   -0.964538  \n",
+       "  57 -0.232991  1.787869   -4.110275    1.402369    0.606416  \n",
+       "  58 -1.996565 -0.252800   -0.539942    2.077366    3.243322  \n",
+       "  59 -1.479916 -0.460586    1.963485    0.778663    1.210486  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.338309   \n",
+       "  3   1.338309  1.239916  1.571174 -0.892004  0.546488 -0.829465  0.193348   \n",
+       "  4   0.193348 -0.346820 -0.336436 -0.240901  2.088110 -2.613916 -1.184867   \n",
+       "  5  -1.184867 -1.193287 -1.015828 -0.827546  1.160168 -0.820899 -0.571423   \n",
+       "  6  -0.571423 -2.663916 -1.909330 -1.195443 -1.518701 -0.631229 -0.461552   \n",
+       "  7  -0.461552 -2.066294  0.669652 -0.219736 -2.497438  0.168027  0.238436   \n",
+       "  8   0.238436 -1.466368  0.963040 -1.074059 -2.622271  0.779781  0.116608   \n",
+       "  9   0.116608 -0.960936  0.674871 -0.141407 -0.282669  2.380615  0.631690   \n",
+       "  10  0.631690  3.075384  1.253655 -0.466512  2.136354  0.211212 -0.530169   \n",
+       "  11 -0.530169  1.167654  0.050321  0.311804  3.736011 -0.091790 -0.143697   \n",
+       "  12 -0.143697 -0.463600 -0.840960  0.671118  0.671534 -0.408424  0.746750   \n",
+       "  13  0.746750 -1.464402 -0.735677  2.274224 -1.078687 -0.309293  0.255830   \n",
+       "  14  0.255830 -1.287899  0.806659  1.156641  0.562994 -0.296644  0.725667   \n",
+       "  15  0.725667 -0.409877  2.224765 -0.299318  0.219868  0.899372 -0.150024   \n",
+       "  16 -0.150024  1.421866  4.025960 -2.792018 -0.732217  1.561153  0.887213   \n",
+       "  17  0.887213  1.636128  1.803608 -0.859390 -2.010676  0.237291  0.802424   \n",
+       "  18  0.802424  0.240325 -3.182136 -1.349971 -0.550954 -1.020401  0.300626   \n",
+       "  19  0.300626  0.091958 -4.837395  0.696349  0.071376 -2.592055 -0.377739   \n",
+       "  20 -0.377739 -4.228778 -3.839992  0.794389  3.552787 -3.128705 -1.536553   \n",
+       "  21 -1.536553 -3.309383  0.377136  0.568852  2.067811 -0.822845 -1.180998   \n",
+       "  22 -1.180998 -1.370621  2.481398  0.832174 -0.955425  0.878134 -0.127665   \n",
+       "  23 -0.127665  1.609493  2.894463 -1.216669 -3.822762  2.399564  0.574187   \n",
+       "  24  0.574187  5.328339  0.725370 -1.144596 -3.554372  4.070938  0.945314   \n",
+       "  25  0.945314  2.940368 -3.206664 -0.869524 -0.269874  3.457920 -0.994090   \n",
+       "  26 -0.994090  0.546670 -4.066988  1.012696  0.457706 -1.197314 -1.587215   \n",
+       "  27 -1.587215 -1.021276 -1.654239  1.012306  1.464667 -3.658615 -0.014457   \n",
+       "  28 -0.014457 -1.147469  1.570268  1.677478  0.844537 -3.531715  0.581224   \n",
+       "  29  0.581224 -1.234892  2.892802 -1.082077 -0.701064  0.433363  1.870181   \n",
+       "  30  1.870181  1.049141  0.724023 -2.090009 -2.879625  3.948528  0.313159   \n",
+       "  31  0.313159  0.240629 -1.770090 -1.685802 -2.263010  5.968175 -1.641057   \n",
+       "  32 -1.641057  0.561385 -3.071928  0.168831 -0.677292  4.635834 -0.968898   \n",
+       "  33 -0.968898  0.877811 -1.164311  0.940499  0.753966 -0.818041 -1.173603   \n",
+       "  34 -1.173603 -0.110649  1.534619  1.341966  1.547380 -6.206645  0.732160   \n",
+       "  35  0.732160  1.551152  3.036576 -0.308112 -0.188393 -7.219594  0.539778   \n",
+       "  36  0.539778  2.183240  1.055115 -2.640709 -1.371694 -2.578747  1.234298   \n",
+       "  37  1.234298  0.424569 -2.824566 -3.342321 -0.621152  2.247463  0.894424   \n",
+       "  38  0.894424 -1.994758 -3.211256 -0.694773  0.583239  5.499868 -0.271940   \n",
+       "  39 -0.271940 -3.172545 -3.198703  0.773074  0.866656  3.379220 -0.332874   \n",
+       "  40 -0.332874 -2.276418  0.930634  3.158289 -0.490709 -0.109997  1.322127   \n",
+       "  41  1.322127 -0.164832  2.606760  4.002746 -1.153614 -4.733259  2.030830   \n",
+       "  42  2.030830  2.900892  2.022500  1.794425 -0.839694 -4.205335 -0.659941   \n",
+       "  43 -0.659941  2.492746 -0.815861 -0.955178  0.555967 -1.436538  0.001947   \n",
+       "  44  0.001947  0.332070 -2.498185 -2.955366  2.059587  3.498017 -0.489280   \n",
+       "  45 -0.489280  0.428482 -2.376467 -3.082320  3.229807  6.488336  0.198256   \n",
+       "  46  0.198256 -0.779333 -1.912477 -1.124814  1.366353  4.543602  2.248602   \n",
+       "  47  2.248602 -0.946542  1.106943  0.470886 -0.588900  0.175839  0.911839   \n",
+       "  48  0.911839 -1.892924  2.393848  0.792847 -2.864493 -2.956281  0.802042   \n",
+       "  49  0.802042 -1.194447  1.724925  0.314364 -2.495426 -4.605053 -1.482921   \n",
+       "  50 -1.482921  0.438803 -1.527381  0.961918 -1.229564 -3.058697 -1.061495   \n",
+       "  51 -1.061495  0.226547 -2.830723 -1.225512  3.221573  0.737460 -0.669184   \n",
+       "  52 -0.669184  2.709804 -2.043994 -0.304723  2.622729  4.016091 -0.222681   \n",
+       "  53 -0.222681  2.195913  0.220208 -0.426993 -0.248895  3.814734  0.588891   \n",
+       "  54  0.588891 -0.242546  1.269376 -0.375089 -2.893622  0.597495  0.474515   \n",
+       "  55  0.474515 -1.565277  2.951817  0.247749 -2.160946 -2.243680  1.201312   \n",
+       "  56  1.201312 -1.455102  1.067762 -0.795755 -0.870163 -4.033355  1.014242   \n",
+       "  57  1.014242 -1.399840  0.193147 -0.205155  1.751227 -2.344347  1.748328   \n",
+       "  58  1.748328 -0.173840 -1.568960  1.124883  3.462560 -0.171906  0.040639   \n",
+       "  59  0.040639  1.938967 -2.073092  3.275354  0.206372  1.622923 -0.209775   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2   1.239916  1.571174   -0.892004    0.546488   -0.829465  \n",
+       "  3  -0.346820 -0.336436   -0.240901    2.088110   -2.613916  \n",
+       "  4  -1.193287 -1.015828   -0.827546    1.160168   -0.820899  \n",
+       "  5  -2.663916 -1.909330   -1.195443   -1.518701   -0.631229  \n",
+       "  6  -2.066294  0.669652   -0.219736   -2.497438    0.168027  \n",
+       "  7  -1.466368  0.963040   -1.074059   -2.622271    0.779781  \n",
+       "  8  -0.960936  0.674871   -0.141407   -0.282669    2.380615  \n",
+       "  9   3.075384  1.253655   -0.466512    2.136354    0.211212  \n",
+       "  10  1.167654  0.050321    0.311804    3.736011   -0.091790  \n",
+       "  11 -0.463600 -0.840960    0.671118    0.671534   -0.408424  \n",
+       "  12 -1.464402 -0.735677    2.274224   -1.078687   -0.309293  \n",
+       "  13 -1.287899  0.806659    1.156641    0.562994   -0.296644  \n",
+       "  14 -0.409877  2.224765   -0.299318    0.219868    0.899372  \n",
+       "  15  1.421866  4.025960   -2.792018   -0.732217    1.561153  \n",
+       "  16  1.636128  1.803608   -0.859390   -2.010676    0.237291  \n",
+       "  17  0.240325 -3.182136   -1.349971   -0.550954   -1.020401  \n",
+       "  18  0.091958 -4.837395    0.696349    0.071376   -2.592055  \n",
+       "  19 -4.228778 -3.839992    0.794389    3.552787   -3.128705  \n",
+       "  20 -3.309383  0.377136    0.568852    2.067811   -0.822845  \n",
+       "  21 -1.370621  2.481398    0.832174   -0.955425    0.878134  \n",
+       "  22  1.609493  2.894463   -1.216669   -3.822762    2.399564  \n",
+       "  23  5.328339  0.725370   -1.144596   -3.554372    4.070938  \n",
+       "  24  2.940368 -3.206664   -0.869524   -0.269874    3.457920  \n",
+       "  25  0.546670 -4.066988    1.012696    0.457706   -1.197314  \n",
+       "  26 -1.021276 -1.654239    1.012306    1.464667   -3.658615  \n",
+       "  27 -1.147469  1.570268    1.677478    0.844537   -3.531715  \n",
+       "  28 -1.234892  2.892802   -1.082077   -0.701064    0.433363  \n",
+       "  29  1.049141  0.724023   -2.090009   -2.879625    3.948528  \n",
+       "  30  0.240629 -1.770090   -1.685802   -2.263010    5.968175  \n",
+       "  31  0.561385 -3.071928    0.168831   -0.677292    4.635834  \n",
+       "  32  0.877811 -1.164311    0.940499    0.753966   -0.818041  \n",
+       "  33 -0.110649  1.534619    1.341966    1.547380   -6.206645  \n",
+       "  34  1.551152  3.036576   -0.308112   -0.188393   -7.219594  \n",
+       "  35  2.183240  1.055115   -2.640709   -1.371694   -2.578747  \n",
+       "  36  0.424569 -2.824566   -3.342321   -0.621152    2.247463  \n",
+       "  37 -1.994758 -3.211256   -0.694773    0.583239    5.499868  \n",
+       "  38 -3.172545 -3.198703    0.773074    0.866656    3.379220  \n",
+       "  39 -2.276418  0.930634    3.158289   -0.490709   -0.109997  \n",
+       "  40 -0.164832  2.606760    4.002746   -1.153614   -4.733259  \n",
+       "  41  2.900892  2.022500    1.794425   -0.839694   -4.205335  \n",
+       "  42  2.492746 -0.815861   -0.955178    0.555967   -1.436538  \n",
+       "  43  0.332070 -2.498185   -2.955366    2.059587    3.498017  \n",
+       "  44  0.428482 -2.376467   -3.082320    3.229807    6.488336  \n",
+       "  45 -0.779333 -1.912477   -1.124814    1.366353    4.543602  \n",
+       "  46 -0.946542  1.106943    0.470886   -0.588900    0.175839  \n",
+       "  47 -1.892924  2.393848    0.792847   -2.864493   -2.956281  \n",
+       "  48 -1.194447  1.724925    0.314364   -2.495426   -4.605053  \n",
+       "  49  0.438803 -1.527381    0.961918   -1.229564   -3.058697  \n",
+       "  50  0.226547 -2.830723   -1.225512    3.221573    0.737460  \n",
+       "  51  2.709804 -2.043994   -0.304723    2.622729    4.016091  \n",
+       "  52  2.195913  0.220208   -0.426993   -0.248895    3.814734  \n",
+       "  53 -0.242546  1.269376   -0.375089   -2.893622    0.597495  \n",
+       "  54 -1.565277  2.951817    0.247749   -2.160946   -2.243680  \n",
+       "  55 -1.455102  1.067762   -0.795755   -0.870163   -4.033355  \n",
+       "  56 -1.399840  0.193147   -0.205155    1.751227   -2.344347  \n",
+       "  57 -0.173840 -1.568960    1.124883    3.462560   -0.171906  \n",
+       "  58  1.938967 -2.073092    3.275354    0.206372    1.622923  \n",
+       "  59  1.983916 -1.399654    2.702434   -3.618466    2.779231  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  0   1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  0.500000   \n",
+       "  1   0.500000  0.500000  0.500000  0.500000  0.500000  0.500000  1.500000   \n",
+       "  2   1.500000  1.500000  1.500000  1.500000  1.500000  1.500000  1.322669   \n",
+       "  3   1.322669 -1.073856 -0.360598 -0.639121  1.197858 -0.205817  2.510263   \n",
+       "  4   2.510263 -0.565204 -2.478859 -0.717986  0.647639 -2.091676  0.323034   \n",
+       "  5   0.323034  0.338847 -3.789155 -1.005255 -1.123641 -2.977187 -1.605918   \n",
+       "  6  -1.605918  1.230190 -0.554889 -1.775058 -1.446165 -0.944520 -1.420973   \n",
+       "  7  -1.420973  1.190286  1.460068 -1.468567 -0.256982 -1.247431 -1.012452   \n",
+       "  8  -1.012452  1.815916  2.449132 -0.009113  2.452757  0.591694  2.095039   \n",
+       "  9   2.095039  1.491358  0.043126  0.196783  2.758861  0.618226  2.623170   \n",
+       "  10  2.623170  1.632743 -0.294231  1.236214  0.322675  1.085057  2.078787   \n",
+       "  11  2.078787  0.968508 -0.846462 -2.320426 -1.535425  1.174601  0.034280   \n",
+       "  12  0.034280  1.158253  0.011142 -2.309954 -1.422649 -0.828008 -0.122131   \n",
+       "  13 -0.122131  0.077336 -0.862352 -2.630876 -1.418250 -1.994943  0.726749   \n",
+       "  14  0.726749 -1.478667  1.097544  0.825356 -0.064301 -3.362385  0.833736   \n",
+       "  15  0.833736 -0.433520  2.138389  4.291489  0.470519 -1.875515  0.813208   \n",
+       "  16  0.813208 -0.355047  1.344081  3.323074 -0.815626  0.564168  0.035998   \n",
+       "  17  0.035998  1.355150  0.840755 -0.076541  0.803810  2.524096 -1.828161   \n",
+       "  18 -1.828161  2.150303 -1.401906 -3.804238  0.934146  3.089948 -0.941750   \n",
+       "  19 -0.941750  0.918759 -3.379011 -4.054902 -0.980777  0.601736  0.106525   \n",
+       "  20  0.106525 -1.446499 -3.158946 -1.781609 -1.024188 -0.525708  1.298312   \n",
+       "  21  1.298312 -2.789575 -0.446798  2.820197 -0.907281 -2.005337 -0.179871   \n",
+       "  22 -0.179871 -0.459416  1.531272  3.783056 -0.044915 -0.995895 -1.700322   \n",
+       "  23 -1.700322 -0.195161  1.863918  0.882964  0.793622 -0.231587 -1.179222   \n",
+       "  24 -1.179222  1.446843  0.121950 -3.539409  0.634979  1.132661 -0.440035   \n",
+       "  25 -0.440035 -0.627308 -0.808423 -5.647924 -0.338748  2.448696 -0.265108   \n",
+       "  26 -0.265108 -2.724156 -0.453038 -4.913438 -1.548702  1.737043  1.519972   \n",
+       "  27  1.519972 -1.943032 -1.465711 -0.237609 -2.572542  1.009947 -0.238025   \n",
+       "  28 -0.238025 -0.211654  0.271651  5.405525 -1.495874 -0.747289  0.997322   \n",
+       "  29  0.997322  1.865793  1.164737  5.752823  0.849461 -2.222375  1.126955   \n",
+       "  30  1.126955  1.657125  0.054583  0.490554  1.676146 -2.869834  0.828750   \n",
+       "  31  0.828750 -1.744726 -0.366993 -2.882978  2.692979 -0.883644 -2.899828   \n",
+       "  32 -2.899828 -1.296072 -2.797796 -4.296804 -0.678162  0.311387 -2.727071   \n",
+       "  33 -2.727071 -1.652893  0.232557 -2.528537 -3.273847  1.271765 -1.171937   \n",
+       "  34 -1.171937 -0.727839 -0.068474  0.420098 -4.252787 -0.266374  0.467029   \n",
+       "  35  0.467029  0.427376  2.114212  3.524802 -1.199888  0.333229  0.451245   \n",
+       "  36  0.451245  0.366676  2.744155  3.405958  2.659586 -1.356285 -0.341985   \n",
+       "  37 -0.341985 -0.198995  1.856955  0.811830  4.309568 -1.166964  0.062717   \n",
+       "  38  0.062717  0.393540 -0.452677 -0.936002  3.467572 -0.314183  1.317140   \n",
+       "  39  1.317140 -0.627812 -1.987246 -1.216615 -1.092155  0.856996  0.378135   \n",
+       "  40  0.378135 -0.022925 -1.116950 -0.104648 -2.913378  1.448316 -1.560567   \n",
+       "  41 -1.560567  0.182331  0.838370 -0.185038 -3.675088  2.111512 -2.929228   \n",
+       "  42 -2.929228  1.793229  1.981621  0.004065 -2.128783  1.599536 -1.578514   \n",
+       "  43 -1.578514  0.940468  1.009385 -0.262679 -1.304996 -0.063792  0.684106   \n",
+       "  44  0.684106  0.758988  0.090768  0.538934  1.290003 -0.531291  2.030198   \n",
+       "  45  2.030198 -2.195700 -1.666064  0.095841  3.270584 -2.540783  0.513336   \n",
+       "  46  0.513336 -1.669783 -2.113832 -0.455991  4.100888 -2.335447  0.568999   \n",
+       "  47  0.568999  1.442164 -0.314349  0.197814  1.850889  0.725559  0.211756   \n",
+       "  48  0.211756  2.322177 -1.157165 -0.721328 -1.734549  1.223539 -0.230006   \n",
+       "  49 -0.230006  1.114213 -0.665391 -0.551266 -4.625515  1.876033 -0.100277   \n",
+       "  50 -0.100277 -0.656010 -0.319658 -0.906447 -2.413765  0.152761 -0.888056   \n",
+       "  51 -0.888056 -1.112970  1.226341  0.998480  1.031764  0.751723 -0.712557   \n",
+       "  52 -0.712557 -2.261739  3.186915  2.594016  4.748402 -0.452217  0.186130   \n",
+       "  53  0.186130 -1.687970  3.340955  3.187527  3.521991 -2.294189 -1.494039   \n",
+       "  54 -1.494039 -1.194116  0.024968  3.169680  3.749017 -3.304637 -1.279332   \n",
+       "  55 -1.279332  0.790812 -2.911261 -0.793772 -1.377800 -0.954743  0.113382   \n",
+       "  56  0.113382  1.620593 -6.010261 -1.130635 -3.036922 -0.270530  2.990234   \n",
+       "  57  2.990234  0.090309 -1.647299 -1.092450 -2.251337  0.715011  2.838134   \n",
+       "  58  2.838134 -0.972754  3.614769 -1.833016 -0.130595  0.894186  0.998217   \n",
+       "  59  0.998217 -2.355062  5.281619 -0.016088 -0.195771 -0.644363 -2.165656   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  0   0.500000  0.500000    0.500000    0.500000    0.500000  \n",
+       "  1   1.500000  1.500000    1.500000    1.500000    1.500000  \n",
+       "  2  -1.073856 -0.360598   -0.639121    1.197858   -0.205817  \n",
+       "  3  -0.565204 -2.478859   -0.717986    0.647639   -2.091676  \n",
+       "  4   0.338847 -3.789155   -1.005255   -1.123641   -2.977187  \n",
+       "  5   1.230190 -0.554889   -1.775058   -1.446165   -0.944520  \n",
+       "  6   1.190286  1.460068   -1.468567   -0.256982   -1.247431  \n",
+       "  7   1.815916  2.449132   -0.009113    2.452757    0.591694  \n",
+       "  8   1.491358  0.043126    0.196783    2.758861    0.618226  \n",
+       "  9   1.632743 -0.294231    1.236214    0.322675    1.085057  \n",
+       "  10  0.968508 -0.846462   -2.320426   -1.535425    1.174601  \n",
+       "  11  1.158253  0.011142   -2.309954   -1.422649   -0.828008  \n",
+       "  12  0.077336 -0.862352   -2.630876   -1.418250   -1.994943  \n",
+       "  13 -1.478667  1.097544    0.825356   -0.064301   -3.362385  \n",
+       "  14 -0.433520  2.138389    4.291489    0.470519   -1.875515  \n",
+       "  15 -0.355047  1.344081    3.323074   -0.815626    0.564168  \n",
+       "  16  1.355150  0.840755   -0.076541    0.803810    2.524096  \n",
+       "  17  2.150303 -1.401906   -3.804238    0.934146    3.089948  \n",
+       "  18  0.918759 -3.379011   -4.054902   -0.980777    0.601736  \n",
+       "  19 -1.446499 -3.158946   -1.781609   -1.024188   -0.525708  \n",
+       "  20 -2.789575 -0.446798    2.820197   -0.907281   -2.005337  \n",
+       "  21 -0.459416  1.531272    3.783056   -0.044915   -0.995895  \n",
+       "  22 -0.195161  1.863918    0.882964    0.793622   -0.231587  \n",
+       "  23  1.446843  0.121950   -3.539409    0.634979    1.132661  \n",
+       "  24 -0.627308 -0.808423   -5.647924   -0.338748    2.448696  \n",
+       "  25 -2.724156 -0.453038   -4.913438   -1.548702    1.737043  \n",
+       "  26 -1.943032 -1.465711   -0.237609   -2.572542    1.009947  \n",
+       "  27 -0.211654  0.271651    5.405525   -1.495874   -0.747289  \n",
+       "  28  1.865793  1.164737    5.752823    0.849461   -2.222375  \n",
+       "  29  1.657125  0.054583    0.490554    1.676146   -2.869834  \n",
+       "  30 -1.744726 -0.366993   -2.882978    2.692979   -0.883644  \n",
+       "  31 -1.296072 -2.797796   -4.296804   -0.678162    0.311387  \n",
+       "  32 -1.652893  0.232557   -2.528537   -3.273847    1.271765  \n",
+       "  33 -0.727839 -0.068474    0.420098   -4.252787   -0.266374  \n",
+       "  34  0.427376  2.114212    3.524802   -1.199888    0.333229  \n",
+       "  35  0.366676  2.744155    3.405958    2.659586   -1.356285  \n",
+       "  36 -0.198995  1.856955    0.811830    4.309568   -1.166964  \n",
+       "  37  0.393540 -0.452677   -0.936002    3.467572   -0.314183  \n",
+       "  38 -0.627812 -1.987246   -1.216615   -1.092155    0.856996  \n",
+       "  39 -0.022925 -1.116950   -0.104648   -2.913378    1.448316  \n",
+       "  40  0.182331  0.838370   -0.185038   -3.675088    2.111512  \n",
+       "  41  1.793229  1.981621    0.004065   -2.128783    1.599536  \n",
+       "  42  0.940468  1.009385   -0.262679   -1.304996   -0.063792  \n",
+       "  43  0.758988  0.090768    0.538934    1.290003   -0.531291  \n",
+       "  44 -2.195700 -1.666064    0.095841    3.270584   -2.540783  \n",
+       "  45 -1.669783 -2.113832   -0.455991    4.100888   -2.335447  \n",
+       "  46  1.442164 -0.314349    0.197814    1.850889    0.725559  \n",
+       "  47  2.322177 -1.157165   -0.721328   -1.734549    1.223539  \n",
+       "  48  1.114213 -0.665391   -0.551266   -4.625515    1.876033  \n",
+       "  49 -0.656010 -0.319658   -0.906447   -2.413765    0.152761  \n",
+       "  50 -1.112970  1.226341    0.998480    1.031764    0.751723  \n",
+       "  51 -2.261739  3.186915    2.594016    4.748402   -0.452217  \n",
+       "  52 -1.687970  3.340955    3.187527    3.521991   -2.294189  \n",
+       "  53 -1.194116  0.024968    3.169680    3.749017   -3.304637  \n",
+       "  54  0.790812 -2.911261   -0.793772   -1.377800   -0.954743  \n",
+       "  55  1.620593 -6.010261   -1.130635   -3.036922   -0.270530  \n",
+       "  56  0.090309 -1.647299   -1.092450   -2.251337    0.715011  \n",
+       "  57 -0.972754  3.614769   -1.833016   -0.130595    0.894186  \n",
+       "  58 -2.355062  5.281619   -0.016088   -0.195771   -0.644363  \n",
+       "  59 -1.012311  4.460661    0.512352    0.084778   -2.726044  ],\n",
+       " [    position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.276321  1.175908 -0.046573 -0.701116 -2.762168 -0.184531  0.229981   \n",
+       "  61  0.229981  2.912632 -2.056867  1.960296 -1.995118  3.331075  0.480058   \n",
+       "  62  0.480058  1.975850 -0.115905  2.246031  1.978832  3.041328 -0.433619   \n",
+       "  63 -0.433619  0.775029 -0.144141  1.192732  3.063638  1.277464  0.584008   \n",
+       "  64  0.584008 -1.984043  1.416942 -1.459473  3.004140 -0.788803 -0.391652   \n",
+       "  65 -0.391652 -1.476831  1.128444 -0.384518  1.196304 -1.449656 -0.707547   \n",
+       "  66 -0.707547 -0.836991  1.139407  0.589694 -0.713512 -1.637819 -0.841956   \n",
+       "  67 -0.841956  1.448158  0.854983  1.380548 -2.889077 -0.982843 -1.042850   \n",
+       "  68 -1.042850  2.804673 -1.398676  0.832539 -3.532846  0.877447  1.405279   \n",
+       "  69  1.405279  0.643454 -2.150745  1.547339 -1.588754  1.223204  1.919757   \n",
+       "  70  1.919757 -0.243278 -1.550826 -1.195242  1.326635  2.487983  0.330992   \n",
+       "  71  0.330992 -2.869274  0.876031  0.146910  1.991782  2.060763 -1.552618   \n",
+       "  72 -1.552618 -0.923266  1.976451 -0.156453  2.220137  0.512256 -0.792384   \n",
+       "  73 -0.792384 -0.627573 -0.624488 -0.246063  1.330245 -0.185149 -0.637666   \n",
+       "  74 -0.637666  0.784245 -2.352963 -1.872971 -1.298334 -0.275924 -0.081866   \n",
+       "  75 -0.081866  0.098037 -1.426145 -0.882271 -0.097513 -1.299011 -0.213911   \n",
+       "  76 -0.213911 -0.127642  1.494361  1.197127 -0.460895 -0.484491  0.478412   \n",
+       "  77  0.478412  1.234350  3.185637  0.881037  1.306265 -0.483908  1.106064   \n",
+       "  78  1.106064  0.889429  2.295463  1.583239 -0.148019 -0.199952  0.577496   \n",
+       "  79  0.577496  0.625240  1.782571  0.073935 -0.253748  0.164830  0.698031   \n",
+       "  80  0.698031  0.171395  0.320584 -0.269983 -0.696875 -0.208571  0.560380   \n",
+       "  81  0.560380 -0.135518 -0.314842 -1.429950 -1.775536 -0.112018 -0.823916   \n",
+       "  82 -0.823916 -1.038572 -1.168207  0.030445 -1.317336 -0.517681 -1.217763   \n",
+       "  83 -1.217763 -0.659569  2.271856 -0.869669  0.453073 -0.156963 -0.707226   \n",
+       "  84 -0.707226  0.039605  3.113719 -0.441320  2.770108  0.127964 -0.222394   \n",
+       "  85 -0.222394  2.793012  3.418856 -0.609548  3.244101 -0.517071  0.928520   \n",
+       "  86  0.928520  0.995549 -0.136191  1.887204  1.213577 -1.109178 -0.110281   \n",
+       "  87 -0.110281 -0.174229 -3.029662  3.277809  0.883814 -2.846425 -1.611923   \n",
+       "  88 -1.611923 -0.446286 -4.461082  1.781383 -0.575246 -1.734604 -1.009215   \n",
+       "  89 -1.009215 -2.660918 -0.704742 -0.561204 -0.357839  1.723583  1.416700   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  2.912632 -2.056867    1.960296   -1.995118    3.331075  \n",
+       "  61  1.975850 -0.115905    2.246031    1.978832    3.041328  \n",
+       "  62  0.775029 -0.144141    1.192732    3.063638    1.277464  \n",
+       "  63 -1.984043  1.416942   -1.459473    3.004140   -0.788803  \n",
+       "  64 -1.476831  1.128444   -0.384518    1.196304   -1.449656  \n",
+       "  65 -0.836991  1.139407    0.589694   -0.713512   -1.637819  \n",
+       "  66  1.448158  0.854983    1.380548   -2.889077   -0.982843  \n",
+       "  67  2.804673 -1.398676    0.832539   -3.532846    0.877447  \n",
+       "  68  0.643454 -2.150745    1.547339   -1.588754    1.223204  \n",
+       "  69 -0.243278 -1.550826   -1.195242    1.326635    2.487983  \n",
+       "  70 -2.869274  0.876031    0.146910    1.991782    2.060763  \n",
+       "  71 -0.923266  1.976451   -0.156453    2.220137    0.512256  \n",
+       "  72 -0.627573 -0.624488   -0.246063    1.330245   -0.185149  \n",
+       "  73  0.784245 -2.352963   -1.872971   -1.298334   -0.275924  \n",
+       "  74  0.098037 -1.426145   -0.882271   -0.097513   -1.299011  \n",
+       "  75 -0.127642  1.494361    1.197127   -0.460895   -0.484491  \n",
+       "  76  1.234350  3.185637    0.881037    1.306265   -0.483908  \n",
+       "  77  0.889429  2.295463    1.583239   -0.148019   -0.199952  \n",
+       "  78  0.625240  1.782571    0.073935   -0.253748    0.164830  \n",
+       "  79  0.171395  0.320584   -0.269983   -0.696875   -0.208571  \n",
+       "  80 -0.135518 -0.314842   -1.429950   -1.775536   -0.112018  \n",
+       "  81 -1.038572 -1.168207    0.030445   -1.317336   -0.517681  \n",
+       "  82 -0.659569  2.271856   -0.869669    0.453073   -0.156963  \n",
+       "  83  0.039605  3.113719   -0.441320    2.770108    0.127964  \n",
+       "  84  2.793012  3.418856   -0.609548    3.244101   -0.517071  \n",
+       "  85  0.995549 -0.136191    1.887204    1.213577   -1.109178  \n",
+       "  86 -0.174229 -3.029662    3.277809    0.883814   -2.846425  \n",
+       "  87 -0.446286 -4.461082    1.781383   -0.575246   -1.734604  \n",
+       "  88 -2.660918 -0.704742   -0.561204   -0.357839    1.723583  \n",
+       "  89 -3.624810  3.284369   -4.247110   -0.258408    2.567445  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.469514  0.103457 -0.802459 -2.725664 -1.994039  0.407783 -2.256171   \n",
+       "  61 -2.256171  0.880938 -2.624300 -4.545854 -3.483966 -0.544306 -2.388437   \n",
+       "  62 -2.388437 -1.231535 -2.836981 -2.463529 -1.704870  1.483900 -0.516786   \n",
+       "  63 -0.516786 -2.560109 -1.427392  0.010935  2.772029  1.386838  0.023360   \n",
+       "  64  0.023360 -0.694294 -0.378691  3.350143  1.951600  0.306524  0.572220   \n",
+       "  65  0.572220  0.829257  0.309406  3.067670  2.703840 -1.737762 -0.860067   \n",
+       "  66 -0.860067  3.812554  0.568659 -0.188545  0.040733 -1.688782 -0.335730   \n",
+       "  67 -0.335730  2.610420 -0.763881 -2.012488 -1.009280 -0.508252 -1.907241   \n",
+       "  68 -1.907241  0.155504 -1.621027 -3.176074 -1.959239  1.144293 -0.651316   \n",
+       "  69 -0.651316 -1.630768 -1.793754 -1.774773 -2.260725  1.545429 -0.480714   \n",
+       "  70 -0.480714 -2.315909 -0.047617  1.369779 -1.584368  2.956849  0.097207   \n",
+       "  71  0.097207 -2.321884  1.310265  3.688323  1.563985 -0.352294  0.037829   \n",
+       "  72  0.037829  0.486936  1.017956  1.823392  3.327315 -2.395582  0.439039   \n",
+       "  73  0.439039  1.163212  0.237456 -0.017896  3.778363 -1.305033  0.250165   \n",
+       "  74  0.250165  2.169630 -0.345965 -1.342560 -0.248445 -0.503040 -1.061608   \n",
+       "  75 -1.061608  2.213478 -1.854024 -1.563028 -3.849806  0.947720  0.121998   \n",
+       "  76  0.121998  0.250484 -1.589768 -0.414737 -4.686626  2.684668  0.982136   \n",
+       "  77  0.982136 -1.105513  1.884374  0.670541 -1.279674  1.326287  0.727317   \n",
+       "  78  0.727317 -1.132330  3.483393  1.907769  1.314452  0.321852 -1.061512   \n",
+       "  79 -1.061512 -0.634647  2.784628 -1.317431  2.163222 -1.953135 -2.861755   \n",
+       "  80 -2.861755 -0.455104  0.022665 -0.892410  0.783500 -2.679596 -2.275027   \n",
+       "  81 -2.275027  1.236303 -2.026244 -0.337999 -1.834884 -2.029932 -1.804792   \n",
+       "  82 -1.804792  0.523059 -1.193114 -0.967617 -3.698754  1.025246 -0.619368   \n",
+       "  83 -0.619368  0.889813 -1.353900 -0.988101 -1.112809  3.878795  0.535418   \n",
+       "  84  0.535418  0.591931  1.042365 -1.013526  1.033272  3.069998 -0.037580   \n",
+       "  85 -0.037580  0.485839  3.442096 -0.155054  4.191992  1.942901 -0.118691   \n",
+       "  86 -0.118691  1.490582  2.545007  0.545318  3.348967  0.280317  0.443738   \n",
+       "  87  0.443738  2.173728  1.756465  1.626241 -0.545568 -2.307091  0.281587   \n",
+       "  88  0.281587  1.171451 -1.599966  0.069828 -3.360435 -2.778937  0.390411   \n",
+       "  89  0.390411 -0.580119 -1.485209 -0.209339 -4.334685 -1.104659 -0.844775   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.880938 -2.624300   -4.545854   -3.483966   -0.544306  \n",
+       "  61 -1.231535 -2.836981   -2.463529   -1.704870    1.483900  \n",
+       "  62 -2.560109 -1.427392    0.010935    2.772029    1.386838  \n",
+       "  63 -0.694294 -0.378691    3.350143    1.951600    0.306524  \n",
+       "  64  0.829257  0.309406    3.067670    2.703840   -1.737762  \n",
+       "  65  3.812554  0.568659   -0.188545    0.040733   -1.688782  \n",
+       "  66  2.610420 -0.763881   -2.012488   -1.009280   -0.508252  \n",
+       "  67  0.155504 -1.621027   -3.176074   -1.959239    1.144293  \n",
+       "  68 -1.630768 -1.793754   -1.774773   -2.260725    1.545429  \n",
+       "  69 -2.315909 -0.047617    1.369779   -1.584368    2.956849  \n",
+       "  70 -2.321884  1.310265    3.688323    1.563985   -0.352294  \n",
+       "  71  0.486936  1.017956    1.823392    3.327315   -2.395582  \n",
+       "  72  1.163212  0.237456   -0.017896    3.778363   -1.305033  \n",
+       "  73  2.169630 -0.345965   -1.342560   -0.248445   -0.503040  \n",
+       "  74  2.213478 -1.854024   -1.563028   -3.849806    0.947720  \n",
+       "  75  0.250484 -1.589768   -0.414737   -4.686626    2.684668  \n",
+       "  76 -1.105513  1.884374    0.670541   -1.279674    1.326287  \n",
+       "  77 -1.132330  3.483393    1.907769    1.314452    0.321852  \n",
+       "  78 -0.634647  2.784628   -1.317431    2.163222   -1.953135  \n",
+       "  79 -0.455104  0.022665   -0.892410    0.783500   -2.679596  \n",
+       "  80  1.236303 -2.026244   -0.337999   -1.834884   -2.029932  \n",
+       "  81  0.523059 -1.193114   -0.967617   -3.698754    1.025246  \n",
+       "  82  0.889813 -1.353900   -0.988101   -1.112809    3.878795  \n",
+       "  83  0.591931  1.042365   -1.013526    1.033272    3.069998  \n",
+       "  84  0.485839  3.442096   -0.155054    4.191992    1.942901  \n",
+       "  85  1.490582  2.545007    0.545318    3.348967    0.280317  \n",
+       "  86  2.173728  1.756465    1.626241   -0.545568   -2.307091  \n",
+       "  87  1.171451 -1.599966    0.069828   -3.360435   -2.778937  \n",
+       "  88 -0.580119 -1.485209   -0.209339   -4.334685   -1.104659  \n",
+       "  89 -0.683084 -2.389418   -2.194385   -2.167888    0.776664  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  1.917445  0.424083  1.814160 -2.762027 -0.682391  0.843818  1.869385   \n",
+       "  61  1.869385 -1.755448  2.664031  1.133596  0.241122  0.310329 -0.686127   \n",
+       "  62 -0.686127 -2.694686  1.792288  0.912631  1.270610  0.488950 -0.283638   \n",
+       "  63 -0.283638 -1.862041 -0.633342  1.049329  1.635332  0.632759  0.276158   \n",
+       "  64  0.276158  0.645076 -0.998123 -1.643615  0.573137 -0.767240 -1.240333   \n",
+       "  65 -1.240333  0.764994 -2.247086 -0.430288 -2.237500 -1.028582 -0.902524   \n",
+       "  66 -0.902524 -1.107498 -1.648195  0.256712 -3.618189  0.683230 -1.021247   \n",
+       "  67 -1.021247 -1.084977 -0.594077  0.855786 -2.024912  0.685636  0.257097   \n",
+       "  68  0.257097 -0.447848  0.972901  0.357159 -0.189848 -0.487249  0.188777   \n",
+       "  69  0.188777  1.464411  1.764915 -0.566384  0.801793 -2.149286 -0.145540   \n",
+       "  70 -0.145540  0.475805 -0.245339 -1.439117  2.931704 -2.304466  1.057804   \n",
+       "  71  1.057804 -0.937455 -0.571110  0.072073  1.129652 -0.852281  0.538032   \n",
+       "  72  0.538032 -0.446670 -1.977667  1.578310 -1.754780  2.114868 -0.757036   \n",
+       "  73 -0.757036  2.334789 -0.847188  2.404196 -3.166514  2.692548 -2.219570   \n",
+       "  74 -2.219570  2.566968 -0.429742  0.743144 -1.989451  3.258139 -1.989348   \n",
+       "  75 -1.989348  0.382244  0.145981 -2.909963 -1.190354 -1.076767  0.148989   \n",
+       "  76  0.148989 -1.148737 -1.036127 -2.274326 -0.775251 -2.754596  0.308413   \n",
+       "  77  0.308413 -1.239253  1.607746 -1.924590  1.446499 -2.778188  0.096484   \n",
+       "  78  0.096484 -0.793640 -0.914520  0.686321  1.216066 -0.138531 -0.772739   \n",
+       "  79 -0.772739  0.484218 -1.405677  2.310222  0.713558  2.250154  0.047967   \n",
+       "  80  0.047967  0.937725 -0.846066  2.846707  1.488698  3.024919 -0.002955   \n",
+       "  81 -0.002955 -0.706795  0.150337  1.395966  2.504515  0.134513  1.580253   \n",
+       "  82  1.580253 -1.853587  1.421121  1.017553  1.222741 -2.804850  1.938247   \n",
+       "  83  1.938247 -0.917574  1.733568 -1.010442 -0.158253 -3.228200  0.241149   \n",
+       "  84  0.241149 -0.113724 -1.113042 -0.635299 -1.208446 -1.328762 -1.924521   \n",
+       "  85 -1.924521  2.740505 -1.677377  0.595868 -0.655033  1.084313 -4.191472   \n",
+       "  86 -4.191472  2.724548 -3.101098  1.928213 -0.691312  2.829752 -3.333084   \n",
+       "  87 -3.333084  0.552443 -1.390827  2.238340 -0.798946  2.342494 -0.637297   \n",
+       "  88 -0.637297 -1.959596 -0.402732  1.898234 -0.365378  0.827025  1.195065   \n",
+       "  89  1.195065 -2.386260 -0.459044 -0.069700  1.767076 -0.323808  1.788060   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.755448  2.664031    1.133596    0.241122    0.310329  \n",
+       "  61 -2.694686  1.792288    0.912631    1.270610    0.488950  \n",
+       "  62 -1.862041 -0.633342    1.049329    1.635332    0.632759  \n",
+       "  63  0.645076 -0.998123   -1.643615    0.573137   -0.767240  \n",
+       "  64  0.764994 -2.247086   -0.430288   -2.237500   -1.028582  \n",
+       "  65 -1.107498 -1.648195    0.256712   -3.618189    0.683230  \n",
+       "  66 -1.084977 -0.594077    0.855786   -2.024912    0.685636  \n",
+       "  67 -0.447848  0.972901    0.357159   -0.189848   -0.487249  \n",
+       "  68  1.464411  1.764915   -0.566384    0.801793   -2.149286  \n",
+       "  69  0.475805 -0.245339   -1.439117    2.931704   -2.304466  \n",
+       "  70 -0.937455 -0.571110    0.072073    1.129652   -0.852281  \n",
+       "  71 -0.446670 -1.977667    1.578310   -1.754780    2.114868  \n",
+       "  72  2.334789 -0.847188    2.404196   -3.166514    2.692548  \n",
+       "  73  2.566968 -0.429742    0.743144   -1.989451    3.258139  \n",
+       "  74  0.382244  0.145981   -2.909963   -1.190354   -1.076767  \n",
+       "  75 -1.148737 -1.036127   -2.274326   -0.775251   -2.754596  \n",
+       "  76 -1.239253  1.607746   -1.924590    1.446499   -2.778188  \n",
+       "  77 -0.793640 -0.914520    0.686321    1.216066   -0.138531  \n",
+       "  78  0.484218 -1.405677    2.310222    0.713558    2.250154  \n",
+       "  79  0.937725 -0.846066    2.846707    1.488698    3.024919  \n",
+       "  80 -0.706795  0.150337    1.395966    2.504515    0.134513  \n",
+       "  81 -1.853587  1.421121    1.017553    1.222741   -2.804850  \n",
+       "  82 -0.917574  1.733568   -1.010442   -0.158253   -3.228200  \n",
+       "  83 -0.113724 -1.113042   -0.635299   -1.208446   -1.328762  \n",
+       "  84  2.740505 -1.677377    0.595868   -0.655033    1.084313  \n",
+       "  85  2.724548 -3.101098    1.928213   -0.691312    2.829752  \n",
+       "  86  0.552443 -1.390827    2.238340   -0.798946    2.342494  \n",
+       "  87 -1.959596 -0.402732    1.898234   -0.365378    0.827025  \n",
+       "  88 -2.386260 -0.459044   -0.069700    1.767076   -0.323808  \n",
+       "  89 -1.480080 -0.636910   -1.396105   -0.471885   -1.756906  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.713908  0.320904 -0.782775 -0.722663  0.071847  1.164273  1.682919   \n",
+       "  61  1.682919 -2.388572 -1.300749 -0.141636  1.930598  0.751260  1.681935   \n",
+       "  62  1.681935 -2.657078 -2.196242  0.785881  2.080726  0.561226  1.576851   \n",
+       "  63  1.576851 -0.351374  0.118508 -1.014508  2.146039 -0.376912  0.085250   \n",
+       "  64  0.085250  1.281852  2.867076  0.150232 -1.340815  0.791626 -0.953586   \n",
+       "  65 -0.953586  1.815711  2.989039 -1.266645 -4.015517 -0.756670 -0.923559   \n",
+       "  66 -0.923559  2.474341  2.672111 -1.906676 -2.769358 -0.235033 -0.292216   \n",
+       "  67 -0.292216  1.864875 -0.131480 -1.747659 -1.328787  1.461536  0.924116   \n",
+       "  68  0.924116  0.942738 -3.643499 -0.157823  3.000651  0.974917  1.230502   \n",
+       "  69  1.230502  0.383336 -2.019988  0.148953  4.699028 -0.321534  2.768788   \n",
+       "  70  2.768788 -1.599424 -0.881621  0.380715  1.175693 -1.226649  0.450128   \n",
+       "  71  0.450128 -0.099952  2.078545 -0.827020 -1.932328 -0.597282 -2.772836   \n",
+       "  72 -2.772836  1.544877  2.278044  0.034980 -4.652404  0.668702 -3.456068   \n",
+       "  73 -3.456068  1.516595  2.541595 -2.063500 -3.681807  0.658552 -2.029494   \n",
+       "  74 -2.029494 -0.128450  0.669977 -2.342384 -0.482825  1.025233 -0.653047   \n",
+       "  75 -0.653047 -0.167821  0.379226  0.296982  4.572365 -0.091393  2.040508   \n",
+       "  76  2.040508 -0.368822 -0.872117  2.697534  5.208068 -0.266616  2.631915   \n",
+       "  77  2.631915 -0.446267 -0.181989 -0.153423  3.547596  1.250459  1.603041   \n",
+       "  78  1.603041 -1.845806 -0.166413 -0.192891 -0.293278  2.662481 -0.865082   \n",
+       "  79 -0.865082 -1.458011 -1.234499 -1.067211 -4.464443  0.435587 -2.205227   \n",
+       "  80 -2.205227 -0.176463  0.878637 -0.048069 -4.893215 -0.123116 -2.042816   \n",
+       "  81 -2.042816  1.434881  2.314891  0.957918 -0.909170  0.027510  0.443151   \n",
+       "  82  0.443151  2.041466  0.721612  0.235677  3.670453  0.616757  0.547022   \n",
+       "  83  0.547022  1.244023 -1.378619  0.049037  4.998566  0.118599  0.155189   \n",
+       "  84  0.155189 -0.778814 -2.643225  0.158892  3.916415  0.208525 -0.817764   \n",
+       "  85 -0.817764 -3.060236 -1.900758  2.556272 -0.306462 -0.447871  0.431376   \n",
+       "  86  0.431376 -1.440388 -1.776193  1.435471 -2.885586  1.543672  2.773271   \n",
+       "  87  2.773271  0.694225  1.270376  1.563404 -3.793343  0.472818  0.875524   \n",
+       "  88  0.875524  0.658465  1.937401 -1.070127 -0.724260 -0.918481 -0.399359   \n",
+       "  89 -0.399359  2.298706  3.582988 -1.733143  2.067901 -2.857918  0.301190   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -2.388572 -1.300749   -0.141636    1.930598    0.751260  \n",
+       "  61 -2.657078 -2.196242    0.785881    2.080726    0.561226  \n",
+       "  62 -0.351374  0.118508   -1.014508    2.146039   -0.376912  \n",
+       "  63  1.281852  2.867076    0.150232   -1.340815    0.791626  \n",
+       "  64  1.815711  2.989039   -1.266645   -4.015517   -0.756670  \n",
+       "  65  2.474341  2.672111   -1.906676   -2.769358   -0.235033  \n",
+       "  66  1.864875 -0.131480   -1.747659   -1.328787    1.461536  \n",
+       "  67  0.942738 -3.643499   -0.157823    3.000651    0.974917  \n",
+       "  68  0.383336 -2.019988    0.148953    4.699028   -0.321534  \n",
+       "  69 -1.599424 -0.881621    0.380715    1.175693   -1.226649  \n",
+       "  70 -0.099952  2.078545   -0.827020   -1.932328   -0.597282  \n",
+       "  71  1.544877  2.278044    0.034980   -4.652404    0.668702  \n",
+       "  72  1.516595  2.541595   -2.063500   -3.681807    0.658552  \n",
+       "  73 -0.128450  0.669977   -2.342384   -0.482825    1.025233  \n",
+       "  74 -0.167821  0.379226    0.296982    4.572365   -0.091393  \n",
+       "  75 -0.368822 -0.872117    2.697534    5.208068   -0.266616  \n",
+       "  76 -0.446267 -0.181989   -0.153423    3.547596    1.250459  \n",
+       "  77 -1.845806 -0.166413   -0.192891   -0.293278    2.662481  \n",
+       "  78 -1.458011 -1.234499   -1.067211   -4.464443    0.435587  \n",
+       "  79 -0.176463  0.878637   -0.048069   -4.893215   -0.123116  \n",
+       "  80  1.434881  2.314891    0.957918   -0.909170    0.027510  \n",
+       "  81  2.041466  0.721612    0.235677    3.670453    0.616757  \n",
+       "  82  1.244023 -1.378619    0.049037    4.998566    0.118599  \n",
+       "  83 -0.778814 -2.643225    0.158892    3.916415    0.208525  \n",
+       "  84 -3.060236 -1.900758    2.556272   -0.306462   -0.447871  \n",
+       "  85 -1.440388 -1.776193    1.435471   -2.885586    1.543672  \n",
+       "  86  0.694225  1.270376    1.563404   -3.793343    0.472818  \n",
+       "  87  0.658465  1.937401   -1.070127   -0.724260   -0.918481  \n",
+       "  88  2.298706  3.582988   -1.733143    2.067901   -2.857918  \n",
+       "  89  0.380842  1.606308   -1.286544    2.109026   -3.293401  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.243095  1.506121  1.096045 -0.004722  0.324182  0.155714 -1.580972   \n",
+       "  61 -1.580972  3.371454  1.971686 -2.747544 -0.879979  1.183650 -1.474558   \n",
+       "  62 -1.474558  2.530278  0.095790 -0.471255 -1.366920  2.401096  1.788893   \n",
+       "  63  1.788893  0.693493 -2.254300 -0.317789 -2.077374  0.412545  2.737864   \n",
+       "  64  2.737864 -1.886433 -2.507595  1.821527 -0.838620 -0.939984  2.073186   \n",
+       "  65  2.073186 -1.759916 -1.178534  2.103039  0.571481 -3.408172 -0.945736   \n",
+       "  66 -0.945736 -1.271095  1.229019  1.564490  0.103958 -4.528126 -1.756272   \n",
+       "  67 -1.756272  0.236963  2.252189 -2.237433  0.262045 -4.643308 -1.999418   \n",
+       "  68 -1.999418  0.481479  1.225703 -2.338164 -0.777021  1.030072 -1.725606   \n",
+       "  69 -1.725606  2.219166 -1.170252 -0.744256 -0.065610  3.484983  1.224078   \n",
+       "  70  1.224078  2.066992 -2.544909  1.115314  0.219856  5.308886  0.082589   \n",
+       "  71  0.082589  1.524231  0.291775  2.084647  2.637385  1.659821 -1.128185   \n",
+       "  72 -1.128185 -1.926884  1.263244  1.149052  1.353942 -0.776538 -2.381389   \n",
+       "  73 -2.381389 -2.859932  1.411599 -0.540712  1.137165 -2.514076 -1.854532   \n",
+       "  74 -1.854532 -1.033483  0.012817 -0.001867 -3.698228 -2.515087 -0.930382   \n",
+       "  75 -0.930382  1.327529 -0.650056  0.148061 -2.391957  0.530017  0.655270   \n",
+       "  76  0.655270  2.383808  0.367766 -0.698972  1.127949  3.831907  2.336527   \n",
+       "  77  2.336527  1.772249  1.323985 -1.627222  0.963098  3.223289  0.297191   \n",
+       "  78  0.297191  0.915412  1.726209 -0.936250  1.204873  1.601381 -1.653547   \n",
+       "  79 -1.653547 -0.993067  1.567010 -1.658474  0.674699 -1.093461 -2.707865   \n",
+       "  80 -2.707865 -2.540437  1.834388 -0.489827  0.050653 -3.627862 -0.677792   \n",
+       "  81 -0.677792 -1.850082  0.379170  1.420762 -0.512126 -4.632063  0.975186   \n",
+       "  82  0.975186 -0.013807 -0.307042  2.555231 -0.810940 -0.797186  1.914860   \n",
+       "  83  1.914860  2.976574 -1.347095 -1.531805 -0.084930  1.867111  0.734887   \n",
+       "  84  0.734887  3.116367 -1.401106 -1.792021  0.540145  3.214132 -1.565813   \n",
+       "  85 -1.565813  0.226883 -2.479774 -3.671394  1.702125  1.948937 -2.287481   \n",
+       "  86 -2.287481 -1.783491  0.280745  0.187260  2.298550 -1.406441 -2.138083   \n",
+       "  87 -2.138083  0.225059  1.130979  1.691229  2.487135 -4.248973 -0.696683   \n",
+       "  88 -0.696683  0.540923 -0.424952  1.635476  2.895723 -2.772123  0.943704   \n",
+       "  89  0.943704  3.518086  1.949599  0.937306 -2.032653 -1.953112  1.980842   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  3.371454  1.971686   -2.747544   -0.879979    1.183650  \n",
+       "  61  2.530278  0.095790   -0.471255   -1.366920    2.401096  \n",
+       "  62  0.693493 -2.254300   -0.317789   -2.077374    0.412545  \n",
+       "  63 -1.886433 -2.507595    1.821527   -0.838620   -0.939984  \n",
+       "  64 -1.759916 -1.178534    2.103039    0.571481   -3.408172  \n",
+       "  65 -1.271095  1.229019    1.564490    0.103958   -4.528126  \n",
+       "  66  0.236963  2.252189   -2.237433    0.262045   -4.643308  \n",
+       "  67  0.481479  1.225703   -2.338164   -0.777021    1.030072  \n",
+       "  68  2.219166 -1.170252   -0.744256   -0.065610    3.484983  \n",
+       "  69  2.066992 -2.544909    1.115314    0.219856    5.308886  \n",
+       "  70  1.524231  0.291775    2.084647    2.637385    1.659821  \n",
+       "  71 -1.926884  1.263244    1.149052    1.353942   -0.776538  \n",
+       "  72 -2.859932  1.411599   -0.540712    1.137165   -2.514076  \n",
+       "  73 -1.033483  0.012817   -0.001867   -3.698228   -2.515087  \n",
+       "  74  1.327529 -0.650056    0.148061   -2.391957    0.530017  \n",
+       "  75  2.383808  0.367766   -0.698972    1.127949    3.831907  \n",
+       "  76  1.772249  1.323985   -1.627222    0.963098    3.223289  \n",
+       "  77  0.915412  1.726209   -0.936250    1.204873    1.601381  \n",
+       "  78 -0.993067  1.567010   -1.658474    0.674699   -1.093461  \n",
+       "  79 -2.540437  1.834388   -0.489827    0.050653   -3.627862  \n",
+       "  80 -1.850082  0.379170    1.420762   -0.512126   -4.632063  \n",
+       "  81 -0.013807 -0.307042    2.555231   -0.810940   -0.797186  \n",
+       "  82  2.976574 -1.347095   -1.531805   -0.084930    1.867111  \n",
+       "  83  3.116367 -1.401106   -1.792021    0.540145    3.214132  \n",
+       "  84  0.226883 -2.479774   -3.671394    1.702125    1.948937  \n",
+       "  85 -1.783491  0.280745    0.187260    2.298550   -1.406441  \n",
+       "  86  0.225059  1.130979    1.691229    2.487135   -4.248973  \n",
+       "  87  0.540923 -0.424952    1.635476    2.895723   -2.772123  \n",
+       "  88  3.518086  1.949599    0.937306   -2.032653   -1.953112  \n",
+       "  89  0.350935  1.159034   -2.432277   -3.455090    1.105144  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -1.844121  1.404062  0.133012 -2.177573 -4.991557  2.725737  0.394410   \n",
+       "  61  0.394410  0.832687 -1.347120 -0.570855 -5.310494  2.483180  0.771116   \n",
+       "  62  0.771116  0.274412 -1.630075  0.112338 -1.686917  0.240140  0.073239   \n",
+       "  63  0.073239 -1.676866  1.340263  1.344791  2.412299 -0.641510  0.275131   \n",
+       "  64  0.275131  1.034524  1.010338 -0.187143  3.900790 -1.606793  0.819826   \n",
+       "  65  0.819826  1.170432  1.411689  1.384278  2.032221 -1.999902  0.909827   \n",
+       "  66  0.909827  1.714484  0.915232  1.562684 -1.734225 -1.693617  0.936131   \n",
+       "  67  0.936131  0.404081  0.680444  0.330203 -4.752708  0.181486 -1.940606   \n",
+       "  68 -1.940606 -0.677543 -1.520043 -0.905971 -3.153794  0.891268 -4.674094   \n",
+       "  69 -4.674094 -1.013700 -2.593136 -0.260203  0.993908 -0.050491 -3.867371   \n",
+       "  70 -3.867371 -0.429870  0.075243  0.356997  5.432793 -1.126745  0.111385   \n",
+       "  71  0.111385 -1.146121  0.179036  0.435176  5.089377 -0.844994  1.378994   \n",
+       "  72  1.378994  0.320967  1.983980 -0.464431  2.287764 -0.106176  2.017123   \n",
+       "  73  2.017123  0.584136  2.476780 -0.084046 -0.671684  2.503050  1.233768   \n",
+       "  74  1.233768  0.120178  0.750613  0.018464 -2.960181  1.912911  0.762412   \n",
+       "  75  0.762412  0.596608 -1.073506  1.334353 -2.587975  1.101905 -2.314392   \n",
+       "  76 -2.314392  0.363519 -2.231148  2.545316 -1.544592 -0.805722 -1.409856   \n",
+       "  77 -1.409856 -0.786142 -1.913215 -0.672591  1.466574 -1.457238  0.479192   \n",
+       "  78  0.479192 -0.123929 -0.458485 -1.635850  0.935421 -1.786358  0.914005   \n",
+       "  79  0.914005  0.749372  0.143247 -1.458564  3.364298 -0.879340  1.535945   \n",
+       "  80  1.535945 -0.097074  1.549831  0.485956  2.780015  0.171350  2.982823   \n",
+       "  81  2.982823 -0.391851  1.755939  0.657316  0.462876  0.885935  0.937896   \n",
+       "  82  0.937896  1.185015  1.024291 -0.136350 -0.693837  0.176263 -1.156280   \n",
+       "  83 -1.156280  1.492098 -0.947821  0.174189 -1.398964 -0.362087 -2.623793   \n",
+       "  84 -2.623793 -0.270297 -1.909480 -0.150980 -2.150991  0.050971 -2.395558   \n",
+       "  85 -2.395558  0.386757 -2.406142  0.163438 -0.804404  0.879161 -0.693770   \n",
+       "  86 -0.693770 -0.421078 -0.224656  0.496727  1.184898  1.655206  1.081732   \n",
+       "  87  1.081732 -1.417222  0.408448  0.169962  1.723554  1.162921  1.353910   \n",
+       "  88  1.353910 -2.110803  2.159743 -0.146318  0.674121  1.681720 -0.162605   \n",
+       "  89 -0.162605 -0.653505  1.739176 -0.624810 -0.001498  1.489634 -0.734624   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.832687 -1.347120   -0.570855   -5.310494    2.483180  \n",
+       "  61  0.274412 -1.630075    0.112338   -1.686917    0.240140  \n",
+       "  62 -1.676866  1.340263    1.344791    2.412299   -0.641510  \n",
+       "  63  1.034524  1.010338   -0.187143    3.900790   -1.606793  \n",
+       "  64  1.170432  1.411689    1.384278    2.032221   -1.999902  \n",
+       "  65  1.714484  0.915232    1.562684   -1.734225   -1.693617  \n",
+       "  66  0.404081  0.680444    0.330203   -4.752708    0.181486  \n",
+       "  67 -0.677543 -1.520043   -0.905971   -3.153794    0.891268  \n",
+       "  68 -1.013700 -2.593136   -0.260203    0.993908   -0.050491  \n",
+       "  69 -0.429870  0.075243    0.356997    5.432793   -1.126745  \n",
+       "  70 -1.146121  0.179036    0.435176    5.089377   -0.844994  \n",
+       "  71  0.320967  1.983980   -0.464431    2.287764   -0.106176  \n",
+       "  72  0.584136  2.476780   -0.084046   -0.671684    2.503050  \n",
+       "  73  0.120178  0.750613    0.018464   -2.960181    1.912911  \n",
+       "  74  0.596608 -1.073506    1.334353   -2.587975    1.101905  \n",
+       "  75  0.363519 -2.231148    2.545316   -1.544592   -0.805722  \n",
+       "  76 -0.786142 -1.913215   -0.672591    1.466574   -1.457238  \n",
+       "  77 -0.123929 -0.458485   -1.635850    0.935421   -1.786358  \n",
+       "  78  0.749372  0.143247   -1.458564    3.364298   -0.879340  \n",
+       "  79 -0.097074  1.549831    0.485956    2.780015    0.171350  \n",
+       "  80 -0.391851  1.755939    0.657316    0.462876    0.885935  \n",
+       "  81  1.185015  1.024291   -0.136350   -0.693837    0.176263  \n",
+       "  82  1.492098 -0.947821    0.174189   -1.398964   -0.362087  \n",
+       "  83 -0.270297 -1.909480   -0.150980   -2.150991    0.050971  \n",
+       "  84  0.386757 -2.406142    0.163438   -0.804404    0.879161  \n",
+       "  85 -0.421078 -0.224656    0.496727    1.184898    1.655206  \n",
+       "  86 -1.417222  0.408448    0.169962    1.723554    1.162921  \n",
+       "  87 -2.110803  2.159743   -0.146318    0.674121    1.681720  \n",
+       "  88 -0.653505  1.739176   -0.624810   -0.001498    1.489634  \n",
+       "  89 -0.609222 -1.036570   -1.747476    0.232383   -0.234142  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  1.670596  0.616349  4.417277  3.862959  3.691000 -0.454728  1.581596   \n",
+       "  61  1.581596 -2.715455  4.128548  2.365504  2.329975 -0.789331  1.327521   \n",
+       "  62  1.327521 -0.864444  0.988653  0.014531  2.393706 -0.906599 -0.278283   \n",
+       "  63 -0.278283  0.974031 -1.578165 -2.837002  1.204810  0.978109 -1.914628   \n",
+       "  64 -1.914628  2.424988 -1.852094 -1.449292 -0.864971  2.557071 -2.005962   \n",
+       "  65 -2.005962 -0.554845 -0.929136 -0.574730 -1.248962  1.702240 -1.314553   \n",
+       "  66 -1.314553 -1.736235  1.016063  0.421975  0.360696  1.689439  1.037877   \n",
+       "  67  1.037877 -0.741015  0.667932  0.451218  1.118886 -0.812725  4.282860   \n",
+       "  68  4.282860  1.466067 -1.437994 -1.655084 -0.696777 -1.030200  4.685458   \n",
+       "  69  4.685458  1.972627 -2.735001 -3.438087  0.995428 -1.598803  1.995482   \n",
+       "  70  1.995482  0.451713 -2.999481 -3.213851  0.474564 -2.065249  0.335514   \n",
+       "  71  0.335514  0.138057  0.307220 -1.808266 -1.283386 -0.347561 -2.404472   \n",
+       "  72 -2.404472 -1.588186  1.773128  1.580360 -1.050652  1.965277 -2.040535   \n",
+       "  73 -2.040535  0.109352  2.014625  3.584152 -0.963639  0.973528 -0.692867   \n",
+       "  74 -0.692867 -0.270418 -0.850798  1.314733  1.633540 -0.480920  0.929582   \n",
+       "  75  0.929582 -1.334952 -1.990637 -1.156940  1.011405 -3.690130  1.191523   \n",
+       "  76  1.191523 -1.303284 -2.429174 -1.998664  1.102686 -2.191351 -0.408214   \n",
+       "  77 -0.408214  2.003381 -0.423213 -1.116427 -0.424795 -2.961186 -0.742585   \n",
+       "  78 -0.742585  2.698595  1.792179 -0.465684 -1.580955  0.021245 -0.332454   \n",
+       "  79 -0.332454  2.706294 -0.385880  1.822709 -0.980779  0.854112 -1.366267   \n",
+       "  80 -1.366267 -0.078494 -0.789336  1.619052  1.382581  1.616160 -0.174300   \n",
+       "  81 -0.174300 -1.512272  0.486939  1.275763  0.739995  0.882558 -0.255620   \n",
+       "  82 -0.255620 -0.598363  1.141060  0.690001  1.264074 -0.963984  0.818776   \n",
+       "  83  0.818776  1.677166 -0.622007 -0.231115  0.174242 -2.719487  2.024036   \n",
+       "  84  2.024036  1.709465 -2.240311 -0.224401 -0.296712 -0.402779  2.509383   \n",
+       "  85  2.509383  0.081859 -3.468236 -0.240561 -2.503979  0.844787 -0.010822   \n",
+       "  86 -0.010822 -1.344137 -2.677623  1.861581 -2.104714  2.214538 -0.392137   \n",
+       "  87 -0.392137 -1.180357  1.679591  1.801429 -1.123552  1.510170 -0.811060   \n",
+       "  88 -0.811060  1.742062  2.055151  1.391134 -0.148826  0.402289 -1.524603   \n",
+       "  89 -1.524603  2.113404  0.905446 -1.261162 -0.221992 -0.003482 -0.712535   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -2.715455  4.128548    2.365504    2.329975   -0.789331  \n",
+       "  61 -0.864444  0.988653    0.014531    2.393706   -0.906599  \n",
+       "  62  0.974031 -1.578165   -2.837002    1.204810    0.978109  \n",
+       "  63  2.424988 -1.852094   -1.449292   -0.864971    2.557071  \n",
+       "  64 -0.554845 -0.929136   -0.574730   -1.248962    1.702240  \n",
+       "  65 -1.736235  1.016063    0.421975    0.360696    1.689439  \n",
+       "  66 -0.741015  0.667932    0.451218    1.118886   -0.812725  \n",
+       "  67  1.466067 -1.437994   -1.655084   -0.696777   -1.030200  \n",
+       "  68  1.972627 -2.735001   -3.438087    0.995428   -1.598803  \n",
+       "  69  0.451713 -2.999481   -3.213851    0.474564   -2.065249  \n",
+       "  70  0.138057  0.307220   -1.808266   -1.283386   -0.347561  \n",
+       "  71 -1.588186  1.773128    1.580360   -1.050652    1.965277  \n",
+       "  72  0.109352  2.014625    3.584152   -0.963639    0.973528  \n",
+       "  73 -0.270418 -0.850798    1.314733    1.633540   -0.480920  \n",
+       "  74 -1.334952 -1.990637   -1.156940    1.011405   -3.690130  \n",
+       "  75 -1.303284 -2.429174   -1.998664    1.102686   -2.191351  \n",
+       "  76  2.003381 -0.423213   -1.116427   -0.424795   -2.961186  \n",
+       "  77  2.698595  1.792179   -0.465684   -1.580955    0.021245  \n",
+       "  78  2.706294 -0.385880    1.822709   -0.980779    0.854112  \n",
+       "  79 -0.078494 -0.789336    1.619052    1.382581    1.616160  \n",
+       "  80 -1.512272  0.486939    1.275763    0.739995    0.882558  \n",
+       "  81 -0.598363  1.141060    0.690001    1.264074   -0.963984  \n",
+       "  82  1.677166 -0.622007   -0.231115    0.174242   -2.719487  \n",
+       "  83  1.709465 -2.240311   -0.224401   -0.296712   -0.402779  \n",
+       "  84  0.081859 -3.468236   -0.240561   -2.503979    0.844787  \n",
+       "  85 -1.344137 -2.677623    1.861581   -2.104714    2.214538  \n",
+       "  86 -1.180357  1.679591    1.801429   -1.123552    1.510170  \n",
+       "  87  1.742062  2.055151    1.391134   -0.148826    0.402289  \n",
+       "  88  2.113404  0.905446   -1.261162   -0.221992   -0.003482  \n",
+       "  89  2.147108 -0.908203   -2.797310    0.687622    0.925929  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.017873  0.998343  2.111248 -1.558481  2.200494 -1.872177 -1.251739   \n",
+       "  61 -1.251739  0.848566  2.473541 -0.791963  2.673677 -1.270513  0.723868   \n",
+       "  62  0.723868  0.391377  2.392263 -0.242586 -0.397609 -1.693993  2.724819   \n",
+       "  63  2.724819  1.754132  0.179259  1.368340 -2.727276  0.708650  1.395681   \n",
+       "  64  1.395681  1.374729 -2.566563 -0.281858 -6.209252  3.069244 -1.432575   \n",
+       "  65 -1.432575  1.151260 -2.543684 -2.689262 -4.252493  2.282797 -2.238352   \n",
+       "  66 -2.238352 -0.953206 -1.099552 -1.192947 -0.753698  2.353096 -1.036583   \n",
+       "  67 -1.036583 -1.066286  1.181577  1.879787  1.361354  2.049168  0.531463   \n",
+       "  68  0.531463 -0.270451  2.572654  1.762864  3.165220 -0.629316  1.533889   \n",
+       "  69  1.533889  2.347786  1.113827  2.604645  1.898512 -1.774677  1.456108   \n",
+       "  70  1.456108  3.086798  0.115505  0.564985 -1.278563 -1.483599  0.816150   \n",
+       "  71  0.816150  0.316060 -2.514096 -2.772503 -1.891591 -0.538174 -0.024618   \n",
+       "  72 -0.024618 -3.973625 -2.024249 -4.056873 -1.675018  0.621292 -1.748735   \n",
+       "  73 -1.748735 -3.437163 -0.779410 -1.131295 -0.488545  1.022468 -1.709991   \n",
+       "  74 -1.709991 -1.178595 -1.412287  0.765995  1.965889  1.507141 -0.503010   \n",
+       "  75 -0.503010  1.970133  1.290897  2.483629  2.442585  0.933141  1.248043   \n",
+       "  76  1.248043  2.630753  1.069681  1.297316  2.161965  0.270163  0.800279   \n",
+       "  77  0.800279  1.855084  1.223793  1.224042 -1.497402 -1.313838  1.830052   \n",
+       "  78  1.830052  1.993346 -0.798478 -0.963500 -2.932943 -1.667031  1.238788   \n",
+       "  79  1.238788 -0.328507  0.215491 -1.370384 -3.726840  0.021059  0.900776   \n",
+       "  80  0.900776 -0.090369 -0.630829 -2.687735 -0.791409  1.953376 -1.211910   \n",
+       "  81 -1.211910 -1.206408 -0.459830 -0.399888  1.493901  0.311651 -3.828413   \n",
+       "  82 -3.828413 -1.667926  0.179738 -0.857677  3.030625  0.471078 -2.683339   \n",
+       "  83 -2.683339 -0.173424  0.472495  1.148234  1.352692  0.284218  1.027778   \n",
+       "  84  1.027778  1.128056 -1.109142  2.782332 -0.068425  1.176986  3.456398   \n",
+       "  85  3.456398  2.198664 -2.492617  0.531102 -2.556358  1.615380  3.869826   \n",
+       "  86  3.869826  3.192362 -1.620808 -0.352022 -2.859071  1.838077  2.640704   \n",
+       "  87  2.640704  2.264215 -0.713156 -0.318175  0.943941  1.292033 -0.108306   \n",
+       "  88 -0.108306  0.765994  1.533329 -0.143521  1.728885 -1.449028 -2.275552   \n",
+       "  89 -2.275552 -1.436440  1.631104 -0.197039  0.344418 -1.243634 -3.178840   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.848566  2.473541   -0.791963    2.673677   -1.270513  \n",
+       "  61  0.391377  2.392263   -0.242586   -0.397609   -1.693993  \n",
+       "  62  1.754132  0.179259    1.368340   -2.727276    0.708650  \n",
+       "  63  1.374729 -2.566563   -0.281858   -6.209252    3.069244  \n",
+       "  64  1.151260 -2.543684   -2.689262   -4.252493    2.282797  \n",
+       "  65 -0.953206 -1.099552   -1.192947   -0.753698    2.353096  \n",
+       "  66 -1.066286  1.181577    1.879787    1.361354    2.049168  \n",
+       "  67 -0.270451  2.572654    1.762864    3.165220   -0.629316  \n",
+       "  68  2.347786  1.113827    2.604645    1.898512   -1.774677  \n",
+       "  69  3.086798  0.115505    0.564985   -1.278563   -1.483599  \n",
+       "  70  0.316060 -2.514096   -2.772503   -1.891591   -0.538174  \n",
+       "  71 -3.973625 -2.024249   -4.056873   -1.675018    0.621292  \n",
+       "  72 -3.437163 -0.779410   -1.131295   -0.488545    1.022468  \n",
+       "  73 -1.178595 -1.412287    0.765995    1.965889    1.507141  \n",
+       "  74  1.970133  1.290897    2.483629    2.442585    0.933141  \n",
+       "  75  2.630753  1.069681    1.297316    2.161965    0.270163  \n",
+       "  76  1.855084  1.223793    1.224042   -1.497402   -1.313838  \n",
+       "  77  1.993346 -0.798478   -0.963500   -2.932943   -1.667031  \n",
+       "  78 -0.328507  0.215491   -1.370384   -3.726840    0.021059  \n",
+       "  79 -0.090369 -0.630829   -2.687735   -0.791409    1.953376  \n",
+       "  80 -1.206408 -0.459830   -0.399888    1.493901    0.311651  \n",
+       "  81 -1.667926  0.179738   -0.857677    3.030625    0.471078  \n",
+       "  82 -0.173424  0.472495    1.148234    1.352692    0.284218  \n",
+       "  83  1.128056 -1.109142    2.782332   -0.068425    1.176986  \n",
+       "  84  2.198664 -2.492617    0.531102   -2.556358    1.615380  \n",
+       "  85  3.192362 -1.620808   -0.352022   -2.859071    1.838077  \n",
+       "  86  2.264215 -0.713156   -0.318175    0.943941    1.292033  \n",
+       "  87  0.765994  1.533329   -0.143521    1.728885   -1.449028  \n",
+       "  88 -1.436440  1.631104   -0.197039    0.344418   -1.243634  \n",
+       "  89 -1.799920  0.717556   -0.342118   -1.629275   -1.918805  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  2.364563 -0.042790  1.147040  0.660839  0.086087 -3.001265 -0.562276   \n",
+       "  61 -0.562276 -0.429933  0.452815  0.562511 -0.682730 -1.043968 -2.882237   \n",
+       "  62 -2.882237 -0.162607 -0.350148 -2.535652 -0.350821  2.203811 -2.121254   \n",
+       "  63 -2.121254 -0.145104  0.711416 -1.053733 -2.046611  4.291309 -1.922117   \n",
+       "  64 -1.922117 -0.187077  0.638806  0.623556 -0.054828  2.454799  0.477348   \n",
+       "  65  0.477348 -0.542394  0.163157  0.583265  1.171090  0.333063  1.407008   \n",
+       "  66  1.407008 -0.168180 -1.148828  0.265036  2.417641 -3.565903  0.331318   \n",
+       "  67  0.331318  0.730488 -2.349223 -0.511083  0.584984 -4.770478 -1.131506   \n",
+       "  68 -1.131506  0.201428 -3.224776 -1.218035 -1.017036 -1.558036 -1.467184   \n",
+       "  69 -1.467184  1.045220 -1.248807 -1.881918 -1.142161  0.881184  0.370394   \n",
+       "  70  0.370394  0.135816  1.322255 -1.267708 -1.396164  3.977848  1.298459   \n",
+       "  71  1.298459 -1.601027  2.546740  0.042202 -0.909344  2.897931  1.908366   \n",
+       "  72  1.908366 -0.630105  2.180186  1.984879  0.244527  1.138793  0.692011   \n",
+       "  73  0.692011  1.185104  1.428940  1.774400 -1.017583 -2.094205 -0.083625   \n",
+       "  74 -0.083625  1.493910 -3.797683  0.466759  0.210236 -2.813392 -3.012324   \n",
+       "  75 -3.012324  0.045480 -4.632264 -0.709940  1.238994 -2.055418 -2.783666   \n",
+       "  76 -2.783666 -1.611140 -2.509458 -1.777194 -1.161332  0.646860 -0.942087   \n",
+       "  77 -0.942087 -3.958247  2.593708 -0.736231 -1.375484  4.528596  0.501027   \n",
+       "  78  0.501027 -2.883184  3.639628 -0.640993 -1.531078  5.054282  0.799336   \n",
+       "  79  0.799336  0.044399  5.611852  1.933917 -0.701771  2.120019  1.133170   \n",
+       "  80  1.133170  3.639978  0.695154  0.300094  0.325186 -1.784560  0.546814   \n",
+       "  81  0.546814  3.227774 -3.642505 -0.373600  0.721698 -3.481736  1.036912   \n",
+       "  82  1.036912  1.033386 -3.455092 -0.197902  0.992185 -0.978900  0.539420   \n",
+       "  83  0.539420 -2.354147 -1.591416 -0.253831  0.085228  1.748377 -1.085687   \n",
+       "  84 -1.085687 -3.004755  1.068982  0.671847 -0.099498  2.181924  0.131862   \n",
+       "  85  0.131862 -1.661746  2.982417  0.649484 -0.242619  1.376137 -0.092005   \n",
+       "  86 -0.092005  1.499914  3.984058  0.482092 -1.457332  1.222571  0.201454   \n",
+       "  87  0.201454  3.039629  2.893773 -2.103268 -1.416149 -1.645970 -0.042993   \n",
+       "  88 -0.042993  1.741077 -2.013600 -3.667351 -0.472534 -1.562210  0.875786   \n",
+       "  89  0.875786 -0.475424 -3.678648 -0.327363  0.836716 -1.560100  0.170462   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -0.429933  0.452815    0.562511   -0.682730   -1.043968  \n",
+       "  61 -0.162607 -0.350148   -2.535652   -0.350821    2.203811  \n",
+       "  62 -0.145104  0.711416   -1.053733   -2.046611    4.291309  \n",
+       "  63 -0.187077  0.638806    0.623556   -0.054828    2.454799  \n",
+       "  64 -0.542394  0.163157    0.583265    1.171090    0.333063  \n",
+       "  65 -0.168180 -1.148828    0.265036    2.417641   -3.565903  \n",
+       "  66  0.730488 -2.349223   -0.511083    0.584984   -4.770478  \n",
+       "  67  0.201428 -3.224776   -1.218035   -1.017036   -1.558036  \n",
+       "  68  1.045220 -1.248807   -1.881918   -1.142161    0.881184  \n",
+       "  69  0.135816  1.322255   -1.267708   -1.396164    3.977848  \n",
+       "  70 -1.601027  2.546740    0.042202   -0.909344    2.897931  \n",
+       "  71 -0.630105  2.180186    1.984879    0.244527    1.138793  \n",
+       "  72  1.185104  1.428940    1.774400   -1.017583   -2.094205  \n",
+       "  73  1.493910 -3.797683    0.466759    0.210236   -2.813392  \n",
+       "  74  0.045480 -4.632264   -0.709940    1.238994   -2.055418  \n",
+       "  75 -1.611140 -2.509458   -1.777194   -1.161332    0.646860  \n",
+       "  76 -3.958247  2.593708   -0.736231   -1.375484    4.528596  \n",
+       "  77 -2.883184  3.639628   -0.640993   -1.531078    5.054282  \n",
+       "  78  0.044399  5.611852    1.933917   -0.701771    2.120019  \n",
+       "  79  3.639978  0.695154    0.300094    0.325186   -1.784560  \n",
+       "  80  3.227774 -3.642505   -0.373600    0.721698   -3.481736  \n",
+       "  81  1.033386 -3.455092   -0.197902    0.992185   -0.978900  \n",
+       "  82 -2.354147 -1.591416   -0.253831    0.085228    1.748377  \n",
+       "  83 -3.004755  1.068982    0.671847   -0.099498    2.181924  \n",
+       "  84 -1.661746  2.982417    0.649484   -0.242619    1.376137  \n",
+       "  85  1.499914  3.984058    0.482092   -1.457332    1.222571  \n",
+       "  86  3.039629  2.893773   -2.103268   -1.416149   -1.645970  \n",
+       "  87  1.741077 -2.013600   -3.667351   -0.472534   -1.562210  \n",
+       "  88 -0.475424 -3.678648   -0.327363    0.836716   -1.560100  \n",
+       "  89 -0.206762 -5.520207    0.519898    2.393559    0.636117  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.872374  1.990135  0.297583 -1.066695  0.091423 -4.943615 -1.687076   \n",
+       "  61 -1.687076  0.853637  1.025386 -0.473731 -0.433259 -3.077235 -0.006757   \n",
+       "  62 -0.006757 -0.248643  2.652306  1.437589  0.104676 -0.729568  1.570910   \n",
+       "  63  1.570910 -3.601251  0.592856  0.731229  0.308387  1.144441  0.102240   \n",
+       "  64  0.102240 -3.719388 -1.047996  0.163092  1.190545  2.769590 -1.319377   \n",
+       "  65 -1.319377 -0.596706 -2.237035 -2.454960  1.353396  1.941065 -3.662447   \n",
+       "  66 -3.662447  1.656436 -0.562023 -3.088563 -1.224186  0.882441 -1.824493   \n",
+       "  67 -1.824493  3.169102  0.981356 -2.709030 -1.809005 -0.704677 -1.693505   \n",
+       "  68 -1.693505  2.675753  1.083249  0.938331 -1.571572 -1.272493  0.116976   \n",
+       "  69  0.116976  0.210827  1.037542  3.640067  1.038964  0.158655  2.439815   \n",
+       "  70  2.439815 -1.861021 -0.402030  2.759186  1.840223  0.709158  1.836236   \n",
+       "  71  1.836236 -2.470441 -0.983812 -0.750075 -0.775418  1.238954 -0.806980   \n",
+       "  72 -0.806980 -0.799926 -0.460736 -1.555724 -3.051348  0.508151 -1.180050   \n",
+       "  73 -1.180050  0.583908 -0.369243 -2.894906 -3.572248 -1.240955 -1.849694   \n",
+       "  74 -1.849694  2.012127 -1.919617 -1.685410 -0.625655 -2.919089  0.663516   \n",
+       "  75  0.663516  2.295114 -1.631332  1.399342  2.177067 -1.554732  2.750167   \n",
+       "  76  2.750167  1.013816  1.072757  3.917486  5.145858 -0.405237  4.028440   \n",
+       "  77  4.028440 -1.675394  1.015182  2.624576  3.081509  2.133440  2.457844   \n",
+       "  78  2.457844 -1.086703  1.404511  0.910725  1.123848  1.420362  0.442924   \n",
+       "  79  0.442924 -0.658064 -1.026345 -1.415294 -4.096098  0.530235 -3.190911   \n",
+       "  80 -3.190911  1.146276 -0.274903 -1.157838 -4.237729 -1.593334 -4.521673   \n",
+       "  81 -4.521673  1.824385  0.068958 -1.200381 -0.580161 -3.594429 -2.068363   \n",
+       "  82 -2.068363  2.231203  0.736491  0.444919  2.980921 -2.014504  0.441453   \n",
+       "  83  0.441453  1.477714  2.871922  1.265464  5.629423  1.303676  1.703133   \n",
+       "  84  1.703133  0.805023  1.900766 -0.703000  2.625176  2.354439  0.200737   \n",
+       "  85  0.200737 -1.583263 -1.835399 -0.281823 -1.952698  2.351439 -0.444060   \n",
+       "  86 -0.444060 -0.200055 -2.206059  0.545808 -2.637749 -0.661999 -1.427726   \n",
+       "  87 -1.427726 -0.646934 -3.911207 -0.099012 -2.126432 -1.996235 -0.892147   \n",
+       "  88 -0.892147  0.788741 -0.242570  0.969093  1.272153 -3.390167 -1.507731   \n",
+       "  89 -1.507731 -0.832920  1.110772 -1.116961  4.435864 -1.043411  0.381322   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.853637  1.025386   -0.473731   -0.433259   -3.077235  \n",
+       "  61 -0.248643  2.652306    1.437589    0.104676   -0.729568  \n",
+       "  62 -3.601251  0.592856    0.731229    0.308387    1.144441  \n",
+       "  63 -3.719388 -1.047996    0.163092    1.190545    2.769590  \n",
+       "  64 -0.596706 -2.237035   -2.454960    1.353396    1.941065  \n",
+       "  65  1.656436 -0.562023   -3.088563   -1.224186    0.882441  \n",
+       "  66  3.169102  0.981356   -2.709030   -1.809005   -0.704677  \n",
+       "  67  2.675753  1.083249    0.938331   -1.571572   -1.272493  \n",
+       "  68  0.210827  1.037542    3.640067    1.038964    0.158655  \n",
+       "  69 -1.861021 -0.402030    2.759186    1.840223    0.709158  \n",
+       "  70 -2.470441 -0.983812   -0.750075   -0.775418    1.238954  \n",
+       "  71 -0.799926 -0.460736   -1.555724   -3.051348    0.508151  \n",
+       "  72  0.583908 -0.369243   -2.894906   -3.572248   -1.240955  \n",
+       "  73  2.012127 -1.919617   -1.685410   -0.625655   -2.919089  \n",
+       "  74  2.295114 -1.631332    1.399342    2.177067   -1.554732  \n",
+       "  75  1.013816  1.072757    3.917486    5.145858   -0.405237  \n",
+       "  76 -1.675394  1.015182    2.624576    3.081509    2.133440  \n",
+       "  77 -1.086703  1.404511    0.910725    1.123848    1.420362  \n",
+       "  78 -0.658064 -1.026345   -1.415294   -4.096098    0.530235  \n",
+       "  79  1.146276 -0.274903   -1.157838   -4.237729   -1.593334  \n",
+       "  80  1.824385  0.068958   -1.200381   -0.580161   -3.594429  \n",
+       "  81  2.231203  0.736491    0.444919    2.980921   -2.014504  \n",
+       "  82  1.477714  2.871922    1.265464    5.629423    1.303676  \n",
+       "  83  0.805023  1.900766   -0.703000    2.625176    2.354439  \n",
+       "  84 -1.583263 -1.835399   -0.281823   -1.952698    2.351439  \n",
+       "  85 -0.200055 -2.206059    0.545808   -2.637749   -0.661999  \n",
+       "  86 -0.646934 -3.911207   -0.099012   -2.126432   -1.996235  \n",
+       "  87  0.788741 -0.242570    0.969093    1.272153   -3.390167  \n",
+       "  88 -0.832920  1.110772   -1.116961    4.435864   -1.043411  \n",
+       "  89 -0.079558  1.889477   -1.504298    5.291423    0.359237  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -3.052695  1.771650 -0.104490 -0.244687 -2.180743 -1.086017 -0.078010   \n",
+       "  61 -0.078010 -1.853162 -1.102825  0.235088 -0.464934 -1.368802  2.977445   \n",
+       "  62  2.977445 -2.555221  0.164024  1.747016 -0.253511 -0.223016  4.064077   \n",
+       "  63  4.064077 -1.438553  0.248250  1.982387 -0.385925  1.829349  1.885844   \n",
+       "  64  1.885844  1.408925 -0.431548  1.481537  2.298905  2.133446 -1.531526   \n",
+       "  65 -1.531526  2.210591 -0.642280 -0.999472  2.756987  0.837043 -2.716657   \n",
+       "  66 -2.716657  0.262184 -0.828387 -1.384352 -0.219925 -0.088460 -2.070463   \n",
+       "  67 -2.070463 -2.022905 -1.519772 -0.503828 -3.811856 -0.664499  0.055344   \n",
+       "  68  0.055344 -1.319796 -0.026377  0.341965 -2.863804 -0.843450  1.431172   \n",
+       "  69  1.431172 -1.316418  1.478163 -0.195328  0.394254  0.889683  3.659692   \n",
+       "  70  3.659692 -0.557773  2.067663  0.104477  1.675980  0.875243  1.429766   \n",
+       "  71  1.429766  1.111478  0.541016  0.293202  2.046106  0.075073 -1.763373   \n",
+       "  72 -1.763373  0.702531  0.217729 -0.049927  0.401732 -1.667984 -3.750701   \n",
+       "  73 -3.750701 -1.680985 -1.579559  0.817121 -0.466799  0.062963 -2.135473   \n",
+       "  74 -2.135473 -1.480057 -0.692093  0.232470 -1.739530  2.639617 -0.123265   \n",
+       "  75 -0.123265 -1.222746 -0.024331 -1.451444 -0.269269  3.063041  3.733472   \n",
+       "  76  3.733472  0.131112  1.111105 -0.779720 -0.731027  0.878202  2.935438   \n",
+       "  77  2.935438  0.103386  1.553818 -0.412173 -0.978933 -2.838855  2.012739   \n",
+       "  78  2.012739  0.470691  0.988479  0.385488  0.798346 -1.907548  0.016641   \n",
+       "  79  0.016641 -0.669352 -0.116288  0.294540 -2.269996 -0.447544 -1.960698   \n",
+       "  80 -1.960698 -1.335370 -2.696311  1.671726 -0.497392 -0.652222 -2.008170   \n",
+       "  81 -2.008170 -0.025607 -1.341542  0.861241  1.014186  0.498689 -0.944127   \n",
+       "  82 -0.944127  1.178309  1.016620  0.357319  0.388295 -0.100110  0.961161   \n",
+       "  83  0.961161  1.524301  2.311915 -2.246697  0.162937  1.013521  2.732004   \n",
+       "  84  2.732004  0.544196  3.458618 -2.858678 -1.179666  0.222193  1.417702   \n",
+       "  85  1.417702  0.251495  1.871802 -0.414931 -1.330393 -0.628870 -0.969844   \n",
+       "  86 -0.969844 -1.054716 -0.984595  1.146568 -0.940306 -1.143957 -1.322673   \n",
+       "  87 -1.322673 -2.296717 -2.596043  3.307855 -0.534392 -0.405950  1.442348   \n",
+       "  88  1.442348 -0.281453  0.379432  1.734172  1.710747 -0.800667  3.613439   \n",
+       "  89  3.613439  0.475857  1.588164 -0.247938  0.197369 -1.213023  4.200121   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.853162 -1.102825    0.235088   -0.464934   -1.368802  \n",
+       "  61 -2.555221  0.164024    1.747016   -0.253511   -0.223016  \n",
+       "  62 -1.438553  0.248250    1.982387   -0.385925    1.829349  \n",
+       "  63  1.408925 -0.431548    1.481537    2.298905    2.133446  \n",
+       "  64  2.210591 -0.642280   -0.999472    2.756987    0.837043  \n",
+       "  65  0.262184 -0.828387   -1.384352   -0.219925   -0.088460  \n",
+       "  66 -2.022905 -1.519772   -0.503828   -3.811856   -0.664499  \n",
+       "  67 -1.319796 -0.026377    0.341965   -2.863804   -0.843450  \n",
+       "  68 -1.316418  1.478163   -0.195328    0.394254    0.889683  \n",
+       "  69 -0.557773  2.067663    0.104477    1.675980    0.875243  \n",
+       "  70  1.111478  0.541016    0.293202    2.046106    0.075073  \n",
+       "  71  0.702531  0.217729   -0.049927    0.401732   -1.667984  \n",
+       "  72 -1.680985 -1.579559    0.817121   -0.466799    0.062963  \n",
+       "  73 -1.480057 -0.692093    0.232470   -1.739530    2.639617  \n",
+       "  74 -1.222746 -0.024331   -1.451444   -0.269269    3.063041  \n",
+       "  75  0.131112  1.111105   -0.779720   -0.731027    0.878202  \n",
+       "  76  0.103386  1.553818   -0.412173   -0.978933   -2.838855  \n",
+       "  77  0.470691  0.988479    0.385488    0.798346   -1.907548  \n",
+       "  78 -0.669352 -0.116288    0.294540   -2.269996   -0.447544  \n",
+       "  79 -1.335370 -2.696311    1.671726   -0.497392   -0.652222  \n",
+       "  80 -0.025607 -1.341542    0.861241    1.014186    0.498689  \n",
+       "  81  1.178309  1.016620    0.357319    0.388295   -0.100110  \n",
+       "  82  1.524301  2.311915   -2.246697    0.162937    1.013521  \n",
+       "  83  0.544196  3.458618   -2.858678   -1.179666    0.222193  \n",
+       "  84  0.251495  1.871802   -0.414931   -1.330393   -0.628870  \n",
+       "  85 -1.054716 -0.984595    1.146568   -0.940306   -1.143957  \n",
+       "  86 -2.296717 -2.596043    3.307855   -0.534392   -0.405950  \n",
+       "  87 -0.281453  0.379432    1.734172    1.710747   -0.800667  \n",
+       "  88  0.475857  1.588164   -0.247938    0.197369   -1.213023  \n",
+       "  89  2.047084  1.861377   -2.360137    1.350237   -1.784683  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  0.100819 -1.442561  2.752056 -3.877231  2.416107 -2.059157  0.579495   \n",
+       "  61  0.579495  0.300315  2.842137 -4.682121  0.955683 -3.674331  2.082137   \n",
+       "  62  2.082137  0.817274  0.320434 -2.381796 -1.784697 -0.708090  2.494787   \n",
+       "  63  2.494787 -0.016161 -2.221860  0.818036 -2.087814  0.798084  0.426360   \n",
+       "  64  0.426360 -0.613260 -3.650533  2.120057 -1.206045  1.627200 -1.296240   \n",
+       "  65 -1.296240 -0.463113 -1.731341  1.485343 -1.537819  1.598191 -0.176719   \n",
+       "  66 -0.176719  0.309851  1.660857  0.383506 -0.289393  1.204664  2.743494   \n",
+       "  67  2.743494 -0.850736  2.778975 -0.681526  2.997422 -0.107259  1.592957   \n",
+       "  68  1.592957 -0.684063  1.802925 -0.928021  3.802495 -0.185951  0.524456   \n",
+       "  69  0.524456 -0.589943 -0.353531 -1.514259  2.440624 -3.049610 -1.991043   \n",
+       "  70 -1.991043  0.714601 -1.074122 -0.787149  0.620037 -3.418158 -1.162900   \n",
+       "  71 -1.162900  2.265915 -1.535150  0.643999 -1.100083 -1.737074  0.982258   \n",
+       "  72  0.982258  1.723122 -0.892006  2.363095 -3.173811  0.396197  1.827840   \n",
+       "  73  1.827840  0.286614 -0.459562  1.583189 -2.199253  1.922818  0.942047   \n",
+       "  74  0.942047 -1.670859  1.505813  1.009048 -1.070964  1.260829 -1.269387   \n",
+       "  75 -1.269387 -3.725436  1.973417 -1.534379  0.938300 -0.196523 -0.168504   \n",
+       "  76 -0.168504 -2.558517  1.259268 -3.164184  2.381426 -1.315538 -0.128876   \n",
+       "  77 -0.128876  0.940935 -1.068779 -4.388107  0.544819 -1.439003  1.433897   \n",
+       "  78  1.433897  2.047320 -1.864022 -0.289828 -0.308408 -0.311740 -0.331085   \n",
+       "  79 -0.331085  2.746225 -1.217183  3.632759 -1.361276  0.487468 -0.315361   \n",
+       "  80 -0.315361  0.589196  0.571483  5.028331 -1.849564 -0.230044 -0.762210   \n",
+       "  81 -0.762210 -0.485875  3.897827  2.999021 -0.167528  1.194289 -1.567906   \n",
+       "  82 -1.567906 -1.008032  4.004619 -1.935326  2.737665  1.748598 -2.331511   \n",
+       "  83 -2.331511 -1.027063  2.714900 -5.849283  2.856831  0.042363 -1.839644   \n",
+       "  84 -1.839644  0.472226 -1.618325 -2.457965  1.975780 -0.808627  0.973316   \n",
+       "  85  0.973316  0.740306 -2.047034  0.256547  0.393028 -2.052007  2.451531   \n",
+       "  86  2.451531 -0.021556 -1.603006  3.698459 -1.553931  0.174903  0.724204   \n",
+       "  87  0.724204 -0.577354  0.497699  3.755430 -0.508810  1.267854 -1.044896   \n",
+       "  88 -1.044896  0.430316 -0.050029  0.727209 -1.732228  3.409055 -1.835064   \n",
+       "  89 -1.835064 -1.620588  0.894233 -2.078245 -0.793673  1.343310 -0.409001   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.300315  2.842137   -4.682121    0.955683   -3.674331  \n",
+       "  61  0.817274  0.320434   -2.381796   -1.784697   -0.708090  \n",
+       "  62 -0.016161 -2.221860    0.818036   -2.087814    0.798084  \n",
+       "  63 -0.613260 -3.650533    2.120057   -1.206045    1.627200  \n",
+       "  64 -0.463113 -1.731341    1.485343   -1.537819    1.598191  \n",
+       "  65  0.309851  1.660857    0.383506   -0.289393    1.204664  \n",
+       "  66 -0.850736  2.778975   -0.681526    2.997422   -0.107259  \n",
+       "  67 -0.684063  1.802925   -0.928021    3.802495   -0.185951  \n",
+       "  68 -0.589943 -0.353531   -1.514259    2.440624   -3.049610  \n",
+       "  69  0.714601 -1.074122   -0.787149    0.620037   -3.418158  \n",
+       "  70  2.265915 -1.535150    0.643999   -1.100083   -1.737074  \n",
+       "  71  1.723122 -0.892006    2.363095   -3.173811    0.396197  \n",
+       "  72  0.286614 -0.459562    1.583189   -2.199253    1.922818  \n",
+       "  73 -1.670859  1.505813    1.009048   -1.070964    1.260829  \n",
+       "  74 -3.725436  1.973417   -1.534379    0.938300   -0.196523  \n",
+       "  75 -2.558517  1.259268   -3.164184    2.381426   -1.315538  \n",
+       "  76  0.940935 -1.068779   -4.388107    0.544819   -1.439003  \n",
+       "  77  2.047320 -1.864022   -0.289828   -0.308408   -0.311740  \n",
+       "  78  2.746225 -1.217183    3.632759   -1.361276    0.487468  \n",
+       "  79  0.589196  0.571483    5.028331   -1.849564   -0.230044  \n",
+       "  80 -0.485875  3.897827    2.999021   -0.167528    1.194289  \n",
+       "  81 -1.008032  4.004619   -1.935326    2.737665    1.748598  \n",
+       "  82 -1.027063  2.714900   -5.849283    2.856831    0.042363  \n",
+       "  83  0.472226 -1.618325   -2.457965    1.975780   -0.808627  \n",
+       "  84  0.740306 -2.047034    0.256547    0.393028   -2.052007  \n",
+       "  85 -0.021556 -1.603006    3.698459   -1.553931    0.174903  \n",
+       "  86 -0.577354  0.497699    3.755430   -0.508810    1.267854  \n",
+       "  87  0.430316 -0.050029    0.727209   -1.732228    3.409055  \n",
+       "  88 -1.620588  0.894233   -2.078245   -0.793673    1.343310  \n",
+       "  89 -2.268185  1.036461   -1.735795    0.027985    0.455108  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  2.953675 -0.018045  1.151584  2.071645 -0.155312  0.391748  2.874661   \n",
+       "  61  2.874661 -0.915966  0.856123  0.735260  0.464869  2.804945 -0.118125   \n",
+       "  62 -0.118125 -1.192170 -0.576937 -1.090330  0.215668  1.309739 -2.161309   \n",
+       "  63 -2.161309  1.905697 -1.044975 -2.072771 -1.133193  0.394498 -1.260517   \n",
+       "  64 -1.260517  0.941612 -3.445848 -3.223891 -1.356922  0.195925 -1.567283   \n",
+       "  65 -1.567283  0.196419 -0.638335 -1.673107 -1.566498 -0.495712  0.404715   \n",
+       "  66  0.404715 -0.716043  2.145362 -0.751011 -0.135251  0.423986  3.283947   \n",
+       "  67  3.283947  0.217225  3.184663 -0.734542  0.767995 -1.316109  3.328817   \n",
+       "  68  3.328817 -0.272207  1.887753  1.307161  1.028541 -2.500597  1.278807   \n",
+       "  69  1.278807  0.346272 -1.306695  1.495824  2.398555 -0.074978  0.412002   \n",
+       "  70  0.412002  1.248201 -3.970933  0.430463  1.713423  0.509253 -1.914785   \n",
+       "  71 -1.914785  1.000311 -2.443263 -1.711100 -0.242145  0.251758 -1.440251   \n",
+       "  72 -1.440251  0.639010  0.839803 -2.452806 -0.921488 -0.266757 -0.137047   \n",
+       "  73 -0.137047 -0.996662  2.156574 -0.988178 -2.417547 -0.533882  1.125329   \n",
+       "  74  1.125329 -0.905213  3.915176 -1.323470 -0.674155  0.053638  1.718797   \n",
+       "  75  1.718797  0.317731  4.268954  2.014932 -0.943008  1.515069  0.218969   \n",
+       "  76  0.218969  0.206986 -1.123494  1.847477  0.298050 -0.229476 -0.737161   \n",
+       "  77 -0.737161 -0.366422 -4.425411  1.210680 -1.325329 -0.379311 -1.175968   \n",
+       "  78 -1.175968  1.295247 -5.572420  0.734280 -1.045959  1.384640 -1.043135   \n",
+       "  79 -1.043135  2.717379 -0.624004 -0.970908 -0.874260  0.082085 -0.234479   \n",
+       "  80 -0.234479 -0.739749  0.897162 -3.418340 -0.978525  0.546884  0.064335   \n",
+       "  81  0.064335 -3.204158  2.741729 -1.370648  0.094981 -0.776590 -0.497992   \n",
+       "  82 -0.497992 -2.628104  0.825883 -1.793776 -0.293073 -0.082658 -0.359867   \n",
+       "  83 -0.359867 -0.057035 -2.460002  0.479688  2.355541 -0.487903 -1.465025   \n",
+       "  84 -1.465025  2.843161 -3.521029  2.251233  2.716463 -0.714129  0.973762   \n",
+       "  85  0.973762  3.532325 -1.890408  1.635554  0.450045 -2.499476  0.068790   \n",
+       "  86  0.068790  0.657102 -0.376189 -0.692458 -2.077838 -1.233716  1.259926   \n",
+       "  87  1.259926 -3.081980  3.010169 -0.809858 -3.141109  0.672850  0.657541   \n",
+       "  88  0.657541 -2.949787  2.438469 -0.846516 -1.150520  2.763086  0.928001   \n",
+       "  89  0.928001 -2.493788  1.924277 -0.023458  1.368444  2.741882 -1.673787   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -0.915966  0.856123    0.735260    0.464869    2.804945  \n",
+       "  61 -1.192170 -0.576937   -1.090330    0.215668    1.309739  \n",
+       "  62  1.905697 -1.044975   -2.072771   -1.133193    0.394498  \n",
+       "  63  0.941612 -3.445848   -3.223891   -1.356922    0.195925  \n",
+       "  64  0.196419 -0.638335   -1.673107   -1.566498   -0.495712  \n",
+       "  65 -0.716043  2.145362   -0.751011   -0.135251    0.423986  \n",
+       "  66  0.217225  3.184663   -0.734542    0.767995   -1.316109  \n",
+       "  67 -0.272207  1.887753    1.307161    1.028541   -2.500597  \n",
+       "  68  0.346272 -1.306695    1.495824    2.398555   -0.074978  \n",
+       "  69  1.248201 -3.970933    0.430463    1.713423    0.509253  \n",
+       "  70  1.000311 -2.443263   -1.711100   -0.242145    0.251758  \n",
+       "  71  0.639010  0.839803   -2.452806   -0.921488   -0.266757  \n",
+       "  72 -0.996662  2.156574   -0.988178   -2.417547   -0.533882  \n",
+       "  73 -0.905213  3.915176   -1.323470   -0.674155    0.053638  \n",
+       "  74  0.317731  4.268954    2.014932   -0.943008    1.515069  \n",
+       "  75  0.206986 -1.123494    1.847477    0.298050   -0.229476  \n",
+       "  76 -0.366422 -4.425411    1.210680   -1.325329   -0.379311  \n",
+       "  77  1.295247 -5.572420    0.734280   -1.045959    1.384640  \n",
+       "  78  2.717379 -0.624004   -0.970908   -0.874260    0.082085  \n",
+       "  79 -0.739749  0.897162   -3.418340   -0.978525    0.546884  \n",
+       "  80 -3.204158  2.741729   -1.370648    0.094981   -0.776590  \n",
+       "  81 -2.628104  0.825883   -1.793776   -0.293073   -0.082658  \n",
+       "  82 -0.057035 -2.460002    0.479688    2.355541   -0.487903  \n",
+       "  83  2.843161 -3.521029    2.251233    2.716463   -0.714129  \n",
+       "  84  3.532325 -1.890408    1.635554    0.450045   -2.499476  \n",
+       "  85  0.657102 -0.376189   -0.692458   -2.077838   -1.233716  \n",
+       "  86 -3.081980  3.010169   -0.809858   -3.141109    0.672850  \n",
+       "  87 -2.949787  2.438469   -0.846516   -1.150520    2.763086  \n",
+       "  88 -2.493788  1.924277   -0.023458    1.368444    2.741882  \n",
+       "  89 -1.349448 -0.352789    0.959449    1.988303    1.542615  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  0.912505 -1.512408  1.835188 -1.239491 -4.682574 -2.325343  0.638431   \n",
+       "  61  0.638431 -4.037491  0.070889 -0.178650 -2.211860 -0.788304  0.802165   \n",
+       "  62  0.802165 -3.533287  0.009426  0.336691  1.029385  1.010560 -0.977291   \n",
+       "  63 -0.977291 -0.422322 -0.886461  0.529838  3.348708  2.425526 -1.398203   \n",
+       "  64 -1.398203  3.242548 -2.162930  1.009574  4.057376  2.275013 -0.595266   \n",
+       "  65 -0.595266  4.351941 -2.574902  0.430132  0.342781 -1.518534 -0.264999   \n",
+       "  66 -0.264999  0.978562 -1.251600  0.550960 -2.736930 -1.592556  0.688283   \n",
+       "  67  0.688283 -0.772963  1.584695  0.169261 -2.950381 -0.380488  1.698439   \n",
+       "  68  1.698439 -4.306863  3.821107 -0.280592 -2.744430 -0.229182  1.018202   \n",
+       "  69  1.018202 -4.473335  3.571151  0.674721 -0.047673  0.094599  0.348752   \n",
+       "  70  0.348752 -1.008368  1.173110 -0.576932  3.175341  1.140847 -0.638908   \n",
+       "  71 -0.638908  2.459737 -1.984907 -1.042074  3.752499  1.954112 -1.448191   \n",
+       "  72 -1.448191  3.990645 -3.779784 -0.202316  2.370760 -0.054110 -0.908514   \n",
+       "  73 -0.908514  1.823621 -3.367505 -0.596076 -0.959559 -0.735746 -1.374165   \n",
+       "  74 -1.374165 -0.863308  0.993574 -1.195400 -2.579410 -2.113064  1.073098   \n",
+       "  75  1.073098 -2.159723  2.716188 -1.130006 -2.140445 -2.007964 -0.918034   \n",
+       "  76 -0.918034 -3.671358  1.935725 -2.345269  2.415344 -0.058130 -1.010007   \n",
+       "  77 -1.010007 -2.023703  1.400723  0.683650  2.467657  1.689828 -2.020112   \n",
+       "  78 -2.020112 -0.042314  0.500651  2.105881  4.273030  1.333344  0.049062   \n",
+       "  79  0.049062  0.467313  3.425469  0.470709  2.948775  1.628385  1.814465   \n",
+       "  80  1.814465  2.007260  0.678345 -1.991109 -1.016776 -0.478031  2.557999   \n",
+       "  81  2.557999  0.052934 -0.947832 -0.925824 -5.359199 -0.968552  0.869773   \n",
+       "  82  0.869773 -0.069402 -1.356054 -0.268876 -5.703679 -1.480841 -0.267202   \n",
+       "  83 -0.267202 -0.965937 -0.879207  1.058603 -0.610162 -0.195064 -1.986643   \n",
+       "  84 -1.986643 -0.610991  0.785625  0.699832  4.016378  0.379526 -0.340882   \n",
+       "  85 -0.340882  0.453180  0.910186 -0.067159  5.759486  0.021904  0.892066   \n",
+       "  86  0.892066  2.277608  1.523195 -1.051397  3.528289  1.130149  2.390404   \n",
+       "  87  2.390404  1.853892 -0.844085 -0.408741 -1.114235  1.775119  1.338230   \n",
+       "  88  1.338230  0.493892  0.103921 -1.304480 -3.327790  2.744288  0.140582   \n",
+       "  89  0.140582  0.112699 -0.175311  0.475266 -3.226895  0.533065 -0.128760   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -4.037491  0.070889   -0.178650   -2.211860   -0.788304  \n",
+       "  61 -3.533287  0.009426    0.336691    1.029385    1.010560  \n",
+       "  62 -0.422322 -0.886461    0.529838    3.348708    2.425526  \n",
+       "  63  3.242548 -2.162930    1.009574    4.057376    2.275013  \n",
+       "  64  4.351941 -2.574902    0.430132    0.342781   -1.518534  \n",
+       "  65  0.978562 -1.251600    0.550960   -2.736930   -1.592556  \n",
+       "  66 -0.772963  1.584695    0.169261   -2.950381   -0.380488  \n",
+       "  67 -4.306863  3.821107   -0.280592   -2.744430   -0.229182  \n",
+       "  68 -4.473335  3.571151    0.674721   -0.047673    0.094599  \n",
+       "  69 -1.008368  1.173110   -0.576932    3.175341    1.140847  \n",
+       "  70  2.459737 -1.984907   -1.042074    3.752499    1.954112  \n",
+       "  71  3.990645 -3.779784   -0.202316    2.370760   -0.054110  \n",
+       "  72  1.823621 -3.367505   -0.596076   -0.959559   -0.735746  \n",
+       "  73 -0.863308  0.993574   -1.195400   -2.579410   -2.113064  \n",
+       "  74 -2.159723  2.716188   -1.130006   -2.140445   -2.007964  \n",
+       "  75 -3.671358  1.935725   -2.345269    2.415344   -0.058130  \n",
+       "  76 -2.023703  1.400723    0.683650    2.467657    1.689828  \n",
+       "  77 -0.042314  0.500651    2.105881    4.273030    1.333344  \n",
+       "  78  0.467313  3.425469    0.470709    2.948775    1.628385  \n",
+       "  79  2.007260  0.678345   -1.991109   -1.016776   -0.478031  \n",
+       "  80  0.052934 -0.947832   -0.925824   -5.359199   -0.968552  \n",
+       "  81 -0.069402 -1.356054   -0.268876   -5.703679   -1.480841  \n",
+       "  82 -0.965937 -0.879207    1.058603   -0.610162   -0.195064  \n",
+       "  83 -0.610991  0.785625    0.699832    4.016378    0.379526  \n",
+       "  84  0.453180  0.910186   -0.067159    5.759486    0.021904  \n",
+       "  85  2.277608  1.523195   -1.051397    3.528289    1.130149  \n",
+       "  86  1.853892 -0.844085   -0.408741   -1.114235    1.775119  \n",
+       "  87  0.493892  0.103921   -1.304480   -3.327790    2.744288  \n",
+       "  88  0.112699 -0.175311    0.475266   -3.226895    0.533065  \n",
+       "  89 -0.001318 -1.215088   -1.031362   -1.285630   -0.312166  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.541825  1.120159 -3.811405  0.083991  0.808471 -2.597957 -0.258621   \n",
+       "  61 -0.258621  3.354138 -0.434448  1.147658  0.744841 -1.083955 -1.193483   \n",
+       "  62 -1.193483  1.827391  2.787805  1.514345  0.271237  1.253287 -0.015886   \n",
+       "  63 -0.015886  0.475725  2.331243  1.234283 -0.246986  1.860868  0.147868   \n",
+       "  64  0.147868 -1.275006  1.786470 -0.423528 -0.286664  0.461110  1.246658   \n",
+       "  65  1.246658 -1.310302 -1.592064 -0.394603 -0.898844 -0.611727  0.551620   \n",
+       "  66  0.551620  1.251550  0.101952  0.148827 -0.376403 -0.279978 -1.466841   \n",
+       "  67 -1.466841  1.725379 -0.863156  1.450324 -0.596003 -0.175088 -2.050649   \n",
+       "  68 -2.050649  4.506352  0.521717 -0.515446  0.694077 -1.519883 -1.113994   \n",
+       "  69 -1.113994  0.784093  0.853355 -1.009782  2.287767 -0.317357 -0.677212   \n",
+       "  70 -0.677212  0.453301  1.709507 -0.120520  1.793377  0.086223  0.275864   \n",
+       "  71  0.275864 -1.942727  1.555109  0.635124  0.798136  1.705499 -0.355449   \n",
+       "  72 -0.355449 -1.493376 -0.964329  0.519558 -0.391140 -0.135953  0.734065   \n",
+       "  73  0.734065 -1.486809 -1.263921 -0.246104 -1.044259  0.286109  0.194473   \n",
+       "  74  0.194473  1.597110 -0.832935 -0.168239  0.112321 -0.440165 -1.530858   \n",
+       "  75 -1.530858  1.868198  1.054238 -0.070644 -1.462346 -2.112274 -0.790124   \n",
+       "  76 -0.790124  1.627032  0.074164  0.062115  0.403590 -2.220162 -0.067797   \n",
+       "  77 -0.067797 -0.504092  1.436010 -0.618412  0.598467 -0.936203  1.473607   \n",
+       "  78  1.473607 -3.337738  1.198604 -0.824122  0.453057  1.770174  1.109526   \n",
+       "  79  1.109526 -3.011664  0.076764  0.406991  1.974256  2.820162 -1.577588   \n",
+       "  80 -1.577588 -0.918120 -0.448286 -0.475381 -1.429105  2.414385 -2.890452   \n",
+       "  81 -2.890452 -0.799209 -0.070208 -2.424808 -1.914444  0.577235 -1.653448   \n",
+       "  82 -1.653448  0.492866 -1.820824 -0.798814 -1.196111 -1.455887  0.100210   \n",
+       "  83  0.100210  2.144391  0.068399 -0.644657  0.633674 -2.271418  0.366661   \n",
+       "  84  0.366661  1.743662  1.122079 -1.158773  2.018689 -1.617997  1.861555   \n",
+       "  85  1.861555 -0.834139 -0.395158  0.001227  2.817887 -0.090428  1.286897   \n",
+       "  86  1.286897 -0.496548 -0.804785  0.834663 -0.563643  2.690321 -1.277605   \n",
+       "  87 -1.277605 -0.406843 -1.667944  1.478758 -2.090977  1.570284 -1.813501   \n",
+       "  88 -1.813501 -0.177253 -1.215594  0.515979 -2.866923 -0.632807 -0.252096   \n",
+       "  89 -0.252096  0.965131 -0.956625 -0.021032 -1.759588 -2.537146  0.842326   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  3.354138 -0.434448    1.147658    0.744841   -1.083955  \n",
+       "  61  1.827391  2.787805    1.514345    0.271237    1.253287  \n",
+       "  62  0.475725  2.331243    1.234283   -0.246986    1.860868  \n",
+       "  63 -1.275006  1.786470   -0.423528   -0.286664    0.461110  \n",
+       "  64 -1.310302 -1.592064   -0.394603   -0.898844   -0.611727  \n",
+       "  65  1.251550  0.101952    0.148827   -0.376403   -0.279978  \n",
+       "  66  1.725379 -0.863156    1.450324   -0.596003   -0.175088  \n",
+       "  67  4.506352  0.521717   -0.515446    0.694077   -1.519883  \n",
+       "  68  0.784093  0.853355   -1.009782    2.287767   -0.317357  \n",
+       "  69  0.453301  1.709507   -0.120520    1.793377    0.086223  \n",
+       "  70 -1.942727  1.555109    0.635124    0.798136    1.705499  \n",
+       "  71 -1.493376 -0.964329    0.519558   -0.391140   -0.135953  \n",
+       "  72 -1.486809 -1.263921   -0.246104   -1.044259    0.286109  \n",
+       "  73  1.597110 -0.832935   -0.168239    0.112321   -0.440165  \n",
+       "  74  1.868198  1.054238   -0.070644   -1.462346   -2.112274  \n",
+       "  75  1.627032  0.074164    0.062115    0.403590   -2.220162  \n",
+       "  76 -0.504092  1.436010   -0.618412    0.598467   -0.936203  \n",
+       "  77 -3.337738  1.198604   -0.824122    0.453057    1.770174  \n",
+       "  78 -3.011664  0.076764    0.406991    1.974256    2.820162  \n",
+       "  79 -0.918120 -0.448286   -0.475381   -1.429105    2.414385  \n",
+       "  80 -0.799209 -0.070208   -2.424808   -1.914444    0.577235  \n",
+       "  81  0.492866 -1.820824   -0.798814   -1.196111   -1.455887  \n",
+       "  82  2.144391  0.068399   -0.644657    0.633674   -2.271418  \n",
+       "  83  1.743662  1.122079   -1.158773    2.018689   -1.617997  \n",
+       "  84 -0.834139 -0.395158    0.001227    2.817887   -0.090428  \n",
+       "  85 -0.496548 -0.804785    0.834663   -0.563643    2.690321  \n",
+       "  86 -0.406843 -1.667944    1.478758   -2.090977    1.570284  \n",
+       "  87 -0.177253 -1.215594    0.515979   -2.866923   -0.632807  \n",
+       "  88  0.965131 -0.956625   -0.021032   -1.759588   -2.537146  \n",
+       "  89  2.453053  0.986591   -0.818892    0.534551   -1.500883  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.610707  1.371179 -0.034546  0.575024  0.063405 -1.284970  1.230269   \n",
+       "  61  1.230269  0.977326  0.191987  1.296904  0.831318 -2.163235  3.476596   \n",
+       "  62  3.476596  0.143280  2.241575  1.707632  0.507086  0.089134  1.881142   \n",
+       "  63  1.881142  0.261148  0.235130  1.043072  0.648907  0.993807  1.698983   \n",
+       "  64  1.698983 -2.295103 -2.658509  0.451769  1.353231  0.959745  0.181180   \n",
+       "  65  0.181180  0.446498 -3.298504 -1.564741  0.573507  0.064898 -2.152398   \n",
+       "  66 -2.152398 -0.293900 -1.780434  0.161818 -0.974486  0.719820 -0.056564   \n",
+       "  67 -0.056564  1.595197  0.550574  0.397405  0.329018 -0.886243 -0.802238   \n",
+       "  68 -0.802238  1.780317  2.569567  0.962017 -0.769759 -0.850789 -0.912028   \n",
+       "  69 -0.912028  1.550546  4.023653 -0.408617 -1.469642  0.460816  0.397690   \n",
+       "  70  0.397690  1.100039  2.667615 -0.037787 -1.990070  0.689738  1.192882   \n",
+       "  71  1.192882  1.891119 -0.859181 -1.341961 -1.194899  0.875529 -0.413597   \n",
+       "  72 -0.413597  0.083400 -3.444629  1.276378  0.266088  0.597908 -1.967082   \n",
+       "  73 -1.967082 -0.929074 -2.467368  1.241989  1.076004 -0.194670 -1.466065   \n",
+       "  74 -1.466065 -1.895080 -0.546580  1.477755  0.666273 -0.105443 -0.390681   \n",
+       "  75 -0.390681 -1.134304  1.028580 -0.530955  0.235136  1.008962  2.370573   \n",
+       "  76  2.370573  1.143074  1.257146 -1.161119 -0.429170  0.435294  2.519267   \n",
+       "  77  2.519267  1.716484  1.322954  0.515357 -0.860545  1.003338  2.329886   \n",
+       "  78  2.329886  1.795702  0.606135  0.484185 -0.644405 -0.618935  0.733668   \n",
+       "  79  0.733668  1.099595 -1.954766  0.380603  0.827316 -1.487622 -2.341298   \n",
+       "  80 -2.341298  0.222770 -3.129682 -0.568563  0.109213 -0.708357 -1.741419   \n",
+       "  81 -1.741419  0.179238 -1.156191  0.004197 -0.691917  1.341180 -1.094898   \n",
+       "  82 -1.094898 -2.306750  0.511482 -1.433657 -2.519554  1.312169 -0.871998   \n",
+       "  83 -0.871998 -2.450142  4.064651  0.264109 -1.525674  0.161924  1.369335   \n",
+       "  84  1.369335 -0.228935  3.167370  2.030271 -0.366488 -0.892391  2.673040   \n",
+       "  85  2.673040  2.081544 -0.412855  1.793252  1.412931 -0.062202  3.788712   \n",
+       "  86  3.788712  3.139995 -2.181413  0.291079  1.727583 -0.625297  1.101140   \n",
+       "  87  1.101140  3.477356 -1.549714 -1.861248  0.660776 -0.588776 -3.465928   \n",
+       "  88 -3.465928  0.916347  1.234603 -2.463092 -0.807784 -0.184374 -3.251520   \n",
+       "  89 -3.251520  0.196648  2.403762 -1.794867 -1.992312  0.611719 -1.784604   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.977326  0.191987    1.296904    0.831318   -2.163235  \n",
+       "  61  0.143280  2.241575    1.707632    0.507086    0.089134  \n",
+       "  62  0.261148  0.235130    1.043072    0.648907    0.993807  \n",
+       "  63 -2.295103 -2.658509    0.451769    1.353231    0.959745  \n",
+       "  64  0.446498 -3.298504   -1.564741    0.573507    0.064898  \n",
+       "  65 -0.293900 -1.780434    0.161818   -0.974486    0.719820  \n",
+       "  66  1.595197  0.550574    0.397405    0.329018   -0.886243  \n",
+       "  67  1.780317  2.569567    0.962017   -0.769759   -0.850789  \n",
+       "  68  1.550546  4.023653   -0.408617   -1.469642    0.460816  \n",
+       "  69  1.100039  2.667615   -0.037787   -1.990070    0.689738  \n",
+       "  70  1.891119 -0.859181   -1.341961   -1.194899    0.875529  \n",
+       "  71  0.083400 -3.444629    1.276378    0.266088    0.597908  \n",
+       "  72 -0.929074 -2.467368    1.241989    1.076004   -0.194670  \n",
+       "  73 -1.895080 -0.546580    1.477755    0.666273   -0.105443  \n",
+       "  74 -1.134304  1.028580   -0.530955    0.235136    1.008962  \n",
+       "  75  1.143074  1.257146   -1.161119   -0.429170    0.435294  \n",
+       "  76  1.716484  1.322954    0.515357   -0.860545    1.003338  \n",
+       "  77  1.795702  0.606135    0.484185   -0.644405   -0.618935  \n",
+       "  78  1.099595 -1.954766    0.380603    0.827316   -1.487622  \n",
+       "  79  0.222770 -3.129682   -0.568563    0.109213   -0.708357  \n",
+       "  80  0.179238 -1.156191    0.004197   -0.691917    1.341180  \n",
+       "  81 -2.306750  0.511482   -1.433657   -2.519554    1.312169  \n",
+       "  82 -2.450142  4.064651    0.264109   -1.525674    0.161924  \n",
+       "  83 -0.228935  3.167370    2.030271   -0.366488   -0.892391  \n",
+       "  84  2.081544 -0.412855    1.793252    1.412931   -0.062202  \n",
+       "  85  3.139995 -2.181413    0.291079    1.727583   -0.625297  \n",
+       "  86  3.477356 -1.549714   -1.861248    0.660776   -0.588776  \n",
+       "  87  0.916347  1.234603   -2.463092   -0.807784   -0.184374  \n",
+       "  88  0.196648  2.403762   -1.794867   -1.992312    0.611719  \n",
+       "  89  0.125869  1.477406    1.349440   -1.322504    0.509294  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.234760  2.989016  0.528748 -1.182286  1.231493  1.072577  0.526181   \n",
+       "  61  0.526181  3.277077  0.501605 -0.312934 -0.948925  0.825625  0.019918   \n",
+       "  62  0.019918  0.664222  0.179991 -0.217420 -0.943029 -0.024018 -1.304581   \n",
+       "  63 -1.304581 -2.456909  0.082226 -0.832791 -0.317924 -2.106387 -0.479873   \n",
+       "  64 -0.479873 -1.993448  0.290292 -0.403452 -0.470986 -3.028290 -0.450147   \n",
+       "  65 -0.450147 -1.030192 -0.834576 -0.411997 -0.125073 -1.041438  1.536032   \n",
+       "  66  1.536032  0.725868 -1.796604  1.994818 -0.274982 -0.550775  0.393386   \n",
+       "  67  0.393386  1.572938 -0.940266  1.484033 -0.891856  1.877125  1.457135   \n",
+       "  68  1.457135  0.167545  0.896997 -1.026276 -0.765759  2.639266 -0.963552   \n",
+       "  69 -0.963552 -0.227954  3.923042 -2.502902 -0.241628  1.286070 -2.976237   \n",
+       "  70 -2.976237 -1.919862  3.621893 -1.581883  0.122843  0.323945 -1.534757   \n",
+       "  71 -1.534757 -3.261174  0.658382 -0.314782 -1.712093 -1.820405 -0.191403   \n",
+       "  72 -0.191403 -3.035443 -2.221915  1.646071 -1.994747 -1.222010  3.569117   \n",
+       "  73  3.569117 -0.064941 -3.931866  4.447516 -1.731809 -1.264840  2.120177   \n",
+       "  74  2.120177  2.000763 -2.688302  4.418267  0.720911 -0.552541  0.559687   \n",
+       "  75  0.559687  2.388950 -0.558741  0.342316  2.211136  0.160668 -2.004504   \n",
+       "  76 -2.004504  2.387879  2.791549 -3.626864  2.497297 -1.042424 -2.502157   \n",
+       "  77 -2.502157  0.225871  1.300311 -6.163266  1.114514 -0.478726 -1.687455   \n",
+       "  78 -1.687455 -1.278735  1.386269 -1.250504 -1.298757 -1.029316 -0.479914   \n",
+       "  79 -0.479914 -1.022931  0.302015  2.182299 -3.049618  1.704622  0.872687   \n",
+       "  80  0.872687 -1.029589  0.327059  3.429953 -0.741949  2.711257  0.469743   \n",
+       "  81  0.469743  0.406448 -0.060700  2.236191 -0.016861  1.268259 -0.105023   \n",
+       "  82 -0.105023  2.615751 -0.495436 -0.390006  1.891217  0.173120 -1.289290   \n",
+       "  83 -1.289290  1.197222 -0.563314 -2.925364  2.998844 -1.859861  0.139991   \n",
+       "  84  0.139991  0.309326 -0.834606 -1.311656  2.022687 -1.437861  1.028792   \n",
+       "  85  1.028792 -2.505739 -1.896065  1.533578  0.234542 -0.798793  0.963609   \n",
+       "  86  0.963609 -0.187461 -1.299613  3.289499 -1.583584  1.945300  1.085450   \n",
+       "  87  1.085450 -0.590949  1.377019  2.286042 -2.612805  3.066540  0.344841   \n",
+       "  88  0.344841  0.609448  0.552117  0.132806 -2.030065  0.043373  0.665908   \n",
+       "  89  0.665908  1.928572  0.312337 -2.564483 -1.023827 -2.105581 -1.557568   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  3.277077  0.501605   -0.312934   -0.948925    0.825625  \n",
+       "  61  0.664222  0.179991   -0.217420   -0.943029   -0.024018  \n",
+       "  62 -2.456909  0.082226   -0.832791   -0.317924   -2.106387  \n",
+       "  63 -1.993448  0.290292   -0.403452   -0.470986   -3.028290  \n",
+       "  64 -1.030192 -0.834576   -0.411997   -0.125073   -1.041438  \n",
+       "  65  0.725868 -1.796604    1.994818   -0.274982   -0.550775  \n",
+       "  66  1.572938 -0.940266    1.484033   -0.891856    1.877125  \n",
+       "  67  0.167545  0.896997   -1.026276   -0.765759    2.639266  \n",
+       "  68 -0.227954  3.923042   -2.502902   -0.241628    1.286070  \n",
+       "  69 -1.919862  3.621893   -1.581883    0.122843    0.323945  \n",
+       "  70 -3.261174  0.658382   -0.314782   -1.712093   -1.820405  \n",
+       "  71 -3.035443 -2.221915    1.646071   -1.994747   -1.222010  \n",
+       "  72 -0.064941 -3.931866    4.447516   -1.731809   -1.264840  \n",
+       "  73  2.000763 -2.688302    4.418267    0.720911   -0.552541  \n",
+       "  74  2.388950 -0.558741    0.342316    2.211136    0.160668  \n",
+       "  75  2.387879  2.791549   -3.626864    2.497297   -1.042424  \n",
+       "  76  0.225871  1.300311   -6.163266    1.114514   -0.478726  \n",
+       "  77 -1.278735  1.386269   -1.250504   -1.298757   -1.029316  \n",
+       "  78 -1.022931  0.302015    2.182299   -3.049618    1.704622  \n",
+       "  79 -1.029589  0.327059    3.429953   -0.741949    2.711257  \n",
+       "  80  0.406448 -0.060700    2.236191   -0.016861    1.268259  \n",
+       "  81  2.615751 -0.495436   -0.390006    1.891217    0.173120  \n",
+       "  82  1.197222 -0.563314   -2.925364    2.998844   -1.859861  \n",
+       "  83  0.309326 -0.834606   -1.311656    2.022687   -1.437861  \n",
+       "  84 -2.505739 -1.896065    1.533578    0.234542   -0.798793  \n",
+       "  85 -0.187461 -1.299613    3.289499   -1.583584    1.945300  \n",
+       "  86 -0.590949  1.377019    2.286042   -2.612805    3.066540  \n",
+       "  87  0.609448  0.552117    0.132806   -2.030065    0.043373  \n",
+       "  88  1.928572  0.312337   -2.564483   -1.023827   -2.105581  \n",
+       "  89  1.879642 -0.257159   -2.380335    1.071873   -1.540923  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  3.262865 -0.998738 -2.225457 -0.270655 -0.335106  1.169663  2.857702   \n",
+       "  61  2.857702 -1.651232 -2.075401  0.811543 -0.396383 -0.012729  1.592541   \n",
+       "  62  1.592541  0.588509 -0.766591  2.884348 -0.788493  1.064877 -1.371235   \n",
+       "  63 -1.371235  2.838621  1.765412  1.528076  0.623929 -0.053066 -2.974887   \n",
+       "  64 -2.974887  2.720293  2.050827  1.383186  1.379242  0.750671 -1.561395   \n",
+       "  65 -1.561395  1.331196 -0.522120 -1.220484  0.159438  0.275418 -0.493095   \n",
+       "  66 -0.493095  0.026952 -1.268773 -3.354351  2.348704  0.639935  0.890087   \n",
+       "  67  0.890087 -2.124379 -2.046520 -0.950884  2.855904  0.307000  2.020316   \n",
+       "  68  2.020316 -2.670335 -0.902512  1.245655  0.629129  0.299759  1.064006   \n",
+       "  69  1.064006 -1.056181 -0.184485  2.437298 -0.982714 -0.860268  0.330127   \n",
+       "  70  0.330127  0.804237  1.176660  2.251727 -2.526648 -1.382603 -3.237305   \n",
+       "  71 -3.237305  2.999485  0.830707  0.150727 -3.139435 -2.488903 -3.593213   \n",
+       "  72 -3.593213  3.290378 -0.738335 -1.129431  0.415106 -0.785124  0.006466   \n",
+       "  73  0.006466  0.761416 -1.664562 -2.280732  2.928816  1.001666  3.117567   \n",
+       "  74  3.117567 -1.726211 -2.009004 -2.158772  5.648352  1.312691  5.297028   \n",
+       "  75  5.297028 -2.558293 -1.357651 -0.624157  3.396497  2.918646  3.037272   \n",
+       "  76  3.037272 -1.208592 -0.855416  0.110215 -2.830853  0.987387  0.347522   \n",
+       "  77  0.347522 -0.037173  0.055371  1.490620 -4.308259 -0.839575 -3.997416   \n",
+       "  78 -3.997416  0.549323  1.306851  2.933926 -3.233216 -2.790849 -4.269360   \n",
+       "  79 -4.269360 -0.660096  1.827394  1.147987  0.053580 -2.457523 -4.304405   \n",
+       "  80 -4.304405 -3.365532  1.361072 -0.496627  2.380230 -0.306221  3.086323   \n",
+       "  81  3.086323 -4.955508  0.323198 -2.673871  3.455040  1.229024  5.625039   \n",
+       "  82  5.625039 -2.562852 -0.990488 -3.923446  2.916201  4.535887  5.368636   \n",
+       "  83  5.368636 -1.573926 -0.570342 -0.832130 -0.146385  2.184667 -0.781668   \n",
+       "  84 -0.781668  1.693602 -0.580889  2.296095 -2.086119  0.347865 -5.433085   \n",
+       "  85 -5.433085  2.198580 -1.130030  5.082360 -0.594642 -2.189126 -4.287193   \n",
+       "  86 -4.287193  2.273405 -0.808077  4.206239 -1.127258 -3.180984 -0.340714   \n",
+       "  87 -0.340714  1.075434  0.365584  1.835434  0.073062 -1.855402  3.804668   \n",
+       "  88  3.804668 -1.140799 -0.665286 -1.199595 -1.464257  1.947387  4.658658   \n",
+       "  89  4.658658 -3.060021  0.818628 -1.717086  0.441083  4.775016  2.428994   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.651232 -2.075401    0.811543   -0.396383   -0.012729  \n",
+       "  61  0.588509 -0.766591    2.884348   -0.788493    1.064877  \n",
+       "  62  2.838621  1.765412    1.528076    0.623929   -0.053066  \n",
+       "  63  2.720293  2.050827    1.383186    1.379242    0.750671  \n",
+       "  64  1.331196 -0.522120   -1.220484    0.159438    0.275418  \n",
+       "  65  0.026952 -1.268773   -3.354351    2.348704    0.639935  \n",
+       "  66 -2.124379 -2.046520   -0.950884    2.855904    0.307000  \n",
+       "  67 -2.670335 -0.902512    1.245655    0.629129    0.299759  \n",
+       "  68 -1.056181 -0.184485    2.437298   -0.982714   -0.860268  \n",
+       "  69  0.804237  1.176660    2.251727   -2.526648   -1.382603  \n",
+       "  70  2.999485  0.830707    0.150727   -3.139435   -2.488903  \n",
+       "  71  3.290378 -0.738335   -1.129431    0.415106   -0.785124  \n",
+       "  72  0.761416 -1.664562   -2.280732    2.928816    1.001666  \n",
+       "  73 -1.726211 -2.009004   -2.158772    5.648352    1.312691  \n",
+       "  74 -2.558293 -1.357651   -0.624157    3.396497    2.918646  \n",
+       "  75 -1.208592 -0.855416    0.110215   -2.830853    0.987387  \n",
+       "  76 -0.037173  0.055371    1.490620   -4.308259   -0.839575  \n",
+       "  77  0.549323  1.306851    2.933926   -3.233216   -2.790849  \n",
+       "  78 -0.660096  1.827394    1.147987    0.053580   -2.457523  \n",
+       "  79 -3.365532  1.361072   -0.496627    2.380230   -0.306221  \n",
+       "  80 -4.955508  0.323198   -2.673871    3.455040    1.229024  \n",
+       "  81 -2.562852 -0.990488   -3.923446    2.916201    4.535887  \n",
+       "  82 -1.573926 -0.570342   -0.832130   -0.146385    2.184667  \n",
+       "  83  1.693602 -0.580889    2.296095   -2.086119    0.347865  \n",
+       "  84  2.198580 -1.130030    5.082360   -0.594642   -2.189126  \n",
+       "  85  2.273405 -0.808077    4.206239   -1.127258   -3.180984  \n",
+       "  86  1.075434  0.365584    1.835434    0.073062   -1.855402  \n",
+       "  87 -1.140799 -0.665286   -1.199595   -1.464257    1.947387  \n",
+       "  88 -3.060021  0.818628   -1.717086    0.441083    4.775016  \n",
+       "  89 -1.438413 -0.838479   -0.242172   -1.434628    2.037590  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  0.061899 -4.148564 -1.765435 -0.359470 -1.822180 -0.247190 -0.700963   \n",
+       "  61 -0.700963 -0.820251 -1.043994  1.356703 -1.423421  1.382552 -1.744184   \n",
+       "  62 -1.744184  1.497204 -0.798447  1.996459 -0.210120  2.269137 -1.685723   \n",
+       "  63 -1.685723  2.463315  1.225354 -1.036232  1.958403  1.046931  0.023875   \n",
+       "  64  0.023875  1.900196  1.742493 -1.840338  3.789354 -1.510794  0.439851   \n",
+       "  65  0.439851 -1.511178  1.122066 -3.238754  3.033248 -3.030950  1.241101   \n",
+       "  66  1.241101 -3.249206 -1.156793 -1.175318 -1.562454 -2.286322 -0.712275   \n",
+       "  67 -0.712275 -2.426949 -1.005932  1.021686 -4.712102  0.025392 -1.301948   \n",
+       "  68 -1.301948 -0.537148 -0.892291  3.412579 -5.668334  1.311899 -2.281669   \n",
+       "  69 -2.281669  2.370137  1.303178  1.935428 -2.952765  2.068329  2.300175   \n",
+       "  70  2.300175  3.727753 -0.317049  0.649624  0.080242  0.292405  2.272390   \n",
+       "  71  2.272390  3.545140 -0.471687 -1.292702  2.223902 -1.060196  2.157472   \n",
+       "  72  2.157472 -0.598735 -2.743018 -1.901808  1.393607 -0.972781 -0.344465   \n",
+       "  73 -0.344465 -4.223598 -2.839396 -0.822359  0.678123 -0.344902 -2.358678   \n",
+       "  74 -2.358678 -4.661940 -1.181193 -2.027079 -0.148825 -0.741945 -2.135220   \n",
+       "  75 -2.135220 -0.590039  0.646658  0.079636 -2.427659  0.555466 -0.087501   \n",
+       "  76 -0.087501  3.174174  2.094352  1.150575 -0.802575  1.065682  0.029646   \n",
+       "  77  0.029646  2.738902  0.922025  2.351633  0.047470  2.226185  2.445064   \n",
+       "  78  2.445064 -1.325723  1.081020  2.855624  0.623979  2.570099  2.307159   \n",
+       "  79  2.307159 -2.318471 -0.738894  0.540435  0.560705  0.967681  2.451906   \n",
+       "  80  2.451906 -3.086457 -2.098244 -0.920443  0.045118 -0.246631  0.225767   \n",
+       "  81  0.225767 -1.040014 -0.839991 -2.576032  0.592540  0.488488 -3.234246   \n",
+       "  82 -3.234246  1.134267 -0.445092 -2.639505 -0.421573 -0.102867 -3.387468   \n",
+       "  83 -3.387468  1.347078  1.692721 -0.603946 -1.804525 -2.424867 -1.301384   \n",
+       "  84 -1.301384  0.724904  1.039654  2.816397 -0.900884 -1.244191  0.120735   \n",
+       "  85  0.120735  0.159092  0.756535  3.325421 -0.257398 -1.375548  2.986653   \n",
+       "  86  2.986653  0.060471 -0.824702  2.394721 -0.577602  0.271222  3.773625   \n",
+       "  87  3.773625  0.631030 -0.135607 -0.560903  1.162573  0.483151  3.536276   \n",
+       "  88  3.536276  0.982720 -1.439663 -2.529233 -0.896999 -0.888065 -1.845284   \n",
+       "  89 -1.845284 -0.871012 -0.665207 -1.018938 -0.360740 -1.069991 -4.584388   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -0.820251 -1.043994    1.356703   -1.423421    1.382552  \n",
+       "  61  1.497204 -0.798447    1.996459   -0.210120    2.269137  \n",
+       "  62  2.463315  1.225354   -1.036232    1.958403    1.046931  \n",
+       "  63  1.900196  1.742493   -1.840338    3.789354   -1.510794  \n",
+       "  64 -1.511178  1.122066   -3.238754    3.033248   -3.030950  \n",
+       "  65 -3.249206 -1.156793   -1.175318   -1.562454   -2.286322  \n",
+       "  66 -2.426949 -1.005932    1.021686   -4.712102    0.025392  \n",
+       "  67 -0.537148 -0.892291    3.412579   -5.668334    1.311899  \n",
+       "  68  2.370137  1.303178    1.935428   -2.952765    2.068329  \n",
+       "  69  3.727753 -0.317049    0.649624    0.080242    0.292405  \n",
+       "  70  3.545140 -0.471687   -1.292702    2.223902   -1.060196  \n",
+       "  71 -0.598735 -2.743018   -1.901808    1.393607   -0.972781  \n",
+       "  72 -4.223598 -2.839396   -0.822359    0.678123   -0.344902  \n",
+       "  73 -4.661940 -1.181193   -2.027079   -0.148825   -0.741945  \n",
+       "  74 -0.590039  0.646658    0.079636   -2.427659    0.555466  \n",
+       "  75  3.174174  2.094352    1.150575   -0.802575    1.065682  \n",
+       "  76  2.738902  0.922025    2.351633    0.047470    2.226185  \n",
+       "  77 -1.325723  1.081020    2.855624    0.623979    2.570099  \n",
+       "  78 -2.318471 -0.738894    0.540435    0.560705    0.967681  \n",
+       "  79 -3.086457 -2.098244   -0.920443    0.045118   -0.246631  \n",
+       "  80 -1.040014 -0.839991   -2.576032    0.592540    0.488488  \n",
+       "  81  1.134267 -0.445092   -2.639505   -0.421573   -0.102867  \n",
+       "  82  1.347078  1.692721   -0.603946   -1.804525   -2.424867  \n",
+       "  83  0.724904  1.039654    2.816397   -0.900884   -1.244191  \n",
+       "  84  0.159092  0.756535    3.325421   -0.257398   -1.375548  \n",
+       "  85  0.060471 -0.824702    2.394721   -0.577602    0.271222  \n",
+       "  86  0.631030 -0.135607   -0.560903    1.162573    0.483151  \n",
+       "  87  0.982720 -1.439663   -2.529233   -0.896999   -0.888065  \n",
+       "  88 -0.871012 -0.665207   -1.018938   -0.360740   -1.069991  \n",
+       "  89 -1.153338 -0.779293    0.124251   -1.208025   -0.678118  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  0.491014  2.158864 -1.276885  1.538736 -1.786920  1.667961  0.280436   \n",
+       "  61  0.280436  0.629828 -1.827539  2.738483 -0.675962  0.172913 -0.785412   \n",
+       "  62 -0.785412 -1.769622 -1.002571  1.206167 -1.015079 -2.298656 -0.255673   \n",
+       "  63 -0.255673 -1.397822  2.405598 -0.567687 -0.181514 -2.829452  0.789342   \n",
+       "  64  0.789342 -0.895802  2.850276 -0.486300  0.703019 -3.399185 -0.629827   \n",
+       "  65 -0.629827  2.204206  1.028156  0.065218  0.388578 -0.763919 -1.189322   \n",
+       "  66 -1.189322  1.335813  0.257509 -0.769415  1.118270  0.760246 -3.030687   \n",
+       "  67 -3.030687  0.178033 -2.305563  0.177095 -1.695217  3.286245 -2.577645   \n",
+       "  68 -2.577645  0.100602 -1.660623  0.000750 -3.169408  2.514765 -1.391244   \n",
+       "  69 -1.391244 -1.074354 -0.195576  0.345218 -2.156164 -2.185370  2.452457   \n",
+       "  70  2.452457  0.931697  1.813115  0.295440  0.635099 -2.817262  2.818569   \n",
+       "  71  2.818569  0.590252  1.821645  0.376092  2.004902 -3.015877  0.083823   \n",
+       "  72  0.083823  0.848107  2.361806  0.408268  1.611082 -0.377758 -2.610488   \n",
+       "  73 -2.610488  0.691511  0.446377 -1.146696  0.048779  1.061810 -2.793538   \n",
+       "  74 -2.793538 -1.263998 -0.897091 -0.651766 -0.923699  1.105273 -2.733693   \n",
+       "  75 -2.733693 -1.822542 -0.826907  0.189818 -1.025302  0.159337  1.052965   \n",
+       "  76  1.052965 -0.663824 -2.358854  0.729730 -0.844431 -0.777146  4.181226   \n",
+       "  77  4.181226  0.938109  0.444279  1.031860  1.317978 -0.731373  4.557585   \n",
+       "  78  4.557585  0.720967  0.126482 -0.165671  0.436859 -2.060981  1.273518   \n",
+       "  79  1.273518  1.283758  0.244413  0.296860  1.168375 -1.020748 -1.948375   \n",
+       "  80 -1.948375 -1.226101  0.604486 -0.500869  0.298280  0.102682 -4.386791   \n",
+       "  81 -4.386791 -0.494508  0.418634  0.330353 -1.064894  0.146473 -1.879109   \n",
+       "  82 -1.879109  0.551062  1.043869  1.191543 -0.902560  1.936496  0.522988   \n",
+       "  83  0.522988  1.626518  0.072699  0.947041 -0.343573 -0.945035  3.649777   \n",
+       "  84  3.649777 -0.783859 -1.389610 -0.776206 -0.959019 -1.789426  3.331701   \n",
+       "  85  3.331701 -2.114244 -3.808466 -0.808139 -0.509048 -0.221618  2.746009   \n",
+       "  86  2.746009 -2.032002 -2.923907  0.084494  0.615174  1.306685  0.686721   \n",
+       "  87  0.686721 -0.700041 -1.386485 -0.021244  0.453305  2.093774 -2.459898   \n",
+       "  88 -2.459898  1.614380  1.552895  1.463764  0.414330  1.323549 -3.215049   \n",
+       "  89 -3.215049  2.174911  2.495080  1.953343  0.109284  0.027797 -0.961253   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.629828 -1.827539    2.738483   -0.675962    0.172913  \n",
+       "  61 -1.769622 -1.002571    1.206167   -1.015079   -2.298656  \n",
+       "  62 -1.397822  2.405598   -0.567687   -0.181514   -2.829452  \n",
+       "  63 -0.895802  2.850276   -0.486300    0.703019   -3.399185  \n",
+       "  64  2.204206  1.028156    0.065218    0.388578   -0.763919  \n",
+       "  65  1.335813  0.257509   -0.769415    1.118270    0.760246  \n",
+       "  66  0.178033 -2.305563    0.177095   -1.695217    3.286245  \n",
+       "  67  0.100602 -1.660623    0.000750   -3.169408    2.514765  \n",
+       "  68 -1.074354 -0.195576    0.345218   -2.156164   -2.185370  \n",
+       "  69  0.931697  1.813115    0.295440    0.635099   -2.817262  \n",
+       "  70  0.590252  1.821645    0.376092    2.004902   -3.015877  \n",
+       "  71  0.848107  2.361806    0.408268    1.611082   -0.377758  \n",
+       "  72  0.691511  0.446377   -1.146696    0.048779    1.061810  \n",
+       "  73 -1.263998 -0.897091   -0.651766   -0.923699    1.105273  \n",
+       "  74 -1.822542 -0.826907    0.189818   -1.025302    0.159337  \n",
+       "  75 -0.663824 -2.358854    0.729730   -0.844431   -0.777146  \n",
+       "  76  0.938109  0.444279    1.031860    1.317978   -0.731373  \n",
+       "  77  0.720967  0.126482   -0.165671    0.436859   -2.060981  \n",
+       "  78  1.283758  0.244413    0.296860    1.168375   -1.020748  \n",
+       "  79 -1.226101  0.604486   -0.500869    0.298280    0.102682  \n",
+       "  80 -0.494508  0.418634    0.330353   -1.064894    0.146473  \n",
+       "  81  0.551062  1.043869    1.191543   -0.902560    1.936496  \n",
+       "  82  1.626518  0.072699    0.947041   -0.343573   -0.945035  \n",
+       "  83 -0.783859 -1.389610   -0.776206   -0.959019   -1.789426  \n",
+       "  84 -2.114244 -3.808466   -0.808139   -0.509048   -0.221618  \n",
+       "  85 -2.032002 -2.923907    0.084494    0.615174    1.306685  \n",
+       "  86 -0.700041 -1.386485   -0.021244    0.453305    2.093774  \n",
+       "  87  1.614380  1.552895    1.463764    0.414330    1.323549  \n",
+       "  88  2.174911  2.495080    1.953343    0.109284    0.027797  \n",
+       "  89  0.801807  1.495661    1.848330    1.010062   -0.901927  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -2.234305  1.057904 -2.431879  3.996343 -1.888671 -1.001321  0.041524   \n",
+       "  61  0.041524  2.914817  0.385592  2.592526 -2.418986 -0.047214  2.287534   \n",
+       "  62  2.287534  3.124593  2.264874 -0.142733 -0.886073  0.324981  2.216548   \n",
+       "  63  2.216548  1.219234  2.305431 -2.934141  2.347037  0.206114 -0.362595   \n",
+       "  64 -0.362595 -1.958035 -0.583588 -4.545260  2.058527 -1.870397 -1.367243   \n",
+       "  65 -1.367243 -3.331922 -4.031091 -1.366025  1.066488 -2.304902 -0.917193   \n",
+       "  66 -0.917193 -2.439897 -3.071789  0.781930 -1.612261 -1.936815 -1.442161   \n",
+       "  67 -1.442161 -0.740961 -2.488142  4.855436 -1.977300  0.561281  1.126792   \n",
+       "  68  1.126792  1.082806  1.557145  1.915990 -0.985257  1.058603  2.010138   \n",
+       "  69  2.010138  1.830127  1.503359 -0.613999 -0.749473  0.612084  1.229726   \n",
+       "  70  1.229726 -0.717689  1.413590 -3.363352  1.080882 -1.115603 -0.634088   \n",
+       "  71 -0.634088 -0.529395  0.339459 -4.449658  1.054359 -1.497560 -1.883727   \n",
+       "  72 -1.883727 -1.136922  0.085997 -1.681215  1.922623 -1.185294 -3.411172   \n",
+       "  73 -3.411172 -0.166210 -0.905001  1.339099  1.822293  1.152559 -1.271114   \n",
+       "  74 -1.271114  1.318300 -0.040674  2.362472  0.752660  2.067758 -0.630225   \n",
+       "  75 -0.630225  2.885983  1.128876  2.354871 -0.949773  0.849242 -0.906440   \n",
+       "  76 -0.906440  0.547165 -0.106878  0.856628 -1.610376 -0.559398 -0.217868   \n",
+       "  77 -0.217868 -0.357722 -0.361163  0.016239  0.949850 -0.775302  2.076068   \n",
+       "  78  2.076068 -1.824887  0.838648 -1.416676  1.955123  0.846376  1.357089   \n",
+       "  79  1.357089 -1.793211  0.648775 -0.997433  0.423559  1.921088  2.084392   \n",
+       "  80  2.084392  0.635117  1.285481  0.643497 -1.113981  1.165691  1.420715   \n",
+       "  81  1.420715  3.318562  1.157885  1.633008  0.163491 -0.369407 -0.957550   \n",
+       "  82 -0.957550  1.099338  0.062756 -0.335165  0.926208 -0.206248 -2.269373   \n",
+       "  83 -2.269373  0.262264 -0.021714 -0.616804  1.308775 -1.926899 -0.903314   \n",
+       "  84 -0.903314 -0.536685 -1.631701 -1.395834 -0.100663 -1.897773  1.933164   \n",
+       "  85  1.933164 -1.561369 -0.884576  0.187045 -0.293740  0.619188  1.875089   \n",
+       "  86  1.875089 -0.873307 -0.258200  0.982630 -0.913993  2.654418 -0.533306   \n",
+       "  87 -0.533306  1.226978  0.512267  1.350733  0.134545  1.754514 -2.496145   \n",
+       "  88 -2.496145  1.826498  1.345719  1.232539 -0.075482 -0.591318 -2.060195   \n",
+       "  89 -2.060195  1.611081 -0.312066  0.496698 -0.087888 -2.544625 -0.817834   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  2.914817  0.385592    2.592526   -2.418986   -0.047214  \n",
+       "  61  3.124593  2.264874   -0.142733   -0.886073    0.324981  \n",
+       "  62  1.219234  2.305431   -2.934141    2.347037    0.206114  \n",
+       "  63 -1.958035 -0.583588   -4.545260    2.058527   -1.870397  \n",
+       "  64 -3.331922 -4.031091   -1.366025    1.066488   -2.304902  \n",
+       "  65 -2.439897 -3.071789    0.781930   -1.612261   -1.936815  \n",
+       "  66 -0.740961 -2.488142    4.855436   -1.977300    0.561281  \n",
+       "  67  1.082806  1.557145    1.915990   -0.985257    1.058603  \n",
+       "  68  1.830127  1.503359   -0.613999   -0.749473    0.612084  \n",
+       "  69 -0.717689  1.413590   -3.363352    1.080882   -1.115603  \n",
+       "  70 -0.529395  0.339459   -4.449658    1.054359   -1.497560  \n",
+       "  71 -1.136922  0.085997   -1.681215    1.922623   -1.185294  \n",
+       "  72 -0.166210 -0.905001    1.339099    1.822293    1.152559  \n",
+       "  73  1.318300 -0.040674    2.362472    0.752660    2.067758  \n",
+       "  74  2.885983  1.128876    2.354871   -0.949773    0.849242  \n",
+       "  75  0.547165 -0.106878    0.856628   -1.610376   -0.559398  \n",
+       "  76 -0.357722 -0.361163    0.016239    0.949850   -0.775302  \n",
+       "  77 -1.824887  0.838648   -1.416676    1.955123    0.846376  \n",
+       "  78 -1.793211  0.648775   -0.997433    0.423559    1.921088  \n",
+       "  79  0.635117  1.285481    0.643497   -1.113981    1.165691  \n",
+       "  80  3.318562  1.157885    1.633008    0.163491   -0.369407  \n",
+       "  81  1.099338  0.062756   -0.335165    0.926208   -0.206248  \n",
+       "  82  0.262264 -0.021714   -0.616804    1.308775   -1.926899  \n",
+       "  83 -0.536685 -1.631701   -1.395834   -0.100663   -1.897773  \n",
+       "  84 -1.561369 -0.884576    0.187045   -0.293740    0.619188  \n",
+       "  85 -0.873307 -0.258200    0.982630   -0.913993    2.654418  \n",
+       "  86  1.226978  0.512267    1.350733    0.134545    1.754514  \n",
+       "  87  1.826498  1.345719    1.232539   -0.075482   -0.591318  \n",
+       "  88  1.611081 -0.312066    0.496698   -0.087888   -2.544625  \n",
+       "  89 -0.736320 -1.193022    0.021372    0.505670   -1.416145  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  1.881652  1.504533  0.310889  0.624089  1.772759  0.824027  2.998425   \n",
+       "  61  2.998425 -1.230983  0.279751  0.052622  1.526846 -1.181696  2.398990   \n",
+       "  62  2.398990 -2.905943 -0.105857 -2.101467  0.732558 -1.561028 -0.508791   \n",
+       "  63 -0.508791 -0.424025  1.308285 -1.674693 -0.125756 -2.083691 -3.191761   \n",
+       "  64 -3.191761  2.385969  1.355117 -0.893754 -2.439220  0.728704 -3.572512   \n",
+       "  65 -3.572512  2.175467 -0.257525 -1.001727 -2.949535  2.217689 -3.145538   \n",
+       "  66 -3.145538  0.599689 -1.597158 -0.577174 -0.423198  3.604072 -0.778352   \n",
+       "  67 -0.778352 -1.352991  0.305684  0.246157  1.916006  2.587846  2.802134   \n",
+       "  68  2.802134 -1.481878  0.533175  2.813115  2.723080 -0.790438  4.230165   \n",
+       "  69  4.230165 -1.792216  1.141789  2.059568  2.128772 -4.536541  1.802283   \n",
+       "  70  1.802283 -1.393381  0.864187  0.714310  0.711769 -3.123274 -1.552948   \n",
+       "  71 -1.552948  1.120297 -2.272515  0.283128 -2.328881 -0.879676 -2.780352   \n",
+       "  72 -2.780352  0.473938 -3.843004 -0.818302 -1.308259  0.414675 -2.447021   \n",
+       "  73 -2.447021 -0.177863 -2.315591 -0.067213  1.289557  0.459030 -1.718889   \n",
+       "  74 -1.718889 -1.017653  0.183627 -0.573849  2.004149  1.627870  2.058176   \n",
+       "  75  2.058176  0.996134  1.197163 -1.256176  0.668059  1.677391  2.444938   \n",
+       "  76  2.444938  1.645735  1.747388 -1.352645  0.674871  0.621077  2.659391   \n",
+       "  77  2.659391  1.129096  1.211868  0.182050  0.434929 -2.501776  0.068282   \n",
+       "  78  0.068282 -1.935578  0.910026  0.008372  0.531915 -2.830916 -3.026511   \n",
+       "  79 -3.026511 -2.754679 -0.022815 -0.830554 -0.610918 -2.492386 -4.297696   \n",
+       "  80 -4.297696 -0.569996 -0.812599  0.892167 -1.078383  0.515900  0.723050   \n",
+       "  81  0.723050  0.995382 -2.007675  0.391013  0.543290  2.406645  4.058503   \n",
+       "  82  4.058503  1.479418 -1.438861 -2.167264  1.015501  0.878988  7.084350   \n",
+       "  83  7.084350  2.229069 -0.097604 -1.267306  0.583885 -2.346794  3.441263   \n",
+       "  84  3.441263  1.318623  2.313682 -1.662196 -0.946596 -1.819218 -0.776058   \n",
+       "  85 -0.776058  0.278031  2.568129  0.699151 -1.765235 -0.620273 -4.931686   \n",
+       "  86 -4.931686 -2.833365  1.603982  2.260929 -0.771172  1.790663 -4.838825   \n",
+       "  87 -4.838825 -3.367167 -0.341341  2.019524 -0.069833  1.431138 -2.728682   \n",
+       "  88 -2.728682 -2.251032 -1.931032 -0.664019 -0.951134 -0.163226  3.013876   \n",
+       "  89  3.013876 -0.619195 -2.369783 -1.670191  0.329694 -1.325283  6.090772   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.230983  0.279751    0.052622    1.526846   -1.181696  \n",
+       "  61 -2.905943 -0.105857   -2.101467    0.732558   -1.561028  \n",
+       "  62 -0.424025  1.308285   -1.674693   -0.125756   -2.083691  \n",
+       "  63  2.385969  1.355117   -0.893754   -2.439220    0.728704  \n",
+       "  64  2.175467 -0.257525   -1.001727   -2.949535    2.217689  \n",
+       "  65  0.599689 -1.597158   -0.577174   -0.423198    3.604072  \n",
+       "  66 -1.352991  0.305684    0.246157    1.916006    2.587846  \n",
+       "  67 -1.481878  0.533175    2.813115    2.723080   -0.790438  \n",
+       "  68 -1.792216  1.141789    2.059568    2.128772   -4.536541  \n",
+       "  69 -1.393381  0.864187    0.714310    0.711769   -3.123274  \n",
+       "  70  1.120297 -2.272515    0.283128   -2.328881   -0.879676  \n",
+       "  71  0.473938 -3.843004   -0.818302   -1.308259    0.414675  \n",
+       "  72 -0.177863 -2.315591   -0.067213    1.289557    0.459030  \n",
+       "  73 -1.017653  0.183627   -0.573849    2.004149    1.627870  \n",
+       "  74  0.996134  1.197163   -1.256176    0.668059    1.677391  \n",
+       "  75  1.645735  1.747388   -1.352645    0.674871    0.621077  \n",
+       "  76  1.129096  1.211868    0.182050    0.434929   -2.501776  \n",
+       "  77 -1.935578  0.910026    0.008372    0.531915   -2.830916  \n",
+       "  78 -2.754679 -0.022815   -0.830554   -0.610918   -2.492386  \n",
+       "  79 -0.569996 -0.812599    0.892167   -1.078383    0.515900  \n",
+       "  80  0.995382 -2.007675    0.391013    0.543290    2.406645  \n",
+       "  81  1.479418 -1.438861   -2.167264    1.015501    0.878988  \n",
+       "  82  2.229069 -0.097604   -1.267306    0.583885   -2.346794  \n",
+       "  83  1.318623  2.313682   -1.662196   -0.946596   -1.819218  \n",
+       "  84  0.278031  2.568129    0.699151   -1.765235   -0.620273  \n",
+       "  85 -2.833365  1.603982    2.260929   -0.771172    1.790663  \n",
+       "  86 -3.367167 -0.341341    2.019524   -0.069833    1.431138  \n",
+       "  87 -2.251032 -1.931032   -0.664019   -0.951134   -0.163226  \n",
+       "  88 -0.619195 -2.369783   -1.670191    0.329694   -1.325283  \n",
+       "  89  0.612835 -0.554521   -0.578938   -0.357559   -2.341110  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  1.680819 -0.681254  2.627465  3.273730  0.650328 -0.936166  1.228992   \n",
+       "  61  1.228992 -1.488935  2.518781  0.615162  1.407563 -0.456516  1.862195   \n",
+       "  62  1.862195 -2.393755  0.913320 -2.585124  2.090041 -0.175354  0.602650   \n",
+       "  63  0.602650 -0.339711 -0.172080 -4.447160  0.778187  1.535135 -0.260039   \n",
+       "  64 -0.260039  0.580616 -1.571830 -4.902183 -0.959584  2.936794 -1.515716   \n",
+       "  65 -1.515716  1.828092 -1.974693  0.534747 -2.503464  2.438435 -1.485518   \n",
+       "  66 -1.485518  1.525046 -2.592006  5.342490 -2.864387 -0.399905 -2.626184   \n",
+       "  67 -2.626184  2.466658  0.018118  4.875281 -1.056073 -3.616328  0.397835   \n",
+       "  68  0.397835 -0.737224  1.761882  0.142659  1.353457 -4.357649  0.911542   \n",
+       "  69  0.911542 -0.633794  1.874507 -3.083685  0.885859 -1.754117  1.755674   \n",
+       "  70  1.755674 -1.201601  0.705752 -3.612896  0.055418  1.849641  0.446253   \n",
+       "  71  0.446253  0.539970 -2.176662 -2.245288  0.117804  3.525875  0.508387   \n",
+       "  72  0.508387  1.562250 -2.297061  0.360295 -1.002668  3.286808  0.805489   \n",
+       "  73  0.805489  0.306215 -0.476938  2.049031 -0.716267  0.627413 -0.519585   \n",
+       "  74 -0.519585  0.783023  1.966242  4.850647  0.041063 -0.541945 -1.826379   \n",
+       "  75 -1.826379  1.926417  1.034913  2.162924 -0.389304 -0.569663 -2.143826   \n",
+       "  76 -2.143826  2.832732  0.753649 -0.769983 -0.508989 -0.459738 -1.301600   \n",
+       "  77 -1.301600  2.680499 -1.030914 -3.172170 -0.217104  0.991162  0.554854   \n",
+       "  78  0.554854  0.830306 -0.495523 -1.587060 -2.304652  0.108613  0.533382   \n",
+       "  79  0.533382 -0.936879 -0.918761  1.427294 -0.636389  1.352739  1.015069   \n",
+       "  80  1.015069 -0.877705  0.377456  1.509370 -0.601471  0.356580 -0.494456   \n",
+       "  81 -0.494456 -1.644547 -0.025527  0.617111  0.471710 -1.428557 -0.226623   \n",
+       "  82 -0.226623 -0.601503  0.625554 -0.996891  1.807628 -1.050636  0.314559   \n",
+       "  83  0.314559  0.193089  2.324045 -1.012351  0.453360 -0.635838  1.237596   \n",
+       "  84  1.237596 -0.540120  0.475041  0.678177 -0.362982  0.700509  1.071946   \n",
+       "  85  1.071946 -0.659231 -0.439229  1.357625 -1.090722  0.188836  0.581215   \n",
+       "  86  0.581215 -1.962852 -1.432475  1.499102 -1.557974 -0.761958 -0.231633   \n",
+       "  87 -0.231633 -2.553362 -0.461556  2.323088 -1.339376 -1.702678  0.170262   \n",
+       "  88  0.170262 -1.219019  0.981423 -0.596623 -0.059411 -2.055866  0.035747   \n",
+       "  89  0.035747  2.006200  0.880483 -0.514165  1.093089 -1.288274 -1.685527   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.488935  2.518781    0.615162    1.407563   -0.456516  \n",
+       "  61 -2.393755  0.913320   -2.585124    2.090041   -0.175354  \n",
+       "  62 -0.339711 -0.172080   -4.447160    0.778187    1.535135  \n",
+       "  63  0.580616 -1.571830   -4.902183   -0.959584    2.936794  \n",
+       "  64  1.828092 -1.974693    0.534747   -2.503464    2.438435  \n",
+       "  65  1.525046 -2.592006    5.342490   -2.864387   -0.399905  \n",
+       "  66  2.466658  0.018118    4.875281   -1.056073   -3.616328  \n",
+       "  67 -0.737224  1.761882    0.142659    1.353457   -4.357649  \n",
+       "  68 -0.633794  1.874507   -3.083685    0.885859   -1.754117  \n",
+       "  69 -1.201601  0.705752   -3.612896    0.055418    1.849641  \n",
+       "  70  0.539970 -2.176662   -2.245288    0.117804    3.525875  \n",
+       "  71  1.562250 -2.297061    0.360295   -1.002668    3.286808  \n",
+       "  72  0.306215 -0.476938    2.049031   -0.716267    0.627413  \n",
+       "  73  0.783023  1.966242    4.850647    0.041063   -0.541945  \n",
+       "  74  1.926417  1.034913    2.162924   -0.389304   -0.569663  \n",
+       "  75  2.832732  0.753649   -0.769983   -0.508989   -0.459738  \n",
+       "  76  2.680499 -1.030914   -3.172170   -0.217104    0.991162  \n",
+       "  77  0.830306 -0.495523   -1.587060   -2.304652    0.108613  \n",
+       "  78 -0.936879 -0.918761    1.427294   -0.636389    1.352739  \n",
+       "  79 -0.877705  0.377456    1.509370   -0.601471    0.356580  \n",
+       "  80 -1.644547 -0.025527    0.617111    0.471710   -1.428557  \n",
+       "  81 -0.601503  0.625554   -0.996891    1.807628   -1.050636  \n",
+       "  82  0.193089  2.324045   -1.012351    0.453360   -0.635838  \n",
+       "  83 -0.540120  0.475041    0.678177   -0.362982    0.700509  \n",
+       "  84 -0.659231 -0.439229    1.357625   -1.090722    0.188836  \n",
+       "  85 -1.962852 -1.432475    1.499102   -1.557974   -0.761958  \n",
+       "  86 -2.553362 -0.461556    2.323088   -1.339376   -1.702678  \n",
+       "  87 -1.219019  0.981423   -0.596623   -0.059411   -2.055866  \n",
+       "  88  2.006200  0.880483   -0.514165    1.093089   -1.288274  \n",
+       "  89  1.205162  1.054529   -1.784525    2.460425    1.442798  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  1.823529 -1.293195 -0.172053  1.729222  0.207518  1.370205  0.467817   \n",
+       "  61  0.467817  1.293634 -0.448187  2.197368  1.549577  2.595173 -0.593424   \n",
+       "  62 -0.593424  1.369111 -1.399389  0.745228  2.536789  1.738505 -1.543991   \n",
+       "  63 -1.543991  0.502487 -1.110471 -1.961757  1.235868  0.979272 -0.615584   \n",
+       "  64 -0.615584 -0.658409 -0.924924 -3.200424  0.611048 -1.191724  0.077924   \n",
+       "  65  0.077924 -0.924853  0.695470 -3.079045 -1.357561 -2.122748  2.660185   \n",
+       "  66  2.660185 -1.240581  2.849480 -0.147059 -3.113116 -0.327884  2.288580   \n",
+       "  67  2.288580 -0.336916  0.858441  1.838624 -1.959108  0.060819  0.920028   \n",
+       "  68  0.920028  0.607202 -1.506267  3.093163 -0.513181  3.062244  0.556107   \n",
+       "  69  0.556107  1.426576 -2.550172  1.128137  1.867712  1.849391 -1.955670   \n",
+       "  70 -1.955670  1.117844 -3.188923 -1.018385  1.518742  1.813964 -1.105488   \n",
+       "  71 -1.105488  0.746730 -0.037030 -1.949714  2.629842 -2.299988  1.052119   \n",
+       "  72  1.052119 -1.433000  3.579984 -0.862773  0.810627 -3.261968  2.731219   \n",
+       "  73  2.731219 -2.716599  3.015616  0.989027 -0.838462 -1.869832  1.901297   \n",
+       "  74  1.901297 -2.411058  2.051466  2.702027 -0.617981 -0.882119  0.194531   \n",
+       "  75  0.194531  0.311926 -0.541453  0.679058  0.342511 -0.292818 -1.589595   \n",
+       "  76 -1.589595 -1.040254 -0.603181  1.092594  0.781053  0.660527 -1.912187   \n",
+       "  77 -1.912187  0.140156 -0.029513 -1.022639  1.744593  1.131131 -0.466819   \n",
+       "  78 -0.466819 -1.586535  1.543429 -0.957549  1.894467  0.934099  0.902537   \n",
+       "  79  0.902537 -1.516142  1.063423 -0.245065 -0.871214 -0.100747  1.520499   \n",
+       "  80  1.520499  1.142301 -0.758222  0.094534 -0.779546 -1.784133  1.128114   \n",
+       "  81  1.128114  2.790647 -2.470233  1.386057 -1.212917 -2.509134 -0.494991   \n",
+       "  82 -0.494991  2.900042 -2.084146  0.263426 -1.342913 -3.674438 -1.031726   \n",
+       "  83 -1.031726  1.111313 -0.117841 -0.064657 -0.887552 -1.275401 -0.771518   \n",
+       "  84 -0.771518 -0.734321  3.656258 -0.707595  0.614799  0.920814 -0.615447   \n",
+       "  85 -0.615447 -2.042885  4.232662 -0.427151  2.064965  1.218059  1.506048   \n",
+       "  86  1.506048 -3.275256  3.436325 -0.517421  2.811083 -0.015527  0.556946   \n",
+       "  87  0.556946 -3.159522 -0.177244 -0.115255  2.193561  0.065165  0.676699   \n",
+       "  88  0.676699 -1.591200 -3.069664 -0.819659 -0.881490 -0.598842 -1.552696   \n",
+       "  89 -1.552696  0.490795 -4.077221 -1.054793 -3.329401  0.420326 -2.032222   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  1.293634 -0.448187    2.197368    1.549577    2.595173  \n",
+       "  61  1.369111 -1.399389    0.745228    2.536789    1.738505  \n",
+       "  62  0.502487 -1.110471   -1.961757    1.235868    0.979272  \n",
+       "  63 -0.658409 -0.924924   -3.200424    0.611048   -1.191724  \n",
+       "  64 -0.924853  0.695470   -3.079045   -1.357561   -2.122748  \n",
+       "  65 -1.240581  2.849480   -0.147059   -3.113116   -0.327884  \n",
+       "  66 -0.336916  0.858441    1.838624   -1.959108    0.060819  \n",
+       "  67  0.607202 -1.506267    3.093163   -0.513181    3.062244  \n",
+       "  68  1.426576 -2.550172    1.128137    1.867712    1.849391  \n",
+       "  69  1.117844 -3.188923   -1.018385    1.518742    1.813964  \n",
+       "  70  0.746730 -0.037030   -1.949714    2.629842   -2.299988  \n",
+       "  71 -1.433000  3.579984   -0.862773    0.810627   -3.261968  \n",
+       "  72 -2.716599  3.015616    0.989027   -0.838462   -1.869832  \n",
+       "  73 -2.411058  2.051466    2.702027   -0.617981   -0.882119  \n",
+       "  74  0.311926 -0.541453    0.679058    0.342511   -0.292818  \n",
+       "  75 -1.040254 -0.603181    1.092594    0.781053    0.660527  \n",
+       "  76  0.140156 -0.029513   -1.022639    1.744593    1.131131  \n",
+       "  77 -1.586535  1.543429   -0.957549    1.894467    0.934099  \n",
+       "  78 -1.516142  1.063423   -0.245065   -0.871214   -0.100747  \n",
+       "  79  1.142301 -0.758222    0.094534   -0.779546   -1.784133  \n",
+       "  80  2.790647 -2.470233    1.386057   -1.212917   -2.509134  \n",
+       "  81  2.900042 -2.084146    0.263426   -1.342913   -3.674438  \n",
+       "  82  1.111313 -0.117841   -0.064657   -0.887552   -1.275401  \n",
+       "  83 -0.734321  3.656258   -0.707595    0.614799    0.920814  \n",
+       "  84 -2.042885  4.232662   -0.427151    2.064965    1.218059  \n",
+       "  85 -3.275256  3.436325   -0.517421    2.811083   -0.015527  \n",
+       "  86 -3.159522 -0.177244   -0.115255    2.193561    0.065165  \n",
+       "  87 -1.591200 -3.069664   -0.819659   -0.881490   -0.598842  \n",
+       "  88  0.490795 -4.077221   -1.054793   -3.329401    0.420326  \n",
+       "  89  3.723229 -2.239790    0.396676   -3.437313   -1.579182  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -1.259116 -0.385834  1.429974  0.201847 -2.462000  0.740260  1.930155   \n",
+       "  61  1.930155  0.580334  2.082634 -1.909071 -1.135760  0.043369  2.205342   \n",
+       "  62  2.205342  0.161111  0.718701 -1.009798 -0.109405 -0.909381  4.576691   \n",
+       "  63  4.576691  0.311150  0.167796 -1.981883  2.027704 -0.958609 -0.295993   \n",
+       "  64 -0.295993 -1.010519 -0.745160 -1.158973  1.847801 -0.260147 -3.509607   \n",
+       "  65 -3.509607  0.180367  0.338989 -0.486259 -0.228531 -0.427020 -4.343406   \n",
+       "  66 -4.343406  1.171590  0.043313  1.529249 -0.007335 -0.043079 -3.419318   \n",
+       "  67 -3.419318  0.789004  1.119576  1.582930 -1.286082 -0.727652  0.996668   \n",
+       "  68  0.996668  0.351666 -0.610564  0.333912 -0.260968 -0.007976  3.033692   \n",
+       "  69  3.033692  0.243130  0.778245 -1.212264  1.050911  0.869296  3.236630   \n",
+       "  70  3.236630 -0.727589  0.151605 -1.689701  1.522070  0.802358 -0.457178   \n",
+       "  71 -0.457178 -0.690474 -0.825098 -1.492085  0.718846  0.396840 -2.663826   \n",
+       "  72 -2.663826  0.387668 -2.120943  0.097154  0.201686  0.017166 -3.515396   \n",
+       "  73 -3.515396  1.601491 -1.830478  2.796904 -0.454042 -0.360521 -1.087144   \n",
+       "  74 -1.087144  0.121117 -0.084974  3.489552 -1.554192 -1.145096  2.866796   \n",
+       "  75  2.866796 -0.339617  2.371980  1.542942 -0.478600 -0.071287  3.969419   \n",
+       "  76  3.969419 -1.048349  1.328269 -1.705329  1.220301 -1.369072  1.750849   \n",
+       "  77  1.750849 -0.689999  0.216438 -3.741396  0.101721 -0.777888 -2.950256   \n",
+       "  78 -2.950256  0.417833 -0.490479 -1.733803 -1.151889 -1.026007 -4.898972   \n",
+       "  79 -4.898972 -0.245090 -3.979437  0.199305 -0.421011  0.933132 -2.682809   \n",
+       "  80 -2.682809 -0.822971 -4.202475  1.321274  0.475866  0.705312 -0.768914   \n",
+       "  81 -0.768914 -2.403704 -2.757711 -0.388212  2.518883  1.426113  1.347788   \n",
+       "  82  1.347788 -1.885154  1.933246 -0.944390  2.757962 -1.447239  2.515485   \n",
+       "  83  2.515485  1.463268  3.488321 -1.583489  0.784340 -1.549164  1.396114   \n",
+       "  84  1.396114  2.797969  3.546152 -3.137961  0.504622 -1.667585  0.088689   \n",
+       "  85  0.088689  2.419981  0.952885  0.112620  0.968212  0.847453 -1.149665   \n",
+       "  86 -1.149665  1.003526 -1.626336  2.766710  1.479246  1.454935 -1.246927   \n",
+       "  87 -1.246927 -1.689242 -3.194519  1.460712  1.434484  1.952309 -0.071667   \n",
+       "  88 -0.071667 -3.619822 -1.786819 -0.609705 -0.439697 -0.148688  1.717559   \n",
+       "  89  1.717559 -1.891868 -2.613131 -0.905189 -1.677754 -1.617548  3.128830   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.580334  2.082634   -1.909071   -1.135760    0.043369  \n",
+       "  61  0.161111  0.718701   -1.009798   -0.109405   -0.909381  \n",
+       "  62  0.311150  0.167796   -1.981883    2.027704   -0.958609  \n",
+       "  63 -1.010519 -0.745160   -1.158973    1.847801   -0.260147  \n",
+       "  64  0.180367  0.338989   -0.486259   -0.228531   -0.427020  \n",
+       "  65  1.171590  0.043313    1.529249   -0.007335   -0.043079  \n",
+       "  66  0.789004  1.119576    1.582930   -1.286082   -0.727652  \n",
+       "  67  0.351666 -0.610564    0.333912   -0.260968   -0.007976  \n",
+       "  68  0.243130  0.778245   -1.212264    1.050911    0.869296  \n",
+       "  69 -0.727589  0.151605   -1.689701    1.522070    0.802358  \n",
+       "  70 -0.690474 -0.825098   -1.492085    0.718846    0.396840  \n",
+       "  71  0.387668 -2.120943    0.097154    0.201686    0.017166  \n",
+       "  72  1.601491 -1.830478    2.796904   -0.454042   -0.360521  \n",
+       "  73  0.121117 -0.084974    3.489552   -1.554192   -1.145096  \n",
+       "  74 -0.339617  2.371980    1.542942   -0.478600   -0.071287  \n",
+       "  75 -1.048349  1.328269   -1.705329    1.220301   -1.369072  \n",
+       "  76 -0.689999  0.216438   -3.741396    0.101721   -0.777888  \n",
+       "  77  0.417833 -0.490479   -1.733803   -1.151889   -1.026007  \n",
+       "  78 -0.245090 -3.979437    0.199305   -0.421011    0.933132  \n",
+       "  79 -0.822971 -4.202475    1.321274    0.475866    0.705312  \n",
+       "  80 -2.403704 -2.757711   -0.388212    2.518883    1.426113  \n",
+       "  81 -1.885154  1.933246   -0.944390    2.757962   -1.447239  \n",
+       "  82  1.463268  3.488321   -1.583489    0.784340   -1.549164  \n",
+       "  83  2.797969  3.546152   -3.137961    0.504622   -1.667585  \n",
+       "  84  2.419981  0.952885    0.112620    0.968212    0.847453  \n",
+       "  85  1.003526 -1.626336    2.766710    1.479246    1.454935  \n",
+       "  86 -1.689242 -3.194519    1.460712    1.434484    1.952309  \n",
+       "  87 -3.619822 -1.786819   -0.609705   -0.439697   -0.148688  \n",
+       "  88 -1.891868 -2.613131   -0.905189   -1.677754   -1.617548  \n",
+       "  89 -0.048761 -3.352714    0.058197   -2.414288   -1.918953  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.019892  0.208132 -0.662958  0.811238  1.353678 -0.705613  0.915694   \n",
+       "  61  0.915694  0.619417 -2.307087 -2.678355  3.951085  0.148669  0.406500   \n",
+       "  62  0.406500  0.664277  0.683767 -3.798121  2.854007  0.455178 -0.386453   \n",
+       "  63 -0.386453  1.493993  3.222729 -3.078924 -0.398409  2.002940 -2.167966   \n",
+       "  64 -2.167966  1.769673  3.029283 -0.218307 -0.685532  0.605028 -2.122616   \n",
+       "  65 -2.122616 -0.299664  0.996874  2.339748 -1.873393  0.241406 -0.096937   \n",
+       "  66 -0.096937  1.456160 -2.672620  2.867809 -1.082162 -2.597974  1.602911   \n",
+       "  67  1.602911 -1.828873 -3.888179  2.129829 -0.954547 -2.809588  3.880245   \n",
+       "  68  3.880245 -0.608335 -2.126572  0.707961  0.391498 -2.593880  1.882875   \n",
+       "  69  1.882875 -1.514213  0.816344 -1.120501  1.784354 -1.657929 -0.809506   \n",
+       "  70 -0.809506  1.165726  2.131644 -2.356211  1.291720  1.277860 -2.480903   \n",
+       "  71 -2.480903  1.383812  1.362319 -0.389929  1.870995  1.097376 -2.932448   \n",
+       "  72 -2.932448  1.158270  0.026803  0.330682  0.505978  0.053642 -1.781076   \n",
+       "  73 -1.781076  1.048062 -2.703495  1.350165 -2.733252 -0.617690 -0.418806   \n",
+       "  74 -0.418806  0.715334 -1.483783  0.711120 -2.127758 -0.443826  2.309667   \n",
+       "  75  2.309667 -0.922348 -1.969357 -1.827422 -0.313921  1.772170  3.381397   \n",
+       "  76  3.381397 -1.274413 -0.291370 -3.087099  1.959135  1.705189 -0.104565   \n",
+       "  77 -0.104565 -0.254445  0.861890 -1.700481  2.194608 -0.361499 -0.682030   \n",
+       "  78 -0.682030  0.420411  2.078084  1.364096  0.578161 -1.112355 -2.818104   \n",
+       "  79 -2.818104  0.941557  1.118324  2.253539 -0.799357 -1.196283 -1.439287   \n",
+       "  80 -1.439287 -1.246934  0.411409  1.821385 -0.457688 -1.456430  1.423554   \n",
+       "  81  1.423554  0.065390 -1.073365  0.428865  1.987304 -0.957867  2.890136   \n",
+       "  82  2.890136 -0.525534  0.959167 -0.373553 -0.822852  1.741427  2.742616   \n",
+       "  83  2.742616  0.479479  1.143947 -0.474494 -0.486087  0.644314  0.538207   \n",
+       "  84  0.538207  0.067565  0.608003 -1.539780 -0.702191  0.585251 -2.768805   \n",
+       "  85 -2.768805 -1.575151  0.983666 -0.799864  0.525615 -0.342741 -3.047394   \n",
+       "  86 -3.047394  0.447492  1.795983  0.291184  0.372567  0.564388 -3.312656   \n",
+       "  87 -3.312656  0.348356 -0.891524  2.213649  2.091079 -1.249898 -0.587037   \n",
+       "  88 -0.587037  0.298050 -1.772421  2.750544  1.072840 -1.085764  0.343382   \n",
+       "  89  0.343382 -0.394445 -1.689085  1.400441 -0.599305 -2.032167  1.997551   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.619417 -2.307087   -2.678355    3.951085    0.148669  \n",
+       "  61  0.664277  0.683767   -3.798121    2.854007    0.455178  \n",
+       "  62  1.493993  3.222729   -3.078924   -0.398409    2.002940  \n",
+       "  63  1.769673  3.029283   -0.218307   -0.685532    0.605028  \n",
+       "  64 -0.299664  0.996874    2.339748   -1.873393    0.241406  \n",
+       "  65  1.456160 -2.672620    2.867809   -1.082162   -2.597974  \n",
+       "  66 -1.828873 -3.888179    2.129829   -0.954547   -2.809588  \n",
+       "  67 -0.608335 -2.126572    0.707961    0.391498   -2.593880  \n",
+       "  68 -1.514213  0.816344   -1.120501    1.784354   -1.657929  \n",
+       "  69  1.165726  2.131644   -2.356211    1.291720    1.277860  \n",
+       "  70  1.383812  1.362319   -0.389929    1.870995    1.097376  \n",
+       "  71  1.158270  0.026803    0.330682    0.505978    0.053642  \n",
+       "  72  1.048062 -2.703495    1.350165   -2.733252   -0.617690  \n",
+       "  73  0.715334 -1.483783    0.711120   -2.127758   -0.443826  \n",
+       "  74 -0.922348 -1.969357   -1.827422   -0.313921    1.772170  \n",
+       "  75 -1.274413 -0.291370   -3.087099    1.959135    1.705189  \n",
+       "  76 -0.254445  0.861890   -1.700481    2.194608   -0.361499  \n",
+       "  77  0.420411  2.078084    1.364096    0.578161   -1.112355  \n",
+       "  78  0.941557  1.118324    2.253539   -0.799357   -1.196283  \n",
+       "  79 -1.246934  0.411409    1.821385   -0.457688   -1.456430  \n",
+       "  80  0.065390 -1.073365    0.428865    1.987304   -0.957867  \n",
+       "  81 -0.525534  0.959167   -0.373553   -0.822852    1.741427  \n",
+       "  82  0.479479  1.143947   -0.474494   -0.486087    0.644314  \n",
+       "  83  0.067565  0.608003   -1.539780   -0.702191    0.585251  \n",
+       "  84 -1.575151  0.983666   -0.799864    0.525615   -0.342741  \n",
+       "  85  0.447492  1.795983    0.291184    0.372567    0.564388  \n",
+       "  86  0.348356 -0.891524    2.213649    2.091079   -1.249898  \n",
+       "  87  0.298050 -1.772421    2.750544    1.072840   -1.085764  \n",
+       "  88 -0.394445 -1.689085    1.400441   -0.599305   -2.032167  \n",
+       "  89  0.198883 -1.409954    0.252679   -2.525278   -0.619233  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -3.187256 -1.845119  1.464419 -1.450202 -0.886686 -0.839873 -3.401291   \n",
+       "  61 -3.401291 -1.301804  1.825605 -1.379630  1.735251 -0.273759 -0.449865   \n",
+       "  62 -0.449865  0.108435  0.264935  0.268095  2.876003  0.789275  2.146334   \n",
+       "  63  2.146334  0.597059 -1.503790  2.142922  2.218576 -0.169037  2.812775   \n",
+       "  64  2.812775 -0.206871 -1.056144  4.122208  0.915995 -0.254108  0.559734   \n",
+       "  65  0.559734 -1.805391 -1.299688  3.118547 -2.210113 -1.803311  1.468527   \n",
+       "  66  1.468527 -1.233604 -0.442405 -2.042858 -2.918931 -0.656228  0.426712   \n",
+       "  67  0.426712  0.617130 -0.408477 -5.287627 -2.154943  0.934242 -0.405993   \n",
+       "  68 -0.405993  1.263328  1.457087 -4.153228 -0.861197  3.709693  0.538758   \n",
+       "  69  0.538758  3.659157  2.608475 -1.564166  0.694228  3.995520  0.293024   \n",
+       "  70  0.293024  1.398618  0.663049  1.376945  1.292930  2.406879 -0.704256   \n",
+       "  71 -0.704256 -1.188806 -0.717721  1.954026  1.729189 -0.921697 -0.624342   \n",
+       "  72 -0.624342 -1.723299 -0.767618  3.502768  1.282859 -2.325294 -0.031506   \n",
+       "  73 -0.031506 -0.501007 -0.526395  0.821508  0.723188 -1.522760  0.443492   \n",
+       "  74  0.443492  1.419256 -1.124909 -2.899890 -1.378862  0.000049 -0.442575   \n",
+       "  75 -0.442575  3.330602  0.441650 -4.173796 -0.884340  3.029700 -1.440500   \n",
+       "  76 -1.440500  2.435017  0.858189 -1.107863 -0.508333  3.028390 -1.081777   \n",
+       "  77 -1.081777  0.783598 -0.627353  0.586467  0.762079  2.943569  0.344009   \n",
+       "  78  0.344009 -1.926856  0.077327  1.418995  1.387388  0.546161  1.257616   \n",
+       "  79  1.257616 -4.606872 -1.181787  2.220228  0.685110 -1.722096  1.571903   \n",
+       "  80  1.571903 -4.830979 -1.014661  1.302769 -1.031445 -2.115464 -0.526730   \n",
+       "  81 -0.526730 -1.475407  0.656636  0.314291 -1.954660 -2.893362 -1.113223   \n",
+       "  82 -1.113223  2.696480  1.514883 -2.133322 -2.217674  0.104310  0.357160   \n",
+       "  83  0.357160  4.735158  0.795844 -1.804582  0.695342  1.098099  1.572319   \n",
+       "  84  1.572319  3.137866 -0.535226 -0.441267  2.688439  1.449070  0.366246   \n",
+       "  85  0.366246 -1.100956 -0.757385  0.833024  2.411659 -0.357270 -0.282046   \n",
+       "  86 -0.282046 -4.752973 -1.930996  0.535051 -0.856112  0.101478 -1.764550   \n",
+       "  87 -1.764550 -5.009690 -1.352952  0.148031 -3.669774 -0.643931 -2.092768   \n",
+       "  88 -2.092768 -3.505833  0.117653  0.044182 -1.562934 -1.487753 -0.363194   \n",
+       "  89 -0.363194 -0.441448  1.440173 -0.804545  1.190181 -1.489404  0.484759   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.301804  1.825605   -1.379630    1.735251   -0.273759  \n",
+       "  61  0.108435  0.264935    0.268095    2.876003    0.789275  \n",
+       "  62  0.597059 -1.503790    2.142922    2.218576   -0.169037  \n",
+       "  63 -0.206871 -1.056144    4.122208    0.915995   -0.254108  \n",
+       "  64 -1.805391 -1.299688    3.118547   -2.210113   -1.803311  \n",
+       "  65 -1.233604 -0.442405   -2.042858   -2.918931   -0.656228  \n",
+       "  66  0.617130 -0.408477   -5.287627   -2.154943    0.934242  \n",
+       "  67  1.263328  1.457087   -4.153228   -0.861197    3.709693  \n",
+       "  68  3.659157  2.608475   -1.564166    0.694228    3.995520  \n",
+       "  69  1.398618  0.663049    1.376945    1.292930    2.406879  \n",
+       "  70 -1.188806 -0.717721    1.954026    1.729189   -0.921697  \n",
+       "  71 -1.723299 -0.767618    3.502768    1.282859   -2.325294  \n",
+       "  72 -0.501007 -0.526395    0.821508    0.723188   -1.522760  \n",
+       "  73  1.419256 -1.124909   -2.899890   -1.378862    0.000049  \n",
+       "  74  3.330602  0.441650   -4.173796   -0.884340    3.029700  \n",
+       "  75  2.435017  0.858189   -1.107863   -0.508333    3.028390  \n",
+       "  76  0.783598 -0.627353    0.586467    0.762079    2.943569  \n",
+       "  77 -1.926856  0.077327    1.418995    1.387388    0.546161  \n",
+       "  78 -4.606872 -1.181787    2.220228    0.685110   -1.722096  \n",
+       "  79 -4.830979 -1.014661    1.302769   -1.031445   -2.115464  \n",
+       "  80 -1.475407  0.656636    0.314291   -1.954660   -2.893362  \n",
+       "  81  2.696480  1.514883   -2.133322   -2.217674    0.104310  \n",
+       "  82  4.735158  0.795844   -1.804582    0.695342    1.098099  \n",
+       "  83  3.137866 -0.535226   -0.441267    2.688439    1.449070  \n",
+       "  84 -1.100956 -0.757385    0.833024    2.411659   -0.357270  \n",
+       "  85 -4.752973 -1.930996    0.535051   -0.856112    0.101478  \n",
+       "  86 -5.009690 -1.352952    0.148031   -3.669774   -0.643931  \n",
+       "  87 -3.505833  0.117653    0.044182   -1.562934   -1.487753  \n",
+       "  88 -0.441448  1.440173   -0.804545    1.190181   -1.489404  \n",
+       "  89  4.207526  2.900076   -1.209055    1.964081    0.979124  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.407831  0.258702  1.856324  2.974512 -3.065267  1.754975  0.584454   \n",
+       "  61  0.584454 -0.952814  0.676367  3.795046  0.048520 -0.733174  1.257573   \n",
+       "  62  1.257573 -0.751845 -0.551305  0.679185  2.942517 -2.749238  1.615134   \n",
+       "  63  1.615134 -1.817687 -1.973145 -0.183444  3.361640 -2.058496 -1.298270   \n",
+       "  64 -1.298270 -0.919491 -0.781548 -1.306657  1.500147 -1.343489 -2.368049   \n",
+       "  65 -2.368049  1.188613  0.524110  0.211374 -1.453643  1.589049 -1.840431   \n",
+       "  66 -1.840431  2.690977  0.385371 -0.330676 -2.357146  2.086022 -0.511025   \n",
+       "  67 -0.511025  3.080276  1.117569 -1.091092 -2.195654 -0.233135  0.523720   \n",
+       "  68  0.523720  2.697995  1.485507 -0.216731 -0.983252 -4.290945 -0.449713   \n",
+       "  69 -0.449713  1.511309 -0.077010  1.666030 -0.178062 -4.960821 -0.619492   \n",
+       "  70 -0.619492  0.648589  0.375064  1.862518  0.160215 -2.952665 -1.228636   \n",
+       "  71 -1.228636 -0.057061  1.449743  1.354601  1.901197  1.047147 -0.558444   \n",
+       "  72 -0.558444 -1.914726  1.029643  0.727461  0.860336  2.210802  1.196906   \n",
+       "  73  1.196906 -2.863734  1.994683 -0.238202 -0.947966  1.499250  1.443962   \n",
+       "  74  1.443962 -3.308421  1.847669 -1.204619 -0.531323 -0.666080  1.416854   \n",
+       "  75  1.416854 -2.366726 -0.650543 -0.002047  0.735484 -0.232453 -0.360158   \n",
+       "  76 -0.360158  1.296114 -0.007590  2.269306  0.522603  0.383166 -0.074382   \n",
+       "  77 -0.074382  2.667595  0.189075  2.950817 -0.285898  0.259685 -0.303069   \n",
+       "  78 -0.303069  3.515666  1.895875  1.577165 -0.730545 -0.208155 -0.910866   \n",
+       "  79 -0.910866  2.689167  2.503987 -1.264165  0.940923 -0.476323 -1.417594   \n",
+       "  80 -1.417594  0.708374  0.546987 -2.404092  1.070615  0.465916  0.072690   \n",
+       "  81  0.072690 -0.128555 -0.882959 -1.555883  0.813279  0.035211  0.769823   \n",
+       "  82  0.769823 -1.284352  0.109954 -1.600760 -0.693911  0.554286  0.714587   \n",
+       "  83  0.714587 -1.635079  0.797104  1.398549 -0.898859 -1.805065 -1.500985   \n",
+       "  84 -1.500985  0.638803  0.406405  0.779131 -0.890101 -1.587988 -0.506558   \n",
+       "  85 -0.506558  1.747592  0.407406  0.855629 -0.345264 -0.293160  0.036192   \n",
+       "  86  0.036192  0.406347  0.944317  0.356863  1.725088  1.302567  1.950017   \n",
+       "  87  1.950017  0.793906  1.184842 -0.084412  2.719791  1.885940  2.457749   \n",
+       "  88  2.457749 -1.467929  0.771107 -1.456646  0.385921  0.219383 -0.355610   \n",
+       "  89 -0.355610 -2.455799 -0.148358 -0.013728 -0.262992 -2.275728 -3.780854   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -0.952814  0.676367    3.795046    0.048520   -0.733174  \n",
+       "  61 -0.751845 -0.551305    0.679185    2.942517   -2.749238  \n",
+       "  62 -1.817687 -1.973145   -0.183444    3.361640   -2.058496  \n",
+       "  63 -0.919491 -0.781548   -1.306657    1.500147   -1.343489  \n",
+       "  64  1.188613  0.524110    0.211374   -1.453643    1.589049  \n",
+       "  65  2.690977  0.385371   -0.330676   -2.357146    2.086022  \n",
+       "  66  3.080276  1.117569   -1.091092   -2.195654   -0.233135  \n",
+       "  67  2.697995  1.485507   -0.216731   -0.983252   -4.290945  \n",
+       "  68  1.511309 -0.077010    1.666030   -0.178062   -4.960821  \n",
+       "  69  0.648589  0.375064    1.862518    0.160215   -2.952665  \n",
+       "  70 -0.057061  1.449743    1.354601    1.901197    1.047147  \n",
+       "  71 -1.914726  1.029643    0.727461    0.860336    2.210802  \n",
+       "  72 -2.863734  1.994683   -0.238202   -0.947966    1.499250  \n",
+       "  73 -3.308421  1.847669   -1.204619   -0.531323   -0.666080  \n",
+       "  74 -2.366726 -0.650543   -0.002047    0.735484   -0.232453  \n",
+       "  75  1.296114 -0.007590    2.269306    0.522603    0.383166  \n",
+       "  76  2.667595  0.189075    2.950817   -0.285898    0.259685  \n",
+       "  77  3.515666  1.895875    1.577165   -0.730545   -0.208155  \n",
+       "  78  2.689167  2.503987   -1.264165    0.940923   -0.476323  \n",
+       "  79  0.708374  0.546987   -2.404092    1.070615    0.465916  \n",
+       "  80 -0.128555 -0.882959   -1.555883    0.813279    0.035211  \n",
+       "  81 -1.284352  0.109954   -1.600760   -0.693911    0.554286  \n",
+       "  82 -1.635079  0.797104    1.398549   -0.898859   -1.805065  \n",
+       "  83  0.638803  0.406405    0.779131   -0.890101   -1.587988  \n",
+       "  84  1.747592  0.407406    0.855629   -0.345264   -0.293160  \n",
+       "  85  0.406347  0.944317    0.356863    1.725088    1.302567  \n",
+       "  86  0.793906  1.184842   -0.084412    2.719791    1.885940  \n",
+       "  87 -1.467929  0.771107   -1.456646    0.385921    0.219383  \n",
+       "  88 -2.455799 -0.148358   -0.013728   -0.262992   -2.275728  \n",
+       "  89 -2.299102 -0.049291   -0.926701   -1.939716   -3.456137  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  2.275064  1.214050 -1.003962 -1.830210 -1.776676  0.730259 -2.174047   \n",
+       "  61 -2.174047 -0.500938 -2.287466 -3.712164 -1.393612 -0.684774 -5.154045   \n",
+       "  62 -5.154045 -2.334924 -2.277957 -2.407873 -1.425446 -1.415450 -4.205746   \n",
+       "  63 -4.205746 -0.395803  0.184118  0.692220 -0.692846 -1.424968 -1.859623   \n",
+       "  64 -1.859623  0.325206  1.302703  3.848622  1.243915  1.405249  0.901769   \n",
+       "  65  0.901769  1.669984  1.753428  3.160101  2.770854  0.421429  2.517161   \n",
+       "  66  2.517161  0.600389  0.850770  1.659653  0.604455  1.200923  3.477921   \n",
+       "  67  3.477921 -1.175858  0.096899 -2.220268 -0.779784  0.656155  3.360906   \n",
+       "  68  3.360906 -1.639218 -0.671374 -3.693891 -1.535182 -1.243399 -1.791352   \n",
+       "  69 -1.791352 -0.464805  0.298828 -4.432723 -0.813568 -2.405867 -4.222123   \n",
+       "  70 -4.222123 -0.459963  0.903088  0.244423  0.641671 -2.638526 -3.848828   \n",
+       "  71 -3.848828  0.481153  0.411295  2.384573  0.388771 -1.443261 -0.855934   \n",
+       "  72 -0.855934 -0.382533 -0.539600  2.934057  0.305116  0.695714  5.112448   \n",
+       "  73  5.112448 -1.185565 -1.888231  1.927258 -1.801545  1.551224  4.475796   \n",
+       "  74  4.475796 -0.723249 -1.716462 -0.428376 -2.329085  1.992312  0.825471   \n",
+       "  75  0.825471  1.508598  0.274270 -3.079473 -0.882989 -0.989872 -4.098704   \n",
+       "  76 -4.098704  0.982265  1.093108 -1.868835 -0.282550 -0.959873 -4.767684   \n",
+       "  77 -4.767684 -0.182674  0.558376 -0.729730  2.094086 -0.258074 -1.448489   \n",
+       "  78 -1.448489 -0.511974 -0.023360  0.659419  2.942761  1.676490  2.410955   \n",
+       "  79  2.410955 -0.484561 -1.035641  1.046625  1.592212  0.241093  3.842161   \n",
+       "  80  3.842161  1.140564 -1.443598  0.855280  1.368638  0.478754  1.971986   \n",
+       "  81  1.971986  0.031126  0.033102  1.500066 -1.295631  0.417822  0.351041   \n",
+       "  82  0.351041  0.663884 -0.097229  0.827577 -2.803568  0.109030 -2.460459   \n",
+       "  83 -2.460459  1.786770 -0.372456  0.865618 -1.060345  1.729813 -2.913920   \n",
+       "  84 -2.913920  2.479557 -1.382946 -0.637149  2.062460  0.243097 -0.966230   \n",
+       "  85 -0.966230  0.819615  0.174440 -0.878729  4.434980  0.165777  0.025901   \n",
+       "  86  0.025901 -1.942628  1.088861 -1.238199  3.243673 -1.454689  1.721090   \n",
+       "  87  1.721090 -2.971954 -0.236020 -0.060381  0.966560 -1.047664  2.369250   \n",
+       "  88  2.369250 -2.485609  0.198822  1.063708 -2.691862  0.073366  1.699654   \n",
+       "  89  1.699654  0.894051 -0.888475  2.218064 -1.679164  1.394735  1.103396   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -0.500938 -2.287466   -3.712164   -1.393612   -0.684774  \n",
+       "  61 -2.334924 -2.277957   -2.407873   -1.425446   -1.415450  \n",
+       "  62 -0.395803  0.184118    0.692220   -0.692846   -1.424968  \n",
+       "  63  0.325206  1.302703    3.848622    1.243915    1.405249  \n",
+       "  64  1.669984  1.753428    3.160101    2.770854    0.421429  \n",
+       "  65  0.600389  0.850770    1.659653    0.604455    1.200923  \n",
+       "  66 -1.175858  0.096899   -2.220268   -0.779784    0.656155  \n",
+       "  67 -1.639218 -0.671374   -3.693891   -1.535182   -1.243399  \n",
+       "  68 -0.464805  0.298828   -4.432723   -0.813568   -2.405867  \n",
+       "  69 -0.459963  0.903088    0.244423    0.641671   -2.638526  \n",
+       "  70  0.481153  0.411295    2.384573    0.388771   -1.443261  \n",
+       "  71 -0.382533 -0.539600    2.934057    0.305116    0.695714  \n",
+       "  72 -1.185565 -1.888231    1.927258   -1.801545    1.551224  \n",
+       "  73 -0.723249 -1.716462   -0.428376   -2.329085    1.992312  \n",
+       "  74  1.508598  0.274270   -3.079473   -0.882989   -0.989872  \n",
+       "  75  0.982265  1.093108   -1.868835   -0.282550   -0.959873  \n",
+       "  76 -0.182674  0.558376   -0.729730    2.094086   -0.258074  \n",
+       "  77 -0.511974 -0.023360    0.659419    2.942761    1.676490  \n",
+       "  78 -0.484561 -1.035641    1.046625    1.592212    0.241093  \n",
+       "  79  1.140564 -1.443598    0.855280    1.368638    0.478754  \n",
+       "  80  0.031126  0.033102    1.500066   -1.295631    0.417822  \n",
+       "  81  0.663884 -0.097229    0.827577   -2.803568    0.109030  \n",
+       "  82  1.786770 -0.372456    0.865618   -1.060345    1.729813  \n",
+       "  83  2.479557 -1.382946   -0.637149    2.062460    0.243097  \n",
+       "  84  0.819615  0.174440   -0.878729    4.434980    0.165777  \n",
+       "  85 -1.942628  1.088861   -1.238199    3.243673   -1.454689  \n",
+       "  86 -2.971954 -0.236020   -0.060381    0.966560   -1.047664  \n",
+       "  87 -2.485609  0.198822    1.063708   -2.691862    0.073366  \n",
+       "  88  0.894051 -0.888475    2.218064   -1.679164    1.394735  \n",
+       "  89  2.147638 -0.871294    3.280611    2.810044    0.287354  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  2.474403 -1.038674 -0.990974  1.332450 -0.164939 -3.103476 -0.935532   \n",
+       "  61 -0.935532 -1.093257 -3.254390  0.676791  1.422578 -3.410078 -3.157073   \n",
+       "  62 -3.157073  0.027427 -1.279689  0.434824  1.646681 -1.255057 -3.089318   \n",
+       "  63 -3.089318 -1.331961  1.038962  0.449984  0.784442  2.158697 -1.625094   \n",
+       "  64 -1.625094 -2.319425  3.341327 -0.061277 -0.374307  0.948896  1.083417   \n",
+       "  65  1.083417 -0.127085  1.573187  0.422325 -2.542050  1.394117  3.303262   \n",
+       "  66  3.303262  1.385573 -1.797623 -1.142012 -1.833158  0.701534  3.722426   \n",
+       "  67  3.722426  0.432194 -2.141439  0.161413 -1.940078  0.505609  0.774891   \n",
+       "  68  0.774891 -0.988772 -0.478429 -1.365863 -0.033471 -1.256974 -1.271740   \n",
+       "  69 -1.271740 -0.531680  1.938098  0.903977  0.852073 -1.421019 -2.892119   \n",
+       "  70 -2.892119 -0.178172  1.888405  1.198443  0.464888  0.264409 -1.128108   \n",
+       "  71 -1.128108  1.059931  0.753565  0.985608  0.466084  1.347699  0.385350   \n",
+       "  72  0.385350  1.188412 -1.432428 -0.423096 -1.602360  1.728931  1.836885   \n",
+       "  73  1.836885  0.172500 -1.191346 -2.335520 -1.454776  1.556865  0.057572   \n",
+       "  74  0.057572  0.086041 -2.336974 -1.858567 -1.656595 -0.015476 -0.668584   \n",
+       "  75 -0.668584 -1.498036 -2.182759 -1.372958 -0.388241 -0.264109 -0.251022   \n",
+       "  76 -0.251022 -0.869322 -1.416885  0.666934  1.983643 -1.246599  1.682677   \n",
+       "  77  1.682677  2.464102  0.027237  2.232649  2.897965 -0.106515  0.636836   \n",
+       "  78  0.636836  3.951575  0.924600  2.972474  1.111272  1.222890 -0.206404   \n",
+       "  79 -0.206404  1.834323  3.084592 -0.082621 -0.441140  2.169595 -1.724948   \n",
+       "  80 -1.724948 -1.099744  1.625883 -0.558089 -2.001482  1.405565 -1.735261   \n",
+       "  81 -1.735261 -2.799802  0.974156 -1.498868  0.019154  1.258082 -0.004554   \n",
+       "  82 -0.004554 -2.111255  0.723079 -1.992782 -1.053823 -0.795676  1.205392   \n",
+       "  83  1.205392 -0.324236 -0.757468 -0.812215 -1.835174  0.506768  1.355163   \n",
+       "  84  1.355163  3.502629 -2.926913  1.051642 -0.782736  0.362942  1.675425   \n",
+       "  85  1.675425  2.709646 -2.563197  1.971909 -0.488619 -0.233639 -1.499944   \n",
+       "  86 -1.499944  0.504846 -0.508225  1.201894  1.491629  0.645217 -0.752378   \n",
+       "  87 -0.752378 -2.860298  1.517849  0.299131  0.383057  0.249469 -1.070096   \n",
+       "  88 -1.070096 -1.897392  1.258929 -0.190099  0.461740 -1.365965  0.227962   \n",
+       "  89  0.227962 -1.253612  1.086257 -2.335870 -0.651303 -3.339594  1.546406   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.093257 -3.254390    0.676791    1.422578   -3.410078  \n",
+       "  61  0.027427 -1.279689    0.434824    1.646681   -1.255057  \n",
+       "  62 -1.331961  1.038962    0.449984    0.784442    2.158697  \n",
+       "  63 -2.319425  3.341327   -0.061277   -0.374307    0.948896  \n",
+       "  64 -0.127085  1.573187    0.422325   -2.542050    1.394117  \n",
+       "  65  1.385573 -1.797623   -1.142012   -1.833158    0.701534  \n",
+       "  66  0.432194 -2.141439    0.161413   -1.940078    0.505609  \n",
+       "  67 -0.988772 -0.478429   -1.365863   -0.033471   -1.256974  \n",
+       "  68 -0.531680  1.938098    0.903977    0.852073   -1.421019  \n",
+       "  69 -0.178172  1.888405    1.198443    0.464888    0.264409  \n",
+       "  70  1.059931  0.753565    0.985608    0.466084    1.347699  \n",
+       "  71  1.188412 -1.432428   -0.423096   -1.602360    1.728931  \n",
+       "  72  0.172500 -1.191346   -2.335520   -1.454776    1.556865  \n",
+       "  73  0.086041 -2.336974   -1.858567   -1.656595   -0.015476  \n",
+       "  74 -1.498036 -2.182759   -1.372958   -0.388241   -0.264109  \n",
+       "  75 -0.869322 -1.416885    0.666934    1.983643   -1.246599  \n",
+       "  76  2.464102  0.027237    2.232649    2.897965   -0.106515  \n",
+       "  77  3.951575  0.924600    2.972474    1.111272    1.222890  \n",
+       "  78  1.834323  3.084592   -0.082621   -0.441140    2.169595  \n",
+       "  79 -1.099744  1.625883   -0.558089   -2.001482    1.405565  \n",
+       "  80 -2.799802  0.974156   -1.498868    0.019154    1.258082  \n",
+       "  81 -2.111255  0.723079   -1.992782   -1.053823   -0.795676  \n",
+       "  82 -0.324236 -0.757468   -0.812215   -1.835174    0.506768  \n",
+       "  83  3.502629 -2.926913    1.051642   -0.782736    0.362942  \n",
+       "  84  2.709646 -2.563197    1.971909   -0.488619   -0.233639  \n",
+       "  85  0.504846 -0.508225    1.201894    1.491629    0.645217  \n",
+       "  86 -2.860298  1.517849    0.299131    0.383057    0.249469  \n",
+       "  87 -1.897392  1.258929   -0.190099    0.461740   -1.365965  \n",
+       "  88 -1.253612  1.086257   -2.335870   -0.651303   -3.339594  \n",
+       "  89  0.577922 -0.076296   -1.554651   -1.357715   -2.559836  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.492635  1.193488 -0.964220  2.831891 -1.269955  0.728819 -2.060793   \n",
+       "  61 -2.060793  2.172567 -0.293455  3.796578 -0.047988  1.293631 -2.636127   \n",
+       "  62 -2.636127  1.845931 -0.470276  0.363265  0.779729  0.382279 -2.680137   \n",
+       "  63 -2.680137  1.136325 -2.203184 -2.789683  0.005814 -1.286493 -1.656874   \n",
+       "  64 -1.656874 -1.552302 -1.246983 -4.307581  0.100406 -0.253156  0.181772   \n",
+       "  65  0.181772 -2.712956 -0.628700 -1.848399 -0.207035  0.936197  2.062190   \n",
+       "  66  2.062190 -2.128917 -1.253546  0.382256  0.128504 -0.502786  3.215845   \n",
+       "  67  3.215845 -0.240419  0.358938  3.714183 -0.052284 -1.455593  0.888318   \n",
+       "  68  0.888318  1.924889 -0.031177  3.220500 -1.172009 -3.021120 -3.823115   \n",
+       "  69 -3.823115  4.412772  0.523425  3.072120 -0.535665 -1.914405 -3.021261   \n",
+       "  70 -3.021261  2.691115  0.948435  1.697189  1.746470 -0.412968 -1.586674   \n",
+       "  71 -1.586674 -0.238007 -0.086537 -3.147830  2.511956  1.533213  1.605648   \n",
+       "  72  1.605648 -2.535294  1.843477 -5.728953  1.004609  1.826675  2.001086   \n",
+       "  73  2.001086 -1.358214  0.361318 -2.775036 -1.910376  0.245942  1.149361   \n",
+       "  74  1.149361  0.330379  0.855159 -0.221556 -3.772159 -2.583453  1.084362   \n",
+       "  75  1.084362  1.499392  0.505004  3.315236 -3.954455 -4.185574  0.424443   \n",
+       "  76  0.424443  1.624651  2.942868  4.346914  0.030224 -3.948526 -0.577916   \n",
+       "  77 -0.577916 -0.320824  1.707707  2.170419  3.798617  0.352397 -2.195715   \n",
+       "  78 -2.195715  0.192140  0.256077 -1.935862  2.621184  3.097828 -2.175718   \n",
+       "  79 -2.175718 -1.822955 -0.386627 -3.333789 -0.205787  4.175043 -0.214011   \n",
+       "  80 -0.214011 -0.709557  0.093560 -2.171547 -2.816909  1.794360  0.420515   \n",
+       "  81  0.420515  0.310025  1.435536  0.382372 -4.272931 -2.447567  2.151949   \n",
+       "  82  2.151949  0.551033  0.465772  3.810615 -3.171912 -3.538989  1.197920   \n",
+       "  83  1.197920 -0.268349 -0.266228  2.773418 -0.217766 -2.001551  1.062872   \n",
+       "  84  1.062872 -1.616365  0.207241  0.644424  2.415299  0.969353  0.085975   \n",
+       "  85  0.085975 -0.638142 -0.594434 -3.424642  1.409866  4.066861  0.475105   \n",
+       "  86  0.475105 -1.047459 -0.446301 -2.072921 -0.230156  4.167821 -1.256427   \n",
+       "  87 -1.256427 -0.397899 -0.171541 -2.178718 -2.019383  3.583835  0.054771   \n",
+       "  88  0.054771  0.531370  1.528750 -0.605347 -1.853846  0.466993  0.540725   \n",
+       "  89  0.540725  0.308185  0.809842  0.757465 -1.056238 -2.857040  1.571757   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  2.172567 -0.293455    3.796578   -0.047988    1.293631  \n",
+       "  61  1.845931 -0.470276    0.363265    0.779729    0.382279  \n",
+       "  62  1.136325 -2.203184   -2.789683    0.005814   -1.286493  \n",
+       "  63 -1.552302 -1.246983   -4.307581    0.100406   -0.253156  \n",
+       "  64 -2.712956 -0.628700   -1.848399   -0.207035    0.936197  \n",
+       "  65 -2.128917 -1.253546    0.382256    0.128504   -0.502786  \n",
+       "  66 -0.240419  0.358938    3.714183   -0.052284   -1.455593  \n",
+       "  67  1.924889 -0.031177    3.220500   -1.172009   -3.021120  \n",
+       "  68  4.412772  0.523425    3.072120   -0.535665   -1.914405  \n",
+       "  69  2.691115  0.948435    1.697189    1.746470   -0.412968  \n",
+       "  70 -0.238007 -0.086537   -3.147830    2.511956    1.533213  \n",
+       "  71 -2.535294  1.843477   -5.728953    1.004609    1.826675  \n",
+       "  72 -1.358214  0.361318   -2.775036   -1.910376    0.245942  \n",
+       "  73  0.330379  0.855159   -0.221556   -3.772159   -2.583453  \n",
+       "  74  1.499392  0.505004    3.315236   -3.954455   -4.185574  \n",
+       "  75  1.624651  2.942868    4.346914    0.030224   -3.948526  \n",
+       "  76 -0.320824  1.707707    2.170419    3.798617    0.352397  \n",
+       "  77  0.192140  0.256077   -1.935862    2.621184    3.097828  \n",
+       "  78 -1.822955 -0.386627   -3.333789   -0.205787    4.175043  \n",
+       "  79 -0.709557  0.093560   -2.171547   -2.816909    1.794360  \n",
+       "  80  0.310025  1.435536    0.382372   -4.272931   -2.447567  \n",
+       "  81  0.551033  0.465772    3.810615   -3.171912   -3.538989  \n",
+       "  82 -0.268349 -0.266228    2.773418   -0.217766   -2.001551  \n",
+       "  83 -1.616365  0.207241    0.644424    2.415299    0.969353  \n",
+       "  84 -0.638142 -0.594434   -3.424642    1.409866    4.066861  \n",
+       "  85 -1.047459 -0.446301   -2.072921   -0.230156    4.167821  \n",
+       "  86 -0.397899 -0.171541   -2.178718   -2.019383    3.583835  \n",
+       "  87  0.531370  1.528750   -0.605347   -1.853846    0.466993  \n",
+       "  88  0.308185  0.809842    0.757465   -1.056238   -2.857040  \n",
+       "  89  0.748470 -0.632171    2.906095   -0.278676   -2.841532  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -3.464854 -1.832816 -0.174653  0.259981 -1.209566 -2.210490 -1.717688   \n",
+       "  61 -1.717688 -1.297281  3.293169 -0.628000 -0.079306 -1.007285  0.036674   \n",
+       "  62  0.036674  0.017890  3.839258 -1.642813  0.871061 -0.727099  1.535039   \n",
+       "  63  1.535039 -2.055124  2.629554 -1.351879  2.253430 -0.418324  1.615826   \n",
+       "  64  1.615826 -1.813167  0.129153  0.042975  2.094149  2.049318  0.352764   \n",
+       "  65  0.352764 -0.208869 -3.238566  2.010057  0.715761  2.545818 -2.852743   \n",
+       "  66 -2.852743 -0.036032 -3.133320  2.732940 -0.152530  1.624888 -2.644120   \n",
+       "  67 -2.644120  1.575628 -0.762283  1.389004 -0.746639 -0.184327 -1.860332   \n",
+       "  68 -1.860332  3.000297  0.414687 -1.493348 -2.392509 -2.315378  2.498602   \n",
+       "  69  2.498602  1.317396  3.951138 -3.904944 -0.206032 -5.014243  3.917813   \n",
+       "  70  3.917813 -1.183196  0.682501 -1.218465  0.980888 -1.797228  3.851384   \n",
+       "  71  3.851384 -3.788339 -0.794494  0.820048  1.515677  4.554011 -0.761284   \n",
+       "  72 -0.761284 -3.443180 -2.336929  3.360153 -0.026353  5.226525 -4.469422   \n",
+       "  73 -4.469422 -0.857480 -0.801321  2.054508 -1.699304  2.038723 -6.148874   \n",
+       "  74 -6.148874  2.103143 -0.032828  1.800791 -1.317875 -0.052055 -3.009429   \n",
+       "  75 -3.009429  3.388492  1.854603 -0.095451  1.065260 -4.631018  2.452576   \n",
+       "  76  2.452576  0.850402  2.134153  0.133786  2.569712 -4.281377  2.556381   \n",
+       "  77  2.556381  0.792891  1.487130 -0.973488  2.109466 -1.432639  1.523439   \n",
+       "  78  1.523439 -1.069978 -0.820207 -0.836315  0.122994  1.552846 -0.293542   \n",
+       "  79 -0.293542 -2.503558 -0.659449  0.860871 -0.057828  3.680980 -0.396512   \n",
+       "  80 -0.396512 -2.315952  0.413559  1.034675 -2.740701  1.505930 -1.061620   \n",
+       "  81 -1.061620 -1.476704 -0.064930 -0.868044 -1.633860 -1.194747  0.273424   \n",
+       "  82  0.273424 -0.112162 -0.930887 -2.783061 -1.003453 -3.236857 -0.144922   \n",
+       "  83 -0.144922  1.282381 -1.324384 -0.966959  2.565751 -2.240504 -1.858278   \n",
+       "  84 -1.858278  0.949938 -0.753315 -0.540983  1.765948  0.505677 -1.102670   \n",
+       "  85 -1.102670  1.144074  1.095962  0.801202  1.691550  3.380342  0.703083   \n",
+       "  86  0.703083  0.086111  1.977977  0.676387  0.254059  2.387153  2.097831   \n",
+       "  87  2.097831  0.169518  1.132813 -0.397354 -1.434396  0.147590  2.500092   \n",
+       "  88  2.500092 -1.154931  0.674632 -1.555009 -1.155983 -3.104066  2.744039   \n",
+       "  89  2.744039 -1.971793 -0.497200 -2.199325 -1.097270 -3.520772  0.427064   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.297281  3.293169   -0.628000   -0.079306   -1.007285  \n",
+       "  61  0.017890  3.839258   -1.642813    0.871061   -0.727099  \n",
+       "  62 -2.055124  2.629554   -1.351879    2.253430   -0.418324  \n",
+       "  63 -1.813167  0.129153    0.042975    2.094149    2.049318  \n",
+       "  64 -0.208869 -3.238566    2.010057    0.715761    2.545818  \n",
+       "  65 -0.036032 -3.133320    2.732940   -0.152530    1.624888  \n",
+       "  66  1.575628 -0.762283    1.389004   -0.746639   -0.184327  \n",
+       "  67  3.000297  0.414687   -1.493348   -2.392509   -2.315378  \n",
+       "  68  1.317396  3.951138   -3.904944   -0.206032   -5.014243  \n",
+       "  69 -1.183196  0.682501   -1.218465    0.980888   -1.797228  \n",
+       "  70 -3.788339 -0.794494    0.820048    1.515677    4.554011  \n",
+       "  71 -3.443180 -2.336929    3.360153   -0.026353    5.226525  \n",
+       "  72 -0.857480 -0.801321    2.054508   -1.699304    2.038723  \n",
+       "  73  2.103143 -0.032828    1.800791   -1.317875   -0.052055  \n",
+       "  74  3.388492  1.854603   -0.095451    1.065260   -4.631018  \n",
+       "  75  0.850402  2.134153    0.133786    2.569712   -4.281377  \n",
+       "  76  0.792891  1.487130   -0.973488    2.109466   -1.432639  \n",
+       "  77 -1.069978 -0.820207   -0.836315    0.122994    1.552846  \n",
+       "  78 -2.503558 -0.659449    0.860871   -0.057828    3.680980  \n",
+       "  79 -2.315952  0.413559    1.034675   -2.740701    1.505930  \n",
+       "  80 -1.476704 -0.064930   -0.868044   -1.633860   -1.194747  \n",
+       "  81 -0.112162 -0.930887   -2.783061   -1.003453   -3.236857  \n",
+       "  82  1.282381 -1.324384   -0.966959    2.565751   -2.240504  \n",
+       "  83  0.949938 -0.753315   -0.540983    1.765948    0.505677  \n",
+       "  84  1.144074  1.095962    0.801202    1.691550    3.380342  \n",
+       "  85  0.086111  1.977977    0.676387    0.254059    2.387153  \n",
+       "  86  0.169518  1.132813   -0.397354   -1.434396    0.147590  \n",
+       "  87 -1.154931  0.674632   -1.555009   -1.155983   -3.104066  \n",
+       "  88 -1.971793 -0.497200   -2.199325   -1.097270   -3.520772  \n",
+       "  89 -1.086998 -0.605018   -1.008407   -0.755047    0.004602  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.118219 -1.343190 -1.671193 -2.355654 -1.460661 -1.251164  1.412238   \n",
+       "  61  1.412238 -1.662818  0.662902  0.841870  0.141020 -0.799783  0.121210   \n",
+       "  62  0.121210 -0.268880  2.440944  3.221333  1.811004 -0.215863  1.452086   \n",
+       "  63  1.452086  0.218387  3.024580  4.153766  2.187800  0.722705  0.346343   \n",
+       "  64  0.346343  1.676698  0.577293  2.334207 -0.063633  0.988152  1.288118   \n",
+       "  65  1.288118  1.570718 -3.161838 -0.501500 -1.155203  0.237235  2.315858   \n",
+       "  66  2.315858 -1.292739 -4.671818 -0.942924 -1.205894 -0.747141  2.194168   \n",
+       "  67  2.194168 -1.675680 -1.618224 -0.470986 -2.307518 -0.238243  1.654346   \n",
+       "  68  1.654346 -1.060476  1.421196  0.604180 -0.666402  1.718830 -1.384830   \n",
+       "  69 -1.384830  1.805043  4.226801  3.089848 -0.601553  1.458479 -2.310157   \n",
+       "  70 -2.310157  2.364306  1.617193  1.872666  2.161644  1.385825 -1.166171   \n",
+       "  71 -1.166171  1.928742  0.310046  0.235568  1.993690  0.295746  0.630508   \n",
+       "  72  0.630508  0.603648 -3.925560 -1.652914  0.937297 -0.934204  1.424101   \n",
+       "  73  1.424101 -1.897066 -2.099158  0.321535 -1.870298 -0.724650  1.174852   \n",
+       "  74  1.174852 -0.515554  1.182205  1.312451 -2.576679 -1.724582  0.781981   \n",
+       "  75  0.781981  0.451242  4.941707  2.496174 -1.450808  0.976864 -1.062353   \n",
+       "  76 -1.062353  1.730637  4.742309 -0.013192  0.677435 -0.483924 -2.115014   \n",
+       "  77 -2.115014  0.542071  1.920541 -2.567696  0.766889  0.858731 -1.864331   \n",
+       "  78 -1.864331 -0.523618 -2.984521 -1.814380  1.083094  0.204137 -1.011608   \n",
+       "  79 -1.011608 -1.198533 -3.977388  0.660579 -0.587013 -0.837585  2.045365   \n",
+       "  80  2.045365 -0.206723 -3.262028  1.735203  1.257549 -1.094069  3.668072   \n",
+       "  81  3.668072 -1.398233 -0.506589  1.501881 -0.163434 -2.026354  1.521936   \n",
+       "  82  1.521936 -1.662251 -0.026460  0.049090  1.126376 -2.530342 -1.804469   \n",
+       "  83 -1.804469 -0.536962  4.062030 -2.240342 -1.145242 -1.494980 -3.515592   \n",
+       "  84 -3.515592  1.445655  4.237833 -2.748244 -0.213658  0.701970 -3.260573   \n",
+       "  85 -3.260573  1.810823  2.582224 -0.119447 -0.384254  2.130112  0.631721   \n",
+       "  86  0.631721  0.114376  0.163953  1.697186  1.832048  2.349327  3.207158   \n",
+       "  87  3.207158 -2.543991 -2.663228  1.397582  2.721974  0.431706  2.333897   \n",
+       "  88  2.333897 -3.087011 -3.447807 -0.859844  2.630075 -2.384398 -0.087764   \n",
+       "  89 -0.087764 -2.861110  0.177002 -0.318104  0.393445 -2.718577 -2.111828   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -1.662818  0.662902    0.841870    0.141020   -0.799783  \n",
+       "  61 -0.268880  2.440944    3.221333    1.811004   -0.215863  \n",
+       "  62  0.218387  3.024580    4.153766    2.187800    0.722705  \n",
+       "  63  1.676698  0.577293    2.334207   -0.063633    0.988152  \n",
+       "  64  1.570718 -3.161838   -0.501500   -1.155203    0.237235  \n",
+       "  65 -1.292739 -4.671818   -0.942924   -1.205894   -0.747141  \n",
+       "  66 -1.675680 -1.618224   -0.470986   -2.307518   -0.238243  \n",
+       "  67 -1.060476  1.421196    0.604180   -0.666402    1.718830  \n",
+       "  68  1.805043  4.226801    3.089848   -0.601553    1.458479  \n",
+       "  69  2.364306  1.617193    1.872666    2.161644    1.385825  \n",
+       "  70  1.928742  0.310046    0.235568    1.993690    0.295746  \n",
+       "  71  0.603648 -3.925560   -1.652914    0.937297   -0.934204  \n",
+       "  72 -1.897066 -2.099158    0.321535   -1.870298   -0.724650  \n",
+       "  73 -0.515554  1.182205    1.312451   -2.576679   -1.724582  \n",
+       "  74  0.451242  4.941707    2.496174   -1.450808    0.976864  \n",
+       "  75  1.730637  4.742309   -0.013192    0.677435   -0.483924  \n",
+       "  76  0.542071  1.920541   -2.567696    0.766889    0.858731  \n",
+       "  77 -0.523618 -2.984521   -1.814380    1.083094    0.204137  \n",
+       "  78 -1.198533 -3.977388    0.660579   -0.587013   -0.837585  \n",
+       "  79 -0.206723 -3.262028    1.735203    1.257549   -1.094069  \n",
+       "  80 -1.398233 -0.506589    1.501881   -0.163434   -2.026354  \n",
+       "  81 -1.662251 -0.026460    0.049090    1.126376   -2.530342  \n",
+       "  82 -0.536962  4.062030   -2.240342   -1.145242   -1.494980  \n",
+       "  83  1.445655  4.237833   -2.748244   -0.213658    0.701970  \n",
+       "  84  1.810823  2.582224   -0.119447   -0.384254    2.130112  \n",
+       "  85  0.114376  0.163953    1.697186    1.832048    2.349327  \n",
+       "  86 -2.543991 -2.663228    1.397582    2.721974    0.431706  \n",
+       "  87 -3.087011 -3.447807   -0.859844    2.630075   -2.384398  \n",
+       "  88 -2.861110  0.177002   -0.318104    0.393445   -2.718577  \n",
+       "  89  0.830879  1.491398   -0.821948   -2.538050   -0.908552  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  4.569306 -0.798498  0.609071 -0.021529 -0.209514  0.621347  3.147458   \n",
+       "  61  3.147458  0.008732 -0.552263 -0.167876 -3.046541  0.543985 -1.262464   \n",
+       "  62 -1.262464  0.217695 -1.304316  0.022754 -1.759758 -1.091869 -2.239359   \n",
+       "  63 -2.239359  0.631366 -1.119518  1.761280 -0.167343 -0.157578 -2.333374   \n",
+       "  64 -2.333374  1.792723  1.201710  2.785211  2.411954  0.790412 -0.193492   \n",
+       "  65 -0.193492 -1.201408  1.170694  3.485478  2.634566  0.182407  0.630173   \n",
+       "  66  0.630173 -1.735033  0.970036  0.700816  2.282324  0.096216  1.273013   \n",
+       "  67  1.273013 -1.884537 -1.001683 -2.745488 -0.533986  0.070440  0.578896   \n",
+       "  68  0.578896 -0.790935 -0.350655 -2.510823 -2.377003  0.627108 -0.026394   \n",
+       "  69 -0.026394  0.038736  0.058842 -1.911890 -2.232081  0.165764  0.141427   \n",
+       "  70  0.141427  1.834455  0.774156  0.665298 -1.227418 -1.223745  1.095692   \n",
+       "  71  1.095692  1.577170  1.293903  1.399337 -0.455383 -1.275127  2.195790   \n",
+       "  72  2.195790 -0.143484 -1.542062  1.367575  1.755822 -1.249703  0.554360   \n",
+       "  73  0.554360 -0.461189 -0.531467 -0.526743  1.767643 -0.958754 -0.379276   \n",
+       "  74 -0.379276 -0.146485 -2.084130 -3.173413  0.761212  0.471554 -0.704083   \n",
+       "  75 -0.704083  0.541631 -2.262198 -3.233491 -1.778068  1.215338 -0.307140   \n",
+       "  76 -0.307140  0.416681 -1.322426 -1.995688 -2.211341 -0.347646  1.961538   \n",
+       "  77  1.961538  1.786280 -0.387510  0.400428 -1.572515 -0.324425  3.752041   \n",
+       "  78  3.752041  1.457652 -0.230724  2.196113  0.303147 -0.355870  2.980880   \n",
+       "  79  2.980880 -2.170035 -0.577750  3.068385  2.008266 -0.392184  0.385406   \n",
+       "  80  0.385406 -1.825065 -0.567154  1.716316  3.178034 -0.938433 -1.872168   \n",
+       "  81 -1.872168  0.688344 -0.122636  1.033442  2.022348 -1.371062 -2.095597   \n",
+       "  82 -2.095597  1.599356 -0.941269 -0.613189  1.034829 -0.566376 -0.018585   \n",
+       "  83 -0.018585  0.000766 -1.211274 -2.079798 -0.114404  0.706195  0.867245   \n",
+       "  84  0.867245 -0.017016 -1.390916 -1.138061 -0.480119  2.738785  0.794309   \n",
+       "  85  0.794309 -0.176876  1.628998  0.774603 -2.014705  3.506099  1.397612   \n",
+       "  86  1.397612  0.420227  1.970413  2.372274 -1.661993  2.796578  0.951862   \n",
+       "  87  0.951862  1.356625  0.765103  0.769257 -2.514691 -1.584423  0.045636   \n",
+       "  88  0.045636 -0.450817 -3.508267 -0.857880  0.074091 -4.040436 -2.015435   \n",
+       "  89 -2.015435 -1.061422 -4.314483 -2.622413  1.898410 -1.345288 -1.996302   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.008732 -0.552263   -0.167876   -3.046541    0.543985  \n",
+       "  61  0.217695 -1.304316    0.022754   -1.759758   -1.091869  \n",
+       "  62  0.631366 -1.119518    1.761280   -0.167343   -0.157578  \n",
+       "  63  1.792723  1.201710    2.785211    2.411954    0.790412  \n",
+       "  64 -1.201408  1.170694    3.485478    2.634566    0.182407  \n",
+       "  65 -1.735033  0.970036    0.700816    2.282324    0.096216  \n",
+       "  66 -1.884537 -1.001683   -2.745488   -0.533986    0.070440  \n",
+       "  67 -0.790935 -0.350655   -2.510823   -2.377003    0.627108  \n",
+       "  68  0.038736  0.058842   -1.911890   -2.232081    0.165764  \n",
+       "  69  1.834455  0.774156    0.665298   -1.227418   -1.223745  \n",
+       "  70  1.577170  1.293903    1.399337   -0.455383   -1.275127  \n",
+       "  71 -0.143484 -1.542062    1.367575    1.755822   -1.249703  \n",
+       "  72 -0.461189 -0.531467   -0.526743    1.767643   -0.958754  \n",
+       "  73 -0.146485 -2.084130   -3.173413    0.761212    0.471554  \n",
+       "  74  0.541631 -2.262198   -3.233491   -1.778068    1.215338  \n",
+       "  75  0.416681 -1.322426   -1.995688   -2.211341   -0.347646  \n",
+       "  76  1.786280 -0.387510    0.400428   -1.572515   -0.324425  \n",
+       "  77  1.457652 -0.230724    2.196113    0.303147   -0.355870  \n",
+       "  78 -2.170035 -0.577750    3.068385    2.008266   -0.392184  \n",
+       "  79 -1.825065 -0.567154    1.716316    3.178034   -0.938433  \n",
+       "  80  0.688344 -0.122636    1.033442    2.022348   -1.371062  \n",
+       "  81  1.599356 -0.941269   -0.613189    1.034829   -0.566376  \n",
+       "  82  0.000766 -1.211274   -2.079798   -0.114404    0.706195  \n",
+       "  83 -0.017016 -1.390916   -1.138061   -0.480119    2.738785  \n",
+       "  84 -0.176876  1.628998    0.774603   -2.014705    3.506099  \n",
+       "  85  0.420227  1.970413    2.372274   -1.661993    2.796578  \n",
+       "  86  1.356625  0.765103    0.769257   -2.514691   -1.584423  \n",
+       "  87 -0.450817 -3.508267   -0.857880    0.074091   -4.040436  \n",
+       "  88 -1.061422 -4.314483   -2.622413    1.898410   -1.345288  \n",
+       "  89  0.841850 -1.592179   -2.488018    2.516441    1.451898  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60  0.154244  1.363363 -0.600139  4.702588  0.078029  1.259880  0.793144   \n",
+       "  61  0.793144 -2.609666 -1.141711  5.109981 -1.266998 -0.258288  0.700250   \n",
+       "  62  0.700250 -5.336132 -1.321961  0.306438 -3.033890  0.200533 -1.455859   \n",
+       "  63 -1.455859 -1.870145 -0.863670 -2.127923 -2.263305 -0.614713 -0.798163   \n",
+       "  64 -0.798163  2.170096 -1.617134 -4.756598  0.492297 -2.062416  0.910867   \n",
+       "  65  0.910867  5.789576 -1.728239 -2.049161  0.770258 -1.351842  1.225478   \n",
+       "  66  1.225478  3.050609 -1.312519 -0.632181  0.153491  0.951488  1.572787   \n",
+       "  67  1.572787 -0.759152  0.436962  2.004270 -1.178278  1.231687  0.136821   \n",
+       "  68  0.136821 -3.540880  1.824918  2.537212 -0.692231  0.772661 -0.264216   \n",
+       "  69 -0.264216 -2.844267  1.501819  1.186685  2.019131 -0.802338 -1.626922   \n",
+       "  70 -1.626922 -1.580944 -0.685232 -1.999756  2.773578 -2.542120 -0.420178   \n",
+       "  71 -0.420178  0.576604 -1.596060 -3.063344  2.042677 -0.718184  1.359884   \n",
+       "  72  1.359884  3.212726 -1.689383 -4.139951 -0.648250 -0.258600  1.061475   \n",
+       "  73  1.061475  5.307505 -0.443206  1.965477 -2.803724  1.240522  0.219517   \n",
+       "  74  0.219517  3.419164  1.955569  4.946192 -2.239255  0.727797 -0.224321   \n",
+       "  75 -0.224321 -0.209690  2.595755  5.127648 -0.485151 -1.048553 -0.224782   \n",
+       "  76 -0.224782 -4.166616  2.434316  0.811661  1.957396 -0.971907 -0.161303   \n",
+       "  77 -0.161303 -3.308008  0.418675 -4.096251  3.057698 -1.595461 -0.572904   \n",
+       "  78 -0.572904 -0.657048  0.158499 -6.464860  1.443851 -1.069809 -1.125856   \n",
+       "  79 -1.125856  1.926940  0.884323 -5.234382 -1.380808  1.775812 -1.827453   \n",
+       "  80 -1.827453  3.455210  0.130247 -0.574002 -2.916684  1.551780 -1.258977   \n",
+       "  81 -1.258977  3.181148 -1.940312  2.617914 -5.305719  0.954069 -0.004844   \n",
+       "  82 -0.004844  0.795904 -1.159582  3.972387 -4.430579 -1.588166  1.358367   \n",
+       "  83  1.358367 -2.176082 -1.175309  2.232671 -1.086524 -2.464509  2.681692   \n",
+       "  84  2.681692 -3.295164  0.973188 -0.826057  3.844225 -2.241165  3.047643   \n",
+       "  85  3.047643 -2.411864  2.890455 -2.465340  6.373428 -1.129394 -1.127837   \n",
+       "  86 -1.127837 -2.035201  2.785620 -2.200440  2.490472 -0.043273 -3.117791   \n",
+       "  87 -3.117791 -0.590106  1.923935 -2.355443 -3.290635  2.239354 -3.078187   \n",
+       "  88 -3.078187  0.930937 -1.537186 -0.826715 -5.179500  2.657779 -1.628601   \n",
+       "  89 -1.628601  2.916959 -2.285918  0.781669 -4.334814  1.486367  1.052797   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -2.609666 -1.141711    5.109981   -1.266998   -0.258288  \n",
+       "  61 -5.336132 -1.321961    0.306438   -3.033890    0.200533  \n",
+       "  62 -1.870145 -0.863670   -2.127923   -2.263305   -0.614713  \n",
+       "  63  2.170096 -1.617134   -4.756598    0.492297   -2.062416  \n",
+       "  64  5.789576 -1.728239   -2.049161    0.770258   -1.351842  \n",
+       "  65  3.050609 -1.312519   -0.632181    0.153491    0.951488  \n",
+       "  66 -0.759152  0.436962    2.004270   -1.178278    1.231687  \n",
+       "  67 -3.540880  1.824918    2.537212   -0.692231    0.772661  \n",
+       "  68 -2.844267  1.501819    1.186685    2.019131   -0.802338  \n",
+       "  69 -1.580944 -0.685232   -1.999756    2.773578   -2.542120  \n",
+       "  70  0.576604 -1.596060   -3.063344    2.042677   -0.718184  \n",
+       "  71  3.212726 -1.689383   -4.139951   -0.648250   -0.258600  \n",
+       "  72  5.307505 -0.443206    1.965477   -2.803724    1.240522  \n",
+       "  73  3.419164  1.955569    4.946192   -2.239255    0.727797  \n",
+       "  74 -0.209690  2.595755    5.127648   -0.485151   -1.048553  \n",
+       "  75 -4.166616  2.434316    0.811661    1.957396   -0.971907  \n",
+       "  76 -3.308008  0.418675   -4.096251    3.057698   -1.595461  \n",
+       "  77 -0.657048  0.158499   -6.464860    1.443851   -1.069809  \n",
+       "  78  1.926940  0.884323   -5.234382   -1.380808    1.775812  \n",
+       "  79  3.455210  0.130247   -0.574002   -2.916684    1.551780  \n",
+       "  80  3.181148 -1.940312    2.617914   -5.305719    0.954069  \n",
+       "  81  0.795904 -1.159582    3.972387   -4.430579   -1.588166  \n",
+       "  82 -2.176082 -1.175309    2.232671   -1.086524   -2.464509  \n",
+       "  83 -3.295164  0.973188   -0.826057    3.844225   -2.241165  \n",
+       "  84 -2.411864  2.890455   -2.465340    6.373428   -1.129394  \n",
+       "  85 -2.035201  2.785620   -2.200440    2.490472   -0.043273  \n",
+       "  86 -0.590106  1.923935   -2.355443   -3.290635    2.239354  \n",
+       "  87  0.930937 -1.537186   -0.826715   -5.179500    2.657779  \n",
+       "  88  2.916959 -2.285918    0.781669   -4.334814    1.486367  \n",
+       "  89  1.620549 -1.929854    1.632944   -1.455596   -1.793962  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.618623 -1.851727 -2.646047  1.723866 -0.569919  0.135567  0.436616   \n",
+       "  61  0.436616  1.423434 -1.185700  2.743809 -0.655317 -1.128150 -1.075877   \n",
+       "  62 -1.075877  2.851996 -1.086912  0.049283  1.689472 -2.246365  1.368340   \n",
+       "  63  1.368340  2.811002  0.570809 -1.584925  1.936455 -1.650213  0.645653   \n",
+       "  64  0.645653  1.103224  1.346946 -1.514554  1.638320 -0.738145 -0.907032   \n",
+       "  65 -0.907032 -2.130953  0.729087 -0.045363 -1.176770  1.520549 -0.745589   \n",
+       "  66 -0.745589 -3.798937  0.301078  0.627036 -1.957944  2.207844 -0.874023   \n",
+       "  67 -0.874023 -2.324778 -2.021133  0.172672 -1.773560  1.735508 -1.175872   \n",
+       "  68 -1.175872 -0.145077 -0.714506 -0.581567 -0.562292  1.439571 -0.776126   \n",
+       "  69 -0.776126  2.354991  0.882150 -0.292824  0.553696 -0.086498  1.257944   \n",
+       "  70  1.257944  2.982970  1.172265 -1.023023  1.770174  0.897156  2.189200   \n",
+       "  71  2.189200  1.974453 -1.138415 -0.671705  0.684873 -1.118832  1.137647   \n",
+       "  72  1.137647 -1.696935 -1.936380 -0.012390  0.462524 -1.376543 -1.813177   \n",
+       "  73 -1.813177 -3.230779 -0.339893  0.170044 -0.845914 -0.740985 -2.358637   \n",
+       "  74 -2.358637 -2.505974  1.481134  2.114529 -0.555209 -1.311588 -1.857516   \n",
+       "  75 -1.857516  0.844192  4.115092  0.999567 -0.703949 -0.151682 -0.205376   \n",
+       "  76 -0.205376  3.166252  0.756737 -0.885138  0.293985  1.075243  0.973583   \n",
+       "  77  0.973583  3.618910 -2.232593 -2.303783  0.784390  1.041726  1.931186   \n",
+       "  78  1.931186  1.082722 -2.987955 -1.226331 -0.748084  0.048225  0.356001   \n",
+       "  79  0.356001 -1.455449 -1.134376 -0.891216  0.000256 -1.695465 -0.475582   \n",
+       "  80 -0.475582 -1.407977  0.389047  0.812076 -1.538098 -1.833660 -2.786787   \n",
+       "  81 -2.786787 -0.270902  1.342302  0.943521 -0.669215 -0.334537 -1.494407   \n",
+       "  82 -1.494407  0.484254  0.450467 -0.649942 -0.487784  0.708484  0.732837   \n",
+       "  83  0.732837  2.321132 -0.574330 -2.603086  0.808731  1.440377  1.560527   \n",
+       "  84  1.560527  1.819291 -2.266004 -0.450379  0.601264 -0.261853  0.988805   \n",
+       "  85  0.988805 -0.289290 -1.867312  0.240841  1.271201 -2.307314  1.235644   \n",
+       "  86  1.235644 -1.729803  0.404489  1.293507 -1.089716 -2.324197  0.406064   \n",
+       "  87  0.406064 -1.008360  1.714899  2.481590 -2.145235 -1.427575 -0.136433   \n",
+       "  88 -0.136433 -1.011929  2.937061  0.577854 -1.854742  1.741697  0.110671   \n",
+       "  89  0.110671 -0.779808  1.216857  1.430736 -0.399076  1.532006 -0.238795   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  1.423434 -1.185700    2.743809   -0.655317   -1.128150  \n",
+       "  61  2.851996 -1.086912    0.049283    1.689472   -2.246365  \n",
+       "  62  2.811002  0.570809   -1.584925    1.936455   -1.650213  \n",
+       "  63  1.103224  1.346946   -1.514554    1.638320   -0.738145  \n",
+       "  64 -2.130953  0.729087   -0.045363   -1.176770    1.520549  \n",
+       "  65 -3.798937  0.301078    0.627036   -1.957944    2.207844  \n",
+       "  66 -2.324778 -2.021133    0.172672   -1.773560    1.735508  \n",
+       "  67 -0.145077 -0.714506   -0.581567   -0.562292    1.439571  \n",
+       "  68  2.354991  0.882150   -0.292824    0.553696   -0.086498  \n",
+       "  69  2.982970  1.172265   -1.023023    1.770174    0.897156  \n",
+       "  70  1.974453 -1.138415   -0.671705    0.684873   -1.118832  \n",
+       "  71 -1.696935 -1.936380   -0.012390    0.462524   -1.376543  \n",
+       "  72 -3.230779 -0.339893    0.170044   -0.845914   -0.740985  \n",
+       "  73 -2.505974  1.481134    2.114529   -0.555209   -1.311588  \n",
+       "  74  0.844192  4.115092    0.999567   -0.703949   -0.151682  \n",
+       "  75  3.166252  0.756737   -0.885138    0.293985    1.075243  \n",
+       "  76  3.618910 -2.232593   -2.303783    0.784390    1.041726  \n",
+       "  77  1.082722 -2.987955   -1.226331   -0.748084    0.048225  \n",
+       "  78 -1.455449 -1.134376   -0.891216    0.000256   -1.695465  \n",
+       "  79 -1.407977  0.389047    0.812076   -1.538098   -1.833660  \n",
+       "  80 -0.270902  1.342302    0.943521   -0.669215   -0.334537  \n",
+       "  81  0.484254  0.450467   -0.649942   -0.487784    0.708484  \n",
+       "  82  2.321132 -0.574330   -2.603086    0.808731    1.440377  \n",
+       "  83  1.819291 -2.266004   -0.450379    0.601264   -0.261853  \n",
+       "  84 -0.289290 -1.867312    0.240841    1.271201   -2.307314  \n",
+       "  85 -1.729803  0.404489    1.293507   -1.089716   -2.324197  \n",
+       "  86 -1.008360  1.714899    2.481590   -2.145235   -1.427575  \n",
+       "  87 -1.011929  2.937061    0.577854   -1.854742    1.741697  \n",
+       "  88 -0.779808  1.216857    1.430736   -0.399076    1.532006  \n",
+       "  89  1.386718 -1.104284    0.500996    2.119447    1.809279  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -1.167226  0.167392 -1.685509 -1.247271 -1.132011 -1.283324 -2.280404   \n",
+       "  61 -2.280404 -0.025239 -1.916570  0.295656 -3.049798  0.919540 -3.239596   \n",
+       "  62 -3.239596  0.883136  0.095351  0.763694 -2.187441  1.969424 -2.940880   \n",
+       "  63 -2.940880 -0.385556 -0.050009  2.480736  1.412647  1.743876  0.800873   \n",
+       "  64  0.800873 -0.413936  2.068421 -0.120846  1.688452  0.344982  3.344545   \n",
+       "  65  3.344545 -0.043613  2.858649 -1.348447  2.039165 -0.250046  1.858965   \n",
+       "  66  1.858965  0.491425  3.507978 -2.062056  1.071336 -0.306025 -1.111941   \n",
+       "  67 -1.111941 -0.590985  1.625797 -2.523370  0.823870 -0.607660 -3.540877   \n",
+       "  68 -3.540877 -0.666781 -0.166255 -1.393848 -1.710233 -0.401415 -3.396411   \n",
+       "  69 -3.396411 -1.846702 -1.578918  2.095835 -1.059427  0.299222 -1.745039   \n",
+       "  70 -1.745039 -1.540209 -2.098739  2.101022 -0.616314 -0.688610  0.614357   \n",
+       "  71  0.614357  0.152666 -2.039708  0.672615  0.871450 -0.298649  1.972368   \n",
+       "  72  1.972368  1.019862 -0.044612 -0.636590  3.507761  1.290824  2.461228   \n",
+       "  73  2.461228  0.000129  2.865856 -2.004953  1.552899  1.770791 -1.199805   \n",
+       "  74 -1.199805 -0.144117  4.000769 -1.678536  0.306273  1.268093 -1.060845   \n",
+       "  75 -1.060845 -0.498612  1.978117 -1.656998 -1.237523 -1.985477 -2.486280   \n",
+       "  76 -2.486280  0.525568  1.075937  0.236648 -0.712883 -2.864928 -1.029292   \n",
+       "  77 -1.029292  0.883893 -0.566037  2.263940  2.194865 -1.601640  0.517514   \n",
+       "  78  0.517514  0.206294 -1.132402  1.208318  3.698926  0.388490  1.255694   \n",
+       "  79  1.255694 -0.962525 -0.857602  0.969281  2.100742  2.188003 -0.006574   \n",
+       "  80 -0.006574 -1.930397  0.286045  1.569053 -1.391181  2.500662  0.187281   \n",
+       "  81  0.187281 -1.526384  0.735018 -0.150289 -2.973972  0.473920  0.532088   \n",
+       "  82  0.532088 -0.175339  1.540847 -1.312730 -4.698008  0.075215 -0.149244   \n",
+       "  83 -0.149244  1.037076  0.971530 -2.219011 -1.744916 -2.206001 -0.206520   \n",
+       "  84 -0.206520  1.620385  1.097709 -0.844839  1.806090 -1.115976  0.091740   \n",
+       "  85  0.091740  2.242596 -1.252491 -0.005468  1.629252 -1.309366  0.970703   \n",
+       "  86  0.970703  0.244445 -0.889020  0.328863  2.298506 -0.497965  1.590650   \n",
+       "  87  1.590650 -1.800840  0.751319  0.795303  0.720622  0.192357  0.578302   \n",
+       "  88  0.578302 -0.499254 -0.608451  0.792281  0.625734  1.910050  0.780563   \n",
+       "  89  0.780563 -1.054341 -0.948198  1.532694 -1.636653  1.116860  1.719407   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -0.025239 -1.916570    0.295656   -3.049798    0.919540  \n",
+       "  61  0.883136  0.095351    0.763694   -2.187441    1.969424  \n",
+       "  62 -0.385556 -0.050009    2.480736    1.412647    1.743876  \n",
+       "  63 -0.413936  2.068421   -0.120846    1.688452    0.344982  \n",
+       "  64 -0.043613  2.858649   -1.348447    2.039165   -0.250046  \n",
+       "  65  0.491425  3.507978   -2.062056    1.071336   -0.306025  \n",
+       "  66 -0.590985  1.625797   -2.523370    0.823870   -0.607660  \n",
+       "  67 -0.666781 -0.166255   -1.393848   -1.710233   -0.401415  \n",
+       "  68 -1.846702 -1.578918    2.095835   -1.059427    0.299222  \n",
+       "  69 -1.540209 -2.098739    2.101022   -0.616314   -0.688610  \n",
+       "  70  0.152666 -2.039708    0.672615    0.871450   -0.298649  \n",
+       "  71  1.019862 -0.044612   -0.636590    3.507761    1.290824  \n",
+       "  72  0.000129  2.865856   -2.004953    1.552899    1.770791  \n",
+       "  73 -0.144117  4.000769   -1.678536    0.306273    1.268093  \n",
+       "  74 -0.498612  1.978117   -1.656998   -1.237523   -1.985477  \n",
+       "  75  0.525568  1.075937    0.236648   -0.712883   -2.864928  \n",
+       "  76  0.883893 -0.566037    2.263940    2.194865   -1.601640  \n",
+       "  77  0.206294 -1.132402    1.208318    3.698926    0.388490  \n",
+       "  78 -0.962525 -0.857602    0.969281    2.100742    2.188003  \n",
+       "  79 -1.930397  0.286045    1.569053   -1.391181    2.500662  \n",
+       "  80 -1.526384  0.735018   -0.150289   -2.973972    0.473920  \n",
+       "  81 -0.175339  1.540847   -1.312730   -4.698008    0.075215  \n",
+       "  82  1.037076  0.971530   -2.219011   -1.744916   -2.206001  \n",
+       "  83  1.620385  1.097709   -0.844839    1.806090   -1.115976  \n",
+       "  84  2.242596 -1.252491   -0.005468    1.629252   -1.309366  \n",
+       "  85  0.244445 -0.889020    0.328863    2.298506   -0.497965  \n",
+       "  86 -1.800840  0.751319    0.795303    0.720622    0.192357  \n",
+       "  87 -0.499254 -0.608451    0.792281    0.625734    1.910050  \n",
+       "  88 -1.054341 -0.948198    1.532694   -1.636653    1.116860  \n",
+       "  89  1.121406 -2.246503   -0.045191   -1.734408   -0.390020  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.398007 -1.479916 -0.460586  1.963485  0.778663  1.210486  0.882067   \n",
+       "  61  0.882067 -0.855101 -0.035233  4.074258 -1.066623 -1.343082  1.628291   \n",
+       "  62  1.628291  0.162431 -0.288115  1.099491 -2.725116 -0.726502  0.801720   \n",
+       "  63  0.801720 -0.475885 -3.177662 -3.396770 -2.776347 -0.637670 -0.620168   \n",
+       "  64 -0.620168  0.515000 -2.293142 -4.911863 -1.002465  0.816826 -0.861045   \n",
+       "  65 -0.861045  0.778586  0.805629 -1.780978  1.854739  1.291458 -1.070533   \n",
+       "  66 -1.070533  1.209739  4.369712  2.743951  3.258460 -0.209997 -1.912532   \n",
+       "  67 -1.912532 -1.977688  3.903134  5.127530  2.357577  0.363131  0.366923   \n",
+       "  68  0.366923 -1.232676  0.606916  3.151103 -0.574317  0.545037  0.887142   \n",
+       "  69  0.887142  2.599536 -2.886806  0.641680  0.023141  1.622852 -1.358916   \n",
+       "  70 -1.358916  3.479275 -4.479379 -2.211291 -1.753701  0.733647 -0.675350   \n",
+       "  71 -0.675350  3.838734 -2.998618 -4.513093 -0.751182  0.256657  0.133476   \n",
+       "  72  0.133476  1.275202  0.108603 -3.096559 -0.160155 -0.934443  0.676577   \n",
+       "  73  0.676577 -1.545327  3.349526  0.036517  1.473372 -0.347145  1.978592   \n",
+       "  74  1.978592 -2.655303  2.492451  1.975053  1.033512  1.746959  0.510410   \n",
+       "  75  0.510410 -1.747708  1.902057  2.143028 -0.153508 -0.027923 -1.807043   \n",
+       "  76 -1.807043 -0.213928  0.385088 -0.828867  0.666566 -0.863924 -4.338421   \n",
+       "  77 -4.338421  0.433653  0.063883 -2.684510 -0.087626 -1.836943 -4.083309   \n",
+       "  78 -4.083309  0.977052 -2.228163 -2.034469  0.443623 -0.016114 -0.256001   \n",
+       "  79 -0.256001  0.586525  0.197333 -0.869808  1.282626  0.850809  5.958040   \n",
+       "  80  5.958040  0.140962 -0.255633  4.122751  1.469220  1.962489  5.987298   \n",
+       "  81  5.987298 -0.296900 -0.665429  2.996892  0.275355 -0.321202  2.205598   \n",
+       "  82  2.205598 -0.403897 -3.168002  1.226043 -1.447568 -2.720313 -4.044254   \n",
+       "  83 -4.044254 -0.614493 -3.255016 -2.155671 -0.851214 -3.946684 -5.737718   \n",
+       "  84 -5.737718 -1.134317 -1.426159 -1.953780  0.890659 -2.981015 -2.924716   \n",
+       "  85 -2.924716 -1.579553  1.445963 -0.923854  1.559216 -0.568282  0.677553   \n",
+       "  86  0.677553 -0.794114  4.044008  0.717635  1.533358  2.080238  3.655744   \n",
+       "  87  3.655744  0.546354  3.126001  1.300627 -0.480809  1.500773  3.030372   \n",
+       "  88  3.030372 -0.476754 -0.755059  0.960152 -2.798714  0.372368  2.008380   \n",
+       "  89  2.008380  0.026488 -3.103756 -0.454796 -2.215750  0.187846 -0.328257   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60 -0.855101 -0.035233    4.074258   -1.066623   -1.343082  \n",
+       "  61  0.162431 -0.288115    1.099491   -2.725116   -0.726502  \n",
+       "  62 -0.475885 -3.177662   -3.396770   -2.776347   -0.637670  \n",
+       "  63  0.515000 -2.293142   -4.911863   -1.002465    0.816826  \n",
+       "  64  0.778586  0.805629   -1.780978    1.854739    1.291458  \n",
+       "  65  1.209739  4.369712    2.743951    3.258460   -0.209997  \n",
+       "  66 -1.977688  3.903134    5.127530    2.357577    0.363131  \n",
+       "  67 -1.232676  0.606916    3.151103   -0.574317    0.545037  \n",
+       "  68  2.599536 -2.886806    0.641680    0.023141    1.622852  \n",
+       "  69  3.479275 -4.479379   -2.211291   -1.753701    0.733647  \n",
+       "  70  3.838734 -2.998618   -4.513093   -0.751182    0.256657  \n",
+       "  71  1.275202  0.108603   -3.096559   -0.160155   -0.934443  \n",
+       "  72 -1.545327  3.349526    0.036517    1.473372   -0.347145  \n",
+       "  73 -2.655303  2.492451    1.975053    1.033512    1.746959  \n",
+       "  74 -1.747708  1.902057    2.143028   -0.153508   -0.027923  \n",
+       "  75 -0.213928  0.385088   -0.828867    0.666566   -0.863924  \n",
+       "  76  0.433653  0.063883   -2.684510   -0.087626   -1.836943  \n",
+       "  77  0.977052 -2.228163   -2.034469    0.443623   -0.016114  \n",
+       "  78  0.586525  0.197333   -0.869808    1.282626    0.850809  \n",
+       "  79  0.140962 -0.255633    4.122751    1.469220    1.962489  \n",
+       "  80 -0.296900 -0.665429    2.996892    0.275355   -0.321202  \n",
+       "  81 -0.403897 -3.168002    1.226043   -1.447568   -2.720313  \n",
+       "  82 -0.614493 -3.255016   -2.155671   -0.851214   -3.946684  \n",
+       "  83 -1.134317 -1.426159   -1.953780    0.890659   -2.981015  \n",
+       "  84 -1.579553  1.445963   -0.923854    1.559216   -0.568282  \n",
+       "  85 -0.794114  4.044008    0.717635    1.533358    2.080238  \n",
+       "  86  0.546354  3.126001    1.300627   -0.480809    1.500773  \n",
+       "  87 -0.476754 -0.755059    0.960152   -2.798714    0.372368  \n",
+       "  88  0.026488 -3.103756   -0.454796   -2.215750    0.187846  \n",
+       "  89  2.003878 -4.872825   -1.095859   -0.139129   -1.012713  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -0.209775  1.983916 -1.399654  2.702434 -3.618466  2.779231 -0.761360   \n",
+       "  61 -0.761360  1.758685  0.859538  1.056490 -1.900676  2.514305  0.354054   \n",
+       "  62  0.354054  0.274470  0.152621 -1.655514  0.812150 -1.019162  1.203846   \n",
+       "  63  1.203846 -1.388322  1.126554 -1.869503  3.724072 -2.609569  0.225827   \n",
+       "  64  0.225827 -3.229540  1.071901 -1.110651  1.660682 -1.586151 -0.754077   \n",
+       "  65 -0.754077 -1.901526  2.611333  1.399496 -0.766115 -0.429593  0.314103   \n",
+       "  66  0.314103  0.741687  0.111993  2.635956 -2.249805  2.616262  0.101230   \n",
+       "  67  0.101230  3.352516 -0.580449  2.052722 -3.195358  1.762890  0.068388   \n",
+       "  68  0.068388  4.921416 -2.388240  1.233698 -1.175603  0.164272  0.125049   \n",
+       "  69  0.125049  1.977655 -2.473697 -1.529232  1.361067 -2.702633  1.158777   \n",
+       "  70  1.158777 -0.672836  0.224110 -3.440139  1.533563 -4.883118  2.025432   \n",
+       "  71  2.025432 -4.428374  2.122866 -2.867199  0.313816 -3.942198  0.145822   \n",
+       "  72  0.145822 -2.604815  2.365404 -0.794905 -0.125253 -0.293663 -0.384198   \n",
+       "  73 -0.384198  1.681565  0.526083  1.587665 -1.224827  3.362266 -1.979570   \n",
+       "  74 -1.979570  3.991158 -2.004997  2.629875 -1.142648  5.910755 -2.575205   \n",
+       "  75 -2.575205  4.393863 -1.519879  0.874901 -0.236475  1.205169 -0.524899   \n",
+       "  76 -0.524899  0.577445  0.320540  1.100972  1.773889 -0.133791  2.490564   \n",
+       "  77  2.490564 -1.490734  1.598248 -0.551581  1.379639 -3.893544  2.959845   \n",
+       "  78  2.959845 -2.297707  0.378391  0.042724  1.198809 -4.085242  1.045900   \n",
+       "  79  1.045900  0.032022 -0.808208  2.238310  0.038341 -0.983553 -0.899231   \n",
+       "  80 -0.899231  1.018718 -2.093362  0.310942 -1.813785  2.472030 -1.845194   \n",
+       "  81 -1.845194  1.332143 -0.779706 -0.175863 -2.035967  4.882394 -1.392098   \n",
+       "  82 -1.392098  0.469300  1.020278 -2.451785 -0.870250  1.910514  0.745574   \n",
+       "  83  0.745574 -0.565977  2.639429 -2.489304  0.884485 -0.145968  1.673265   \n",
+       "  84  1.673265  0.185552  2.615073  0.238968  0.817064 -2.389345  2.795449   \n",
+       "  85  2.795449 -0.004722 -0.325815  2.104353  0.658313 -2.383934  1.352611   \n",
+       "  86  1.352611 -0.695171 -2.703843  3.319148  0.571645 -0.435923 -0.766970   \n",
+       "  87 -0.766970 -2.411104 -2.744937  0.687423  0.234186  0.599716 -1.372550   \n",
+       "  88 -1.372550 -0.158052 -2.040457 -0.301968  1.964977  0.370966 -0.665064   \n",
+       "  89 -0.665064 -1.034281  0.923198 -2.121550  1.026455  0.140262  1.057973   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  1.758685  0.859538    1.056490   -1.900676    2.514305  \n",
+       "  61  0.274470  0.152621   -1.655514    0.812150   -1.019162  \n",
+       "  62 -1.388322  1.126554   -1.869503    3.724072   -2.609569  \n",
+       "  63 -3.229540  1.071901   -1.110651    1.660682   -1.586151  \n",
+       "  64 -1.901526  2.611333    1.399496   -0.766115   -0.429593  \n",
+       "  65  0.741687  0.111993    2.635956   -2.249805    2.616262  \n",
+       "  66  3.352516 -0.580449    2.052722   -3.195358    1.762890  \n",
+       "  67  4.921416 -2.388240    1.233698   -1.175603    0.164272  \n",
+       "  68  1.977655 -2.473697   -1.529232    1.361067   -2.702633  \n",
+       "  69 -0.672836  0.224110   -3.440139    1.533563   -4.883118  \n",
+       "  70 -4.428374  2.122866   -2.867199    0.313816   -3.942198  \n",
+       "  71 -2.604815  2.365404   -0.794905   -0.125253   -0.293663  \n",
+       "  72  1.681565  0.526083    1.587665   -1.224827    3.362266  \n",
+       "  73  3.991158 -2.004997    2.629875   -1.142648    5.910755  \n",
+       "  74  4.393863 -1.519879    0.874901   -0.236475    1.205169  \n",
+       "  75  0.577445  0.320540    1.100972    1.773889   -0.133791  \n",
+       "  76 -1.490734  1.598248   -0.551581    1.379639   -3.893544  \n",
+       "  77 -2.297707  0.378391    0.042724    1.198809   -4.085242  \n",
+       "  78  0.032022 -0.808208    2.238310    0.038341   -0.983553  \n",
+       "  79  1.018718 -2.093362    0.310942   -1.813785    2.472030  \n",
+       "  80  1.332143 -0.779706   -0.175863   -2.035967    4.882394  \n",
+       "  81  0.469300  1.020278   -2.451785   -0.870250    1.910514  \n",
+       "  82 -0.565977  2.639429   -2.489304    0.884485   -0.145968  \n",
+       "  83  0.185552  2.615073    0.238968    0.817064   -2.389345  \n",
+       "  84 -0.004722 -0.325815    2.104353    0.658313   -2.383934  \n",
+       "  85 -0.695171 -2.703843    3.319148    0.571645   -0.435923  \n",
+       "  86 -2.411104 -2.744937    0.687423    0.234186    0.599716  \n",
+       "  87 -0.158052 -2.040457   -0.301968    1.964977    0.370966  \n",
+       "  88 -1.034281  0.923198   -2.121550    1.026455    0.140262  \n",
+       "  89  1.422899  4.488055   -1.171351    0.445268   -1.498079  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  60 -2.165656 -1.012311  4.460661  0.512352  0.084778 -2.726044 -2.855503   \n",
+       "  61 -2.855503  0.290858  0.388224 -0.095945  0.367747 -1.614404 -0.791065   \n",
+       "  62 -0.791065  3.258051 -4.737279 -1.387328  0.905106  0.653974  0.549689   \n",
+       "  63  0.549689  2.324396 -5.277272 -0.615716  0.256732  1.775130  0.681464   \n",
+       "  64  0.681464  2.187001 -1.264876 -1.251307 -1.242144  1.298649  0.134990   \n",
+       "  65  0.134990 -0.565480  2.036034 -1.630925 -0.865789  0.191516  0.288091   \n",
+       "  66  0.288091 -1.475902  4.548979 -2.467309  0.393827 -1.263533 -0.377747   \n",
+       "  67 -0.377747 -1.813656  4.782790 -0.978624  0.420092  0.726369 -1.436444   \n",
+       "  68 -1.436444 -0.206226  0.791167  2.552580  0.583373  0.727112  1.043709   \n",
+       "  69  1.043709  1.454386 -2.358628  2.971459  0.950932  0.602520  1.682215   \n",
+       "  70  1.682215  2.846495 -3.373910  0.124101 -0.052988 -0.538958  0.751184   \n",
+       "  71  0.751184 -0.651571 -1.970679 -3.125021 -0.337056 -2.436883  1.470732   \n",
+       "  72  1.470732 -1.130288  1.025356 -2.714964 -0.243951 -2.717292  0.625061   \n",
+       "  73  0.625061 -2.189104  1.670263 -1.416479  0.840228  0.299973  0.401571   \n",
+       "  74  0.401571  0.270148  0.829678  0.631770  1.610272  1.610117 -0.837196   \n",
+       "  75 -0.837196  1.370522 -1.600171  1.402540  0.537670  4.202027 -1.974223   \n",
+       "  76 -1.974223  1.392759 -0.662995  1.153663 -1.028711  2.083353 -1.149414   \n",
+       "  77 -1.149414 -0.146609  0.547633 -1.459172 -0.636692 -1.718239 -0.232300   \n",
+       "  78 -0.232300 -0.717104  0.501159 -1.807283 -0.864730 -4.611572  0.391479   \n",
+       "  79  0.391479 -1.581055  1.098984  0.778674  0.210781 -3.338497  2.493381   \n",
+       "  80  2.493381 -2.813428  0.143602  2.532044  0.287317 -1.027477  4.402519   \n",
+       "  81  4.402519 -0.230272  0.222516  0.967888 -1.188864 -0.888017  2.296136   \n",
+       "  82  2.296136  3.165116 -2.382624  1.225946 -1.323221  1.130519 -0.623352   \n",
+       "  83 -0.623352  2.897938 -1.604568 -1.751727 -0.649017  1.133186 -1.186037   \n",
+       "  84 -1.186037  0.262927 -1.272783 -1.607198  0.073505  0.557602 -1.164215   \n",
+       "  85 -1.164215 -4.002295  0.173476 -1.130770  1.287545  0.416290 -0.196504   \n",
+       "  86 -0.196504 -2.560250  2.748453 -1.432013  0.309054 -0.868056 -1.004020   \n",
+       "  87 -1.004020 -0.366731  2.894229 -0.168462 -1.335828 -2.101592  0.764309   \n",
+       "  88  0.764309  0.404532  1.843497 -0.328352 -3.324994 -0.535436  0.978711   \n",
+       "  89  0.978711  1.218457 -0.220437  0.578928 -1.649496  0.580766  0.866420   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  60  0.290858  0.388224   -0.095945    0.367747   -1.614404  \n",
+       "  61  3.258051 -4.737279   -1.387328    0.905106    0.653974  \n",
+       "  62  2.324396 -5.277272   -0.615716    0.256732    1.775130  \n",
+       "  63  2.187001 -1.264876   -1.251307   -1.242144    1.298649  \n",
+       "  64 -0.565480  2.036034   -1.630925   -0.865789    0.191516  \n",
+       "  65 -1.475902  4.548979   -2.467309    0.393827   -1.263533  \n",
+       "  66 -1.813656  4.782790   -0.978624    0.420092    0.726369  \n",
+       "  67 -0.206226  0.791167    2.552580    0.583373    0.727112  \n",
+       "  68  1.454386 -2.358628    2.971459    0.950932    0.602520  \n",
+       "  69  2.846495 -3.373910    0.124101   -0.052988   -0.538958  \n",
+       "  70 -0.651571 -1.970679   -3.125021   -0.337056   -2.436883  \n",
+       "  71 -1.130288  1.025356   -2.714964   -0.243951   -2.717292  \n",
+       "  72 -2.189104  1.670263   -1.416479    0.840228    0.299973  \n",
+       "  73  0.270148  0.829678    0.631770    1.610272    1.610117  \n",
+       "  74  1.370522 -1.600171    1.402540    0.537670    4.202027  \n",
+       "  75  1.392759 -0.662995    1.153663   -1.028711    2.083353  \n",
+       "  76 -0.146609  0.547633   -1.459172   -0.636692   -1.718239  \n",
+       "  77 -0.717104  0.501159   -1.807283   -0.864730   -4.611572  \n",
+       "  78 -1.581055  1.098984    0.778674    0.210781   -3.338497  \n",
+       "  79 -2.813428  0.143602    2.532044    0.287317   -1.027477  \n",
+       "  80 -0.230272  0.222516    0.967888   -1.188864   -0.888017  \n",
+       "  81  3.165116 -2.382624    1.225946   -1.323221    1.130519  \n",
+       "  82  2.897938 -1.604568   -1.751727   -0.649017    1.133186  \n",
+       "  83  0.262927 -1.272783   -1.607198    0.073505    0.557602  \n",
+       "  84 -4.002295  0.173476   -1.130770    1.287545    0.416290  \n",
+       "  85 -2.560250  2.748453   -1.432013    0.309054   -0.868056  \n",
+       "  86 -0.366731  2.894229   -0.168462   -1.335828   -2.101592  \n",
+       "  87  0.404532  1.843497   -0.328352   -3.324994   -0.535436  \n",
+       "  88  1.218457 -0.220437    0.578928   -1.649496    0.580766  \n",
+       "  89  1.084599 -2.596926    1.565112   -0.591769    1.397244  ],\n",
+       " [    position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.416700 -3.624810  3.284369 -4.247110 -0.258408  2.567445  1.393611   \n",
+       "  91  1.393611 -3.025457  4.306449 -4.607767  0.477560  1.766001  0.141995   \n",
+       "  92  0.141995 -0.315108  1.603595 -1.078277  0.611742  0.464117 -0.475689   \n",
+       "  93 -0.475689 -0.307528 -2.917162  1.390820  1.040833 -2.616601 -2.048299   \n",
+       "  94 -2.048299  1.604193 -3.286767  3.564031  0.666178 -3.682880 -1.920410   \n",
+       "  95 -1.920410  0.301301 -1.509458  2.717610  0.591750 -2.220386 -0.277497   \n",
+       "  96 -0.277497 -0.310946  0.937258 -0.978405  0.615388  1.024304  1.892707   \n",
+       "  97  1.892707  1.222579  2.077502 -1.598360  0.901812  2.575396  0.700152   \n",
+       "  98  0.700152  0.989836  1.990585 -0.731666  0.373581  1.945908 -1.150664   \n",
+       "  99 -1.150664  0.248047 -1.251445  1.471908  1.369095 -1.219077       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -3.025457  4.306449   -4.607767    0.477560    1.766001  \n",
+       "  91 -0.315108  1.603595   -1.078277    0.611742    0.464117  \n",
+       "  92 -0.307528 -2.917162    1.390820    1.040833   -2.616601  \n",
+       "  93  1.604193 -3.286767    3.564031    0.666178   -3.682880  \n",
+       "  94  0.301301 -1.509458    2.717610    0.591750   -2.220386  \n",
+       "  95 -0.310946  0.937258   -0.978405    0.615388    1.024304  \n",
+       "  96  1.222579  2.077502   -1.598360    0.901812    2.575396  \n",
+       "  97  0.989836  1.990585   -0.731666    0.373581    1.945908  \n",
+       "  98  0.248047 -1.251445    1.471908    1.369095   -1.219077  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.844775 -0.683084 -2.389418 -2.194385 -2.167888  0.776664 -0.073000   \n",
+       "  91 -0.073000 -0.612067 -0.437435 -1.148200  1.766697  3.276472  0.607724   \n",
+       "  92  0.607724  0.024935  1.486925  0.263627  4.525540  2.903643  2.961431   \n",
+       "  93  2.961431 -0.555491  1.260348  4.018761  3.114657  0.761845  3.263648   \n",
+       "  94  3.263648  0.587949  0.819413  4.453367 -1.469920 -3.829786 -0.022117   \n",
+       "  95 -0.022117  1.950978  0.104085  3.201953 -3.258048 -3.697476 -3.453358   \n",
+       "  96 -3.453358  2.411187 -1.695725 -2.025692 -4.250793 -1.505105 -3.636218   \n",
+       "  97 -3.636218  1.516836 -2.001407 -3.260210 -0.967584  1.452558 -1.259054   \n",
+       "  98 -1.259054 -1.320138 -0.346712 -3.937003  1.067736  2.395416  1.423157   \n",
+       "  99  1.423157 -2.750100  1.145481 -0.759939  2.611100  1.958985       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.612067 -0.437435   -1.148200    1.766697    3.276472  \n",
+       "  91  0.024935  1.486925    0.263627    4.525540    2.903643  \n",
+       "  92 -0.555491  1.260348    4.018761    3.114657    0.761845  \n",
+       "  93  0.587949  0.819413    4.453367   -1.469920   -3.829786  \n",
+       "  94  1.950978  0.104085    3.201953   -3.258048   -3.697476  \n",
+       "  95  2.411187 -1.695725   -2.025692   -4.250793   -1.505105  \n",
+       "  96  1.516836 -2.001407   -3.260210   -0.967584    1.452558  \n",
+       "  97 -1.320138 -0.346712   -3.937003    1.067736    2.395416  \n",
+       "  98 -2.750100  1.145481   -0.759939    2.611100    1.958985  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.788060 -1.480080 -0.636910 -1.396105 -0.471885 -1.756906  0.336026   \n",
+       "  91  0.336026 -0.074360 -0.074487 -1.923061 -1.192424 -0.741124 -0.491042   \n",
+       "  92 -0.491042  1.514327  0.559967 -0.888019 -1.435148  0.580355 -0.780028   \n",
+       "  93 -0.780028  1.685748  0.934281 -0.161589 -1.654368  1.343423 -0.208817   \n",
+       "  94 -0.208817  1.830475  1.707827  0.461274 -0.739353  0.920172 -0.780844   \n",
+       "  95 -0.780844  1.484224 -0.129986  0.318603 -0.488717 -0.336269  0.311185   \n",
+       "  96  0.311185 -0.386321  0.265115  0.491511  1.176548  0.376266  2.000436   \n",
+       "  97  2.000436 -1.253333 -0.196009 -0.762807  1.452829  1.153834  2.471127   \n",
+       "  98  2.471127  0.449355  0.033815 -1.793604  1.039659  1.761873  1.088058   \n",
+       "  99  1.088058  1.596194 -0.678505 -2.149846 -1.891386  0.461521       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.074360 -0.074487   -1.923061   -1.192424   -0.741124  \n",
+       "  91  1.514327  0.559967   -0.888019   -1.435148    0.580355  \n",
+       "  92  1.685748  0.934281   -0.161589   -1.654368    1.343423  \n",
+       "  93  1.830475  1.707827    0.461274   -0.739353    0.920172  \n",
+       "  94  1.484224 -0.129986    0.318603   -0.488717   -0.336269  \n",
+       "  95 -0.386321  0.265115    0.491511    1.176548    0.376266  \n",
+       "  96 -1.253333 -0.196009   -0.762807    1.452829    1.153834  \n",
+       "  97  0.449355  0.033815   -1.793604    1.039659    1.761873  \n",
+       "  98  1.596194 -0.678505   -2.149846   -1.891386    0.461521  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  0.301190  0.380842  1.606308 -1.286544  2.109026 -3.293401  0.730551   \n",
+       "  91  0.730551 -0.381916 -0.347121 -0.768725  2.094923 -3.565978  3.020000   \n",
+       "  92  3.020000 -1.983131 -3.561172  0.850795  1.142193 -1.955739  1.306717   \n",
+       "  93  1.306717 -2.100363 -2.842159  0.197859 -1.750342  2.886875  0.600805   \n",
+       "  94  0.600805 -0.913524  0.173386 -0.318022 -2.647185  4.338383 -0.439271   \n",
+       "  95 -0.439271  2.257758  2.493722 -0.939630 -2.067235  1.764715 -1.379650   \n",
+       "  96 -1.379650  3.928516  1.339030 -1.091258 -1.033788 -0.898601  0.081235   \n",
+       "  97  0.081235  3.587624 -0.092580 -0.743741  3.194531 -1.635289 -1.600291   \n",
+       "  98 -1.600291 -0.434914 -0.805256  0.364718  5.011984 -1.750213 -1.300325   \n",
+       "  99 -1.300325 -2.504268 -1.643029  1.174850  4.858573  0.370479       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.381916 -0.347121   -0.768725    2.094923   -3.565978  \n",
+       "  91 -1.983131 -3.561172    0.850795    1.142193   -1.955739  \n",
+       "  92 -2.100363 -2.842159    0.197859   -1.750342    2.886875  \n",
+       "  93 -0.913524  0.173386   -0.318022   -2.647185    4.338383  \n",
+       "  94  2.257758  2.493722   -0.939630   -2.067235    1.764715  \n",
+       "  95  3.928516  1.339030   -1.091258   -1.033788   -0.898601  \n",
+       "  96  3.587624 -0.092580   -0.743741    3.194531   -1.635289  \n",
+       "  97 -0.434914 -0.805256    0.364718    5.011984   -1.750213  \n",
+       "  98 -2.504268 -1.643029    1.174850    4.858573    0.370479  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.980842  0.350935  1.159034 -2.432277 -3.455090  1.105144  1.479669   \n",
+       "  91  1.479669  0.265045 -0.071244 -0.719727 -3.762730  1.986603 -0.243755   \n",
+       "  92 -0.243755 -1.017233 -0.663129  0.145985 -0.992996  1.675404 -1.798941   \n",
+       "  93 -1.798941 -0.307191  0.178933  1.116960  2.559951 -0.848825 -2.315550   \n",
+       "  94 -2.315550 -0.243347  0.143555  0.395417  3.236177 -2.462995 -1.594520   \n",
+       "  95 -1.594520 -0.730589  1.225854 -0.779284  1.150345 -4.339275 -0.476648   \n",
+       "  96 -0.476648  0.078115 -1.052917 -1.436326 -0.579653 -2.657774  0.295173   \n",
+       "  97  0.295173  1.025137 -3.075420 -1.031647 -2.061050  1.068201  1.476599   \n",
+       "  98  1.476599  0.322530 -3.052370  1.325596 -2.959582  4.242178  2.106233   \n",
+       "  99  2.106233 -1.597711 -1.135695  1.837659 -1.251309  3.966337       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.265045 -0.071244   -0.719727   -3.762730    1.986603  \n",
+       "  91 -1.017233 -0.663129    0.145985   -0.992996    1.675404  \n",
+       "  92 -0.307191  0.178933    1.116960    2.559951   -0.848825  \n",
+       "  93 -0.243347  0.143555    0.395417    3.236177   -2.462995  \n",
+       "  94 -0.730589  1.225854   -0.779284    1.150345   -4.339275  \n",
+       "  95  0.078115 -1.052917   -1.436326   -0.579653   -2.657774  \n",
+       "  96  1.025137 -3.075420   -1.031647   -2.061050    1.068201  \n",
+       "  97  0.322530 -3.052370    1.325596   -2.959582    4.242178  \n",
+       "  98 -1.597711 -1.135695    1.837659   -1.251309    3.966337  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.734624 -0.609222 -1.036570 -1.747476  0.232383 -0.234142 -1.343739   \n",
+       "  91 -1.343739  0.970877 -1.130455 -1.461228 -0.445302 -1.399234 -0.297883   \n",
+       "  92 -0.297883  0.760777 -2.320275  0.183841 -0.846643  0.398287  1.610080   \n",
+       "  93  1.610080 -0.370841 -1.055738  2.529339  0.229553 -0.774070  2.056509   \n",
+       "  94  2.056509 -1.348628  1.934080  1.099374 -0.922645  0.245889  1.388162   \n",
+       "  95  1.388162 -0.729026  2.207346  0.664876  0.037179  1.019552 -0.126700   \n",
+       "  96 -0.126700  0.916343  2.213808 -2.654876  0.895148  1.226401 -4.014663   \n",
+       "  97 -4.014663  1.385940 -0.290279 -2.908185  1.638980 -0.310469 -1.594719   \n",
+       "  98 -1.594719  1.110614 -2.283005 -2.660561  2.920590 -0.696967 -0.678632   \n",
+       "  99 -0.678632  1.899536 -3.123920  0.573857  1.083805 -0.894776       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.970877 -1.130455   -1.461228   -0.445302   -1.399234  \n",
+       "  91  0.760777 -2.320275    0.183841   -0.846643    0.398287  \n",
+       "  92 -0.370841 -1.055738    2.529339    0.229553   -0.774070  \n",
+       "  93 -1.348628  1.934080    1.099374   -0.922645    0.245889  \n",
+       "  94 -0.729026  2.207346    0.664876    0.037179    1.019552  \n",
+       "  95  0.916343  2.213808   -2.654876    0.895148    1.226401  \n",
+       "  96  1.385940 -0.290279   -2.908185    1.638980   -0.310469  \n",
+       "  97  1.110614 -2.283005   -2.660561    2.920590   -0.696967  \n",
+       "  98  1.899536 -3.123920    0.573857    1.083805   -0.894776  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.712535  2.147108 -0.908203 -2.797310  0.687622  0.925929  0.817156   \n",
+       "  91  0.817156  0.856563 -1.416775 -3.181914 -2.315316  0.196571  0.705327   \n",
+       "  92  0.705327 -1.364279  0.466378 -2.575465 -2.623876 -0.240482  1.609313   \n",
+       "  93  1.609313 -2.520184  1.737394 -0.775011 -1.694601 -1.450493  0.320309   \n",
+       "  94  0.320309 -2.238890  2.912343  1.441508  0.035432 -1.416718 -1.909092   \n",
+       "  95 -1.909092  1.740160  1.530704  1.489631  1.305091  1.419014 -2.382876   \n",
+       "  96 -2.382876  0.956422 -1.219333  0.817287  0.770867  2.049496 -0.681677   \n",
+       "  97 -0.681677  0.539551 -1.394952 -0.573453 -0.146953  1.939897  0.963765   \n",
+       "  98  0.963765 -1.406308  0.253741 -1.251408  0.357917  0.327781  2.850471   \n",
+       "  99  2.850471 -1.591889  0.285962 -1.081273 -0.739715 -1.237475       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.856563 -1.416775   -3.181914   -2.315316    0.196571  \n",
+       "  91 -1.364279  0.466378   -2.575465   -2.623876   -0.240482  \n",
+       "  92 -2.520184  1.737394   -0.775011   -1.694601   -1.450493  \n",
+       "  93 -2.238890  2.912343    1.441508    0.035432   -1.416718  \n",
+       "  94  1.740160  1.530704    1.489631    1.305091    1.419014  \n",
+       "  95  0.956422 -1.219333    0.817287    0.770867    2.049496  \n",
+       "  96  0.539551 -1.394952   -0.573453   -0.146953    1.939897  \n",
+       "  97 -1.406308  0.253741   -1.251408    0.357917    0.327781  \n",
+       "  98 -1.591889  0.285962   -1.081273   -0.739715   -1.237475  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -3.178840 -1.799920  0.717556 -0.342118 -1.629275 -1.918805 -2.888127   \n",
+       "  91 -2.888127 -1.930604  0.330201 -2.599804 -2.442455 -1.704478  1.828623   \n",
+       "  92  1.828623  1.667593 -1.226489 -3.029020  0.197057 -0.174359  3.258455   \n",
+       "  93  3.258455  2.235124 -1.747547 -1.699449  2.908731 -0.743774  1.905558   \n",
+       "  94  1.905558  0.735210  0.196228  0.593102  2.268146  0.228313 -0.136383   \n",
+       "  95 -0.136383 -1.120542  1.155516  2.572626  0.613238  0.448844 -1.285613   \n",
+       "  96 -1.285613 -1.945686  1.446742  0.143859 -1.449183  1.366526 -0.944357   \n",
+       "  97 -0.944357 -1.236941  1.067758 -2.180683 -2.871160  0.697951  1.062332   \n",
+       "  98  1.062332 -1.314128 -0.549369 -1.680980 -2.073369 -1.409427  2.662931   \n",
+       "  99  2.662931  0.083840 -0.801368 -0.572412  1.366569 -2.305168       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -1.930604  0.330201   -2.599804   -2.442455   -1.704478  \n",
+       "  91  1.667593 -1.226489   -3.029020    0.197057   -0.174359  \n",
+       "  92  2.235124 -1.747547   -1.699449    2.908731   -0.743774  \n",
+       "  93  0.735210  0.196228    0.593102    2.268146    0.228313  \n",
+       "  94 -1.120542  1.155516    2.572626    0.613238    0.448844  \n",
+       "  95 -1.945686  1.446742    0.143859   -1.449183    1.366526  \n",
+       "  96 -1.236941  1.067758   -2.180683   -2.871160    0.697951  \n",
+       "  97 -1.314128 -0.549369   -1.680980   -2.073369   -1.409427  \n",
+       "  98  0.083840 -0.801368   -0.572412    1.366569   -2.305168  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  0.170462 -0.206762 -5.520207  0.519898  2.393559  0.636117 -0.499703   \n",
+       "  91 -0.499703 -2.126351 -2.298413  1.753857  0.945569  1.654151 -1.362139   \n",
+       "  92 -1.362139 -2.205586  0.637329  1.635533 -0.892059  3.557487  0.288782   \n",
+       "  93  0.288782 -0.792425  3.647277 -0.798907 -3.474222  1.135377  0.728279   \n",
+       "  94  0.728279  0.876429  3.698717 -0.351217 -2.729466 -0.188353  0.605427   \n",
+       "  95  0.605427 -0.050133  1.390027  0.292534  0.018617 -2.556738 -0.437724   \n",
+       "  96 -0.437724  0.302272 -2.561111 -0.834191  1.762622 -1.515827 -0.224150   \n",
+       "  97 -0.224150 -1.315926 -6.004213 -0.627657  2.438206  1.975867 -0.093526   \n",
+       "  98 -0.093526 -1.898786 -2.528429 -0.062092  1.799746  1.366656 -1.387700   \n",
+       "  99 -1.387700 -0.481198  2.562267  0.094629 -1.196622 -0.295730       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -2.126351 -2.298413    1.753857    0.945569    1.654151  \n",
+       "  91 -2.205586  0.637329    1.635533   -0.892059    3.557487  \n",
+       "  92 -0.792425  3.647277   -0.798907   -3.474222    1.135377  \n",
+       "  93  0.876429  3.698717   -0.351217   -2.729466   -0.188353  \n",
+       "  94 -0.050133  1.390027    0.292534    0.018617   -2.556738  \n",
+       "  95  0.302272 -2.561111   -0.834191    1.762622   -1.515827  \n",
+       "  96 -1.315926 -6.004213   -0.627657    2.438206    1.975867  \n",
+       "  97 -1.898786 -2.528429   -0.062092    1.799746    1.366656  \n",
+       "  98 -0.481198  2.562267    0.094629   -1.196622   -0.295730  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  0.381322 -0.079558  1.889477 -1.504298  5.291423  0.359237  0.885682   \n",
+       "  91  0.885682 -0.626669  1.697695  0.489302  2.488088 -0.337720  0.109572   \n",
+       "  92  0.109572  0.893173 -1.177124  1.694801 -0.362700 -1.456001 -0.998924   \n",
+       "  93 -0.998924  1.378959 -1.741618  0.924012 -4.362658  0.751636 -0.840795   \n",
+       "  94 -0.840795  0.643344 -1.124233  0.212207 -4.450997  1.586131  0.397245   \n",
+       "  95  0.397245  0.230374 -1.943202 -2.034669 -2.172055  1.573719 -0.819265   \n",
+       "  96 -0.819265 -2.715234  0.168784 -1.985317  1.767079  0.557304 -0.777425   \n",
+       "  97 -0.777425 -1.082671  0.684544  1.550787  3.394596 -2.243046 -1.688990   \n",
+       "  98 -1.688990  0.963625  1.773586  3.740746  3.840164 -4.000069 -0.489485   \n",
+       "  99 -0.489485  1.790031  1.758096  4.597142  0.359536 -3.317297       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.626669  1.697695    0.489302    2.488088   -0.337720  \n",
+       "  91  0.893173 -1.177124    1.694801   -0.362700   -1.456001  \n",
+       "  92  1.378959 -1.741618    0.924012   -4.362658    0.751636  \n",
+       "  93  0.643344 -1.124233    0.212207   -4.450997    1.586131  \n",
+       "  94  0.230374 -1.943202   -2.034669   -2.172055    1.573719  \n",
+       "  95 -2.715234  0.168784   -1.985317    1.767079    0.557304  \n",
+       "  96 -1.082671  0.684544    1.550787    3.394596   -2.243046  \n",
+       "  97  0.963625  1.773586    3.740746    3.840164   -4.000069  \n",
+       "  98  1.790031  1.758096    4.597142    0.359536   -3.317297  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  4.200121  2.047084  1.861377 -2.360137  1.350237 -1.784683  1.359283   \n",
+       "  91  1.359283  0.616726 -0.574292 -1.849790  0.795604 -0.613929 -1.588165   \n",
+       "  92 -1.588165  1.470134 -2.578510 -0.704915  0.493295  1.033427 -3.074070   \n",
+       "  93 -3.074070 -0.029495 -2.980658  1.144438 -1.280428  1.439158 -1.794587   \n",
+       "  94 -1.794587 -1.927643 -0.364741  1.788206 -1.974179 -0.348176 -2.104354   \n",
+       "  95 -2.104354 -1.755520  2.350406  1.059132 -1.539940 -0.332644  1.555891   \n",
+       "  96  1.555891  1.279955  2.752953 -0.827841 -0.495685 -2.092978  3.083921   \n",
+       "  97  3.083921  1.706086  3.059997 -0.959199 -0.832420 -0.164629  3.349823   \n",
+       "  98  3.349823  2.331061 -0.285553 -0.750800 -0.837988  0.818107 -0.658499   \n",
+       "  99 -0.658499  0.533129 -3.243543  3.570284  0.031715  2.521802       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.616726 -0.574292   -1.849790    0.795604   -0.613929  \n",
+       "  91  1.470134 -2.578510   -0.704915    0.493295    1.033427  \n",
+       "  92 -0.029495 -2.980658    1.144438   -1.280428    1.439158  \n",
+       "  93 -1.927643 -0.364741    1.788206   -1.974179   -0.348176  \n",
+       "  94 -1.755520  2.350406    1.059132   -1.539940   -0.332644  \n",
+       "  95  1.279955  2.752953   -0.827841   -0.495685   -2.092978  \n",
+       "  96  1.706086  3.059997   -0.959199   -0.832420   -0.164629  \n",
+       "  97  2.331061 -0.285553   -0.750800   -0.837988    0.818107  \n",
+       "  98  0.533129 -3.243543    3.570284    0.031715    2.521802  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.409001 -2.268185  1.036461 -1.735795  0.027985  0.455108 -0.149952   \n",
+       "  91 -0.149952 -0.408547  1.792189  1.508157 -0.885200 -1.288625  0.272225   \n",
+       "  92  0.272225  0.451708  2.080444  3.386795 -1.113402 -0.503827 -0.942843   \n",
+       "  93 -0.942843  1.645946  1.934227  3.563382  0.119331 -0.462251  0.013892   \n",
+       "  94  0.013892  1.834810 -1.873057 -0.325089  1.011893 -1.632715 -0.319490   \n",
+       "  95 -0.319490  1.704404 -2.384175 -4.377852 -0.185862  0.889781 -1.030820   \n",
+       "  96 -1.030820  0.289090 -0.664006 -6.060491 -0.328157  2.253597 -0.091125   \n",
+       "  97 -0.091125 -0.573907  0.100565 -2.866875  0.074889 -1.666824  1.164653   \n",
+       "  98  1.164653 -2.133627  0.756022  1.305472 -0.048460 -2.953035  2.070156   \n",
+       "  99  2.070156 -0.878057 -1.115139  6.159124 -2.018786 -1.257729       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.408547  1.792189    1.508157   -0.885200   -1.288625  \n",
+       "  91  0.451708  2.080444    3.386795   -1.113402   -0.503827  \n",
+       "  92  1.645946  1.934227    3.563382    0.119331   -0.462251  \n",
+       "  93  1.834810 -1.873057   -0.325089    1.011893   -1.632715  \n",
+       "  94  1.704404 -2.384175   -4.377852   -0.185862    0.889781  \n",
+       "  95  0.289090 -0.664006   -6.060491   -0.328157    2.253597  \n",
+       "  96 -0.573907  0.100565   -2.866875    0.074889   -1.666824  \n",
+       "  97 -2.133627  0.756022    1.305472   -0.048460   -2.953035  \n",
+       "  98 -0.878057 -1.115139    6.159124   -2.018786   -1.257729  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -1.673787 -1.349448 -0.352789  0.959449  1.988303  1.542615 -2.392087   \n",
+       "  91 -2.392087  2.255310 -1.557876  0.483670  2.471669 -0.411587 -0.991263   \n",
+       "  92 -0.991263  2.902964 -0.337278 -0.027840  1.517651  0.154496  0.142078   \n",
+       "  93  0.142078  0.576191 -1.689508  0.845783  0.298816 -2.994765  1.112360   \n",
+       "  94  1.112360 -3.203814 -0.617898  2.403638 -0.861312 -3.536520  1.863384   \n",
+       "  95  1.863384 -2.491900 -0.367934  1.415864 -0.907380 -2.698254  0.500003   \n",
+       "  96  0.500003  0.272266  1.882679 -0.417702  1.279041 -1.686848  1.005211   \n",
+       "  97  1.005211  3.550583  2.063878 -2.253511  1.485022  0.821456 -1.649635   \n",
+       "  98 -1.649635  2.105833  0.001193 -0.731013 -0.242957  2.241449 -1.183455   \n",
+       "  99 -1.183455  0.761874 -2.387485 -0.179972 -0.813268  1.343294       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  2.255310 -1.557876    0.483670    2.471669   -0.411587  \n",
+       "  91  2.902964 -0.337278   -0.027840    1.517651    0.154496  \n",
+       "  92  0.576191 -1.689508    0.845783    0.298816   -2.994765  \n",
+       "  93 -3.203814 -0.617898    2.403638   -0.861312   -3.536520  \n",
+       "  94 -2.491900 -0.367934    1.415864   -0.907380   -2.698254  \n",
+       "  95  0.272266  1.882679   -0.417702    1.279041   -1.686848  \n",
+       "  96  3.550583  2.063878   -2.253511    1.485022    0.821456  \n",
+       "  97  2.105833  0.001193   -0.731013   -0.242957    2.241449  \n",
+       "  98  0.761874 -2.387485   -0.179972   -0.813268    1.343294  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.128760 -0.001318 -1.215088 -1.031362 -1.285630 -0.312166 -2.406231   \n",
+       "  91 -2.406231 -0.845530 -0.691537  0.662617  1.934451 -0.660321 -2.218893   \n",
+       "  92 -2.218893 -0.919579  0.140481  1.681514  1.078343 -1.118342  0.655845   \n",
+       "  93  0.655845 -0.441153  1.660510  2.051384  2.094735  0.641433  2.739785   \n",
+       "  94  2.739785  0.938520  1.166559  0.215687 -0.621988  0.238601  2.910587   \n",
+       "  95  2.910587 -0.461965 -1.727631 -0.849011 -1.894747 -0.451046  2.200952   \n",
+       "  96  2.200952  0.329820 -2.082580 -2.605897 -2.437916 -1.536423  1.348362   \n",
+       "  97  1.348362 -1.126405 -1.591295 -1.089121 -0.669075 -0.795198 -1.677558   \n",
+       "  98 -1.677558 -0.441709  1.331189 -0.486211  1.850179  0.037579 -3.482500   \n",
+       "  99 -3.482500 -0.374082  1.814353  2.642065  3.029059  1.808283       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.845530 -0.691537    0.662617    1.934451   -0.660321  \n",
+       "  91 -0.919579  0.140481    1.681514    1.078343   -1.118342  \n",
+       "  92 -0.441153  1.660510    2.051384    2.094735    0.641433  \n",
+       "  93  0.938520  1.166559    0.215687   -0.621988    0.238601  \n",
+       "  94 -0.461965 -1.727631   -0.849011   -1.894747   -0.451046  \n",
+       "  95  0.329820 -2.082580   -2.605897   -2.437916   -1.536423  \n",
+       "  96 -1.126405 -1.591295   -1.089121   -0.669075   -0.795198  \n",
+       "  97 -0.441709  1.331189   -0.486211    1.850179    0.037579  \n",
+       "  98 -0.374082  1.814353    2.642065    3.029059    1.808283  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  0.842326  2.453053  0.986591 -0.818892  0.534551 -1.500883  1.298417   \n",
+       "  91  1.298417  1.670302  2.291539 -1.038953  2.504449  0.223376  0.310061   \n",
+       "  92  0.310061  0.815880  2.729195 -0.466936  1.524962  1.576621 -0.592760   \n",
+       "  93 -0.592760  0.218903 -0.859873  0.481274 -0.166645  1.575826 -0.340990   \n",
+       "  94 -0.340990  0.630732 -0.911381  1.666105 -3.089551  1.092998 -0.906161   \n",
+       "  95 -0.906161 -2.217112 -1.484805  1.109717 -1.259790  0.169056  0.166948   \n",
+       "  96  0.166948 -1.447475 -0.537587 -0.407250  0.507757 -0.000323 -0.431307   \n",
+       "  97 -0.431307 -0.494502  0.710585  0.770675  2.119923 -0.441230 -1.985260   \n",
+       "  98 -1.985260  2.073460  2.066489 -0.180241  2.179703  1.170776 -1.255326   \n",
+       "  99 -1.255326  2.538230  1.654843 -0.277629 -0.852216 -0.757340       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  1.670302  2.291539   -1.038953    2.504449    0.223376  \n",
+       "  91  0.815880  2.729195   -0.466936    1.524962    1.576621  \n",
+       "  92  0.218903 -0.859873    0.481274   -0.166645    1.575826  \n",
+       "  93  0.630732 -0.911381    1.666105   -3.089551    1.092998  \n",
+       "  94 -2.217112 -1.484805    1.109717   -1.259790    0.169056  \n",
+       "  95 -1.447475 -0.537587   -0.407250    0.507757   -0.000323  \n",
+       "  96 -0.494502  0.710585    0.770675    2.119923   -0.441230  \n",
+       "  97  2.073460  2.066489   -0.180241    2.179703    1.170776  \n",
+       "  98  2.538230  1.654843   -0.277629   -0.852216   -0.757340  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -1.784604  0.125869  1.477406  1.349440 -1.322504  0.509294  0.631772   \n",
+       "  91  0.631772  0.515575  1.296251  1.614020  1.251285 -0.568131  2.975698   \n",
+       "  92  2.975698 -0.159361 -1.639891  1.533836  2.193172 -0.519741  2.543485   \n",
+       "  93  2.543485  0.046601 -1.373430  1.454027  1.685606 -2.210292  0.714626   \n",
+       "  94  0.714626 -1.808487 -3.131696  0.600562 -0.257495 -0.593565  0.093389   \n",
+       "  95  0.093389 -3.302220 -1.085377 -1.741075 -1.609240  1.250664 -0.980969   \n",
+       "  96 -0.980969 -1.728807  0.018565 -4.474539 -2.351791  2.126155 -0.451659   \n",
+       "  97 -0.451659  1.644256  1.884805 -3.730649 -0.851714  0.575999 -0.534408   \n",
+       "  98 -0.534408  3.578701  1.148037  2.088193  1.091947 -1.683833  1.529494   \n",
+       "  99  1.529494  4.090263  1.242445  4.124656  1.584801 -4.077229       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.515575  1.296251    1.614020    1.251285   -0.568131  \n",
+       "  91 -0.159361 -1.639891    1.533836    2.193172   -0.519741  \n",
+       "  92  0.046601 -1.373430    1.454027    1.685606   -2.210292  \n",
+       "  93 -1.808487 -3.131696    0.600562   -0.257495   -0.593565  \n",
+       "  94 -3.302220 -1.085377   -1.741075   -1.609240    1.250664  \n",
+       "  95 -1.728807  0.018565   -4.474539   -2.351791    2.126155  \n",
+       "  96  1.644256  1.884805   -3.730649   -0.851714    0.575999  \n",
+       "  97  3.578701  1.148037    2.088193    1.091947   -1.683833  \n",
+       "  98  4.090263  1.242445    4.124656    1.584801   -4.077229  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -1.557568  1.879642 -0.257159 -2.380335  1.071873 -1.540923 -0.360807   \n",
+       "  91 -0.360807 -1.087779  0.378761 -0.155245  1.989710 -0.936055 -0.300128   \n",
+       "  92 -0.300128 -1.706857  0.786891  1.877030  2.114213  0.883765  0.656311   \n",
+       "  93  0.656311 -0.430280  1.920578  2.646555  0.727919  2.823792  0.608920   \n",
+       "  94  0.608920  1.016828  1.559764 -0.130094 -0.743455  1.476100 -1.321975   \n",
+       "  95 -1.321975  2.982809  0.605819 -2.199770 -2.139028  0.777442 -1.259387   \n",
+       "  96 -1.259387  2.673109 -0.699011 -1.544666 -1.327937 -1.538700  0.592476   \n",
+       "  97  0.592476  1.372027 -2.211685  2.556170 -1.506432 -3.437078  0.350529   \n",
+       "  98  0.350529 -2.248556 -1.729400  3.089402 -0.035075 -2.515380 -1.346575   \n",
+       "  99 -1.346575 -2.808909  0.893396  1.307010  1.267311 -0.850422       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -1.087779  0.378761   -0.155245    1.989710   -0.936055  \n",
+       "  91 -1.706857  0.786891    1.877030    2.114213    0.883765  \n",
+       "  92 -0.430280  1.920578    2.646555    0.727919    2.823792  \n",
+       "  93  1.016828  1.559764   -0.130094   -0.743455    1.476100  \n",
+       "  94  2.982809  0.605819   -2.199770   -2.139028    0.777442  \n",
+       "  95  2.673109 -0.699011   -1.544666   -1.327937   -1.538700  \n",
+       "  96  1.372027 -2.211685    2.556170   -1.506432   -3.437078  \n",
+       "  97 -2.248556 -1.729400    3.089402   -0.035075   -2.515380  \n",
+       "  98 -2.808909  0.893396    1.307010    1.267311   -0.850422  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  2.428994 -1.438413 -0.838479 -0.242172 -1.434628  2.037590 -2.538198   \n",
+       "  91 -2.538198  1.492844  1.379604  1.138242 -0.882032  0.779170 -3.450957   \n",
+       "  92 -3.450957  4.609503  1.466612  0.287957  0.042796 -0.493009 -1.373594   \n",
+       "  93 -1.373594  2.653226  0.127196  0.853433  0.726961 -1.943584  2.741439   \n",
+       "  94  2.741439  0.670387  0.853268 -0.618125  1.573063 -3.138267  4.695468   \n",
+       "  95  4.695468 -1.506623  1.273260 -2.030426  2.030398 -1.343562  2.186398   \n",
+       "  96  2.186398 -4.278121  0.223753 -1.677035 -0.797954  1.138394 -3.640679   \n",
+       "  97 -3.640679 -1.241571  1.315692 -1.261810 -3.259736  1.250836 -5.556547   \n",
+       "  98 -5.556547  2.006398  2.990594 -1.144630 -3.090990  1.665750 -3.483941   \n",
+       "  99 -3.483941  2.661199  3.690363 -0.620511 -0.997891  0.045620       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  1.492844  1.379604    1.138242   -0.882032    0.779170  \n",
+       "  91  4.609503  1.466612    0.287957    0.042796   -0.493009  \n",
+       "  92  2.653226  0.127196    0.853433    0.726961   -1.943584  \n",
+       "  93  0.670387  0.853268   -0.618125    1.573063   -3.138267  \n",
+       "  94 -1.506623  1.273260   -2.030426    2.030398   -1.343562  \n",
+       "  95 -4.278121  0.223753   -1.677035   -0.797954    1.138394  \n",
+       "  96 -1.241571  1.315692   -1.261810   -3.259736    1.250836  \n",
+       "  97  2.006398  2.990594   -1.144630   -3.090990    1.665750  \n",
+       "  98  2.661199  3.690363   -0.620511   -0.997891    0.045620  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -4.584388 -1.153338 -0.779293  0.124251 -1.208025 -0.678118 -2.914027   \n",
+       "  91 -2.914027 -1.025116 -0.132026  0.723385 -1.367595  0.695482 -0.853751   \n",
+       "  92 -0.853751  0.201046  0.976236  1.510146 -0.534232  1.976445  3.041583   \n",
+       "  93  3.041583  0.479305 -0.188422  0.821715  1.765074  0.698424  4.889114   \n",
+       "  94  4.889114  0.453017 -0.115774 -1.104901  2.372423  0.285643  2.493208   \n",
+       "  95  2.493208  1.471280  0.419042 -2.273542  3.785738 -1.284611 -2.386726   \n",
+       "  96 -2.386726  1.146833  0.193981 -0.707685  1.664648 -1.990530 -4.391433   \n",
+       "  97 -4.391433 -0.528513  0.429134 -0.155892  0.243099 -2.240177 -2.267162   \n",
+       "  98 -2.267162 -2.145199  0.106813  2.410789 -2.583812 -0.284934  1.453498   \n",
+       "  99  1.453498 -2.031952 -0.507126  0.223801 -4.978832  0.735950       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -1.025116 -0.132026    0.723385   -1.367595    0.695482  \n",
+       "  91  0.201046  0.976236    1.510146   -0.534232    1.976445  \n",
+       "  92  0.479305 -0.188422    0.821715    1.765074    0.698424  \n",
+       "  93  0.453017 -0.115774   -1.104901    2.372423    0.285643  \n",
+       "  94  1.471280  0.419042   -2.273542    3.785738   -1.284611  \n",
+       "  95  1.146833  0.193981   -0.707685    1.664648   -1.990530  \n",
+       "  96 -0.528513  0.429134   -0.155892    0.243099   -2.240177  \n",
+       "  97 -2.145199  0.106813    2.410789   -2.583812   -0.284934  \n",
+       "  98 -2.031952 -0.507126    0.223801   -4.978832    0.735950  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.961253  0.801807  1.495661  1.848330  1.010062 -0.901927  0.453260   \n",
+       "  91  0.453260 -1.596908  0.775081  0.354458  0.539005 -2.101045  0.995235   \n",
+       "  92  0.995235 -3.081264 -0.669370 -0.633921 -0.643825 -1.235146 -1.051168   \n",
+       "  93 -1.051168  0.649300 -2.123535 -1.026631 -2.349627  0.117550 -0.378713   \n",
+       "  94 -0.378713  2.269672 -1.904151  1.149286 -1.787756  2.330172 -0.582859   \n",
+       "  95 -0.582859  1.766747  0.971626  1.953500  0.801523  2.504008  0.942515   \n",
+       "  96  0.942515 -0.991386  2.674905  1.918494  1.897207 -0.021272  1.657742   \n",
+       "  97  1.657742 -1.931950  3.165102  0.290494  1.474629 -2.052938  1.615868   \n",
+       "  98  1.615868 -2.244423  1.513529  0.344516  0.731063 -1.420814  2.339970   \n",
+       "  99  2.339970  0.761077 -0.657147 -1.599035 -0.828132 -0.699249       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -1.596908  0.775081    0.354458    0.539005   -2.101045  \n",
+       "  91 -3.081264 -0.669370   -0.633921   -0.643825   -1.235146  \n",
+       "  92  0.649300 -2.123535   -1.026631   -2.349627    0.117550  \n",
+       "  93  2.269672 -1.904151    1.149286   -1.787756    2.330172  \n",
+       "  94  1.766747  0.971626    1.953500    0.801523    2.504008  \n",
+       "  95 -0.991386  2.674905    1.918494    1.897207   -0.021272  \n",
+       "  96 -1.931950  3.165102    0.290494    1.474629   -2.052938  \n",
+       "  97 -2.244423  1.513529    0.344516    0.731063   -1.420814  \n",
+       "  98  0.761077 -0.657147   -1.599035   -0.828132   -0.699249  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.817834 -0.736320 -1.193022  0.021372  0.505670 -1.416145  2.219357   \n",
+       "  91  2.219357 -0.181495 -1.977444 -0.433216  1.170412  0.790175  2.811889   \n",
+       "  92  2.811889 -0.116320 -0.903011 -1.345688  2.770863  0.432529  2.215013   \n",
+       "  93  2.215013  0.020624  0.204632 -2.411333  1.843807  1.254942 -0.373686   \n",
+       "  94 -0.373686  0.542533  0.582122 -3.268499  2.063669 -2.092810 -1.504307   \n",
+       "  95 -1.504307  1.666317  0.449826 -1.917534 -1.204373 -1.666268 -2.733504   \n",
+       "  96 -2.733504  2.522774  0.236388  1.071735 -1.897336  0.415175 -0.894683   \n",
+       "  97 -0.894683  1.113929  0.321216  3.583580 -2.052233  2.305358  0.333576   \n",
+       "  98  0.333576 -1.451915  0.137137  2.948614 -2.029266  1.804470  1.559505   \n",
+       "  99  1.559505 -3.371175  0.282433  1.383540 -0.565837  0.393738       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.181495 -1.977444   -0.433216    1.170412    0.790175  \n",
+       "  91 -0.116320 -0.903011   -1.345688    2.770863    0.432529  \n",
+       "  92  0.020624  0.204632   -2.411333    1.843807    1.254942  \n",
+       "  93  0.542533  0.582122   -3.268499    2.063669   -2.092810  \n",
+       "  94  1.666317  0.449826   -1.917534   -1.204373   -1.666268  \n",
+       "  95  2.522774  0.236388    1.071735   -1.897336    0.415175  \n",
+       "  96  1.113929  0.321216    3.583580   -2.052233    2.305358  \n",
+       "  97 -1.451915  0.137137    2.948614   -2.029266    1.804470  \n",
+       "  98 -3.371175  0.282433    1.383540   -0.565837    0.393738  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  6.090772  0.612835 -0.554521 -0.578938 -0.357559 -2.341110  3.950198   \n",
+       "  91  3.950198  3.339571  0.726317  0.657525 -0.182980 -1.439997  0.069264   \n",
+       "  92  0.069264  3.768624  1.577777  0.932507 -0.471971 -0.411604 -3.779693   \n",
+       "  93 -3.779693 -0.211379  0.565511 -0.164628 -1.644236  2.118790 -5.225218   \n",
+       "  94 -5.225218 -3.190342 -0.965481 -0.924976 -0.388732  2.288138 -2.208530   \n",
+       "  95 -2.208530 -4.338285  0.188654  0.339516  0.461394  2.338308  2.819084   \n",
+       "  96  2.819084 -1.845277 -0.740722 -0.338346  0.230674 -0.193532  2.977697   \n",
+       "  97  2.977697 -0.033545  1.018156  1.264151 -0.237959 -1.926113  3.539424   \n",
+       "  98  3.539424  1.026904  1.663807 -1.455952  0.306195 -4.459252 -1.281671   \n",
+       "  99 -1.281671  3.083101  1.270306 -1.262548  1.637945 -1.952002       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  3.339571  0.726317    0.657525   -0.182980   -1.439997  \n",
+       "  91  3.768624  1.577777    0.932507   -0.471971   -0.411604  \n",
+       "  92 -0.211379  0.565511   -0.164628   -1.644236    2.118790  \n",
+       "  93 -3.190342 -0.965481   -0.924976   -0.388732    2.288138  \n",
+       "  94 -4.338285  0.188654    0.339516    0.461394    2.338308  \n",
+       "  95 -1.845277 -0.740722   -0.338346    0.230674   -0.193532  \n",
+       "  96 -0.033545  1.018156    1.264151   -0.237959   -1.926113  \n",
+       "  97  1.026904  1.663807   -1.455952    0.306195   -4.459252  \n",
+       "  98  3.083101  1.270306   -1.262548    1.637945   -1.952002  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -1.685527  1.205162  1.054529 -1.784525  2.460425  1.442798 -0.274905   \n",
+       "  91 -0.274905  2.079570 -0.705762 -1.626996  3.513856  2.521425  1.063194   \n",
+       "  92  1.063194  0.212986  0.189532 -0.622026  2.424569  2.158121 -0.127547   \n",
+       "  93 -0.127547 -1.970494  0.422704  2.331040  0.719916  1.904722 -2.432755   \n",
+       "  94 -2.432755 -2.590695  1.179097  3.505741 -0.707999  1.765216 -2.078837   \n",
+       "  95 -2.078837 -0.451053 -0.362980  3.526929 -1.944419  0.735935 -1.254051   \n",
+       "  96 -1.254051  1.072575 -0.317852  0.070186  0.347888 -0.262548  0.200557   \n",
+       "  97  0.200557  1.082743  0.094596 -2.993759  1.565085 -0.519796  1.702001   \n",
+       "  98  1.702001  1.513972  1.382439 -4.594542  0.824472 -0.604470  1.351353   \n",
+       "  99  1.351353 -1.166462  1.693758 -2.036611  0.290932 -0.374048       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  2.079570 -0.705762   -1.626996    3.513856    2.521425  \n",
+       "  91  0.212986  0.189532   -0.622026    2.424569    2.158121  \n",
+       "  92 -1.970494  0.422704    2.331040    0.719916    1.904722  \n",
+       "  93 -2.590695  1.179097    3.505741   -0.707999    1.765216  \n",
+       "  94 -0.451053 -0.362980    3.526929   -1.944419    0.735935  \n",
+       "  95  1.072575 -0.317852    0.070186    0.347888   -0.262548  \n",
+       "  96  1.082743  0.094596   -2.993759    1.565085   -0.519796  \n",
+       "  97  1.513972  1.382439   -4.594542    0.824472   -0.604470  \n",
+       "  98 -1.166462  1.693758   -2.036611    0.290932   -0.374048  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -2.032222  3.723229 -2.239790  0.396676 -3.437313 -1.579182 -1.960648   \n",
+       "  91 -1.960648  4.767730  1.761792  1.545038 -0.145135 -1.522122 -0.379624   \n",
+       "  92 -0.379624  1.220771  5.297002  1.147595  2.775979 -0.718540 -0.235264   \n",
+       "  93 -0.235264 -0.313998  3.614661 -0.167223  4.101994  1.047673  0.561974   \n",
+       "  94  0.561974 -1.946655  0.436293 -2.612323  2.360011  1.744728  2.230361   \n",
+       "  95  2.230361 -2.816225 -1.961076 -3.439321 -0.334411  2.310912 -0.799519   \n",
+       "  96 -0.799519 -1.091374 -0.977973 -0.808677 -2.201392  0.179878 -0.138255   \n",
+       "  97 -0.138255 -0.409765 -0.300230  1.067965 -1.537342 -0.536087 -0.237031   \n",
+       "  98 -0.237031  1.674529  3.058697  2.113988  0.322217 -2.272228  1.287630   \n",
+       "  99  1.287630  0.191619  3.236867  2.059731  0.861357 -1.373915       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  4.767730  1.761792    1.545038   -0.145135   -1.522122  \n",
+       "  91  1.220771  5.297002    1.147595    2.775979   -0.718540  \n",
+       "  92 -0.313998  3.614661   -0.167223    4.101994    1.047673  \n",
+       "  93 -1.946655  0.436293   -2.612323    2.360011    1.744728  \n",
+       "  94 -2.816225 -1.961076   -3.439321   -0.334411    2.310912  \n",
+       "  95 -1.091374 -0.977973   -0.808677   -2.201392    0.179878  \n",
+       "  96 -0.409765 -0.300230    1.067965   -1.537342   -0.536087  \n",
+       "  97  1.674529  3.058697    2.113988    0.322217   -2.272228  \n",
+       "  98  0.191619  3.236867    2.059731    0.861357   -1.373915  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  3.128830 -0.048761 -3.352714  0.058197 -2.414288 -1.918953  0.655042   \n",
+       "  91  0.655042  2.759179 -2.698145  0.369580  0.646926 -0.979541 -1.167612   \n",
+       "  92 -1.167612  2.697995  0.916626 -1.386310  1.049110 -1.363745 -1.440374   \n",
+       "  93 -1.440374  0.637609  2.456934 -1.013163  2.178561  0.409131 -0.847872   \n",
+       "  94 -0.847872 -0.672023  2.460198 -1.110510  1.448662  2.867871 -0.144968   \n",
+       "  95 -0.144968 -1.747992  1.150353  0.223192  1.611473  2.681234 -0.367839   \n",
+       "  96 -0.367839 -0.309310 -0.536399  3.545427 -0.227506  0.432730 -0.126800   \n",
+       "  97 -0.126800  0.442574 -1.536364  3.587848 -0.432021 -2.947919  1.317033   \n",
+       "  98  1.317033  0.993629 -3.990106 -0.452320  0.947816 -2.744352  1.867593   \n",
+       "  99  1.867593  0.709994 -1.936384 -2.561923 -1.810053 -0.605121       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  2.759179 -2.698145    0.369580    0.646926   -0.979541  \n",
+       "  91  2.697995  0.916626   -1.386310    1.049110   -1.363745  \n",
+       "  92  0.637609  2.456934   -1.013163    2.178561    0.409131  \n",
+       "  93 -0.672023  2.460198   -1.110510    1.448662    2.867871  \n",
+       "  94 -1.747992  1.150353    0.223192    1.611473    2.681234  \n",
+       "  95 -0.309310 -0.536399    3.545427   -0.227506    0.432730  \n",
+       "  96  0.442574 -1.536364    3.587848   -0.432021   -2.947919  \n",
+       "  97  0.993629 -3.990106   -0.452320    0.947816   -2.744352  \n",
+       "  98  0.709994 -1.936384   -2.561923   -1.810053   -0.605121  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.997551  0.198883 -1.409954  0.252679 -2.525278 -0.619233  1.251816   \n",
+       "  91  1.251816  0.039320  0.385739 -1.840886 -1.058905  0.689383 -0.192436   \n",
+       "  92 -0.192436 -0.950879  3.239751 -2.282709  1.208176  1.773226 -1.654916   \n",
+       "  93 -1.654916 -0.493634  0.986766 -1.215266  2.696146  1.530108 -3.304474   \n",
+       "  94 -3.304474 -1.001467 -1.505230 -0.088945  2.935221  0.996852 -0.258885   \n",
+       "  95 -0.258885 -0.584546 -4.818128  1.203502  0.272261  0.151744  0.453997   \n",
+       "  96  0.453997 -0.467148 -2.380127  0.101296 -0.574522 -0.819681  3.039810   \n",
+       "  97  3.039810 -0.454228  0.096177 -0.896568 -2.483677 -1.726702  1.993273   \n",
+       "  98  1.993273  0.693591  4.894651 -0.600893 -2.731607  0.402097  1.012162   \n",
+       "  99  1.012162  1.493311  6.060897 -1.417386 -1.209081  0.819461       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.039320  0.385739   -1.840886   -1.058905    0.689383  \n",
+       "  91 -0.950879  3.239751   -2.282709    1.208176    1.773226  \n",
+       "  92 -0.493634  0.986766   -1.215266    2.696146    1.530108  \n",
+       "  93 -1.001467 -1.505230   -0.088945    2.935221    0.996852  \n",
+       "  94 -0.584546 -4.818128    1.203502    0.272261    0.151744  \n",
+       "  95 -0.467148 -2.380127    0.101296   -0.574522   -0.819681  \n",
+       "  96 -0.454228  0.096177   -0.896568   -2.483677   -1.726702  \n",
+       "  97  0.693591  4.894651   -0.600893   -2.731607    0.402097  \n",
+       "  98  1.493311  6.060897   -1.417386   -1.209081    0.819461  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  0.484759  4.207526  2.900076 -1.209055  1.964081  0.979124  1.354418   \n",
+       "  91  1.354418  4.864026  0.212240 -1.934153  1.192941  1.182687 -1.187561   \n",
+       "  92 -1.187561  4.166835 -1.148710  0.429727 -0.079279  2.181212 -0.819075   \n",
+       "  93 -0.819075  0.761227 -0.956843  3.824880 -1.704885  0.058145 -0.550488   \n",
+       "  94 -0.550488 -3.723728  0.302841  4.338240 -0.170154 -1.846881 -0.151132   \n",
+       "  95 -0.151132 -2.901306 -0.196919  2.714597  0.810312 -2.481809 -0.737217   \n",
+       "  96 -0.737217  0.574301 -0.623220 -0.432920  0.238950 -0.245892  0.797838   \n",
+       "  97  0.797838  2.395862  0.628293 -3.152225 -0.270460  1.066593  1.938229   \n",
+       "  98  1.938229  2.268271  0.401700 -2.511890 -1.288560  2.606097  1.819082   \n",
+       "  99  1.819082  2.099445  2.800786  0.838799  0.846398  1.338840       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  4.864026  0.212240   -1.934153    1.192941    1.182687  \n",
+       "  91  4.166835 -1.148710    0.429727   -0.079279    2.181212  \n",
+       "  92  0.761227 -0.956843    3.824880   -1.704885    0.058145  \n",
+       "  93 -3.723728  0.302841    4.338240   -0.170154   -1.846881  \n",
+       "  94 -2.901306 -0.196919    2.714597    0.810312   -2.481809  \n",
+       "  95  0.574301 -0.623220   -0.432920    0.238950   -0.245892  \n",
+       "  96  2.395862  0.628293   -3.152225   -0.270460    1.066593  \n",
+       "  97  2.268271  0.401700   -2.511890   -1.288560    2.606097  \n",
+       "  98  2.099445  2.800786    0.838799    0.846398    1.338840  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -3.780854 -2.299102 -0.049291 -0.926701 -1.939716 -3.456137 -2.685156   \n",
+       "  91 -2.685156 -0.191933  0.207991  0.093969 -0.418946  0.064402 -0.170834   \n",
+       "  92 -0.170834  0.339413  0.272200 -0.922871  0.811263  0.389024  0.595421   \n",
+       "  93  0.595421  0.551413 -0.150667  0.181605  2.526760  3.302493  3.367615   \n",
+       "  94  3.367615  1.558597  0.392370 -2.175594  1.500473  2.766155  3.299455   \n",
+       "  95  3.299455  1.882657 -1.373768 -2.934319 -0.809594  1.345297  1.693369   \n",
+       "  96  1.693369  1.603983 -1.235806 -2.684808 -3.189110 -0.102380 -2.496646   \n",
+       "  97 -2.496646 -0.655314 -2.442021 -1.691552 -2.518296 -3.364120 -3.686123   \n",
+       "  98 -3.686123 -1.559038 -0.722338  1.523279 -2.014962 -2.931216 -1.435255   \n",
+       "  99 -1.435255 -2.038513  1.912585  1.931658  0.681482 -1.721297       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.191933  0.207991    0.093969   -0.418946    0.064402  \n",
+       "  91  0.339413  0.272200   -0.922871    0.811263    0.389024  \n",
+       "  92  0.551413 -0.150667    0.181605    2.526760    3.302493  \n",
+       "  93  1.558597  0.392370   -2.175594    1.500473    2.766155  \n",
+       "  94  1.882657 -1.373768   -2.934319   -0.809594    1.345297  \n",
+       "  95  1.603983 -1.235806   -2.684808   -3.189110   -0.102380  \n",
+       "  96 -0.655314 -2.442021   -1.691552   -2.518296   -3.364120  \n",
+       "  97 -1.559038 -0.722338    1.523279   -2.014962   -2.931216  \n",
+       "  98 -2.038513  1.912585    1.931658    0.681482   -1.721297  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.103396  2.147638 -0.871294  3.280611  2.810044  0.287354 -1.122029   \n",
+       "  91 -1.122029  2.009304  1.134213  0.473581  4.513882 -0.404126 -1.176446   \n",
+       "  92 -1.176446 -1.390107  1.385663 -0.550349  2.409626 -0.257057 -0.066151   \n",
+       "  93 -0.066151 -2.992267  0.820787 -0.806997 -0.132691  2.095596  0.261284   \n",
+       "  94  0.261284 -2.760590 -0.031311 -0.288143 -3.445424  1.820980  1.558862   \n",
+       "  95  1.558862 -0.217200  0.942383 -2.769124 -2.776748  0.734111  0.983341   \n",
+       "  96  0.983341  1.265795 -0.990979 -0.431504 -1.321108 -0.304573 -0.173709   \n",
+       "  97 -0.173709  1.829996 -1.665507 -0.224381  2.594147 -1.465082 -1.032453   \n",
+       "  98 -1.032453  1.017769 -2.617224 -0.542388  3.900821 -2.175392 -1.037418   \n",
+       "  99 -1.037418 -0.312221 -1.880827 -0.506428  1.391266  1.051700       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  2.009304  1.134213    0.473581    4.513882   -0.404126  \n",
+       "  91 -1.390107  1.385663   -0.550349    2.409626   -0.257057  \n",
+       "  92 -2.992267  0.820787   -0.806997   -0.132691    2.095596  \n",
+       "  93 -2.760590 -0.031311   -0.288143   -3.445424    1.820980  \n",
+       "  94 -0.217200  0.942383   -2.769124   -2.776748    0.734111  \n",
+       "  95  1.265795 -0.990979   -0.431504   -1.321108   -0.304573  \n",
+       "  96  1.829996 -1.665507   -0.224381    2.594147   -1.465082  \n",
+       "  97  1.017769 -2.617224   -0.542388    3.900821   -2.175392  \n",
+       "  98 -0.312221 -1.880827   -0.506428    1.391266    1.051700  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.546406  0.577922 -0.076296 -1.554651 -1.357715 -2.559836  0.323374   \n",
+       "  91  0.323374  1.180765 -2.198102  0.518310 -0.166672 -0.820337 -0.317329   \n",
+       "  92 -0.317329  1.630925 -2.858941  0.933308 -0.750687  2.537062 -0.885428   \n",
+       "  93 -0.885428  1.181459 -1.916389  1.201085 -1.341031  4.052563 -0.609215   \n",
+       "  94 -0.609215 -2.081963 -0.143135 -1.281749 -0.622391  1.724875 -0.629023   \n",
+       "  95 -0.629023 -1.673150  2.163743 -3.673209  0.840323  0.134532  1.030110   \n",
+       "  96  1.030110 -1.262512  1.820833 -2.248333  1.076242 -2.175558  2.302945   \n",
+       "  97  2.302945  0.447270  1.557092  1.737566  2.436075 -2.300389  0.950351   \n",
+       "  98  0.950351  0.713166  0.363389  2.298880 -0.549328 -0.984767 -1.127914   \n",
+       "  99 -1.127914  0.694117 -1.541399  0.557168 -3.162430  2.593879       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  1.180765 -2.198102    0.518310   -0.166672   -0.820337  \n",
+       "  91  1.630925 -2.858941    0.933308   -0.750687    2.537062  \n",
+       "  92  1.181459 -1.916389    1.201085   -1.341031    4.052563  \n",
+       "  93 -2.081963 -0.143135   -1.281749   -0.622391    1.724875  \n",
+       "  94 -1.673150  2.163743   -3.673209    0.840323    0.134532  \n",
+       "  95 -1.262512  1.820833   -2.248333    1.076242   -2.175558  \n",
+       "  96  0.447270  1.557092    1.737566    2.436075   -2.300389  \n",
+       "  97  0.713166  0.363389    2.298880   -0.549328   -0.984767  \n",
+       "  98  0.694117 -1.541399    0.557168   -3.162430    2.593879  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.571757  0.748470 -0.632171  2.906095 -0.278676 -2.841532  1.864670   \n",
+       "  91  1.864670  0.183655 -2.080737  2.301732  0.890273 -0.981771 -1.102150   \n",
+       "  92 -1.102150  0.145925 -0.484781  0.980484  1.363877  1.636137 -2.627694   \n",
+       "  93 -2.627694 -0.723561  0.556160  0.737863  2.921294  2.623652 -2.739893   \n",
+       "  94 -2.739893 -0.248379  1.323471  0.286051  1.615864  1.081099 -0.117375   \n",
+       "  95 -0.117375  0.692906  1.554493 -0.776562  0.009469 -1.405719  2.009376   \n",
+       "  96  2.009376  0.101329  0.118414 -3.218140 -2.501485 -2.844531  3.122712   \n",
+       "  97  3.122712  0.721199  0.056297 -3.178994 -1.693403 -2.960276  1.948807   \n",
+       "  98  1.948807 -0.264103  1.614927 -2.106019  0.475588 -0.477515  2.438477   \n",
+       "  99  2.438477 -0.937620  0.059752 -0.096596  1.736721  0.781023       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.183655 -2.080737    2.301732    0.890273   -0.981771  \n",
+       "  91  0.145925 -0.484781    0.980484    1.363877    1.636137  \n",
+       "  92 -0.723561  0.556160    0.737863    2.921294    2.623652  \n",
+       "  93 -0.248379  1.323471    0.286051    1.615864    1.081099  \n",
+       "  94  0.692906  1.554493   -0.776562    0.009469   -1.405719  \n",
+       "  95  0.101329  0.118414   -3.218140   -2.501485   -2.844531  \n",
+       "  96  0.721199  0.056297   -3.178994   -1.693403   -2.960276  \n",
+       "  97 -0.264103  1.614927   -2.106019    0.475588   -0.477515  \n",
+       "  98 -0.937620  0.059752   -0.096596    1.736721    0.781023  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  0.427064 -1.086998 -0.605018 -1.008407 -0.755047  0.004602 -1.992831   \n",
+       "  91 -1.992831  0.418268 -0.488370 -1.028571 -0.196170  2.302570 -2.630215   \n",
+       "  92 -2.630215  2.361271 -1.216912 -0.130298  1.564002  2.877779 -1.219828   \n",
+       "  93 -1.219828  1.689643 -2.219595 -0.488474  0.973460 -0.690383  0.395041   \n",
+       "  94  0.395041  1.760676 -1.983052  0.522326  0.507187 -1.534666  3.118752   \n",
+       "  95  3.118752  1.492517 -1.683800 -0.316018 -0.804022 -0.878563  3.341877   \n",
+       "  96  3.341877 -1.425087  0.159954 -0.210370 -0.926491 -0.984057  2.824296   \n",
+       "  97  2.824296 -2.360862  1.698672 -0.405069 -0.599191  0.216936  0.935832   \n",
+       "  98  0.935832 -2.174572  0.765492 -0.603147  0.908420  1.437372 -2.252940   \n",
+       "  99 -2.252940 -1.532402  1.149925 -0.546272  2.782206  1.589004       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.418268 -0.488370   -1.028571   -0.196170    2.302570  \n",
+       "  91  2.361271 -1.216912   -0.130298    1.564002    2.877779  \n",
+       "  92  1.689643 -2.219595   -0.488474    0.973460   -0.690383  \n",
+       "  93  1.760676 -1.983052    0.522326    0.507187   -1.534666  \n",
+       "  94  1.492517 -1.683800   -0.316018   -0.804022   -0.878563  \n",
+       "  95 -1.425087  0.159954   -0.210370   -0.926491   -0.984057  \n",
+       "  96 -2.360862  1.698672   -0.405069   -0.599191    0.216936  \n",
+       "  97 -2.174572  0.765492   -0.603147    0.908420    1.437372  \n",
+       "  98 -1.532402  1.149925   -0.546272    2.782206    1.589004  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -2.111828  0.830879  1.491398 -0.821948 -2.538050 -0.908552 -2.840747   \n",
+       "  91 -2.840747  2.118040  2.223518  0.806322 -3.708871  1.772600 -0.811224   \n",
+       "  92 -0.811224  1.827185  1.194115  1.304459 -2.376526  2.283941  1.651588   \n",
+       "  93  1.651588  1.470540 -0.380306  1.181152 -0.696426  1.668966  0.633571   \n",
+       "  94  0.633571  0.399457 -2.019406 -0.415849 -0.028241  0.167519  0.289263   \n",
+       "  95  0.289263 -0.654052 -0.824404 -2.197527  2.529407 -0.197107  0.473276   \n",
+       "  96  0.473276 -1.590447  2.450673 -2.052120  2.414469 -0.338258  0.201388   \n",
+       "  97  0.201388 -0.717935  3.981636 -1.316953  2.721881 -1.990192  0.710283   \n",
+       "  98  0.710283 -0.664567  3.521806 -0.865626  1.232372 -0.644510 -0.209132   \n",
+       "  99 -0.209132 -1.046806  0.513747  0.657512 -3.283061  0.539511       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  2.118040  2.223518    0.806322   -3.708871    1.772600  \n",
+       "  91  1.827185  1.194115    1.304459   -2.376526    2.283941  \n",
+       "  92  1.470540 -0.380306    1.181152   -0.696426    1.668966  \n",
+       "  93  0.399457 -2.019406   -0.415849   -0.028241    0.167519  \n",
+       "  94 -0.654052 -0.824404   -2.197527    2.529407   -0.197107  \n",
+       "  95 -1.590447  2.450673   -2.052120    2.414469   -0.338258  \n",
+       "  96 -0.717935  3.981636   -1.316953    2.721881   -1.990192  \n",
+       "  97 -0.664567  3.521806   -0.865626    1.232372   -0.644510  \n",
+       "  98 -1.046806  0.513747    0.657512   -3.283061    0.539511  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -1.996302  0.841850 -1.592179 -2.488018  2.516441  1.451898 -0.616387   \n",
+       "  91 -0.616387  1.750831  1.950846  0.086467  0.377596  3.681402 -1.770126   \n",
+       "  92 -1.770126 -0.354060  4.190139  1.666806 -0.507569  3.882892  1.008703   \n",
+       "  93  1.008703 -0.449403  3.225635  2.650498 -1.124460  0.775557  2.705874   \n",
+       "  94  2.705874 -0.920154 -0.321589  2.123559  0.349715 -0.561927  1.023788   \n",
+       "  95  1.023788 -0.144676 -1.885265 -0.972536  0.355381 -2.532173 -0.503571   \n",
+       "  96 -0.503571  0.653448 -0.753684 -3.231821  1.374061 -1.733715 -2.095444   \n",
+       "  97 -2.095444  1.253179 -1.698495 -3.786626  2.397480  0.722855 -2.391770   \n",
+       "  98 -2.391770 -0.828247  0.079662  0.508385  0.751839  2.164962 -0.943947   \n",
+       "  99 -0.943947 -2.041943  0.797652  1.966253 -0.654143  1.787804       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  1.750831  1.950846    0.086467    0.377596    3.681402  \n",
+       "  91 -0.354060  4.190139    1.666806   -0.507569    3.882892  \n",
+       "  92 -0.449403  3.225635    2.650498   -1.124460    0.775557  \n",
+       "  93 -0.920154 -0.321589    2.123559    0.349715   -0.561927  \n",
+       "  94 -0.144676 -1.885265   -0.972536    0.355381   -2.532173  \n",
+       "  95  0.653448 -0.753684   -3.231821    1.374061   -1.733715  \n",
+       "  96  1.253179 -1.698495   -3.786626    2.397480    0.722855  \n",
+       "  97 -0.828247  0.079662    0.508385    0.751839    2.164962  \n",
+       "  98 -2.041943  0.797652    1.966253   -0.654143    1.787804  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.052797  1.620549 -1.929854  1.632944 -1.455596 -1.793962  3.376248   \n",
+       "  91  3.376248  0.398279  1.295416  3.570689  2.584588 -5.000246  0.455166   \n",
+       "  92  0.455166 -3.285486  1.676346  2.609159  3.599354 -4.567709  0.139741   \n",
+       "  93  0.139741 -3.407771 -0.368108 -1.090563  1.841568 -1.565976 -0.918778   \n",
+       "  94 -0.918778 -3.380849  0.649965 -3.260663 -0.228585  2.752291 -0.895310   \n",
+       "  95 -0.895310 -0.000640 -0.203638 -1.446359 -1.243435  4.990225 -1.247916   \n",
+       "  96 -1.247916  1.312863  0.221157  0.574059 -3.088533  4.862169  1.640914   \n",
+       "  97  1.640914  1.237940 -0.102135  1.690182 -1.661185 -0.901648  2.063300   \n",
+       "  98  2.063300  1.019497 -1.414061  0.594443 -2.227290 -4.515423  0.219240   \n",
+       "  99  0.219240 -0.721042 -1.986455  0.187650  0.616716 -5.249820       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  0.398279  1.295416    3.570689    2.584588   -5.000246  \n",
+       "  91 -3.285486  1.676346    2.609159    3.599354   -4.567709  \n",
+       "  92 -3.407771 -0.368108   -1.090563    1.841568   -1.565976  \n",
+       "  93 -3.380849  0.649965   -3.260663   -0.228585    2.752291  \n",
+       "  94 -0.000640 -0.203638   -1.446359   -1.243435    4.990225  \n",
+       "  95  1.312863  0.221157    0.574059   -3.088533    4.862169  \n",
+       "  96  1.237940 -0.102135    1.690182   -1.661185   -0.901648  \n",
+       "  97  1.019497 -1.414061    0.594443   -2.227290   -4.515423  \n",
+       "  98 -0.721042 -1.986455    0.187650    0.616716   -5.249820  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.238795  1.386718 -1.104284  0.500996  2.119447  1.809279 -0.883474   \n",
+       "  91 -0.883474  1.644697 -1.133443  0.570626  1.840193  1.851916  0.147737   \n",
+       "  92  0.147737  1.688116 -0.284994 -0.740141  2.521258  0.428410  0.470783   \n",
+       "  93  0.470783 -0.996581  1.082340 -0.297879  0.012362 -1.584376 -0.130021   \n",
+       "  94 -0.130021 -1.707698  1.977666 -0.337853 -0.988263 -2.138036  0.025838   \n",
+       "  95  0.025838 -0.413297  0.243390 -0.353106 -1.985771 -2.668837 -0.069460   \n",
+       "  96 -0.069460  0.393597 -1.599124  1.061641 -0.491637  0.574642  0.181442   \n",
+       "  97  0.181442  1.399342 -2.250317  0.762428  0.292990  0.705980  0.288991   \n",
+       "  98  0.288991  2.168686 -1.797098  0.828200 -0.402600  1.606075  0.260047   \n",
+       "  99  0.260047  2.026128  1.258081  0.278334 -0.750835  0.110668       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  1.644697 -1.133443    0.570626    1.840193    1.851916  \n",
+       "  91  1.688116 -0.284994   -0.740141    2.521258    0.428410  \n",
+       "  92 -0.996581  1.082340   -0.297879    0.012362   -1.584376  \n",
+       "  93 -1.707698  1.977666   -0.337853   -0.988263   -2.138036  \n",
+       "  94 -0.413297  0.243390   -0.353106   -1.985771   -2.668837  \n",
+       "  95  0.393597 -1.599124    1.061641   -0.491637    0.574642  \n",
+       "  96  1.399342 -2.250317    0.762428    0.292990    0.705980  \n",
+       "  97  2.168686 -1.797098    0.828200   -0.402600    1.606075  \n",
+       "  98  2.026128  1.258081    0.278334   -0.750835    0.110668  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.719407  1.121406 -2.246503 -0.045191 -1.734408 -0.390020  1.240183   \n",
+       "  91  1.240183  2.148678 -1.464874 -0.574242 -0.993017 -1.932865  0.580915   \n",
+       "  92  0.580915  1.018482  0.421388 -0.464178 -0.575167 -3.923609 -0.575272   \n",
+       "  93 -0.575272 -0.803863  0.045040  1.085461  1.934320 -1.341015 -0.357746   \n",
+       "  94 -0.357746 -2.675854  0.429844  0.204403  2.573536 -0.180793  1.376032   \n",
+       "  95  1.376032 -2.133823 -0.495761 -0.129178  2.164885  1.391484  1.800865   \n",
+       "  96  1.800865 -2.052738 -0.243025 -0.315088  0.083855  1.877381  0.740137   \n",
+       "  97  0.740137 -0.002328  1.734448 -1.268275 -1.929025  1.205941 -1.254576   \n",
+       "  98 -1.254576  0.413330  0.201210 -1.081200 -0.918645 -2.085511  0.563808   \n",
+       "  99  0.563808  1.521711  1.665783 -0.526091  1.472599 -4.400250       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90  2.148678 -1.464874   -0.574242   -0.993017   -1.932865  \n",
+       "  91  1.018482  0.421388   -0.464178   -0.575167   -3.923609  \n",
+       "  92 -0.803863  0.045040    1.085461    1.934320   -1.341015  \n",
+       "  93 -2.675854  0.429844    0.204403    2.573536   -0.180793  \n",
+       "  94 -2.133823 -0.495761   -0.129178    2.164885    1.391484  \n",
+       "  95 -2.052738 -0.243025   -0.315088    0.083855    1.877381  \n",
+       "  96 -0.002328  1.734448   -1.268275   -1.929025    1.205941  \n",
+       "  97  0.413330  0.201210   -1.081200   -0.918645   -2.085511  \n",
+       "  98  1.521711  1.665783   -0.526091    1.472599   -4.400250  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90 -0.328257  2.003878 -4.872825 -1.095859 -0.139129 -1.012713 -1.465825   \n",
+       "  91 -1.465825 -0.448425 -1.798118 -1.552690 -0.359433 -0.913222 -0.756326   \n",
+       "  92 -0.756326 -1.402398  1.488469 -1.339670  0.040523  0.989225 -0.361212   \n",
+       "  93 -0.361212 -1.552164  3.415856  0.382732  0.558238  1.519227 -0.567170   \n",
+       "  94 -0.567170 -0.735934  2.566101  0.762839  0.973118  2.046286  0.917057   \n",
+       "  95  0.917057  1.237586 -1.223859  1.288567  1.412155  1.306062  1.380277   \n",
+       "  96  1.380277  1.195142 -3.177719  1.144851  0.622592 -2.139431  0.667791   \n",
+       "  97  0.667791  1.943209 -1.916920  0.268094  0.053041 -2.777536  0.117971   \n",
+       "  98  0.117971  0.489678 -0.703515  0.278949 -0.453831 -2.799854 -0.393481   \n",
+       "  99 -0.393481 -0.718960  2.596901 -1.508228  0.816409  0.938007       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -0.448425 -1.798118   -1.552690   -0.359433   -0.913222  \n",
+       "  91 -1.402398  1.488469   -1.339670    0.040523    0.989225  \n",
+       "  92 -1.552164  3.415856    0.382732    0.558238    1.519227  \n",
+       "  93 -0.735934  2.566101    0.762839    0.973118    2.046286  \n",
+       "  94  1.237586 -1.223859    1.288567    1.412155    1.306062  \n",
+       "  95  1.195142 -3.177719    1.144851    0.622592   -2.139431  \n",
+       "  96  1.943209 -1.916920    0.268094    0.053041   -2.777536  \n",
+       "  97  0.489678 -0.703515    0.278949   -0.453831   -2.799854  \n",
+       "  98 -0.718960  2.596901   -1.508228    0.816409    0.938007  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  1.057973  1.422899  4.488055 -1.171351  0.445268 -1.498079  0.881147   \n",
+       "  91  0.881147 -1.135295  3.527412  0.020703 -2.426884 -0.752752 -1.555459   \n",
+       "  92 -1.555459 -2.947879  0.973125  1.053436 -1.281413 -1.770734 -2.098078   \n",
+       "  93 -2.098078 -1.052008 -3.432153  1.072897 -0.949869  0.575539 -0.536686   \n",
+       "  94 -0.536686  0.571528 -3.201514 -1.488237 -0.927765 -0.515264  1.923833   \n",
+       "  95  1.923833  2.588356 -1.546300 -3.307662 -0.377515  0.880116  2.646125   \n",
+       "  96  2.646125  1.589499  2.349990 -1.045222 -0.052937  0.796079  1.426403   \n",
+       "  97  1.426403 -0.685496  3.639358  0.556975 -0.121314 -0.023159  0.265301   \n",
+       "  98  0.265301 -2.905392  3.930807  2.520412  0.256544 -1.469228 -1.903496   \n",
+       "  99 -1.903496 -2.256664 -1.031043  0.393905  0.752899 -2.762937       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -1.135295  3.527412    0.020703   -2.426884   -0.752752  \n",
+       "  91 -2.947879  0.973125    1.053436   -1.281413   -1.770734  \n",
+       "  92 -1.052008 -3.432153    1.072897   -0.949869    0.575539  \n",
+       "  93  0.571528 -3.201514   -1.488237   -0.927765   -0.515264  \n",
+       "  94  2.588356 -1.546300   -3.307662   -0.377515    0.880116  \n",
+       "  95  1.589499  2.349990   -1.045222   -0.052937    0.796079  \n",
+       "  96 -0.685496  3.639358    0.556975   -0.121314   -0.023159  \n",
+       "  97 -2.905392  3.930807    2.520412    0.256544   -1.469228  \n",
+       "  98 -2.256664 -1.031043    0.393905    0.752899   -2.762937  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ,\n",
+       "      position                         r-xyz                      position  \\\n",
+       "             x         y         z   alpha_0   alpha_1   alpha_2     x_tar   \n",
+       "  90  0.866420  1.084599 -2.596926  1.565112 -0.591769  1.397244  1.763729   \n",
+       "  91  1.763729 -2.022973 -2.382188  2.512027  0.197335 -0.308777  0.730131   \n",
+       "  92  0.730131 -1.687481 -1.098141 -0.105426  1.351000 -0.917809 -0.681705   \n",
+       "  93 -0.681705  0.173699  0.239967 -2.448540  1.955613 -2.225990 -1.213109   \n",
+       "  94 -1.213109  3.018919  2.182310 -3.533449  1.713715 -1.692590 -0.338798   \n",
+       "  95 -0.338798  3.121372  3.261087 -1.207832 -0.760052 -0.803866  0.693446   \n",
+       "  96  0.693446  1.275434  0.032587  2.365354 -3.510923 -0.313984  1.734673   \n",
+       "  97  1.734673 -0.827296  0.499353  3.786802 -3.427673 -0.371170  1.295753   \n",
+       "  98  1.295753 -2.108120 -1.130036  2.828813 -0.246133  2.772462 -0.517895   \n",
+       "  99 -0.517895 -2.281592 -2.183573 -1.304478 -0.340119  1.192214       NaN   \n",
+       "  \n",
+       "                               r-xyz                          \n",
+       "         y_tar     z_tar alpha_0_tar alpha_1_tar alpha_2_tar  \n",
+       "  90 -2.022973 -2.382188    2.512027    0.197335   -0.308777  \n",
+       "  91 -1.687481 -1.098141   -0.105426    1.351000   -0.917809  \n",
+       "  92  0.173699  0.239967   -2.448540    1.955613   -2.225990  \n",
+       "  93  3.018919  2.182310   -3.533449    1.713715   -1.692590  \n",
+       "  94  3.121372  3.261087   -1.207832   -0.760052   -0.803866  \n",
+       "  95  1.275434  0.032587    2.365354   -3.510923   -0.313984  \n",
+       "  96 -0.827296  0.499353    3.786802   -3.427673   -0.371170  \n",
+       "  97 -2.108120 -1.130036    2.828813   -0.246133    2.772462  \n",
+       "  98 -2.281592 -2.183573   -1.304478   -0.340119    1.192214  \n",
+       "  99       NaN       NaN         NaN         NaN         NaN  ])"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Mom_ar1.setup_data(pred_size=-1, split_type='intra')\n",
+    "Mom_ar3.setup_data(pred_size=-1, split_type='intra')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "C:\\Users\\Stefan(local)\\Documents\\Coding\\trajectory_prediction\\src\\Python\\reworked\\predictor_box.py:623: UserWarning: n_preds > len(obs)!\n",
+      "  warnings.warn('n_preds > len(obs)!')\n",
+      "C:\\Users\\Stefan(local)\\Documents\\Coding\\trajectory_prediction\\src\\Python\\reworked\\predictor_box.py:623: UserWarning: n_preds > len(obs)!\n",
+      "  warnings.warn('n_preds > len(obs)!')\n",
+      "C:\\Users\\Stefan(local)\\Documents\\Coding\\trajectory_prediction\\src\\Python\\reworked\\predictor_box.py:623: UserWarning: n_preds > len(obs)!\n",
+      "  warnings.warn('n_preds > len(obs)!')\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>TrialID</th>\n",
+       "      <th>Model</th>\n",
+       "      <th>Feature</th>\n",
+       "      <th>Lag</th>\n",
+       "      <th>Diff</th>\n",
+       "      <th>Order</th>\n",
+       "      <th>Error</th>\n",
+       "      <th>Estimates</th>\n",
+       "      <th>Targets</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>0</td>\n",
+       "      <td>&lt;statsmodels.tsa.arima_model.ARMA object at 0x...</td>\n",
+       "      <td>(position, x)</td>\n",
+       "      <td>2</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0.527052</td>\n",
+       "      <td>[-0.0645277349362258, 0.1301659896513196, 0.26...</td>\n",
+       "      <td>[-0.276320823391778, 0.22998104566612665, 0.48...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>1</td>\n",
+       "      <td>&lt;statsmodels.tsa.arima_model.ARMA object at 0x...</td>\n",
+       "      <td>(position, x)</td>\n",
+       "      <td>2</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0.816722</td>\n",
+       "      <td>[1.0006648375191916, -1.8025224877788146, -1.8...</td>\n",
+       "      <td>[-0.46951414155077487, -2.2561705878075404, -2...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>20</td>\n",
+       "      <td>&lt;statsmodels.tsa.arima_model.ARMA object at 0x...</td>\n",
+       "      <td>(position, x)</td>\n",
+       "      <td>2</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1.070597</td>\n",
+       "      <td>[-1.4138710136262314, 0.8020384338929414, 1.42...</td>\n",
+       "      <td>[-2.234305461742375, 0.04152361335067889, 2.28...</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  TrialID                                              Model        Feature  \\\n",
+       "0       0  <statsmodels.tsa.arima_model.ARMA object at 0x...  (position, x)   \n",
+       "1       1  <statsmodels.tsa.arima_model.ARMA object at 0x...  (position, x)   \n",
+       "2      20  <statsmodels.tsa.arima_model.ARMA object at 0x...  (position, x)   \n",
+       "\n",
+       "  Lag Diff Order     Error                                          Estimates  \\\n",
+       "0   2    0     0  0.527052  [-0.0645277349362258, 0.1301659896513196, 0.26...   \n",
+       "1   2    0     0  0.816722  [1.0006648375191916, -1.8025224877788146, -1.8...   \n",
+       "2   2    0     0  1.070597  [-1.4138710136262314, 0.8020384338929414, 1.42...   \n",
+       "\n",
+       "                                             Targets  \n",
+       "0  [-0.276320823391778, 0.22998104566612665, 0.48...  \n",
+       "1  [-0.46951414155077487, -2.2561705878075404, -2...  \n",
+       "2  [-2.234305461742375, 0.04152361335067889, 2.28...  "
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# The warning only means that there won't be n_preds=40 predictions, but only \n",
+    "# as much as there are observations\n",
+    "Mom_ar3.apply_arima_models(trial_id=[0,1,20], pred_step=1, p=2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x1c3cef5f518>]"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "Results = Mom_ar3.results\n",
+    "y_hat = Results.loc[Results.TrialID == 20]['Estimates'].iloc[0]\n",
+    "y = Results.loc[Results.TrialID == 20]['Targets'].iloc[0]\n",
+    "plt.plot(y)\n",
+    "plt.plot(y_hat)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/navipy/forecasting/src/Python/reworked/data_generator.py b/navipy/forecasting/src/Python/reworked/data_generator.py
new file mode 100644
index 0000000000000000000000000000000000000000..329fc4112f75e4a865b35fa9355207adf61f82f1
--- /dev/null
+++ b/navipy/forecasting/src/Python/reworked/data_generator.py
@@ -0,0 +1,17 @@
+import pandas as pd
+import numpy as np
+
+frame = range(0,100)
+columns = pd.MultiIndex.from_tuples([('position','x'),
+									('position','y'),
+									('position','z'),
+									('r-xyz','alpha_0'),
+									('r-xyz','alpha_1'),
+									('r-xyz','alpha_2')])
+									
+df = pd.DataFrame(index=frame, columns=columns)
+
+for key in df.keys():
+	df[key] = np.random.rand(100)
+	
+	
\ No newline at end of file
diff --git a/navipy/forecasting/src/Python/reworked/predictor_box.py b/navipy/forecasting/src/Python/reworked/predictor_box.py
new file mode 100644
index 0000000000000000000000000000000000000000..ba6a498658c3c65890dec772fc728315ee8afa69
--- /dev/null
+++ b/navipy/forecasting/src/Python/reworked/predictor_box.py
@@ -0,0 +1,640 @@
+''' This moule contains all supporting class for the main program'''
+
+# standard imports
+import pandas as pd
+import random
+from math import isnan
+
+# model related imports
+from statsmodels.tsa.stattools import adfuller as df_test
+from statsmodels.graphics.tsaplots import plot_acf
+from statsmodels.graphics.tsaplots import plot_pacf
+from statsmodels.tsa.stattools import acf
+from statsmodels.tsa.stattools import pacf
+from statsmodels.tsa.arima_model import ARIMA
+from sklearn.metrics import mean_squared_error as MSE
+
+# maintenance/development imports
+import pdb
+import warnings
+
+class Investigator:
+    ''' This class provides methods for time series analysis like
+    ACF and PACF, as well as stability checks. Invoking an instance of this
+    class requires the data which is wished to be investigated. The expected
+    data structure is equal to the one used in navipy, which is given by 
+    
+    pd.MultiIndex.from_tuples([('position', 'x'),
+                                             ('position', 'y'),
+                                             ('position', 'z'),
+                                             ('r-xyz', 'alpha_0'),
+                                             ('r-xyz', 'alpha_1'),
+                                             ('r-xyz', 'alpha_2')])
+    
+    You can provide a single MultiIndex or a list of MultiIndex.
+    '''
+
+    def __init__(self, data):
+
+        if isinstance(data, list):
+            self.data = data
+        elif isinstance(data, pd.core.frame.DataFrame):
+            self.data = [data]
+        else:
+            print('Investigator not initilaized due to bad data format.\n' +
+                  'Please make sure data is either a pandas.MultiIndex \n' +
+                  'or a list of pandas.MultiIndex.')
+
+    '''####################################################'''
+    '''### Stationarity investigation related functions ###'''
+    '''####################################################'''
+
+    def check_stationary(self, trial_id=-1,
+                         sig_level=None,
+                         print_res=False,
+                         diff_order=0):
+        ''' Checks selected data for stationarity.
+
+        This function checks selected data for stationarity in a time-series
+        context with a dickey-fuller test. It returns a pandas dataframe of
+        booleans, where each row is one trial and each column one feature dim-
+        emnsion.
+
+        Keyword arguments:
+        trial_id -- int or [int] containing the id of the trials to be investi
+                    gated. If trial_id = -1, all trials are checked.
+                    Default = -1
+        sig_level -- float level of significance.
+                    Default = 0.05
+        print_res -- boolean value, if true, results are printed.
+                    Default = False
+        diff_order -- int in [0,3]. Number of times the time-series is
+                    differenced befor it is checked for stability.
+                    Default = 0
+            
+        Returns:
+        stationarity_df -- pandas dataframe of booleans.
+        '''
+        
+        _valid_id_ = True
+        if not isinstance(trial_id, list):
+            if isinstance(trial_id, int):
+                if trial_id is -1:
+                    trial_id = range(0, len(self.data))
+                else:
+                    trial_id = [trial_id]
+        else:
+            if not isinstance(trial_id[0], int):
+                _valid_id_ = False
+                warnings.warn(
+                    'trial_id not valid format. Must be int or [int]'+
+                    'Returned stationarity_df is empty.')
+            elif trial_id[0] is -1:
+                trial_id = range(0, len(self.data))
+        
+        if sig_level is None:
+            sig_level = 0.05
+        _valid_, sig_level = self._stability_args_validation_(sig_level)
+        stationarity_df = self._create_df_template_(trial_id=trial_id)
+        if _valid_ and _valid_id_:
+            t = 0
+            for ID in trial_id:
+                trial = self.data[ID]
+                for dim in trial.columns:
+                    series = trial[dim]
+                    series = self._diff_series_(series, diff_order)
+                    res = df_test(series)
+                    p_val = res[1]
+
+                    if p_val > sig_level:
+                        stationarity_df[dim][t] = False
+                    else:
+                        stationarity_df[dim][t] = True
+                t = t+1
+        else:
+            warnings.warn(
+                'Input sig_level is not in valid format.\n' +
+                'Returned stationarity_df is empty.')
+        return stationarity_df
+
+    def _stability_args_validation_(self, sig_level):
+        valid = True
+        if isinstance(sig_level, float):
+            if sig_level >= 1 or sig_level <= 0:
+                valid = False
+                print('Significance level outside of valid boundaries (0,1)')
+        if isinstance(sig_level, str):
+            try:
+                sig_level = float(sig_level)
+            except:
+                valid = False
+                print('Significance level is string' +
+                      'that can not be casted onto float')
+        if isinstance(sig_level, float):
+            if sig_level >= 1 or sig_level <= 0:
+                valid = False
+                print('Significance level outside of valid boundaries (0,1)')
+
+        return valid, sig_level
+
+    '''####################################################################'''
+    '''### Autocorrelation and Partial autocorelation related functions ###'''
+    '''####################################################################'''
+
+    def plot_cf_function(self, function_type='acf',
+                         trial_id=0, dim=('position', 'x'),
+                         ):
+        ''' Plots results of either ACF or PACF for a single dimension.
+        
+        This function plots the results of an auto-correlation-function (ACF)
+        or partial ACF (PACF), depending on the selected funtion_type, for a 
+        single dimension. 
+        It is basically acting as a tunnel-implementation of plot_acf/_pacf
+        of the statsmodels.graphics.tsaplots module. 
+        
+         Keyword arguments:
+        trial_id -- int or [int] containing the id of the trials to be investi
+                    gated. If trial_id = -1, all trials are checked.
+                    Default = -1
+        dim -- tuple of features like ('position','x'). This column in data
+                is used as a time series and plotted 
+        
+        Returns:
+        figs -- list of pyplot figures [fig]. 
+        '''
+        
+        valid = True
+        if not isinstance(trial_id, list):
+            if isinstance(trial_id, int):
+                if trial_id is -1:
+                    trial_id = range(0, len(self.data))
+                else:
+                    trial_id = [trial_id]
+        else:
+            if not isinstance(trial_id[0], int):
+                valid = False
+                warnings.warn(
+                    'trial_id not valid format. Must be int or [int]')
+            elif trial_id[0] is -1:
+                trial_id = range(0, len(self.data))
+
+        if not isinstance(dim, list):
+            if isinstance(dim, tuple):
+                dim = [dim]
+        else:
+            if (not isinstance(dim[0], str) or
+                not isinstance(dim[1], str)):
+                valid = False
+                warnings.warn(
+                    'dim not valid format. Must be tuple or [tuple] of str')
+        figs = []
+        if valid is True:
+            num = 1
+            for ti in trial_id:
+                trial = self.data[ti]
+                for d in dim:
+                    series = trial[d]
+                    if function_type is 'acf':
+                        fig = plot_acf(series)
+                    elif function_type is 'pacf':
+                        fig = plot_pacf(series)
+                    figs.append(fig)
+                    num = num+1
+        return figs
+
+    def get_significant_lags(self,trial_id=-1, function_type='acf', n_lags=40,
+                             sig_level=0.05, diff_order=0):
+        ''' This function analysis the data for the number of significant
+        legs with respect to either autocorrelation fucntion (acf) or
+        partial acf (pacf). It returns the last significant lag.'''
+        valid_input = True
+        if not isinstance(trial_id, list):
+            if isinstance(trial_id, int):
+                if trial_id is -1:
+                    trial_id = range(0, len(self.data))
+                else:
+                    trial_id = [trial_id]
+        else:
+            if not isinstance(trial_id[0], int):
+                valid_input = False
+                warnings.warn(
+                    'trial_id not valid format. Must be int or [int]'+
+                    'Returned stationarity_df is empty.')
+            elif trial_id[0] is -1:
+                trial_id = range(0, len(self.data))        
+        if function_type is not 'acf' and function_type is not 'pacf':
+            valid_input = False
+            print('function_type must be either \'acf\' or \'pacf\'')
+        elif not isinstance(n_lags, int):
+            valid_input = False
+            print('n_lags should be int type, but is sth. else.')
+        elif (not isinstance(sig_level, float) and
+              not isinstance(sig_level, int)):
+            valid_input = False
+            print('Significance level should be either' +
+                  'float or int, but is not')
+        elif sig_level >= 1 or sig_level <= 0:
+            valid_input = False
+            print('Significance level outside of valid boundaries (0,1)')
+        significant_lags_df = self._create_df_template_(trial_id=trial_id)
+        if valid_input is True:
+            t = 0
+            for ID in trial_id:
+                trial = self.data[ID]
+                for key in trial:
+                    series = trial[key]
+                    series = self._diff_series_(series, diff_order)
+                    if function_type is 'acf':
+                        cf_val, cf_conf_val = acf(
+                            series, nlags=n_lags, alpha=sig_level)
+                    elif function_type is 'pacf':
+                        cf_val, cf_conf_val = pacf(
+                            series, nlags=n_lags, alpha=sig_level)
+                    significant_lags_df.iloc[t][key] = self._find_last_significant_lag_value_(
+                        cf_val, cf_conf_val)
+                t = t+1
+        else:
+            warnings.warn(
+                'Input Arguments not valid! Returned dataframe is empty!')
+        return significant_lags_df
+
+    def _diff_series_(self, series, order):
+        ''' This function differs the time series, which is used to introduce stability
+        It returns a new time series, which is differed.'''
+        if order is not 0:
+            diff = list()
+            for i in range(order, len(series)):
+                val = series[i]-series[i-order]
+                diff.append(val)
+                res = pd.Series(diff)
+        else:
+            res = series
+        return res
+
+    def _find_last_significant_lag_value_(self, cf_val, cf_conf_val):
+        ''' This function finds the last lag value that is significant by
+        comparing the calculated correlation function value cf_val with the
+        corresponding confidence intervalls '''
+        t = 0
+        is_in_interv = False
+        while (is_in_interv is False and t < len(cf_val)):
+            if t < len(cf_val):
+                upper_margin = cf_conf_val[t, 1] - cf_val[t]
+                lower_margin = cf_conf_val[t, 0] - cf_val[t]
+                if cf_val[t] < upper_margin:
+                    is_in_interv = True
+                if cf_val[t] < 0 and cf_val[t] > lower_margin:
+                    is_in_interv = True
+            else:
+                t = t-1
+            t = t+1
+
+        return (t-1)
+
+    '''###################################'''
+    '''### General assisting functions ###'''
+    '''###################################'''
+
+    def _create_df_template_(self, trial_id):
+        n_trials = range(0, len(trial_id))
+        
+        columns=self.data[0].columns
+        df = pd.DataFrame(index=n_trials, columns=columns)
+        return df
+
+
+class Modelmaker:
+
+    def __init__(self, data):
+        if isinstance(data, list):
+            self.data = data
+            self.model = {}
+            self.tr_set = None
+            self.te_set = None
+            self.ev_set = None
+            '''
+            temp_dict = {'TrialID': None,
+                         'Model': None,
+                         'Feature': None,
+                         'Lag': None,
+                         'Diff': None,
+                         'Order': None,
+                         'Error': None,
+                         'Estimates': None,
+                         'Targets': None
+                         }
+            '''
+            columns = ['TrialID','Model','Feature','Lag','Diff','Order',
+                       'Error','Estimates','Targets']
+            self.results = pd.DataFrame(columns=columns)
+
+        elif isinstance(data, pd.core.frame.DataFrame):
+            self.data = [data]
+        else:
+            print('Investigator not initilaized due to bad data format.\n' +
+                  'Please make sure data is either a pandas.MultiIndex or' +
+                  'a list of pandas.MultiIndex.')
+
+    '''##################################'''
+    '''### Train/Test/Eval allocation ###'''
+    '''##################################'''
+
+    def setup_data(self, random_split=True,
+                   tr_size=.6,
+                   te_size=.3,
+                   ev_size=.1,
+                   pred_size=-1,
+                   split_type='inter'):
+        ''' This function put data into train, test and eval set
+    
+        This function splits all trials in data into training, test 
+        and evaluation set and creates targets from a given shift.
+        The number of trials in each set depends on 
+        the user specified allocation. 
+        Furthermore, the user has to select pred_size, which determines
+        how far into the future the prediction shall take place
+        
+        Keyword arguments:
+        random_split -- bool determining if data is allocated randomly to each set
+                        Default = True
+        tr_size -- float determining the percentage of over all data allocated to 
+                    training set.
+                    Default = .6
+        te_size -- float determining the percentage of over all data allocated to 
+                    test set.
+                    Default = .3                
+        ev_size -- float determining the percentage of over all data allocated to 
+                    evaluation set.
+                    Default = .1
+                MIND THAT tr_size + te_size + ev_size = 1 HAS TO BE TRUE
+        
+        pred_size -- int <= 0 determining the shift of target to input data. Number
+                    has to be negative to be consistent with numpy shift method.
+                    Default = -1
+        split_type -- string 'inter' or 'intra' determining how the sets are created.
+                    When 'inter', each set consists of complete, independent trajectories
+                        - Use this for neural networks
+                    When 'intra', each trajectory is cut into a training and a test part
+                        - Use this for ARIMA models
+                    Default = 'intra' 
+                    
+        Returns:
+        ls_df_tr -- list of pandas.DataFrames, one entry per trajectory in training set
+        ls_df_te -- list of pandas.DataFrames, one entry per trajectory in test set
+        ls_df_ev -- list of pandas.DataFrames, one entry per trajectory in evaluation set'''               
+                
+        if split_type is 'inter':
+            ls_df_tr, ls_df_te, ls_df_ev = self._inter_split_data_set_(
+                tr_sz=tr_size,
+                te_sz=te_size,
+                ev_sz=ev_size,
+                rn_splt=random_split)
+            ls_df_tr = self._extend_df_by_shifted_targets_(ls_df_tr, pred_size)
+            ls_df_te = self._extend_df_by_shifted_targets_(ls_df_te, pred_size)
+            ls_df_ev = self._extend_df_by_shifted_targets_(ls_df_ev, pred_size)
+        elif split_type is 'intra':
+            extended_shifted_data = self._extend_df_by_shifted_targets_(
+                self.data, pred_size)
+            ls_df_tr, ls_df_te, ls_df_ev = self._intra_split_data_set_(
+                    extended_shifted_data, tr_sz=tr_size, te_sz=te_size,
+                    ev_sz=ev_size)
+        self.tr_set = ls_df_tr
+        self.te_set = ls_df_te
+        self.ev_set = ls_df_ev
+
+        return ls_df_tr, ls_df_te, ls_df_ev
+
+    def _extend_df_by_shifted_targets_(self, df, pred_size):
+        '''This function shifts the df against itself by a shift
+        of pred size'''
+        trial_i = 0
+        for trial in df:
+            # for each key
+            for key in trial.keys():
+                # shift the rows
+                target = trial[key].shift(pred_size)
+                # add to df
+                t_key = key[1]+'_tar'
+                df[trial_i][key[0], t_key] = target
+            df[trial_i].sort_index(axis=1)
+            trial_i = trial_i+1
+        return df
+
+    def _intra_split_data_set_(self, df, tr_sz, te_sz, ev_sz):
+
+        data = df
+        ls_df_tr = []
+        ls_df_te = []
+        ls_df_ev = []
+
+        for trial in data:
+            n_samples = len(trial)
+            n_tr_elem = round(tr_sz*n_samples)
+            n_te_elem = round(te_sz*n_samples)
+
+            start = 0
+            stop = n_tr_elem
+            ls_df_tr.append(trial.iloc[start:stop])
+
+            start = stop
+            stop = n_tr_elem+n_te_elem
+            ls_df_te.append(trial.iloc[start:stop])
+
+            start = stop
+            stop = n_samples
+            ls_df_ev.append(trial.iloc[start:stop])
+        return ls_df_tr, ls_df_te, ls_df_ev
+
+    def _inter_split_data_set_(self, tr_sz, te_sz, ev_sz, rn_splt):
+
+        data = self.data
+
+        ls_df_tr = []
+        ls_df_te = []
+        ls_df_ev = []
+
+        n_trials = len(data)
+        n_tr_elem = round(tr_sz*n_trials)
+        n_te_elem = round(te_sz*n_trials)
+        n_ev_elem = round(ev_sz*n_trials)
+        if (n_tr_elem is 0 or
+                n_te_elem is 0):
+            print('0 allocation to one set!' +
+                  'User more data or change allocation!')
+        if rn_splt is True:
+            rn = random.sample(range(0, n_trials), n_trials)
+        else:
+            rn = range(0, n_trials)
+
+        start = 0
+        stop = n_tr_elem
+        for i in range(start, stop):
+            trial_i = rn[i]
+            ls_df_tr.append(data[trial_i])
+
+        start = stop
+        stop = n_tr_elem+n_te_elem
+        for i in range(start, stop):
+            trial_i = rn[i]
+            ls_df_te.append(data[trial_i])
+
+        if n_ev_elem is not 0:
+            start = stop
+            stop = n_trials
+        for i in range(start, stop):
+            trial_i = rn[i]
+            ls_df_ev.append(data[trial_i])
+
+        return ls_df_tr, ls_df_te, ls_df_ev
+
+    '''#######################'''
+    '''### ARIMA modelling ###'''
+    '''#######################'''
+
+    def apply_arima_models(self,
+                           p=1,
+                           d=0,
+                           q=0,
+                           pred_step=1,
+                           dim=('position', 'x'),
+                           trial_id=-1,
+                           n_preds=40,
+                           rolling=True,
+                           override=True,
+                           metric = MSE
+                           ):
+        ''' This function applies ARIMA models to data and saves results internally
+        
+        This function applies an ARIMA(p,d,q) model to all trials selected with trial_id.
+        The results are internally saved in Modelmaker.results, where you can see predictions
+        or directly access the model instance. 
+        
+        Keyword arguments:
+        p -- int > 0, number of lag observations
+            Default = 1
+        d -- int > 0, order of differentiation
+            Default = 0
+        q -- int > 0, size of MA window
+            Default = 0
+        pred_step -- int > 0, forecasting horizon
+        dim -- str tuple matching any feature in data, determining which feature values are used in 
+                this model.
+                Default = ('position','x')
+        trial_id -- [int >0] or int >= -1, If list of int, all trials which ID matches any element of
+                said list will be fitted by an ARIMA model. If int  is -1, all trials will be fitted by
+                and ARIMA model
+                Default = -1
+        n_preds -- int > 0, number of predictions that shall be made. If this number is largere than the
+                number of observations estimates can be compared to, it will throw a warning and will only
+                produce len(observation) estimates.
+                Default = 40
+        rolling -- bool, if True, after each estimate, the actual observation is added to the history,
+                   and the model parameters are fitted to the updated history, befor making the next 
+                   estimate
+                   Default = True
+        override -- bool, if True, if the trial_id has already been fitted by an ARIMA, these results will 
+                    be deleted and the new results will be shown for this row in results. If False,
+                    a new row is added (MIND that TrialID is not unique anymore in this case)
+                    Default = True
+        metric -- function(list,list), user defined metric funtcion that handles two list arguments of the 
+                    same length as inputs. Takes EXACTLY two list inputs, so modify before passing as argument.
+                    Note: Pass without brackets e.g. metric = my_metric BUT NOT LIKE metric = my_metric()
+                    Default = sklearn.metrics.mean_squared_error
+        Returns:
+        self.results -- Pandas dataframe, where each row contains informations about the fitted model 
+                           to the respective trial id
+        '''
+        valid = True
+        if not isinstance(trial_id, list):
+            if isinstance(trial_id, int):
+                if trial_id is -1:
+                    trial_id = range(0, len(self.data))
+                else:
+                    trial_id = [trial_id]
+        else:
+            if not isinstance(trial_id[0], int):
+                valid = False
+                warnings.warn(
+                    'trial_id not valid format. Must be int or [int]' +
+                    'Returned stationarity_df is empty.')
+            elif trial_id[0] is -1:
+                trial_id = range(0, len(self.data))
+        if valid is True:
+            for ti in trial_id:
+                history = [x for x in self.tr_set[ti][dim]]
+                observations = [x for x in self.te_set[ti][dim]]
+                model, predictions, observations = self._create_single_arima_(
+                        p=p,
+                        d=d,
+                        q=q,
+                        hist=history,
+                        obs=observations,
+                        n_preds=n_preds,
+                        pred_step=pred_step,
+                        rolling=rolling
+                        )
+                if not callable(metric):
+                    error = None
+                    warnings.warn('metric not valid format. Must be callable' +\
+                                  ' function')
+                else:
+                    try:
+                        error = metric(predictions,observations)
+                    except:
+                        warnings.warn('metric not valid format. Function must'+\
+                                      ' have two input arguments')
+                        error = None
+                if ti in self.results.TrialID.values and\
+                        override is True:
+                    self.results.loc[ti]['TrialID'] = ti
+                    self.results.loc[ti]['Model'] = model
+                    self.results.loc[ti]['Feature'] = dim
+                    self.results.loc[ti]['Lag'] = p
+                    self.results.loc[ti]['Diff'] = d
+                    self.results.loc[ti]['Order'] = q
+                    self.results.loc[ti]['Error'] = error
+                    self.results.loc[ti]['Estimates'] = predictions
+                    self.results.loc[ti]['Targets'] = observations
+                elif ti not in self.results.TrialID.values or\
+                        override is False:
+                    temp_dict = {'TrialID': ti,
+                                 'Model': model,
+                                 'Feature': [dim],
+                                 'Lag': p,
+                                 'Diff': d,
+                                 'Order': q,
+                                 'Error': error,
+                                 'Estimates': [predictions],
+                                 'Targets': [observations]
+                                 }
+                    self.results = self.results.append(
+                            pd.DataFrame(temp_dict,
+                                         index=[0 if isnan(self.results.index.max())\
+                                                else self.results.index.max()+1]))
+        return self.results
+
+    def _create_single_arima_(self, hist, p, d, q, obs, n_preds,
+                              pred_step, rolling):
+        if n_preds > len(obs):
+            n_preds = len(obs)
+            warnings.warn('n_preds > len(obs)!')
+        predictions = []
+        relevant_obs = []
+        if rolling is True:
+            for t in range(0, n_preds):
+                model = ARIMA(hist, order=(p, d, q))
+                model_fit = model.fit(disp=0)
+                output = model_fit.forecast(pred_step)
+                hat = output[0][-1]
+                predictions.append(hat)
+                relevant_obs.append(obs[t])
+                hist.append(obs[t])
+
+        elif rolling is False:
+            model = ARIMA(hist, order=(p, d, q))
+            model_fit = model.fit(disp=0)
+            output = model_fit.forecast(n_preds)
+            predictions = output[0]
+            relevant_obs = obs[0:n_preds]
+
+        return model, predictions, relevant_obs
diff --git a/navipy/forecasting/src/Python/reworked/test_predictor_box.py b/navipy/forecasting/src/Python/reworked/test_predictor_box.py
new file mode 100644
index 0000000000000000000000000000000000000000..c61a96b114e60d1b31b45c9cdadc33c14a7a346e
--- /dev/null
+++ b/navipy/forecasting/src/Python/reworked/test_predictor_box.py
@@ -0,0 +1,340 @@
+import predictor_box as pbox
+from matplotlib import pyplot as plt
+import unittest
+import pandas as pd
+import numpy as np
+import pdb
+from statsmodels.tsa.arima_process import ArmaProcess
+import math
+import copy
+
+
+class GeneralProvider():
+
+    def _generate_random_data_(self, is_stationary, n_samples=1000):
+        frame = range(0, n_samples)
+        columns = pd.MultiIndex.from_tuples([('position', 'x'),
+                                             ('position', 'y'),
+                                             ('position', 'z'),
+                                             ('r-xyz', 'alpha_0'),
+                                             ('r-xyz', 'alpha_1'),
+                                             ('r-xyz', 'alpha_2')])
+
+        df = pd.DataFrame(index=frame, columns=columns)
+        for key in df.keys():
+            if is_stationary:
+                df[key] = np.random.rand(n_samples)
+            if not is_stationary:
+                df[key] = np.linspace(0, 100, n_samples)
+
+        return df
+
+    def _generate_ar1_data_(self, n_samples=1000):
+        frame = range(0, n_samples)
+        columns = pd.MultiIndex.from_tuples([('position', 'x'),
+                                             ('position', 'y'),
+                                             ('position', 'z'),
+                                             ('r-xyz', 'alpha_0'),
+                                             ('r-xyz', 'alpha_1'),
+                                             ('r-xyz', 'alpha_2')])
+        df = pd.DataFrame(index=frame, columns=columns)
+        for key in df.keys():
+            ar = np.array([1, 1])
+            ma = np.array([1])
+            ar1_object = ArmaProcess(ar, ma)
+            ar1_series = ar1_object.generate_sample(n_samples)
+            df[key] = ar1_series
+        return df
+
+    def _generate_ar3_data_(self, n_samples=100):
+        frame = range(0, n_samples)
+        columns = pd.MultiIndex.from_tuples([('position', 'x'),
+                                             ('position', 'y'),
+                                             ('position', 'z'),
+                                             ('r-xyz', 'alpha_0'),
+                                             ('r-xyz', 'alpha_1'),
+                                             ('r-xyz', 'alpha_2')])
+        df = pd.DataFrame(index=frame, columns=columns)
+        rho = np.array([.3, .3, .4])
+        sigma = 1
+        mu_e = 0
+        for key in df.keys():
+            y = np.array([1, .5, 1.5])
+            for i in range(3, n_samples):
+                n_lagged_val = np.array([y[i-1], y[i-2], y[i-3]])
+                # AR model
+                new_val = rho.dot(n_lagged_val) + \
+                    np.random.normal(mu_e, sigma, 1)[0]
+                new_val = y[-1]-new_val
+                y = np.append(y, new_val)
+            df[key] = y
+        return df
+
+    def _check_for_homogeneous_values_(self, df, expected_h_value):
+        is_homogen = True
+        if expected_h_value is 'NaN':
+            for key in df.keys():
+                for val in df[key]:
+                    if not math.isnan(val):
+                        is_homogen = False
+        else:
+            for key in df.keys():
+                for val in df[key]:
+                    if val is not expected_h_value:
+                        is_homogen = False
+        return is_homogen
+
+    def _check_for_correct_structure_and_shift_for_intra_split_(
+            self, df, expected_shift):
+        is_correct = True
+        mainkey = 'position'
+        subkeys_x = ['x', 'y', 'z']
+        subkeys_tar = ['x_tar', 'y_tar', 'z_tar']
+        for trial in df:
+            for k in range(0, len(subkeys_x)):
+                base = trial[mainkey, subkeys_x[k]]
+                shifted = trial[mainkey, subkeys_tar[k]]
+                difference = base.shift(expected_shift)-shifted
+                if difference.sum() != 0.0:
+                    is_correct = False
+        return is_correct
+
+    def _check_for_correct_structure_and_shift_for_inter_split_(
+            self, df, expected_shift):
+        is_correct = True
+        mainkey = 'position'
+        subkeys_x = ['x', 'y', 'z']
+        subkeys_tar = ['x_tar', 'y_tar', 'z_tar']
+        for trial in df:
+            for k in range(0, len(subkeys_x)):
+                base = trial[mainkey, subkeys_x[k]]
+                shifted = trial[mainkey, subkeys_tar[k]]
+                if not self.__is_matching_in_difference_and_number_of_nan__(
+                        base, shifted, expected_shift):
+                    is_correct = False
+        return is_correct
+
+    def __is_matching_in_difference_and_number_of_nan__(self,
+                                                        base,
+                                                        shifted,
+                                                        expected_shift):
+        is_matching = True
+        difference = base.shift(expected_shift)-shifted
+        n_NaN = difference.isnull().values.sum()
+        expected_n_NaN = -expected_shift
+        if n_NaN != expected_n_NaN or difference.sum() != 0.0:
+            is_matching = False
+        return is_matching
+
+
+class TestInvestigatorClass(unittest.TestCase):
+
+    '''####################'''
+    '''### Stationarity ###'''
+    '''####################'''
+
+    def test_stability_function_on_stationary_data(self):
+        gp = GeneralProvider()
+        data = gp._generate_random_data_(is_stationary=True)
+        investigator = pbox.Investigator(data)
+        sig_level = '0.05'
+        df_stationary = investigator.check_stationary(sig_level=sig_level)
+        self.assertTrue(gp._check_for_homogeneous_values_(df_stationary, True))
+
+    def test_stability_function_on_stationary_data_array(self):
+        gp = GeneralProvider()
+        data = []
+        data.append(gp._generate_random_data_(is_stationary=True))
+        data.append(gp._generate_random_data_(is_stationary=True))
+        data.append(gp._generate_random_data_(is_stationary=True))
+        investigator = pbox.Investigator(data)
+        sig_level = '0.05'
+        df_stationary = investigator.check_stationary(sig_level=sig_level)
+        self.assertTrue(gp._check_for_homogeneous_values_(df_stationary, True))
+
+    def test_stability_function_on_non_stationary_data_array(self):
+        gp = GeneralProvider()
+        data = []
+        data.append(gp._generate_random_data_(is_stationary=False))
+        data.append(gp._generate_random_data_(is_stationary=False))
+        data.append(gp._generate_random_data_(is_stationary=False))
+        investigator = pbox.Investigator(data)
+        sig_level = '0.05'
+        df_stationary = investigator.check_stationary(sig_level=sig_level)
+        self.assertTrue(
+            gp._check_for_homogeneous_values_(df_stationary, False))
+
+    def test_stability_function_on_not_stationary_data(self):
+        gp = GeneralProvider()
+        data = gp._generate_random_data_(is_stationary=False)
+        investigator = pbox.Investigator(data)
+        sig_level = '0.05'
+        df_stationary = investigator.check_stationary(sig_level=sig_level)
+        self.assertTrue(
+            gp._check_for_homogeneous_values_(df_stationary, False))
+
+    def test_stability_function_on_not_stationary_data_with_diff_order_1(self):
+        gp = GeneralProvider()
+        data = gp._generate_random_data_(is_stationary=False)
+        investigator = pbox.Investigator(data)
+        sig_level = '0.05'
+        df_stationary = investigator.check_stationary(sig_level=sig_level, diff_order=1)
+        self.assertTrue(gp._check_for_homogeneous_values_(df_stationary, True))
+
+    def test_stability_function_on_user_input_sig_level_format_str(self):
+        gp = GeneralProvider()
+        data = gp._generate_random_data_(is_stationary=False)
+        investigator = pbox.Investigator(data)
+        sig_level = '0.05'
+        valid, s = investigator._stability_args_validation_(sig_level=sig_level)
+        self.assertTrue(valid)
+
+    def test_stability_function_on_user_input_sig_level_format_float(self):
+        gp = GeneralProvider()
+        data = gp._generate_random_data_(is_stationary=False)
+        investigator = pbox.Investigator(data)
+        sig_level = 0.05
+        valid, s = investigator._stability_args_validation_(sig_level=sig_level)
+        self.assertTrue(valid)
+
+    '''###################'''
+    '''### Correlation ###'''
+    '''###################'''
+
+    def test_get_significant_lag_function_with_ar1_process_lag_finding(self):
+        gp = GeneralProvider()
+        data = gp._generate_ar1_data_()
+        investigator = pbox.Investigator(data)
+        lags = investigator.get_significant_lags()
+        self.assertTrue(gp._check_for_homogeneous_values_(lags, 1))
+
+    def test_get_significant_lag_function_with_ar3_process_lag_finding(self):
+        gp = GeneralProvider()
+        data = gp._generate_ar3_data_()
+        investigator = pbox.Investigator(data)
+        lags = investigator.get_significant_lags()
+        self.assertTrue(gp._check_for_homogeneous_values_(lags, 2))
+
+    def test_get_signifcant_lag_function_user_wrong_input_catch(self):
+        gp = GeneralProvider()
+        data = gp._generate_ar1_data_()
+        investigator = pbox.Investigator(data)
+        lags = investigator.get_significant_lags(function_type='Not acf')
+        self.assertTrue(gp._check_for_homogeneous_values_(lags, 'NaN'))
+
+
+'''
+This code is commented, because it was only used for visual inspectation during
+debugging. If non of the other test functions is throwing an error, plotting
+functionallity is covered as well.
+
+    def test_plot_cf_function_test_acf_type(self):
+        gp = GeneralProvider()
+        data = []
+        data.append(gp._generate_ar1_data_())
+        data.append(gp._generate_ar3_data_())
+        data.append(gp._generate_random_data_(is_stationary=True))
+        investigator = pbox.Investigator(data)
+        figs = investigator.plot_cf_function(function_type='acf',
+                                             trial_id=-1, dim=('position', 'x'))
+        
+    def test_plot_cf_function_test_pacf_type(self):
+        gp = GeneralProvider()
+        data = []
+        data.append(gp._generate_ar1_data_())
+        data.append(gp._generate_ar3_data_())
+        data.append(gp._generate_random_data_(is_stationary=True))
+        investigator = pbox.Investigator(data)
+        figs = investigator.plot_cf_function(function_type='pacf',
+                                             trial_id=-1, dim=('position', 'x'))
+        plt.show(block=False)
+'''
+     
+
+class TestModelmakerClass(unittest.TestCase):
+
+    def test_intra_setup_data_with_pred_step_1(self):
+        gp = GeneralProvider()
+        forecasting_horizon = -1
+        data = []
+        for i in range(0, 20):
+            data.append(gp._generate_ar1_data_())
+        MM = pbox.Modelmaker(data)
+        df_tr, df_te, df_ev = MM.setup_data(
+            pred_size=forecasting_horizon, split_type='inter')
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_inter_split_(
+                        df_tr, forecasting_horizon))
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_inter_split_(
+                        df_te, forecasting_horizon))
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_inter_split_(
+                        df_ev, forecasting_horizon))
+
+    def test_intra_setup_data_with_pred_step_10(self):
+        gp = GeneralProvider()
+        forecasting_horizon = -10
+        data = []
+        for i in range(0, 20):
+            data.append(gp._generate_ar1_data_())
+        MM = pbox.Modelmaker(data)
+        df_tr, df_te, df_ev = MM.setup_data(
+            pred_size=forecasting_horizon, split_type='inter')
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_inter_split_(
+                        df_tr, forecasting_horizon))
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_inter_split_(
+                        df_te, forecasting_horizon))
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_inter_split_(
+                        df_ev, forecasting_horizon))
+
+    def test_inter_setup_data_with_pred_step_1(self):
+        gp = GeneralProvider()
+        forecasting_horizon = -1
+        data = []
+        for i in range(0, 20):
+            data.append(gp._generate_ar1_data_())
+        MM = pbox.Modelmaker(data)
+        df_tr, df_te, df_ev = MM.setup_data(
+            pred_size=forecasting_horizon, split_type='intra')
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_intra_split_(
+                        df_tr, forecasting_horizon))
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_intra_split_(
+                        df_te, forecasting_horizon))
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_intra_split_(
+                        df_ev, forecasting_horizon))
+
+    def test_inter_setup_data_with_pred_step_10(self):
+        gp = GeneralProvider()
+        forecasting_horizon = -10
+        data = []
+        for i in range(0, 20):
+            data.append(gp._generate_ar1_data_())
+        MM = pbox.Modelmaker(data)
+        df_tr, df_te, df_ev = MM.setup_data(
+            pred_size=forecasting_horizon, split_type='intra')
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_intra_split_(
+                        df_tr, forecasting_horizon))
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_intra_split_(
+                        df_te, forecasting_horizon))
+        self.assertTrue(
+                gp._check_for_correct_structure_and_shift_for_intra_split_(
+                        df_ev, forecasting_horizon))
+
+    def test_invoke_arima_function_for_correct_override(self):
+        pass
+
+    def test_invoke_arima_function_for_correct_output_structure(self):
+        pass
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/navipy/forecasting/src/Python/reworked/test_script.py b/navipy/forecasting/src/Python/reworked/test_script.py
new file mode 100644
index 0000000000000000000000000000000000000000..f1aca848d76f66c08ed4d8c3781eedfebea2e7d5
--- /dev/null
+++ b/navipy/forecasting/src/Python/reworked/test_script.py
@@ -0,0 +1,59 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Aug 14 11:07:45 2018
+
+@author: Stefan(local)
+"""
+
+from test_predictor_box import GeneralProvider
+from predictor_box import Investigator
+from predictor_box import Modelmaker
+import pandas
+import numpy as np
+
+def my_metric(a,b):
+    a = np.array(a)
+    b = np.array(b)
+    return (a+b).sum()
+
+''' Generate Artificial Data '''
+TOTAL_NUM_TRIALS = 40
+
+gp = GeneralProvider()
+data = []
+for t in range(0, TOTAL_NUM_TRIALS):
+    data.append(gp._generate_random_data_(is_stationary=True))
+
+''' Showcase Investigator Class '''
+
+Inv = Investigator(data)
+statdf = Inv.check_stationary()
+print(statdf)
+lagsdf = Inv.get_significant_lags()
+print(lagsdf)
+# plotting
+#Inv.plot_cf_function(trial_id=0, dim=('position', 'y'), function_type='acf')
+#Inv.plot_cf_function(trial_id=0, dim=('position', 'z'), function_type='pacf')
+
+''' Showcase Modelmaker Class '''
+
+Mom = Modelmaker(data)
+
+tr, te, ev = Mom.setup_data(pred_size=-1, split_type='intra')
+x_example = tr[0][('position', 'x')]
+x_tar_example = tr[0][('position', 'x_tar')]
+df_show = pandas.DataFrame()
+df_show['x'] = x_example
+df_show['x_tar'] = x_tar_example
+df_show.plot()
+
+Mom.apply_arima_models(trial_id=[0, 1, 20], pred_step=1)
+Mom.apply_arima_models(trial_id=[30], pred_step=1)
+#Mom.apply_arima_models(trial_id=[30], pred_step=1, dim=('position', 'y'))
+Mom.apply_arima_models(trial_id=[30], override=False, pred_step=1,
+                       dim=('position', 'y'))
+print(Mom.results)
+
+
+Mom.apply_arima_models(trial_id=[30], override=False, pred_step=1, metric = my_metric,
+                       dim=('position', 'y'))
diff --git a/navipy/forecasting/src/Python/shorty.py b/navipy/forecasting/src/Python/shorty.py
new file mode 100644
index 0000000000000000000000000000000000000000..0824d554958c54a401e339d5c331f4fb3972e718
--- /dev/null
+++ b/navipy/forecasting/src/Python/shorty.py
@@ -0,0 +1,77 @@
+import statistics as stats
+from fastdtw import fastdtw as dtw
+import cozybank as cbank
+from scipy import stats
+'''
+trial = 0
+#sh=0
+sh = int(spc['pr_step'][0])
+single_target = te[trial].shift(-sh).head(100)
+single_pred_esn = esn_r[trial].head(100)
+single_pred_ids = ids_r[trial].head(100)
+single_arima_110 = ari_res['L1_D1_O0'][trial]
+single_arima_210 = ari_res['L2_D1_O0'][trial]
+#single_arima_120 = ari_res['L1_D2_O0'][46]
+#single_arima_220 = ari_res['L2_D2_O0'][46]
+#single_arima_320 = ari_res['L3_D2_O0'][46]
+
+for dim in single_pred_esn.keys():
+	plt.figure()
+	plt.title(dim)
+	plt_arima, = plt.plot(single_arima_110[dim], color='#ACA6FF', label= 'ARIMA')
+	#plt_arima_120, = plt.plot(single_arima_120[dim], color='#737DFF', label= 'ARIMA_120')
+	plt_arima_210, = plt.plot(single_arima_210[dim], color='#3A2CFF', label= 'ARIMA_210')
+	#plt_arima_320, = plt.plot(single_arima_320[dim], color='#1100FF', label= 'ARIMA_320')
+	plt_esn, = plt.plot(single_pred_esn[dim], 'r', label= 'ESN')
+	#plt_ids, = plt.plot(single_pred_ids[dim], 'g', label= 'EBM')
+	plt_tar, = plt.plot(single_target[dim], 'k', label= 'Target')
+	plt.legend(handles=[plt_arima,plt_esn,plt_arima_210])
+	plt.show(block=False)
+	if dim == 'xPos':
+		plt.ylim([-140,250])
+	if dim == 'yPos':
+		plt.ylim([-120,250])
+	if dim == 'zPos':
+		plt.ylim([0,400])
+	if dim == 'Cos' or dim == 'Sin':
+		plt.ylim([-1.5,1.5])
+
+p_val_esn_vs_ebm = []
+p_val_ebm_vs_arima = []
+p_val_esn_vs_arima = []
+for dim in cost_esn.keys():
+	plt.figure()
+	plt.title(dim)
+	mydata = [cost_esn[dim]]
+	label = ['ESN']
+	#for mo in ari_res.keys():
+	#	label.append(mo)
+	#	mydata.append(arima_costs[mo][dim])
+	mydata.append(arima_costs['L1_D1_O0'][dim])
+	label.append('ARIMA')
+	plt.boxplot(mydata, labels=label)
+	plt.show(block=False)
+	#_, p_esn_vs_ebm = stats.ks_2samp(mydata[0],mydata[1])
+	#_, p_ebm_vs_arima = stats.ks_2samp(mydata[1],mydata[2])
+	_, p_esn_vs_arima = stats.ks_2samp(mydata[0],mydata[1])
+	
+	#p_val_esn_vs_ebm.append(p_esn_vs_ebm)
+	#p_val_ebm_vs_arima.append(p_ebm_vs_arima)
+	p_val_esn_vs_arima.append(p_esn_vs_arima)
+	
+#print('esn vs ebm')	
+#print(p_val_esn_vs_ebm)	
+#print('ebm vs arima')
+#print(p_val_ebm_vs_arima)
+#print('esn vs arima')
+print(p_val_esn_vs_arima)	
+'''
+
+for dim in cost_esn.keys():
+	plt.figure()
+	plt.title(dim)
+	plt_esn, = plt.plot(esn_costs_final[dim][:25], 'r', label= 'ESN')
+	plt_ids, = plt.plot(ids_costs_final[dim][:25], 'g', label= 'EBM')
+	plt_arima, = plt.plot(arima_costs_final['L1_D1_O0'][dim][:25], color='#ACA6FF', label= 'ARIMA')
+	plt.legend(handles=[plt_arima,plt_esn])
+	plt.show(block=False)
\ No newline at end of file