function [new_config, new_ctrm, new_norms]  = cicero_tmp_km(sp_coords,Theta)

% This code represents the kinematic model created by 'Build_data_frame' as a function.

%%% INPUTS %%%
% sp_coords: a 4 x 1 vector for global position, R3, and rotation, [-pi,pi], in the spatial frame.
% Theta: a vector of N x 1 angles, where N is the number of rotation axes.
%%% Outputs %%%
% new_config: a point cloud from the surface of the kinematic model in the new configuration.
% new_ctrm: a new center of mass estimate for the kinematic model.

% new_norms: a new norm associated with the model point is calculated to reflect the new pose.

%%% Sampled meshes for each segment
I1  = [  0.055528  0.064213  0.072310  0.066108  0.071599  0.059032  0.070055  0.064211  0.065692  0.055251  0.067291  0.063914  0.068070  0.078052  0.060872  0.059084  0.057119  0.064690  0.071898  0.056292  0.058676  0.066773  0.078199  0.061360  0.067131  0.064705  0.056280  0.073106  0.075840  0.012871  0.022041  0.018729  0.011941  0.018957  0.011703  0.022517  0.020240  0.006553  0.005329  0.008110  0.004354 -0.010243  0.014149  0.021090  0.027600  0.033132  0.040578  0.021252  0.031072  0.025789  0.034900  0.029198  0.037374  0.040742  0.048804  0.041153  0.049743  0.036353  0.039882  0.044468  0.048283  0.049750  0.034461  0.039495  0.053565  0.047493  0.045301  0.049724  0.061163  0.059577  0.042893  0.052653  0.039637  0.050883  0.060690  0.090868  0.073303  0.082768  0.071067  0.084789  0.073079  0.087780  0.077122  0.088719  0.087079  0.101303  0.090740  0.103849  0.099751  0.102452  0.110842  0.095630  0.102143  0.094438  0.105680  0.110031  0.126425  0.106948  0.109769  0.127558  0.116151  0.110610  0.108336  0.105687  0.117484  0.124176  0.132488  0.144343  0.145693  0.147986  0.163531  0.172850  0.180336  0.163473  0.163505  0.185913  0.194906  0.176757  0.178706  0.188347  0.188597  0.144492  0.152602  0.153094  0.142485  0.163377  0.160328  0.153425  0.154331  0.146011  0.164051  0.160646  0.154598  0.164057  0.145856  0.134964  0.127518  0.136462  0.145642  0.131880  0.139600  0.134357  0.143702  0.142615  0.130980  0.118461  0.105740  0.105787  0.119455  0.152122  0.151925  0.108197  0.107900  0.101089  0.110469  0.094578  0.106590  0.093893  0.106844  0.100940  0.111842  0.102732  0.091840  0.107834  0.101415  0.080871  0.095310  0.089799  0.086867  0.083878  0.101393  0.072474  0.124936  0.134173  0.135568  0.141875  0.087194  0.118524  0.079035  0.125160  0.116511  0.128694  0.127131  0.137043  0.136942  0.136584  0.108246  0.084558  0.118097  0.169738  0.169825  0.169990  0.136088  0.141047  0.169807  0.170019  0.170890  0.170234  0.206815  0.150787  0.153507  0.127067  0.127494  0.126278  0.112253  0.138570  0.135650  0.122356  0.134229  0.097956  0.087272  0.133071  0.115439  0.111481  0.087580  0.085856  0.118518  0.117550  0.075672  0.103656  0.105295  0.023602  0.027203  0.021548  0.028960  0.067053  0.067255  0.036156  0.059094  0.010617 -0.005045  0.014883  0.013127  0.030248  0.035460  0.038058  0.047532 -0.001859  0.027955  0.040731  0.024279  0.037232  0.048008  0.072653  0.083590  0.050626  0.053453  0.077003  0.069614  0.081642  0.086335  0.051844  0.077008  0.055065  0.078611  0.054794
        -0.015008 -0.013335 -0.005352 -0.030709 -0.043337 -0.049979 -0.053776 -0.065620 -0.094271 -0.102301 -0.105319 -0.120054 -0.146299 -0.145481 -0.128927 -0.151452 -0.165483 -0.173184 -0.176350 -0.171102 -0.181770 -0.195339 -0.196584 -0.193516 -0.201008 -0.209467 -0.209851 -0.212424 -0.217778 -0.171743 -0.170269 -0.162541 -0.148369 -0.148610 -0.137246 -0.130061 -0.120040 -0.121461 -0.108024 -0.096533 -0.074710 -0.135556 -0.025811 -0.038652 -0.038539 -0.053537 -0.041252 -0.077302 -0.077247 -0.085455 -0.071246 -0.102797 -0.102055 -0.119052 -0.105280 -0.125629 -0.144470 -0.139602 -0.152992 -0.097859 -0.076409 -0.058966 -0.062730 -0.031751 -0.024266 -0.007639  0.003655  0.012853  0.012607  0.021430  0.036950  0.045249  0.037062  0.062088  0.071200  0.082676  0.075010  0.062836  0.059407  0.045773  0.041163  0.040195  0.011153  0.012698  0.005934  0.014523 -0.025260 -0.016620 -0.032252 -0.056353 -0.048279 -0.050237 -0.076460 -0.093950 -0.085471 -0.094284 -0.103421 -0.105001 -0.129741 -0.130922 -0.135031 -0.151117 -0.168091 -0.173405 -0.171275 -0.187762 -0.182152 -0.060639 -0.013811 -0.006292  0.013335  0.033831  0.033825  0.035117  0.053687 -0.199640 -0.199825 -0.206570 -0.205802 -0.197995 -0.197255 -0.201372 -0.198811 -0.207092 -0.208125 -0.208144 -0.207623 -0.209376 -0.209246 -0.212292 -0.205343 -0.206172 -0.208437 -0.203957  0.082537  0.075687  0.069208  0.061326  0.047941  0.036596  0.028265  0.019279  0.011958  0.005944  0.002502  0.016673  0.029751  0.036075  0.053023  0.062562  0.067767  0.090340 -0.223215 -0.222484 -0.219069 -0.215290 -0.214528 -0.210053 -0.207911 -0.204659 -0.203286 -0.197355 -0.189950 -0.190284 -0.186045 -0.180327 -0.183165 -0.175564 -0.158193 -0.150968 -0.165086 -0.174696 -0.194472 -0.202258 -0.196690 -0.194458 -0.191691 -0.206210 -0.199534 -0.209645 -0.210277 -0.214651 -0.216173 -0.213987 -0.215194 -0.215546 -0.215816 -0.216445 -0.221037 -0.202283 -0.202712 -0.203145 -0.209795 -0.198291 -0.203521 -0.207355 -0.207148 -0.203602 -0.190136  0.044106  0.003021 -0.031680 -0.060069 -0.067279 -0.062102 -0.090048 -0.187992 -0.167396 -0.137901 -0.132355 -0.125830 -0.115623 -0.081520 -0.076963 -0.080230 -0.063761 -0.029185 -0.005398 -0.005260  0.053328  0.077042  0.011102  0.003230 -0.013974  0.020060  0.073471  0.032142 -0.002118 -0.029927 -0.049610 -0.134884 -0.063478 -0.097713 -0.161740 -0.163818 -0.172911 -0.162012 -0.148186 -0.171730 -0.185996 -0.179463 -0.192953 -0.199368 -0.215666 -0.208788 -0.193618 -0.182955 -0.179201 -0.169810 -0.135540 -0.098383 -0.088930 -0.068827 -0.046924 -0.010928 -0.006722
         0.415362  0.424396  0.428530  0.429359  0.434588  0.420071  0.427803  0.423779  0.427425  0.423855  0.431287  0.432015  0.430588  0.438020  0.427897  0.419416  0.407694  0.396556  0.409835  0.388514  0.370487  0.359907  0.367533  0.357961  0.349149  0.327191  0.311892  0.321888  0.304494  0.342578  0.352152  0.360098  0.375268  0.382075  0.379879  0.389725  0.388610  0.378161  0.378435  0.381782  0.379128  0.366692  0.381124  0.391812  0.397442  0.399739  0.404621  0.390127  0.398407  0.393801  0.400958  0.397310  0.409928  0.413109  0.419980  0.412278  0.413732  0.399401  0.396505  0.415698  0.414286  0.413467  0.399927  0.404045  0.412621  0.409856  0.408494  0.411994  0.419251  0.418020  0.399845  0.404224  0.396524  0.387317  0.378580  0.378231  0.380343  0.398342  0.398613  0.414154  0.414429  0.419586  0.428634  0.434768  0.436079  0.437044  0.443269  0.447694  0.448748  0.448987  0.455276  0.446553  0.443821  0.439559  0.445913  0.448072  0.450015  0.444930  0.443579  0.443997  0.442035  0.437299  0.430152  0.428394  0.431372  0.414975  0.432375  0.461311  0.455545  0.456061  0.457432  0.428696  0.424474  0.430637  0.388125  0.324880  0.332885  0.363027  0.369239  0.379293  0.396303  0.392686  0.407973  0.377571  0.363756  0.370414  0.345862  0.338332  0.309026  0.295023  0.298989  0.274969  0.267693  0.246167  0.352317  0.370505  0.388819  0.394870  0.406607  0.427754  0.438006  0.442619  0.450325  0.451270  0.445536  0.438067  0.430205  0.426024  0.412237  0.378246  0.368649  0.361716  0.274623  0.289284  0.298438  0.315089  0.316583  0.336212  0.346422  0.358935  0.367345  0.380685  0.387830  0.398036  0.410341  0.413816  0.417247  0.427192  0.435438  0.437676  0.431406  0.416515  0.392799  0.376734  0.396103  0.409590  0.381487  0.359922  0.362499  0.346752  0.339948  0.326656  0.312140  0.322767  0.299881  0.273978  0.309715  0.312796  0.282695  0.270894  0.288539  0.306138  0.355917  0.397755  0.393399  0.377970  0.360537  0.323816  0.395427  0.412901  0.459234  0.455183  0.459911  0.457761  0.453083  0.454399  0.424247  0.434716  0.444711  0.445403  0.445714  0.448027  0.449236  0.447820  0.435196  0.436737  0.454074  0.445263  0.430984  0.411168  0.382916  0.386990  0.390743  0.386988  0.391349  0.379550  0.417733  0.400970  0.417972  0.379809  0.370182  0.385482  0.384685  0.378317  0.380795  0.363583  0.397210  0.365247  0.355465  0.349950  0.343471  0.338657  0.338382  0.309653  0.337682  0.348729  0.364431  0.396166  0.419884  0.441476  0.436594  0.419094  0.429813  0.417003  0.434020  0.415494
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N1  = [ -0.653047 -0.614342 -0.481661 -0.743519 -0.673986 -0.528897 -0.526305 -0.386779 -0.314265 -0.478974 -0.341147 -0.545507 -0.638005 -0.252440 -0.620922 -0.595925 -0.602058 -0.406230 -0.470646 -0.391841 -0.411777 -0.358799 -0.300963 -0.381664 -0.221506 -0.140384 -0.258411 -0.074892 -0.119101 -0.476951 -0.456119 -0.434615 -0.550449 -0.594419 -0.574042 -0.612846 -0.610782 -0.545348 -0.585955 -0.555229 -0.599633 -0.591465 -0.722609 -0.797642 -0.471702 -0.544484 -0.525290 -0.585434 -0.622724 -0.633001 -0.603239 -0.743616 -0.757939 -0.733962 -0.508327 -0.709152 -0.634442 -0.690007 -0.622963 -0.556111 -0.616615 -0.618109 -0.576807 -0.506232 -0.474134 -0.546984 -0.603761 -0.609266 -0.415301 -0.358854 -0.655696 -0.403469 -0.613059 -0.283325 -0.260945 -0.080622 -0.228546 -0.077404 -0.137132 -0.136533 -0.149973 -0.172813 -0.432133 -0.274534 -0.360175 -0.014938 -0.333224 -0.168293 -0.351711 -0.394560 -0.307150 -0.349739 -0.339896 -0.328591 -0.328238 -0.277485 -0.067143 -0.173659  0.211911 -0.055360  0.111978  0.052677  0.055088  0.072534 -0.228573 -0.056171 -0.262373  0.032467 -0.304525 -0.387095  0.039663  0.441136  0.483851  0.316579  0.285901  0.387780  0.513551  0.374029  0.568398  0.656566  0.515928 -0.169146 -0.099027  0.004680  0.101160  0.169930  0.370888  0.366111  0.511357  0.483750  0.543925  0.538256  0.529241  0.562243  0.408166  0.432187  0.351045  0.547648  0.348800  0.114060 -0.053331 -0.207983 -0.293220 -0.367355 -0.224288 -0.067003  0.006118  0.010707  0.211027  0.581333  0.625691  0.295438  0.269849  0.195863  0.251693  0.161687  0.083234  0.032212  0.046764  0.024415  0.004709 -0.015404 -0.255059 -0.063773 -0.071027 -0.276916 -0.069925  0.003927  0.076450 -0.024426  0.195737 -0.494543 -0.073628 -0.089574 -0.187765 -0.179699 -0.290383 -0.010571 -0.219606  0.024164  0.055556  0.177884  0.191475  0.374548  0.367093  0.483686  0.158945  0.041438  0.311708  0.602108  0.573140  0.548194  0.068008 -0.197955  0.390046  0.400439  0.259453  0.488411  0.661112  0.196856 -0.450720  0.050301 -0.073812 -0.164850 -0.385177 -0.090904 -0.221313 -0.261916 -0.193658  0.219909 -0.377287 -0.112808 -0.246228 -0.275130 -0.402998 -0.469585  0.036219  0.056793 -0.470368  0.010979  0.302611 -0.612806 -0.682178 -0.680840 -0.610278 -0.246877 -0.207758 -0.643186 -0.684234 -0.712865 -0.498959 -0.643092 -0.501237 -0.459142 -0.412768 -0.451149 -0.579458 -0.446457 -0.462486 -0.436463 -0.465175 -0.424929 -0.323130 -0.167678 -0.027101 -0.372997 -0.430268 -0.376460 -0.568855 -0.204903 -0.264494 -0.516612 -0.397070 -0.563803 -0.427515 -0.597298
        -0.114056  0.111173  0.198318 -0.045023 -0.293796 -0.001013 -0.188658 -0.055049  0.110635  0.037228  0.142081 -0.108250 -0.363032 -0.380551 -0.287944 -0.437782 -0.826220 -1.039118 -1.010072 -1.007229 -0.891973 -0.968485 -0.991405 -0.941191 -1.064737 -1.141542 -1.145000 -1.164597 -1.159971 -0.835379 -0.849822 -0.944220 -0.638576 -0.557079 -0.315402 -0.245849 -0.176873 -0.180972 -0.180024 -0.182019  0.066558 -0.357678  0.013451 -0.070814  0.047376 -0.124206 -0.033362 -0.101426 -0.019333 -0.081158  0.001375 -0.094114  0.013312 -0.298902 -0.001355 -0.303085 -0.459790 -0.405101 -0.577700  0.068015  0.035558  0.020341 -0.066887 -0.025016  0.051996 -0.053960  0.019523  0.036982  0.066482  0.141846  0.287038  0.574670  0.266858  0.794206  0.916984  0.924800  0.894476  0.751687  0.748683  0.660487  0.584512  0.617717  0.206480  0.324681  0.210700  0.386829  0.118131  0.252383  0.062128 -0.298298 -0.082126 -0.206083 -0.130462 -0.028177 -0.057698 -0.201366 -0.322910 -0.173135 -0.283281 -0.290355 -0.334191 -0.470594 -0.447562 -0.610581 -0.486095 -1.106535 -0.832507 -0.097198  0.129972  0.072232  0.730576  0.834907  0.837297  0.855376  0.978726 -1.155540 -1.139872 -1.186531 -1.115213 -1.075209 -1.142031 -1.110715 -1.135063 -1.186942 -1.181295 -1.208123 -1.184985 -1.186484 -1.143183 -1.153522 -1.130253 -1.131857 -1.135412 -1.119162  0.878905  0.935902  0.928595  0.795653  0.886903  0.778589  0.698623  0.430201  0.328759  0.169276  0.196376  0.368136  0.530561  0.616433  0.768299  0.857229  0.850321  0.942631 -1.207079 -1.201180 -1.174742 -1.161309 -1.197328 -1.177340 -1.176793 -1.163143 -1.153271 -1.082814 -1.019002 -1.139758 -1.139646 -1.091778 -1.102890 -0.833710 -0.464602 -0.451463 -0.481322 -0.910801 -1.132402 -1.106634 -1.106399 -1.097438 -0.948804 -1.170882 -1.055307 -1.190276 -1.176089 -1.189989 -1.207866 -1.172073 -1.188343 -1.153150 -1.180372 -1.172174 -1.198849 -1.103934 -1.117476 -1.128695 -1.194740 -1.088654 -1.142570 -1.159934 -1.199291 -1.150028 -1.080975  0.953813  0.226895  0.259228 -0.163487 -0.337052 -0.360118 -0.277492 -1.061172 -0.449667 -0.251641 -0.446233 -0.121878 -0.366665 -0.131885 -0.143712 -0.085935 -0.320234  0.259037  0.325605  0.179927  0.750839  0.853801  0.033576  0.072309  0.103396  0.082566  0.902040  0.420232  0.061797  0.021918  0.036583 -0.353165 -0.014441 -0.154891 -0.925492 -0.941695 -0.905982 -0.822233 -0.789005 -0.851503 -0.857058 -0.836340 -0.902765 -1.001496 -1.153937 -1.162690 -0.917636 -0.874905 -1.062248 -0.728471 -0.359211  0.101602  0.056748 -0.138605  0.048382  0.187608 -0.061601
         1.114012  1.148317  1.235769  1.016130  1.052142  1.227500  1.219107  1.316246  1.329449  1.257603  1.309906  1.224774  1.104743  1.352086  1.141950  1.118686  0.766738  0.565059  0.512571  0.704849  0.894211  0.830155  0.841342  0.852644  0.762263  0.625810  0.474573  0.589213  0.577019  0.907963  0.908543  0.788417  1.041161  1.058037  1.170551  1.153208  1.162290  1.209944  1.181678  1.203573  1.163502  1.149535  1.056140  0.965087  1.259600  1.212983  1.229079  1.184702  1.152858  1.146116  1.167447  1.031883  1.005047  1.019316  1.243876  1.049108  1.071352  1.033366  1.013156  1.197869  1.152781  1.153517  1.191340  1.241981  1.258622  1.212634  1.169064  1.163758  1.296793  1.318251  1.070240  1.119532  1.118453  0.980874  0.804257  0.889522  0.867541  1.105328  1.092553  1.171217  1.223762  1.193253  1.266791  1.312672  1.306730  1.357846  1.337525  1.371586  1.336033  1.282319  1.363096  1.328232  1.339190  1.343286  1.346437  1.363694  1.406234  1.402331  1.426428  1.414111  1.421993  1.383121  1.388829  1.327159  1.315190  0.766159  1.081316  1.454361  1.336811  1.297204  1.143159  0.963767  0.936638  0.981756  0.747739  0.111561  0.211323  0.335459  0.514539  0.485443  0.412148  0.666044  0.653159  0.511237  0.590100  0.370014  0.325153  0.333390  0.326161  0.299231  0.283573  0.252187  0.248706  0.184133  0.897287  0.784857  0.848699  0.934953  0.911453  1.097925  1.154524  1.287573  1.292189  1.295814  1.359974  1.355714  1.290010  1.234816  1.105054  0.807528  0.772574  0.850123  0.350673  0.471413  0.556786  0.632176  0.499773  0.582284  0.586541  0.633621  0.660691  0.830135  0.826389  0.660809  0.657138  0.616907  0.773344  1.175170  1.387281  1.385290  1.375383  0.786166  0.677156  0.740108  0.656649  0.694577  0.914606  0.589579  0.784952  0.514572  0.591922  0.541818  0.423514  0.482963  0.303419  0.294441  0.568677  0.603870  0.362689  0.261858  0.265204  0.288290  0.514811  0.701618  0.657371  0.576717  0.272172  0.268674  0.390880  0.825588  1.223950  1.408850  1.433965  1.375621  1.267792  1.409494  0.756110  1.313726  1.382556  1.387002  1.331248  1.384254  1.380182  1.367644  1.306575  1.227753  1.408094  1.386934  1.248019  1.121724  0.981006  1.158015  1.092175  1.089038  1.157813  0.843145  1.297366  1.132003  1.084888  1.064750  1.211848  1.136923  1.240348  0.799246  0.821248  0.836112  0.810722  0.991093  0.900786  0.917367  0.917010  0.870235  0.806193  0.558425  0.616643  0.893102  0.900360  0.516999  0.949276  1.373068  1.351430  1.228808  1.307527  1.196694  1.273317  1.171645
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

I4  = [  0.054739  0.070302  0.054477  0.064923  0.019832  0.013603  0.020253  0.028603  0.005605  0.012977 -0.018314 -0.029810 -0.022102 -0.030368 -0.024905 -0.029439 -0.013642 -0.019731 -0.014481 -0.008191 -0.012873 -0.054284 -0.055305 -0.063853 -0.076917 -0.080940 -0.070814 -0.068661 -0.082953 -0.073708 -0.075948 -0.083535 -0.072779 -0.064789 -0.065260 -0.059956 -0.046028 -0.036988 -0.051280 -0.049633 -0.056502 -0.061748 -0.053303 -0.050170 -0.094536 -0.099186 -0.088870 -0.086168 -0.084385 -0.079381 -0.074630 -0.064302 -0.066503 -0.065716 -0.050128 -0.064972 -0.062828 -0.084312 -0.082711 -0.077106 -0.081843 -0.084476 -0.072015 -0.039156 -0.078940 -0.078312 -0.038496 -0.078401 -0.090973 -0.095154 -0.100221 -0.103200 -0.103492 -0.102278 -0.106115 -0.101921 -0.098887 -0.091957 -0.087279 -0.092066 -0.092509 -0.094541 -0.084114 -0.099143 -0.105131 -0.108434 -0.092559 -0.102233 -0.100102 -0.093937 -0.091230 -0.100009 -0.049300 -0.043217 -0.032297 -0.047047 -0.033663 -0.061139 -0.084938 -0.081944 -0.076467 -0.070083  0.039970  0.040485  0.035705  0.090264  0.014061  0.022142  0.024602  0.002428  0.019214  0.030436  0.067177 -0.030541 -0.038408 -0.004394 -0.040935 -0.013758 -0.037061 -0.003285  0.037777  0.042631  0.052505  0.025425  0.041573  0.031283  0.049235  0.048184
        -0.222255 -0.203145 -0.182988 -0.165754 -0.160436 -0.174113 -0.186173 -0.199267 -0.216636 -0.215145 -0.192771 -0.201184 -0.206139 -0.193629 -0.164407  0.126682  0.115503  0.099946  0.093818  0.084851  0.070398 -0.036721 -0.061773 -0.076672 -0.076061 -0.041524 -0.029072  0.010288 -0.004718  0.021124  0.028445  0.030213  0.049096  0.056454  0.046083  0.038640  0.037170  0.056971  0.073345  0.083080  0.073931  0.085500  0.114181  0.101548 -0.143604 -0.133631 -0.146440 -0.124568 -0.116908 -0.132898 -0.118462 -0.166377 -0.172273 -0.184119 -0.193229 -0.186839 -0.162702 -0.152215 -0.174832 -0.181794 -0.175241 -0.158101 -0.178534 -0.197662 -0.159262 -0.143812 -0.178884 -0.109035 -0.084135 -0.073820 -0.091677 -0.098230 -0.097313 -0.023293 -0.049220 -0.049754 -0.044502 -0.037918 -0.006876 -0.013764 -0.006705 -0.002855  0.006626 -0.029415 -0.066346 -0.065965  0.021002 -0.095687 -0.118787 -0.065769 -0.118845 -0.124522  0.094814  0.100487  0.070456  0.003151  0.007600  0.015719  0.040273  0.014870 -0.013585 -0.054524  0.090798  0.102609  0.111589 -0.200987  0.121116  0.112651  0.105107  0.093463  0.086354  0.126279  0.094670  0.064748  0.094534  0.118401 -0.172550 -0.212831 -0.195460 -0.205395 -0.228994 -0.208166 -0.202520 -0.181479 -0.161991 -0.154668 -0.187841 -0.225333
         0.221037  0.192499  0.149889  0.116274  0.115378  0.145518  0.174802  0.188458  0.209442  0.239148  0.260190  0.217213  0.213755  0.177181  0.136993  0.203022  0.221408  0.265475  0.282171  0.317591  0.335337  0.308900  0.311414  0.300072  0.286351  0.281926  0.297767  0.288945  0.267961  0.272388  0.223228  0.198840  0.211433  0.237313  0.275122  0.291286  0.315544  0.322642  0.287918  0.279272  0.249527  0.212830  0.204659  0.227744  0.160900  0.192423  0.220460  0.243280  0.262692  0.277537  0.289422  0.270170  0.240421  0.218198  0.208133  0.176284  0.140963  0.134116  0.162593  0.169911  0.199070  0.224183  0.160091  0.212882  0.236011  0.266702  0.272955  0.283949  0.254766  0.247906  0.221366  0.207949  0.168225  0.190039  0.196440  0.229143  0.240355  0.264177  0.255886  0.249374  0.205549  0.195703  0.236288  0.244380  0.213041  0.184497  0.185652  0.170697  0.203734  0.255547  0.231493  0.166429  0.238070  0.255519  0.322082  0.316778  0.324165  0.299695  0.190506  0.253267  0.285275  0.296663  0.310205  0.284385  0.247509  0.182907  0.205616  0.228249  0.265213  0.291096  0.329918  0.187422  0.289332  0.327151  0.271394  0.213888  0.153382  0.203693  0.227552  0.247887  0.219235  0.199082  0.193292  0.167048  0.116872  0.097987  0.166214  0.232188
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N4  = [  0.166168  0.023384 -0.052513 -0.142032  0.047952 -0.095138  0.118371  0.077880 -0.116647 -0.365603 -0.475356 -0.447672 -0.450869  0.007387 -0.289509 -0.078091  0.112642 -0.125045 -0.043898 -0.401057 -0.572611 -0.566015 -0.791352 -0.872758 -0.741072 -0.940787 -0.813241 -0.942660 -0.997326 -0.964339 -1.022100 -0.947502 -0.982514 -0.967740 -0.939007 -0.931841 -0.778113 -0.792674 -0.894735 -0.763649 -0.981833 -0.938159 -0.777588 -0.937356 -1.056925 -1.040135 -1.018302 -1.026087 -1.067505 -0.987678 -0.891314 -0.674735 -0.693838 -0.549498 -0.461960 -0.394876 -0.105916 -0.551429 -0.803463 -0.571639 -0.956444 -0.980561 -0.186651 -0.471582 -0.896365 -1.035551 -0.444459 -0.980268 -1.029113 -1.033068 -1.037125 -1.057864 -1.025753 -0.989163 -1.063622 -1.092280 -1.084537 -0.959806 -1.012524 -0.995079 -1.026030 -0.997922 -0.989054 -1.078179 -1.092640 -1.103346 -0.964715 -1.089077 -1.051450 -1.042430 -1.022244 -1.043891 -0.944204 -0.336631 -0.597890 -0.624671 -0.568371 -0.882844 -0.954245 -1.023225 -0.941877 -0.855849  0.246630  0.147321 -0.278413 -0.084795  0.045764  0.028895 -0.274590 -0.279036  0.193587  0.081063  0.194153 -0.543193 -0.316980  0.036880 -0.083227 -0.448449 -0.420999 -0.426654 -0.225912  0.076176  0.038210 -0.176518 -0.044706 -0.136670 -0.119465 -0.011613
        -1.159958 -1.046034 -1.093462 -1.059041 -1.077391 -1.094821 -0.935790 -0.920324 -1.195866 -1.103999 -0.999732 -1.084124 -1.072745 -0.978560 -1.044300  1.079605  1.006164  1.046577  1.027206  0.972586  0.474223 -0.127682  0.038240 -0.175158 -0.030105 -0.062666  0.014949  0.226009  0.188391  0.280127  0.331477  0.287330  0.303012  0.479077  0.364018  0.277351  0.156885  0.205164  0.450313  0.669847  0.452796  0.341244  0.705876  0.432713 -0.388775 -0.458876 -0.373586 -0.328247 -0.221975 -0.363477 -0.186602 -0.955393 -0.803930 -1.043506 -1.084706 -1.105197 -0.971750 -0.919010 -0.788009 -1.050885 -0.646355 -0.461824 -0.979634 -1.084413 -0.556951 -0.415449 -1.084704 -0.191372 -0.258293 -0.238397 -0.270936 -0.262499  0.114069  0.200733  0.121232  0.036793  0.012170  0.106872  0.282147  0.336101  0.288740  0.254228  0.431478  0.007886 -0.050701 -0.163445  0.256072  0.050282 -0.312565 -0.196587 -0.315699 -0.446233  0.490247  0.990613  0.586303  0.008118  0.009608  0.210090  0.276624  0.343759  0.165896 -0.184769  0.966716  1.034988  1.049192 -1.099850  1.076748  1.070366  1.046298  1.038004  0.974219  1.070761  1.020745  0.420346  0.989276  1.039892 -0.944595 -1.108517 -1.085228 -1.078833 -0.905387 -0.938596 -0.968852 -1.117609 -1.060712 -1.100893 -1.124642 -1.221383
        -0.108049 -0.343538 -0.249599 -0.282735 -0.282621 -0.229279 -0.479757 -0.502663  0.047693  0.497246  0.634258  0.431241  0.469007 -0.441251 -0.257688  0.502308  0.658187  0.570105  0.639832  0.557554  1.058951  1.163217  0.980916  0.879704  1.032533  0.792038  0.966246  0.724364  0.623814  0.646143  0.337113  0.631797  0.539928  0.315217  0.643202  0.718878  0.986156  0.960590  0.670643  0.661223  0.264487  0.620872  0.558649  0.549039  0.277940  0.286387  0.511256  0.517264  0.412479  0.626578  0.862470  0.339638  0.695901  0.383756  0.396980 -0.042307 -0.445198 -0.306143 -0.160718  0.159032  0.084507  0.547885 -0.427358  0.376223  0.652737  0.366239  0.394134  0.708045  0.554036  0.553246  0.521494  0.456206  0.491878  0.594077  0.429090  0.337304  0.399355  0.739440  0.501624  0.498697  0.408650  0.538939  0.260416  0.444623  0.369826  0.209955  0.614703  0.240215  0.443288  0.544074  0.538841  0.091676  0.444900  0.604210  0.965515  1.133066  1.169200  0.835439  0.624607  0.329572  0.753091  0.901318  0.746163  0.629719  0.396603 -0.218839  0.498469  0.515889  0.422198  0.460274  0.755699  0.512062  0.644666  1.108648  0.620444  0.600089 -0.480777  0.109929  0.474343  0.488434 -0.468486 -0.483082 -0.448995 -0.120841 -0.313077 -0.178511 -0.140291  0.166550
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

I5  = [  0.002764  0.005804  0.015107  0.014045  0.003342 -0.020860 -0.015258 -0.031529 -0.021339 -0.021279 -0.011115 -0.024749 -0.011054 -0.008858 -0.012011 -0.021266 -0.061188 -0.061232 -0.062642 -0.053378 -0.056225 -0.055818 -0.051005 -0.099711 -0.097519 -0.092144 -0.100377 -0.101718 -0.049440 -0.056757 -0.054789 -0.054230 -0.052858 -0.063597 -0.039975 -0.070464 -0.081725 -0.042681 -0.110632 -0.108019 -0.111866 -0.109683 -0.121889 -0.130721 -0.126189 -0.121613 -0.121821 -0.125540 -0.116597 -0.105864 -0.107405 -0.104789 -0.105232 -0.116378 -0.114587 -0.116663 -0.122665 -0.118069 -0.119872 -0.132921 -0.130417 -0.129252 -0.125930 -0.121064 -0.117036 -0.122091 -0.134777 -0.135613 -0.139185 -0.137235 -0.137122 -0.141383 -0.139900 -0.142463 -0.139113 -0.129270 -0.116035 -0.114388 -0.114548 -0.117739 -0.117549 -0.092531 -0.093164 -0.090002 -0.096412 -0.100238 -0.094880 -0.089825 -0.098487 -0.109643 -0.103673 -0.111544 -0.115279 -0.072952 -0.100997 -0.079708 -0.076656 -0.064775 -0.078767 -0.074308 -0.081030 -0.083113 -0.101971 -0.095413 -0.102228 -0.109342 -0.112362 -0.114498 -0.131509 -0.115710 -0.116109 -0.118445 -0.112249 -0.087836 -0.107234 -0.073700 -0.035334 -0.044402 -0.075236 -0.068047 -0.065957 -0.004433 -0.036528 -0.034969 -0.033209 -0.003332 -0.003994 -0.004832
        -0.119480 -0.124978 -0.131801 -0.135474 -0.137918 -0.132935 -0.128331 -0.123943 -0.120945 -0.116240 -0.118185  0.171468  0.170834  0.167630  0.163090  0.152901  0.139830  0.138740  0.144631  0.151765  0.154825  0.159666  0.162682 -0.094815 -0.097710 -0.104249 -0.101575 -0.102304 -0.127520 -0.120577 -0.114188 -0.109725 -0.108577 -0.101879 -0.110518 -0.111972 -0.112103 -0.129604 -0.083845 -0.083381 -0.074119 -0.095442 -0.080400 -0.060398 -0.066261  0.068149  0.061995  0.045486  0.072763  0.073020  0.055907  0.037152  0.027137 -0.029327 -0.042639 -0.026125 -0.012940  0.012079  0.027829  0.011262  0.002694 -0.025449 -0.031599 -0.046481 -0.058328 -0.055048 -0.048557 -0.036806 -0.024252  0.025183  0.013492 -0.007244 -0.013389  0.003664 -0.030818 -0.014486  0.034130 -0.050022 -0.046060 -0.021008 -0.002162  0.075139  0.064437  0.073673  0.091179  0.109152  0.129153  0.135831  0.126120  0.101961  0.112469  0.091652  0.079544  0.149290  0.119854  0.131712  0.125828  0.133157  0.100013  0.122677  0.086530  0.108996  0.099208  0.056236  0.051445  0.038232  0.049426  0.056199  0.043446 -0.083069 -0.080878 -0.073970 -0.095424 -0.112193 -0.097127 -0.098924  0.167741  0.159478  0.146686  0.139267  0.135413  0.152751  0.158930 -0.112160 -0.128493 -0.134896 -0.123880 -0.115904
        -0.092274 -0.047779 -0.016609  0.009175  0.047953  0.054653  0.012295  0.015075 -0.029713 -0.079048 -0.085842 -0.004616  0.040322  0.068821  0.088768  0.125406  0.133667  0.127837  0.078429  0.073062  0.037914 -0.006014 -0.014599 -0.062887 -0.036331 -0.005850  0.029380  0.064800  0.067054  0.040052 -0.010484 -0.043287 -0.052627 -0.085762 -0.084210 -0.000525  0.024086  0.067170  0.092449  0.044272  0.038541  0.006653 -0.017253 -0.020917 -0.066073 -0.017403 -0.006937  0.029952  0.027715  0.056086  0.062425  0.079643  0.098136  0.098065  0.069950  0.063265  0.053503  0.064324  0.052888  0.025712  0.030252  0.014783  0.021943  0.035380  0.045925  0.016783 -0.023983 -0.046256 -0.042447 -0.024160  0.008307 -0.023340 -0.015073 -0.042980 -0.033102  0.023076  0.057109  0.061030  0.082742  0.096984  0.097957  0.133914  0.101082  0.091957  0.065001  0.045771  0.030360  0.020714 -0.009569 -0.015217  0.012272  0.023603  0.011309  0.013837  0.028511  0.070225  0.081469  0.100968  0.123522  0.136633  0.115714  0.081791  0.049325  0.099858  0.115865  0.127362  0.056074  0.047946 -0.006322 -0.077503 -0.052498 -0.041099 -0.004623  0.049684 -0.016528 -0.085152  0.002979  0.044891  0.027886  0.080292  0.135338  0.125951  0.081358 -0.072875  0.048133  0.038195 -0.039895 -0.119632
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N5  = [ -0.126749 -0.183170 -0.260639 -0.239892 -0.229024 -0.263892 -0.280792 -0.295649 -0.267227 -0.266107 -0.170043 -0.239017 -0.107312  0.086314 -0.022920 -0.005595 -0.707944 -0.816628 -0.689332 -0.542048 -0.476174 -0.465376 -0.453577 -0.480014 -0.541979 -0.410722 -0.790363 -0.932644 -0.236135 -0.297290 -0.319979 -0.331781 -0.328168 -0.367053 -0.390692 -0.335365 -0.416320 -0.327536 -1.098385 -1.048473 -1.053645 -0.756523 -0.989684 -1.059162 -1.043273 -0.949073 -0.913807 -1.030065 -1.034694 -0.975758 -0.976731 -0.984244 -0.931045 -1.099921 -1.114042 -1.073761 -1.067101 -1.005506 -0.991665 -1.075469 -1.080208 -1.066970 -1.080662 -1.091044 -1.062638 -1.060118 -1.091404 -1.085665 -1.112513 -1.052314 -1.132761 -1.134428 -1.123312 -1.141278 -1.110922 -1.081317 -0.988370 -1.094862 -1.111946 -1.098031 -1.098736 -0.948934 -1.018297 -1.001157 -0.965348 -0.965850 -0.907293 -0.829163 -0.940423 -1.023139 -1.035919 -1.076536 -1.032007 -0.562005 -0.971175 -0.732727 -0.862868 -0.808219 -0.973769 -0.908420 -0.965081 -0.955995 -0.969151 -1.053517 -1.005951 -1.065178 -0.981732 -0.988641 -1.069073 -0.785194 -0.944587 -0.983538 -0.712178 -0.553276 -0.591429 -0.329850 -0.397039 -0.453972 -0.579839 -0.798574 -0.824258 -0.047127 -0.407537 -0.346004 -0.326939 -0.247843 -0.219017 -0.014796
        -1.096893 -1.101205 -1.081477 -1.095247 -1.104304 -1.092941 -1.083570 -1.081462 -1.083915 -1.085768 -1.104677  1.147995  1.164446  1.127744  1.145073  1.094161  0.901321  0.765909  0.901169  1.014866  1.056625  1.066917  1.074902 -1.017489 -0.985782 -1.047419 -0.825103 -0.604141 -1.037855 -1.080880 -1.064251 -1.058717 -1.057433 -1.035409 -1.046920 -1.058314 -1.049584 -1.018155 -0.238448 -0.409343 -0.372427 -0.838848 -0.539984 -0.431863 -0.405599  0.515779  0.641347  0.324877  0.421931  0.312411  0.294904  0.362282  0.589700 -0.189797 -0.070926 -0.189158 -0.129899  0.186243  0.261079 -0.048716 -0.114817 -0.228133 -0.231156 -0.280298 -0.357088 -0.263193 -0.337964 -0.312733 -0.215153  0.358016 -0.030840 -0.028495 -0.105410 -0.039384 -0.242248 -0.202546  0.272383 -0.154227 -0.020135 -0.146202  0.185120  0.588165  0.437551  0.428330  0.332287  0.438445  0.700531  0.808221  0.590944  0.390774  0.463073  0.353758  0.478930  1.017204  0.599164  0.725809  0.585173  0.663954  0.436728  0.528657  0.528279  0.350763  0.365042  0.283968  0.375505  0.290769  0.288875  0.306480  0.391188 -0.813800 -0.610295 -0.563892 -0.893341 -0.992300 -0.945089 -1.040637  1.097657  1.066172  1.002713  0.782322  0.770015  1.114079  1.076363 -1.062313 -1.072977 -1.092371 -1.093923 -1.095503
        -0.259276 -0.153935 -0.165201 -0.110628 -0.062071 -0.084356 -0.118121 -0.100678 -0.140300 -0.087742 -0.125536  0.017425  0.099222  0.331731  0.277424  0.462726  0.090785 -0.061996  0.265271  0.200575  0.139891  0.089685  0.061494 -0.126466 -0.153724 -0.100399  0.050012 -0.175452 -0.302318 -0.101235 -0.174968 -0.192889 -0.207149 -0.276644 -0.072068 -0.185633 -0.071697 -0.292462  0.071428  0.140680  0.193666  0.176788 -0.206237 -0.024228  0.143229  0.321619  0.185699  0.352092  0.215276  0.487335  0.495036  0.427277  0.137585  0.015038  0.086927  0.302814  0.360684  0.491082  0.483667  0.354353  0.320231  0.296923  0.242544  0.102223  0.174687  0.293875  0.009310 -0.192081 -0.169686  0.203552  0.090388  0.092465  0.141237 -0.020264 -0.137428  0.264402  0.484037  0.227797  0.150009 -0.055839  0.051081  0.075793  0.030986  0.301756  0.497225  0.422973  0.146600  0.056355  0.264442  0.271334 -0.077138  0.014018  0.021316  0.100738  0.142760  0.539921  0.494837  0.507842 -0.169044 -0.236781 -0.036965  0.505614  0.470431 -0.073853 -0.163902 -0.022980  0.488347  0.464158 -0.013242 -0.211003  0.130101 -0.148763  0.053802 -0.044009 -0.232203 -0.303245  0.069509  0.145671  0.140113  0.310099 -0.013854  0.398026  0.225123 -0.094472 -0.099081 -0.114955 -0.152951 -0.320346
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

I6  = [ -0.014489 -0.016844 -0.019752 -0.022925 -0.027736 -0.062689 -0.058151 -0.050708 -0.064829 -0.065586 -0.056831 -0.061330 -0.054190 -0.059272 -0.092612 -0.089267 -0.104412 -0.090943 -0.079608 -0.081006 -0.089072 -0.101023 -0.087110 -0.083758 -0.088844 -0.090085 -0.093201 -0.102544 -0.055662 -0.046828 -0.063083 -0.062951 -0.056082 -0.054703 -0.048672 -0.064624 -0.069665 -0.065836 -0.066599 -0.052144 -0.054464 -0.046964 -0.078859 -0.075411 -0.039144 -0.038513 -0.040287 -0.082537 -0.076152 -0.129404 -0.120044 -0.119188 -0.124680 -0.124302 -0.126674 -0.127022 -0.122511 -0.131067 -0.119229 -0.125199 -0.128043 -0.118077 -0.115656 -0.115697 -0.119676 -0.116393 -0.125740 -0.129304 -0.130282 -0.132531 -0.125689 -0.114117 -0.112357 -0.124299 -0.120608 -0.116354 -0.120745 -0.129167 -0.123841 -0.125010 -0.117539 -0.138323 -0.141258 -0.137129 -0.140006 -0.134301 -0.141046 -0.140970 -0.141821 -0.142282 -0.142883 -0.149002 -0.146110 -0.151946 -0.149930 -0.151046 -0.154878 -0.159135 -0.160344 -0.157382 -0.155777 -0.161373 -0.159942 -0.155045 -0.155002 -0.150836 -0.158186 -0.153524 -0.157541 -0.153295 -0.151882 -0.150871 -0.147079 -0.142382 -0.138465 -0.136992 -0.141018 -0.136809 -0.143872 -0.143733 -0.143814 -0.143938 -0.144611 -0.149899 -0.143636 -0.141281 -0.142794 -0.143810 -0.142091 -0.142489 -0.133983 -0.137308 -0.134423 -0.144198 -0.139459 -0.151923 -0.148605 -0.152758 -0.147403 -0.148255 -0.144646 -0.141178 -0.138147 -0.133624 -0.146370 -0.145816 -0.139661 -0.160355 -0.163126 -0.160117 -0.159517 -0.153309 -0.167052 -0.165241 -0.162691 -0.158402 -0.154825 -0.165074 -0.163046 -0.167567 -0.165392 -0.161610 -0.170721 -0.166133 -0.166749 -0.167343 -0.149857 -0.171837 -0.172079 -0.171270 -0.167411 -0.171433 -0.170647 -0.151757 -0.135217 -0.137673 -0.154377 -0.142550 -0.150615 -0.133670 -0.131055 -0.133566 -0.146879 -0.161089 -0.151986 -0.146519 -0.160409 -0.149826 -0.152702 -0.163562 -0.148711 -0.138314 -0.143303 -0.132717 -0.140709 -0.137235 -0.136818 -0.133366 -0.137023 -0.089589 -0.098772 -0.095659 -0.088300 -0.093129 -0.099900 -0.094008 -0.089454 -0.080254 -0.097030 -0.097551 -0.091492 -0.092738 -0.086341 -0.080850 -0.079911 -0.073988 -0.072826 -0.108372 -0.081102 -0.084908 -0.083845 -0.105787 -0.078449 -0.105850 -0.109019 -0.108619 -0.113979 -0.118000 -0.129138 -0.115944 -0.110178 -0.129949 -0.109314 -0.109661 -0.134538 -0.143820 -0.138665 -0.112615 -0.131815 -0.109349 -0.112142 -0.086727 -0.074309 -0.112818 -0.077923 -0.109146 -0.108911 -0.065753 -0.073778 -0.037331 -0.037336 -0.042423 -0.031643 -0.039049 -0.036045 -0.005376
        -0.103967 -0.097524 -0.100012 -0.084917 -0.074783  0.158898  0.157644  0.159406  0.156456  0.160564  0.158514  0.166750  0.167734  0.172035 -0.032332 -0.038922 -0.039713 -0.048412 -0.054703 -0.058097 -0.061394 -0.064758 -0.073242 -0.076280 -0.080394 -0.082872 -0.086962 -0.086098 -0.086257 -0.089965 -0.084699 -0.077357 -0.080878 -0.076557 -0.076525 -0.068102 -0.072125 -0.058744 -0.046716 -0.055187 -0.043692 -0.051780 -0.043607 -0.060269 -0.073810 -0.082204 -0.089023 -0.092164 -0.090804 -0.057041 -0.070747 -0.070994 -0.064542 -0.057759 -0.059042 -0.049487 -0.054608 -0.044048 -0.052082 -0.041062 -0.040365 -0.038203 -0.041005 -0.035596  0.163605  0.159299  0.155971  0.150571  0.143410  0.135132  0.132924  0.141712  0.140494  0.125346  0.114859  0.115854  0.102040  0.081084  0.090718  0.083651  0.100708 -0.038083 -0.020411 -0.027094 -0.022423 -0.041012 -0.029983 -0.022486 -0.039270 -0.030794 -0.038460 -0.023387 -0.031695 -0.023213 -0.027316 -0.023600 -0.016119 -0.006745 -0.005244 -0.011793 -0.010425  0.003491  0.012208  0.008219  0.015030  0.007332  0.029047  0.026371  0.039601  0.037497  0.040547  0.059099  0.056490  0.063015  0.066919  0.059538  0.044116  0.057525  0.021312  0.021182  0.021381  0.014381  0.031711  0.025647 -0.007171 -0.004813  0.003869  0.003756  0.038574  0.038579  0.065049  0.075364  0.080788  0.090984  0.090610  0.080727  0.098274  0.100313  0.120423  0.124180  0.126542  0.118925  0.114872  0.115779  0.126071  0.117292  0.134308  0.081020  0.081442  0.090429  0.090524  0.110444  0.072238  0.074287  0.066642  0.073453  0.075301  0.045281  0.055991  0.046629  0.026260  0.028090  0.035597  0.008883  0.020674  0.011198 -0.030684  0.052374  0.055322  0.061764  0.071216  0.027061  0.045527  0.106703  0.146479  0.147443  0.101049  0.108448  0.073598  0.100121  0.098273  0.074041  0.038768  0.032117  0.026474 -0.008142  0.021451 -0.001021 -0.004046  0.002797 -0.015894 -0.044614 -0.014029 -0.042927 -0.012788 -0.019987 -0.025349 -0.048236 -0.043945  0.148339  0.141266  0.148638  0.150819  0.152379  0.152167  0.156019  0.159083  0.161513  0.156506  0.160672  0.161036  0.165665  0.167046  0.168575  0.167057  0.167678  0.166328  0.149852  0.159394  0.153559  0.152167  0.135831  0.154095  0.131657  0.126381  0.126531  0.113471  0.102136  0.091390  0.109387  0.126503  0.129114  0.145623  0.156066  0.151984 -0.033475 -0.039950 -0.060335 -0.054092 -0.075676 -0.079405 -0.092219 -0.087853 -0.071709 -0.073101 -0.037746 -0.036020  0.169588  0.161755  0.153920  0.152635  0.158940  0.151011 -0.067223 -0.075138 -0.107830
        -0.150958 -0.156614 -0.148719 -0.170865 -0.191375 -0.059245 -0.073135 -0.064449 -0.082921 -0.110580 -0.101160 -0.128454 -0.127903 -0.145757 -0.257423 -0.244421 -0.227721 -0.224479 -0.224744 -0.217093 -0.203115 -0.182001 -0.175639 -0.171379 -0.156356 -0.148576 -0.134421 -0.116801 -0.146322 -0.135271 -0.155015 -0.185138 -0.172287 -0.192016 -0.192989 -0.207458 -0.193821 -0.227416 -0.252306 -0.246385 -0.273520 -0.259163 -0.246398 -0.217345 -0.198542 -0.165682 -0.144212 -0.130156 -0.135251 -0.102369 -0.125757 -0.117402 -0.138203 -0.165602 -0.154439 -0.182455 -0.176173 -0.195327 -0.187123 -0.216709 -0.222957 -0.229205 -0.215358 -0.241129 -0.191268 -0.179956 -0.170162 -0.158872 -0.149144 -0.139213 -0.127329 -0.120960 -0.112452 -0.112915 -0.096170 -0.088096 -0.087257 -0.091383 -0.083555 -0.066901 -0.068254 -0.088088 -0.087717 -0.112211 -0.129328 -0.119938 -0.149705 -0.138533 -0.164312 -0.154143 -0.182800 -0.167827 -0.198881 -0.190462 -0.211897 -0.208028 -0.197358 -0.217125 -0.198575 -0.186136 -0.177436 -0.182850 -0.172271 -0.160171 -0.150106 -0.141171 -0.147717 -0.134420 -0.139536 -0.127872 -0.123238 -0.125701 -0.116946 -0.110564 -0.104273 -0.093907 -0.075154 -0.067555 -0.077806 -0.095028 -0.083656 -0.103347 -0.102956 -0.123827 -0.127619 -0.112094 -0.101605 -0.083279 -0.078107 -0.095664 -0.088811 -0.107247 -0.104455 -0.129777 -0.120129 -0.139412 -0.142652 -0.152384 -0.155972 -0.166540 -0.153499 -0.139480 -0.131161 -0.123067 -0.181274 -0.196466 -0.190713 -0.198037 -0.178541 -0.170724 -0.165259 -0.173798 -0.182570 -0.168982 -0.155007 -0.148570 -0.142169 -0.160385 -0.152481 -0.167399 -0.177601 -0.162672 -0.188208 -0.195491 -0.185433 -0.204773 -0.228391 -0.199412 -0.190562 -0.183392 -0.191124 -0.196700 -0.180106 -0.188972 -0.183823 -0.164697 -0.157409 -0.136301 -0.132825 -0.113947 -0.107701 -0.097745 -0.111555 -0.156097 -0.129525 -0.144310 -0.165639 -0.150060 -0.163744 -0.204697 -0.161219 -0.159447 -0.135995 -0.131632 -0.121208 -0.111826 -0.109577 -0.103774 -0.090452 -0.056331 -0.067871 -0.093892 -0.084043 -0.108920 -0.128068 -0.136921 -0.145948 -0.131037 -0.154299 -0.182717 -0.172666 -0.200247 -0.200087 -0.198344 -0.180492 -0.160790 -0.143671 -0.143597 -0.120256 -0.092636 -0.074961 -0.086387 -0.066410 -0.057435 -0.077315 -0.059619 -0.059062 -0.059679 -0.099745 -0.081420 -0.082885 -0.128622 -0.120765 -0.171648 -0.164185 -0.234789 -0.214712 -0.177324 -0.149435 -0.146302 -0.126382 -0.125940 -0.144112 -0.151294 -0.184865 -0.231853 -0.238340 -0.145375 -0.120447 -0.094962 -0.078559 -0.064360 -0.075566 -0.222527 -0.190336 -0.153123
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N6  = [ -0.623021 -0.613724 -0.641404 -0.405737 -0.098512 -0.270205 -0.058467 -0.048487 -0.138617 -0.181205 -0.056233 -0.248753 -0.199821 -0.373744 -0.295879 -0.477336 -0.389096 -0.544091 -0.459512 -0.443942 -0.464222 -0.524600 -0.410058 -0.383762 -0.381700 -0.381195 -0.438519 -0.617204 -0.051331 -0.289833 -0.034496 -0.250052 -0.032524 -0.158864  0.021448 -0.328757 -0.344727 -0.373219 -0.453884 -0.377013 -0.408701 -0.369070 -0.512221 -0.391234  0.124575 -0.194021 -0.326981 -0.225020 -0.028143 -1.013004 -0.944420 -0.934204 -0.953996 -0.722103 -0.826661 -0.601144 -0.632562 -0.539319 -0.566151 -0.081298 -0.139723 -0.084673 -0.278168 -0.112626 -0.466873 -0.140432 -0.242925 -0.225409 -0.434957 -0.686724 -0.834724 -0.763693 -0.723251 -0.938105 -0.980054 -0.999632 -0.982574 -1.039642 -1.032837 -1.018165 -1.068570 -1.116123 -1.131494 -1.131160 -1.098781 -1.061478 -1.062465 -1.082625 -1.007350 -1.060795 -0.883791 -1.064463 -0.969726 -1.030251 -0.999661 -1.045534 -1.038154 -1.090599 -1.060942 -1.082733 -1.076946 -1.081691 -1.079402 -1.085284 -1.094955 -1.088790 -1.098262 -1.088646 -1.094620 -1.094764 -1.069437 -1.022903 -1.034834 -1.025661 -1.019823 -1.040971 -1.108974 -1.067680 -1.143003 -1.142914 -1.142710 -1.137886 -1.124484 -1.085175 -1.090834 -1.124584 -1.137010 -1.141785 -1.126146 -1.121437 -1.069395 -1.002716 -1.017961 -1.010828 -1.005955 -1.018420 -1.013771 -1.056268 -1.043849 -1.030776 -1.067740 -1.010962 -0.996682 -0.966533 -1.034566 -1.047561 -1.007502 -1.036201 -1.098402 -1.107598 -1.095510 -1.106989 -1.057259 -1.122252 -1.081345 -1.045869 -1.031762 -1.111265 -1.101982 -1.111685 -1.088311 -1.096614 -1.130027 -1.106005 -1.091413 -1.092469 -0.670726 -1.154061 -1.166433 -1.157365 -1.057940 -1.139064 -1.137667 -1.064459 -1.002423 -0.953369 -1.088806 -1.014354 -1.017048 -0.998940 -0.997873 -1.041614 -1.086973 -1.103580 -1.085355 -1.085688 -1.090802 -1.084634 -1.070830 -1.067205 -1.065604 -0.987532 -1.090573 -1.067333 -1.088591 -1.103374 -1.133621 -1.056094 -1.087537 -0.633407 -0.810832 -0.654195 -0.506766 -0.569450 -0.542152 -0.512296 -0.501880 -0.461010 -0.509413 -0.285734 -0.467473 -0.174770 -0.344655 -0.439103 -0.489990 -0.486010 -0.466684 -0.557342 -0.428784 -0.410387 -0.512142 -0.900064 -0.441556 -0.963063 -0.999222 -1.007451 -1.049326 -1.060479 -1.007658 -1.056863 -0.977174 -0.834552 -0.670446 -0.194972 -0.728915 -0.416263 -0.612221 -0.598823 -0.960795 -0.581893 -0.708167 -0.354646 -0.123945 -0.631799 -0.377080 -0.199981 -0.152720 -0.430562 -0.316328  0.237977  0.254641  0.090239  0.295058 -0.080592  0.029767 -0.160459
        -0.753903 -0.764660 -0.762079 -0.911667 -1.007406  1.134462  1.151531  1.120701  1.153425  1.119612  1.125142  1.103648  1.096754  1.100668 -0.960333 -0.877633 -0.939313 -0.820944 -0.867904 -0.885506 -0.908003 -0.893061 -0.954215 -0.969834 -0.971855 -0.978219 -0.978628 -0.940671 -1.060030 -1.018232 -1.056572 -1.015163 -1.058435 -1.031786 -1.054160 -0.956521 -0.963701 -0.921455 -0.889755 -0.925116 -0.913667 -0.931291 -0.850550 -0.915732 -1.041784 -1.019424 -0.991795 -1.047898 -1.053134 -0.505509 -0.629505 -0.650142 -0.621020 -0.809204 -0.754781 -0.888912 -0.851587 -0.943050 -0.886876 -1.032567 -1.011271 -1.015471 -0.969970 -1.009936  1.061140  1.097967  1.110915  1.000300  0.930660  0.781962  0.747852  0.876366  0.873740  0.565359  0.409047  0.418756  0.454878  0.384272  0.451030  0.529944  0.403770 -0.247553 -0.154901  0.008729 -0.288193 -0.404156 -0.291668 -0.335986 -0.530925 -0.296513 -0.704403 -0.301161 -0.598778 -0.494084 -0.526731 -0.455154 -0.477979 -0.335088 -0.436453 -0.372618 -0.279309 -0.246129 -0.230607 -0.266078 -0.261369 -0.262952 -0.187040 -0.168395 -0.060349 -0.076644  0.005639  0.255452  0.242010  0.293220  0.337949  0.404573  0.291590  0.415262  0.062227  0.023031  0.068162 -0.078581  0.056550 -0.152595 -0.231882 -0.182503 -0.101997 -0.057689  0.209829  0.175195  0.384622  0.333279  0.326772  0.335271  0.335297  0.326542  0.352632  0.324372  0.454450  0.577274  0.415311  0.381382  0.375658  0.433157  0.546168  0.496305  0.575153  0.521156  0.434464  0.406874  0.400949  0.397692  0.524456  0.329693  0.236859  0.295253  0.304702 -0.081704  0.096405 -0.095192 -0.200028 -0.237069 -0.091785 -0.304108 -0.213443 -0.364881 -0.865130  0.223479  0.132148  0.224774  0.505568 -0.163022 -0.125363  0.445191  0.583816  0.719460  0.334174  0.353352  0.314129  0.346723  0.349893  0.341898  0.076302 -0.200633 -0.167865 -0.308994 -0.246043 -0.298808 -0.253671 -0.416302 -0.259728 -0.569011 -0.305067 -0.392945 -0.211519 -0.274110  0.001258 -0.417368 -0.345837  0.987266  0.841266  0.963143  1.049356  1.018325  1.038688  1.057823  1.064873  1.076220  1.061788  1.117025  1.079677  1.133160  1.117185  1.092635  1.073911  1.073834  1.077971  1.031424  1.083912  1.090130  1.055804  0.703468  1.085555  0.645835  0.562241  0.564009  0.464612  0.427972  0.362516  0.369689  0.575423  0.688177  0.951438  1.097021  0.933224 -0.994742 -0.920547 -0.852108 -0.612882 -0.894178 -0.882280 -1.046849 -1.036077 -0.866773 -0.963591 -1.002422 -1.006308  1.089231  1.106935  1.061043  1.103270  1.093398  1.077551 -1.022886 -1.036813 -1.014454
        -0.606230 -0.602332 -0.567307 -0.583103 -0.545220 -0.131440 -0.183535 -0.339964 -0.107587  0.147994  0.155023  0.166665  0.212263  0.051089 -0.569668 -0.626477 -0.558893 -0.669283 -0.665626 -0.645664 -0.580625 -0.548739 -0.521459 -0.505384 -0.502091 -0.485636 -0.427146 -0.186304 -0.373802 -0.416818 -0.388781 -0.477562 -0.381639 -0.468942 -0.391266 -0.582885 -0.553589 -0.628969 -0.625529 -0.617442 -0.616536 -0.609461 -0.647697 -0.627758 -0.388867 -0.477829 -0.464852 -0.387589 -0.402864 -0.237012 -0.035248 -0.099096 -0.188864 -0.444823 -0.315578 -0.448112 -0.499704 -0.353831 -0.508652 -0.339144 -0.462134 -0.438562 -0.547944 -0.466190  0.080551  0.164029  0.102512  0.359513  0.386962  0.384696  0.217828  0.074834  0.186143  0.266702  0.321928  0.269772  0.277098  0.189886  0.125975 -0.011257 -0.129025 -0.082603 -0.124392 -0.009165 -0.028740 -0.211974  0.137537 -0.016048 -0.068743  0.138647 -0.269835  0.123328 -0.207466 -0.273291 -0.042952 -0.091184 -0.278036 -0.060390 -0.253186 -0.069814  0.103898  0.118320  0.136978  0.083584  0.050122  0.076058  0.116029  0.161575  0.194970  0.189317  0.272836  0.322636  0.304330  0.297875  0.282703  0.158624 -0.117794 -0.141754 -0.085807 -0.054594 -0.088107 -0.044826  0.095114  0.181932  0.101117 -0.072831 -0.119726 -0.099702 -0.126131  0.055985  0.062441  0.322344  0.294107  0.305282  0.314971  0.295051  0.289540  0.212948  0.135250 -0.040591  0.100490  0.278363  0.310322  0.330291 -0.367357 -0.404321 -0.419859 -0.395961 -0.203724 -0.124436  0.000732 -0.263152 -0.127524 -0.031509  0.201508  0.255419  0.280154  0.137269  0.189228  0.130138  0.133872  0.072825  0.063796 -0.058826  0.114877 -0.256800 -0.048399 -0.276619 -0.263768 -0.215699 -0.326389 -0.030692  0.008757 -0.417884 -0.421921 -0.078454  0.111840  0.287938  0.304712  0.322511  0.322779  0.224282  0.227289  0.083778  0.172226  0.021374  0.084991  0.043478  0.144036 -0.292934  0.154777 -0.097504 -0.001920 -0.068542  0.127842 -0.156506 -0.184912 -0.214746 -0.163833 -0.034797 -0.013375  0.063012  0.048303  0.043577  0.007923 -0.028361 -0.048744  0.004370 -0.052300  0.040840 -0.051267  0.038968 -0.025417 -0.065052 -0.083277 -0.065294 -0.026270  0.002205  0.035897  0.037353 -0.073560  0.130201 -0.089576 -0.085828  0.055217 -0.086349 -0.101785 -0.134267  0.293565  0.135180  0.133418  0.308395  0.068427  0.155958  0.026549 -0.276512 -0.197611 -0.547050 -0.126061 -0.473040 -0.138503 -0.255944 -0.457810 -0.465191 -0.527696 -0.479139 -0.476290  0.000126  0.098192  0.223369 -0.183638 -0.394798 -0.262084 -0.514045 -0.456515 -0.545530
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

I8  = [ -0.029024 -0.024675 -0.016186 -0.025867 -0.025193 -0.013795 -0.011391 -0.027388 -0.012581 -0.019103 -0.015031 -0.030969 -0.067768 -0.046925 -0.062116 -0.051228 -0.065497 -0.063852 -0.046544 -0.063843 -0.051154 -0.046703 -0.054261 -0.058574 -0.055780 -0.063603 -0.047473 -0.066413 -0.068086 -0.055443 -0.061573 -0.067830 -0.053040 -0.058539 -0.068182 -0.053199 -0.083677 -0.102121 -0.101958 -0.083708 -0.099424 -0.093740 -0.100830 -0.059103 -0.137202 -0.118430 -0.123062 -0.117863 -0.136188 -0.113848 -0.119006 -0.131042 -0.151694 -0.150904 -0.138876 -0.132154 -0.132284 -0.131773 -0.145788 -0.151951 -0.152551 -0.152955 -0.143683 -0.132115 -0.125310 -0.117062 -0.127685 -0.125231 -0.120651 -0.138044 -0.124378 -0.128429 -0.127126 -0.130613 -0.133019 -0.125149 -0.131913 -0.162559 -0.169093 -0.161990 -0.173023 -0.159862 -0.157708 -0.167156 -0.178515 -0.192298 -0.189248 -0.186050 -0.179691 -0.168152 -0.173405 -0.189664 -0.187335 -0.183276 -0.174272 -0.167812 -0.179597 -0.169135 -0.181304 -0.171313 -0.173673 -0.179722 -0.180658 -0.177804 -0.185257 -0.173181 -0.172024 -0.179886 -0.177048 -0.167854 -0.172938 -0.186969 -0.203722 -0.201081 -0.206926 -0.198362 -0.209615 -0.195193 -0.190699 -0.195582 -0.196647 -0.193957 -0.203916 -0.207870 -0.203472 -0.207575 -0.215242 -0.212923 -0.202484 -0.224545 -0.221454 -0.222293 -0.220602 -0.211665 -0.205739 -0.210279 -0.224015 -0.222204 -0.216440 -0.210159 -0.200837 -0.207864 -0.218439 -0.205950 -0.206727 -0.214797 -0.225494 -0.222505 -0.209742 -0.214132 -0.215315 -0.222239 -0.212401 -0.206746 -0.208298 -0.219538 -0.210530 -0.211818 -0.210705 -0.205150 -0.202249 -0.191229 -0.194236 -0.198542 -0.214742 -0.203613 -0.217469 -0.217086 -0.224967 -0.223348 -0.213012 -0.213989 -0.208310 -0.204098 -0.212686 -0.217131 -0.231542 -0.241149 -0.224221 -0.230991 -0.238712 -0.238716 -0.225765 -0.240360 -0.233245 -0.243759 -0.233439 -0.225113 -0.244471 -0.240390 -0.252346 -0.256823 -0.245533 -0.256902 -0.242674 -0.258966 -0.247677 -0.252467 -0.243307 -0.240538 -0.248554 -0.250748 -0.241924 -0.256062 -0.265983 -0.268631 -0.276468 -0.282982 -0.290858 -0.294100 -0.301443 -0.294477 -0.304021 -0.288388 -0.314093 -0.308574 -0.296773 -0.305448 -0.309218 -0.298393 -0.300668 -0.288010 -0.296878 -0.313341 -0.311624 -0.332497 -0.328870 -0.310847 -0.299828 -0.290771 -0.302277 -0.291212 -0.309156 -0.302707 -0.289951 -0.302002 -0.308698 -0.301718 -0.291223 -0.290438 -0.331826 -0.329470 -0.337438 -0.330799 -0.338001 -0.344641 -0.346118 -0.323479 -0.307948 -0.326485 -0.329396 -0.324242 -0.309149 -0.319707 -0.311972 -0.320549 -0.315418 -0.319519 -0.276685 -0.275034 -0.276197 -0.269333 -0.275028 -0.278154 -0.277212 -0.266724 -0.259214 -0.265785 -0.265472 -0.254506 -0.278156 -0.274001 -0.260699 -0.257311 -0.274476 -0.259677 -0.266293 -0.253803 -0.265466 -0.274114 -0.276876 -0.259973 -0.278887 -0.263651 -0.267983 -0.275051 -0.261319 -0.276941 -0.260590 -0.275377 -0.255098 -0.268966 -0.265854 -0.263530 -0.263794 -0.267839 -0.254825 -0.270135 -0.266124 -0.256533 -0.265470 -0.253099 -0.283087 -0.249820 -0.241282 -0.229408 -0.221023 -0.238226 -0.222081 -0.232588 -0.221450 -0.239214 -0.239207 -0.252426 -0.279394 -0.241277 -0.242343 -0.233348 -0.227282 -0.248639 -0.252716 -0.235634 -0.256527 -0.245718 -0.250514 -0.238954 -0.245906 -0.246790 -0.239693 -0.236380 -0.234102 -0.229878 -0.256572 -0.283654 -0.283625 -0.243315 -0.240824 -0.246463 -0.278566 -0.243797 -0.283099 -0.249889 -0.284911 -0.254707 -0.285617 -0.274876 -0.284259 -0.318723 -0.284146 -0.285606 -0.320836 -0.283805 -0.314076 -0.311577 -0.283717 -0.314579 -0.315893 -0.282785 -0.290485 -0.265274 -0.233284 -0.234179 -0.230492 -0.264947 -0.242028 -0.230530 -0.231387 -0.267135 -0.218094 -0.211036 -0.209399 -0.214200 -0.218430 -0.212932 -0.214166 -0.204967 -0.219073 -0.221940 -0.252178 -0.226473 -0.247152 -0.223098 -0.230170 -0.230835 -0.227115 -0.201758 -0.197472 -0.230630 -0.233358 -0.219745 -0.193532 -0.187265 -0.218463 -0.195735 -0.186160 -0.189732 -0.197107 -0.187394 -0.191147 -0.228399 -0.224751 -0.222286 -0.197810 -0.226319 -0.219289 -0.206704 -0.199875 -0.179225 -0.201594 -0.208514 -0.208775 -0.160020 -0.155730 -0.163683 -0.146580 -0.145539 -0.157948 -0.156539 -0.165649 -0.151493 -0.168501 -0.153307 -0.143464 -0.143126 -0.142826 -0.169665 -0.172836 -0.161206 -0.166803 -0.164771 -0.194665 -0.193820 -0.161797 -0.192315 -0.195147 -0.153074 -0.178998 -0.095778 -0.079112 -0.094169 -0.096733 -0.088772 -0.094634 -0.096452 -0.082553 -0.097142 -0.082166 -0.100985 -0.087093 -0.097052 -0.087918 -0.097039 -0.083491 -0.080894 -0.090676 -0.078228 -0.099124 -0.101751 -0.084246 -0.111004 -0.125684 -0.125123 -0.108918 -0.107536 -0.106841 -0.125270 -0.071534 -0.069228 -0.076963 -0.067808 -0.079430 -0.108817 -0.107751 -0.114609 -0.079629 -0.109639 -0.111746 -0.105702 -0.117387 -0.107383 -0.109147 -0.139059 -0.143504 -0.144213 -0.137112 -0.146702 -0.153991 -0.125158 -0.158109 -0.142103 -0.128970 -0.141028 -0.109465 -0.071466 -0.108483 -0.038073 -0.073607 -0.036621 -0.029266 -0.041145 -0.036571 -0.076503 -0.075028 -0.038878 -0.039747 -0.016568 -0.011651 -0.037219 -0.026489 -0.044268 -0.007772 -0.035384
         0.081555  0.090342  0.102199  0.117661  0.131796  0.124232  0.137744  0.155592  0.151365  0.161986  0.165172  0.177104  0.200490  0.199622  0.201551  0.204537  0.195200  0.187010  0.185039  0.178586  0.170999  0.170640  0.151770  0.160505  0.145433  0.118973  0.134191  0.103719  0.098313  0.089333  0.077993  0.069737  0.069760  0.055036  0.040300  0.042627  0.063531  0.056946  0.029617  0.031031  0.015875  0.007795 -0.000801  0.015631 -0.011927 -0.010632 -0.007195 -0.002927  0.011388  0.007200  0.028144  0.041291  0.028755  0.047142  0.048054  0.050338  0.083794  0.100336  0.104954  0.107406  0.121799  0.137580  0.125749  0.129593  0.133317  0.149884  0.157444  0.170127  0.180636  0.180761  0.200546  0.203600  0.202731  0.199660  0.196886  0.197228  0.191237 -0.013825 -0.002900  0.005494 -0.001194  0.010651  0.014779  0.030951  0.015130  0.020027  0.027340  0.045576  0.058775  0.064128  0.077942  0.082584  0.097918  0.107859  0.103872  0.099454  0.127129  0.125081  0.143370  0.144390  0.158835  0.164690  0.165829  0.171570  0.170490  0.182897  0.181588  0.175009  0.176374  0.177933  0.172725  0.163424  0.096772  0.081518  0.018836  0.020649  0.014942 -0.001539 -0.000168 -0.004427 -0.004274 -0.000001 -0.001931  0.005043  0.008951  0.011046  0.010403  0.031130  0.023555  0.013275  0.028747  0.045389  0.050086  0.068857  0.062839  0.076908  0.083089  0.098065  0.107968  0.116221  0.100323  0.129832  0.143599  0.142159  0.157036  0.168094  0.177822  0.184983  0.182551  0.181630  0.177112  0.171389  0.166351  0.158971  0.154480  0.145121  0.141366  0.133849  0.134917  0.155139  0.159110  0.164290  0.166291  0.157964  0.126168  0.152354  0.126514  0.108135  0.090113  0.062312  0.063310  0.045412  0.060184  0.038793  0.031981  0.024034  0.028665  0.024792  0.021620  0.012686  0.009968  0.004392 -0.001100  0.003197 -0.006057 -0.003704 -0.007206 -0.007397  0.004318  0.014431  0.005173  0.031337  0.051607  0.057511  0.069166  0.073183  0.073745  0.098956  0.094275  0.097378  0.119285  0.128721  0.131219  0.118202  0.101051  0.113924  0.117741  0.136867  0.164988  0.178219  0.178555  0.179642  0.173217  0.174255  0.162015  0.152215  0.142054  0.126985  0.098018  0.097365  0.080838  0.091716  0.068749  0.064576  0.080153  0.054020  0.061578  0.044005  0.043846  0.047073  0.034283  0.025097  0.017745  0.022655  0.014373  0.010580  0.008049  0.003991  0.004344  0.014131  0.134964  0.125066  0.100089  0.092010  0.064859  0.064229  0.038040  0.012906  0.011560  0.015223  0.023426  0.030330  0.025769  0.086796  0.090392  0.108345  0.133338  0.169139  0.071473  0.063232  0.051424  0.040329  0.022480  0.007550  0.003155  0.001983  0.001459  0.007828  0.011499  0.010724  0.019562  0.022054  0.023792  0.025422  0.030976  0.034211  0.048021  0.044721  0.065876  0.083149  0.092092  0.100181  0.107699  0.106718  0.128513  0.145275  0.155388  0.154707  0.167536  0.169447  0.174737  0.182162  0.185240  0.187278  0.187033  0.180836  0.183082  0.176358  0.156709  0.164122  0.137274  0.148358  0.152072  0.163874  0.165887  0.137633  0.133112  0.136719  0.125613  0.166982  0.161122  0.181757  0.171196  0.185434  0.184515  0.182053  0.181397  0.184567  0.186537  0.177802  0.172815  0.172534  0.158845  0.157741  0.142664  0.133012  0.128741  0.108948  0.101547  0.094963  0.134051  0.153969  0.166399  0.133652  0.100154  0.081639  0.073853  0.071625  0.064302  0.059756  0.047015  0.039422  0.031984  0.031049  0.029938  0.012158  0.004791  0.007913  0.015953  0.026076  0.038076  0.072171  0.112377  0.129093  0.153019  0.156866  0.173015  0.170667  0.154321  0.130881  0.107507  0.089929  0.063318  0.066493  0.077682  0.056214  0.038363  0.020250 -0.000319 -0.005152 -0.006145 -0.008553 -0.007221 -0.007311 -0.002983 -0.004689  0.003380 -0.003543 -0.000493 -0.006872  0.013915  0.012634  0.043396  0.076260  0.112480  0.157419  0.161756  0.161374  0.180478  0.186952  0.173769  0.164005  0.186876  0.153759  0.150151  0.144558  0.133135  0.130350  0.123650  0.084274  0.064414  0.066733  0.055423  0.050967  0.004807 -0.003918 -0.005159 -0.005462  0.032511  0.086357  0.114370  0.177019  0.182623  0.181732  0.188363  0.190153  0.184842  0.190420  0.185458  0.193613  0.171482  0.173702  0.186396  0.150741  0.171548  0.186124  0.171756  0.137192  0.114512  0.107857  0.101733  0.071736  0.077212  0.050709  0.033355  0.014780  0.003957  0.203895  0.202488  0.208131  0.205127  0.206179  0.202794  0.189745  0.192842  0.182356  0.177779  0.162012  0.168725  0.132189  0.145421  0.118185  0.129836  0.103619  0.099130  0.099955  0.082266  0.065025  0.072274  0.075102  0.063016  0.087697  0.102837  0.116983  0.131102  0.119149  0.132154  0.139522  0.144851  0.164060  0.168100  0.153827  0.169005  0.170068  0.187695  0.198241  0.205344  0.206178  0.206795  0.208811  0.205936  0.191728  0.194290  0.195449  0.171896  0.142453  0.102364  0.098088  0.054242  0.011912  0.017186 -0.007145 -0.000377  0.009341  0.047355  0.082508  0.102996  0.156385  0.166970  0.185406  0.190923  0.195648  0.201106  0.178325  0.176517  0.151235  0.144474  0.149934  0.136872  0.123395  0.107984  0.071773
        -0.444425 -0.457230 -0.467878 -0.479199 -0.481267 -0.475589 -0.474030 -0.476037 -0.460702 -0.464186 -0.448268 -0.442097 -0.392742 -0.401297 -0.414837 -0.411460 -0.416767 -0.426270 -0.433131 -0.432871 -0.458423 -0.462732 -0.468187 -0.459283 -0.469524 -0.471441 -0.477296 -0.467936 -0.462767 -0.451396 -0.437332 -0.432497 -0.429780 -0.425531 -0.422698 -0.421259 -0.430881 -0.425585 -0.409424 -0.414550 -0.400152 -0.391846 -0.370428 -0.410405 -0.338107 -0.340245 -0.355991 -0.365772 -0.370705 -0.386407 -0.401041 -0.404578 -0.382589 -0.391401 -0.402910 -0.412772 -0.419947 -0.416518 -0.400833 -0.391882 -0.389727 -0.385712 -0.398800 -0.411533 -0.413948 -0.412265 -0.404524 -0.402849 -0.398943 -0.383695 -0.388064 -0.370060 -0.352891 -0.337764 -0.323884 -0.314163 -0.294357 -0.311845 -0.330718 -0.358015 -0.334170 -0.371277 -0.376042 -0.386189 -0.381101 -0.396321 -0.396807 -0.399190 -0.400709 -0.400044 -0.405554 -0.412531 -0.416097 -0.413181 -0.405069 -0.401490 -0.400095 -0.390523 -0.391374 -0.381275 -0.371892 -0.366494 -0.356946 -0.346953 -0.330355 -0.329291 -0.321986 -0.302181 -0.294738 -0.287807 -0.268225 -0.253456 -0.270243 -0.273394 -0.301141 -0.291995 -0.306330 -0.320269 -0.308125 -0.331275 -0.347724 -0.372862 -0.387826 -0.407638 -0.402121 -0.411627 -0.423384 -0.418738 -0.403941 -0.431602 -0.435210 -0.433693 -0.427431 -0.420167 -0.415268 -0.421090 -0.431978 -0.433822 -0.431675 -0.428302 -0.421108 -0.423492 -0.427309 -0.415182 -0.406591 -0.407915 -0.406213 -0.395896 -0.386586 -0.367917 -0.355184 -0.338835 -0.334508 -0.317631 -0.308869 -0.300125 -0.286838 -0.268265 -0.260245 -0.253053 -0.260810 -0.259923 -0.285171 -0.295991 -0.286592 -0.287504 -0.291801 -0.292217 -0.294668 -0.292212 -0.285884 -0.291259 -0.283330 -0.286422 -0.297423 -0.304827 -0.309264 -0.323175 -0.311373 -0.330521 -0.345694 -0.356709 -0.342785 -0.363994 -0.389165 -0.393765 -0.410649 -0.402729 -0.423519 -0.435203 -0.425010 -0.451069 -0.456870 -0.464822 -0.458980 -0.470138 -0.463796 -0.465896 -0.457456 -0.450391 -0.454041 -0.452923 -0.448009 -0.461019 -0.469595 -0.463745 -0.461963 -0.454872 -0.439228 -0.424664 -0.408431 -0.400103 -0.381825 -0.372515 -0.363841 -0.349172 -0.342249 -0.335800 -0.329495 -0.322988 -0.320687 -0.318227 -0.316686 -0.323224 -0.326559 -0.324430 -0.324371 -0.320563 -0.317341 -0.313222 -0.325337 -0.341521 -0.346841 -0.340160 -0.361031 -0.377992 -0.384511 -0.410335 -0.401028 -0.437633 -0.352006 -0.347139 -0.337680 -0.334146 -0.323754 -0.322247 -0.329206 -0.369896 -0.361843 -0.363449 -0.339632 -0.331832 -0.334912 -0.330973 -0.329115 -0.338664 -0.341334 -0.380602 -0.476355 -0.476893 -0.469925 -0.460001 -0.445885 -0.426769 -0.407415 -0.409094 -0.396965 -0.383822 -0.373036 -0.365345 -0.353177 -0.348059 -0.338526 -0.332133 -0.321876 -0.316855 -0.304361 -0.303161 -0.305571 -0.313326 -0.317839 -0.318407 -0.325166 -0.322238 -0.330242 -0.339825 -0.334057 -0.346532 -0.348002 -0.363197 -0.364618 -0.392162 -0.400473 -0.407321 -0.417515 -0.426095 -0.422608 -0.431035 -0.442717 -0.437878 -0.452872 -0.445825 -0.445211 -0.436076 -0.431006 -0.438458 -0.434937 -0.444435 -0.436647 -0.425094 -0.420064 -0.410663 -0.426652 -0.415333 -0.399983 -0.392579 -0.374511 -0.370030 -0.371495 -0.365085 -0.347915 -0.338248 -0.331327 -0.324245 -0.321527 -0.312413 -0.315518 -0.311676 -0.304410 -0.301451 -0.309443 -0.315183 -0.336560 -0.337471 -0.321521 -0.305888 -0.302636 -0.304695 -0.306575 -0.300878 -0.310677 -0.305735 -0.322165 -0.322007 -0.328940 -0.374494 -0.398812 -0.383269 -0.359393 -0.340662 -0.327015 -0.310536 -0.335654 -0.337674 -0.347419 -0.356112 -0.389363 -0.434854 -0.445148 -0.456029 -0.443208 -0.442275 -0.443834 -0.471095 -0.459325 -0.445906 -0.445026 -0.443207 -0.415701 -0.391958 -0.384608 -0.366585 -0.353690 -0.344946 -0.329516 -0.327702 -0.325060 -0.340432 -0.394258 -0.371227 -0.348674 -0.320449 -0.299233 -0.296764 -0.300582 -0.310500 -0.319540 -0.322687 -0.356614 -0.376904 -0.377108 -0.384979 -0.392329 -0.399657 -0.393267 -0.399828 -0.413414 -0.408233 -0.414066 -0.435843 -0.430354 -0.426658 -0.408494 -0.439571 -0.423244 -0.390276 -0.325595 -0.311849 -0.288645 -0.283242 -0.264676 -0.259589 -0.287114 -0.304179 -0.301394 -0.312645 -0.312288 -0.338275 -0.347768 -0.354729 -0.358403 -0.369123 -0.375143 -0.391224 -0.383024 -0.337085 -0.354090 -0.382464 -0.393773 -0.395832 -0.418882 -0.410325 -0.402715 -0.403904 -0.401784 -0.374765 -0.362484 -0.343404 -0.359016 -0.368889 -0.384671 -0.374668 -0.390711 -0.404135 -0.406523 -0.406667 -0.417453 -0.416221 -0.420049 -0.431643 -0.433632 -0.437455 -0.445553 -0.462758 -0.446012 -0.463212 -0.436603 -0.430014 -0.434794 -0.432254 -0.421879 -0.425247 -0.431821 -0.429201 -0.425213 -0.417344 -0.459435 -0.459356 -0.444943 -0.443674 -0.427460 -0.414810 -0.409578 -0.408389 -0.411725 -0.399689 -0.393667 -0.385799 -0.378905 -0.363141 -0.344532 -0.303577 -0.338345 -0.347240 -0.390126 -0.389380 -0.393368 -0.421838 -0.394481 -0.368820 -0.382220 -0.347598 -0.373303 -0.400289 -0.418386 -0.444222 -0.466357 -0.473228 -0.468341 -0.431581 -0.421233 -0.408972 -0.394054 -0.443405 -0.450639 -0.478421 -0.474879 -0.475281 -0.480414 -0.479966 -0.465780 -0.430836
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N8  = [ -0.113888 -0.050271  0.201164  0.036737  0.185654  0.646057  0.599571 -0.201076  0.896594  0.723450  0.718114  0.252051  0.057196  0.316922 -0.435752  0.137910 -0.468802 -0.492633 -0.008544 -0.541561 -0.594217 -0.496866 -0.495717 -0.661012 -0.542040 -0.606774 -0.422808 -0.174718 -0.150417 -0.119059 -0.008392  0.051336  0.050139  0.212218 -0.123941  0.205443 -0.102540 -0.258989 -0.345257 -0.266718 -0.260103 -0.183398 -0.029861 -0.116351 -0.304540  0.044019 -0.185286 -0.278996 -0.517598 -0.432678 -0.600452 -0.618785 -0.131864 -0.487463 -0.826963 -0.604790 -0.769495 -0.737522 -0.946628 -0.638410 -0.635588 -0.677562 -0.946904 -0.697173 -0.569062 -0.551882 -0.730179 -0.658477 -0.575788 -0.858041 -0.768983 -0.506086 -0.477050 -0.505960 -0.480872 -0.269875 -0.252538 -0.600549 -0.421709 -0.146592 -0.297344 -0.044405 -0.015952  0.067660  0.210276  0.329944  0.344456  0.256879  0.091952  0.002339  0.179469  0.099138  0.178257  0.438014  0.484792  0.298872  0.542897  0.358409  0.529445  0.258518  0.239002  0.241205 -0.182484 -0.778056 -0.888654 -0.689761 -0.532731 -0.680715 -0.536907 -0.481582 -0.539168 -0.576707 -1.117209 -1.082186 -0.778337 -0.964092 -0.737247 -0.134925 -0.686717  0.014172  0.087434  0.311558  0.431482  0.515017  0.652694  0.639895  0.508849  0.683119  0.438351  0.019689  0.461848  0.664221  0.664832  0.312926  0.324726  0.329019  0.367648  0.339756  0.325004  0.406298  0.188573  0.454121  0.428964  0.422537  0.446657  0.462861  0.176566 -0.301541  0.314166  0.121654  0.043077 -0.016138 -0.000639 -0.314511 -0.346554 -0.451020 -1.110367 -1.207459 -1.195995 -0.869249 -0.848186 -0.506958 -0.889567 -0.968677 -1.126691 -1.027362 -1.028465 -0.943764 -0.699546 -0.759974 -0.721148 -0.734698 -0.772371 -0.921778 -0.664857 -0.665362 -0.591786 -0.672196 -0.691477 -0.823857 -0.810126 -0.809228 -0.857133 -0.779137 -0.462143 -0.584932 -0.231789 -0.034600 -0.309896 -0.101818 -0.291361 -0.118338  0.200675  0.135063  0.396924  0.127369  0.335580  0.245155  0.603693  0.606258  0.303441  0.135754  0.182952  0.232629 -0.083780 -0.273723 -0.124410 -0.139878 -0.192484 -0.319683 -0.417541 -0.602232 -0.607002 -0.366181 -0.716984 -0.485942 -0.319429 -0.481256 -0.808584 -0.723934 -0.793535 -0.423135 -0.767655 -0.530303 -0.677559 -0.380332 -0.335651 -0.657536 -0.577073 -0.646260 -0.529751 -0.141458 -0.240915 -0.124357 -0.097693 -0.387363 -0.228761 -0.255217 -0.304657 -0.252908 -0.662633 -0.667012 -0.227375 -0.299790 -0.166946 -0.228057 -0.308750 -0.299104 -0.455429 -0.408989 -0.440884 -0.464109 -0.222490 -0.531942 -0.741923 -0.759667 -0.850005 -0.386125  0.020511  0.006799 -0.154342 -0.075413 -0.203636 -0.310427 -0.347260 -0.399551 -0.560702 -0.434039 -0.467297 -0.606191 -0.245982 -0.354951 -0.467864 -0.430900 -0.275636 -0.420651 -0.506054 -0.404435 -0.246177 -0.348818 -0.313618 -0.627825 -0.317755 -0.598730 -0.699095 -0.664968 -0.940972 -0.569763 -0.842813 -0.347350 -0.649162 -0.223575 -0.197795 -0.192381 -0.259444 -0.302146 -0.056915 -0.276782 -0.264607 -0.082228 -0.159555 -0.003166 -0.154717  0.065149  0.157975  0.278293  0.324250  0.234778  0.312743  0.278429  0.384771  0.049105  0.205913  0.050294 -0.486989 -0.352779 -0.631088 -0.493110 -0.322297 -0.660502 -0.724853 -0.252202 -0.801118 -0.627842 -0.778048 -0.755588 -0.757533 -0.883428 -0.773233 -0.763053 -0.791584 -0.597769 -0.763574 -0.426044 -0.266794 -0.679790 -0.660693 -0.593945 -0.688479 -0.560626 -0.581773 -0.458291 -0.461805 -0.472905 -0.418976 -0.254483 -0.318979 -0.303205 -0.151895 -0.292429 -0.463656 -0.653688 -0.817291 -0.691319 -0.462753 -0.743268 -0.322593 -0.266858 -0.147988 -0.140424  0.361162  0.531694  0.656618  0.117423  0.505361  0.595877  0.347848 -0.206658  0.275793  0.149479  0.182625 -0.184442 -0.401521 -0.246894 -0.608103 -0.324546 -0.879619 -0.751951 -0.594973 -0.519990 -0.694935 -0.872886 -0.495583 -0.801759 -0.757649 -0.641503 -0.608824 -0.277637 -0.257673  0.018073  0.347346  0.507837  0.122445  0.354007  0.504212  0.422571  0.327546  0.452161  0.341938  0.466731  0.638159  0.468740  0.331864  0.639485  0.234471  0.322319 -0.082703 -0.590922 -0.948553 -0.930769 -1.135899 -0.476950 -0.542983 -0.506556 -0.528962 -0.531865 -0.514579 -0.399289 -0.860602 -0.624804 -0.716871 -0.810891 -0.865781 -0.835024 -0.875233 -0.730832 -0.747816 -0.267175  0.394796  0.351962  0.157777  0.218148 -0.167411  0.308495  0.307892  0.101294  0.076795  0.077608  0.279444  0.085165  0.051113  0.153879 -0.008452 -0.255351 -0.512019 -0.390712 -0.646491 -0.495533 -0.637123 -0.658336 -0.721204 -0.758102 -0.773715 -0.946420 -0.728715 -0.394835 -0.328436 -0.239833 -0.128224 -0.376235 -0.582938 -0.712694 -0.691449 -0.697042 -0.637051 -0.621618 -0.793398 -0.829508 -0.828823 -0.741415 -0.680396 -0.530787 -0.250540 -0.287718 -0.596599 -0.311757 -0.100951 -0.037374 -0.340326 -0.165772 -0.118908 -0.454426 -0.490010 -0.444586 -0.849303 -0.812063 -0.091565 -0.692601 -0.174054 -0.322598 -0.679663 -0.499592 -0.185679 -0.289767 -0.325086 -0.153238 -0.199488 -0.298552  0.190170  0.142303  0.402862 -0.558521 -0.041845  0.054370  0.001149  0.136978  0.767002 -0.267305  0.229571 -0.236415  0.667999 -0.030648
        -0.749125 -0.657663 -0.511698 -0.235046  0.252540  0.149206  0.057584  0.482996  0.544822  0.756980  0.724629  1.075129  1.173579  1.011934  0.810016  1.177659  0.787769  0.759532  0.980473  0.788020  0.838957  0.732135  0.476974  0.677891  0.390772  0.221307  0.366698 -0.336705 -0.659240 -0.731325 -0.583158 -0.381777 -0.489072 -0.154421 -0.394933 -0.205482 -0.329939 -0.421859 -0.483687 -0.489976 -0.651196 -0.820728 -0.956099 -0.555862 -0.953673 -0.977801 -0.919026 -0.872452 -0.630958 -0.829779 -0.477218 -0.627996 -0.423731 -0.417314 -0.434036 -0.379031  0.170291  0.272630  0.367293  0.277350  0.275048  0.389903  0.291137  0.319093  0.390184  0.421482  0.334113  0.592743  0.526736  0.477755  0.716359  1.129134  1.135056  1.120458  1.124290  1.163655  1.155755 -0.829702 -0.919511 -0.943153 -0.959580 -0.835318 -0.637116 -0.362646 -0.614839 -0.284686 -0.214263 -0.184506 -0.255610 -0.261001 -0.136627 -0.235878 -0.013993  0.266293  0.346495  0.391458  0.495178  0.522191  0.522847  0.594211  0.824320  1.057948  1.149232  0.899517  0.856731  1.031764  1.081971  1.040085  1.106459  1.114671  1.090013  1.023929 -0.169744 -0.109066 -0.433231 -0.279176 -0.540568 -0.919877 -0.864050 -0.982150 -0.960657 -0.843333 -0.741287 -0.486944 -0.255054 -0.171554 -0.353191  0.172751 -0.117551 -0.486286 -0.062994  0.219766  0.224509 -0.115853 -0.115581 -0.108341 -0.103133 -0.054498 -0.032482  0.106897 -0.055448  0.416275  0.544373  0.546330  0.550365  0.718983  1.032813  0.942785  1.021283  1.059785  1.073264  1.024095  1.043550  1.088497  1.004874  0.555998  0.567543  0.217331  0.148821  0.836945  0.905695  1.062229  0.871813  0.794166  0.210259  0.715080  0.209807  0.110717  0.239553 -0.044698 -0.005633 -0.301460 -0.031072 -0.331080 -0.407065 -0.488671 -0.637091 -0.769627 -0.596256 -0.633870 -0.699509 -0.753520 -0.710625 -0.800629 -0.971285 -0.909829 -0.953164 -0.988778 -0.800602 -0.679869 -0.852419 -0.528451 -0.218958 -0.261107 -0.032346 -0.067006 -0.054733  0.360643  0.294275  0.239090  0.347898  0.405700  0.351898  0.645637  0.439198  0.516723  0.576102  0.605595  0.673168  1.127058  1.167516  1.128274  1.091861  1.075658  0.945494  0.772511  0.625825  0.427443  0.299387  0.342963  0.239268  0.416127  0.192605  0.305088  0.301634 -0.083642  0.142098 -0.274985 -0.229685 -0.150831 -0.773279 -0.796732 -0.835537 -0.755911 -0.897318 -0.970082 -0.930006 -0.994363 -0.982665 -0.796658  0.511894  0.443538  0.548383  0.535648  0.155249  0.006482 -0.330154 -0.911684 -0.977079 -0.950043 -0.791801 -0.535172 -0.699137  0.419112  0.320411  0.341124  0.395069  1.053757  0.224820 -0.219747 -0.523672 -0.539331 -0.673949 -0.887922 -0.993845 -0.987802 -0.929863 -0.906069 -0.931807 -0.861278 -0.877617 -0.881069 -0.893923 -0.851178 -0.832565 -0.822767 -0.293737 -0.312377  0.394804  0.504011  0.525270  0.394982  0.510632  0.399585  0.375939  0.569003  0.510172  0.746580  0.925732  1.019961  1.075334  1.115041  1.128862  1.165960  1.126643  1.013838  0.987942  0.902609  0.639813  0.622235  0.596985  0.560722  0.679951  0.625262  0.629166  0.433738  0.362711  0.445207  0.201266  0.678425  0.575602  1.121024  0.733387  1.123729  1.144169  1.175802  1.101769  1.135540  1.156844  1.081915  1.031565  1.049213  0.549998  0.647454  0.358665  0.318378  0.317924  0.256522  0.276246  0.170722  0.309106  0.776524  0.806378  0.543136  0.513961  0.262635  0.277146  0.307227  0.152853  0.174600 -0.258656 -0.587676 -0.837540 -0.852095 -0.918173 -0.934007 -0.971889 -0.951800 -0.894707 -0.865655 -0.361204  0.295190  0.298881  0.348966  0.712594  0.847759  1.105245  0.767574  0.687253  0.549705  0.017605  0.116268  0.224224 -0.117617  0.083608  0.116503 -0.169557 -0.665352 -0.721639 -0.909171 -0.920019 -1.006865 -0.977589 -0.993678 -0.852889 -0.993323 -0.624806 -0.772725 -0.904012 -0.954455 -0.789103 -0.567302 -0.284030  0.121733  0.276045  1.003112  1.057324  0.915634  1.108207  1.151482  1.008697  0.673427  1.096655  0.546278  0.522155  0.546094  0.539349  0.528124  0.439295 -0.011456  0.164686 -0.026248 -0.128271  0.176938 -0.596483 -0.812919 -0.982666 -0.893843 -0.402562  0.058607 -0.195319  1.106363  1.097482  1.115062  1.105282  1.105248  1.111798  1.138105  0.777900  1.063836  0.705257  0.487440  0.515432  0.377588  0.565240  1.012715  0.823149  0.493144  0.481885  0.528823 -0.012329 -0.206068 -0.051051 -0.140266 -0.178456 -0.640222 -0.928266  1.163938  1.130379  1.191876  1.153562  1.165732  1.135400  0.589141  0.699224  0.521230  0.653195  0.583190  0.686875  0.444597  0.476588  0.395286  0.565806  0.311701 -0.109216 -0.629063 -0.121929 -0.356353 -0.351148 -0.197570 -0.278130  0.259512  0.266899  0.349991  0.402798  0.291827  0.405686  0.385607  0.390651  0.661481  0.688686  0.415846  0.753997  0.734505  0.731541  0.561424  1.122710  1.167100  1.170177  1.205965  1.194113  1.128754  1.121375  1.136376  0.510900  0.329111  0.800015  0.306563 -0.398406 -0.708712 -0.573146 -0.822279 -0.911591 -0.803555 -0.488328 -0.715036 -0.341260  0.507055  0.845152  0.986179  0.896441  0.723974  1.198325  1.088134  1.125834  0.242093  0.167438  0.410867  0.527303  0.130311 -0.168265 -0.644382
        -0.994669 -1.120429 -1.226751 -1.412836 -1.451300 -1.226570 -1.261621 -1.404821 -0.597051 -0.771753 -0.834929 -0.778921 -0.199141  0.054515 -1.114956 -0.542838 -1.114053 -1.125102 -1.037978 -1.065623 -0.967260 -1.157049 -1.304463 -1.067048 -1.308190 -1.304803 -1.374550 -1.359169 -1.110329 -1.019263 -1.185698 -1.316768 -1.252617 -1.365115 -1.321288 -1.354826 -1.350025 -1.289378 -1.232422 -1.248252 -1.127611 -0.944578 -0.657425 -1.229012 -0.629848 -0.535679 -0.761816 -0.832636 -1.035475 -0.831168 -1.117155 -0.965080 -1.274140 -1.210552 -0.945243 -1.182354 -1.185767 -1.193295 -0.939194 -1.248898 -1.251811 -1.198804 -0.971061 -1.214527 -1.272495 -1.270848 -1.182849 -1.135682 -1.219348 -1.010911 -0.952352 -0.397664 -0.261653 -0.231716 -0.186332 -0.101855 -0.059506 -0.689347 -0.640574 -0.673977 -0.591154 -0.891858 -1.120983 -1.274977 -1.053396 -1.192822 -1.207231 -1.265721 -1.310309 -1.330218 -1.316290 -1.315401 -1.340119 -1.180577 -1.116946 -1.236319 -0.985366 -1.141523 -0.983685 -1.164159 -0.993847 -0.524330 -0.538373 -0.678299 -0.515572 -0.217173 -0.078672 -0.330712 -0.220954 -0.132576 -0.111838  0.074623  0.037180  0.159424  0.383785  0.277005  0.336332  0.070913 -0.220526 -0.323483 -0.415765 -0.555200 -0.610588 -0.892801 -0.846285 -0.910076 -1.009465 -0.839512 -1.158540 -1.262739 -1.159559 -0.862278 -0.858226 -1.251243 -1.243986 -1.242577 -1.216361 -1.246796 -1.260598 -1.215635 -1.328905 -1.116114 -1.075576 -1.079749 -1.053416 -0.895050 -0.733837 -1.043576 -0.535074 -0.027196  0.005574  0.141180  0.096395  0.035028  0.198788  0.581689 -0.193742 -0.226674 -0.089924  0.053725 -0.101510  0.046706 -0.422112 -0.342224  0.115002 -0.356620  0.287291  0.394756  0.572766  0.544796  0.572629  0.488832  0.537345  0.303604  0.478967  0.427446  0.344183  0.104724  0.321005  0.149557  0.066772 -0.040346 -0.029817 -0.111837 -0.262909 -0.143687 -0.734934 -0.427171 -1.013285 -1.141422 -0.937857 -1.268051 -1.309919 -1.327867 -1.220957 -1.381780 -1.265859 -1.292874 -0.949992 -0.963083 -1.255938 -1.332638 -1.325951 -1.155997 -1.392882 -1.379020 -1.337625 -1.326546 -1.294843 -0.739386 -0.316363 -0.326717 -0.128261  0.053419  0.109275  0.414879  0.532652  0.601652  0.513170  0.547987  0.534872  0.617988  0.556830  0.622863  0.577342  0.664894  0.672359  0.561510  0.603699  0.600266  0.218813  0.208179  0.170123  0.261526  0.002089 -0.201884 -0.047372 -0.443905 -0.240925 -1.021766  0.513148  0.538661  0.549405  0.561524  0.657353  0.669253  0.599792  0.010287 -0.332839 -0.115550  0.228676  0.480969  0.348463  0.588006  0.543945  0.529086  0.462229  0.080934 -1.418777 -1.393677 -1.278885 -1.251449 -1.159950 -0.870715 -0.374481 -0.460884 -0.192647 -0.014385 -0.109519 -0.024862  0.087316  0.073622  0.000418  0.116688  0.182401  0.172713  0.604328  0.618680  0.638587  0.590717  0.582720  0.563509  0.589238  0.573280  0.537469  0.477744  0.307970  0.404429 -0.054481  0.157808 -0.181208 -0.034842 -0.076520 -0.214658 -0.759734 -0.978301 -0.982101 -1.118432 -1.318279 -1.309515 -1.334603 -1.321889 -1.284773 -1.265483 -1.222187 -1.247508 -1.241139 -1.269724 -1.278217 -1.115954 -1.098814 -0.596811 -1.123652 -0.582556 -0.210329 -0.398178 -0.332151 -0.202180 -0.149063 -0.251292 -0.148831  0.142543  0.410576  0.459440  0.500088  0.523487  0.522603  0.445235  0.523126  0.545234  0.502080  0.375528  0.240827  0.563666  0.588689  0.575435  0.581887  0.602911  0.601241  0.640626  0.593402  0.444809  0.138960  0.093259 -0.040321 -0.051452 -0.186936 -0.102716  0.032025  0.111852  0.578622  0.591378  0.508142  0.560909  0.461791  0.226033 -0.027558 -1.237007 -1.279221 -1.355473 -1.242303 -1.084728 -0.876435 -1.376577 -1.123686 -1.005741 -1.233224 -1.168668 -0.901267 -0.621693 -0.490209 -0.416452 -0.196009 -0.183926  0.020445 -0.236574  0.086111  0.016566 -0.137070 -0.244994  0.044583  0.170925  0.607601  0.522979  0.531151 -0.008133 -0.149988  0.332204  0.015848 -0.262342 -0.478822 -0.892248 -0.629149 -1.137026 -1.013750 -1.080897 -1.161565 -1.066067 -1.199043 -1.148326 -0.925664 -1.143482 -1.236565 -0.923838 -1.080930 -0.646505 -0.150234 -0.515037  0.214112  0.407828 -0.053644 -0.070181 -0.172800 -0.197721 -0.187189 -0.197092 -0.195809 -0.130990 -0.755264 -0.491439 -1.002123 -1.054069 -0.983414 -1.076656 -0.938529 -0.379977 -0.849150 -1.310941 -1.135153 -1.141335 -1.347738 -1.278142 -1.394440 -1.248130 -1.239691 -1.086291 -0.618474 -0.123737 -0.256760 -0.378129 -0.665051 -0.517418 -0.741165 -1.307038 -1.154278 -1.300524 -1.092373 -1.232886 -1.075019 -1.198038 -1.133116 -1.134743 -1.023066 -0.918353 -1.187293 -1.070083 -1.388296 -1.326325 -1.339658 -1.357080 -1.243182 -1.215969 -1.227899 -1.202629 -1.228369 -1.268121 -1.095118 -1.060535 -1.056734 -0.990324 -1.033949 -1.282731 -1.207948 -1.215510 -1.072765 -1.309220 -0.791564 -0.654050 -0.527877 -0.315448 -0.191522 -0.153487 -0.195353 -0.190935 -1.004829 -1.112190 -1.107081 -1.218422 -1.286028 -1.038239 -0.972344 -0.802558 -0.778123 -0.940238 -1.234552 -1.036387 -1.353369 -1.372351 -1.169709 -1.001764 -0.977239 -1.107922 -0.327324 -0.847821 -0.762287 -1.462376 -1.101914 -1.412817 -1.364720 -1.461308 -1.149169 -1.128761
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

%%% Ordered transformation matrices
%Root Node
% Global rotation operator
w1a = [-0.912693 -0.242616 0.328830]';
q1a = [0.0, 0.0, 0.0]';
t1b = twist_matrix_fast(w1a,q1a,sp_coords(4));

% Global translation operator
t1a = twist_matrix_fast(sp_coords(1:3),0,0);

w1c = [0.578426 0.222244 -0.784876]';
q1c = [0.166766 -0.095816 0.408682]';
t1c = twist_matrix_fast(w1c,q1c,Theta(1));

w1d = [-0.815108 0.119747 -0.566798]';
q1d = [0.166766 -0.095816 0.408682]';
t1d = twist_matrix_fast(w1d,q1d,Theta(2));

w1e = [-0.031981 0.967609 0.250418]';
q1e = [0.166766 -0.095816 0.408682]';
t1e = twist_matrix_fast(w1e,q1e,Theta(3));

w4a = [-0.073919 0.948907 0.306777]';
q4a = [0.012602 -0.073168 0.301482]';
t4a = twist_matrix_fast(w4a,q4a,Theta(4));

w4b = [-0.278356 0.275761 -0.920040]';
q4b = [0.012602 -0.073168 0.301482]';
t4b = twist_matrix_fast(w4b,q4b,Theta(5));

w4c = [0.957629 0.153401 -0.243750]';
q4c = [0.012602 -0.073168 0.301482]';
t4c = twist_matrix_fast(w4c,q4c,Theta(6));

w5a = [0.134603 0.959645 0.246908]';
q5a = [-0.039071 -0.021976 0.130688]';
t5a = twist_matrix_fast(w5a,q5a,Theta(7));

w5b = [-0.163397 0.267260 -0.949670]';
q5b = [-0.039071 -0.021976 0.130688]';
t5b = twist_matrix_fast(w5b,q5b,Theta(8));

w5c = [0.977335 -0.087484 -0.192777]';
q5c = [-0.039071 -0.021976 0.130688]';
t5c = twist_matrix_fast(w5c,q5c,Theta(9));

w6a = [-0.265878 0.915062 0.303267]';
q6a = [-0.073871 0.034944 -0.071569]';
t6a = twist_matrix_fast(w6a,q6a,Theta(10));

w6b = [-0.330813 0.208879 -0.920289]';
q6b = [-0.073871 0.034944 -0.071569]';
t6b = twist_matrix_fast(w6b,q6b,Theta(11));

w6c = [0.905468 0.345010 -0.247178]';
q6c = [-0.073871 0.034944 -0.071569]';
t6c = twist_matrix_fast(w6c,q6c,Theta(12));

w7a = [0.026383 0.976862 0.212235]';
q7a = [-0.132058 0.071684 -0.233441]';
t7a = twist_matrix_fast(w7a,q7a,Theta(13));

w7b = [-0.589389 0.186683 -0.785983]';
q7b = [-0.132058 0.071684 -0.233441]';
t7b = twist_matrix_fast(w7b,q7b,Theta(14));

w7c = [0.807418 0.104353 -0.580677]';
q7c = [-0.132058 0.071684 -0.233441]';
t7c = twist_matrix_fast(w7c,q7c,Theta(15));

w8a = [-0.034875 0.966146 0.255626]';
q8a = [-0.182555 0.087679 -0.300782]';
t8a = twist_matrix_fast(w8a,q8a,Theta(16));

w8b = [0.670875 0.212218 -0.710557]';
q8b = [-0.182555 0.087679 -0.300782]';
t8b = twist_matrix_fast(w8b,q8b,Theta(17));

w8c = [0.740750 -0.146712 0.655564]';
q8c = [-0.182555 0.087679 -0.300782]';
t8c = twist_matrix_fast(w8c,q8c,Theta(18));

%%% Construct kinematic chains of transformations
% Generate new_config and new_norms
U1 = t1a*t1b*t1c*t1d*t1e*I1;
V1 = t1a*t1b*t1c*t1d*t1e*N1;
V1 = V1-U1;

U4 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*I4;
V4 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*N4;
V4 = V4-U4;

U5 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*I5;
V5 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*N5;
V5 = V5-U5;

U6 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*I6;
V6 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*N6;
V6 = V6-U6;

U8 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*t8a*t8b*t8c*I8;
V8 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*t8a*t8b*t8c*N8;
V8 = V8-U8;

%%% Construct complete update
new_config = [U1(1:3,:) U4(1:3,:) U5(1:3,:) U6(1:3,:) U8(1:3,:)];
new_norms  = [V1(1:3,:) V4(1:3,:) V5(1:3,:) V6(1:3,:) V8(1:3,:)];

% Update center of mass estimate
new_ctrm = mean(new_config,2);

%%% Twist matrix function
function [twist] = twist_matrix_fast(w,q,theta)
% Overview:
% This code generates an exponential map matrix for rotation and translation
% using the Rodrigues' formula for the matrix exponential, from "A Mathematical 
% Introduction to Robotic Manipulation" by Murray, Li, and Sastry (1994) p. 28. 
% The equation for the exponential map for twists is from Ibid. 42.
%
% This code has very little error checking to increase speed.
%
% [twist] = twist_matrix_fast(w,q,theta)
% INPUTS %
% w: a 3d vector pointing: 1) in the direction of translation or 2) 
%      along the axis of rotation relative to the origin.
% q: a 3d point along the axis of rotation, providing the offset
% theta: the amount of rotation, in radians
%
% OUTPUTS %
% twist: the resulting matrix for left multiplication
%
% I treat 2 cases: 1) pure translation and 2) pure rotation
if numel(q) < 3 && (q == 0 || theta == 0)
    
    % we want column vectors
    if size(w,1)<size(w,2)
        w = w';
    end
    
    % 1) pure translation
	% pure translation in absolute frame
	twist = [eye(3) w;zeros(1,3) 1];
else
    % 2) pure rotation twist
    % correct for case where w is the origin
    if sum(w) == 0
        w = q;
        W = 0;
    else
        W = 1;
    end
    
    % Generate cross product operator so(3)
    w_hat = [0   -w(3) w(2);
             w(3) 0   -w(1);
            -w(2) w(1) 0];
    
    v = -w_hat*q;
    % Generate rotation matrix using the Rodrigues' equation pg. 28
    Id3x3  = eye(3);
    w_hat2 = w*w'-W*Id3x3;
    R      = Id3x3+w_hat*sin(theta)+w_hat2*(1-cos(theta));
    
    % Generate relative frame twist, pg. 42
    twist  = [R (Id3x3-R)*w_hat*v+w*w'*v*theta;
              zeros(1,3) 1];
end
