Character table for the D72d point group

D72d    E         2 S144    2 C72     2 S48     2 C36     2 S144^5  2 C24     2 S144^7  2 C18     2 S16     2 C72^5   2 S144^11 2 C12     2 S144^13 2 C72^7   2 S48^5   2 C9      2 S144^17 2 C8      2 S144^19 2 C36^5   2 S48^7   2 C72^11  2 S144^23 2 C6      2 S144^25 2 C72^13  2 S16^3   2 C36^7   2 S144^29 2 C24^5   2 S144^31 2 C9^2    2 S48^11  2 C72^17  2 S144^35 2 C4      2 S144^37 2 C72^19  2 S48^13  2 C18^5   2 S144^41 2 C24^7   2 S144^43 2 C36^11  2 S16^5   2 C72^23  2 S144^47 2 C3      2 S144^49 2 C72^25  2 S48^17  2 C36^13  2 S144^53 2 C8^3    2 S144^55 2 C18^7   2 S48^19  2 C72^29  2 S144^59 2 C12^5   2 S144^61 2 C72^31  2 S16^7   2 C9^4    2 S144^65 2 C24^11  2 S144^67 2 C36^17  2 S48^23  2 C72^35  2 S144^71 C2        72 C2'    72 sd        <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A1       1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000     ... ... ....T ....... ........T ........... ............T
A2       1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000  -1.00000  -1.00000     ..T ... ..... ....... ......... ........... .............
B1       1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000   1.00000  -1.00000     ... ... ..... ....... ......... ........... .............
B2       1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000     ... ..T ..... ......T ......... ..........T .............
E1       2.00000   1.99810   1.99239   1.98289   1.96962   1.95259   1.93185   1.90743   1.87939   1.84776   1.81262   1.77402   1.73205   1.68678   1.63830   1.58671   1.53209   1.47455   1.41421   1.35118   1.28558   1.21752   1.14715   1.07460   1.00000   0.92350   0.84524   0.76537   0.68404   0.60141   0.51764   0.43288   0.34730   0.26105   0.17431   0.08724   0.00000  -0.08724  -0.17431  -0.26105  -0.34730  -0.43288  -0.51764  -0.60141  -0.68404  -0.76537  -0.84524  -0.92350  -1.00000  -1.07460  -1.14715  -1.21752  -1.28558  -1.35118  -1.41421  -1.47455  -1.53209  -1.58671  -1.63830  -1.68678  -1.73205  -1.77402  -1.81262  -1.84776  -1.87939  -1.90743  -1.93185  -1.95259  -1.96962  -1.98289  -1.99239  -1.99810  -2.00000   0.00000   0.00000     ... TT. ..... ....TT. ......... ........TT. .............
E2       2.00000   1.99239   1.96962   1.93185   1.87939   1.81262   1.73205   1.63830   1.53209   1.41421   1.28558   1.14715   1.00000   0.84524   0.68404   0.51764   0.34730   0.17431   0.00000  -0.17431  -0.34730  -0.51764  -0.68404  -0.84524  -1.00000  -1.14715  -1.28558  -1.41421  -1.53209  -1.63830  -1.73205  -1.81262  -1.87939  -1.93185  -1.96962  -1.99239  -2.00000  -1.99239  -1.96962  -1.93185  -1.87939  -1.81262  -1.73205  -1.63830  -1.53209  -1.41421  -1.28558  -1.14715  -1.00000  -0.84524  -0.68404  -0.51764  -0.34730  -0.17431   0.00000   0.17431   0.34730   0.51764   0.68404   0.84524   1.00000   1.14715   1.28558   1.41421   1.53209   1.63830   1.73205   1.81262   1.87939   1.93185   1.96962   1.99239   2.00000   0.00000   0.00000     ... ... TT... ....... ....TT... ........... ........TT...
E3       2.00000   1.98289   1.93185   1.84776   1.73205   1.58671   1.41421   1.21752   1.00000   0.76537   0.51764   0.26105   0.00000  -0.26105  -0.51764  -0.76537  -1.00000  -1.21752  -1.41421  -1.58671  -1.73205  -1.84776  -1.93185  -1.98289  -2.00000  -1.98289  -1.93185  -1.84776  -1.73205  -1.58671  -1.41421  -1.21752  -1.00000  -0.76537  -0.51764  -0.26105   0.00000   0.26105   0.51764   0.76537   1.00000   1.21752   1.41421   1.58671   1.73205   1.84776   1.93185   1.98289   2.00000   1.98289   1.93185   1.84776   1.73205   1.58671   1.41421   1.21752   1.00000   0.76537   0.51764   0.26105   0.00000  -0.26105  -0.51764  -0.76537  -1.00000  -1.21752  -1.41421  -1.58671  -1.73205  -1.84776  -1.93185  -1.98289  -2.00000   0.00000   0.00000     ... ... ..... TT..... ......... ....TT..... .............
E4       2.00000   1.96962   1.87939   1.73205   1.53209   1.28558   1.00000   0.68404   0.34730   0.00000  -0.34730  -0.68404  -1.00000  -1.28558  -1.53209  -1.73205  -1.87939  -1.96962  -2.00000  -1.96962  -1.87939  -1.73205  -1.53209  -1.28558  -1.00000  -0.68404  -0.34730   0.00000   0.34730   0.68404   1.00000   1.28558   1.53209   1.73205   1.87939   1.96962   2.00000   1.96962   1.87939   1.73205   1.53209   1.28558   1.00000   0.68404   0.34730   0.00000  -0.34730  -0.68404  -1.00000  -1.28558  -1.53209  -1.73205  -1.87939  -1.96962  -2.00000  -1.96962  -1.87939  -1.73205  -1.53209  -1.28558  -1.00000  -0.68404  -0.34730   0.00000   0.34730   0.68404   1.00000   1.28558   1.53209   1.73205   1.87939   1.96962   2.00000   0.00000   0.00000     ... ... ..... ....... TT....... ........... ....TT.......
E5       2.00000   1.95259   1.81262   1.58671   1.28558   0.92350   0.51764   0.08724  -0.34730  -0.76537  -1.14715  -1.47455  -1.73205  -1.90743  -1.99239  -1.98289  -1.87939  -1.68678  -1.41421  -1.07460  -0.68404  -0.26105   0.17431   0.60141   1.00000   1.35118   1.63830   1.84776   1.96962   1.99810   1.93185   1.77402   1.53209   1.21752   0.84524   0.43288   0.00000  -0.43288  -0.84524  -1.21752  -1.53209  -1.77402  -1.93185  -1.99810  -1.96962  -1.84776  -1.63830  -1.35118  -1.00000  -0.60141  -0.17431   0.26105   0.68404   1.07460   1.41421   1.68678   1.87939   1.98289   1.99239   1.90743   1.73205   1.47455   1.14715   0.76537   0.34730  -0.08724  -0.51764  -0.92350  -1.28558  -1.58671  -1.81262  -1.95259  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... TT......... .............
E6       2.00000   1.93185   1.73205   1.41421   1.00000   0.51764   0.00000  -0.51764  -1.00000  -1.41421  -1.73205  -1.93185  -2.00000  -1.93185  -1.73205  -1.41421  -1.00000  -0.51764   0.00000   0.51764   1.00000   1.41421   1.73205   1.93185   2.00000   1.93185   1.73205   1.41421   1.00000   0.51764   0.00000  -0.51764  -1.00000  -1.41421  -1.73205  -1.93185  -2.00000  -1.93185  -1.73205  -1.41421  -1.00000  -0.51764   0.00000   0.51764   1.00000   1.41421   1.73205   1.93185   2.00000   1.93185   1.73205   1.41421   1.00000   0.51764   0.00000  -0.51764  -1.00000  -1.41421  -1.73205  -1.93185  -2.00000  -1.93185  -1.73205  -1.41421  -1.00000  -0.51764   0.00000   0.51764   1.00000   1.41421   1.73205   1.93185   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... TT...........
E7       2.00000   1.90743   1.63830   1.21752   0.68404   0.08724  -0.51764  -1.07460  -1.53209  -1.84776  -1.99239  -1.95259  -1.73205  -1.35118  -0.84524  -0.26105   0.34730   0.92350   1.41421   1.77402   1.96962   1.98289   1.81262   1.47455   1.00000   0.43288  -0.17431  -0.76537  -1.28558  -1.68678  -1.93185  -1.99810  -1.87939  -1.58671  -1.14715  -0.60141   0.00000   0.60141   1.14715   1.58671   1.87939   1.99810   1.93185   1.68678   1.28558   0.76537   0.17431  -0.43288  -1.00000  -1.47455  -1.81262  -1.98289  -1.96962  -1.77402  -1.41421  -0.92350  -0.34730   0.26105   0.84524   1.35118   1.73205   1.95259   1.99239   1.84776   1.53209   1.07460   0.51764  -0.08724  -0.68404  -1.21752  -1.63830  -1.90743  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E8       2.00000   1.87939   1.53209   1.00000   0.34730  -0.34730  -1.00000  -1.53209  -1.87939  -2.00000  -1.87939  -1.53209  -1.00000  -0.34730   0.34730   1.00000   1.53209   1.87939   2.00000   1.87939   1.53209   1.00000   0.34730  -0.34730  -1.00000  -1.53209  -1.87939  -2.00000  -1.87939  -1.53209  -1.00000  -0.34730   0.34730   1.00000   1.53209   1.87939   2.00000   1.87939   1.53209   1.00000   0.34730  -0.34730  -1.00000  -1.53209  -1.87939  -2.00000  -1.87939  -1.53209  -1.00000  -0.34730   0.34730   1.00000   1.53209   1.87939   2.00000   1.87939   1.53209   1.00000   0.34730  -0.34730  -1.00000  -1.53209  -1.87939  -2.00000  -1.87939  -1.53209  -1.00000  -0.34730   0.34730   1.00000   1.53209   1.87939   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E9       2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E10      2.00000   1.81262   1.28558   0.51764  -0.34730  -1.14715  -1.73205  -1.99239  -1.87939  -1.41421  -0.68404   0.17431   1.00000   1.63830   1.96962   1.93185   1.53209   0.84524   0.00000  -0.84524  -1.53209  -1.93185  -1.96962  -1.63830  -1.00000  -0.17431   0.68404   1.41421   1.87939   1.99239   1.73205   1.14715   0.34730  -0.51764  -1.28558  -1.81262  -2.00000  -1.81262  -1.28558  -0.51764   0.34730   1.14715   1.73205   1.99239   1.87939   1.41421   0.68404  -0.17431  -1.00000  -1.63830  -1.96962  -1.93185  -1.53209  -0.84524   0.00000   0.84524   1.53209   1.93185   1.96962   1.63830   1.00000   0.17431  -0.68404  -1.41421  -1.87939  -1.99239  -1.73205  -1.14715  -0.34730   0.51764   1.28558   1.81262   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E11      2.00000   1.77402   1.14715   0.26105  -0.68404  -1.47455  -1.93185  -1.95259  -1.53209  -0.76537   0.17431   1.07460   1.73205   1.99810   1.81262   1.21752   0.34730  -0.60141  -1.41421  -1.90743  -1.96962  -1.58671  -0.84524   0.08724   1.00000   1.68678   1.99239   1.84776   1.28558   0.43288  -0.51764  -1.35118  -1.87939  -1.98289  -1.63830  -0.92350   0.00000   0.92350   1.63830   1.98289   1.87939   1.35118   0.51764  -0.43288  -1.28558  -1.84776  -1.99239  -1.68678  -1.00000  -0.08724   0.84524   1.58671   1.96962   1.90743   1.41421   0.60141  -0.34730  -1.21752  -1.81262  -1.99810  -1.73205  -1.07460  -0.17431   0.76537   1.53209   1.95259   1.93185   1.47455   0.68404  -0.26105  -1.14715  -1.77402  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E12      2.00000   1.73205   1.00000   0.00000  -1.00000  -1.73205  -2.00000  -1.73205  -1.00000   0.00000   1.00000   1.73205   2.00000   1.73205   1.00000   0.00000  -1.00000  -1.73205  -2.00000  -1.73205  -1.00000   0.00000   1.00000   1.73205   2.00000   1.73205   1.00000   0.00000  -1.00000  -1.73205  -2.00000  -1.73205  -1.00000   0.00000   1.00000   1.73205   2.00000   1.73205   1.00000   0.00000  -1.00000  -1.73205  -2.00000  -1.73205  -1.00000   0.00000   1.00000   1.73205   2.00000   1.73205   1.00000   0.00000  -1.00000  -1.73205  -2.00000  -1.73205  -1.00000   0.00000   1.00000   1.73205   2.00000   1.73205   1.00000   0.00000  -1.00000  -1.73205  -2.00000  -1.73205  -1.00000   0.00000   1.00000   1.73205   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E13      2.00000   1.68678   0.84524  -0.26105  -1.28558  -1.90743  -1.93185  -1.35118  -0.34730   0.76537   1.63830   1.99810   1.73205   0.92350  -0.17431  -1.21752  -1.87939  -1.95259  -1.41421  -0.43288   0.68404   1.58671   1.99239   1.77402   1.00000  -0.08724  -1.14715  -1.84776  -1.96962  -1.47455  -0.51764   0.60141   1.53209   1.98289   1.81262   1.07460   0.00000  -1.07460  -1.81262  -1.98289  -1.53209  -0.60141   0.51764   1.47455   1.96962   1.84776   1.14715   0.08724  -1.00000  -1.77402  -1.99239  -1.58671  -0.68404   0.43288   1.41421   1.95259   1.87939   1.21752   0.17431  -0.92350  -1.73205  -1.99810  -1.63830  -0.76537   0.34730   1.35118   1.93185   1.90743   1.28558   0.26105  -0.84524  -1.68678  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E14      2.00000   1.63830   0.68404  -0.51764  -1.53209  -1.99239  -1.73205  -0.84524   0.34730   1.41421   1.96962   1.81262   1.00000  -0.17431  -1.28558  -1.93185  -1.87939  -1.14715   0.00000   1.14715   1.87939   1.93185   1.28558   0.17431  -1.00000  -1.81262  -1.96962  -1.41421  -0.34730   0.84524   1.73205   1.99239   1.53209   0.51764  -0.68404  -1.63830  -2.00000  -1.63830  -0.68404   0.51764   1.53209   1.99239   1.73205   0.84524  -0.34730  -1.41421  -1.96962  -1.81262  -1.00000   0.17431   1.28558   1.93185   1.87939   1.14715   0.00000  -1.14715  -1.87939  -1.93185  -1.28558  -0.17431   1.00000   1.81262   1.96962   1.41421   0.34730  -0.84524  -1.73205  -1.99239  -1.53209  -0.51764   0.68404   1.63830   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E15      2.00000   1.58671   0.51764  -0.76537  -1.73205  -1.98289  -1.41421  -0.26105   1.00000   1.84776   1.93185   1.21752   0.00000  -1.21752  -1.93185  -1.84776  -1.00000   0.26105   1.41421   1.98289   1.73205   0.76537  -0.51764  -1.58671  -2.00000  -1.58671  -0.51764   0.76537   1.73205   1.98289   1.41421   0.26105  -1.00000  -1.84776  -1.93185  -1.21752   0.00000   1.21752   1.93185   1.84776   1.00000  -0.26105  -1.41421  -1.98289  -1.73205  -0.76537   0.51764   1.58671   2.00000   1.58671   0.51764  -0.76537  -1.73205  -1.98289  -1.41421  -0.26105   1.00000   1.84776   1.93185   1.21752   0.00000  -1.21752  -1.93185  -1.84776  -1.00000   0.26105   1.41421   1.98289   1.73205   0.76537  -0.51764  -1.58671  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E16      2.00000   1.53209   0.34730  -1.00000  -1.87939  -1.87939  -1.00000   0.34730   1.53209   2.00000   1.53209   0.34730  -1.00000  -1.87939  -1.87939  -1.00000   0.34730   1.53209   2.00000   1.53209   0.34730  -1.00000  -1.87939  -1.87939  -1.00000   0.34730   1.53209   2.00000   1.53209   0.34730  -1.00000  -1.87939  -1.87939  -1.00000   0.34730   1.53209   2.00000   1.53209   0.34730  -1.00000  -1.87939  -1.87939  -1.00000   0.34730   1.53209   2.00000   1.53209   0.34730  -1.00000  -1.87939  -1.87939  -1.00000   0.34730   1.53209   2.00000   1.53209   0.34730  -1.00000  -1.87939  -1.87939  -1.00000   0.34730   1.53209   2.00000   1.53209   0.34730  -1.00000  -1.87939  -1.87939  -1.00000   0.34730   1.53209   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E17      2.00000   1.47455   0.17431  -1.21752  -1.96962  -1.68678  -0.51764   0.92350   1.87939   1.84776   0.84524  -0.60141  -1.73205  -1.95259  -1.14715   0.26105   1.53209   1.99810   1.41421   0.08724  -1.28558  -1.98289  -1.63830  -0.43288   1.00000   1.90743   1.81262   0.76537  -0.68404  -1.77402  -1.93185  -1.07460   0.34730   1.58671   1.99239   1.35118   0.00000  -1.35118  -1.99239  -1.58671  -0.34730   1.07460   1.93185   1.77402   0.68404  -0.76537  -1.81262  -1.90743  -1.00000   0.43288   1.63830   1.98289   1.28558  -0.08724  -1.41421  -1.99810  -1.53209  -0.26105   1.14715   1.95259   1.73205   0.60141  -0.84524  -1.84776  -1.87939  -0.92350   0.51764   1.68678   1.96962   1.21752  -0.17431  -1.47455  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E18      2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E19      2.00000   1.35118  -0.17431  -1.58671  -1.96962  -1.07460   0.51764   1.77402   1.87939   0.76537  -0.84524  -1.90743  -1.73205  -0.43288   1.14715   1.98289   1.53209   0.08724  -1.41421  -1.99810  -1.28558   0.26105   1.63830   1.95259   1.00000  -0.60141  -1.81262  -1.84776  -0.68404   0.92350   1.93185   1.68678   0.34730  -1.21752  -1.99239  -1.47455   0.00000   1.47455   1.99239   1.21752  -0.34730  -1.68678  -1.93185  -0.92350   0.68404   1.84776   1.81262   0.60141  -1.00000  -1.95259  -1.63830  -0.26105   1.28558   1.99810   1.41421  -0.08724  -1.53209  -1.98289  -1.14715   0.43288   1.73205   1.90743   0.84524  -0.76537  -1.87939  -1.77402  -0.51764   1.07460   1.96962   1.58671   0.17431  -1.35118  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E20      2.00000   1.28558  -0.34730  -1.73205  -1.87939  -0.68404   1.00000   1.96962   1.53209   0.00000  -1.53209  -1.96962  -1.00000   0.68404   1.87939   1.73205   0.34730  -1.28558  -2.00000  -1.28558   0.34730   1.73205   1.87939   0.68404  -1.00000  -1.96962  -1.53209   0.00000   1.53209   1.96962   1.00000  -0.68404  -1.87939  -1.73205  -0.34730   1.28558   2.00000   1.28558  -0.34730  -1.73205  -1.87939  -0.68404   1.00000   1.96962   1.53209   0.00000  -1.53209  -1.96962  -1.00000   0.68404   1.87939   1.73205   0.34730  -1.28558  -2.00000  -1.28558   0.34730   1.73205   1.87939   0.68404  -1.00000  -1.96962  -1.53209   0.00000   1.53209   1.96962   1.00000  -0.68404  -1.87939  -1.73205  -0.34730   1.28558   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E21      2.00000   1.21752  -0.51764  -1.84776  -1.73205  -0.26105   1.41421   1.98289   1.00000  -0.76537  -1.93185  -1.58671   0.00000   1.58671   1.93185   0.76537  -1.00000  -1.98289  -1.41421   0.26105   1.73205   1.84776   0.51764  -1.21752  -2.00000  -1.21752   0.51764   1.84776   1.73205   0.26105  -1.41421  -1.98289  -1.00000   0.76537   1.93185   1.58671   0.00000  -1.58671  -1.93185  -0.76537   1.00000   1.98289   1.41421  -0.26105  -1.73205  -1.84776  -0.51764   1.21752   2.00000   1.21752  -0.51764  -1.84776  -1.73205  -0.26105   1.41421   1.98289   1.00000  -0.76537  -1.93185  -1.58671   0.00000   1.58671   1.93185   0.76537  -1.00000  -1.98289  -1.41421   0.26105   1.73205   1.84776   0.51764  -1.21752  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E22      2.00000   1.14715  -0.68404  -1.93185  -1.53209   0.17431   1.73205   1.81262   0.34730  -1.41421  -1.96962  -0.84524   1.00000   1.99239   1.28558  -0.51764  -1.87939  -1.63830   0.00000   1.63830   1.87939   0.51764  -1.28558  -1.99239  -1.00000   0.84524   1.96962   1.41421  -0.34730  -1.81262  -1.73205  -0.17431   1.53209   1.93185   0.68404  -1.14715  -2.00000  -1.14715   0.68404   1.93185   1.53209  -0.17431  -1.73205  -1.81262  -0.34730   1.41421   1.96962   0.84524  -1.00000  -1.99239  -1.28558   0.51764   1.87939   1.63830   0.00000  -1.63830  -1.87939  -0.51764   1.28558   1.99239   1.00000  -0.84524  -1.96962  -1.41421   0.34730   1.81262   1.73205   0.17431  -1.53209  -1.93185  -0.68404   1.14715   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E23      2.00000   1.07460  -0.84524  -1.98289  -1.28558   0.60141   1.93185   1.47455  -0.34730  -1.84776  -1.63830   0.08724   1.73205   1.77402   0.17431  -1.58671  -1.87939  -0.43288   1.41421   1.95259   0.68404  -1.21752  -1.99239  -0.92350   1.00000   1.99810   1.14715  -0.76537  -1.96962  -1.35118   0.51764   1.90743   1.53209  -0.26105  -1.81262  -1.68678   0.00000   1.68678   1.81262   0.26105  -1.53209  -1.90743  -0.51764   1.35118   1.96962   0.76537  -1.14715  -1.99810  -1.00000   0.92350   1.99239   1.21752  -0.68404  -1.95259  -1.41421   0.43288   1.87939   1.58671  -0.17431  -1.77402  -1.73205  -0.08724   1.63830   1.84776   0.34730  -1.47455  -1.93185  -0.60141   1.28558   1.98289   0.84524  -1.07460  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E24      2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E25      2.00000   0.92350  -1.14715  -1.98289  -0.68404   1.35118   1.93185   0.43288  -1.53209  -1.84776  -0.17431   1.68678   1.73205  -0.08724  -1.81262  -1.58671   0.34730   1.90743   1.41421  -0.60141  -1.96962  -1.21752   0.84524   1.99810   1.00000  -1.07460  -1.99239  -0.76537   1.28558   1.95259   0.51764  -1.47455  -1.87939  -0.26105   1.63830   1.77402   0.00000  -1.77402  -1.63830   0.26105   1.87939   1.47455  -0.51764  -1.95259  -1.28558   0.76537   1.99239   1.07460  -1.00000  -1.99810  -0.84524   1.21752   1.96962   0.60141  -1.41421  -1.90743  -0.34730   1.58671   1.81262   0.08724  -1.73205  -1.68678   0.17431   1.84776   1.53209  -0.43288  -1.93185  -1.35118   0.68404   1.98289   1.14715  -0.92350  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E26      2.00000   0.84524  -1.28558  -1.93185  -0.34730   1.63830   1.73205  -0.17431  -1.87939  -1.41421   0.68404   1.99239   1.00000  -1.14715  -1.96962  -0.51764   1.53209   1.81262   0.00000  -1.81262  -1.53209   0.51764   1.96962   1.14715  -1.00000  -1.99239  -0.68404   1.41421   1.87939   0.17431  -1.73205  -1.63830   0.34730   1.93185   1.28558  -0.84524  -2.00000  -0.84524   1.28558   1.93185   0.34730  -1.63830  -1.73205   0.17431   1.87939   1.41421  -0.68404  -1.99239  -1.00000   1.14715   1.96962   0.51764  -1.53209  -1.81262   0.00000   1.81262   1.53209  -0.51764  -1.96962  -1.14715   1.00000   1.99239   0.68404  -1.41421  -1.87939  -0.17431   1.73205   1.63830  -0.34730  -1.93185  -1.28558   0.84524   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E27      2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E28      2.00000   0.68404  -1.53209  -1.73205   0.34730   1.96962   1.00000  -1.28558  -1.87939   0.00000   1.87939   1.28558  -1.00000  -1.96962  -0.34730   1.73205   1.53209  -0.68404  -2.00000  -0.68404   1.53209   1.73205  -0.34730  -1.96962  -1.00000   1.28558   1.87939   0.00000  -1.87939  -1.28558   1.00000   1.96962   0.34730  -1.73205  -1.53209   0.68404   2.00000   0.68404  -1.53209  -1.73205   0.34730   1.96962   1.00000  -1.28558  -1.87939   0.00000   1.87939   1.28558  -1.00000  -1.96962  -0.34730   1.73205   1.53209  -0.68404  -2.00000  -0.68404   1.53209   1.73205  -0.34730  -1.96962  -1.00000   1.28558   1.87939   0.00000  -1.87939  -1.28558   1.00000   1.96962   0.34730  -1.73205  -1.53209   0.68404   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E29      2.00000   0.60141  -1.63830  -1.58671   0.68404   1.99810   0.51764  -1.68678  -1.53209   0.76537   1.99239   0.43288  -1.73205  -1.47455   0.84524   1.98289   0.34730  -1.77402  -1.41421   0.92350   1.96962   0.26105  -1.81262  -1.35118   1.00000   1.95259   0.17431  -1.84776  -1.28558   1.07460   1.93185   0.08724  -1.87939  -1.21752   1.14715   1.90743   0.00000  -1.90743  -1.14715   1.21752   1.87939  -0.08724  -1.93185  -1.07460   1.28558   1.84776  -0.17431  -1.95259  -1.00000   1.35118   1.81262  -0.26105  -1.96962  -0.92350   1.41421   1.77402  -0.34730  -1.98289  -0.84524   1.47455   1.73205  -0.43288  -1.99239  -0.76537   1.53209   1.68678  -0.51764  -1.99810  -0.68404   1.58671   1.63830  -0.60141  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E30      2.00000   0.51764  -1.73205  -1.41421   1.00000   1.93185   0.00000  -1.93185  -1.00000   1.41421   1.73205  -0.51764  -2.00000  -0.51764   1.73205   1.41421  -1.00000  -1.93185   0.00000   1.93185   1.00000  -1.41421  -1.73205   0.51764   2.00000   0.51764  -1.73205  -1.41421   1.00000   1.93185   0.00000  -1.93185  -1.00000   1.41421   1.73205  -0.51764  -2.00000  -0.51764   1.73205   1.41421  -1.00000  -1.93185   0.00000   1.93185   1.00000  -1.41421  -1.73205   0.51764   2.00000   0.51764  -1.73205  -1.41421   1.00000   1.93185   0.00000  -1.93185  -1.00000   1.41421   1.73205  -0.51764  -2.00000  -0.51764   1.73205   1.41421  -1.00000  -1.93185   0.00000   1.93185   1.00000  -1.41421  -1.73205   0.51764   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E31      2.00000   0.43288  -1.81262  -1.21752   1.28558   1.77402  -0.51764  -1.99810  -0.34730   1.84776   1.14715  -1.35118  -1.73205   0.60141   1.99239   0.26105  -1.87939  -1.07460   1.41421   1.68678  -0.68404  -1.98289  -0.17431   1.90743   1.00000  -1.47455  -1.63830   0.76537   1.96962   0.08724  -1.93185  -0.92350   1.53209   1.58671  -0.84524  -1.95259   0.00000   1.95259   0.84524  -1.58671  -1.53209   0.92350   1.93185  -0.08724  -1.96962  -0.76537   1.63830   1.47455  -1.00000  -1.90743   0.17431   1.98289   0.68404  -1.68678  -1.41421   1.07460   1.87939  -0.26105  -1.99239  -0.60141   1.73205   1.35118  -1.14715  -1.84776   0.34730   1.99810   0.51764  -1.77402  -1.28558   1.21752   1.81262  -0.43288  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E32      2.00000   0.34730  -1.87939  -1.00000   1.53209   1.53209  -1.00000  -1.87939   0.34730   2.00000   0.34730  -1.87939  -1.00000   1.53209   1.53209  -1.00000  -1.87939   0.34730   2.00000   0.34730  -1.87939  -1.00000   1.53209   1.53209  -1.00000  -1.87939   0.34730   2.00000   0.34730  -1.87939  -1.00000   1.53209   1.53209  -1.00000  -1.87939   0.34730   2.00000   0.34730  -1.87939  -1.00000   1.53209   1.53209  -1.00000  -1.87939   0.34730   2.00000   0.34730  -1.87939  -1.00000   1.53209   1.53209  -1.00000  -1.87939   0.34730   2.00000   0.34730  -1.87939  -1.00000   1.53209   1.53209  -1.00000  -1.87939   0.34730   2.00000   0.34730  -1.87939  -1.00000   1.53209   1.53209  -1.00000  -1.87939   0.34730   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
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E50      2.00000  -1.14715  -0.68404   1.93185  -1.53209  -0.17431   1.73205  -1.81262   0.34730   1.41421  -1.96962   0.84524   1.00000  -1.99239   1.28558   0.51764  -1.87939   1.63830   0.00000  -1.63830   1.87939  -0.51764  -1.28558   1.99239  -1.00000  -0.84524   1.96962  -1.41421  -0.34730   1.81262  -1.73205   0.17431   1.53209  -1.93185   0.68404   1.14715  -2.00000   1.14715   0.68404  -1.93185   1.53209   0.17431  -1.73205   1.81262  -0.34730  -1.41421   1.96962  -0.84524  -1.00000   1.99239  -1.28558  -0.51764   1.87939  -1.63830   0.00000   1.63830  -1.87939   0.51764   1.28558  -1.99239   1.00000   0.84524  -1.96962   1.41421   0.34730  -1.81262   1.73205  -0.17431  -1.53209   1.93185  -0.68404  -1.14715   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E51      2.00000  -1.21752  -0.51764   1.84776  -1.73205   0.26105   1.41421  -1.98289   1.00000   0.76537  -1.93185   1.58671   0.00000  -1.58671   1.93185  -0.76537  -1.00000   1.98289  -1.41421  -0.26105   1.73205  -1.84776   0.51764   1.21752  -2.00000   1.21752   0.51764  -1.84776   1.73205  -0.26105  -1.41421   1.98289  -1.00000  -0.76537   1.93185  -1.58671   0.00000   1.58671  -1.93185   0.76537   1.00000  -1.98289   1.41421   0.26105  -1.73205   1.84776  -0.51764  -1.21752   2.00000  -1.21752  -0.51764   1.84776  -1.73205   0.26105   1.41421  -1.98289   1.00000   0.76537  -1.93185   1.58671   0.00000  -1.58671   1.93185  -0.76537  -1.00000   1.98289  -1.41421  -0.26105   1.73205  -1.84776   0.51764   1.21752  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E52      2.00000  -1.28558  -0.34730   1.73205  -1.87939   0.68404   1.00000  -1.96962   1.53209   0.00000  -1.53209   1.96962  -1.00000  -0.68404   1.87939  -1.73205   0.34730   1.28558  -2.00000   1.28558   0.34730  -1.73205   1.87939  -0.68404  -1.00000   1.96962  -1.53209   0.00000   1.53209  -1.96962   1.00000   0.68404  -1.87939   1.73205  -0.34730  -1.28558   2.00000  -1.28558  -0.34730   1.73205  -1.87939   0.68404   1.00000  -1.96962   1.53209   0.00000  -1.53209   1.96962  -1.00000  -0.68404   1.87939  -1.73205   0.34730   1.28558  -2.00000   1.28558   0.34730  -1.73205   1.87939  -0.68404  -1.00000   1.96962  -1.53209   0.00000   1.53209  -1.96962   1.00000   0.68404  -1.87939   1.73205  -0.34730  -1.28558   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E53      2.00000  -1.35118  -0.17431   1.58671  -1.96962   1.07460   0.51764  -1.77402   1.87939  -0.76537  -0.84524   1.90743  -1.73205   0.43288   1.14715  -1.98289   1.53209  -0.08724  -1.41421   1.99810  -1.28558  -0.26105   1.63830  -1.95259   1.00000   0.60141  -1.81262   1.84776  -0.68404  -0.92350   1.93185  -1.68678   0.34730   1.21752  -1.99239   1.47455   0.00000  -1.47455   1.99239  -1.21752  -0.34730   1.68678  -1.93185   0.92350   0.68404  -1.84776   1.81262  -0.60141  -1.00000   1.95259  -1.63830   0.26105   1.28558  -1.99810   1.41421   0.08724  -1.53209   1.98289  -1.14715  -0.43288   1.73205  -1.90743   0.84524   0.76537  -1.87939   1.77402  -0.51764  -1.07460   1.96962  -1.58671   0.17431   1.35118  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E54      2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E55      2.00000  -1.47455   0.17431   1.21752  -1.96962   1.68678  -0.51764  -0.92350   1.87939  -1.84776   0.84524   0.60141  -1.73205   1.95259  -1.14715  -0.26105   1.53209  -1.99810   1.41421  -0.08724  -1.28558   1.98289  -1.63830   0.43288   1.00000  -1.90743   1.81262  -0.76537  -0.68404   1.77402  -1.93185   1.07460   0.34730  -1.58671   1.99239  -1.35118   0.00000   1.35118  -1.99239   1.58671  -0.34730  -1.07460   1.93185  -1.77402   0.68404   0.76537  -1.81262   1.90743  -1.00000  -0.43288   1.63830  -1.98289   1.28558   0.08724  -1.41421   1.99810  -1.53209   0.26105   1.14715  -1.95259   1.73205  -0.60141  -0.84524   1.84776  -1.87939   0.92350   0.51764  -1.68678   1.96962  -1.21752  -0.17431   1.47455  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E56      2.00000  -1.53209   0.34730   1.00000  -1.87939   1.87939  -1.00000  -0.34730   1.53209  -2.00000   1.53209  -0.34730  -1.00000   1.87939  -1.87939   1.00000   0.34730  -1.53209   2.00000  -1.53209   0.34730   1.00000  -1.87939   1.87939  -1.00000  -0.34730   1.53209  -2.00000   1.53209  -0.34730  -1.00000   1.87939  -1.87939   1.00000   0.34730  -1.53209   2.00000  -1.53209   0.34730   1.00000  -1.87939   1.87939  -1.00000  -0.34730   1.53209  -2.00000   1.53209  -0.34730  -1.00000   1.87939  -1.87939   1.00000   0.34730  -1.53209   2.00000  -1.53209   0.34730   1.00000  -1.87939   1.87939  -1.00000  -0.34730   1.53209  -2.00000   1.53209  -0.34730  -1.00000   1.87939  -1.87939   1.00000   0.34730  -1.53209   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E57      2.00000  -1.58671   0.51764   0.76537  -1.73205   1.98289  -1.41421   0.26105   1.00000  -1.84776   1.93185  -1.21752   0.00000   1.21752  -1.93185   1.84776  -1.00000  -0.26105   1.41421  -1.98289   1.73205  -0.76537  -0.51764   1.58671  -2.00000   1.58671  -0.51764  -0.76537   1.73205  -1.98289   1.41421  -0.26105  -1.00000   1.84776  -1.93185   1.21752   0.00000  -1.21752   1.93185  -1.84776   1.00000   0.26105  -1.41421   1.98289  -1.73205   0.76537   0.51764  -1.58671   2.00000  -1.58671   0.51764   0.76537  -1.73205   1.98289  -1.41421   0.26105   1.00000  -1.84776   1.93185  -1.21752   0.00000   1.21752  -1.93185   1.84776  -1.00000  -0.26105   1.41421  -1.98289   1.73205  -0.76537  -0.51764   1.58671  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E58      2.00000  -1.63830   0.68404   0.51764  -1.53209   1.99239  -1.73205   0.84524   0.34730  -1.41421   1.96962  -1.81262   1.00000   0.17431  -1.28558   1.93185  -1.87939   1.14715   0.00000  -1.14715   1.87939  -1.93185   1.28558  -0.17431  -1.00000   1.81262  -1.96962   1.41421  -0.34730  -0.84524   1.73205  -1.99239   1.53209  -0.51764  -0.68404   1.63830  -2.00000   1.63830  -0.68404  -0.51764   1.53209  -1.99239   1.73205  -0.84524  -0.34730   1.41421  -1.96962   1.81262  -1.00000  -0.17431   1.28558  -1.93185   1.87939  -1.14715   0.00000   1.14715  -1.87939   1.93185  -1.28558   0.17431   1.00000  -1.81262   1.96962  -1.41421   0.34730   0.84524  -1.73205   1.99239  -1.53209   0.51764   0.68404  -1.63830   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E59      2.00000  -1.68678   0.84524   0.26105  -1.28558   1.90743  -1.93185   1.35118  -0.34730  -0.76537   1.63830  -1.99810   1.73205  -0.92350  -0.17431   1.21752  -1.87939   1.95259  -1.41421   0.43288   0.68404  -1.58671   1.99239  -1.77402   1.00000   0.08724  -1.14715   1.84776  -1.96962   1.47455  -0.51764  -0.60141   1.53209  -1.98289   1.81262  -1.07460   0.00000   1.07460  -1.81262   1.98289  -1.53209   0.60141   0.51764  -1.47455   1.96962  -1.84776   1.14715  -0.08724  -1.00000   1.77402  -1.99239   1.58671  -0.68404  -0.43288   1.41421  -1.95259   1.87939  -1.21752   0.17431   0.92350  -1.73205   1.99810  -1.63830   0.76537   0.34730  -1.35118   1.93185  -1.90743   1.28558  -0.26105  -0.84524   1.68678  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E60      2.00000  -1.73205   1.00000   0.00000  -1.00000   1.73205  -2.00000   1.73205  -1.00000   0.00000   1.00000  -1.73205   2.00000  -1.73205   1.00000   0.00000  -1.00000   1.73205  -2.00000   1.73205  -1.00000   0.00000   1.00000  -1.73205   2.00000  -1.73205   1.00000   0.00000  -1.00000   1.73205  -2.00000   1.73205  -1.00000   0.00000   1.00000  -1.73205   2.00000  -1.73205   1.00000   0.00000  -1.00000   1.73205  -2.00000   1.73205  -1.00000   0.00000   1.00000  -1.73205   2.00000  -1.73205   1.00000   0.00000  -1.00000   1.73205  -2.00000   1.73205  -1.00000   0.00000   1.00000  -1.73205   2.00000  -1.73205   1.00000   0.00000  -1.00000   1.73205  -2.00000   1.73205  -1.00000   0.00000   1.00000  -1.73205   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E61      2.00000  -1.77402   1.14715  -0.26105  -0.68404   1.47455  -1.93185   1.95259  -1.53209   0.76537   0.17431  -1.07460   1.73205  -1.99810   1.81262  -1.21752   0.34730   0.60141  -1.41421   1.90743  -1.96962   1.58671  -0.84524  -0.08724   1.00000  -1.68678   1.99239  -1.84776   1.28558  -0.43288  -0.51764   1.35118  -1.87939   1.98289  -1.63830   0.92350   0.00000  -0.92350   1.63830  -1.98289   1.87939  -1.35118   0.51764   0.43288  -1.28558   1.84776  -1.99239   1.68678  -1.00000   0.08724   0.84524  -1.58671   1.96962  -1.90743   1.41421  -0.60141  -0.34730   1.21752  -1.81262   1.99810  -1.73205   1.07460  -0.17431  -0.76537   1.53209  -1.95259   1.93185  -1.47455   0.68404   0.26105  -1.14715   1.77402  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E62      2.00000  -1.81262   1.28558  -0.51764  -0.34730   1.14715  -1.73205   1.99239  -1.87939   1.41421  -0.68404  -0.17431   1.00000  -1.63830   1.96962  -1.93185   1.53209  -0.84524   0.00000   0.84524  -1.53209   1.93185  -1.96962   1.63830  -1.00000   0.17431   0.68404  -1.41421   1.87939  -1.99239   1.73205  -1.14715   0.34730   0.51764  -1.28558   1.81262  -2.00000   1.81262  -1.28558   0.51764   0.34730  -1.14715   1.73205  -1.99239   1.87939  -1.41421   0.68404   0.17431  -1.00000   1.63830  -1.96962   1.93185  -1.53209   0.84524   0.00000  -0.84524   1.53209  -1.93185   1.96962  -1.63830   1.00000  -0.17431  -0.68404   1.41421  -1.87939   1.99239  -1.73205   1.14715  -0.34730  -0.51764   1.28558  -1.81262   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E63      2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E64      2.00000  -1.87939   1.53209  -1.00000   0.34730   0.34730  -1.00000   1.53209  -1.87939   2.00000  -1.87939   1.53209  -1.00000   0.34730   0.34730  -1.00000   1.53209  -1.87939   2.00000  -1.87939   1.53209  -1.00000   0.34730   0.34730  -1.00000   1.53209  -1.87939   2.00000  -1.87939   1.53209  -1.00000   0.34730   0.34730  -1.00000   1.53209  -1.87939   2.00000  -1.87939   1.53209  -1.00000   0.34730   0.34730  -1.00000   1.53209  -1.87939   2.00000  -1.87939   1.53209  -1.00000   0.34730   0.34730  -1.00000   1.53209  -1.87939   2.00000  -1.87939   1.53209  -1.00000   0.34730   0.34730  -1.00000   1.53209  -1.87939   2.00000  -1.87939   1.53209  -1.00000   0.34730   0.34730  -1.00000   1.53209  -1.87939   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E65      2.00000  -1.90743   1.63830  -1.21752   0.68404  -0.08724  -0.51764   1.07460  -1.53209   1.84776  -1.99239   1.95259  -1.73205   1.35118  -0.84524   0.26105   0.34730  -0.92350   1.41421  -1.77402   1.96962  -1.98289   1.81262  -1.47455   1.00000  -0.43288  -0.17431   0.76537  -1.28558   1.68678  -1.93185   1.99810  -1.87939   1.58671  -1.14715   0.60141   0.00000  -0.60141   1.14715  -1.58671   1.87939  -1.99810   1.93185  -1.68678   1.28558  -0.76537   0.17431   0.43288  -1.00000   1.47455  -1.81262   1.98289  -1.96962   1.77402  -1.41421   0.92350  -0.34730  -0.26105   0.84524  -1.35118   1.73205  -1.95259   1.99239  -1.84776   1.53209  -1.07460   0.51764   0.08724  -0.68404   1.21752  -1.63830   1.90743  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E66      2.00000  -1.93185   1.73205  -1.41421   1.00000  -0.51764   0.00000   0.51764  -1.00000   1.41421  -1.73205   1.93185  -2.00000   1.93185  -1.73205   1.41421  -1.00000   0.51764   0.00000  -0.51764   1.00000  -1.41421   1.73205  -1.93185   2.00000  -1.93185   1.73205  -1.41421   1.00000  -0.51764   0.00000   0.51764  -1.00000   1.41421  -1.73205   1.93185  -2.00000   1.93185  -1.73205   1.41421  -1.00000   0.51764   0.00000  -0.51764   1.00000  -1.41421   1.73205  -1.93185   2.00000  -1.93185   1.73205  -1.41421   1.00000  -0.51764   0.00000   0.51764  -1.00000   1.41421  -1.73205   1.93185  -2.00000   1.93185  -1.73205   1.41421  -1.00000   0.51764   0.00000  -0.51764   1.00000  -1.41421   1.73205  -1.93185   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E67      2.00000  -1.95259   1.81262  -1.58671   1.28558  -0.92350   0.51764  -0.08724  -0.34730   0.76537  -1.14715   1.47455  -1.73205   1.90743  -1.99239   1.98289  -1.87939   1.68678  -1.41421   1.07460  -0.68404   0.26105   0.17431  -0.60141   1.00000  -1.35118   1.63830  -1.84776   1.96962  -1.99810   1.93185  -1.77402   1.53209  -1.21752   0.84524  -0.43288   0.00000   0.43288  -0.84524   1.21752  -1.53209   1.77402  -1.93185   1.99810  -1.96962   1.84776  -1.63830   1.35118  -1.00000   0.60141  -0.17431  -0.26105   0.68404  -1.07460   1.41421  -1.68678   1.87939  -1.98289   1.99239  -1.90743   1.73205  -1.47455   1.14715  -0.76537   0.34730   0.08724  -0.51764   0.92350  -1.28558   1.58671  -1.81262   1.95259  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... ..TT.........
E68      2.00000  -1.96962   1.87939  -1.73205   1.53209  -1.28558   1.00000  -0.68404   0.34730   0.00000  -0.34730   0.68404  -1.00000   1.28558  -1.53209   1.73205  -1.87939   1.96962  -2.00000   1.96962  -1.87939   1.73205  -1.53209   1.28558  -1.00000   0.68404  -0.34730   0.00000   0.34730  -0.68404   1.00000  -1.28558   1.53209  -1.73205   1.87939  -1.96962   2.00000  -1.96962   1.87939  -1.73205   1.53209  -1.28558   1.00000  -0.68404   0.34730   0.00000  -0.34730   0.68404  -1.00000   1.28558  -1.53209   1.73205  -1.87939   1.96962  -2.00000   1.96962  -1.87939   1.73205  -1.53209   1.28558  -1.00000   0.68404  -0.34730   0.00000   0.34730  -0.68404   1.00000  -1.28558   1.53209  -1.73205   1.87939  -1.96962   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ..TT....... .............
E69      2.00000  -1.98289   1.93185  -1.84776   1.73205  -1.58671   1.41421  -1.21752   1.00000  -0.76537   0.51764  -0.26105   0.00000   0.26105  -0.51764   0.76537  -1.00000   1.21752  -1.41421   1.58671  -1.73205   1.84776  -1.93185   1.98289  -2.00000   1.98289  -1.93185   1.84776  -1.73205   1.58671  -1.41421   1.21752  -1.00000   0.76537  -0.51764   0.26105   0.00000  -0.26105   0.51764  -0.76537   1.00000  -1.21752   1.41421  -1.58671   1.73205  -1.84776   1.93185  -1.98289   2.00000  -1.98289   1.93185  -1.84776   1.73205  -1.58671   1.41421  -1.21752   1.00000  -0.76537   0.51764  -0.26105   0.00000   0.26105  -0.51764   0.76537  -1.00000   1.21752  -1.41421   1.58671  -1.73205   1.84776  -1.93185   1.98289  -2.00000   0.00000   0.00000     ... ... ..... ....... ..TT..... ........... ......TT.....
E70      2.00000  -1.99239   1.96962  -1.93185   1.87939  -1.81262   1.73205  -1.63830   1.53209  -1.41421   1.28558  -1.14715   1.00000  -0.84524   0.68404  -0.51764   0.34730  -0.17431   0.00000   0.17431  -0.34730   0.51764  -0.68404   0.84524  -1.00000   1.14715  -1.28558   1.41421  -1.53209   1.63830  -1.73205   1.81262  -1.87939   1.93185  -1.96962   1.99239  -2.00000   1.99239  -1.96962   1.93185  -1.87939   1.81262  -1.73205   1.63830  -1.53209   1.41421  -1.28558   1.14715  -1.00000   0.84524  -0.68404   0.51764  -0.34730   0.17431   0.00000  -0.17431   0.34730  -0.51764   0.68404  -0.84524   1.00000  -1.14715   1.28558  -1.41421   1.53209  -1.63830   1.73205  -1.81262   1.87939  -1.93185   1.96962  -1.99239   2.00000   0.00000   0.00000     ... ... ..... ..TT... ......... ......TT... .............
E71      2.00000  -1.99810   1.99239  -1.98289   1.96962  -1.95259   1.93185  -1.90743   1.87939  -1.84776   1.81262  -1.77402   1.73205  -1.68678   1.63830  -1.58671   1.53209  -1.47455   1.41421  -1.35118   1.28558  -1.21752   1.14715  -1.07460   1.00000  -0.92350   0.84524  -0.76537   0.68404  -0.60141   0.51764  -0.43288   0.34730  -0.26105   0.17431  -0.08724   0.00000   0.08724  -0.17431   0.26105  -0.34730   0.43288  -0.51764   0.60141  -0.68404   0.76537  -0.84524   0.92350  -1.00000   1.07460  -1.14715   1.21752  -1.28558   1.35118  -1.41421   1.47455  -1.53209   1.58671  -1.63830   1.68678  -1.73205   1.77402  -1.81262   1.84776  -1.87939   1.90743  -1.93185   1.95259  -1.96962   1.98289  -1.99239   1.99810  -2.00000   0.00000   0.00000     TT. ... ..TT. ....... ......TT. ........... ..........TT.

 Irrational character values:  1.998096443164 = 2*cos(2*π/144) = 2*cos(π/72)
                               1.992389396183 = 2*cos(4*π/144) = 2*cos(π/36)
                               1.982889722748 = 2*cos(6*π/144) = 2*cos(π/24) = √2+√2+√3
                               1.969615506024 = 2*cos(8*π/144) = 2*cos(π/18)
                               1.952592014240 = 2*cos(10*π/144) = 2*cos(5*π/72)
                               1.931851652578 = 2*cos(12*π/144) = 2*cos(π/12) = √2+√3
                               1.907433901496 = 2*cos(14*π/144) = 2*cos(7*π/72)
                               1.879385241572 = 2*cos(16*π/144) = 2*cos(π/9)
                               1.847759065023 = 2*cos(18*π/144) = 2*cos(π/8) = √2+√2
                               1.812615574073 = 2*cos(20*π/144) = 2*cos(5*π/36)
                               1.774021666356 = 2*cos(22*π/144) = 2*cos(11*π/72)
                               1.732050807569 = 2*cos(24*π/144) = 2*cos(π/6) = √3
                               1.686782891626 = 2*cos(26*π/144) = 2*cos(13*π/72)
                               1.638304088578 = 2*cos(28*π/144) = 2*cos(7*π/36)
                               1.586706680582 = 2*cos(30*π/144) = 2*cos(5*π/24) = √2+√2−√3
                               1.532088886238 = 2*cos(32*π/144) = 2*cos(2*π/9)
                               1.474554673620 = 2*cos(34*π/144) = 2*cos(17*π/72)
                               1.414213562373 = 2*cos(36*π/144) = 2*cos(π/4) = √2
                               1.351180415231 = 2*cos(38*π/144) = 2*cos(19*π/72)
                               1.285575219373 = 2*cos(40*π/144) = 2*cos(5*π/18)
                               1.217522858017 = 2*cos(42*π/144) = 2*cos(7*π/24) = √2−√2−√3
                               1.147152872702 = 2*cos(44*π/144) = 2*cos(11*π/36)
                               1.074599216694 = 2*cos(46*π/144) = 2*cos(23*π/72)
                               0.923497226470 = 2*cos(50*π/144) = 2*cos(25*π/72)
                               0.845236523481 = 2*cos(52*π/144) = 2*cos(13*π/36)
                               0.765366864730 = 2*cos(54*π/144) = 2*cos(3*π/8) = √2−√2
                               0.684040286651 = 2*cos(56*π/144) = 2*cos(7*π/18)
                               0.601411599009 = 2*cos(58*π/144) = 2*cos(29*π/72)
                               0.517638090205 = 2*cos(60*π/144) = 2*cos(5*π/12) = √2−√3
                               0.432879227876 = 2*cos(62*π/144) = 2*cos(31*π/72)
                               0.347296355334 = 2*cos(64*π/144) = 2*cos(4*π/9)
                               0.261052384440 = 2*cos(66*π/144) = 2*cos(11*π/24) = √2−√2+√3
                               0.174311485495 = 2*cos(68*π/144) = 2*cos(17*π/36)
                               0.087238774731 = 2*cos(70*π/144) = 2*cos(35*π/72)



 Symmetry of Rotations and Cartesian products

A1   d+g+i+k+m    z2, z4, z6 
A2   R            Rz 
B2   p+f+h+j+l    z, z3, z5 
E1   p+f+h+j+l    {x, y}, {xz2, yz2}, {xz4, yz4} 
E2   d+g+i+k+m    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E3   f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E4   g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E5   h+j+l        {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)} 
E6   i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7   j+l 
E8   k+m 
E9   l 
E10  m 
E63  m 
E64  l 
E65  k+m 
E66  j+l 
E67  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E68  h+j+l        {z((x2y2)2−4x2y2), xyz(x2y2)} 
E69  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E70  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E71  R+d+g+i+k+m  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 

 Notes:

    α  The order of the D72d point group is 288, and the order of the principal axis (S144) is 144. The group has 75 irreducible representations.

    β  The D72d point group is isomorphic to C144v and D144.

    γ  The D72d point group is generated by two symmetry elements, S144 and either a perpendicular C2 or a vertical σd.
       Also, the group may be generated from a C2 plus a σd (some pairs will yield smaller groups, though; choosing a minimum angle is safe).

    δ  The group contains one set of twofold symmetry axes (C2) perpendicular to the principal (z) axis. Both x and y axes are members of that set.

    ε  The single σd set of symmetry planes contains neither the xz nor the yz planes; but it contains the median plane (x+y)z.

    ζ  The lowest nonvanishing multipole moment in D72d is 4 (quadrupole moment).

    η  This point group is non-Abelian (some symmetry operations are not commutative).
       Therefore, the character table contains multi-membered classes and degenerate irreducible representations.

    θ  Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6.
       These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1.
       All characters are algebraic integers of a degree much less than half the order of the principal axis.

    ι  The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible
       if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given
       by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three.
       While some characters of this group can be expressed using real integers and square roots alone, others need complex numbers and third roots.

    κ  The regular nonagon or enneagon is not constructible by ruler and compass because cos(2*π/9) has an algebraic degree of 3.
       (It can be constructed by extended methods that allow angle trisection, as this corresponds to solving cubic equations).
       The value of cos(2*π/9) can be expressed using cubic roots and complex numbers, which, however, is not very useful
       for a real-valued quantity: 2*cos(2π/9) = (3−4+i*4*√3 + 3−4−i*4*√3)/2.
       Therefore, regular polygons of order 18,27,36,45,54 etc. are also inconstructible, and their cosines have no representation in real radicals.

This Character Table for the D72d point group was created by Gernot Katzer.

For other groups and some explanations, see the Main Page.