Character table for the D115 point group

D115    E         2 C115    2 C115^2  2 C115^3  2 C115^4  2 C23     2 C115^6  2 C115^7  2 C115^8  2 C115^9  2 C23^2   2 C115^11 2 C115^12 2 C115^13 2 C115^14 2 C23^3   2 C115^16 2 C115^17 2 C115^18 2 C115^19 2 C23^4   2 C115^21 2 C115^22 2 C5      2 C115^24 2 C23^5   2 C115^26 2 C115^27 2 C115^28 2 C115^29 2 C23^6   2 C115^31 2 C115^32 2 C115^33 2 C115^34 2 C23^7   2 C115^36 2 C115^37 2 C115^38 2 C115^39 2 C23^8   2 C115^41 2 C115^42 2 C115^43 2 C115^44 2 C23^9   2 C5^2    2 C115^47 2 C115^48 2 C115^49 2 C23^10  2 C115^51 2 C115^52 2 C115^53 2 C115^54 2 C23^11  2 C115^56 2 C115^57 115 C2'      <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     ... ... ....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     ..T ..T ..... ......T ......... ..........T .............
E1       2.00000   1.99702   1.98807   1.97319   1.95243   1.92583   1.89349   1.85550   1.81197   1.76304   1.70884   1.64954   1.58532   1.51637   1.44289   1.36511   1.28325   1.19756   1.10830   1.01573   0.92013   0.82178   0.72098   0.61803   0.51324   0.40691   0.29937   0.19094   0.08193  -0.02732  -0.13648  -0.24524  -0.35327  -0.46025  -0.56585  -0.66976  -0.77167  -0.87128  -0.96829  -1.06241  -1.15336  -1.24087  -1.32467  -1.40452  -1.48018  -1.55142  -1.61803  -1.67982  -1.73659  -1.78817  -1.83442  -1.87520  -1.91038  -1.93985  -1.96354  -1.98137  -1.99329  -1.99925   0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2       2.00000   1.98807   1.95243   1.89349   1.81197   1.70884   1.58532   1.44289   1.28325   1.10830   0.92013   0.72098   0.51324   0.29937   0.08193  -0.13648  -0.35327  -0.56585  -0.77167  -0.96829  -1.15336  -1.32467  -1.48018  -1.61803  -1.73659  -1.83442  -1.91038  -1.96354  -1.99329  -1.99925  -1.98137  -1.93985  -1.87520  -1.78817  -1.67982  -1.55142  -1.40452  -1.24087  -1.06241  -0.87128  -0.66976  -0.46025  -0.24524  -0.02732   0.19094   0.40691   0.61803   0.82178   1.01573   1.19756   1.36511   1.51637   1.64954   1.76304   1.85550   1.92583   1.97319   1.99702   0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3       2.00000   1.97319   1.89349   1.76304   1.58532   1.36511   1.10830   0.82178   0.51324   0.19094  -0.13648  -0.46025  -0.77167  -1.06241  -1.32467  -1.55142  -1.73659  -1.87520  -1.96354  -1.99925  -1.98137  -1.91038  -1.78817  -1.61803  -1.40452  -1.15336  -0.87128  -0.56585  -0.24524   0.08193   0.40691   0.72098   1.01573   1.28325   1.51637   1.70884   1.85550   1.95243   1.99702   1.98807   1.92583   1.81197   1.64954   1.44289   1.19756   0.92013   0.61803   0.29937  -0.02732  -0.35327  -0.66976  -0.96829  -1.24087  -1.48018  -1.67982  -1.83442  -1.93985  -1.99329   0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4       2.00000   1.95243   1.81197   1.58532   1.28325   0.92013   0.51324   0.08193  -0.35327  -0.77167  -1.15336  -1.48018  -1.73659  -1.91038  -1.99329  -1.98137  -1.87520  -1.67982  -1.40452  -1.06241  -0.66976  -0.24524   0.19094   0.61803   1.01573   1.36511   1.64954   1.85550   1.97319   1.99702   1.92583   1.76304   1.51637   1.19756   0.82178   0.40691  -0.02732  -0.46025  -0.87128  -1.24087  -1.55142  -1.78817  -1.93985  -1.99925  -1.96354  -1.83442  -1.61803  -1.32467  -0.96829  -0.56585  -0.13648   0.29937   0.72098   1.10830   1.44289   1.70884   1.89349   1.98807   0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5       2.00000   1.92583   1.70884   1.36511   0.92013   0.40691  -0.13648  -0.66976  -1.15336  -1.55142  -1.83442  -1.98137  -1.98137  -1.83442  -1.55142  -1.15336  -0.66976  -0.13648   0.40691   0.92013   1.36511   1.70884   1.92583   2.00000   1.92583   1.70884   1.36511   0.92013   0.40691  -0.13648  -0.66976  -1.15336  -1.55142  -1.83442  -1.98137  -1.98137  -1.83442  -1.55142  -1.15336  -0.66976  -0.13648   0.40691   0.92013   1.36511   1.70884   1.92583   2.00000   1.92583   1.70884   1.36511   0.92013   0.40691  -0.13648  -0.66976  -1.15336  -1.55142  -1.83442  -1.98137   0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6       2.00000   1.89349   1.58532   1.10830   0.51324  -0.13648  -0.77167  -1.32467  -1.73659  -1.96354  -1.98137  -1.78817  -1.40452  -0.87128  -0.24524   0.40691   1.01573   1.51637   1.85550   1.99702   1.92583   1.64954   1.19756   0.61803  -0.02732  -0.66976  -1.24087  -1.67982  -1.93985  -1.99329  -1.83442  -1.48018  -0.96829  -0.35327   0.29937   0.92013   1.44289   1.81197   1.98807   1.95243   1.70884   1.28325   0.72098   0.08193  -0.56585  -1.15336  -1.61803  -1.91038  -1.99925  -1.87520  -1.55142  -1.06241  -0.46025   0.19094   0.82178   1.36511   1.76304   1.97319   0.00000     ... ... ..... ....... ......... ........... TT...........
E7       2.00000   1.85550   1.44289   0.82178   0.08193  -0.66976  -1.32467  -1.78817  -1.99329  -1.91038  -1.55142  -0.96829  -0.24524   0.51324   1.19756   1.70884   1.97319   1.95243   1.64954   1.10830   0.40691  -0.35327  -1.06241  -1.61803  -1.93985  -1.98137  -1.73659  -1.24087  -0.56585   0.19094   0.92013   1.51637   1.89349   1.99702   1.81197   1.36511   0.72098  -0.02732  -0.77167  -1.40452  -1.83442  -1.99925  -1.87520  -1.48018  -0.87128  -0.13648   0.61803   1.28325   1.76304   1.98807   1.92583   1.58532   1.01573   0.29937  -0.46025  -1.15336  -1.67982  -1.96354   0.00000     ... ... ..... ....... ......... ........... .............
E8       2.00000   1.81197   1.28325   0.51324  -0.35327  -1.15336  -1.73659  -1.99329  -1.87520  -1.40452  -0.66976   0.19094   1.01573   1.64954   1.97319   1.92583   1.51637   0.82178  -0.02732  -0.87128  -1.55142  -1.93985  -1.96354  -1.61803  -0.96829  -0.13648   0.72098   1.44289   1.89349   1.98807   1.70884   1.10830   0.29937  -0.56585  -1.32467  -1.83442  -1.99925  -1.78817  -1.24087  -0.46025   0.40691   1.19756   1.76304   1.99702   1.85550   1.36511   0.61803  -0.24524  -1.06241  -1.67982  -1.98137  -1.91038  -1.48018  -0.77167   0.08193   0.92013   1.58532   1.95243   0.00000     ... ... ..... ....... ......... ........... .............
E9       2.00000   1.76304   1.10830   0.19094  -0.77167  -1.55142  -1.96354  -1.91038  -1.40452  -0.56585   0.40691   1.28325   1.85550   1.98807   1.64954   0.92013  -0.02732  -0.96829  -1.67982  -1.99329  -1.83442  -1.24087  -0.35327   0.61803   1.44289   1.92583   1.95243   1.51637   0.72098  -0.24524  -1.15336  -1.78817  -1.99925  -1.73659  -1.06241  -0.13648   0.82178   1.58532   1.97319   1.89349   1.36511   0.51324  -0.46025  -1.32467  -1.87520  -1.98137  -1.61803  -0.87128   0.08193   1.01573   1.70884   1.99702   1.81197   1.19756   0.29937  -0.66976  -1.48018  -1.93985   0.00000     ... ... ..... ....... ......... ........... .............
E10      2.00000   1.70884   0.92013  -0.13648  -1.15336  -1.83442  -1.98137  -1.55142  -0.66976   0.40691   1.36511   1.92583   1.92583   1.36511   0.40691  -0.66976  -1.55142  -1.98137  -1.83442  -1.15336  -0.13648   0.92013   1.70884   2.00000   1.70884   0.92013  -0.13648  -1.15336  -1.83442  -1.98137  -1.55142  -0.66976   0.40691   1.36511   1.92583   1.92583   1.36511   0.40691  -0.66976  -1.55142  -1.98137  -1.83442  -1.15336  -0.13648   0.92013   1.70884   2.00000   1.70884   0.92013  -0.13648  -1.15336  -1.83442  -1.98137  -1.55142  -0.66976   0.40691   1.36511   1.92583   0.00000     ... ... ..... ....... ......... ........... .............
E11      2.00000   1.64954   0.72098  -0.46025  -1.48018  -1.98137  -1.78817  -0.96829   0.19094   1.28325   1.92583   1.89349   1.19756   0.08193  -1.06241  -1.83442  -1.96354  -1.40452  -0.35327   0.82178   1.70884   1.99702   1.58532   0.61803  -0.56585  -1.55142  -1.99329  -1.73659  -0.87128   0.29937   1.36511   1.95243   1.85550   1.10830  -0.02732  -1.15336  -1.87520  -1.93985  -1.32467  -0.24524   0.92013   1.76304   1.98807   1.51637   0.51324  -0.66976  -1.61803  -1.99925  -1.67982  -0.77167   0.40691   1.44289   1.97319   1.81197   1.01573  -0.13648  -1.24087  -1.91038   0.00000     ... ... ..... ....... ......... ........... .............
E12      2.00000   1.58532   0.51324  -0.77167  -1.73659  -1.98137  -1.40452  -0.24524   1.01573   1.85550   1.92583   1.19756  -0.02732  -1.24087  -1.93985  -1.83442  -0.96829   0.29937   1.44289   1.98807   1.70884   0.72098  -0.56585  -1.61803  -1.99925  -1.55142  -0.46025   0.82178   1.76304   1.97319   1.36511   0.19094  -1.06241  -1.87520  -1.91038  -1.15336   0.08193   1.28325   1.95243   1.81197   0.92013  -0.35327  -1.48018  -1.99329  -1.67982  -0.66976   0.61803   1.64954   1.99702   1.51637   0.40691  -0.87128  -1.78817  -1.96354  -1.32467  -0.13648   1.10830   1.89349   0.00000     ... ... ..... ....... ......... ........... .............
E13      2.00000   1.51637   0.29937  -1.06241  -1.91038  -1.83442  -0.87128   0.51324   1.64954   1.98807   1.36511   0.08193  -1.24087  -1.96354  -1.73659  -0.66976   0.72098   1.76304   1.95243   1.19756  -0.13648  -1.40452  -1.99329  -1.61803  -0.46025   0.92013   1.85550   1.89349   1.01573  -0.35327  -1.55142  -1.99925  -1.48018  -0.24524   1.10830   1.92583   1.81197   0.82178  -0.56585  -1.67982  -1.98137  -1.32467  -0.02732   1.28325   1.97319   1.70884   0.61803  -0.77167  -1.78817  -1.93985  -1.15336   0.19094   1.44289   1.99702   1.58532   0.40691  -0.96829  -1.87520   0.00000     ... ... ..... ....... ......... ........... .............
E14      2.00000   1.44289   0.08193  -1.32467  -1.99329  -1.55142  -0.24524   1.19756   1.97319   1.64954   0.40691  -1.06241  -1.93985  -1.73659  -0.56585   0.92013   1.89349   1.81197   0.72098  -0.77167  -1.83442  -1.87520  -0.87128   0.61803   1.76304   1.92583   1.01573  -0.46025  -1.67982  -1.96354  -1.15336   0.29937   1.58532   1.98807   1.28325  -0.13648  -1.48018  -1.99925  -1.40452  -0.02732   1.36511   1.99702   1.51637   0.19094  -1.24087  -1.98137  -1.61803  -0.35327   1.10830   1.95243   1.70884   0.51324  -0.96829  -1.91038  -1.78817  -0.66976   0.82178   1.85550   0.00000     ... ... ..... ....... ......... ........... .............
E15      2.00000   1.36511  -0.13648  -1.55142  -1.98137  -1.15336   0.40691   1.70884   1.92583   0.92013  -0.66976  -1.83442  -1.83442  -0.66976   0.92013   1.92583   1.70884   0.40691  -1.15336  -1.98137  -1.55142  -0.13648   1.36511   2.00000   1.36511  -0.13648  -1.55142  -1.98137  -1.15336   0.40691   1.70884   1.92583   0.92013  -0.66976  -1.83442  -1.83442  -0.66976   0.92013   1.92583   1.70884   0.40691  -1.15336  -1.98137  -1.55142  -0.13648   1.36511   2.00000   1.36511  -0.13648  -1.55142  -1.98137  -1.15336   0.40691   1.70884   1.92583   0.92013  -0.66976  -1.83442   0.00000     ... ... ..... ....... ......... ........... .............
E16      2.00000   1.28325  -0.35327  -1.73659  -1.87520  -0.66976   1.01573   1.97319   1.51637  -0.02732  -1.55142  -1.96354  -0.96829   0.72098   1.89349   1.70884   0.29937  -1.32467  -1.99925  -1.24087   0.40691   1.76304   1.85550   0.61803  -1.06241  -1.98137  -1.48018   0.08193   1.58532   1.95243   0.92013  -0.77167  -1.91038  -1.67982  -0.24524   1.36511   1.99702   1.19756  -0.46025  -1.78817  -1.83442  -0.56585   1.10830   1.98807   1.44289  -0.13648  -1.61803  -1.93985  -0.87128   0.82178   1.92583   1.64954   0.19094  -1.40452  -1.99329  -1.15336   0.51324   1.81197   0.00000     ... ... ..... ....... ......... ........... .............
E17      2.00000   1.19756  -0.56585  -1.87520  -1.67982  -0.13648   1.51637   1.95243   0.82178  -0.96829  -1.98137  -1.40452   0.29937   1.76304   1.81197   0.40691  -1.32467  -1.99329  -1.06241   0.72098   1.92583   1.58532  -0.02732  -1.61803  -1.91038  -0.66976   1.10830   1.99702   1.28325  -0.46025  -1.83442  -1.73659  -0.24524   1.44289   1.97319   0.92013  -0.87128  -1.96354  -1.48018   0.19094   1.70884   1.85550   0.51324  -1.24087  -1.99925  -1.15336   0.61803   1.89349   1.64954   0.08193  -1.55142  -1.93985  -0.77167   1.01573   1.98807   1.36511  -0.35327  -1.78817   0.00000     ... ... ..... ....... ......... ........... .............
E18      2.00000   1.10830  -0.77167  -1.96354  -1.40452   0.40691   1.85550   1.64954  -0.02732  -1.67982  -1.83442  -0.35327   1.44289   1.95243   0.72098  -1.15336  -1.99925  -1.06241   0.82178   1.97319   1.36511  -0.46025  -1.87520  -1.61803   0.08193   1.70884   1.81197   0.29937  -1.48018  -1.93985  -0.66976   1.19756   1.99702   1.01573  -0.87128  -1.98137  -1.32467   0.51324   1.89349   1.58532  -0.13648  -1.73659  -1.78817  -0.24524   1.51637   1.92583   0.61803  -1.24087  -1.99329  -0.96829   0.92013   1.98807   1.28325  -0.56585  -1.91038  -1.55142   0.19094   1.76304   0.00000     ... ... ..... ....... ......... ........... .............
E19      2.00000   1.01573  -0.96829  -1.99925  -1.06241   0.92013   1.99702   1.10830  -0.87128  -1.99329  -1.15336   0.82178   1.98807   1.19756  -0.77167  -1.98137  -1.24087   0.72098   1.97319   1.28325  -0.66976  -1.96354  -1.32467   0.61803   1.95243   1.36511  -0.56585  -1.93985  -1.40452   0.51324   1.92583   1.44289  -0.46025  -1.91038  -1.48018   0.40691   1.89349   1.51637  -0.35327  -1.87520  -1.55142   0.29937   1.85550   1.58532  -0.24524  -1.83442  -1.61803   0.19094   1.81197   1.64954  -0.13648  -1.78817  -1.67982   0.08193   1.76304   1.70884  -0.02732  -1.73659   0.00000     ... ... ..... ....... ......... ........... .............
E20      2.00000   0.92013  -1.15336  -1.98137  -0.66976   1.36511   1.92583   0.40691  -1.55142  -1.83442  -0.13648   1.70884   1.70884  -0.13648  -1.83442  -1.55142   0.40691   1.92583   1.36511  -0.66976  -1.98137  -1.15336   0.92013   2.00000   0.92013  -1.15336  -1.98137  -0.66976   1.36511   1.92583   0.40691  -1.55142  -1.83442  -0.13648   1.70884   1.70884  -0.13648  -1.83442  -1.55142   0.40691   1.92583   1.36511  -0.66976  -1.98137  -1.15336   0.92013   2.00000   0.92013  -1.15336  -1.98137  -0.66976   1.36511   1.92583   0.40691  -1.55142  -1.83442  -0.13648   1.70884   0.00000     ... ... ..... ....... ......... ........... .............
E21      2.00000   0.82178  -1.32467  -1.91038  -0.24524   1.70884   1.64954  -0.35327  -1.93985  -1.24087   0.92013   1.99702   0.72098  -1.40452  -1.87520  -0.13648   1.76304   1.58532  -0.46025  -1.96354  -1.15336   1.01573   1.98807   0.61803  -1.48018  -1.83442  -0.02732   1.81197   1.51637  -0.56585  -1.98137  -1.06241   1.10830   1.97319   0.51324  -1.55142  -1.78817   0.08193   1.85550   1.44289  -0.66976  -1.99329  -0.96829   1.19756   1.95243   0.40691  -1.61803  -1.73659   0.19094   1.89349   1.36511  -0.77167  -1.99925  -0.87128   1.28325   1.92583   0.29937  -1.67982   0.00000     ... ... ..... ....... ......... ........... .............
E22      2.00000   0.72098  -1.48018  -1.78817   0.19094   1.92583   1.19756  -1.06241  -1.96354  -0.35327   1.70884   1.58532  -0.56585  -1.99329  -0.87128   1.36511   1.85550  -0.02732  -1.87520  -1.32467   0.92013   1.98807   0.51324  -1.61803  -1.67982   0.40691   1.97319   1.01573  -1.24087  -1.91038  -0.13648   1.81197   1.44289  -0.77167  -1.99925  -0.66976   1.51637   1.76304  -0.24524  -1.93985  -1.15336   1.10830   1.95243   0.29937  -1.73659  -1.55142   0.61803   1.99702   0.82178  -1.40452  -1.83442   0.08193   1.89349   1.28325  -0.96829  -1.98137  -0.46025   1.64954   0.00000     ... ... ..... ....... ......... ........... .............
E23      2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803   0.00000     ... ... ..... ....... ......... ........... .............
E24      2.00000   0.51324  -1.73659  -1.40452   1.01573   1.92583  -0.02732  -1.93985  -0.96829   1.44289   1.70884  -0.56585  -1.99925  -0.46025   1.76304   1.36511  -1.06241  -1.91038   0.08193   1.95243   0.92013  -1.48018  -1.67982   0.61803   1.99702   0.40691  -1.78817  -1.32467   1.10830   1.89349  -0.13648  -1.96354  -0.87128   1.51637   1.64954  -0.66976  -1.99329  -0.35327   1.81197   1.28325  -1.15336  -1.87520   0.19094   1.97319   0.82178  -1.55142  -1.61803   0.72098   1.98807   0.29937  -1.83442  -1.24087   1.19756   1.85550  -0.24524  -1.98137  -0.77167   1.58532   0.00000     ... ... ..... ....... ......... ........... .............
E25      2.00000   0.40691  -1.83442  -1.15336   1.36511   1.70884  -0.66976  -1.98137  -0.13648   1.92583   0.92013  -1.55142  -1.55142   0.92013   1.92583  -0.13648  -1.98137  -0.66976   1.70884   1.36511  -1.15336  -1.83442   0.40691   2.00000   0.40691  -1.83442  -1.15336   1.36511   1.70884  -0.66976  -1.98137  -0.13648   1.92583   0.92013  -1.55142  -1.55142   0.92013   1.92583  -0.13648  -1.98137  -0.66976   1.70884   1.36511  -1.15336  -1.83442   0.40691   2.00000   0.40691  -1.83442  -1.15336   1.36511   1.70884  -0.66976  -1.98137  -0.13648   1.92583   0.92013  -1.55142   0.00000     ... ... ..... ....... ......... ........... .............
E26      2.00000   0.29937  -1.91038  -0.87128   1.64954   1.36511  -1.24087  -1.73659   0.72098   1.95243  -0.13648  -1.99329  -0.46025   1.85550   1.01573  -1.55142  -1.48018   1.10830   1.81197  -0.56585  -1.98137  -0.02732   1.97319   0.61803  -1.78817  -1.15336   1.44289   1.58532  -0.96829  -1.87520   0.40691   1.99702   0.19094  -1.93985  -0.77167   1.70884   1.28325  -1.32467  -1.67982   0.82178   1.92583  -0.24524  -1.99925  -0.35327   1.89349   0.92013  -1.61803  -1.40452   1.19756   1.76304  -0.66976  -1.96354   0.08193   1.98807   0.51324  -1.83442  -1.06241   1.51637   0.00000     ... ... ..... ....... ......... ........... .............
E27      2.00000   0.19094  -1.96354  -0.56585   1.85550   0.92013  -1.67982  -1.24087   1.44289   1.51637  -1.15336  -1.73659   0.82178   1.89349  -0.46025  -1.98137   0.08193   1.99702   0.29937  -1.93985  -0.66976   1.81197   1.01573  -1.61803  -1.32467   1.36511   1.58532  -1.06241  -1.78817   0.72098   1.92583  -0.35327  -1.99329  -0.02732   1.98807   0.40691  -1.91038  -0.77167   1.76304   1.10830  -1.55142  -1.40452   1.28325   1.64954  -0.96829  -1.83442   0.61803   1.95243  -0.24524  -1.99925  -0.13648   1.97319   0.51324  -1.87520  -0.87128   1.70884   1.19756  -1.48018   0.00000     ... ... ..... ....... ......... ........... .............
E28      2.00000   0.08193  -1.99329  -0.24524   1.97319   0.40691  -1.93985  -0.56585   1.89349   0.72098  -1.83442  -0.87128   1.76304   1.01573  -1.67982  -1.15336   1.58532   1.28325  -1.48018  -1.40452   1.36511   1.51637  -1.24087  -1.61803   1.10830   1.70884  -0.96829  -1.78817   0.82178   1.85550  -0.66976  -1.91038   0.51324   1.95243  -0.35327  -1.98137   0.19094   1.99702  -0.02732  -1.99925  -0.13648   1.98807   0.29937  -1.96354  -0.46025   1.92583   0.61803  -1.87520  -0.77167   1.81197   0.92013  -1.73659  -1.06241   1.64954   1.19756  -1.55142  -1.32467   1.44289   0.00000     ... ... ..... ....... ......... ........... .............
E29      2.00000  -0.02732  -1.99925   0.08193   1.99702  -0.13648  -1.99329   0.19094   1.98807  -0.24524  -1.98137   0.29937   1.97319  -0.35327  -1.96354   0.40691   1.95243  -0.46025  -1.93985   0.51324   1.92583  -0.56585  -1.91038   0.61803   1.89349  -0.66976  -1.87520   0.72098   1.85550  -0.77167  -1.83442   0.82178   1.81197  -0.87128  -1.78817   0.92013   1.76304  -0.96829  -1.73659   1.01573   1.70884  -1.06241  -1.67982   1.10830   1.64954  -1.15336  -1.61803   1.19756   1.58532  -1.24087  -1.55142   1.28325   1.51637  -1.32467  -1.48018   1.36511   1.44289  -1.40452   0.00000     ... ... ..... ....... ......... ........... .............
E30      2.00000  -0.13648  -1.98137   0.40691   1.92583  -0.66976  -1.83442   0.92013   1.70884  -1.15336  -1.55142   1.36511   1.36511  -1.55142  -1.15336   1.70884   0.92013  -1.83442  -0.66976   1.92583   0.40691  -1.98137  -0.13648   2.00000  -0.13648  -1.98137   0.40691   1.92583  -0.66976  -1.83442   0.92013   1.70884  -1.15336  -1.55142   1.36511   1.36511  -1.55142  -1.15336   1.70884   0.92013  -1.83442  -0.66976   1.92583   0.40691  -1.98137  -0.13648   2.00000  -0.13648  -1.98137   0.40691   1.92583  -0.66976  -1.83442   0.92013   1.70884  -1.15336  -1.55142   1.36511   0.00000     ... ... ..... ....... ......... ........... .............
E31      2.00000  -0.24524  -1.93985   0.72098   1.76304  -1.15336  -1.48018   1.51637   1.10830  -1.78817  -0.66976   1.95243   0.19094  -1.99925   0.29937   1.92583  -0.77167  -1.73659   1.19756   1.44289  -1.55142  -1.06241   1.81197   0.61803  -1.96354  -0.13648   1.99702  -0.35327  -1.91038   0.82178   1.70884  -1.24087  -1.40452   1.58532   1.01573  -1.83442  -0.56585   1.97319   0.08193  -1.99329   0.40691   1.89349  -0.87128  -1.67982   1.28325   1.36511  -1.61803  -0.96829   1.85550   0.51324  -1.98137  -0.02732   1.98807  -0.46025  -1.87520   0.92013   1.64954  -1.32467   0.00000     ... ... ..... ....... ......... ........... .............
E32      2.00000  -0.35327  -1.87520   1.01573   1.51637  -1.55142  -0.96829   1.89349   0.29937  -1.99925   0.40691   1.85550  -1.06241  -1.48018   1.58532   0.92013  -1.91038  -0.24524   1.99702  -0.46025  -1.83442   1.10830   1.44289  -1.61803  -0.87128   1.92583   0.19094  -1.99329   0.51324   1.81197  -1.15336  -1.40452   1.64954   0.82178  -1.93985  -0.13648   1.98807  -0.56585  -1.78817   1.19756   1.36511  -1.67982  -0.77167   1.95243   0.08193  -1.98137   0.61803   1.76304  -1.24087  -1.32467   1.70884   0.72098  -1.96354  -0.02732   1.97319  -0.66976  -1.73659   1.28325   0.00000     ... ... ..... ....... ......... ........... .............
E33      2.00000  -0.46025  -1.78817   1.28325   1.19756  -1.83442  -0.35327   1.99702  -0.56585  -1.73659   1.36511   1.10830  -1.87520  -0.24524   1.98807  -0.66976  -1.67982   1.44289   1.01573  -1.91038  -0.13648   1.97319  -0.77167  -1.61803   1.51637   0.92013  -1.93985  -0.02732   1.95243  -0.87128  -1.55142   1.58532   0.82178  -1.96354   0.08193   1.92583  -0.96829  -1.48018   1.64954   0.72098  -1.98137   0.19094   1.89349  -1.06241  -1.40452   1.70884   0.61803  -1.99329   0.29937   1.85550  -1.15336  -1.32467   1.76304   0.51324  -1.99925   0.40691   1.81197  -1.24087   0.00000     ... ... ..... ....... ......... ........... .............
E34      2.00000  -0.56585  -1.67982   1.51637   0.82178  -1.98137   0.29937   1.81197  -1.32467  -1.06241   1.92583  -0.02732  -1.91038   1.10830   1.28325  -1.83442  -0.24524   1.97319  -0.87128  -1.48018   1.70884   0.51324  -1.99925   0.61803   1.64954  -1.55142  -0.77167   1.98807  -0.35327  -1.78817   1.36511   1.01573  -1.93985   0.08193   1.89349  -1.15336  -1.24087   1.85550   0.19094  -1.96354   0.92013   1.44289  -1.73659  -0.46025   1.99702  -0.66976  -1.61803   1.58532   0.72098  -1.99329   0.40691   1.76304  -1.40452  -0.96829   1.95243  -0.13648  -1.87520   1.19756   0.00000     ... ... ..... ....... ......... ........... .............
E35      2.00000  -0.66976  -1.55142   1.70884   0.40691  -1.98137   0.92013   1.36511  -1.83442  -0.13648   1.92583  -1.15336  -1.15336   1.92583  -0.13648  -1.83442   1.36511   0.92013  -1.98137   0.40691   1.70884  -1.55142  -0.66976   2.00000  -0.66976  -1.55142   1.70884   0.40691  -1.98137   0.92013   1.36511  -1.83442  -0.13648   1.92583  -1.15336  -1.15336   1.92583  -0.13648  -1.83442   1.36511   0.92013  -1.98137   0.40691   1.70884  -1.55142  -0.66976   2.00000  -0.66976  -1.55142   1.70884   0.40691  -1.98137   0.92013   1.36511  -1.83442  -0.13648   1.92583  -1.15336   0.00000     ... ... ..... ....... ......... ........... .............
E36      2.00000  -0.77167  -1.40452   1.85550  -0.02732  -1.83442   1.44289   0.72098  -1.99925   0.82178   1.36511  -1.87520   0.08193   1.81197  -1.48018  -0.66976   1.99702  -0.87128  -1.32467   1.89349  -0.13648  -1.78817   1.51637   0.61803  -1.99329   0.92013   1.28325  -1.91038   0.19094   1.76304  -1.55142  -0.56585   1.98807  -0.96829  -1.24087   1.92583  -0.24524  -1.73659   1.58532   0.51324  -1.98137   1.01573   1.19756  -1.93985   0.29937   1.70884  -1.61803  -0.46025   1.97319  -1.06241  -1.15336   1.95243  -0.35327  -1.67982   1.64954   0.40691  -1.96354   1.10830   0.00000     ... ... ..... ....... ......... ........... .............
E37      2.00000  -0.87128  -1.24087   1.95243  -0.46025  -1.55142   1.81197  -0.02732  -1.78817   1.58532   0.40691  -1.93985   1.28325   0.82178  -1.99925   0.92013   1.19756  -1.96354   0.51324   1.51637  -1.83442   0.08193   1.76304  -1.61803  -0.35327   1.92583  -1.32467  -0.77167   1.99702  -0.96829  -1.15336   1.97319  -0.56585  -1.48018   1.85550  -0.13648  -1.73659   1.64954   0.29937  -1.91038   1.36511   0.72098  -1.99329   1.01573   1.10830  -1.98137   0.61803   1.44289  -1.87520   0.19094   1.70884  -1.67982  -0.24524   1.89349  -1.40452  -0.66976   1.98807  -1.06241   0.00000     ... ... ..... ....... ......... ........... .............
E38      2.00000  -0.96829  -1.06241   1.99702  -0.87128  -1.15336   1.98807  -0.77167  -1.24087   1.97319  -0.66976  -1.32467   1.95243  -0.56585  -1.40452   1.92583  -0.46025  -1.48018   1.89349  -0.35327  -1.55142   1.85550  -0.24524  -1.61803   1.81197  -0.13648  -1.67982   1.76304  -0.02732  -1.73659   1.70884   0.08193  -1.78817   1.64954   0.19094  -1.83442   1.58532   0.29937  -1.87520   1.51637   0.40691  -1.91038   1.44289   0.51324  -1.93985   1.36511   0.61803  -1.96354   1.28325   0.72098  -1.98137   1.19756   0.82178  -1.99329   1.10830   0.92013  -1.99925   1.01573   0.00000     ... ... ..... ....... ......... ........... .............
E39      2.00000  -1.06241  -0.87128   1.98807  -1.24087  -0.66976   1.95243  -1.40452  -0.46025   1.89349  -1.55142  -0.24524   1.81197  -1.67982  -0.02732   1.70884  -1.78817   0.19094   1.58532  -1.87520   0.40691   1.44289  -1.93985   0.61803   1.28325  -1.98137   0.82178   1.10830  -1.99925   1.01573   0.92013  -1.99329   1.19756   0.72098  -1.96354   1.36511   0.51324  -1.91038   1.51637   0.29937  -1.83442   1.64954   0.08193  -1.73659   1.76304  -0.13648  -1.61803   1.85550  -0.35327  -1.48018   1.92583  -0.56585  -1.32467   1.97319  -0.77167  -1.15336   1.99702  -0.96829   0.00000     ... ... ..... ....... ......... ........... .............
E40      2.00000  -1.15336  -0.66976   1.92583  -1.55142  -0.13648   1.70884  -1.83442   0.40691   1.36511  -1.98137   0.92013   0.92013  -1.98137   1.36511   0.40691  -1.83442   1.70884  -0.13648  -1.55142   1.92583  -0.66976  -1.15336   2.00000  -1.15336  -0.66976   1.92583  -1.55142  -0.13648   1.70884  -1.83442   0.40691   1.36511  -1.98137   0.92013   0.92013  -1.98137   1.36511   0.40691  -1.83442   1.70884  -0.13648  -1.55142   1.92583  -0.66976  -1.15336   2.00000  -1.15336  -0.66976   1.92583  -1.55142  -0.13648   1.70884  -1.83442   0.40691   1.36511  -1.98137   0.92013   0.00000     ... ... ..... ....... ......... ........... .............
E41      2.00000  -1.24087  -0.46025   1.81197  -1.78817   0.40691   1.28325  -1.99925   1.19756   0.51324  -1.83442   1.76304  -0.35327  -1.32467   1.99702  -1.15336  -0.56585   1.85550  -1.73659   0.29937   1.36511  -1.99329   1.10830   0.61803  -1.87520   1.70884  -0.24524  -1.40452   1.98807  -1.06241  -0.66976   1.89349  -1.67982   0.19094   1.44289  -1.98137   1.01573   0.72098  -1.91038   1.64954  -0.13648  -1.48018   1.97319  -0.96829  -0.77167   1.92583  -1.61803   0.08193   1.51637  -1.96354   0.92013   0.82178  -1.93985   1.58532  -0.02732  -1.55142   1.95243  -0.87128   0.00000     ... ... ..... ....... ......... ........... .............
E42      2.00000  -1.32467  -0.24524   1.64954  -1.93985   0.92013   0.72098  -1.87520   1.76304  -0.46025  -1.15336   1.98807  -1.48018  -0.02732   1.51637  -1.98137   1.10830   0.51324  -1.78817   1.85550  -0.66976  -0.96829   1.95243  -1.61803   0.19094   1.36511  -1.99925   1.28325   0.29937  -1.67982   1.92583  -0.87128  -0.77167   1.89349  -1.73659   0.40691   1.19756  -1.99329   1.44289   0.08193  -1.55142   1.97319  -1.06241  -0.56585   1.81197  -1.83442   0.61803   1.01573  -1.96354   1.58532  -0.13648  -1.40452   1.99702  -1.24087  -0.35327   1.70884  -1.91038   0.82178   0.00000     ... ... ..... ....... ......... ........... .............
E43      2.00000  -1.40452  -0.02732   1.44289  -1.99925   1.36511   0.08193  -1.48018   1.99702  -1.32467  -0.13648   1.51637  -1.99329   1.28325   0.19094  -1.55142   1.98807  -1.24087  -0.24524   1.58532  -1.98137   1.19756   0.29937  -1.61803   1.97319  -1.15336  -0.35327   1.64954  -1.96354   1.10830   0.40691  -1.67982   1.95243  -1.06241  -0.46025   1.70884  -1.93985   1.01573   0.51324  -1.73659   1.92583  -0.96829  -0.56585   1.76304  -1.91038   0.92013   0.61803  -1.78817   1.89349  -0.87128  -0.66976   1.81197  -1.87520   0.82178   0.72098  -1.83442   1.85550  -0.77167   0.00000     ... ... ..... ....... ......... ........... .............
E44      2.00000  -1.48018   0.19094   1.19756  -1.96354   1.70884  -0.56585  -0.87128   1.85550  -1.87520   0.92013   0.51324  -1.67982   1.97319  -1.24087  -0.13648   1.44289  -1.99925   1.51637  -0.24524  -1.15336   1.95243  -1.73659   0.61803   0.82178  -1.83442   1.89349  -0.96829  -0.46025   1.64954  -1.98137   1.28325   0.08193  -1.40452   1.99702  -1.55142   0.29937   1.10830  -1.93985   1.76304  -0.66976  -0.77167   1.81197  -1.91038   1.01573   0.40691  -1.61803   1.98807  -1.32467  -0.02732   1.36511  -1.99329   1.58532  -0.35327  -1.06241   1.92583  -1.78817   0.72098   0.00000     ... ... ..... ....... ......... ........... .............
E45      2.00000  -1.55142   0.40691   0.92013  -1.83442   1.92583  -1.15336  -0.13648   1.36511  -1.98137   1.70884  -0.66976  -0.66976   1.70884  -1.98137   1.36511  -0.13648  -1.15336   1.92583  -1.83442   0.92013   0.40691  -1.55142   2.00000  -1.55142   0.40691   0.92013  -1.83442   1.92583  -1.15336  -0.13648   1.36511  -1.98137   1.70884  -0.66976  -0.66976   1.70884  -1.98137   1.36511  -0.13648  -1.15336   1.92583  -1.83442   0.92013   0.40691  -1.55142   2.00000  -1.55142   0.40691   0.92013  -1.83442   1.92583  -1.15336  -0.13648   1.36511  -1.98137   1.70884  -0.66976   0.00000     ... ... ..... ....... ......... ........... .............
E46      2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.00000     ... ... ..... ....... ......... ........... .............
E47      2.00000  -1.67982   0.82178   0.29937  -1.32467   1.92583  -1.91038   1.28325  -0.24524  -0.87128   1.70884  -1.99925   1.64954  -0.77167  -0.35327   1.36511  -1.93985   1.89349  -1.24087   0.19094   0.92013  -1.73659   1.99702  -1.61803   0.72098   0.40691  -1.40452   1.95243  -1.87520   1.19756  -0.13648  -0.96829   1.76304  -1.99329   1.58532  -0.66976  -0.46025   1.44289  -1.96354   1.85550  -1.15336   0.08193   1.01573  -1.78817   1.98807  -1.55142   0.61803   0.51324  -1.48018   1.97319  -1.83442   1.10830  -0.02732  -1.06241   1.81197  -1.98137   1.51637  -0.56585   0.00000     ... ... ..... ....... ......... ........... .............
E48      2.00000  -1.73659   1.01573  -0.02732  -0.96829   1.70884  -1.99925   1.76304  -1.06241   0.08193   0.92013  -1.67982   1.99702  -1.78817   1.10830  -0.13648  -0.87128   1.64954  -1.99329   1.81197  -1.15336   0.19094   0.82178  -1.61803   1.98807  -1.83442   1.19756  -0.24524  -0.77167   1.58532  -1.98137   1.85550  -1.24087   0.29937   0.72098  -1.55142   1.97319  -1.87520   1.28325  -0.35327  -0.66976   1.51637  -1.96354   1.89349  -1.32467   0.40691   0.61803  -1.48018   1.95243  -1.91038   1.36511  -0.46025  -0.56585   1.44289  -1.93985   1.92583  -1.40452   0.51324   0.00000     ... ... ..... ....... ......... ........... .............
E49      2.00000  -1.78817   1.19756  -0.35327  -0.56585   1.36511  -1.87520   1.98807  -1.67982   1.01573  -0.13648  -0.77167   1.51637  -1.93985   1.95243  -1.55142   0.82178   0.08193  -0.96829   1.64954  -1.98137   1.89349  -1.40452   0.61803   0.29937  -1.15336   1.76304  -1.99925   1.81197  -1.24087   0.40691   0.51324  -1.32467   1.85550  -1.99329   1.70884  -1.06241   0.19094   0.72098  -1.48018   1.92583  -1.96354   1.58532  -0.87128  -0.02732   0.92013  -1.61803   1.97319  -1.91038   1.44289  -0.66976  -0.24524   1.10830  -1.73659   1.99702  -1.83442   1.28325  -0.46025   0.00000     ... ... ..... ....... ......... ........... .............
E50      2.00000  -1.83442   1.36511  -0.66976  -0.13648   0.92013  -1.55142   1.92583  -1.98137   1.70884  -1.15336   0.40691   0.40691  -1.15336   1.70884  -1.98137   1.92583  -1.55142   0.92013  -0.13648  -0.66976   1.36511  -1.83442   2.00000  -1.83442   1.36511  -0.66976  -0.13648   0.92013  -1.55142   1.92583  -1.98137   1.70884  -1.15336   0.40691   0.40691  -1.15336   1.70884  -1.98137   1.92583  -1.55142   0.92013  -0.13648  -0.66976   1.36511  -1.83442   2.00000  -1.83442   1.36511  -0.66976  -0.13648   0.92013  -1.55142   1.92583  -1.98137   1.70884  -1.15336   0.40691   0.00000     ... ... ..... ....... ......... ........... .............
E51      2.00000  -1.87520   1.51637  -0.96829   0.29937   0.40691  -1.06241   1.58532  -1.91038   1.99702  -1.83442   1.44289  -0.87128   0.19094   0.51324  -1.15336   1.64954  -1.93985   1.98807  -1.78817   1.36511  -0.77167   0.08193   0.61803  -1.24087   1.70884  -1.96354   1.97319  -1.73659   1.28325  -0.66976  -0.02732   0.72098  -1.32467   1.76304  -1.98137   1.95243  -1.67982   1.19756  -0.56585  -0.13648   0.82178  -1.40452   1.81197  -1.99329   1.92583  -1.61803   1.10830  -0.46025  -0.24524   0.92013  -1.48018   1.85550  -1.99925   1.89349  -1.55142   1.01573  -0.35327   0.00000     ... ... ..... ....... ......... ........... .............
E52      2.00000  -1.91038   1.64954  -1.24087   0.72098  -0.13648  -0.46025   1.01573  -1.48018   1.81197  -1.98137   1.97319  -1.78817   1.44289  -0.96829   0.40691   0.19094  -0.77167   1.28325  -1.67982   1.92583  -1.99925   1.89349  -1.61803   1.19756  -0.66976   0.08193   0.51324  -1.06241   1.51637  -1.83442   1.98807  -1.96354   1.76304  -1.40452   0.92013  -0.35327  -0.24524   0.82178  -1.32467   1.70884  -1.93985   1.99702  -1.87520   1.58532  -1.15336   0.61803  -0.02732  -0.56585   1.10830  -1.55142   1.85550  -1.99329   1.95243  -1.73659   1.36511  -0.87128   0.29937   0.00000     ... ... ..... ....... ......... ........... .............
E53      2.00000  -1.93985   1.76304  -1.48018   1.10830  -0.66976   0.19094   0.29937  -0.77167   1.19756  -1.55142   1.81197  -1.96354   1.99702  -1.91038   1.70884  -1.40452   1.01573  -0.56585   0.08193   0.40691  -0.87128   1.28325  -1.61803   1.85550  -1.98137   1.98807  -1.87520   1.64954  -1.32467   0.92013  -0.46025  -0.02732   0.51324  -0.96829   1.36511  -1.67982   1.89349  -1.99329   1.97319  -1.83442   1.58532  -1.24087   0.82178  -0.35327  -0.13648   0.61803  -1.06241   1.44289  -1.73659   1.92583  -1.99925   1.95243  -1.78817   1.51637  -1.15336   0.72098  -0.24524   0.00000     ... ... ..... ....... ......... ........... .............
E54      2.00000  -1.96354   1.85550  -1.67982   1.44289  -1.15336   0.82178  -0.46025   0.08193   0.29937  -0.66976   1.01573  -1.32467   1.58532  -1.78817   1.92583  -1.99329   1.98807  -1.91038   1.76304  -1.55142   1.28325  -0.96829   0.61803  -0.24524  -0.13648   0.51324  -0.87128   1.19756  -1.48018   1.70884  -1.87520   1.97319  -1.99925   1.95243  -1.83442   1.64954  -1.40452   1.10830  -0.77167   0.40691  -0.02732  -0.35327   0.72098  -1.06241   1.36511  -1.61803   1.81197  -1.93985   1.99702  -1.98137   1.89349  -1.73659   1.51637  -1.24087   0.92013  -0.56585   0.19094   0.00000     ... ... ..... ....... ......... ........... .............
E55      2.00000  -1.98137   1.92583  -1.83442   1.70884  -1.55142   1.36511  -1.15336   0.92013  -0.66976   0.40691  -0.13648  -0.13648   0.40691  -0.66976   0.92013  -1.15336   1.36511  -1.55142   1.70884  -1.83442   1.92583  -1.98137   2.00000  -1.98137   1.92583  -1.83442   1.70884  -1.55142   1.36511  -1.15336   0.92013  -0.66976   0.40691  -0.13648  -0.13648   0.40691  -0.66976   0.92013  -1.15336   1.36511  -1.55142   1.70884  -1.83442   1.92583  -1.98137   2.00000  -1.98137   1.92583  -1.83442   1.70884  -1.55142   1.36511  -1.15336   0.92013  -0.66976   0.40691  -0.13648   0.00000     ... ... ..... ....... ......... ........... .............
E56      2.00000  -1.99329   1.97319  -1.93985   1.89349  -1.83442   1.76304  -1.67982   1.58532  -1.48018   1.36511  -1.24087   1.10830  -0.96829   0.82178  -0.66976   0.51324  -0.35327   0.19094  -0.02732  -0.13648   0.29937  -0.46025   0.61803  -0.77167   0.92013  -1.06241   1.19756  -1.32467   1.44289  -1.55142   1.64954  -1.73659   1.81197  -1.87520   1.92583  -1.96354   1.98807  -1.99925   1.99702  -1.98137   1.95243  -1.91038   1.85550  -1.78817   1.70884  -1.61803   1.51637  -1.40452   1.28325  -1.15336   1.01573  -0.87128   0.72098  -0.56585   0.40691  -0.24524   0.08193   0.00000     ... ... ..... ....... ......... ........... .............
E57      2.00000  -1.99925   1.99702  -1.99329   1.98807  -1.98137   1.97319  -1.96354   1.95243  -1.93985   1.92583  -1.91038   1.89349  -1.87520   1.85550  -1.83442   1.81197  -1.78817   1.76304  -1.73659   1.70884  -1.67982   1.64954  -1.61803   1.58532  -1.55142   1.51637  -1.48018   1.44289  -1.40452   1.36511  -1.32467   1.28325  -1.24087   1.19756  -1.15336   1.10830  -1.06241   1.01573  -0.96829   0.92013  -0.87128   0.82178  -0.77167   0.72098  -0.66976   0.61803  -0.56585   0.51324  -0.46025   0.40691  -0.35327   0.29937  -0.24524   0.19094  -0.13648   0.08193  -0.02732   0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.997015606966 = 2*cos(2*π/115)
                               1.988071334464 = 2*cos(4*π/115)
                               1.973193875721 = 2*cos(6*π/115)
                               1.952427630919 = 2*cos(8*π/115)
                               1.925834574696 = 2*cos(10*π/115) = 2*cos(2*π/23)
                               1.893494071182 = 2*cos(12*π/115)
                               1.855502637152 = 2*cos(14*π/115)
                               1.811973653976 = 2*cos(16*π/115)
                               1.763037029249 = 2*cos(18*π/115)
                               1.708838809093 = 2*cos(20*π/115) = 2*cos(4*π/23)
                               1.649540742298 = 2*cos(22*π/115)
                               1.585319797602 = 2*cos(24*π/115)
                               1.516367635544 = 2*cos(26*π/115)
                               1.442890036478 = 2*cos(28*π/115)
                               1.365106286437 = 2*cos(30*π/115) = 2*cos(6*π/23)
                               1.283248522704 = 2*cos(32*π/115)
                               1.197561041019 = 2*cos(34*π/115)
                               1.108299566504 = 2*cos(36*π/115)
                               1.015730490484 = 2*cos(38*π/115)
                               0.920130075462 = 2*cos(40*π/115) = 2*cos(8*π/23)
                               0.821783630653 = 2*cos(42*π/115)
                               0.720984660501 = 2*cos(44*π/115)
                               0.618033988750 = 2*cos(46*π/115) = 2*cos(2*π/5) = (√5−1)/2
                               0.513238860668 = 2*cos(48*π/115)
                               0.406912026105 = 2*cos(50*π/115) = 2*cos(10*π/23)
                               0.299370806126 = 2*cos(52*π/115)
                               0.190936145999 = 2*cos(54*π/115)
                               0.081931657367 = 2*cos(56*π/115)
                              -0.027317347532 = 2*cos(58*π/115)
                              -0.136484826729 = 2*cos(60*π/115) = 2*cos(12*π/23)
                              -0.245244981561 = 2*cos(62*π/115)
                              -0.353273228977 = 2*cos(64*π/115)
                              -0.460247170230 = 2*cos(66*π/115)
                              -0.565847553034 = 2*cos(68*π/115)
                              -0.669759224342 = 2*cos(70*π/115) = 2*cos(14*π/23)
                              -0.771672070886 = 2*cos(72*π/115)
                              -0.871281944677 = 2*cos(74*π/115)
                              -0.968291570702 = 2*cos(76*π/115)
                              -1.062411434108 = 2*cos(78*π/115)
                              -1.153360644230 = 2*cos(80*π/115) = 2*cos(16*π/23)
                              -1.240867772879 = 2*cos(82*π/115)
                              -1.324671664391 = 2*cos(84*π/115)
                              -1.404522215014 = 2*cos(86*π/115)
                              -1.480181119323 = 2*cos(88*π/115)
                              -1.551422581409 = 2*cos(90*π/115) = 2*cos(18*π/23)
                              -1.618033988750 = 2*cos(92*π/115) = 2*cos(4*π/5) = −(√5+1)/2
                              -1.679816546726 = 2*cos(94*π/115)
                              -1.736585871900 = 2*cos(96*π/115)
                              -1.788172542295 = 2*cos(98*π/115)
                              -1.834422603011 = 2*cos(100*π/115) = 2*cos(20*π/23)
                              -1.875198025688 = 2*cos(102*π/115)
                              -1.910377120439 = 2*cos(104*π/115)
                              -1.939854899019 = 2*cos(106*π/115)
                              -1.963543388151 = 2*cos(108*π/115)
                              -1.981371892073 = 2*cos(110*π/115) = 2*cos(22*π/23)
                              -1.993287203521 = 2*cos(112*π/115)
                              -1.999253762524 = 2*cos(114*π/115)



 Symmetry of Rotations and Cartesian products

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

 Notes:

    α  The order of the D115 point group is 230, and the order of the principal axis (C115) is 115. The group has 59 irreducible representations.

    β  The D115 point group is isomorphic to C115v.

    γ  The D115 point group is generated by two symmetry elements, C115 and a perpendicular C2.
       Also, the group may be generated from two C2 axes (some pairs will yield smaller groups, though; choosing a minimum angle is safe).

    δ  The lowest nonvanishing multipole moment in D115 is 4 (quadrupole moment).

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

    ζ  The point group is chiral, as it does not contain any mirroring operation.

    η  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.
       For this group, however, some of the irrational characters cannot be expressed by a closed algebraic form using real numbers only.

This Character Table for the D115 point group was created by Gernot Katzer.

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