Character table for the C123 point group

C123    E         2 C123    2 C123^2  2 C41     2 C123^4  2 C123^5  2 C41^2   2 C123^7  2 C123^8  2 C41^3   2 C123^10 2 C123^11 2 C41^4   2 C123^13 2 C123^14 2 C41^5   2 C123^16 2 C123^17 2 C41^6   2 C123^19 2 C123^20 2 C41^7   2 C123^22 2 C123^23 2 C41^8   2 C123^25 2 C123^26 2 C41^9   2 C123^28 2 C123^29 2 C41^10  2 C123^31 2 C123^32 2 C41^11  2 C123^34 2 C123^35 2 C41^12  2 C123^37 2 C123^38 2 C41^13  2 C123^40 2 C3      2 C41^14  2 C123^43 2 C123^44 2 C41^15  2 C123^46 2 C123^47 2 C41^16  2 C123^49 2 C123^50 2 C41^17  2 C123^52 2 C123^53 2 C41^18  2 C123^55 2 C123^56 2 C41^19  2 C123^58 2 C123^59 2 C41^20  2 C123^61    <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A        1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   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 ........T ..........T ............T
E1  *    2.00000   1.99739   1.98957   1.97656   1.95839   1.93512   1.90679   1.87349   1.83531   1.79233   1.74468   1.69248   1.63586   1.57497   1.50998   1.44104   1.36835   1.29209   1.21245   1.12965   1.04391   0.95544   0.86448   0.77126   0.67603   0.57904   0.48054   0.38078   0.28003   0.17855   0.07661  -0.02554  -0.12762  -0.22937  -0.33052  -0.43080  -0.52996  -0.62774  -0.72388  -0.81814  -0.91026  -1.00000  -1.08714  -1.17143  -1.25268  -1.33065  -1.40515  -1.47599  -1.54298  -1.60594  -1.66471  -1.71914  -1.76908  -1.81441  -1.85500  -1.89076  -1.92158  -1.94739  -1.96812  -1.98371  -1.99413  -1.99935     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2  *    2.00000   1.98957   1.95839   1.90679   1.83531   1.74468   1.63586   1.50998   1.36835   1.21245   1.04391   0.86448   0.67603   0.48054   0.28003   0.07661  -0.12762  -0.33052  -0.52996  -0.72388  -0.91026  -1.08714  -1.25268  -1.40515  -1.54298  -1.66471  -1.76908  -1.85500  -1.92158  -1.96812  -1.99413  -1.99935  -1.98371  -1.94739  -1.89076  -1.81441  -1.71914  -1.60594  -1.47599  -1.33065  -1.17143  -1.00000  -0.81814  -0.62774  -0.43080  -0.22937  -0.02554   0.17855   0.38078   0.57904   0.77126   0.95544   1.12965   1.29209   1.44104   1.57497   1.69248   1.79233   1.87349   1.93512   1.97656   1.99739     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3  *    2.00000   1.97656   1.90679   1.79233   1.63586   1.44104   1.21245   0.95544   0.67603   0.38078   0.07661  -0.22937  -0.52996  -0.81814  -1.08714  -1.33065  -1.54298  -1.71914  -1.85500  -1.94739  -1.99413  -1.99413  -1.94739  -1.85500  -1.71914  -1.54298  -1.33065  -1.08714  -0.81814  -0.52996  -0.22937   0.07661   0.38078   0.67603   0.95544   1.21245   1.44104   1.63586   1.79233   1.90679   1.97656   2.00000   1.97656   1.90679   1.79233   1.63586   1.44104   1.21245   0.95544   0.67603   0.38078   0.07661  -0.22937  -0.52996  -0.81814  -1.08714  -1.33065  -1.54298  -1.71914  -1.85500  -1.94739  -1.99413     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4  *    2.00000   1.95839   1.83531   1.63586   1.36835   1.04391   0.67603   0.28003  -0.12762  -0.52996  -0.91026  -1.25268  -1.54298  -1.76908  -1.92158  -1.99413  -1.98371  -1.89076  -1.71914  -1.47599  -1.17143  -0.81814  -0.43080  -0.02554   0.38078   0.77126   1.12965   1.44104   1.69248   1.87349   1.97656   1.99739   1.93512   1.79233   1.57497   1.29209   0.95544   0.57904   0.17855  -0.22937  -0.62774  -1.00000  -1.33065  -1.60594  -1.81441  -1.94739  -1.99935  -1.96812  -1.85500  -1.66471  -1.40515  -1.08714  -0.72388  -0.33052   0.07661   0.48054   0.86448   1.21245   1.50998   1.74468   1.90679   1.98957     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5  *    2.00000   1.93512   1.74468   1.44104   1.04391   0.57904   0.07661  -0.43080  -0.91026  -1.33065  -1.66471  -1.89076  -1.99413  -1.96812  -1.81441  -1.54298  -1.17143  -0.72388  -0.22937   0.28003   0.77126   1.21245   1.57497   1.83531   1.97656   1.98957   1.87349   1.63586   1.29209   0.86448   0.38078  -0.12762  -0.62774  -1.08714  -1.47599  -1.76908  -1.94739  -1.99935  -1.92158  -1.71914  -1.40515  -1.00000  -0.52996  -0.02554   0.48054   0.95544   1.36835   1.69248   1.90679   1.99739   1.95839   1.79233   1.50998   1.12965   0.67603   0.17855  -0.33052  -0.81814  -1.25268  -1.60594  -1.85500  -1.98371     ... ... ..... ....... ......... TT......... ..TT.........
E6  *    2.00000   1.90679   1.63586   1.21245   0.67603   0.07661  -0.52996  -1.08714  -1.54298  -1.85500  -1.99413  -1.94739  -1.71914  -1.33065  -0.81814  -0.22937   0.38078   0.95544   1.44104   1.79233   1.97656   1.97656   1.79233   1.44104   0.95544   0.38078  -0.22937  -0.81814  -1.33065  -1.71914  -1.94739  -1.99413  -1.85500  -1.54298  -1.08714  -0.52996   0.07661   0.67603   1.21245   1.63586   1.90679   2.00000   1.90679   1.63586   1.21245   0.67603   0.07661  -0.52996  -1.08714  -1.54298  -1.85500  -1.99413  -1.94739  -1.71914  -1.33065  -0.81814  -0.22937   0.38078   0.95544   1.44104   1.79233   1.97656     ... ... ..... ....... ......... ........... TT...........
E7  *    2.00000   1.87349   1.50998   0.95544   0.28003  -0.43080  -1.08714  -1.60594  -1.92158  -1.99413  -1.81441  -1.40515  -0.81814  -0.12762   0.57904   1.21245   1.69248   1.95839   1.97656   1.74468   1.29209   0.67603  -0.02554  -0.72388  -1.33065  -1.76908  -1.98371  -1.94739  -1.66471  -1.17143  -0.52996   0.17855   0.86448   1.44104   1.83531   1.99739   1.90679   1.57497   1.04391   0.38078  -0.33052  -1.00000  -1.54298  -1.89076  -1.99935  -1.85500  -1.47599  -0.91026  -0.22937   0.48054   1.12965   1.63586   1.93512   1.98957   1.79233   1.36835   0.77126   0.07661  -0.62774  -1.25268  -1.71914  -1.96812     ... ... ..... ....... ......... ........... .............
E8  *    2.00000   1.83531   1.36835   0.67603  -0.12762  -0.91026  -1.54298  -1.92158  -1.98371  -1.71914  -1.17143  -0.43080   0.38078   1.12965   1.69248   1.97656   1.93512   1.57497   0.95544   0.17855  -0.62774  -1.33065  -1.81441  -1.99935  -1.85500  -1.40515  -0.72388   0.07661   0.86448   1.50998   1.90679   1.98957   1.74468   1.21245   0.48054  -0.33052  -1.08714  -1.66471  -1.96812  -1.94739  -1.60594  -1.00000  -0.22937   0.57904   1.29209   1.79233   1.99739   1.87349   1.44104   0.77126  -0.02554  -0.81814  -1.47599  -1.89076  -1.99413  -1.76908  -1.25268  -0.52996   0.28003   1.04391   1.63586   1.95839     ... ... ..... ....... ......... ........... .............
E9  *    2.00000   1.79233   1.21245   0.38078  -0.52996  -1.33065  -1.85500  -1.99413  -1.71914  -1.08714  -0.22937   0.67603   1.44104   1.90679   1.97656   1.63586   0.95544   0.07661  -0.81814  -1.54298  -1.94739  -1.94739  -1.54298  -0.81814   0.07661   0.95544   1.63586   1.97656   1.90679   1.44104   0.67603  -0.22937  -1.08714  -1.71914  -1.99413  -1.85500  -1.33065  -0.52996   0.38078   1.21245   1.79233   2.00000   1.79233   1.21245   0.38078  -0.52996  -1.33065  -1.85500  -1.99413  -1.71914  -1.08714  -0.22937   0.67603   1.44104   1.90679   1.97656   1.63586   0.95544   0.07661  -0.81814  -1.54298  -1.94739     ... ... ..... ....... ......... ........... .............
E10 *    2.00000   1.74468   1.04391   0.07661  -0.91026  -1.66471  -1.99413  -1.81441  -1.17143  -0.22937   0.77126   1.57497   1.97656   1.87349   1.29209   0.38078  -0.62774  -1.47599  -1.94739  -1.92158  -1.40515  -0.52996   0.48054   1.36835   1.90679   1.95839   1.50998   0.67603  -0.33052  -1.25268  -1.85500  -1.98371  -1.60594  -0.81814   0.17855   1.12965   1.79233   1.99739   1.69248   0.95544  -0.02554  -1.00000  -1.71914  -1.99935  -1.76908  -1.08714  -0.12762   0.86448   1.63586   1.98957   1.83531   1.21245   0.28003  -0.72388  -1.54298  -1.96812  -1.89076  -1.33065  -0.43080   0.57904   1.44104   1.93512     ... ... ..... ....... ......... ........... .............
E11 *    2.00000   1.69248   0.86448  -0.22937  -1.25268  -1.89076  -1.94739  -1.40515  -0.43080   0.67603   1.57497   1.98957   1.79233   1.04391  -0.02554  -1.08714  -1.81441  -1.98371  -1.54298  -0.62774   0.48054   1.44104   1.95839   1.87349   1.21245   0.17855  -0.91026  -1.71914  -1.99935  -1.66471  -0.81814   0.28003   1.29209   1.90679   1.93512   1.36835   0.38078  -0.72388  -1.60594  -1.99413  -1.76908  -1.00000   0.07661   1.12965   1.83531   1.97656   1.50998   0.57904  -0.52996  -1.47599  -1.96812  -1.85500  -1.17143  -0.12762   0.95544   1.74468   1.99739   1.63586   0.77126  -0.33052  -1.33065  -1.92158     ... ... ..... ....... ......... ........... .............
E12 *    2.00000   1.63586   0.67603  -0.52996  -1.54298  -1.99413  -1.71914  -0.81814   0.38078   1.44104   1.97656   1.79233   0.95544  -0.22937  -1.33065  -1.94739  -1.85500  -1.08714   0.07661   1.21245   1.90679   1.90679   1.21245   0.07661  -1.08714  -1.85500  -1.94739  -1.33065  -0.22937   0.95544   1.79233   1.97656   1.44104   0.38078  -0.81814  -1.71914  -1.99413  -1.54298  -0.52996   0.67603   1.63586   2.00000   1.63586   0.67603  -0.52996  -1.54298  -1.99413  -1.71914  -0.81814   0.38078   1.44104   1.97656   1.79233   0.95544  -0.22937  -1.33065  -1.94739  -1.85500  -1.08714   0.07661   1.21245   1.90679     ... ... ..... ....... ......... ........... .............
E13 *    2.00000   1.57497   0.48054  -0.81814  -1.76908  -1.96812  -1.33065  -0.12762   1.12965   1.90679   1.87349   1.04391  -0.22937  -1.40515  -1.98371  -1.71914  -0.72388   0.57904   1.63586   1.99739   1.50998   0.38078  -0.91026  -1.81441  -1.94739  -1.25268  -0.02554   1.21245   1.93512   1.83531   0.95544  -0.33052  -1.47599  -1.99413  -1.66471  -0.62774   0.67603   1.69248   1.98957   1.44104   0.28003  -1.00000  -1.85500  -1.92158  -1.17143   0.07661   1.29209   1.95839   1.79233   0.86448  -0.43080  -1.54298  -1.99935  -1.60594  -0.52996   0.77126   1.74468   1.97656   1.36835   0.17855  -1.08714  -1.89076     ... ... ..... ....... ......... ........... .............
E14 *    2.00000   1.50998   0.28003  -1.08714  -1.92158  -1.81441  -0.81814   0.57904   1.69248   1.97656   1.29209  -0.02554  -1.33065  -1.98371  -1.66471  -0.52996   0.86448   1.83531   1.90679   1.04391  -0.33052  -1.54298  -1.99935  -1.47599  -0.22937   1.12965   1.93512   1.79233   0.77126  -0.62774  -1.71914  -1.96812  -1.25268   0.07661   1.36835   1.98957   1.63586   0.48054  -0.91026  -1.85500  -1.89076  -1.00000   0.38078   1.57497   1.99739   1.44104   0.17855  -1.17143  -1.94739  -1.76908  -0.72388   0.67603   1.74468   1.95839   1.21245  -0.12762  -1.40515  -1.99413  -1.60594  -0.43080   0.95544   1.87349     ... ... ..... ....... ......... ........... .............
E15 *    2.00000   1.44104   0.07661  -1.33065  -1.99413  -1.54298  -0.22937   1.21245   1.97656   1.63586   0.38078  -1.08714  -1.94739  -1.71914  -0.52996   0.95544   1.90679   1.79233   0.67603  -0.81814  -1.85500  -1.85500  -0.81814   0.67603   1.79233   1.90679   0.95544  -0.52996  -1.71914  -1.94739  -1.08714   0.38078   1.63586   1.97656   1.21245  -0.22937  -1.54298  -1.99413  -1.33065   0.07661   1.44104   2.00000   1.44104   0.07661  -1.33065  -1.99413  -1.54298  -0.22937   1.21245   1.97656   1.63586   0.38078  -1.08714  -1.94739  -1.71914  -0.52996   0.95544   1.90679   1.79233   0.67603  -0.81814  -1.85500     ... ... ..... ....... ......... ........... .............
E16 *    2.00000   1.36835  -0.12762  -1.54298  -1.98371  -1.17143   0.38078   1.69248   1.93512   0.95544  -0.62774  -1.81441  -1.85500  -0.72388   0.86448   1.90679   1.74468   0.48054  -1.08714  -1.96812  -1.60594  -0.22937   1.29209   1.99739   1.44104  -0.02554  -1.47599  -1.99413  -1.25268   0.28003   1.63586   1.95839   1.04391  -0.52996  -1.76908  -1.89076  -0.81814   0.77126   1.87349   1.79233   0.57904  -1.00000  -1.94739  -1.66471  -0.33052   1.21245   1.98957   1.50998   0.07661  -1.40515  -1.99935  -1.33065   0.17855   1.57497   1.97656   1.12965  -0.43080  -1.71914  -1.92158  -0.91026   0.67603   1.83531     ... ... ..... ....... ......... ........... .............
E17 *    2.00000   1.29209  -0.33052  -1.71914  -1.89076  -0.72388   0.95544   1.95839   1.57497   0.07661  -1.47599  -1.98371  -1.08714   0.57904   1.83531   1.79233   0.48054  -1.17143  -1.99413  -1.40515   0.17855   1.63586   1.93512   0.86448  -0.81814  -1.92158  -1.66471  -0.22937   1.36835   1.99739   1.21245  -0.43080  -1.76908  -1.85500  -0.62774   1.04391   1.97656   1.50998  -0.02554  -1.54298  -1.96812  -1.00000   0.67603   1.87349   1.74468   0.38078  -1.25268  -1.99935  -1.33065   0.28003   1.69248   1.90679   0.77126  -0.91026  -1.94739  -1.60594  -0.12762   1.44104   1.98957   1.12965  -0.52996  -1.81441     ... ... ..... ....... ......... ........... .............
E18 *    2.00000   1.21245  -0.52996  -1.85500  -1.71914  -0.22937   1.44104   1.97656   0.95544  -0.81814  -1.94739  -1.54298   0.07661   1.63586   1.90679   0.67603  -1.08714  -1.99413  -1.33065   0.38078   1.79233   1.79233   0.38078  -1.33065  -1.99413  -1.08714   0.67603   1.90679   1.63586   0.07661  -1.54298  -1.94739  -0.81814   0.95544   1.97656   1.44104  -0.22937  -1.71914  -1.85500  -0.52996   1.21245   2.00000   1.21245  -0.52996  -1.85500  -1.71914  -0.22937   1.44104   1.97656   0.95544  -0.81814  -1.94739  -1.54298   0.07661   1.63586   1.90679   0.67603  -1.08714  -1.99413  -1.33065   0.38078   1.79233     ... ... ..... ....... ......... ........... .............
E19 *    2.00000   1.12965  -0.72388  -1.94739  -1.47599   0.28003   1.79233   1.74468   0.17855  -1.54298  -1.92158  -0.62774   1.21245   1.99739   1.04391  -0.81814  -1.96812  -1.40515   0.38078   1.83531   1.69248   0.07661  -1.60594  -1.89076  -0.52996   1.29209   1.98957   0.95544  -0.91026  -1.98371  -1.33065   0.48054   1.87349   1.63586  -0.02554  -1.66471  -1.85500  -0.43080   1.36835   1.97656   0.86448  -1.00000  -1.99413  -1.25268   0.57904   1.90679   1.57497  -0.12762  -1.71914  -1.81441  -0.33052   1.44104   1.95839   0.77126  -1.08714  -1.99935  -1.17143   0.67603   1.93512   1.50998  -0.22937  -1.76908     ... ... ..... ....... ......... ........... .............
E20 *    2.00000   1.04391  -0.91026  -1.99413  -1.17143   0.77126   1.97656   1.29209  -0.62774  -1.94739  -1.40515   0.48054   1.90679   1.50998  -0.33052  -1.85500  -1.60594   0.17855   1.79233   1.69248  -0.02554  -1.71914  -1.76908  -0.12762   1.63586   1.83531   0.28003  -1.54298  -1.89076  -0.43080   1.44104   1.93512   0.57904  -1.33065  -1.96812  -0.72388   1.21245   1.98957   0.86448  -1.08714  -1.99935  -1.00000   0.95544   1.99739   1.12965  -0.81814  -1.98371  -1.25268   0.67603   1.95839   1.36835  -0.52996  -1.92158  -1.47599   0.38078   1.87349   1.57497  -0.22937  -1.81441  -1.66471   0.07661   1.74468     ... ... ..... ....... ......... ........... .............
E21 *    2.00000   0.95544  -1.08714  -1.99413  -0.81814   1.21245   1.97656   0.67603  -1.33065  -1.94739  -0.52996   1.44104   1.90679   0.38078  -1.54298  -1.85500  -0.22937   1.63586   1.79233   0.07661  -1.71914  -1.71914   0.07661   1.79233   1.63586  -0.22937  -1.85500  -1.54298   0.38078   1.90679   1.44104  -0.52996  -1.94739  -1.33065   0.67603   1.97656   1.21245  -0.81814  -1.99413  -1.08714   0.95544   2.00000   0.95544  -1.08714  -1.99413  -0.81814   1.21245   1.97656   0.67603  -1.33065  -1.94739  -0.52996   1.44104   1.90679   0.38078  -1.54298  -1.85500  -0.22937   1.63586   1.79233   0.07661  -1.71914     ... ... ..... ....... ......... ........... .............
E22 *    2.00000   0.86448  -1.25268  -1.94739  -0.43080   1.57497   1.79233  -0.02554  -1.81441  -1.54298   0.48054   1.95839   1.21245  -0.91026  -1.99935  -0.81814   1.29209   1.93512   0.38078  -1.60594  -1.76908   0.07661   1.83531   1.50998  -0.52996  -1.96812  -1.17143   0.95544   1.99739   0.77126  -1.33065  -1.92158  -0.33052   1.63586   1.74468  -0.12762  -1.85500  -1.47599   0.57904   1.97656   1.12965  -1.00000  -1.99413  -0.72388   1.36835   1.90679   0.28003  -1.66471  -1.71914   0.17855   1.87349   1.44104  -0.62774  -1.98371  -1.08714   1.04391   1.98957   0.67603  -1.40515  -1.89076  -0.22937   1.69248     ... ... ..... ....... ......... ........... .............
E23 *    2.00000   0.77126  -1.40515  -1.85500  -0.02554   1.83531   1.44104  -0.72388  -1.99935  -0.81814   1.36835   1.87349   0.07661  -1.81441  -1.47599   0.67603   1.99739   0.86448  -1.33065  -1.89076  -0.12762   1.79233   1.50998  -0.62774  -1.99413  -0.91026   1.29209   1.90679   0.17855  -1.76908  -1.54298   0.57904   1.98957   0.95544  -1.25268  -1.92158  -0.22937   1.74468   1.57497  -0.52996  -1.98371  -1.00000   1.21245   1.93512   0.28003  -1.71914  -1.60594   0.48054   1.97656   1.04391  -1.17143  -1.94739  -0.33052   1.69248   1.63586  -0.43080  -1.96812  -1.08714   1.12965   1.95839   0.38078  -1.66471     ... ... ..... ....... ......... ........... .............
E24 *    2.00000   0.67603  -1.54298  -1.71914   0.38078   1.97656   0.95544  -1.33065  -1.85500   0.07661   1.90679   1.21245  -1.08714  -1.94739  -0.22937   1.79233   1.44104  -0.81814  -1.99413  -0.52996   1.63586   1.63586  -0.52996  -1.99413  -0.81814   1.44104   1.79233  -0.22937  -1.94739  -1.08714   1.21245   1.90679   0.07661  -1.85500  -1.33065   0.95544   1.97656   0.38078  -1.71914  -1.54298   0.67603   2.00000   0.67603  -1.54298  -1.71914   0.38078   1.97656   0.95544  -1.33065  -1.85500   0.07661   1.90679   1.21245  -1.08714  -1.94739  -0.22937   1.79233   1.44104  -0.81814  -1.99413  -0.52996   1.63586     ... ... ..... ....... ......... ........... .............
E25 *    2.00000   0.57904  -1.66471  -1.54298   0.77126   1.98957   0.38078  -1.76908  -1.40515   0.95544   1.95839   0.17855  -1.85500  -1.25268   1.12965   1.90679  -0.02554  -1.92158  -1.08714   1.29209   1.83531  -0.22937  -1.96812  -0.91026   1.44104   1.74468  -0.43080  -1.99413  -0.72388   1.57497   1.63586  -0.62774  -1.99935  -0.52996   1.69248   1.50998  -0.81814  -1.98371  -0.33052   1.79233   1.36835  -1.00000  -1.94739  -0.12762   1.87349   1.21245  -1.17143  -1.89076   0.07661   1.93512   1.04391  -1.33065  -1.81441   0.28003   1.97656   0.86448  -1.47599  -1.71914   0.48054   1.99739   0.67603  -1.60594     ... ... ..... ....... ......... ........... .............
E26 *    2.00000   0.48054  -1.76908  -1.33065   1.12965   1.87349  -0.22937  -1.98371  -0.72388   1.63586   1.50998  -0.91026  -1.94739  -0.02554   1.93512   0.95544  -1.47599  -1.66471   0.67603   1.98957   0.28003  -1.85500  -1.17143   1.29209   1.79233  -0.43080  -1.99935  -0.52996   1.74468   1.36835  -1.08714  -1.89076   0.17855   1.97656   0.77126  -1.60594  -1.54298   0.86448   1.95839   0.07661  -1.92158  -1.00000   1.44104   1.69248  -0.62774  -1.99413  -0.33052   1.83531   1.21245  -1.25268  -1.81441   0.38078   1.99739   0.57904  -1.71914  -1.40515   1.04391   1.90679  -0.12762  -1.96812  -0.81814   1.57497     ... ... ..... ....... ......... ........... .............
E27 *    2.00000   0.38078  -1.85500  -1.08714   1.44104   1.63586  -0.81814  -1.94739   0.07661   1.97656   0.67603  -1.71914  -1.33065   1.21245   1.79233  -0.52996  -1.99413  -0.22937   1.90679   0.95544  -1.54298  -1.54298   0.95544   1.90679  -0.22937  -1.99413  -0.52996   1.79233   1.21245  -1.33065  -1.71914   0.67603   1.97656   0.07661  -1.94739  -0.81814   1.63586   1.44104  -1.08714  -1.85500   0.38078   2.00000   0.38078  -1.85500  -1.08714   1.44104   1.63586  -0.81814  -1.94739   0.07661   1.97656   0.67603  -1.71914  -1.33065   1.21245   1.79233  -0.52996  -1.99413  -0.22937   1.90679   0.95544  -1.54298     ... ... ..... ....... ......... ........... .............
E28 *    2.00000   0.28003  -1.92158  -0.81814   1.69248   1.29209  -1.33065  -1.66471   0.86448   1.90679  -0.33052  -1.99935  -0.22937   1.93512   0.77126  -1.71914  -1.25268   1.36835   1.63586  -0.91026  -1.89076   0.38078   1.99739   0.17855  -1.94739  -0.72388   1.74468   1.21245  -1.40515  -1.60594   0.95544   1.87349  -0.43080  -1.99413  -0.12762   1.95839   0.67603  -1.76908  -1.17143   1.44104   1.57497  -1.00000  -1.85500   0.48054   1.98957   0.07661  -1.96812  -0.62774   1.79233   1.12965  -1.47599  -1.54298   1.04391   1.83531  -0.52996  -1.98371  -0.02554   1.97656   0.57904  -1.81441  -1.08714   1.50998     ... ... ..... ....... ......... ........... .............
E29 *    2.00000   0.17855  -1.96812  -0.52996   1.87349   0.86448  -1.71914  -1.17143   1.50998   1.44104  -1.25268  -1.66471   0.95544   1.83531  -0.62774  -1.94739   0.28003   1.99739   0.07661  -1.98371  -0.43080   1.90679   0.77126  -1.76908  -1.08714   1.57497   1.36835  -1.33065  -1.60594   1.04391   1.79233  -0.72388  -1.92158   0.38078   1.98957  -0.02554  -1.99413  -0.33052   1.93512   0.67603  -1.81441  -1.00000   1.63586   1.29209  -1.40515  -1.54298   1.12965   1.74468  -0.81814  -1.89076   0.48054   1.97656  -0.12762  -1.99935  -0.22937   1.95839   0.57904  -1.85500  -0.91026   1.69248   1.21245  -1.47599     ... ... ..... ....... ......... ........... .............
E30 *    2.00000   0.07661  -1.99413  -0.22937   1.97656   0.38078  -1.94739  -0.52996   1.90679   0.67603  -1.85500  -0.81814   1.79233   0.95544  -1.71914  -1.08714   1.63586   1.21245  -1.54298  -1.33065   1.44104   1.44104  -1.33065  -1.54298   1.21245   1.63586  -1.08714  -1.71914   0.95544   1.79233  -0.81814  -1.85500   0.67603   1.90679  -0.52996  -1.94739   0.38078   1.97656  -0.22937  -1.99413   0.07661   2.00000   0.07661  -1.99413  -0.22937   1.97656   0.38078  -1.94739  -0.52996   1.90679   0.67603  -1.85500  -0.81814   1.79233   0.95544  -1.71914  -1.08714   1.63586   1.21245  -1.54298  -1.33065   1.44104     ... ... ..... ....... ......... ........... .............
E31 *    2.00000  -0.02554  -1.99935   0.07661   1.99739  -0.12762  -1.99413   0.17855   1.98957  -0.22937  -1.98371   0.28003   1.97656  -0.33052  -1.96812   0.38078   1.95839  -0.43080  -1.94739   0.48054   1.93512  -0.52996  -1.92158   0.57904   1.90679  -0.62774  -1.89076   0.67603   1.87349  -0.72388  -1.85500   0.77126   1.83531  -0.81814  -1.81441   0.86448   1.79233  -0.91026  -1.76908   0.95544   1.74468  -1.00000  -1.71914   1.04391   1.69248  -1.08714  -1.66471   1.12965   1.63586  -1.17143  -1.60594   1.21245   1.57497  -1.25268  -1.54298   1.29209   1.50998  -1.33065  -1.47599   1.36835   1.44104  -1.40515     ... ... ..... ....... ......... ........... .............
E32 *    2.00000  -0.12762  -1.98371   0.38078   1.93512  -0.62774  -1.85500   0.86448   1.74468  -1.08714  -1.60594   1.29209   1.44104  -1.47599  -1.25268   1.63586   1.04391  -1.76908  -0.81814   1.87349   0.57904  -1.94739  -0.33052   1.98957   0.07661  -1.99935   0.17855   1.97656  -0.43080  -1.92158   0.67603   1.83531  -0.91026  -1.71914   1.12965   1.57497  -1.33065  -1.40515   1.50998   1.21245  -1.66471  -1.00000   1.79233   0.77126  -1.89076  -0.52996   1.95839   0.28003  -1.99413  -0.02554   1.99739  -0.22937  -1.96812   0.48054   1.90679  -0.72388  -1.81441   0.95544   1.69248  -1.17143  -1.54298   1.36835     ... ... ..... ....... ......... ........... .............
E33 *    2.00000  -0.22937  -1.94739   0.67603   1.79233  -1.08714  -1.54298   1.44104   1.21245  -1.71914  -0.81814   1.90679   0.38078  -1.99413   0.07661   1.97656  -0.52996  -1.85500   0.95544   1.63586  -1.33065  -1.33065   1.63586   0.95544  -1.85500  -0.52996   1.97656   0.07661  -1.99413   0.38078   1.90679  -0.81814  -1.71914   1.21245   1.44104  -1.54298  -1.08714   1.79233   0.67603  -1.94739  -0.22937   2.00000  -0.22937  -1.94739   0.67603   1.79233  -1.08714  -1.54298   1.44104   1.21245  -1.71914  -0.81814   1.90679   0.38078  -1.99413   0.07661   1.97656  -0.52996  -1.85500   0.95544   1.63586  -1.33065     ... ... ..... ....... ......... ........... .............
E34 *    2.00000  -0.33052  -1.89076   0.95544   1.57497  -1.47599  -1.08714   1.83531   0.48054  -1.99413   0.17855   1.93512  -0.81814  -1.66471   1.36835   1.21245  -1.76908  -0.62774   1.97656  -0.02554  -1.96812   0.67603   1.74468  -1.25268  -1.33065   1.69248   0.77126  -1.94739  -0.12762   1.98957  -0.52996  -1.81441   1.12965   1.44104  -1.60594  -0.91026   1.90679   0.28003  -1.99935   0.38078   1.87349  -1.00000  -1.54298   1.50998   1.04391  -1.85500  -0.43080   1.99739  -0.22937  -1.92158   0.86448   1.63586  -1.40515  -1.17143   1.79233   0.57904  -1.98371   0.07661   1.95839  -0.72388  -1.71914   1.29209     ... ... ..... ....... ......... ........... .............
E35 *    2.00000  -0.43080  -1.81441   1.21245   1.29209  -1.76908  -0.52996   1.99739  -0.33052  -1.85500   1.12965   1.36835  -1.71914  -0.62774   1.98957  -0.22937  -1.89076   1.04391   1.44104  -1.66471  -0.72388   1.97656  -0.12762  -1.92158   0.95544   1.50998  -1.60594  -0.81814   1.95839  -0.02554  -1.94739   0.86448   1.57497  -1.54298  -0.91026   1.93512   0.07661  -1.96812   0.77126   1.63586  -1.47599  -1.00000   1.90679   0.17855  -1.98371   0.67603   1.69248  -1.40515  -1.08714   1.87349   0.28003  -1.99413   0.57904   1.74468  -1.33065  -1.17143   1.83531   0.38078  -1.99935   0.48054   1.79233  -1.25268     ... ... ..... ....... ......... ........... .............
E36 *    2.00000  -0.52996  -1.71914   1.44104   0.95544  -1.94739   0.07661   1.90679  -1.08714  -1.33065   1.79233   0.38078  -1.99413   0.67603   1.63586  -1.54298  -0.81814   1.97656  -0.22937  -1.85500   1.21245   1.21245  -1.85500  -0.22937   1.97656  -0.81814  -1.54298   1.63586   0.67603  -1.99413   0.38078   1.79233  -1.33065  -1.08714   1.90679   0.07661  -1.94739   0.95544   1.44104  -1.71914  -0.52996   2.00000  -0.52996  -1.71914   1.44104   0.95544  -1.94739   0.07661   1.90679  -1.08714  -1.33065   1.79233   0.38078  -1.99413   0.67603   1.63586  -1.54298  -0.81814   1.97656  -0.22937  -1.85500   1.21245     ... ... ..... ....... ......... ........... .............
E37 *    2.00000  -0.62774  -1.60594   1.63586   0.57904  -1.99935   0.67603   1.57497  -1.66471  -0.52996   1.99739  -0.72388  -1.54298   1.69248   0.48054  -1.99413   0.77126   1.50998  -1.71914  -0.43080   1.98957  -0.81814  -1.47599   1.74468   0.38078  -1.98371   0.86448   1.44104  -1.76908  -0.33052   1.97656  -0.91026  -1.40515   1.79233   0.28003  -1.96812   0.95544   1.36835  -1.81441  -0.22937   1.95839  -1.00000  -1.33065   1.83531   0.17855  -1.94739   1.04391   1.29209  -1.85500  -0.12762   1.93512  -1.08714  -1.25268   1.87349   0.07661  -1.92158   1.12965   1.21245  -1.89076  -0.02554   1.90679  -1.17143     ... ... ..... ....... ......... ........... .............
E38 *    2.00000  -0.72388  -1.47599   1.79233   0.17855  -1.92158   1.21245   1.04391  -1.96812   0.38078   1.69248  -1.60594  -0.52996   1.98957  -0.91026  -1.33065   1.87349  -0.02554  -1.85500   1.36835   0.86448  -1.99413   0.57904   1.57497  -1.71914  -0.33052   1.95839  -1.08714  -1.17143   1.93512  -0.22937  -1.76908   1.50998   0.67603  -1.99935   0.77126   1.44104  -1.81441  -0.12762   1.90679  -1.25268  -1.00000   1.97656  -0.43080  -1.66471   1.63586   0.48054  -1.98371   0.95544   1.29209  -1.89076   0.07661   1.83531  -1.40515  -0.81814   1.99739  -0.62774  -1.54298   1.74468   0.28003  -1.94739   1.12965     ... ... ..... ....... ......... ........... .............
E39 *    2.00000  -0.81814  -1.33065   1.90679  -0.22937  -1.71914   1.63586   0.38078  -1.94739   1.21245   0.95544  -1.99413   0.67603   1.44104  -1.85500   0.07661   1.79233  -1.54298  -0.52996   1.97656  -1.08714  -1.08714   1.97656  -0.52996  -1.54298   1.79233   0.07661  -1.85500   1.44104   0.67603  -1.99413   0.95544   1.21245  -1.94739   0.38078   1.63586  -1.71914  -0.22937   1.90679  -1.33065  -0.81814   2.00000  -0.81814  -1.33065   1.90679  -0.22937  -1.71914   1.63586   0.38078  -1.94739   1.21245   0.95544  -1.99413   0.67603   1.44104  -1.85500   0.07661   1.79233  -1.54298  -0.52996   1.97656  -1.08714     ... ... ..... ....... ......... ........... .............
E40 *    2.00000  -0.91026  -1.17143   1.97656  -0.62774  -1.40515   1.90679  -0.33052  -1.60594   1.79233  -0.02554  -1.76908   1.63586   0.28003  -1.89076   1.44104   0.57904  -1.96812   1.21245   0.86448  -1.99935   0.95544   1.12965  -1.98371   0.67603   1.36835  -1.92158   0.38078   1.57497  -1.81441   0.07661   1.74468  -1.66471  -0.22937   1.87349  -1.47599  -0.52996   1.95839  -1.25268  -0.81814   1.99739  -1.00000  -1.08714   1.98957  -0.72388  -1.33065   1.93512  -0.43080  -1.54298   1.83531  -0.12762  -1.71914   1.69248   0.17855  -1.85500   1.50998   0.48054  -1.94739   1.29209   0.77126  -1.99413   1.04391     ... ... ..... ....... ......... ........... .............
E41 *    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     ... ... ..... ....... ......... ........... .............
E42 *    2.00000  -1.08714  -0.81814   1.97656  -1.33065  -0.52996   1.90679  -1.54298  -0.22937   1.79233  -1.71914   0.07661   1.63586  -1.85500   0.38078   1.44104  -1.94739   0.67603   1.21245  -1.99413   0.95544   0.95544  -1.99413   1.21245   0.67603  -1.94739   1.44104   0.38078  -1.85500   1.63586   0.07661  -1.71914   1.79233  -0.22937  -1.54298   1.90679  -0.52996  -1.33065   1.97656  -0.81814  -1.08714   2.00000  -1.08714  -0.81814   1.97656  -1.33065  -0.52996   1.90679  -1.54298  -0.22937   1.79233  -1.71914   0.07661   1.63586  -1.85500   0.38078   1.44104  -1.94739   0.67603   1.21245  -1.99413   0.95544     ... ... ..... ....... ......... ........... .............
E43 *    2.00000  -1.17143  -0.62774   1.90679  -1.60594  -0.02554   1.63586  -1.89076   0.57904   1.21245  -1.99935   1.12965   0.67603  -1.92158   1.57497   0.07661  -1.66471   1.87349  -0.52996  -1.25268   1.99739  -1.08714  -0.72388   1.93512  -1.54298  -0.12762   1.69248  -1.85500   0.48054   1.29209  -1.99413   1.04391   0.77126  -1.94739   1.50998   0.17855  -1.71914   1.83531  -0.43080  -1.33065   1.98957  -1.00000  -0.81814   1.95839  -1.47599  -0.22937   1.74468  -1.81441   0.38078   1.36835  -1.98371   0.95544   0.86448  -1.96812   1.44104   0.28003  -1.76908   1.79233  -0.33052  -1.40515   1.97656  -0.91026     ... ... ..... ....... ......... ........... .............
E44 *    2.00000  -1.25268  -0.43080   1.79233  -1.81441   0.48054   1.21245  -1.99935   1.29209   0.38078  -1.76908   1.83531  -0.52996  -1.17143   1.99739  -1.33065  -0.33052   1.74468  -1.85500   0.57904   1.12965  -1.99413   1.36835   0.28003  -1.71914   1.87349  -0.62774  -1.08714   1.98957  -1.40515  -0.22937   1.69248  -1.89076   0.67603   1.04391  -1.98371   1.44104   0.17855  -1.66471   1.90679  -0.72388  -1.00000   1.97656  -1.47599  -0.12762   1.63586  -1.92158   0.77126   0.95544  -1.96812   1.50998   0.07661  -1.60594   1.93512  -0.81814  -0.91026   1.95839  -1.54298  -0.02554   1.57497  -1.94739   0.86448     ... ... ..... ....... ......... ........... .............
E45 *    2.00000  -1.33065  -0.22937   1.63586  -1.94739   0.95544   0.67603  -1.85500   1.79233  -0.52996  -1.08714   1.97656  -1.54298   0.07661   1.44104  -1.99413   1.21245   0.38078  -1.71914   1.90679  -0.81814  -0.81814   1.90679  -1.71914   0.38078   1.21245  -1.99413   1.44104   0.07661  -1.54298   1.97656  -1.08714  -0.52996   1.79233  -1.85500   0.67603   0.95544  -1.94739   1.63586  -0.22937  -1.33065   2.00000  -1.33065  -0.22937   1.63586  -1.94739   0.95544   0.67603  -1.85500   1.79233  -0.52996  -1.08714   1.97656  -1.54298   0.07661   1.44104  -1.99413   1.21245   0.38078  -1.71914   1.90679  -0.81814     ... ... ..... ....... ......... ........... .............
E46 *    2.00000  -1.40515  -0.02554   1.44104  -1.99935   1.36835   0.07661  -1.47599   1.99739  -1.33065  -0.12762   1.50998  -1.99413   1.29209   0.17855  -1.54298   1.98957  -1.25268  -0.22937   1.57497  -1.98371   1.21245   0.28003  -1.60594   1.97656  -1.17143  -0.33052   1.63586  -1.96812   1.12965   0.38078  -1.66471   1.95839  -1.08714  -0.43080   1.69248  -1.94739   1.04391   0.48054  -1.71914   1.93512  -1.00000  -0.52996   1.74468  -1.92158   0.95544   0.57904  -1.76908   1.90679  -0.91026  -0.62774   1.79233  -1.89076   0.86448   0.67603  -1.81441   1.87349  -0.81814  -0.72388   1.83531  -1.85500   0.77126     ... ... ..... ....... ......... ........... .............
E47 *    2.00000  -1.47599   0.17855   1.21245  -1.96812   1.69248  -0.52996  -0.91026   1.87349  -1.85500   0.86448   0.57904  -1.71914   1.95839  -1.17143  -0.22937   1.50998  -1.99935   1.44104  -0.12762  -1.25268   1.97656  -1.66471   0.48054   0.95544  -1.89076   1.83531  -0.81814  -0.62774   1.74468  -1.94739   1.12965   0.28003  -1.54298   1.99739  -1.40515   0.07661   1.29209  -1.98371   1.63586  -0.43080  -1.00000   1.90679  -1.81441   0.77126   0.67603  -1.76908   1.93512  -1.08714  -0.33052   1.57497  -1.99413   1.36835  -0.02554  -1.33065   1.98957  -1.60594   0.38078   1.04391  -1.92158   1.79233  -0.72388     ... ... ..... ....... ......... ........... .............
E48 *    2.00000  -1.54298   0.38078   0.95544  -1.85500   1.90679  -1.08714  -0.22937   1.44104  -1.99413   1.63586  -0.52996  -0.81814   1.79233  -1.94739   1.21245   0.07661  -1.33065   1.97656  -1.71914   0.67603   0.67603  -1.71914   1.97656  -1.33065   0.07661   1.21245  -1.94739   1.79233  -0.81814  -0.52996   1.63586  -1.99413   1.44104  -0.22937  -1.08714   1.90679  -1.85500   0.95544   0.38078  -1.54298   2.00000  -1.54298   0.38078   0.95544  -1.85500   1.90679  -1.08714  -0.22937   1.44104  -1.99413   1.63586  -0.52996  -0.81814   1.79233  -1.94739   1.21245   0.07661  -1.33065   1.97656  -1.71914   0.67603     ... ... ..... ....... ......... ........... .............
E49 *    2.00000  -1.60594   0.57904   0.67603  -1.66471   1.99739  -1.54298   0.48054   0.77126  -1.71914   1.98957  -1.47599   0.38078   0.86448  -1.76908   1.97656  -1.40515   0.28003   0.95544  -1.81441   1.95839  -1.33065   0.17855   1.04391  -1.85500   1.93512  -1.25268   0.07661   1.12965  -1.89076   1.90679  -1.17143  -0.02554   1.21245  -1.92158   1.87349  -1.08714  -0.12762   1.29209  -1.94739   1.83531  -1.00000  -0.22937   1.36835  -1.96812   1.79233  -0.91026  -0.33052   1.44104  -1.98371   1.74468  -0.81814  -0.43080   1.50998  -1.99413   1.69248  -0.72388  -0.52996   1.57497  -1.99935   1.63586  -0.62774     ... ... ..... ....... ......... ........... .............
E50 *    2.00000  -1.66471   0.77126   0.38078  -1.40515   1.95839  -1.85500   1.12965  -0.02554  -1.08714   1.83531  -1.96812   1.44104  -0.43080  -0.72388   1.63586  -1.99935   1.69248  -0.81814  -0.33052   1.36835  -1.94739   1.87349  -1.17143   0.07661   1.04391  -1.81441   1.97656  -1.47599   0.48054   0.67603  -1.60594   1.99739  -1.71914   0.86448   0.28003  -1.33065   1.93512  -1.89076   1.21245  -0.12762  -1.00000   1.79233  -1.98371   1.50998  -0.52996  -0.62774   1.57497  -1.99413   1.74468  -0.91026  -0.22937   1.29209  -1.92158   1.90679  -1.25268   0.17855   0.95544  -1.76908   1.98957  -1.54298   0.57904     ... ... ..... ....... ......... ........... .............
E51 *    2.00000  -1.71914   0.95544   0.07661  -1.08714   1.79233  -1.99413   1.63586  -0.81814  -0.22937   1.21245  -1.85500   1.97656  -1.54298   0.67603   0.38078  -1.33065   1.90679  -1.94739   1.44104  -0.52996  -0.52996   1.44104  -1.94739   1.90679  -1.33065   0.38078   0.67603  -1.54298   1.97656  -1.85500   1.21245  -0.22937  -0.81814   1.63586  -1.99413   1.79233  -1.08714   0.07661   0.95544  -1.71914   2.00000  -1.71914   0.95544   0.07661  -1.08714   1.79233  -1.99413   1.63586  -0.81814  -0.22937   1.21245  -1.85500   1.97656  -1.54298   0.67603   0.38078  -1.33065   1.90679  -1.94739   1.44104  -0.52996     ... ... ..... ....... ......... ........... .............
E52 *    2.00000  -1.76908   1.12965  -0.22937  -0.72388   1.50998  -1.94739   1.93512  -1.47599   0.67603   0.28003  -1.17143   1.79233  -1.99935   1.74468  -1.08714   0.17855   0.77126  -1.54298   1.95839  -1.92158   1.44104  -0.62774  -0.33052   1.21245  -1.81441   1.99739  -1.71914   1.04391  -0.12762  -0.81814   1.57497  -1.96812   1.90679  -1.40515   0.57904   0.38078  -1.25268   1.83531  -1.99413   1.69248  -1.00000   0.07661   0.86448  -1.60594   1.97656  -1.89076   1.36835  -0.52996  -0.43080   1.29209  -1.85500   1.98957  -1.66471   0.95544  -0.02554  -0.91026   1.63586  -1.98371   1.87349  -1.33065   0.48054     ... ... ..... ....... ......... ........... .............
E53 *    2.00000  -1.81441   1.29209  -0.52996  -0.33052   1.12965  -1.71914   1.98957  -1.89076   1.44104  -0.72388  -0.12762   0.95544  -1.60594   1.95839  -1.94739   1.57497  -0.91026   0.07661   0.77126  -1.47599   1.90679  -1.98371   1.69248  -1.08714   0.28003   0.57904  -1.33065   1.83531  -1.99935   1.79233  -1.25268   0.48054   0.38078  -1.17143   1.74468  -1.99413   1.87349  -1.40515   0.67603   0.17855  -1.00000   1.63586  -1.96812   1.93512  -1.54298   0.86448  -0.02554  -0.81814   1.50998  -1.92158   1.97656  -1.66471   1.04391  -0.22937  -0.62774   1.36835  -1.85500   1.99739  -1.76908   1.21245  -0.43080     ... ... ..... ....... ......... ........... .............
E54 *    2.00000  -1.85500   1.44104  -0.81814   0.07661   0.67603  -1.33065   1.79233  -1.99413   1.90679  -1.54298   0.95544  -0.22937  -0.52996   1.21245  -1.71914   1.97656  -1.94739   1.63586  -1.08714   0.38078   0.38078  -1.08714   1.63586  -1.94739   1.97656  -1.71914   1.21245  -0.52996  -0.22937   0.95544  -1.54298   1.90679  -1.99413   1.79233  -1.33065   0.67603   0.07661  -0.81814   1.44104  -1.85500   2.00000  -1.85500   1.44104  -0.81814   0.07661   0.67603  -1.33065   1.79233  -1.99413   1.90679  -1.54298   0.95544  -0.22937  -0.52996   1.21245  -1.71914   1.97656  -1.94739   1.63586  -1.08714   0.38078     ... ... ..... ....... ......... ........... .............
E55 *    2.00000  -1.89076   1.57497  -1.08714   0.48054   0.17855  -0.81814   1.36835  -1.76908   1.97656  -1.96812   1.74468  -1.33065   0.77126  -0.12762  -0.52996   1.12965  -1.60594   1.90679  -1.99935   1.87349  -1.54298   1.04391  -0.43080  -0.22937   0.86448  -1.40515   1.79233  -1.98371   1.95839  -1.71914   1.29209  -0.72388   0.07661   0.57904  -1.17143   1.63586  -1.92158   1.99739  -1.85500   1.50998  -1.00000   0.38078   0.28003  -0.91026   1.44104  -1.81441   1.98957  -1.94739   1.69248  -1.25268   0.67603  -0.02554  -0.62774   1.21245  -1.66471   1.93512  -1.99413   1.83531  -1.47599   0.95544  -0.33052     ... ... ..... ....... ......... ........... .............
E56 *    2.00000  -1.92158   1.69248  -1.33065   0.86448  -0.33052  -0.22937   0.77126  -1.25268   1.63586  -1.89076   1.99739  -1.94739   1.74468  -1.40515   0.95544  -0.43080  -0.12762   0.67603  -1.17143   1.57497  -1.85500   1.98957  -1.96812   1.79233  -1.47599   1.04391  -0.52996  -0.02554   0.57904  -1.08714   1.50998  -1.81441   1.97656  -1.98371   1.83531  -1.54298   1.12965  -0.62774   0.07661   0.48054  -1.00000   1.44104  -1.76908   1.95839  -1.99413   1.87349  -1.60594   1.21245  -0.72388   0.17855   0.38078  -0.91026   1.36835  -1.71914   1.93512  -1.99935   1.90679  -1.66471   1.29209  -0.81814   0.28003     ... ... ..... ....... ......... ........... .............
E57 *    2.00000  -1.94739   1.79233  -1.54298   1.21245  -0.81814   0.38078   0.07661  -0.52996   0.95544  -1.33065   1.63586  -1.85500   1.97656  -1.99413   1.90679  -1.71914   1.44104  -1.08714   0.67603  -0.22937  -0.22937   0.67603  -1.08714   1.44104  -1.71914   1.90679  -1.99413   1.97656  -1.85500   1.63586  -1.33065   0.95544  -0.52996   0.07661   0.38078  -0.81814   1.21245  -1.54298   1.79233  -1.94739   2.00000  -1.94739   1.79233  -1.54298   1.21245  -0.81814   0.38078   0.07661  -0.52996   0.95544  -1.33065   1.63586  -1.85500   1.97656  -1.99413   1.90679  -1.71914   1.44104  -1.08714   0.67603  -0.22937     ... ... ..... ....... ......... ........... .............
E58 *    2.00000  -1.96812   1.87349  -1.71914   1.50998  -1.25268   0.95544  -0.62774   0.28003   0.07661  -0.43080   0.77126  -1.08714   1.36835  -1.60594   1.79233  -1.92158   1.98957  -1.99413   1.93512  -1.81441   1.63586  -1.40515   1.12965  -0.81814   0.48054  -0.12762  -0.22937   0.57904  -0.91026   1.21245  -1.47599   1.69248  -1.85500   1.95839  -1.99935   1.97656  -1.89076   1.74468  -1.54298   1.29209  -1.00000   0.67603  -0.33052  -0.02554   0.38078  -0.72388   1.04391  -1.33065   1.57497  -1.76908   1.90679  -1.98371   1.99739  -1.94739   1.83531  -1.66471   1.44104  -1.17143   0.86448  -0.52996   0.17855     ... ... ..... ....... ......... ........... .............
E59 *    2.00000  -1.98371   1.93512  -1.85500   1.74468  -1.60594   1.44104  -1.25268   1.04391  -0.81814   0.57904  -0.33052   0.07661   0.17855  -0.43080   0.67603  -0.91026   1.12965  -1.33065   1.50998  -1.66471   1.79233  -1.89076   1.95839  -1.99413   1.99739  -1.96812   1.90679  -1.81441   1.69248  -1.54298   1.36835  -1.17143   0.95544  -0.72388   0.48054  -0.22937  -0.02554   0.28003  -0.52996   0.77126  -1.00000   1.21245  -1.40515   1.57497  -1.71914   1.83531  -1.92158   1.97656  -1.99935   1.98957  -1.94739   1.87349  -1.76908   1.63586  -1.47599   1.29209  -1.08714   0.86448  -0.62774   0.38078  -0.12762     ... ... ..... ....... ......... ........... .............
E60 *    2.00000  -1.99413   1.97656  -1.94739   1.90679  -1.85500   1.79233  -1.71914   1.63586  -1.54298   1.44104  -1.33065   1.21245  -1.08714   0.95544  -0.81814   0.67603  -0.52996   0.38078  -0.22937   0.07661   0.07661  -0.22937   0.38078  -0.52996   0.67603  -0.81814   0.95544  -1.08714   1.21245  -1.33065   1.44104  -1.54298   1.63586  -1.71914   1.79233  -1.85500   1.90679  -1.94739   1.97656  -1.99413   2.00000  -1.99413   1.97656  -1.94739   1.90679  -1.85500   1.79233  -1.71914   1.63586  -1.54298   1.44104  -1.33065   1.21245  -1.08714   0.95544  -0.81814   0.67603  -0.52996   0.38078  -0.22937   0.07661     ... ... ..... ....... ......... ........... .............
E61 *    2.00000  -1.99935   1.99739  -1.99413   1.98957  -1.98371   1.97656  -1.96812   1.95839  -1.94739   1.93512  -1.92158   1.90679  -1.89076   1.87349  -1.85500   1.83531  -1.81441   1.79233  -1.76908   1.74468  -1.71914   1.69248  -1.66471   1.63586  -1.60594   1.57497  -1.54298   1.50998  -1.47599   1.44104  -1.40515   1.36835  -1.33065   1.29209  -1.25268   1.21245  -1.17143   1.12965  -1.08714   1.04391  -1.00000   0.95544  -0.91026   0.86448  -0.81814   0.77126  -0.72388   0.67603  -0.62774   0.57904  -0.52996   0.48054  -0.43080   0.38078  -0.33052   0.28003  -0.22937   0.17855  -0.12762   0.07661  -0.02554     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.997391114178 = 2*cos(2*π/123)
                               1.989571262999 = 2*cos(4*π/123)
                               1.976560847561 = 2*cos(6*π/123) = 2*cos(2*π/41)
                               1.958393810552 = 2*cos(8*π/123)
                               1.935117547697 = 2*cos(10*π/123)
                               1.906792784110 = 2*cos(12*π/123) = 2*cos(4*π/41)
                               1.873493415863 = 2*cos(14*π/123)
                               1.835306317207 = 2*cos(16*π/123)
                               1.792331113922 = 2*cos(18*π/123) = 2*cos(6*π/41)
                               1.744679923406 = 2*cos(20*π/123)
                               1.692477062175 = 2*cos(22*π/123)
                               1.635858721533 = 2*cos(24*π/123) = 2*cos(8*π/41)
                               1.574972612267 = 2*cos(26*π/123)
                               1.509977579283 = 2*cos(28*π/123)
                               1.441043187202 = 2*cos(30*π/123) = 2*cos(10*π/41)
                               1.368349277981 = 2*cos(32*π/123)
                               1.292085501730 = 2*cos(34*π/123)
                               1.212450821933 = 2*cos(36*π/123) = 2*cos(12*π/41)
                               1.129652996378 = 2*cos(38*π/123)
                               1.043908035137 = 2*cos(40*π/123)
                               0.955439637025 = 2*cos(42*π/123) = 2*cos(14*π/41)
                               0.864478605989 = 2*cos(44*π/123)
                               0.771262248976 = 2*cos(46*π/123)
                               0.676033756817 = 2*cos(48*π/123) = 2*cos(16*π/41)
                               0.579041569775 = 2*cos(50*π/123)
                               0.480538729391 = 2*cos(52*π/123)
                               0.380782218329 = 2*cos(54*π/123) = 2*cos(18*π/41)
                               0.280032289937 = 2*cos(56*π/123)
                               0.178551789274 = 2*cos(58*π/123)
                               0.076605467380 = 2*cos(60*π/123) = 2*cos(20*π/41)
                              -0.025540709432 = 2*cos(62*π/123)
                              -0.127620253449 = 2*cos(64*π/123)
                              -0.229366850797 = 2*cos(66*π/123) = 2*cos(22*π/41)
                              -0.330515056219 = 2*cos(68*π/123)
                              -0.430800985598 = 2*cos(70*π/123)
                              -0.529963004393 = 2*cos(72*π/123) = 2*cos(24*π/41)
                              -0.627742410221 = 2*cos(74*π/123)
                              -0.723884107774 = 2*cos(76*π/123)
                              -0.818137274343 = 2*cos(78*π/123) = 2*cos(26*π/41)
                              -0.910256014176 = 2*cos(80*π/123)
                              -1.087135100002 = 2*cos(84*π/123) = 2*cos(28*π/41)
                              -1.171433988656 = 2*cos(86*π/123)
                              -1.252676739786 = 2*cos(88*π/123)
                              -1.330651400331 = 2*cos(90*π/123) = 2*cos(30*π/41)
                              -1.405154543304 = 2*cos(92*π/123)
                              -1.475991798512 = 2*cos(94*π/123)
                              -1.542978359644 = 2*cos(96*π/123) = 2*cos(32*π/41)
                              -1.605939466410 = 2*cos(98*π/123)
                              -1.664710860473 = 2*cos(100*π/123)
                              -1.719139213974 = 2*cos(102*π/123) = 2*cos(34*π/41)
                              -1.769082529555 = 2*cos(104*π/123)
                              -1.814410510808 = 2*cos(106*π/123)
                              -1.855004902204 = 2*cos(108*π/123) = 2*cos(36*π/41)
                              -1.890759797612 = 2*cos(110*π/123)
                              -1.921581916592 = 2*cos(112*π/123)
                              -1.947390847756 = 2*cos(114*π/123) = 2*cos(38*π/41)
                              -1.968119258547 = 2*cos(116*π/123)
                              -1.983713070910 = 2*cos(118*π/123)
                              -1.994131602367 = 2*cos(120*π/123) = 2*cos(40*π/41)
                              -1.999347672162 = 2*cos(122*π/123)



 Symmetry of Rotations and Cartesian products

A    R+p+d+f+g+h+i+j+k+l+m  Rz, z, z2, z3, z4, z5, z6 
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 C123 point group is 123, and the order of the principal axis (C123) is 123. The group has 62 irreducible representations.

    β  The C123 point group is generated by one single symmetry element, C123. Therefore, it is a cyclic group.

    γ  The lowest nonvanishing multipole moment in C123 is 2 (dipole moment).

    δ  This is an Abelian point group (the commutative law holds between all symmetry operations).
       The C123 group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition).
       In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional.

    ε  Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters.
       These 122 cases have been combined into 61 two-dimensional representations that are no longer irreducible but have real-valued characters.
       Accordingly, 61 pairs of left and right rotations have been combined into one two-membered pseudo-class each.

    ζ  The 61 reducible “E” representations almost behave like true irreducible representations.
       Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table.
       This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula.

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

    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.
       For this group, however, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the C123 point group was created by Gernot Katzer.

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