Character table for the C103v point group

C103v   E         2 C103    2 C103^2  2 C103^3  2 C103^4  2 C103^5  2 C103^6  2 C103^7  2 C103^8  2 C103^9  2 C103^10 2 C103^11 2 C103^12 2 C103^13 2 C103^14 2 C103^15 2 C103^16 2 C103^17 2 C103^18 2 C103^19 2 C103^20 2 C103^21 2 C103^22 2 C103^23 2 C103^24 2 C103^25 2 C103^26 2 C103^27 2 C103^28 2 C103^29 2 C103^30 2 C103^31 2 C103^32 2 C103^33 2 C103^34 2 C103^35 2 C103^36 2 C103^37 2 C103^38 2 C103^39 2 C103^40 2 C103^41 2 C103^42 2 C103^43 2 C103^44 2 C103^45 2 C103^46 2 C103^47 2 C103^48 2 C103^49 2 C103^50 2 C103^51 103 sv       <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     ... ..T ....T ......T ........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     ..T ... ..... ....... ......... ........... .............
E1       2.00000   1.99628   1.98513   1.96660   1.94076   1.90769   1.86752   1.82041   1.76653   1.70608   1.63928   1.56638   1.48765   1.40339   1.31391   1.21954   1.12063   1.01756   0.91070   0.80045   0.68722   0.57144   0.45353   0.33394   0.21310   0.09147  -0.03050  -0.15236  -0.27365  -0.39392  -0.51273  -0.62963  -0.74418  -0.85597  -0.96458  -1.06959  -1.17063  -1.26731  -1.35928  -1.44619  -1.52772  -1.60357  -1.67345  -1.73711  -1.79431  -1.84483  -1.88849  -1.92512  -1.95459  -1.97679  -1.99163  -1.99907   0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2       2.00000   1.98513   1.94076   1.86752   1.76653   1.63928   1.48765   1.31391   1.12063   0.91070   0.68722   0.45353   0.21310  -0.03050  -0.27365  -0.51273  -0.74418  -0.96458  -1.17063  -1.35928  -1.52772  -1.67345  -1.79431  -1.88849  -1.95459  -1.99163  -1.99907  -1.97679  -1.92512  -1.84483  -1.73711  -1.60357  -1.44619  -1.26731  -1.06959  -0.85597  -0.62963  -0.39392  -0.15236   0.09147   0.33394   0.57144   0.80045   1.01756   1.21954   1.40339   1.56638   1.70608   1.82041   1.90769   1.96660   1.99628   0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3       2.00000   1.96660   1.86752   1.70608   1.48765   1.21954   0.91070   0.57144   0.21310  -0.15236  -0.51273  -0.85597  -1.17063  -1.44619  -1.67345  -1.84483  -1.95459  -1.99907  -1.97679  -1.88849  -1.73711  -1.52772  -1.26731  -0.96458  -0.62963  -0.27365   0.09147   0.45353   0.80045   1.12063   1.40339   1.63928   1.82041   1.94076   1.99628   1.98513   1.90769   1.76653   1.56638   1.31391   1.01756   0.68722   0.33394  -0.03050  -0.39392  -0.74418  -1.06959  -1.35928  -1.60357  -1.79431  -1.92512  -1.99163   0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4       2.00000   1.94076   1.76653   1.48765   1.12063   0.68722   0.21310  -0.27365  -0.74418  -1.17063  -1.52772  -1.79431  -1.95459  -1.99907  -1.92512  -1.73711  -1.44619  -1.06959  -0.62963  -0.15236   0.33394   0.80045   1.21954   1.56638   1.82041   1.96660   1.99628   1.90769   1.70608   1.40339   1.01756   0.57144   0.09147  -0.39392  -0.85597  -1.26731  -1.60357  -1.84483  -1.97679  -1.99163  -1.88849  -1.67345  -1.35928  -0.96458  -0.51273  -0.03050   0.45353   0.91070   1.31391   1.63928   1.86752   1.98513   0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5       2.00000   1.90769   1.63928   1.21954   0.68722   0.09147  -0.51273  -1.06959  -1.52772  -1.84483  -1.99163  -1.95459  -1.73711  -1.35928  -0.85597  -0.27365   0.33394   0.91070   1.40339   1.76653   1.96660   1.98513   1.82041   1.48765   1.01756   0.45353  -0.15236  -0.74418  -1.26731  -1.67345  -1.92512  -1.99907  -1.88849  -1.60357  -1.17063  -0.62963  -0.03050   0.57144   1.12063   1.56638   1.86752   1.99628   1.94076   1.70608   1.31391   0.80045   0.21310  -0.39392  -0.96458  -1.44619  -1.79431  -1.97679   0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6       2.00000   1.86752   1.48765   0.91070   0.21310  -0.51273  -1.17063  -1.67345  -1.95459  -1.97679  -1.73711  -1.26731  -0.62963   0.09147   0.80045   1.40339   1.82041   1.99628   1.90769   1.56638   1.01756   0.33394  -0.39392  -1.06959  -1.60357  -1.92512  -1.99163  -1.79431  -1.35928  -0.74418  -0.03050   0.68722   1.31391   1.76653   1.98513   1.94076   1.63928   1.12063   0.45353  -0.27365  -0.96458  -1.52772  -1.88849  -1.99907  -1.84483  -1.44619  -0.85597  -0.15236   0.57144   1.21954   1.70608   1.96660   0.00000     ... ... ..... ....... ......... ........... TT...........
E7       2.00000   1.82041   1.31391   0.57144  -0.27365  -1.06959  -1.67345  -1.97679  -1.92512  -1.52772  -0.85597  -0.03050   0.80045   1.48765   1.90769   1.98513   1.70608   1.12063   0.33394  -0.51273  -1.26731  -1.79431  -1.99907  -1.84483  -1.35928  -0.62963   0.21310   1.01756   1.63928   1.96660   1.94076   1.56638   0.91070   0.09147  -0.74418  -1.44619  -1.88849  -1.99163  -1.73711  -1.17063  -0.39392   0.45353   1.21954   1.76653   1.99628   1.86752   1.40339   0.68722  -0.15236  -0.96458  -1.60357  -1.95459   0.00000     ... ... ..... ....... ......... ........... .............
E8       2.00000   1.76653   1.12063   0.21310  -0.74418  -1.52772  -1.95459  -1.92512  -1.44619  -0.62963   0.33394   1.21954   1.82041   1.99628   1.70608   1.01756   0.09147  -0.85597  -1.60357  -1.97679  -1.88849  -1.35928  -0.51273   0.45353   1.31391   1.86752   1.98513   1.63928   0.91070  -0.03050  -0.96458  -1.67345  -1.99163  -1.84483  -1.26731  -0.39392   0.57144   1.40339   1.90769   1.96660   1.56638   0.80045  -0.15236  -1.06959  -1.73711  -1.99907  -1.79431  -1.17063  -0.27365   0.68722   1.48765   1.94076   0.00000     ... ... ..... ....... ......... ........... .............
E9       2.00000   1.70608   0.91070  -0.15236  -1.17063  -1.84483  -1.97679  -1.52772  -0.62963   0.45353   1.40339   1.94076   1.90769   1.31391   0.33394  -0.74418  -1.60357  -1.99163  -1.79431  -1.06959  -0.03050   1.01756   1.76653   1.99628   1.63928   0.80045  -0.27365  -1.26731  -1.88849  -1.95459  -1.44619  -0.51273   0.57144   1.48765   1.96660   1.86752   1.21954   0.21310  -0.85597  -1.67345  -1.99907  -1.73711  -0.96458   0.09147   1.12063   1.82041   1.98513   1.56638   0.68722  -0.39392  -1.35928  -1.92512   0.00000     ... ... ..... ....... ......... ........... .............
E10      2.00000   1.63928   0.68722  -0.51273  -1.52772  -1.99163  -1.73711  -0.85597   0.33394   1.40339   1.96660   1.82041   1.01756  -0.15236  -1.26731  -1.92512  -1.88849  -1.17063  -0.03050   1.12063   1.86752   1.94076   1.31391   0.21310  -0.96458  -1.79431  -1.97679  -1.44619  -0.39392   0.80045   1.70608   1.99628   1.56638   0.57144  -0.62963  -1.60357  -1.99907  -1.67345  -0.74418   0.45353   1.48765   1.98513   1.76653   0.91070  -0.27365  -1.35928  -1.95459  -1.84483  -1.06959   0.09147   1.21954   1.90769   0.00000     ... ... ..... ....... ......... ........... .............
E11      2.00000   1.56638   0.45353  -0.85597  -1.79431  -1.95459  -1.26731  -0.03050   1.21954   1.94076   1.82041   0.91070  -0.39392  -1.52772  -1.99907  -1.60357  -0.51273   0.80045   1.76653   1.96660   1.31391   0.09147  -1.17063  -1.92512  -1.84483  -0.96458   0.33394   1.48765   1.99628   1.63928   0.57144  -0.74418  -1.73711  -1.97679  -1.35928  -0.15236   1.12063   1.90769   1.86752   1.01756  -0.27365  -1.44619  -1.99163  -1.67345  -0.62963   0.68722   1.70608   1.98513   1.40339   0.21310  -1.06959  -1.88849   0.00000     ... ... ..... ....... ......... ........... .............
E12      2.00000   1.48765   0.21310  -1.17063  -1.95459  -1.73711  -0.62963   0.80045   1.82041   1.90769   1.01756  -0.39392  -1.60357  -1.99163  -1.35928  -0.03050   1.31391   1.98513   1.63928   0.45353  -0.96458  -1.88849  -1.84483  -0.85597   0.57144   1.70608   1.96660   1.21954  -0.15236  -1.44619  -1.99907  -1.52772  -0.27365   1.12063   1.94076   1.76653   0.68722  -0.74418  -1.79431  -1.92512  -1.06959   0.33394   1.56638   1.99628   1.40339   0.09147  -1.26731  -1.97679  -1.67345  -0.51273   0.91070   1.86752   0.00000     ... ... ..... ....... ......... ........... .............
E13      2.00000   1.40339  -0.03050  -1.44619  -1.99907  -1.35928   0.09147   1.48765   1.99628   1.31391  -0.15236  -1.52772  -1.99163  -1.26731   0.21310   1.56638   1.98513   1.21954  -0.27365  -1.60357  -1.97679  -1.17063   0.33394   1.63928   1.96660   1.12063  -0.39392  -1.67345  -1.95459  -1.06959   0.45353   1.70608   1.94076   1.01756  -0.51273  -1.73711  -1.92512  -0.96458   0.57144   1.76653   1.90769   0.91070  -0.62963  -1.79431  -1.88849  -0.85597   0.68722   1.82041   1.86752   0.80045  -0.74418  -1.84483   0.00000     ... ... ..... ....... ......... ........... .............
E14      2.00000   1.31391  -0.27365  -1.67345  -1.92512  -0.85597   0.80045   1.90769   1.70608   0.33394  -1.26731  -1.99907  -1.35928   0.21310   1.63928   1.94076   0.91070  -0.74418  -1.88849  -1.73711  -0.39392   1.21954   1.99628   1.40339  -0.15236  -1.60357  -1.95459  -0.96458   0.68722   1.86752   1.76653   0.45353  -1.17063  -1.99163  -1.44619   0.09147   1.56638   1.96660   1.01756  -0.62963  -1.84483  -1.79431  -0.51273   1.12063   1.98513   1.48765  -0.03050  -1.52772  -1.97679  -1.06959   0.57144   1.82041   0.00000     ... ... ..... ....... ......... ........... .............
E15      2.00000   1.21954  -0.51273  -1.84483  -1.73711  -0.27365   1.40339   1.98513   1.01756  -0.74418  -1.92512  -1.60357  -0.03050   1.56638   1.94076   0.80045  -0.96458  -1.97679  -1.44619   0.21310   1.70608   1.86752   0.57144  -1.17063  -1.99907  -1.26731   0.45353   1.82041   1.76653   0.33394  -1.35928  -1.99163  -1.06959   0.68722   1.90769   1.63928   0.09147  -1.52772  -1.95459  -0.85597   0.91070   1.96660   1.48765  -0.15236  -1.67345  -1.88849  -0.62963   1.12063   1.99628   1.31391  -0.39392  -1.79431   0.00000     ... ... ..... ....... ......... ........... .............
E16      2.00000   1.12063  -0.74418  -1.95459  -1.44619   0.33394   1.82041   1.70608   0.09147  -1.60357  -1.88849  -0.51273   1.31391   1.98513   0.91070  -0.96458  -1.99163  -1.26731   0.57144   1.90769   1.56638  -0.15236  -1.73711  -1.79431  -0.27365   1.48765   1.94076   0.68722  -1.17063  -1.99907  -1.06959   0.80045   1.96660   1.40339  -0.39392  -1.84483  -1.67345  -0.03050   1.63928   1.86752   0.45353  -1.35928  -1.97679  -0.85597   1.01756   1.99628   1.21954  -0.62963  -1.92512  -1.52772   0.21310   1.76653   0.00000     ... ... ..... ....... ......... ........... .............
E17      2.00000   1.01756  -0.96458  -1.99907  -1.06959   0.91070   1.99628   1.12063  -0.85597  -1.99163  -1.17063   0.80045   1.98513   1.21954  -0.74418  -1.97679  -1.26731   0.68722   1.96660   1.31391  -0.62963  -1.95459  -1.35928   0.57144   1.94076   1.40339  -0.51273  -1.92512  -1.44619   0.45353   1.90769   1.48765  -0.39392  -1.88849  -1.52772   0.33394   1.86752   1.56638  -0.27365  -1.84483  -1.60357   0.21310   1.82041   1.63928  -0.15236  -1.79431  -1.67345   0.09147   1.76653   1.70608  -0.03050  -1.73711   0.00000     ... ... ..... ....... ......... ........... .............
E18      2.00000   0.91070  -1.17063  -1.97679  -0.62963   1.40339   1.90769   0.33394  -1.60357  -1.79431  -0.03050   1.76653   1.63928  -0.27365  -1.88849  -1.44619   0.57144   1.96660   1.21954  -0.85597  -1.99907  -0.96458   1.12063   1.98513   0.68722  -1.35928  -1.92512  -0.39392   1.56638   1.82041   0.09147  -1.73711  -1.67345   0.21310   1.86752   1.48765  -0.51273  -1.95459  -1.26731   0.80045   1.99628   1.01756  -1.06959  -1.99163  -0.74418   1.31391   1.94076   0.45353  -1.52772  -1.84483  -0.15236   1.70608   0.00000     ... ... ..... ....... ......... ........... .............
E19      2.00000   0.80045  -1.35928  -1.88849  -0.15236   1.76653   1.56638  -0.51273  -1.97679  -1.06959   1.12063   1.96660   0.45353  -1.60357  -1.73711   0.21310   1.90769   1.31391  -0.85597  -1.99907  -0.74418   1.40339   1.86752   0.09147  -1.79431  -1.52772   0.57144   1.98513   1.01756  -1.17063  -1.95459  -0.39392   1.63928   1.70608  -0.27365  -1.92512  -1.26731   0.91070   1.99628   0.68722  -1.44619  -1.84483  -0.03050   1.82041   1.48765  -0.62963  -1.99163  -0.96458   1.21954   1.94076   0.33394  -1.67345   0.00000     ... ... ..... ....... ......... ........... .............
E20      2.00000   0.68722  -1.52772  -1.73711   0.33394   1.96660   1.01756  -1.26731  -1.88849  -0.03050   1.86752   1.31391  -0.96458  -1.97679  -0.39392   1.70608   1.56638  -0.62963  -1.99907  -0.74418   1.48765   1.76653  -0.27365  -1.95459  -1.06959   1.21954   1.90769   0.09147  -1.84483  -1.35928   0.91070   1.98513   0.45353  -1.67345  -1.60357   0.57144   1.99628   0.80045  -1.44619  -1.79431   0.21310   1.94076   1.12063  -1.17063  -1.92512  -0.15236   1.82041   1.40339  -0.85597  -1.99163  -0.51273   1.63928   0.00000     ... ... ..... ....... ......... ........... .............
E21      2.00000   0.57144  -1.67345  -1.52772   0.80045   1.98513   0.33394  -1.79431  -1.35928   1.01756   1.94076   0.09147  -1.88849  -1.17063   1.21954   1.86752  -0.15236  -1.95459  -0.96458   1.40339   1.76653  -0.39392  -1.99163  -0.74418   1.56638   1.63928  -0.62963  -1.99907  -0.51273   1.70608   1.48765  -0.85597  -1.97679  -0.27365   1.82041   1.31391  -1.06959  -1.92512  -0.03050   1.90769   1.12063  -1.26731  -1.84483   0.21310   1.96660   0.91070  -1.44619  -1.73711   0.45353   1.99628   0.68722  -1.60357   0.00000     ... ... ..... ....... ......... ........... .............
E22      2.00000   0.45353  -1.79431  -1.26731   1.21954   1.82041  -0.39392  -1.99907  -0.51273   1.76653   1.31391  -1.17063  -1.84483   0.33394   1.99628   0.57144  -1.73711  -1.35928   1.12063   1.86752  -0.27365  -1.99163  -0.62963   1.70608   1.40339  -1.06959  -1.88849   0.21310   1.98513   0.68722  -1.67345  -1.44619   1.01756   1.90769  -0.15236  -1.97679  -0.74418   1.63928   1.48765  -0.96458  -1.92512   0.09147   1.96660   0.80045  -1.60357  -1.52772   0.91070   1.94076  -0.03050  -1.95459  -0.85597   1.56638   0.00000     ... ... ..... ....... ......... ........... .............
E23      2.00000   0.33394  -1.88849  -0.96458   1.56638   1.48765  -1.06959  -1.84483   0.45353   1.99628   0.21310  -1.92512  -0.85597   1.63928   1.40339  -1.17063  -1.79431   0.57144   1.98513   0.09147  -1.95459  -0.74418   1.70608   1.31391  -1.26731  -1.73711   0.68722   1.96660  -0.03050  -1.97679  -0.62963   1.76653   1.21954  -1.35928  -1.67345   0.80045   1.94076  -0.15236  -1.99163  -0.51273   1.82041   1.12063  -1.44619  -1.60357   0.91070   1.90769  -0.27365  -1.99907  -0.39392   1.86752   1.01756  -1.52772   0.00000     ... ... ..... ....... ......... ........... .............
E24      2.00000   0.21310  -1.95459  -0.62963   1.82041   1.01756  -1.60357  -1.35928   1.31391   1.63928  -0.96458  -1.84483   0.57144   1.96660  -0.15236  -1.99907  -0.27365   1.94076   0.68722  -1.79431  -1.06959   1.56638   1.40339  -1.26731  -1.67345   0.91070   1.86752  -0.51273  -1.97679   0.09147   1.99628   0.33394  -1.92512  -0.74418   1.76653   1.12063  -1.52772  -1.44619   1.21954   1.70608  -0.85597  -1.88849   0.45353   1.98513  -0.03050  -1.99163  -0.39392   1.90769   0.80045  -1.73711  -1.17063   1.48765   0.00000     ... ... ..... ....... ......... ........... .............
E25      2.00000   0.09147  -1.99163  -0.27365   1.96660   0.45353  -1.92512  -0.62963   1.86752   0.80045  -1.79431  -0.96458   1.70608   1.12063  -1.60357  -1.26731   1.48765   1.40339  -1.35928  -1.52772   1.21954   1.63928  -1.06959  -1.73711   0.91070   1.82041  -0.74418  -1.88849   0.57144   1.94076  -0.39392  -1.97679   0.21310   1.99628  -0.03050  -1.99907  -0.15236   1.98513   0.33394  -1.95459  -0.51273   1.90769   0.68722  -1.84483  -0.85597   1.76653   1.01756  -1.67345  -1.17063   1.56638   1.31391  -1.44619   0.00000     ... ... ..... ....... ......... ........... .............
E26      2.00000  -0.03050  -1.99907   0.09147   1.99628  -0.15236  -1.99163   0.21310   1.98513  -0.27365  -1.97679   0.33394   1.96660  -0.39392  -1.95459   0.45353   1.94076  -0.51273  -1.92512   0.57144   1.90769  -0.62963  -1.88849   0.68722   1.86752  -0.74418  -1.84483   0.80045   1.82041  -0.85597  -1.79431   0.91070   1.76653  -0.96458  -1.73711   1.01756   1.70608  -1.06959  -1.67345   1.12063   1.63928  -1.17063  -1.60357   1.21954   1.56638  -1.26731  -1.52772   1.31391   1.48765  -1.35928  -1.44619   1.40339   0.00000     ... ... ..... ....... ......... ........... .............
E27      2.00000  -0.15236  -1.97679   0.45353   1.90769  -0.74418  -1.79431   1.01756   1.63928  -1.26731  -1.44619   1.48765   1.21954  -1.67345  -0.96458   1.82041   0.68722  -1.92512  -0.39392   1.98513   0.09147  -1.99907   0.21310   1.96660  -0.51273  -1.88849   0.80045   1.76653  -1.06959  -1.60357   1.31391   1.40339  -1.52772  -1.17063   1.70608   0.91070  -1.84483  -0.62963   1.94076   0.33394  -1.99163  -0.03050   1.99628  -0.27365  -1.95459   0.57144   1.86752  -0.85597  -1.73711   1.12063   1.56638  -1.35928   0.00000     ... ... ..... ....... ......... ........... .............
E28      2.00000  -0.27365  -1.92512   0.80045   1.70608  -1.26731  -1.35928   1.63928   0.91070  -1.88849  -0.39392   1.99628  -0.15236  -1.95459   0.68722   1.76653  -1.17063  -1.44619   1.56638   1.01756  -1.84483  -0.51273   1.98513  -0.03050  -1.97679   0.57144   1.82041  -1.06959  -1.52772   1.48765   1.12063  -1.79431  -0.62963   1.96660   0.09147  -1.99163   0.45353   1.86752  -0.96458  -1.60357   1.40339   1.21954  -1.73711  -0.74418   1.94076   0.21310  -1.99907   0.33394   1.90769  -0.85597  -1.67345   1.31391   0.00000     ... ... ..... ....... ......... ........... .............
E29      2.00000  -0.39392  -1.84483   1.12063   1.40339  -1.67345  -0.74418   1.96660  -0.03050  -1.95459   0.80045   1.63928  -1.44619  -1.06959   1.86752   0.33394  -1.99907   0.45353   1.82041  -1.17063  -1.35928   1.70608   0.68722  -1.97679   0.09147   1.94076  -0.85597  -1.60357   1.48765   1.01756  -1.88849  -0.27365   1.99628  -0.51273  -1.79431   1.21954   1.31391  -1.73711  -0.62963   1.98513  -0.15236  -1.92512   0.91070   1.56638  -1.52772  -0.96458   1.90769   0.21310  -1.99163   0.57144   1.76653  -1.26731   0.00000     ... ... ..... ....... ......... ........... .............
E30      2.00000  -0.51273  -1.73711   1.40339   1.01756  -1.92512  -0.03050   1.94076  -0.96458  -1.44619   1.70608   0.57144  -1.99907   0.45353   1.76653  -1.35928  -1.06959   1.90769   0.09147  -1.95459   0.91070   1.48765  -1.67345  -0.62963   1.99628  -0.39392  -1.79431   1.31391   1.12063  -1.88849  -0.15236   1.96660  -0.85597  -1.52772   1.63928   0.68722  -1.99163   0.33394   1.82041  -1.26731  -1.17063   1.86752   0.21310  -1.97679   0.80045   1.56638  -1.60357  -0.74418   1.98513  -0.27365  -1.84483   1.21954   0.00000     ... ... ..... ....... ......... ........... .............
E31      2.00000  -0.62963  -1.60357   1.63928   0.57144  -1.99907   0.68722   1.56638  -1.67345  -0.51273   1.99628  -0.74418  -1.52772   1.70608   0.45353  -1.99163   0.80045   1.48765  -1.73711  -0.39392   1.98513  -0.85597  -1.44619   1.76653   0.33394  -1.97679   0.91070   1.40339  -1.79431  -0.27365   1.96660  -0.96458  -1.35928   1.82041   0.21310  -1.95459   1.01756   1.31391  -1.84483  -0.15236   1.94076  -1.06959  -1.26731   1.86752   0.09147  -1.92512   1.12063   1.21954  -1.88849  -0.03050   1.90769  -1.17063   0.00000     ... ... ..... ....... ......... ........... .............
E32      2.00000  -0.74418  -1.44619   1.82041   0.09147  -1.88849   1.31391   0.91070  -1.99163   0.57144   1.56638  -1.73711  -0.27365   1.94076  -1.17063  -1.06959   1.96660  -0.39392  -1.67345   1.63928   0.45353  -1.97679   1.01756   1.21954  -1.92512   0.21310   1.76653  -1.52772  -0.62963   1.99628  -0.85597  -1.35928   1.86752  -0.03050  -1.84483   1.40339   0.80045  -1.99907   0.68722   1.48765  -1.79431  -0.15236   1.90769  -1.26731  -0.96458   1.98513  -0.51273  -1.60357   1.70608   0.33394  -1.95459   1.12063   0.00000     ... ... ..... ....... ......... ........... .............
E33      2.00000  -0.85597  -1.26731   1.94076  -0.39392  -1.60357   1.76653   0.09147  -1.84483   1.48765   0.57144  -1.97679   1.12063   1.01756  -1.99163   0.68722   1.40339  -1.88849   0.21310   1.70608  -1.67345  -0.27365   1.90769  -1.35928  -0.74418   1.99628  -0.96458  -1.17063   1.96660  -0.51273  -1.52772   1.82041  -0.03050  -1.79431   1.56638   0.45353  -1.95459   1.21954   0.91070  -1.99907   0.80045   1.31391  -1.92512   0.33394   1.63928  -1.73711  -0.15236   1.86752  -1.44619  -0.62963   1.98513  -1.06959   0.00000     ... ... ..... ....... ......... ........... .............
E34      2.00000  -0.96458  -1.06959   1.99628  -0.85597  -1.17063   1.98513  -0.74418  -1.26731   1.96660  -0.62963  -1.35928   1.94076  -0.51273  -1.44619   1.90769  -0.39392  -1.52772   1.86752  -0.27365  -1.60357   1.82041  -0.15236  -1.67345   1.76653  -0.03050  -1.73711   1.70608   0.09147  -1.79431   1.63928   0.21310  -1.84483   1.56638   0.33394  -1.88849   1.48765   0.45353  -1.92512   1.40339   0.57144  -1.95459   1.31391   0.68722  -1.97679   1.21954   0.80045  -1.99163   1.12063   0.91070  -1.99907   1.01756   0.00000     ... ... ..... ....... ......... ........... .............
E35      2.00000  -1.06959  -0.85597   1.98513  -1.26731  -0.62963   1.94076  -1.44619  -0.39392   1.86752  -1.60357  -0.15236   1.76653  -1.73711   0.09147   1.63928  -1.84483   0.33394   1.48765  -1.92512   0.57144   1.31391  -1.97679   0.80045   1.12063  -1.99907   1.01756   0.91070  -1.99163   1.21954   0.68722  -1.95459   1.40339   0.45353  -1.88849   1.56638   0.21310  -1.79431   1.70608  -0.03050  -1.67345   1.82041  -0.27365  -1.52772   1.90769  -0.51273  -1.35928   1.96660  -0.74418  -1.17063   1.99628  -0.96458   0.00000     ... ... ..... ....... ......... ........... .............
E36      2.00000  -1.17063  -0.62963   1.90769  -1.60357  -0.03050   1.63928  -1.88849   0.57144   1.21954  -1.99907   1.12063   0.68722  -1.92512   1.56638   0.09147  -1.67345   1.86752  -0.51273  -1.26731   1.99628  -1.06959  -0.74418   1.94076  -1.52772  -0.15236   1.70608  -1.84483   0.45353   1.31391  -1.99163   1.01756   0.80045  -1.95459   1.48765   0.21310  -1.73711   1.82041  -0.39392  -1.35928   1.98513  -0.96458  -0.85597   1.96660  -1.44619  -0.27365   1.76653  -1.79431   0.33394   1.40339  -1.97679   0.91070   0.00000     ... ... ..... ....... ......... ........... .............
E37      2.00000  -1.26731  -0.39392   1.76653  -1.84483   0.57144   1.12063  -1.99163   1.40339   0.21310  -1.67345   1.90769  -0.74418  -0.96458   1.96660  -1.52772  -0.03050   1.56638  -1.95459   0.91070   0.80045  -1.92512   1.63928  -0.15236  -1.44619   1.98513  -1.06959  -0.62963   1.86752  -1.73711   0.33394   1.31391  -1.99907   1.21954   0.45353  -1.79431   1.82041  -0.51273  -1.17063   1.99628  -1.35928  -0.27365   1.70608  -1.88849   0.68722   1.01756  -1.97679   1.48765   0.09147  -1.60357   1.94076  -0.85597   0.00000     ... ... ..... ....... ......... ........... .............
E38      2.00000  -1.35928  -0.15236   1.56638  -1.97679   1.12063   0.45353  -1.73711   1.90769  -0.85597  -0.74418   1.86752  -1.79431   0.57144   1.01756  -1.95459   1.63928  -0.27365  -1.26731   1.99628  -1.44619  -0.03050   1.48765  -1.99163   1.21954   0.33394  -1.67345   1.94076  -0.96458  -0.62963   1.82041  -1.84483   0.68722   0.91070  -1.92512   1.70608  -0.39392  -1.17063   1.98513  -1.52772   0.09147   1.40339  -1.99907   1.31391   0.21310  -1.60357   1.96660  -1.06959  -0.51273   1.76653  -1.88849   0.80045   0.00000     ... ... ..... ....... ......... ........... .............
E39      2.00000  -1.44619   0.09147   1.31391  -1.99163   1.56638  -0.27365  -1.17063   1.96660  -1.67345   0.45353   1.01756  -1.92512   1.76653  -0.62963  -0.85597   1.86752  -1.84483   0.80045   0.68722  -1.79431   1.90769  -0.96458  -0.51273   1.70608  -1.95459   1.12063   0.33394  -1.60357   1.98513  -1.26731  -0.15236   1.48765  -1.99907   1.40339  -0.03050  -1.35928   1.99628  -1.52772   0.21310   1.21954  -1.97679   1.63928  -0.39392  -1.06959   1.94076  -1.73711   0.57144   0.91070  -1.88849   1.82041  -0.74418   0.00000     ... ... ..... ....... ......... ........... .............
E40      2.00000  -1.52772   0.33394   1.01756  -1.88849   1.86752  -0.96458  -0.39392   1.56638  -1.99907   1.48765  -0.27365  -1.06959   1.90769  -1.84483   0.91070   0.45353  -1.60357   1.99628  -1.44619   0.21310   1.12063  -1.92512   1.82041  -0.85597  -0.51273   1.63928  -1.99163   1.40339  -0.15236  -1.17063   1.94076  -1.79431   0.80045   0.57144  -1.67345   1.98513  -1.35928   0.09147   1.21954  -1.95459   1.76653  -0.74418  -0.62963   1.70608  -1.97679   1.31391  -0.03050  -1.26731   1.96660  -1.73711   0.68722   0.00000     ... ... ..... ....... ......... ........... .............
E41      2.00000  -1.60357   0.57144   0.68722  -1.67345   1.99628  -1.52772   0.45353   0.80045  -1.73711   1.98513  -1.44619   0.33394   0.91070  -1.79431   1.96660  -1.35928   0.21310   1.01756  -1.84483   1.94076  -1.26731   0.09147   1.12063  -1.88849   1.90769  -1.17063  -0.03050   1.21954  -1.92512   1.86752  -1.06959  -0.15236   1.31391  -1.95459   1.82041  -0.96458  -0.27365   1.40339  -1.97679   1.76653  -0.85597  -0.39392   1.48765  -1.99163   1.70608  -0.74418  -0.51273   1.56638  -1.99907   1.63928  -0.62963   0.00000     ... ... ..... ....... ......... ........... .............
E42      2.00000  -1.67345   0.80045   0.33394  -1.35928   1.94076  -1.88849   1.21954  -0.15236  -0.96458   1.76653  -1.99163   1.56638  -0.62963  -0.51273   1.48765  -1.97679   1.82041  -1.06959  -0.03050   1.12063  -1.84483   1.96660  -1.44619   0.45353   0.68722  -1.60357   1.99628  -1.73711   0.91070   0.21310  -1.26731   1.90769  -1.92512   1.31391  -0.27365  -0.85597   1.70608  -1.99907   1.63928  -0.74418  -0.39392   1.40339  -1.95459   1.86752  -1.17063   0.09147   1.01756  -1.79431   1.98513  -1.52772   0.57144   0.00000     ... ... ..... ....... ......... ........... .............
E43      2.00000  -1.73711   1.01756  -0.03050  -0.96458   1.70608  -1.99907   1.76653  -1.06959   0.09147   0.91070  -1.67345   1.99628  -1.79431   1.12063  -0.15236  -0.85597   1.63928  -1.99163   1.82041  -1.17063   0.21310   0.80045  -1.60357   1.98513  -1.84483   1.21954  -0.27365  -0.74418   1.56638  -1.97679   1.86752  -1.26731   0.33394   0.68722  -1.52772   1.96660  -1.88849   1.31391  -0.39392  -0.62963   1.48765  -1.95459   1.90769  -1.35928   0.45353   0.57144  -1.44619   1.94076  -1.92512   1.40339  -0.51273   0.00000     ... ... ..... ....... ......... ........... .............
E44      2.00000  -1.79431   1.21954  -0.39392  -0.51273   1.31391  -1.84483   1.99628  -1.73711   1.12063  -0.27365  -0.62963   1.40339  -1.88849   1.98513  -1.67345   1.01756  -0.15236  -0.74418   1.48765  -1.92512   1.96660  -1.60357   0.91070  -0.03050  -0.85597   1.56638  -1.95459   1.94076  -1.52772   0.80045   0.09147  -0.96458   1.63928  -1.97679   1.90769  -1.44619   0.68722   0.21310  -1.06959   1.70608  -1.99163   1.86752  -1.35928   0.57144   0.33394  -1.17063   1.76653  -1.99907   1.82041  -1.26731   0.45353   0.00000     ... ... ..... ....... ......... ........... .............
E45      2.00000  -1.84483   1.40339  -0.74418  -0.03050   0.80045  -1.44619   1.86752  -1.99907   1.82041  -1.35928   0.68722   0.09147  -0.85597   1.48765  -1.88849   1.99628  -1.79431   1.31391  -0.62963  -0.15236   0.91070  -1.52772   1.90769  -1.99163   1.76653  -1.26731   0.57144   0.21310  -0.96458   1.56638  -1.92512   1.98513  -1.73711   1.21954  -0.51273  -0.27365   1.01756  -1.60357   1.94076  -1.97679   1.70608  -1.17063   0.45353   0.33394  -1.06959   1.63928  -1.95459   1.96660  -1.67345   1.12063  -0.39392   0.00000     ... ... ..... ....... ......... ........... .............
E46      2.00000  -1.88849   1.56638  -1.06959   0.45353   0.21310  -0.85597   1.40339  -1.79431   1.98513  -1.95459   1.70608  -1.26731   0.68722  -0.03050  -0.62963   1.21954  -1.67345   1.94076  -1.99163   1.82041  -1.44619   0.91070  -0.27365  -0.39392   1.01756  -1.52772   1.86752  -1.99907   1.90769  -1.60357   1.12063  -0.51273  -0.15236   0.80045  -1.35928   1.76653  -1.97679   1.96660  -1.73711   1.31391  -0.74418   0.09147   0.57144  -1.17063   1.63928  -1.92512   1.99628  -1.84483   1.48765  -0.96458   0.33394   0.00000     ... ... ..... ....... ......... ........... .............
E47      2.00000  -1.92512   1.70608  -1.35928   0.91070  -0.39392  -0.15236   0.68722  -1.17063   1.56638  -1.84483   1.98513  -1.97679   1.82041  -1.52772   1.12063  -0.62963   0.09147   0.45353  -0.96458   1.40339  -1.73711   1.94076  -1.99907   1.90769  -1.67345   1.31391  -0.85597   0.33394   0.21310  -0.74418   1.21954  -1.60357   1.86752  -1.99163   1.96660  -1.79431   1.48765  -1.06959   0.57144  -0.03050  -0.51273   1.01756  -1.44619   1.76653  -1.95459   1.99628  -1.88849   1.63928  -1.26731   0.80045  -0.27365   0.00000     ... ... ..... ....... ......... ........... .............
E48      2.00000  -1.95459   1.82041  -1.60357   1.31391  -0.96458   0.57144  -0.15236  -0.27365   0.68722  -1.06959   1.40339  -1.67345   1.86752  -1.97679   1.99628  -1.92512   1.76653  -1.52772   1.21954  -0.85597   0.45353  -0.03050  -0.39392   0.80045  -1.17063   1.48765  -1.73711   1.90769  -1.99163   1.98513  -1.88849   1.70608  -1.44619   1.12063  -0.74418   0.33394   0.09147  -0.51273   0.91070  -1.26731   1.56638  -1.79431   1.94076  -1.99907   1.96660  -1.84483   1.63928  -1.35928   1.01756  -0.62963   0.21310   0.00000     ... ... ..... ....... ......... ........... .............
E49      2.00000  -1.97679   1.90769  -1.79431   1.63928  -1.44619   1.21954  -0.96458   0.68722  -0.39392   0.09147   0.21310  -0.51273   0.80045  -1.06959   1.31391  -1.52772   1.70608  -1.84483   1.94076  -1.99163   1.99628  -1.95459   1.86752  -1.73711   1.56638  -1.35928   1.12063  -0.85597   0.57144  -0.27365  -0.03050   0.33394  -0.62963   0.91070  -1.17063   1.40339  -1.60357   1.76653  -1.88849   1.96660  -1.99907   1.98513  -1.92512   1.82041  -1.67345   1.48765  -1.26731   1.01756  -0.74418   0.45353  -0.15236   0.00000     ... ... ..... ....... ......... ........... .............
E50      2.00000  -1.99163   1.96660  -1.92512   1.86752  -1.79431   1.70608  -1.60357   1.48765  -1.35928   1.21954  -1.06959   0.91070  -0.74418   0.57144  -0.39392   0.21310  -0.03050  -0.15236   0.33394  -0.51273   0.68722  -0.85597   1.01756  -1.17063   1.31391  -1.44619   1.56638  -1.67345   1.76653  -1.84483   1.90769  -1.95459   1.98513  -1.99907   1.99628  -1.97679   1.94076  -1.88849   1.82041  -1.73711   1.63928  -1.52772   1.40339  -1.26731   1.12063  -0.96458   0.80045  -0.62963   0.45353  -0.27365   0.09147   0.00000     ... ... ..... ....... ......... ........... .............
E51      2.00000  -1.99907   1.99628  -1.99163   1.98513  -1.97679   1.96660  -1.95459   1.94076  -1.92512   1.90769  -1.88849   1.86752  -1.84483   1.82041  -1.79431   1.76653  -1.73711   1.70608  -1.67345   1.63928  -1.60357   1.56638  -1.52772   1.48765  -1.44619   1.40339  -1.35928   1.31391  -1.26731   1.21954  -1.17063   1.12063  -1.06959   1.01756  -0.96458   0.91070  -0.85597   0.80045  -0.74418   0.68722  -0.62963   0.57144  -0.51273   0.45353  -0.39392   0.33394  -0.27365   0.21310  -0.15236   0.09147  -0.03050   0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.996279934320 = 2*cos(2*π/103)
                               1.985133576168 = 2*cos(4*π/103)
                               1.966602390729 = 2*cos(6*π/103)
                               1.940755315229 = 2*cos(8*π/103)
                               1.907688502487 = 2*cos(10*π/103)
                               1.867524963219 = 2*cos(12*π/103)
                               1.820414108428 = 2*cos(14*π/103)
                               1.766531193589 = 2*cos(16*π/103)
                               1.706076666683 = 2*cos(18*π/103)
                               1.639275422522 = 2*cos(20*π/103)
                               1.566375966121 = 2*cos(22*π/103)
                               1.487649488246 = 2*cos(24*π/103)
                               1.403388856566 = 2*cos(26*π/103)
                               1.313907526165 = 2*cos(28*π/103)
                               1.219538373468 = 2*cos(30*π/103)
                               1.120632457923 = 2*cos(32*π/103)
                               1.017557716030 = 2*cos(34*π/103)
                               0.910697592601 = 2*cos(36*π/103)
                               0.800449614313 = 2*cos(38*π/103)
                               0.687223910885 = 2*cos(40*π/103)
                               0.571441689372 = 2*cos(42*π/103)
                               0.453533667242 = 2*cos(44*π/103)
                               0.333938470082 = 2*cos(46*π/103)
                               0.213100999880 = 2*cos(48*π/103)
                               0.091470779962 = 2*cos(50*π/103)
                              -0.030499717266 = 2*cos(52*π/103)
                              -0.152356753542 = 2*cos(54*π/103)
                              -0.273647012688 = 2*cos(56*π/103)
                              -0.393919286973 = 2*cos(58*π/103)
                              -0.512726155639 = 2*cos(60*π/103)
                              -0.629625649329 = 2*cos(62*π/103)
                              -0.744182894250 = 2*cos(64*π/103)
                              -0.855971729926 = 2*cos(66*π/103)
                              -0.964576294547 = 2*cos(68*π/103)
                              -1.069592571998 = 2*cos(70*π/103)
                              -1.170629894830 = 2*cos(72*π/103)
                              -1.267312397567 = 2*cos(74*π/103)
                              -1.359280414947 = 2*cos(76*π/103)
                              -1.446191819906 = 2*cos(78*π/103)
                              -1.527723296308 = 2*cos(80*π/103)
                              -1.603571541707 = 2*cos(82*π/103)
                              -1.673454395648 = 2*cos(84*π/103)
                              -1.737111889324 = 2*cos(86*π/103)
                              -1.794307212678 = 2*cos(88*π/103)
                              -1.844827595350 = 2*cos(90*π/103)
                              -1.888485098199 = 2*cos(92*π/103)
                              -1.925117312447 = 2*cos(94*π/103)
                              -1.954587963850 = 2*cos(96*π/103)
                              -1.976787419650 = 2*cos(98*π/103)
                              -1.991633096413 = 2*cos(100*π/103)
                              -1.999069767247 = 2*cos(102*π/103)



 Symmetry of Rotations and Cartesian products

A1   p+d+f+g+h+i+j+k+l+m    z, z2, z3, z4, z5, z6 
A2   R                      Rz 
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 C103v point group is 206, and the order of the principal axis (C103) is 103. The group has 53 irreducible representations.

    β  The C103v point group is isomorphic to D103.

    γ  The C103v point group is generated by two symmetry elements, C103 and any σv.
       Also, the group may be generated from any two σv planes.

    δ  The lowest nonvanishing multipole moment in C103v is 2 (dipole 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  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 just 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 C103v point group was created by Gernot Katzer.

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