Character table for the D61d point group

D61d     E         2 C61     2 C61^2   2 C61^3   2 C61^4   2 C61^5   2 C61^6   2 C61^7   2 C61^8   2 C61^9   2 C61^10  2 C61^11  2 C61^12  2 C61^13  2 C61^14  2 C61^15  2 C61^16  2 C61^17  2 C61^18  2 C61^19  2 C61^20  2 C61^21  2 C61^22  2 C61^23  2 C61^24  2 C61^25  2 C61^26  2 C61^27  2 C61^28  2 C61^29  2 C61^30  61 C2'    i         2 S122    2 S122^3  2 S122^5  2 S122^7  2 S122^9  2 S122^11 2 S122^13 2 S122^15 2 S122^17 2 S122^19 2 S122^21 2 S122^23 2 S122^25 2 S122^27 2 S122^29 2 S122^31 2 S122^33 2 S122^35 2 S122^37 2 S122^39 2 S122^41 2 S122^43 2 S122^45 2 S122^47 2 S122^49 2 S122^51 2 S122^53 2 S122^55 2 S122^57 2 S122^59 61 sd       <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A1g      1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   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
A2g      1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000  -1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   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 ... ..... ....... ......... ........... .............
E1g      2.00000   1.98940   1.95771   1.90527   1.83263   1.74057   1.63006   1.50226   1.35855   1.20043   1.02959   0.84783   0.65708   0.45938   0.25680   0.05150  -0.15435  -0.35856  -0.55897  -0.75346  -0.93995  -1.11649  -1.28119  -1.43230  -1.56824  -1.68755  -1.78897  -1.87143  -1.93406  -1.97618  -1.99735   0.00000   2.00000  -1.99735  -1.97618  -1.93406  -1.87143  -1.78897  -1.68755  -1.56824  -1.43230  -1.28119  -1.11649  -0.93995  -0.75346  -0.55897  -0.35856  -0.15435   0.05150   0.25680   0.45938   0.65708   0.84783   1.02959   1.20043   1.35855   1.50226   1.63006   1.74057   1.83263   1.90527   1.95771   1.98940   0.00000     TT. ... ..TT. ....... ......TT. ........... ..........TT.
E2g      2.00000   1.95771   1.83263   1.63006   1.35855   1.02959   0.65708   0.25680  -0.15435  -0.55897  -0.93995  -1.28119  -1.56824  -1.78897  -1.93406  -1.99735  -1.97618  -1.87143  -1.68755  -1.43230  -1.11649  -0.75346  -0.35856   0.05150   0.45938   0.84783   1.20043   1.50226   1.74057   1.90527   1.98940   0.00000   2.00000   1.98940   1.90527   1.74057   1.50226   1.20043   0.84783   0.45938   0.05150  -0.35856  -0.75346  -1.11649  -1.43230  -1.68755  -1.87143  -1.97618  -1.99735  -1.93406  -1.78897  -1.56824  -1.28119  -0.93995  -0.55897  -0.15435   0.25680   0.65708   1.02959   1.35855   1.63006   1.83263   1.95771   0.00000     ... ... TT... ....... ....TT... ........... ........TT...
E3g      2.00000   1.90527   1.63006   1.20043   0.65708   0.05150  -0.55897  -1.11649  -1.56824  -1.87143  -1.99735  -1.93406  -1.68755  -1.28119  -0.75346  -0.15435   0.45938   1.02959   1.50226   1.83263   1.98940   1.95771   1.74057   1.35855   0.84783   0.25680  -0.35856  -0.93995  -1.43230  -1.78897  -1.97618   0.00000   2.00000  -1.97618  -1.78897  -1.43230  -0.93995  -0.35856   0.25680   0.84783   1.35855   1.74057   1.95771   1.98940   1.83263   1.50226   1.02959   0.45938  -0.15435  -0.75346  -1.28119  -1.68755  -1.93406  -1.99735  -1.87143  -1.56824  -1.11649  -0.55897   0.05150   0.65708   1.20043   1.63006   1.90527   0.00000     ... ... ..... ....... ..TT..... ........... ......TT.....
E4g      2.00000   1.83263   1.35855   0.65708  -0.15435  -0.93995  -1.56824  -1.93406  -1.97618  -1.68755  -1.11649  -0.35856   0.45938   1.20043   1.74057   1.98940   1.90527   1.50226   0.84783   0.05150  -0.75346  -1.43230  -1.87143  -1.99735  -1.78897  -1.28119  -0.55897   0.25680   1.02959   1.63006   1.95771   0.00000   2.00000   1.95771   1.63006   1.02959   0.25680  -0.55897  -1.28119  -1.78897  -1.99735  -1.87143  -1.43230  -0.75346   0.05150   0.84783   1.50226   1.90527   1.98940   1.74057   1.20043   0.45938  -0.35856  -1.11649  -1.68755  -1.97618  -1.93406  -1.56824  -0.93995  -0.15435   0.65708   1.35855   1.83263   0.00000     ... ... ..... ....... TT....... ........... ....TT.......
E5g      2.00000   1.74057   1.02959   0.05150  -0.93995  -1.68755  -1.99735  -1.78897  -1.11649  -0.15435   0.84783   1.63006   1.98940   1.83263   1.20043   0.25680  -0.75346  -1.56824  -1.97618  -1.87143  -1.28119  -0.35856   0.65708   1.50226   1.95771   1.90527   1.35855   0.45938  -0.55897  -1.43230  -1.93406   0.00000   2.00000  -1.93406  -1.43230  -0.55897   0.45938   1.35855   1.90527   1.95771   1.50226   0.65708  -0.35856  -1.28119  -1.87143  -1.97618  -1.56824  -0.75346   0.25680   1.20043   1.83263   1.98940   1.63006   0.84783  -0.15435  -1.11649  -1.78897  -1.99735  -1.68755  -0.93995   0.05150   1.02959   1.74057   0.00000     ... ... ..... ....... ......... ........... ..TT.........
E6g      2.00000   1.63006   0.65708  -0.55897  -1.56824  -1.99735  -1.68755  -0.75346   0.45938   1.50226   1.98940   1.74057   0.84783  -0.35856  -1.43230  -1.97618  -1.78897  -0.93995   0.25680   1.35855   1.95771   1.83263   1.02959  -0.15435  -1.28119  -1.93406  -1.87143  -1.11649   0.05150   1.20043   1.90527   0.00000   2.00000   1.90527   1.20043   0.05150  -1.11649  -1.87143  -1.93406  -1.28119  -0.15435   1.02959   1.83263   1.95771   1.35855   0.25680  -0.93995  -1.78897  -1.97618  -1.43230  -0.35856   0.84783   1.74057   1.98940   1.50226   0.45938  -0.75346  -1.68755  -1.99735  -1.56824  -0.55897   0.65708   1.63006   0.00000     ... ... ..... ....... ......... ........... TT...........
E7g      2.00000   1.50226   0.25680  -1.11649  -1.93406  -1.78897  -0.75346   0.65708   1.74057   1.95771   1.20043  -0.15435  -1.43230  -1.99735  -1.56824  -0.35856   1.02959   1.90527   1.83263   0.84783  -0.55897  -1.68755  -1.97618  -1.28119   0.05150   1.35855   1.98940   1.63006   0.45938  -0.93995  -1.87143   0.00000   2.00000  -1.87143  -0.93995   0.45938   1.63006   1.98940   1.35855   0.05150  -1.28119  -1.97618  -1.68755  -0.55897   0.84783   1.83263   1.90527   1.02959  -0.35856  -1.56824  -1.99735  -1.43230  -0.15435   1.20043   1.95771   1.74057   0.65708  -0.75346  -1.78897  -1.93406  -1.11649   0.25680   1.50226   0.00000     ... ... ..... ....... ......... ........... .............
E8g      2.00000   1.35855  -0.15435  -1.56824  -1.97618  -1.11649   0.45938   1.74057   1.90527   0.84783  -0.75346  -1.87143  -1.78897  -0.55897   1.02959   1.95771   1.63006   0.25680  -1.28119  -1.99735  -1.43230   0.05150   1.50226   1.98940   1.20043  -0.35856  -1.68755  -1.93406  -0.93995   0.65708   1.83263   0.00000   2.00000   1.83263   0.65708  -0.93995  -1.93406  -1.68755  -0.35856   1.20043   1.98940   1.50226   0.05150  -1.43230  -1.99735  -1.28119   0.25680   1.63006   1.95771   1.02959  -0.55897  -1.78897  -1.87143  -0.75346   0.84783   1.90527   1.74057   0.45938  -1.11649  -1.97618  -1.56824  -0.15435   1.35855   0.00000     ... ... ..... ....... ......... ........... .............
E9g      2.00000   1.20043  -0.55897  -1.87143  -1.68755  -0.15435   1.50226   1.95771   0.84783  -0.93995  -1.97618  -1.43230   0.25680   1.74057   1.83263   0.45938  -1.28119  -1.99735  -1.11649   0.65708   1.90527   1.63006   0.05150  -1.56824  -1.93406  -0.75346   1.02959   1.98940   1.35855  -0.35856  -1.78897   0.00000   2.00000  -1.78897  -0.35856   1.35855   1.98940   1.02959  -0.75346  -1.93406  -1.56824   0.05150   1.63006   1.90527   0.65708  -1.11649  -1.99735  -1.28119   0.45938   1.83263   1.74057   0.25680  -1.43230  -1.97618  -0.93995   0.84783   1.95771   1.50226  -0.15435  -1.68755  -1.87143  -0.55897   1.20043   0.00000     ... ... ..... ....... ......... ........... .............
E10g     2.00000   1.02959  -0.93995  -1.99735  -1.11649   0.84783   1.98940   1.20043  -0.75346  -1.97618  -1.28119   0.65708   1.95771   1.35855  -0.55897  -1.93406  -1.43230   0.45938   1.90527   1.50226  -0.35856  -1.87143  -1.56824   0.25680   1.83263   1.63006  -0.15435  -1.78897  -1.68755   0.05150   1.74057   0.00000   2.00000   1.74057   0.05150  -1.68755  -1.78897  -0.15435   1.63006   1.83263   0.25680  -1.56824  -1.87143  -0.35856   1.50226   1.90527   0.45938  -1.43230  -1.93406  -0.55897   1.35855   1.95771   0.65708  -1.28119  -1.97618  -0.75346   1.20043   1.98940   0.84783  -1.11649  -1.99735  -0.93995   1.02959   0.00000     ... ... ..... ....... ......... ........... .............
E11g     2.00000   0.84783  -1.28119  -1.93406  -0.35856   1.63006   1.74057  -0.15435  -1.87143  -1.43230   0.65708   1.98940   1.02959  -1.11649  -1.97618  -0.55897   1.50226   1.83263   0.05150  -1.78897  -1.56824   0.45938   1.95771   1.20043  -0.93995  -1.99735  -0.75346   1.35855   1.90527   0.25680  -1.68755   0.00000   2.00000  -1.68755   0.25680   1.90527   1.35855  -0.75346  -1.99735  -0.93995   1.20043   1.95771   0.45938  -1.56824  -1.78897   0.05150   1.83263   1.50226  -0.55897  -1.97618  -1.11649   1.02959   1.98940   0.65708  -1.43230  -1.87143  -0.15435   1.74057   1.63006  -0.35856  -1.93406  -1.28119   0.84783   0.00000     ... ... ..... ....... ......... ........... .............
E12g     2.00000   0.65708  -1.56824  -1.68755   0.45938   1.98940   0.84783  -1.43230  -1.78897   0.25680   1.95771   1.02959  -1.28119  -1.87143   0.05150   1.90527   1.20043  -1.11649  -1.93406  -0.15435   1.83263   1.35855  -0.93995  -1.97618  -0.35856   1.74057   1.50226  -0.75346  -1.99735  -0.55897   1.63006   0.00000   2.00000   1.63006  -0.55897  -1.99735  -0.75346   1.50226   1.74057  -0.35856  -1.97618  -0.93995   1.35855   1.83263  -0.15435  -1.93406  -1.11649   1.20043   1.90527   0.05150  -1.87143  -1.28119   1.02959   1.95771   0.25680  -1.78897  -1.43230   0.84783   1.98940   0.45938  -1.68755  -1.56824   0.65708   0.00000     ... ... ..... ....... ......... ........... .............
E13g     2.00000   0.45938  -1.78897  -1.28119   1.20043   1.83263  -0.35856  -1.99735  -0.55897   1.74057   1.35855  -1.11649  -1.87143   0.25680   1.98940   0.65708  -1.68755  -1.43230   1.02959   1.90527  -0.15435  -1.97618  -0.75346   1.63006   1.50226  -0.93995  -1.93406   0.05150   1.95771   0.84783  -1.56824   0.00000   2.00000  -1.56824   0.84783   1.95771   0.05150  -1.93406  -0.93995   1.50226   1.63006  -0.75346  -1.97618  -0.15435   1.90527   1.02959  -1.43230  -1.68755   0.65708   1.98940   0.25680  -1.87143  -1.11649   1.35855   1.74057  -0.55897  -1.99735  -0.35856   1.83263   1.20043  -1.28119  -1.78897   0.45938   0.00000     ... ... ..... ....... ......... ........... .............
E14g     2.00000   0.25680  -1.93406  -0.75346   1.74057   1.20043  -1.43230  -1.56824   1.02959   1.83263  -0.55897  -1.97618   0.05150   1.98940   0.45938  -1.87143  -0.93995   1.63006   1.35855  -1.28119  -1.68755   0.84783   1.90527  -0.35856  -1.99735  -0.15435   1.95771   0.65708  -1.78897  -1.11649   1.50226   0.00000   2.00000   1.50226  -1.11649  -1.78897   0.65708   1.95771  -0.15435  -1.99735  -0.35856   1.90527   0.84783  -1.68755  -1.28119   1.35855   1.63006  -0.93995  -1.87143   0.45938   1.98940   0.05150  -1.97618  -0.55897   1.83263   1.02959  -1.56824  -1.43230   1.20043   1.74057  -0.75346  -1.93406   0.25680   0.00000     ... ... ..... ....... ......... ........... .............
E15g     2.00000   0.05150  -1.99735  -0.15435   1.98940   0.25680  -1.97618  -0.35856   1.95771   0.45938  -1.93406  -0.55897   1.90527   0.65708  -1.87143  -0.75346   1.83263   0.84783  -1.78897  -0.93995   1.74057   1.02959  -1.68755  -1.11649   1.63006   1.20043  -1.56824  -1.28119   1.50226   1.35855  -1.43230   0.00000   2.00000  -1.43230   1.35855   1.50226  -1.28119  -1.56824   1.20043   1.63006  -1.11649  -1.68755   1.02959   1.74057  -0.93995  -1.78897   0.84783   1.83263  -0.75346  -1.87143   0.65708   1.90527  -0.55897  -1.93406   0.45938   1.95771  -0.35856  -1.97618   0.25680   1.98940  -0.15435  -1.99735   0.05150   0.00000     ... ... ..... ....... ......... ........... .............
E16g     2.00000  -0.15435  -1.97618   0.45938   1.90527  -0.75346  -1.78897   1.02959   1.63006  -1.28119  -1.43230   1.50226   1.20043  -1.68755  -0.93995   1.83263   0.65708  -1.93406  -0.35856   1.98940   0.05150  -1.99735   0.25680   1.95771  -0.55897  -1.87143   0.84783   1.74057  -1.11649  -1.56824   1.35855   0.00000   2.00000   1.35855  -1.56824  -1.11649   1.74057   0.84783  -1.87143  -0.55897   1.95771   0.25680  -1.99735   0.05150   1.98940  -0.35856  -1.93406   0.65708   1.83263  -0.93995  -1.68755   1.20043   1.50226  -1.43230  -1.28119   1.63006   1.02959  -1.78897  -0.75346   1.90527   0.45938  -1.97618  -0.15435   0.00000     ... ... ..... ....... ......... ........... .............
E17g     2.00000  -0.35856  -1.87143   1.02959   1.50226  -1.56824  -0.93995   1.90527   0.25680  -1.99735   0.45938   1.83263  -1.11649  -1.43230   1.63006   0.84783  -1.93406  -0.15435   1.98940  -0.55897  -1.78897   1.20043   1.35855  -1.68755  -0.75346   1.95771   0.05150  -1.97618   0.65708   1.74057  -1.28119   0.00000   2.00000  -1.28119   1.74057   0.65708  -1.97618   0.05150   1.95771  -0.75346  -1.68755   1.35855   1.20043  -1.78897  -0.55897   1.98940  -0.15435  -1.93406   0.84783   1.63006  -1.43230  -1.11649   1.83263   0.45938  -1.99735   0.25680   1.90527  -0.93995  -1.56824   1.50226   1.02959  -1.87143  -0.35856   0.00000     ... ... ..... ....... ......... ........... .............
E18g     2.00000  -0.55897  -1.68755   1.50226   0.84783  -1.97618   0.25680   1.83263  -1.28119  -1.11649   1.90527   0.05150  -1.93406   1.02959   1.35855  -1.78897  -0.35856   1.98940  -0.75346  -1.56824   1.63006   0.65708  -1.99735   0.45938   1.74057  -1.43230  -0.93995   1.95771  -0.15435  -1.87143   1.20043   0.00000   2.00000   1.20043  -1.87143  -0.15435   1.95771  -0.93995  -1.43230   1.74057   0.45938  -1.99735   0.65708   1.63006  -1.56824  -0.75346   1.98940  -0.35856  -1.78897   1.35855   1.02959  -1.93406   0.05150   1.90527  -1.11649  -1.28119   1.83263   0.25680  -1.97618   0.84783   1.50226  -1.68755  -0.55897   0.00000     ... ... ..... ....... ......... ........... .............
E19g     2.00000  -0.75346  -1.43230   1.83263   0.05150  -1.87143   1.35855   0.84783  -1.99735   0.65708   1.50226  -1.78897  -0.15435   1.90527  -1.28119  -0.93995   1.98940  -0.55897  -1.56824   1.74057   0.25680  -1.93406   1.20043   1.02959  -1.97618   0.45938   1.63006  -1.68755  -0.35856   1.95771  -1.11649   0.00000   2.00000  -1.11649   1.95771  -0.35856  -1.68755   1.63006   0.45938  -1.97618   1.02959   1.20043  -1.93406   0.25680   1.74057  -1.56824  -0.55897   1.98940  -0.93995  -1.28119   1.90527  -0.15435  -1.78897   1.50226   0.65708  -1.99735   0.84783   1.35855  -1.87143   0.05150   1.83263  -1.43230  -0.75346   0.00000     ... ... ..... ....... ......... ........... .............
E20g     2.00000  -0.93995  -1.11649   1.98940  -0.75346  -1.28119   1.95771  -0.55897  -1.43230   1.90527  -0.35856  -1.56824   1.83263  -0.15435  -1.68755   1.74057   0.05150  -1.78897   1.63006   0.25680  -1.87143   1.50226   0.45938  -1.93406   1.35855   0.65708  -1.97618   1.20043   0.84783  -1.99735   1.02959   0.00000   2.00000   1.02959  -1.99735   0.84783   1.20043  -1.97618   0.65708   1.35855  -1.93406   0.45938   1.50226  -1.87143   0.25680   1.63006  -1.78897   0.05150   1.74057  -1.68755  -0.15435   1.83263  -1.56824  -0.35856   1.90527  -1.43230  -0.55897   1.95771  -1.28119  -0.75346   1.98940  -1.11649  -0.93995   0.00000     ... ... ..... ....... ......... ........... .............
E21g     2.00000  -1.11649  -0.75346   1.95771  -1.43230  -0.35856   1.83263  -1.68755   0.05150   1.63006  -1.87143   0.45938   1.35855  -1.97618   0.84783   1.02959  -1.99735   1.20043   0.65708  -1.93406   1.50226   0.25680  -1.78897   1.74057  -0.15435  -1.56824   1.90527  -0.55897  -1.28119   1.98940  -0.93995   0.00000   2.00000  -0.93995   1.98940  -1.28119  -0.55897   1.90527  -1.56824  -0.15435   1.74057  -1.78897   0.25680   1.50226  -1.93406   0.65708   1.20043  -1.99735   1.02959   0.84783  -1.97618   1.35855   0.45938  -1.87143   1.63006   0.05150  -1.68755   1.83263  -0.35856  -1.43230   1.95771  -0.75346  -1.11649   0.00000     ... ... ..... ....... ......... ........... .............
E22g     2.00000  -1.28119  -0.35856   1.74057  -1.87143   0.65708   1.02959  -1.97618   1.50226   0.05150  -1.56824   1.95771  -0.93995  -0.75346   1.90527  -1.68755   0.25680   1.35855  -1.99735   1.20043   0.45938  -1.78897   1.83263  -0.55897  -1.11649   1.98940  -1.43230  -0.15435   1.63006  -1.93406   0.84783   0.00000   2.00000   0.84783  -1.93406   1.63006  -0.15435  -1.43230   1.98940  -1.11649  -0.55897   1.83263  -1.78897   0.45938   1.20043  -1.99735   1.35855   0.25680  -1.68755   1.90527  -0.75346  -0.93995   1.95771  -1.56824   0.05150   1.50226  -1.97618   1.02959   0.65708  -1.87143   1.74057  -0.35856  -1.28119   0.00000     ... ... ..... ....... ......... ........... .............
E23g     2.00000  -1.43230   0.05150   1.35855  -1.99735   1.50226  -0.15435  -1.28119   1.98940  -1.56824   0.25680   1.20043  -1.97618   1.63006  -0.35856  -1.11649   1.95771  -1.68755   0.45938   1.02959  -1.93406   1.74057  -0.55897  -0.93995   1.90527  -1.78897   0.65708   0.84783  -1.87143   1.83263  -0.75346   0.00000   2.00000  -0.75346   1.83263  -1.87143   0.84783   0.65708  -1.78897   1.90527  -0.93995  -0.55897   1.74057  -1.93406   1.02959   0.45938  -1.68755   1.95771  -1.11649  -0.35856   1.63006  -1.97618   1.20043   0.25680  -1.56824   1.98940  -1.28119  -0.15435   1.50226  -1.99735   1.35855   0.05150  -1.43230   0.00000     ... ... ..... ....... ......... ........... .............
E24g     2.00000  -1.56824   0.45938   0.84783  -1.78897   1.95771  -1.28119   0.05150   1.20043  -1.93406   1.83263  -0.93995  -0.35856   1.50226  -1.99735   1.63006  -0.55897  -0.75346   1.74057  -1.97618   1.35855  -0.15435  -1.11649   1.90527  -1.87143   1.02959   0.25680  -1.43230   1.98940  -1.68755   0.65708   0.00000   2.00000   0.65708  -1.68755   1.98940  -1.43230   0.25680   1.02959  -1.87143   1.90527  -1.11649  -0.15435   1.35855  -1.97618   1.74057  -0.75346  -0.55897   1.63006  -1.99735   1.50226  -0.35856  -0.93995   1.83263  -1.93406   1.20043   0.05150  -1.28119   1.95771  -1.78897   0.84783   0.45938  -1.56824   0.00000     ... ... ..... ....... ......... ........... .............
E25g     2.00000  -1.68755   0.84783   0.25680  -1.28119   1.90527  -1.93406   1.35855  -0.35856  -0.75346   1.63006  -1.99735   1.74057  -0.93995  -0.15435   1.20043  -1.87143   1.95771  -1.43230   0.45938   0.65708  -1.56824   1.98940  -1.78897   1.02959   0.05150  -1.11649   1.83263  -1.97618   1.50226  -0.55897   0.00000   2.00000  -0.55897   1.50226  -1.97618   1.83263  -1.11649   0.05150   1.02959  -1.78897   1.98940  -1.56824   0.65708   0.45938  -1.43230   1.95771  -1.87143   1.20043  -0.15435  -0.93995   1.74057  -1.99735   1.63006  -0.75346  -0.35856   1.35855  -1.93406   1.90527  -1.28119   0.25680   0.84783  -1.68755   0.00000     ... ... ..... ....... ......... ........... .............
E26g     2.00000  -1.78897   1.20043  -0.35856  -0.55897   1.35855  -1.87143   1.98940  -1.68755   1.02959  -0.15435  -0.75346   1.50226  -1.93406   1.95771  -1.56824   0.84783   0.05150  -0.93995   1.63006  -1.97618   1.90527  -1.43230   0.65708   0.25680  -1.11649   1.74057  -1.99735   1.83263  -1.28119   0.45938   0.00000   2.00000   0.45938  -1.28119   1.83263  -1.99735   1.74057  -1.11649   0.25680   0.65708  -1.43230   1.90527  -1.97618   1.63006  -0.93995   0.05150   0.84783  -1.56824   1.95771  -1.93406   1.50226  -0.75346  -0.15435   1.02959  -1.68755   1.98940  -1.87143   1.35855  -0.55897  -0.35856   1.20043  -1.78897   0.00000     ... ... ..... ....... ......... ........... .............
E27g     2.00000  -1.87143   1.50226  -0.93995   0.25680   0.45938  -1.11649   1.63006  -1.93406   1.98940  -1.78897   1.35855  -0.75346   0.05150   0.65708  -1.28119   1.74057  -1.97618   1.95771  -1.68755   1.20043  -0.55897  -0.15435   0.84783  -1.43230   1.83263  -1.99735   1.90527  -1.56824   1.02959  -0.35856   0.00000   2.00000  -0.35856   1.02959  -1.56824   1.90527  -1.99735   1.83263  -1.43230   0.84783  -0.15435  -0.55897   1.20043  -1.68755   1.95771  -1.97618   1.74057  -1.28119   0.65708   0.05150  -0.75346   1.35855  -1.78897   1.98940  -1.93406   1.63006  -1.11649   0.45938   0.25680  -0.93995   1.50226  -1.87143   0.00000     ... ... ..... ....... ......... ........... .............
E28g     2.00000  -1.93406   1.74057  -1.43230   1.02959  -0.55897   0.05150   0.45938  -0.93995   1.35855  -1.68755   1.90527  -1.99735   1.95771  -1.78897   1.50226  -1.11649   0.65708  -0.15435  -0.35856   0.84783  -1.28119   1.63006  -1.87143   1.98940  -1.97618   1.83263  -1.56824   1.20043  -0.75346   0.25680   0.00000   2.00000   0.25680  -0.75346   1.20043  -1.56824   1.83263  -1.97618   1.98940  -1.87143   1.63006  -1.28119   0.84783  -0.35856  -0.15435   0.65708  -1.11649   1.50226  -1.78897   1.95771  -1.99735   1.90527  -1.68755   1.35855  -0.93995   0.45938   0.05150  -0.55897   1.02959  -1.43230   1.74057  -1.93406   0.00000     ... ... ..... ....... ......... ........... .............
E29g     2.00000  -1.97618   1.90527  -1.78897   1.63006  -1.43230   1.20043  -0.93995   0.65708  -0.35856   0.05150   0.25680  -0.55897   0.84783  -1.11649   1.35855  -1.56824   1.74057  -1.87143   1.95771  -1.99735   1.98940  -1.93406   1.83263  -1.68755   1.50226  -1.28119   1.02959  -0.75346   0.45938  -0.15435   0.00000   2.00000  -0.15435   0.45938  -0.75346   1.02959  -1.28119   1.50226  -1.68755   1.83263  -1.93406   1.98940  -1.99735   1.95771  -1.87143   1.74057  -1.56824   1.35855  -1.11649   0.84783  -0.55897   0.25680   0.05150  -0.35856   0.65708  -0.93995   1.20043  -1.43230   1.63006  -1.78897   1.90527  -1.97618   0.00000     ... ... ..... ....... ......... ........... .............
E30g     2.00000  -1.99735   1.98940  -1.97618   1.95771  -1.93406   1.90527  -1.87143   1.83263  -1.78897   1.74057  -1.68755   1.63006  -1.56824   1.50226  -1.43230   1.35855  -1.28119   1.20043  -1.11649   1.02959  -0.93995   0.84783  -0.75346   0.65708  -0.55897   0.45938  -0.35856   0.25680  -0.15435   0.05150   0.00000   2.00000   0.05150  -0.15435   0.25680  -0.35856   0.45938  -0.55897   0.65708  -0.75346   0.84783  -0.93995   1.02959  -1.11649   1.20043  -1.28119   1.35855  -1.43230   1.50226  -1.56824   1.63006  -1.68755   1.74057  -1.78897   1.83263  -1.87143   1.90527  -1.93406   1.95771  -1.97618   1.98940  -1.99735   0.00000     ... ... ..... ....... ......... ........... .............
A1u      1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000     ... ... ..... ....... ......... ........... .............
A2u      1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -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 .............
E1u      2.00000   1.98940   1.95771   1.90527   1.83263   1.74057   1.63006   1.50226   1.35855   1.20043   1.02959   0.84783   0.65708   0.45938   0.25680   0.05150  -0.15435  -0.35856  -0.55897  -0.75346  -0.93995  -1.11649  -1.28119  -1.43230  -1.56824  -1.68755  -1.78897  -1.87143  -1.93406  -1.97618  -1.99735   0.00000  -2.00000   1.99735   1.97618   1.93406   1.87143   1.78897   1.68755   1.56824   1.43230   1.28119   1.11649   0.93995   0.75346   0.55897   0.35856   0.15435  -0.05150  -0.25680  -0.45938  -0.65708  -0.84783  -1.02959  -1.20043  -1.35855  -1.50226  -1.63006  -1.74057  -1.83263  -1.90527  -1.95771  -1.98940   0.00000     ... TT. ..... ....TT. ......... ........TT. .............
E2u      2.00000   1.95771   1.83263   1.63006   1.35855   1.02959   0.65708   0.25680  -0.15435  -0.55897  -0.93995  -1.28119  -1.56824  -1.78897  -1.93406  -1.99735  -1.97618  -1.87143  -1.68755  -1.43230  -1.11649  -0.75346  -0.35856   0.05150   0.45938   0.84783   1.20043   1.50226   1.74057   1.90527   1.98940   0.00000  -2.00000  -1.98940  -1.90527  -1.74057  -1.50226  -1.20043  -0.84783  -0.45938  -0.05150   0.35856   0.75346   1.11649   1.43230   1.68755   1.87143   1.97618   1.99735   1.93406   1.78897   1.56824   1.28119   0.93995   0.55897   0.15435  -0.25680  -0.65708  -1.02959  -1.35855  -1.63006  -1.83263  -1.95771   0.00000     ... ... ..... ..TT... ......... ......TT... .............
E3u      2.00000   1.90527   1.63006   1.20043   0.65708   0.05150  -0.55897  -1.11649  -1.56824  -1.87143  -1.99735  -1.93406  -1.68755  -1.28119  -0.75346  -0.15435   0.45938   1.02959   1.50226   1.83263   1.98940   1.95771   1.74057   1.35855   0.84783   0.25680  -0.35856  -0.93995  -1.43230  -1.78897  -1.97618   0.00000  -2.00000   1.97618   1.78897   1.43230   0.93995   0.35856  -0.25680  -0.84783  -1.35855  -1.74057  -1.95771  -1.98940  -1.83263  -1.50226  -1.02959  -0.45938   0.15435   0.75346   1.28119   1.68755   1.93406   1.99735   1.87143   1.56824   1.11649   0.55897  -0.05150  -0.65708  -1.20043  -1.63006  -1.90527   0.00000     ... ... ..... TT..... ......... ....TT..... .............
E4u      2.00000   1.83263   1.35855   0.65708  -0.15435  -0.93995  -1.56824  -1.93406  -1.97618  -1.68755  -1.11649  -0.35856   0.45938   1.20043   1.74057   1.98940   1.90527   1.50226   0.84783   0.05150  -0.75346  -1.43230  -1.87143  -1.99735  -1.78897  -1.28119  -0.55897   0.25680   1.02959   1.63006   1.95771   0.00000  -2.00000  -1.95771  -1.63006  -1.02959  -0.25680   0.55897   1.28119   1.78897   1.99735   1.87143   1.43230   0.75346  -0.05150  -0.84783  -1.50226  -1.90527  -1.98940  -1.74057  -1.20043  -0.45938   0.35856   1.11649   1.68755   1.97618   1.93406   1.56824   0.93995   0.15435  -0.65708  -1.35855  -1.83263   0.00000     ... ... ..... ....... ......... ..TT....... .............
E5u      2.00000   1.74057   1.02959   0.05150  -0.93995  -1.68755  -1.99735  -1.78897  -1.11649  -0.15435   0.84783   1.63006   1.98940   1.83263   1.20043   0.25680  -0.75346  -1.56824  -1.97618  -1.87143  -1.28119  -0.35856   0.65708   1.50226   1.95771   1.90527   1.35855   0.45938  -0.55897  -1.43230  -1.93406   0.00000  -2.00000   1.93406   1.43230   0.55897  -0.45938  -1.35855  -1.90527  -1.95771  -1.50226  -0.65708   0.35856   1.28119   1.87143   1.97618   1.56824   0.75346  -0.25680  -1.20043  -1.83263  -1.98940  -1.63006  -0.84783   0.15435   1.11649   1.78897   1.99735   1.68755   0.93995  -0.05150  -1.02959  -1.74057   0.00000     ... ... ..... ....... ......... TT......... .............
E6u      2.00000   1.63006   0.65708  -0.55897  -1.56824  -1.99735  -1.68755  -0.75346   0.45938   1.50226   1.98940   1.74057   0.84783  -0.35856  -1.43230  -1.97618  -1.78897  -0.93995   0.25680   1.35855   1.95771   1.83263   1.02959  -0.15435  -1.28119  -1.93406  -1.87143  -1.11649   0.05150   1.20043   1.90527   0.00000  -2.00000  -1.90527  -1.20043  -0.05150   1.11649   1.87143   1.93406   1.28119   0.15435  -1.02959  -1.83263  -1.95771  -1.35855  -0.25680   0.93995   1.78897   1.97618   1.43230   0.35856  -0.84783  -1.74057  -1.98940  -1.50226  -0.45938   0.75346   1.68755   1.99735   1.56824   0.55897  -0.65708  -1.63006   0.00000     ... ... ..... ....... ......... ........... .............
E7u      2.00000   1.50226   0.25680  -1.11649  -1.93406  -1.78897  -0.75346   0.65708   1.74057   1.95771   1.20043  -0.15435  -1.43230  -1.99735  -1.56824  -0.35856   1.02959   1.90527   1.83263   0.84783  -0.55897  -1.68755  -1.97618  -1.28119   0.05150   1.35855   1.98940   1.63006   0.45938  -0.93995  -1.87143   0.00000  -2.00000   1.87143   0.93995  -0.45938  -1.63006  -1.98940  -1.35855  -0.05150   1.28119   1.97618   1.68755   0.55897  -0.84783  -1.83263  -1.90527  -1.02959   0.35856   1.56824   1.99735   1.43230   0.15435  -1.20043  -1.95771  -1.74057  -0.65708   0.75346   1.78897   1.93406   1.11649  -0.25680  -1.50226   0.00000     ... ... ..... ....... ......... ........... .............
E8u      2.00000   1.35855  -0.15435  -1.56824  -1.97618  -1.11649   0.45938   1.74057   1.90527   0.84783  -0.75346  -1.87143  -1.78897  -0.55897   1.02959   1.95771   1.63006   0.25680  -1.28119  -1.99735  -1.43230   0.05150   1.50226   1.98940   1.20043  -0.35856  -1.68755  -1.93406  -0.93995   0.65708   1.83263   0.00000  -2.00000  -1.83263  -0.65708   0.93995   1.93406   1.68755   0.35856  -1.20043  -1.98940  -1.50226  -0.05150   1.43230   1.99735   1.28119  -0.25680  -1.63006  -1.95771  -1.02959   0.55897   1.78897   1.87143   0.75346  -0.84783  -1.90527  -1.74057  -0.45938   1.11649   1.97618   1.56824   0.15435  -1.35855   0.00000     ... ... ..... ....... ......... ........... .............
E9u      2.00000   1.20043  -0.55897  -1.87143  -1.68755  -0.15435   1.50226   1.95771   0.84783  -0.93995  -1.97618  -1.43230   0.25680   1.74057   1.83263   0.45938  -1.28119  -1.99735  -1.11649   0.65708   1.90527   1.63006   0.05150  -1.56824  -1.93406  -0.75346   1.02959   1.98940   1.35855  -0.35856  -1.78897   0.00000  -2.00000   1.78897   0.35856  -1.35855  -1.98940  -1.02959   0.75346   1.93406   1.56824  -0.05150  -1.63006  -1.90527  -0.65708   1.11649   1.99735   1.28119  -0.45938  -1.83263  -1.74057  -0.25680   1.43230   1.97618   0.93995  -0.84783  -1.95771  -1.50226   0.15435   1.68755   1.87143   0.55897  -1.20043   0.00000     ... ... ..... ....... ......... ........... .............
E10u     2.00000   1.02959  -0.93995  -1.99735  -1.11649   0.84783   1.98940   1.20043  -0.75346  -1.97618  -1.28119   0.65708   1.95771   1.35855  -0.55897  -1.93406  -1.43230   0.45938   1.90527   1.50226  -0.35856  -1.87143  -1.56824   0.25680   1.83263   1.63006  -0.15435  -1.78897  -1.68755   0.05150   1.74057   0.00000  -2.00000  -1.74057  -0.05150   1.68755   1.78897   0.15435  -1.63006  -1.83263  -0.25680   1.56824   1.87143   0.35856  -1.50226  -1.90527  -0.45938   1.43230   1.93406   0.55897  -1.35855  -1.95771  -0.65708   1.28119   1.97618   0.75346  -1.20043  -1.98940  -0.84783   1.11649   1.99735   0.93995  -1.02959   0.00000     ... ... ..... ....... ......... ........... .............
E11u     2.00000   0.84783  -1.28119  -1.93406  -0.35856   1.63006   1.74057  -0.15435  -1.87143  -1.43230   0.65708   1.98940   1.02959  -1.11649  -1.97618  -0.55897   1.50226   1.83263   0.05150  -1.78897  -1.56824   0.45938   1.95771   1.20043  -0.93995  -1.99735  -0.75346   1.35855   1.90527   0.25680  -1.68755   0.00000  -2.00000   1.68755  -0.25680  -1.90527  -1.35855   0.75346   1.99735   0.93995  -1.20043  -1.95771  -0.45938   1.56824   1.78897  -0.05150  -1.83263  -1.50226   0.55897   1.97618   1.11649  -1.02959  -1.98940  -0.65708   1.43230   1.87143   0.15435  -1.74057  -1.63006   0.35856   1.93406   1.28119  -0.84783   0.00000     ... ... ..... ....... ......... ........... .............
E12u     2.00000   0.65708  -1.56824  -1.68755   0.45938   1.98940   0.84783  -1.43230  -1.78897   0.25680   1.95771   1.02959  -1.28119  -1.87143   0.05150   1.90527   1.20043  -1.11649  -1.93406  -0.15435   1.83263   1.35855  -0.93995  -1.97618  -0.35856   1.74057   1.50226  -0.75346  -1.99735  -0.55897   1.63006   0.00000  -2.00000  -1.63006   0.55897   1.99735   0.75346  -1.50226  -1.74057   0.35856   1.97618   0.93995  -1.35855  -1.83263   0.15435   1.93406   1.11649  -1.20043  -1.90527  -0.05150   1.87143   1.28119  -1.02959  -1.95771  -0.25680   1.78897   1.43230  -0.84783  -1.98940  -0.45938   1.68755   1.56824  -0.65708   0.00000     ... ... ..... ....... ......... ........... .............
E13u     2.00000   0.45938  -1.78897  -1.28119   1.20043   1.83263  -0.35856  -1.99735  -0.55897   1.74057   1.35855  -1.11649  -1.87143   0.25680   1.98940   0.65708  -1.68755  -1.43230   1.02959   1.90527  -0.15435  -1.97618  -0.75346   1.63006   1.50226  -0.93995  -1.93406   0.05150   1.95771   0.84783  -1.56824   0.00000  -2.00000   1.56824  -0.84783  -1.95771  -0.05150   1.93406   0.93995  -1.50226  -1.63006   0.75346   1.97618   0.15435  -1.90527  -1.02959   1.43230   1.68755  -0.65708  -1.98940  -0.25680   1.87143   1.11649  -1.35855  -1.74057   0.55897   1.99735   0.35856  -1.83263  -1.20043   1.28119   1.78897  -0.45938   0.00000     ... ... ..... ....... ......... ........... .............
E14u     2.00000   0.25680  -1.93406  -0.75346   1.74057   1.20043  -1.43230  -1.56824   1.02959   1.83263  -0.55897  -1.97618   0.05150   1.98940   0.45938  -1.87143  -0.93995   1.63006   1.35855  -1.28119  -1.68755   0.84783   1.90527  -0.35856  -1.99735  -0.15435   1.95771   0.65708  -1.78897  -1.11649   1.50226   0.00000  -2.00000  -1.50226   1.11649   1.78897  -0.65708  -1.95771   0.15435   1.99735   0.35856  -1.90527  -0.84783   1.68755   1.28119  -1.35855  -1.63006   0.93995   1.87143  -0.45938  -1.98940  -0.05150   1.97618   0.55897  -1.83263  -1.02959   1.56824   1.43230  -1.20043  -1.74057   0.75346   1.93406  -0.25680   0.00000     ... ... ..... ....... ......... ........... .............
E15u     2.00000   0.05150  -1.99735  -0.15435   1.98940   0.25680  -1.97618  -0.35856   1.95771   0.45938  -1.93406  -0.55897   1.90527   0.65708  -1.87143  -0.75346   1.83263   0.84783  -1.78897  -0.93995   1.74057   1.02959  -1.68755  -1.11649   1.63006   1.20043  -1.56824  -1.28119   1.50226   1.35855  -1.43230   0.00000  -2.00000   1.43230  -1.35855  -1.50226   1.28119   1.56824  -1.20043  -1.63006   1.11649   1.68755  -1.02959  -1.74057   0.93995   1.78897  -0.84783  -1.83263   0.75346   1.87143  -0.65708  -1.90527   0.55897   1.93406  -0.45938  -1.95771   0.35856   1.97618  -0.25680  -1.98940   0.15435   1.99735  -0.05150   0.00000     ... ... ..... ....... ......... ........... .............
E16u     2.00000  -0.15435  -1.97618   0.45938   1.90527  -0.75346  -1.78897   1.02959   1.63006  -1.28119  -1.43230   1.50226   1.20043  -1.68755  -0.93995   1.83263   0.65708  -1.93406  -0.35856   1.98940   0.05150  -1.99735   0.25680   1.95771  -0.55897  -1.87143   0.84783   1.74057  -1.11649  -1.56824   1.35855   0.00000  -2.00000  -1.35855   1.56824   1.11649  -1.74057  -0.84783   1.87143   0.55897  -1.95771  -0.25680   1.99735  -0.05150  -1.98940   0.35856   1.93406  -0.65708  -1.83263   0.93995   1.68755  -1.20043  -1.50226   1.43230   1.28119  -1.63006  -1.02959   1.78897   0.75346  -1.90527  -0.45938   1.97618   0.15435   0.00000     ... ... ..... ....... ......... ........... .............
E17u     2.00000  -0.35856  -1.87143   1.02959   1.50226  -1.56824  -0.93995   1.90527   0.25680  -1.99735   0.45938   1.83263  -1.11649  -1.43230   1.63006   0.84783  -1.93406  -0.15435   1.98940  -0.55897  -1.78897   1.20043   1.35855  -1.68755  -0.75346   1.95771   0.05150  -1.97618   0.65708   1.74057  -1.28119   0.00000  -2.00000   1.28119  -1.74057  -0.65708   1.97618  -0.05150  -1.95771   0.75346   1.68755  -1.35855  -1.20043   1.78897   0.55897  -1.98940   0.15435   1.93406  -0.84783  -1.63006   1.43230   1.11649  -1.83263  -0.45938   1.99735  -0.25680  -1.90527   0.93995   1.56824  -1.50226  -1.02959   1.87143   0.35856   0.00000     ... ... ..... ....... ......... ........... .............
E18u     2.00000  -0.55897  -1.68755   1.50226   0.84783  -1.97618   0.25680   1.83263  -1.28119  -1.11649   1.90527   0.05150  -1.93406   1.02959   1.35855  -1.78897  -0.35856   1.98940  -0.75346  -1.56824   1.63006   0.65708  -1.99735   0.45938   1.74057  -1.43230  -0.93995   1.95771  -0.15435  -1.87143   1.20043   0.00000  -2.00000  -1.20043   1.87143   0.15435  -1.95771   0.93995   1.43230  -1.74057  -0.45938   1.99735  -0.65708  -1.63006   1.56824   0.75346  -1.98940   0.35856   1.78897  -1.35855  -1.02959   1.93406  -0.05150  -1.90527   1.11649   1.28119  -1.83263  -0.25680   1.97618  -0.84783  -1.50226   1.68755   0.55897   0.00000     ... ... ..... ....... ......... ........... .............
E19u     2.00000  -0.75346  -1.43230   1.83263   0.05150  -1.87143   1.35855   0.84783  -1.99735   0.65708   1.50226  -1.78897  -0.15435   1.90527  -1.28119  -0.93995   1.98940  -0.55897  -1.56824   1.74057   0.25680  -1.93406   1.20043   1.02959  -1.97618   0.45938   1.63006  -1.68755  -0.35856   1.95771  -1.11649   0.00000  -2.00000   1.11649  -1.95771   0.35856   1.68755  -1.63006  -0.45938   1.97618  -1.02959  -1.20043   1.93406  -0.25680  -1.74057   1.56824   0.55897  -1.98940   0.93995   1.28119  -1.90527   0.15435   1.78897  -1.50226  -0.65708   1.99735  -0.84783  -1.35855   1.87143  -0.05150  -1.83263   1.43230   0.75346   0.00000     ... ... ..... ....... ......... ........... .............
E20u     2.00000  -0.93995  -1.11649   1.98940  -0.75346  -1.28119   1.95771  -0.55897  -1.43230   1.90527  -0.35856  -1.56824   1.83263  -0.15435  -1.68755   1.74057   0.05150  -1.78897   1.63006   0.25680  -1.87143   1.50226   0.45938  -1.93406   1.35855   0.65708  -1.97618   1.20043   0.84783  -1.99735   1.02959   0.00000  -2.00000  -1.02959   1.99735  -0.84783  -1.20043   1.97618  -0.65708  -1.35855   1.93406  -0.45938  -1.50226   1.87143  -0.25680  -1.63006   1.78897  -0.05150  -1.74057   1.68755   0.15435  -1.83263   1.56824   0.35856  -1.90527   1.43230   0.55897  -1.95771   1.28119   0.75346  -1.98940   1.11649   0.93995   0.00000     ... ... ..... ....... ......... ........... .............
E21u     2.00000  -1.11649  -0.75346   1.95771  -1.43230  -0.35856   1.83263  -1.68755   0.05150   1.63006  -1.87143   0.45938   1.35855  -1.97618   0.84783   1.02959  -1.99735   1.20043   0.65708  -1.93406   1.50226   0.25680  -1.78897   1.74057  -0.15435  -1.56824   1.90527  -0.55897  -1.28119   1.98940  -0.93995   0.00000  -2.00000   0.93995  -1.98940   1.28119   0.55897  -1.90527   1.56824   0.15435  -1.74057   1.78897  -0.25680  -1.50226   1.93406  -0.65708  -1.20043   1.99735  -1.02959  -0.84783   1.97618  -1.35855  -0.45938   1.87143  -1.63006  -0.05150   1.68755  -1.83263   0.35856   1.43230  -1.95771   0.75346   1.11649   0.00000     ... ... ..... ....... ......... ........... .............
E22u     2.00000  -1.28119  -0.35856   1.74057  -1.87143   0.65708   1.02959  -1.97618   1.50226   0.05150  -1.56824   1.95771  -0.93995  -0.75346   1.90527  -1.68755   0.25680   1.35855  -1.99735   1.20043   0.45938  -1.78897   1.83263  -0.55897  -1.11649   1.98940  -1.43230  -0.15435   1.63006  -1.93406   0.84783   0.00000  -2.00000  -0.84783   1.93406  -1.63006   0.15435   1.43230  -1.98940   1.11649   0.55897  -1.83263   1.78897  -0.45938  -1.20043   1.99735  -1.35855  -0.25680   1.68755  -1.90527   0.75346   0.93995  -1.95771   1.56824  -0.05150  -1.50226   1.97618  -1.02959  -0.65708   1.87143  -1.74057   0.35856   1.28119   0.00000     ... ... ..... ....... ......... ........... .............
E23u     2.00000  -1.43230   0.05150   1.35855  -1.99735   1.50226  -0.15435  -1.28119   1.98940  -1.56824   0.25680   1.20043  -1.97618   1.63006  -0.35856  -1.11649   1.95771  -1.68755   0.45938   1.02959  -1.93406   1.74057  -0.55897  -0.93995   1.90527  -1.78897   0.65708   0.84783  -1.87143   1.83263  -0.75346   0.00000  -2.00000   0.75346  -1.83263   1.87143  -0.84783  -0.65708   1.78897  -1.90527   0.93995   0.55897  -1.74057   1.93406  -1.02959  -0.45938   1.68755  -1.95771   1.11649   0.35856  -1.63006   1.97618  -1.20043  -0.25680   1.56824  -1.98940   1.28119   0.15435  -1.50226   1.99735  -1.35855  -0.05150   1.43230   0.00000     ... ... ..... ....... ......... ........... .............
E24u     2.00000  -1.56824   0.45938   0.84783  -1.78897   1.95771  -1.28119   0.05150   1.20043  -1.93406   1.83263  -0.93995  -0.35856   1.50226  -1.99735   1.63006  -0.55897  -0.75346   1.74057  -1.97618   1.35855  -0.15435  -1.11649   1.90527  -1.87143   1.02959   0.25680  -1.43230   1.98940  -1.68755   0.65708   0.00000  -2.00000  -0.65708   1.68755  -1.98940   1.43230  -0.25680  -1.02959   1.87143  -1.90527   1.11649   0.15435  -1.35855   1.97618  -1.74057   0.75346   0.55897  -1.63006   1.99735  -1.50226   0.35856   0.93995  -1.83263   1.93406  -1.20043  -0.05150   1.28119  -1.95771   1.78897  -0.84783  -0.45938   1.56824   0.00000     ... ... ..... ....... ......... ........... .............
E25u     2.00000  -1.68755   0.84783   0.25680  -1.28119   1.90527  -1.93406   1.35855  -0.35856  -0.75346   1.63006  -1.99735   1.74057  -0.93995  -0.15435   1.20043  -1.87143   1.95771  -1.43230   0.45938   0.65708  -1.56824   1.98940  -1.78897   1.02959   0.05150  -1.11649   1.83263  -1.97618   1.50226  -0.55897   0.00000  -2.00000   0.55897  -1.50226   1.97618  -1.83263   1.11649  -0.05150  -1.02959   1.78897  -1.98940   1.56824  -0.65708  -0.45938   1.43230  -1.95771   1.87143  -1.20043   0.15435   0.93995  -1.74057   1.99735  -1.63006   0.75346   0.35856  -1.35855   1.93406  -1.90527   1.28119  -0.25680  -0.84783   1.68755   0.00000     ... ... ..... ....... ......... ........... .............
E26u     2.00000  -1.78897   1.20043  -0.35856  -0.55897   1.35855  -1.87143   1.98940  -1.68755   1.02959  -0.15435  -0.75346   1.50226  -1.93406   1.95771  -1.56824   0.84783   0.05150  -0.93995   1.63006  -1.97618   1.90527  -1.43230   0.65708   0.25680  -1.11649   1.74057  -1.99735   1.83263  -1.28119   0.45938   0.00000  -2.00000  -0.45938   1.28119  -1.83263   1.99735  -1.74057   1.11649  -0.25680  -0.65708   1.43230  -1.90527   1.97618  -1.63006   0.93995  -0.05150  -0.84783   1.56824  -1.95771   1.93406  -1.50226   0.75346   0.15435  -1.02959   1.68755  -1.98940   1.87143  -1.35855   0.55897   0.35856  -1.20043   1.78897   0.00000     ... ... ..... ....... ......... ........... .............
E27u     2.00000  -1.87143   1.50226  -0.93995   0.25680   0.45938  -1.11649   1.63006  -1.93406   1.98940  -1.78897   1.35855  -0.75346   0.05150   0.65708  -1.28119   1.74057  -1.97618   1.95771  -1.68755   1.20043  -0.55897  -0.15435   0.84783  -1.43230   1.83263  -1.99735   1.90527  -1.56824   1.02959  -0.35856   0.00000  -2.00000   0.35856  -1.02959   1.56824  -1.90527   1.99735  -1.83263   1.43230  -0.84783   0.15435   0.55897  -1.20043   1.68755  -1.95771   1.97618  -1.74057   1.28119  -0.65708  -0.05150   0.75346  -1.35855   1.78897  -1.98940   1.93406  -1.63006   1.11649  -0.45938  -0.25680   0.93995  -1.50226   1.87143   0.00000     ... ... ..... ....... ......... ........... .............
E28u     2.00000  -1.93406   1.74057  -1.43230   1.02959  -0.55897   0.05150   0.45938  -0.93995   1.35855  -1.68755   1.90527  -1.99735   1.95771  -1.78897   1.50226  -1.11649   0.65708  -0.15435  -0.35856   0.84783  -1.28119   1.63006  -1.87143   1.98940  -1.97618   1.83263  -1.56824   1.20043  -0.75346   0.25680   0.00000  -2.00000  -0.25680   0.75346  -1.20043   1.56824  -1.83263   1.97618  -1.98940   1.87143  -1.63006   1.28119  -0.84783   0.35856   0.15435  -0.65708   1.11649  -1.50226   1.78897  -1.95771   1.99735  -1.90527   1.68755  -1.35855   0.93995  -0.45938  -0.05150   0.55897  -1.02959   1.43230  -1.74057   1.93406   0.00000     ... ... ..... ....... ......... ........... .............
E29u     2.00000  -1.97618   1.90527  -1.78897   1.63006  -1.43230   1.20043  -0.93995   0.65708  -0.35856   0.05150   0.25680  -0.55897   0.84783  -1.11649   1.35855  -1.56824   1.74057  -1.87143   1.95771  -1.99735   1.98940  -1.93406   1.83263  -1.68755   1.50226  -1.28119   1.02959  -0.75346   0.45938  -0.15435   0.00000  -2.00000   0.15435  -0.45938   0.75346  -1.02959   1.28119  -1.50226   1.68755  -1.83263   1.93406  -1.98940   1.99735  -1.95771   1.87143  -1.74057   1.56824  -1.35855   1.11649  -0.84783   0.55897  -0.25680  -0.05150   0.35856  -0.65708   0.93995  -1.20043   1.43230  -1.63006   1.78897  -1.90527   1.97618   0.00000     ... ... ..... ....... ......... ........... .............
E30u     2.00000  -1.99735   1.98940  -1.97618   1.95771  -1.93406   1.90527  -1.87143   1.83263  -1.78897   1.74057  -1.68755   1.63006  -1.56824   1.50226  -1.43230   1.35855  -1.28119   1.20043  -1.11649   1.02959  -0.93995   0.84783  -0.75346   0.65708  -0.55897   0.45938  -0.35856   0.25680  -0.15435   0.05150   0.00000  -2.00000  -0.05150   0.15435  -0.25680   0.35856  -0.45938   0.55897  -0.65708   0.75346  -0.84783   0.93995  -1.02959   1.11649  -1.20043   1.28119  -1.35855   1.43230  -1.50226   1.56824  -1.63006   1.68755  -1.74057   1.78897  -1.83263   1.87143  -1.90527   1.93406  -1.95771   1.97618  -1.98940   1.99735   0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.997348179770 = 2*cos(2*π/122) = 2*cos(π/61)
                               1.989399751229 = 2*cos(4*π/122) = 2*cos(2*π/61)
                               1.976175792182 = 2*cos(6*π/122) = 2*cos(3*π/61)
                               1.957711370191 = 2*cos(8*π/122) = 2*cos(4*π/61)
                               1.934055449583 = 2*cos(10*π/122) = 2*cos(5*π/61)
                               1.905270761607 = 2*cos(12*π/122) = 2*cos(6*π/61)
                               1.871433638081 = 2*cos(14*π/122) = 2*cos(7*π/61)
                               1.832633808974 = 2*cos(16*π/122) = 2*cos(8*π/61)
                               1.788974164458 = 2*cos(18*π/122) = 2*cos(9*π/61)
                               1.740570482060 = 2*cos(20*π/122) = 2*cos(10*π/61)
                               1.687551119646 = 2*cos(22*π/122) = 2*cos(11*π/61)
                               1.630056675034 = 2*cos(24*π/122) = 2*cos(12*π/61)
                               1.568239613153 = 2*cos(26*π/122) = 2*cos(13*π/61)
                               1.502263861741 = 2*cos(28*π/122) = 2*cos(14*π/61)
                               1.432304376629 = 2*cos(30*π/122) = 2*cos(15*π/61)
                               1.358546677795 = 2*cos(32*π/122) = 2*cos(16*π/61)
                               1.281186357396 = 2*cos(34*π/122) = 2*cos(17*π/61)
                               1.200428561097 = 2*cos(36*π/122) = 2*cos(18*π/61)
                               1.116487444054 = 2*cos(38*π/122) = 2*cos(19*π/61)
                               1.029585603020 = 2*cos(40*π/122) = 2*cos(20*π/61)
                               0.939953486055 = 2*cos(42*π/122) = 2*cos(21*π/61)
                               0.847828781420 = 2*cos(44*π/122) = 2*cos(22*π/61)
                               0.753455787270 = 2*cos(46*π/122) = 2*cos(23*π/61)
                               0.657084763822 = 2*cos(48*π/122) = 2*cos(24*π/61)
                               0.558971269703 = 2*cos(50*π/122) = 2*cos(25*π/61)
                               0.459375484264 = 2*cos(52*π/122) = 2*cos(26*π/61)
                               0.358561517621 = 2*cos(54*π/122) = 2*cos(27*π/61)
                               0.256796710293 = 2*cos(56*π/122) = 2*cos(28*π/61)
                               0.154350924253 = 2*cos(58*π/122) = 2*cos(29*π/61)
                               0.051495827310 = 2*cos(60*π/122) = 2*cos(30*π/61)



 Symmetry of Rotations and Cartesian products

A1g  d+g+i+k+m    z2, z4, z6 
A2g  R            Rz 
E1g  R+d+g+i+k+m  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 
E2g  d+g+i+k+m    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E3g  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E4g  g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E5g  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E6g  i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7g  k+m 
E8g  k+m 
E9g  m 
E10g m 
A2u  p+f+h+j+l    z, z3, z5 
E1u  p+f+h+j+l    {x, y}, {xz2, yz2}, {xz4, yz4} 
E2u  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E3u  f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E4u  h+j+l        {z((x2y2)2−4x2y2), xyz(x2y2)} 
E5u  h+j+l        {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)} 
E6u  j+l 
E7u  j+l 
E8u  l 
E9u  l 

 Notes:

    α  The order of the D61d point group is 244, and the order of the principal axis (S122) is 122. The group has 64 irreducible representations.

    β  The D61d point group is isomorphic to D61h, C122v and D122.

    γ  The D61d point group is generated by two symmetry elements, S122 and either a perpendicular C2 or a vertical σd.
       Also, the group may be generated from any C2 plus any σd plane.
       The canonical choice, however, is to use redundant generators: C61, C2 and i.

    δ  The group contains one set of C2 symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set.
       Reversely, the single set of symmetry planes denoted σd contains the yz plane but not the xz plane.

    ε  The lowest nonvanishing multipole moment in D61d is 4 (quadrupole moment).

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

    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 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 D61d point group was created by Gernot Katzer.

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