Character table for the D65d point group

D65d     E         2 C65     2 C65^2   2 C65^3   2 C65^4   2 C13     2 C65^6   2 C65^7   2 C65^8   2 C65^9   2 C13^2   2 C65^11  2 C65^12  2 C5      2 C65^14  2 C13^3   2 C65^16  2 C65^17  2 C65^18  2 C65^19  2 C13^4   2 C65^21  2 C65^22  2 C65^23  2 C65^24  2 C13^5   2 C5^2    2 C65^27  2 C65^28  2 C65^29  2 C13^6   2 C65^31  2 C65^32  65 C2'    i         2 S130    2 S130^3  2 S26     2 S130^7  2 S130^9  2 S130^11 2 S10     2 S26^3   2 S130^17 2 S130^19 2 S130^21 2 S130^23 2 S26^5   2 S130^27 2 S130^29 2 S130^31 2 S130^33 2 S26^7   2 S130^37 2 S10^3   2 S130^41 2 S130^43 2 S26^9   2 S130^47 2 S130^49 2 S130^51 2 S130^53 2 S26^11  2 S130^57 2 S130^59 2 S130^61 2 S130^63 65 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   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   1.00000   1.00000   1.00000  -1.00000     ..T ... ..... ....... ......... ........... .............
E1g      2.00000   1.99066   1.96274   1.91649   1.85235   1.77091   1.67294   1.55935   1.43120   1.28968   1.13613   0.97197   0.79873   0.61803   0.43157   0.24107   0.04833  -0.14487  -0.33671  -0.52541  -0.70921  -0.88638  -1.05528  -1.21433  -1.36203  -1.49702  -1.61803  -1.72394  -1.81375  -1.88662  -1.94188  -1.97901  -1.99766   0.00000   2.00000  -1.99766  -1.97901  -1.94188  -1.88662  -1.81375  -1.72394  -1.61803  -1.49702  -1.36203  -1.21433  -1.05528  -0.88638  -0.70921  -0.52541  -0.33671  -0.14487   0.04833   0.24107   0.43157   0.61803   0.79873   0.97197   1.13613   1.28968   1.43120   1.55935   1.67294   1.77091   1.85235   1.91649   1.96274   1.99066   0.00000     TT. ... ..TT. ....... ......TT. ........... ..........TT.
E2g      2.00000   1.96274   1.85235   1.67294   1.43120   1.13613   0.79873   0.43157   0.04833  -0.33671  -0.70921  -1.05528  -1.36203  -1.61803  -1.81375  -1.94188  -1.99766  -1.97901  -1.88662  -1.72394  -1.49702  -1.21433  -0.88638  -0.52541  -0.14487   0.24107   0.61803   0.97197   1.28968   1.55935   1.77091   1.91649   1.99066   0.00000   2.00000   1.99066   1.91649   1.77091   1.55935   1.28968   0.97197   0.61803   0.24107  -0.14487  -0.52541  -0.88638  -1.21433  -1.49702  -1.72394  -1.88662  -1.97901  -1.99766  -1.94188  -1.81375  -1.61803  -1.36203  -1.05528  -0.70921  -0.33671   0.04833   0.43157   0.79873   1.13613   1.43120   1.67294   1.85235   1.96274   0.00000     ... ... TT... ....... ....TT... ........... ........TT...
E3g      2.00000   1.91649   1.67294   1.28968   0.79873   0.24107  -0.33671  -0.88638  -1.36203  -1.72394  -1.94188  -1.99766  -1.88662  -1.61803  -1.21433  -0.70921  -0.14487   0.43157   0.97197   1.43120   1.77091   1.96274   1.99066   1.85235   1.55935   1.13613   0.61803   0.04833  -0.52541  -1.05528  -1.49702  -1.81375  -1.97901   0.00000   2.00000  -1.97901  -1.81375  -1.49702  -1.05528  -0.52541   0.04833   0.61803   1.13613   1.55935   1.85235   1.99066   1.96274   1.77091   1.43120   0.97197   0.43157  -0.14487  -0.70921  -1.21433  -1.61803  -1.88662  -1.99766  -1.94188  -1.72394  -1.36203  -0.88638  -0.33671   0.24107   0.79873   1.28968   1.67294   1.91649   0.00000     ... ... ..... ....... ..TT..... ........... ......TT.....
E4g      2.00000   1.85235   1.43120   0.79873   0.04833  -0.70921  -1.36203  -1.81375  -1.99766  -1.88662  -1.49702  -0.88638  -0.14487   0.61803   1.28968   1.77091   1.99066   1.91649   1.55935   0.97197   0.24107  -0.52541  -1.21433  -1.72394  -1.97901  -1.94188  -1.61803  -1.05528  -0.33671   0.43157   1.13613   1.67294   1.96274   0.00000   2.00000   1.96274   1.67294   1.13613   0.43157  -0.33671  -1.05528  -1.61803  -1.94188  -1.97901  -1.72394  -1.21433  -0.52541   0.24107   0.97197   1.55935   1.91649   1.99066   1.77091   1.28968   0.61803  -0.14487  -0.88638  -1.49702  -1.88662  -1.99766  -1.81375  -1.36203  -0.70921   0.04833   0.79873   1.43120   1.85235   0.00000     ... ... ..... ....... TT....... ........... ....TT.......
E5g      2.00000   1.77091   1.13613   0.24107  -0.70921  -1.49702  -1.94188  -1.94188  -1.49702  -0.70921   0.24107   1.13613   1.77091   2.00000   1.77091   1.13613   0.24107  -0.70921  -1.49702  -1.94188  -1.94188  -1.49702  -0.70921   0.24107   1.13613   1.77091   2.00000   1.77091   1.13613   0.24107  -0.70921  -1.49702  -1.94188   0.00000   2.00000  -1.94188  -1.49702  -0.70921   0.24107   1.13613   1.77091   2.00000   1.77091   1.13613   0.24107  -0.70921  -1.49702  -1.94188  -1.94188  -1.49702  -0.70921   0.24107   1.13613   1.77091   2.00000   1.77091   1.13613   0.24107  -0.70921  -1.49702  -1.94188  -1.94188  -1.49702  -0.70921   0.24107   1.13613   1.77091   0.00000     ... ... ..... ....... ......... ........... ..TT.........
E6g      2.00000   1.67294   0.79873  -0.33671  -1.36203  -1.94188  -1.88662  -1.21433  -0.14487   0.97197   1.77091   1.99066   1.55935   0.61803  -0.52541  -1.49702  -1.97901  -1.81375  -1.05528   0.04833   1.13613   1.85235   1.96274   1.43120   0.43157  -0.70921  -1.61803  -1.99766  -1.72394  -0.88638   0.24107   1.28968   1.91649   0.00000   2.00000   1.91649   1.28968   0.24107  -0.88638  -1.72394  -1.99766  -1.61803  -0.70921   0.43157   1.43120   1.96274   1.85235   1.13613   0.04833  -1.05528  -1.81375  -1.97901  -1.49702  -0.52541   0.61803   1.55935   1.99066   1.77091   0.97197  -0.14487  -1.21433  -1.88662  -1.94188  -1.36203  -0.33671   0.79873   1.67294   0.00000     ... ... ..... ....... ......... ........... TT...........
E7g      2.00000   1.55935   0.43157  -0.88638  -1.81375  -1.94188  -1.21433   0.04833   1.28968   1.96274   1.77091   0.79873  -0.52541  -1.61803  -1.99766  -1.49702  -0.33671   0.97197   1.85235   1.91649   1.13613  -0.14487  -1.36203  -1.97901  -1.72394  -0.70921   0.61803   1.67294   1.99066   1.43120   0.24107  -1.05528  -1.88662   0.00000   2.00000  -1.88662  -1.05528   0.24107   1.43120   1.99066   1.67294   0.61803  -0.70921  -1.72394  -1.97901  -1.36203  -0.14487   1.13613   1.91649   1.85235   0.97197  -0.33671  -1.49702  -1.99766  -1.61803  -0.52541   0.79873   1.77091   1.96274   1.28968   0.04833  -1.21433  -1.94188  -1.81375  -0.88638   0.43157   1.55935   0.00000     ... ... ..... ....... ......... ........... .............
E8g      2.00000   1.43120   0.04833  -1.36203  -1.99766  -1.49702  -0.14487   1.28968   1.99066   1.55935   0.24107  -1.21433  -1.97901  -1.61803  -0.33671   1.13613   1.96274   1.67294   0.43157  -1.05528  -1.94188  -1.72394  -0.52541   0.97197   1.91649   1.77091   0.61803  -0.88638  -1.88662  -1.81375  -0.70921   0.79873   1.85235   0.00000   2.00000   1.85235   0.79873  -0.70921  -1.81375  -1.88662  -0.88638   0.61803   1.77091   1.91649   0.97197  -0.52541  -1.72394  -1.94188  -1.05528   0.43157   1.67294   1.96274   1.13613  -0.33671  -1.61803  -1.97901  -1.21433   0.24107   1.55935   1.99066   1.28968  -0.14487  -1.49702  -1.99766  -1.36203   0.04833   1.43120   0.00000     ... ... ..... ....... ......... ........... .............
E9g      2.00000   1.28968  -0.33671  -1.72394  -1.88662  -0.70921   0.97197   1.96274   1.55935   0.04833  -1.49702  -1.97901  -1.05528   0.61803   1.85235   1.77091   0.43157  -1.21433  -1.99766  -1.36203   0.24107   1.67294   1.91649   0.79873  -0.88638  -1.94188  -1.61803  -0.14487   1.43120   1.99066   1.13613  -0.52541  -1.81375   0.00000   2.00000  -1.81375  -0.52541   1.13613   1.99066   1.43120  -0.14487  -1.61803  -1.94188  -0.88638   0.79873   1.91649   1.67294   0.24107  -1.36203  -1.99766  -1.21433   0.43157   1.77091   1.85235   0.61803  -1.05528  -1.97901  -1.49702   0.04833   1.55935   1.96274   0.97197  -0.70921  -1.88662  -1.72394  -0.33671   1.28968   0.00000     ... ... ..... ....... ......... ........... .............
E10g     2.00000   1.13613  -0.70921  -1.94188  -1.49702   0.24107   1.77091   1.77091   0.24107  -1.49702  -1.94188  -0.70921   1.13613   2.00000   1.13613  -0.70921  -1.94188  -1.49702   0.24107   1.77091   1.77091   0.24107  -1.49702  -1.94188  -0.70921   1.13613   2.00000   1.13613  -0.70921  -1.94188  -1.49702   0.24107   1.77091   0.00000   2.00000   1.77091   0.24107  -1.49702  -1.94188  -0.70921   1.13613   2.00000   1.13613  -0.70921  -1.94188  -1.49702   0.24107   1.77091   1.77091   0.24107  -1.49702  -1.94188  -0.70921   1.13613   2.00000   1.13613  -0.70921  -1.94188  -1.49702   0.24107   1.77091   1.77091   0.24107  -1.49702  -1.94188  -0.70921   1.13613   0.00000     ... ... ..... ....... ......... ........... .............
E11g     2.00000   0.97197  -1.05528  -1.99766  -0.88638   1.13613   1.99066   0.79873  -1.21433  -1.97901  -0.70921   1.28968   1.96274   0.61803  -1.36203  -1.94188  -0.52541   1.43120   1.91649   0.43157  -1.49702  -1.88662  -0.33671   1.55935   1.85235   0.24107  -1.61803  -1.81375  -0.14487   1.67294   1.77091   0.04833  -1.72394   0.00000   2.00000  -1.72394   0.04833   1.77091   1.67294  -0.14487  -1.81375  -1.61803   0.24107   1.85235   1.55935  -0.33671  -1.88662  -1.49702   0.43157   1.91649   1.43120  -0.52541  -1.94188  -1.36203   0.61803   1.96274   1.28968  -0.70921  -1.97901  -1.21433   0.79873   1.99066   1.13613  -0.88638  -1.99766  -1.05528   0.97197   0.00000     ... ... ..... ....... ......... ........... .............
E12g     2.00000   0.79873  -1.36203  -1.88662  -0.14487   1.77091   1.55935  -0.52541  -1.97901  -1.05528   1.13613   1.96274   0.43157  -1.61803  -1.72394   0.24107   1.91649   1.28968  -0.88638  -1.99766  -0.70921   1.43120   1.85235   0.04833  -1.81375  -1.49702   0.61803   1.99066   0.97197  -1.21433  -1.94188  -0.33671   1.67294   0.00000   2.00000   1.67294  -0.33671  -1.94188  -1.21433   0.97197   1.99066   0.61803  -1.49702  -1.81375   0.04833   1.85235   1.43120  -0.70921  -1.99766  -0.88638   1.28968   1.91649   0.24107  -1.72394  -1.61803   0.43157   1.96274   1.13613  -1.05528  -1.97901  -0.52541   1.55935   1.77091  -0.14487  -1.88662  -1.36203   0.79873   0.00000     ... ... ..... ....... ......... ........... .............
E13g     2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803   0.00000   2.00000  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   0.00000     ... ... ..... ....... ......... ........... .............
E14g     2.00000   0.43157  -1.81375  -1.21433   1.28968   1.77091  -0.52541  -1.99766  -0.33671   1.85235   1.13613  -1.36203  -1.72394   0.61803   1.99066   0.24107  -1.88662  -1.05528   1.43120   1.67294  -0.70921  -1.97901  -0.14487   1.91649   0.97197  -1.49702  -1.61803   0.79873   1.96274   0.04833  -1.94188  -0.88638   1.55935   0.00000   2.00000   1.55935  -0.88638  -1.94188   0.04833   1.96274   0.79873  -1.61803  -1.49702   0.97197   1.91649  -0.14487  -1.97901  -0.70921   1.67294   1.43120  -1.05528  -1.88662   0.24107   1.99066   0.61803  -1.72394  -1.36203   1.13613   1.85235  -0.33671  -1.99766  -0.52541   1.77091   1.28968  -1.21433  -1.81375   0.43157   0.00000     ... ... ..... ....... ......... ........... .............
E15g     2.00000   0.24107  -1.94188  -0.70921   1.77091   1.13613  -1.49702  -1.49702   1.13613   1.77091  -0.70921  -1.94188   0.24107   2.00000   0.24107  -1.94188  -0.70921   1.77091   1.13613  -1.49702  -1.49702   1.13613   1.77091  -0.70921  -1.94188   0.24107   2.00000   0.24107  -1.94188  -0.70921   1.77091   1.13613  -1.49702   0.00000   2.00000  -1.49702   1.13613   1.77091  -0.70921  -1.94188   0.24107   2.00000   0.24107  -1.94188  -0.70921   1.77091   1.13613  -1.49702  -1.49702   1.13613   1.77091  -0.70921  -1.94188   0.24107   2.00000   0.24107  -1.94188  -0.70921   1.77091   1.13613  -1.49702  -1.49702   1.13613   1.77091  -0.70921  -1.94188   0.24107   0.00000     ... ... ..... ....... ......... ........... .............
E16g     2.00000   0.04833  -1.99766  -0.14487   1.99066   0.24107  -1.97901  -0.33671   1.96274   0.43157  -1.94188  -0.52541   1.91649   0.61803  -1.88662  -0.70921   1.85235   0.79873  -1.81375  -0.88638   1.77091   0.97197  -1.72394  -1.05528   1.67294   1.13613  -1.61803  -1.21433   1.55935   1.28968  -1.49702  -1.36203   1.43120   0.00000   2.00000   1.43120  -1.36203  -1.49702   1.28968   1.55935  -1.21433  -1.61803   1.13613   1.67294  -1.05528  -1.72394   0.97197   1.77091  -0.88638  -1.81375   0.79873   1.85235  -0.70921  -1.88662   0.61803   1.91649  -0.52541  -1.94188   0.43157   1.96274  -0.33671  -1.97901   0.24107   1.99066  -0.14487  -1.99766   0.04833   0.00000     ... ... ..... ....... ......... ........... .............
E17g     2.00000  -0.14487  -1.97901   0.43157   1.91649  -0.70921  -1.81375   0.97197   1.67294  -1.21433  -1.49702   1.43120   1.28968  -1.61803  -1.05528   1.77091   0.79873  -1.88662  -0.52541   1.96274   0.24107  -1.99766   0.04833   1.99066  -0.33671  -1.94188   0.61803   1.85235  -0.88638  -1.72394   1.13613   1.55935  -1.36203   0.00000   2.00000  -1.36203   1.55935   1.13613  -1.72394  -0.88638   1.85235   0.61803  -1.94188  -0.33671   1.99066   0.04833  -1.99766   0.24107   1.96274  -0.52541  -1.88662   0.79873   1.77091  -1.05528  -1.61803   1.28968   1.43120  -1.49702  -1.21433   1.67294   0.97197  -1.81375  -0.70921   1.91649   0.43157  -1.97901  -0.14487   0.00000     ... ... ..... ....... ......... ........... .............
E18g     2.00000  -0.33671  -1.88662   0.97197   1.55935  -1.49702  -1.05528   1.85235   0.43157  -1.99766   0.24107   1.91649  -0.88638  -1.61803   1.43120   1.13613  -1.81375  -0.52541   1.99066  -0.14487  -1.94188   0.79873   1.67294  -1.36203  -1.21433   1.77091   0.61803  -1.97901   0.04833   1.96274  -0.70921  -1.72394   1.28968   0.00000   2.00000   1.28968  -1.72394  -0.70921   1.96274   0.04833  -1.97901   0.61803   1.77091  -1.21433  -1.36203   1.67294   0.79873  -1.94188  -0.14487   1.99066  -0.52541  -1.81375   1.13613   1.43120  -1.61803  -0.88638   1.91649   0.24107  -1.99766   0.43157   1.85235  -1.05528  -1.49702   1.55935   0.97197  -1.88662  -0.33671   0.00000     ... ... ..... ....... ......... ........... .............
E19g     2.00000  -0.52541  -1.72394   1.43120   0.97197  -1.94188   0.04833   1.91649  -1.05528  -1.36203   1.77091   0.43157  -1.99766   0.61803   1.67294  -1.49702  -0.88638   1.96274  -0.14487  -1.88662   1.13613   1.28968  -1.81375  -0.33671   1.99066  -0.70921  -1.61803   1.55935   0.79873  -1.97901   0.24107   1.85235  -1.21433   0.00000   2.00000  -1.21433   1.85235   0.24107  -1.97901   0.79873   1.55935  -1.61803  -0.70921   1.99066  -0.33671  -1.81375   1.28968   1.13613  -1.88662  -0.14487   1.96274  -0.88638  -1.49702   1.67294   0.61803  -1.99766   0.43157   1.77091  -1.36203  -1.05528   1.91649   0.04833  -1.94188   0.97197   1.43120  -1.72394  -0.52541   0.00000     ... ... ..... ....... ......... ........... .............
E20g     2.00000  -0.70921  -1.49702   1.77091   0.24107  -1.94188   1.13613   1.13613  -1.94188   0.24107   1.77091  -1.49702  -0.70921   2.00000  -0.70921  -1.49702   1.77091   0.24107  -1.94188   1.13613   1.13613  -1.94188   0.24107   1.77091  -1.49702  -0.70921   2.00000  -0.70921  -1.49702   1.77091   0.24107  -1.94188   1.13613   0.00000   2.00000   1.13613  -1.94188   0.24107   1.77091  -1.49702  -0.70921   2.00000  -0.70921  -1.49702   1.77091   0.24107  -1.94188   1.13613   1.13613  -1.94188   0.24107   1.77091  -1.49702  -0.70921   2.00000  -0.70921  -1.49702   1.77091   0.24107  -1.94188   1.13613   1.13613  -1.94188   0.24107   1.77091  -1.49702  -0.70921   0.00000     ... ... ..... ....... ......... ........... .............
E21g     2.00000  -0.88638  -1.21433   1.96274  -0.52541  -1.49702   1.85235  -0.14487  -1.72394   1.67294   0.24107  -1.88662   1.43120   0.61803  -1.97901   1.13613   0.97197  -1.99766   0.79873   1.28968  -1.94188   0.43157   1.55935  -1.81375   0.04833   1.77091  -1.61803  -0.33671   1.91649  -1.36203  -0.70921   1.99066  -1.05528   0.00000   2.00000  -1.05528   1.99066  -0.70921  -1.36203   1.91649  -0.33671  -1.61803   1.77091   0.04833  -1.81375   1.55935   0.43157  -1.94188   1.28968   0.79873  -1.99766   0.97197   1.13613  -1.97901   0.61803   1.43120  -1.88662   0.24107   1.67294  -1.72394  -0.14487   1.85235  -1.49702  -0.52541   1.96274  -1.21433  -0.88638   0.00000     ... ... ..... ....... ......... ........... .............
E22g     2.00000  -1.05528  -0.88638   1.99066  -1.21433  -0.70921   1.96274  -1.36203  -0.52541   1.91649  -1.49702  -0.33671   1.85235  -1.61803  -0.14487   1.77091  -1.72394   0.04833   1.67294  -1.81375   0.24107   1.55935  -1.88662   0.43157   1.43120  -1.94188   0.61803   1.28968  -1.97901   0.79873   1.13613  -1.99766   0.97197   0.00000   2.00000   0.97197  -1.99766   1.13613   0.79873  -1.97901   1.28968   0.61803  -1.94188   1.43120   0.43157  -1.88662   1.55935   0.24107  -1.81375   1.67294   0.04833  -1.72394   1.77091  -0.14487  -1.61803   1.85235  -0.33671  -1.49702   1.91649  -0.52541  -1.36203   1.96274  -0.70921  -1.21433   1.99066  -0.88638  -1.05528   0.00000     ... ... ..... ....... ......... ........... .............
E23g     2.00000  -1.21433  -0.52541   1.85235  -1.72394   0.24107   1.43120  -1.97901   0.97197   0.79873  -1.94188   1.55935   0.04833  -1.61803   1.91649  -0.70921  -1.05528   1.99066  -1.36203  -0.33671   1.77091  -1.81375   0.43157   1.28968  -1.99766   1.13613   0.61803  -1.88662   1.67294  -0.14487  -1.49702   1.96274  -0.88638   0.00000   2.00000  -0.88638   1.96274  -1.49702  -0.14487   1.67294  -1.88662   0.61803   1.13613  -1.99766   1.28968   0.43157  -1.81375   1.77091  -0.33671  -1.36203   1.99066  -1.05528  -0.70921   1.91649  -1.61803   0.04833   1.55935  -1.94188   0.79873   0.97197  -1.97901   1.43120   0.24107  -1.72394   1.85235  -0.52541  -1.21433   0.00000     ... ... ..... ....... ......... ........... .............
E24g     2.00000  -1.36203  -0.14487   1.55935  -1.97901   1.13613   0.43157  -1.72394   1.91649  -0.88638  -0.70921   1.85235  -1.81375   0.61803   0.97197  -1.94188   1.67294  -0.33671  -1.21433   1.99066  -1.49702   0.04833   1.43120  -1.99766   1.28968   0.24107  -1.61803   1.96274  -1.05528  -0.52541   1.77091  -1.88662   0.79873   0.00000   2.00000   0.79873  -1.88662   1.77091  -0.52541  -1.05528   1.96274  -1.61803   0.24107   1.28968  -1.99766   1.43120   0.04833  -1.49702   1.99066  -1.21433  -0.33671   1.67294  -1.94188   0.97197   0.61803  -1.81375   1.85235  -0.70921  -0.88638   1.91649  -1.72394   0.43157   1.13613  -1.97901   1.55935  -0.14487  -1.36203   0.00000     ... ... ..... ....... ......... ........... .............
E25g     2.00000  -1.49702   0.24107   1.13613  -1.94188   1.77091  -0.70921  -0.70921   1.77091  -1.94188   1.13613   0.24107  -1.49702   2.00000  -1.49702   0.24107   1.13613  -1.94188   1.77091  -0.70921  -0.70921   1.77091  -1.94188   1.13613   0.24107  -1.49702   2.00000  -1.49702   0.24107   1.13613  -1.94188   1.77091  -0.70921   0.00000   2.00000  -0.70921   1.77091  -1.94188   1.13613   0.24107  -1.49702   2.00000  -1.49702   0.24107   1.13613  -1.94188   1.77091  -0.70921  -0.70921   1.77091  -1.94188   1.13613   0.24107  -1.49702   2.00000  -1.49702   0.24107   1.13613  -1.94188   1.77091  -0.70921  -0.70921   1.77091  -1.94188   1.13613   0.24107  -1.49702   0.00000     ... ... ..... ....... ......... ........... .............
E26g     2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.00000   2.00000   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   0.00000     ... ... ..... ....... ......... ........... .............
E27g     2.00000  -1.72394   0.97197   0.04833  -1.05528   1.77091  -1.99766   1.67294  -0.88638  -0.14487   1.13613  -1.81375   1.99066  -1.61803   0.79873   0.24107  -1.21433   1.85235  -1.97901   1.55935  -0.70921  -0.33671   1.28968  -1.88662   1.96274  -1.49702   0.61803   0.43157  -1.36203   1.91649  -1.94188   1.43120  -0.52541   0.00000   2.00000  -0.52541   1.43120  -1.94188   1.91649  -1.36203   0.43157   0.61803  -1.49702   1.96274  -1.88662   1.28968  -0.33671  -0.70921   1.55935  -1.97901   1.85235  -1.21433   0.24107   0.79873  -1.61803   1.99066  -1.81375   1.13613  -0.14487  -0.88638   1.67294  -1.99766   1.77091  -1.05528   0.04833   0.97197  -1.72394   0.00000     ... ... ..... ....... ......... ........... .............
E28g     2.00000  -1.81375   1.28968  -0.52541  -0.33671   1.13613  -1.72394   1.99066  -1.88662   1.43120  -0.70921  -0.14487   0.97197  -1.61803   1.96274  -1.94188   1.55935  -0.88638   0.04833   0.79873  -1.49702   1.91649  -1.97901   1.67294  -1.05528   0.24107   0.61803  -1.36203   1.85235  -1.99766   1.77091  -1.21433   0.43157   0.00000   2.00000   0.43157  -1.21433   1.77091  -1.99766   1.85235  -1.36203   0.61803   0.24107  -1.05528   1.67294  -1.97901   1.91649  -1.49702   0.79873   0.04833  -0.88638   1.55935  -1.94188   1.96274  -1.61803   0.97197  -0.14487  -0.70921   1.43120  -1.88662   1.99066  -1.72394   1.13613  -0.33671  -0.52541   1.28968  -1.81375   0.00000     ... ... ..... ....... ......... ........... .............
E29g     2.00000  -1.88662   1.55935  -1.05528   0.43157   0.24107  -0.88638   1.43120  -1.81375   1.99066  -1.94188   1.67294  -1.21433   0.61803   0.04833  -0.70921   1.28968  -1.72394   1.96274  -1.97901   1.77091  -1.36203   0.79873  -0.14487  -0.52541   1.13613  -1.61803   1.91649  -1.99766   1.85235  -1.49702   0.97197  -0.33671   0.00000   2.00000  -0.33671   0.97197  -1.49702   1.85235  -1.99766   1.91649  -1.61803   1.13613  -0.52541  -0.14487   0.79873  -1.36203   1.77091  -1.97901   1.96274  -1.72394   1.28968  -0.70921   0.04833   0.61803  -1.21433   1.67294  -1.94188   1.99066  -1.81375   1.43120  -0.88638   0.24107   0.43157  -1.05528   1.55935  -1.88662   0.00000     ... ... ..... ....... ......... ........... .............
E30g     2.00000  -1.94188   1.77091  -1.49702   1.13613  -0.70921   0.24107   0.24107  -0.70921   1.13613  -1.49702   1.77091  -1.94188   2.00000  -1.94188   1.77091  -1.49702   1.13613  -0.70921   0.24107   0.24107  -0.70921   1.13613  -1.49702   1.77091  -1.94188   2.00000  -1.94188   1.77091  -1.49702   1.13613  -0.70921   0.24107   0.00000   2.00000   0.24107  -0.70921   1.13613  -1.49702   1.77091  -1.94188   2.00000  -1.94188   1.77091  -1.49702   1.13613  -0.70921   0.24107   0.24107  -0.70921   1.13613  -1.49702   1.77091  -1.94188   2.00000  -1.94188   1.77091  -1.49702   1.13613  -0.70921   0.24107   0.24107  -0.70921   1.13613  -1.49702   1.77091  -1.94188   0.00000     ... ... ..... ....... ......... ........... .............
E31g     2.00000  -1.97901   1.91649  -1.81375   1.67294  -1.49702   1.28968  -1.05528   0.79873  -0.52541   0.24107   0.04833  -0.33671   0.61803  -0.88638   1.13613  -1.36203   1.55935  -1.72394   1.85235  -1.94188   1.99066  -1.99766   1.96274  -1.88662   1.77091  -1.61803   1.43120  -1.21433   0.97197  -0.70921   0.43157  -0.14487   0.00000   2.00000  -0.14487   0.43157  -0.70921   0.97197  -1.21433   1.43120  -1.61803   1.77091  -1.88662   1.96274  -1.99766   1.99066  -1.94188   1.85235  -1.72394   1.55935  -1.36203   1.13613  -0.88638   0.61803  -0.33671   0.04833   0.24107  -0.52541   0.79873  -1.05528   1.28968  -1.49702   1.67294  -1.81375   1.91649  -1.97901   0.00000     ... ... ..... ....... ......... ........... .............
E32g     2.00000  -1.99766   1.99066  -1.97901   1.96274  -1.94188   1.91649  -1.88662   1.85235  -1.81375   1.77091  -1.72394   1.67294  -1.61803   1.55935  -1.49702   1.43120  -1.36203   1.28968  -1.21433   1.13613  -1.05528   0.97197  -0.88638   0.79873  -0.70921   0.61803  -0.52541   0.43157  -0.33671   0.24107  -0.14487   0.04833   0.00000   2.00000   0.04833  -0.14487   0.24107  -0.33671   0.43157  -0.52541   0.61803  -0.70921   0.79873  -0.88638   0.97197  -1.05528   1.13613  -1.21433   1.28968  -1.36203   1.43120  -1.49702   1.55935  -1.61803   1.67294  -1.72394   1.77091  -1.81375   1.85235  -1.88662   1.91649  -1.94188   1.96274  -1.97901   1.99066  -1.99766   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  -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  -1.00000  -1.00000  -1.00000   1.00000     ... ..T ..... ......T ......... ..........T .............
E1u      2.00000   1.99066   1.96274   1.91649   1.85235   1.77091   1.67294   1.55935   1.43120   1.28968   1.13613   0.97197   0.79873   0.61803   0.43157   0.24107   0.04833  -0.14487  -0.33671  -0.52541  -0.70921  -0.88638  -1.05528  -1.21433  -1.36203  -1.49702  -1.61803  -1.72394  -1.81375  -1.88662  -1.94188  -1.97901  -1.99766   0.00000  -2.00000   1.99766   1.97901   1.94188   1.88662   1.81375   1.72394   1.61803   1.49702   1.36203   1.21433   1.05528   0.88638   0.70921   0.52541   0.33671   0.14487  -0.04833  -0.24107  -0.43157  -0.61803  -0.79873  -0.97197  -1.13613  -1.28968  -1.43120  -1.55935  -1.67294  -1.77091  -1.85235  -1.91649  -1.96274  -1.99066   0.00000     ... TT. ..... ....TT. ......... ........TT. .............
E2u      2.00000   1.96274   1.85235   1.67294   1.43120   1.13613   0.79873   0.43157   0.04833  -0.33671  -0.70921  -1.05528  -1.36203  -1.61803  -1.81375  -1.94188  -1.99766  -1.97901  -1.88662  -1.72394  -1.49702  -1.21433  -0.88638  -0.52541  -0.14487   0.24107   0.61803   0.97197   1.28968   1.55935   1.77091   1.91649   1.99066   0.00000  -2.00000  -1.99066  -1.91649  -1.77091  -1.55935  -1.28968  -0.97197  -0.61803  -0.24107   0.14487   0.52541   0.88638   1.21433   1.49702   1.72394   1.88662   1.97901   1.99766   1.94188   1.81375   1.61803   1.36203   1.05528   0.70921   0.33671  -0.04833  -0.43157  -0.79873  -1.13613  -1.43120  -1.67294  -1.85235  -1.96274   0.00000     ... ... ..... ..TT... ......... ......TT... .............
E3u      2.00000   1.91649   1.67294   1.28968   0.79873   0.24107  -0.33671  -0.88638  -1.36203  -1.72394  -1.94188  -1.99766  -1.88662  -1.61803  -1.21433  -0.70921  -0.14487   0.43157   0.97197   1.43120   1.77091   1.96274   1.99066   1.85235   1.55935   1.13613   0.61803   0.04833  -0.52541  -1.05528  -1.49702  -1.81375  -1.97901   0.00000  -2.00000   1.97901   1.81375   1.49702   1.05528   0.52541  -0.04833  -0.61803  -1.13613  -1.55935  -1.85235  -1.99066  -1.96274  -1.77091  -1.43120  -0.97197  -0.43157   0.14487   0.70921   1.21433   1.61803   1.88662   1.99766   1.94188   1.72394   1.36203   0.88638   0.33671  -0.24107  -0.79873  -1.28968  -1.67294  -1.91649   0.00000     ... ... ..... TT..... ......... ....TT..... .............
E4u      2.00000   1.85235   1.43120   0.79873   0.04833  -0.70921  -1.36203  -1.81375  -1.99766  -1.88662  -1.49702  -0.88638  -0.14487   0.61803   1.28968   1.77091   1.99066   1.91649   1.55935   0.97197   0.24107  -0.52541  -1.21433  -1.72394  -1.97901  -1.94188  -1.61803  -1.05528  -0.33671   0.43157   1.13613   1.67294   1.96274   0.00000  -2.00000  -1.96274  -1.67294  -1.13613  -0.43157   0.33671   1.05528   1.61803   1.94188   1.97901   1.72394   1.21433   0.52541  -0.24107  -0.97197  -1.55935  -1.91649  -1.99066  -1.77091  -1.28968  -0.61803   0.14487   0.88638   1.49702   1.88662   1.99766   1.81375   1.36203   0.70921  -0.04833  -0.79873  -1.43120  -1.85235   0.00000     ... ... ..... ....... ......... ..TT....... .............
E5u      2.00000   1.77091   1.13613   0.24107  -0.70921  -1.49702  -1.94188  -1.94188  -1.49702  -0.70921   0.24107   1.13613   1.77091   2.00000   1.77091   1.13613   0.24107  -0.70921  -1.49702  -1.94188  -1.94188  -1.49702  -0.70921   0.24107   1.13613   1.77091   2.00000   1.77091   1.13613   0.24107  -0.70921  -1.49702  -1.94188   0.00000  -2.00000   1.94188   1.49702   0.70921  -0.24107  -1.13613  -1.77091  -2.00000  -1.77091  -1.13613  -0.24107   0.70921   1.49702   1.94188   1.94188   1.49702   0.70921  -0.24107  -1.13613  -1.77091  -2.00000  -1.77091  -1.13613  -0.24107   0.70921   1.49702   1.94188   1.94188   1.49702   0.70921  -0.24107  -1.13613  -1.77091   0.00000     ... ... ..... ....... ......... TT......... .............
E6u      2.00000   1.67294   0.79873  -0.33671  -1.36203  -1.94188  -1.88662  -1.21433  -0.14487   0.97197   1.77091   1.99066   1.55935   0.61803  -0.52541  -1.49702  -1.97901  -1.81375  -1.05528   0.04833   1.13613   1.85235   1.96274   1.43120   0.43157  -0.70921  -1.61803  -1.99766  -1.72394  -0.88638   0.24107   1.28968   1.91649   0.00000  -2.00000  -1.91649  -1.28968  -0.24107   0.88638   1.72394   1.99766   1.61803   0.70921  -0.43157  -1.43120  -1.96274  -1.85235  -1.13613  -0.04833   1.05528   1.81375   1.97901   1.49702   0.52541  -0.61803  -1.55935  -1.99066  -1.77091  -0.97197   0.14487   1.21433   1.88662   1.94188   1.36203   0.33671  -0.79873  -1.67294   0.00000     ... ... ..... ....... ......... ........... .............
E7u      2.00000   1.55935   0.43157  -0.88638  -1.81375  -1.94188  -1.21433   0.04833   1.28968   1.96274   1.77091   0.79873  -0.52541  -1.61803  -1.99766  -1.49702  -0.33671   0.97197   1.85235   1.91649   1.13613  -0.14487  -1.36203  -1.97901  -1.72394  -0.70921   0.61803   1.67294   1.99066   1.43120   0.24107  -1.05528  -1.88662   0.00000  -2.00000   1.88662   1.05528  -0.24107  -1.43120  -1.99066  -1.67294  -0.61803   0.70921   1.72394   1.97901   1.36203   0.14487  -1.13613  -1.91649  -1.85235  -0.97197   0.33671   1.49702   1.99766   1.61803   0.52541  -0.79873  -1.77091  -1.96274  -1.28968  -0.04833   1.21433   1.94188   1.81375   0.88638  -0.43157  -1.55935   0.00000     ... ... ..... ....... ......... ........... .............
E8u      2.00000   1.43120   0.04833  -1.36203  -1.99766  -1.49702  -0.14487   1.28968   1.99066   1.55935   0.24107  -1.21433  -1.97901  -1.61803  -0.33671   1.13613   1.96274   1.67294   0.43157  -1.05528  -1.94188  -1.72394  -0.52541   0.97197   1.91649   1.77091   0.61803  -0.88638  -1.88662  -1.81375  -0.70921   0.79873   1.85235   0.00000  -2.00000  -1.85235  -0.79873   0.70921   1.81375   1.88662   0.88638  -0.61803  -1.77091  -1.91649  -0.97197   0.52541   1.72394   1.94188   1.05528  -0.43157  -1.67294  -1.96274  -1.13613   0.33671   1.61803   1.97901   1.21433  -0.24107  -1.55935  -1.99066  -1.28968   0.14487   1.49702   1.99766   1.36203  -0.04833  -1.43120   0.00000     ... ... ..... ....... ......... ........... .............
E9u      2.00000   1.28968  -0.33671  -1.72394  -1.88662  -0.70921   0.97197   1.96274   1.55935   0.04833  -1.49702  -1.97901  -1.05528   0.61803   1.85235   1.77091   0.43157  -1.21433  -1.99766  -1.36203   0.24107   1.67294   1.91649   0.79873  -0.88638  -1.94188  -1.61803  -0.14487   1.43120   1.99066   1.13613  -0.52541  -1.81375   0.00000  -2.00000   1.81375   0.52541  -1.13613  -1.99066  -1.43120   0.14487   1.61803   1.94188   0.88638  -0.79873  -1.91649  -1.67294  -0.24107   1.36203   1.99766   1.21433  -0.43157  -1.77091  -1.85235  -0.61803   1.05528   1.97901   1.49702  -0.04833  -1.55935  -1.96274  -0.97197   0.70921   1.88662   1.72394   0.33671  -1.28968   0.00000     ... ... ..... ....... ......... ........... .............
E10u     2.00000   1.13613  -0.70921  -1.94188  -1.49702   0.24107   1.77091   1.77091   0.24107  -1.49702  -1.94188  -0.70921   1.13613   2.00000   1.13613  -0.70921  -1.94188  -1.49702   0.24107   1.77091   1.77091   0.24107  -1.49702  -1.94188  -0.70921   1.13613   2.00000   1.13613  -0.70921  -1.94188  -1.49702   0.24107   1.77091   0.00000  -2.00000  -1.77091  -0.24107   1.49702   1.94188   0.70921  -1.13613  -2.00000  -1.13613   0.70921   1.94188   1.49702  -0.24107  -1.77091  -1.77091  -0.24107   1.49702   1.94188   0.70921  -1.13613  -2.00000  -1.13613   0.70921   1.94188   1.49702  -0.24107  -1.77091  -1.77091  -0.24107   1.49702   1.94188   0.70921  -1.13613   0.00000     ... ... ..... ....... ......... ........... .............
E11u     2.00000   0.97197  -1.05528  -1.99766  -0.88638   1.13613   1.99066   0.79873  -1.21433  -1.97901  -0.70921   1.28968   1.96274   0.61803  -1.36203  -1.94188  -0.52541   1.43120   1.91649   0.43157  -1.49702  -1.88662  -0.33671   1.55935   1.85235   0.24107  -1.61803  -1.81375  -0.14487   1.67294   1.77091   0.04833  -1.72394   0.00000  -2.00000   1.72394  -0.04833  -1.77091  -1.67294   0.14487   1.81375   1.61803  -0.24107  -1.85235  -1.55935   0.33671   1.88662   1.49702  -0.43157  -1.91649  -1.43120   0.52541   1.94188   1.36203  -0.61803  -1.96274  -1.28968   0.70921   1.97901   1.21433  -0.79873  -1.99066  -1.13613   0.88638   1.99766   1.05528  -0.97197   0.00000     ... ... ..... ....... ......... ........... .............
E12u     2.00000   0.79873  -1.36203  -1.88662  -0.14487   1.77091   1.55935  -0.52541  -1.97901  -1.05528   1.13613   1.96274   0.43157  -1.61803  -1.72394   0.24107   1.91649   1.28968  -0.88638  -1.99766  -0.70921   1.43120   1.85235   0.04833  -1.81375  -1.49702   0.61803   1.99066   0.97197  -1.21433  -1.94188  -0.33671   1.67294   0.00000  -2.00000  -1.67294   0.33671   1.94188   1.21433  -0.97197  -1.99066  -0.61803   1.49702   1.81375  -0.04833  -1.85235  -1.43120   0.70921   1.99766   0.88638  -1.28968  -1.91649  -0.24107   1.72394   1.61803  -0.43157  -1.96274  -1.13613   1.05528   1.97901   0.52541  -1.55935  -1.77091   0.14487   1.88662   1.36203  -0.79873   0.00000     ... ... ..... ....... ......... ........... .............
E13u     2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803   0.00000  -2.00000   1.61803  -0.61803  -2.00000  -0.61803   1.61803   1.61803  -0.61803  -2.00000  -0.61803   1.61803   1.61803  -0.61803  -2.00000  -0.61803   1.61803   1.61803  -0.61803  -2.00000  -0.61803   1.61803   1.61803  -0.61803  -2.00000  -0.61803   1.61803   1.61803  -0.61803  -2.00000  -0.61803   1.61803   1.61803  -0.61803   0.00000     ... ... ..... ....... ......... ........... .............
E14u     2.00000   0.43157  -1.81375  -1.21433   1.28968   1.77091  -0.52541  -1.99766  -0.33671   1.85235   1.13613  -1.36203  -1.72394   0.61803   1.99066   0.24107  -1.88662  -1.05528   1.43120   1.67294  -0.70921  -1.97901  -0.14487   1.91649   0.97197  -1.49702  -1.61803   0.79873   1.96274   0.04833  -1.94188  -0.88638   1.55935   0.00000  -2.00000  -1.55935   0.88638   1.94188  -0.04833  -1.96274  -0.79873   1.61803   1.49702  -0.97197  -1.91649   0.14487   1.97901   0.70921  -1.67294  -1.43120   1.05528   1.88662  -0.24107  -1.99066  -0.61803   1.72394   1.36203  -1.13613  -1.85235   0.33671   1.99766   0.52541  -1.77091  -1.28968   1.21433   1.81375  -0.43157   0.00000     ... ... ..... ....... ......... ........... .............
E15u     2.00000   0.24107  -1.94188  -0.70921   1.77091   1.13613  -1.49702  -1.49702   1.13613   1.77091  -0.70921  -1.94188   0.24107   2.00000   0.24107  -1.94188  -0.70921   1.77091   1.13613  -1.49702  -1.49702   1.13613   1.77091  -0.70921  -1.94188   0.24107   2.00000   0.24107  -1.94188  -0.70921   1.77091   1.13613  -1.49702   0.00000  -2.00000   1.49702  -1.13613  -1.77091   0.70921   1.94188  -0.24107  -2.00000  -0.24107   1.94188   0.70921  -1.77091  -1.13613   1.49702   1.49702  -1.13613  -1.77091   0.70921   1.94188  -0.24107  -2.00000  -0.24107   1.94188   0.70921  -1.77091  -1.13613   1.49702   1.49702  -1.13613  -1.77091   0.70921   1.94188  -0.24107   0.00000     ... ... ..... ....... ......... ........... .............
E16u     2.00000   0.04833  -1.99766  -0.14487   1.99066   0.24107  -1.97901  -0.33671   1.96274   0.43157  -1.94188  -0.52541   1.91649   0.61803  -1.88662  -0.70921   1.85235   0.79873  -1.81375  -0.88638   1.77091   0.97197  -1.72394  -1.05528   1.67294   1.13613  -1.61803  -1.21433   1.55935   1.28968  -1.49702  -1.36203   1.43120   0.00000  -2.00000  -1.43120   1.36203   1.49702  -1.28968  -1.55935   1.21433   1.61803  -1.13613  -1.67294   1.05528   1.72394  -0.97197  -1.77091   0.88638   1.81375  -0.79873  -1.85235   0.70921   1.88662  -0.61803  -1.91649   0.52541   1.94188  -0.43157  -1.96274   0.33671   1.97901  -0.24107  -1.99066   0.14487   1.99766  -0.04833   0.00000     ... ... ..... ....... ......... ........... .............
E17u     2.00000  -0.14487  -1.97901   0.43157   1.91649  -0.70921  -1.81375   0.97197   1.67294  -1.21433  -1.49702   1.43120   1.28968  -1.61803  -1.05528   1.77091   0.79873  -1.88662  -0.52541   1.96274   0.24107  -1.99766   0.04833   1.99066  -0.33671  -1.94188   0.61803   1.85235  -0.88638  -1.72394   1.13613   1.55935  -1.36203   0.00000  -2.00000   1.36203  -1.55935  -1.13613   1.72394   0.88638  -1.85235  -0.61803   1.94188   0.33671  -1.99066  -0.04833   1.99766  -0.24107  -1.96274   0.52541   1.88662  -0.79873  -1.77091   1.05528   1.61803  -1.28968  -1.43120   1.49702   1.21433  -1.67294  -0.97197   1.81375   0.70921  -1.91649  -0.43157   1.97901   0.14487   0.00000     ... ... ..... ....... ......... ........... .............
E18u     2.00000  -0.33671  -1.88662   0.97197   1.55935  -1.49702  -1.05528   1.85235   0.43157  -1.99766   0.24107   1.91649  -0.88638  -1.61803   1.43120   1.13613  -1.81375  -0.52541   1.99066  -0.14487  -1.94188   0.79873   1.67294  -1.36203  -1.21433   1.77091   0.61803  -1.97901   0.04833   1.96274  -0.70921  -1.72394   1.28968   0.00000  -2.00000  -1.28968   1.72394   0.70921  -1.96274  -0.04833   1.97901  -0.61803  -1.77091   1.21433   1.36203  -1.67294  -0.79873   1.94188   0.14487  -1.99066   0.52541   1.81375  -1.13613  -1.43120   1.61803   0.88638  -1.91649  -0.24107   1.99766  -0.43157  -1.85235   1.05528   1.49702  -1.55935  -0.97197   1.88662   0.33671   0.00000     ... ... ..... ....... ......... ........... .............
E19u     2.00000  -0.52541  -1.72394   1.43120   0.97197  -1.94188   0.04833   1.91649  -1.05528  -1.36203   1.77091   0.43157  -1.99766   0.61803   1.67294  -1.49702  -0.88638   1.96274  -0.14487  -1.88662   1.13613   1.28968  -1.81375  -0.33671   1.99066  -0.70921  -1.61803   1.55935   0.79873  -1.97901   0.24107   1.85235  -1.21433   0.00000  -2.00000   1.21433  -1.85235  -0.24107   1.97901  -0.79873  -1.55935   1.61803   0.70921  -1.99066   0.33671   1.81375  -1.28968  -1.13613   1.88662   0.14487  -1.96274   0.88638   1.49702  -1.67294  -0.61803   1.99766  -0.43157  -1.77091   1.36203   1.05528  -1.91649  -0.04833   1.94188  -0.97197  -1.43120   1.72394   0.52541   0.00000     ... ... ..... ....... ......... ........... .............
E20u     2.00000  -0.70921  -1.49702   1.77091   0.24107  -1.94188   1.13613   1.13613  -1.94188   0.24107   1.77091  -1.49702  -0.70921   2.00000  -0.70921  -1.49702   1.77091   0.24107  -1.94188   1.13613   1.13613  -1.94188   0.24107   1.77091  -1.49702  -0.70921   2.00000  -0.70921  -1.49702   1.77091   0.24107  -1.94188   1.13613   0.00000  -2.00000  -1.13613   1.94188  -0.24107  -1.77091   1.49702   0.70921  -2.00000   0.70921   1.49702  -1.77091  -0.24107   1.94188  -1.13613  -1.13613   1.94188  -0.24107  -1.77091   1.49702   0.70921  -2.00000   0.70921   1.49702  -1.77091  -0.24107   1.94188  -1.13613  -1.13613   1.94188  -0.24107  -1.77091   1.49702   0.70921   0.00000     ... ... ..... ....... ......... ........... .............
E21u     2.00000  -0.88638  -1.21433   1.96274  -0.52541  -1.49702   1.85235  -0.14487  -1.72394   1.67294   0.24107  -1.88662   1.43120   0.61803  -1.97901   1.13613   0.97197  -1.99766   0.79873   1.28968  -1.94188   0.43157   1.55935  -1.81375   0.04833   1.77091  -1.61803  -0.33671   1.91649  -1.36203  -0.70921   1.99066  -1.05528   0.00000  -2.00000   1.05528  -1.99066   0.70921   1.36203  -1.91649   0.33671   1.61803  -1.77091  -0.04833   1.81375  -1.55935  -0.43157   1.94188  -1.28968  -0.79873   1.99766  -0.97197  -1.13613   1.97901  -0.61803  -1.43120   1.88662  -0.24107  -1.67294   1.72394   0.14487  -1.85235   1.49702   0.52541  -1.96274   1.21433   0.88638   0.00000     ... ... ..... ....... ......... ........... .............
E22u     2.00000  -1.05528  -0.88638   1.99066  -1.21433  -0.70921   1.96274  -1.36203  -0.52541   1.91649  -1.49702  -0.33671   1.85235  -1.61803  -0.14487   1.77091  -1.72394   0.04833   1.67294  -1.81375   0.24107   1.55935  -1.88662   0.43157   1.43120  -1.94188   0.61803   1.28968  -1.97901   0.79873   1.13613  -1.99766   0.97197   0.00000  -2.00000  -0.97197   1.99766  -1.13613  -0.79873   1.97901  -1.28968  -0.61803   1.94188  -1.43120  -0.43157   1.88662  -1.55935  -0.24107   1.81375  -1.67294  -0.04833   1.72394  -1.77091   0.14487   1.61803  -1.85235   0.33671   1.49702  -1.91649   0.52541   1.36203  -1.96274   0.70921   1.21433  -1.99066   0.88638   1.05528   0.00000     ... ... ..... ....... ......... ........... .............
E23u     2.00000  -1.21433  -0.52541   1.85235  -1.72394   0.24107   1.43120  -1.97901   0.97197   0.79873  -1.94188   1.55935   0.04833  -1.61803   1.91649  -0.70921  -1.05528   1.99066  -1.36203  -0.33671   1.77091  -1.81375   0.43157   1.28968  -1.99766   1.13613   0.61803  -1.88662   1.67294  -0.14487  -1.49702   1.96274  -0.88638   0.00000  -2.00000   0.88638  -1.96274   1.49702   0.14487  -1.67294   1.88662  -0.61803  -1.13613   1.99766  -1.28968  -0.43157   1.81375  -1.77091   0.33671   1.36203  -1.99066   1.05528   0.70921  -1.91649   1.61803  -0.04833  -1.55935   1.94188  -0.79873  -0.97197   1.97901  -1.43120  -0.24107   1.72394  -1.85235   0.52541   1.21433   0.00000     ... ... ..... ....... ......... ........... .............
E24u     2.00000  -1.36203  -0.14487   1.55935  -1.97901   1.13613   0.43157  -1.72394   1.91649  -0.88638  -0.70921   1.85235  -1.81375   0.61803   0.97197  -1.94188   1.67294  -0.33671  -1.21433   1.99066  -1.49702   0.04833   1.43120  -1.99766   1.28968   0.24107  -1.61803   1.96274  -1.05528  -0.52541   1.77091  -1.88662   0.79873   0.00000  -2.00000  -0.79873   1.88662  -1.77091   0.52541   1.05528  -1.96274   1.61803  -0.24107  -1.28968   1.99766  -1.43120  -0.04833   1.49702  -1.99066   1.21433   0.33671  -1.67294   1.94188  -0.97197  -0.61803   1.81375  -1.85235   0.70921   0.88638  -1.91649   1.72394  -0.43157  -1.13613   1.97901  -1.55935   0.14487   1.36203   0.00000     ... ... ..... ....... ......... ........... .............
E25u     2.00000  -1.49702   0.24107   1.13613  -1.94188   1.77091  -0.70921  -0.70921   1.77091  -1.94188   1.13613   0.24107  -1.49702   2.00000  -1.49702   0.24107   1.13613  -1.94188   1.77091  -0.70921  -0.70921   1.77091  -1.94188   1.13613   0.24107  -1.49702   2.00000  -1.49702   0.24107   1.13613  -1.94188   1.77091  -0.70921   0.00000  -2.00000   0.70921  -1.77091   1.94188  -1.13613  -0.24107   1.49702  -2.00000   1.49702  -0.24107  -1.13613   1.94188  -1.77091   0.70921   0.70921  -1.77091   1.94188  -1.13613  -0.24107   1.49702  -2.00000   1.49702  -0.24107  -1.13613   1.94188  -1.77091   0.70921   0.70921  -1.77091   1.94188  -1.13613  -0.24107   1.49702   0.00000     ... ... ..... ....... ......... ........... .............
E26u     2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.00000  -2.00000  -0.61803   1.61803  -2.00000   1.61803  -0.61803  -0.61803   1.61803  -2.00000   1.61803  -0.61803  -0.61803   1.61803  -2.00000   1.61803  -0.61803  -0.61803   1.61803  -2.00000   1.61803  -0.61803  -0.61803   1.61803  -2.00000   1.61803  -0.61803  -0.61803   1.61803  -2.00000   1.61803  -0.61803  -0.61803   1.61803   0.00000     ... ... ..... ....... ......... ........... .............
E27u     2.00000  -1.72394   0.97197   0.04833  -1.05528   1.77091  -1.99766   1.67294  -0.88638  -0.14487   1.13613  -1.81375   1.99066  -1.61803   0.79873   0.24107  -1.21433   1.85235  -1.97901   1.55935  -0.70921  -0.33671   1.28968  -1.88662   1.96274  -1.49702   0.61803   0.43157  -1.36203   1.91649  -1.94188   1.43120  -0.52541   0.00000  -2.00000   0.52541  -1.43120   1.94188  -1.91649   1.36203  -0.43157  -0.61803   1.49702  -1.96274   1.88662  -1.28968   0.33671   0.70921  -1.55935   1.97901  -1.85235   1.21433  -0.24107  -0.79873   1.61803  -1.99066   1.81375  -1.13613   0.14487   0.88638  -1.67294   1.99766  -1.77091   1.05528  -0.04833  -0.97197   1.72394   0.00000     ... ... ..... ....... ......... ........... .............
E28u     2.00000  -1.81375   1.28968  -0.52541  -0.33671   1.13613  -1.72394   1.99066  -1.88662   1.43120  -0.70921  -0.14487   0.97197  -1.61803   1.96274  -1.94188   1.55935  -0.88638   0.04833   0.79873  -1.49702   1.91649  -1.97901   1.67294  -1.05528   0.24107   0.61803  -1.36203   1.85235  -1.99766   1.77091  -1.21433   0.43157   0.00000  -2.00000  -0.43157   1.21433  -1.77091   1.99766  -1.85235   1.36203  -0.61803  -0.24107   1.05528  -1.67294   1.97901  -1.91649   1.49702  -0.79873  -0.04833   0.88638  -1.55935   1.94188  -1.96274   1.61803  -0.97197   0.14487   0.70921  -1.43120   1.88662  -1.99066   1.72394  -1.13613   0.33671   0.52541  -1.28968   1.81375   0.00000     ... ... ..... ....... ......... ........... .............
E29u     2.00000  -1.88662   1.55935  -1.05528   0.43157   0.24107  -0.88638   1.43120  -1.81375   1.99066  -1.94188   1.67294  -1.21433   0.61803   0.04833  -0.70921   1.28968  -1.72394   1.96274  -1.97901   1.77091  -1.36203   0.79873  -0.14487  -0.52541   1.13613  -1.61803   1.91649  -1.99766   1.85235  -1.49702   0.97197  -0.33671   0.00000  -2.00000   0.33671  -0.97197   1.49702  -1.85235   1.99766  -1.91649   1.61803  -1.13613   0.52541   0.14487  -0.79873   1.36203  -1.77091   1.97901  -1.96274   1.72394  -1.28968   0.70921  -0.04833  -0.61803   1.21433  -1.67294   1.94188  -1.99066   1.81375  -1.43120   0.88638  -0.24107  -0.43157   1.05528  -1.55935   1.88662   0.00000     ... ... ..... ....... ......... ........... .............
E30u     2.00000  -1.94188   1.77091  -1.49702   1.13613  -0.70921   0.24107   0.24107  -0.70921   1.13613  -1.49702   1.77091  -1.94188   2.00000  -1.94188   1.77091  -1.49702   1.13613  -0.70921   0.24107   0.24107  -0.70921   1.13613  -1.49702   1.77091  -1.94188   2.00000  -1.94188   1.77091  -1.49702   1.13613  -0.70921   0.24107   0.00000  -2.00000  -0.24107   0.70921  -1.13613   1.49702  -1.77091   1.94188  -2.00000   1.94188  -1.77091   1.49702  -1.13613   0.70921  -0.24107  -0.24107   0.70921  -1.13613   1.49702  -1.77091   1.94188  -2.00000   1.94188  -1.77091   1.49702  -1.13613   0.70921  -0.24107  -0.24107   0.70921  -1.13613   1.49702  -1.77091   1.94188   0.00000     ... ... ..... ....... ......... ........... .............
E31u     2.00000  -1.97901   1.91649  -1.81375   1.67294  -1.49702   1.28968  -1.05528   0.79873  -0.52541   0.24107   0.04833  -0.33671   0.61803  -0.88638   1.13613  -1.36203   1.55935  -1.72394   1.85235  -1.94188   1.99066  -1.99766   1.96274  -1.88662   1.77091  -1.61803   1.43120  -1.21433   0.97197  -0.70921   0.43157  -0.14487   0.00000  -2.00000   0.14487  -0.43157   0.70921  -0.97197   1.21433  -1.43120   1.61803  -1.77091   1.88662  -1.96274   1.99766  -1.99066   1.94188  -1.85235   1.72394  -1.55935   1.36203  -1.13613   0.88638  -0.61803   0.33671  -0.04833  -0.24107   0.52541  -0.79873   1.05528  -1.28968   1.49702  -1.67294   1.81375  -1.91649   1.97901   0.00000     ... ... ..... ....... ......... ........... .............
E32u     2.00000  -1.99766   1.99066  -1.97901   1.96274  -1.94188   1.91649  -1.88662   1.85235  -1.81375   1.77091  -1.72394   1.67294  -1.61803   1.55935  -1.49702   1.43120  -1.36203   1.28968  -1.21433   1.13613  -1.05528   0.97197  -0.88638   0.79873  -0.70921   0.61803  -0.52541   0.43157  -0.33671   0.24107  -0.14487   0.04833   0.00000  -2.00000  -0.04833   0.14487  -0.24107   0.33671  -0.43157   0.52541  -0.61803   0.70921  -0.79873   0.88638  -0.97197   1.05528  -1.13613   1.21433  -1.28968   1.36203  -1.43120   1.49702  -1.55935   1.61803  -1.67294   1.72394  -1.77091   1.81375  -1.85235   1.88662  -1.91649   1.94188  -1.96274   1.97901  -1.99066   1.99766   0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.997664453665 = 2*cos(2*π/130) = 2*cos(π/65)
                               1.990663269435 = 2*cos(4*π/130) = 2*cos(2*π/65)
                               1.979012798902 = 2*cos(6*π/130) = 2*cos(3*π/65)
                               1.962740252279 = 2*cos(8*π/130) = 2*cos(4*π/65)
                               1.941883634852 = 2*cos(10*π/130) = 2*cos(π/13)
                               1.916491658218 = 2*cos(12*π/130) = 2*cos(6*π/65)
                               1.886623626515 = 2*cos(14*π/130) = 2*cos(7*π/65)
                               1.852349297916 = 2*cos(16*π/130) = 2*cos(8*π/65)
                               1.813748721701 = 2*cos(18*π/130) = 2*cos(9*π/65)
                               1.770912051306 = 2*cos(20*π/130) = 2*cos(2*π/13)
                               1.723939333760 = 2*cos(22*π/130) = 2*cos(11*π/65)
                               1.672940276020 = 2*cos(24*π/130) = 2*cos(12*π/65)
                               1.618033988750 = 2*cos(26*π/130) = 2*cos(π/5) = (√5+1)/2
                               1.559348708126 = 2*cos(28*π/130) = 2*cos(14*π/65)
                               1.497021496342 = 2*cos(30*π/130) = 2*cos(3*π/13)
                               1.431197921488 = 2*cos(32*π/130) = 2*cos(16*π/65)
                               1.362031717574 = 2*cos(34*π/130) = 2*cos(17*π/65)
                               1.289684425472 = 2*cos(36*π/130) = 2*cos(18*π/65)
                               1.214325015637 = 2*cos(38*π/130) = 2*cos(19*π/65)
                               1.136129493462 = 2*cos(40*π/130) = 2*cos(4*π/13)
                               1.055280488212 = 2*cos(42*π/130) = 2*cos(21*π/65)
                               0.971966826485 = 2*cos(44*π/130) = 2*cos(22*π/65)
                               0.886383091198 = 2*cos(46*π/130) = 2*cos(23*π/65)
                               0.798729167131 = 2*cos(48*π/130) = 2*cos(24*π/65)
                               0.709209774085 = 2*cos(50*π/130) = 2*cos(5*π/13)
                               0.618033988750 = 2*cos(52*π/130) = 2*cos(2*π/5) = (√5−1)/2
                               0.525414756397 = 2*cos(54*π/130) = 2*cos(27*π/65)
                               0.431568393536 = 2*cos(56*π/130) = 2*cos(28*π/65)
                               0.336714082694 = 2*cos(58*π/130) = 2*cos(29*π/65)
                               0.241073360511 = 2*cos(60*π/130) = 2*cos(6*π/13)
                               0.144869600324 = 2*cos(62*π/130) = 2*cos(31*π/65)
                               0.048327490472 = 2*cos(64*π/130) = 2*cos(32*π/65)



 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 D65d point group is 260, and the order of the principal axis (S130) is 130. The group has 68 irreducible representations.

    β  The D65d point group is isomorphic to D65h, C130v and D130.

    γ  The D65d point group is generated by two symmetry elements, S130 and either a perpendicular C2 or a vertical σd.
       Also, the group may be generated from a C2 plus a σd (some pairs will yield smaller groups, though; choosing a minimum angle is safe).
       The canonical choice, however, is to use redundant generators: C65, 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 D65d 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 much less than half the order of the principal axis.

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

This Character Table for the D65d point group was created by Gernot Katzer.

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