Character table for the D99 point group

D99     E        2 C99    2 C99^2  2 C33    2 C99^4  2 C99^5  2 C33^2  2 C99^7  2 C99^8  2 C11    2 C99^10 2 C9     2 C33^4  2 C99^13 2 C99^14 2 C33^5  2 C99^16 2 C99^17 2 C11^2  2 C99^19 2 C99^20 2 C33^7  2 C9^2   2 C99^23 2 C33^8  2 C99^25 2 C99^26 2 C11^3  2 C99^28 2 C99^29 2 C33^10 2 C99^31 2 C99^32 2 C3     2 C99^34 2 C99^35 2 C11^4  2 C99^37 2 C99^38 2 C33^13 2 C99^40 2 C99^41 2 C33^14 2 C99^43 2 C9^4   2 C11^5  2 C99^46 2 C99^47 2 C33^16 2 C99^49 99 C2'      <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A1      1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000     ... ... ....T ....... ........T ........... ............T
A2      1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000 -1.00000     ..T ..T ..... ......T ......... ..........T .............
E1      2.00000  1.99597  1.98391  1.96386  1.93590  1.90014  1.85674  1.80585  1.74770  1.68251  1.61054  1.53209  1.44747  1.35702  1.26111  1.16011  1.05445  0.94454  0.83083  0.71377  0.59384  0.47152  0.34730  0.22168  0.09516 -0.03173 -0.15850 -0.28463 -0.40961 -0.53295 -0.65414 -0.77269 -0.88813 -1.00000 -1.10784 -1.21122 -1.30972 -1.40295 -1.49053 -1.57211 -1.64735 -1.71597 -1.77767 -1.83222 -1.87939 -1.91899 -1.95086 -1.97488 -1.99094 -1.99899  0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2      2.00000  1.98391  1.93590  1.85674  1.74770  1.61054  1.44747  1.26111  1.05445  0.83083  0.59384  0.34730  0.09516 -0.15850 -0.40961 -0.65414 -0.88813 -1.10784 -1.30972 -1.49053 -1.64735 -1.77767 -1.87939 -1.95086 -1.99094 -1.99899 -1.97488 -1.91899 -1.83222 -1.71597 -1.57211 -1.40295 -1.21122 -1.00000 -0.77269 -0.53295 -0.28463 -0.03173  0.22168  0.47152  0.71377  0.94454  1.16011  1.35702  1.53209  1.68251  1.80585  1.90014  1.96386  1.99597  0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3      2.00000  1.96386  1.85674  1.68251  1.44747  1.16011  0.83083  0.47152  0.09516 -0.28463 -0.65414 -1.00000 -1.30972 -1.57211 -1.77767 -1.91899 -1.99094 -1.99094 -1.91899 -1.77767 -1.57211 -1.30972 -1.00000 -0.65414 -0.28463  0.09516  0.47152  0.83083  1.16011  1.44747  1.68251  1.85674  1.96386  2.00000  1.96386  1.85674  1.68251  1.44747  1.16011  0.83083  0.47152  0.09516 -0.28463 -0.65414 -1.00000 -1.30972 -1.57211 -1.77767 -1.91899 -1.99094  0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4      2.00000  1.93590  1.74770  1.44747  1.05445  0.59384  0.09516 -0.40961 -0.88813 -1.30972 -1.64735 -1.87939 -1.99094 -1.97488 -1.83222 -1.57211 -1.21122 -0.77269 -0.28463  0.22168  0.71377  1.16011  1.53209  1.80585  1.96386  1.99597  1.90014  1.68251  1.35702  0.94454  0.47152 -0.03173 -0.53295 -1.00000 -1.40295 -1.71597 -1.91899 -1.99899 -1.95086 -1.77767 -1.49053 -1.10784 -0.65414 -0.15850  0.34730  0.83083  1.26111  1.61054  1.85674  1.98391  0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5      2.00000  1.90014  1.61054  1.16011  0.59384 -0.03173 -0.65414 -1.21122 -1.64735 -1.91899 -1.99899 -1.87939 -1.57211 -1.10784 -0.53295  0.09516  0.71377  1.26111  1.68251  1.93590  1.99597  1.85674  1.53209  1.05445  0.47152 -0.15850 -0.77269 -1.30972 -1.71597 -1.95086 -1.99094 -1.83222 -1.49053 -1.00000 -0.40961  0.22168  0.83083  1.35702  1.74770  1.96386  1.98391  1.80585  1.44747  0.94454  0.34730 -0.28463 -0.88813 -1.40295 -1.77767 -1.97488  0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6      2.00000  1.85674  1.44747  0.83083  0.09516 -0.65414 -1.30972 -1.77767 -1.99094 -1.91899 -1.57211 -1.00000 -0.28463  0.47152  1.16011  1.68251  1.96386  1.96386  1.68251  1.16011  0.47152 -0.28463 -1.00000 -1.57211 -1.91899 -1.99094 -1.77767 -1.30972 -0.65414  0.09516  0.83083  1.44747  1.85674  2.00000  1.85674  1.44747  0.83083  0.09516 -0.65414 -1.30972 -1.77767 -1.99094 -1.91899 -1.57211 -1.00000 -0.28463  0.47152  1.16011  1.68251  1.96386  0.00000     ... ... ..... ....... ......... ........... TT...........
E7      2.00000  1.80585  1.26111  0.47152 -0.40961 -1.21122 -1.77767 -1.99899 -1.83222 -1.30972 -0.53295  0.34730  1.16011  1.74770  1.99597  1.85674  1.35702  0.59384 -0.28463 -1.10784 -1.71597 -1.99094 -1.87939 -1.40295 -0.65414  0.22168  1.05445  1.68251  1.98391  1.90014  1.44747  0.71377 -0.15850 -1.00000 -1.64735 -1.97488 -1.91899 -1.49053 -0.77269  0.09516  0.94454  1.61054  1.96386  1.93590  1.53209  0.83083 -0.03173 -0.88813 -1.57211 -1.95086  0.00000     ... ... ..... ....... ......... ........... .............
E8      2.00000  1.74770  1.05445  0.09516 -0.88813 -1.64735 -1.99094 -1.83222 -1.21122 -0.28463  0.71377  1.53209  1.96386  1.90014  1.35702  0.47152 -0.53295 -1.40295 -1.91899 -1.95086 -1.49053 -0.65414  0.34730  1.26111  1.85674  1.98391  1.61054  0.83083 -0.15850 -1.10784 -1.77767 -1.99899 -1.71597 -1.00000 -0.03173  0.94454  1.68251  1.99597  1.80585  1.16011  0.22168 -0.77269 -1.57211 -1.97488 -1.87939 -1.30972 -0.40961  0.59384  1.44747  1.93590  0.00000     ... ... ..... ....... ......... ........... .............
E9      2.00000  1.68251  0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463  0.83083  1.68251  2.00000  1.68251  0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463  0.83083  1.68251  2.00000  1.68251  0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463  0.83083  1.68251  2.00000  1.68251  0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463  0.83083  1.68251  2.00000  1.68251  0.83083 -0.28463 -1.30972 -1.91899  0.00000     ... ... ..... ....... ......... ........... .............
E10     2.00000  1.61054  0.59384 -0.65414 -1.64735 -1.99899 -1.57211 -0.53295  0.71377  1.68251  1.99597  1.53209  0.47152 -0.77269 -1.71597 -1.99094 -1.49053 -0.40961  0.83083  1.74770  1.98391  1.44747  0.34730 -0.88813 -1.77767 -1.97488 -1.40295 -0.28463  0.94454  1.80585  1.96386  1.35702  0.22168 -1.00000 -1.83222 -1.95086 -1.30972 -0.15850  1.05445  1.85674  1.93590  1.26111  0.09516 -1.10784 -1.87939 -1.91899 -1.21122 -0.03173  1.16011  1.90014  0.00000     ... ... ..... ....... ......... ........... .............
E11     2.00000  1.53209  0.34730 -1.00000 -1.87939 -1.87939 -1.00000  0.34730  1.53209  2.00000  1.53209  0.34730 -1.00000 -1.87939 -1.87939 -1.00000  0.34730  1.53209  2.00000  1.53209  0.34730 -1.00000 -1.87939 -1.87939 -1.00000  0.34730  1.53209  2.00000  1.53209  0.34730 -1.00000 -1.87939 -1.87939 -1.00000  0.34730  1.53209  2.00000  1.53209  0.34730 -1.00000 -1.87939 -1.87939 -1.00000  0.34730  1.53209  2.00000  1.53209  0.34730 -1.00000 -1.87939  0.00000     ... ... ..... ....... ......... ........... .............
E12     2.00000  1.44747  0.09516 -1.30972 -1.99094 -1.57211 -0.28463  1.16011  1.96386  1.68251  0.47152 -1.00000 -1.91899 -1.77767 -0.65414  0.83083  1.85674  1.85674  0.83083 -0.65414 -1.77767 -1.91899 -1.00000  0.47152  1.68251  1.96386  1.16011 -0.28463 -1.57211 -1.99094 -1.30972  0.09516  1.44747  2.00000  1.44747  0.09516 -1.30972 -1.99094 -1.57211 -0.28463  1.16011  1.96386  1.68251  0.47152 -1.00000 -1.91899 -1.77767 -0.65414  0.83083  1.85674  0.00000     ... ... ..... ....... ......... ........... .............
E13     2.00000  1.35702 -0.15850 -1.57211 -1.97488 -1.10784  0.47152  1.74770  1.90014  0.83083 -0.77269 -1.87939 -1.77767 -0.53295  1.05445  1.96386  1.61054  0.22168 -1.30972 -1.99899 -1.40295  0.09516  1.53209  1.98391  1.16011 -0.40961 -1.71597 -1.91899 -0.88813  0.71377  1.85674  1.80585  0.59384 -1.00000 -1.95086 -1.64735 -0.28463  1.26111  1.99597  1.44747 -0.03173 -1.49053 -1.99094 -1.21122  0.34730  1.68251  1.93590  0.94454 -0.65414 -1.83222  0.00000     ... ... ..... ....... ......... ........... .............
E14     2.00000  1.26111 -0.40961 -1.77767 -1.83222 -0.53295  1.16011  1.99597  1.35702 -0.28463 -1.71597 -1.87939 -0.65414  1.05445  1.98391  1.44747 -0.15850 -1.64735 -1.91899 -0.77269  0.94454  1.96386  1.53209 -0.03173 -1.57211 -1.95086 -0.88813  0.83083  1.93590  1.61054  0.09516 -1.49053 -1.97488 -1.00000  0.71377  1.90014  1.68251  0.22168 -1.40295 -1.99094 -1.10784  0.59384  1.85674  1.74770  0.34730 -1.30972 -1.99899 -1.21122  0.47152  1.80585  0.00000     ... ... ..... ....... ......... ........... .............
E15     2.00000  1.16011 -0.65414 -1.91899 -1.57211  0.09516  1.68251  1.85674  0.47152 -1.30972 -1.99094 -1.00000  0.83083  1.96386  1.44747 -0.28463 -1.77767 -1.77767 -0.28463  1.44747  1.96386  0.83083 -1.00000 -1.99094 -1.30972  0.47152  1.85674  1.68251  0.09516 -1.57211 -1.91899 -0.65414  1.16011  2.00000  1.16011 -0.65414 -1.91899 -1.57211  0.09516  1.68251  1.85674  0.47152 -1.30972 -1.99094 -1.00000  0.83083  1.96386  1.44747 -0.28463 -1.77767  0.00000     ... ... ..... ....... ......... ........... .............
E16     2.00000  1.05445 -0.88813 -1.99094 -1.21122  0.71377  1.96386  1.35702 -0.53295 -1.91899 -1.49053  0.34730  1.85674  1.61054 -0.15850 -1.77767 -1.71597 -0.03173  1.68251  1.80585  0.22168 -1.57211 -1.87939 -0.40961  1.44747  1.93590  0.59384 -1.30972 -1.97488 -0.77269  1.16011  1.99597  0.94454 -1.00000 -1.99899 -1.10784  0.83083  1.98391  1.26111 -0.65414 -1.95086 -1.40295  0.47152  1.90014  1.53209 -0.28463 -1.83222 -1.64735  0.09516  1.74770  0.00000     ... ... ..... ....... ......... ........... .............
E17     2.00000  0.94454 -1.10784 -1.99094 -0.77269  1.26111  1.96386  0.59384 -1.40295 -1.91899 -0.40961  1.53209  1.85674  0.22168 -1.64735 -1.77767 -0.03173  1.74770  1.68251 -0.15850 -1.83222 -1.57211  0.34730  1.90014  1.44747 -0.53295 -1.95086 -1.30972  0.71377  1.98391  1.16011 -0.88813 -1.99899 -1.00000  1.05445  1.99597  0.83083 -1.21122 -1.97488 -0.65414  1.35702  1.93590  0.47152 -1.49053 -1.87939 -0.28463  1.61054  1.80585  0.09516 -1.71597  0.00000     ... ... ..... ....... ......... ........... .............
E18     2.00000  0.83083 -1.30972 -1.91899 -0.28463  1.68251  1.68251 -0.28463 -1.91899 -1.30972  0.83083  2.00000  0.83083 -1.30972 -1.91899 -0.28463  1.68251  1.68251 -0.28463 -1.91899 -1.30972  0.83083  2.00000  0.83083 -1.30972 -1.91899 -0.28463  1.68251  1.68251 -0.28463 -1.91899 -1.30972  0.83083  2.00000  0.83083 -1.30972 -1.91899 -0.28463  1.68251  1.68251 -0.28463 -1.91899 -1.30972  0.83083  2.00000  0.83083 -1.30972 -1.91899 -0.28463  1.68251  0.00000     ... ... ..... ....... ......... ........... .............
E19     2.00000  0.71377 -1.49053 -1.77767  0.22168  1.93590  1.16011 -1.10784 -1.95086 -0.28463  1.74770  1.53209 -0.65414 -1.99899 -0.77269  1.44747  1.80585 -0.15850 -1.91899 -1.21122  1.05445  1.96386  0.34730 -1.71597 -1.57211  0.59384  1.99597  0.83083 -1.40295 -1.83222  0.09516  1.90014  1.26111 -1.00000 -1.97488 -0.40961  1.68251  1.61054 -0.53295 -1.99094 -0.88813  1.35702  1.85674 -0.03173 -1.87939 -1.30972  0.94454  1.98391  0.47152 -1.64735  0.00000     ... ... ..... ....... ......... ........... .............
E20     2.00000  0.59384 -1.64735 -1.57211  0.71377  1.99597  0.47152 -1.71597 -1.49053  0.83083  1.98391  0.34730 -1.77767 -1.40295  0.94454  1.96386  0.22168 -1.83222 -1.30972  1.05445  1.93590  0.09516 -1.87939 -1.21122  1.16011  1.90014 -0.03173 -1.91899 -1.10784  1.26111  1.85674 -0.15850 -1.95086 -1.00000  1.35702  1.80585 -0.28463 -1.97488 -0.88813  1.44747  1.74770 -0.40961 -1.99094 -0.77269  1.53209  1.68251 -0.53295 -1.99899 -0.65414  1.61054  0.00000     ... ... ..... ....... ......... ........... .............
E21     2.00000  0.47152 -1.77767 -1.30972  1.16011  1.85674 -0.28463 -1.99094 -0.65414  1.68251  1.44747 -1.00000 -1.91899  0.09516  1.96386  0.83083 -1.57211 -1.57211  0.83083  1.96386  0.09516 -1.91899 -1.00000  1.44747  1.68251 -0.65414 -1.99094 -0.28463  1.85674  1.16011 -1.30972 -1.77767  0.47152  2.00000  0.47152 -1.77767 -1.30972  1.16011  1.85674 -0.28463 -1.99094 -0.65414  1.68251  1.44747 -1.00000 -1.91899  0.09516  1.96386  0.83083 -1.57211  0.00000     ... ... ..... ....... ......... ........... .............
E22     2.00000  0.34730 -1.87939 -1.00000  1.53209  1.53209 -1.00000 -1.87939  0.34730  2.00000  0.34730 -1.87939 -1.00000  1.53209  1.53209 -1.00000 -1.87939  0.34730  2.00000  0.34730 -1.87939 -1.00000  1.53209  1.53209 -1.00000 -1.87939  0.34730  2.00000  0.34730 -1.87939 -1.00000  1.53209  1.53209 -1.00000 -1.87939  0.34730  2.00000  0.34730 -1.87939 -1.00000  1.53209  1.53209 -1.00000 -1.87939  0.34730  2.00000  0.34730 -1.87939 -1.00000  1.53209  0.00000     ... ... ..... ....... ......... ........... .............
E23     2.00000  0.22168 -1.95086 -0.65414  1.80585  1.05445 -1.57211 -1.40295  1.26111  1.68251 -0.88813 -1.87939  0.47152  1.98391 -0.03173 -1.99094 -0.40961  1.90014  0.83083 -1.71597 -1.21122  1.44747  1.53209 -1.10784 -1.77767  0.71377  1.93590 -0.28463 -1.99899 -0.15850  1.96386  0.59384 -1.83222 -1.00000  1.61054  1.35702 -1.30972 -1.64735  0.94454  1.85674 -0.53295 -1.97488  0.09516  1.99597  0.34730 -1.91899 -0.77269  1.74770  1.16011 -1.49053  0.00000     ... ... ..... ....... ......... ........... .............
E24     2.00000  0.09516 -1.99094 -0.28463  1.96386  0.47152 -1.91899 -0.65414  1.85674  0.83083 -1.77767 -1.00000  1.68251  1.16011 -1.57211 -1.30972  1.44747  1.44747 -1.30972 -1.57211  1.16011  1.68251 -1.00000 -1.77767  0.83083  1.85674 -0.65414 -1.91899  0.47152  1.96386 -0.28463 -1.99094  0.09516  2.00000  0.09516 -1.99094 -0.28463  1.96386  0.47152 -1.91899 -0.65414  1.85674  0.83083 -1.77767 -1.00000  1.68251  1.16011 -1.57211 -1.30972  1.44747  0.00000     ... ... ..... ....... ......... ........... .............
E25     2.00000 -0.03173 -1.99899  0.09516  1.99597 -0.15850 -1.99094  0.22168  1.98391 -0.28463 -1.97488  0.34730  1.96386 -0.40961 -1.95086  0.47152  1.93590 -0.53295 -1.91899  0.59384  1.90014 -0.65414 -1.87939  0.71377  1.85674 -0.77269 -1.83222  0.83083  1.80585 -0.88813 -1.77767  0.94454  1.74770 -1.00000 -1.71597  1.05445  1.68251 -1.10784 -1.64735  1.16011  1.61054 -1.21122 -1.57211  1.26111  1.53209 -1.30972 -1.49053  1.35702  1.44747 -1.40295  0.00000     ... ... ..... ....... ......... ........... .............
E26     2.00000 -0.15850 -1.97488  0.47152  1.90014 -0.77269 -1.77767  1.05445  1.61054 -1.30972 -1.40295  1.53209  1.16011 -1.71597 -0.88813  1.85674  0.59384 -1.95086 -0.28463  1.99597 -0.03173 -1.99094  0.34730  1.93590 -0.65414 -1.83222  0.94454  1.68251 -1.21122 -1.49053  1.44747  1.26111 -1.64735 -1.00000  1.80585  0.71377 -1.91899 -0.40961  1.98391  0.09516 -1.99899  0.22168  1.96386 -0.53295 -1.87939  0.83083  1.74770 -1.10784 -1.57211  1.35702  0.00000     ... ... ..... ....... ......... ........... .............
E27     2.00000 -0.28463 -1.91899  0.83083  1.68251 -1.30972 -1.30972  1.68251  0.83083 -1.91899 -0.28463  2.00000 -0.28463 -1.91899  0.83083  1.68251 -1.30972 -1.30972  1.68251  0.83083 -1.91899 -0.28463  2.00000 -0.28463 -1.91899  0.83083  1.68251 -1.30972 -1.30972  1.68251  0.83083 -1.91899 -0.28463  2.00000 -0.28463 -1.91899  0.83083  1.68251 -1.30972 -1.30972  1.68251  0.83083 -1.91899 -0.28463  2.00000 -0.28463 -1.91899  0.83083  1.68251 -1.30972  0.00000     ... ... ..... ....... ......... ........... .............
E28     2.00000 -0.40961 -1.83222  1.16011  1.35702 -1.71597 -0.65414  1.98391 -0.15850 -1.91899  0.94454  1.53209 -1.57211 -0.88813  1.93590  0.09516 -1.97488  0.71377  1.68251 -1.40295 -1.10784  1.85674  0.34730 -1.99899  0.47152  1.80585 -1.21122 -1.30972  1.74770  0.59384 -1.99094  0.22168  1.90014 -1.00000 -1.49053  1.61054  0.83083 -1.95086 -0.03173  1.96386 -0.77269 -1.64735  1.44747  1.05445 -1.87939 -0.28463  1.99597 -0.53295 -1.77767  1.26111  0.00000     ... ... ..... ....... ......... ........... .............
E29     2.00000 -0.53295 -1.71597  1.44747  0.94454 -1.95086  0.09516  1.90014 -1.10784 -1.30972  1.80585  0.34730 -1.99094  0.71377  1.61054 -1.57211 -0.77269  1.98391 -0.28463 -1.83222  1.26111  1.16011 -1.87939 -0.15850  1.96386 -0.88813 -1.49053  1.68251  0.59384 -1.99899  0.47152  1.74770 -1.40295 -1.00000  1.93590 -0.03173 -1.91899  1.05445  1.35702 -1.77767 -0.40961  1.99597 -0.65414 -1.64735  1.53209  0.83083 -1.97488  0.22168  1.85674 -1.21122  0.00000     ... ... ..... ....... ......... ........... .............
E30     2.00000 -0.65414 -1.57211  1.68251  0.47152 -1.99094  0.83083  1.44747 -1.77767 -0.28463  1.96386 -1.00000 -1.30972  1.85674  0.09516 -1.91899  1.16011  1.16011 -1.91899  0.09516  1.85674 -1.30972 -1.00000  1.96386 -0.28463 -1.77767  1.44747  0.83083 -1.99094  0.47152  1.68251 -1.57211 -0.65414  2.00000 -0.65414 -1.57211  1.68251  0.47152 -1.99094  0.83083  1.44747 -1.77767 -0.28463  1.96386 -1.00000 -1.30972  1.85674  0.09516 -1.91899  1.16011  0.00000     ... ... ..... ....... ......... ........... .............
E31     2.00000 -0.77269 -1.40295  1.85674 -0.03173 -1.83222  1.44747  0.71377 -1.99899  0.83083  1.35702 -1.87939  0.09516  1.80585 -1.49053 -0.65414  1.99597 -0.88813 -1.30972  1.90014 -0.15850 -1.77767  1.53209  0.59384 -1.99094  0.94454  1.26111 -1.91899  0.22168  1.74770 -1.57211 -0.53295  1.98391 -1.00000 -1.21122  1.93590 -0.28463 -1.71597  1.61054  0.47152 -1.97488  1.05445  1.16011 -1.95086  0.34730  1.68251 -1.64735 -0.40961  1.96386 -1.10784  0.00000     ... ... ..... ....... ......... ........... .............
E32     2.00000 -0.88813 -1.21122  1.96386 -0.53295 -1.49053  1.85674 -0.15850 -1.71597  1.68251  0.22168 -1.87939  1.44747  0.59384 -1.97488  1.16011  0.94454 -1.99899  0.83083  1.26111 -1.95086  0.47152  1.53209 -1.83222  0.09516  1.74770 -1.64735 -0.28463  1.90014 -1.40295 -0.65414  1.98391 -1.10784 -1.00000  1.99597 -0.77269 -1.30972  1.93590 -0.40961 -1.57211  1.80585 -0.03173 -1.77767  1.61054  0.34730 -1.91899  1.35702  0.71377 -1.99094  1.05445  0.00000     ... ... ..... ....... ......... ........... .............
E33     2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000 -1.00000  2.00000 -1.00000  0.00000     ... ... ..... ....... ......... ........... .............
E34     2.00000 -1.10784 -0.77269  1.96386 -1.40295 -0.40961  1.85674 -1.64735 -0.03173  1.68251 -1.83222  0.34730  1.44747 -1.95086  0.71377  1.16011 -1.99899  1.05445  0.83083 -1.97488  1.35702  0.47152 -1.87939  1.61054  0.09516 -1.71597  1.80585 -0.28463 -1.49053  1.93590 -0.65414 -1.21122  1.99597 -1.00000 -0.88813  1.98391 -1.30972 -0.53295  1.90014 -1.57211 -0.15850  1.74770 -1.77767  0.22168  1.53209 -1.91899  0.59384  1.26111 -1.99094  0.94454  0.00000     ... ... ..... ....... ......... ........... .............
E35     2.00000 -1.21122 -0.53295  1.85674 -1.71597  0.22168  1.44747 -1.97488  0.94454  0.83083 -1.95086  1.53209  0.09516 -1.64735  1.90014 -0.65414 -1.10784  1.99597 -1.30972 -0.40961  1.80585 -1.77767  0.34730  1.35702 -1.99094  1.05445  0.71377 -1.91899  1.61054 -0.03173 -1.57211  1.93590 -0.77269 -1.00000  1.98391 -1.40295 -0.28463  1.74770 -1.83222  0.47152  1.26111 -1.99899  1.16011  0.59384 -1.87939  1.68251 -0.15850 -1.49053  1.96386 -0.88813  0.00000     ... ... ..... ....... ......... ........... .............
E36     2.00000 -1.30972 -0.28463  1.68251 -1.91899  0.83083  0.83083 -1.91899  1.68251 -0.28463 -1.30972  2.00000 -1.30972 -0.28463  1.68251 -1.91899  0.83083  0.83083 -1.91899  1.68251 -0.28463 -1.30972  2.00000 -1.30972 -0.28463  1.68251 -1.91899  0.83083  0.83083 -1.91899  1.68251 -0.28463 -1.30972  2.00000 -1.30972 -0.28463  1.68251 -1.91899  0.83083  0.83083 -1.91899  1.68251 -0.28463 -1.30972  2.00000 -1.30972 -0.28463  1.68251 -1.91899  0.83083  0.00000     ... ... ..... ....... ......... ........... .............
E37     2.00000 -1.40295 -0.03173  1.44747 -1.99899  1.35702  0.09516 -1.49053  1.99597 -1.30972 -0.15850  1.53209 -1.99094  1.26111  0.22168 -1.57211  1.98391 -1.21122 -0.28463  1.61054 -1.97488  1.16011  0.34730 -1.64735  1.96386 -1.10784 -0.40961  1.68251 -1.95086  1.05445  0.47152 -1.71597  1.93590 -1.00000 -0.53295  1.74770 -1.91899  0.94454  0.59384 -1.77767  1.90014 -0.88813 -0.65414  1.80585 -1.87939  0.83083  0.71377 -1.83222  1.85674 -0.77269  0.00000     ... ... ..... ....... ......... ........... .............
E38     2.00000 -1.49053  0.22168  1.16011 -1.95086  1.74770 -0.65414 -0.77269  1.80585 -1.91899  1.05445  0.34730 -1.57211  1.99597 -1.40295  0.09516  1.26111 -1.97488  1.68251 -0.53295 -0.88813  1.85674 -1.87939  0.94454  0.47152 -1.64735  1.98391 -1.30972 -0.03173  1.35702 -1.99094  1.61054 -0.40961 -1.00000  1.90014 -1.83222  0.83083  0.59384 -1.71597  1.96386 -1.21122 -0.15850  1.44747 -1.99899  1.53209 -0.28463 -1.10784  1.93590 -1.77767  0.71377  0.00000     ... ... ..... ....... ......... ........... .............
E39     2.00000 -1.57211  0.47152  0.83083 -1.77767  1.96386 -1.30972  0.09516  1.16011 -1.91899  1.85674 -1.00000 -0.28463  1.44747 -1.99094  1.68251 -0.65414 -0.65414  1.68251 -1.99094  1.44747 -0.28463 -1.00000  1.85674 -1.91899  1.16011  0.09516 -1.30972  1.96386 -1.77767  0.83083  0.47152 -1.57211  2.00000 -1.57211  0.47152  0.83083 -1.77767  1.96386 -1.30972  0.09516  1.16011 -1.91899  1.85674 -1.00000 -0.28463  1.44747 -1.99094  1.68251 -0.65414  0.00000     ... ... ..... ....... ......... ........... .............
E40     2.00000 -1.64735  0.71377  0.47152 -1.49053  1.98391 -1.77767  0.94454  0.22168 -1.30972  1.93590 -1.87939  1.16011 -0.03173 -1.10784  1.85674 -1.95086  1.35702 -0.28463 -0.88813  1.74770 -1.99094  1.53209 -0.53295 -0.65414  1.61054 -1.99899  1.68251 -0.77269 -0.40961  1.44747 -1.97488  1.80585 -1.00000 -0.15850  1.26111 -1.91899  1.90014 -1.21122  0.09516  1.05445 -1.83222  1.96386 -1.40295  0.34730  0.83083 -1.71597  1.99597 -1.57211  0.59384  0.00000     ... ... ..... ....... ......... ........... .............
E41     2.00000 -1.71597  0.94454  0.09516 -1.10784  1.80585 -1.99094  1.61054 -0.77269 -0.28463  1.26111 -1.87939  1.96386 -1.49053  0.59384  0.47152 -1.40295  1.93590 -1.91899  1.35702 -0.40961 -0.65414  1.53209 -1.97488  1.85674 -1.21122  0.22168  0.83083 -1.64735  1.99597 -1.77767  1.05445 -0.03173 -1.00000  1.74770 -1.99899  1.68251 -0.88813 -0.15850  1.16011 -1.83222  1.98391 -1.57211  0.71377  0.34730 -1.30972  1.90014 -1.95086  1.44747 -0.53295  0.00000     ... ... ..... ....... ......... ........... .............
E42     2.00000 -1.77767  1.16011 -0.28463 -0.65414  1.44747 -1.91899  1.96386 -1.57211  0.83083  0.09516 -1.00000  1.68251 -1.99094  1.85674 -1.30972  0.47152  0.47152 -1.30972  1.85674 -1.99094  1.68251 -1.00000  0.09516  0.83083 -1.57211  1.96386 -1.91899  1.44747 -0.65414 -0.28463  1.16011 -1.77767  2.00000 -1.77767  1.16011 -0.28463 -0.65414  1.44747 -1.91899  1.96386 -1.57211  0.83083  0.09516 -1.00000  1.68251 -1.99094  1.85674 -1.30972  0.47152  0.00000     ... ... ..... ....... ......... ........... .............
E43     2.00000 -1.83222  1.35702 -0.65414 -0.15850  0.94454 -1.57211  1.93590 -1.97488  1.68251 -1.10784  0.34730  0.47152 -1.21122  1.74770 -1.99094  1.90014 -1.49053  0.83083 -0.03173 -0.77269  1.44747 -1.87939  1.99597 -1.77767  1.26111 -0.53295 -0.28463  1.05445 -1.64735  1.96386 -1.95086  1.61054 -1.00000  0.22168  0.59384 -1.30972  1.80585 -1.99899  1.85674 -1.40295  0.71377  0.09516 -0.88813  1.53209 -1.91899  1.98391 -1.71597  1.16011 -0.40961  0.00000     ... ... ..... ....... ......... ........... .............
E44     2.00000 -1.87939  1.53209 -1.00000  0.34730  0.34730 -1.00000  1.53209 -1.87939  2.00000 -1.87939  1.53209 -1.00000  0.34730  0.34730 -1.00000  1.53209 -1.87939  2.00000 -1.87939  1.53209 -1.00000  0.34730  0.34730 -1.00000  1.53209 -1.87939  2.00000 -1.87939  1.53209 -1.00000  0.34730  0.34730 -1.00000  1.53209 -1.87939  2.00000 -1.87939  1.53209 -1.00000  0.34730  0.34730 -1.00000  1.53209 -1.87939  2.00000 -1.87939  1.53209 -1.00000  0.34730  0.00000     ... ... ..... ....... ......... ........... .............
E45     2.00000 -1.91899  1.68251 -1.30972  0.83083 -0.28463 -0.28463  0.83083 -1.30972  1.68251 -1.91899  2.00000 -1.91899  1.68251 -1.30972  0.83083 -0.28463 -0.28463  0.83083 -1.30972  1.68251 -1.91899  2.00000 -1.91899  1.68251 -1.30972  0.83083 -0.28463 -0.28463  0.83083 -1.30972  1.68251 -1.91899  2.00000 -1.91899  1.68251 -1.30972  0.83083 -0.28463 -0.28463  0.83083 -1.30972  1.68251 -1.91899  2.00000 -1.91899  1.68251 -1.30972  0.83083 -0.28463  0.00000     ... ... ..... ....... ......... ........... .............
E46     2.00000 -1.95086  1.80585 -1.57211  1.26111 -0.88813  0.47152 -0.03173 -0.40961  0.83083 -1.21122  1.53209 -1.77767  1.93590 -1.99899  1.96386 -1.83222  1.61054 -1.30972  0.94454 -0.53295  0.09516  0.34730 -0.77269  1.16011 -1.49053  1.74770 -1.91899  1.99597 -1.97488  1.85674 -1.64735  1.35702 -1.00000  0.59384 -0.15850 -0.28463  0.71377 -1.10784  1.44747 -1.71597  1.90014 -1.99094  1.98391 -1.87939  1.68251 -1.40295  1.05445 -0.65414  0.22168  0.00000     ... ... ..... ....... ......... ........... .............
E47     2.00000 -1.97488  1.90014 -1.77767  1.61054 -1.40295  1.16011 -0.88813  0.59384 -0.28463 -0.03173  0.34730 -0.65414  0.94454 -1.21122  1.44747 -1.64735  1.80585 -1.91899  1.98391 -1.99899  1.96386 -1.87939  1.74770 -1.57211  1.35702 -1.10784  0.83083 -0.53295  0.22168  0.09516 -0.40961  0.71377 -1.00000  1.26111 -1.49053  1.68251 -1.83222  1.93590 -1.99094  1.99597 -1.95086  1.85674 -1.71597  1.53209 -1.30972  1.05445 -0.77269  0.47152 -0.15850  0.00000     ... ... ..... ....... ......... ........... .............
E48     2.00000 -1.99094  1.96386 -1.91899  1.85674 -1.77767  1.68251 -1.57211  1.44747 -1.30972  1.16011 -1.00000  0.83083 -0.65414  0.47152 -0.28463  0.09516  0.09516 -0.28463  0.47152 -0.65414  0.83083 -1.00000  1.16011 -1.30972  1.44747 -1.57211  1.68251 -1.77767  1.85674 -1.91899  1.96386 -1.99094  2.00000 -1.99094  1.96386 -1.91899  1.85674 -1.77767  1.68251 -1.57211  1.44747 -1.30972  1.16011 -1.00000  0.83083 -0.65414  0.47152 -0.28463  0.09516  0.00000     ... ... ..... ....... ......... ........... .............
E49     2.00000 -1.99899  1.99597 -1.99094  1.98391 -1.97488  1.96386 -1.95086  1.93590 -1.91899  1.90014 -1.87939  1.85674 -1.83222  1.80585 -1.77767  1.74770 -1.71597  1.68251 -1.64735  1.61054 -1.57211  1.53209 -1.49053  1.44747 -1.40295  1.35702 -1.30972  1.26111 -1.21122  1.16011 -1.10784  1.05445 -1.00000  0.94454 -0.88813  0.83083 -0.77269  0.71377 -0.65414  0.59384 -0.53295  0.47152 -0.40961  0.34730 -0.28463  0.22168 -0.15850  0.09516 -0.03173  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.995973352944 = 2*cos(2*π/99)
                               1.983909625662 = 2*cos(4*π/99)
                               1.963857394525 = 2*cos(6*π/99) = 2*cos(2*π/33)
                               1.935897402793 = 2*cos(8*π/99)
                               1.900142235482 = 2*cos(10*π/99)
                               1.856735866032 = 2*cos(12*π/99) = 2*cos(4*π/33)
                               1.805853076573 = 2*cos(14*π/99)
                               1.747698754140 = 2*cos(16*π/99)
                               1.682507065662 = 2*cos(18*π/99) = 2*cos(2*π/11)
                               1.610540515062 = 2*cos(20*π/99)
                               1.532088886238 = 2*cos(22*π/99) = 2*cos(2*π/9)
                               1.447468076210 = 2*cos(24*π/99) = 2*cos(8*π/33)
                               1.357018823114 = 2*cos(26*π/99)
                               1.261105334169 = 2*cos(28*π/99)
                               1.160113819142 = 2*cos(30*π/99) = 2*cos(10*π/33)
                               1.054450935221 = 2*cos(32*π/99)
                               0.944542149545 = 2*cos(34*π/99)
                               0.830830026004 = 2*cos(36*π/99) = 2*cos(4*π/11)
                               0.713772443184 = 2*cos(38*π/99)
                               0.593840750657 = 2*cos(40*π/99)
                               0.471517871019 = 2*cos(42*π/99) = 2*cos(14*π/33)
                               0.347296355334 = 2*cos(44*π/99) = 2*cos(4*π/9)
                               0.221676399802 = 2*cos(46*π/99)
                               0.095163831647 = 2*cos(48*π/99) = 2*cos(16*π/33)
                              -0.031731927670 = 2*cos(50*π/99)
                              -0.158499913714 = 2*cos(52*π/99)
                              -0.284629676547 = 2*cos(54*π/99) = 2*cos(6*π/11)
                              -0.409613336130 = 2*cos(56*π/99)
                              -0.532947627380 = 2*cos(58*π/99)
                              -0.654135926635 = 2*cos(60*π/99) = 2*cos(20*π/33)
                              -0.772690251386 = 2*cos(62*π/99)
                              -0.888133225212 = 2*cos(64*π/99)
                              -1.107840127732 = 2*cos(68*π/99)
                              -1.211219374275 = 2*cos(70*π/99)
                              -1.309721467891 = 2*cos(72*π/99) = 2*cos(8*π/11)
                              -1.402949775413 = 2*cos(74*π/99)
                              -1.490528899352 = 2*cos(76*π/99)
                              -1.572106189486 = 2*cos(78*π/99) = 2*cos(26*π/33)
                              -1.647353162860 = 2*cos(80*π/99)
                              -1.715966826470 = 2*cos(82*π/99)
                              -1.777670897310 = 2*cos(84*π/99) = 2*cos(28*π/33)
                              -1.832216914864 = 2*cos(86*π/99)
                              -1.879385241572 = 2*cos(88*π/99) = 2*cos(8*π/9)
                              -1.918985947229 = 2*cos(90*π/99) = 2*cos(10*π/11)
                              -1.950859573771 = 2*cos(92*π/99)
                              -1.974877777353 = 2*cos(94*π/99)
                              -1.990943845146 = 2*cos(96*π/99) = 2*cos(32*π/33)
                              -1.998993084766 = 2*cos(98*π/99)



 Symmetry of Rotations and Cartesian products

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

 Notes:

    α  The order of the D99 point group is 198, and the order of the principal axis (C99) is 99. The group has 51 irreducible representations.

    β  The D99 point group is isomorphic to C99v.

    γ  The D99 point group is generated by two symmetry elements, C99 and a perpendicular C2.
       Also, the group may be generated from two C2 axes (some pairs will yield smaller groups, though; choosing a minimum angle is safe).

    δ  The 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.

    ε  The lowest nonvanishing multipole moment in D99 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  The point group is chiral, as it does not contain any mirroring operation.

    θ  Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6.
       These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1.
       All characters are algebraic integers of a degree much less than half the order of the principal axis.
       For this group, however, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the D99 point group was created by Gernot Katzer.

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