Character table for the D56h point group

D56h     E        2 C56    2 C28    2 C56^3  2 C14    2 C56^5  2 C28^3  2 C8     2 C7     2 C56^9  2 C28^5  2 C56^11 2 C14^3  2 C56^13 2 C4     2 C56^15 2 C7^2   2 C56^17 2 C28^9  2 C56^19 2 C14^5  2 C8^3   2 C28^11 2 C56^23 2 C7^3   2 C56^25 2 C28^13 2 C56^27 C2       28 C2'   28 C2"   i        2 S56    2 S28    2 S56^3  2 S14    2 S56^5  2 S28^3  2 S8     2 S7     2 S56^9  2 S28^5  2 S56^11 2 S14^3  2 S56^13 2 S4     2 S56^15 2 S7^2   2 S56^17 2 S28^9  2 S56^19 2 S14^5  2 S8^3   2 S28^11 2 S56^23 2 S7^3   2 S56^25 2 S28^13 2 S56^27 sh       28 sv    28 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     ... ... ....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     ..T ... ..... ....... ......... ........... .............
B1g     1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000  1.00000 -1.00000     ... ... ..... ....... ......... ........... .............
B2g     1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000     ... ... ..... ....... ......... ........... .............
E1g     2.00000  1.98742  1.94986  1.88777  1.80194  1.69345  1.56366  1.41421  1.24698  1.06406  0.86777  0.66056  0.44504  0.22393  0.00000 -0.22393 -0.44504 -0.66056 -0.86777 -1.06406 -1.24698 -1.41421 -1.56366 -1.69345 -1.80194 -1.88777 -1.94986 -1.98742 -2.00000  0.00000  0.00000  2.00000 -1.98742 -1.94986 -1.88777 -1.80194 -1.69345 -1.56366 -1.41421 -1.24698 -1.06406 -0.86777 -0.66056 -0.44504 -0.22393  0.00000  0.22393  0.44504  0.66056  0.86777  1.06406  1.24698  1.41421  1.56366  1.69345  1.80194  1.88777  1.94986  1.98742 -2.00000  0.00000  0.00000     TT. ... ..TT. ....... ......TT. ........... ..........TT.
E2g     2.00000  1.94986  1.80194  1.56366  1.24698  0.86777  0.44504  0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 -1.94986 -1.80194 -1.56366 -1.24698 -0.86777 -0.44504  0.00000  0.44504  0.86777  1.24698  1.56366  1.80194  1.94986  2.00000  0.00000  0.00000  2.00000  1.94986  1.80194  1.56366  1.24698  0.86777  0.44504  0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 -1.94986 -1.80194 -1.56366 -1.24698 -0.86777 -0.44504  0.00000  0.44504  0.86777  1.24698  1.56366  1.80194  1.94986  2.00000  0.00000  0.00000     ... ... TT... ....... ....TT... ........... ........TT...
E3g     2.00000  1.88777  1.56366  1.06406  0.44504 -0.22393 -0.86777 -1.41421 -1.80194 -1.98742 -1.94986 -1.69345 -1.24698 -0.66056  0.00000  0.66056  1.24698  1.69345  1.94986  1.98742  1.80194  1.41421  0.86777  0.22393 -0.44504 -1.06406 -1.56366 -1.88777 -2.00000  0.00000  0.00000  2.00000 -1.88777 -1.56366 -1.06406 -0.44504  0.22393  0.86777  1.41421  1.80194  1.98742  1.94986  1.69345  1.24698  0.66056  0.00000 -0.66056 -1.24698 -1.69345 -1.94986 -1.98742 -1.80194 -1.41421 -0.86777 -0.22393  0.44504  1.06406  1.56366  1.88777 -2.00000  0.00000  0.00000     ... ... ..... ....... ..TT..... ........... ......TT.....
E4g     2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  0.00000  0.00000  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  0.00000  0.00000     ... ... ..... ....... TT....... ........... ....TT.......
E5g     2.00000  1.69345  0.86777 -0.22393 -1.24698 -1.88777 -1.94986 -1.41421 -0.44504  0.66056  1.56366  1.98742  1.80194  1.06406  0.00000 -1.06406 -1.80194 -1.98742 -1.56366 -0.66056  0.44504  1.41421  1.94986  1.88777  1.24698  0.22393 -0.86777 -1.69345 -2.00000  0.00000  0.00000  2.00000 -1.69345 -0.86777  0.22393  1.24698  1.88777  1.94986  1.41421  0.44504 -0.66056 -1.56366 -1.98742 -1.80194 -1.06406  0.00000  1.06406  1.80194  1.98742  1.56366  0.66056 -0.44504 -1.41421 -1.94986 -1.88777 -1.24698 -0.22393  0.86777  1.69345 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... ..TT.........
E6g     2.00000  1.56366  0.44504 -0.86777 -1.80194 -1.94986 -1.24698  0.00000  1.24698  1.94986  1.80194  0.86777 -0.44504 -1.56366 -2.00000 -1.56366 -0.44504  0.86777  1.80194  1.94986  1.24698  0.00000 -1.24698 -1.94986 -1.80194 -0.86777  0.44504  1.56366  2.00000  0.00000  0.00000  2.00000  1.56366  0.44504 -0.86777 -1.80194 -1.94986 -1.24698  0.00000  1.24698  1.94986  1.80194  0.86777 -0.44504 -1.56366 -2.00000 -1.56366 -0.44504  0.86777  1.80194  1.94986  1.24698  0.00000 -1.24698 -1.94986 -1.80194 -0.86777  0.44504  1.56366  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... TT...........
E7g     2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000  0.00000  0.00000  2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E8g     2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  0.00000  0.00000  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E9g     2.00000  1.06406 -0.86777 -1.98742 -1.24698  0.66056  1.94986  1.41421 -0.44504 -1.88777 -1.56366  0.22393  1.80194  1.69345  0.00000 -1.69345 -1.80194 -0.22393  1.56366  1.88777  0.44504 -1.41421 -1.94986 -0.66056  1.24698  1.98742  0.86777 -1.06406 -2.00000  0.00000  0.00000  2.00000 -1.06406  0.86777  1.98742  1.24698 -0.66056 -1.94986 -1.41421  0.44504  1.88777  1.56366 -0.22393 -1.80194 -1.69345  0.00000  1.69345  1.80194  0.22393 -1.56366 -1.88777 -0.44504  1.41421  1.94986  0.66056 -1.24698 -1.98742 -0.86777  1.06406 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E10g    2.00000  0.86777 -1.24698 -1.94986 -0.44504  1.56366  1.80194  0.00000 -1.80194 -1.56366  0.44504  1.94986  1.24698 -0.86777 -2.00000 -0.86777  1.24698  1.94986  0.44504 -1.56366 -1.80194  0.00000  1.80194  1.56366 -0.44504 -1.94986 -1.24698  0.86777  2.00000  0.00000  0.00000  2.00000  0.86777 -1.24698 -1.94986 -0.44504  1.56366  1.80194  0.00000 -1.80194 -1.56366  0.44504  1.94986  1.24698 -0.86777 -2.00000 -0.86777  1.24698  1.94986  0.44504 -1.56366 -1.80194  0.00000  1.80194  1.56366 -0.44504 -1.94986 -1.24698  0.86777  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E11g    2.00000  0.66056 -1.56366 -1.69345  0.44504  1.98742  0.86777 -1.41421 -1.80194  0.22393  1.94986  1.06406 -1.24698 -1.88777  0.00000  1.88777  1.24698 -1.06406 -1.94986 -0.22393  1.80194  1.41421 -0.86777 -1.98742 -0.44504  1.69345  1.56366 -0.66056 -2.00000  0.00000  0.00000  2.00000 -0.66056  1.56366  1.69345 -0.44504 -1.98742 -0.86777  1.41421  1.80194 -0.22393 -1.94986 -1.06406  1.24698  1.88777  0.00000 -1.88777 -1.24698  1.06406  1.94986  0.22393 -1.80194 -1.41421  0.86777  1.98742  0.44504 -1.69345 -1.56366  0.66056 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E12g    2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.00000  0.00000  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E13g    2.00000  0.22393 -1.94986 -0.66056  1.80194  1.06406 -1.56366 -1.41421  1.24698  1.69345 -0.86777 -1.88777  0.44504  1.98742  0.00000 -1.98742 -0.44504  1.88777  0.86777 -1.69345 -1.24698  1.41421  1.56366 -1.06406 -1.80194  0.66056  1.94986 -0.22393 -2.00000  0.00000  0.00000  2.00000 -0.22393  1.94986  0.66056 -1.80194 -1.06406  1.56366  1.41421 -1.24698 -1.69345  0.86777  1.88777 -0.44504 -1.98742  0.00000  1.98742  0.44504 -1.88777 -0.86777  1.69345  1.24698 -1.41421 -1.56366  1.06406  1.80194 -0.66056 -1.94986  0.22393 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E14g    2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E15g    2.00000 -0.22393 -1.94986  0.66056  1.80194 -1.06406 -1.56366  1.41421  1.24698 -1.69345 -0.86777  1.88777  0.44504 -1.98742  0.00000  1.98742 -0.44504 -1.88777  0.86777  1.69345 -1.24698 -1.41421  1.56366  1.06406 -1.80194 -0.66056  1.94986  0.22393 -2.00000  0.00000  0.00000  2.00000  0.22393  1.94986 -0.66056 -1.80194  1.06406  1.56366 -1.41421 -1.24698  1.69345  0.86777 -1.88777 -0.44504  1.98742  0.00000 -1.98742  0.44504  1.88777 -0.86777 -1.69345  1.24698  1.41421 -1.56366 -1.06406  1.80194  0.66056 -1.94986 -0.22393 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E16g    2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000  0.00000  0.00000  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E17g    2.00000 -0.66056 -1.56366  1.69345  0.44504 -1.98742  0.86777  1.41421 -1.80194 -0.22393  1.94986 -1.06406 -1.24698  1.88777  0.00000 -1.88777  1.24698  1.06406 -1.94986  0.22393  1.80194 -1.41421 -0.86777  1.98742 -0.44504 -1.69345  1.56366  0.66056 -2.00000  0.00000  0.00000  2.00000  0.66056  1.56366 -1.69345 -0.44504  1.98742 -0.86777 -1.41421  1.80194  0.22393 -1.94986  1.06406  1.24698 -1.88777  0.00000  1.88777 -1.24698 -1.06406  1.94986 -0.22393 -1.80194  1.41421  0.86777 -1.98742  0.44504  1.69345 -1.56366 -0.66056 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E18g    2.00000 -0.86777 -1.24698  1.94986 -0.44504 -1.56366  1.80194  0.00000 -1.80194  1.56366  0.44504 -1.94986  1.24698  0.86777 -2.00000  0.86777  1.24698 -1.94986  0.44504  1.56366 -1.80194  0.00000  1.80194 -1.56366 -0.44504  1.94986 -1.24698 -0.86777  2.00000  0.00000  0.00000  2.00000 -0.86777 -1.24698  1.94986 -0.44504 -1.56366  1.80194  0.00000 -1.80194  1.56366  0.44504 -1.94986  1.24698  0.86777 -2.00000  0.86777  1.24698 -1.94986  0.44504  1.56366 -1.80194  0.00000  1.80194 -1.56366 -0.44504  1.94986 -1.24698 -0.86777  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E19g    2.00000 -1.06406 -0.86777  1.98742 -1.24698 -0.66056  1.94986 -1.41421 -0.44504  1.88777 -1.56366 -0.22393  1.80194 -1.69345  0.00000  1.69345 -1.80194  0.22393  1.56366 -1.88777  0.44504  1.41421 -1.94986  0.66056  1.24698 -1.98742  0.86777  1.06406 -2.00000  0.00000  0.00000  2.00000  1.06406  0.86777 -1.98742  1.24698  0.66056 -1.94986  1.41421  0.44504 -1.88777  1.56366  0.22393 -1.80194  1.69345  0.00000 -1.69345  1.80194 -0.22393 -1.56366  1.88777 -0.44504 -1.41421  1.94986 -0.66056 -1.24698  1.98742 -0.86777 -1.06406 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E20g    2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000  0.00000  0.00000  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E21g    2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  0.00000  0.00000  2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E22g    2.00000 -1.56366  0.44504  0.86777 -1.80194  1.94986 -1.24698  0.00000  1.24698 -1.94986  1.80194 -0.86777 -0.44504  1.56366 -2.00000  1.56366 -0.44504 -0.86777  1.80194 -1.94986  1.24698  0.00000 -1.24698  1.94986 -1.80194  0.86777  0.44504 -1.56366  2.00000  0.00000  0.00000  2.00000 -1.56366  0.44504  0.86777 -1.80194  1.94986 -1.24698  0.00000  1.24698 -1.94986  1.80194 -0.86777 -0.44504  1.56366 -2.00000  1.56366 -0.44504 -0.86777  1.80194 -1.94986  1.24698  0.00000 -1.24698  1.94986 -1.80194  0.86777  0.44504 -1.56366  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E23g    2.00000 -1.69345  0.86777  0.22393 -1.24698  1.88777 -1.94986  1.41421 -0.44504 -0.66056  1.56366 -1.98742  1.80194 -1.06406  0.00000  1.06406 -1.80194  1.98742 -1.56366  0.66056  0.44504 -1.41421  1.94986 -1.88777  1.24698 -0.22393 -0.86777  1.69345 -2.00000  0.00000  0.00000  2.00000  1.69345 -0.86777 -0.22393  1.24698 -1.88777  1.94986 -1.41421  0.44504  0.66056 -1.56366  1.98742 -1.80194  1.06406  0.00000 -1.06406  1.80194 -1.98742  1.56366 -0.66056 -0.44504  1.41421 -1.94986  1.88777 -1.24698  0.22393  0.86777 -1.69345 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E24g    2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000  0.00000  0.00000  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E25g    2.00000 -1.88777  1.56366 -1.06406  0.44504  0.22393 -0.86777  1.41421 -1.80194  1.98742 -1.94986  1.69345 -1.24698  0.66056  0.00000 -0.66056  1.24698 -1.69345  1.94986 -1.98742  1.80194 -1.41421  0.86777 -0.22393 -0.44504  1.06406 -1.56366  1.88777 -2.00000  0.00000  0.00000  2.00000  1.88777 -1.56366  1.06406 -0.44504 -0.22393  0.86777 -1.41421  1.80194 -1.98742  1.94986 -1.69345  1.24698 -0.66056  0.00000  0.66056 -1.24698  1.69345 -1.94986  1.98742 -1.80194  1.41421 -0.86777  0.22393  0.44504 -1.06406  1.56366 -1.88777 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E26g    2.00000 -1.94986  1.80194 -1.56366  1.24698 -0.86777  0.44504  0.00000 -0.44504  0.86777 -1.24698  1.56366 -1.80194  1.94986 -2.00000  1.94986 -1.80194  1.56366 -1.24698  0.86777 -0.44504  0.00000  0.44504 -0.86777  1.24698 -1.56366  1.80194 -1.94986  2.00000  0.00000  0.00000  2.00000 -1.94986  1.80194 -1.56366  1.24698 -0.86777  0.44504  0.00000 -0.44504  0.86777 -1.24698  1.56366 -1.80194  1.94986 -2.00000  1.94986 -1.80194  1.56366 -1.24698  0.86777 -0.44504  0.00000  0.44504 -0.86777  1.24698 -1.56366  1.80194 -1.94986  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E27g    2.00000 -1.98742  1.94986 -1.88777  1.80194 -1.69345  1.56366 -1.41421  1.24698 -1.06406  0.86777 -0.66056  0.44504 -0.22393  0.00000  0.22393 -0.44504  0.66056 -0.86777  1.06406 -1.24698  1.41421 -1.56366  1.69345 -1.80194  1.88777 -1.94986  1.98742 -2.00000  0.00000  0.00000  2.00000  1.98742 -1.94986  1.88777 -1.80194  1.69345 -1.56366  1.41421 -1.24698  1.06406 -0.86777  0.66056 -0.44504  0.22393  0.00000 -0.22393  0.44504 -0.66056  0.86777 -1.06406  1.24698 -1.41421  1.56366 -1.69345  1.80194 -1.88777  1.94986 -1.98742 -2.00000  0.00000  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     ... ... ..... ....... ......... ........... .............
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     ... ..T ..... ......T ......... ..........T .............
B1u     1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000  1.00000 -1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000 -1.00000  1.00000     ... ... ..... ....... ......... ........... .............
B2u     1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000     ... ... ..... ....... ......... ........... .............
E1u     2.00000  1.98742  1.94986  1.88777  1.80194  1.69345  1.56366  1.41421  1.24698  1.06406  0.86777  0.66056  0.44504  0.22393  0.00000 -0.22393 -0.44504 -0.66056 -0.86777 -1.06406 -1.24698 -1.41421 -1.56366 -1.69345 -1.80194 -1.88777 -1.94986 -1.98742 -2.00000  0.00000  0.00000 -2.00000  1.98742  1.94986  1.88777  1.80194  1.69345  1.56366  1.41421  1.24698  1.06406  0.86777  0.66056  0.44504  0.22393  0.00000 -0.22393 -0.44504 -0.66056 -0.86777 -1.06406 -1.24698 -1.41421 -1.56366 -1.69345 -1.80194 -1.88777 -1.94986 -1.98742  2.00000  0.00000  0.00000     ... TT. ..... ....TT. ......... ........TT. .............
E2u     2.00000  1.94986  1.80194  1.56366  1.24698  0.86777  0.44504  0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 -1.94986 -1.80194 -1.56366 -1.24698 -0.86777 -0.44504  0.00000  0.44504  0.86777  1.24698  1.56366  1.80194  1.94986  2.00000  0.00000  0.00000 -2.00000 -1.94986 -1.80194 -1.56366 -1.24698 -0.86777 -0.44504  0.00000  0.44504  0.86777  1.24698  1.56366  1.80194  1.94986  2.00000  1.94986  1.80194  1.56366  1.24698  0.86777  0.44504  0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000  0.00000  0.00000     ... ... ..... ..TT... ......... ......TT... .............
E3u     2.00000  1.88777  1.56366  1.06406  0.44504 -0.22393 -0.86777 -1.41421 -1.80194 -1.98742 -1.94986 -1.69345 -1.24698 -0.66056  0.00000  0.66056  1.24698  1.69345  1.94986  1.98742  1.80194  1.41421  0.86777  0.22393 -0.44504 -1.06406 -1.56366 -1.88777 -2.00000  0.00000  0.00000 -2.00000  1.88777  1.56366  1.06406  0.44504 -0.22393 -0.86777 -1.41421 -1.80194 -1.98742 -1.94986 -1.69345 -1.24698 -0.66056  0.00000  0.66056  1.24698  1.69345  1.94986  1.98742  1.80194  1.41421  0.86777  0.22393 -0.44504 -1.06406 -1.56366 -1.88777  2.00000  0.00000  0.00000     ... ... ..... TT..... ......... ....TT..... .............
E4u     2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  0.00000  0.00000 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ..TT....... .............
E5u     2.00000  1.69345  0.86777 -0.22393 -1.24698 -1.88777 -1.94986 -1.41421 -0.44504  0.66056  1.56366  1.98742  1.80194  1.06406  0.00000 -1.06406 -1.80194 -1.98742 -1.56366 -0.66056  0.44504  1.41421  1.94986  1.88777  1.24698  0.22393 -0.86777 -1.69345 -2.00000  0.00000  0.00000 -2.00000  1.69345  0.86777 -0.22393 -1.24698 -1.88777 -1.94986 -1.41421 -0.44504  0.66056  1.56366  1.98742  1.80194  1.06406  0.00000 -1.06406 -1.80194 -1.98742 -1.56366 -0.66056  0.44504  1.41421  1.94986  1.88777  1.24698  0.22393 -0.86777 -1.69345  2.00000  0.00000  0.00000     ... ... ..... ....... ......... TT......... .............
E6u     2.00000  1.56366  0.44504 -0.86777 -1.80194 -1.94986 -1.24698  0.00000  1.24698  1.94986  1.80194  0.86777 -0.44504 -1.56366 -2.00000 -1.56366 -0.44504  0.86777  1.80194  1.94986  1.24698  0.00000 -1.24698 -1.94986 -1.80194 -0.86777  0.44504  1.56366  2.00000  0.00000  0.00000 -2.00000 -1.56366 -0.44504  0.86777  1.80194  1.94986  1.24698  0.00000 -1.24698 -1.94986 -1.80194 -0.86777  0.44504  1.56366  2.00000  1.56366  0.44504 -0.86777 -1.80194 -1.94986 -1.24698  0.00000  1.24698  1.94986  1.80194  0.86777 -0.44504 -1.56366 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E7u     2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000  0.00000  0.00000 -2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421 -2.00000 -1.41421  0.00000  1.41421  2.00000  1.41421  0.00000 -1.41421  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E8u     2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  0.00000  0.00000 -2.00000 -1.24698  0.44504  1.80194  1.80194  0.44504 -1.24698 -2.00000 -1.24698  0.44504  1.80194  1.80194  0.44504 -1.24698 -2.00000 -1.24698  0.44504  1.80194  1.80194  0.44504 -1.24698 -2.00000 -1.24698  0.44504  1.80194  1.80194  0.44504 -1.24698 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E9u     2.00000  1.06406 -0.86777 -1.98742 -1.24698  0.66056  1.94986  1.41421 -0.44504 -1.88777 -1.56366  0.22393  1.80194  1.69345  0.00000 -1.69345 -1.80194 -0.22393  1.56366  1.88777  0.44504 -1.41421 -1.94986 -0.66056  1.24698  1.98742  0.86777 -1.06406 -2.00000  0.00000  0.00000 -2.00000  1.06406 -0.86777 -1.98742 -1.24698  0.66056  1.94986  1.41421 -0.44504 -1.88777 -1.56366  0.22393  1.80194  1.69345  0.00000 -1.69345 -1.80194 -0.22393  1.56366  1.88777  0.44504 -1.41421 -1.94986 -0.66056  1.24698  1.98742  0.86777 -1.06406  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E10u    2.00000  0.86777 -1.24698 -1.94986 -0.44504  1.56366  1.80194  0.00000 -1.80194 -1.56366  0.44504  1.94986  1.24698 -0.86777 -2.00000 -0.86777  1.24698  1.94986  0.44504 -1.56366 -1.80194  0.00000  1.80194  1.56366 -0.44504 -1.94986 -1.24698  0.86777  2.00000  0.00000  0.00000 -2.00000 -0.86777  1.24698  1.94986  0.44504 -1.56366 -1.80194  0.00000  1.80194  1.56366 -0.44504 -1.94986 -1.24698  0.86777  2.00000  0.86777 -1.24698 -1.94986 -0.44504  1.56366  1.80194  0.00000 -1.80194 -1.56366  0.44504  1.94986  1.24698 -0.86777 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E11u    2.00000  0.66056 -1.56366 -1.69345  0.44504  1.98742  0.86777 -1.41421 -1.80194  0.22393  1.94986  1.06406 -1.24698 -1.88777  0.00000  1.88777  1.24698 -1.06406 -1.94986 -0.22393  1.80194  1.41421 -0.86777 -1.98742 -0.44504  1.69345  1.56366 -0.66056 -2.00000  0.00000  0.00000 -2.00000  0.66056 -1.56366 -1.69345  0.44504  1.98742  0.86777 -1.41421 -1.80194  0.22393  1.94986  1.06406 -1.24698 -1.88777  0.00000  1.88777  1.24698 -1.06406 -1.94986 -0.22393  1.80194  1.41421 -0.86777 -1.98742 -0.44504  1.69345  1.56366 -0.66056  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E12u    2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.00000  0.00000 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E13u    2.00000  0.22393 -1.94986 -0.66056  1.80194  1.06406 -1.56366 -1.41421  1.24698  1.69345 -0.86777 -1.88777  0.44504  1.98742  0.00000 -1.98742 -0.44504  1.88777  0.86777 -1.69345 -1.24698  1.41421  1.56366 -1.06406 -1.80194  0.66056  1.94986 -0.22393 -2.00000  0.00000  0.00000 -2.00000  0.22393 -1.94986 -0.66056  1.80194  1.06406 -1.56366 -1.41421  1.24698  1.69345 -0.86777 -1.88777  0.44504  1.98742  0.00000 -1.98742 -0.44504  1.88777  0.86777 -1.69345 -1.24698  1.41421  1.56366 -1.06406 -1.80194  0.66056  1.94986 -0.22393  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E14u    2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E15u    2.00000 -0.22393 -1.94986  0.66056  1.80194 -1.06406 -1.56366  1.41421  1.24698 -1.69345 -0.86777  1.88777  0.44504 -1.98742  0.00000  1.98742 -0.44504 -1.88777  0.86777  1.69345 -1.24698 -1.41421  1.56366  1.06406 -1.80194 -0.66056  1.94986  0.22393 -2.00000  0.00000  0.00000 -2.00000 -0.22393 -1.94986  0.66056  1.80194 -1.06406 -1.56366  1.41421  1.24698 -1.69345 -0.86777  1.88777  0.44504 -1.98742  0.00000  1.98742 -0.44504 -1.88777  0.86777  1.69345 -1.24698 -1.41421  1.56366  1.06406 -1.80194 -0.66056  1.94986  0.22393  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E16u    2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000  0.00000  0.00000 -2.00000  0.44504  1.80194 -1.24698 -1.24698  1.80194  0.44504 -2.00000  0.44504  1.80194 -1.24698 -1.24698  1.80194  0.44504 -2.00000  0.44504  1.80194 -1.24698 -1.24698  1.80194  0.44504 -2.00000  0.44504  1.80194 -1.24698 -1.24698  1.80194  0.44504 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E17u    2.00000 -0.66056 -1.56366  1.69345  0.44504 -1.98742  0.86777  1.41421 -1.80194 -0.22393  1.94986 -1.06406 -1.24698  1.88777  0.00000 -1.88777  1.24698  1.06406 -1.94986  0.22393  1.80194 -1.41421 -0.86777  1.98742 -0.44504 -1.69345  1.56366  0.66056 -2.00000  0.00000  0.00000 -2.00000 -0.66056 -1.56366  1.69345  0.44504 -1.98742  0.86777  1.41421 -1.80194 -0.22393  1.94986 -1.06406 -1.24698  1.88777  0.00000 -1.88777  1.24698  1.06406 -1.94986  0.22393  1.80194 -1.41421 -0.86777  1.98742 -0.44504 -1.69345  1.56366  0.66056  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E18u    2.00000 -0.86777 -1.24698  1.94986 -0.44504 -1.56366  1.80194  0.00000 -1.80194  1.56366  0.44504 -1.94986  1.24698  0.86777 -2.00000  0.86777  1.24698 -1.94986  0.44504  1.56366 -1.80194  0.00000  1.80194 -1.56366 -0.44504  1.94986 -1.24698 -0.86777  2.00000  0.00000  0.00000 -2.00000  0.86777  1.24698 -1.94986  0.44504  1.56366 -1.80194  0.00000  1.80194 -1.56366 -0.44504  1.94986 -1.24698 -0.86777  2.00000 -0.86777 -1.24698  1.94986 -0.44504 -1.56366  1.80194  0.00000 -1.80194  1.56366  0.44504 -1.94986  1.24698  0.86777 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E19u    2.00000 -1.06406 -0.86777  1.98742 -1.24698 -0.66056  1.94986 -1.41421 -0.44504  1.88777 -1.56366 -0.22393  1.80194 -1.69345  0.00000  1.69345 -1.80194  0.22393  1.56366 -1.88777  0.44504  1.41421 -1.94986  0.66056  1.24698 -1.98742  0.86777  1.06406 -2.00000  0.00000  0.00000 -2.00000 -1.06406 -0.86777  1.98742 -1.24698 -0.66056  1.94986 -1.41421 -0.44504  1.88777 -1.56366 -0.22393  1.80194 -1.69345  0.00000  1.69345 -1.80194  0.22393  1.56366 -1.88777  0.44504  1.41421 -1.94986  0.66056  1.24698 -1.98742  0.86777  1.06406  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E20u    2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000  0.00000  0.00000 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E21u    2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  0.00000  0.00000 -2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421 -2.00000  1.41421  0.00000 -1.41421  2.00000 -1.41421  0.00000  1.41421  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E22u    2.00000 -1.56366  0.44504  0.86777 -1.80194  1.94986 -1.24698  0.00000  1.24698 -1.94986  1.80194 -0.86777 -0.44504  1.56366 -2.00000  1.56366 -0.44504 -0.86777  1.80194 -1.94986  1.24698  0.00000 -1.24698  1.94986 -1.80194  0.86777  0.44504 -1.56366  2.00000  0.00000  0.00000 -2.00000  1.56366 -0.44504 -0.86777  1.80194 -1.94986  1.24698  0.00000 -1.24698  1.94986 -1.80194  0.86777  0.44504 -1.56366  2.00000 -1.56366  0.44504  0.86777 -1.80194  1.94986 -1.24698  0.00000  1.24698 -1.94986  1.80194 -0.86777 -0.44504  1.56366 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E23u    2.00000 -1.69345  0.86777  0.22393 -1.24698  1.88777 -1.94986  1.41421 -0.44504 -0.66056  1.56366 -1.98742  1.80194 -1.06406  0.00000  1.06406 -1.80194  1.98742 -1.56366  0.66056  0.44504 -1.41421  1.94986 -1.88777  1.24698 -0.22393 -0.86777  1.69345 -2.00000  0.00000  0.00000 -2.00000 -1.69345  0.86777  0.22393 -1.24698  1.88777 -1.94986  1.41421 -0.44504 -0.66056  1.56366 -1.98742  1.80194 -1.06406  0.00000  1.06406 -1.80194  1.98742 -1.56366  0.66056  0.44504 -1.41421  1.94986 -1.88777  1.24698 -0.22393 -0.86777  1.69345  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E24u    2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000  0.00000  0.00000 -2.00000  1.80194 -1.24698  0.44504  0.44504 -1.24698  1.80194 -2.00000  1.80194 -1.24698  0.44504  0.44504 -1.24698  1.80194 -2.00000  1.80194 -1.24698  0.44504  0.44504 -1.24698  1.80194 -2.00000  1.80194 -1.24698  0.44504  0.44504 -1.24698  1.80194 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E25u    2.00000 -1.88777  1.56366 -1.06406  0.44504  0.22393 -0.86777  1.41421 -1.80194  1.98742 -1.94986  1.69345 -1.24698  0.66056  0.00000 -0.66056  1.24698 -1.69345  1.94986 -1.98742  1.80194 -1.41421  0.86777 -0.22393 -0.44504  1.06406 -1.56366  1.88777 -2.00000  0.00000  0.00000 -2.00000 -1.88777  1.56366 -1.06406  0.44504  0.22393 -0.86777  1.41421 -1.80194  1.98742 -1.94986  1.69345 -1.24698  0.66056  0.00000 -0.66056  1.24698 -1.69345  1.94986 -1.98742  1.80194 -1.41421  0.86777 -0.22393 -0.44504  1.06406 -1.56366  1.88777  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E26u    2.00000 -1.94986  1.80194 -1.56366  1.24698 -0.86777  0.44504  0.00000 -0.44504  0.86777 -1.24698  1.56366 -1.80194  1.94986 -2.00000  1.94986 -1.80194  1.56366 -1.24698  0.86777 -0.44504  0.00000  0.44504 -0.86777  1.24698 -1.56366  1.80194 -1.94986  2.00000  0.00000  0.00000 -2.00000  1.94986 -1.80194  1.56366 -1.24698  0.86777 -0.44504  0.00000  0.44504 -0.86777  1.24698 -1.56366  1.80194 -1.94986  2.00000 -1.94986  1.80194 -1.56366  1.24698 -0.86777  0.44504  0.00000 -0.44504  0.86777 -1.24698  1.56366 -1.80194  1.94986 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E27u    2.00000 -1.98742  1.94986 -1.88777  1.80194 -1.69345  1.56366 -1.41421  1.24698 -1.06406  0.86777 -0.66056  0.44504 -0.22393  0.00000  0.22393 -0.44504  0.66056 -0.86777  1.06406 -1.24698  1.41421 -1.56366  1.69345 -1.80194  1.88777 -1.94986  1.98742 -2.00000  0.00000  0.00000 -2.00000 -1.98742  1.94986 -1.88777  1.80194 -1.69345  1.56366 -1.41421  1.24698 -1.06406  0.86777 -0.66056  0.44504 -0.22393  0.00000  0.22393 -0.44504  0.66056 -0.86777  1.06406 -1.24698  1.41421 -1.56366  1.69345 -1.80194  1.88777 -1.94986  1.98742  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.987424419786 = 2*cos(2*π/56) = 2*cos(π/28)
                               1.949855824364 = 2*cos(4*π/56) = 2*cos(π/14)
                               1.887766660617 = 2*cos(6*π/56) = 2*cos(3*π/28)
                               1.801937735805 = 2*cos(8*π/56) = 2*cos(π/7)
                               1.693448398457 = 2*cos(10*π/56) = 2*cos(5*π/28)
                               1.563662964936 = 2*cos(12*π/56) = 2*cos(3*π/14)
                               1.414213562373 = 2*cos(14*π/56) = 2*cos(π/4) = √2
                               1.246979603717 = 2*cos(16*π/56) = 2*cos(2*π/7)
                               1.064064153031 = 2*cos(18*π/56) = 2*cos(9*π/28)
                               0.867767478235 = 2*cos(20*π/56) = 2*cos(5*π/14)
                               0.660558123910 = 2*cos(22*π/56) = 2*cos(11*π/28)
                               0.445041867913 = 2*cos(24*π/56) = 2*cos(3*π/7)
                               0.223928952207 = 2*cos(26*π/56) = 2*cos(13*π/28)



 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 D56h point group is 224, and the order of the principal axis (C56) is 56. The group has 62 irreducible representations.

    β  The D56h point group is generated by three symmetry elements that are canonically chosen C56, C2 and i.
       Other choices include σh instead of i, or any of C2, σv or σd instead of C2. Also, some ternary combinations of C2, C2, σv and σd act as generators.
       Lastly, the S56 can be chosen, together with i or σh and any one of C2, C2, σv or σd.

    γ  There are two different sets of twofold symmetry axes perpendicular to the principal axis (z axis in standard orientation).
       By convention, the set denoted as C2 contains both the x and y axes.

    δ  There are two different sets of symmetry planes containing the principal axis (z axis in standard orientation).
       By convention, the set denoted as σv contains both the xz and the yz planes.

    ε  The lowest nonvanishing multipole moment in D56h 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.

    ι  The regular heptagon is the lowest regular polygon that cannot be constructed by compass and ruler alone, which has mystified
       mathematicians since antiquity. The reason for the inconstructibility of the heptagon is that cos(2π/7) has an algebraic degree of 3 and
       thus can not be represented by square roots and integer numbers. An algebraic representation becomes possible if cubic roots and complex numbers
       are used: 2*cos(2π/7) = (328+i*84*√3 + 328−i*84*√3 − 2)/6. This complex expression for a real value is hardly useful.
       Therefore, regular polygons of order 14,21,28,35,42 etc. are also inconstructible, and their cosines have no representation in real radicals.

This Character Table for the D56h point group was created by Gernot Katzer.

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