Character table for the D56d point group

D56d    E         2 S112    2 C56     2 S112^3  2 C28     2 S112^5  2 C56^3   2 S16     2 C14     2 S112^9  2 C56^5   2 S112^11 2 C28^3   2 S112^13 2 C8      2 S112^15 2 C7      2 S112^17 2 C56^9   2 S112^19 2 C28^5   2 S16^3   2 C56^11  2 S112^23 2 C14^3   2 S112^25 2 C56^13  2 S112^27 2 C4      2 S112^29 2 C56^15  2 S112^31 2 C7^2    2 S112^33 2 C56^17  2 S16^5   2 C28^9   2 S112^37 2 C56^19  2 S112^39 2 C14^5   2 S112^41 2 C8^3    2 S112^43 2 C28^11  2 S112^45 2 C56^23  2 S112^47 2 C7^3    2 S16^7   2 C56^25  2 S112^51 2 C28^13  2 S112^53 2 C56^27  2 S112^55 C2        56 C2'    56 sd        <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A1       1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   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   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000  -1.00000  -1.00000     ..T ... ..... ....... ......... ........... .............
B1       1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000   1.00000  -1.00000     ... ... ..... ....... ......... ........... .............
B2       1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -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 .............
E1       2.00000   1.99685   1.98742   1.97174   1.94986   1.92183   1.88777   1.84776   1.80194   1.75045   1.69345   1.63112   1.56366   1.49128   1.41421   1.33269   1.24698   1.15734   1.06406   0.96744   0.86777   0.76537   0.66056   0.55367   0.44504   0.33501   0.22393   0.11214   0.00000  -0.11214  -0.22393  -0.33501  -0.44504  -0.55367  -0.66056  -0.76537  -0.86777  -0.96744  -1.06406  -1.15734  -1.24698  -1.33269  -1.41421  -1.49128  -1.56366  -1.63112  -1.69345  -1.75045  -1.80194  -1.84776  -1.88777  -1.92183  -1.94986  -1.97174  -1.98742  -1.99685  -2.00000   0.00000   0.00000     ... TT. ..... ....TT. ......... ........TT. .............
E2       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  -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...
E3       2.00000   1.97174   1.88777   1.75045   1.56366   1.33269   1.06406   0.76537   0.44504   0.11214  -0.22393  -0.55367  -0.86777  -1.15734  -1.41421  -1.63112  -1.80194  -1.92183  -1.98742  -1.99685  -1.94986  -1.84776  -1.69345  -1.49128  -1.24698  -0.96744  -0.66056  -0.33501   0.00000   0.33501   0.66056   0.96744   1.24698   1.49128   1.69345   1.84776   1.94986   1.99685   1.98742   1.92183   1.80194   1.63112   1.41421   1.15734   0.86777   0.55367   0.22393  -0.11214  -0.44504  -0.76537  -1.06406  -1.33269  -1.56366  -1.75045  -1.88777  -1.97174  -2.00000   0.00000   0.00000     ... ... ..... TT..... ......... ....TT..... .............
E4       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   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.......
E5       2.00000   1.92183   1.69345   1.33269   0.86777   0.33501  -0.22393  -0.76537  -1.24698  -1.63112  -1.88777  -1.99685  -1.94986  -1.75045  -1.41421  -0.96744  -0.44504   0.11214   0.66056   1.15734   1.56366   1.84776   1.98742   1.97174   1.80194   1.49128   1.06406   0.55367   0.00000  -0.55367  -1.06406  -1.49128  -1.80194  -1.97174  -1.98742  -1.84776  -1.56366  -1.15734  -0.66056  -0.11214   0.44504   0.96744   1.41421   1.75045   1.94986   1.99685   1.88777   1.63112   1.24698   0.76537   0.22393  -0.33501  -0.86777  -1.33269  -1.69345  -1.92183  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... TT......... .............
E6       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  -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...........
E7       2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E8       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   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     ... ... ..... ....... ......... ........... .............
E9       2.00000   1.75045   1.06406   0.11214  -0.86777  -1.63112  -1.98742  -1.84776  -1.24698  -0.33501   0.66056   1.49128   1.94986   1.92183   1.41421   0.55367  -0.44504  -1.33269  -1.88777  -1.97174  -1.56366  -0.76537   0.22393   1.15734   1.80194   1.99685   1.69345   0.96744   0.00000  -0.96744  -1.69345  -1.99685  -1.80194  -1.15734  -0.22393   0.76537   1.56366   1.97174   1.88777   1.33269   0.44504  -0.55367  -1.41421  -1.92183  -1.94986  -1.49128  -0.66056   0.33501   1.24698   1.84776   1.98742   1.63112   0.86777  -0.11214  -1.06406  -1.75045  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E10      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  -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     ... ... ..... ....... ......... ........... .............
E11      2.00000   1.63112   0.66056  -0.55367  -1.56366  -1.99685  -1.69345  -0.76537   0.44504   1.49128   1.98742   1.75045   0.86777  -0.33501  -1.41421  -1.97174  -1.80194  -0.96744   0.22393   1.33269   1.94986   1.84776   1.06406  -0.11214  -1.24698  -1.92183  -1.88777  -1.15734   0.00000   1.15734   1.88777   1.92183   1.24698   0.11214  -1.06406  -1.84776  -1.94986  -1.33269  -0.22393   0.96744   1.80194   1.97174   1.41421   0.33501  -0.86777  -1.75045  -1.98742  -1.49128  -0.44504   0.76537   1.69345   1.99685   1.56366   0.55367  -0.66056  -1.63112  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E12      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   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     ... ... ..... ....... ......... ........... .............
E13      2.00000   1.49128   0.22393  -1.15734  -1.94986  -1.75045  -0.66056   0.76537   1.80194   1.92183   1.06406  -0.33501  -1.56366  -1.99685  -1.41421  -0.11214   1.24698   1.97174   1.69345   0.55367  -0.86777  -1.84776  -1.88777  -0.96744   0.44504   1.63112   1.98742   1.33269   0.00000  -1.33269  -1.98742  -1.63112  -0.44504   0.96744   1.88777   1.84776   0.86777  -0.55367  -1.69345  -1.97174  -1.24698   0.11214   1.41421   1.99685   1.56366   0.33501  -1.06406  -1.92183  -1.80194  -0.76537   0.66056   1.75045   1.94986   1.15734  -0.22393  -1.49128  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E14      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  -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     ... ... ..... ....... ......... ........... .............
E15      2.00000   1.33269  -0.22393  -1.63112  -1.94986  -0.96744   0.66056   1.84776   1.80194   0.55367  -1.06406  -1.97174  -1.56366  -0.11214   1.41421   1.99685   1.24698  -0.33501  -1.69345  -1.92183  -0.86777   0.76537   1.88777   1.75045   0.44504  -1.15734  -1.98742  -1.49128   0.00000   1.49128   1.98742   1.15734  -0.44504  -1.75045  -1.88777  -0.76537   0.86777   1.92183   1.69345   0.33501  -1.24698  -1.99685  -1.41421   0.11214   1.56366   1.97174   1.06406  -0.55367  -1.80194  -1.84776  -0.66056   0.96744   1.94986   1.63112   0.22393  -1.33269  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E16      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   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     ... ... ..... ....... ......... ........... .............
E17      2.00000   1.15734  -0.66056  -1.92183  -1.56366   0.11214   1.69345   1.84776   0.44504  -1.33269  -1.98742  -0.96744   0.86777   1.97174   1.41421  -0.33501  -1.80194  -1.75045  -0.22393   1.49128   1.94986   0.76537  -1.06406  -1.99685  -1.24698   0.55367   1.88777   1.63112   0.00000  -1.63112  -1.88777  -0.55367   1.24698   1.99685   1.06406  -0.76537  -1.94986  -1.49128   0.22393   1.75045   1.80194   0.33501  -1.41421  -1.97174  -0.86777   0.96744   1.98742   1.33269  -0.44504  -1.84776  -1.69345  -0.11214   1.56366   1.92183   0.66056  -1.15734  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E18      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  -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     ... ... ..... ....... ......... ........... .............
E19      2.00000   0.96744  -1.06406  -1.99685  -0.86777   1.15734   1.98742   0.76537  -1.24698  -1.97174  -0.66056   1.33269   1.94986   0.55367  -1.41421  -1.92183  -0.44504   1.49128   1.88777   0.33501  -1.56366  -1.84776  -0.22393   1.63112   1.80194   0.11214  -1.69345  -1.75045   0.00000   1.75045   1.69345  -0.11214  -1.80194  -1.63112   0.22393   1.84776   1.56366  -0.33501  -1.88777  -1.49128   0.44504   1.92183   1.41421  -0.55367  -1.94986  -1.33269   0.66056   1.97174   1.24698  -0.76537  -1.98742  -1.15734   0.86777   1.99685   1.06406  -0.96744  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E20      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   0.86777  -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     ... ... ..... ....... ......... ........... .............
E21      2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E22      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  -0.66056   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     ... ... ..... ....... ......... ........... .............
E23      2.00000   0.55367  -1.69345  -1.49128   0.86777   1.97174   0.22393  -1.84776  -1.24698   1.15734   1.88777  -0.11214  -1.94986  -0.96744   1.41421   1.75045  -0.44504  -1.99685  -0.66056   1.63112   1.56366  -0.76537  -1.98742  -0.33501   1.80194   1.33269  -1.06406  -1.92183   0.00000   1.92183   1.06406  -1.33269  -1.80194   0.33501   1.98742   0.76537  -1.56366  -1.63112   0.66056   1.99685   0.44504  -1.75045  -1.41421   0.96744   1.94986   0.11214  -1.88777  -1.15734   1.24698   1.84776  -0.22393  -1.97174  -0.86777   1.49128   1.69345  -0.55367  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E24      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   0.44504  -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     ... ... ..... ....... ......... ........... .............
E25      2.00000   0.33501  -1.88777  -0.96744   1.56366   1.49128  -1.06406  -1.84776   0.44504   1.99685   0.22393  -1.92183  -0.86777   1.63112   1.41421  -1.15734  -1.80194   0.55367   1.98742   0.11214  -1.94986  -0.76537   1.69345   1.33269  -1.24698  -1.75045   0.66056   1.97174   0.00000  -1.97174  -0.66056   1.75045   1.24698  -1.33269  -1.69345   0.76537   1.94986  -0.11214  -1.98742  -0.55367   1.80194   1.15734  -1.41421  -1.63112   0.86777   1.92183  -0.22393  -1.99685  -0.44504   1.84776   1.06406  -1.49128  -1.56366   0.96744   1.88777  -0.33501  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E26      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  -0.22393   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     ... ... ..... ....... ......... ........... .............
E27      2.00000   0.11214  -1.98742  -0.33501   1.94986   0.55367  -1.88777  -0.76537   1.80194   0.96744  -1.69345  -1.15734   1.56366   1.33269  -1.41421  -1.49128   1.24698   1.63112  -1.06406  -1.75045   0.86777   1.84776  -0.66056  -1.92183   0.44504   1.97174  -0.22393  -1.99685   0.00000   1.99685   0.22393  -1.97174  -0.44504   1.92183   0.66056  -1.84776  -0.86777   1.75045   1.06406  -1.63112  -1.24698   1.49128   1.41421  -1.33269  -1.56366   1.15734   1.69345  -0.96744  -1.80194   0.76537   1.88777  -0.55367  -1.94986   0.33501   1.98742  -0.11214  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E28      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  -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     ... ... ..... ....... ......... ........... .............
E29      2.00000  -0.11214  -1.98742   0.33501   1.94986  -0.55367  -1.88777   0.76537   1.80194  -0.96744  -1.69345   1.15734   1.56366  -1.33269  -1.41421   1.49128   1.24698  -1.63112  -1.06406   1.75045   0.86777  -1.84776  -0.66056   1.92183   0.44504  -1.97174  -0.22393   1.99685   0.00000  -1.99685   0.22393   1.97174  -0.44504  -1.92183   0.66056   1.84776  -0.86777  -1.75045   1.06406   1.63112  -1.24698  -1.49128   1.41421   1.33269  -1.56366  -1.15734   1.69345   0.96744  -1.80194  -0.76537   1.88777   0.55367  -1.94986  -0.33501   1.98742   0.11214  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E30      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   0.22393   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     ... ... ..... ....... ......... ........... .............
E31      2.00000  -0.33501  -1.88777   0.96744   1.56366  -1.49128  -1.06406   1.84776   0.44504  -1.99685   0.22393   1.92183  -0.86777  -1.63112   1.41421   1.15734  -1.80194  -0.55367   1.98742  -0.11214  -1.94986   0.76537   1.69345  -1.33269  -1.24698   1.75045   0.66056  -1.97174   0.00000   1.97174  -0.66056  -1.75045   1.24698   1.33269  -1.69345  -0.76537   1.94986   0.11214  -1.98742   0.55367   1.80194  -1.15734  -1.41421   1.63112   0.86777  -1.92183  -0.22393   1.99685  -0.44504  -1.84776   1.06406   1.49128  -1.56366  -0.96744   1.88777   0.33501  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E32      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  -0.44504  -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     ... ... ..... ....... ......... ........... .............
E33      2.00000  -0.55367  -1.69345   1.49128   0.86777  -1.97174   0.22393   1.84776  -1.24698  -1.15734   1.88777   0.11214  -1.94986   0.96744   1.41421  -1.75045  -0.44504   1.99685  -0.66056  -1.63112   1.56366   0.76537  -1.98742   0.33501   1.80194  -1.33269  -1.06406   1.92183   0.00000  -1.92183   1.06406   1.33269  -1.80194  -0.33501   1.98742  -0.76537  -1.56366   1.63112   0.66056  -1.99685   0.44504   1.75045  -1.41421  -0.96744   1.94986  -0.11214  -1.88777   1.15734   1.24698  -1.84776  -0.22393   1.97174  -0.86777  -1.49128   1.69345   0.55367  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E34      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   0.66056   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     ... ... ..... ....... ......... ........... .............
E35      2.00000  -0.76537  -1.41421   1.84776   0.00000  -1.84776   1.41421   0.76537  -2.00000   0.76537   1.41421  -1.84776   0.00000   1.84776  -1.41421  -0.76537   2.00000  -0.76537  -1.41421   1.84776   0.00000  -1.84776   1.41421   0.76537  -2.00000   0.76537   1.41421  -1.84776   0.00000   1.84776  -1.41421  -0.76537   2.00000  -0.76537  -1.41421   1.84776   0.00000  -1.84776   1.41421   0.76537  -2.00000   0.76537   1.41421  -1.84776   0.00000   1.84776  -1.41421  -0.76537   2.00000  -0.76537  -1.41421   1.84776   0.00000  -1.84776   1.41421   0.76537  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E36      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  -0.86777  -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     ... ... ..... ....... ......... ........... .............
E37      2.00000  -0.96744  -1.06406   1.99685  -0.86777  -1.15734   1.98742  -0.76537  -1.24698   1.97174  -0.66056  -1.33269   1.94986  -0.55367  -1.41421   1.92183  -0.44504  -1.49128   1.88777  -0.33501  -1.56366   1.84776  -0.22393  -1.63112   1.80194  -0.11214  -1.69345   1.75045   0.00000  -1.75045   1.69345   0.11214  -1.80194   1.63112   0.22393  -1.84776   1.56366   0.33501  -1.88777   1.49128   0.44504  -1.92183   1.41421   0.55367  -1.94986   1.33269   0.66056  -1.97174   1.24698   0.76537  -1.98742   1.15734   0.86777  -1.99685   1.06406   0.96744  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E38      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   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     ... ... ..... ....... ......... ........... .............
E39      2.00000  -1.15734  -0.66056   1.92183  -1.56366  -0.11214   1.69345  -1.84776   0.44504   1.33269  -1.98742   0.96744   0.86777  -1.97174   1.41421   0.33501  -1.80194   1.75045  -0.22393  -1.49128   1.94986  -0.76537  -1.06406   1.99685  -1.24698  -0.55367   1.88777  -1.63112   0.00000   1.63112  -1.88777   0.55367   1.24698  -1.99685   1.06406   0.76537  -1.94986   1.49128   0.22393  -1.75045   1.80194  -0.33501  -1.41421   1.97174  -0.86777  -0.96744   1.98742  -1.33269  -0.44504   1.84776  -1.69345   0.11214   1.56366  -1.92183   0.66056   1.15734  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E40      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  -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     ... ... ..... ....... ......... ........... .............
E41      2.00000  -1.33269  -0.22393   1.63112  -1.94986   0.96744   0.66056  -1.84776   1.80194  -0.55367  -1.06406   1.97174  -1.56366   0.11214   1.41421  -1.99685   1.24698   0.33501  -1.69345   1.92183  -0.86777  -0.76537   1.88777  -1.75045   0.44504   1.15734  -1.98742   1.49128   0.00000  -1.49128   1.98742  -1.15734  -0.44504   1.75045  -1.88777   0.76537   0.86777  -1.92183   1.69345  -0.33501  -1.24698   1.99685  -1.41421  -0.11214   1.56366  -1.97174   1.06406   0.55367  -1.80194   1.84776  -0.66056  -0.96744   1.94986  -1.63112   0.22393   1.33269  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E42      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   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     ... ... ..... ....... ......... ........... .............
E43      2.00000  -1.49128   0.22393   1.15734  -1.94986   1.75045  -0.66056  -0.76537   1.80194  -1.92183   1.06406   0.33501  -1.56366   1.99685  -1.41421   0.11214   1.24698  -1.97174   1.69345  -0.55367  -0.86777   1.84776  -1.88777   0.96744   0.44504  -1.63112   1.98742  -1.33269   0.00000   1.33269  -1.98742   1.63112  -0.44504  -0.96744   1.88777  -1.84776   0.86777   0.55367  -1.69345   1.97174  -1.24698  -0.11214   1.41421  -1.99685   1.56366  -0.33501  -1.06406   1.92183  -1.80194   0.76537   0.66056  -1.75045   1.94986  -1.15734  -0.22393   1.49128  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E44      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  -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     ... ... ..... ....... ......... ........... .............
E45      2.00000  -1.63112   0.66056   0.55367  -1.56366   1.99685  -1.69345   0.76537   0.44504  -1.49128   1.98742  -1.75045   0.86777   0.33501  -1.41421   1.97174  -1.80194   0.96744   0.22393  -1.33269   1.94986  -1.84776   1.06406   0.11214  -1.24698   1.92183  -1.88777   1.15734   0.00000  -1.15734   1.88777  -1.92183   1.24698  -0.11214  -1.06406   1.84776  -1.94986   1.33269  -0.22393  -0.96744   1.80194  -1.97174   1.41421  -0.33501  -0.86777   1.75045  -1.98742   1.49128  -0.44504  -0.76537   1.69345  -1.99685   1.56366  -0.55367  -0.66056   1.63112  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E46      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   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     ... ... ..... ....... ......... ........... .............
E47      2.00000  -1.75045   1.06406  -0.11214  -0.86777   1.63112  -1.98742   1.84776  -1.24698   0.33501   0.66056  -1.49128   1.94986  -1.92183   1.41421  -0.55367  -0.44504   1.33269  -1.88777   1.97174  -1.56366   0.76537   0.22393  -1.15734   1.80194  -1.99685   1.69345  -0.96744   0.00000   0.96744  -1.69345   1.99685  -1.80194   1.15734  -0.22393  -0.76537   1.56366  -1.97174   1.88777  -1.33269   0.44504   0.55367  -1.41421   1.92183  -1.94986   1.49128  -0.66056  -0.33501   1.24698  -1.84776   1.98742  -1.63112   0.86777   0.11214  -1.06406   1.75045  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E48      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  -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     ... ... ..... ....... ......... ........... .............
E49      2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E50      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   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     ... ... ..... ....... ......... ........... .............
E51      2.00000  -1.92183   1.69345  -1.33269   0.86777  -0.33501  -0.22393   0.76537  -1.24698   1.63112  -1.88777   1.99685  -1.94986   1.75045  -1.41421   0.96744  -0.44504  -0.11214   0.66056  -1.15734   1.56366  -1.84776   1.98742  -1.97174   1.80194  -1.49128   1.06406  -0.55367   0.00000   0.55367  -1.06406   1.49128  -1.80194   1.97174  -1.98742   1.84776  -1.56366   1.15734  -0.66056   0.11214   0.44504  -0.96744   1.41421  -1.75045   1.94986  -1.99685   1.88777  -1.63112   1.24698  -0.76537   0.22393   0.33501  -0.86777   1.33269  -1.69345   1.92183  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... ..TT.........
E52      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  -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....... .............
E53      2.00000  -1.97174   1.88777  -1.75045   1.56366  -1.33269   1.06406  -0.76537   0.44504  -0.11214  -0.22393   0.55367  -0.86777   1.15734  -1.41421   1.63112  -1.80194   1.92183  -1.98742   1.99685  -1.94986   1.84776  -1.69345   1.49128  -1.24698   0.96744  -0.66056   0.33501   0.00000  -0.33501   0.66056  -0.96744   1.24698  -1.49128   1.69345  -1.84776   1.94986  -1.99685   1.98742  -1.92183   1.80194  -1.63112   1.41421  -1.15734   0.86777  -0.55367   0.22393   0.11214  -0.44504   0.76537  -1.06406   1.33269  -1.56366   1.75045  -1.88777   1.97174  -2.00000   0.00000   0.00000     ... ... ..... ....... ..TT..... ........... ......TT.....
E54      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   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... .............
E55      2.00000  -1.99685   1.98742  -1.97174   1.94986  -1.92183   1.88777  -1.84776   1.80194  -1.75045   1.69345  -1.63112   1.56366  -1.49128   1.41421  -1.33269   1.24698  -1.15734   1.06406  -0.96744   0.86777  -0.76537   0.66056  -0.55367   0.44504  -0.33501   0.22393  -0.11214   0.00000   0.11214  -0.22393   0.33501  -0.44504   0.55367  -0.66056   0.76537  -0.86777   0.96744  -1.06406   1.15734  -1.24698   1.33269  -1.41421   1.49128  -1.56366   1.63112  -1.69345   1.75045  -1.80194   1.84776  -1.88777   1.92183  -1.94986   1.97174  -1.98742   1.99685  -2.00000   0.00000   0.00000     TT. ... ..TT. ....... ......TT. ........... ..........TT.

 Irrational character values:  1.996853630036 = 2*cos(2*π/112) = 2*cos(π/56)
                               1.987424419786 = 2*cos(4*π/112) = 2*cos(π/28)
                               1.971742037036 = 2*cos(6*π/112) = 2*cos(3*π/56)
                               1.949855824364 = 2*cos(8*π/112) = 2*cos(π/14)
                               1.921834643890 = 2*cos(10*π/112) = 2*cos(5*π/56)
                               1.887766660617 = 2*cos(12*π/112) = 2*cos(3*π/28)
                               1.847759065023 = 2*cos(14*π/112) = 2*cos(π/8) = √2+√2
                               1.801937735805 = 2*cos(16*π/112) = 2*cos(π/7)
                               1.750446843818 = 2*cos(18*π/112) = 2*cos(9*π/56)
                               1.693448398457 = 2*cos(20*π/112) = 2*cos(5*π/28)
                               1.631121737919 = 2*cos(22*π/112) = 2*cos(11*π/56)
                               1.563662964936 = 2*cos(24*π/112) = 2*cos(3*π/14)
                               1.491284329766 = 2*cos(26*π/112) = 2*cos(13*π/56)
                               1.414213562373 = 2*cos(28*π/112) = 2*cos(π/4) = √2
                               1.332693155904 = 2*cos(30*π/112) = 2*cos(15*π/56)
                               1.246979603717 = 2*cos(32*π/112) = 2*cos(2*π/7)
                               1.157342592360 = 2*cos(34*π/112) = 2*cos(17*π/56)
                               1.064064153031 = 2*cos(36*π/112) = 2*cos(9*π/28)
                               0.967437774210 = 2*cos(38*π/112) = 2*cos(19*π/56)
                               0.867767478235 = 2*cos(40*π/112) = 2*cos(5*π/14)
                               0.765366864730 = 2*cos(42*π/112) = 2*cos(3*π/8) = √2−√2
                               0.660558123910 = 2*cos(44*π/112) = 2*cos(11*π/28)
                               0.553671022850 = 2*cos(46*π/112) = 2*cos(23*π/56)
                               0.445041867913 = 2*cos(48*π/112) = 2*cos(3*π/7)
                               0.335012446609 = 2*cos(50*π/112) = 2*cos(25*π/56)
                               0.223928952207 = 2*cos(52*π/112) = 2*cos(13*π/28)
                               0.112140894474 = 2*cos(54*π/112) = 2*cos(27*π/56)



 Symmetry of Rotations and Cartesian products

A1   d+g+i+k+m    z2, z4, z6 
A2   R            Rz 
B2   p+f+h+j+l    z, z3, z5 
E1   p+f+h+j+l    {x, y}, {xz2, yz2}, {xz4, yz4} 
E2   d+g+i+k+m    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E3   f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E4   g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E5   h+j+l        {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)} 
E6   i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7   j+l 
E8   k+m 
E9   l 
E10  m 
E47  m 
E48  l 
E49  k+m 
E50  j+l 
E51  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E52  h+j+l        {z((x2y2)2−4x2y2), xyz(x2y2)} 
E53  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E54  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E55  R+d+g+i+k+m  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 

 Notes:

    α  The order of the D56d point group is 224, and the order of the principal axis (S112) is 112. The group has 59 irreducible representations.

    β  The D56d point group is isomorphic to C112v and D112.

    γ  The D56d point group is generated by two symmetry elements, S112 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).

    δ  The group contains one set of twofold symmetry axes (C2) perpendicular to the principal (z) axis. Both x and y axes are members of that set.

    ε  The single σd set of symmetry planes contains neither the xz nor the yz planes; but it contains the median plane (x+y)z.

    ζ  The lowest nonvanishing multipole moment in D56d is 4 (quadrupole moment).

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

    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.

    ι  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.

    κ  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 D56d point group was created by Gernot Katzer.

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