Character Table for Point Group C64h

Character table for the C_64h point group

C64h E 2 C64 2 C32 2 C64^3 2 C16 2 C64^5 2 C32^3 2 C64^7 2 C8 2 C64^9 2 C32^5 2 C64^11 2 C16^3 2 C64^13 2 C32^7 2 C64^15 2 C4 2 C64^17 2 C32^9 2 C64^19 2 C16^5 2 C64^21 2 C32^11 2 C64^23 2 C8^3 2 C64^25 2 C32^13 2 C64^27 2 C16^7 2 C64^29 2 C32^15 2 C64^31 C2 i 2 S64 2 S32 2 S64^3 2 S16 2 S64^5 2 S32^3 2 S64^7 2 S8 2 S64^9 2 S32^5 2 S64^11 2 S16^3 2 S64^13 2 S32^7 2 S64^15 2 S4 2 S64^17 2 S32^9 2 S64^19 2 S16^5 2 S64^21 2 S32^11 2 S64^23 2 S8^3 2 S64^25 2 S32^13 2 S64^27 2 S16^7 2 S64^29 2 S32^15 2 S64^31 sh <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> Ag 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 Bg 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -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 1.99037 1.96157 1.91388 1.84776 1.76384 1.66294 1.54602 1.41421 1.26879 1.11114 0.94279 0.76537 0.58057 0.39018 0.19603 0.00000 -0.19603 -0.39018 -0.58057 -0.76537 -0.94279 -1.11114 -1.26879 -1.41421 -1.54602 -1.66294 -1.76384 -1.84776 -1.91388 -1.96157 -1.99037 -2.00000 2.00000 -1.99037 -1.96157 -1.91388 -1.84776 -1.76384 -1.66294 -1.54602 -1.41421 -1.26879 -1.11114 -0.94279 -0.76537 -0.58057 -0.39018 -0.19603 0.00000 0.19603 0.39018 0.58057 0.76537 0.94279 1.11114 1.26879 1.41421 1.54602 1.66294 1.76384 1.84776 1.91388 1.96157 1.99037 -2.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g * 2.00000 1.96157 1.84776 1.66294 1.41421 1.11114 0.76537 0.39018 0.00000 -0.39018 -0.76537 -1.11114 -1.41421 -1.66294 -1.84776 -1.96157 -2.00000 -1.96157 -1.84776 -1.66294 -1.41421 -1.11114 -0.76537 -0.39018 0.00000 0.39018 0.76537 1.11114 1.41421 1.66294 1.84776 1.96157 2.00000 2.00000 1.96157 1.84776 1.66294 1.41421 1.11114 0.76537 0.39018 0.00000 -0.39018 -0.76537 -1.11114 -1.41421 -1.66294 -1.84776 -1.96157 -2.00000 -1.96157 -1.84776 -1.66294 -1.41421 -1.11114 -0.76537 -0.39018 0.00000 0.39018 0.76537 1.11114 1.41421 1.66294 1.84776 1.96157 2.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g * 2.00000 1.91388 1.66294 1.26879 0.76537 0.19603 -0.39018 -0.94279 -1.41421 -1.76384 -1.96157 -1.99037 -1.84776 -1.54602 -1.11114 -0.58057 0.00000 0.58057 1.11114 1.54602 1.84776 1.99037 1.96157 1.76384 1.41421 0.94279 0.39018 -0.19603 -0.76537 -1.26879 -1.66294 -1.91388 -2.00000 2.00000 -1.91388 -1.66294 -1.26879 -0.76537 -0.19603 0.39018 0.94279 1.41421 1.76384 1.96157 1.99037 1.84776 1.54602 1.11114 0.58057 0.00000 -0.58057 -1.11114 -1.54602 -1.84776 -1.99037 -1.96157 -1.76384 -1.41421 -0.94279 -0.39018 0.19603 0.76537 1.26879 1.66294 1.91388 -2.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g * 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 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 ... ... ..... ....... TT....... ........... ....TT....... E5g * 2.00000 1.76384 1.11114 0.19603 -0.76537 -1.54602 -1.96157 -1.91388 -1.41421 -0.58057 0.39018 1.26879 1.84776 1.99037 1.66294 0.94279 0.00000 -0.94279 -1.66294 -1.99037 -1.84776 -1.26879 -0.39018 0.58057 1.41421 1.91388 1.96157 1.54602 0.76537 -0.19603 -1.11114 -1.76384 -2.00000 2.00000 -1.76384 -1.11114 -0.19603 0.76537 1.54602 1.96157 1.91388 1.41421 0.58057 -0.39018 -1.26879 -1.84776 -1.99037 -1.66294 -0.94279 0.00000 0.94279 1.66294 1.99037 1.84776 1.26879 0.39018 -0.58057 -1.41421 -1.91388 -1.96157 -1.54602 -0.76537 0.19603 1.11114 1.76384 -2.00000 ... ... ..... ....... ......... ........... ..TT......... E6g * 2.00000 1.66294 0.76537 -0.39018 -1.41421 -1.96157 -1.84776 -1.11114 0.00000 1.11114 1.84776 1.96157 1.41421 0.39018 -0.76537 -1.66294 -2.00000 -1.66294 -0.76537 0.39018 1.41421 1.96157 1.84776 1.11114 0.00000 -1.11114 -1.84776 -1.96157 -1.41421 -0.39018 0.76537 1.66294 2.00000 2.00000 1.66294 0.76537 -0.39018 -1.41421 -1.96157 -1.84776 -1.11114 0.00000 1.11114 1.84776 1.96157 1.41421 0.39018 -0.76537 -1.66294 -2.00000 -1.66294 -0.76537 0.39018 1.41421 1.96157 1.84776 1.11114 0.00000 -1.11114 -1.84776 -1.96157 -1.41421 -0.39018 0.76537 1.66294 2.00000 ... ... ..... ....... ......... ........... TT........... E7g * 2.00000 1.54602 0.39018 -0.94279 -1.84776 -1.91388 -1.11114 0.19603 1.41421 1.99037 1.66294 0.58057 -0.76537 -1.76384 -1.96157 -1.26879 0.00000 1.26879 1.96157 1.76384 0.76537 -0.58057 -1.66294 -1.99037 -1.41421 -0.19603 1.11114 1.91388 1.84776 0.94279 -0.39018 -1.54602 -2.00000 2.00000 -1.54602 -0.39018 0.94279 1.84776 1.91388 1.11114 -0.19603 -1.41421 -1.99037 -1.66294 -0.58057 0.76537 1.76384 1.96157 1.26879 0.00000 -1.26879 -1.96157 -1.76384 -0.76537 0.58057 1.66294 1.99037 1.41421 0.19603 -1.11114 -1.91388 -1.84776 -0.94279 0.39018 1.54602 -2.00000 ... ... ..... ....... ......... ........... ............. E8g * 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 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 ... ... ..... ....... ......... ........... ............. E9g * 2.00000 1.26879 -0.39018 -1.76384 -1.84776 -0.58057 1.11114 1.99037 1.41421 -0.19603 -1.66294 -1.91388 -0.76537 0.94279 1.96157 1.54602 0.00000 -1.54602 -1.96157 -0.94279 0.76537 1.91388 1.66294 0.19603 -1.41421 -1.99037 -1.11114 0.58057 1.84776 1.76384 0.39018 -1.26879 -2.00000 2.00000 -1.26879 0.39018 1.76384 1.84776 0.58057 -1.11114 -1.99037 -1.41421 0.19603 1.66294 1.91388 0.76537 -0.94279 -1.96157 -1.54602 0.00000 1.54602 1.96157 0.94279 -0.76537 -1.91388 -1.66294 -0.19603 1.41421 1.99037 1.11114 -0.58057 -1.84776 -1.76384 -0.39018 1.26879 -2.00000 ... ... ..... ....... ......... ........... ............. E10g * 2.00000 1.11114 -0.76537 -1.96157 -1.41421 0.39018 1.84776 1.66294 0.00000 -1.66294 -1.84776 -0.39018 1.41421 1.96157 0.76537 -1.11114 -2.00000 -1.11114 0.76537 1.96157 1.41421 -0.39018 -1.84776 -1.66294 0.00000 1.66294 1.84776 0.39018 -1.41421 -1.96157 -0.76537 1.11114 2.00000 2.00000 1.11114 -0.76537 -1.96157 -1.41421 0.39018 1.84776 1.66294 0.00000 -1.66294 -1.84776 -0.39018 1.41421 1.96157 0.76537 -1.11114 -2.00000 -1.11114 0.76537 1.96157 1.41421 -0.39018 -1.84776 -1.66294 0.00000 1.66294 1.84776 0.39018 -1.41421 -1.96157 -0.76537 1.11114 2.00000 ... ... ..... ....... ......... ........... ............. E11g * 2.00000 0.94279 -1.11114 -1.99037 -0.76537 1.26879 1.96157 0.58057 -1.41421 -1.91388 -0.39018 1.54602 1.84776 0.19603 -1.66294 -1.76384 0.00000 1.76384 1.66294 -0.19603 -1.84776 -1.54602 0.39018 1.91388 1.41421 -0.58057 -1.96157 -1.26879 0.76537 1.99037 1.11114 -0.94279 -2.00000 2.00000 -0.94279 1.11114 1.99037 0.76537 -1.26879 -1.96157 -0.58057 1.41421 1.91388 0.39018 -1.54602 -1.84776 -0.19603 1.66294 1.76384 0.00000 -1.76384 -1.66294 0.19603 1.84776 1.54602 -0.39018 -1.91388 -1.41421 0.58057 1.96157 1.26879 -0.76537 -1.99037 -1.11114 0.94279 -2.00000 ... ... ..... ....... ......... ........... ............. E12g * 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 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 ... ... ..... ....... ......... ........... ............. E13g * 2.00000 0.58057 -1.66294 -1.54602 0.76537 1.99037 0.39018 -1.76384 -1.41421 0.94279 1.96157 0.19603 -1.84776 -1.26879 1.11114 1.91388 0.00000 -1.91388 -1.11114 1.26879 1.84776 -0.19603 -1.96157 -0.94279 1.41421 1.76384 -0.39018 -1.99037 -0.76537 1.54602 1.66294 -0.58057 -2.00000 2.00000 -0.58057 1.66294 1.54602 -0.76537 -1.99037 -0.39018 1.76384 1.41421 -0.94279 -1.96157 -0.19603 1.84776 1.26879 -1.11114 -1.91388 0.00000 1.91388 1.11114 -1.26879 -1.84776 0.19603 1.96157 0.94279 -1.41421 -1.76384 0.39018 1.99037 0.76537 -1.54602 -1.66294 0.58057 -2.00000 ... ... ..... ....... ......... ........... ............. E14g * 2.00000 0.39018 -1.84776 -1.11114 1.41421 1.66294 -0.76537 -1.96157 0.00000 1.96157 0.76537 -1.66294 -1.41421 1.11114 1.84776 -0.39018 -2.00000 -0.39018 1.84776 1.11114 -1.41421 -1.66294 0.76537 1.96157 0.00000 -1.96157 -0.76537 1.66294 1.41421 -1.11114 -1.84776 0.39018 2.00000 2.00000 0.39018 -1.84776 -1.11114 1.41421 1.66294 -0.76537 -1.96157 0.00000 1.96157 0.76537 -1.66294 -1.41421 1.11114 1.84776 -0.39018 -2.00000 -0.39018 1.84776 1.11114 -1.41421 -1.66294 0.76537 1.96157 0.00000 -1.96157 -0.76537 1.66294 1.41421 -1.11114 -1.84776 0.39018 2.00000 ... ... ..... ....... ......... ........... ............. E15g * 2.00000 0.19603 -1.96157 -0.58057 1.84776 0.94279 -1.66294 -1.26879 1.41421 1.54602 -1.11114 -1.76384 0.76537 1.91388 -0.39018 -1.99037 0.00000 1.99037 0.39018 -1.91388 -0.76537 1.76384 1.11114 -1.54602 -1.41421 1.26879 1.66294 -0.94279 -1.84776 0.58057 1.96157 -0.19603 -2.00000 2.00000 -0.19603 1.96157 0.58057 -1.84776 -0.94279 1.66294 1.26879 -1.41421 -1.54602 1.11114 1.76384 -0.76537 -1.91388 0.39018 1.99037 0.00000 -1.99037 -0.39018 1.91388 0.76537 -1.76384 -1.11114 1.54602 1.41421 -1.26879 -1.66294 0.94279 1.84776 -0.58057 -1.96157 0.19603 -2.00000 ... ... ..... ....... ......... ........... ............. E16g * 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 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 ... ... ..... ....... ......... ........... ............. E17g * 2.00000 -0.19603 -1.96157 0.58057 1.84776 -0.94279 -1.66294 1.26879 1.41421 -1.54602 -1.11114 1.76384 0.76537 -1.91388 -0.39018 1.99037 0.00000 -1.99037 0.39018 1.91388 -0.76537 -1.76384 1.11114 1.54602 -1.41421 -1.26879 1.66294 0.94279 -1.84776 -0.58057 1.96157 0.19603 -2.00000 2.00000 0.19603 1.96157 -0.58057 -1.84776 0.94279 1.66294 -1.26879 -1.41421 1.54602 1.11114 -1.76384 -0.76537 1.91388 0.39018 -1.99037 0.00000 1.99037 -0.39018 -1.91388 0.76537 1.76384 -1.11114 -1.54602 1.41421 1.26879 -1.66294 -0.94279 1.84776 0.58057 -1.96157 -0.19603 -2.00000 ... ... ..... ....... ......... ........... ............. E18g * 2.00000 -0.39018 -1.84776 1.11114 1.41421 -1.66294 -0.76537 1.96157 0.00000 -1.96157 0.76537 1.66294 -1.41421 -1.11114 1.84776 0.39018 -2.00000 0.39018 1.84776 -1.11114 -1.41421 1.66294 0.76537 -1.96157 0.00000 1.96157 -0.76537 -1.66294 1.41421 1.11114 -1.84776 -0.39018 2.00000 2.00000 -0.39018 -1.84776 1.11114 1.41421 -1.66294 -0.76537 1.96157 0.00000 -1.96157 0.76537 1.66294 -1.41421 -1.11114 1.84776 0.39018 -2.00000 0.39018 1.84776 -1.11114 -1.41421 1.66294 0.76537 -1.96157 0.00000 1.96157 -0.76537 -1.66294 1.41421 1.11114 -1.84776 -0.39018 2.00000 ... ... ..... ....... ......... ........... ............. E19g * 2.00000 -0.58057 -1.66294 1.54602 0.76537 -1.99037 0.39018 1.76384 -1.41421 -0.94279 1.96157 -0.19603 -1.84776 1.26879 1.11114 -1.91388 0.00000 1.91388 -1.11114 -1.26879 1.84776 0.19603 -1.96157 0.94279 1.41421 -1.76384 -0.39018 1.99037 -0.76537 -1.54602 1.66294 0.58057 -2.00000 2.00000 0.58057 1.66294 -1.54602 -0.76537 1.99037 -0.39018 -1.76384 1.41421 0.94279 -1.96157 0.19603 1.84776 -1.26879 -1.11114 1.91388 0.00000 -1.91388 1.11114 1.26879 -1.84776 -0.19603 1.96157 -0.94279 -1.41421 1.76384 0.39018 -1.99037 0.76537 1.54602 -1.66294 -0.58057 -2.00000 ... ... ..... ....... ......... ........... ............. E20g * 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 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 ... ... ..... ....... ......... ........... ............. E21g * 2.00000 -0.94279 -1.11114 1.99037 -0.76537 -1.26879 1.96157 -0.58057 -1.41421 1.91388 -0.39018 -1.54602 1.84776 -0.19603 -1.66294 1.76384 0.00000 -1.76384 1.66294 0.19603 -1.84776 1.54602 0.39018 -1.91388 1.41421 0.58057 -1.96157 1.26879 0.76537 -1.99037 1.11114 0.94279 -2.00000 2.00000 0.94279 1.11114 -1.99037 0.76537 1.26879 -1.96157 0.58057 1.41421 -1.91388 0.39018 1.54602 -1.84776 0.19603 1.66294 -1.76384 0.00000 1.76384 -1.66294 -0.19603 1.84776 -1.54602 -0.39018 1.91388 -1.41421 -0.58057 1.96157 -1.26879 -0.76537 1.99037 -1.11114 -0.94279 -2.00000 ... ... ..... ....... ......... ........... ............. E22g * 2.00000 -1.11114 -0.76537 1.96157 -1.41421 -0.39018 1.84776 -1.66294 0.00000 1.66294 -1.84776 0.39018 1.41421 -1.96157 0.76537 1.11114 -2.00000 1.11114 0.76537 -1.96157 1.41421 0.39018 -1.84776 1.66294 0.00000 -1.66294 1.84776 -0.39018 -1.41421 1.96157 -0.76537 -1.11114 2.00000 2.00000 -1.11114 -0.76537 1.96157 -1.41421 -0.39018 1.84776 -1.66294 0.00000 1.66294 -1.84776 0.39018 1.41421 -1.96157 0.76537 1.11114 -2.00000 1.11114 0.76537 -1.96157 1.41421 0.39018 -1.84776 1.66294 0.00000 -1.66294 1.84776 -0.39018 -1.41421 1.96157 -0.76537 -1.11114 2.00000 ... ... ..... ....... ......... ........... ............. E23g * 2.00000 -1.26879 -0.39018 1.76384 -1.84776 0.58057 1.11114 -1.99037 1.41421 0.19603 -1.66294 1.91388 -0.76537 -0.94279 1.96157 -1.54602 0.00000 1.54602 -1.96157 0.94279 0.76537 -1.91388 1.66294 -0.19603 -1.41421 1.99037 -1.11114 -0.58057 1.84776 -1.76384 0.39018 1.26879 -2.00000 2.00000 1.26879 0.39018 -1.76384 1.84776 -0.58057 -1.11114 1.99037 -1.41421 -0.19603 1.66294 -1.91388 0.76537 0.94279 -1.96157 1.54602 0.00000 -1.54602 1.96157 -0.94279 -0.76537 1.91388 -1.66294 0.19603 1.41421 -1.99037 1.11114 0.58057 -1.84776 1.76384 -0.39018 -1.26879 -2.00000 ... ... ..... ....... ......... ........... ............. E24g * 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 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 ... ... ..... ....... ......... ........... ............. E25g * 2.00000 -1.54602 0.39018 0.94279 -1.84776 1.91388 -1.11114 -0.19603 1.41421 -1.99037 1.66294 -0.58057 -0.76537 1.76384 -1.96157 1.26879 0.00000 -1.26879 1.96157 -1.76384 0.76537 0.58057 -1.66294 1.99037 -1.41421 0.19603 1.11114 -1.91388 1.84776 -0.94279 -0.39018 1.54602 -2.00000 2.00000 1.54602 -0.39018 -0.94279 1.84776 -1.91388 1.11114 0.19603 -1.41421 1.99037 -1.66294 0.58057 0.76537 -1.76384 1.96157 -1.26879 0.00000 1.26879 -1.96157 1.76384 -0.76537 -0.58057 1.66294 -1.99037 1.41421 -0.19603 -1.11114 1.91388 -1.84776 0.94279 0.39018 -1.54602 -2.00000 ... ... ..... ....... ......... ........... ............. E26g * 2.00000 -1.66294 0.76537 0.39018 -1.41421 1.96157 -1.84776 1.11114 0.00000 -1.11114 1.84776 -1.96157 1.41421 -0.39018 -0.76537 1.66294 -2.00000 1.66294 -0.76537 -0.39018 1.41421 -1.96157 1.84776 -1.11114 0.00000 1.11114 -1.84776 1.96157 -1.41421 0.39018 0.76537 -1.66294 2.00000 2.00000 -1.66294 0.76537 0.39018 -1.41421 1.96157 -1.84776 1.11114 0.00000 -1.11114 1.84776 -1.96157 1.41421 -0.39018 -0.76537 1.66294 -2.00000 1.66294 -0.76537 -0.39018 1.41421 -1.96157 1.84776 -1.11114 0.00000 1.11114 -1.84776 1.96157 -1.41421 0.39018 0.76537 -1.66294 2.00000 ... ... ..... ....... ......... ........... ............. E27g * 2.00000 -1.76384 1.11114 -0.19603 -0.76537 1.54602 -1.96157 1.91388 -1.41421 0.58057 0.39018 -1.26879 1.84776 -1.99037 1.66294 -0.94279 0.00000 0.94279 -1.66294 1.99037 -1.84776 1.26879 -0.39018 -0.58057 1.41421 -1.91388 1.96157 -1.54602 0.76537 0.19603 -1.11114 1.76384 -2.00000 2.00000 1.76384 -1.11114 0.19603 0.76537 -1.54602 1.96157 -1.91388 1.41421 -0.58057 -0.39018 1.26879 -1.84776 1.99037 -1.66294 0.94279 0.00000 -0.94279 1.66294 -1.99037 1.84776 -1.26879 0.39018 0.58057 -1.41421 1.91388 -1.96157 1.54602 -0.76537 -0.19603 1.11114 -1.76384 -2.00000 ... ... ..... ....... ......... ........... ............. E28g * 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 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 ... ... ..... ....... ......... ........... ............. E29g * 2.00000 -1.91388 1.66294 -1.26879 0.76537 -0.19603 -0.39018 0.94279 -1.41421 1.76384 -1.96157 1.99037 -1.84776 1.54602 -1.11114 0.58057 0.00000 -0.58057 1.11114 -1.54602 1.84776 -1.99037 1.96157 -1.76384 1.41421 -0.94279 0.39018 0.19603 -0.76537 1.26879 -1.66294 1.91388 -2.00000 2.00000 1.91388 -1.66294 1.26879 -0.76537 0.19603 0.39018 -0.94279 1.41421 -1.76384 1.96157 -1.99037 1.84776 -1.54602 1.11114 -0.58057 0.00000 0.58057 -1.11114 1.54602 -1.84776 1.99037 -1.96157 1.76384 -1.41421 0.94279 -0.39018 -0.19603 0.76537 -1.26879 1.66294 -1.91388 -2.00000 ... ... ..... ....... ......... ........... ............. E30g * 2.00000 -1.96157 1.84776 -1.66294 1.41421 -1.11114 0.76537 -0.39018 0.00000 0.39018 -0.76537 1.11114 -1.41421 1.66294 -1.84776 1.96157 -2.00000 1.96157 -1.84776 1.66294 -1.41421 1.11114 -0.76537 0.39018 0.00000 -0.39018 0.76537 -1.11114 1.41421 -1.66294 1.84776 -1.96157 2.00000 2.00000 -1.96157 1.84776 -1.66294 1.41421 -1.11114 0.76537 -0.39018 0.00000 0.39018 -0.76537 1.11114 -1.41421 1.66294 -1.84776 1.96157 -2.00000 1.96157 -1.84776 1.66294 -1.41421 1.11114 -0.76537 0.39018 0.00000 -0.39018 0.76537 -1.11114 1.41421 -1.66294 1.84776 -1.96157 2.00000 ... ... ..... ....... ......... ........... ............. E31g * 2.00000 -1.99037 1.96157 -1.91388 1.84776 -1.76384 1.66294 -1.54602 1.41421 -1.26879 1.11114 -0.94279 0.76537 -0.58057 0.39018 -0.19603 0.00000 0.19603 -0.39018 0.58057 -0.76537 0.94279 -1.11114 1.26879 -1.41421 1.54602 -1.66294 1.76384 -1.84776 1.91388 -1.96157 1.99037 -2.00000 2.00000 1.99037 -1.96157 1.91388 -1.84776 1.76384 -1.66294 1.54602 -1.41421 1.26879 -1.11114 0.94279 -0.76537 0.58057 -0.39018 0.19603 0.00000 -0.19603 0.39018 -0.58057 0.76537 -0.94279 1.11114 -1.26879 1.41421 -1.54602 1.66294 -1.76384 1.84776 -1.91388 1.96157 -1.99037 -2.00000 ... ... ..... ....... ......... ........... ............. Au 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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 ............. Bu 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 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 1.99037 1.96157 1.91388 1.84776 1.76384 1.66294 1.54602 1.41421 1.26879 1.11114 0.94279 0.76537 0.58057 0.39018 0.19603 0.00000 -0.19603 -0.39018 -0.58057 -0.76537 -0.94279 -1.11114 -1.26879 -1.41421 -1.54602 -1.66294 -1.76384 -1.84776 -1.91388 -1.96157 -1.99037 -2.00000 -2.00000 1.99037 1.96157 1.91388 1.84776 1.76384 1.66294 1.54602 1.41421 1.26879 1.11114 0.94279 0.76537 0.58057 0.39018 0.19603 0.00000 -0.19603 -0.39018 -0.58057 -0.76537 -0.94279 -1.11114 -1.26879 -1.41421 -1.54602 -1.66294 -1.76384 -1.84776 -1.91388 -1.96157 -1.99037 2.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u * 2.00000 1.96157 1.84776 1.66294 1.41421 1.11114 0.76537 0.39018 0.00000 -0.39018 -0.76537 -1.11114 -1.41421 -1.66294 -1.84776 -1.96157 -2.00000 -1.96157 -1.84776 -1.66294 -1.41421 -1.11114 -0.76537 -0.39018 0.00000 0.39018 0.76537 1.11114 1.41421 1.66294 1.84776 1.96157 2.00000 -2.00000 -1.96157 -1.84776 -1.66294 -1.41421 -1.11114 -0.76537 -0.39018 0.00000 0.39018 0.76537 1.11114 1.41421 1.66294 1.84776 1.96157 2.00000 1.96157 1.84776 1.66294 1.41421 1.11114 0.76537 0.39018 0.00000 -0.39018 -0.76537 -1.11114 -1.41421 -1.66294 -1.84776 -1.96157 -2.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u * 2.00000 1.91388 1.66294 1.26879 0.76537 0.19603 -0.39018 -0.94279 -1.41421 -1.76384 -1.96157 -1.99037 -1.84776 -1.54602 -1.11114 -0.58057 0.00000 0.58057 1.11114 1.54602 1.84776 1.99037 1.96157 1.76384 1.41421 0.94279 0.39018 -0.19603 -0.76537 -1.26879 -1.66294 -1.91388 -2.00000 -2.00000 1.91388 1.66294 1.26879 0.76537 0.19603 -0.39018 -0.94279 -1.41421 -1.76384 -1.96157 -1.99037 -1.84776 -1.54602 -1.11114 -0.58057 0.00000 0.58057 1.11114 1.54602 1.84776 1.99037 1.96157 1.76384 1.41421 0.94279 0.39018 -0.19603 -0.76537 -1.26879 -1.66294 -1.91388 2.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u * 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 -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 ... ... ..... ....... ......... ..TT....... ............. E5u * 2.00000 1.76384 1.11114 0.19603 -0.76537 -1.54602 -1.96157 -1.91388 -1.41421 -0.58057 0.39018 1.26879 1.84776 1.99037 1.66294 0.94279 0.00000 -0.94279 -1.66294 -1.99037 -1.84776 -1.26879 -0.39018 0.58057 1.41421 1.91388 1.96157 1.54602 0.76537 -0.19603 -1.11114 -1.76384 -2.00000 -2.00000 1.76384 1.11114 0.19603 -0.76537 -1.54602 -1.96157 -1.91388 -1.41421 -0.58057 0.39018 1.26879 1.84776 1.99037 1.66294 0.94279 0.00000 -0.94279 -1.66294 -1.99037 -1.84776 -1.26879 -0.39018 0.58057 1.41421 1.91388 1.96157 1.54602 0.76537 -0.19603 -1.11114 -1.76384 2.00000 ... ... ..... ....... ......... TT......... ............. E6u * 2.00000 1.66294 0.76537 -0.39018 -1.41421 -1.96157 -1.84776 -1.11114 0.00000 1.11114 1.84776 1.96157 1.41421 0.39018 -0.76537 -1.66294 -2.00000 -1.66294 -0.76537 0.39018 1.41421 1.96157 1.84776 1.11114 0.00000 -1.11114 -1.84776 -1.96157 -1.41421 -0.39018 0.76537 1.66294 2.00000 -2.00000 -1.66294 -0.76537 0.39018 1.41421 1.96157 1.84776 1.11114 0.00000 -1.11114 -1.84776 -1.96157 -1.41421 -0.39018 0.76537 1.66294 2.00000 1.66294 0.76537 -0.39018 -1.41421 -1.96157 -1.84776 -1.11114 0.00000 1.11114 1.84776 1.96157 1.41421 0.39018 -0.76537 -1.66294 -2.00000 ... ... ..... ....... ......... ........... ............. E7u * 2.00000 1.54602 0.39018 -0.94279 -1.84776 -1.91388 -1.11114 0.19603 1.41421 1.99037 1.66294 0.58057 -0.76537 -1.76384 -1.96157 -1.26879 0.00000 1.26879 1.96157 1.76384 0.76537 -0.58057 -1.66294 -1.99037 -1.41421 -0.19603 1.11114 1.91388 1.84776 0.94279 -0.39018 -1.54602 -2.00000 -2.00000 1.54602 0.39018 -0.94279 -1.84776 -1.91388 -1.11114 0.19603 1.41421 1.99037 1.66294 0.58057 -0.76537 -1.76384 -1.96157 -1.26879 0.00000 1.26879 1.96157 1.76384 0.76537 -0.58057 -1.66294 -1.99037 -1.41421 -0.19603 1.11114 1.91388 1.84776 0.94279 -0.39018 -1.54602 2.00000 ... ... ..... ....... ......... ........... ............. E8u * 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 -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 ... ... ..... ....... ......... ........... ............. E9u * 2.00000 1.26879 -0.39018 -1.76384 -1.84776 -0.58057 1.11114 1.99037 1.41421 -0.19603 -1.66294 -1.91388 -0.76537 0.94279 1.96157 1.54602 0.00000 -1.54602 -1.96157 -0.94279 0.76537 1.91388 1.66294 0.19603 -1.41421 -1.99037 -1.11114 0.58057 1.84776 1.76384 0.39018 -1.26879 -2.00000 -2.00000 1.26879 -0.39018 -1.76384 -1.84776 -0.58057 1.11114 1.99037 1.41421 -0.19603 -1.66294 -1.91388 -0.76537 0.94279 1.96157 1.54602 0.00000 -1.54602 -1.96157 -0.94279 0.76537 1.91388 1.66294 0.19603 -1.41421 -1.99037 -1.11114 0.58057 1.84776 1.76384 0.39018 -1.26879 2.00000 ... ... ..... ....... ......... ........... ............. E10u * 2.00000 1.11114 -0.76537 -1.96157 -1.41421 0.39018 1.84776 1.66294 0.00000 -1.66294 -1.84776 -0.39018 1.41421 1.96157 0.76537 -1.11114 -2.00000 -1.11114 0.76537 1.96157 1.41421 -0.39018 -1.84776 -1.66294 0.00000 1.66294 1.84776 0.39018 -1.41421 -1.96157 -0.76537 1.11114 2.00000 -2.00000 -1.11114 0.76537 1.96157 1.41421 -0.39018 -1.84776 -1.66294 0.00000 1.66294 1.84776 0.39018 -1.41421 -1.96157 -0.76537 1.11114 2.00000 1.11114 -0.76537 -1.96157 -1.41421 0.39018 1.84776 1.66294 0.00000 -1.66294 -1.84776 -0.39018 1.41421 1.96157 0.76537 -1.11114 -2.00000 ... ... ..... ....... ......... ........... ............. E11u * 2.00000 0.94279 -1.11114 -1.99037 -0.76537 1.26879 1.96157 0.58057 -1.41421 -1.91388 -0.39018 1.54602 1.84776 0.19603 -1.66294 -1.76384 0.00000 1.76384 1.66294 -0.19603 -1.84776 -1.54602 0.39018 1.91388 1.41421 -0.58057 -1.96157 -1.26879 0.76537 1.99037 1.11114 -0.94279 -2.00000 -2.00000 0.94279 -1.11114 -1.99037 -0.76537 1.26879 1.96157 0.58057 -1.41421 -1.91388 -0.39018 1.54602 1.84776 0.19603 -1.66294 -1.76384 0.00000 1.76384 1.66294 -0.19603 -1.84776 -1.54602 0.39018 1.91388 1.41421 -0.58057 -1.96157 -1.26879 0.76537 1.99037 1.11114 -0.94279 2.00000 ... ... ..... ....... ......... ........... ............. E12u * 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 -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 ... ... ..... ....... ......... ........... ............. E13u * 2.00000 0.58057 -1.66294 -1.54602 0.76537 1.99037 0.39018 -1.76384 -1.41421 0.94279 1.96157 0.19603 -1.84776 -1.26879 1.11114 1.91388 0.00000 -1.91388 -1.11114 1.26879 1.84776 -0.19603 -1.96157 -0.94279 1.41421 1.76384 -0.39018 -1.99037 -0.76537 1.54602 1.66294 -0.58057 -2.00000 -2.00000 0.58057 -1.66294 -1.54602 0.76537 1.99037 0.39018 -1.76384 -1.41421 0.94279 1.96157 0.19603 -1.84776 -1.26879 1.11114 1.91388 0.00000 -1.91388 -1.11114 1.26879 1.84776 -0.19603 -1.96157 -0.94279 1.41421 1.76384 -0.39018 -1.99037 -0.76537 1.54602 1.66294 -0.58057 2.00000 ... ... ..... ....... ......... ........... ............. E14u * 2.00000 0.39018 -1.84776 -1.11114 1.41421 1.66294 -0.76537 -1.96157 0.00000 1.96157 0.76537 -1.66294 -1.41421 1.11114 1.84776 -0.39018 -2.00000 -0.39018 1.84776 1.11114 -1.41421 -1.66294 0.76537 1.96157 0.00000 -1.96157 -0.76537 1.66294 1.41421 -1.11114 -1.84776 0.39018 2.00000 -2.00000 -0.39018 1.84776 1.11114 -1.41421 -1.66294 0.76537 1.96157 0.00000 -1.96157 -0.76537 1.66294 1.41421 -1.11114 -1.84776 0.39018 2.00000 0.39018 -1.84776 -1.11114 1.41421 1.66294 -0.76537 -1.96157 0.00000 1.96157 0.76537 -1.66294 -1.41421 1.11114 1.84776 -0.39018 -2.00000 ... ... ..... ....... ......... ........... ............. E15u * 2.00000 0.19603 -1.96157 -0.58057 1.84776 0.94279 -1.66294 -1.26879 1.41421 1.54602 -1.11114 -1.76384 0.76537 1.91388 -0.39018 -1.99037 0.00000 1.99037 0.39018 -1.91388 -0.76537 1.76384 1.11114 -1.54602 -1.41421 1.26879 1.66294 -0.94279 -1.84776 0.58057 1.96157 -0.19603 -2.00000 -2.00000 0.19603 -1.96157 -0.58057 1.84776 0.94279 -1.66294 -1.26879 1.41421 1.54602 -1.11114 -1.76384 0.76537 1.91388 -0.39018 -1.99037 0.00000 1.99037 0.39018 -1.91388 -0.76537 1.76384 1.11114 -1.54602 -1.41421 1.26879 1.66294 -0.94279 -1.84776 0.58057 1.96157 -0.19603 2.00000 ... ... ..... ....... ......... ........... ............. E16u * 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 -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 ... ... ..... ....... ......... ........... ............. E17u * 2.00000 -0.19603 -1.96157 0.58057 1.84776 -0.94279 -1.66294 1.26879 1.41421 -1.54602 -1.11114 1.76384 0.76537 -1.91388 -0.39018 1.99037 0.00000 -1.99037 0.39018 1.91388 -0.76537 -1.76384 1.11114 1.54602 -1.41421 -1.26879 1.66294 0.94279 -1.84776 -0.58057 1.96157 0.19603 -2.00000 -2.00000 -0.19603 -1.96157 0.58057 1.84776 -0.94279 -1.66294 1.26879 1.41421 -1.54602 -1.11114 1.76384 0.76537 -1.91388 -0.39018 1.99037 0.00000 -1.99037 0.39018 1.91388 -0.76537 -1.76384 1.11114 1.54602 -1.41421 -1.26879 1.66294 0.94279 -1.84776 -0.58057 1.96157 0.19603 2.00000 ... ... ..... ....... ......... ........... ............. E18u * 2.00000 -0.39018 -1.84776 1.11114 1.41421 -1.66294 -0.76537 1.96157 0.00000 -1.96157 0.76537 1.66294 -1.41421 -1.11114 1.84776 0.39018 -2.00000 0.39018 1.84776 -1.11114 -1.41421 1.66294 0.76537 -1.96157 0.00000 1.96157 -0.76537 -1.66294 1.41421 1.11114 -1.84776 -0.39018 2.00000 -2.00000 0.39018 1.84776 -1.11114 -1.41421 1.66294 0.76537 -1.96157 0.00000 1.96157 -0.76537 -1.66294 1.41421 1.11114 -1.84776 -0.39018 2.00000 -0.39018 -1.84776 1.11114 1.41421 -1.66294 -0.76537 1.96157 0.00000 -1.96157 0.76537 1.66294 -1.41421 -1.11114 1.84776 0.39018 -2.00000 ... ... ..... ....... ......... ........... ............. E19u * 2.00000 -0.58057 -1.66294 1.54602 0.76537 -1.99037 0.39018 1.76384 -1.41421 -0.94279 1.96157 -0.19603 -1.84776 1.26879 1.11114 -1.91388 0.00000 1.91388 -1.11114 -1.26879 1.84776 0.19603 -1.96157 0.94279 1.41421 -1.76384 -0.39018 1.99037 -0.76537 -1.54602 1.66294 0.58057 -2.00000 -2.00000 -0.58057 -1.66294 1.54602 0.76537 -1.99037 0.39018 1.76384 -1.41421 -0.94279 1.96157 -0.19603 -1.84776 1.26879 1.11114 -1.91388 0.00000 1.91388 -1.11114 -1.26879 1.84776 0.19603 -1.96157 0.94279 1.41421 -1.76384 -0.39018 1.99037 -0.76537 -1.54602 1.66294 0.58057 2.00000 ... ... ..... ....... ......... ........... ............. E20u * 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 -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 ... ... ..... ....... ......... ........... ............. E21u * 2.00000 -0.94279 -1.11114 1.99037 -0.76537 -1.26879 1.96157 -0.58057 -1.41421 1.91388 -0.39018 -1.54602 1.84776 -0.19603 -1.66294 1.76384 0.00000 -1.76384 1.66294 0.19603 -1.84776 1.54602 0.39018 -1.91388 1.41421 0.58057 -1.96157 1.26879 0.76537 -1.99037 1.11114 0.94279 -2.00000 -2.00000 -0.94279 -1.11114 1.99037 -0.76537 -1.26879 1.96157 -0.58057 -1.41421 1.91388 -0.39018 -1.54602 1.84776 -0.19603 -1.66294 1.76384 0.00000 -1.76384 1.66294 0.19603 -1.84776 1.54602 0.39018 -1.91388 1.41421 0.58057 -1.96157 1.26879 0.76537 -1.99037 1.11114 0.94279 2.00000 ... ... ..... ....... ......... ........... ............. E22u * 2.00000 -1.11114 -0.76537 1.96157 -1.41421 -0.39018 1.84776 -1.66294 0.00000 1.66294 -1.84776 0.39018 1.41421 -1.96157 0.76537 1.11114 -2.00000 1.11114 0.76537 -1.96157 1.41421 0.39018 -1.84776 1.66294 0.00000 -1.66294 1.84776 -0.39018 -1.41421 1.96157 -0.76537 -1.11114 2.00000 -2.00000 1.11114 0.76537 -1.96157 1.41421 0.39018 -1.84776 1.66294 0.00000 -1.66294 1.84776 -0.39018 -1.41421 1.96157 -0.76537 -1.11114 2.00000 -1.11114 -0.76537 1.96157 -1.41421 -0.39018 1.84776 -1.66294 0.00000 1.66294 -1.84776 0.39018 1.41421 -1.96157 0.76537 1.11114 -2.00000 ... ... ..... ....... ......... ........... ............. E23u * 2.00000 -1.26879 -0.39018 1.76384 -1.84776 0.58057 1.11114 -1.99037 1.41421 0.19603 -1.66294 1.91388 -0.76537 -0.94279 1.96157 -1.54602 0.00000 1.54602 -1.96157 0.94279 0.76537 -1.91388 1.66294 -0.19603 -1.41421 1.99037 -1.11114 -0.58057 1.84776 -1.76384 0.39018 1.26879 -2.00000 -2.00000 -1.26879 -0.39018 1.76384 -1.84776 0.58057 1.11114 -1.99037 1.41421 0.19603 -1.66294 1.91388 -0.76537 -0.94279 1.96157 -1.54602 0.00000 1.54602 -1.96157 0.94279 0.76537 -1.91388 1.66294 -0.19603 -1.41421 1.99037 -1.11114 -0.58057 1.84776 -1.76384 0.39018 1.26879 2.00000 ... ... ..... ....... ......... ........... ............. E24u * 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 -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 ... ... ..... ....... ......... ........... ............. E25u * 2.00000 -1.54602 0.39018 0.94279 -1.84776 1.91388 -1.11114 -0.19603 1.41421 -1.99037 1.66294 -0.58057 -0.76537 1.76384 -1.96157 1.26879 0.00000 -1.26879 1.96157 -1.76384 0.76537 0.58057 -1.66294 1.99037 -1.41421 0.19603 1.11114 -1.91388 1.84776 -0.94279 -0.39018 1.54602 -2.00000 -2.00000 -1.54602 0.39018 0.94279 -1.84776 1.91388 -1.11114 -0.19603 1.41421 -1.99037 1.66294 -0.58057 -0.76537 1.76384 -1.96157 1.26879 0.00000 -1.26879 1.96157 -1.76384 0.76537 0.58057 -1.66294 1.99037 -1.41421 0.19603 1.11114 -1.91388 1.84776 -0.94279 -0.39018 1.54602 2.00000 ... ... ..... ....... ......... ........... ............. E26u * 2.00000 -1.66294 0.76537 0.39018 -1.41421 1.96157 -1.84776 1.11114 0.00000 -1.11114 1.84776 -1.96157 1.41421 -0.39018 -0.76537 1.66294 -2.00000 1.66294 -0.76537 -0.39018 1.41421 -1.96157 1.84776 -1.11114 0.00000 1.11114 -1.84776 1.96157 -1.41421 0.39018 0.76537 -1.66294 2.00000 -2.00000 1.66294 -0.76537 -0.39018 1.41421 -1.96157 1.84776 -1.11114 0.00000 1.11114 -1.84776 1.96157 -1.41421 0.39018 0.76537 -1.66294 2.00000 -1.66294 0.76537 0.39018 -1.41421 1.96157 -1.84776 1.11114 0.00000 -1.11114 1.84776 -1.96157 1.41421 -0.39018 -0.76537 1.66294 -2.00000 ... ... ..... ....... ......... ........... ............. E27u * 2.00000 -1.76384 1.11114 -0.19603 -0.76537 1.54602 -1.96157 1.91388 -1.41421 0.58057 0.39018 -1.26879 1.84776 -1.99037 1.66294 -0.94279 0.00000 0.94279 -1.66294 1.99037 -1.84776 1.26879 -0.39018 -0.58057 1.41421 -1.91388 1.96157 -1.54602 0.76537 0.19603 -1.11114 1.76384 -2.00000 -2.00000 -1.76384 1.11114 -0.19603 -0.76537 1.54602 -1.96157 1.91388 -1.41421 0.58057 0.39018 -1.26879 1.84776 -1.99037 1.66294 -0.94279 0.00000 0.94279 -1.66294 1.99037 -1.84776 1.26879 -0.39018 -0.58057 1.41421 -1.91388 1.96157 -1.54602 0.76537 0.19603 -1.11114 1.76384 2.00000 ... ... ..... ....... ......... ........... ............. E28u * 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 -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 ... ... ..... ....... ......... ........... ............. E29u * 2.00000 -1.91388 1.66294 -1.26879 0.76537 -0.19603 -0.39018 0.94279 -1.41421 1.76384 -1.96157 1.99037 -1.84776 1.54602 -1.11114 0.58057 0.00000 -0.58057 1.11114 -1.54602 1.84776 -1.99037 1.96157 -1.76384 1.41421 -0.94279 0.39018 0.19603 -0.76537 1.26879 -1.66294 1.91388 -2.00000 -2.00000 -1.91388 1.66294 -1.26879 0.76537 -0.19603 -0.39018 0.94279 -1.41421 1.76384 -1.96157 1.99037 -1.84776 1.54602 -1.11114 0.58057 0.00000 -0.58057 1.11114 -1.54602 1.84776 -1.99037 1.96157 -1.76384 1.41421 -0.94279 0.39018 0.19603 -0.76537 1.26879 -1.66294 1.91388 2.00000 ... ... ..... ....... ......... ........... ............. E30u * 2.00000 -1.96157 1.84776 -1.66294 1.41421 -1.11114 0.76537 -0.39018 0.00000 0.39018 -0.76537 1.11114 -1.41421 1.66294 -1.84776 1.96157 -2.00000 1.96157 -1.84776 1.66294 -1.41421 1.11114 -0.76537 0.39018 0.00000 -0.39018 0.76537 -1.11114 1.41421 -1.66294 1.84776 -1.96157 2.00000 -2.00000 1.96157 -1.84776 1.66294 -1.41421 1.11114 -0.76537 0.39018 0.00000 -0.39018 0.76537 -1.11114 1.41421 -1.66294 1.84776 -1.96157 2.00000 -1.96157 1.84776 -1.66294 1.41421 -1.11114 0.76537 -0.39018 0.00000 0.39018 -0.76537 1.11114 -1.41421 1.66294 -1.84776 1.96157 -2.00000 ... ... ..... ....... ......... ........... ............. E31u * 2.00000 -1.99037 1.96157 -1.91388 1.84776 -1.76384 1.66294 -1.54602 1.41421 -1.26879 1.11114 -0.94279 0.76537 -0.58057 0.39018 -0.19603 0.00000 0.19603 -0.39018 0.58057 -0.76537 0.94279 -1.11114 1.26879 -1.41421 1.54602 -1.66294 1.76384 -1.84776 1.91388 -1.96157 1.99037 -2.00000 -2.00000 -1.99037 1.96157 -1.91388 1.84776 -1.76384 1.66294 -1.54602 1.41421 -1.26879 1.11114 -0.94279 0.76537 -0.58057 0.39018 -0.19603 0.00000 0.19603 -0.39018 0.58057 -0.76537 0.94279 -1.11114 1.26879 -1.41421 1.54602 -1.66294 1.76384 -1.84776 1.91388 -1.96157 1.99037 2.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.990369453344 = 2*cos(2*π/64) = 2*cos(π/32) = √2+√2+√2+√2 1.961570560806 = 2*cos(4*π/64) = 2*cos(π/16) = √2+√2+√2 1.913880671464 = 2*cos(6*π/64) = 2*cos(3*π/32) = √2+√2+√2−√2 1.847759065023 = 2*cos(8*π/64) = 2*cos(π/8) = √2+√2 1.763842528697 = 2*cos(10*π/64) = 2*cos(5*π/32) = √2+√2−√2−√2 1.662939224605 = 2*cos(12*π/64) = 2*cos(3*π/16) = √2+√2−√2 1.546020906725 = 2*cos(14*π/64) = 2*cos(7*π/32) = √2+√2−√2+√2 1.414213562373 = 2*cos(16*π/64) = 2*cos(π/4) = √2 1.268786568327 = 2*cos(18*π/64) = 2*cos(9*π/32) = √2−√2−√2+√2 1.111140466039 = 2*cos(20*π/64) = 2*cos(5*π/16) = √2−√2−√2 0.942793473652 = 2*cos(22*π/64) = 2*cos(11*π/32) = √2−√2−√2−√2 0.765366864730 = 2*cos(24*π/64) = 2*cos(3*π/8) = √2−√2 0.580569354509 = 2*cos(26*π/64) = 2*cos(13*π/32) = √2−√2+√2−√2 0.390180644032 = 2*cos(28*π/64) = 2*cos(7*π/16) = √2−√2+√2 0.196034280659 = 2*cos(30*π/64) = 2*cos(15*π/32) = √2−√2+√2+√2 Symmetry of Rotations and Cartesian products Ag R+d+g+i+k+m R_z, z², z⁴, z⁶ E1g R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2g d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E3g g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4g g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5g i+k+m {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6g i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7g k+m E8g k+m E9g m E10g m Au 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(x²−y²), xyz}, {z³(x²−y²), xyz³} E3u f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E4u h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5u h+j+l {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)} E6u j+l E7u j+l E8u l E9u l Notes: α The order of the C_64h point group is 128, and the order of the principal axis (C₆₄) is 64. The group has 66 irreducible representations. β The C_64h point group is generated by two symmetry elements, which are canonically chosen as C₆₄ and i. Other possible choices are C₆₄ and σ_h, or less commonly S₆₄ with either i or σ_h. γ The lowest nonvanishing multipole moment in C_64h is 4 (quadrupole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C_64h group is Abelian because all its symmetry operations are coaxial. This is a sufficient condition. In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. ε Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 124 cases have been combined into 62 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 62 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 62 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. 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 constructible polygon, as the order of the principal axis is a product of any number of different Fermat primes (3,5,17,257,65537) times an arbitrary power of two. Therefore, all characters have an algebraic degree which is a power of two and can be expressed as radicals involving only square roots and integer numbers.

This Character Table for the C_64h point group was created by Gernot Katzer.

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

	C_62h
	C_63h
C₆₄ C_64v	C_64h	D₆₄ D_64h D_64d S₆₄
	C_65h
	C_66h

Character table for the C64h point group

Character table for the C_64h point group