Character Table for Point Group S126

Character table for the S₁₂₆ point group

S126 E 2 C63 2 C63^2 2 C21 2 C63^4 2 C63^5 2 C21^2 2 C9 2 C63^8 2 C7 2 C63^10 2 C63^11 2 C21^4 2 C63^13 2 C9^2 2 C21^5 2 C63^16 2 C63^17 2 C7^2 2 C63^19 2 C63^20 2 C3 2 C63^22 2 C63^23 2 C21^8 2 C63^25 2 C63^26 2 C7^3 2 C9^4 2 C63^29 2 C21^10 2 C63^31 i 2 S126 2 S42 2 S126^5 2 S18 2 S14 2 S126^11 2 S126^13 2 S126^15 2 S126^17 2 S126^19 2 S6 2 S126^23 2 S126^25 2 S126^27 2 S126^29 2 S126^31 2 S126^33 2 S126^35 2 S126^37 2 S126^39 2 S126^41 2 S126^43 2 S126^45 2 S126^47 2 S126^49 2 S126^51 2 S126^53 2 S126^55 2 S126^57 2 S126^59 2 S126^61 <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 ..T ... ....T ....... ........T ........... ............T E1g * 2.00000 1.99006 1.96034 1.91115 1.84295 1.75644 1.65248 1.53209 1.39647 1.24698 1.08509 0.91242 0.73068 0.54168 0.34730 0.14946 -0.04986 -0.24869 -0.44504 -0.63697 -0.82257 -1.00000 -1.16749 -1.32337 -1.46610 -1.59427 -1.70658 -1.80194 -1.87939 -1.93815 -1.97766 -1.99751 2.00000 -1.99751 -1.97766 -1.93815 -1.87939 -1.80194 -1.70658 -1.59427 -1.46610 -1.32337 -1.16749 -1.00000 -0.82257 -0.63697 -0.44504 -0.24869 -0.04986 0.14946 0.34730 0.54168 0.73068 0.91242 1.08509 1.24698 1.39647 1.53209 1.65248 1.75644 1.84295 1.91115 1.96034 1.99006 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g * 2.00000 1.96034 1.84295 1.65248 1.39647 1.08509 0.73068 0.34730 -0.04986 -0.44504 -0.82257 -1.16749 -1.46610 -1.70658 -1.87939 -1.97766 -1.99751 -1.93815 -1.80194 -1.59427 -1.32337 -1.00000 -0.63697 -0.24869 0.14946 0.54168 0.91242 1.24698 1.53209 1.75644 1.91115 1.99006 2.00000 1.99006 1.91115 1.75644 1.53209 1.24698 0.91242 0.54168 0.14946 -0.24869 -0.63697 -1.00000 -1.32337 -1.59427 -1.80194 -1.93815 -1.99751 -1.97766 -1.87939 -1.70658 -1.46610 -1.16749 -0.82257 -0.44504 -0.04986 0.34730 0.73068 1.08509 1.39647 1.65248 1.84295 1.96034 ... ... TT... ....... ....TT... ........... ........TT... E3g * 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766 -1.97766 -1.80194 -1.46610 -1.00000 -0.44504 0.14946 0.73068 1.24698 1.65248 1.91115 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766 2.00000 -1.97766 -1.80194 -1.46610 -1.00000 -0.44504 0.14946 0.73068 1.24698 1.65248 1.91115 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766 -1.97766 -1.80194 -1.46610 -1.00000 -0.44504 0.14946 0.73068 1.24698 1.65248 1.91115 ... ... ..... ....... ..TT..... ........... ......TT..... E4g * 2.00000 1.84295 1.39647 0.73068 -0.04986 -0.82257 -1.46610 -1.87939 -1.99751 -1.80194 -1.32337 -0.63697 0.14946 0.91242 1.53209 1.91115 1.99006 1.75644 1.24698 0.54168 -0.24869 -1.00000 -1.59427 -1.93815 -1.97766 -1.70658 -1.16749 -0.44504 0.34730 1.08509 1.65248 1.96034 2.00000 1.96034 1.65248 1.08509 0.34730 -0.44504 -1.16749 -1.70658 -1.97766 -1.93815 -1.59427 -1.00000 -0.24869 0.54168 1.24698 1.75644 1.99006 1.91115 1.53209 0.91242 0.14946 -0.63697 -1.32337 -1.80194 -1.99751 -1.87939 -1.46610 -0.82257 -0.04986 0.73068 1.39647 1.84295 ... ... ..... ....... TT....... ........... ....TT....... E5g * 2.00000 1.75644 1.08509 0.14946 -0.82257 -1.59427 -1.97766 -1.87939 -1.32337 -0.44504 0.54168 1.39647 1.91115 1.96034 1.53209 0.73068 -0.24869 -1.16749 -1.80194 -1.99751 -1.70658 -1.00000 -0.04986 0.91242 1.65248 1.99006 1.84295 1.24698 0.34730 -0.63697 -1.46610 -1.93815 2.00000 -1.93815 -1.46610 -0.63697 0.34730 1.24698 1.84295 1.99006 1.65248 0.91242 -0.04986 -1.00000 -1.70658 -1.99751 -1.80194 -1.16749 -0.24869 0.73068 1.53209 1.96034 1.91115 1.39647 0.54168 -0.44504 -1.32337 -1.87939 -1.97766 -1.59427 -0.82257 0.14946 1.08509 1.75644 ... ... ..... ....... ......... ........... ..TT......... E6g * 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115 1.91115 1.24698 0.14946 -1.00000 -1.80194 -1.97766 -1.46610 -0.44504 0.73068 1.65248 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115 2.00000 1.91115 1.24698 0.14946 -1.00000 -1.80194 -1.97766 -1.46610 -0.44504 0.73068 1.65248 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115 1.91115 1.24698 0.14946 -1.00000 -1.80194 -1.97766 -1.46610 -0.44504 0.73068 1.65248 ... ... ..... ....... ......... ........... TT........... E7g * 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 2.00000 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 ... ... ..... ....... ......... ........... ............. E8g * 2.00000 1.39647 -0.04986 -1.46610 -1.99751 -1.32337 0.14946 1.53209 1.99006 1.24698 -0.24869 -1.59427 -1.97766 -1.16749 0.34730 1.65248 1.96034 1.08509 -0.44504 -1.70658 -1.93815 -1.00000 0.54168 1.75644 1.91115 0.91242 -0.63697 -1.80194 -1.87939 -0.82257 0.73068 1.84295 2.00000 1.84295 0.73068 -0.82257 -1.87939 -1.80194 -0.63697 0.91242 1.91115 1.75644 0.54168 -1.00000 -1.93815 -1.70658 -0.44504 1.08509 1.96034 1.65248 0.34730 -1.16749 -1.97766 -1.59427 -0.24869 1.24698 1.99006 1.53209 0.14946 -1.32337 -1.99751 -1.46610 -0.04986 1.39647 ... ... ..... ....... ......... ........... ............. E9g * 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 2.00000 -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 ... ... ..... ....... ......... ........... ............. E10g * 2.00000 1.08509 -0.82257 -1.97766 -1.32337 0.54168 1.91115 1.53209 -0.24869 -1.80194 -1.70658 -0.04986 1.65248 1.84295 0.34730 -1.46610 -1.93815 -0.63697 1.24698 1.99006 0.91242 -1.00000 -1.99751 -1.16749 0.73068 1.96034 1.39647 -0.44504 -1.87939 -1.59427 0.14946 1.75644 2.00000 1.75644 0.14946 -1.59427 -1.87939 -0.44504 1.39647 1.96034 0.73068 -1.16749 -1.99751 -1.00000 0.91242 1.99006 1.24698 -0.63697 -1.93815 -1.46610 0.34730 1.84295 1.65248 -0.04986 -1.70658 -1.80194 -0.24869 1.53209 1.91115 0.54168 -1.32337 -1.97766 -0.82257 1.08509 ... ... ..... ....... ......... ........... ............. E11g * 2.00000 0.91242 -1.16749 -1.97766 -0.63697 1.39647 1.91115 0.34730 -1.59427 -1.80194 -0.04986 1.75644 1.65248 -0.24869 -1.87939 -1.46610 0.54168 1.96034 1.24698 -0.82257 -1.99751 -1.00000 1.08509 1.99006 0.73068 -1.32337 -1.93815 -0.44504 1.53209 1.84295 0.14946 -1.70658 2.00000 -1.70658 0.14946 1.84295 1.53209 -0.44504 -1.93815 -1.32337 0.73068 1.99006 1.08509 -1.00000 -1.99751 -0.82257 1.24698 1.96034 0.54168 -1.46610 -1.87939 -0.24869 1.65248 1.75644 -0.04986 -1.80194 -1.59427 0.34730 1.91115 1.39647 -0.63697 -1.97766 -1.16749 0.91242 ... ... ..... ....... ......... ........... ............. E12g * 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248 1.65248 -0.44504 -1.97766 -1.00000 1.24698 1.91115 0.14946 -1.80194 -1.46610 0.73068 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248 2.00000 1.65248 -0.44504 -1.97766 -1.00000 1.24698 1.91115 0.14946 -1.80194 -1.46610 0.73068 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248 1.65248 -0.44504 -1.97766 -1.00000 1.24698 1.91115 0.14946 -1.80194 -1.46610 0.73068 ... ... ..... ....... ......... ........... ............. E13g * 2.00000 0.54168 -1.70658 -1.46610 0.91242 1.96034 0.14946 -1.87939 -1.16749 1.24698 1.84295 -0.24869 -1.97766 -0.82257 1.53209 1.65248 -0.63697 -1.99751 -0.44504 1.75644 1.39647 -1.00000 -1.93815 -0.04986 1.91115 1.08509 -1.32337 -1.80194 0.34730 1.99006 0.73068 -1.59427 2.00000 -1.59427 0.73068 1.99006 0.34730 -1.80194 -1.32337 1.08509 1.91115 -0.04986 -1.93815 -1.00000 1.39647 1.75644 -0.44504 -1.99751 -0.63697 1.65248 1.53209 -0.82257 -1.97766 -0.24869 1.84295 1.24698 -1.16749 -1.87939 0.14946 1.96034 0.91242 -1.46610 -1.70658 0.54168 ... ... ..... ....... ......... ........... ............. E14g * 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 2.00000 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 ... ... ..... ....... ......... ........... ............. E15g * 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610 -1.46610 1.24698 1.65248 -1.00000 -1.80194 0.73068 1.91115 -0.44504 -1.97766 0.14946 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610 2.00000 -1.46610 1.24698 1.65248 -1.00000 -1.80194 0.73068 1.91115 -0.44504 -1.97766 0.14946 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610 -1.46610 1.24698 1.65248 -1.00000 -1.80194 0.73068 1.91115 -0.44504 -1.97766 0.14946 ... ... ..... ....... ......... ........... ............. E16g * 2.00000 -0.04986 -1.99751 0.14946 1.99006 -0.24869 -1.97766 0.34730 1.96034 -0.44504 -1.93815 0.54168 1.91115 -0.63697 -1.87939 0.73068 1.84295 -0.82257 -1.80194 0.91242 1.75644 -1.00000 -1.70658 1.08509 1.65248 -1.16749 -1.59427 1.24698 1.53209 -1.32337 -1.46610 1.39647 2.00000 1.39647 -1.46610 -1.32337 1.53209 1.24698 -1.59427 -1.16749 1.65248 1.08509 -1.70658 -1.00000 1.75644 0.91242 -1.80194 -0.82257 1.84295 0.73068 -1.87939 -0.63697 1.91115 0.54168 -1.93815 -0.44504 1.96034 0.34730 -1.97766 -0.24869 1.99006 0.14946 -1.99751 -0.04986 ... ... ..... ....... ......... ........... ............. E17g * 2.00000 -0.24869 -1.93815 0.73068 1.75644 -1.16749 -1.46610 1.53209 1.08509 -1.80194 -0.63697 1.96034 0.14946 -1.99751 0.34730 1.91115 -0.82257 -1.70658 1.24698 1.39647 -1.59427 -1.00000 1.84295 0.54168 -1.97766 -0.04986 1.99006 -0.44504 -1.87939 0.91242 1.65248 -1.32337 2.00000 -1.32337 1.65248 0.91242 -1.87939 -0.44504 1.99006 -0.04986 -1.97766 0.54168 1.84295 -1.00000 -1.59427 1.39647 1.24698 -1.70658 -0.82257 1.91115 0.34730 -1.99751 0.14946 1.96034 -0.63697 -1.80194 1.08509 1.53209 -1.46610 -1.16749 1.75644 0.73068 -1.93815 -0.24869 ... ... ..... ....... ......... ........... ............. E18g * 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 2.00000 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 ... ... ..... ....... ......... ........... ............. E19g * 2.00000 -0.63697 -1.59427 1.65248 0.54168 -1.99751 0.73068 1.53209 -1.70658 -0.44504 1.99006 -0.82257 -1.46610 1.75644 0.34730 -1.97766 0.91242 1.39647 -1.80194 -0.24869 1.96034 -1.00000 -1.32337 1.84295 0.14946 -1.93815 1.08509 1.24698 -1.87939 -0.04986 1.91115 -1.16749 2.00000 -1.16749 1.91115 -0.04986 -1.87939 1.24698 1.08509 -1.93815 0.14946 1.84295 -1.32337 -1.00000 1.96034 -0.24869 -1.80194 1.39647 0.91242 -1.97766 0.34730 1.75644 -1.46610 -0.82257 1.99006 -0.44504 -1.70658 1.53209 0.73068 -1.99751 0.54168 1.65248 -1.59427 -0.63697 ... ... ..... ....... ......... ........... ............. E20g * 2.00000 -0.82257 -1.32337 1.91115 -0.24869 -1.70658 1.65248 0.34730 -1.93815 1.24698 0.91242 -1.99751 0.73068 1.39647 -1.87939 0.14946 1.75644 -1.59427 -0.44504 1.96034 -1.16749 -1.00000 1.99006 -0.63697 -1.46610 1.84295 -0.04986 -1.80194 1.53209 0.54168 -1.97766 1.08509 2.00000 1.08509 -1.97766 0.54168 1.53209 -1.80194 -0.04986 1.84295 -1.46610 -0.63697 1.99006 -1.00000 -1.16749 1.96034 -0.44504 -1.59427 1.75644 0.14946 -1.87939 1.39647 0.73068 -1.99751 0.91242 1.24698 -1.93815 0.34730 1.65248 -1.70658 -0.24869 1.91115 -1.32337 -0.82257 ... ... ..... ....... ......... ........... ............. E21g * 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 2.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E22g * 2.00000 -1.16749 -0.63697 1.91115 -1.59427 -0.04986 1.65248 -1.87939 0.54168 1.24698 -1.99751 1.08509 0.73068 -1.93815 1.53209 0.14946 -1.70658 1.84295 -0.44504 -1.32337 1.99006 -1.00000 -0.82257 1.96034 -1.46610 -0.24869 1.75644 -1.80194 0.34730 1.39647 -1.97766 0.91242 2.00000 0.91242 -1.97766 1.39647 0.34730 -1.80194 1.75644 -0.24869 -1.46610 1.96034 -0.82257 -1.00000 1.99006 -1.32337 -0.44504 1.84295 -1.70658 0.14946 1.53209 -1.93815 0.73068 1.08509 -1.99751 1.24698 0.54168 -1.87939 1.65248 -0.04986 -1.59427 1.91115 -0.63697 -1.16749 ... ... ..... ....... ......... ........... ............. E23g * 2.00000 -1.32337 -0.24869 1.65248 -1.93815 0.91242 0.73068 -1.87939 1.75644 -0.44504 -1.16749 1.99006 -1.46610 -0.04986 1.53209 -1.97766 1.08509 0.54168 -1.80194 1.84295 -0.63697 -1.00000 1.96034 -1.59427 0.14946 1.39647 -1.99751 1.24698 0.34730 -1.70658 1.91115 -0.82257 2.00000 -0.82257 1.91115 -1.70658 0.34730 1.24698 -1.99751 1.39647 0.14946 -1.59427 1.96034 -1.00000 -0.63697 1.84295 -1.80194 0.54168 1.08509 -1.97766 1.53209 -0.04986 -1.46610 1.99006 -1.16749 -0.44504 1.75644 -1.87939 0.73068 0.91242 -1.93815 1.65248 -0.24869 -1.32337 ... ... ..... ....... ......... ........... ............. E24g * 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068 0.73068 -1.80194 1.91115 -1.00000 -0.44504 1.65248 -1.97766 1.24698 0.14946 -1.46610 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068 2.00000 0.73068 -1.80194 1.91115 -1.00000 -0.44504 1.65248 -1.97766 1.24698 0.14946 -1.46610 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068 0.73068 -1.80194 1.91115 -1.00000 -0.44504 1.65248 -1.97766 1.24698 0.14946 -1.46610 ... ... ..... ....... ......... ........... ............. E25g * 2.00000 -1.59427 0.54168 0.73068 -1.70658 1.99006 -1.46610 0.34730 0.91242 -1.80194 1.96034 -1.32337 0.14946 1.08509 -1.87939 1.91115 -1.16749 -0.04986 1.24698 -1.93815 1.84295 -1.00000 -0.24869 1.39647 -1.97766 1.75644 -0.82257 -0.44504 1.53209 -1.99751 1.65248 -0.63697 2.00000 -0.63697 1.65248 -1.99751 1.53209 -0.44504 -0.82257 1.75644 -1.97766 1.39647 -0.24869 -1.00000 1.84295 -1.93815 1.24698 -0.04986 -1.16749 1.91115 -1.87939 1.08509 0.14946 -1.32337 1.96034 -1.80194 0.91242 0.34730 -1.46610 1.99006 -1.70658 0.73068 0.54168 -1.59427 ... ... ..... ....... ......... ........... ............. E26g * 2.00000 -1.70658 0.91242 0.14946 -1.16749 1.84295 -1.97766 1.53209 -0.63697 -0.44504 1.39647 -1.93815 1.91115 -1.32337 0.34730 0.73068 -1.59427 1.99006 -1.80194 1.08509 -0.04986 -1.00000 1.75644 -1.99751 1.65248 -0.82257 -0.24869 1.24698 -1.87939 1.96034 -1.46610 0.54168 2.00000 0.54168 -1.46610 1.96034 -1.87939 1.24698 -0.24869 -0.82257 1.65248 -1.99751 1.75644 -1.00000 -0.04986 1.08509 -1.80194 1.99006 -1.59427 0.73068 0.34730 -1.32337 1.91115 -1.93815 1.39647 -0.44504 -0.63697 1.53209 -1.97766 1.84295 -1.16749 0.14946 0.91242 -1.70658 ... ... ..... ....... ......... ........... ............. E27g * 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 2.00000 -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 ... ... ..... ....... ......... ........... ............. E28g * 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 2.00000 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 ... ... ..... ....... ......... ........... ............. E29g * 2.00000 -1.93815 1.75644 -1.46610 1.08509 -0.63697 0.14946 0.34730 -0.82257 1.24698 -1.59427 1.84295 -1.97766 1.99006 -1.87939 1.65248 -1.32337 0.91242 -0.44504 -0.04986 0.54168 -1.00000 1.39647 -1.70658 1.91115 -1.99751 1.96034 -1.80194 1.53209 -1.16749 0.73068 -0.24869 2.00000 -0.24869 0.73068 -1.16749 1.53209 -1.80194 1.96034 -1.99751 1.91115 -1.70658 1.39647 -1.00000 0.54168 -0.04986 -0.44504 0.91242 -1.32337 1.65248 -1.87939 1.99006 -1.97766 1.84295 -1.59427 1.24698 -0.82257 0.34730 0.14946 -0.63697 1.08509 -1.46610 1.75644 -1.93815 ... ... ..... ....... ......... ........... ............. E30g * 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946 0.14946 -0.44504 0.73068 -1.00000 1.24698 -1.46610 1.65248 -1.80194 1.91115 -1.97766 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946 2.00000 0.14946 -0.44504 0.73068 -1.00000 1.24698 -1.46610 1.65248 -1.80194 1.91115 -1.97766 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946 0.14946 -0.44504 0.73068 -1.00000 1.24698 -1.46610 1.65248 -1.80194 1.91115 -1.97766 ... ... ..... ....... ......... ........... ............. E31g * 2.00000 -1.99751 1.99006 -1.97766 1.96034 -1.93815 1.91115 -1.87939 1.84295 -1.80194 1.75644 -1.70658 1.65248 -1.59427 1.53209 -1.46610 1.39647 -1.32337 1.24698 -1.16749 1.08509 -1.00000 0.91242 -0.82257 0.73068 -0.63697 0.54168 -0.44504 0.34730 -0.24869 0.14946 -0.04986 2.00000 -0.04986 0.14946 -0.24869 0.34730 -0.44504 0.54168 -0.63697 0.73068 -0.82257 0.91242 -1.00000 1.08509 -1.16749 1.24698 -1.32337 1.39647 -1.46610 1.53209 -1.59427 1.65248 -1.70658 1.75644 -1.80194 1.84295 -1.87939 1.91115 -1.93815 1.96034 -1.97766 1.99006 -1.99751 ... ... ..... ....... ......... ........... ............. 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 ... ..T ..... ......T ......... ..........T ............. E1u * 2.00000 1.99006 1.96034 1.91115 1.84295 1.75644 1.65248 1.53209 1.39647 1.24698 1.08509 0.91242 0.73068 0.54168 0.34730 0.14946 -0.04986 -0.24869 -0.44504 -0.63697 -0.82257 -1.00000 -1.16749 -1.32337 -1.46610 -1.59427 -1.70658 -1.80194 -1.87939 -1.93815 -1.97766 -1.99751 -2.00000 1.99751 1.97766 1.93815 1.87939 1.80194 1.70658 1.59427 1.46610 1.32337 1.16749 1.00000 0.82257 0.63697 0.44504 0.24869 0.04986 -0.14946 -0.34730 -0.54168 -0.73068 -0.91242 -1.08509 -1.24698 -1.39647 -1.53209 -1.65248 -1.75644 -1.84295 -1.91115 -1.96034 -1.99006 ... TT. ..... ....TT. ......... ........TT. ............. E2u * 2.00000 1.96034 1.84295 1.65248 1.39647 1.08509 0.73068 0.34730 -0.04986 -0.44504 -0.82257 -1.16749 -1.46610 -1.70658 -1.87939 -1.97766 -1.99751 -1.93815 -1.80194 -1.59427 -1.32337 -1.00000 -0.63697 -0.24869 0.14946 0.54168 0.91242 1.24698 1.53209 1.75644 1.91115 1.99006 -2.00000 -1.99006 -1.91115 -1.75644 -1.53209 -1.24698 -0.91242 -0.54168 -0.14946 0.24869 0.63697 1.00000 1.32337 1.59427 1.80194 1.93815 1.99751 1.97766 1.87939 1.70658 1.46610 1.16749 0.82257 0.44504 0.04986 -0.34730 -0.73068 -1.08509 -1.39647 -1.65248 -1.84295 -1.96034 ... ... ..... ..TT... ......... ......TT... ............. E3u * 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766 -1.97766 -1.80194 -1.46610 -1.00000 -0.44504 0.14946 0.73068 1.24698 1.65248 1.91115 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766 -2.00000 1.97766 1.80194 1.46610 1.00000 0.44504 -0.14946 -0.73068 -1.24698 -1.65248 -1.91115 -2.00000 -1.91115 -1.65248 -1.24698 -0.73068 -0.14946 0.44504 1.00000 1.46610 1.80194 1.97766 1.97766 1.80194 1.46610 1.00000 0.44504 -0.14946 -0.73068 -1.24698 -1.65248 -1.91115 ... ... ..... TT..... ......... ....TT..... ............. E4u * 2.00000 1.84295 1.39647 0.73068 -0.04986 -0.82257 -1.46610 -1.87939 -1.99751 -1.80194 -1.32337 -0.63697 0.14946 0.91242 1.53209 1.91115 1.99006 1.75644 1.24698 0.54168 -0.24869 -1.00000 -1.59427 -1.93815 -1.97766 -1.70658 -1.16749 -0.44504 0.34730 1.08509 1.65248 1.96034 -2.00000 -1.96034 -1.65248 -1.08509 -0.34730 0.44504 1.16749 1.70658 1.97766 1.93815 1.59427 1.00000 0.24869 -0.54168 -1.24698 -1.75644 -1.99006 -1.91115 -1.53209 -0.91242 -0.14946 0.63697 1.32337 1.80194 1.99751 1.87939 1.46610 0.82257 0.04986 -0.73068 -1.39647 -1.84295 ... ... ..... ....... ......... ..TT....... ............. E5u * 2.00000 1.75644 1.08509 0.14946 -0.82257 -1.59427 -1.97766 -1.87939 -1.32337 -0.44504 0.54168 1.39647 1.91115 1.96034 1.53209 0.73068 -0.24869 -1.16749 -1.80194 -1.99751 -1.70658 -1.00000 -0.04986 0.91242 1.65248 1.99006 1.84295 1.24698 0.34730 -0.63697 -1.46610 -1.93815 -2.00000 1.93815 1.46610 0.63697 -0.34730 -1.24698 -1.84295 -1.99006 -1.65248 -0.91242 0.04986 1.00000 1.70658 1.99751 1.80194 1.16749 0.24869 -0.73068 -1.53209 -1.96034 -1.91115 -1.39647 -0.54168 0.44504 1.32337 1.87939 1.97766 1.59427 0.82257 -0.14946 -1.08509 -1.75644 ... ... ..... ....... ......... TT......... ............. E6u * 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115 1.91115 1.24698 0.14946 -1.00000 -1.80194 -1.97766 -1.46610 -0.44504 0.73068 1.65248 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115 -2.00000 -1.91115 -1.24698 -0.14946 1.00000 1.80194 1.97766 1.46610 0.44504 -0.73068 -1.65248 -2.00000 -1.65248 -0.73068 0.44504 1.46610 1.97766 1.80194 1.00000 -0.14946 -1.24698 -1.91115 -1.91115 -1.24698 -0.14946 1.00000 1.80194 1.97766 1.46610 0.44504 -0.73068 -1.65248 ... ... ..... ....... ......... ........... ............. E7u * 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -2.00000 1.87939 1.00000 -0.34730 -1.53209 -2.00000 -1.53209 -0.34730 1.00000 1.87939 1.87939 1.00000 -0.34730 -1.53209 -2.00000 -1.53209 -0.34730 1.00000 1.87939 1.87939 1.00000 -0.34730 -1.53209 -2.00000 -1.53209 -0.34730 1.00000 1.87939 1.87939 1.00000 -0.34730 -1.53209 ... ... ..... ....... ......... ........... ............. E8u * 2.00000 1.39647 -0.04986 -1.46610 -1.99751 -1.32337 0.14946 1.53209 1.99006 1.24698 -0.24869 -1.59427 -1.97766 -1.16749 0.34730 1.65248 1.96034 1.08509 -0.44504 -1.70658 -1.93815 -1.00000 0.54168 1.75644 1.91115 0.91242 -0.63697 -1.80194 -1.87939 -0.82257 0.73068 1.84295 -2.00000 -1.84295 -0.73068 0.82257 1.87939 1.80194 0.63697 -0.91242 -1.91115 -1.75644 -0.54168 1.00000 1.93815 1.70658 0.44504 -1.08509 -1.96034 -1.65248 -0.34730 1.16749 1.97766 1.59427 0.24869 -1.24698 -1.99006 -1.53209 -0.14946 1.32337 1.99751 1.46610 0.04986 -1.39647 ... ... ..... ....... ......... ........... ............. E9u * 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 -2.00000 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 ... ... ..... ....... ......... ........... ............. E10u * 2.00000 1.08509 -0.82257 -1.97766 -1.32337 0.54168 1.91115 1.53209 -0.24869 -1.80194 -1.70658 -0.04986 1.65248 1.84295 0.34730 -1.46610 -1.93815 -0.63697 1.24698 1.99006 0.91242 -1.00000 -1.99751 -1.16749 0.73068 1.96034 1.39647 -0.44504 -1.87939 -1.59427 0.14946 1.75644 -2.00000 -1.75644 -0.14946 1.59427 1.87939 0.44504 -1.39647 -1.96034 -0.73068 1.16749 1.99751 1.00000 -0.91242 -1.99006 -1.24698 0.63697 1.93815 1.46610 -0.34730 -1.84295 -1.65248 0.04986 1.70658 1.80194 0.24869 -1.53209 -1.91115 -0.54168 1.32337 1.97766 0.82257 -1.08509 ... ... ..... ....... ......... ........... ............. E11u * 2.00000 0.91242 -1.16749 -1.97766 -0.63697 1.39647 1.91115 0.34730 -1.59427 -1.80194 -0.04986 1.75644 1.65248 -0.24869 -1.87939 -1.46610 0.54168 1.96034 1.24698 -0.82257 -1.99751 -1.00000 1.08509 1.99006 0.73068 -1.32337 -1.93815 -0.44504 1.53209 1.84295 0.14946 -1.70658 -2.00000 1.70658 -0.14946 -1.84295 -1.53209 0.44504 1.93815 1.32337 -0.73068 -1.99006 -1.08509 1.00000 1.99751 0.82257 -1.24698 -1.96034 -0.54168 1.46610 1.87939 0.24869 -1.65248 -1.75644 0.04986 1.80194 1.59427 -0.34730 -1.91115 -1.39647 0.63697 1.97766 1.16749 -0.91242 ... ... ..... ....... ......... ........... ............. E12u * 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248 1.65248 -0.44504 -1.97766 -1.00000 1.24698 1.91115 0.14946 -1.80194 -1.46610 0.73068 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248 -2.00000 -1.65248 0.44504 1.97766 1.00000 -1.24698 -1.91115 -0.14946 1.80194 1.46610 -0.73068 -2.00000 -0.73068 1.46610 1.80194 -0.14946 -1.91115 -1.24698 1.00000 1.97766 0.44504 -1.65248 -1.65248 0.44504 1.97766 1.00000 -1.24698 -1.91115 -0.14946 1.80194 1.46610 -0.73068 ... ... ..... ....... ......... ........... ............. E13u * 2.00000 0.54168 -1.70658 -1.46610 0.91242 1.96034 0.14946 -1.87939 -1.16749 1.24698 1.84295 -0.24869 -1.97766 -0.82257 1.53209 1.65248 -0.63697 -1.99751 -0.44504 1.75644 1.39647 -1.00000 -1.93815 -0.04986 1.91115 1.08509 -1.32337 -1.80194 0.34730 1.99006 0.73068 -1.59427 -2.00000 1.59427 -0.73068 -1.99006 -0.34730 1.80194 1.32337 -1.08509 -1.91115 0.04986 1.93815 1.00000 -1.39647 -1.75644 0.44504 1.99751 0.63697 -1.65248 -1.53209 0.82257 1.97766 0.24869 -1.84295 -1.24698 1.16749 1.87939 -0.14946 -1.96034 -0.91242 1.46610 1.70658 -0.54168 ... ... ..... ....... ......... ........... ............. E14u * 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 -2.00000 -1.53209 1.00000 1.87939 -0.34730 -2.00000 -0.34730 1.87939 1.00000 -1.53209 -1.53209 1.00000 1.87939 -0.34730 -2.00000 -0.34730 1.87939 1.00000 -1.53209 -1.53209 1.00000 1.87939 -0.34730 -2.00000 -0.34730 1.87939 1.00000 -1.53209 -1.53209 1.00000 1.87939 -0.34730 ... ... ..... ....... ......... ........... ............. E15u * 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610 -1.46610 1.24698 1.65248 -1.00000 -1.80194 0.73068 1.91115 -0.44504 -1.97766 0.14946 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610 -2.00000 1.46610 -1.24698 -1.65248 1.00000 1.80194 -0.73068 -1.91115 0.44504 1.97766 -0.14946 -2.00000 -0.14946 1.97766 0.44504 -1.91115 -0.73068 1.80194 1.00000 -1.65248 -1.24698 1.46610 1.46610 -1.24698 -1.65248 1.00000 1.80194 -0.73068 -1.91115 0.44504 1.97766 -0.14946 ... ... ..... ....... ......... ........... ............. E16u * 2.00000 -0.04986 -1.99751 0.14946 1.99006 -0.24869 -1.97766 0.34730 1.96034 -0.44504 -1.93815 0.54168 1.91115 -0.63697 -1.87939 0.73068 1.84295 -0.82257 -1.80194 0.91242 1.75644 -1.00000 -1.70658 1.08509 1.65248 -1.16749 -1.59427 1.24698 1.53209 -1.32337 -1.46610 1.39647 -2.00000 -1.39647 1.46610 1.32337 -1.53209 -1.24698 1.59427 1.16749 -1.65248 -1.08509 1.70658 1.00000 -1.75644 -0.91242 1.80194 0.82257 -1.84295 -0.73068 1.87939 0.63697 -1.91115 -0.54168 1.93815 0.44504 -1.96034 -0.34730 1.97766 0.24869 -1.99006 -0.14946 1.99751 0.04986 ... ... ..... ....... ......... ........... ............. E17u * 2.00000 -0.24869 -1.93815 0.73068 1.75644 -1.16749 -1.46610 1.53209 1.08509 -1.80194 -0.63697 1.96034 0.14946 -1.99751 0.34730 1.91115 -0.82257 -1.70658 1.24698 1.39647 -1.59427 -1.00000 1.84295 0.54168 -1.97766 -0.04986 1.99006 -0.44504 -1.87939 0.91242 1.65248 -1.32337 -2.00000 1.32337 -1.65248 -0.91242 1.87939 0.44504 -1.99006 0.04986 1.97766 -0.54168 -1.84295 1.00000 1.59427 -1.39647 -1.24698 1.70658 0.82257 -1.91115 -0.34730 1.99751 -0.14946 -1.96034 0.63697 1.80194 -1.08509 -1.53209 1.46610 1.16749 -1.75644 -0.73068 1.93815 0.24869 ... ... ..... ....... ......... ........... ............. E18u * 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 -2.00000 -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 ... ... ..... ....... ......... ........... ............. E19u * 2.00000 -0.63697 -1.59427 1.65248 0.54168 -1.99751 0.73068 1.53209 -1.70658 -0.44504 1.99006 -0.82257 -1.46610 1.75644 0.34730 -1.97766 0.91242 1.39647 -1.80194 -0.24869 1.96034 -1.00000 -1.32337 1.84295 0.14946 -1.93815 1.08509 1.24698 -1.87939 -0.04986 1.91115 -1.16749 -2.00000 1.16749 -1.91115 0.04986 1.87939 -1.24698 -1.08509 1.93815 -0.14946 -1.84295 1.32337 1.00000 -1.96034 0.24869 1.80194 -1.39647 -0.91242 1.97766 -0.34730 -1.75644 1.46610 0.82257 -1.99006 0.44504 1.70658 -1.53209 -0.73068 1.99751 -0.54168 -1.65248 1.59427 0.63697 ... ... ..... ....... ......... ........... ............. E20u * 2.00000 -0.82257 -1.32337 1.91115 -0.24869 -1.70658 1.65248 0.34730 -1.93815 1.24698 0.91242 -1.99751 0.73068 1.39647 -1.87939 0.14946 1.75644 -1.59427 -0.44504 1.96034 -1.16749 -1.00000 1.99006 -0.63697 -1.46610 1.84295 -0.04986 -1.80194 1.53209 0.54168 -1.97766 1.08509 -2.00000 -1.08509 1.97766 -0.54168 -1.53209 1.80194 0.04986 -1.84295 1.46610 0.63697 -1.99006 1.00000 1.16749 -1.96034 0.44504 1.59427 -1.75644 -0.14946 1.87939 -1.39647 -0.73068 1.99751 -0.91242 -1.24698 1.93815 -0.34730 -1.65248 1.70658 0.24869 -1.91115 1.32337 0.82257 ... ... ..... ....... ......... ........... ............. E21u * 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -2.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E22u * 2.00000 -1.16749 -0.63697 1.91115 -1.59427 -0.04986 1.65248 -1.87939 0.54168 1.24698 -1.99751 1.08509 0.73068 -1.93815 1.53209 0.14946 -1.70658 1.84295 -0.44504 -1.32337 1.99006 -1.00000 -0.82257 1.96034 -1.46610 -0.24869 1.75644 -1.80194 0.34730 1.39647 -1.97766 0.91242 -2.00000 -0.91242 1.97766 -1.39647 -0.34730 1.80194 -1.75644 0.24869 1.46610 -1.96034 0.82257 1.00000 -1.99006 1.32337 0.44504 -1.84295 1.70658 -0.14946 -1.53209 1.93815 -0.73068 -1.08509 1.99751 -1.24698 -0.54168 1.87939 -1.65248 0.04986 1.59427 -1.91115 0.63697 1.16749 ... ... ..... ....... ......... ........... ............. E23u * 2.00000 -1.32337 -0.24869 1.65248 -1.93815 0.91242 0.73068 -1.87939 1.75644 -0.44504 -1.16749 1.99006 -1.46610 -0.04986 1.53209 -1.97766 1.08509 0.54168 -1.80194 1.84295 -0.63697 -1.00000 1.96034 -1.59427 0.14946 1.39647 -1.99751 1.24698 0.34730 -1.70658 1.91115 -0.82257 -2.00000 0.82257 -1.91115 1.70658 -0.34730 -1.24698 1.99751 -1.39647 -0.14946 1.59427 -1.96034 1.00000 0.63697 -1.84295 1.80194 -0.54168 -1.08509 1.97766 -1.53209 0.04986 1.46610 -1.99006 1.16749 0.44504 -1.75644 1.87939 -0.73068 -0.91242 1.93815 -1.65248 0.24869 1.32337 ... ... ..... ....... ......... ........... ............. E24u * 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068 0.73068 -1.80194 1.91115 -1.00000 -0.44504 1.65248 -1.97766 1.24698 0.14946 -1.46610 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068 -2.00000 -0.73068 1.80194 -1.91115 1.00000 0.44504 -1.65248 1.97766 -1.24698 -0.14946 1.46610 -2.00000 1.46610 -0.14946 -1.24698 1.97766 -1.65248 0.44504 1.00000 -1.91115 1.80194 -0.73068 -0.73068 1.80194 -1.91115 1.00000 0.44504 -1.65248 1.97766 -1.24698 -0.14946 1.46610 ... ... ..... ....... ......... ........... ............. E25u * 2.00000 -1.59427 0.54168 0.73068 -1.70658 1.99006 -1.46610 0.34730 0.91242 -1.80194 1.96034 -1.32337 0.14946 1.08509 -1.87939 1.91115 -1.16749 -0.04986 1.24698 -1.93815 1.84295 -1.00000 -0.24869 1.39647 -1.97766 1.75644 -0.82257 -0.44504 1.53209 -1.99751 1.65248 -0.63697 -2.00000 0.63697 -1.65248 1.99751 -1.53209 0.44504 0.82257 -1.75644 1.97766 -1.39647 0.24869 1.00000 -1.84295 1.93815 -1.24698 0.04986 1.16749 -1.91115 1.87939 -1.08509 -0.14946 1.32337 -1.96034 1.80194 -0.91242 -0.34730 1.46610 -1.99006 1.70658 -0.73068 -0.54168 1.59427 ... ... ..... ....... ......... ........... ............. E26u * 2.00000 -1.70658 0.91242 0.14946 -1.16749 1.84295 -1.97766 1.53209 -0.63697 -0.44504 1.39647 -1.93815 1.91115 -1.32337 0.34730 0.73068 -1.59427 1.99006 -1.80194 1.08509 -0.04986 -1.00000 1.75644 -1.99751 1.65248 -0.82257 -0.24869 1.24698 -1.87939 1.96034 -1.46610 0.54168 -2.00000 -0.54168 1.46610 -1.96034 1.87939 -1.24698 0.24869 0.82257 -1.65248 1.99751 -1.75644 1.00000 0.04986 -1.08509 1.80194 -1.99006 1.59427 -0.73068 -0.34730 1.32337 -1.91115 1.93815 -1.39647 0.44504 0.63697 -1.53209 1.97766 -1.84295 1.16749 -0.14946 -0.91242 1.70658 ... ... ..... ....... ......... ........... ............. E27u * 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 -2.00000 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 ... ... ..... ....... ......... ........... ............. E28u * 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 -2.00000 -0.34730 1.00000 -1.53209 1.87939 -2.00000 1.87939 -1.53209 1.00000 -0.34730 -0.34730 1.00000 -1.53209 1.87939 -2.00000 1.87939 -1.53209 1.00000 -0.34730 -0.34730 1.00000 -1.53209 1.87939 -2.00000 1.87939 -1.53209 1.00000 -0.34730 -0.34730 1.00000 -1.53209 1.87939 ... ... ..... ....... ......... ........... ............. E29u * 2.00000 -1.93815 1.75644 -1.46610 1.08509 -0.63697 0.14946 0.34730 -0.82257 1.24698 -1.59427 1.84295 -1.97766 1.99006 -1.87939 1.65248 -1.32337 0.91242 -0.44504 -0.04986 0.54168 -1.00000 1.39647 -1.70658 1.91115 -1.99751 1.96034 -1.80194 1.53209 -1.16749 0.73068 -0.24869 -2.00000 0.24869 -0.73068 1.16749 -1.53209 1.80194 -1.96034 1.99751 -1.91115 1.70658 -1.39647 1.00000 -0.54168 0.04986 0.44504 -0.91242 1.32337 -1.65248 1.87939 -1.99006 1.97766 -1.84295 1.59427 -1.24698 0.82257 -0.34730 -0.14946 0.63697 -1.08509 1.46610 -1.75644 1.93815 ... ... ..... ....... ......... ........... ............. E30u * 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946 0.14946 -0.44504 0.73068 -1.00000 1.24698 -1.46610 1.65248 -1.80194 1.91115 -1.97766 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946 -2.00000 -0.14946 0.44504 -0.73068 1.00000 -1.24698 1.46610 -1.65248 1.80194 -1.91115 1.97766 -2.00000 1.97766 -1.91115 1.80194 -1.65248 1.46610 -1.24698 1.00000 -0.73068 0.44504 -0.14946 -0.14946 0.44504 -0.73068 1.00000 -1.24698 1.46610 -1.65248 1.80194 -1.91115 1.97766 ... ... ..... ....... ......... ........... ............. E31u * 2.00000 -1.99751 1.99006 -1.97766 1.96034 -1.93815 1.91115 -1.87939 1.84295 -1.80194 1.75644 -1.70658 1.65248 -1.59427 1.53209 -1.46610 1.39647 -1.32337 1.24698 -1.16749 1.08509 -1.00000 0.91242 -0.82257 0.73068 -0.63697 0.54168 -0.44504 0.34730 -0.24869 0.14946 -0.04986 -2.00000 0.04986 -0.14946 0.24869 -0.34730 0.44504 -0.54168 0.63697 -0.73068 0.82257 -0.91242 1.00000 -1.08509 1.16749 -1.24698 1.32337 -1.39647 1.46610 -1.53209 1.59427 -1.65248 1.70658 -1.75644 1.80194 -1.84295 1.87939 -1.91115 1.93815 -1.96034 1.97766 -1.99006 1.99751 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.997513842438 = 2*cos(2*π/126) = 2*cos(π/63) 1.990061550731 = 2*cos(4*π/126) = 2*cos(2*π/63) 1.977661652450 = 2*cos(6*π/126) = 2*cos(π/21) 1.960344975697 = 2*cos(8*π/126) = 2*cos(4*π/63) 1.938154572458 = 2*cos(10*π/126) = 2*cos(5*π/63) 1.911145611572 = 2*cos(12*π/126) = 2*cos(2*π/21) 1.879385241572 = 2*cos(14*π/126) = 2*cos(π/9) 1.842952423741 = 2*cos(16*π/126) = 2*cos(8*π/63) 1.801937735805 = 2*cos(18*π/126) = 2*cos(π/7) 1.756443146740 = 2*cos(20*π/126) = 2*cos(10*π/63) 1.706581763264 = 2*cos(22*π/126) = 2*cos(11*π/63) 1.652477548632 = 2*cos(24*π/126) = 2*cos(4*π/21) 1.594265014446 = 2*cos(26*π/126) = 2*cos(13*π/63) 1.532088886238 = 2*cos(28*π/126) = 2*cos(2*π/9) 1.466103743660 = 2*cos(30*π/126) = 2*cos(5*π/21) 1.396473636172 = 2*cos(32*π/126) = 2*cos(16*π/63) 1.323371675194 = 2*cos(34*π/126) = 2*cos(17*π/63) 1.246979603717 = 2*cos(36*π/126) = 2*cos(2*π/7) 1.167487344469 = 2*cos(38*π/126) = 2*cos(19*π/63) 1.085092527731 = 2*cos(40*π/126) = 2*cos(20*π/63) 0.912421314706 = 2*cos(44*π/126) = 2*cos(22*π/63) 0.822574206261 = 2*cos(46*π/126) = 2*cos(23*π/63) 0.730682048733 = 2*cos(48*π/126) = 2*cos(8*π/21) 0.636973300503 = 2*cos(50*π/126) = 2*cos(25*π/63) 0.541680936286 = 2*cos(52*π/126) = 2*cos(26*π/63) 0.445041867912 = 2*cos(54*π/126) = 2*cos(3*π/7) 0.347296355334 = 2*cos(56*π/126) = 2*cos(4*π/9) 0.248687409295 = 2*cos(58*π/126) = 2*cos(29*π/63) 0.149460187173 = 2*cos(60*π/126) = 2*cos(10*π/21) 0.049861383476 = 2*cos(62*π/126) = 2*cos(31*π/63) Symmetry of Rotations and Cartesian products Ag R+d+g+i R_z, z², z⁴, z⁶ E1g R+d+g+i {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2g d+g+i {x²–y², xy}, {z²(x²–y²), xyz²}, {z⁴(x²–y²), xyz⁴} E3g g+i {xz(x²–3y²), yz(3x²–y²)}, {xz³(x²–3y²), yz³(3x²–y²)} E4g g+i {(x²–y²)²–2x²y², xy(x²–y²)}, {z²((x²–y²)²–4x²y²), xyz²(x²–y²)} E5g i {xz(x²–(5+2√5)y²)(x²–(5–2√5)y²), yz(y²–(5+2√5)x²)(y²–(5–2√5)x²)(y²–(5–2√5)x²)} E6g i {x²(x²–3y²)²–y²(3x²–y²)², xy(x²–3y²)(3x²–y²)} Au p+f+h z, z³, z⁵ E1u p+f+h {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2u f+h {z(x²–y²), xyz}, {z³(x²–y²), xyz³} E3u f+h {x(x²–3y²), y(3x²–y²)}, {xz²(x²–3y²), yz²(3x²–y²)} E4u h {z((x²–y²)²–4x²y²), xyz(x²–y²)} E5u h {x(x²–(5+2√5)y²)(x²–(5–2√5)y²), y(y²–(5+2√5)x²)(y²–(5–2√5)x²)(y²–(5–2√5)x²)} Notes: α The order of the S₁₂₆ point group is 126, and the order of the principal axis is 126. β The S₁₂₆ point group could also be named C_63i, because the S₁₂₆ axis is identical to a roto-inversion axis of order 63. γ This is an Abelian point group (the commutative law holds between all symmetry operations). The S₁₂₆ group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition). In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. δ 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. ε 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. ζ 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 less than half the order of the principal axis (and often much less). For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the S₁₂₆ point group was created by Gernot Katzer.

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

	S₁₂₄
C₁₂₆ C_126v C_126h D₁₂₆ D_126h D_126d	S₁₂₆
	S₁₂₈

Character table for the S126 point group

Character table for the S₁₂₆ point group