Character Table for Point Group D63h

Character table for the D_63h point group

D63h 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 63 C2' sh 2 S63 2 S21 2 S63^5 2 S9 2 S7 2 S63^11 2 S63^13 2 S21^5 2 S63^17 2 S63^19 2 S3 2 S63^23 2 S63^25 2 S7^3 2 S63^29 2 S63^31 2 S21^11 2 S9^5 2 S63^37 2 S21^13 2 S63^41 2 S63^43 2 S7^5 2 S63^47 2 S9^7 2 S21^17 2 S63^53 2 S63^55 2 S21^19 2 S63^59 2 S63^61 63 sv <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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ... ....T ....... ........T ........... ............T 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 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. 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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 ..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 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 1.00000 ... ..T ..... ......T ......... ..........T ............. E1' 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 0.00000 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 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E1" 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 0.00000 -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 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2' 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 0.00000 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 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E2" 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 0.00000 -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 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3' 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 0.00000 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 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E3" 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 0.00000 -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 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4' 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 0.00000 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 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E4" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5' 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 0.00000 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 0.00000 ... ... ..... ....... ......... TT......... ............. E5" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... TT........... E6" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E7' 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E7" 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E8' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E8" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E9' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E9" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E10' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E10" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E11' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E11" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E12' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E12" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E13' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E13" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E14' 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E14" 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E15' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E15" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E16' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E16" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E17' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E17" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E18' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E18" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E19' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E19" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E20' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E20" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E21' 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E21" 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E22' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E22" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E23' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E23" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E24' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E24" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E25' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E25" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E26' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E26" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E27' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E27" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E28' 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E28" 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E29' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E29" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E30' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E30" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E31' 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 0.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E31" 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 0.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. 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) 1.167487344470 = 2*cos(38*π/126) = 2*cos(19*π/63) 1.085092527732 = 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) 0.445041867913 = 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 A1' d+g+i+k+m z², z⁴, z⁶ A2' R R_z A2" p+f+h+j+l z, z³, z⁵ E1' p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E1" R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2' d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E2" f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3' f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E3" g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4' g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E4" h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5' 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)} E5" 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)} E6' i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E6" j+l E7' j+l E7" k+m E8' k+m E8" l E9' l E9" m E10' m Notes: α The order of the D_63h point group is 252, and the order of the principal axis (S₆₃) is 126. The group has 66 irreducible representations. β The D_63h point group is isomorphic to D_63d, C_126v and D₁₂₆. γ The D_63h point group is generated by two symmetry elements, S₆₃ and either a perpendicular C₂^′ or a vertical σ_v. Also, the group may be generated from two σ_v planes, or a σ_v and a C₂^′ (some pairs will yield smaller groups, though; choosing a minimum angle is safe). The canonical choice, however, is to use redundant generators: C₆₃, C₂^′ and σ_h. δ The group contains one set of C₂^′ symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set. Similarly, the single set of symmetry planes denoted σ_d contains the xz plane but not the yz plane. ε The lowest nonvanishing multipole moment in D_63h is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. η Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. θ The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. All characters of this group can be expressed using complex numbers, elementary arithmetic operations, square roots and third roots.

This Character Table for the D_63h point group was created by Gernot Katzer.

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

	D_61h
	D_62h
C₆₃ C_63v C_63h D₆₃	D_63h	D_63d
	D_64h
	D_65h

Character table for the D63h point group

Character table for the D_63h point group