D72h E 2 C72 2 C36 2 C24 2 C18 2 C72^5 2 C12 2 C72^7 2 C9 2 C8 2 C36^5 2 C72^11 2 C6 2 C72^13 2 C36^7 2 C24^5 2 C9^2 2 C72^17 2 C4 2 C72^19 2 C18^5 2 C24^7 2 C36^11 2 C72^23 2 C3 2 C72^25 2 C36^13 2 C8^3 2 C18^7 2 C72^29 2 C12^5 2 C72^31 2 C9^4 2 C24^11 2 C36^17 2 C72^35 C2 36 C2' 36 C2" i 2 S72 2 S36 2 S24 2 S18 2 S72^5 2 S12 2 S72^7 2 S9 2 S8 2 S36^5 2 S72^11 2 S6 2 S72^13 2 S36^7 2 S24^5 2 S9^2 2 S72^17 2 S4 2 S72^19 2 S18^5 2 S24^7 2 S36^11 2 S72^23 2 S3 2 S72^25 2 S36^13 2 S8^3 2 S18^7 2 S72^29 2 S12^5 2 S72^31 2 S9^4 2 S24^11 2 S36^17 2 S72^35 sh 36 sv 36 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ... ....T ....... ........T ........... ............T A2g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. B1g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. B2g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -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 1.99239 1.96962 1.93185 1.87939 1.81262 1.73205 1.63830 1.53209 1.41421 1.28558 1.14715 1.00000 0.84524 0.68404 0.51764 0.34730 0.17431 0.00000 -0.17431 -0.34730 -0.51764 -0.68404 -0.84524 -1.00000 -1.14715 -1.28558 -1.41421 -1.53209 -1.63830 -1.73205 -1.81262 -1.87939 -1.93185 -1.96962 -1.99239 -2.00000 0.00000 0.00000 2.00000 -1.99239 -1.96962 -1.93185 -1.87939 -1.81262 -1.73205 -1.63830 -1.53209 -1.41421 -1.28558 -1.14715 -1.00000 -0.84524 -0.68404 -0.51764 -0.34730 -0.17431 0.00000 0.17431 0.34730 0.51764 0.68404 0.84524 1.00000 1.14715 1.28558 1.41421 1.53209 1.63830 1.73205 1.81262 1.87939 1.93185 1.96962 1.99239 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.96962 1.87939 1.73205 1.53209 1.28558 1.00000 0.68404 0.34730 0.00000 -0.34730 -0.68404 -1.00000 -1.28558 -1.53209 -1.73205 -1.87939 -1.96962 -2.00000 -1.96962 -1.87939 -1.73205 -1.53209 -1.28558 -1.00000 -0.68404 -0.34730 0.00000 0.34730 0.68404 1.00000 1.28558 1.53209 1.73205 1.87939 1.96962 2.00000 0.00000 0.00000 2.00000 1.96962 1.87939 1.73205 1.53209 1.28558 1.00000 0.68404 0.34730 0.00000 -0.34730 -0.68404 -1.00000 -1.28558 -1.53209 -1.73205 -1.87939 -1.96962 -2.00000 -1.96962 -1.87939 -1.73205 -1.53209 -1.28558 -1.00000 -0.68404 -0.34730 0.00000 0.34730 0.68404 1.00000 1.28558 1.53209 1.73205 1.87939 1.96962 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 2.00000 1.93185 1.73205 1.41421 1.00000 0.51764 0.00000 -0.51764 -1.00000 -1.41421 -1.73205 -1.93185 -2.00000 -1.93185 -1.73205 -1.41421 -1.00000 -0.51764 0.00000 0.51764 1.00000 1.41421 1.73205 1.93185 2.00000 1.93185 1.73205 1.41421 1.00000 0.51764 0.00000 -0.51764 -1.00000 -1.41421 -1.73205 -1.93185 -2.00000 0.00000 0.00000 2.00000 -1.93185 -1.73205 -1.41421 -1.00000 -0.51764 0.00000 0.51764 1.00000 1.41421 1.73205 1.93185 2.00000 1.93185 1.73205 1.41421 1.00000 0.51764 0.00000 -0.51764 -1.00000 -1.41421 -1.73205 -1.93185 -2.00000 -1.93185 -1.73205 -1.41421 -1.00000 -0.51764 0.00000 0.51764 1.00000 1.41421 1.73205 1.93185 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g 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 0.34730 1.00000 1.53209 1.87939 2.00000 0.00000 0.00000 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 0.34730 1.00000 1.53209 1.87939 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.81262 1.28558 0.51764 -0.34730 -1.14715 -1.73205 -1.99239 -1.87939 -1.41421 -0.68404 0.17431 1.00000 1.63830 1.96962 1.93185 1.53209 0.84524 0.00000 -0.84524 -1.53209 -1.93185 -1.96962 -1.63830 -1.00000 -0.17431 0.68404 1.41421 1.87939 1.99239 1.73205 1.14715 0.34730 -0.51764 -1.28558 -1.81262 -2.00000 0.00000 0.00000 2.00000 -1.81262 -1.28558 -0.51764 0.34730 1.14715 1.73205 1.99239 1.87939 1.41421 0.68404 -0.17431 -1.00000 -1.63830 -1.96962 -1.93185 -1.53209 -0.84524 0.00000 0.84524 1.53209 1.93185 1.96962 1.63830 1.00000 0.17431 -0.68404 -1.41421 -1.87939 -1.99239 -1.73205 -1.14715 -0.34730 0.51764 1.28558 1.81262 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 0.00000 0.00000 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7g 2.00000 1.63830 0.68404 -0.51764 -1.53209 -1.99239 -1.73205 -0.84524 0.34730 1.41421 1.96962 1.81262 1.00000 -0.17431 -1.28558 -1.93185 -1.87939 -1.14715 0.00000 1.14715 1.87939 1.93185 1.28558 0.17431 -1.00000 -1.81262 -1.96962 -1.41421 -0.34730 0.84524 1.73205 1.99239 1.53209 0.51764 -0.68404 -1.63830 -2.00000 0.00000 0.00000 2.00000 -1.63830 -0.68404 0.51764 1.53209 1.99239 1.73205 0.84524 -0.34730 -1.41421 -1.96962 -1.81262 -1.00000 0.17431 1.28558 1.93185 1.87939 1.14715 0.00000 -1.14715 -1.87939 -1.93185 -1.28558 -0.17431 1.00000 1.81262 1.96962 1.41421 0.34730 -0.84524 -1.73205 -1.99239 -1.53209 -0.51764 0.68404 1.63830 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8g 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 -1.87939 -1.00000 0.34730 1.53209 2.00000 0.00000 0.00000 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 -1.87939 -1.00000 0.34730 1.53209 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9g 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 0.00000 0.00000 2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10g 2.00000 1.28558 -0.34730 -1.73205 -1.87939 -0.68404 1.00000 1.96962 1.53209 0.00000 -1.53209 -1.96962 -1.00000 0.68404 1.87939 1.73205 0.34730 -1.28558 -2.00000 -1.28558 0.34730 1.73205 1.87939 0.68404 -1.00000 -1.96962 -1.53209 0.00000 1.53209 1.96962 1.00000 -0.68404 -1.87939 -1.73205 -0.34730 1.28558 2.00000 0.00000 0.00000 2.00000 1.28558 -0.34730 -1.73205 -1.87939 -0.68404 1.00000 1.96962 1.53209 0.00000 -1.53209 -1.96962 -1.00000 0.68404 1.87939 1.73205 0.34730 -1.28558 -2.00000 -1.28558 0.34730 1.73205 1.87939 0.68404 -1.00000 -1.96962 -1.53209 0.00000 1.53209 1.96962 1.00000 -0.68404 -1.87939 -1.73205 -0.34730 1.28558 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 1.14715 -0.68404 -1.93185 -1.53209 0.17431 1.73205 1.81262 0.34730 -1.41421 -1.96962 -0.84524 1.00000 1.99239 1.28558 -0.51764 -1.87939 -1.63830 0.00000 1.63830 1.87939 0.51764 -1.28558 -1.99239 -1.00000 0.84524 1.96962 1.41421 -0.34730 -1.81262 -1.73205 -0.17431 1.53209 1.93185 0.68404 -1.14715 -2.00000 0.00000 0.00000 2.00000 -1.14715 0.68404 1.93185 1.53209 -0.17431 -1.73205 -1.81262 -0.34730 1.41421 1.96962 0.84524 -1.00000 -1.99239 -1.28558 0.51764 1.87939 1.63830 0.00000 -1.63830 -1.87939 -0.51764 1.28558 1.99239 1.00000 -0.84524 -1.96962 -1.41421 0.34730 1.81262 1.73205 0.17431 -1.53209 -1.93185 -0.68404 1.14715 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12g 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 -1.00000 -2.00000 -1.00000 1.00000 2.00000 0.00000 0.00000 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 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 0.84524 -1.28558 -1.93185 -0.34730 1.63830 1.73205 -0.17431 -1.87939 -1.41421 0.68404 1.99239 1.00000 -1.14715 -1.96962 -0.51764 1.53209 1.81262 0.00000 -1.81262 -1.53209 0.51764 1.96962 1.14715 -1.00000 -1.99239 -0.68404 1.41421 1.87939 0.17431 -1.73205 -1.63830 0.34730 1.93185 1.28558 -0.84524 -2.00000 0.00000 0.00000 2.00000 -0.84524 1.28558 1.93185 0.34730 -1.63830 -1.73205 0.17431 1.87939 1.41421 -0.68404 -1.99239 -1.00000 1.14715 1.96962 0.51764 -1.53209 -1.81262 0.00000 1.81262 1.53209 -0.51764 -1.96962 -1.14715 1.00000 1.99239 0.68404 -1.41421 -1.87939 -0.17431 1.73205 1.63830 -0.34730 -1.93185 -1.28558 0.84524 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 0.68404 -1.53209 -1.73205 0.34730 1.96962 1.00000 -1.28558 -1.87939 0.00000 1.87939 1.28558 -1.00000 -1.96962 -0.34730 1.73205 1.53209 -0.68404 -2.00000 -0.68404 1.53209 1.73205 -0.34730 -1.96962 -1.00000 1.28558 1.87939 0.00000 -1.87939 -1.28558 1.00000 1.96962 0.34730 -1.73205 -1.53209 0.68404 2.00000 0.00000 0.00000 2.00000 0.68404 -1.53209 -1.73205 0.34730 1.96962 1.00000 -1.28558 -1.87939 0.00000 1.87939 1.28558 -1.00000 -1.96962 -0.34730 1.73205 1.53209 -0.68404 -2.00000 -0.68404 1.53209 1.73205 -0.34730 -1.96962 -1.00000 1.28558 1.87939 0.00000 -1.87939 -1.28558 1.00000 1.96962 0.34730 -1.73205 -1.53209 0.68404 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15g 2.00000 0.51764 -1.73205 -1.41421 1.00000 1.93185 0.00000 -1.93185 -1.00000 1.41421 1.73205 -0.51764 -2.00000 -0.51764 1.73205 1.41421 -1.00000 -1.93185 0.00000 1.93185 1.00000 -1.41421 -1.73205 0.51764 2.00000 0.51764 -1.73205 -1.41421 1.00000 1.93185 0.00000 -1.93185 -1.00000 1.41421 1.73205 -0.51764 -2.00000 0.00000 0.00000 2.00000 -0.51764 1.73205 1.41421 -1.00000 -1.93185 0.00000 1.93185 1.00000 -1.41421 -1.73205 0.51764 2.00000 0.51764 -1.73205 -1.41421 1.00000 1.93185 0.00000 -1.93185 -1.00000 1.41421 1.73205 -0.51764 -2.00000 -0.51764 1.73205 1.41421 -1.00000 -1.93185 0.00000 1.93185 1.00000 -1.41421 -1.73205 0.51764 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16g 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 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.00000 0.00000 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 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17g 2.00000 0.17431 -1.96962 -0.51764 1.87939 0.84524 -1.73205 -1.14715 1.53209 1.41421 -1.28558 -1.63830 1.00000 1.81262 -0.68404 -1.93185 0.34730 1.99239 0.00000 -1.99239 -0.34730 1.93185 0.68404 -1.81262 -1.00000 1.63830 1.28558 -1.41421 -1.53209 1.14715 1.73205 -0.84524 -1.87939 0.51764 1.96962 -0.17431 -2.00000 0.00000 0.00000 2.00000 -0.17431 1.96962 0.51764 -1.87939 -0.84524 1.73205 1.14715 -1.53209 -1.41421 1.28558 1.63830 -1.00000 -1.81262 0.68404 1.93185 -0.34730 -1.99239 0.00000 1.99239 0.34730 -1.93185 -0.68404 1.81262 1.00000 -1.63830 -1.28558 1.41421 1.53209 -1.14715 -1.73205 0.84524 1.87939 -0.51764 -1.96962 0.17431 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18g 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19g 2.00000 -0.17431 -1.96962 0.51764 1.87939 -0.84524 -1.73205 1.14715 1.53209 -1.41421 -1.28558 1.63830 1.00000 -1.81262 -0.68404 1.93185 0.34730 -1.99239 0.00000 1.99239 -0.34730 -1.93185 0.68404 1.81262 -1.00000 -1.63830 1.28558 1.41421 -1.53209 -1.14715 1.73205 0.84524 -1.87939 -0.51764 1.96962 0.17431 -2.00000 0.00000 0.00000 2.00000 0.17431 1.96962 -0.51764 -1.87939 0.84524 1.73205 -1.14715 -1.53209 1.41421 1.28558 -1.63830 -1.00000 1.81262 0.68404 -1.93185 -0.34730 1.99239 0.00000 -1.99239 0.34730 1.93185 -0.68404 -1.81262 1.00000 1.63830 -1.28558 -1.41421 1.53209 1.14715 -1.73205 -0.84524 1.87939 0.51764 -1.96962 -0.17431 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20g 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 1.53209 1.00000 -1.87939 -0.34730 2.00000 0.00000 0.00000 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 1.53209 1.00000 -1.87939 -0.34730 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21g 2.00000 -0.51764 -1.73205 1.41421 1.00000 -1.93185 0.00000 1.93185 -1.00000 -1.41421 1.73205 0.51764 -2.00000 0.51764 1.73205 -1.41421 -1.00000 1.93185 0.00000 -1.93185 1.00000 1.41421 -1.73205 -0.51764 2.00000 -0.51764 -1.73205 1.41421 1.00000 -1.93185 0.00000 1.93185 -1.00000 -1.41421 1.73205 0.51764 -2.00000 0.00000 0.00000 2.00000 0.51764 1.73205 -1.41421 -1.00000 1.93185 0.00000 -1.93185 1.00000 1.41421 -1.73205 -0.51764 2.00000 -0.51764 -1.73205 1.41421 1.00000 -1.93185 0.00000 1.93185 -1.00000 -1.41421 1.73205 0.51764 -2.00000 0.51764 1.73205 -1.41421 -1.00000 1.93185 0.00000 -1.93185 1.00000 1.41421 -1.73205 -0.51764 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E22g 2.00000 -0.68404 -1.53209 1.73205 0.34730 -1.96962 1.00000 1.28558 -1.87939 0.00000 1.87939 -1.28558 -1.00000 1.96962 -0.34730 -1.73205 1.53209 0.68404 -2.00000 0.68404 1.53209 -1.73205 -0.34730 1.96962 -1.00000 -1.28558 1.87939 0.00000 -1.87939 1.28558 1.00000 -1.96962 0.34730 1.73205 -1.53209 -0.68404 2.00000 0.00000 0.00000 2.00000 -0.68404 -1.53209 1.73205 0.34730 -1.96962 1.00000 1.28558 -1.87939 0.00000 1.87939 -1.28558 -1.00000 1.96962 -0.34730 -1.73205 1.53209 0.68404 -2.00000 0.68404 1.53209 -1.73205 -0.34730 1.96962 -1.00000 -1.28558 1.87939 0.00000 -1.87939 1.28558 1.00000 -1.96962 0.34730 1.73205 -1.53209 -0.68404 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E23g 2.00000 -0.84524 -1.28558 1.93185 -0.34730 -1.63830 1.73205 0.17431 -1.87939 1.41421 0.68404 -1.99239 1.00000 1.14715 -1.96962 0.51764 1.53209 -1.81262 0.00000 1.81262 -1.53209 -0.51764 1.96962 -1.14715 -1.00000 1.99239 -0.68404 -1.41421 1.87939 -0.17431 -1.73205 1.63830 0.34730 -1.93185 1.28558 0.84524 -2.00000 0.00000 0.00000 2.00000 0.84524 1.28558 -1.93185 0.34730 1.63830 -1.73205 -0.17431 1.87939 -1.41421 -0.68404 1.99239 -1.00000 -1.14715 1.96962 -0.51764 -1.53209 1.81262 0.00000 -1.81262 1.53209 0.51764 -1.96962 1.14715 1.00000 -1.99239 0.68404 1.41421 -1.87939 0.17431 1.73205 -1.63830 -0.34730 1.93185 -1.28558 -0.84524 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E24g 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 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000 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 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E25g 2.00000 -1.14715 -0.68404 1.93185 -1.53209 -0.17431 1.73205 -1.81262 0.34730 1.41421 -1.96962 0.84524 1.00000 -1.99239 1.28558 0.51764 -1.87939 1.63830 0.00000 -1.63830 1.87939 -0.51764 -1.28558 1.99239 -1.00000 -0.84524 1.96962 -1.41421 -0.34730 1.81262 -1.73205 0.17431 1.53209 -1.93185 0.68404 1.14715 -2.00000 0.00000 0.00000 2.00000 1.14715 0.68404 -1.93185 1.53209 0.17431 -1.73205 1.81262 -0.34730 -1.41421 1.96962 -0.84524 -1.00000 1.99239 -1.28558 -0.51764 1.87939 -1.63830 0.00000 1.63830 -1.87939 0.51764 1.28558 -1.99239 1.00000 0.84524 -1.96962 1.41421 0.34730 -1.81262 1.73205 -0.17431 -1.53209 1.93185 -0.68404 -1.14715 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E26g 2.00000 -1.28558 -0.34730 1.73205 -1.87939 0.68404 1.00000 -1.96962 1.53209 0.00000 -1.53209 1.96962 -1.00000 -0.68404 1.87939 -1.73205 0.34730 1.28558 -2.00000 1.28558 0.34730 -1.73205 1.87939 -0.68404 -1.00000 1.96962 -1.53209 0.00000 1.53209 -1.96962 1.00000 0.68404 -1.87939 1.73205 -0.34730 -1.28558 2.00000 0.00000 0.00000 2.00000 -1.28558 -0.34730 1.73205 -1.87939 0.68404 1.00000 -1.96962 1.53209 0.00000 -1.53209 1.96962 -1.00000 -0.68404 1.87939 -1.73205 0.34730 1.28558 -2.00000 1.28558 0.34730 -1.73205 1.87939 -0.68404 -1.00000 1.96962 -1.53209 0.00000 1.53209 -1.96962 1.00000 0.68404 -1.87939 1.73205 -0.34730 -1.28558 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E27g 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 0.00000 0.00000 2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E28g 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 -1.87939 1.00000 0.34730 -1.53209 2.00000 0.00000 0.00000 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 -1.87939 1.00000 0.34730 -1.53209 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E29g 2.00000 -1.63830 0.68404 0.51764 -1.53209 1.99239 -1.73205 0.84524 0.34730 -1.41421 1.96962 -1.81262 1.00000 0.17431 -1.28558 1.93185 -1.87939 1.14715 0.00000 -1.14715 1.87939 -1.93185 1.28558 -0.17431 -1.00000 1.81262 -1.96962 1.41421 -0.34730 -0.84524 1.73205 -1.99239 1.53209 -0.51764 -0.68404 1.63830 -2.00000 0.00000 0.00000 2.00000 1.63830 -0.68404 -0.51764 1.53209 -1.99239 1.73205 -0.84524 -0.34730 1.41421 -1.96962 1.81262 -1.00000 -0.17431 1.28558 -1.93185 1.87939 -1.14715 0.00000 1.14715 -1.87939 1.93185 -1.28558 0.17431 1.00000 -1.81262 1.96962 -1.41421 0.34730 0.84524 -1.73205 1.99239 -1.53209 0.51764 0.68404 -1.63830 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E30g 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 0.00000 0.00000 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E31g 2.00000 -1.81262 1.28558 -0.51764 -0.34730 1.14715 -1.73205 1.99239 -1.87939 1.41421 -0.68404 -0.17431 1.00000 -1.63830 1.96962 -1.93185 1.53209 -0.84524 0.00000 0.84524 -1.53209 1.93185 -1.96962 1.63830 -1.00000 0.17431 0.68404 -1.41421 1.87939 -1.99239 1.73205 -1.14715 0.34730 0.51764 -1.28558 1.81262 -2.00000 0.00000 0.00000 2.00000 1.81262 -1.28558 0.51764 0.34730 -1.14715 1.73205 -1.99239 1.87939 -1.41421 0.68404 0.17431 -1.00000 1.63830 -1.96962 1.93185 -1.53209 0.84524 0.00000 -0.84524 1.53209 -1.93185 1.96962 -1.63830 1.00000 -0.17431 -0.68404 1.41421 -1.87939 1.99239 -1.73205 1.14715 -0.34730 -0.51764 1.28558 -1.81262 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E32g 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 0.34730 -1.00000 1.53209 -1.87939 2.00000 0.00000 0.00000 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 0.34730 -1.00000 1.53209 -1.87939 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E33g 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 1.93185 -1.73205 1.41421 -1.00000 0.51764 0.00000 -0.51764 1.00000 -1.41421 1.73205 -1.93185 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 0.00000 0.00000 2.00000 1.93185 -1.73205 1.41421 -1.00000 0.51764 0.00000 -0.51764 1.00000 -1.41421 1.73205 -1.93185 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 1.93185 -1.73205 1.41421 -1.00000 0.51764 0.00000 -0.51764 1.00000 -1.41421 1.73205 -1.93185 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E34g 2.00000 -1.96962 1.87939 -1.73205 1.53209 -1.28558 1.00000 -0.68404 0.34730 0.00000 -0.34730 0.68404 -1.00000 1.28558 -1.53209 1.73205 -1.87939 1.96962 -2.00000 1.96962 -1.87939 1.73205 -1.53209 1.28558 -1.00000 0.68404 -0.34730 0.00000 0.34730 -0.68404 1.00000 -1.28558 1.53209 -1.73205 1.87939 -1.96962 2.00000 0.00000 0.00000 2.00000 -1.96962 1.87939 -1.73205 1.53209 -1.28558 1.00000 -0.68404 0.34730 0.00000 -0.34730 0.68404 -1.00000 1.28558 -1.53209 1.73205 -1.87939 1.96962 -2.00000 1.96962 -1.87939 1.73205 -1.53209 1.28558 -1.00000 0.68404 -0.34730 0.00000 0.34730 -0.68404 1.00000 -1.28558 1.53209 -1.73205 1.87939 -1.96962 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E35g 2.00000 -1.99239 1.96962 -1.93185 1.87939 -1.81262 1.73205 -1.63830 1.53209 -1.41421 1.28558 -1.14715 1.00000 -0.84524 0.68404 -0.51764 0.34730 -0.17431 0.00000 0.17431 -0.34730 0.51764 -0.68404 0.84524 -1.00000 1.14715 -1.28558 1.41421 -1.53209 1.63830 -1.73205 1.81262 -1.87939 1.93185 -1.96962 1.99239 -2.00000 0.00000 0.00000 2.00000 1.99239 -1.96962 1.93185 -1.87939 1.81262 -1.73205 1.63830 -1.53209 1.41421 -1.28558 1.14715 -1.00000 0.84524 -0.68404 0.51764 -0.34730 0.17431 0.00000 -0.17431 0.34730 -0.51764 0.68404 -0.84524 1.00000 -1.14715 1.28558 -1.41421 1.53209 -1.63830 1.73205 -1.81262 1.87939 -1.93185 1.96962 -1.99239 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. A1u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. A2u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 1.00000 1.00000 ... ..T ..... ......T ......... ..........T ............. B1u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. B2u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 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 1.99239 1.96962 1.93185 1.87939 1.81262 1.73205 1.63830 1.53209 1.41421 1.28558 1.14715 1.00000 0.84524 0.68404 0.51764 0.34730 0.17431 0.00000 -0.17431 -0.34730 -0.51764 -0.68404 -0.84524 -1.00000 -1.14715 -1.28558 -1.41421 -1.53209 -1.63830 -1.73205 -1.81262 -1.87939 -1.93185 -1.96962 -1.99239 -2.00000 0.00000 0.00000 -2.00000 1.99239 1.96962 1.93185 1.87939 1.81262 1.73205 1.63830 1.53209 1.41421 1.28558 1.14715 1.00000 0.84524 0.68404 0.51764 0.34730 0.17431 0.00000 -0.17431 -0.34730 -0.51764 -0.68404 -0.84524 -1.00000 -1.14715 -1.28558 -1.41421 -1.53209 -1.63830 -1.73205 -1.81262 -1.87939 -1.93185 -1.96962 -1.99239 2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.96962 1.87939 1.73205 1.53209 1.28558 1.00000 0.68404 0.34730 0.00000 -0.34730 -0.68404 -1.00000 -1.28558 -1.53209 -1.73205 -1.87939 -1.96962 -2.00000 -1.96962 -1.87939 -1.73205 -1.53209 -1.28558 -1.00000 -0.68404 -0.34730 0.00000 0.34730 0.68404 1.00000 1.28558 1.53209 1.73205 1.87939 1.96962 2.00000 0.00000 0.00000 -2.00000 -1.96962 -1.87939 -1.73205 -1.53209 -1.28558 -1.00000 -0.68404 -0.34730 0.00000 0.34730 0.68404 1.00000 1.28558 1.53209 1.73205 1.87939 1.96962 2.00000 1.96962 1.87939 1.73205 1.53209 1.28558 1.00000 0.68404 0.34730 0.00000 -0.34730 -0.68404 -1.00000 -1.28558 -1.53209 -1.73205 -1.87939 -1.96962 -2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. 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E25u 2.00000 -1.14715 -0.68404 1.93185 -1.53209 -0.17431 1.73205 -1.81262 0.34730 1.41421 -1.96962 0.84524 1.00000 -1.99239 1.28558 0.51764 -1.87939 1.63830 0.00000 -1.63830 1.87939 -0.51764 -1.28558 1.99239 -1.00000 -0.84524 1.96962 -1.41421 -0.34730 1.81262 -1.73205 0.17431 1.53209 -1.93185 0.68404 1.14715 -2.00000 0.00000 0.00000 -2.00000 -1.14715 -0.68404 1.93185 -1.53209 -0.17431 1.73205 -1.81262 0.34730 1.41421 -1.96962 0.84524 1.00000 -1.99239 1.28558 0.51764 -1.87939 1.63830 0.00000 -1.63830 1.87939 -0.51764 -1.28558 1.99239 -1.00000 -0.84524 1.96962 -1.41421 -0.34730 1.81262 -1.73205 0.17431 1.53209 -1.93185 0.68404 1.14715 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E26u 2.00000 -1.28558 -0.34730 1.73205 -1.87939 0.68404 1.00000 -1.96962 1.53209 0.00000 -1.53209 1.96962 -1.00000 -0.68404 1.87939 -1.73205 0.34730 1.28558 -2.00000 1.28558 0.34730 -1.73205 1.87939 -0.68404 -1.00000 1.96962 -1.53209 0.00000 1.53209 -1.96962 1.00000 0.68404 -1.87939 1.73205 -0.34730 -1.28558 2.00000 0.00000 0.00000 -2.00000 1.28558 0.34730 -1.73205 1.87939 -0.68404 -1.00000 1.96962 -1.53209 0.00000 1.53209 -1.96962 1.00000 0.68404 -1.87939 1.73205 -0.34730 -1.28558 2.00000 -1.28558 -0.34730 1.73205 -1.87939 0.68404 1.00000 -1.96962 1.53209 0.00000 -1.53209 1.96962 -1.00000 -0.68404 1.87939 -1.73205 0.34730 1.28558 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E27u 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 0.00000 0.00000 -2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E28u 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 -1.87939 1.00000 0.34730 -1.53209 2.00000 0.00000 0.00000 -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 1.87939 -1.00000 -0.34730 1.53209 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E29u 2.00000 -1.63830 0.68404 0.51764 -1.53209 1.99239 -1.73205 0.84524 0.34730 -1.41421 1.96962 -1.81262 1.00000 0.17431 -1.28558 1.93185 -1.87939 1.14715 0.00000 -1.14715 1.87939 -1.93185 1.28558 -0.17431 -1.00000 1.81262 -1.96962 1.41421 -0.34730 -0.84524 1.73205 -1.99239 1.53209 -0.51764 -0.68404 1.63830 -2.00000 0.00000 0.00000 -2.00000 -1.63830 0.68404 0.51764 -1.53209 1.99239 -1.73205 0.84524 0.34730 -1.41421 1.96962 -1.81262 1.00000 0.17431 -1.28558 1.93185 -1.87939 1.14715 0.00000 -1.14715 1.87939 -1.93185 1.28558 -0.17431 -1.00000 1.81262 -1.96962 1.41421 -0.34730 -0.84524 1.73205 -1.99239 1.53209 -0.51764 -0.68404 1.63830 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E30u 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 0.00000 0.00000 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E31u 2.00000 -1.81262 1.28558 -0.51764 -0.34730 1.14715 -1.73205 1.99239 -1.87939 1.41421 -0.68404 -0.17431 1.00000 -1.63830 1.96962 -1.93185 1.53209 -0.84524 0.00000 0.84524 -1.53209 1.93185 -1.96962 1.63830 -1.00000 0.17431 0.68404 -1.41421 1.87939 -1.99239 1.73205 -1.14715 0.34730 0.51764 -1.28558 1.81262 -2.00000 0.00000 0.00000 -2.00000 -1.81262 1.28558 -0.51764 -0.34730 1.14715 -1.73205 1.99239 -1.87939 1.41421 -0.68404 -0.17431 1.00000 -1.63830 1.96962 -1.93185 1.53209 -0.84524 0.00000 0.84524 -1.53209 1.93185 -1.96962 1.63830 -1.00000 0.17431 0.68404 -1.41421 1.87939 -1.99239 1.73205 -1.14715 0.34730 0.51764 -1.28558 1.81262 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E32u 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 0.34730 -1.00000 1.53209 -1.87939 2.00000 0.00000 0.00000 -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 -0.34730 1.00000 -1.53209 1.87939 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E33u 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 1.93185 -1.73205 1.41421 -1.00000 0.51764 0.00000 -0.51764 1.00000 -1.41421 1.73205 -1.93185 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 0.00000 0.00000 -2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 1.93185 -1.73205 1.41421 -1.00000 0.51764 0.00000 -0.51764 1.00000 -1.41421 1.73205 -1.93185 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E34u 2.00000 -1.96962 1.87939 -1.73205 1.53209 -1.28558 1.00000 -0.68404 0.34730 0.00000 -0.34730 0.68404 -1.00000 1.28558 -1.53209 1.73205 -1.87939 1.96962 -2.00000 1.96962 -1.87939 1.73205 -1.53209 1.28558 -1.00000 0.68404 -0.34730 0.00000 0.34730 -0.68404 1.00000 -1.28558 1.53209 -1.73205 1.87939 -1.96962 2.00000 0.00000 0.00000 -2.00000 1.96962 -1.87939 1.73205 -1.53209 1.28558 -1.00000 0.68404 -0.34730 0.00000 0.34730 -0.68404 1.00000 -1.28558 1.53209 -1.73205 1.87939 -1.96962 2.00000 -1.96962 1.87939 -1.73205 1.53209 -1.28558 1.00000 -0.68404 0.34730 0.00000 -0.34730 0.68404 -1.00000 1.28558 -1.53209 1.73205 -1.87939 1.96962 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E35u 2.00000 -1.99239 1.96962 -1.93185 1.87939 -1.81262 1.73205 -1.63830 1.53209 -1.41421 1.28558 -1.14715 1.00000 -0.84524 0.68404 -0.51764 0.34730 -0.17431 0.00000 0.17431 -0.34730 0.51764 -0.68404 0.84524 -1.00000 1.14715 -1.28558 1.41421 -1.53209 1.63830 -1.73205 1.81262 -1.87939 1.93185 -1.96962 1.99239 -2.00000 0.00000 0.00000 -2.00000 -1.99239 1.96962 -1.93185 1.87939 -1.81262 1.73205 -1.63830 1.53209 -1.41421 1.28558 -1.14715 1.00000 -0.84524 0.68404 -0.51764 0.34730 -0.17431 0.00000 0.17431 -0.34730 0.51764 -0.68404 0.84524 -1.00000 1.14715 -1.28558 1.41421 -1.53209 1.63830 -1.73205 1.81262 -1.87939 1.93185 -1.96962 1.99239 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.992389396183 = 2*cos(2*π/72) = 2*cos(π/36) 1.969615506024 = 2*cos(4*π/72) = 2*cos(π/18) 1.931851652578 = 2*cos(6*π/72) = 2*cos(π/12) = √2+√3 1.879385241572 = 2*cos(8*π/72) = 2*cos(π/9) 1.812615574073 = 2*cos(10*π/72) = 2*cos(5*π/36) 1.732050807569 = 2*cos(12*π/72) = 2*cos(π/6) = √3 1.638304088578 = 2*cos(14*π/72) = 2*cos(7*π/36) 1.532088886238 = 2*cos(16*π/72) = 2*cos(2*π/9) 1.414213562373 = 2*cos(18*π/72) = 2*cos(π/4) = √2 1.285575219373 = 2*cos(20*π/72) = 2*cos(5*π/18) 1.147152872702 = 2*cos(22*π/72) = 2*cos(11*π/36) 0.845236523481 = 2*cos(26*π/72) = 2*cos(13*π/36) 0.684040286651 = 2*cos(28*π/72) = 2*cos(7*π/18) 0.517638090205 = 2*cos(30*π/72) = 2*cos(5*π/12) = √2−√3 0.347296355334 = 2*cos(32*π/72) = 2*cos(4*π/9) 0.174311485495 = 2*cos(34*π/72) = 2*cos(17*π/36) Symmetry of Rotations and Cartesian products A1g d+g+i+k+m z2, z4, z6 A2g R Rz E1g R+d+g+i+k+m {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} E2g d+g+i+k+m {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 A2u p+f+h+j+l z, z3, z5 E1u p+f+h+j+l {x, y}, {xz2, yz2}, {xz4, yz4} E2u f+h+j+l {z(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 D72h point group is 288, and the order of the principal axis (C72) is 72. The group has 78 irreducible representations. β The D72h point group is generated by three symmetry elements that are canonically chosen C72, C2′ and i. Other choices include σh instead of i, or any of C2″, σv or σd instead of C2′. Also, some ternary combinations of C2′, C2″, σv and σd act as generators. Lastly, the S72 can be chosen, together with i or σh and any one of C2′, C2″, σv or σd. γ There are two different sets of twofold symmetry axes perpendicular to the principal axis (z axis in standard orientation). By convention, the set denoted as C2′ contains both the x and y axes. δ There are two different sets of symmetry planes containing the principal axis (z axis in standard orientation). By convention, the set denoted as σv contains both the xz and the yz planes. ε The lowest nonvanishing multipole moment in D72h 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. While some characters of this group can be expressed using real integers and square roots alone, others need complex numbers and third roots. ι The regular nonagon or enneagon is not constructible by ruler and compass because cos(2*π/9) has an algebraic degree of 3. (It can be constructed by extended methods that allow angle trisection, as this corresponds to solving cubic equations). The value of cos(2*π/9) can be expressed using cubic roots and complex numbers, which, however, is not very useful for a real-valued quantity: 2*cos(2π/9) = (3√−4+i*4*√3 + 3√−4−i*4*√3)/2. Therefore, regular polygons of order 18,27,36,45,54 etc. are also inconstructible, and their cosines have no representation in real radicals.
D70h | ||
D71h | ||
C72 C72v C72h D72 | D72h | D72d S72 |
D73h | ||
D74h |
This Character Table for the D72h point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.