Character Table for Point Group C72h

Character table for the C_72h point group

C72h 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 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 <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> Ag 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ..T ... ....T ....... ........T ........... ............T Bg 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -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 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 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 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 ... ... 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 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 ... ... ..... ....... ..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 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 ... ... ..... ....... 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 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 ... ... ..... ....... ......... ........... ..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 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 ... ... ..... ....... ......... ........... 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. Au 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ..T ..... ......T ......... ..........T ............. Bu 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 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 -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 ... 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 -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 ... ... ..... ..TT... ......... ......TT... ............. E3u * 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 -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 ... ... ..... TT..... ......... ....TT..... ............. E4u * 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 -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 ... ... ..... ....... ......... ..TT....... ............. E5u * 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 -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 ... ... ..... ....... ......... TT......... ............. E6u * 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 -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 ... ... ..... ....... ......... ........... ............. E7u * 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 -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 ... ... ..... ....... ......... ........... ............. E8u * 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 -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 ... ... ..... ....... ......... ........... ............. E9u * 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 -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 ... ... ..... ....... ......... ........... ............. E10u * 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 -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 ... ... ..... ....... ......... ........... ............. E11u * 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 -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 ... ... ..... ....... ......... ........... ............. E12u * 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 -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 ... ... ..... ....... ......... ........... ............. E13u * 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 -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 ... ... ..... ....... ......... ........... ............. E14u * 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 -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 ... ... ..... ....... ......... ........... ............. E15u * 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 -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 ... ... ..... ....... ......... ........... ............. E16u * 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 -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 ... ... ..... ....... ......... ........... ............. E17u * 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 -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 ... ... ..... ....... ......... ........... ............. E18u * 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 -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 ... ... ..... ....... ......... ........... ............. E19u * 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 -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 ... ... ..... ....... ......... ........... ............. E20u * 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 -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 ... ... ..... ....... ......... ........... ............. E21u * 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 -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 ... ... ..... ....... ......... ........... ............. E22u * 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 -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 ... ... ..... ....... ......... ........... ............. E23u * 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 -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 ... ... ..... ....... ......... ........... ............. E24u * 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 Ag R+d+g+i+k+m R_z, z², z⁴, z⁶ E1g R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2g d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E3g g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4g g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5g i+k+m {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6g i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7g k+m E8g k+m E9g m E10g m Au p+f+h+j+l z, z³, z⁵ E1u p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2u f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3u f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E4u h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5u h+j+l {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)} E6u j+l E7u j+l E8u l E9u l Notes: α The order of the C_72h point group is 144, and the order of the principal axis (C₇₂) is 72. The group has 74 irreducible representations. β The C_72h point group is generated by two symmetry elements, which are canonically chosen as C₇₂ and i. Other possible choices are C₇₂ and σ_h, or less commonly S₇₂ with either i or σ_h. γ The lowest nonvanishing multipole moment in C_72h is 4 (quadrupole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C_72h group is Abelian because all its symmetry operations are coaxial. This is a sufficient condition. In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. ε Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 140 cases have been combined into 70 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 70 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 70 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. η Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. θ The point group corresponds to a 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.

This Character Table for the C_72h point group was created by Gernot Katzer.

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

	C_70h
	C_71h
C₇₂ C_72v	C_72h	D₇₂ D_72h D_72d S₇₂
	C_73h
	C_74h

Character table for the C72h point group

Character table for the C_72h point group