Character Table for Point Group C80h

Character table for the C_80h point group

C80h E 2 C80 2 C40 2 C80^3 2 C20 2 C16 2 C40^3 2 C80^7 2 C10 2 C80^9 2 C8 2 C80^11 2 C20^3 2 C80^13 2 C40^7 2 C16^3 2 C5 2 C80^17 2 C40^9 2 C80^19 2 C4 2 C80^21 2 C40^11 2 C80^23 2 C10^3 2 C16^5 2 C40^13 2 C80^27 2 C20^7 2 C80^29 2 C8^3 2 C80^31 2 C5^2 2 C80^33 2 C40^17 2 C16^7 2 C20^9 2 C80^37 2 C40^19 2 C80^39 C2 i 2 S80 2 S40 2 S80^3 2 S20 2 S16 2 S40^3 2 S80^7 2 S10 2 S80^9 2 S8 2 S80^11 2 S20^3 2 S80^13 2 S40^7 2 S16^3 2 S5 2 S80^17 2 S40^9 2 S80^19 2 S4 2 S80^21 2 S40^11 2 S80^23 2 S10^3 2 S16^5 2 S40^13 2 S80^27 2 S20^7 2 S80^29 2 S8^3 2 S80^31 2 S5^2 2 S80^33 2 S40^17 2 S16^7 2 S20^9 2 S80^37 2 S40^19 2 S80^39 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 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 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E1g * 2.00000 1.99383 1.97538 1.94474 1.90211 1.84776 1.78201 1.70528 1.61803 1.52081 1.41421 1.29890 1.17557 1.04500 0.90798 0.76537 0.61803 0.46689 0.31287 0.15692 0.00000 -0.15692 -0.31287 -0.46689 -0.61803 -0.76537 -0.90798 -1.04500 -1.17557 -1.29890 -1.41421 -1.52081 -1.61803 -1.70528 -1.78201 -1.84776 -1.90211 -1.94474 -1.97538 -1.99383 -2.00000 2.00000 -1.99383 -1.97538 -1.94474 -1.90211 -1.84776 -1.78201 -1.70528 -1.61803 -1.52081 -1.41421 -1.29890 -1.17557 -1.04500 -0.90798 -0.76537 -0.61803 -0.46689 -0.31287 -0.15692 0.00000 0.15692 0.31287 0.46689 0.61803 0.76537 0.90798 1.04500 1.17557 1.29890 1.41421 1.52081 1.61803 1.70528 1.78201 1.84776 1.90211 1.94474 1.97538 1.99383 -2.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g * 2.00000 1.97538 1.90211 1.78201 1.61803 1.41421 1.17557 0.90798 0.61803 0.31287 0.00000 -0.31287 -0.61803 -0.90798 -1.17557 -1.41421 -1.61803 -1.78201 -1.90211 -1.97538 -2.00000 -1.97538 -1.90211 -1.78201 -1.61803 -1.41421 -1.17557 -0.90798 -0.61803 -0.31287 0.00000 0.31287 0.61803 0.90798 1.17557 1.41421 1.61803 1.78201 1.90211 1.97538 2.00000 2.00000 1.97538 1.90211 1.78201 1.61803 1.41421 1.17557 0.90798 0.61803 0.31287 0.00000 -0.31287 -0.61803 -0.90798 -1.17557 -1.41421 -1.61803 -1.78201 -1.90211 -1.97538 -2.00000 -1.97538 -1.90211 -1.78201 -1.61803 -1.41421 -1.17557 -0.90798 -0.61803 -0.31287 0.00000 0.31287 0.61803 0.90798 1.17557 1.41421 1.61803 1.78201 1.90211 1.97538 2.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g * 2.00000 1.94474 1.78201 1.52081 1.17557 0.76537 0.31287 -0.15692 -0.61803 -1.04500 -1.41421 -1.70528 -1.90211 -1.99383 -1.97538 -1.84776 -1.61803 -1.29890 -0.90798 -0.46689 0.00000 0.46689 0.90798 1.29890 1.61803 1.84776 1.97538 1.99383 1.90211 1.70528 1.41421 1.04500 0.61803 0.15692 -0.31287 -0.76537 -1.17557 -1.52081 -1.78201 -1.94474 -2.00000 2.00000 -1.94474 -1.78201 -1.52081 -1.17557 -0.76537 -0.31287 0.15692 0.61803 1.04500 1.41421 1.70528 1.90211 1.99383 1.97538 1.84776 1.61803 1.29890 0.90798 0.46689 0.00000 -0.46689 -0.90798 -1.29890 -1.61803 -1.84776 -1.97538 -1.99383 -1.90211 -1.70528 -1.41421 -1.04500 -0.61803 -0.15692 0.31287 0.76537 1.17557 1.52081 1.78201 1.94474 -2.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g * 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g * 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 -2.00000 ... ... ..... ....... ......... ........... ..TT......... E6g * 2.00000 1.78201 1.17557 0.31287 -0.61803 -1.41421 -1.90211 -1.97538 -1.61803 -0.90798 0.00000 0.90798 1.61803 1.97538 1.90211 1.41421 0.61803 -0.31287 -1.17557 -1.78201 -2.00000 -1.78201 -1.17557 -0.31287 0.61803 1.41421 1.90211 1.97538 1.61803 0.90798 0.00000 -0.90798 -1.61803 -1.97538 -1.90211 -1.41421 -0.61803 0.31287 1.17557 1.78201 2.00000 2.00000 1.78201 1.17557 0.31287 -0.61803 -1.41421 -1.90211 -1.97538 -1.61803 -0.90798 0.00000 0.90798 1.61803 1.97538 1.90211 1.41421 0.61803 -0.31287 -1.17557 -1.78201 -2.00000 -1.78201 -1.17557 -0.31287 0.61803 1.41421 1.90211 1.97538 1.61803 0.90798 0.00000 -0.90798 -1.61803 -1.97538 -1.90211 -1.41421 -0.61803 0.31287 1.17557 1.78201 2.00000 ... ... ..... ....... ......... ........... TT........... E7g * 2.00000 1.70528 0.90798 -0.15692 -1.17557 -1.84776 -1.97538 -1.52081 -0.61803 0.46689 1.41421 1.94474 1.90211 1.29890 0.31287 -0.76537 -1.61803 -1.99383 -1.78201 -1.04500 0.00000 1.04500 1.78201 1.99383 1.61803 0.76537 -0.31287 -1.29890 -1.90211 -1.94474 -1.41421 -0.46689 0.61803 1.52081 1.97538 1.84776 1.17557 0.15692 -0.90798 -1.70528 -2.00000 2.00000 -1.70528 -0.90798 0.15692 1.17557 1.84776 1.97538 1.52081 0.61803 -0.46689 -1.41421 -1.94474 -1.90211 -1.29890 -0.31287 0.76537 1.61803 1.99383 1.78201 1.04500 0.00000 -1.04500 -1.78201 -1.99383 -1.61803 -0.76537 0.31287 1.29890 1.90211 1.94474 1.41421 0.46689 -0.61803 -1.52081 -1.97538 -1.84776 -1.17557 -0.15692 0.90798 1.70528 -2.00000 ... ... ..... ....... ......... ........... ............. E8g * 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 ... ... ..... ....... ......... ........... ............. E9g * 2.00000 1.52081 0.31287 -1.04500 -1.90211 -1.84776 -0.90798 0.46689 1.61803 1.99383 1.41421 0.15692 -1.17557 -1.94474 -1.78201 -0.76537 0.61803 1.70528 1.97538 1.29890 0.00000 -1.29890 -1.97538 -1.70528 -0.61803 0.76537 1.78201 1.94474 1.17557 -0.15692 -1.41421 -1.99383 -1.61803 -0.46689 0.90798 1.84776 1.90211 1.04500 -0.31287 -1.52081 -2.00000 2.00000 -1.52081 -0.31287 1.04500 1.90211 1.84776 0.90798 -0.46689 -1.61803 -1.99383 -1.41421 -0.15692 1.17557 1.94474 1.78201 0.76537 -0.61803 -1.70528 -1.97538 -1.29890 0.00000 1.29890 1.97538 1.70528 0.61803 -0.76537 -1.78201 -1.94474 -1.17557 0.15692 1.41421 1.99383 1.61803 0.46689 -0.90798 -1.84776 -1.90211 -1.04500 0.31287 1.52081 -2.00000 ... ... ..... ....... ......... ........... ............. E10g * 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 -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 -1.41421 0.00000 1.41421 2.00000 ... ... ..... ....... ......... ........... ............. E11g * 2.00000 1.29890 -0.31287 -1.70528 -1.90211 -0.76537 0.90798 1.94474 1.61803 0.15692 -1.41421 -1.99383 -1.17557 0.46689 1.78201 1.84776 0.61803 -1.04500 -1.97538 -1.52081 0.00000 1.52081 1.97538 1.04500 -0.61803 -1.84776 -1.78201 -0.46689 1.17557 1.99383 1.41421 -0.15692 -1.61803 -1.94474 -0.90798 0.76537 1.90211 1.70528 0.31287 -1.29890 -2.00000 2.00000 -1.29890 0.31287 1.70528 1.90211 0.76537 -0.90798 -1.94474 -1.61803 -0.15692 1.41421 1.99383 1.17557 -0.46689 -1.78201 -1.84776 -0.61803 1.04500 1.97538 1.52081 0.00000 -1.52081 -1.97538 -1.04500 0.61803 1.84776 1.78201 0.46689 -1.17557 -1.99383 -1.41421 0.15692 1.61803 1.94474 0.90798 -0.76537 -1.90211 -1.70528 -0.31287 1.29890 -2.00000 ... ... ..... ....... ......... ........... ............. E12g * 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 ... ... ..... ....... ......... ........... ............. E13g * 2.00000 1.04500 -0.90798 -1.99383 -1.17557 0.76537 1.97538 1.29890 -0.61803 -1.94474 -1.41421 0.46689 1.90211 1.52081 -0.31287 -1.84776 -1.61803 0.15692 1.78201 1.70528 0.00000 -1.70528 -1.78201 -0.15692 1.61803 1.84776 0.31287 -1.52081 -1.90211 -0.46689 1.41421 1.94474 0.61803 -1.29890 -1.97538 -0.76537 1.17557 1.99383 0.90798 -1.04500 -2.00000 2.00000 -1.04500 0.90798 1.99383 1.17557 -0.76537 -1.97538 -1.29890 0.61803 1.94474 1.41421 -0.46689 -1.90211 -1.52081 0.31287 1.84776 1.61803 -0.15692 -1.78201 -1.70528 0.00000 1.70528 1.78201 0.15692 -1.61803 -1.84776 -0.31287 1.52081 1.90211 0.46689 -1.41421 -1.94474 -0.61803 1.29890 1.97538 0.76537 -1.17557 -1.99383 -0.90798 1.04500 -2.00000 ... ... ..... ....... ......... ........... ............. E14g * 2.00000 0.90798 -1.17557 -1.97538 -0.61803 1.41421 1.90211 0.31287 -1.61803 -1.78201 0.00000 1.78201 1.61803 -0.31287 -1.90211 -1.41421 0.61803 1.97538 1.17557 -0.90798 -2.00000 -0.90798 1.17557 1.97538 0.61803 -1.41421 -1.90211 -0.31287 1.61803 1.78201 0.00000 -1.78201 -1.61803 0.31287 1.90211 1.41421 -0.61803 -1.97538 -1.17557 0.90798 2.00000 2.00000 0.90798 -1.17557 -1.97538 -0.61803 1.41421 1.90211 0.31287 -1.61803 -1.78201 0.00000 1.78201 1.61803 -0.31287 -1.90211 -1.41421 0.61803 1.97538 1.17557 -0.90798 -2.00000 -0.90798 1.17557 1.97538 0.61803 -1.41421 -1.90211 -0.31287 1.61803 1.78201 0.00000 -1.78201 -1.61803 0.31287 1.90211 1.41421 -0.61803 -1.97538 -1.17557 0.90798 2.00000 ... ... ..... ....... ......... ........... ............. E15g * 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 -2.00000 ... ... ..... ....... ......... ........... ............. E16g * 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 ... ... ..... ....... ......... ........... ............. E17g * 2.00000 0.46689 -1.78201 -1.29890 1.17557 1.84776 -0.31287 -1.99383 -0.61803 1.70528 1.41421 -1.04500 -1.90211 0.15692 1.97538 0.76537 -1.61803 -1.52081 0.90798 1.94474 0.00000 -1.94474 -0.90798 1.52081 1.61803 -0.76537 -1.97538 -0.15692 1.90211 1.04500 -1.41421 -1.70528 0.61803 1.99383 0.31287 -1.84776 -1.17557 1.29890 1.78201 -0.46689 -2.00000 2.00000 -0.46689 1.78201 1.29890 -1.17557 -1.84776 0.31287 1.99383 0.61803 -1.70528 -1.41421 1.04500 1.90211 -0.15692 -1.97538 -0.76537 1.61803 1.52081 -0.90798 -1.94474 0.00000 1.94474 0.90798 -1.52081 -1.61803 0.76537 1.97538 0.15692 -1.90211 -1.04500 1.41421 1.70528 -0.61803 -1.99383 -0.31287 1.84776 1.17557 -1.29890 -1.78201 0.46689 -2.00000 ... ... ..... ....... ......... ........... ............. E18g * 2.00000 0.31287 -1.90211 -0.90798 1.61803 1.41421 -1.17557 -1.78201 0.61803 1.97538 0.00000 -1.97538 -0.61803 1.78201 1.17557 -1.41421 -1.61803 0.90798 1.90211 -0.31287 -2.00000 -0.31287 1.90211 0.90798 -1.61803 -1.41421 1.17557 1.78201 -0.61803 -1.97538 0.00000 1.97538 0.61803 -1.78201 -1.17557 1.41421 1.61803 -0.90798 -1.90211 0.31287 2.00000 2.00000 0.31287 -1.90211 -0.90798 1.61803 1.41421 -1.17557 -1.78201 0.61803 1.97538 0.00000 -1.97538 -0.61803 1.78201 1.17557 -1.41421 -1.61803 0.90798 1.90211 -0.31287 -2.00000 -0.31287 1.90211 0.90798 -1.61803 -1.41421 1.17557 1.78201 -0.61803 -1.97538 0.00000 1.97538 0.61803 -1.78201 -1.17557 1.41421 1.61803 -0.90798 -1.90211 0.31287 2.00000 ... ... ..... ....... ......... ........... ............. E19g * 2.00000 0.15692 -1.97538 -0.46689 1.90211 0.76537 -1.78201 -1.04500 1.61803 1.29890 -1.41421 -1.52081 1.17557 1.70528 -0.90798 -1.84776 0.61803 1.94474 -0.31287 -1.99383 0.00000 1.99383 0.31287 -1.94474 -0.61803 1.84776 0.90798 -1.70528 -1.17557 1.52081 1.41421 -1.29890 -1.61803 1.04500 1.78201 -0.76537 -1.90211 0.46689 1.97538 -0.15692 -2.00000 2.00000 -0.15692 1.97538 0.46689 -1.90211 -0.76537 1.78201 1.04500 -1.61803 -1.29890 1.41421 1.52081 -1.17557 -1.70528 0.90798 1.84776 -0.61803 -1.94474 0.31287 1.99383 0.00000 -1.99383 -0.31287 1.94474 0.61803 -1.84776 -0.90798 1.70528 1.17557 -1.52081 -1.41421 1.29890 1.61803 -1.04500 -1.78201 0.76537 1.90211 -0.46689 -1.97538 0.15692 -2.00000 ... ... ..... ....... ......... ........... ............. E20g * 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 -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 0.00000 -2.00000 0.00000 2.00000 ... ... ..... ....... ......... ........... ............. E21g * 2.00000 -0.15692 -1.97538 0.46689 1.90211 -0.76537 -1.78201 1.04500 1.61803 -1.29890 -1.41421 1.52081 1.17557 -1.70528 -0.90798 1.84776 0.61803 -1.94474 -0.31287 1.99383 0.00000 -1.99383 0.31287 1.94474 -0.61803 -1.84776 0.90798 1.70528 -1.17557 -1.52081 1.41421 1.29890 -1.61803 -1.04500 1.78201 0.76537 -1.90211 -0.46689 1.97538 0.15692 -2.00000 2.00000 0.15692 1.97538 -0.46689 -1.90211 0.76537 1.78201 -1.04500 -1.61803 1.29890 1.41421 -1.52081 -1.17557 1.70528 0.90798 -1.84776 -0.61803 1.94474 0.31287 -1.99383 0.00000 1.99383 -0.31287 -1.94474 0.61803 1.84776 -0.90798 -1.70528 1.17557 1.52081 -1.41421 -1.29890 1.61803 1.04500 -1.78201 -0.76537 1.90211 0.46689 -1.97538 -0.15692 -2.00000 ... ... ..... ....... ......... ........... ............. E22g * 2.00000 -0.31287 -1.90211 0.90798 1.61803 -1.41421 -1.17557 1.78201 0.61803 -1.97538 0.00000 1.97538 -0.61803 -1.78201 1.17557 1.41421 -1.61803 -0.90798 1.90211 0.31287 -2.00000 0.31287 1.90211 -0.90798 -1.61803 1.41421 1.17557 -1.78201 -0.61803 1.97538 0.00000 -1.97538 0.61803 1.78201 -1.17557 -1.41421 1.61803 0.90798 -1.90211 -0.31287 2.00000 2.00000 -0.31287 -1.90211 0.90798 1.61803 -1.41421 -1.17557 1.78201 0.61803 -1.97538 0.00000 1.97538 -0.61803 -1.78201 1.17557 1.41421 -1.61803 -0.90798 1.90211 0.31287 -2.00000 0.31287 1.90211 -0.90798 -1.61803 1.41421 1.17557 -1.78201 -0.61803 1.97538 0.00000 -1.97538 0.61803 1.78201 -1.17557 -1.41421 1.61803 0.90798 -1.90211 -0.31287 2.00000 ... ... ..... ....... ......... ........... ............. E23g * 2.00000 -0.46689 -1.78201 1.29890 1.17557 -1.84776 -0.31287 1.99383 -0.61803 -1.70528 1.41421 1.04500 -1.90211 -0.15692 1.97538 -0.76537 -1.61803 1.52081 0.90798 -1.94474 0.00000 1.94474 -0.90798 -1.52081 1.61803 0.76537 -1.97538 0.15692 1.90211 -1.04500 -1.41421 1.70528 0.61803 -1.99383 0.31287 1.84776 -1.17557 -1.29890 1.78201 0.46689 -2.00000 2.00000 0.46689 1.78201 -1.29890 -1.17557 1.84776 0.31287 -1.99383 0.61803 1.70528 -1.41421 -1.04500 1.90211 0.15692 -1.97538 0.76537 1.61803 -1.52081 -0.90798 1.94474 0.00000 -1.94474 0.90798 1.52081 -1.61803 -0.76537 1.97538 -0.15692 -1.90211 1.04500 1.41421 -1.70528 -0.61803 1.99383 -0.31287 -1.84776 1.17557 1.29890 -1.78201 -0.46689 -2.00000 ... ... ..... ....... ......... ........... ............. E24g * 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 ... ... ..... ....... ......... ........... ............. E25g * 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 -2.00000 ... ... ..... ....... ......... ........... ............. E26g * 2.00000 -0.90798 -1.17557 1.97538 -0.61803 -1.41421 1.90211 -0.31287 -1.61803 1.78201 0.00000 -1.78201 1.61803 0.31287 -1.90211 1.41421 0.61803 -1.97538 1.17557 0.90798 -2.00000 0.90798 1.17557 -1.97538 0.61803 1.41421 -1.90211 0.31287 1.61803 -1.78201 0.00000 1.78201 -1.61803 -0.31287 1.90211 -1.41421 -0.61803 1.97538 -1.17557 -0.90798 2.00000 2.00000 -0.90798 -1.17557 1.97538 -0.61803 -1.41421 1.90211 -0.31287 -1.61803 1.78201 0.00000 -1.78201 1.61803 0.31287 -1.90211 1.41421 0.61803 -1.97538 1.17557 0.90798 -2.00000 0.90798 1.17557 -1.97538 0.61803 1.41421 -1.90211 0.31287 1.61803 -1.78201 0.00000 1.78201 -1.61803 -0.31287 1.90211 -1.41421 -0.61803 1.97538 -1.17557 -0.90798 2.00000 ... ... ..... ....... ......... ........... ............. E27g * 2.00000 -1.04500 -0.90798 1.99383 -1.17557 -0.76537 1.97538 -1.29890 -0.61803 1.94474 -1.41421 -0.46689 1.90211 -1.52081 -0.31287 1.84776 -1.61803 -0.15692 1.78201 -1.70528 0.00000 1.70528 -1.78201 0.15692 1.61803 -1.84776 0.31287 1.52081 -1.90211 0.46689 1.41421 -1.94474 0.61803 1.29890 -1.97538 0.76537 1.17557 -1.99383 0.90798 1.04500 -2.00000 2.00000 1.04500 0.90798 -1.99383 1.17557 0.76537 -1.97538 1.29890 0.61803 -1.94474 1.41421 0.46689 -1.90211 1.52081 0.31287 -1.84776 1.61803 0.15692 -1.78201 1.70528 0.00000 -1.70528 1.78201 -0.15692 -1.61803 1.84776 -0.31287 -1.52081 1.90211 -0.46689 -1.41421 1.94474 -0.61803 -1.29890 1.97538 -0.76537 -1.17557 1.99383 -0.90798 -1.04500 -2.00000 ... ... ..... ....... ......... ........... ............. E28g * 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 ... ... ..... ....... ......... ........... ............. E29g * 2.00000 -1.29890 -0.31287 1.70528 -1.90211 0.76537 0.90798 -1.94474 1.61803 -0.15692 -1.41421 1.99383 -1.17557 -0.46689 1.78201 -1.84776 0.61803 1.04500 -1.97538 1.52081 0.00000 -1.52081 1.97538 -1.04500 -0.61803 1.84776 -1.78201 0.46689 1.17557 -1.99383 1.41421 0.15692 -1.61803 1.94474 -0.90798 -0.76537 1.90211 -1.70528 0.31287 1.29890 -2.00000 2.00000 1.29890 0.31287 -1.70528 1.90211 -0.76537 -0.90798 1.94474 -1.61803 0.15692 1.41421 -1.99383 1.17557 0.46689 -1.78201 1.84776 -0.61803 -1.04500 1.97538 -1.52081 0.00000 1.52081 -1.97538 1.04500 0.61803 -1.84776 1.78201 -0.46689 -1.17557 1.99383 -1.41421 -0.15692 1.61803 -1.94474 0.90798 0.76537 -1.90211 1.70528 -0.31287 -1.29890 -2.00000 ... ... ..... ....... ......... ........... ............. E30g * 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 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 1.41421 0.00000 -1.41421 2.00000 ... ... ..... ....... ......... ........... ............. E31g * 2.00000 -1.52081 0.31287 1.04500 -1.90211 1.84776 -0.90798 -0.46689 1.61803 -1.99383 1.41421 -0.15692 -1.17557 1.94474 -1.78201 0.76537 0.61803 -1.70528 1.97538 -1.29890 0.00000 1.29890 -1.97538 1.70528 -0.61803 -0.76537 1.78201 -1.94474 1.17557 0.15692 -1.41421 1.99383 -1.61803 0.46689 0.90798 -1.84776 1.90211 -1.04500 -0.31287 1.52081 -2.00000 2.00000 1.52081 -0.31287 -1.04500 1.90211 -1.84776 0.90798 0.46689 -1.61803 1.99383 -1.41421 0.15692 1.17557 -1.94474 1.78201 -0.76537 -0.61803 1.70528 -1.97538 1.29890 0.00000 -1.29890 1.97538 -1.70528 0.61803 0.76537 -1.78201 1.94474 -1.17557 -0.15692 1.41421 -1.99383 1.61803 -0.46689 -0.90798 1.84776 -1.90211 1.04500 0.31287 -1.52081 -2.00000 ... ... ..... ....... ......... ........... ............. E32g * 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 ... ... ..... ....... ......... ........... ............. E33g * 2.00000 -1.70528 0.90798 0.15692 -1.17557 1.84776 -1.97538 1.52081 -0.61803 -0.46689 1.41421 -1.94474 1.90211 -1.29890 0.31287 0.76537 -1.61803 1.99383 -1.78201 1.04500 0.00000 -1.04500 1.78201 -1.99383 1.61803 -0.76537 -0.31287 1.29890 -1.90211 1.94474 -1.41421 0.46689 0.61803 -1.52081 1.97538 -1.84776 1.17557 -0.15692 -0.90798 1.70528 -2.00000 2.00000 1.70528 -0.90798 -0.15692 1.17557 -1.84776 1.97538 -1.52081 0.61803 0.46689 -1.41421 1.94474 -1.90211 1.29890 -0.31287 -0.76537 1.61803 -1.99383 1.78201 -1.04500 0.00000 1.04500 -1.78201 1.99383 -1.61803 0.76537 0.31287 -1.29890 1.90211 -1.94474 1.41421 -0.46689 -0.61803 1.52081 -1.97538 1.84776 -1.17557 0.15692 0.90798 -1.70528 -2.00000 ... ... ..... ....... ......... ........... ............. E34g * 2.00000 -1.78201 1.17557 -0.31287 -0.61803 1.41421 -1.90211 1.97538 -1.61803 0.90798 0.00000 -0.90798 1.61803 -1.97538 1.90211 -1.41421 0.61803 0.31287 -1.17557 1.78201 -2.00000 1.78201 -1.17557 0.31287 0.61803 -1.41421 1.90211 -1.97538 1.61803 -0.90798 0.00000 0.90798 -1.61803 1.97538 -1.90211 1.41421 -0.61803 -0.31287 1.17557 -1.78201 2.00000 2.00000 -1.78201 1.17557 -0.31287 -0.61803 1.41421 -1.90211 1.97538 -1.61803 0.90798 0.00000 -0.90798 1.61803 -1.97538 1.90211 -1.41421 0.61803 0.31287 -1.17557 1.78201 -2.00000 1.78201 -1.17557 0.31287 0.61803 -1.41421 1.90211 -1.97538 1.61803 -0.90798 0.00000 0.90798 -1.61803 1.97538 -1.90211 1.41421 -0.61803 -0.31287 1.17557 -1.78201 2.00000 ... ... ..... ....... ......... ........... ............. E35g * 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 -2.00000 ... ... ..... ....... ......... ........... ............. E36g * 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 ... ... ..... ....... ......... ........... ............. E37g * 2.00000 -1.94474 1.78201 -1.52081 1.17557 -0.76537 0.31287 0.15692 -0.61803 1.04500 -1.41421 1.70528 -1.90211 1.99383 -1.97538 1.84776 -1.61803 1.29890 -0.90798 0.46689 0.00000 -0.46689 0.90798 -1.29890 1.61803 -1.84776 1.97538 -1.99383 1.90211 -1.70528 1.41421 -1.04500 0.61803 -0.15692 -0.31287 0.76537 -1.17557 1.52081 -1.78201 1.94474 -2.00000 2.00000 1.94474 -1.78201 1.52081 -1.17557 0.76537 -0.31287 -0.15692 0.61803 -1.04500 1.41421 -1.70528 1.90211 -1.99383 1.97538 -1.84776 1.61803 -1.29890 0.90798 -0.46689 0.00000 0.46689 -0.90798 1.29890 -1.61803 1.84776 -1.97538 1.99383 -1.90211 1.70528 -1.41421 1.04500 -0.61803 0.15692 0.31287 -0.76537 1.17557 -1.52081 1.78201 -1.94474 -2.00000 ... ... ..... ....... ......... ........... ............. E38g * 2.00000 -1.97538 1.90211 -1.78201 1.61803 -1.41421 1.17557 -0.90798 0.61803 -0.31287 0.00000 0.31287 -0.61803 0.90798 -1.17557 1.41421 -1.61803 1.78201 -1.90211 1.97538 -2.00000 1.97538 -1.90211 1.78201 -1.61803 1.41421 -1.17557 0.90798 -0.61803 0.31287 0.00000 -0.31287 0.61803 -0.90798 1.17557 -1.41421 1.61803 -1.78201 1.90211 -1.97538 2.00000 2.00000 -1.97538 1.90211 -1.78201 1.61803 -1.41421 1.17557 -0.90798 0.61803 -0.31287 0.00000 0.31287 -0.61803 0.90798 -1.17557 1.41421 -1.61803 1.78201 -1.90211 1.97538 -2.00000 1.97538 -1.90211 1.78201 -1.61803 1.41421 -1.17557 0.90798 -0.61803 0.31287 0.00000 -0.31287 0.61803 -0.90798 1.17557 -1.41421 1.61803 -1.78201 1.90211 -1.97538 2.00000 ... ... ..... ....... ......... ........... ............. E39g * 2.00000 -1.99383 1.97538 -1.94474 1.90211 -1.84776 1.78201 -1.70528 1.61803 -1.52081 1.41421 -1.29890 1.17557 -1.04500 0.90798 -0.76537 0.61803 -0.46689 0.31287 -0.15692 0.00000 0.15692 -0.31287 0.46689 -0.61803 0.76537 -0.90798 1.04500 -1.17557 1.29890 -1.41421 1.52081 -1.61803 1.70528 -1.78201 1.84776 -1.90211 1.94474 -1.97538 1.99383 -2.00000 2.00000 1.99383 -1.97538 1.94474 -1.90211 1.84776 -1.78201 1.70528 -1.61803 1.52081 -1.41421 1.29890 -1.17557 1.04500 -0.90798 0.76537 -0.61803 0.46689 -0.31287 0.15692 0.00000 -0.15692 0.31287 -0.46689 0.61803 -0.76537 0.90798 -1.04500 1.17557 -1.29890 1.41421 -1.52081 1.61803 -1.70528 1.78201 -1.84776 1.90211 -1.94474 1.97538 -1.99383 -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 -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 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E1u * 2.00000 1.99383 1.97538 1.94474 1.90211 1.84776 1.78201 1.70528 1.61803 1.52081 1.41421 1.29890 1.17557 1.04500 0.90798 0.76537 0.61803 0.46689 0.31287 0.15692 0.00000 -0.15692 -0.31287 -0.46689 -0.61803 -0.76537 -0.90798 -1.04500 -1.17557 -1.29890 -1.41421 -1.52081 -1.61803 -1.70528 -1.78201 -1.84776 -1.90211 -1.94474 -1.97538 -1.99383 -2.00000 -2.00000 1.99383 1.97538 1.94474 1.90211 1.84776 1.78201 1.70528 1.61803 1.52081 1.41421 1.29890 1.17557 1.04500 0.90798 0.76537 0.61803 0.46689 0.31287 0.15692 0.00000 -0.15692 -0.31287 -0.46689 -0.61803 -0.76537 -0.90798 -1.04500 -1.17557 -1.29890 -1.41421 -1.52081 -1.61803 -1.70528 -1.78201 -1.84776 -1.90211 -1.94474 -1.97538 -1.99383 2.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u * 2.00000 1.97538 1.90211 1.78201 1.61803 1.41421 1.17557 0.90798 0.61803 0.31287 0.00000 -0.31287 -0.61803 -0.90798 -1.17557 -1.41421 -1.61803 -1.78201 -1.90211 -1.97538 -2.00000 -1.97538 -1.90211 -1.78201 -1.61803 -1.41421 -1.17557 -0.90798 -0.61803 -0.31287 0.00000 0.31287 0.61803 0.90798 1.17557 1.41421 1.61803 1.78201 1.90211 1.97538 2.00000 -2.00000 -1.97538 -1.90211 -1.78201 -1.61803 -1.41421 -1.17557 -0.90798 -0.61803 -0.31287 0.00000 0.31287 0.61803 0.90798 1.17557 1.41421 1.61803 1.78201 1.90211 1.97538 2.00000 1.97538 1.90211 1.78201 1.61803 1.41421 1.17557 0.90798 0.61803 0.31287 0.00000 -0.31287 -0.61803 -0.90798 -1.17557 -1.41421 -1.61803 -1.78201 -1.90211 -1.97538 -2.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u * 2.00000 1.94474 1.78201 1.52081 1.17557 0.76537 0.31287 -0.15692 -0.61803 -1.04500 -1.41421 -1.70528 -1.90211 -1.99383 -1.97538 -1.84776 -1.61803 -1.29890 -0.90798 -0.46689 0.00000 0.46689 0.90798 1.29890 1.61803 1.84776 1.97538 1.99383 1.90211 1.70528 1.41421 1.04500 0.61803 0.15692 -0.31287 -0.76537 -1.17557 -1.52081 -1.78201 -1.94474 -2.00000 -2.00000 1.94474 1.78201 1.52081 1.17557 0.76537 0.31287 -0.15692 -0.61803 -1.04500 -1.41421 -1.70528 -1.90211 -1.99383 -1.97538 -1.84776 -1.61803 -1.29890 -0.90798 -0.46689 0.00000 0.46689 0.90798 1.29890 1.61803 1.84776 1.97538 1.99383 1.90211 1.70528 1.41421 1.04500 0.61803 0.15692 -0.31287 -0.76537 -1.17557 -1.52081 -1.78201 -1.94474 2.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u * 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 ... ... ..... ....... ......... ..TT....... ............. E5u * 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 -2.00000 -1.84776 -1.41421 -0.76537 0.00000 0.76537 1.41421 1.84776 2.00000 1.84776 1.41421 0.76537 0.00000 -0.76537 -1.41421 -1.84776 2.00000 ... ... ..... ....... ......... TT......... ............. E6u * 2.00000 1.78201 1.17557 0.31287 -0.61803 -1.41421 -1.90211 -1.97538 -1.61803 -0.90798 0.00000 0.90798 1.61803 1.97538 1.90211 1.41421 0.61803 -0.31287 -1.17557 -1.78201 -2.00000 -1.78201 -1.17557 -0.31287 0.61803 1.41421 1.90211 1.97538 1.61803 0.90798 0.00000 -0.90798 -1.61803 -1.97538 -1.90211 -1.41421 -0.61803 0.31287 1.17557 1.78201 2.00000 -2.00000 -1.78201 -1.17557 -0.31287 0.61803 1.41421 1.90211 1.97538 1.61803 0.90798 0.00000 -0.90798 -1.61803 -1.97538 -1.90211 -1.41421 -0.61803 0.31287 1.17557 1.78201 2.00000 1.78201 1.17557 0.31287 -0.61803 -1.41421 -1.90211 -1.97538 -1.61803 -0.90798 0.00000 0.90798 1.61803 1.97538 1.90211 1.41421 0.61803 -0.31287 -1.17557 -1.78201 -2.00000 ... ... ..... ....... ......... ........... ............. E7u * 2.00000 1.70528 0.90798 -0.15692 -1.17557 -1.84776 -1.97538 -1.52081 -0.61803 0.46689 1.41421 1.94474 1.90211 1.29890 0.31287 -0.76537 -1.61803 -1.99383 -1.78201 -1.04500 0.00000 1.04500 1.78201 1.99383 1.61803 0.76537 -0.31287 -1.29890 -1.90211 -1.94474 -1.41421 -0.46689 0.61803 1.52081 1.97538 1.84776 1.17557 0.15692 -0.90798 -1.70528 -2.00000 -2.00000 1.70528 0.90798 -0.15692 -1.17557 -1.84776 -1.97538 -1.52081 -0.61803 0.46689 1.41421 1.94474 1.90211 1.29890 0.31287 -0.76537 -1.61803 -1.99383 -1.78201 -1.04500 0.00000 1.04500 1.78201 1.99383 1.61803 0.76537 -0.31287 -1.29890 -1.90211 -1.94474 -1.41421 -0.46689 0.61803 1.52081 1.97538 1.84776 1.17557 0.15692 -0.90798 -1.70528 2.00000 ... ... ..... ....... ......... ........... ............. E8u * 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 ... ... ..... ....... ......... ........... ............. E9u * 2.00000 1.52081 0.31287 -1.04500 -1.90211 -1.84776 -0.90798 0.46689 1.61803 1.99383 1.41421 0.15692 -1.17557 -1.94474 -1.78201 -0.76537 0.61803 1.70528 1.97538 1.29890 0.00000 -1.29890 -1.97538 -1.70528 -0.61803 0.76537 1.78201 1.94474 1.17557 -0.15692 -1.41421 -1.99383 -1.61803 -0.46689 0.90798 1.84776 1.90211 1.04500 -0.31287 -1.52081 -2.00000 -2.00000 1.52081 0.31287 -1.04500 -1.90211 -1.84776 -0.90798 0.46689 1.61803 1.99383 1.41421 0.15692 -1.17557 -1.94474 -1.78201 -0.76537 0.61803 1.70528 1.97538 1.29890 0.00000 -1.29890 -1.97538 -1.70528 -0.61803 0.76537 1.78201 1.94474 1.17557 -0.15692 -1.41421 -1.99383 -1.61803 -0.46689 0.90798 1.84776 1.90211 1.04500 -0.31287 -1.52081 2.00000 ... ... ..... ....... ......... ........... ............. E10u * 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 -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 1.41421 0.00000 -1.41421 -2.00000 ... ... ..... ....... ......... ........... ............. E11u * 2.00000 1.29890 -0.31287 -1.70528 -1.90211 -0.76537 0.90798 1.94474 1.61803 0.15692 -1.41421 -1.99383 -1.17557 0.46689 1.78201 1.84776 0.61803 -1.04500 -1.97538 -1.52081 0.00000 1.52081 1.97538 1.04500 -0.61803 -1.84776 -1.78201 -0.46689 1.17557 1.99383 1.41421 -0.15692 -1.61803 -1.94474 -0.90798 0.76537 1.90211 1.70528 0.31287 -1.29890 -2.00000 -2.00000 1.29890 -0.31287 -1.70528 -1.90211 -0.76537 0.90798 1.94474 1.61803 0.15692 -1.41421 -1.99383 -1.17557 0.46689 1.78201 1.84776 0.61803 -1.04500 -1.97538 -1.52081 0.00000 1.52081 1.97538 1.04500 -0.61803 -1.84776 -1.78201 -0.46689 1.17557 1.99383 1.41421 -0.15692 -1.61803 -1.94474 -0.90798 0.76537 1.90211 1.70528 0.31287 -1.29890 2.00000 ... ... ..... ....... ......... ........... ............. E12u * 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 ... ... ..... ....... ......... ........... ............. E13u * 2.00000 1.04500 -0.90798 -1.99383 -1.17557 0.76537 1.97538 1.29890 -0.61803 -1.94474 -1.41421 0.46689 1.90211 1.52081 -0.31287 -1.84776 -1.61803 0.15692 1.78201 1.70528 0.00000 -1.70528 -1.78201 -0.15692 1.61803 1.84776 0.31287 -1.52081 -1.90211 -0.46689 1.41421 1.94474 0.61803 -1.29890 -1.97538 -0.76537 1.17557 1.99383 0.90798 -1.04500 -2.00000 -2.00000 1.04500 -0.90798 -1.99383 -1.17557 0.76537 1.97538 1.29890 -0.61803 -1.94474 -1.41421 0.46689 1.90211 1.52081 -0.31287 -1.84776 -1.61803 0.15692 1.78201 1.70528 0.00000 -1.70528 -1.78201 -0.15692 1.61803 1.84776 0.31287 -1.52081 -1.90211 -0.46689 1.41421 1.94474 0.61803 -1.29890 -1.97538 -0.76537 1.17557 1.99383 0.90798 -1.04500 2.00000 ... ... ..... ....... ......... ........... ............. E14u * 2.00000 0.90798 -1.17557 -1.97538 -0.61803 1.41421 1.90211 0.31287 -1.61803 -1.78201 0.00000 1.78201 1.61803 -0.31287 -1.90211 -1.41421 0.61803 1.97538 1.17557 -0.90798 -2.00000 -0.90798 1.17557 1.97538 0.61803 -1.41421 -1.90211 -0.31287 1.61803 1.78201 0.00000 -1.78201 -1.61803 0.31287 1.90211 1.41421 -0.61803 -1.97538 -1.17557 0.90798 2.00000 -2.00000 -0.90798 1.17557 1.97538 0.61803 -1.41421 -1.90211 -0.31287 1.61803 1.78201 0.00000 -1.78201 -1.61803 0.31287 1.90211 1.41421 -0.61803 -1.97538 -1.17557 0.90798 2.00000 0.90798 -1.17557 -1.97538 -0.61803 1.41421 1.90211 0.31287 -1.61803 -1.78201 0.00000 1.78201 1.61803 -0.31287 -1.90211 -1.41421 0.61803 1.97538 1.17557 -0.90798 -2.00000 ... ... ..... ....... ......... ........... ............. E15u * 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 -2.00000 -0.76537 1.41421 1.84776 0.00000 -1.84776 -1.41421 0.76537 2.00000 0.76537 -1.41421 -1.84776 0.00000 1.84776 1.41421 -0.76537 2.00000 ... ... ..... ....... ......... ........... ............. E16u * 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 ... ... ..... ....... ......... ........... ............. E17u * 2.00000 0.46689 -1.78201 -1.29890 1.17557 1.84776 -0.31287 -1.99383 -0.61803 1.70528 1.41421 -1.04500 -1.90211 0.15692 1.97538 0.76537 -1.61803 -1.52081 0.90798 1.94474 0.00000 -1.94474 -0.90798 1.52081 1.61803 -0.76537 -1.97538 -0.15692 1.90211 1.04500 -1.41421 -1.70528 0.61803 1.99383 0.31287 -1.84776 -1.17557 1.29890 1.78201 -0.46689 -2.00000 -2.00000 0.46689 -1.78201 -1.29890 1.17557 1.84776 -0.31287 -1.99383 -0.61803 1.70528 1.41421 -1.04500 -1.90211 0.15692 1.97538 0.76537 -1.61803 -1.52081 0.90798 1.94474 0.00000 -1.94474 -0.90798 1.52081 1.61803 -0.76537 -1.97538 -0.15692 1.90211 1.04500 -1.41421 -1.70528 0.61803 1.99383 0.31287 -1.84776 -1.17557 1.29890 1.78201 -0.46689 2.00000 ... ... ..... ....... ......... ........... ............. E18u * 2.00000 0.31287 -1.90211 -0.90798 1.61803 1.41421 -1.17557 -1.78201 0.61803 1.97538 0.00000 -1.97538 -0.61803 1.78201 1.17557 -1.41421 -1.61803 0.90798 1.90211 -0.31287 -2.00000 -0.31287 1.90211 0.90798 -1.61803 -1.41421 1.17557 1.78201 -0.61803 -1.97538 0.00000 1.97538 0.61803 -1.78201 -1.17557 1.41421 1.61803 -0.90798 -1.90211 0.31287 2.00000 -2.00000 -0.31287 1.90211 0.90798 -1.61803 -1.41421 1.17557 1.78201 -0.61803 -1.97538 0.00000 1.97538 0.61803 -1.78201 -1.17557 1.41421 1.61803 -0.90798 -1.90211 0.31287 2.00000 0.31287 -1.90211 -0.90798 1.61803 1.41421 -1.17557 -1.78201 0.61803 1.97538 0.00000 -1.97538 -0.61803 1.78201 1.17557 -1.41421 -1.61803 0.90798 1.90211 -0.31287 -2.00000 ... ... ..... ....... ......... ........... ............. E19u * 2.00000 0.15692 -1.97538 -0.46689 1.90211 0.76537 -1.78201 -1.04500 1.61803 1.29890 -1.41421 -1.52081 1.17557 1.70528 -0.90798 -1.84776 0.61803 1.94474 -0.31287 -1.99383 0.00000 1.99383 0.31287 -1.94474 -0.61803 1.84776 0.90798 -1.70528 -1.17557 1.52081 1.41421 -1.29890 -1.61803 1.04500 1.78201 -0.76537 -1.90211 0.46689 1.97538 -0.15692 -2.00000 -2.00000 0.15692 -1.97538 -0.46689 1.90211 0.76537 -1.78201 -1.04500 1.61803 1.29890 -1.41421 -1.52081 1.17557 1.70528 -0.90798 -1.84776 0.61803 1.94474 -0.31287 -1.99383 0.00000 1.99383 0.31287 -1.94474 -0.61803 1.84776 0.90798 -1.70528 -1.17557 1.52081 1.41421 -1.29890 -1.61803 1.04500 1.78201 -0.76537 -1.90211 0.46689 1.97538 -0.15692 2.00000 ... ... ..... ....... ......... ........... ............. E20u * 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 -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 0.00000 2.00000 0.00000 -2.00000 ... ... ..... ....... ......... ........... ............. E21u * 2.00000 -0.15692 -1.97538 0.46689 1.90211 -0.76537 -1.78201 1.04500 1.61803 -1.29890 -1.41421 1.52081 1.17557 -1.70528 -0.90798 1.84776 0.61803 -1.94474 -0.31287 1.99383 0.00000 -1.99383 0.31287 1.94474 -0.61803 -1.84776 0.90798 1.70528 -1.17557 -1.52081 1.41421 1.29890 -1.61803 -1.04500 1.78201 0.76537 -1.90211 -0.46689 1.97538 0.15692 -2.00000 -2.00000 -0.15692 -1.97538 0.46689 1.90211 -0.76537 -1.78201 1.04500 1.61803 -1.29890 -1.41421 1.52081 1.17557 -1.70528 -0.90798 1.84776 0.61803 -1.94474 -0.31287 1.99383 0.00000 -1.99383 0.31287 1.94474 -0.61803 -1.84776 0.90798 1.70528 -1.17557 -1.52081 1.41421 1.29890 -1.61803 -1.04500 1.78201 0.76537 -1.90211 -0.46689 1.97538 0.15692 2.00000 ... ... ..... ....... ......... ........... ............. E22u * 2.00000 -0.31287 -1.90211 0.90798 1.61803 -1.41421 -1.17557 1.78201 0.61803 -1.97538 0.00000 1.97538 -0.61803 -1.78201 1.17557 1.41421 -1.61803 -0.90798 1.90211 0.31287 -2.00000 0.31287 1.90211 -0.90798 -1.61803 1.41421 1.17557 -1.78201 -0.61803 1.97538 0.00000 -1.97538 0.61803 1.78201 -1.17557 -1.41421 1.61803 0.90798 -1.90211 -0.31287 2.00000 -2.00000 0.31287 1.90211 -0.90798 -1.61803 1.41421 1.17557 -1.78201 -0.61803 1.97538 0.00000 -1.97538 0.61803 1.78201 -1.17557 -1.41421 1.61803 0.90798 -1.90211 -0.31287 2.00000 -0.31287 -1.90211 0.90798 1.61803 -1.41421 -1.17557 1.78201 0.61803 -1.97538 0.00000 1.97538 -0.61803 -1.78201 1.17557 1.41421 -1.61803 -0.90798 1.90211 0.31287 -2.00000 ... ... ..... ....... ......... ........... ............. E23u * 2.00000 -0.46689 -1.78201 1.29890 1.17557 -1.84776 -0.31287 1.99383 -0.61803 -1.70528 1.41421 1.04500 -1.90211 -0.15692 1.97538 -0.76537 -1.61803 1.52081 0.90798 -1.94474 0.00000 1.94474 -0.90798 -1.52081 1.61803 0.76537 -1.97538 0.15692 1.90211 -1.04500 -1.41421 1.70528 0.61803 -1.99383 0.31287 1.84776 -1.17557 -1.29890 1.78201 0.46689 -2.00000 -2.00000 -0.46689 -1.78201 1.29890 1.17557 -1.84776 -0.31287 1.99383 -0.61803 -1.70528 1.41421 1.04500 -1.90211 -0.15692 1.97538 -0.76537 -1.61803 1.52081 0.90798 -1.94474 0.00000 1.94474 -0.90798 -1.52081 1.61803 0.76537 -1.97538 0.15692 1.90211 -1.04500 -1.41421 1.70528 0.61803 -1.99383 0.31287 1.84776 -1.17557 -1.29890 1.78201 0.46689 2.00000 ... ... ..... ....... ......... ........... ............. E24u * 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 ... ... ..... ....... ......... ........... ............. E25u * 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 -2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 -2.00000 0.76537 1.41421 -1.84776 0.00000 1.84776 -1.41421 -0.76537 2.00000 -0.76537 -1.41421 1.84776 0.00000 -1.84776 1.41421 0.76537 2.00000 ... ... ..... ....... ......... ........... ............. E26u * 2.00000 -0.90798 -1.17557 1.97538 -0.61803 -1.41421 1.90211 -0.31287 -1.61803 1.78201 0.00000 -1.78201 1.61803 0.31287 -1.90211 1.41421 0.61803 -1.97538 1.17557 0.90798 -2.00000 0.90798 1.17557 -1.97538 0.61803 1.41421 -1.90211 0.31287 1.61803 -1.78201 0.00000 1.78201 -1.61803 -0.31287 1.90211 -1.41421 -0.61803 1.97538 -1.17557 -0.90798 2.00000 -2.00000 0.90798 1.17557 -1.97538 0.61803 1.41421 -1.90211 0.31287 1.61803 -1.78201 0.00000 1.78201 -1.61803 -0.31287 1.90211 -1.41421 -0.61803 1.97538 -1.17557 -0.90798 2.00000 -0.90798 -1.17557 1.97538 -0.61803 -1.41421 1.90211 -0.31287 -1.61803 1.78201 0.00000 -1.78201 1.61803 0.31287 -1.90211 1.41421 0.61803 -1.97538 1.17557 0.90798 -2.00000 ... ... ..... ....... ......... ........... ............. E27u * 2.00000 -1.04500 -0.90798 1.99383 -1.17557 -0.76537 1.97538 -1.29890 -0.61803 1.94474 -1.41421 -0.46689 1.90211 -1.52081 -0.31287 1.84776 -1.61803 -0.15692 1.78201 -1.70528 0.00000 1.70528 -1.78201 0.15692 1.61803 -1.84776 0.31287 1.52081 -1.90211 0.46689 1.41421 -1.94474 0.61803 1.29890 -1.97538 0.76537 1.17557 -1.99383 0.90798 1.04500 -2.00000 -2.00000 -1.04500 -0.90798 1.99383 -1.17557 -0.76537 1.97538 -1.29890 -0.61803 1.94474 -1.41421 -0.46689 1.90211 -1.52081 -0.31287 1.84776 -1.61803 -0.15692 1.78201 -1.70528 0.00000 1.70528 -1.78201 0.15692 1.61803 -1.84776 0.31287 1.52081 -1.90211 0.46689 1.41421 -1.94474 0.61803 1.29890 -1.97538 0.76537 1.17557 -1.99383 0.90798 1.04500 2.00000 ... ... ..... ....... ......... ........... ............. E28u * 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 ... ... ..... ....... ......... ........... ............. E29u * 2.00000 -1.29890 -0.31287 1.70528 -1.90211 0.76537 0.90798 -1.94474 1.61803 -0.15692 -1.41421 1.99383 -1.17557 -0.46689 1.78201 -1.84776 0.61803 1.04500 -1.97538 1.52081 0.00000 -1.52081 1.97538 -1.04500 -0.61803 1.84776 -1.78201 0.46689 1.17557 -1.99383 1.41421 0.15692 -1.61803 1.94474 -0.90798 -0.76537 1.90211 -1.70528 0.31287 1.29890 -2.00000 -2.00000 -1.29890 -0.31287 1.70528 -1.90211 0.76537 0.90798 -1.94474 1.61803 -0.15692 -1.41421 1.99383 -1.17557 -0.46689 1.78201 -1.84776 0.61803 1.04500 -1.97538 1.52081 0.00000 -1.52081 1.97538 -1.04500 -0.61803 1.84776 -1.78201 0.46689 1.17557 -1.99383 1.41421 0.15692 -1.61803 1.94474 -0.90798 -0.76537 1.90211 -1.70528 0.31287 1.29890 2.00000 ... ... ..... ....... ......... ........... ............. E30u * 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 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 -1.41421 0.00000 1.41421 -2.00000 ... ... ..... ....... ......... ........... ............. E31u * 2.00000 -1.52081 0.31287 1.04500 -1.90211 1.84776 -0.90798 -0.46689 1.61803 -1.99383 1.41421 -0.15692 -1.17557 1.94474 -1.78201 0.76537 0.61803 -1.70528 1.97538 -1.29890 0.00000 1.29890 -1.97538 1.70528 -0.61803 -0.76537 1.78201 -1.94474 1.17557 0.15692 -1.41421 1.99383 -1.61803 0.46689 0.90798 -1.84776 1.90211 -1.04500 -0.31287 1.52081 -2.00000 -2.00000 -1.52081 0.31287 1.04500 -1.90211 1.84776 -0.90798 -0.46689 1.61803 -1.99383 1.41421 -0.15692 -1.17557 1.94474 -1.78201 0.76537 0.61803 -1.70528 1.97538 -1.29890 0.00000 1.29890 -1.97538 1.70528 -0.61803 -0.76537 1.78201 -1.94474 1.17557 0.15692 -1.41421 1.99383 -1.61803 0.46689 0.90798 -1.84776 1.90211 -1.04500 -0.31287 1.52081 2.00000 ... ... ..... ....... ......... ........... ............. E32u * 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 ... ... ..... ....... ......... ........... ............. E33u * 2.00000 -1.70528 0.90798 0.15692 -1.17557 1.84776 -1.97538 1.52081 -0.61803 -0.46689 1.41421 -1.94474 1.90211 -1.29890 0.31287 0.76537 -1.61803 1.99383 -1.78201 1.04500 0.00000 -1.04500 1.78201 -1.99383 1.61803 -0.76537 -0.31287 1.29890 -1.90211 1.94474 -1.41421 0.46689 0.61803 -1.52081 1.97538 -1.84776 1.17557 -0.15692 -0.90798 1.70528 -2.00000 -2.00000 -1.70528 0.90798 0.15692 -1.17557 1.84776 -1.97538 1.52081 -0.61803 -0.46689 1.41421 -1.94474 1.90211 -1.29890 0.31287 0.76537 -1.61803 1.99383 -1.78201 1.04500 0.00000 -1.04500 1.78201 -1.99383 1.61803 -0.76537 -0.31287 1.29890 -1.90211 1.94474 -1.41421 0.46689 0.61803 -1.52081 1.97538 -1.84776 1.17557 -0.15692 -0.90798 1.70528 2.00000 ... ... ..... ....... ......... ........... ............. E34u * 2.00000 -1.78201 1.17557 -0.31287 -0.61803 1.41421 -1.90211 1.97538 -1.61803 0.90798 0.00000 -0.90798 1.61803 -1.97538 1.90211 -1.41421 0.61803 0.31287 -1.17557 1.78201 -2.00000 1.78201 -1.17557 0.31287 0.61803 -1.41421 1.90211 -1.97538 1.61803 -0.90798 0.00000 0.90798 -1.61803 1.97538 -1.90211 1.41421 -0.61803 -0.31287 1.17557 -1.78201 2.00000 -2.00000 1.78201 -1.17557 0.31287 0.61803 -1.41421 1.90211 -1.97538 1.61803 -0.90798 0.00000 0.90798 -1.61803 1.97538 -1.90211 1.41421 -0.61803 -0.31287 1.17557 -1.78201 2.00000 -1.78201 1.17557 -0.31287 -0.61803 1.41421 -1.90211 1.97538 -1.61803 0.90798 0.00000 -0.90798 1.61803 -1.97538 1.90211 -1.41421 0.61803 0.31287 -1.17557 1.78201 -2.00000 ... ... ..... ....... ......... ........... ............. E35u * 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 -2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 -2.00000 1.84776 -1.41421 0.76537 0.00000 -0.76537 1.41421 -1.84776 2.00000 -1.84776 1.41421 -0.76537 0.00000 0.76537 -1.41421 1.84776 2.00000 ... ... ..... ....... ......... ........... ............. E36u * 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 ... ... ..... ....... ......... ........... ............. E37u * 2.00000 -1.94474 1.78201 -1.52081 1.17557 -0.76537 0.31287 0.15692 -0.61803 1.04500 -1.41421 1.70528 -1.90211 1.99383 -1.97538 1.84776 -1.61803 1.29890 -0.90798 0.46689 0.00000 -0.46689 0.90798 -1.29890 1.61803 -1.84776 1.97538 -1.99383 1.90211 -1.70528 1.41421 -1.04500 0.61803 -0.15692 -0.31287 0.76537 -1.17557 1.52081 -1.78201 1.94474 -2.00000 -2.00000 -1.94474 1.78201 -1.52081 1.17557 -0.76537 0.31287 0.15692 -0.61803 1.04500 -1.41421 1.70528 -1.90211 1.99383 -1.97538 1.84776 -1.61803 1.29890 -0.90798 0.46689 0.00000 -0.46689 0.90798 -1.29890 1.61803 -1.84776 1.97538 -1.99383 1.90211 -1.70528 1.41421 -1.04500 0.61803 -0.15692 -0.31287 0.76537 -1.17557 1.52081 -1.78201 1.94474 2.00000 ... ... ..... ....... ......... ........... ............. E38u * 2.00000 -1.97538 1.90211 -1.78201 1.61803 -1.41421 1.17557 -0.90798 0.61803 -0.31287 0.00000 0.31287 -0.61803 0.90798 -1.17557 1.41421 -1.61803 1.78201 -1.90211 1.97538 -2.00000 1.97538 -1.90211 1.78201 -1.61803 1.41421 -1.17557 0.90798 -0.61803 0.31287 0.00000 -0.31287 0.61803 -0.90798 1.17557 -1.41421 1.61803 -1.78201 1.90211 -1.97538 2.00000 -2.00000 1.97538 -1.90211 1.78201 -1.61803 1.41421 -1.17557 0.90798 -0.61803 0.31287 0.00000 -0.31287 0.61803 -0.90798 1.17557 -1.41421 1.61803 -1.78201 1.90211 -1.97538 2.00000 -1.97538 1.90211 -1.78201 1.61803 -1.41421 1.17557 -0.90798 0.61803 -0.31287 0.00000 0.31287 -0.61803 0.90798 -1.17557 1.41421 -1.61803 1.78201 -1.90211 1.97538 -2.00000 ... ... ..... ....... ......... ........... ............. E39u * 2.00000 -1.99383 1.97538 -1.94474 1.90211 -1.84776 1.78201 -1.70528 1.61803 -1.52081 1.41421 -1.29890 1.17557 -1.04500 0.90798 -0.76537 0.61803 -0.46689 0.31287 -0.15692 0.00000 0.15692 -0.31287 0.46689 -0.61803 0.76537 -0.90798 1.04500 -1.17557 1.29890 -1.41421 1.52081 -1.61803 1.70528 -1.78201 1.84776 -1.90211 1.94474 -1.97538 1.99383 -2.00000 -2.00000 -1.99383 1.97538 -1.94474 1.90211 -1.84776 1.78201 -1.70528 1.61803 -1.52081 1.41421 -1.29890 1.17557 -1.04500 0.90798 -0.76537 0.61803 -0.46689 0.31287 -0.15692 0.00000 0.15692 -0.31287 0.46689 -0.61803 0.76537 -0.90798 1.04500 -1.17557 1.29890 -1.41421 1.52081 -1.61803 1.70528 -1.78201 1.84776 -1.90211 1.94474 -1.97538 1.99383 2.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.993834667466 = 2*cos(2*π/80) = 2*cos(π/40) = √8+√2+√10+2*√5−√5/2 1.975376681190 = 2*cos(4*π/80) = 2*cos(π/20) = (√2+√10+2*(√5−√5))/4 1.944739840795 = 2*cos(6*π/80) = 2*cos(3*π/40) = √8−√2+√10+2*√5+√5/2 1.902113032590 = 2*cos(8*π/80) = 2*cos(π/10) = (√10+2*√5)/2 1.847759065023 = 2*cos(10*π/80) = 2*cos(π/8) = √2+√2 1.782013048377 = 2*cos(12*π/80) = 2*cos(3*π/20) = (√10−√2+2*√5+√5)/4 1.705280328708 = 2*cos(14*π/80) = 2*cos(7*π/40) = √8+√2−√10+2*√5+√5/2 1.618033988750 = 2*cos(16*π/80) = 2*cos(π/5) = (√5+1)/2 1.520811931200 = 2*cos(18*π/80) = 2*cos(9*π/40) = √8+√2+√10−2*√5−√5/2 1.414213562373 = 2*cos(20*π/80) = 2*cos(π/4) = √2 1.298896096660 = 2*cos(22*π/80) = 2*cos(11*π/40) = √8−√2−√10+2*√5−√5/2 1.175570504585 = 2*cos(24*π/80) = 2*cos(3*π/10) = (√10−2*√5)/2 1.044997129432 = 2*cos(26*π/80) = 2*cos(13*π/40) = √8−√2+√10−2*√5+√5/2 0.907980999479 = 2*cos(28*π/80) = 2*cos(7*π/20) = (√2−√10+2*√5+√5)/4 0.765366864730 = 2*cos(30*π/80) = 2*cos(3*π/8) = √2−√2 0.618033988750 = 2*cos(32*π/80) = 2*cos(2*π/5) = (√5−1)/2 0.466890727712 = 2*cos(34*π/80) = 2*cos(17*π/40) = √8+√2−√10−2*√5+√5/2 0.312868930080 = 2*cos(36*π/80) = 2*cos(9*π/20) = (√2+√10−2*(√5−√5))/4 0.156918191456 = 2*cos(38*π/80) = 2*cos(19*π/40) = √8−√2−√10−2*√5−√5/2 Symmetry of Rotations and Cartesian products Ag R+d+g+i+k+m R_z, z², z⁴, z⁶ E1g R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2g d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E3g g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4g g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5g i+k+m {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6g i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7g k+m E8g k+m E9g m E10g m Au p+f+h+j+l z, z³, z⁵ E1u p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2u f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3u f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E4u h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5u h+j+l {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)} E6u j+l E7u j+l E8u l E9u l Notes: α The order of the C_80h point group is 160, and the order of the principal axis (C₈₀) is 80. The group has 82 irreducible representations. β The C_80h point group is generated by two symmetry elements, which are canonically chosen as C₈₀ and i. Other possible choices are C₈₀ and σ_h, or less commonly S₈₀ with either i or σ_h. γ The lowest nonvanishing multipole moment in C_80h is 4 (quadrupole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C_80h 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 156 cases have been combined into 78 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 78 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 78 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. η Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. θ The point group corresponds to a constructible polygon, as the order of the principal axis is a product of any number of different Fermat primes (3,5,17,257,65537) times an arbitrary power of two. Therefore, all characters have an algebraic degree which is a power of two and can be expressed as radicals involving only square roots and integer numbers. ι The fact that the regular pentagon is constructible is known since antiquity; Eukleides already discovered a construction for it. The double cosine of 2π/5 is equal to the reciprocal of the Golden Ratio of (1+√5)/2 = 1.61803. Regular polygons of order 10,20,40,80 etc. are easily derived from the regular pentagon by successive halving of angles.

This Character Table for the C_80h point group was created by Gernot Katzer.

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

	C_78h
	C_79h
C₈₀ C_80v	C_80h	D₈₀ D_80h D_80d S₈₀
	C_81h
	C_82h

Character table for the C80h point group

Character table for the C_80h point group