D44h E 2 C44 2 C22 2 C44^3 2 C11 2 C44^5 2 C22^3 2 C44^7 2 C11^2 2 C44^9 2 C22^5 2 C4 2 C11^3 2 C44^13 2 C22^7 2 C44^15 2 C11^4 2 C44^17 2 C22^9 2 C44^19 2 C11^5 2 C44^21 C2 22 C2' 22 C2" i 2 S44 2 S22 2 S44^3 2 S11 2 S44^5 2 S22^3 2 S44^7 2 S11^2 2 S44^9 2 S22^5 2 S4 2 S11^3 2 S44^13 2 S22^7 2 S44^15 2 S11^4 2 S44^17 2 S22^9 2 S44^19 2 S11^5 2 S44^21 sh 22 sv 22 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ... ....T ....... ........T ........... ............T A2g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. B1g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. B2g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E1g 2.00000 1.97964 1.91899 1.81926 1.68251 1.51150 1.30972 1.08128 0.83083 0.56347 0.28463 0.00000 -0.28463 -0.56347 -0.83083 -1.08128 -1.30972 -1.51150 -1.68251 -1.81926 -1.91899 -1.97964 -2.00000 0.00000 0.00000 2.00000 -1.97964 -1.91899 -1.81926 -1.68251 -1.51150 -1.30972 -1.08128 -0.83083 -0.56347 -0.28463 0.00000 0.28463 0.56347 0.83083 1.08128 1.30972 1.51150 1.68251 1.81926 1.91899 1.97964 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.91899 1.68251 1.30972 0.83083 0.28463 -0.28463 -0.83083 -1.30972 -1.68251 -1.91899 -2.00000 -1.91899 -1.68251 -1.30972 -0.83083 -0.28463 0.28463 0.83083 1.30972 1.68251 1.91899 2.00000 0.00000 0.00000 2.00000 1.91899 1.68251 1.30972 0.83083 0.28463 -0.28463 -0.83083 -1.30972 -1.68251 -1.91899 -2.00000 -1.91899 -1.68251 -1.30972 -0.83083 -0.28463 0.28463 0.83083 1.30972 1.68251 1.91899 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 2.00000 1.81926 1.30972 0.56347 -0.28463 -1.08128 -1.68251 -1.97964 -1.91899 -1.51150 -0.83083 0.00000 0.83083 1.51150 1.91899 1.97964 1.68251 1.08128 0.28463 -0.56347 -1.30972 -1.81926 -2.00000 0.00000 0.00000 2.00000 -1.81926 -1.30972 -0.56347 0.28463 1.08128 1.68251 1.97964 1.91899 1.51150 0.83083 0.00000 -0.83083 -1.51150 -1.91899 -1.97964 -1.68251 -1.08128 -0.28463 0.56347 1.30972 1.81926 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 0.00000 0.00000 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.51150 0.28463 -1.08128 -1.91899 -1.81926 -0.83083 0.56347 1.68251 1.97964 1.30972 0.00000 -1.30972 -1.97964 -1.68251 -0.56347 0.83083 1.81926 1.91899 1.08128 -0.28463 -1.51150 -2.00000 0.00000 0.00000 2.00000 -1.51150 -0.28463 1.08128 1.91899 1.81926 0.83083 -0.56347 -1.68251 -1.97964 -1.30972 0.00000 1.30972 1.97964 1.68251 0.56347 -0.83083 -1.81926 -1.91899 -1.08128 0.28463 1.51150 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 2.00000 1.30972 -0.28463 -1.68251 -1.91899 -0.83083 0.83083 1.91899 1.68251 0.28463 -1.30972 -2.00000 -1.30972 0.28463 1.68251 1.91899 0.83083 -0.83083 -1.91899 -1.68251 -0.28463 1.30972 2.00000 0.00000 0.00000 2.00000 1.30972 -0.28463 -1.68251 -1.91899 -0.83083 0.83083 1.91899 1.68251 0.28463 -1.30972 -2.00000 -1.30972 0.28463 1.68251 1.91899 0.83083 -0.83083 -1.91899 -1.68251 -0.28463 1.30972 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7g 2.00000 1.08128 -0.83083 -1.97964 -1.30972 0.56347 1.91899 1.51150 -0.28463 -1.81926 -1.68251 0.00000 1.68251 1.81926 0.28463 -1.51150 -1.91899 -0.56347 1.30972 1.97964 0.83083 -1.08128 -2.00000 0.00000 0.00000 2.00000 -1.08128 0.83083 1.97964 1.30972 -0.56347 -1.91899 -1.51150 0.28463 1.81926 1.68251 0.00000 -1.68251 -1.81926 -0.28463 1.51150 1.91899 0.56347 -1.30972 -1.97964 -0.83083 1.08128 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8g 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.00000 0.00000 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9g 2.00000 0.56347 -1.68251 -1.51150 0.83083 1.97964 0.28463 -1.81926 -1.30972 1.08128 1.91899 0.00000 -1.91899 -1.08128 1.30972 1.81926 -0.28463 -1.97964 -0.83083 1.51150 1.68251 -0.56347 -2.00000 0.00000 0.00000 2.00000 -0.56347 1.68251 1.51150 -0.83083 -1.97964 -0.28463 1.81926 1.30972 -1.08128 -1.91899 0.00000 1.91899 1.08128 -1.30972 -1.81926 0.28463 1.97964 0.83083 -1.51150 -1.68251 0.56347 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10g 2.00000 0.28463 -1.91899 -0.83083 1.68251 1.30972 -1.30972 -1.68251 0.83083 1.91899 -0.28463 -2.00000 -0.28463 1.91899 0.83083 -1.68251 -1.30972 1.30972 1.68251 -0.83083 -1.91899 0.28463 2.00000 0.00000 0.00000 2.00000 0.28463 -1.91899 -0.83083 1.68251 1.30972 -1.30972 -1.68251 0.83083 1.91899 -0.28463 -2.00000 -0.28463 1.91899 0.83083 -1.68251 -1.30972 1.30972 1.68251 -0.83083 -1.91899 0.28463 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 0.00000 2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12g 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 0.00000 0.00000 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 -0.56347 -1.68251 1.51150 0.83083 -1.97964 0.28463 1.81926 -1.30972 -1.08128 1.91899 0.00000 -1.91899 1.08128 1.30972 -1.81926 -0.28463 1.97964 -0.83083 -1.51150 1.68251 0.56347 -2.00000 0.00000 0.00000 2.00000 0.56347 1.68251 -1.51150 -0.83083 1.97964 -0.28463 -1.81926 1.30972 1.08128 -1.91899 0.00000 1.91899 -1.08128 -1.30972 1.81926 0.28463 -1.97964 0.83083 1.51150 -1.68251 -0.56347 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 -0.83083 -1.30972 1.91899 -0.28463 -1.68251 1.68251 0.28463 -1.91899 1.30972 0.83083 -2.00000 0.83083 1.30972 -1.91899 0.28463 1.68251 -1.68251 -0.28463 1.91899 -1.30972 -0.83083 2.00000 0.00000 0.00000 2.00000 -0.83083 -1.30972 1.91899 -0.28463 -1.68251 1.68251 0.28463 -1.91899 1.30972 0.83083 -2.00000 0.83083 1.30972 -1.91899 0.28463 1.68251 -1.68251 -0.28463 1.91899 -1.30972 -0.83083 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15g 2.00000 -1.08128 -0.83083 1.97964 -1.30972 -0.56347 1.91899 -1.51150 -0.28463 1.81926 -1.68251 0.00000 1.68251 -1.81926 0.28463 1.51150 -1.91899 0.56347 1.30972 -1.97964 0.83083 1.08128 -2.00000 0.00000 0.00000 2.00000 1.08128 0.83083 -1.97964 1.30972 0.56347 -1.91899 1.51150 0.28463 -1.81926 1.68251 0.00000 -1.68251 1.81926 -0.28463 -1.51150 1.91899 -0.56347 -1.30972 1.97964 -0.83083 -1.08128 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16g 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 0.00000 0.00000 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17g 2.00000 -1.51150 0.28463 1.08128 -1.91899 1.81926 -0.83083 -0.56347 1.68251 -1.97964 1.30972 0.00000 -1.30972 1.97964 -1.68251 0.56347 0.83083 -1.81926 1.91899 -1.08128 -0.28463 1.51150 -2.00000 0.00000 0.00000 2.00000 1.51150 -0.28463 -1.08128 1.91899 -1.81926 0.83083 0.56347 -1.68251 1.97964 -1.30972 0.00000 1.30972 -1.97964 1.68251 -0.56347 -0.83083 1.81926 -1.91899 1.08128 0.28463 -1.51150 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18g 2.00000 -1.68251 0.83083 0.28463 -1.30972 1.91899 -1.91899 1.30972 -0.28463 -0.83083 1.68251 -2.00000 1.68251 -0.83083 -0.28463 1.30972 -1.91899 1.91899 -1.30972 0.28463 0.83083 -1.68251 2.00000 0.00000 0.00000 2.00000 -1.68251 0.83083 0.28463 -1.30972 1.91899 -1.91899 1.30972 -0.28463 -0.83083 1.68251 -2.00000 1.68251 -0.83083 -0.28463 1.30972 -1.91899 1.91899 -1.30972 0.28463 0.83083 -1.68251 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19g 2.00000 -1.81926 1.30972 -0.56347 -0.28463 1.08128 -1.68251 1.97964 -1.91899 1.51150 -0.83083 0.00000 0.83083 -1.51150 1.91899 -1.97964 1.68251 -1.08128 0.28463 0.56347 -1.30972 1.81926 -2.00000 0.00000 0.00000 2.00000 1.81926 -1.30972 0.56347 0.28463 -1.08128 1.68251 -1.97964 1.91899 -1.51150 0.83083 0.00000 -0.83083 1.51150 -1.91899 1.97964 -1.68251 1.08128 -0.28463 -0.56347 1.30972 -1.81926 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20g 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 0.00000 0.00000 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21g 2.00000 -1.97964 1.91899 -1.81926 1.68251 -1.51150 1.30972 -1.08128 0.83083 -0.56347 0.28463 0.00000 -0.28463 0.56347 -0.83083 1.08128 -1.30972 1.51150 -1.68251 1.81926 -1.91899 1.97964 -2.00000 0.00000 0.00000 2.00000 1.97964 -1.91899 1.81926 -1.68251 1.51150 -1.30972 1.08128 -0.83083 0.56347 -0.28463 0.00000 0.28463 -0.56347 0.83083 -1.08128 1.30972 -1.51150 1.68251 -1.81926 1.91899 -1.97964 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. A1u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. A2u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 1.00000 1.00000 ... ..T ..... ......T ......... ..........T ............. B1u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. B2u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E1u 2.00000 1.97964 1.91899 1.81926 1.68251 1.51150 1.30972 1.08128 0.83083 0.56347 0.28463 0.00000 -0.28463 -0.56347 -0.83083 -1.08128 -1.30972 -1.51150 -1.68251 -1.81926 -1.91899 -1.97964 -2.00000 0.00000 0.00000 -2.00000 1.97964 1.91899 1.81926 1.68251 1.51150 1.30972 1.08128 0.83083 0.56347 0.28463 0.00000 -0.28463 -0.56347 -0.83083 -1.08128 -1.30972 -1.51150 -1.68251 -1.81926 -1.91899 -1.97964 2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.91899 1.68251 1.30972 0.83083 0.28463 -0.28463 -0.83083 -1.30972 -1.68251 -1.91899 -2.00000 -1.91899 -1.68251 -1.30972 -0.83083 -0.28463 0.28463 0.83083 1.30972 1.68251 1.91899 2.00000 0.00000 0.00000 -2.00000 -1.91899 -1.68251 -1.30972 -0.83083 -0.28463 0.28463 0.83083 1.30972 1.68251 1.91899 2.00000 1.91899 1.68251 1.30972 0.83083 0.28463 -0.28463 -0.83083 -1.30972 -1.68251 -1.91899 -2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u 2.00000 1.81926 1.30972 0.56347 -0.28463 -1.08128 -1.68251 -1.97964 -1.91899 -1.51150 -0.83083 0.00000 0.83083 1.51150 1.91899 1.97964 1.68251 1.08128 0.28463 -0.56347 -1.30972 -1.81926 -2.00000 0.00000 0.00000 -2.00000 1.81926 1.30972 0.56347 -0.28463 -1.08128 -1.68251 -1.97964 -1.91899 -1.51150 -0.83083 0.00000 0.83083 1.51150 1.91899 1.97964 1.68251 1.08128 0.28463 -0.56347 -1.30972 -1.81926 2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 0.00000 0.00000 -2.00000 -1.68251 -0.83083 0.28463 1.30972 1.91899 1.91899 1.30972 0.28463 -0.83083 -1.68251 -2.00000 -1.68251 -0.83083 0.28463 1.30972 1.91899 1.91899 1.30972 0.28463 -0.83083 -1.68251 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5u 2.00000 1.51150 0.28463 -1.08128 -1.91899 -1.81926 -0.83083 0.56347 1.68251 1.97964 1.30972 0.00000 -1.30972 -1.97964 -1.68251 -0.56347 0.83083 1.81926 1.91899 1.08128 -0.28463 -1.51150 -2.00000 0.00000 0.00000 -2.00000 1.51150 0.28463 -1.08128 -1.91899 -1.81926 -0.83083 0.56347 1.68251 1.97964 1.30972 0.00000 -1.30972 -1.97964 -1.68251 -0.56347 0.83083 1.81926 1.91899 1.08128 -0.28463 -1.51150 2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6u 2.00000 1.30972 -0.28463 -1.68251 -1.91899 -0.83083 0.83083 1.91899 1.68251 0.28463 -1.30972 -2.00000 -1.30972 0.28463 1.68251 1.91899 0.83083 -0.83083 -1.91899 -1.68251 -0.28463 1.30972 2.00000 0.00000 0.00000 -2.00000 -1.30972 0.28463 1.68251 1.91899 0.83083 -0.83083 -1.91899 -1.68251 -0.28463 1.30972 2.00000 1.30972 -0.28463 -1.68251 -1.91899 -0.83083 0.83083 1.91899 1.68251 0.28463 -1.30972 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E7u 2.00000 1.08128 -0.83083 -1.97964 -1.30972 0.56347 1.91899 1.51150 -0.28463 -1.81926 -1.68251 0.00000 1.68251 1.81926 0.28463 -1.51150 -1.91899 -0.56347 1.30972 1.97964 0.83083 -1.08128 -2.00000 0.00000 0.00000 -2.00000 1.08128 -0.83083 -1.97964 -1.30972 0.56347 1.91899 1.51150 -0.28463 -1.81926 -1.68251 0.00000 1.68251 1.81926 0.28463 -1.51150 -1.91899 -0.56347 1.30972 1.97964 0.83083 -1.08128 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8u 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.00000 0.00000 -2.00000 -0.83083 1.30972 1.91899 0.28463 -1.68251 -1.68251 0.28463 1.91899 1.30972 -0.83083 -2.00000 -0.83083 1.30972 1.91899 0.28463 -1.68251 -1.68251 0.28463 1.91899 1.30972 -0.83083 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9u 2.00000 0.56347 -1.68251 -1.51150 0.83083 1.97964 0.28463 -1.81926 -1.30972 1.08128 1.91899 0.00000 -1.91899 -1.08128 1.30972 1.81926 -0.28463 -1.97964 -0.83083 1.51150 1.68251 -0.56347 -2.00000 0.00000 0.00000 -2.00000 0.56347 -1.68251 -1.51150 0.83083 1.97964 0.28463 -1.81926 -1.30972 1.08128 1.91899 0.00000 -1.91899 -1.08128 1.30972 1.81926 -0.28463 -1.97964 -0.83083 1.51150 1.68251 -0.56347 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10u 2.00000 0.28463 -1.91899 -0.83083 1.68251 1.30972 -1.30972 -1.68251 0.83083 1.91899 -0.28463 -2.00000 -0.28463 1.91899 0.83083 -1.68251 -1.30972 1.30972 1.68251 -0.83083 -1.91899 0.28463 2.00000 0.00000 0.00000 -2.00000 -0.28463 1.91899 0.83083 -1.68251 -1.30972 1.30972 1.68251 -0.83083 -1.91899 0.28463 2.00000 0.28463 -1.91899 -0.83083 1.68251 1.30972 -1.30972 -1.68251 0.83083 1.91899 -0.28463 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11u 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 0.00000 -2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12u 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 0.00000 0.00000 -2.00000 0.28463 1.91899 -0.83083 -1.68251 1.30972 1.30972 -1.68251 -0.83083 1.91899 0.28463 -2.00000 0.28463 1.91899 -0.83083 -1.68251 1.30972 1.30972 -1.68251 -0.83083 1.91899 0.28463 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13u 2.00000 -0.56347 -1.68251 1.51150 0.83083 -1.97964 0.28463 1.81926 -1.30972 -1.08128 1.91899 0.00000 -1.91899 1.08128 1.30972 -1.81926 -0.28463 1.97964 -0.83083 -1.51150 1.68251 0.56347 -2.00000 0.00000 0.00000 -2.00000 -0.56347 -1.68251 1.51150 0.83083 -1.97964 0.28463 1.81926 -1.30972 -1.08128 1.91899 0.00000 -1.91899 1.08128 1.30972 -1.81926 -0.28463 1.97964 -0.83083 -1.51150 1.68251 0.56347 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14u 2.00000 -0.83083 -1.30972 1.91899 -0.28463 -1.68251 1.68251 0.28463 -1.91899 1.30972 0.83083 -2.00000 0.83083 1.30972 -1.91899 0.28463 1.68251 -1.68251 -0.28463 1.91899 -1.30972 -0.83083 2.00000 0.00000 0.00000 -2.00000 0.83083 1.30972 -1.91899 0.28463 1.68251 -1.68251 -0.28463 1.91899 -1.30972 -0.83083 2.00000 -0.83083 -1.30972 1.91899 -0.28463 -1.68251 1.68251 0.28463 -1.91899 1.30972 0.83083 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15u 2.00000 -1.08128 -0.83083 1.97964 -1.30972 -0.56347 1.91899 -1.51150 -0.28463 1.81926 -1.68251 0.00000 1.68251 -1.81926 0.28463 1.51150 -1.91899 0.56347 1.30972 -1.97964 0.83083 1.08128 -2.00000 0.00000 0.00000 -2.00000 -1.08128 -0.83083 1.97964 -1.30972 -0.56347 1.91899 -1.51150 -0.28463 1.81926 -1.68251 0.00000 1.68251 -1.81926 0.28463 1.51150 -1.91899 0.56347 1.30972 -1.97964 0.83083 1.08128 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16u 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 0.00000 0.00000 -2.00000 1.30972 0.28463 -1.68251 1.91899 -0.83083 -0.83083 1.91899 -1.68251 0.28463 1.30972 -2.00000 1.30972 0.28463 -1.68251 1.91899 -0.83083 -0.83083 1.91899 -1.68251 0.28463 1.30972 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17u 2.00000 -1.51150 0.28463 1.08128 -1.91899 1.81926 -0.83083 -0.56347 1.68251 -1.97964 1.30972 0.00000 -1.30972 1.97964 -1.68251 0.56347 0.83083 -1.81926 1.91899 -1.08128 -0.28463 1.51150 -2.00000 0.00000 0.00000 -2.00000 -1.51150 0.28463 1.08128 -1.91899 1.81926 -0.83083 -0.56347 1.68251 -1.97964 1.30972 0.00000 -1.30972 1.97964 -1.68251 0.56347 0.83083 -1.81926 1.91899 -1.08128 -0.28463 1.51150 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18u 2.00000 -1.68251 0.83083 0.28463 -1.30972 1.91899 -1.91899 1.30972 -0.28463 -0.83083 1.68251 -2.00000 1.68251 -0.83083 -0.28463 1.30972 -1.91899 1.91899 -1.30972 0.28463 0.83083 -1.68251 2.00000 0.00000 0.00000 -2.00000 1.68251 -0.83083 -0.28463 1.30972 -1.91899 1.91899 -1.30972 0.28463 0.83083 -1.68251 2.00000 -1.68251 0.83083 0.28463 -1.30972 1.91899 -1.91899 1.30972 -0.28463 -0.83083 1.68251 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19u 2.00000 -1.81926 1.30972 -0.56347 -0.28463 1.08128 -1.68251 1.97964 -1.91899 1.51150 -0.83083 0.00000 0.83083 -1.51150 1.91899 -1.97964 1.68251 -1.08128 0.28463 0.56347 -1.30972 1.81926 -2.00000 0.00000 0.00000 -2.00000 -1.81926 1.30972 -0.56347 -0.28463 1.08128 -1.68251 1.97964 -1.91899 1.51150 -0.83083 0.00000 0.83083 -1.51150 1.91899 -1.97964 1.68251 -1.08128 0.28463 0.56347 -1.30972 1.81926 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20u 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 0.00000 0.00000 -2.00000 1.91899 -1.68251 1.30972 -0.83083 0.28463 0.28463 -0.83083 1.30972 -1.68251 1.91899 -2.00000 1.91899 -1.68251 1.30972 -0.83083 0.28463 0.28463 -0.83083 1.30972 -1.68251 1.91899 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21u 2.00000 -1.97964 1.91899 -1.81926 1.68251 -1.51150 1.30972 -1.08128 0.83083 -0.56347 0.28463 0.00000 -0.28463 0.56347 -0.83083 1.08128 -1.30972 1.51150 -1.68251 1.81926 -1.91899 1.97964 -2.00000 0.00000 0.00000 -2.00000 -1.97964 1.91899 -1.81926 1.68251 -1.51150 1.30972 -1.08128 0.83083 -0.56347 0.28463 0.00000 -0.28463 0.56347 -0.83083 1.08128 -1.30972 1.51150 -1.68251 1.81926 -1.91899 1.97964 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.979642883762 = 2*cos(2*π/44) = 2*cos(π/22) 1.918985947229 = 2*cos(4*π/44) = 2*cos(π/11) 1.819263990709 = 2*cos(6*π/44) = 2*cos(3*π/22) 1.682507065662 = 2*cos(8*π/44) = 2*cos(2*π/11) 1.511499148709 = 2*cos(10*π/44) = 2*cos(5*π/22) 1.309721467891 = 2*cos(12*π/44) = 2*cos(3*π/11) 1.081281634911 = 2*cos(14*π/44) = 2*cos(7*π/22) 0.830830026004 = 2*cos(16*π/44) = 2*cos(4*π/11) 0.563465113683 = 2*cos(18*π/44) = 2*cos(9*π/22) 0.284629676547 = 2*cos(20*π/44) = 2*cos(5*π/11) Symmetry of Rotations and Cartesian products A1g d+g+i+k+m z2, z4, z6 A2g R Rz E1g R+d+g+i+k+m {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} E2g d+g+i+k+m {x2−y2, xy}, {z2(x2−y2), xyz2}, {z4(x2−y2), xyz4} E3g g+i+k+m {xz(x2−3y2), yz(3x2−y2)}, {xz3(x2−3y2), yz3(3x2−y2)} E4g g+i+k+m {(x2−y2)2−4x2y2, xy(x2−y2)}, {z2((x2−y2)2−4x2y2), xyz2(x2−y2)} E5g i+k+m {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2−y2)((5−2√5)x2−y2)} E6g i+k+m {x2(x2−3y2)2−y2(3x2−y2)2, xy(x2−3y2)(3x2−y2)} E7g k+m E8g k+m E9g m E10g m A2u p+f+h+j+l z, z3, z5 E1u p+f+h+j+l {x, y}, {xz2, yz2}, {xz4, yz4} E2u f+h+j+l {z(x2−y2), xyz}, {z3(x2−y2), xyz3} E3u f+h+j+l {x(x2−3y2), y(3x2−y2)}, {xz2(x2−3y2), yz2(3x2−y2)} E4u h+j+l {z((x2−y2)2−4x2y2), xyz(x2−y2)} E5u h+j+l {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2−y2)((5−2√5)x2−y2)} E6u j+l E7u j+l E8u l E9u l Notes: α The order of the D44h point group is 176, and the order of the principal axis (C44) is 44. The group has 50 irreducible representations. β The D44h point group is generated by three symmetry elements that are canonically chosen C44, C2′ and i. Other choices include σh instead of i, or any of C2″, σv or σd instead of C2′. Also, some ternary combinations of C2′, C2″, σv and σd act as generators. Lastly, the S44 can be chosen, together with i or σh and any one of C2′, C2″, σv or σd. γ There are two different sets of twofold symmetry axes perpendicular to the principal axis (z axis in standard orientation). By convention, the set denoted as C2′ contains both the x and y axes. δ There are two different sets of symmetry planes containing the principal axis (z axis in standard orientation). By convention, the set denoted as σv contains both the xz and the yz planes. ε The lowest nonvanishing multipole moment in D44h is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. η Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. For this group, however, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.
D42h | ||
D43h | ||
C44 C44v C44h D44 | D44h | D44d S44 |
D45h | ||
D46h |
This Character Table for the D44h point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.