D38h E 2 C38 2 C19 2 C38^3 2 C19^2 2 C38^5 2 C19^3 2 C38^7 2 C19^4 2 C38^9 2 C19^5 2 C38^11 2 C19^6 2 C38^13 2 C19^7 2 C38^15 2 C19^8 2 C38^17 2 C19^9 C2 19 C2' 19 C2" i 2 S38 2 S19 2 S38^3 2 S19^2 2 S38^5 2 S19^3 2 S38^7 2 S19^4 2 S38^9 2 S19^5 2 S38^11 2 S19^6 2 S38^13 2 S19^7 2 S38^15 2 S19^8 2 S38^17 2 S19^9 sh 19 sv 19 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 ... ... ....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 ..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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. E1g 2.00000 1.97272 1.89163 1.75895 1.57828 1.35456 1.09390 0.80339 0.49097 0.16516 -0.16516 -0.49097 -0.80339 -1.09390 -1.35456 -1.57828 -1.75895 -1.89163 -1.97272 -2.00000 0.00000 0.00000 2.00000 -1.97272 -1.89163 -1.75895 -1.57828 -1.35456 -1.09390 -0.80339 -0.49097 -0.16516 0.16516 0.49097 0.80339 1.09390 1.35456 1.57828 1.75895 1.89163 1.97272 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.89163 1.57828 1.09390 0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516 0.49097 1.09390 1.57828 1.89163 2.00000 0.00000 0.00000 2.00000 1.89163 1.57828 1.09390 0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516 0.49097 1.09390 1.57828 1.89163 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 2.00000 1.75895 1.09390 0.16516 -0.80339 -1.57828 -1.97272 -1.89163 -1.35456 -0.49097 0.49097 1.35456 1.89163 1.97272 1.57828 0.80339 -0.16516 -1.09390 -1.75895 -2.00000 0.00000 0.00000 2.00000 -1.75895 -1.09390 -0.16516 0.80339 1.57828 1.97272 1.89163 1.35456 0.49097 -0.49097 -1.35456 -1.89163 -1.97272 -1.57828 -0.80339 0.16516 1.09390 1.75895 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g 2.00000 1.57828 0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516 1.09390 1.89163 1.89163 1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339 0.49097 1.57828 2.00000 0.00000 0.00000 2.00000 1.57828 0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516 1.09390 1.89163 1.89163 1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339 0.49097 1.57828 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.35456 -0.16516 -1.57828 -1.97272 -1.09390 0.49097 1.75895 1.89163 0.80339 -0.80339 -1.89163 -1.75895 -0.49097 1.09390 1.97272 1.57828 0.16516 -1.35456 -2.00000 0.00000 0.00000 2.00000 -1.35456 0.16516 1.57828 1.97272 1.09390 -0.49097 -1.75895 -1.89163 -0.80339 0.80339 1.89163 1.75895 0.49097 -1.09390 -1.97272 -1.57828 -0.16516 1.35456 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 2.00000 1.09390 -0.80339 -1.97272 -1.35456 0.49097 1.89163 1.57828 -0.16516 -1.75895 -1.75895 -0.16516 1.57828 1.89163 0.49097 -1.35456 -1.97272 -0.80339 1.09390 2.00000 0.00000 0.00000 2.00000 1.09390 -0.80339 -1.97272 -1.35456 0.49097 1.89163 1.57828 -0.16516 -1.75895 -1.75895 -0.16516 1.57828 1.89163 0.49097 -1.35456 -1.97272 -0.80339 1.09390 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7g 2.00000 0.80339 -1.35456 -1.89163 -0.16516 1.75895 1.57828 -0.49097 -1.97272 -1.09390 1.09390 1.97272 0.49097 -1.57828 -1.75895 0.16516 1.89163 1.35456 -0.80339 -2.00000 0.00000 0.00000 2.00000 -0.80339 1.35456 1.89163 0.16516 -1.75895 -1.57828 0.49097 1.97272 1.09390 -1.09390 -1.97272 -0.49097 1.57828 1.75895 -0.16516 -1.89163 -1.35456 0.80339 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8g 2.00000 0.49097 -1.75895 -1.35456 1.09390 1.89163 -0.16516 -1.97272 -0.80339 1.57828 1.57828 -0.80339 -1.97272 -0.16516 1.89163 1.09390 -1.35456 -1.75895 0.49097 2.00000 0.00000 0.00000 2.00000 0.49097 -1.75895 -1.35456 1.09390 1.89163 -0.16516 -1.97272 -0.80339 1.57828 1.57828 -0.80339 -1.97272 -0.16516 1.89163 1.09390 -1.35456 -1.75895 0.49097 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9g 2.00000 0.16516 -1.97272 -0.49097 1.89163 0.80339 -1.75895 -1.09390 1.57828 1.35456 -1.35456 -1.57828 1.09390 1.75895 -0.80339 -1.89163 0.49097 1.97272 -0.16516 -2.00000 0.00000 0.00000 2.00000 -0.16516 1.97272 0.49097 -1.89163 -0.80339 1.75895 1.09390 -1.57828 -1.35456 1.35456 1.57828 -1.09390 -1.75895 0.80339 1.89163 -0.49097 -1.97272 0.16516 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10g 2.00000 -0.16516 -1.97272 0.49097 1.89163 -0.80339 -1.75895 1.09390 1.57828 -1.35456 -1.35456 1.57828 1.09390 -1.75895 -0.80339 1.89163 0.49097 -1.97272 -0.16516 2.00000 0.00000 0.00000 2.00000 -0.16516 -1.97272 0.49097 1.89163 -0.80339 -1.75895 1.09390 1.57828 -1.35456 -1.35456 1.57828 1.09390 -1.75895 -0.80339 1.89163 0.49097 -1.97272 -0.16516 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 -0.49097 -1.75895 1.35456 1.09390 -1.89163 -0.16516 1.97272 -0.80339 -1.57828 1.57828 0.80339 -1.97272 0.16516 1.89163 -1.09390 -1.35456 1.75895 0.49097 -2.00000 0.00000 0.00000 2.00000 0.49097 1.75895 -1.35456 -1.09390 1.89163 0.16516 -1.97272 0.80339 1.57828 -1.57828 -0.80339 1.97272 -0.16516 -1.89163 1.09390 1.35456 -1.75895 -0.49097 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12g 2.00000 -0.80339 -1.35456 1.89163 -0.16516 -1.75895 1.57828 0.49097 -1.97272 1.09390 1.09390 -1.97272 0.49097 1.57828 -1.75895 -0.16516 1.89163 -1.35456 -0.80339 2.00000 0.00000 0.00000 2.00000 -0.80339 -1.35456 1.89163 -0.16516 -1.75895 1.57828 0.49097 -1.97272 1.09390 1.09390 -1.97272 0.49097 1.57828 -1.75895 -0.16516 1.89163 -1.35456 -0.80339 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 -1.09390 -0.80339 1.97272 -1.35456 -0.49097 1.89163 -1.57828 -0.16516 1.75895 -1.75895 0.16516 1.57828 -1.89163 0.49097 1.35456 -1.97272 0.80339 1.09390 -2.00000 0.00000 0.00000 2.00000 1.09390 0.80339 -1.97272 1.35456 0.49097 -1.89163 1.57828 0.16516 -1.75895 1.75895 -0.16516 -1.57828 1.89163 -0.49097 -1.35456 1.97272 -0.80339 -1.09390 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 -1.35456 -0.16516 1.57828 -1.97272 1.09390 0.49097 -1.75895 1.89163 -0.80339 -0.80339 1.89163 -1.75895 0.49097 1.09390 -1.97272 1.57828 -0.16516 -1.35456 2.00000 0.00000 0.00000 2.00000 -1.35456 -0.16516 1.57828 -1.97272 1.09390 0.49097 -1.75895 1.89163 -0.80339 -0.80339 1.89163 -1.75895 0.49097 1.09390 -1.97272 1.57828 -0.16516 -1.35456 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15g 2.00000 -1.57828 0.49097 0.80339 -1.75895 1.97272 -1.35456 0.16516 1.09390 -1.89163 1.89163 -1.09390 -0.16516 1.35456 -1.97272 1.75895 -0.80339 -0.49097 1.57828 -2.00000 0.00000 0.00000 2.00000 1.57828 -0.49097 -0.80339 1.75895 -1.97272 1.35456 -0.16516 -1.09390 1.89163 -1.89163 1.09390 0.16516 -1.35456 1.97272 -1.75895 0.80339 0.49097 -1.57828 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16g 2.00000 -1.75895 1.09390 -0.16516 -0.80339 1.57828 -1.97272 1.89163 -1.35456 0.49097 0.49097 -1.35456 1.89163 -1.97272 1.57828 -0.80339 -0.16516 1.09390 -1.75895 2.00000 0.00000 0.00000 2.00000 -1.75895 1.09390 -0.16516 -0.80339 1.57828 -1.97272 1.89163 -1.35456 0.49097 0.49097 -1.35456 1.89163 -1.97272 1.57828 -0.80339 -0.16516 1.09390 -1.75895 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17g 2.00000 -1.89163 1.57828 -1.09390 0.49097 0.16516 -0.80339 1.35456 -1.75895 1.97272 -1.97272 1.75895 -1.35456 0.80339 -0.16516 -0.49097 1.09390 -1.57828 1.89163 -2.00000 0.00000 0.00000 2.00000 1.89163 -1.57828 1.09390 -0.49097 -0.16516 0.80339 -1.35456 1.75895 -1.97272 1.97272 -1.75895 1.35456 -0.80339 0.16516 0.49097 -1.09390 1.57828 -1.89163 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18g 2.00000 -1.97272 1.89163 -1.75895 1.57828 -1.35456 1.09390 -0.80339 0.49097 -0.16516 -0.16516 0.49097 -0.80339 1.09390 -1.35456 1.57828 -1.75895 1.89163 -1.97272 2.00000 0.00000 0.00000 2.00000 -1.97272 1.89163 -1.75895 1.57828 -1.35456 1.09390 -0.80339 0.49097 -0.16516 -0.16516 0.49097 -0.80339 1.09390 -1.35456 1.57828 -1.75895 1.89163 -1.97272 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 ... ... ..... ....... ......... ........... ............. 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 ... ..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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. E1u 2.00000 1.97272 1.89163 1.75895 1.57828 1.35456 1.09390 0.80339 0.49097 0.16516 -0.16516 -0.49097 -0.80339 -1.09390 -1.35456 -1.57828 -1.75895 -1.89163 -1.97272 -2.00000 0.00000 0.00000 -2.00000 1.97272 1.89163 1.75895 1.57828 1.35456 1.09390 0.80339 0.49097 0.16516 -0.16516 -0.49097 -0.80339 -1.09390 -1.35456 -1.57828 -1.75895 -1.89163 -1.97272 2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.89163 1.57828 1.09390 0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516 0.49097 1.09390 1.57828 1.89163 2.00000 0.00000 0.00000 -2.00000 -1.89163 -1.57828 -1.09390 -0.49097 0.16516 0.80339 1.35456 1.75895 1.97272 1.97272 1.75895 1.35456 0.80339 0.16516 -0.49097 -1.09390 -1.57828 -1.89163 -2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u 2.00000 1.75895 1.09390 0.16516 -0.80339 -1.57828 -1.97272 -1.89163 -1.35456 -0.49097 0.49097 1.35456 1.89163 1.97272 1.57828 0.80339 -0.16516 -1.09390 -1.75895 -2.00000 0.00000 0.00000 -2.00000 1.75895 1.09390 0.16516 -0.80339 -1.57828 -1.97272 -1.89163 -1.35456 -0.49097 0.49097 1.35456 1.89163 1.97272 1.57828 0.80339 -0.16516 -1.09390 -1.75895 2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u 2.00000 1.57828 0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516 1.09390 1.89163 1.89163 1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339 0.49097 1.57828 2.00000 0.00000 0.00000 -2.00000 -1.57828 -0.49097 0.80339 1.75895 1.97272 1.35456 0.16516 -1.09390 -1.89163 -1.89163 -1.09390 0.16516 1.35456 1.97272 1.75895 0.80339 -0.49097 -1.57828 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5u 2.00000 1.35456 -0.16516 -1.57828 -1.97272 -1.09390 0.49097 1.75895 1.89163 0.80339 -0.80339 -1.89163 -1.75895 -0.49097 1.09390 1.97272 1.57828 0.16516 -1.35456 -2.00000 0.00000 0.00000 -2.00000 1.35456 -0.16516 -1.57828 -1.97272 -1.09390 0.49097 1.75895 1.89163 0.80339 -0.80339 -1.89163 -1.75895 -0.49097 1.09390 1.97272 1.57828 0.16516 -1.35456 2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6u 2.00000 1.09390 -0.80339 -1.97272 -1.35456 0.49097 1.89163 1.57828 -0.16516 -1.75895 -1.75895 -0.16516 1.57828 1.89163 0.49097 -1.35456 -1.97272 -0.80339 1.09390 2.00000 0.00000 0.00000 -2.00000 -1.09390 0.80339 1.97272 1.35456 -0.49097 -1.89163 -1.57828 0.16516 1.75895 1.75895 0.16516 -1.57828 -1.89163 -0.49097 1.35456 1.97272 0.80339 -1.09390 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E7u 2.00000 0.80339 -1.35456 -1.89163 -0.16516 1.75895 1.57828 -0.49097 -1.97272 -1.09390 1.09390 1.97272 0.49097 -1.57828 -1.75895 0.16516 1.89163 1.35456 -0.80339 -2.00000 0.00000 0.00000 -2.00000 0.80339 -1.35456 -1.89163 -0.16516 1.75895 1.57828 -0.49097 -1.97272 -1.09390 1.09390 1.97272 0.49097 -1.57828 -1.75895 0.16516 1.89163 1.35456 -0.80339 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8u 2.00000 0.49097 -1.75895 -1.35456 1.09390 1.89163 -0.16516 -1.97272 -0.80339 1.57828 1.57828 -0.80339 -1.97272 -0.16516 1.89163 1.09390 -1.35456 -1.75895 0.49097 2.00000 0.00000 0.00000 -2.00000 -0.49097 1.75895 1.35456 -1.09390 -1.89163 0.16516 1.97272 0.80339 -1.57828 -1.57828 0.80339 1.97272 0.16516 -1.89163 -1.09390 1.35456 1.75895 -0.49097 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9u 2.00000 0.16516 -1.97272 -0.49097 1.89163 0.80339 -1.75895 -1.09390 1.57828 1.35456 -1.35456 -1.57828 1.09390 1.75895 -0.80339 -1.89163 0.49097 1.97272 -0.16516 -2.00000 0.00000 0.00000 -2.00000 0.16516 -1.97272 -0.49097 1.89163 0.80339 -1.75895 -1.09390 1.57828 1.35456 -1.35456 -1.57828 1.09390 1.75895 -0.80339 -1.89163 0.49097 1.97272 -0.16516 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10u 2.00000 -0.16516 -1.97272 0.49097 1.89163 -0.80339 -1.75895 1.09390 1.57828 -1.35456 -1.35456 1.57828 1.09390 -1.75895 -0.80339 1.89163 0.49097 -1.97272 -0.16516 2.00000 0.00000 0.00000 -2.00000 0.16516 1.97272 -0.49097 -1.89163 0.80339 1.75895 -1.09390 -1.57828 1.35456 1.35456 -1.57828 -1.09390 1.75895 0.80339 -1.89163 -0.49097 1.97272 0.16516 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11u 2.00000 -0.49097 -1.75895 1.35456 1.09390 -1.89163 -0.16516 1.97272 -0.80339 -1.57828 1.57828 0.80339 -1.97272 0.16516 1.89163 -1.09390 -1.35456 1.75895 0.49097 -2.00000 0.00000 0.00000 -2.00000 -0.49097 -1.75895 1.35456 1.09390 -1.89163 -0.16516 1.97272 -0.80339 -1.57828 1.57828 0.80339 -1.97272 0.16516 1.89163 -1.09390 -1.35456 1.75895 0.49097 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12u 2.00000 -0.80339 -1.35456 1.89163 -0.16516 -1.75895 1.57828 0.49097 -1.97272 1.09390 1.09390 -1.97272 0.49097 1.57828 -1.75895 -0.16516 1.89163 -1.35456 -0.80339 2.00000 0.00000 0.00000 -2.00000 0.80339 1.35456 -1.89163 0.16516 1.75895 -1.57828 -0.49097 1.97272 -1.09390 -1.09390 1.97272 -0.49097 -1.57828 1.75895 0.16516 -1.89163 1.35456 0.80339 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13u 2.00000 -1.09390 -0.80339 1.97272 -1.35456 -0.49097 1.89163 -1.57828 -0.16516 1.75895 -1.75895 0.16516 1.57828 -1.89163 0.49097 1.35456 -1.97272 0.80339 1.09390 -2.00000 0.00000 0.00000 -2.00000 -1.09390 -0.80339 1.97272 -1.35456 -0.49097 1.89163 -1.57828 -0.16516 1.75895 -1.75895 0.16516 1.57828 -1.89163 0.49097 1.35456 -1.97272 0.80339 1.09390 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14u 2.00000 -1.35456 -0.16516 1.57828 -1.97272 1.09390 0.49097 -1.75895 1.89163 -0.80339 -0.80339 1.89163 -1.75895 0.49097 1.09390 -1.97272 1.57828 -0.16516 -1.35456 2.00000 0.00000 0.00000 -2.00000 1.35456 0.16516 -1.57828 1.97272 -1.09390 -0.49097 1.75895 -1.89163 0.80339 0.80339 -1.89163 1.75895 -0.49097 -1.09390 1.97272 -1.57828 0.16516 1.35456 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15u 2.00000 -1.57828 0.49097 0.80339 -1.75895 1.97272 -1.35456 0.16516 1.09390 -1.89163 1.89163 -1.09390 -0.16516 1.35456 -1.97272 1.75895 -0.80339 -0.49097 1.57828 -2.00000 0.00000 0.00000 -2.00000 -1.57828 0.49097 0.80339 -1.75895 1.97272 -1.35456 0.16516 1.09390 -1.89163 1.89163 -1.09390 -0.16516 1.35456 -1.97272 1.75895 -0.80339 -0.49097 1.57828 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16u 2.00000 -1.75895 1.09390 -0.16516 -0.80339 1.57828 -1.97272 1.89163 -1.35456 0.49097 0.49097 -1.35456 1.89163 -1.97272 1.57828 -0.80339 -0.16516 1.09390 -1.75895 2.00000 0.00000 0.00000 -2.00000 1.75895 -1.09390 0.16516 0.80339 -1.57828 1.97272 -1.89163 1.35456 -0.49097 -0.49097 1.35456 -1.89163 1.97272 -1.57828 0.80339 0.16516 -1.09390 1.75895 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17u 2.00000 -1.89163 1.57828 -1.09390 0.49097 0.16516 -0.80339 1.35456 -1.75895 1.97272 -1.97272 1.75895 -1.35456 0.80339 -0.16516 -0.49097 1.09390 -1.57828 1.89163 -2.00000 0.00000 0.00000 -2.00000 -1.89163 1.57828 -1.09390 0.49097 0.16516 -0.80339 1.35456 -1.75895 1.97272 -1.97272 1.75895 -1.35456 0.80339 -0.16516 -0.49097 1.09390 -1.57828 1.89163 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18u 2.00000 -1.97272 1.89163 -1.75895 1.57828 -1.35456 1.09390 -0.80339 0.49097 -0.16516 -0.16516 0.49097 -0.80339 1.09390 -1.35456 1.57828 -1.75895 1.89163 -1.97272 2.00000 0.00000 0.00000 -2.00000 1.97272 -1.89163 1.75895 -1.57828 1.35456 -1.09390 0.80339 -0.49097 0.16516 0.16516 -0.49097 0.80339 -1.09390 1.35456 -1.57828 1.75895 -1.89163 1.97272 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.972722606805 = 2*cos(2*π/38) = 2*cos(π/19) 1.891634483401 = 2*cos(4*π/38) = 2*cos(2*π/19) 1.758947502413 = 2*cos(6*π/38) = 2*cos(3*π/19) 1.578281018793 = 2*cos(8*π/38) = 2*cos(4*π/19) 1.354563143251 = 2*cos(10*π/38) = 2*cos(5*π/19) 1.093896316245 = 2*cos(12*π/38) = 2*cos(6*π/19) 0.803390849306 = 2*cos(14*π/38) = 2*cos(7*π/19) 0.490970974282 = 2*cos(16*π/38) = 2*cos(8*π/19) 0.165158690945 = 2*cos(18*π/38) = 2*cos(9*π/19) 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 D38h point group is 152, and the order of the principal axis (C38) is 38. The group has 44 irreducible representations. β The D38h point group is generated by three symmetry elements that are canonically chosen C38, 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 S38 can be chosen, together with σh or C2 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′ has the x axis as a member, while the y axis is a member of the C2″ set. 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 has the xz plane as a member, while the yz plane is a member of the σd set. ε The lowest nonvanishing multipole moment in D38h is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. η Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. θ The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. All characters of this group can be expressed using complex numbers, elementary arithmetic operations, square roots and third roots.
D36h | ||
D37h | ||
C38 C38v C38h D38 | D38h | D38d S38 |
D39h | ||
D40h |
This Character Table for the D38h point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.