Character Table for Point Group D66h

Character table for the D_66h point group

D66h E 2 C66 2 C33 2 C22 2 C33^2 2 C66^5 2 C11 2 C66^7 2 C33^4 2 C22^3 2 C33^5 2 C6 2 C11^2 2 C66^13 2 C33^7 2 C22^5 2 C33^8 2 C66^17 2 C11^3 2 C66^19 2 C33^10 2 C22^7 2 C3 2 C66^23 2 C11^4 2 C66^25 2 C33^13 2 C22^9 2 C33^14 2 C66^29 2 C11^5 2 C66^31 2 C33^16 C2 33 C2' 33 C2" i 2 S66 2 S33 2 S22 2 S33^2 2 S66^5 2 S11 2 S66^7 2 S33^4 2 S22^3 2 S33^5 2 S6 2 S11^2 2 S66^13 2 S33^7 2 S22^5 2 S33^8 2 S66^17 2 S11^3 2 S66^19 2 S33^10 2 S22^7 2 S3 2 S66^23 2 S11^4 2 S66^25 2 S33^13 2 S22^9 2 S33^14 2 S66^29 2 S11^5 2 S66^31 2 S33^16 sh 33 sv 33 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ... ....T ....... ........T ........... ............T A2g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. B1g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. B2g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E1g 2.00000 1.99094 1.96386 1.91899 1.85674 1.77767 1.68251 1.57211 1.44747 1.30972 1.16011 1.00000 0.83083 0.65414 0.47152 0.28463 0.09516 -0.09516 -0.28463 -0.47152 -0.65414 -0.83083 -1.00000 -1.16011 -1.30972 -1.44747 -1.57211 -1.68251 -1.77767 -1.85674 -1.91899 -1.96386 -1.99094 -2.00000 0.00000 0.00000 2.00000 -1.99094 -1.96386 -1.91899 -1.85674 -1.77767 -1.68251 -1.57211 -1.44747 -1.30972 -1.16011 -1.00000 -0.83083 -0.65414 -0.47152 -0.28463 -0.09516 0.09516 0.28463 0.47152 0.65414 0.83083 1.00000 1.16011 1.30972 1.44747 1.57211 1.68251 1.77767 1.85674 1.91899 1.96386 1.99094 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.96386 1.85674 1.68251 1.44747 1.16011 0.83083 0.47152 0.09516 -0.28463 -0.65414 -1.00000 -1.30972 -1.57211 -1.77767 -1.91899 -1.99094 -1.99094 -1.91899 -1.77767 -1.57211 -1.30972 -1.00000 -0.65414 -0.28463 0.09516 0.47152 0.83083 1.16011 1.44747 1.68251 1.85674 1.96386 2.00000 0.00000 0.00000 2.00000 1.96386 1.85674 1.68251 1.44747 1.16011 0.83083 0.47152 0.09516 -0.28463 -0.65414 -1.00000 -1.30972 -1.57211 -1.77767 -1.91899 -1.99094 -1.99094 -1.91899 -1.77767 -1.57211 -1.30972 -1.00000 -0.65414 -0.28463 0.09516 0.47152 0.83083 1.16011 1.44747 1.68251 1.85674 1.96386 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 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 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 -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..... E4g 2.00000 1.85674 1.44747 0.83083 0.09516 -0.65414 -1.30972 -1.77767 -1.99094 -1.91899 -1.57211 -1.00000 -0.28463 0.47152 1.16011 1.68251 1.96386 1.96386 1.68251 1.16011 0.47152 -0.28463 -1.00000 -1.57211 -1.91899 -1.99094 -1.77767 -1.30972 -0.65414 0.09516 0.83083 1.44747 1.85674 2.00000 0.00000 0.00000 2.00000 1.85674 1.44747 0.83083 0.09516 -0.65414 -1.30972 -1.77767 -1.99094 -1.91899 -1.57211 -1.00000 -0.28463 0.47152 1.16011 1.68251 1.96386 1.96386 1.68251 1.16011 0.47152 -0.28463 -1.00000 -1.57211 -1.91899 -1.99094 -1.77767 -1.30972 -0.65414 0.09516 0.83083 1.44747 1.85674 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.77767 1.16011 0.28463 -0.65414 -1.44747 -1.91899 -1.96386 -1.57211 -0.83083 0.09516 1.00000 1.68251 1.99094 1.85674 1.30972 0.47152 -0.47152 -1.30972 -1.85674 -1.99094 -1.68251 -1.00000 -0.09516 0.83083 1.57211 1.96386 1.91899 1.44747 0.65414 -0.28463 -1.16011 -1.77767 -2.00000 0.00000 0.00000 2.00000 -1.77767 -1.16011 -0.28463 0.65414 1.44747 1.91899 1.96386 1.57211 0.83083 -0.09516 -1.00000 -1.68251 -1.99094 -1.85674 -1.30972 -0.47152 0.47152 1.30972 1.85674 1.99094 1.68251 1.00000 0.09516 -0.83083 -1.57211 -1.96386 -1.91899 -1.44747 -0.65414 0.28463 1.16011 1.77767 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 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 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 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........... E7g 2.00000 1.57211 0.47152 -0.83083 -1.77767 -1.96386 -1.30972 -0.09516 1.16011 1.91899 1.85674 1.00000 -0.28463 -1.44747 -1.99094 -1.68251 -0.65414 0.65414 1.68251 1.99094 1.44747 0.28463 -1.00000 -1.85674 -1.91899 -1.16011 0.09516 1.30972 1.96386 1.77767 0.83083 -0.47152 -1.57211 -2.00000 0.00000 0.00000 2.00000 -1.57211 -0.47152 0.83083 1.77767 1.96386 1.30972 0.09516 -1.16011 -1.91899 -1.85674 -1.00000 0.28463 1.44747 1.99094 1.68251 0.65414 -0.65414 -1.68251 -1.99094 -1.44747 -0.28463 1.00000 1.85674 1.91899 1.16011 -0.09516 -1.30972 -1.96386 -1.77767 -0.83083 0.47152 1.57211 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8g 2.00000 1.44747 0.09516 -1.30972 -1.99094 -1.57211 -0.28463 1.16011 1.96386 1.68251 0.47152 -1.00000 -1.91899 -1.77767 -0.65414 0.83083 1.85674 1.85674 0.83083 -0.65414 -1.77767 -1.91899 -1.00000 0.47152 1.68251 1.96386 1.16011 -0.28463 -1.57211 -1.99094 -1.30972 0.09516 1.44747 2.00000 0.00000 0.00000 2.00000 1.44747 0.09516 -1.30972 -1.99094 -1.57211 -0.28463 1.16011 1.96386 1.68251 0.47152 -1.00000 -1.91899 -1.77767 -0.65414 0.83083 1.85674 1.85674 0.83083 -0.65414 -1.77767 -1.91899 -1.00000 0.47152 1.68251 1.96386 1.16011 -0.28463 -1.57211 -1.99094 -1.30972 0.09516 1.44747 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9g 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 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 -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 ... ... ..... ....... ......... ........... ............. E10g 2.00000 1.16011 -0.65414 -1.91899 -1.57211 0.09516 1.68251 1.85674 0.47152 -1.30972 -1.99094 -1.00000 0.83083 1.96386 1.44747 -0.28463 -1.77767 -1.77767 -0.28463 1.44747 1.96386 0.83083 -1.00000 -1.99094 -1.30972 0.47152 1.85674 1.68251 0.09516 -1.57211 -1.91899 -0.65414 1.16011 2.00000 0.00000 0.00000 2.00000 1.16011 -0.65414 -1.91899 -1.57211 0.09516 1.68251 1.85674 0.47152 -1.30972 -1.99094 -1.00000 0.83083 1.96386 1.44747 -0.28463 -1.77767 -1.77767 -0.28463 1.44747 1.96386 0.83083 -1.00000 -1.99094 -1.30972 0.47152 1.85674 1.68251 0.09516 -1.57211 -1.91899 -0.65414 1.16011 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 0.00000 0.00000 2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12g 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 0.83083 -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 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 0.65414 -1.57211 -1.68251 0.47152 1.99094 0.83083 -1.44747 -1.77767 0.28463 1.96386 1.00000 -1.30972 -1.85674 0.09516 1.91899 1.16011 -1.16011 -1.91899 -0.09516 1.85674 1.30972 -1.00000 -1.96386 -0.28463 1.77767 1.44747 -0.83083 -1.99094 -0.47152 1.68251 1.57211 -0.65414 -2.00000 0.00000 0.00000 2.00000 -0.65414 1.57211 1.68251 -0.47152 -1.99094 -0.83083 1.44747 1.77767 -0.28463 -1.96386 -1.00000 1.30972 1.85674 -0.09516 -1.91899 -1.16011 1.16011 1.91899 0.09516 -1.85674 -1.30972 1.00000 1.96386 0.28463 -1.77767 -1.44747 0.83083 1.99094 0.47152 -1.68251 -1.57211 0.65414 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 0.47152 -1.77767 -1.30972 1.16011 1.85674 -0.28463 -1.99094 -0.65414 1.68251 1.44747 -1.00000 -1.91899 0.09516 1.96386 0.83083 -1.57211 -1.57211 0.83083 1.96386 0.09516 -1.91899 -1.00000 1.44747 1.68251 -0.65414 -1.99094 -0.28463 1.85674 1.16011 -1.30972 -1.77767 0.47152 2.00000 0.00000 0.00000 2.00000 0.47152 -1.77767 -1.30972 1.16011 1.85674 -0.28463 -1.99094 -0.65414 1.68251 1.44747 -1.00000 -1.91899 0.09516 1.96386 0.83083 -1.57211 -1.57211 0.83083 1.96386 0.09516 -1.91899 -1.00000 1.44747 1.68251 -0.65414 -1.99094 -0.28463 1.85674 1.16011 -1.30972 -1.77767 0.47152 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15g 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 0.28463 -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 -0.28463 1.91899 0.83083 -1.68251 -1.30972 1.30972 1.68251 -0.83083 -1.91899 0.28463 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16g 2.00000 0.09516 -1.99094 -0.28463 1.96386 0.47152 -1.91899 -0.65414 1.85674 0.83083 -1.77767 -1.00000 1.68251 1.16011 -1.57211 -1.30972 1.44747 1.44747 -1.30972 -1.57211 1.16011 1.68251 -1.00000 -1.77767 0.83083 1.85674 -0.65414 -1.91899 0.47152 1.96386 -0.28463 -1.99094 0.09516 2.00000 0.00000 0.00000 2.00000 0.09516 -1.99094 -0.28463 1.96386 0.47152 -1.91899 -0.65414 1.85674 0.83083 -1.77767 -1.00000 1.68251 1.16011 -1.57211 -1.30972 1.44747 1.44747 -1.30972 -1.57211 1.16011 1.68251 -1.00000 -1.77767 0.83083 1.85674 -0.65414 -1.91899 0.47152 1.96386 -0.28463 -1.99094 0.09516 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17g 2.00000 -0.09516 -1.99094 0.28463 1.96386 -0.47152 -1.91899 0.65414 1.85674 -0.83083 -1.77767 1.00000 1.68251 -1.16011 -1.57211 1.30972 1.44747 -1.44747 -1.30972 1.57211 1.16011 -1.68251 -1.00000 1.77767 0.83083 -1.85674 -0.65414 1.91899 0.47152 -1.96386 -0.28463 1.99094 0.09516 -2.00000 0.00000 0.00000 2.00000 0.09516 1.99094 -0.28463 -1.96386 0.47152 1.91899 -0.65414 -1.85674 0.83083 1.77767 -1.00000 -1.68251 1.16011 1.57211 -1.30972 -1.44747 1.44747 1.30972 -1.57211 -1.16011 1.68251 1.00000 -1.77767 -0.83083 1.85674 0.65414 -1.91899 -0.47152 1.96386 0.28463 -1.99094 -0.09516 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18g 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 -0.28463 -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 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19g 2.00000 -0.47152 -1.77767 1.30972 1.16011 -1.85674 -0.28463 1.99094 -0.65414 -1.68251 1.44747 1.00000 -1.91899 -0.09516 1.96386 -0.83083 -1.57211 1.57211 0.83083 -1.96386 0.09516 1.91899 -1.00000 -1.44747 1.68251 0.65414 -1.99094 0.28463 1.85674 -1.16011 -1.30972 1.77767 0.47152 -2.00000 0.00000 0.00000 2.00000 0.47152 1.77767 -1.30972 -1.16011 1.85674 0.28463 -1.99094 0.65414 1.68251 -1.44747 -1.00000 1.91899 0.09516 -1.96386 0.83083 1.57211 -1.57211 -0.83083 1.96386 -0.09516 -1.91899 1.00000 1.44747 -1.68251 -0.65414 1.99094 -0.28463 -1.85674 1.16011 1.30972 -1.77767 -0.47152 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20g 2.00000 -0.65414 -1.57211 1.68251 0.47152 -1.99094 0.83083 1.44747 -1.77767 -0.28463 1.96386 -1.00000 -1.30972 1.85674 0.09516 -1.91899 1.16011 1.16011 -1.91899 0.09516 1.85674 -1.30972 -1.00000 1.96386 -0.28463 -1.77767 1.44747 0.83083 -1.99094 0.47152 1.68251 -1.57211 -0.65414 2.00000 0.00000 0.00000 2.00000 -0.65414 -1.57211 1.68251 0.47152 -1.99094 0.83083 1.44747 -1.77767 -0.28463 1.96386 -1.00000 -1.30972 1.85674 0.09516 -1.91899 1.16011 1.16011 -1.91899 0.09516 1.85674 -1.30972 -1.00000 1.96386 -0.28463 -1.77767 1.44747 0.83083 -1.99094 0.47152 1.68251 -1.57211 -0.65414 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21g 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 -0.83083 -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 0.83083 1.30972 -1.91899 0.28463 1.68251 -1.68251 -0.28463 1.91899 -1.30972 -0.83083 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E22g 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E23g 2.00000 -1.16011 -0.65414 1.91899 -1.57211 -0.09516 1.68251 -1.85674 0.47152 1.30972 -1.99094 1.00000 0.83083 -1.96386 1.44747 0.28463 -1.77767 1.77767 -0.28463 -1.44747 1.96386 -0.83083 -1.00000 1.99094 -1.30972 -0.47152 1.85674 -1.68251 0.09516 1.57211 -1.91899 0.65414 1.16011 -2.00000 0.00000 0.00000 2.00000 1.16011 0.65414 -1.91899 1.57211 0.09516 -1.68251 1.85674 -0.47152 -1.30972 1.99094 -1.00000 -0.83083 1.96386 -1.44747 -0.28463 1.77767 -1.77767 0.28463 1.44747 -1.96386 0.83083 1.00000 -1.99094 1.30972 0.47152 -1.85674 1.68251 -0.09516 -1.57211 1.91899 -0.65414 -1.16011 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E24g 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 -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 -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 ... ... ..... ....... ......... ........... ............. E25g 2.00000 -1.44747 0.09516 1.30972 -1.99094 1.57211 -0.28463 -1.16011 1.96386 -1.68251 0.47152 1.00000 -1.91899 1.77767 -0.65414 -0.83083 1.85674 -1.85674 0.83083 0.65414 -1.77767 1.91899 -1.00000 -0.47152 1.68251 -1.96386 1.16011 0.28463 -1.57211 1.99094 -1.30972 -0.09516 1.44747 -2.00000 0.00000 0.00000 2.00000 1.44747 -0.09516 -1.30972 1.99094 -1.57211 0.28463 1.16011 -1.96386 1.68251 -0.47152 -1.00000 1.91899 -1.77767 0.65414 0.83083 -1.85674 1.85674 -0.83083 -0.65414 1.77767 -1.91899 1.00000 0.47152 -1.68251 1.96386 -1.16011 -0.28463 1.57211 -1.99094 1.30972 0.09516 -1.44747 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E26g 2.00000 -1.57211 0.47152 0.83083 -1.77767 1.96386 -1.30972 0.09516 1.16011 -1.91899 1.85674 -1.00000 -0.28463 1.44747 -1.99094 1.68251 -0.65414 -0.65414 1.68251 -1.99094 1.44747 -0.28463 -1.00000 1.85674 -1.91899 1.16011 0.09516 -1.30972 1.96386 -1.77767 0.83083 0.47152 -1.57211 2.00000 0.00000 0.00000 2.00000 -1.57211 0.47152 0.83083 -1.77767 1.96386 -1.30972 0.09516 1.16011 -1.91899 1.85674 -1.00000 -0.28463 1.44747 -1.99094 1.68251 -0.65414 -0.65414 1.68251 -1.99094 1.44747 -0.28463 -1.00000 1.85674 -1.91899 1.16011 0.09516 -1.30972 1.96386 -1.77767 0.83083 0.47152 -1.57211 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E27g 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 -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 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 ... ... ..... ....... ......... ........... ............. E28g 2.00000 -1.77767 1.16011 -0.28463 -0.65414 1.44747 -1.91899 1.96386 -1.57211 0.83083 0.09516 -1.00000 1.68251 -1.99094 1.85674 -1.30972 0.47152 0.47152 -1.30972 1.85674 -1.99094 1.68251 -1.00000 0.09516 0.83083 -1.57211 1.96386 -1.91899 1.44747 -0.65414 -0.28463 1.16011 -1.77767 2.00000 0.00000 0.00000 2.00000 -1.77767 1.16011 -0.28463 -0.65414 1.44747 -1.91899 1.96386 -1.57211 0.83083 0.09516 -1.00000 1.68251 -1.99094 1.85674 -1.30972 0.47152 0.47152 -1.30972 1.85674 -1.99094 1.68251 -1.00000 0.09516 0.83083 -1.57211 1.96386 -1.91899 1.44747 -0.65414 -0.28463 1.16011 -1.77767 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E29g 2.00000 -1.85674 1.44747 -0.83083 0.09516 0.65414 -1.30972 1.77767 -1.99094 1.91899 -1.57211 1.00000 -0.28463 -0.47152 1.16011 -1.68251 1.96386 -1.96386 1.68251 -1.16011 0.47152 0.28463 -1.00000 1.57211 -1.91899 1.99094 -1.77767 1.30972 -0.65414 -0.09516 0.83083 -1.44747 1.85674 -2.00000 0.00000 0.00000 2.00000 1.85674 -1.44747 0.83083 -0.09516 -0.65414 1.30972 -1.77767 1.99094 -1.91899 1.57211 -1.00000 0.28463 0.47152 -1.16011 1.68251 -1.96386 1.96386 -1.68251 1.16011 -0.47152 -0.28463 1.00000 -1.57211 1.91899 -1.99094 1.77767 -1.30972 0.65414 0.09516 -0.83083 1.44747 -1.85674 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E30g 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 -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 -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 ... ... ..... ....... ......... ........... ............. E31g 2.00000 -1.96386 1.85674 -1.68251 1.44747 -1.16011 0.83083 -0.47152 0.09516 0.28463 -0.65414 1.00000 -1.30972 1.57211 -1.77767 1.91899 -1.99094 1.99094 -1.91899 1.77767 -1.57211 1.30972 -1.00000 0.65414 -0.28463 -0.09516 0.47152 -0.83083 1.16011 -1.44747 1.68251 -1.85674 1.96386 -2.00000 0.00000 0.00000 2.00000 1.96386 -1.85674 1.68251 -1.44747 1.16011 -0.83083 0.47152 -0.09516 -0.28463 0.65414 -1.00000 1.30972 -1.57211 1.77767 -1.91899 1.99094 -1.99094 1.91899 -1.77767 1.57211 -1.30972 1.00000 -0.65414 0.28463 0.09516 -0.47152 0.83083 -1.16011 1.44747 -1.68251 1.85674 -1.96386 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E32g 2.00000 -1.99094 1.96386 -1.91899 1.85674 -1.77767 1.68251 -1.57211 1.44747 -1.30972 1.16011 -1.00000 0.83083 -0.65414 0.47152 -0.28463 0.09516 0.09516 -0.28463 0.47152 -0.65414 0.83083 -1.00000 1.16011 -1.30972 1.44747 -1.57211 1.68251 -1.77767 1.85674 -1.91899 1.96386 -1.99094 2.00000 0.00000 0.00000 2.00000 -1.99094 1.96386 -1.91899 1.85674 -1.77767 1.68251 -1.57211 1.44747 -1.30972 1.16011 -1.00000 0.83083 -0.65414 0.47152 -0.28463 0.09516 0.09516 -0.28463 0.47152 -0.65414 0.83083 -1.00000 1.16011 -1.30972 1.44747 -1.57211 1.68251 -1.77767 1.85674 -1.91899 1.96386 -1.99094 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. A1u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. A2u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 1.00000 1.00000 ... ..T ..... ......T ......... ..........T ............. B1u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. B2u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E1u 2.00000 1.99094 1.96386 1.91899 1.85674 1.77767 1.68251 1.57211 1.44747 1.30972 1.16011 1.00000 0.83083 0.65414 0.47152 0.28463 0.09516 -0.09516 -0.28463 -0.47152 -0.65414 -0.83083 -1.00000 -1.16011 -1.30972 -1.44747 -1.57211 -1.68251 -1.77767 -1.85674 -1.91899 -1.96386 -1.99094 -2.00000 0.00000 0.00000 -2.00000 1.99094 1.96386 1.91899 1.85674 1.77767 1.68251 1.57211 1.44747 1.30972 1.16011 1.00000 0.83083 0.65414 0.47152 0.28463 0.09516 -0.09516 -0.28463 -0.47152 -0.65414 -0.83083 -1.00000 -1.16011 -1.30972 -1.44747 -1.57211 -1.68251 -1.77767 -1.85674 -1.91899 -1.96386 -1.99094 2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.96386 1.85674 1.68251 1.44747 1.16011 0.83083 0.47152 0.09516 -0.28463 -0.65414 -1.00000 -1.30972 -1.57211 -1.77767 -1.91899 -1.99094 -1.99094 -1.91899 -1.77767 -1.57211 -1.30972 -1.00000 -0.65414 -0.28463 0.09516 0.47152 0.83083 1.16011 1.44747 1.68251 1.85674 1.96386 2.00000 0.00000 0.00000 -2.00000 -1.96386 -1.85674 -1.68251 -1.44747 -1.16011 -0.83083 -0.47152 -0.09516 0.28463 0.65414 1.00000 1.30972 1.57211 1.77767 1.91899 1.99094 1.99094 1.91899 1.77767 1.57211 1.30972 1.00000 0.65414 0.28463 -0.09516 -0.47152 -0.83083 -1.16011 -1.44747 -1.68251 -1.85674 -1.96386 -2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u 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 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 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..... ............. E4u 2.00000 1.85674 1.44747 0.83083 0.09516 -0.65414 -1.30972 -1.77767 -1.99094 -1.91899 -1.57211 -1.00000 -0.28463 0.47152 1.16011 1.68251 1.96386 1.96386 1.68251 1.16011 0.47152 -0.28463 -1.00000 -1.57211 -1.91899 -1.99094 -1.77767 -1.30972 -0.65414 0.09516 0.83083 1.44747 1.85674 2.00000 0.00000 0.00000 -2.00000 -1.85674 -1.44747 -0.83083 -0.09516 0.65414 1.30972 1.77767 1.99094 1.91899 1.57211 1.00000 0.28463 -0.47152 -1.16011 -1.68251 -1.96386 -1.96386 -1.68251 -1.16011 -0.47152 0.28463 1.00000 1.57211 1.91899 1.99094 1.77767 1.30972 0.65414 -0.09516 -0.83083 -1.44747 -1.85674 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5u 2.00000 1.77767 1.16011 0.28463 -0.65414 -1.44747 -1.91899 -1.96386 -1.57211 -0.83083 0.09516 1.00000 1.68251 1.99094 1.85674 1.30972 0.47152 -0.47152 -1.30972 -1.85674 -1.99094 -1.68251 -1.00000 -0.09516 0.83083 1.57211 1.96386 1.91899 1.44747 0.65414 -0.28463 -1.16011 -1.77767 -2.00000 0.00000 0.00000 -2.00000 1.77767 1.16011 0.28463 -0.65414 -1.44747 -1.91899 -1.96386 -1.57211 -0.83083 0.09516 1.00000 1.68251 1.99094 1.85674 1.30972 0.47152 -0.47152 -1.30972 -1.85674 -1.99094 -1.68251 -1.00000 -0.09516 0.83083 1.57211 1.96386 1.91899 1.44747 0.65414 -0.28463 -1.16011 -1.77767 2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6u 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 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 -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 ... ... ..... ....... ......... ........... ............. E7u 2.00000 1.57211 0.47152 -0.83083 -1.77767 -1.96386 -1.30972 -0.09516 1.16011 1.91899 1.85674 1.00000 -0.28463 -1.44747 -1.99094 -1.68251 -0.65414 0.65414 1.68251 1.99094 1.44747 0.28463 -1.00000 -1.85674 -1.91899 -1.16011 0.09516 1.30972 1.96386 1.77767 0.83083 -0.47152 -1.57211 -2.00000 0.00000 0.00000 -2.00000 1.57211 0.47152 -0.83083 -1.77767 -1.96386 -1.30972 -0.09516 1.16011 1.91899 1.85674 1.00000 -0.28463 -1.44747 -1.99094 -1.68251 -0.65414 0.65414 1.68251 1.99094 1.44747 0.28463 -1.00000 -1.85674 -1.91899 -1.16011 0.09516 1.30972 1.96386 1.77767 0.83083 -0.47152 -1.57211 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E9u 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 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 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 ... ... ..... ....... ......... ........... ............. 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E12u 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 0.83083 -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 -0.83083 1.30972 1.91899 0.28463 -1.68251 -1.68251 0.28463 1.91899 1.30972 -0.83083 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E16u 2.00000 0.09516 -1.99094 -0.28463 1.96386 0.47152 -1.91899 -0.65414 1.85674 0.83083 -1.77767 -1.00000 1.68251 1.16011 -1.57211 -1.30972 1.44747 1.44747 -1.30972 -1.57211 1.16011 1.68251 -1.00000 -1.77767 0.83083 1.85674 -0.65414 -1.91899 0.47152 1.96386 -0.28463 -1.99094 0.09516 2.00000 0.00000 0.00000 -2.00000 -0.09516 1.99094 0.28463 -1.96386 -0.47152 1.91899 0.65414 -1.85674 -0.83083 1.77767 1.00000 -1.68251 -1.16011 1.57211 1.30972 -1.44747 -1.44747 1.30972 1.57211 -1.16011 -1.68251 1.00000 1.77767 -0.83083 -1.85674 0.65414 1.91899 -0.47152 -1.96386 0.28463 1.99094 -0.09516 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E18u 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 -0.28463 -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 0.28463 1.91899 -0.83083 -1.68251 1.30972 1.30972 -1.68251 -0.83083 1.91899 0.28463 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19u 2.00000 -0.47152 -1.77767 1.30972 1.16011 -1.85674 -0.28463 1.99094 -0.65414 -1.68251 1.44747 1.00000 -1.91899 -0.09516 1.96386 -0.83083 -1.57211 1.57211 0.83083 -1.96386 0.09516 1.91899 -1.00000 -1.44747 1.68251 0.65414 -1.99094 0.28463 1.85674 -1.16011 -1.30972 1.77767 0.47152 -2.00000 0.00000 0.00000 -2.00000 -0.47152 -1.77767 1.30972 1.16011 -1.85674 -0.28463 1.99094 -0.65414 -1.68251 1.44747 1.00000 -1.91899 -0.09516 1.96386 -0.83083 -1.57211 1.57211 0.83083 -1.96386 0.09516 1.91899 -1.00000 -1.44747 1.68251 0.65414 -1.99094 0.28463 1.85674 -1.16011 -1.30972 1.77767 0.47152 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20u 2.00000 -0.65414 -1.57211 1.68251 0.47152 -1.99094 0.83083 1.44747 -1.77767 -0.28463 1.96386 -1.00000 -1.30972 1.85674 0.09516 -1.91899 1.16011 1.16011 -1.91899 0.09516 1.85674 -1.30972 -1.00000 1.96386 -0.28463 -1.77767 1.44747 0.83083 -1.99094 0.47152 1.68251 -1.57211 -0.65414 2.00000 0.00000 0.00000 -2.00000 0.65414 1.57211 -1.68251 -0.47152 1.99094 -0.83083 -1.44747 1.77767 0.28463 -1.96386 1.00000 1.30972 -1.85674 -0.09516 1.91899 -1.16011 -1.16011 1.91899 -0.09516 -1.85674 1.30972 1.00000 -1.96386 0.28463 1.77767 -1.44747 -0.83083 1.99094 -0.47152 -1.68251 1.57211 0.65414 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E24u 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 -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 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 ... ... ..... ....... ......... ........... ............. E25u 2.00000 -1.44747 0.09516 1.30972 -1.99094 1.57211 -0.28463 -1.16011 1.96386 -1.68251 0.47152 1.00000 -1.91899 1.77767 -0.65414 -0.83083 1.85674 -1.85674 0.83083 0.65414 -1.77767 1.91899 -1.00000 -0.47152 1.68251 -1.96386 1.16011 0.28463 -1.57211 1.99094 -1.30972 -0.09516 1.44747 -2.00000 0.00000 0.00000 -2.00000 -1.44747 0.09516 1.30972 -1.99094 1.57211 -0.28463 -1.16011 1.96386 -1.68251 0.47152 1.00000 -1.91899 1.77767 -0.65414 -0.83083 1.85674 -1.85674 0.83083 0.65414 -1.77767 1.91899 -1.00000 -0.47152 1.68251 -1.96386 1.16011 0.28463 -1.57211 1.99094 -1.30972 -0.09516 1.44747 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E26u 2.00000 -1.57211 0.47152 0.83083 -1.77767 1.96386 -1.30972 0.09516 1.16011 -1.91899 1.85674 -1.00000 -0.28463 1.44747 -1.99094 1.68251 -0.65414 -0.65414 1.68251 -1.99094 1.44747 -0.28463 -1.00000 1.85674 -1.91899 1.16011 0.09516 -1.30972 1.96386 -1.77767 0.83083 0.47152 -1.57211 2.00000 0.00000 0.00000 -2.00000 1.57211 -0.47152 -0.83083 1.77767 -1.96386 1.30972 -0.09516 -1.16011 1.91899 -1.85674 1.00000 0.28463 -1.44747 1.99094 -1.68251 0.65414 0.65414 -1.68251 1.99094 -1.44747 0.28463 1.00000 -1.85674 1.91899 -1.16011 -0.09516 1.30972 -1.96386 1.77767 -0.83083 -0.47152 1.57211 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E27u 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 -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 -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 ... ... ..... ....... ......... ........... ............. E28u 2.00000 -1.77767 1.16011 -0.28463 -0.65414 1.44747 -1.91899 1.96386 -1.57211 0.83083 0.09516 -1.00000 1.68251 -1.99094 1.85674 -1.30972 0.47152 0.47152 -1.30972 1.85674 -1.99094 1.68251 -1.00000 0.09516 0.83083 -1.57211 1.96386 -1.91899 1.44747 -0.65414 -0.28463 1.16011 -1.77767 2.00000 0.00000 0.00000 -2.00000 1.77767 -1.16011 0.28463 0.65414 -1.44747 1.91899 -1.96386 1.57211 -0.83083 -0.09516 1.00000 -1.68251 1.99094 -1.85674 1.30972 -0.47152 -0.47152 1.30972 -1.85674 1.99094 -1.68251 1.00000 -0.09516 -0.83083 1.57211 -1.96386 1.91899 -1.44747 0.65414 0.28463 -1.16011 1.77767 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E29u 2.00000 -1.85674 1.44747 -0.83083 0.09516 0.65414 -1.30972 1.77767 -1.99094 1.91899 -1.57211 1.00000 -0.28463 -0.47152 1.16011 -1.68251 1.96386 -1.96386 1.68251 -1.16011 0.47152 0.28463 -1.00000 1.57211 -1.91899 1.99094 -1.77767 1.30972 -0.65414 -0.09516 0.83083 -1.44747 1.85674 -2.00000 0.00000 0.00000 -2.00000 -1.85674 1.44747 -0.83083 0.09516 0.65414 -1.30972 1.77767 -1.99094 1.91899 -1.57211 1.00000 -0.28463 -0.47152 1.16011 -1.68251 1.96386 -1.96386 1.68251 -1.16011 0.47152 0.28463 -1.00000 1.57211 -1.91899 1.99094 -1.77767 1.30972 -0.65414 -0.09516 0.83083 -1.44747 1.85674 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E30u 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 -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 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 ... ... ..... ....... ......... ........... ............. E31u 2.00000 -1.96386 1.85674 -1.68251 1.44747 -1.16011 0.83083 -0.47152 0.09516 0.28463 -0.65414 1.00000 -1.30972 1.57211 -1.77767 1.91899 -1.99094 1.99094 -1.91899 1.77767 -1.57211 1.30972 -1.00000 0.65414 -0.28463 -0.09516 0.47152 -0.83083 1.16011 -1.44747 1.68251 -1.85674 1.96386 -2.00000 0.00000 0.00000 -2.00000 -1.96386 1.85674 -1.68251 1.44747 -1.16011 0.83083 -0.47152 0.09516 0.28463 -0.65414 1.00000 -1.30972 1.57211 -1.77767 1.91899 -1.99094 1.99094 -1.91899 1.77767 -1.57211 1.30972 -1.00000 0.65414 -0.28463 -0.09516 0.47152 -0.83083 1.16011 -1.44747 1.68251 -1.85674 1.96386 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E32u 2.00000 -1.99094 1.96386 -1.91899 1.85674 -1.77767 1.68251 -1.57211 1.44747 -1.30972 1.16011 -1.00000 0.83083 -0.65414 0.47152 -0.28463 0.09516 0.09516 -0.28463 0.47152 -0.65414 0.83083 -1.00000 1.16011 -1.30972 1.44747 -1.57211 1.68251 -1.77767 1.85674 -1.91899 1.96386 -1.99094 2.00000 0.00000 0.00000 -2.00000 1.99094 -1.96386 1.91899 -1.85674 1.77767 -1.68251 1.57211 -1.44747 1.30972 -1.16011 1.00000 -0.83083 0.65414 -0.47152 0.28463 -0.09516 -0.09516 0.28463 -0.47152 0.65414 -0.83083 1.00000 -1.16011 1.30972 -1.44747 1.57211 -1.68251 1.77767 -1.85674 1.91899 -1.96386 1.99094 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.990943845146 = 2*cos(2*π/66) = 2*cos(π/33) 1.963857394525 = 2*cos(4*π/66) = 2*cos(2*π/33) 1.918985947229 = 2*cos(6*π/66) = 2*cos(π/11) 1.856735866032 = 2*cos(8*π/66) = 2*cos(4*π/33) 1.777670897310 = 2*cos(10*π/66) = 2*cos(5*π/33) 1.682507065662 = 2*cos(12*π/66) = 2*cos(2*π/11) 1.572106189486 = 2*cos(14*π/66) = 2*cos(7*π/33) 1.447468076210 = 2*cos(16*π/66) = 2*cos(8*π/33) 1.309721467891 = 2*cos(18*π/66) = 2*cos(3*π/11) 1.160113819142 = 2*cos(20*π/66) = 2*cos(10*π/33) 0.830830026004 = 2*cos(24*π/66) = 2*cos(4*π/11) 0.654135926635 = 2*cos(26*π/66) = 2*cos(13*π/33) 0.471517871019 = 2*cos(28*π/66) = 2*cos(14*π/33) 0.284629676547 = 2*cos(30*π/66) = 2*cos(5*π/11) 0.095163831647 = 2*cos(32*π/66) = 2*cos(16*π/33) Symmetry of Rotations and Cartesian products A1g d+g+i+k+m z², z⁴, z⁶ A2g R R_z 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 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 D_66h point group is 264, and the order of the principal axis (C₆₆) is 66. The group has 72 irreducible representations. β The D_66h point group is generated by three symmetry elements that are canonically chosen C₆₆, C₂^′ and i. Other choices include σ_h instead of i, or any of C₂^″, σ_v or σ_d instead of C₂^′. Also, some ternary combinations of C₂^′, C₂^″, σ_v and σ_d act as generators. Lastly, the S₆₆ can be chosen, together with σ_h or C₂ and any one of C₂^′, C₂^″, σ_v or σ_d. 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 σ_v has the xz plane as a member, while the yz plane is a member of the σ_d set. ε The lowest nonvanishing multipole moment in D_66h 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.

This Character Table for the D_66h point group was created by Gernot Katzer.

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

	D_64h
	D_65h
C₆₆ C_66v C_66h D₆₆	D_66h	D_66d S₆₆
	D_67h
	D_68h

Character table for the D66h point group

Character table for the D_66h point group