C104 E 2 C104 2 C52 2 C104^3 2 C26 2 C104^5 2 C52^3 2 C104^7 2 C13 2 C104^9 2 C52^5 2 C104^11 2 C26^3 2 C8 2 C52^7 2 C104^15 2 C13^2 2 C104^17 2 C52^9 2 C104^19 2 C26^5 2 C104^21 2 C52^11 2 C104^23 2 C13^3 2 C104^25 2 C4 2 C104^27 2 C26^7 2 C104^29 2 C52^15 2 C104^31 2 C13^4 2 C104^33 2 C52^17 2 C104^35 2 C26^9 2 C104^37 2 C52^19 2 C8^3 2 C13^5 2 C104^41 2 C52^21 2 C104^43 2 C26^11 2 C104^45 2 C52^23 2 C104^47 2 C13^6 2 C104^49 2 C52^25 2 C104^51 C2 <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ..T ..T ....T ......T ........T ..........T ............T B 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E1 * 2.00000 1.99635 1.98542 1.96724 1.94188 1.90944 1.87003 1.82380 1.77091 1.71156 1.64597 1.57437 1.49702 1.41421 1.32625 1.23344 1.13613 1.03468 0.92945 0.82083 0.70921 0.59501 0.47863 0.36051 0.24107 0.12076 0.00000 -0.12076 -0.24107 -0.36051 -0.47863 -0.59501 -0.70921 -0.82083 -0.92945 -1.03468 -1.13613 -1.23344 -1.32625 -1.41421 -1.49702 -1.57437 -1.64597 -1.71156 -1.77091 -1.82380 -1.87003 -1.90944 -1.94188 -1.96724 -1.98542 -1.99635 -2.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98542 1.94188 1.87003 1.77091 1.64597 1.49702 1.32625 1.13613 0.92945 0.70921 0.47863 0.24107 0.00000 -0.24107 -0.47863 -0.70921 -0.92945 -1.13613 -1.32625 -1.49702 -1.64597 -1.77091 -1.87003 -1.94188 -1.98542 -2.00000 -1.98542 -1.94188 -1.87003 -1.77091 -1.64597 -1.49702 -1.32625 -1.13613 -0.92945 -0.70921 -0.47863 -0.24107 0.00000 0.24107 0.47863 0.70921 0.92945 1.13613 1.32625 1.49702 1.64597 1.77091 1.87003 1.94188 1.98542 2.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.96724 1.87003 1.71156 1.49702 1.23344 0.92945 0.59501 0.24107 -0.12076 -0.47863 -0.82083 -1.13613 -1.41421 -1.64597 -1.82380 -1.94188 -1.99635 -1.98542 -1.90944 -1.77091 -1.57437 -1.32625 -1.03468 -0.70921 -0.36051 0.00000 0.36051 0.70921 1.03468 1.32625 1.57437 1.77091 1.90944 1.98542 1.99635 1.94188 1.82380 1.64597 1.41421 1.13613 0.82083 0.47863 0.12076 -0.24107 -0.59501 -0.92945 -1.23344 -1.49702 -1.71156 -1.87003 -1.96724 -2.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.94188 1.77091 1.49702 1.13613 0.70921 0.24107 -0.24107 -0.70921 -1.13613 -1.49702 -1.77091 -1.94188 -2.00000 -1.94188 -1.77091 -1.49702 -1.13613 -0.70921 -0.24107 0.24107 0.70921 1.13613 1.49702 1.77091 1.94188 2.00000 1.94188 1.77091 1.49702 1.13613 0.70921 0.24107 -0.24107 -0.70921 -1.13613 -1.49702 -1.77091 -1.94188 -2.00000 -1.94188 -1.77091 -1.49702 -1.13613 -0.70921 -0.24107 0.24107 0.70921 1.13613 1.49702 1.77091 1.94188 2.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.90944 1.64597 1.23344 0.70921 0.12076 -0.47863 -1.03468 -1.49702 -1.82380 -1.98542 -1.96724 -1.77091 -1.41421 -0.92945 -0.36051 0.24107 0.82083 1.32625 1.71156 1.94188 1.99635 1.87003 1.57437 1.13613 0.59501 0.00000 -0.59501 -1.13613 -1.57437 -1.87003 -1.99635 -1.94188 -1.71156 -1.32625 -0.82083 -0.24107 0.36051 0.92945 1.41421 1.77091 1.96724 1.98542 1.82380 1.49702 1.03468 0.47863 -0.12076 -0.70921 -1.23344 -1.64597 -1.90944 -2.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.87003 1.49702 0.92945 0.24107 -0.47863 -1.13613 -1.64597 -1.94188 -1.98542 -1.77091 -1.32625 -0.70921 0.00000 0.70921 1.32625 1.77091 1.98542 1.94188 1.64597 1.13613 0.47863 -0.24107 -0.92945 -1.49702 -1.87003 -2.00000 -1.87003 -1.49702 -0.92945 -0.24107 0.47863 1.13613 1.64597 1.94188 1.98542 1.77091 1.32625 0.70921 0.00000 -0.70921 -1.32625 -1.77091 -1.98542 -1.94188 -1.64597 -1.13613 -0.47863 0.24107 0.92945 1.49702 1.87003 2.00000 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.82380 1.32625 0.59501 -0.24107 -1.03468 -1.64597 -1.96724 -1.94188 -1.57437 -0.92945 -0.12076 0.70921 1.41421 1.87003 1.99635 1.77091 1.23344 0.47863 -0.36051 -1.13613 -1.71156 -1.98542 -1.90944 -1.49702 -0.82083 0.00000 0.82083 1.49702 1.90944 1.98542 1.71156 1.13613 0.36051 -0.47863 -1.23344 -1.77091 -1.99635 -1.87003 -1.41421 -0.70921 0.12076 0.92945 1.57437 1.94188 1.96724 1.64597 1.03468 0.24107 -0.59501 -1.32625 -1.82380 -2.00000 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.71156 0.92945 -0.12076 -1.13613 -1.82380 -1.98542 -1.57437 -0.70921 0.36051 1.32625 1.90944 1.94188 1.41421 0.47863 -0.59501 -1.49702 -1.96724 -1.87003 -1.23344 -0.24107 0.82083 1.64597 1.99635 1.77091 1.03468 0.00000 -1.03468 -1.77091 -1.99635 -1.64597 -0.82083 0.24107 1.23344 1.87003 1.96724 1.49702 0.59501 -0.47863 -1.41421 -1.94188 -1.90944 -1.32625 -0.36051 0.70921 1.57437 1.98542 1.82380 1.13613 0.12076 -0.92945 -1.71156 -2.00000 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.64597 0.70921 -0.47863 -1.49702 -1.98542 -1.77091 -0.92945 0.24107 1.32625 1.94188 1.87003 1.13613 0.00000 -1.13613 -1.87003 -1.94188 -1.32625 -0.24107 0.92945 1.77091 1.98542 1.49702 0.47863 -0.70921 -1.64597 -2.00000 -1.64597 -0.70921 0.47863 1.49702 1.98542 1.77091 0.92945 -0.24107 -1.32625 -1.94188 -1.87003 -1.13613 0.00000 1.13613 1.87003 1.94188 1.32625 0.24107 -0.92945 -1.77091 -1.98542 -1.49702 -0.47863 0.70921 1.64597 2.00000 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.57437 0.47863 -0.82083 -1.77091 -1.96724 -1.32625 -0.12076 1.13613 1.90944 1.87003 1.03468 -0.24107 -1.41421 -1.98542 -1.71156 -0.70921 0.59501 1.64597 1.99635 1.49702 0.36051 -0.92945 -1.82380 -1.94188 -1.23344 0.00000 1.23344 1.94188 1.82380 0.92945 -0.36051 -1.49702 -1.99635 -1.64597 -0.59501 0.70921 1.71156 1.98542 1.41421 0.24107 -1.03468 -1.87003 -1.90944 -1.13613 0.12076 1.32625 1.96724 1.77091 0.82083 -0.47863 -1.57437 -2.00000 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.49702 0.24107 -1.13613 -1.94188 -1.77091 -0.70921 0.70921 1.77091 1.94188 1.13613 -0.24107 -1.49702 -2.00000 -1.49702 -0.24107 1.13613 1.94188 1.77091 0.70921 -0.70921 -1.77091 -1.94188 -1.13613 0.24107 1.49702 2.00000 1.49702 0.24107 -1.13613 -1.94188 -1.77091 -0.70921 0.70921 1.77091 1.94188 1.13613 -0.24107 -1.49702 -2.00000 -1.49702 -0.24107 1.13613 1.94188 1.77091 0.70921 -0.70921 -1.77091 -1.94188 -1.13613 0.24107 1.49702 2.00000 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.32625 -0.24107 -1.64597 -1.94188 -0.92945 0.70921 1.87003 1.77091 0.47863 -1.13613 -1.98542 -1.49702 0.00000 1.49702 1.98542 1.13613 -0.47863 -1.77091 -1.87003 -0.70921 0.92945 1.94188 1.64597 0.24107 -1.32625 -2.00000 -1.32625 0.24107 1.64597 1.94188 0.92945 -0.70921 -1.87003 -1.77091 -0.47863 1.13613 1.98542 1.49702 0.00000 -1.49702 -1.98542 -1.13613 0.47863 1.77091 1.87003 0.70921 -0.92945 -1.94188 -1.64597 -0.24107 1.32625 2.00000 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.23344 -0.47863 -1.82380 -1.77091 -0.36051 1.32625 1.99635 1.13613 -0.59501 -1.87003 -1.71156 -0.24107 1.41421 1.98542 1.03468 -0.70921 -1.90944 -1.64597 -0.12076 1.49702 1.96724 0.92945 -0.82083 -1.94188 -1.57437 0.00000 1.57437 1.94188 0.82083 -0.92945 -1.96724 -1.49702 0.12076 1.64597 1.90944 0.70921 -1.03468 -1.98542 -1.41421 0.24107 1.71156 1.87003 0.59501 -1.13613 -1.99635 -1.32625 0.36051 1.77091 1.82380 0.47863 -1.23344 -2.00000 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 1.03468 -0.92945 -1.99635 -1.13613 0.82083 1.98542 1.23344 -0.70921 -1.96724 -1.32625 0.59501 1.94188 1.41421 -0.47863 -1.90944 -1.49702 0.36051 1.87003 1.57437 -0.24107 -1.82380 -1.64597 0.12076 1.77091 1.71156 0.00000 -1.71156 -1.77091 -0.12076 1.64597 1.82380 0.24107 -1.57437 -1.87003 -0.36051 1.49702 1.90944 0.47863 -1.41421 -1.94188 -0.59501 1.32625 1.96724 0.70921 -1.23344 -1.98542 -0.82083 1.13613 1.99635 0.92945 -1.03468 -2.00000 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.92945 -1.13613 -1.98542 -0.70921 1.32625 1.94188 0.47863 -1.49702 -1.87003 -0.24107 1.64597 1.77091 0.00000 -1.77091 -1.64597 0.24107 1.87003 1.49702 -0.47863 -1.94188 -1.32625 0.70921 1.98542 1.13613 -0.92945 -2.00000 -0.92945 1.13613 1.98542 0.70921 -1.32625 -1.94188 -0.47863 1.49702 1.87003 0.24107 -1.64597 -1.77091 0.00000 1.77091 1.64597 -0.24107 -1.87003 -1.49702 0.47863 1.94188 1.32625 -0.70921 -1.98542 -1.13613 0.92945 2.00000 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.82083 -1.32625 -1.90944 -0.24107 1.71156 1.64597 -0.36051 -1.94188 -1.23344 0.92945 1.99635 0.70921 -1.41421 -1.87003 -0.12076 1.77091 1.57437 -0.47863 -1.96724 -1.13613 1.03468 1.98542 0.59501 -1.49702 -1.82380 0.00000 1.82380 1.49702 -0.59501 -1.98542 -1.03468 1.13613 1.96724 0.47863 -1.57437 -1.77091 0.12076 1.87003 1.41421 -0.70921 -1.99635 -0.92945 1.23344 1.94188 0.36051 -1.64597 -1.71156 0.24107 1.90944 1.32625 -0.82083 -2.00000 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.70921 -1.49702 -1.77091 0.24107 1.94188 1.13613 -1.13613 -1.94188 -0.24107 1.77091 1.49702 -0.70921 -2.00000 -0.70921 1.49702 1.77091 -0.24107 -1.94188 -1.13613 1.13613 1.94188 0.24107 -1.77091 -1.49702 0.70921 2.00000 0.70921 -1.49702 -1.77091 0.24107 1.94188 1.13613 -1.13613 -1.94188 -0.24107 1.77091 1.49702 -0.70921 -2.00000 -0.70921 1.49702 1.77091 -0.24107 -1.94188 -1.13613 1.13613 1.94188 0.24107 -1.77091 -1.49702 0.70921 2.00000 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.59501 -1.64597 -1.57437 0.70921 1.99635 0.47863 -1.71156 -1.49702 0.82083 1.98542 0.36051 -1.77091 -1.41421 0.92945 1.96724 0.24107 -1.82380 -1.32625 1.03468 1.94188 0.12076 -1.87003 -1.23344 1.13613 1.90944 0.00000 -1.90944 -1.13613 1.23344 1.87003 -0.12076 -1.94188 -1.03468 1.32625 1.82380 -0.24107 -1.96724 -0.92945 1.41421 1.77091 -0.36051 -1.98542 -0.82083 1.49702 1.71156 -0.47863 -1.99635 -0.70921 1.57437 1.64597 -0.59501 -2.00000 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.47863 -1.77091 -1.32625 1.13613 1.87003 -0.24107 -1.98542 -0.70921 1.64597 1.49702 -0.92945 -1.94188 0.00000 1.94188 0.92945 -1.49702 -1.64597 0.70921 1.98542 0.24107 -1.87003 -1.13613 1.32625 1.77091 -0.47863 -2.00000 -0.47863 1.77091 1.32625 -1.13613 -1.87003 0.24107 1.98542 0.70921 -1.64597 -1.49702 0.92945 1.94188 0.00000 -1.94188 -0.92945 1.49702 1.64597 -0.70921 -1.98542 -0.24107 1.87003 1.13613 -1.32625 -1.77091 0.47863 2.00000 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.36051 -1.87003 -1.03468 1.49702 1.57437 -0.92945 -1.90944 0.24107 1.99635 0.47863 -1.82380 -1.13613 1.41421 1.64597 -0.82083 -1.94188 0.12076 1.98542 0.59501 -1.77091 -1.23344 1.32625 1.71156 -0.70921 -1.96724 0.00000 1.96724 0.70921 -1.71156 -1.32625 1.23344 1.77091 -0.59501 -1.98542 -0.12076 1.94188 0.82083 -1.64597 -1.41421 1.13613 1.82380 -0.47863 -1.99635 -0.24107 1.90944 0.92945 -1.57437 -1.49702 1.03468 1.87003 -0.36051 -2.00000 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 0.12076 -1.98542 -0.36051 1.94188 0.59501 -1.87003 -0.82083 1.77091 1.03468 -1.64597 -1.23344 1.49702 1.41421 -1.32625 -1.57437 1.13613 1.71156 -0.92945 -1.82380 0.70921 1.90944 -0.47863 -1.96724 0.24107 1.99635 0.00000 -1.99635 -0.24107 1.96724 0.47863 -1.90944 -0.70921 1.82380 0.92945 -1.71156 -1.13613 1.57437 1.32625 -1.41421 -1.49702 1.23344 1.64597 -1.03468 -1.77091 0.82083 1.87003 -0.59501 -1.94188 0.36051 1.98542 -0.12076 -2.00000 ... ... ..... ....... ......... ........... ............. 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E28 * 2.00000 -0.24107 -1.94188 0.70921 1.77091 -1.13613 -1.49702 1.49702 1.13613 -1.77091 -0.70921 1.94188 0.24107 -2.00000 0.24107 1.94188 -0.70921 -1.77091 1.13613 1.49702 -1.49702 -1.13613 1.77091 0.70921 -1.94188 -0.24107 2.00000 -0.24107 -1.94188 0.70921 1.77091 -1.13613 -1.49702 1.49702 1.13613 -1.77091 -0.70921 1.94188 0.24107 -2.00000 0.24107 1.94188 -0.70921 -1.77091 1.13613 1.49702 -1.49702 -1.13613 1.77091 0.70921 -1.94188 -0.24107 2.00000 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.36051 -1.87003 1.03468 1.49702 -1.57437 -0.92945 1.90944 0.24107 -1.99635 0.47863 1.82380 -1.13613 -1.41421 1.64597 0.82083 -1.94188 -0.12076 1.98542 -0.59501 -1.77091 1.23344 1.32625 -1.71156 -0.70921 1.96724 0.00000 -1.96724 0.70921 1.71156 -1.32625 -1.23344 1.77091 0.59501 -1.98542 0.12076 1.94188 -0.82083 -1.64597 1.41421 1.13613 -1.82380 -0.47863 1.99635 -0.24107 -1.90944 0.92945 1.57437 -1.49702 -1.03468 1.87003 0.36051 -2.00000 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -0.47863 -1.77091 1.32625 1.13613 -1.87003 -0.24107 1.98542 -0.70921 -1.64597 1.49702 0.92945 -1.94188 0.00000 1.94188 -0.92945 -1.49702 1.64597 0.70921 -1.98542 0.24107 1.87003 -1.13613 -1.32625 1.77091 0.47863 -2.00000 0.47863 1.77091 -1.32625 -1.13613 1.87003 0.24107 -1.98542 0.70921 1.64597 -1.49702 -0.92945 1.94188 0.00000 -1.94188 0.92945 1.49702 -1.64597 -0.70921 1.98542 -0.24107 -1.87003 1.13613 1.32625 -1.77091 -0.47863 2.00000 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -0.59501 -1.64597 1.57437 0.70921 -1.99635 0.47863 1.71156 -1.49702 -0.82083 1.98542 -0.36051 -1.77091 1.41421 0.92945 -1.96724 0.24107 1.82380 -1.32625 -1.03468 1.94188 -0.12076 -1.87003 1.23344 1.13613 -1.90944 0.00000 1.90944 -1.13613 -1.23344 1.87003 0.12076 -1.94188 1.03468 1.32625 -1.82380 -0.24107 1.96724 -0.92945 -1.41421 1.77091 0.36051 -1.98542 0.82083 1.49702 -1.71156 -0.47863 1.99635 -0.70921 -1.57437 1.64597 0.59501 -2.00000 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -0.82083 -1.32625 1.90944 -0.24107 -1.71156 1.64597 0.36051 -1.94188 1.23344 0.92945 -1.99635 0.70921 1.41421 -1.87003 0.12076 1.77091 -1.57437 -0.47863 1.96724 -1.13613 -1.03468 1.98542 -0.59501 -1.49702 1.82380 0.00000 -1.82380 1.49702 0.59501 -1.98542 1.03468 1.13613 -1.96724 0.47863 1.57437 -1.77091 -0.12076 1.87003 -1.41421 -0.70921 1.99635 -0.92945 -1.23344 1.94188 -0.36051 -1.64597 1.71156 0.24107 -1.90944 1.32625 0.82083 -2.00000 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -0.92945 -1.13613 1.98542 -0.70921 -1.32625 1.94188 -0.47863 -1.49702 1.87003 -0.24107 -1.64597 1.77091 0.00000 -1.77091 1.64597 0.24107 -1.87003 1.49702 0.47863 -1.94188 1.32625 0.70921 -1.98542 1.13613 0.92945 -2.00000 0.92945 1.13613 -1.98542 0.70921 1.32625 -1.94188 0.47863 1.49702 -1.87003 0.24107 1.64597 -1.77091 0.00000 1.77091 -1.64597 -0.24107 1.87003 -1.49702 -0.47863 1.94188 -1.32625 -0.70921 1.98542 -1.13613 -0.92945 2.00000 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.03468 -0.92945 1.99635 -1.13613 -0.82083 1.98542 -1.23344 -0.70921 1.96724 -1.32625 -0.59501 1.94188 -1.41421 -0.47863 1.90944 -1.49702 -0.36051 1.87003 -1.57437 -0.24107 1.82380 -1.64597 -0.12076 1.77091 -1.71156 0.00000 1.71156 -1.77091 0.12076 1.64597 -1.82380 0.24107 1.57437 -1.87003 0.36051 1.49702 -1.90944 0.47863 1.41421 -1.94188 0.59501 1.32625 -1.96724 0.70921 1.23344 -1.98542 0.82083 1.13613 -1.99635 0.92945 1.03468 -2.00000 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.13613 -0.70921 1.94188 -1.49702 -0.24107 1.77091 -1.77091 0.24107 1.49702 -1.94188 0.70921 1.13613 -2.00000 1.13613 0.70921 -1.94188 1.49702 0.24107 -1.77091 1.77091 -0.24107 -1.49702 1.94188 -0.70921 -1.13613 2.00000 -1.13613 -0.70921 1.94188 -1.49702 -0.24107 1.77091 -1.77091 0.24107 1.49702 -1.94188 0.70921 1.13613 -2.00000 1.13613 0.70921 -1.94188 1.49702 0.24107 -1.77091 1.77091 -0.24107 -1.49702 1.94188 -0.70921 -1.13613 2.00000 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.23344 -0.47863 1.82380 -1.77091 0.36051 1.32625 -1.99635 1.13613 0.59501 -1.87003 1.71156 -0.24107 -1.41421 1.98542 -1.03468 -0.70921 1.90944 -1.64597 0.12076 1.49702 -1.96724 0.92945 0.82083 -1.94188 1.57437 0.00000 -1.57437 1.94188 -0.82083 -0.92945 1.96724 -1.49702 -0.12076 1.64597 -1.90944 0.70921 1.03468 -1.98542 1.41421 0.24107 -1.71156 1.87003 -0.59501 -1.13613 1.99635 -1.32625 -0.36051 1.77091 -1.82380 0.47863 1.23344 -2.00000 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.32625 -0.24107 1.64597 -1.94188 0.92945 0.70921 -1.87003 1.77091 -0.47863 -1.13613 1.98542 -1.49702 0.00000 1.49702 -1.98542 1.13613 0.47863 -1.77091 1.87003 -0.70921 -0.92945 1.94188 -1.64597 0.24107 1.32625 -2.00000 1.32625 0.24107 -1.64597 1.94188 -0.92945 -0.70921 1.87003 -1.77091 0.47863 1.13613 -1.98542 1.49702 0.00000 -1.49702 1.98542 -1.13613 -0.47863 1.77091 -1.87003 0.70921 0.92945 -1.94188 1.64597 -0.24107 -1.32625 2.00000 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.57437 0.47863 0.82083 -1.77091 1.96724 -1.32625 0.12076 1.13613 -1.90944 1.87003 -1.03468 -0.24107 1.41421 -1.98542 1.71156 -0.70921 -0.59501 1.64597 -1.99635 1.49702 -0.36051 -0.92945 1.82380 -1.94188 1.23344 0.00000 -1.23344 1.94188 -1.82380 0.92945 0.36051 -1.49702 1.99635 -1.64597 0.59501 0.70921 -1.71156 1.98542 -1.41421 0.24107 1.03468 -1.87003 1.90944 -1.13613 -0.12076 1.32625 -1.96724 1.77091 -0.82083 -0.47863 1.57437 -2.00000 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.64597 0.70921 0.47863 -1.49702 1.98542 -1.77091 0.92945 0.24107 -1.32625 1.94188 -1.87003 1.13613 0.00000 -1.13613 1.87003 -1.94188 1.32625 -0.24107 -0.92945 1.77091 -1.98542 1.49702 -0.47863 -0.70921 1.64597 -2.00000 1.64597 -0.70921 -0.47863 1.49702 -1.98542 1.77091 -0.92945 -0.24107 1.32625 -1.94188 1.87003 -1.13613 0.00000 1.13613 -1.87003 1.94188 -1.32625 0.24107 0.92945 -1.77091 1.98542 -1.49702 0.47863 0.70921 -1.64597 2.00000 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.71156 0.92945 0.12076 -1.13613 1.82380 -1.98542 1.57437 -0.70921 -0.36051 1.32625 -1.90944 1.94188 -1.41421 0.47863 0.59501 -1.49702 1.96724 -1.87003 1.23344 -0.24107 -0.82083 1.64597 -1.99635 1.77091 -1.03468 0.00000 1.03468 -1.77091 1.99635 -1.64597 0.82083 0.24107 -1.23344 1.87003 -1.96724 1.49702 -0.59501 -0.47863 1.41421 -1.94188 1.90944 -1.32625 0.36051 0.70921 -1.57437 1.98542 -1.82380 1.13613 -0.12076 -0.92945 1.71156 -2.00000 ... ... ..... ....... ......... ........... ............. E44 * 2.00000 -1.77091 1.13613 -0.24107 -0.70921 1.49702 -1.94188 1.94188 -1.49702 0.70921 0.24107 -1.13613 1.77091 -2.00000 1.77091 -1.13613 0.24107 0.70921 -1.49702 1.94188 -1.94188 1.49702 -0.70921 -0.24107 1.13613 -1.77091 2.00000 -1.77091 1.13613 -0.24107 -0.70921 1.49702 -1.94188 1.94188 -1.49702 0.70921 0.24107 -1.13613 1.77091 -2.00000 1.77091 -1.13613 0.24107 0.70921 -1.49702 1.94188 -1.94188 1.49702 -0.70921 -0.24107 1.13613 -1.77091 2.00000 ... ... ..... ....... ......... ........... ............. E45 * 2.00000 -1.82380 1.32625 -0.59501 -0.24107 1.03468 -1.64597 1.96724 -1.94188 1.57437 -0.92945 0.12076 0.70921 -1.41421 1.87003 -1.99635 1.77091 -1.23344 0.47863 0.36051 -1.13613 1.71156 -1.98542 1.90944 -1.49702 0.82083 0.00000 -0.82083 1.49702 -1.90944 1.98542 -1.71156 1.13613 -0.36051 -0.47863 1.23344 -1.77091 1.99635 -1.87003 1.41421 -0.70921 -0.12076 0.92945 -1.57437 1.94188 -1.96724 1.64597 -1.03468 0.24107 0.59501 -1.32625 1.82380 -2.00000 ... ... ..... ....... ......... ........... ............. E46 * 2.00000 -1.87003 1.49702 -0.92945 0.24107 0.47863 -1.13613 1.64597 -1.94188 1.98542 -1.77091 1.32625 -0.70921 0.00000 0.70921 -1.32625 1.77091 -1.98542 1.94188 -1.64597 1.13613 -0.47863 -0.24107 0.92945 -1.49702 1.87003 -2.00000 1.87003 -1.49702 0.92945 -0.24107 -0.47863 1.13613 -1.64597 1.94188 -1.98542 1.77091 -1.32625 0.70921 0.00000 -0.70921 1.32625 -1.77091 1.98542 -1.94188 1.64597 -1.13613 0.47863 0.24107 -0.92945 1.49702 -1.87003 2.00000 ... ... ..... ....... ......... ........... ............. E47 * 2.00000 -1.90944 1.64597 -1.23344 0.70921 -0.12076 -0.47863 1.03468 -1.49702 1.82380 -1.98542 1.96724 -1.77091 1.41421 -0.92945 0.36051 0.24107 -0.82083 1.32625 -1.71156 1.94188 -1.99635 1.87003 -1.57437 1.13613 -0.59501 0.00000 0.59501 -1.13613 1.57437 -1.87003 1.99635 -1.94188 1.71156 -1.32625 0.82083 -0.24107 -0.36051 0.92945 -1.41421 1.77091 -1.96724 1.98542 -1.82380 1.49702 -1.03468 0.47863 0.12076 -0.70921 1.23344 -1.64597 1.90944 -2.00000 ... ... ..... ....... ......... ........... ............. E48 * 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 ... ... ..... ....... ......... ........... ............. E49 * 2.00000 -1.96724 1.87003 -1.71156 1.49702 -1.23344 0.92945 -0.59501 0.24107 0.12076 -0.47863 0.82083 -1.13613 1.41421 -1.64597 1.82380 -1.94188 1.99635 -1.98542 1.90944 -1.77091 1.57437 -1.32625 1.03468 -0.70921 0.36051 0.00000 -0.36051 0.70921 -1.03468 1.32625 -1.57437 1.77091 -1.90944 1.98542 -1.99635 1.94188 -1.82380 1.64597 -1.41421 1.13613 -0.82083 0.47863 -0.12076 -0.24107 0.59501 -0.92945 1.23344 -1.49702 1.71156 -1.87003 1.96724 -2.00000 ... ... ..... ....... ......... ........... ............. E50 * 2.00000 -1.98542 1.94188 -1.87003 1.77091 -1.64597 1.49702 -1.32625 1.13613 -0.92945 0.70921 -0.47863 0.24107 0.00000 -0.24107 0.47863 -0.70921 0.92945 -1.13613 1.32625 -1.49702 1.64597 -1.77091 1.87003 -1.94188 1.98542 -2.00000 1.98542 -1.94188 1.87003 -1.77091 1.64597 -1.49702 1.32625 -1.13613 0.92945 -0.70921 0.47863 -0.24107 0.00000 0.24107 -0.47863 0.70921 -0.92945 1.13613 -1.32625 1.49702 -1.64597 1.77091 -1.87003 1.94188 -1.98542 2.00000 ... ... ..... ....... ......... ........... ............. E51 * 2.00000 -1.99635 1.98542 -1.96724 1.94188 -1.90944 1.87003 -1.82380 1.77091 -1.71156 1.64597 -1.57437 1.49702 -1.41421 1.32625 -1.23344 1.13613 -1.03468 0.92945 -0.82083 0.70921 -0.59501 0.47863 -0.36051 0.24107 -0.12076 0.00000 0.12076 -0.24107 0.36051 -0.47863 0.59501 -0.70921 0.82083 -0.92945 1.03468 -1.13613 1.23344 -1.32625 1.41421 -1.49702 1.57437 -1.64597 1.71156 -1.77091 1.82380 -1.87003 1.90944 -1.94188 1.96724 -1.98542 1.99635 -2.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.996351108447 = 2*cos(2*π/104) = 2*cos(π/52) 1.985417748196 = 2*cos(4*π/104) = 2*cos(π/26) 1.967239813894 = 2*cos(6*π/104) = 2*cos(3*π/52) 1.941883634852 = 2*cos(8*π/104) = 2*cos(π/13) 1.909441733017 = 2*cos(10*π/104) = 2*cos(5*π/52) 1.870032485371 = 2*cos(12*π/104) = 2*cos(3*π/26) 1.823799691984 = 2*cos(14*π/104) = 2*cos(7*π/52) 1.770912051306 = 2*cos(16*π/104) = 2*cos(2*π/13) 1.711562544603 = 2*cos(18*π/104) = 2*cos(9*π/52) 1.645967731787 = 2*cos(20*π/104) = 2*cos(5*π/26) 1.574366961218 = 2*cos(22*π/104) = 2*cos(11*π/52) 1.497021496342 = 2*cos(24*π/104) = 2*cos(3*π/13) 1.414213562373 = 2*cos(26*π/104) = 2*cos(π/4) = √2 1.326245316482 = 2*cos(28*π/104) = 2*cos(7*π/26) 1.233437745257 = 2*cos(30*π/104) = 2*cos(15*π/52) 1.136129493462 = 2*cos(32*π/104) = 2*cos(4*π/13) 1.034675628355 = 2*cos(34*π/104) = 2*cos(17*π/52) 0.929446344088 = 2*cos(36*π/104) = 2*cos(9*π/26) 0.820825610906 = 2*cos(38*π/104) = 2*cos(19*π/52) 0.709209774085 = 2*cos(40*π/104) = 2*cos(5*π/13) 0.595006107710 = 2*cos(42*π/104) = 2*cos(21*π/52) 0.478631328575 = 2*cos(44*π/104) = 2*cos(11*π/26) 0.360510075628 = 2*cos(46*π/104) = 2*cos(23*π/52) 0.241073360511 = 2*cos(48*π/104) = 2*cos(6*π/13) 0.120756994845 = 2*cos(50*π/104) = 2*cos(25*π/52) Symmetry of Rotations and Cartesian products A R+p+d+f+g+h+i+j+k+l+m Rz, z, z2, z3, z4, z5, z6 E1 R+p+d+f+g+h+i+j+k+l+m {Rx, Ry}, {x, y}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} E2 d+f+g+h+i+j+k+l+m {x2−y2, xy}, {z(x2−y2), xyz}, {z2(x2−y2), xyz2}, {z3(x2−y2), xyz3}, {z4(x2−y2), xyz4} E3 f+g+h+i+j+k+l+m {x(x2−3y2), y(3x2−y2)}, {xz(x2−3y2), yz(3x2−y2)}, {xz2(x2−3y2), yz2(3x2−y2)}, {xz3(x2−3y2), yz3(3x2−y2)} E4 g+h+i+j+k+l+m {(x2−y2)2−4x2y2, xy(x2−y2)}, {z((x2−y2)2−4x2y2), xyz(x2−y2)}, {z2((x2−y2)2−4x2y2), xyz2(x2−y2)} E5 h+i+j+k+l+m {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2−y2)((5−2√5)x2−y2)}, {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2−y2)((5−2√5)x2−y2)} E6 i+j+k+l+m {x2(x2−3y2)2−y2(3x2−y2)2, xy(x2−3y2)(3x2−y2)} E7 j+k+l+m E8 k+l+m E9 l+m E10 m Notes: α The order of the C104 point group is 104, and the order of the principal axis (C104) is 104. The group has 53 irreducible representations. β The C104 point group is isomorphic to S104. γ The C104 point group is generated by one single symmetry element, C104. Therefore, it is a cyclic group. δ The lowest nonvanishing multipole moment in C104 is 2 (dipole moment). ε This is an Abelian point group (the commutative law holds between all symmetry operations). The C104 group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition). In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. ζ Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 102 cases have been combined into 51 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 51 pairs of left and right rotations have been combined into one two-membered pseudo-class each. η The 51 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. θ The point group is chiral, as it does not contain any mirroring operation. ι 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. κ The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. While some characters of this group can be expressed using real integers and square roots alone, others need complex numbers and third roots.
C102 | ||
C103 | ||
C104 | C104v C104h D104 D104h D104d S104 | |
C105 | ||
C106 |
This Character Table for the C104 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.