S124 E 2 S124 2 C62 2 S124^3 2 C31 2 S124^5 2 C62^3 2 S124^7 2 C31^2 2 S124^9 2 C62^5 2 S124^11 2 C31^3 2 S124^13 2 C62^7 2 S124^15 2 C31^4 2 S124^17 2 C62^9 2 S124^19 2 C31^5 2 S124^21 2 C62^11 2 S124^23 2 C31^6 2 S124^25 2 C62^13 2 S124^27 2 C31^7 2 S124^29 2 C62^15 2 S4 2 C31^8 2 S124^33 2 C62^17 2 S124^35 2 C31^9 2 S124^37 2 C62^19 2 S124^39 2 C31^10 2 S124^41 2 C62^21 2 S124^43 2 C31^11 2 S124^45 2 C62^23 2 S124^47 2 C31^12 2 S124^49 2 C62^25 2 S124^51 2 C31^13 2 S124^53 2 C62^27 2 S124^55 2 C31^14 2 S124^57 2 C62^29 2 S124^59 2 C31^15 2 S124^61 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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ..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 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 ... ..T ..... ......T ......... ..........T ............. E1 * 2.00000 1.99743 1.98974 1.97694 1.95906 1.93615 1.90828 1.87550 1.83792 1.79561 1.74869 1.69729 1.64153 1.58155 1.51752 1.44959 1.37793 1.30274 1.22421 1.14254 1.05793 0.97060 0.88079 0.78871 0.69461 0.59873 0.50131 0.40260 0.30286 0.20234 0.10130 0.00000 -0.10130 -0.20234 -0.30286 -0.40260 -0.50131 -0.59873 -0.69461 -0.78871 -0.88079 -0.97060 -1.05793 -1.14254 -1.22421 -1.30274 -1.37793 -1.44959 -1.51752 -1.58155 -1.64153 -1.69729 -1.74869 -1.79561 -1.83792 -1.87550 -1.90828 -1.93615 -1.95906 -1.97694 -1.98974 -1.99743 -2.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 * 2.00000 1.98974 1.95906 1.90828 1.83792 1.74869 1.64153 1.51752 1.37793 1.22421 1.05793 0.88079 0.69461 0.50131 0.30286 0.10130 -0.10130 -0.30286 -0.50131 -0.69461 -0.88079 -1.05793 -1.22421 -1.37793 -1.51752 -1.64153 -1.74869 -1.83792 -1.90828 -1.95906 -1.98974 -2.00000 -1.98974 -1.95906 -1.90828 -1.83792 -1.74869 -1.64153 -1.51752 -1.37793 -1.22421 -1.05793 -0.88079 -0.69461 -0.50131 -0.30286 -0.10130 0.10130 0.30286 0.50131 0.69461 0.88079 1.05793 1.22421 1.37793 1.51752 1.64153 1.74869 1.83792 1.90828 1.95906 1.98974 2.00000 ... ... TT... ....... ....TT... ........... ........TT... E3 * 2.00000 1.97694 1.90828 1.79561 1.64153 1.44959 1.22421 0.97060 0.69461 0.40260 0.10130 -0.20234 -0.50131 -0.78871 -1.05793 -1.30274 -1.51752 -1.69729 -1.83792 -1.93615 -1.98974 -1.99743 -1.95906 -1.87550 -1.74869 -1.58155 -1.37793 -1.14254 -0.88079 -0.59873 -0.30286 0.00000 0.30286 0.59873 0.88079 1.14254 1.37793 1.58155 1.74869 1.87550 1.95906 1.99743 1.98974 1.93615 1.83792 1.69729 1.51752 1.30274 1.05793 0.78871 0.50131 0.20234 -0.10130 -0.40260 -0.69461 -0.97060 -1.22421 -1.44959 -1.64153 -1.79561 -1.90828 -1.97694 -2.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 * 2.00000 1.95906 1.83792 1.64153 1.37793 1.05793 0.69461 0.30286 -0.10130 -0.50131 -0.88079 -1.22421 -1.51752 -1.74869 -1.90828 -1.98974 -1.98974 -1.90828 -1.74869 -1.51752 -1.22421 -0.88079 -0.50131 -0.10130 0.30286 0.69461 1.05793 1.37793 1.64153 1.83792 1.95906 2.00000 1.95906 1.83792 1.64153 1.37793 1.05793 0.69461 0.30286 -0.10130 -0.50131 -0.88079 -1.22421 -1.51752 -1.74869 -1.90828 -1.98974 -1.98974 -1.90828 -1.74869 -1.51752 -1.22421 -0.88079 -0.50131 -0.10130 0.30286 0.69461 1.05793 1.37793 1.64153 1.83792 1.95906 2.00000 ... ... ..... ....... TT....... ........... ....TT....... E5 * 2.00000 1.93615 1.74869 1.44959 1.05793 0.59873 0.10130 -0.40260 -0.88079 -1.30274 -1.64153 -1.87550 -1.98974 -1.97694 -1.83792 -1.58155 -1.22421 -0.78871 -0.30286 0.20234 0.69461 1.14254 1.51752 1.79561 1.95906 1.99743 1.90828 1.69729 1.37793 0.97060 0.50131 0.00000 -0.50131 -0.97060 -1.37793 -1.69729 -1.90828 -1.99743 -1.95906 -1.79561 -1.51752 -1.14254 -0.69461 -0.20234 0.30286 0.78871 1.22421 1.58155 1.83792 1.97694 1.98974 1.87550 1.64153 1.30274 0.88079 0.40260 -0.10130 -0.59873 -1.05793 -1.44959 -1.74869 -1.93615 -2.00000 ... ... ..... ....... ......... TT......... ............. E6 * 2.00000 1.90828 1.64153 1.22421 0.69461 0.10130 -0.50131 -1.05793 -1.51752 -1.83792 -1.98974 -1.95906 -1.74869 -1.37793 -0.88079 -0.30286 0.30286 0.88079 1.37793 1.74869 1.95906 1.98974 1.83792 1.51752 1.05793 0.50131 -0.10130 -0.69461 -1.22421 -1.64153 -1.90828 -2.00000 -1.90828 -1.64153 -1.22421 -0.69461 -0.10130 0.50131 1.05793 1.51752 1.83792 1.98974 1.95906 1.74869 1.37793 0.88079 0.30286 -0.30286 -0.88079 -1.37793 -1.74869 -1.95906 -1.98974 -1.83792 -1.51752 -1.05793 -0.50131 0.10130 0.69461 1.22421 1.64153 1.90828 2.00000 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.87550 1.51752 0.97060 0.30286 -0.40260 -1.05793 -1.58155 -1.90828 -1.99743 -1.83792 -1.44959 -0.88079 -0.20234 0.50131 1.14254 1.64153 1.93615 1.98974 1.79561 1.37793 0.78871 0.10130 -0.59873 -1.22421 -1.69729 -1.95906 -1.97694 -1.74869 -1.30274 -0.69461 0.00000 0.69461 1.30274 1.74869 1.97694 1.95906 1.69729 1.22421 0.59873 -0.10130 -0.78871 -1.37793 -1.79561 -1.98974 -1.93615 -1.64153 -1.14254 -0.50131 0.20234 0.88079 1.44959 1.83792 1.99743 1.90828 1.58155 1.05793 0.40260 -0.30286 -0.97060 -1.51752 -1.87550 -2.00000 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.83792 1.37793 0.69461 -0.10130 -0.88079 -1.51752 -1.90828 -1.98974 -1.74869 -1.22421 -0.50131 0.30286 1.05793 1.64153 1.95906 1.95906 1.64153 1.05793 0.30286 -0.50131 -1.22421 -1.74869 -1.98974 -1.90828 -1.51752 -0.88079 -0.10130 0.69461 1.37793 1.83792 2.00000 1.83792 1.37793 0.69461 -0.10130 -0.88079 -1.51752 -1.90828 -1.98974 -1.74869 -1.22421 -0.50131 0.30286 1.05793 1.64153 1.95906 1.95906 1.64153 1.05793 0.30286 -0.50131 -1.22421 -1.74869 -1.98974 -1.90828 -1.51752 -0.88079 -0.10130 0.69461 1.37793 1.83792 2.00000 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.79561 1.22421 0.40260 -0.50131 -1.30274 -1.83792 -1.99743 -1.74869 -1.14254 -0.30286 0.59873 1.37793 1.87550 1.98974 1.69729 1.05793 0.20234 -0.69461 -1.44959 -1.90828 -1.97694 -1.64153 -0.97060 -0.10130 0.78871 1.51752 1.93615 1.95906 1.58155 0.88079 0.00000 -0.88079 -1.58155 -1.95906 -1.93615 -1.51752 -0.78871 0.10130 0.97060 1.64153 1.97694 1.90828 1.44959 0.69461 -0.20234 -1.05793 -1.69729 -1.98974 -1.87550 -1.37793 -0.59873 0.30286 1.14254 1.74869 1.99743 1.83792 1.30274 0.50131 -0.40260 -1.22421 -1.79561 -2.00000 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.74869 1.05793 0.10130 -0.88079 -1.64153 -1.98974 -1.83792 -1.22421 -0.30286 0.69461 1.51752 1.95906 1.90828 1.37793 0.50131 -0.50131 -1.37793 -1.90828 -1.95906 -1.51752 -0.69461 0.30286 1.22421 1.83792 1.98974 1.64153 0.88079 -0.10130 -1.05793 -1.74869 -2.00000 -1.74869 -1.05793 -0.10130 0.88079 1.64153 1.98974 1.83792 1.22421 0.30286 -0.69461 -1.51752 -1.95906 -1.90828 -1.37793 -0.50131 0.50131 1.37793 1.90828 1.95906 1.51752 0.69461 -0.30286 -1.22421 -1.83792 -1.98974 -1.64153 -0.88079 0.10130 1.05793 1.74869 2.00000 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.69729 0.88079 -0.20234 -1.22421 -1.87550 -1.95906 -1.44959 -0.50131 0.59873 1.51752 1.97694 1.83792 1.14254 0.10130 -0.97060 -1.74869 -1.99743 -1.64153 -0.78871 0.30286 1.30274 1.90828 1.93615 1.37793 0.40260 -0.69461 -1.58155 -1.98974 -1.79561 -1.05793 0.00000 1.05793 1.79561 1.98974 1.58155 0.69461 -0.40260 -1.37793 -1.93615 -1.90828 -1.30274 -0.30286 0.78871 1.64153 1.99743 1.74869 0.97060 -0.10130 -1.14254 -1.83792 -1.97694 -1.51752 -0.59873 0.50131 1.44959 1.95906 1.87550 1.22421 0.20234 -0.88079 -1.69729 -2.00000 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.64153 0.69461 -0.50131 -1.51752 -1.98974 -1.74869 -0.88079 0.30286 1.37793 1.95906 1.83792 1.05793 -0.10130 -1.22421 -1.90828 -1.90828 -1.22421 -0.10130 1.05793 1.83792 1.95906 1.37793 0.30286 -0.88079 -1.74869 -1.98974 -1.51752 -0.50131 0.69461 1.64153 2.00000 1.64153 0.69461 -0.50131 -1.51752 -1.98974 -1.74869 -0.88079 0.30286 1.37793 1.95906 1.83792 1.05793 -0.10130 -1.22421 -1.90828 -1.90828 -1.22421 -0.10130 1.05793 1.83792 1.95906 1.37793 0.30286 -0.88079 -1.74869 -1.98974 -1.51752 -0.50131 0.69461 1.64153 2.00000 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.58155 0.50131 -0.78871 -1.74869 -1.97694 -1.37793 -0.20234 1.05793 1.87550 1.90828 1.14254 -0.10130 -1.30274 -1.95906 -1.79561 -0.88079 0.40260 1.51752 1.99743 1.64153 0.59873 -0.69461 -1.69729 -1.98974 -1.44959 -0.30286 0.97060 1.83792 1.93615 1.22421 0.00000 -1.22421 -1.93615 -1.83792 -0.97060 0.30286 1.44959 1.98974 1.69729 0.69461 -0.59873 -1.64153 -1.99743 -1.51752 -0.40260 0.88079 1.79561 1.95906 1.30274 0.10130 -1.14254 -1.90828 -1.87550 -1.05793 0.20234 1.37793 1.97694 1.74869 0.78871 -0.50131 -1.58155 -2.00000 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.51752 0.30286 -1.05793 -1.90828 -1.83792 -0.88079 0.50131 1.64153 1.98974 1.37793 0.10130 -1.22421 -1.95906 -1.74869 -0.69461 0.69461 1.74869 1.95906 1.22421 -0.10130 -1.37793 -1.98974 -1.64153 -0.50131 0.88079 1.83792 1.90828 1.05793 -0.30286 -1.51752 -2.00000 -1.51752 -0.30286 1.05793 1.90828 1.83792 0.88079 -0.50131 -1.64153 -1.98974 -1.37793 -0.10130 1.22421 1.95906 1.74869 0.69461 -0.69461 -1.74869 -1.95906 -1.22421 0.10130 1.37793 1.98974 1.64153 0.50131 -0.88079 -1.83792 -1.90828 -1.05793 0.30286 1.51752 2.00000 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.44959 0.10130 -1.30274 -1.98974 -1.58155 -0.30286 1.14254 1.95906 1.69729 0.50131 -0.97060 -1.90828 -1.79561 -0.69461 0.78871 1.83792 1.87550 0.88079 -0.59873 -1.74869 -1.93615 -1.05793 0.40260 1.64153 1.97694 1.22421 -0.20234 -1.51752 -1.99743 -1.37793 0.00000 1.37793 1.99743 1.51752 0.20234 -1.22421 -1.97694 -1.64153 -0.40260 1.05793 1.93615 1.74869 0.59873 -0.88079 -1.87550 -1.83792 -0.78871 0.69461 1.79561 1.90828 0.97060 -0.50131 -1.69729 -1.95906 -1.14254 0.30286 1.58155 1.98974 1.30274 -0.10130 -1.44959 -2.00000 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.37793 -0.10130 -1.51752 -1.98974 -1.22421 0.30286 1.64153 1.95906 1.05793 -0.50131 -1.74869 -1.90828 -0.88079 0.69461 1.83792 1.83792 0.69461 -0.88079 -1.90828 -1.74869 -0.50131 1.05793 1.95906 1.64153 0.30286 -1.22421 -1.98974 -1.51752 -0.10130 1.37793 2.00000 1.37793 -0.10130 -1.51752 -1.98974 -1.22421 0.30286 1.64153 1.95906 1.05793 -0.50131 -1.74869 -1.90828 -0.88079 0.69461 1.83792 1.83792 0.69461 -0.88079 -1.90828 -1.74869 -0.50131 1.05793 1.95906 1.64153 0.30286 -1.22421 -1.98974 -1.51752 -0.10130 1.37793 2.00000 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 1.30274 -0.30286 -1.69729 -1.90828 -0.78871 0.88079 1.93615 1.64153 0.20234 -1.37793 -1.99743 -1.22421 0.40260 1.74869 1.87550 0.69461 -0.97060 -1.95906 -1.58155 -0.10130 1.44959 1.98974 1.14254 -0.50131 -1.79561 -1.83792 -0.59873 1.05793 1.97694 1.51752 0.00000 -1.51752 -1.97694 -1.05793 0.59873 1.83792 1.79561 0.50131 -1.14254 -1.98974 -1.44959 0.10130 1.58155 1.95906 0.97060 -0.69461 -1.87550 -1.74869 -0.40260 1.22421 1.99743 1.37793 -0.20234 -1.64153 -1.93615 -0.88079 0.78871 1.90828 1.69729 0.30286 -1.30274 -2.00000 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 1.22421 -0.50131 -1.83792 -1.74869 -0.30286 1.37793 1.98974 1.05793 -0.69461 -1.90828 -1.64153 -0.10130 1.51752 1.95906 0.88079 -0.88079 -1.95906 -1.51752 0.10130 1.64153 1.90828 0.69461 -1.05793 -1.98974 -1.37793 0.30286 1.74869 1.83792 0.50131 -1.22421 -2.00000 -1.22421 0.50131 1.83792 1.74869 0.30286 -1.37793 -1.98974 -1.05793 0.69461 1.90828 1.64153 0.10130 -1.51752 -1.95906 -0.88079 0.88079 1.95906 1.51752 -0.10130 -1.64153 -1.90828 -0.69461 1.05793 1.98974 1.37793 -0.30286 -1.74869 -1.83792 -0.50131 1.22421 2.00000 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 1.14254 -0.69461 -1.93615 -1.51752 0.20234 1.74869 1.79561 0.30286 -1.44959 -1.95906 -0.78871 1.05793 1.99743 1.22421 -0.59873 -1.90828 -1.58155 0.10130 1.69729 1.83792 0.40260 -1.37793 -1.97694 -0.88079 0.97060 1.98974 1.30274 -0.50131 -1.87550 -1.64153 0.00000 1.64153 1.87550 0.50131 -1.30274 -1.98974 -0.97060 0.88079 1.97694 1.37793 -0.40260 -1.83792 -1.69729 -0.10130 1.58155 1.90828 0.59873 -1.22421 -1.99743 -1.05793 0.78871 1.95906 1.44959 -0.30286 -1.79561 -1.74869 -0.20234 1.51752 1.93615 0.69461 -1.14254 -2.00000 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 1.05793 -0.88079 -1.98974 -1.22421 0.69461 1.95906 1.37793 -0.50131 -1.90828 -1.51752 0.30286 1.83792 1.64153 -0.10130 -1.74869 -1.74869 -0.10130 1.64153 1.83792 0.30286 -1.51752 -1.90828 -0.50131 1.37793 1.95906 0.69461 -1.22421 -1.98974 -0.88079 1.05793 2.00000 1.05793 -0.88079 -1.98974 -1.22421 0.69461 1.95906 1.37793 -0.50131 -1.90828 -1.51752 0.30286 1.83792 1.64153 -0.10130 -1.74869 -1.74869 -0.10130 1.64153 1.83792 0.30286 -1.51752 -1.90828 -0.50131 1.37793 1.95906 0.69461 -1.22421 -1.98974 -0.88079 1.05793 2.00000 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.97060 -1.05793 -1.99743 -0.88079 1.14254 1.98974 0.78871 -1.22421 -1.97694 -0.69461 1.30274 1.95906 0.59873 -1.37793 -1.93615 -0.50131 1.44959 1.90828 0.40260 -1.51752 -1.87550 -0.30286 1.58155 1.83792 0.20234 -1.64153 -1.79561 -0.10130 1.69729 1.74869 0.00000 -1.74869 -1.69729 0.10130 1.79561 1.64153 -0.20234 -1.83792 -1.58155 0.30286 1.87550 1.51752 -0.40260 -1.90828 -1.44959 0.50131 1.93615 1.37793 -0.59873 -1.95906 -1.30274 0.69461 1.97694 1.22421 -0.78871 -1.98974 -1.14254 0.88079 1.99743 1.05793 -0.97060 -2.00000 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.88079 -1.22421 -1.95906 -0.50131 1.51752 1.83792 0.10130 -1.74869 -1.64153 0.30286 1.90828 1.37793 -0.69461 -1.98974 -1.05793 1.05793 1.98974 0.69461 -1.37793 -1.90828 -0.30286 1.64153 1.74869 -0.10130 -1.83792 -1.51752 0.50131 1.95906 1.22421 -0.88079 -2.00000 -0.88079 1.22421 1.95906 0.50131 -1.51752 -1.83792 -0.10130 1.74869 1.64153 -0.30286 -1.90828 -1.37793 0.69461 1.98974 1.05793 -1.05793 -1.98974 -0.69461 1.37793 1.90828 0.30286 -1.64153 -1.74869 0.10130 1.83792 1.51752 -0.50131 -1.95906 -1.22421 0.88079 2.00000 ... ... ..... ....... ......... ........... ............. 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E24 * 2.00000 0.69461 -1.51752 -1.74869 0.30286 1.95906 1.05793 -1.22421 -1.90828 -0.10130 1.83792 1.37793 -0.88079 -1.98974 -0.50131 1.64153 1.64153 -0.50131 -1.98974 -0.88079 1.37793 1.83792 -0.10130 -1.90828 -1.22421 1.05793 1.95906 0.30286 -1.74869 -1.51752 0.69461 2.00000 0.69461 -1.51752 -1.74869 0.30286 1.95906 1.05793 -1.22421 -1.90828 -0.10130 1.83792 1.37793 -0.88079 -1.98974 -0.50131 1.64153 1.64153 -0.50131 -1.98974 -0.88079 1.37793 1.83792 -0.10130 -1.90828 -1.22421 1.05793 1.95906 0.30286 -1.74869 -1.51752 0.69461 2.00000 ... ... ..... ....... ......... ........... ............. 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E47 * 2.00000 -1.44959 0.10130 1.30274 -1.98974 1.58155 -0.30286 -1.14254 1.95906 -1.69729 0.50131 0.97060 -1.90828 1.79561 -0.69461 -0.78871 1.83792 -1.87550 0.88079 0.59873 -1.74869 1.93615 -1.05793 -0.40260 1.64153 -1.97694 1.22421 0.20234 -1.51752 1.99743 -1.37793 0.00000 1.37793 -1.99743 1.51752 -0.20234 -1.22421 1.97694 -1.64153 0.40260 1.05793 -1.93615 1.74869 -0.59873 -0.88079 1.87550 -1.83792 0.78871 0.69461 -1.79561 1.90828 -0.97060 -0.50131 1.69729 -1.95906 1.14254 0.30286 -1.58155 1.98974 -1.30274 -0.10130 1.44959 -2.00000 ... ... ..... ....... ......... ........... ............. E48 * 2.00000 -1.51752 0.30286 1.05793 -1.90828 1.83792 -0.88079 -0.50131 1.64153 -1.98974 1.37793 -0.10130 -1.22421 1.95906 -1.74869 0.69461 0.69461 -1.74869 1.95906 -1.22421 -0.10130 1.37793 -1.98974 1.64153 -0.50131 -0.88079 1.83792 -1.90828 1.05793 0.30286 -1.51752 2.00000 -1.51752 0.30286 1.05793 -1.90828 1.83792 -0.88079 -0.50131 1.64153 -1.98974 1.37793 -0.10130 -1.22421 1.95906 -1.74869 0.69461 0.69461 -1.74869 1.95906 -1.22421 -0.10130 1.37793 -1.98974 1.64153 -0.50131 -0.88079 1.83792 -1.90828 1.05793 0.30286 -1.51752 2.00000 ... ... ..... ....... ......... ........... ............. E49 * 2.00000 -1.58155 0.50131 0.78871 -1.74869 1.97694 -1.37793 0.20234 1.05793 -1.87550 1.90828 -1.14254 -0.10130 1.30274 -1.95906 1.79561 -0.88079 -0.40260 1.51752 -1.99743 1.64153 -0.59873 -0.69461 1.69729 -1.98974 1.44959 -0.30286 -0.97060 1.83792 -1.93615 1.22421 0.00000 -1.22421 1.93615 -1.83792 0.97060 0.30286 -1.44959 1.98974 -1.69729 0.69461 0.59873 -1.64153 1.99743 -1.51752 0.40260 0.88079 -1.79561 1.95906 -1.30274 0.10130 1.14254 -1.90828 1.87550 -1.05793 -0.20234 1.37793 -1.97694 1.74869 -0.78871 -0.50131 1.58155 -2.00000 ... ... ..... ....... ......... ........... ............. E50 * 2.00000 -1.64153 0.69461 0.50131 -1.51752 1.98974 -1.74869 0.88079 0.30286 -1.37793 1.95906 -1.83792 1.05793 0.10130 -1.22421 1.90828 -1.90828 1.22421 -0.10130 -1.05793 1.83792 -1.95906 1.37793 -0.30286 -0.88079 1.74869 -1.98974 1.51752 -0.50131 -0.69461 1.64153 -2.00000 1.64153 -0.69461 -0.50131 1.51752 -1.98974 1.74869 -0.88079 -0.30286 1.37793 -1.95906 1.83792 -1.05793 -0.10130 1.22421 -1.90828 1.90828 -1.22421 0.10130 1.05793 -1.83792 1.95906 -1.37793 0.30286 0.88079 -1.74869 1.98974 -1.51752 0.50131 0.69461 -1.64153 2.00000 ... ... ..... ....... ......... ........... ............. E51 * 2.00000 -1.69729 0.88079 0.20234 -1.22421 1.87550 -1.95906 1.44959 -0.50131 -0.59873 1.51752 -1.97694 1.83792 -1.14254 0.10130 0.97060 -1.74869 1.99743 -1.64153 0.78871 0.30286 -1.30274 1.90828 -1.93615 1.37793 -0.40260 -0.69461 1.58155 -1.98974 1.79561 -1.05793 0.00000 1.05793 -1.79561 1.98974 -1.58155 0.69461 0.40260 -1.37793 1.93615 -1.90828 1.30274 -0.30286 -0.78871 1.64153 -1.99743 1.74869 -0.97060 -0.10130 1.14254 -1.83792 1.97694 -1.51752 0.59873 0.50131 -1.44959 1.95906 -1.87550 1.22421 -0.20234 -0.88079 1.69729 -2.00000 ... ... ..... ....... ......... ........... ............. E52 * 2.00000 -1.74869 1.05793 -0.10130 -0.88079 1.64153 -1.98974 1.83792 -1.22421 0.30286 0.69461 -1.51752 1.95906 -1.90828 1.37793 -0.50131 -0.50131 1.37793 -1.90828 1.95906 -1.51752 0.69461 0.30286 -1.22421 1.83792 -1.98974 1.64153 -0.88079 -0.10130 1.05793 -1.74869 2.00000 -1.74869 1.05793 -0.10130 -0.88079 1.64153 -1.98974 1.83792 -1.22421 0.30286 0.69461 -1.51752 1.95906 -1.90828 1.37793 -0.50131 -0.50131 1.37793 -1.90828 1.95906 -1.51752 0.69461 0.30286 -1.22421 1.83792 -1.98974 1.64153 -0.88079 -0.10130 1.05793 -1.74869 2.00000 ... ... ..... ....... ......... ........... ............. E53 * 2.00000 -1.79561 1.22421 -0.40260 -0.50131 1.30274 -1.83792 1.99743 -1.74869 1.14254 -0.30286 -0.59873 1.37793 -1.87550 1.98974 -1.69729 1.05793 -0.20234 -0.69461 1.44959 -1.90828 1.97694 -1.64153 0.97060 -0.10130 -0.78871 1.51752 -1.93615 1.95906 -1.58155 0.88079 0.00000 -0.88079 1.58155 -1.95906 1.93615 -1.51752 0.78871 0.10130 -0.97060 1.64153 -1.97694 1.90828 -1.44959 0.69461 0.20234 -1.05793 1.69729 -1.98974 1.87550 -1.37793 0.59873 0.30286 -1.14254 1.74869 -1.99743 1.83792 -1.30274 0.50131 0.40260 -1.22421 1.79561 -2.00000 ... ... ..... ....... ......... ........... ............. E54 * 2.00000 -1.83792 1.37793 -0.69461 -0.10130 0.88079 -1.51752 1.90828 -1.98974 1.74869 -1.22421 0.50131 0.30286 -1.05793 1.64153 -1.95906 1.95906 -1.64153 1.05793 -0.30286 -0.50131 1.22421 -1.74869 1.98974 -1.90828 1.51752 -0.88079 0.10130 0.69461 -1.37793 1.83792 -2.00000 1.83792 -1.37793 0.69461 0.10130 -0.88079 1.51752 -1.90828 1.98974 -1.74869 1.22421 -0.50131 -0.30286 1.05793 -1.64153 1.95906 -1.95906 1.64153 -1.05793 0.30286 0.50131 -1.22421 1.74869 -1.98974 1.90828 -1.51752 0.88079 -0.10130 -0.69461 1.37793 -1.83792 2.00000 ... ... ..... ....... ......... ........... ............. E55 * 2.00000 -1.87550 1.51752 -0.97060 0.30286 0.40260 -1.05793 1.58155 -1.90828 1.99743 -1.83792 1.44959 -0.88079 0.20234 0.50131 -1.14254 1.64153 -1.93615 1.98974 -1.79561 1.37793 -0.78871 0.10130 0.59873 -1.22421 1.69729 -1.95906 1.97694 -1.74869 1.30274 -0.69461 0.00000 0.69461 -1.30274 1.74869 -1.97694 1.95906 -1.69729 1.22421 -0.59873 -0.10130 0.78871 -1.37793 1.79561 -1.98974 1.93615 -1.64153 1.14254 -0.50131 -0.20234 0.88079 -1.44959 1.83792 -1.99743 1.90828 -1.58155 1.05793 -0.40260 -0.30286 0.97060 -1.51752 1.87550 -2.00000 ... ... ..... ....... ......... ........... ............. E56 * 2.00000 -1.90828 1.64153 -1.22421 0.69461 -0.10130 -0.50131 1.05793 -1.51752 1.83792 -1.98974 1.95906 -1.74869 1.37793 -0.88079 0.30286 0.30286 -0.88079 1.37793 -1.74869 1.95906 -1.98974 1.83792 -1.51752 1.05793 -0.50131 -0.10130 0.69461 -1.22421 1.64153 -1.90828 2.00000 -1.90828 1.64153 -1.22421 0.69461 -0.10130 -0.50131 1.05793 -1.51752 1.83792 -1.98974 1.95906 -1.74869 1.37793 -0.88079 0.30286 0.30286 -0.88079 1.37793 -1.74869 1.95906 -1.98974 1.83792 -1.51752 1.05793 -0.50131 -0.10130 0.69461 -1.22421 1.64153 -1.90828 2.00000 ... ... ..... ....... ......... ........... ............. E57 * 2.00000 -1.93615 1.74869 -1.44959 1.05793 -0.59873 0.10130 0.40260 -0.88079 1.30274 -1.64153 1.87550 -1.98974 1.97694 -1.83792 1.58155 -1.22421 0.78871 -0.30286 -0.20234 0.69461 -1.14254 1.51752 -1.79561 1.95906 -1.99743 1.90828 -1.69729 1.37793 -0.97060 0.50131 0.00000 -0.50131 0.97060 -1.37793 1.69729 -1.90828 1.99743 -1.95906 1.79561 -1.51752 1.14254 -0.69461 0.20234 0.30286 -0.78871 1.22421 -1.58155 1.83792 -1.97694 1.98974 -1.87550 1.64153 -1.30274 0.88079 -0.40260 -0.10130 0.59873 -1.05793 1.44959 -1.74869 1.93615 -2.00000 ... ... ..... ....... ......... ........... ..TT......... E58 * 2.00000 -1.95906 1.83792 -1.64153 1.37793 -1.05793 0.69461 -0.30286 -0.10130 0.50131 -0.88079 1.22421 -1.51752 1.74869 -1.90828 1.98974 -1.98974 1.90828 -1.74869 1.51752 -1.22421 0.88079 -0.50131 0.10130 0.30286 -0.69461 1.05793 -1.37793 1.64153 -1.83792 1.95906 -2.00000 1.95906 -1.83792 1.64153 -1.37793 1.05793 -0.69461 0.30286 0.10130 -0.50131 0.88079 -1.22421 1.51752 -1.74869 1.90828 -1.98974 1.98974 -1.90828 1.74869 -1.51752 1.22421 -0.88079 0.50131 -0.10130 -0.30286 0.69461 -1.05793 1.37793 -1.64153 1.83792 -1.95906 2.00000 ... ... ..... ....... ......... ..TT....... ............. E59 * 2.00000 -1.97694 1.90828 -1.79561 1.64153 -1.44959 1.22421 -0.97060 0.69461 -0.40260 0.10130 0.20234 -0.50131 0.78871 -1.05793 1.30274 -1.51752 1.69729 -1.83792 1.93615 -1.98974 1.99743 -1.95906 1.87550 -1.74869 1.58155 -1.37793 1.14254 -0.88079 0.59873 -0.30286 0.00000 0.30286 -0.59873 0.88079 -1.14254 1.37793 -1.58155 1.74869 -1.87550 1.95906 -1.99743 1.98974 -1.93615 1.83792 -1.69729 1.51752 -1.30274 1.05793 -0.78871 0.50131 -0.20234 -0.10130 0.40260 -0.69461 0.97060 -1.22421 1.44959 -1.64153 1.79561 -1.90828 1.97694 -2.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E60 * 2.00000 -1.98974 1.95906 -1.90828 1.83792 -1.74869 1.64153 -1.51752 1.37793 -1.22421 1.05793 -0.88079 0.69461 -0.50131 0.30286 -0.10130 -0.10130 0.30286 -0.50131 0.69461 -0.88079 1.05793 -1.22421 1.37793 -1.51752 1.64153 -1.74869 1.83792 -1.90828 1.95906 -1.98974 2.00000 -1.98974 1.95906 -1.90828 1.83792 -1.74869 1.64153 -1.51752 1.37793 -1.22421 1.05793 -0.88079 0.69461 -0.50131 0.30286 -0.10130 -0.10130 0.30286 -0.50131 0.69461 -0.88079 1.05793 -1.22421 1.37793 -1.51752 1.64153 -1.74869 1.83792 -1.90828 1.95906 -1.98974 2.00000 ... ... ..... ..TT... ......... ......TT... ............. E61 * 2.00000 -1.99743 1.98974 -1.97694 1.95906 -1.93615 1.90828 -1.87550 1.83792 -1.79561 1.74869 -1.69729 1.64153 -1.58155 1.51752 -1.44959 1.37793 -1.30274 1.22421 -1.14254 1.05793 -0.97060 0.88079 -0.78871 0.69461 -0.59873 0.50131 -0.40260 0.30286 -0.20234 0.10130 0.00000 -0.10130 0.20234 -0.30286 0.40260 -0.50131 0.59873 -0.69461 0.78871 -0.88079 0.97060 -1.05793 1.14254 -1.22421 1.30274 -1.37793 1.44959 -1.51752 1.58155 -1.64153 1.69729 -1.74869 1.79561 -1.83792 1.87550 -1.90828 1.93615 -1.95906 1.97694 -1.98974 1.99743 -2.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.997433014342 = 2*cos(2*π/124) = 2*cos(π/62) 1.989738646784 = 2*cos(4*π/124) = 2*cos(π/31) 1.976936648656 = 2*cos(6*π/124) = 2*cos(3*π/62) 1.959059882505 = 2*cos(8*π/124) = 2*cos(2*π/31) 1.936154237732 = 2*cos(10*π/124) = 2*cos(5*π/62) 1.908278512800 = 2*cos(12*π/124) = 2*cos(3*π/31) 1.875504264294 = 2*cos(14*π/124) = 2*cos(7*π/62) 1.837915623240 = 2*cos(16*π/124) = 2*cos(4*π/31) 1.795609079141 = 2*cos(18*π/124) = 2*cos(9*π/62) 1.748693232289 = 2*cos(20*π/124) = 2*cos(5*π/31) 1.697288514989 = 2*cos(22*π/124) = 2*cos(11*π/62) 1.641526882415 = 2*cos(24*π/124) = 2*cos(6*π/31) 1.581551473875 = 2*cos(26*π/124) = 2*cos(13*π/62) 1.517516245386 = 2*cos(28*π/124) = 2*cos(7*π/31) 1.449585574458 = 2*cos(30*π/124) = 2*cos(15*π/62) 1.377933838151 = 2*cos(32*π/124) = 2*cos(8*π/31) 1.302744965444 = 2*cos(34*π/124) = 2*cos(17*π/62) 1.224211965095 = 2*cos(36*π/124) = 2*cos(9*π/31) 1.142536430189 = 2*cos(38*π/124) = 2*cos(19*π/62) 1.057928020654 = 2*cos(40*π/124) = 2*cos(10*π/31) 0.970603925062 = 2*cos(42*π/124) = 2*cos(21*π/62) 0.880788303115 = 2*cos(44*π/124) = 2*cos(11*π/31) 0.788711710226 = 2*cos(46*π/124) = 2*cos(23*π/62) 0.694610505689 = 2*cos(48*π/124) = 2*cos(12*π/31) 0.598726245947 = 2*cos(50*π/124) = 2*cos(25*π/62) 0.501305064517 = 2*cos(52*π/124) = 2*cos(13*π/31) 0.402597040177 = 2*cos(54*π/124) = 2*cos(27*π/62) 0.302855555009 = 2*cos(56*π/124) = 2*cos(14*π/31) 0.202336643975 = 2*cos(58*π/124) = 2*cos(29*π/62) 0.101298337677 = 2*cos(60*π/124) = 2*cos(15*π/31) Symmetry of Rotations and Cartesian products A R+d+g+i Rz, z2, z4, z6 B p+f+h z, z3, z5 E1 p+f+h {x, y}, {xz2, yz2}, {xz4, yz4} E2 d+g+i {x2–y2, xy}, {z2(x2–y2), xyz2}, {z4(x2–y2), xyz4} E3 f+h {x(x2–3y2), y(3x2–y2)}, {xz2(x2–3y2), yz2(3x2–y2)} E4 g+i {(x2–y2)2–2x2y2, xy(x2–y2)}, {z2((x2–y2)2–4x2y2), xyz2(x2–y2)} E5 h {x(x2–(5+2√5)y2)(x2–(5–2√5)y2), y(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)} E6 i {x2(x2–3y2)2–y2(3x2–y2)2, xy(x2–3y2)(3x2–y2)} E57 i {xz(x2–(5+2√5)y2)(x2–(5–2√5)y2), yz(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)} E58 h {z((x2–y2)2–4x2y2), xyz(x2–y2)} E59 g+i {xz(x2–3y2), yz(3x2–y2)}, {xz3(x2–3y2), yz3(3x2–y2)} E60 f+h {z(x2–y2), xyz}, {z3(x2–y2), xyz3} E61 R+d+g+i {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} Notes: α The order of the S124 point group is 124, and the order of the principal axis is 124. β The S124 point group could also be named C124i, because the S124 axis is identical to a roto-inversion axis of order 124. γ This is an Abelian point group (the commutative law holds between all symmetry operations). The S124 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. δ Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 122 cases have been combined into 61 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 61 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ε The 61 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. ζ 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 less than half the order of the principal axis (and often much less). For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.
| S122 | ||
| C124 C124v C124h D124 D124h D124d | S124 | |
| S126 |
This Character Table for the S124 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.