C117 E 2 C117 2 C117^2 2 C39 2 C117^4 2 C117^5 2 C39^2 2 C117^7 2 C117^8 2 C13 2 C117^10 2 C117^11 2 C39^4 2 C9 2 C117^14 2 C39^5 2 C117^16 2 C117^17 2 C13^2 2 C117^19 2 C117^20 2 C39^7 2 C117^22 2 C117^23 2 C39^8 2 C117^25 2 C9^2 2 C13^3 2 C117^28 2 C117^29 2 C39^10 2 C117^31 2 C117^32 2 C39^11 2 C117^34 2 C117^35 2 C13^4 2 C117^37 2 C117^38 2 C3 2 C117^40 2 C117^41 2 C39^14 2 C117^43 2 C117^44 2 C13^5 2 C117^46 2 C117^47 2 C39^16 2 C117^49 2 C117^50 2 C39^17 2 C9^4 2 C117^53 2 C13^6 2 C117^55 2 C117^56 2 C39^19 2 C117^58 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99712 1.98848 1.97410 1.95403 1.92833 1.89707 1.86034 1.81825 1.77091 1.71847 1.66107 1.59889 1.53209 1.46087 1.38545 1.30603 1.22284 1.13613 1.04614 0.95314 0.85739 0.75916 0.65875 0.55643 0.45252 0.34730 0.24107 0.13416 0.02685 -0.08053 -0.18768 -0.29429 -0.40005 -0.50466 -0.60781 -0.70921 -0.80856 -0.90559 -1.00000 -1.09153 -1.17991 -1.26489 -1.34622 -1.42367 -1.49702 -1.56605 -1.63057 -1.69038 -1.74532 -1.79523 -1.83996 -1.87939 -1.91339 -1.94188 -1.96478 -1.98200 -1.99351 -1.99928 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98848 1.95403 1.89707 1.81825 1.71847 1.59889 1.46087 1.30603 1.13613 0.95314 0.75916 0.55643 0.34730 0.13416 -0.08053 -0.29429 -0.50466 -0.70921 -0.90559 -1.09153 -1.26489 -1.42367 -1.56605 -1.69038 -1.79523 -1.87939 -1.94188 -1.98200 -1.99928 -1.99351 -1.96478 -1.91339 -1.83996 -1.74532 -1.63057 -1.49702 -1.34622 -1.17991 -1.00000 -0.80856 -0.60781 -0.40005 -0.18768 0.02685 0.24107 0.45252 0.65875 0.85739 1.04614 1.22284 1.38545 1.53209 1.66107 1.77091 1.86034 1.92833 1.97410 1.99712 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.97410 1.89707 1.77091 1.59889 1.38545 1.13613 0.85739 0.55643 0.24107 -0.08053 -0.40005 -0.70921 -1.00000 -1.26489 -1.49702 -1.69038 -1.83996 -1.94188 -1.99351 -1.99351 -1.94188 -1.83996 -1.69038 -1.49702 -1.26489 -1.00000 -0.70921 -0.40005 -0.08053 0.24107 0.55643 0.85739 1.13613 1.38545 1.59889 1.77091 1.89707 1.97410 2.00000 1.97410 1.89707 1.77091 1.59889 1.38545 1.13613 0.85739 0.55643 0.24107 -0.08053 -0.40005 -0.70921 -1.00000 -1.26489 -1.49702 -1.69038 -1.83996 -1.94188 -1.99351 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.95403 1.81825 1.59889 1.30603 0.95314 0.55643 0.13416 -0.29429 -0.70921 -1.09153 -1.42367 -1.69038 -1.87939 -1.98200 -1.99351 -1.91339 -1.74532 -1.49702 -1.17991 -0.80856 -0.40005 0.02685 0.45252 0.85739 1.22284 1.53209 1.77091 1.92833 1.99712 1.97410 1.86034 1.66107 1.38545 1.04614 0.65875 0.24107 -0.18768 -0.60781 -1.00000 -1.34622 -1.63057 -1.83996 -1.96478 -1.99928 -1.94188 -1.79523 -1.56605 -1.26489 -0.90559 -0.50466 -0.08053 0.34730 0.75916 1.13613 1.46087 1.71847 1.89707 1.98848 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.92833 1.71847 1.38545 0.95314 0.45252 -0.08053 -0.60781 -1.09153 -1.49702 -1.79523 -1.96478 -1.99351 -1.87939 -1.63057 -1.26489 -0.80856 -0.29429 0.24107 0.75916 1.22284 1.59889 1.86034 1.98848 1.97410 1.81825 1.53209 1.13613 0.65875 0.13416 -0.40005 -0.90559 -1.34622 -1.69038 -1.91339 -1.99928 -1.94188 -1.74532 -1.42367 -1.00000 -0.50466 0.02685 0.55643 1.04614 1.46087 1.77091 1.95403 1.99712 1.89707 1.66107 1.30603 0.85739 0.34730 -0.18768 -0.70921 -1.17991 -1.56605 -1.83996 -1.98200 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.89707 1.59889 1.13613 0.55643 -0.08053 -0.70921 -1.26489 -1.69038 -1.94188 -1.99351 -1.83996 -1.49702 -1.00000 -0.40005 0.24107 0.85739 1.38545 1.77091 1.97410 1.97410 1.77091 1.38545 0.85739 0.24107 -0.40005 -1.00000 -1.49702 -1.83996 -1.99351 -1.94188 -1.69038 -1.26489 -0.70921 -0.08053 0.55643 1.13613 1.59889 1.89707 2.00000 1.89707 1.59889 1.13613 0.55643 -0.08053 -0.70921 -1.26489 -1.69038 -1.94188 -1.99351 -1.83996 -1.49702 -1.00000 -0.40005 0.24107 0.85739 1.38545 1.77091 1.97410 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.86034 1.46087 0.85739 0.13416 -0.60781 -1.26489 -1.74532 -1.98200 -1.94188 -1.63057 -1.09153 -0.40005 0.34730 1.04614 1.59889 1.92833 1.98848 1.77091 1.30603 0.65875 -0.08053 -0.80856 -1.42367 -1.83996 -1.99928 -1.87939 -1.49702 -0.90559 -0.18768 0.55643 1.22284 1.71847 1.97410 1.95403 1.66107 1.13613 0.45252 -0.29429 -1.00000 -1.56605 -1.91339 -1.99351 -1.79523 -1.34622 -0.70921 0.02685 0.75916 1.38545 1.81825 1.99712 1.89707 1.53209 0.95314 0.24107 -0.50466 -1.17991 -1.69038 -1.96478 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.81825 1.30603 0.55643 -0.29429 -1.09153 -1.69038 -1.98200 -1.91339 -1.49702 -0.80856 0.02685 0.85739 1.53209 1.92833 1.97410 1.66107 1.04614 0.24107 -0.60781 -1.34622 -1.83996 -1.99928 -1.79523 -1.26489 -0.50466 0.34730 1.13613 1.71847 1.98848 1.89707 1.46087 0.75916 -0.08053 -0.90559 -1.56605 -1.94188 -1.96478 -1.63057 -1.00000 -0.18768 0.65875 1.38545 1.86034 1.99712 1.77091 1.22284 0.45252 -0.40005 -1.17991 -1.74532 -1.99351 -1.87939 -1.42367 -0.70921 0.13416 0.95314 1.59889 1.95403 ... ... ..... ....... ......... ........... ............. E9 * 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 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.71847 0.95314 -0.08053 -1.09153 -1.79523 -1.99351 -1.63057 -0.80856 0.24107 1.22284 1.86034 1.97410 1.53209 0.65875 -0.40005 -1.34622 -1.91339 -1.94188 -1.42367 -0.50466 0.55643 1.46087 1.95403 1.89707 1.30603 0.34730 -0.70921 -1.56605 -1.98200 -1.83996 -1.17991 -0.18768 0.85739 1.66107 1.99712 1.77091 1.04614 0.02685 -1.00000 -1.74532 -1.99928 -1.69038 -0.90559 0.13416 1.13613 1.81825 1.98848 1.59889 0.75916 -0.29429 -1.26489 -1.87939 -1.96478 -1.49702 -0.60781 0.45252 1.38545 1.92833 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.66107 0.75916 -0.40005 -1.42367 -1.96478 -1.83996 -1.09153 0.02685 1.13613 1.86034 1.95403 1.38545 0.34730 -0.80856 -1.69038 -1.99928 -1.63057 -0.70921 0.45252 1.46087 1.97410 1.81825 1.04614 -0.08053 -1.17991 -1.87939 -1.94188 -1.34622 -0.29429 0.85739 1.71847 1.99712 1.59889 0.65875 -0.50466 -1.49702 -1.98200 -1.79523 -1.00000 0.13416 1.22284 1.89707 1.92833 1.30603 0.24107 -0.90559 -1.74532 -1.99351 -1.56605 -0.60781 0.55643 1.53209 1.98848 1.77091 0.95314 -0.18768 -1.26489 -1.91339 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.59889 0.55643 -0.70921 -1.69038 -1.99351 -1.49702 -0.40005 0.85739 1.77091 1.97410 1.38545 0.24107 -1.00000 -1.83996 -1.94188 -1.26489 -0.08053 1.13613 1.89707 1.89707 1.13613 -0.08053 -1.26489 -1.94188 -1.83996 -1.00000 0.24107 1.38545 1.97410 1.77091 0.85739 -0.40005 -1.49702 -1.99351 -1.69038 -0.70921 0.55643 1.59889 2.00000 1.59889 0.55643 -0.70921 -1.69038 -1.99351 -1.49702 -0.40005 0.85739 1.77091 1.97410 1.38545 0.24107 -1.00000 -1.83996 -1.94188 -1.26489 -0.08053 1.13613 1.89707 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.46087 0.13416 -1.26489 -1.98200 -1.63057 -0.40005 1.04614 1.92833 1.77091 0.65875 -0.80856 -1.83996 -1.87939 -0.90559 0.55643 1.71847 1.95403 1.13613 -0.29429 -1.56605 -1.99351 -1.34622 0.02685 1.38545 1.99712 1.53209 0.24107 -1.17991 -1.96478 -1.69038 -0.50466 0.95314 1.89707 1.81825 0.75916 -0.70921 -1.79523 -1.91339 -1.00000 0.45252 1.66107 1.97410 1.22284 -0.18768 -1.49702 -1.99928 -1.42367 -0.08053 1.30603 1.98848 1.59889 0.34730 -1.09153 -1.94188 -1.74532 -0.60781 0.85739 1.86034 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.38545 -0.08053 -1.49702 -1.99351 -1.26489 0.24107 1.59889 1.97410 1.13613 -0.40005 -1.69038 -1.94188 -1.00000 0.55643 1.77091 1.89707 0.85739 -0.70921 -1.83996 -1.83996 -0.70921 0.85739 1.89707 1.77091 0.55643 -1.00000 -1.94188 -1.69038 -0.40005 1.13613 1.97410 1.59889 0.24107 -1.26489 -1.99351 -1.49702 -0.08053 1.38545 2.00000 1.38545 -0.08053 -1.49702 -1.99351 -1.26489 0.24107 1.59889 1.97410 1.13613 -0.40005 -1.69038 -1.94188 -1.00000 0.55643 1.77091 1.89707 0.85739 -0.70921 -1.83996 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.30603 -0.29429 -1.69038 -1.91339 -0.80856 0.85739 1.92833 1.66107 0.24107 -1.34622 -1.99928 -1.26489 0.34730 1.71847 1.89707 0.75916 -0.90559 -1.94188 -1.63057 -0.18768 1.38545 1.99712 1.22284 -0.40005 -1.74532 -1.87939 -0.70921 0.95314 1.95403 1.59889 0.13416 -1.42367 -1.99351 -1.17991 0.45252 1.77091 1.86034 0.65875 -1.00000 -1.96478 -1.56605 -0.08053 1.46087 1.98848 1.13613 -0.50466 -1.79523 -1.83996 -0.60781 1.04614 1.97410 1.53209 0.02685 -1.49702 -1.98200 -1.09153 0.55643 1.81825 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 1.22284 -0.50466 -1.83996 -1.74532 -0.29429 1.38545 1.98848 1.04614 -0.70921 -1.91339 -1.63057 -0.08053 1.53209 1.95403 0.85739 -0.90559 -1.96478 -1.49702 0.13416 1.66107 1.89707 0.65875 -1.09153 -1.99351 -1.34622 0.34730 1.77091 1.81825 0.45252 -1.26489 -1.99928 -1.17991 0.55643 1.86034 1.71847 0.24107 -1.42367 -1.98200 -1.00000 0.75916 1.92833 1.59889 0.02685 -1.56605 -1.94188 -0.80856 0.95314 1.97410 1.46087 -0.18768 -1.69038 -1.87939 -0.60781 1.13613 1.99712 1.30603 -0.40005 -1.79523 ... ... ..... ....... ......... ........... ............. E18 * 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 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 1.04614 -0.90559 -1.99351 -1.17991 0.75916 1.97410 1.30603 -0.60781 -1.94188 -1.42367 0.45252 1.89707 1.53209 -0.29429 -1.83996 -1.63057 0.13416 1.77091 1.71847 0.02685 -1.69038 -1.79523 -0.18768 1.59889 1.86034 0.34730 -1.49702 -1.91339 -0.50466 1.38545 1.95403 0.65875 -1.26489 -1.98200 -0.80856 1.13613 1.99712 0.95314 -1.00000 -1.99928 -1.09153 0.85739 1.98848 1.22284 -0.70921 -1.96478 -1.34622 0.55643 1.92833 1.46087 -0.40005 -1.87939 -1.56605 0.24107 1.81825 1.66107 -0.08053 -1.74532 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.95314 -1.09153 -1.99351 -0.80856 1.22284 1.97410 0.65875 -1.34622 -1.94188 -0.50466 1.46087 1.89707 0.34730 -1.56605 -1.83996 -0.18768 1.66107 1.77091 0.02685 -1.74532 -1.69038 0.13416 1.81825 1.59889 -0.29429 -1.87939 -1.49702 0.45252 1.92833 1.38545 -0.60781 -1.96478 -1.26489 0.75916 1.98848 1.13613 -0.90559 -1.99928 -1.00000 1.04614 1.99712 0.85739 -1.17991 -1.98200 -0.70921 1.30603 1.95403 0.55643 -1.42367 -1.91339 -0.40005 1.53209 1.86034 0.24107 -1.63057 -1.79523 -0.08053 1.71847 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.85739 -1.26489 -1.94188 -0.40005 1.59889 1.77091 -0.08053 -1.83996 -1.49702 0.55643 1.97410 1.13613 -1.00000 -1.99351 -0.70921 1.38545 1.89707 0.24107 -1.69038 -1.69038 0.24107 1.89707 1.38545 -0.70921 -1.99351 -1.00000 1.13613 1.97410 0.55643 -1.49702 -1.83996 -0.08053 1.77091 1.59889 -0.40005 -1.94188 -1.26489 0.85739 2.00000 0.85739 -1.26489 -1.94188 -0.40005 1.59889 1.77091 -0.08053 -1.83996 -1.49702 0.55643 1.97410 1.13613 -1.00000 -1.99351 -0.70921 1.38545 1.89707 0.24107 -1.69038 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.75916 -1.42367 -1.83996 0.02685 1.86034 1.38545 -0.80856 -1.99928 -0.70921 1.46087 1.81825 -0.08053 -1.87939 -1.34622 0.85739 1.99712 0.65875 -1.49702 -1.79523 0.13416 1.89707 1.30603 -0.90559 -1.99351 -0.60781 1.53209 1.77091 -0.18768 -1.91339 -1.26489 0.95314 1.98848 0.55643 -1.56605 -1.74532 0.24107 1.92833 1.22284 -1.00000 -1.98200 -0.50466 1.59889 1.71847 -0.29429 -1.94188 -1.17991 1.04614 1.97410 0.45252 -1.63057 -1.69038 0.34730 1.95403 1.13613 -1.09153 -1.96478 -0.40005 1.66107 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.65875 -1.56605 -1.69038 0.45252 1.98848 0.85739 -1.42367 -1.79523 0.24107 1.95403 1.04614 -1.26489 -1.87939 0.02685 1.89707 1.22284 -1.09153 -1.94188 -0.18768 1.81825 1.38545 -0.90559 -1.98200 -0.40005 1.71847 1.53209 -0.70921 -1.99928 -0.60781 1.59889 1.66107 -0.50466 -1.99351 -0.80856 1.46087 1.77091 -0.29429 -1.96478 -1.00000 1.30603 1.86034 -0.08053 -1.91339 -1.17991 1.13613 1.92833 0.13416 -1.83996 -1.34622 0.95314 1.97410 0.34730 -1.74532 -1.49702 0.75916 1.99712 0.55643 -1.63057 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 0.55643 -1.69038 -1.49702 0.85739 1.97410 0.24107 -1.83996 -1.26489 1.13613 1.89707 -0.08053 -1.94188 -1.00000 1.38545 1.77091 -0.40005 -1.99351 -0.70921 1.59889 1.59889 -0.70921 -1.99351 -0.40005 1.77091 1.38545 -1.00000 -1.94188 -0.08053 1.89707 1.13613 -1.26489 -1.83996 0.24107 1.97410 0.85739 -1.49702 -1.69038 0.55643 2.00000 0.55643 -1.69038 -1.49702 0.85739 1.97410 0.24107 -1.83996 -1.26489 1.13613 1.89707 -0.08053 -1.94188 -1.00000 1.38545 1.77091 -0.40005 -1.99351 -0.70921 1.59889 ... ... ..... ....... ......... ........... ............. 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E26 * 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 ... ... ..... ....... ......... ........... ............. E27 * 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 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 ... ... ..... ....... ......... ........... ............. 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E36 * 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 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 ... ... ..... ....... ......... ........... ............. 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E52 * 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 ... ... ..... ....... ......... ........... ............. E53 * 2.00000 -1.91339 1.66107 -1.26489 0.75916 -0.18768 -0.40005 0.95314 -1.42367 1.77091 -1.96478 1.98848 -1.83996 1.53209 -1.09153 0.55643 0.02685 -0.60781 1.13613 -1.56605 1.86034 -1.99351 1.95403 -1.74532 1.38545 -0.90559 0.34730 0.24107 -0.80856 1.30603 -1.69038 1.92833 -1.99928 1.89707 -1.63057 1.22284 -0.70921 0.13416 0.45252 -1.00000 1.46087 -1.79523 1.97410 -1.98200 1.81825 -1.49702 1.04614 -0.50466 -0.08053 0.65875 -1.17991 1.59889 -1.87939 1.99712 -1.94188 1.71847 -1.34622 0.85739 -0.29429 ... ... ..... ....... ......... ........... ............. E54 * 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 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 ... ... ..... ....... ......... ........... ............. E55 * 2.00000 -1.96478 1.86034 -1.69038 1.46087 -1.17991 0.85739 -0.50466 0.13416 0.24107 -0.60781 0.95314 -1.26489 1.53209 -1.74532 1.89707 -1.98200 1.99712 -1.94188 1.81825 -1.63057 1.38545 -1.09153 0.75916 -0.40005 0.02685 0.34730 -0.70921 1.04614 -1.34622 1.59889 -1.79523 1.92833 -1.99351 1.98848 -1.91339 1.77091 -1.56605 1.30603 -1.00000 0.65875 -0.29429 -0.08053 0.45252 -0.80856 1.13613 -1.42367 1.66107 -1.83996 1.95403 -1.99928 1.97410 -1.87939 1.71847 -1.49702 1.22284 -0.90559 0.55643 -0.18768 ... ... ..... ....... ......... ........... ............. E56 * 2.00000 -1.98200 1.92833 -1.83996 1.71847 -1.56605 1.38545 -1.17991 0.95314 -0.70921 0.45252 -0.18768 -0.08053 0.34730 -0.60781 0.85739 -1.09153 1.30603 -1.49702 1.66107 -1.79523 1.89707 -1.96478 1.99712 -1.99351 1.95403 -1.87939 1.77091 -1.63057 1.46087 -1.26489 1.04614 -0.80856 0.55643 -0.29429 0.02685 0.24107 -0.50466 0.75916 -1.00000 1.22284 -1.42367 1.59889 -1.74532 1.86034 -1.94188 1.98848 -1.99928 1.97410 -1.91339 1.81825 -1.69038 1.53209 -1.34622 1.13613 -0.90559 0.65875 -0.40005 0.13416 ... ... ..... ....... ......... ........... ............. E57 * 2.00000 -1.99351 1.97410 -1.94188 1.89707 -1.83996 1.77091 -1.69038 1.59889 -1.49702 1.38545 -1.26489 1.13613 -1.00000 0.85739 -0.70921 0.55643 -0.40005 0.24107 -0.08053 -0.08053 0.24107 -0.40005 0.55643 -0.70921 0.85739 -1.00000 1.13613 -1.26489 1.38545 -1.49702 1.59889 -1.69038 1.77091 -1.83996 1.89707 -1.94188 1.97410 -1.99351 2.00000 -1.99351 1.97410 -1.94188 1.89707 -1.83996 1.77091 -1.69038 1.59889 -1.49702 1.38545 -1.26489 1.13613 -1.00000 0.85739 -0.70921 0.55643 -0.40005 0.24107 -0.08053 ... ... ..... ....... ......... ........... ............. E58 * 2.00000 -1.99928 1.99712 -1.99351 1.98848 -1.98200 1.97410 -1.96478 1.95403 -1.94188 1.92833 -1.91339 1.89707 -1.87939 1.86034 -1.83996 1.81825 -1.79523 1.77091 -1.74532 1.71847 -1.69038 1.66107 -1.63057 1.59889 -1.56605 1.53209 -1.49702 1.46087 -1.42367 1.38545 -1.34622 1.30603 -1.26489 1.22284 -1.17991 1.13613 -1.09153 1.04614 -1.00000 0.95314 -0.90559 0.85739 -0.80856 0.75916 -0.70921 0.65875 -0.60781 0.55643 -0.50466 0.45252 -0.40005 0.34730 -0.29429 0.24107 -0.18768 0.13416 -0.08053 0.02685 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.997116741128 = 2*cos(2*π/117) 1.988475277695 = 2*cos(4*π/117) 1.974100525276 = 2*cos(6*π/117) = 2*cos(2*π/39) 1.954033930004 = 2*cos(8*π/117) 1.928333349067 = 2*cos(10*π/117) 1.897072883894 = 2*cos(12*π/117) = 2*cos(4*π/39) 1.860342666499 = 2*cos(14*π/117) 1.818248599605 = 2*cos(16*π/117) 1.770912051306 = 2*cos(18*π/117) = 2*cos(2*π/13) 1.718469505124 = 2*cos(20*π/117) 1.661072166496 = 2*cos(22*π/117) 1.598885526807 = 2*cos(24*π/117) = 2*cos(8*π/39) 1.532088886238 = 2*cos(26*π/117) = 2*cos(2*π/9) 1.460874836795 = 2*cos(28*π/117) 1.385448707019 = 2*cos(30*π/117) = 2*cos(10*π/39) 1.306027969967 = 2*cos(32*π/117) 1.222841616184 = 2*cos(34*π/117) 1.136129493462 = 2*cos(36*π/117) = 2*cos(4*π/13) 1.046141615299 = 2*cos(38*π/117) 0.953137440043 = 2*cos(40*π/117) 0.857385122806 = 2*cos(42*π/117) = 2*cos(14*π/39) 0.759160742308 = 2*cos(44*π/117) 0.658747504864 = 2*cos(46*π/117) 0.556434927833 = 2*cos(48*π/117) = 2*cos(16*π/39) 0.452518004859 = 2*cos(50*π/117) 0.347296355334 = 2*cos(52*π/117) = 2*cos(4*π/9) 0.241073360511 = 2*cos(54*π/117) = 2*cos(6*π/13) 0.134155288782 = 2*cos(56*π/117) 0.026850412627 = 2*cos(58*π/117) -0.080531880219 = 2*cos(60*π/117) = 2*cos(20*π/39) -0.187681978806 = 2*cos(62*π/117) -0.294290941663 = 2*cos(64*π/117) -0.400051387552 = 2*cos(66*π/117) = 2*cos(22*π/39) -0.504658381728 = 2*cos(68*π/117) -0.607810315148 = 2*cos(70*π/117) -0.709209774085 = 2*cos(72*π/117) = 2*cos(8*π/13) -0.808564397649 = 2*cos(74*π/117) -0.905587720739 = 2*cos(76*π/117) -1.091529020389 = 2*cos(80*π/117) -1.179910880046 = 2*cos(82*π/117) -1.264890751191 = 2*cos(84*π/117) = 2*cos(28*π/39) -1.346223614855 = 2*cos(86*π/117) -1.423674967339 = 2*cos(88*π/117) -1.497021496342 = 2*cos(90*π/117) = 2*cos(10*π/13) -1.566051724835 = 2*cos(92*π/117) -1.630566620799 = 2*cos(94*π/117) -1.690380171088 = 2*cos(96*π/117) = 2*cos(32*π/39) -1.745319917751 = 2*cos(98*π/117) -1.795227455278 = 2*cos(100*π/117) -1.839958887318 = 2*cos(102*π/117) = 2*cos(34*π/39) -1.879385241572 = 2*cos(104*π/117) = 2*cos(8*π/9) -1.913392841655 = 2*cos(106*π/117) -1.941883634852 = 2*cos(108*π/117) = 2*cos(12*π/13) -1.964775474831 = 2*cos(110*π/117) -1.982002358492 = 2*cos(112*π/117) -1.993514616268 = 2*cos(114*π/117) = 2*cos(38*π/39) -1.999279055342 = 2*cos(116*π/117) 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 C117 point group is 117, and the order of the principal axis (C117) is 117. The group has 59 irreducible representations. β The C117 point group is generated by one single symmetry element, C117. Therefore, it is a cyclic group. γ The lowest nonvanishing multipole moment in C117 is 2 (dipole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C117 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. ε Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 116 cases have been combined into 58 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 58 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 58 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. η The point group is chiral, as it does not contain any mirroring operation. θ 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. ι The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. All characters of this group can be expressed using complex numbers, elementary arithmetic operations, square roots and third roots.
| C115 | ||
| C116 | ||
| C117 | C117v C117h D117 D117h D117d | |
| C118 | ||
| C119 |
This Character Table for the C117 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.