C100 E 2 C100 2 C50 2 C100^3 2 C25 2 C20 2 C50^3 2 C100^7 2 C25^2 2 C100^9 2 C10 2 C100^11 2 C25^3 2 C100^13 2 C50^7 2 C20^3 2 C25^4 2 C100^17 2 C50^9 2 C100^19 2 C5 2 C100^21 2 C50^11 2 C100^23 2 C25^6 2 C4 2 C50^13 2 C100^27 2 C25^7 2 C100^29 2 C10^3 2 C100^31 2 C25^8 2 C100^33 2 C50^17 2 C20^7 2 C25^9 2 C100^37 2 C50^19 2 C100^39 2 C5^2 2 C100^41 2 C50^21 2 C100^43 2 C25^11 2 C20^9 2 C50^23 2 C100^47 2 C25^12 2 C100^49 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 ..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 ... ... ..... ....... ......... ........... ............. E1 * 2.00000 1.99605 1.98423 1.96457 1.93717 1.90211 1.85955 1.80965 1.75261 1.68866 1.61803 1.54103 1.45794 1.36909 1.27485 1.17557 1.07165 0.96351 0.85156 0.73625 0.61803 0.49738 0.37476 0.25067 0.12558 0.00000 -0.12558 -0.25067 -0.37476 -0.49738 -0.61803 -0.73625 -0.85156 -0.96351 -1.07165 -1.17557 -1.27485 -1.36909 -1.45794 -1.54103 -1.61803 -1.68866 -1.75261 -1.80965 -1.85955 -1.90211 -1.93717 -1.96457 -1.98423 -1.99605 -2.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98423 1.93717 1.85955 1.75261 1.61803 1.45794 1.27485 1.07165 0.85156 0.61803 0.37476 0.12558 -0.12558 -0.37476 -0.61803 -0.85156 -1.07165 -1.27485 -1.45794 -1.61803 -1.75261 -1.85955 -1.93717 -1.98423 -2.00000 -1.98423 -1.93717 -1.85955 -1.75261 -1.61803 -1.45794 -1.27485 -1.07165 -0.85156 -0.61803 -0.37476 -0.12558 0.12558 0.37476 0.61803 0.85156 1.07165 1.27485 1.45794 1.61803 1.75261 1.85955 1.93717 1.98423 2.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.96457 1.85955 1.68866 1.45794 1.17557 0.85156 0.49738 0.12558 -0.25067 -0.61803 -0.96351 -1.27485 -1.54103 -1.75261 -1.90211 -1.98423 -1.99605 -1.93717 -1.80965 -1.61803 -1.36909 -1.07165 -0.73625 -0.37476 0.00000 0.37476 0.73625 1.07165 1.36909 1.61803 1.80965 1.93717 1.99605 1.98423 1.90211 1.75261 1.54103 1.27485 0.96351 0.61803 0.25067 -0.12558 -0.49738 -0.85156 -1.17557 -1.45794 -1.68866 -1.85955 -1.96457 -2.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.85955 1.45794 0.85156 0.12558 -0.61803 -1.27485 -1.75261 -1.98423 -1.93717 -1.61803 -1.07165 -0.37476 0.37476 1.07165 1.61803 1.93717 1.98423 1.75261 1.27485 0.61803 -0.12558 -0.85156 -1.45794 -1.85955 -2.00000 -1.85955 -1.45794 -0.85156 -0.12558 0.61803 1.27485 1.75261 1.98423 1.93717 1.61803 1.07165 0.37476 -0.37476 -1.07165 -1.61803 -1.93717 -1.98423 -1.75261 -1.27485 -0.61803 0.12558 0.85156 1.45794 1.85955 2.00000 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.80965 1.27485 0.49738 -0.37476 -1.17557 -1.75261 -1.99605 -1.85955 -1.36909 -0.61803 0.25067 1.07165 1.68866 1.98423 1.90211 1.45794 0.73625 -0.12558 -0.96351 -1.61803 -1.96457 -1.93717 -1.54103 -0.85156 0.00000 0.85156 1.54103 1.93717 1.96457 1.61803 0.96351 0.12558 -0.73625 -1.45794 -1.90211 -1.98423 -1.68866 -1.07165 -0.25067 0.61803 1.36909 1.85955 1.99605 1.75261 1.17557 0.37476 -0.49738 -1.27485 -1.80965 -2.00000 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 1.93717 1.45794 0.61803 -0.37476 -1.27485 -1.85955 -1.98423 -1.61803 -0.85156 0.12558 1.07165 1.75261 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 1.93717 1.45794 0.61803 -0.37476 -1.27485 -1.85955 -1.98423 -1.61803 -0.85156 0.12558 1.07165 1.75261 2.00000 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.68866 0.85156 -0.25067 -1.27485 -1.90211 -1.93717 -1.36909 -0.37476 0.73625 1.61803 1.99605 1.75261 0.96351 -0.12558 -1.17557 -1.85955 -1.96457 -1.45794 -0.49738 0.61803 1.54103 1.98423 1.80965 1.07165 0.00000 -1.07165 -1.80965 -1.98423 -1.54103 -0.61803 0.49738 1.45794 1.96457 1.85955 1.17557 0.12558 -0.96351 -1.75261 -1.99605 -1.61803 -0.73625 0.37476 1.36909 1.93717 1.90211 1.27485 0.25067 -0.85156 -1.68866 -2.00000 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.54103 0.37476 -0.96351 -1.85955 -1.90211 -1.07165 0.25067 1.45794 1.99605 1.61803 0.49738 -0.85156 -1.80965 -1.93717 -1.17557 0.12558 1.36909 1.98423 1.68866 0.61803 -0.73625 -1.75261 -1.96457 -1.27485 0.00000 1.27485 1.96457 1.75261 0.73625 -0.61803 -1.68866 -1.98423 -1.36909 -0.12558 1.17557 1.93717 1.80965 0.85156 -0.49738 -1.61803 -1.99605 -1.45794 -0.25067 1.07165 1.90211 1.85955 0.96351 -0.37476 -1.54103 -2.00000 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 -1.85955 -0.85156 0.61803 1.75261 1.93717 1.07165 -0.37476 -1.61803 -1.98423 -1.27485 0.12558 1.45794 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 -1.85955 -0.85156 0.61803 1.75261 1.93717 1.07165 -0.37476 -1.61803 -1.98423 -1.27485 0.12558 1.45794 2.00000 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.36909 -0.12558 -1.54103 -1.98423 -1.17557 0.37476 1.68866 1.93717 0.96351 -0.61803 -1.80965 -1.85955 -0.73625 0.85156 1.90211 1.75261 0.49738 -1.07165 -1.96457 -1.61803 -0.25067 1.27485 1.99605 1.45794 0.00000 -1.45794 -1.99605 -1.27485 0.25067 1.61803 1.96457 1.07165 -0.49738 -1.75261 -1.90211 -0.85156 0.73625 1.85955 1.80965 0.61803 -0.96351 -1.93717 -1.68866 -0.37476 1.17557 1.98423 1.54103 0.12558 -1.36909 -2.00000 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.27485 -0.37476 -1.75261 -1.85955 -0.61803 1.07165 1.98423 1.45794 -0.12558 -1.61803 -1.93717 -0.85156 0.85156 1.93717 1.61803 0.12558 -1.45794 -1.98423 -1.07165 0.61803 1.85955 1.75261 0.37476 -1.27485 -2.00000 -1.27485 0.37476 1.75261 1.85955 0.61803 -1.07165 -1.98423 -1.45794 0.12558 1.61803 1.93717 0.85156 -0.85156 -1.93717 -1.61803 -0.12558 1.45794 1.98423 1.07165 -0.61803 -1.85955 -1.75261 -0.37476 1.27485 2.00000 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 1.75261 0.12558 -1.61803 -1.85955 -0.37476 1.45794 1.93717 0.61803 -1.27485 -1.98423 -0.85156 1.07165 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 1.75261 0.12558 -1.61803 -1.85955 -0.37476 1.45794 1.93717 0.61803 -1.27485 -1.98423 -0.85156 1.07165 2.00000 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 0.96351 -1.07165 -1.99605 -0.85156 1.17557 1.98423 0.73625 -1.27485 -1.96457 -0.61803 1.36909 1.93717 0.49738 -1.45794 -1.90211 -0.37476 1.54103 1.85955 0.25067 -1.61803 -1.80965 -0.12558 1.68866 1.75261 0.00000 -1.75261 -1.68866 0.12558 1.80965 1.61803 -0.25067 -1.85955 -1.54103 0.37476 1.90211 1.45794 -0.49738 -1.93717 -1.36909 0.61803 1.96457 1.27485 -0.73625 -1.98423 -1.17557 0.85156 1.99605 1.07165 -0.96351 -2.00000 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.85156 -1.27485 -1.93717 -0.37476 1.61803 1.75261 -0.12558 -1.85955 -1.45794 0.61803 1.98423 1.07165 -1.07165 -1.98423 -0.61803 1.45794 1.85955 0.12558 -1.75261 -1.61803 0.37476 1.93717 1.27485 -0.85156 -2.00000 -0.85156 1.27485 1.93717 0.37476 -1.61803 -1.75261 0.12558 1.85955 1.45794 -0.61803 -1.98423 -1.07165 1.07165 1.98423 0.61803 -1.45794 -1.85955 -0.12558 1.75261 1.61803 -0.37476 -1.93717 -1.27485 0.85156 2.00000 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.73625 -1.45794 -1.80965 0.12558 1.90211 1.27485 -0.96351 -1.98423 -0.49738 1.61803 1.68866 -0.37476 -1.96457 -1.07165 1.17557 1.93717 0.25067 -1.75261 -1.54103 0.61803 1.99605 0.85156 -1.36909 -1.85955 0.00000 1.85955 1.36909 -0.85156 -1.99605 -0.61803 1.54103 1.75261 -0.25067 -1.93717 -1.17557 1.07165 1.96457 0.37476 -1.68866 -1.61803 0.49738 1.98423 0.96351 -1.27485 -1.90211 -0.12558 1.80965 1.45794 -0.73625 -2.00000 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.49738 -1.75261 -1.36909 1.07165 1.90211 -0.12558 -1.96457 -0.85156 1.54103 1.61803 -0.73625 -1.98423 -0.25067 1.85955 1.17557 -1.27485 -1.80965 0.37476 1.99605 0.61803 -1.68866 -1.45794 0.96351 1.93717 0.00000 -1.93717 -0.96351 1.45794 1.68866 -0.61803 -1.99605 -0.37476 1.80965 1.27485 -1.17557 -1.85955 0.25067 1.98423 0.73625 -1.61803 -1.54103 0.85156 1.96457 0.12558 -1.90211 -1.07165 1.36909 1.75261 -0.49738 -2.00000 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.37476 -1.85955 -1.07165 1.45794 1.61803 -0.85156 -1.93717 0.12558 1.98423 0.61803 -1.75261 -1.27485 1.27485 1.75261 -0.61803 -1.98423 -0.12558 1.93717 0.85156 -1.61803 -1.45794 1.07165 1.85955 -0.37476 -2.00000 -0.37476 1.85955 1.07165 -1.45794 -1.61803 0.85156 1.93717 -0.12558 -1.98423 -0.61803 1.75261 1.27485 -1.27485 -1.75261 0.61803 1.98423 0.12558 -1.93717 -0.85156 1.61803 1.45794 -1.07165 -1.85955 0.37476 2.00000 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.25067 -1.93717 -0.73625 1.75261 1.17557 -1.45794 -1.54103 1.07165 1.80965 -0.61803 -1.96457 0.12558 1.99605 0.37476 -1.90211 -0.85156 1.68866 1.27485 -1.36909 -1.61803 0.96351 1.85955 -0.49738 -1.98423 0.00000 1.98423 0.49738 -1.85955 -0.96351 1.61803 1.36909 -1.27485 -1.68866 0.85156 1.90211 -0.37476 -1.99605 -0.12558 1.96457 0.61803 -1.80965 -1.07165 1.54103 1.45794 -1.17557 -1.75261 0.73625 1.93717 -0.25067 -2.00000 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 1.45794 -1.27485 -1.61803 1.07165 1.75261 -0.85156 -1.85955 0.61803 1.93717 -0.37476 -1.98423 0.12558 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 1.45794 -1.27485 -1.61803 1.07165 1.75261 -0.85156 -1.85955 0.61803 1.93717 -0.37476 -1.98423 0.12558 2.00000 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.12558 -1.98423 0.37476 1.93717 -0.61803 -1.85955 0.85156 1.75261 -1.07165 -1.61803 1.27485 1.45794 -1.45794 -1.27485 1.61803 1.07165 -1.75261 -0.85156 1.85955 0.61803 -1.93717 -0.37476 1.98423 0.12558 -2.00000 0.12558 1.98423 -0.37476 -1.93717 0.61803 1.85955 -0.85156 -1.75261 1.07165 1.61803 -1.27485 -1.45794 1.45794 1.27485 -1.61803 -1.07165 1.75261 0.85156 -1.85955 -0.61803 1.93717 0.37476 -1.98423 -0.12558 2.00000 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 -0.25067 -1.93717 0.73625 1.75261 -1.17557 -1.45794 1.54103 1.07165 -1.80965 -0.61803 1.96457 0.12558 -1.99605 0.37476 1.90211 -0.85156 -1.68866 1.27485 1.36909 -1.61803 -0.96351 1.85955 0.49738 -1.98423 0.00000 1.98423 -0.49738 -1.85955 0.96351 1.61803 -1.36909 -1.27485 1.68866 0.85156 -1.90211 -0.37476 1.99605 -0.12558 -1.96457 0.61803 1.80965 -1.07165 -1.54103 1.45794 1.17557 -1.75261 -0.73625 1.93717 0.25067 -2.00000 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 -1.27485 1.75261 0.61803 -1.98423 0.12558 1.93717 -0.85156 -1.61803 1.45794 1.07165 -1.85955 -0.37476 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 -1.27485 1.75261 0.61803 -1.98423 0.12558 1.93717 -0.85156 -1.61803 1.45794 1.07165 -1.85955 -0.37476 2.00000 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.49738 -1.75261 1.36909 1.07165 -1.90211 -0.12558 1.96457 -0.85156 -1.54103 1.61803 0.73625 -1.98423 0.25067 1.85955 -1.17557 -1.27485 1.80965 0.37476 -1.99605 0.61803 1.68866 -1.45794 -0.96351 1.93717 0.00000 -1.93717 0.96351 1.45794 -1.68866 -0.61803 1.99605 -0.37476 -1.80965 1.27485 1.17557 -1.85955 -0.25067 1.98423 -0.73625 -1.61803 1.54103 0.85156 -1.96457 0.12558 1.90211 -1.07165 -1.36909 1.75261 0.49738 -2.00000 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -0.73625 -1.45794 1.80965 0.12558 -1.90211 1.27485 0.96351 -1.98423 0.49738 1.61803 -1.68866 -0.37476 1.96457 -1.07165 -1.17557 1.93717 -0.25067 -1.75261 1.54103 0.61803 -1.99605 0.85156 1.36909 -1.85955 0.00000 1.85955 -1.36909 -0.85156 1.99605 -0.61803 -1.54103 1.75261 0.25067 -1.93717 1.17557 1.07165 -1.96457 0.37476 1.68866 -1.61803 -0.49738 1.98423 -0.96351 -1.27485 1.90211 -0.12558 -1.80965 1.45794 0.73625 -2.00000 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 1.07165 -1.98423 0.61803 1.45794 -1.85955 0.12558 1.75261 -1.61803 -0.37476 1.93717 -1.27485 -0.85156 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 1.07165 -1.98423 0.61803 1.45794 -1.85955 0.12558 1.75261 -1.61803 -0.37476 1.93717 -1.27485 -0.85156 2.00000 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -0.96351 -1.07165 1.99605 -0.85156 -1.17557 1.98423 -0.73625 -1.27485 1.96457 -0.61803 -1.36909 1.93717 -0.49738 -1.45794 1.90211 -0.37476 -1.54103 1.85955 -0.25067 -1.61803 1.80965 -0.12558 -1.68866 1.75261 0.00000 -1.75261 1.68866 0.12558 -1.80965 1.61803 0.25067 -1.85955 1.54103 0.37476 -1.90211 1.45794 0.49738 -1.93717 1.36909 0.61803 -1.96457 1.27485 0.73625 -1.98423 1.17557 0.85156 -1.99605 1.07165 0.96351 -2.00000 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.07165 -0.85156 1.98423 -1.27485 -0.61803 1.93717 -1.45794 -0.37476 1.85955 -1.61803 -0.12558 1.75261 -1.75261 0.12558 1.61803 -1.85955 0.37476 1.45794 -1.93717 0.61803 1.27485 -1.98423 0.85156 1.07165 -2.00000 1.07165 0.85156 -1.98423 1.27485 0.61803 -1.93717 1.45794 0.37476 -1.85955 1.61803 0.12558 -1.75261 1.75261 -0.12558 -1.61803 1.85955 -0.37476 -1.45794 1.93717 -0.61803 -1.27485 1.98423 -0.85156 -1.07165 2.00000 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 -0.85156 1.93717 -1.61803 0.12558 1.45794 -1.98423 1.07165 0.61803 -1.85955 1.75261 -0.37476 -1.27485 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 -0.85156 1.93717 -1.61803 0.12558 1.45794 -1.98423 1.07165 0.61803 -1.85955 1.75261 -0.37476 -1.27485 2.00000 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.36909 -0.12558 1.54103 -1.98423 1.17557 0.37476 -1.68866 1.93717 -0.96351 -0.61803 1.80965 -1.85955 0.73625 0.85156 -1.90211 1.75261 -0.49738 -1.07165 1.96457 -1.61803 0.25067 1.27485 -1.99605 1.45794 0.00000 -1.45794 1.99605 -1.27485 -0.25067 1.61803 -1.96457 1.07165 0.49738 -1.75261 1.90211 -0.85156 -0.73625 1.85955 -1.80965 0.61803 0.96351 -1.93717 1.68866 -0.37476 -1.17557 1.98423 -1.54103 0.12558 1.36909 -2.00000 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.45794 0.12558 1.27485 -1.98423 1.61803 -0.37476 -1.07165 1.93717 -1.75261 0.61803 0.85156 -1.85955 1.85955 -0.85156 -0.61803 1.75261 -1.93717 1.07165 0.37476 -1.61803 1.98423 -1.27485 -0.12558 1.45794 -2.00000 1.45794 -0.12558 -1.27485 1.98423 -1.61803 0.37476 1.07165 -1.93717 1.75261 -0.61803 -0.85156 1.85955 -1.85955 0.85156 0.61803 -1.75261 1.93717 -1.07165 -0.37476 1.61803 -1.98423 1.27485 0.12558 -1.45794 2.00000 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.54103 0.37476 0.96351 -1.85955 1.90211 -1.07165 -0.25067 1.45794 -1.99605 1.61803 -0.49738 -0.85156 1.80965 -1.93717 1.17557 0.12558 -1.36909 1.98423 -1.68866 0.61803 0.73625 -1.75261 1.96457 -1.27485 0.00000 1.27485 -1.96457 1.75261 -0.73625 -0.61803 1.68866 -1.98423 1.36909 -0.12558 -1.17557 1.93717 -1.80965 0.85156 0.49738 -1.61803 1.99605 -1.45794 0.25067 1.07165 -1.90211 1.85955 -0.96351 -0.37476 1.54103 -2.00000 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.68866 0.85156 0.25067 -1.27485 1.90211 -1.93717 1.36909 -0.37476 -0.73625 1.61803 -1.99605 1.75261 -0.96351 -0.12558 1.17557 -1.85955 1.96457 -1.45794 0.49738 0.61803 -1.54103 1.98423 -1.80965 1.07165 0.00000 -1.07165 1.80965 -1.98423 1.54103 -0.61803 -0.49738 1.45794 -1.96457 1.85955 -1.17557 0.12558 0.96351 -1.75261 1.99605 -1.61803 0.73625 0.37476 -1.36909 1.93717 -1.90211 1.27485 -0.25067 -0.85156 1.68866 -2.00000 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.75261 1.07165 -0.12558 -0.85156 1.61803 -1.98423 1.85955 -1.27485 0.37476 0.61803 -1.45794 1.93717 -1.93717 1.45794 -0.61803 -0.37476 1.27485 -1.85955 1.98423 -1.61803 0.85156 0.12558 -1.07165 1.75261 -2.00000 1.75261 -1.07165 0.12558 0.85156 -1.61803 1.98423 -1.85955 1.27485 -0.37476 -0.61803 1.45794 -1.93717 1.93717 -1.45794 0.61803 0.37476 -1.27485 1.85955 -1.98423 1.61803 -0.85156 -0.12558 1.07165 -1.75261 2.00000 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.80965 1.27485 -0.49738 -0.37476 1.17557 -1.75261 1.99605 -1.85955 1.36909 -0.61803 -0.25067 1.07165 -1.68866 1.98423 -1.90211 1.45794 -0.73625 -0.12558 0.96351 -1.61803 1.96457 -1.93717 1.54103 -0.85156 0.00000 0.85156 -1.54103 1.93717 -1.96457 1.61803 -0.96351 0.12558 0.73625 -1.45794 1.90211 -1.98423 1.68866 -1.07165 0.25067 0.61803 -1.36909 1.85955 -1.99605 1.75261 -1.17557 0.37476 0.49738 -1.27485 1.80965 -2.00000 ... ... ..... ....... ......... ........... ............. E44 * 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 -0.37476 1.07165 -1.61803 1.93717 -1.98423 1.75261 -1.27485 0.61803 0.12558 -0.85156 1.45794 -1.85955 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 -0.37476 1.07165 -1.61803 1.93717 -1.98423 1.75261 -1.27485 0.61803 0.12558 -0.85156 1.45794 -1.85955 2.00000 ... ... ..... ....... ......... ........... ............. E45 * 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 ... ... ..... ....... ......... ........... ............. E46 * 2.00000 -1.93717 1.75261 -1.45794 1.07165 -0.61803 0.12558 0.37476 -0.85156 1.27485 -1.61803 1.85955 -1.98423 1.98423 -1.85955 1.61803 -1.27485 0.85156 -0.37476 -0.12558 0.61803 -1.07165 1.45794 -1.75261 1.93717 -2.00000 1.93717 -1.75261 1.45794 -1.07165 0.61803 -0.12558 -0.37476 0.85156 -1.27485 1.61803 -1.85955 1.98423 -1.98423 1.85955 -1.61803 1.27485 -0.85156 0.37476 0.12558 -0.61803 1.07165 -1.45794 1.75261 -1.93717 2.00000 ... ... ..... ....... ......... ........... ............. E47 * 2.00000 -1.96457 1.85955 -1.68866 1.45794 -1.17557 0.85156 -0.49738 0.12558 0.25067 -0.61803 0.96351 -1.27485 1.54103 -1.75261 1.90211 -1.98423 1.99605 -1.93717 1.80965 -1.61803 1.36909 -1.07165 0.73625 -0.37476 0.00000 0.37476 -0.73625 1.07165 -1.36909 1.61803 -1.80965 1.93717 -1.99605 1.98423 -1.90211 1.75261 -1.54103 1.27485 -0.96351 0.61803 -0.25067 -0.12558 0.49738 -0.85156 1.17557 -1.45794 1.68866 -1.85955 1.96457 -2.00000 ... ... ..... ....... ......... ........... ............. E48 * 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 0.12558 -0.37476 0.61803 -0.85156 1.07165 -1.27485 1.45794 -1.61803 1.75261 -1.85955 1.93717 -1.98423 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 0.12558 -0.37476 0.61803 -0.85156 1.07165 -1.27485 1.45794 -1.61803 1.75261 -1.85955 1.93717 -1.98423 2.00000 ... ... ..... ....... ......... ........... ............. E49 * 2.00000 -1.99605 1.98423 -1.96457 1.93717 -1.90211 1.85955 -1.80965 1.75261 -1.68866 1.61803 -1.54103 1.45794 -1.36909 1.27485 -1.17557 1.07165 -0.96351 0.85156 -0.73625 0.61803 -0.49738 0.37476 -0.25067 0.12558 0.00000 -0.12558 0.25067 -0.37476 0.49738 -0.61803 0.73625 -0.85156 0.96351 -1.07165 1.17557 -1.27485 1.36909 -1.45794 1.54103 -1.61803 1.68866 -1.75261 1.80965 -1.85955 1.90211 -1.93717 1.96457 -1.98423 1.99605 -2.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.996053456857 = 2*cos(2*π/100) = 2*cos(π/50) 1.984229402629 = 2*cos(4*π/100) = 2*cos(π/25) 1.964574501457 = 2*cos(6*π/100) = 2*cos(3*π/50) 1.937166322257 = 2*cos(8*π/100) = 2*cos(2*π/25) 1.902113032590 = 2*cos(10*π/100) = 2*cos(π/10) = (√10+2*√5)/2 1.859552971777 = 2*cos(12*π/100) = 2*cos(3*π/25) 1.809654104932 = 2*cos(14*π/100) = 2*cos(7*π/50) 1.752613360088 = 2*cos(16*π/100) = 2*cos(4*π/25) 1.688655851004 = 2*cos(18*π/100) = 2*cos(9*π/50) 1.618033988750 = 2*cos(20*π/100) = 2*cos(π/5) = (√5+1)/2 1.541026485552 = 2*cos(22*π/100) = 2*cos(11*π/50) 1.457937254843 = 2*cos(24*π/100) = 2*cos(6*π/25) 1.369094211857 = 2*cos(26*π/100) = 2*cos(13*π/50) 1.274847979497 = 2*cos(28*π/100) = 2*cos(7*π/25) 1.175570504585 = 2*cos(30*π/100) = 2*cos(3*π/10) = (√10−2*√5)/2 1.071653589958 = 2*cos(32*π/100) = 2*cos(8*π/25) 0.963507348203 = 2*cos(34*π/100) = 2*cos(17*π/50) 0.851558583130 = 2*cos(36*π/100) = 2*cos(9*π/25) 0.736249105369 = 2*cos(38*π/100) = 2*cos(19*π/50) 0.618033988750 = 2*cos(40*π/100) = 2*cos(2*π/5) = (√5−1)/2 0.497379774330 = 2*cos(42*π/100) = 2*cos(21*π/50) 0.374762629171 = 2*cos(44*π/100) = 2*cos(11*π/25) 0.250666467129 = 2*cos(46*π/100) = 2*cos(23*π/50) 0.125581039059 = 2*cos(48*π/100) = 2*cos(12*π/25) 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 C100 point group is 100, and the order of the principal axis (C100) is 100. The group has 51 irreducible representations. β The C100 point group is isomorphic to S100. γ The C100 point group is generated by one single symmetry element, C100. Therefore, it is a cyclic group. δ The lowest nonvanishing multipole moment in C100 is 2 (dipole moment). ε This is an Abelian point group (the commutative law holds between all symmetry operations). The C100 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 98 cases have been combined into 49 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 49 pairs of left and right rotations have been combined into one two-membered pseudo-class each. η The 49 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. For this group, however, some of the irrational characters cannot be expressed by a closed algebraic form using real numbers only.
| C98 | ||
| C99 | ||
| C100 | C100v C100h D100 D100h D100d S100 | |
| C101 | ||
| C102 |
This Character Table for the C100 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.