C115 E 2 C115 2 C115^2 2 C115^3 2 C115^4 2 C23 2 C115^6 2 C115^7 2 C115^8 2 C115^9 2 C23^2 2 C115^11 2 C115^12 2 C115^13 2 C115^14 2 C23^3 2 C115^16 2 C115^17 2 C115^18 2 C115^19 2 C23^4 2 C115^21 2 C115^22 2 C5 2 C115^24 2 C23^5 2 C115^26 2 C115^27 2 C115^28 2 C115^29 2 C23^6 2 C115^31 2 C115^32 2 C115^33 2 C115^34 2 C23^7 2 C115^36 2 C115^37 2 C115^38 2 C115^39 2 C23^8 2 C115^41 2 C115^42 2 C115^43 2 C115^44 2 C23^9 2 C5^2 2 C115^47 2 C115^48 2 C115^49 2 C23^10 2 C115^51 2 C115^52 2 C115^53 2 C115^54 2 C23^11 2 C115^56 2 C115^57 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99702 1.98807 1.97319 1.95243 1.92583 1.89349 1.85550 1.81197 1.76304 1.70884 1.64954 1.58532 1.51637 1.44289 1.36511 1.28325 1.19756 1.10830 1.01573 0.92013 0.82178 0.72098 0.61803 0.51324 0.40691 0.29937 0.19094 0.08193 -0.02732 -0.13648 -0.24524 -0.35327 -0.46025 -0.56585 -0.66976 -0.77167 -0.87128 -0.96829 -1.06241 -1.15336 -1.24087 -1.32467 -1.40452 -1.48018 -1.55142 -1.61803 -1.67982 -1.73659 -1.78817 -1.83442 -1.87520 -1.91038 -1.93985 -1.96354 -1.98137 -1.99329 -1.99925 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98807 1.95243 1.89349 1.81197 1.70884 1.58532 1.44289 1.28325 1.10830 0.92013 0.72098 0.51324 0.29937 0.08193 -0.13648 -0.35327 -0.56585 -0.77167 -0.96829 -1.15336 -1.32467 -1.48018 -1.61803 -1.73659 -1.83442 -1.91038 -1.96354 -1.99329 -1.99925 -1.98137 -1.93985 -1.87520 -1.78817 -1.67982 -1.55142 -1.40452 -1.24087 -1.06241 -0.87128 -0.66976 -0.46025 -0.24524 -0.02732 0.19094 0.40691 0.61803 0.82178 1.01573 1.19756 1.36511 1.51637 1.64954 1.76304 1.85550 1.92583 1.97319 1.99702 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.97319 1.89349 1.76304 1.58532 1.36511 1.10830 0.82178 0.51324 0.19094 -0.13648 -0.46025 -0.77167 -1.06241 -1.32467 -1.55142 -1.73659 -1.87520 -1.96354 -1.99925 -1.98137 -1.91038 -1.78817 -1.61803 -1.40452 -1.15336 -0.87128 -0.56585 -0.24524 0.08193 0.40691 0.72098 1.01573 1.28325 1.51637 1.70884 1.85550 1.95243 1.99702 1.98807 1.92583 1.81197 1.64954 1.44289 1.19756 0.92013 0.61803 0.29937 -0.02732 -0.35327 -0.66976 -0.96829 -1.24087 -1.48018 -1.67982 -1.83442 -1.93985 -1.99329 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.95243 1.81197 1.58532 1.28325 0.92013 0.51324 0.08193 -0.35327 -0.77167 -1.15336 -1.48018 -1.73659 -1.91038 -1.99329 -1.98137 -1.87520 -1.67982 -1.40452 -1.06241 -0.66976 -0.24524 0.19094 0.61803 1.01573 1.36511 1.64954 1.85550 1.97319 1.99702 1.92583 1.76304 1.51637 1.19756 0.82178 0.40691 -0.02732 -0.46025 -0.87128 -1.24087 -1.55142 -1.78817 -1.93985 -1.99925 -1.96354 -1.83442 -1.61803 -1.32467 -0.96829 -0.56585 -0.13648 0.29937 0.72098 1.10830 1.44289 1.70884 1.89349 1.98807 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.89349 1.58532 1.10830 0.51324 -0.13648 -0.77167 -1.32467 -1.73659 -1.96354 -1.98137 -1.78817 -1.40452 -0.87128 -0.24524 0.40691 1.01573 1.51637 1.85550 1.99702 1.92583 1.64954 1.19756 0.61803 -0.02732 -0.66976 -1.24087 -1.67982 -1.93985 -1.99329 -1.83442 -1.48018 -0.96829 -0.35327 0.29937 0.92013 1.44289 1.81197 1.98807 1.95243 1.70884 1.28325 0.72098 0.08193 -0.56585 -1.15336 -1.61803 -1.91038 -1.99925 -1.87520 -1.55142 -1.06241 -0.46025 0.19094 0.82178 1.36511 1.76304 1.97319 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.85550 1.44289 0.82178 0.08193 -0.66976 -1.32467 -1.78817 -1.99329 -1.91038 -1.55142 -0.96829 -0.24524 0.51324 1.19756 1.70884 1.97319 1.95243 1.64954 1.10830 0.40691 -0.35327 -1.06241 -1.61803 -1.93985 -1.98137 -1.73659 -1.24087 -0.56585 0.19094 0.92013 1.51637 1.89349 1.99702 1.81197 1.36511 0.72098 -0.02732 -0.77167 -1.40452 -1.83442 -1.99925 -1.87520 -1.48018 -0.87128 -0.13648 0.61803 1.28325 1.76304 1.98807 1.92583 1.58532 1.01573 0.29937 -0.46025 -1.15336 -1.67982 -1.96354 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.81197 1.28325 0.51324 -0.35327 -1.15336 -1.73659 -1.99329 -1.87520 -1.40452 -0.66976 0.19094 1.01573 1.64954 1.97319 1.92583 1.51637 0.82178 -0.02732 -0.87128 -1.55142 -1.93985 -1.96354 -1.61803 -0.96829 -0.13648 0.72098 1.44289 1.89349 1.98807 1.70884 1.10830 0.29937 -0.56585 -1.32467 -1.83442 -1.99925 -1.78817 -1.24087 -0.46025 0.40691 1.19756 1.76304 1.99702 1.85550 1.36511 0.61803 -0.24524 -1.06241 -1.67982 -1.98137 -1.91038 -1.48018 -0.77167 0.08193 0.92013 1.58532 1.95243 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.76304 1.10830 0.19094 -0.77167 -1.55142 -1.96354 -1.91038 -1.40452 -0.56585 0.40691 1.28325 1.85550 1.98807 1.64954 0.92013 -0.02732 -0.96829 -1.67982 -1.99329 -1.83442 -1.24087 -0.35327 0.61803 1.44289 1.92583 1.95243 1.51637 0.72098 -0.24524 -1.15336 -1.78817 -1.99925 -1.73659 -1.06241 -0.13648 0.82178 1.58532 1.97319 1.89349 1.36511 0.51324 -0.46025 -1.32467 -1.87520 -1.98137 -1.61803 -0.87128 0.08193 1.01573 1.70884 1.99702 1.81197 1.19756 0.29937 -0.66976 -1.48018 -1.93985 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.64954 0.72098 -0.46025 -1.48018 -1.98137 -1.78817 -0.96829 0.19094 1.28325 1.92583 1.89349 1.19756 0.08193 -1.06241 -1.83442 -1.96354 -1.40452 -0.35327 0.82178 1.70884 1.99702 1.58532 0.61803 -0.56585 -1.55142 -1.99329 -1.73659 -0.87128 0.29937 1.36511 1.95243 1.85550 1.10830 -0.02732 -1.15336 -1.87520 -1.93985 -1.32467 -0.24524 0.92013 1.76304 1.98807 1.51637 0.51324 -0.66976 -1.61803 -1.99925 -1.67982 -0.77167 0.40691 1.44289 1.97319 1.81197 1.01573 -0.13648 -1.24087 -1.91038 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.58532 0.51324 -0.77167 -1.73659 -1.98137 -1.40452 -0.24524 1.01573 1.85550 1.92583 1.19756 -0.02732 -1.24087 -1.93985 -1.83442 -0.96829 0.29937 1.44289 1.98807 1.70884 0.72098 -0.56585 -1.61803 -1.99925 -1.55142 -0.46025 0.82178 1.76304 1.97319 1.36511 0.19094 -1.06241 -1.87520 -1.91038 -1.15336 0.08193 1.28325 1.95243 1.81197 0.92013 -0.35327 -1.48018 -1.99329 -1.67982 -0.66976 0.61803 1.64954 1.99702 1.51637 0.40691 -0.87128 -1.78817 -1.96354 -1.32467 -0.13648 1.10830 1.89349 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.51637 0.29937 -1.06241 -1.91038 -1.83442 -0.87128 0.51324 1.64954 1.98807 1.36511 0.08193 -1.24087 -1.96354 -1.73659 -0.66976 0.72098 1.76304 1.95243 1.19756 -0.13648 -1.40452 -1.99329 -1.61803 -0.46025 0.92013 1.85550 1.89349 1.01573 -0.35327 -1.55142 -1.99925 -1.48018 -0.24524 1.10830 1.92583 1.81197 0.82178 -0.56585 -1.67982 -1.98137 -1.32467 -0.02732 1.28325 1.97319 1.70884 0.61803 -0.77167 -1.78817 -1.93985 -1.15336 0.19094 1.44289 1.99702 1.58532 0.40691 -0.96829 -1.87520 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.44289 0.08193 -1.32467 -1.99329 -1.55142 -0.24524 1.19756 1.97319 1.64954 0.40691 -1.06241 -1.93985 -1.73659 -0.56585 0.92013 1.89349 1.81197 0.72098 -0.77167 -1.83442 -1.87520 -0.87128 0.61803 1.76304 1.92583 1.01573 -0.46025 -1.67982 -1.96354 -1.15336 0.29937 1.58532 1.98807 1.28325 -0.13648 -1.48018 -1.99925 -1.40452 -0.02732 1.36511 1.99702 1.51637 0.19094 -1.24087 -1.98137 -1.61803 -0.35327 1.10830 1.95243 1.70884 0.51324 -0.96829 -1.91038 -1.78817 -0.66976 0.82178 1.85550 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.28325 -0.35327 -1.73659 -1.87520 -0.66976 1.01573 1.97319 1.51637 -0.02732 -1.55142 -1.96354 -0.96829 0.72098 1.89349 1.70884 0.29937 -1.32467 -1.99925 -1.24087 0.40691 1.76304 1.85550 0.61803 -1.06241 -1.98137 -1.48018 0.08193 1.58532 1.95243 0.92013 -0.77167 -1.91038 -1.67982 -0.24524 1.36511 1.99702 1.19756 -0.46025 -1.78817 -1.83442 -0.56585 1.10830 1.98807 1.44289 -0.13648 -1.61803 -1.93985 -0.87128 0.82178 1.92583 1.64954 0.19094 -1.40452 -1.99329 -1.15336 0.51324 1.81197 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 1.19756 -0.56585 -1.87520 -1.67982 -0.13648 1.51637 1.95243 0.82178 -0.96829 -1.98137 -1.40452 0.29937 1.76304 1.81197 0.40691 -1.32467 -1.99329 -1.06241 0.72098 1.92583 1.58532 -0.02732 -1.61803 -1.91038 -0.66976 1.10830 1.99702 1.28325 -0.46025 -1.83442 -1.73659 -0.24524 1.44289 1.97319 0.92013 -0.87128 -1.96354 -1.48018 0.19094 1.70884 1.85550 0.51324 -1.24087 -1.99925 -1.15336 0.61803 1.89349 1.64954 0.08193 -1.55142 -1.93985 -0.77167 1.01573 1.98807 1.36511 -0.35327 -1.78817 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 1.10830 -0.77167 -1.96354 -1.40452 0.40691 1.85550 1.64954 -0.02732 -1.67982 -1.83442 -0.35327 1.44289 1.95243 0.72098 -1.15336 -1.99925 -1.06241 0.82178 1.97319 1.36511 -0.46025 -1.87520 -1.61803 0.08193 1.70884 1.81197 0.29937 -1.48018 -1.93985 -0.66976 1.19756 1.99702 1.01573 -0.87128 -1.98137 -1.32467 0.51324 1.89349 1.58532 -0.13648 -1.73659 -1.78817 -0.24524 1.51637 1.92583 0.61803 -1.24087 -1.99329 -0.96829 0.92013 1.98807 1.28325 -0.56585 -1.91038 -1.55142 0.19094 1.76304 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 1.01573 -0.96829 -1.99925 -1.06241 0.92013 1.99702 1.10830 -0.87128 -1.99329 -1.15336 0.82178 1.98807 1.19756 -0.77167 -1.98137 -1.24087 0.72098 1.97319 1.28325 -0.66976 -1.96354 -1.32467 0.61803 1.95243 1.36511 -0.56585 -1.93985 -1.40452 0.51324 1.92583 1.44289 -0.46025 -1.91038 -1.48018 0.40691 1.89349 1.51637 -0.35327 -1.87520 -1.55142 0.29937 1.85550 1.58532 -0.24524 -1.83442 -1.61803 0.19094 1.81197 1.64954 -0.13648 -1.78817 -1.67982 0.08193 1.76304 1.70884 -0.02732 -1.73659 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.82178 -1.32467 -1.91038 -0.24524 1.70884 1.64954 -0.35327 -1.93985 -1.24087 0.92013 1.99702 0.72098 -1.40452 -1.87520 -0.13648 1.76304 1.58532 -0.46025 -1.96354 -1.15336 1.01573 1.98807 0.61803 -1.48018 -1.83442 -0.02732 1.81197 1.51637 -0.56585 -1.98137 -1.06241 1.10830 1.97319 0.51324 -1.55142 -1.78817 0.08193 1.85550 1.44289 -0.66976 -1.99329 -0.96829 1.19756 1.95243 0.40691 -1.61803 -1.73659 0.19094 1.89349 1.36511 -0.77167 -1.99925 -0.87128 1.28325 1.92583 0.29937 -1.67982 ... ... ..... ....... ......... ........... ............. 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E27 * 2.00000 0.19094 -1.96354 -0.56585 1.85550 0.92013 -1.67982 -1.24087 1.44289 1.51637 -1.15336 -1.73659 0.82178 1.89349 -0.46025 -1.98137 0.08193 1.99702 0.29937 -1.93985 -0.66976 1.81197 1.01573 -1.61803 -1.32467 1.36511 1.58532 -1.06241 -1.78817 0.72098 1.92583 -0.35327 -1.99329 -0.02732 1.98807 0.40691 -1.91038 -0.77167 1.76304 1.10830 -1.55142 -1.40452 1.28325 1.64954 -0.96829 -1.83442 0.61803 1.95243 -0.24524 -1.99925 -0.13648 1.97319 0.51324 -1.87520 -0.87128 1.70884 1.19756 -1.48018 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 0.08193 -1.99329 -0.24524 1.97319 0.40691 -1.93985 -0.56585 1.89349 0.72098 -1.83442 -0.87128 1.76304 1.01573 -1.67982 -1.15336 1.58532 1.28325 -1.48018 -1.40452 1.36511 1.51637 -1.24087 -1.61803 1.10830 1.70884 -0.96829 -1.78817 0.82178 1.85550 -0.66976 -1.91038 0.51324 1.95243 -0.35327 -1.98137 0.19094 1.99702 -0.02732 -1.99925 -0.13648 1.98807 0.29937 -1.96354 -0.46025 1.92583 0.61803 -1.87520 -0.77167 1.81197 0.92013 -1.73659 -1.06241 1.64954 1.19756 -1.55142 -1.32467 1.44289 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.02732 -1.99925 0.08193 1.99702 -0.13648 -1.99329 0.19094 1.98807 -0.24524 -1.98137 0.29937 1.97319 -0.35327 -1.96354 0.40691 1.95243 -0.46025 -1.93985 0.51324 1.92583 -0.56585 -1.91038 0.61803 1.89349 -0.66976 -1.87520 0.72098 1.85550 -0.77167 -1.83442 0.82178 1.81197 -0.87128 -1.78817 0.92013 1.76304 -0.96829 -1.73659 1.01573 1.70884 -1.06241 -1.67982 1.10830 1.64954 -1.15336 -1.61803 1.19756 1.58532 -1.24087 -1.55142 1.28325 1.51637 -1.32467 -1.48018 1.36511 1.44289 -1.40452 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -0.24524 -1.93985 0.72098 1.76304 -1.15336 -1.48018 1.51637 1.10830 -1.78817 -0.66976 1.95243 0.19094 -1.99925 0.29937 1.92583 -0.77167 -1.73659 1.19756 1.44289 -1.55142 -1.06241 1.81197 0.61803 -1.96354 -0.13648 1.99702 -0.35327 -1.91038 0.82178 1.70884 -1.24087 -1.40452 1.58532 1.01573 -1.83442 -0.56585 1.97319 0.08193 -1.99329 0.40691 1.89349 -0.87128 -1.67982 1.28325 1.36511 -1.61803 -0.96829 1.85550 0.51324 -1.98137 -0.02732 1.98807 -0.46025 -1.87520 0.92013 1.64954 -1.32467 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -0.35327 -1.87520 1.01573 1.51637 -1.55142 -0.96829 1.89349 0.29937 -1.99925 0.40691 1.85550 -1.06241 -1.48018 1.58532 0.92013 -1.91038 -0.24524 1.99702 -0.46025 -1.83442 1.10830 1.44289 -1.61803 -0.87128 1.92583 0.19094 -1.99329 0.51324 1.81197 -1.15336 -1.40452 1.64954 0.82178 -1.93985 -0.13648 1.98807 -0.56585 -1.78817 1.19756 1.36511 -1.67982 -0.77167 1.95243 0.08193 -1.98137 0.61803 1.76304 -1.24087 -1.32467 1.70884 0.72098 -1.96354 -0.02732 1.97319 -0.66976 -1.73659 1.28325 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -0.46025 -1.78817 1.28325 1.19756 -1.83442 -0.35327 1.99702 -0.56585 -1.73659 1.36511 1.10830 -1.87520 -0.24524 1.98807 -0.66976 -1.67982 1.44289 1.01573 -1.91038 -0.13648 1.97319 -0.77167 -1.61803 1.51637 0.92013 -1.93985 -0.02732 1.95243 -0.87128 -1.55142 1.58532 0.82178 -1.96354 0.08193 1.92583 -0.96829 -1.48018 1.64954 0.72098 -1.98137 0.19094 1.89349 -1.06241 -1.40452 1.70884 0.61803 -1.99329 0.29937 1.85550 -1.15336 -1.32467 1.76304 0.51324 -1.99925 0.40691 1.81197 -1.24087 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -0.56585 -1.67982 1.51637 0.82178 -1.98137 0.29937 1.81197 -1.32467 -1.06241 1.92583 -0.02732 -1.91038 1.10830 1.28325 -1.83442 -0.24524 1.97319 -0.87128 -1.48018 1.70884 0.51324 -1.99925 0.61803 1.64954 -1.55142 -0.77167 1.98807 -0.35327 -1.78817 1.36511 1.01573 -1.93985 0.08193 1.89349 -1.15336 -1.24087 1.85550 0.19094 -1.96354 0.92013 1.44289 -1.73659 -0.46025 1.99702 -0.66976 -1.61803 1.58532 0.72098 -1.99329 0.40691 1.76304 -1.40452 -0.96829 1.95243 -0.13648 -1.87520 1.19756 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 ... ... ..... ....... ......... ........... ............. 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E51 * 2.00000 -1.87520 1.51637 -0.96829 0.29937 0.40691 -1.06241 1.58532 -1.91038 1.99702 -1.83442 1.44289 -0.87128 0.19094 0.51324 -1.15336 1.64954 -1.93985 1.98807 -1.78817 1.36511 -0.77167 0.08193 0.61803 -1.24087 1.70884 -1.96354 1.97319 -1.73659 1.28325 -0.66976 -0.02732 0.72098 -1.32467 1.76304 -1.98137 1.95243 -1.67982 1.19756 -0.56585 -0.13648 0.82178 -1.40452 1.81197 -1.99329 1.92583 -1.61803 1.10830 -0.46025 -0.24524 0.92013 -1.48018 1.85550 -1.99925 1.89349 -1.55142 1.01573 -0.35327 ... ... ..... ....... ......... ........... ............. E52 * 2.00000 -1.91038 1.64954 -1.24087 0.72098 -0.13648 -0.46025 1.01573 -1.48018 1.81197 -1.98137 1.97319 -1.78817 1.44289 -0.96829 0.40691 0.19094 -0.77167 1.28325 -1.67982 1.92583 -1.99925 1.89349 -1.61803 1.19756 -0.66976 0.08193 0.51324 -1.06241 1.51637 -1.83442 1.98807 -1.96354 1.76304 -1.40452 0.92013 -0.35327 -0.24524 0.82178 -1.32467 1.70884 -1.93985 1.99702 -1.87520 1.58532 -1.15336 0.61803 -0.02732 -0.56585 1.10830 -1.55142 1.85550 -1.99329 1.95243 -1.73659 1.36511 -0.87128 0.29937 ... ... ..... ....... ......... ........... ............. E53 * 2.00000 -1.93985 1.76304 -1.48018 1.10830 -0.66976 0.19094 0.29937 -0.77167 1.19756 -1.55142 1.81197 -1.96354 1.99702 -1.91038 1.70884 -1.40452 1.01573 -0.56585 0.08193 0.40691 -0.87128 1.28325 -1.61803 1.85550 -1.98137 1.98807 -1.87520 1.64954 -1.32467 0.92013 -0.46025 -0.02732 0.51324 -0.96829 1.36511 -1.67982 1.89349 -1.99329 1.97319 -1.83442 1.58532 -1.24087 0.82178 -0.35327 -0.13648 0.61803 -1.06241 1.44289 -1.73659 1.92583 -1.99925 1.95243 -1.78817 1.51637 -1.15336 0.72098 -0.24524 ... ... ..... ....... ......... ........... ............. E54 * 2.00000 -1.96354 1.85550 -1.67982 1.44289 -1.15336 0.82178 -0.46025 0.08193 0.29937 -0.66976 1.01573 -1.32467 1.58532 -1.78817 1.92583 -1.99329 1.98807 -1.91038 1.76304 -1.55142 1.28325 -0.96829 0.61803 -0.24524 -0.13648 0.51324 -0.87128 1.19756 -1.48018 1.70884 -1.87520 1.97319 -1.99925 1.95243 -1.83442 1.64954 -1.40452 1.10830 -0.77167 0.40691 -0.02732 -0.35327 0.72098 -1.06241 1.36511 -1.61803 1.81197 -1.93985 1.99702 -1.98137 1.89349 -1.73659 1.51637 -1.24087 0.92013 -0.56585 0.19094 ... ... ..... ....... ......... ........... ............. E55 * 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 ... ... ..... ....... ......... ........... ............. E56 * 2.00000 -1.99329 1.97319 -1.93985 1.89349 -1.83442 1.76304 -1.67982 1.58532 -1.48018 1.36511 -1.24087 1.10830 -0.96829 0.82178 -0.66976 0.51324 -0.35327 0.19094 -0.02732 -0.13648 0.29937 -0.46025 0.61803 -0.77167 0.92013 -1.06241 1.19756 -1.32467 1.44289 -1.55142 1.64954 -1.73659 1.81197 -1.87520 1.92583 -1.96354 1.98807 -1.99925 1.99702 -1.98137 1.95243 -1.91038 1.85550 -1.78817 1.70884 -1.61803 1.51637 -1.40452 1.28325 -1.15336 1.01573 -0.87128 0.72098 -0.56585 0.40691 -0.24524 0.08193 ... ... ..... ....... ......... ........... ............. E57 * 2.00000 -1.99925 1.99702 -1.99329 1.98807 -1.98137 1.97319 -1.96354 1.95243 -1.93985 1.92583 -1.91038 1.89349 -1.87520 1.85550 -1.83442 1.81197 -1.78817 1.76304 -1.73659 1.70884 -1.67982 1.64954 -1.61803 1.58532 -1.55142 1.51637 -1.48018 1.44289 -1.40452 1.36511 -1.32467 1.28325 -1.24087 1.19756 -1.15336 1.10830 -1.06241 1.01573 -0.96829 0.92013 -0.87128 0.82178 -0.77167 0.72098 -0.66976 0.61803 -0.56585 0.51324 -0.46025 0.40691 -0.35327 0.29937 -0.24524 0.19094 -0.13648 0.08193 -0.02732 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.997015606966 = 2*cos(2*π/115) 1.988071334464 = 2*cos(4*π/115) 1.973193875721 = 2*cos(6*π/115) 1.952427630919 = 2*cos(8*π/115) 1.925834574696 = 2*cos(10*π/115) = 2*cos(2*π/23) 1.893494071182 = 2*cos(12*π/115) 1.855502637152 = 2*cos(14*π/115) 1.811973653976 = 2*cos(16*π/115) 1.763037029249 = 2*cos(18*π/115) 1.708838809093 = 2*cos(20*π/115) = 2*cos(4*π/23) 1.649540742298 = 2*cos(22*π/115) 1.585319797602 = 2*cos(24*π/115) 1.516367635544 = 2*cos(26*π/115) 1.442890036478 = 2*cos(28*π/115) 1.365106286437 = 2*cos(30*π/115) = 2*cos(6*π/23) 1.283248522704 = 2*cos(32*π/115) 1.197561041019 = 2*cos(34*π/115) 1.108299566504 = 2*cos(36*π/115) 1.015730490484 = 2*cos(38*π/115) 0.920130075462 = 2*cos(40*π/115) = 2*cos(8*π/23) 0.821783630653 = 2*cos(42*π/115) 0.720984660501 = 2*cos(44*π/115) 0.618033988750 = 2*cos(46*π/115) = 2*cos(2*π/5) = (√5−1)/2 0.513238860668 = 2*cos(48*π/115) 0.406912026105 = 2*cos(50*π/115) = 2*cos(10*π/23) 0.299370806126 = 2*cos(52*π/115) 0.190936145999 = 2*cos(54*π/115) 0.081931657367 = 2*cos(56*π/115) -0.027317347532 = 2*cos(58*π/115) -0.136484826729 = 2*cos(60*π/115) = 2*cos(12*π/23) -0.245244981561 = 2*cos(62*π/115) -0.353273228977 = 2*cos(64*π/115) -0.460247170230 = 2*cos(66*π/115) -0.565847553034 = 2*cos(68*π/115) -0.669759224342 = 2*cos(70*π/115) = 2*cos(14*π/23) -0.771672070886 = 2*cos(72*π/115) -0.871281944677 = 2*cos(74*π/115) -0.968291570702 = 2*cos(76*π/115) -1.062411434108 = 2*cos(78*π/115) -1.153360644230 = 2*cos(80*π/115) = 2*cos(16*π/23) -1.240867772879 = 2*cos(82*π/115) -1.324671664391 = 2*cos(84*π/115) -1.404522215014 = 2*cos(86*π/115) -1.480181119323 = 2*cos(88*π/115) -1.551422581409 = 2*cos(90*π/115) = 2*cos(18*π/23) -1.618033988750 = 2*cos(92*π/115) = 2*cos(4*π/5) = −(√5+1)/2 -1.679816546726 = 2*cos(94*π/115) -1.736585871900 = 2*cos(96*π/115) -1.788172542295 = 2*cos(98*π/115) -1.834422603011 = 2*cos(100*π/115) = 2*cos(20*π/23) -1.875198025688 = 2*cos(102*π/115) -1.910377120439 = 2*cos(104*π/115) -1.939854899019 = 2*cos(106*π/115) -1.963543388151 = 2*cos(108*π/115) -1.981371892073 = 2*cos(110*π/115) = 2*cos(22*π/23) -1.993287203521 = 2*cos(112*π/115) -1.999253762524 = 2*cos(114*π/115) 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 C115 point group is 115, and the order of the principal axis (C115) is 115. The group has 58 irreducible representations. β The C115 point group is generated by one single symmetry element, C115. Therefore, it is a cyclic group. γ The lowest nonvanishing multipole moment in C115 is 2 (dipole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C115 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 114 cases have been combined into 57 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 57 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 57 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. For this group, however, some of the irrational characters cannot be expressed by a closed algebraic form using real numbers only.
| C113 | ||
| C114 | ||
| C115 | C115v C115h D115 D115h D115d | |
| C116 | ||
| C117 |
This Character Table for the C115 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.