C86 E 2 C86 2 C43 2 C86^3 2 C43^2 2 C86^5 2 C43^3 2 C86^7 2 C43^4 2 C86^9 2 C43^5 2 C86^11 2 C43^6 2 C86^13 2 C43^7 2 C86^15 2 C43^8 2 C86^17 2 C43^9 2 C86^19 2 C43^10 2 C86^21 2 C43^11 2 C86^23 2 C43^12 2 C86^25 2 C43^13 2 C86^27 2 C43^14 2 C86^29 2 C43^15 2 C86^31 2 C43^16 2 C86^33 2 C43^17 2 C86^35 2 C43^18 2 C86^37 2 C43^19 2 C86^39 2 C43^20 2 C86^41 2 C43^21 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 ..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 ... ... ..... ....... ......... ........... ............. E1 * 2.00000 1.99466 1.97869 1.95215 1.91520 1.86803 1.81090 1.74410 1.66800 1.58299 1.48954 1.38815 1.27935 1.16372 1.04188 0.91448 0.78221 0.64576 0.50587 0.36327 0.21874 0.07304 -0.07304 -0.21874 -0.36327 -0.50587 -0.64576 -0.78221 -0.91448 -1.04188 -1.16372 -1.27935 -1.38815 -1.48954 -1.58299 -1.66800 -1.74410 -1.81090 -1.86803 -1.91520 -1.95215 -1.97869 -1.99466 -2.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.97869 1.91520 1.81090 1.66800 1.48954 1.27935 1.04188 0.78221 0.50587 0.21874 -0.07304 -0.36327 -0.64576 -0.91448 -1.16372 -1.38815 -1.58299 -1.74410 -1.86803 -1.95215 -1.99466 -1.99466 -1.95215 -1.86803 -1.74410 -1.58299 -1.38815 -1.16372 -0.91448 -0.64576 -0.36327 -0.07304 0.21874 0.50587 0.78221 1.04188 1.27935 1.48954 1.66800 1.81090 1.91520 1.97869 2.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.95215 1.81090 1.58299 1.27935 0.91448 0.50587 0.07304 -0.36327 -0.78221 -1.16372 -1.48954 -1.74410 -1.91520 -1.99466 -1.97869 -1.86803 -1.66800 -1.38815 -1.04188 -0.64576 -0.21874 0.21874 0.64576 1.04188 1.38815 1.66800 1.86803 1.97869 1.99466 1.91520 1.74410 1.48954 1.16372 0.78221 0.36327 -0.07304 -0.50587 -0.91448 -1.27935 -1.58299 -1.81090 -1.95215 -2.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.91520 1.66800 1.27935 0.78221 0.21874 -0.36327 -0.91448 -1.38815 -1.74410 -1.95215 -1.99466 -1.86803 -1.58299 -1.16372 -0.64576 -0.07304 0.50587 1.04188 1.48954 1.81090 1.97869 1.97869 1.81090 1.48954 1.04188 0.50587 -0.07304 -0.64576 -1.16372 -1.58299 -1.86803 -1.99466 -1.95215 -1.74410 -1.38815 -0.91448 -0.36327 0.21874 0.78221 1.27935 1.66800 1.91520 2.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.86803 1.48954 0.91448 0.21874 -0.50587 -1.16372 -1.66800 -1.95215 -1.97869 -1.74410 -1.27935 -0.64576 0.07304 0.78221 1.38815 1.81090 1.99466 1.91520 1.58299 1.04188 0.36327 -0.36327 -1.04188 -1.58299 -1.91520 -1.99466 -1.81090 -1.38815 -0.78221 -0.07304 0.64576 1.27935 1.74410 1.97869 1.95215 1.66800 1.16372 0.50587 -0.21874 -0.91448 -1.48954 -1.86803 -2.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.81090 1.27935 0.50587 -0.36327 -1.16372 -1.74410 -1.99466 -1.86803 -1.38815 -0.64576 0.21874 1.04188 1.66800 1.97869 1.91520 1.48954 0.78221 -0.07304 -0.91448 -1.58299 -1.95215 -1.95215 -1.58299 -0.91448 -0.07304 0.78221 1.48954 1.91520 1.97869 1.66800 1.04188 0.21874 -0.64576 -1.38815 -1.86803 -1.99466 -1.74410 -1.16372 -0.36327 0.50587 1.27935 1.81090 2.00000 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.74410 1.04188 0.07304 -0.91448 -1.66800 -1.99466 -1.81090 -1.16372 -0.21874 0.78221 1.58299 1.97869 1.86803 1.27935 0.36327 -0.64576 -1.48954 -1.95215 -1.91520 -1.38815 -0.50587 0.50587 1.38815 1.91520 1.95215 1.48954 0.64576 -0.36327 -1.27935 -1.86803 -1.97869 -1.58299 -0.78221 0.21874 1.16372 1.81090 1.99466 1.66800 0.91448 -0.07304 -1.04188 -1.74410 -2.00000 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.66800 0.78221 -0.36327 -1.38815 -1.95215 -1.86803 -1.16372 -0.07304 1.04188 1.81090 1.97869 1.48954 0.50587 -0.64576 -1.58299 -1.99466 -1.74410 -0.91448 0.21874 1.27935 1.91520 1.91520 1.27935 0.21874 -0.91448 -1.74410 -1.99466 -1.58299 -0.64576 0.50587 1.48954 1.97869 1.81090 1.04188 -0.07304 -1.16372 -1.86803 -1.95215 -1.38815 -0.36327 0.78221 1.66800 2.00000 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.58299 0.50587 -0.78221 -1.74410 -1.97869 -1.38815 -0.21874 1.04188 1.86803 1.91520 1.16372 -0.07304 -1.27935 -1.95215 -1.81090 -0.91448 0.36327 1.48954 1.99466 1.66800 0.64576 -0.64576 -1.66800 -1.99466 -1.48954 -0.36327 0.91448 1.81090 1.95215 1.27935 0.07304 -1.16372 -1.91520 -1.86803 -1.04188 0.21874 1.38815 1.97869 1.74410 0.78221 -0.50587 -1.58299 -2.00000 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.48954 0.21874 -1.16372 -1.95215 -1.74410 -0.64576 0.78221 1.81090 1.91520 1.04188 -0.36327 -1.58299 -1.99466 -1.38815 -0.07304 1.27935 1.97869 1.66800 0.50587 -0.91448 -1.86803 -1.86803 -0.91448 0.50587 1.66800 1.97869 1.27935 -0.07304 -1.38815 -1.99466 -1.58299 -0.36327 1.04188 1.91520 1.81090 0.78221 -0.64576 -1.74410 -1.95215 -1.16372 0.21874 1.48954 2.00000 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.38815 -0.07304 -1.48954 -1.99466 -1.27935 0.21874 1.58299 1.97869 1.16372 -0.36327 -1.66800 -1.95215 -1.04188 0.50587 1.74410 1.91520 0.91448 -0.64576 -1.81090 -1.86803 -0.78221 0.78221 1.86803 1.81090 0.64576 -0.91448 -1.91520 -1.74410 -0.50587 1.04188 1.95215 1.66800 0.36327 -1.16372 -1.97869 -1.58299 -0.21874 1.27935 1.99466 1.48954 0.07304 -1.38815 -2.00000 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.27935 -0.36327 -1.74410 -1.86803 -0.64576 1.04188 1.97869 1.48954 -0.07304 -1.58299 -1.95215 -0.91448 0.78221 1.91520 1.66800 0.21874 -1.38815 -1.99466 -1.16372 0.50587 1.81090 1.81090 0.50587 -1.16372 -1.99466 -1.38815 0.21874 1.66800 1.91520 0.78221 -0.91448 -1.95215 -1.58299 -0.07304 1.48954 1.97869 1.04188 -0.64576 -1.86803 -1.74410 -0.36327 1.27935 2.00000 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.16372 -0.64576 -1.91520 -1.58299 0.07304 1.66800 1.86803 0.50587 -1.27935 -1.99466 -1.04188 0.78221 1.95215 1.48954 -0.21874 -1.74410 -1.81090 -0.36327 1.38815 1.97869 0.91448 -0.91448 -1.97869 -1.38815 0.36327 1.81090 1.74410 0.21874 -1.48954 -1.95215 -0.78221 1.04188 1.99466 1.27935 -0.50587 -1.86803 -1.66800 -0.07304 1.58299 1.91520 0.64576 -1.16372 -2.00000 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.04188 -0.91448 -1.99466 -1.16372 0.78221 1.97869 1.27935 -0.64576 -1.95215 -1.38815 0.50587 1.91520 1.48954 -0.36327 -1.86803 -1.58299 0.21874 1.81090 1.66800 -0.07304 -1.74410 -1.74410 -0.07304 1.66800 1.81090 0.21874 -1.58299 -1.86803 -0.36327 1.48954 1.91520 0.50587 -1.38815 -1.95215 -0.64576 1.27935 1.97869 0.78221 -1.16372 -1.99466 -0.91448 1.04188 2.00000 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 0.91448 -1.16372 -1.97869 -0.64576 1.38815 1.91520 0.36327 -1.58299 -1.81090 -0.07304 1.74410 1.66800 -0.21874 -1.86803 -1.48954 0.50587 1.95215 1.27935 -0.78221 -1.99466 -1.04188 1.04188 1.99466 0.78221 -1.27935 -1.95215 -0.50587 1.48954 1.86803 0.21874 -1.66800 -1.74410 0.07304 1.81090 1.58299 -0.36327 -1.91520 -1.38815 0.64576 1.97869 1.16372 -0.91448 -2.00000 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 0.78221 -1.38815 -1.86803 -0.07304 1.81090 1.48954 -0.64576 -1.99466 -0.91448 1.27935 1.91520 0.21874 -1.74410 -1.58299 0.50587 1.97869 1.04188 -1.16372 -1.95215 -0.36327 1.66800 1.66800 -0.36327 -1.95215 -1.16372 1.04188 1.97869 0.50587 -1.58299 -1.74410 0.21874 1.91520 1.27935 -0.91448 -1.99466 -0.64576 1.48954 1.81090 -0.07304 -1.86803 -1.38815 0.78221 2.00000 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 0.64576 -1.58299 -1.66800 0.50587 1.99466 0.78221 -1.48954 -1.74410 0.36327 1.97869 0.91448 -1.38815 -1.81090 0.21874 1.95215 1.04188 -1.27935 -1.86803 0.07304 1.91520 1.16372 -1.16372 -1.91520 -0.07304 1.86803 1.27935 -1.04188 -1.95215 -0.21874 1.81090 1.38815 -0.91448 -1.97869 -0.36327 1.74410 1.48954 -0.78221 -1.99466 -0.50587 1.66800 1.58299 -0.64576 -2.00000 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.50587 -1.74410 -1.38815 1.04188 1.91520 -0.07304 -1.95215 -0.91448 1.48954 1.66800 -0.64576 -1.99466 -0.36327 1.81090 1.27935 -1.16372 -1.86803 0.21874 1.97869 0.78221 -1.58299 -1.58299 0.78221 1.97869 0.21874 -1.86803 -1.16372 1.27935 1.81090 -0.36327 -1.99466 -0.64576 1.66800 1.48954 -0.91448 -1.95215 -0.07304 1.91520 1.04188 -1.38815 -1.74410 0.50587 2.00000 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.36327 -1.86803 -1.04188 1.48954 1.58299 -0.91448 -1.91520 0.21874 1.99466 0.50587 -1.81090 -1.16372 1.38815 1.66800 -0.78221 -1.95215 0.07304 1.97869 0.64576 -1.74410 -1.27935 1.27935 1.74410 -0.64576 -1.97869 -0.07304 1.95215 0.78221 -1.66800 -1.38815 1.16372 1.81090 -0.50587 -1.99466 -0.21874 1.91520 0.91448 -1.58299 -1.48954 1.04188 1.86803 -0.36327 -2.00000 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.21874 -1.95215 -0.64576 1.81090 1.04188 -1.58299 -1.38815 1.27935 1.66800 -0.91448 -1.86803 0.50587 1.97869 -0.07304 -1.99466 -0.36327 1.91520 0.78221 -1.74410 -1.16372 1.48954 1.48954 -1.16372 -1.74410 0.78221 1.91520 -0.36327 -1.99466 -0.07304 1.97869 0.50587 -1.86803 -0.91448 1.66800 1.27935 -1.38815 -1.58299 1.04188 1.81090 -0.64576 -1.95215 0.21874 2.00000 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.07304 -1.99466 -0.21874 1.97869 0.36327 -1.95215 -0.50587 1.91520 0.64576 -1.86803 -0.78221 1.81090 0.91448 -1.74410 -1.04188 1.66800 1.16372 -1.58299 -1.27935 1.48954 1.38815 -1.38815 -1.48954 1.27935 1.58299 -1.16372 -1.66800 1.04188 1.74410 -0.91448 -1.81090 0.78221 1.86803 -0.64576 -1.91520 0.50587 1.95215 -0.36327 -1.97869 0.21874 1.99466 -0.07304 -2.00000 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 -0.07304 -1.99466 0.21874 1.97869 -0.36327 -1.95215 0.50587 1.91520 -0.64576 -1.86803 0.78221 1.81090 -0.91448 -1.74410 1.04188 1.66800 -1.16372 -1.58299 1.27935 1.48954 -1.38815 -1.38815 1.48954 1.27935 -1.58299 -1.16372 1.66800 1.04188 -1.74410 -0.91448 1.81090 0.78221 -1.86803 -0.64576 1.91520 0.50587 -1.95215 -0.36327 1.97869 0.21874 -1.99466 -0.07304 2.00000 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 -0.21874 -1.95215 0.64576 1.81090 -1.04188 -1.58299 1.38815 1.27935 -1.66800 -0.91448 1.86803 0.50587 -1.97869 -0.07304 1.99466 -0.36327 -1.91520 0.78221 1.74410 -1.16372 -1.48954 1.48954 1.16372 -1.74410 -0.78221 1.91520 0.36327 -1.99466 0.07304 1.97869 -0.50587 -1.86803 0.91448 1.66800 -1.27935 -1.38815 1.58299 1.04188 -1.81090 -0.64576 1.95215 0.21874 -2.00000 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 -0.36327 -1.86803 1.04188 1.48954 -1.58299 -0.91448 1.91520 0.21874 -1.99466 0.50587 1.81090 -1.16372 -1.38815 1.66800 0.78221 -1.95215 -0.07304 1.97869 -0.64576 -1.74410 1.27935 1.27935 -1.74410 -0.64576 1.97869 -0.07304 -1.95215 0.78221 1.66800 -1.38815 -1.16372 1.81090 0.50587 -1.99466 0.21874 1.91520 -0.91448 -1.58299 1.48954 1.04188 -1.86803 -0.36327 2.00000 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 -0.50587 -1.74410 1.38815 1.04188 -1.91520 -0.07304 1.95215 -0.91448 -1.48954 1.66800 0.64576 -1.99466 0.36327 1.81090 -1.27935 -1.16372 1.86803 0.21874 -1.97869 0.78221 1.58299 -1.58299 -0.78221 1.97869 -0.21874 -1.86803 1.16372 1.27935 -1.81090 -0.36327 1.99466 -0.64576 -1.66800 1.48954 0.91448 -1.95215 0.07304 1.91520 -1.04188 -1.38815 1.74410 0.50587 -2.00000 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.64576 -1.58299 1.66800 0.50587 -1.99466 0.78221 1.48954 -1.74410 -0.36327 1.97869 -0.91448 -1.38815 1.81090 0.21874 -1.95215 1.04188 1.27935 -1.86803 -0.07304 1.91520 -1.16372 -1.16372 1.91520 -0.07304 -1.86803 1.27935 1.04188 -1.95215 0.21874 1.81090 -1.38815 -0.91448 1.97869 -0.36327 -1.74410 1.48954 0.78221 -1.99466 0.50587 1.66800 -1.58299 -0.64576 2.00000 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 -0.78221 -1.38815 1.86803 -0.07304 -1.81090 1.48954 0.64576 -1.99466 0.91448 1.27935 -1.91520 0.21874 1.74410 -1.58299 -0.50587 1.97869 -1.04188 -1.16372 1.95215 -0.36327 -1.66800 1.66800 0.36327 -1.95215 1.16372 1.04188 -1.97869 0.50587 1.58299 -1.74410 -0.21874 1.91520 -1.27935 -0.91448 1.99466 -0.64576 -1.48954 1.81090 0.07304 -1.86803 1.38815 0.78221 -2.00000 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.91448 -1.16372 1.97869 -0.64576 -1.38815 1.91520 -0.36327 -1.58299 1.81090 -0.07304 -1.74410 1.66800 0.21874 -1.86803 1.48954 0.50587 -1.95215 1.27935 0.78221 -1.99466 1.04188 1.04188 -1.99466 0.78221 1.27935 -1.95215 0.50587 1.48954 -1.86803 0.21874 1.66800 -1.74410 -0.07304 1.81090 -1.58299 -0.36327 1.91520 -1.38815 -0.64576 1.97869 -1.16372 -0.91448 2.00000 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -1.04188 -0.91448 1.99466 -1.16372 -0.78221 1.97869 -1.27935 -0.64576 1.95215 -1.38815 -0.50587 1.91520 -1.48954 -0.36327 1.86803 -1.58299 -0.21874 1.81090 -1.66800 -0.07304 1.74410 -1.74410 0.07304 1.66800 -1.81090 0.21874 1.58299 -1.86803 0.36327 1.48954 -1.91520 0.50587 1.38815 -1.95215 0.64576 1.27935 -1.97869 0.78221 1.16372 -1.99466 0.91448 1.04188 -2.00000 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -1.16372 -0.64576 1.91520 -1.58299 -0.07304 1.66800 -1.86803 0.50587 1.27935 -1.99466 1.04188 0.78221 -1.95215 1.48954 0.21874 -1.74410 1.81090 -0.36327 -1.38815 1.97869 -0.91448 -0.91448 1.97869 -1.38815 -0.36327 1.81090 -1.74410 0.21874 1.48954 -1.95215 0.78221 1.04188 -1.99466 1.27935 0.50587 -1.86803 1.66800 -0.07304 -1.58299 1.91520 -0.64576 -1.16372 2.00000 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -1.27935 -0.36327 1.74410 -1.86803 0.64576 1.04188 -1.97869 1.48954 0.07304 -1.58299 1.95215 -0.91448 -0.78221 1.91520 -1.66800 0.21874 1.38815 -1.99466 1.16372 0.50587 -1.81090 1.81090 -0.50587 -1.16372 1.99466 -1.38815 -0.21874 1.66800 -1.91520 0.78221 0.91448 -1.95215 1.58299 -0.07304 -1.48954 1.97869 -1.04188 -0.64576 1.86803 -1.74410 0.36327 1.27935 -2.00000 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -1.38815 -0.07304 1.48954 -1.99466 1.27935 0.21874 -1.58299 1.97869 -1.16372 -0.36327 1.66800 -1.95215 1.04188 0.50587 -1.74410 1.91520 -0.91448 -0.64576 1.81090 -1.86803 0.78221 0.78221 -1.86803 1.81090 -0.64576 -0.91448 1.91520 -1.74410 0.50587 1.04188 -1.95215 1.66800 -0.36327 -1.16372 1.97869 -1.58299 0.21874 1.27935 -1.99466 1.48954 -0.07304 -1.38815 2.00000 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -1.48954 0.21874 1.16372 -1.95215 1.74410 -0.64576 -0.78221 1.81090 -1.91520 1.04188 0.36327 -1.58299 1.99466 -1.38815 0.07304 1.27935 -1.97869 1.66800 -0.50587 -0.91448 1.86803 -1.86803 0.91448 0.50587 -1.66800 1.97869 -1.27935 -0.07304 1.38815 -1.99466 1.58299 -0.36327 -1.04188 1.91520 -1.81090 0.78221 0.64576 -1.74410 1.95215 -1.16372 -0.21874 1.48954 -2.00000 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.58299 0.50587 0.78221 -1.74410 1.97869 -1.38815 0.21874 1.04188 -1.86803 1.91520 -1.16372 -0.07304 1.27935 -1.95215 1.81090 -0.91448 -0.36327 1.48954 -1.99466 1.66800 -0.64576 -0.64576 1.66800 -1.99466 1.48954 -0.36327 -0.91448 1.81090 -1.95215 1.27935 -0.07304 -1.16372 1.91520 -1.86803 1.04188 0.21874 -1.38815 1.97869 -1.74410 0.78221 0.50587 -1.58299 2.00000 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.66800 0.78221 0.36327 -1.38815 1.95215 -1.86803 1.16372 -0.07304 -1.04188 1.81090 -1.97869 1.48954 -0.50587 -0.64576 1.58299 -1.99466 1.74410 -0.91448 -0.21874 1.27935 -1.91520 1.91520 -1.27935 0.21874 0.91448 -1.74410 1.99466 -1.58299 0.64576 0.50587 -1.48954 1.97869 -1.81090 1.04188 0.07304 -1.16372 1.86803 -1.95215 1.38815 -0.36327 -0.78221 1.66800 -2.00000 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.74410 1.04188 -0.07304 -0.91448 1.66800 -1.99466 1.81090 -1.16372 0.21874 0.78221 -1.58299 1.97869 -1.86803 1.27935 -0.36327 -0.64576 1.48954 -1.95215 1.91520 -1.38815 0.50587 0.50587 -1.38815 1.91520 -1.95215 1.48954 -0.64576 -0.36327 1.27935 -1.86803 1.97869 -1.58299 0.78221 0.21874 -1.16372 1.81090 -1.99466 1.66800 -0.91448 -0.07304 1.04188 -1.74410 2.00000 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.81090 1.27935 -0.50587 -0.36327 1.16372 -1.74410 1.99466 -1.86803 1.38815 -0.64576 -0.21874 1.04188 -1.66800 1.97869 -1.91520 1.48954 -0.78221 -0.07304 0.91448 -1.58299 1.95215 -1.95215 1.58299 -0.91448 0.07304 0.78221 -1.48954 1.91520 -1.97869 1.66800 -1.04188 0.21874 0.64576 -1.38815 1.86803 -1.99466 1.74410 -1.16372 0.36327 0.50587 -1.27935 1.81090 -2.00000 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.86803 1.48954 -0.91448 0.21874 0.50587 -1.16372 1.66800 -1.95215 1.97869 -1.74410 1.27935 -0.64576 -0.07304 0.78221 -1.38815 1.81090 -1.99466 1.91520 -1.58299 1.04188 -0.36327 -0.36327 1.04188 -1.58299 1.91520 -1.99466 1.81090 -1.38815 0.78221 -0.07304 -0.64576 1.27935 -1.74410 1.97869 -1.95215 1.66800 -1.16372 0.50587 0.21874 -0.91448 1.48954 -1.86803 2.00000 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.91520 1.66800 -1.27935 0.78221 -0.21874 -0.36327 0.91448 -1.38815 1.74410 -1.95215 1.99466 -1.86803 1.58299 -1.16372 0.64576 -0.07304 -0.50587 1.04188 -1.48954 1.81090 -1.97869 1.97869 -1.81090 1.48954 -1.04188 0.50587 0.07304 -0.64576 1.16372 -1.58299 1.86803 -1.99466 1.95215 -1.74410 1.38815 -0.91448 0.36327 0.21874 -0.78221 1.27935 -1.66800 1.91520 -2.00000 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.95215 1.81090 -1.58299 1.27935 -0.91448 0.50587 -0.07304 -0.36327 0.78221 -1.16372 1.48954 -1.74410 1.91520 -1.99466 1.97869 -1.86803 1.66800 -1.38815 1.04188 -0.64576 0.21874 0.21874 -0.64576 1.04188 -1.38815 1.66800 -1.86803 1.97869 -1.99466 1.91520 -1.74410 1.48954 -1.16372 0.78221 -0.36327 -0.07304 0.50587 -0.91448 1.27935 -1.58299 1.81090 -1.95215 2.00000 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.97869 1.91520 -1.81090 1.66800 -1.48954 1.27935 -1.04188 0.78221 -0.50587 0.21874 0.07304 -0.36327 0.64576 -0.91448 1.16372 -1.38815 1.58299 -1.74410 1.86803 -1.95215 1.99466 -1.99466 1.95215 -1.86803 1.74410 -1.58299 1.38815 -1.16372 0.91448 -0.64576 0.36327 -0.07304 -0.21874 0.50587 -0.78221 1.04188 -1.27935 1.48954 -1.66800 1.81090 -1.91520 1.97869 -2.00000 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.99466 1.97869 -1.95215 1.91520 -1.86803 1.81090 -1.74410 1.66800 -1.58299 1.48954 -1.38815 1.27935 -1.16372 1.04188 -0.91448 0.78221 -0.64576 0.50587 -0.36327 0.21874 -0.07304 -0.07304 0.21874 -0.36327 0.50587 -0.64576 0.78221 -0.91448 1.04188 -1.16372 1.27935 -1.38815 1.48954 -1.58299 1.66800 -1.74410 1.81090 -1.86803 1.91520 -1.95215 1.97869 -1.99466 2.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.994664567327 = 2*cos(2*π/86) = 2*cos(π/43) 1.978686736150 = 2*cos(4*π/86) = 2*cos(2*π/43) 1.952151755112 = 2*cos(6*π/86) = 2*cos(3*π/43) 1.915201199817 = 2*cos(8*π/86) = 2*cos(4*π/43) 1.868032217465 = 2*cos(10*π/86) = 2*cos(5*π/43) 1.810896474986 = 2*cos(12*π/86) = 2*cos(6*π/43) 1.744098816288 = 2*cos(14*π/86) = 2*cos(7*π/43) 1.667995635780 = 2*cos(16*π/86) = 2*cos(8*π/43) 1.582992976859 = 2*cos(18*π/86) = 2*cos(9*π/43) 1.489544365488 = 2*cos(20*π/86) = 2*cos(10*π/43) 1.388148390441 = 2*cos(22*π/86) = 2*cos(11*π/43) 1.279346043118 = 2*cos(24*π/86) = 2*cos(12*π/43) 1.163717831116 = 2*cos(26*π/86) = 2*cos(13*π/43) 1.041880680976 = 2*cos(28*π/86) = 2*cos(14*π/43) 0.914484646609 = 2*cos(30*π/86) = 2*cos(15*π/43) 0.782209440980 = 2*cos(32*π/86) = 2*cos(16*π/43) 0.645760809543 = 2*cos(34*π/86) = 2*cos(17*π/43) 0.505866764783 = 2*cos(36*π/86) = 2*cos(18*π/43) 0.363273701959 = 2*cos(38*π/86) = 2*cos(19*π/43) 0.218742416756 = 2*cos(40*π/86) = 2*cos(20*π/43) 0.073044046115 = 2*cos(42*π/86) = 2*cos(21*π/43) 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 C86 point group is 86, and the order of the principal axis (C86) is 86. The group has 44 irreducible representations. β The C86 point group is isomorphic to S86 and C43h. γ The C86 point group is generated by one single symmetry element, C86. Therefore, it is a cyclic group. δ The lowest nonvanishing multipole moment in C86 is 2 (dipole moment). ε This is an Abelian point group (the commutative law holds between all symmetry operations). The C86 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 84 cases have been combined into 42 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 42 pairs of left and right rotations have been combined into one two-membered pseudo-class each. η The 42 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, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.
| C84 | ||
| C85 | ||
| C86 | C86v C86h D86 D86h D86d S86 | |
| C87 | ||
| C88 |
This Character Table for the C86 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.