C99 E 2 C99 2 C99^2 2 C33 2 C99^4 2 C99^5 2 C33^2 2 C99^7 2 C99^8 2 C11 2 C99^10 2 C9 2 C33^4 2 C99^13 2 C99^14 2 C33^5 2 C99^16 2 C99^17 2 C11^2 2 C99^19 2 C99^20 2 C33^7 2 C9^2 2 C99^23 2 C33^8 2 C99^25 2 C99^26 2 C11^3 2 C99^28 2 C99^29 2 C33^10 2 C99^31 2 C99^32 2 C3 2 C99^34 2 C99^35 2 C11^4 2 C99^37 2 C99^38 2 C33^13 2 C99^40 2 C99^41 2 C33^14 2 C99^43 2 C9^4 2 C11^5 2 C99^46 2 C99^47 2 C33^16 2 C99^49 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99597 1.98391 1.96386 1.93590 1.90014 1.85674 1.80585 1.74770 1.68251 1.61054 1.53209 1.44747 1.35702 1.26111 1.16011 1.05445 0.94454 0.83083 0.71377 0.59384 0.47152 0.34730 0.22168 0.09516 -0.03173 -0.15850 -0.28463 -0.40961 -0.53295 -0.65414 -0.77269 -0.88813 -1.00000 -1.10784 -1.21122 -1.30972 -1.40295 -1.49053 -1.57211 -1.64735 -1.71597 -1.77767 -1.83222 -1.87939 -1.91899 -1.95086 -1.97488 -1.99094 -1.99899 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98391 1.93590 1.85674 1.74770 1.61054 1.44747 1.26111 1.05445 0.83083 0.59384 0.34730 0.09516 -0.15850 -0.40961 -0.65414 -0.88813 -1.10784 -1.30972 -1.49053 -1.64735 -1.77767 -1.87939 -1.95086 -1.99094 -1.99899 -1.97488 -1.91899 -1.83222 -1.71597 -1.57211 -1.40295 -1.21122 -1.00000 -0.77269 -0.53295 -0.28463 -0.03173 0.22168 0.47152 0.71377 0.94454 1.16011 1.35702 1.53209 1.68251 1.80585 1.90014 1.96386 1.99597 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.96386 1.85674 1.68251 1.44747 1.16011 0.83083 0.47152 0.09516 -0.28463 -0.65414 -1.00000 -1.30972 -1.57211 -1.77767 -1.91899 -1.99094 -1.99094 -1.91899 -1.77767 -1.57211 -1.30972 -1.00000 -0.65414 -0.28463 0.09516 0.47152 0.83083 1.16011 1.44747 1.68251 1.85674 1.96386 2.00000 1.96386 1.85674 1.68251 1.44747 1.16011 0.83083 0.47152 0.09516 -0.28463 -0.65414 -1.00000 -1.30972 -1.57211 -1.77767 -1.91899 -1.99094 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.93590 1.74770 1.44747 1.05445 0.59384 0.09516 -0.40961 -0.88813 -1.30972 -1.64735 -1.87939 -1.99094 -1.97488 -1.83222 -1.57211 -1.21122 -0.77269 -0.28463 0.22168 0.71377 1.16011 1.53209 1.80585 1.96386 1.99597 1.90014 1.68251 1.35702 0.94454 0.47152 -0.03173 -0.53295 -1.00000 -1.40295 -1.71597 -1.91899 -1.99899 -1.95086 -1.77767 -1.49053 -1.10784 -0.65414 -0.15850 0.34730 0.83083 1.26111 1.61054 1.85674 1.98391 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.90014 1.61054 1.16011 0.59384 -0.03173 -0.65414 -1.21122 -1.64735 -1.91899 -1.99899 -1.87939 -1.57211 -1.10784 -0.53295 0.09516 0.71377 1.26111 1.68251 1.93590 1.99597 1.85674 1.53209 1.05445 0.47152 -0.15850 -0.77269 -1.30972 -1.71597 -1.95086 -1.99094 -1.83222 -1.49053 -1.00000 -0.40961 0.22168 0.83083 1.35702 1.74770 1.96386 1.98391 1.80585 1.44747 0.94454 0.34730 -0.28463 -0.88813 -1.40295 -1.77767 -1.97488 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.85674 1.44747 0.83083 0.09516 -0.65414 -1.30972 -1.77767 -1.99094 -1.91899 -1.57211 -1.00000 -0.28463 0.47152 1.16011 1.68251 1.96386 1.96386 1.68251 1.16011 0.47152 -0.28463 -1.00000 -1.57211 -1.91899 -1.99094 -1.77767 -1.30972 -0.65414 0.09516 0.83083 1.44747 1.85674 2.00000 1.85674 1.44747 0.83083 0.09516 -0.65414 -1.30972 -1.77767 -1.99094 -1.91899 -1.57211 -1.00000 -0.28463 0.47152 1.16011 1.68251 1.96386 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.80585 1.26111 0.47152 -0.40961 -1.21122 -1.77767 -1.99899 -1.83222 -1.30972 -0.53295 0.34730 1.16011 1.74770 1.99597 1.85674 1.35702 0.59384 -0.28463 -1.10784 -1.71597 -1.99094 -1.87939 -1.40295 -0.65414 0.22168 1.05445 1.68251 1.98391 1.90014 1.44747 0.71377 -0.15850 -1.00000 -1.64735 -1.97488 -1.91899 -1.49053 -0.77269 0.09516 0.94454 1.61054 1.96386 1.93590 1.53209 0.83083 -0.03173 -0.88813 -1.57211 -1.95086 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.74770 1.05445 0.09516 -0.88813 -1.64735 -1.99094 -1.83222 -1.21122 -0.28463 0.71377 1.53209 1.96386 1.90014 1.35702 0.47152 -0.53295 -1.40295 -1.91899 -1.95086 -1.49053 -0.65414 0.34730 1.26111 1.85674 1.98391 1.61054 0.83083 -0.15850 -1.10784 -1.77767 -1.99899 -1.71597 -1.00000 -0.03173 0.94454 1.68251 1.99597 1.80585 1.16011 0.22168 -0.77269 -1.57211 -1.97488 -1.87939 -1.30972 -0.40961 0.59384 1.44747 1.93590 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.61054 0.59384 -0.65414 -1.64735 -1.99899 -1.57211 -0.53295 0.71377 1.68251 1.99597 1.53209 0.47152 -0.77269 -1.71597 -1.99094 -1.49053 -0.40961 0.83083 1.74770 1.98391 1.44747 0.34730 -0.88813 -1.77767 -1.97488 -1.40295 -0.28463 0.94454 1.80585 1.96386 1.35702 0.22168 -1.00000 -1.83222 -1.95086 -1.30972 -0.15850 1.05445 1.85674 1.93590 1.26111 0.09516 -1.10784 -1.87939 -1.91899 -1.21122 -0.03173 1.16011 1.90014 ... ... ..... ....... ......... ........... ............. E11 * 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 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.44747 0.09516 -1.30972 -1.99094 -1.57211 -0.28463 1.16011 1.96386 1.68251 0.47152 -1.00000 -1.91899 -1.77767 -0.65414 0.83083 1.85674 1.85674 0.83083 -0.65414 -1.77767 -1.91899 -1.00000 0.47152 1.68251 1.96386 1.16011 -0.28463 -1.57211 -1.99094 -1.30972 0.09516 1.44747 2.00000 1.44747 0.09516 -1.30972 -1.99094 -1.57211 -0.28463 1.16011 1.96386 1.68251 0.47152 -1.00000 -1.91899 -1.77767 -0.65414 0.83083 1.85674 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.35702 -0.15850 -1.57211 -1.97488 -1.10784 0.47152 1.74770 1.90014 0.83083 -0.77269 -1.87939 -1.77767 -0.53295 1.05445 1.96386 1.61054 0.22168 -1.30972 -1.99899 -1.40295 0.09516 1.53209 1.98391 1.16011 -0.40961 -1.71597 -1.91899 -0.88813 0.71377 1.85674 1.80585 0.59384 -1.00000 -1.95086 -1.64735 -0.28463 1.26111 1.99597 1.44747 -0.03173 -1.49053 -1.99094 -1.21122 0.34730 1.68251 1.93590 0.94454 -0.65414 -1.83222 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.26111 -0.40961 -1.77767 -1.83222 -0.53295 1.16011 1.99597 1.35702 -0.28463 -1.71597 -1.87939 -0.65414 1.05445 1.98391 1.44747 -0.15850 -1.64735 -1.91899 -0.77269 0.94454 1.96386 1.53209 -0.03173 -1.57211 -1.95086 -0.88813 0.83083 1.93590 1.61054 0.09516 -1.49053 -1.97488 -1.00000 0.71377 1.90014 1.68251 0.22168 -1.40295 -1.99094 -1.10784 0.59384 1.85674 1.74770 0.34730 -1.30972 -1.99899 -1.21122 0.47152 1.80585 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.16011 -0.65414 -1.91899 -1.57211 0.09516 1.68251 1.85674 0.47152 -1.30972 -1.99094 -1.00000 0.83083 1.96386 1.44747 -0.28463 -1.77767 -1.77767 -0.28463 1.44747 1.96386 0.83083 -1.00000 -1.99094 -1.30972 0.47152 1.85674 1.68251 0.09516 -1.57211 -1.91899 -0.65414 1.16011 2.00000 1.16011 -0.65414 -1.91899 -1.57211 0.09516 1.68251 1.85674 0.47152 -1.30972 -1.99094 -1.00000 0.83083 1.96386 1.44747 -0.28463 -1.77767 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.05445 -0.88813 -1.99094 -1.21122 0.71377 1.96386 1.35702 -0.53295 -1.91899 -1.49053 0.34730 1.85674 1.61054 -0.15850 -1.77767 -1.71597 -0.03173 1.68251 1.80585 0.22168 -1.57211 -1.87939 -0.40961 1.44747 1.93590 0.59384 -1.30972 -1.97488 -0.77269 1.16011 1.99597 0.94454 -1.00000 -1.99899 -1.10784 0.83083 1.98391 1.26111 -0.65414 -1.95086 -1.40295 0.47152 1.90014 1.53209 -0.28463 -1.83222 -1.64735 0.09516 1.74770 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 0.94454 -1.10784 -1.99094 -0.77269 1.26111 1.96386 0.59384 -1.40295 -1.91899 -0.40961 1.53209 1.85674 0.22168 -1.64735 -1.77767 -0.03173 1.74770 1.68251 -0.15850 -1.83222 -1.57211 0.34730 1.90014 1.44747 -0.53295 -1.95086 -1.30972 0.71377 1.98391 1.16011 -0.88813 -1.99899 -1.00000 1.05445 1.99597 0.83083 -1.21122 -1.97488 -0.65414 1.35702 1.93590 0.47152 -1.49053 -1.87939 -0.28463 1.61054 1.80585 0.09516 -1.71597 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 1.68251 -0.28463 -1.91899 -1.30972 0.83083 2.00000 0.83083 -1.30972 -1.91899 -0.28463 1.68251 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.71377 -1.49053 -1.77767 0.22168 1.93590 1.16011 -1.10784 -1.95086 -0.28463 1.74770 1.53209 -0.65414 -1.99899 -0.77269 1.44747 1.80585 -0.15850 -1.91899 -1.21122 1.05445 1.96386 0.34730 -1.71597 -1.57211 0.59384 1.99597 0.83083 -1.40295 -1.83222 0.09516 1.90014 1.26111 -1.00000 -1.97488 -0.40961 1.68251 1.61054 -0.53295 -1.99094 -0.88813 1.35702 1.85674 -0.03173 -1.87939 -1.30972 0.94454 1.98391 0.47152 -1.64735 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.59384 -1.64735 -1.57211 0.71377 1.99597 0.47152 -1.71597 -1.49053 0.83083 1.98391 0.34730 -1.77767 -1.40295 0.94454 1.96386 0.22168 -1.83222 -1.30972 1.05445 1.93590 0.09516 -1.87939 -1.21122 1.16011 1.90014 -0.03173 -1.91899 -1.10784 1.26111 1.85674 -0.15850 -1.95086 -1.00000 1.35702 1.80585 -0.28463 -1.97488 -0.88813 1.44747 1.74770 -0.40961 -1.99094 -0.77269 1.53209 1.68251 -0.53295 -1.99899 -0.65414 1.61054 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.47152 -1.77767 -1.30972 1.16011 1.85674 -0.28463 -1.99094 -0.65414 1.68251 1.44747 -1.00000 -1.91899 0.09516 1.96386 0.83083 -1.57211 -1.57211 0.83083 1.96386 0.09516 -1.91899 -1.00000 1.44747 1.68251 -0.65414 -1.99094 -0.28463 1.85674 1.16011 -1.30972 -1.77767 0.47152 2.00000 0.47152 -1.77767 -1.30972 1.16011 1.85674 -0.28463 -1.99094 -0.65414 1.68251 1.44747 -1.00000 -1.91899 0.09516 1.96386 0.83083 -1.57211 ... ... ..... ....... ......... ........... ............. E22 * 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 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.22168 -1.95086 -0.65414 1.80585 1.05445 -1.57211 -1.40295 1.26111 1.68251 -0.88813 -1.87939 0.47152 1.98391 -0.03173 -1.99094 -0.40961 1.90014 0.83083 -1.71597 -1.21122 1.44747 1.53209 -1.10784 -1.77767 0.71377 1.93590 -0.28463 -1.99899 -0.15850 1.96386 0.59384 -1.83222 -1.00000 1.61054 1.35702 -1.30972 -1.64735 0.94454 1.85674 -0.53295 -1.97488 0.09516 1.99597 0.34730 -1.91899 -0.77269 1.74770 1.16011 -1.49053 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 0.09516 -1.99094 -0.28463 1.96386 0.47152 -1.91899 -0.65414 1.85674 0.83083 -1.77767 -1.00000 1.68251 1.16011 -1.57211 -1.30972 1.44747 1.44747 -1.30972 -1.57211 1.16011 1.68251 -1.00000 -1.77767 0.83083 1.85674 -0.65414 -1.91899 0.47152 1.96386 -0.28463 -1.99094 0.09516 2.00000 0.09516 -1.99094 -0.28463 1.96386 0.47152 -1.91899 -0.65414 1.85674 0.83083 -1.77767 -1.00000 1.68251 1.16011 -1.57211 -1.30972 1.44747 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 -0.03173 -1.99899 0.09516 1.99597 -0.15850 -1.99094 0.22168 1.98391 -0.28463 -1.97488 0.34730 1.96386 -0.40961 -1.95086 0.47152 1.93590 -0.53295 -1.91899 0.59384 1.90014 -0.65414 -1.87939 0.71377 1.85674 -0.77269 -1.83222 0.83083 1.80585 -0.88813 -1.77767 0.94454 1.74770 -1.00000 -1.71597 1.05445 1.68251 -1.10784 -1.64735 1.16011 1.61054 -1.21122 -1.57211 1.26111 1.53209 -1.30972 -1.49053 1.35702 1.44747 -1.40295 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.15850 -1.97488 0.47152 1.90014 -0.77269 -1.77767 1.05445 1.61054 -1.30972 -1.40295 1.53209 1.16011 -1.71597 -0.88813 1.85674 0.59384 -1.95086 -0.28463 1.99597 -0.03173 -1.99094 0.34730 1.93590 -0.65414 -1.83222 0.94454 1.68251 -1.21122 -1.49053 1.44747 1.26111 -1.64735 -1.00000 1.80585 0.71377 -1.91899 -0.40961 1.98391 0.09516 -1.99899 0.22168 1.96386 -0.53295 -1.87939 0.83083 1.74770 -1.10784 -1.57211 1.35702 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.40961 -1.83222 1.16011 1.35702 -1.71597 -0.65414 1.98391 -0.15850 -1.91899 0.94454 1.53209 -1.57211 -0.88813 1.93590 0.09516 -1.97488 0.71377 1.68251 -1.40295 -1.10784 1.85674 0.34730 -1.99899 0.47152 1.80585 -1.21122 -1.30972 1.74770 0.59384 -1.99094 0.22168 1.90014 -1.00000 -1.49053 1.61054 0.83083 -1.95086 -0.03173 1.96386 -0.77269 -1.64735 1.44747 1.05445 -1.87939 -0.28463 1.99597 -0.53295 -1.77767 1.26111 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.53295 -1.71597 1.44747 0.94454 -1.95086 0.09516 1.90014 -1.10784 -1.30972 1.80585 0.34730 -1.99094 0.71377 1.61054 -1.57211 -0.77269 1.98391 -0.28463 -1.83222 1.26111 1.16011 -1.87939 -0.15850 1.96386 -0.88813 -1.49053 1.68251 0.59384 -1.99899 0.47152 1.74770 -1.40295 -1.00000 1.93590 -0.03173 -1.91899 1.05445 1.35702 -1.77767 -0.40961 1.99597 -0.65414 -1.64735 1.53209 0.83083 -1.97488 0.22168 1.85674 -1.21122 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -0.65414 -1.57211 1.68251 0.47152 -1.99094 0.83083 1.44747 -1.77767 -0.28463 1.96386 -1.00000 -1.30972 1.85674 0.09516 -1.91899 1.16011 1.16011 -1.91899 0.09516 1.85674 -1.30972 -1.00000 1.96386 -0.28463 -1.77767 1.44747 0.83083 -1.99094 0.47152 1.68251 -1.57211 -0.65414 2.00000 -0.65414 -1.57211 1.68251 0.47152 -1.99094 0.83083 1.44747 -1.77767 -0.28463 1.96386 -1.00000 -1.30972 1.85674 0.09516 -1.91899 1.16011 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -0.77269 -1.40295 1.85674 -0.03173 -1.83222 1.44747 0.71377 -1.99899 0.83083 1.35702 -1.87939 0.09516 1.80585 -1.49053 -0.65414 1.99597 -0.88813 -1.30972 1.90014 -0.15850 -1.77767 1.53209 0.59384 -1.99094 0.94454 1.26111 -1.91899 0.22168 1.74770 -1.57211 -0.53295 1.98391 -1.00000 -1.21122 1.93590 -0.28463 -1.71597 1.61054 0.47152 -1.97488 1.05445 1.16011 -1.95086 0.34730 1.68251 -1.64735 -0.40961 1.96386 -1.10784 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -0.88813 -1.21122 1.96386 -0.53295 -1.49053 1.85674 -0.15850 -1.71597 1.68251 0.22168 -1.87939 1.44747 0.59384 -1.97488 1.16011 0.94454 -1.99899 0.83083 1.26111 -1.95086 0.47152 1.53209 -1.83222 0.09516 1.74770 -1.64735 -0.28463 1.90014 -1.40295 -0.65414 1.98391 -1.10784 -1.00000 1.99597 -0.77269 -1.30972 1.93590 -0.40961 -1.57211 1.80585 -0.03173 -1.77767 1.61054 0.34730 -1.91899 1.35702 0.71377 -1.99094 1.05445 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.10784 -0.77269 1.96386 -1.40295 -0.40961 1.85674 -1.64735 -0.03173 1.68251 -1.83222 0.34730 1.44747 -1.95086 0.71377 1.16011 -1.99899 1.05445 0.83083 -1.97488 1.35702 0.47152 -1.87939 1.61054 0.09516 -1.71597 1.80585 -0.28463 -1.49053 1.93590 -0.65414 -1.21122 1.99597 -1.00000 -0.88813 1.98391 -1.30972 -0.53295 1.90014 -1.57211 -0.15850 1.74770 -1.77767 0.22168 1.53209 -1.91899 0.59384 1.26111 -1.99094 0.94454 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.21122 -0.53295 1.85674 -1.71597 0.22168 1.44747 -1.97488 0.94454 0.83083 -1.95086 1.53209 0.09516 -1.64735 1.90014 -0.65414 -1.10784 1.99597 -1.30972 -0.40961 1.80585 -1.77767 0.34730 1.35702 -1.99094 1.05445 0.71377 -1.91899 1.61054 -0.03173 -1.57211 1.93590 -0.77269 -1.00000 1.98391 -1.40295 -0.28463 1.74770 -1.83222 0.47152 1.26111 -1.99899 1.16011 0.59384 -1.87939 1.68251 -0.15850 -1.49053 1.96386 -0.88813 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.40295 -0.03173 1.44747 -1.99899 1.35702 0.09516 -1.49053 1.99597 -1.30972 -0.15850 1.53209 -1.99094 1.26111 0.22168 -1.57211 1.98391 -1.21122 -0.28463 1.61054 -1.97488 1.16011 0.34730 -1.64735 1.96386 -1.10784 -0.40961 1.68251 -1.95086 1.05445 0.47152 -1.71597 1.93590 -1.00000 -0.53295 1.74770 -1.91899 0.94454 0.59384 -1.77767 1.90014 -0.88813 -0.65414 1.80585 -1.87939 0.83083 0.71377 -1.83222 1.85674 -0.77269 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.49053 0.22168 1.16011 -1.95086 1.74770 -0.65414 -0.77269 1.80585 -1.91899 1.05445 0.34730 -1.57211 1.99597 -1.40295 0.09516 1.26111 -1.97488 1.68251 -0.53295 -0.88813 1.85674 -1.87939 0.94454 0.47152 -1.64735 1.98391 -1.30972 -0.03173 1.35702 -1.99094 1.61054 -0.40961 -1.00000 1.90014 -1.83222 0.83083 0.59384 -1.71597 1.96386 -1.21122 -0.15850 1.44747 -1.99899 1.53209 -0.28463 -1.10784 1.93590 -1.77767 0.71377 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.57211 0.47152 0.83083 -1.77767 1.96386 -1.30972 0.09516 1.16011 -1.91899 1.85674 -1.00000 -0.28463 1.44747 -1.99094 1.68251 -0.65414 -0.65414 1.68251 -1.99094 1.44747 -0.28463 -1.00000 1.85674 -1.91899 1.16011 0.09516 -1.30972 1.96386 -1.77767 0.83083 0.47152 -1.57211 2.00000 -1.57211 0.47152 0.83083 -1.77767 1.96386 -1.30972 0.09516 1.16011 -1.91899 1.85674 -1.00000 -0.28463 1.44747 -1.99094 1.68251 -0.65414 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.64735 0.71377 0.47152 -1.49053 1.98391 -1.77767 0.94454 0.22168 -1.30972 1.93590 -1.87939 1.16011 -0.03173 -1.10784 1.85674 -1.95086 1.35702 -0.28463 -0.88813 1.74770 -1.99094 1.53209 -0.53295 -0.65414 1.61054 -1.99899 1.68251 -0.77269 -0.40961 1.44747 -1.97488 1.80585 -1.00000 -0.15850 1.26111 -1.91899 1.90014 -1.21122 0.09516 1.05445 -1.83222 1.96386 -1.40295 0.34730 0.83083 -1.71597 1.99597 -1.57211 0.59384 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.71597 0.94454 0.09516 -1.10784 1.80585 -1.99094 1.61054 -0.77269 -0.28463 1.26111 -1.87939 1.96386 -1.49053 0.59384 0.47152 -1.40295 1.93590 -1.91899 1.35702 -0.40961 -0.65414 1.53209 -1.97488 1.85674 -1.21122 0.22168 0.83083 -1.64735 1.99597 -1.77767 1.05445 -0.03173 -1.00000 1.74770 -1.99899 1.68251 -0.88813 -0.15850 1.16011 -1.83222 1.98391 -1.57211 0.71377 0.34730 -1.30972 1.90014 -1.95086 1.44747 -0.53295 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.77767 1.16011 -0.28463 -0.65414 1.44747 -1.91899 1.96386 -1.57211 0.83083 0.09516 -1.00000 1.68251 -1.99094 1.85674 -1.30972 0.47152 0.47152 -1.30972 1.85674 -1.99094 1.68251 -1.00000 0.09516 0.83083 -1.57211 1.96386 -1.91899 1.44747 -0.65414 -0.28463 1.16011 -1.77767 2.00000 -1.77767 1.16011 -0.28463 -0.65414 1.44747 -1.91899 1.96386 -1.57211 0.83083 0.09516 -1.00000 1.68251 -1.99094 1.85674 -1.30972 0.47152 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.83222 1.35702 -0.65414 -0.15850 0.94454 -1.57211 1.93590 -1.97488 1.68251 -1.10784 0.34730 0.47152 -1.21122 1.74770 -1.99094 1.90014 -1.49053 0.83083 -0.03173 -0.77269 1.44747 -1.87939 1.99597 -1.77767 1.26111 -0.53295 -0.28463 1.05445 -1.64735 1.96386 -1.95086 1.61054 -1.00000 0.22168 0.59384 -1.30972 1.80585 -1.99899 1.85674 -1.40295 0.71377 0.09516 -0.88813 1.53209 -1.91899 1.98391 -1.71597 1.16011 -0.40961 ... ... ..... ....... ......... ........... ............. E44 * 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 ... ... ..... ....... ......... ........... ............. E45 * 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 ... ... ..... ....... ......... ........... ............. E46 * 2.00000 -1.95086 1.80585 -1.57211 1.26111 -0.88813 0.47152 -0.03173 -0.40961 0.83083 -1.21122 1.53209 -1.77767 1.93590 -1.99899 1.96386 -1.83222 1.61054 -1.30972 0.94454 -0.53295 0.09516 0.34730 -0.77269 1.16011 -1.49053 1.74770 -1.91899 1.99597 -1.97488 1.85674 -1.64735 1.35702 -1.00000 0.59384 -0.15850 -0.28463 0.71377 -1.10784 1.44747 -1.71597 1.90014 -1.99094 1.98391 -1.87939 1.68251 -1.40295 1.05445 -0.65414 0.22168 ... ... ..... ....... ......... ........... ............. E47 * 2.00000 -1.97488 1.90014 -1.77767 1.61054 -1.40295 1.16011 -0.88813 0.59384 -0.28463 -0.03173 0.34730 -0.65414 0.94454 -1.21122 1.44747 -1.64735 1.80585 -1.91899 1.98391 -1.99899 1.96386 -1.87939 1.74770 -1.57211 1.35702 -1.10784 0.83083 -0.53295 0.22168 0.09516 -0.40961 0.71377 -1.00000 1.26111 -1.49053 1.68251 -1.83222 1.93590 -1.99094 1.99597 -1.95086 1.85674 -1.71597 1.53209 -1.30972 1.05445 -0.77269 0.47152 -0.15850 ... ... ..... ....... ......... ........... ............. E48 * 2.00000 -1.99094 1.96386 -1.91899 1.85674 -1.77767 1.68251 -1.57211 1.44747 -1.30972 1.16011 -1.00000 0.83083 -0.65414 0.47152 -0.28463 0.09516 0.09516 -0.28463 0.47152 -0.65414 0.83083 -1.00000 1.16011 -1.30972 1.44747 -1.57211 1.68251 -1.77767 1.85674 -1.91899 1.96386 -1.99094 2.00000 -1.99094 1.96386 -1.91899 1.85674 -1.77767 1.68251 -1.57211 1.44747 -1.30972 1.16011 -1.00000 0.83083 -0.65414 0.47152 -0.28463 0.09516 ... ... ..... ....... ......... ........... ............. E49 * 2.00000 -1.99899 1.99597 -1.99094 1.98391 -1.97488 1.96386 -1.95086 1.93590 -1.91899 1.90014 -1.87939 1.85674 -1.83222 1.80585 -1.77767 1.74770 -1.71597 1.68251 -1.64735 1.61054 -1.57211 1.53209 -1.49053 1.44747 -1.40295 1.35702 -1.30972 1.26111 -1.21122 1.16011 -1.10784 1.05445 -1.00000 0.94454 -0.88813 0.83083 -0.77269 0.71377 -0.65414 0.59384 -0.53295 0.47152 -0.40961 0.34730 -0.28463 0.22168 -0.15850 0.09516 -0.03173 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.995973352944 = 2*cos(2*π/99) 1.983909625662 = 2*cos(4*π/99) 1.963857394525 = 2*cos(6*π/99) = 2*cos(2*π/33) 1.935897402793 = 2*cos(8*π/99) 1.900142235482 = 2*cos(10*π/99) 1.856735866032 = 2*cos(12*π/99) = 2*cos(4*π/33) 1.805853076573 = 2*cos(14*π/99) 1.747698754140 = 2*cos(16*π/99) 1.682507065662 = 2*cos(18*π/99) = 2*cos(2*π/11) 1.610540515062 = 2*cos(20*π/99) 1.532088886238 = 2*cos(22*π/99) = 2*cos(2*π/9) 1.447468076210 = 2*cos(24*π/99) = 2*cos(8*π/33) 1.357018823114 = 2*cos(26*π/99) 1.261105334169 = 2*cos(28*π/99) 1.160113819142 = 2*cos(30*π/99) = 2*cos(10*π/33) 1.054450935221 = 2*cos(32*π/99) 0.944542149545 = 2*cos(34*π/99) 0.830830026004 = 2*cos(36*π/99) = 2*cos(4*π/11) 0.713772443184 = 2*cos(38*π/99) 0.593840750656 = 2*cos(40*π/99) 0.471517871019 = 2*cos(42*π/99) = 2*cos(14*π/33) 0.347296355334 = 2*cos(44*π/99) = 2*cos(4*π/9) 0.221676399802 = 2*cos(46*π/99) 0.095163831647 = 2*cos(48*π/99) = 2*cos(16*π/33) -0.031731927670 = 2*cos(50*π/99) -0.158499913714 = 2*cos(52*π/99) -0.284629676547 = 2*cos(54*π/99) = 2*cos(6*π/11) -0.409613336131 = 2*cos(56*π/99) -0.532947627380 = 2*cos(58*π/99) -0.654135926635 = 2*cos(60*π/99) = 2*cos(20*π/33) -0.772690251386 = 2*cos(62*π/99) -0.888133225212 = 2*cos(64*π/99) -1.107840127732 = 2*cos(68*π/99) -1.211219374276 = 2*cos(70*π/99) -1.309721467891 = 2*cos(72*π/99) = 2*cos(8*π/11) -1.402949775413 = 2*cos(74*π/99) -1.490528899352 = 2*cos(76*π/99) -1.572106189486 = 2*cos(78*π/99) = 2*cos(26*π/33) -1.647353162860 = 2*cos(80*π/99) -1.715966826470 = 2*cos(82*π/99) -1.777670897310 = 2*cos(84*π/99) = 2*cos(28*π/33) -1.832216914864 = 2*cos(86*π/99) -1.879385241572 = 2*cos(88*π/99) = 2*cos(8*π/9) -1.918985947229 = 2*cos(90*π/99) = 2*cos(10*π/11) -1.950859573771 = 2*cos(92*π/99) -1.974877777353 = 2*cos(94*π/99) -1.990943845146 = 2*cos(96*π/99) = 2*cos(32*π/33) -1.998993084766 = 2*cos(98*π/99) Symmetry of Rotations and Cartesian products A R+p+d+f+g+h+i z, Rz, z2, z3, z4, z5, z6 E1 R+p+d+f+g+h+i {x, y}, {Rx, Ry}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} E2 d+f+g+h+i {x2–y2, xy}, {z(x2–y2), xyz}, {z2(x2–y2), xyz2}, {z3(x2–y2), xyz3}, {z4(x2–y2), xyz4} E3 f+g+h+i {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 {(x2–y2)2–2x2y2, xy(x2–y2)}, {z((x2–y2)2–4x2y2), xyz(x2–y2)}, {z2((x2–y2)2–4x2y2), xyz2(x2–y2)} E5 h+i {x(x2–(5+2√5)y2)(x2–(5–2√5)y2), y(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)}, {xz(x2–(5+2√5)y2)(x2–(5–2√5)y2), yz(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)} E6 i {x2(x2–3y2)2–y2(3x2–y2)2, xy(x2–3y2)(3x2–y2)} Notes: α The order of the C99 point group is 99, and the order of the principal axis is 99. β This is an Abelian point group (the commutative law holds between all symmetry operations). The C99 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. γ 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. δ 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. ε The point group is chiral, as it does not contain any mirroring operation. ζ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree less than half the order of the principal axis (and often much less). For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.
| C98 | ||
| C99 | C99v C99h D99 D99h D99d | |
| C100 |
This Character Table for the C99 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.