D99 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 99 C2' <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 A2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 ............. 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 0.00000 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 0.00000 ... ... 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 0.00000 ... ... ..... 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 0.00000 ... ... ..... ....... 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 0.00000 ... ... ..... ....... ......... 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 0.00000 ... ... ..... ....... ......... ........... 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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) 0.593840750657 = 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) -0.409613336130 = 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) -1.211219374275 = 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 A1 d+g+i+k+m z2, z4, z6 A2 R+p+f+h+j+l Rz, z, z3, z5 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 D99 point group is 198, and the order of the principal axis (C99) is 99. The group has 51 irreducible representations. β The D99 point group is isomorphic to C99v. γ The D99 point group is generated by two symmetry elements, C99 and a perpendicular C2′. Also, the group may be generated from two C2′ axes (some pairs will yield smaller groups, though; choosing a minimum angle is safe). δ The group contains one set of C2′ symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set. ε The lowest nonvanishing multipole moment in D99 is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. 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, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.
D97 | ||
D98 | ||
C99 C99v C99h | D99 | D99h D99d |
D100 | ||
D101 |
This Character Table for the D99 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.