C79 E 2 C79 2 C79^2 2 C79^3 2 C79^4 2 C79^5 2 C79^6 2 C79^7 2 C79^8 2 C79^9 2 C79^10 2 C79^11 2 C79^12 2 C79^13 2 C79^14 2 C79^15 2 C79^16 2 C79^17 2 C79^18 2 C79^19 2 C79^20 2 C79^21 2 C79^22 2 C79^23 2 C79^24 2 C79^25 2 C79^26 2 C79^27 2 C79^28 2 C79^29 2 C79^30 2 C79^31 2 C79^32 2 C79^33 2 C79^34 2 C79^35 2 C79^36 2 C79^37 2 C79^38 2 C79^39 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99368 1.97475 1.94334 1.89964 1.84393 1.77657 1.69797 1.60863 1.50913 1.40008 1.28219 1.15618 1.02287 0.88309 0.73773 0.58770 0.43396 0.27747 0.11923 -0.03976 -0.19851 -0.35600 -0.51123 -0.66324 -0.81105 -0.95374 -1.09039 -1.22015 -1.34220 -1.45576 -1.56011 -1.65461 -1.73864 -1.81168 -1.87327 -1.92301 -1.96059 -1.98578 -1.99842 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.97475 1.89964 1.77657 1.60863 1.40008 1.15618 0.88309 0.58770 0.27747 -0.03976 -0.35600 -0.66324 -0.95374 -1.22015 -1.45576 -1.65461 -1.81168 -1.92301 -1.98578 -1.99842 -1.96059 -1.87327 -1.73864 -1.56011 -1.34220 -1.09039 -0.81105 -0.51123 -0.19851 0.11923 0.43396 0.73773 1.02287 1.28219 1.50913 1.69797 1.84393 1.94334 1.99368 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.94334 1.77657 1.50913 1.15618 0.73773 0.27747 -0.19851 -0.66324 -1.09039 -1.45576 -1.73864 -1.92301 -1.99842 -1.96059 -1.81168 -1.56011 -1.22015 -0.81105 -0.35600 0.11923 0.58770 1.02287 1.40008 1.69797 1.89964 1.99368 1.97475 1.84393 1.60863 1.28219 0.88309 0.43396 -0.03976 -0.51123 -0.95374 -1.34220 -1.65461 -1.87327 -1.98578 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.89964 1.60863 1.15618 0.58770 -0.03976 -0.66324 -1.22015 -1.65461 -1.92301 -1.99842 -1.87327 -1.56011 -1.09039 -0.51123 0.11923 0.73773 1.28219 1.69797 1.94334 1.99368 1.84393 1.50913 1.02287 0.43396 -0.19851 -0.81105 -1.34220 -1.73864 -1.96059 -1.98578 -1.81168 -1.45576 -0.95374 -0.35600 0.27747 0.88309 1.40008 1.77657 1.97475 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.84393 1.40008 0.73773 -0.03976 -0.81105 -1.45576 -1.87327 -1.99842 -1.81168 -1.34220 -0.66324 0.11923 0.88309 1.50913 1.89964 1.99368 1.77657 1.28219 0.58770 -0.19851 -0.95374 -1.56011 -1.92301 -1.98578 -1.73864 -1.22015 -0.51123 0.27747 1.02287 1.60863 1.94334 1.97475 1.69797 1.15618 0.43396 -0.35600 -1.09039 -1.65461 -1.96059 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.77657 1.15618 0.27747 -0.66324 -1.45576 -1.92301 -1.96059 -1.56011 -0.81105 0.11923 1.02287 1.69797 1.99368 1.84393 1.28219 0.43396 -0.51123 -1.34220 -1.87327 -1.98578 -1.65461 -0.95374 -0.03976 0.88309 1.60863 1.97475 1.89964 1.40008 0.58770 -0.35600 -1.22015 -1.81168 -1.99842 -1.73864 -1.09039 -0.19851 0.73773 1.50913 1.94334 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.69797 0.88309 -0.19851 -1.22015 -1.87327 -1.96059 -1.45576 -0.51123 0.58770 1.50913 1.97475 1.84393 1.15618 0.11923 -0.95374 -1.73864 -1.99842 -1.65461 -0.81105 0.27747 1.28219 1.89964 1.94334 1.40008 0.43396 -0.66324 -1.56011 -1.98578 -1.81168 -1.09039 -0.03976 1.02287 1.77657 1.99368 1.60863 0.73773 -0.35600 -1.34220 -1.92301 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.60863 0.58770 -0.66324 -1.65461 -1.99842 -1.56011 -0.51123 0.73773 1.69797 1.99368 1.50913 0.43396 -0.81105 -1.73864 -1.98578 -1.45576 -0.35600 0.88309 1.77657 1.97475 1.40008 0.27747 -0.95374 -1.81168 -1.96059 -1.34220 -0.19851 1.02287 1.84393 1.94334 1.28219 0.11923 -1.09039 -1.87327 -1.92301 -1.22015 -0.03976 1.15618 1.89964 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.50913 0.27747 -1.09039 -1.92301 -1.81168 -0.81105 0.58770 1.69797 1.97475 1.28219 -0.03976 -1.34220 -1.98578 -1.65461 -0.51123 0.88309 1.84393 1.89964 1.02287 -0.35600 -1.56011 -1.99842 -1.45576 -0.19851 1.15618 1.94334 1.77657 0.73773 -0.66324 -1.73864 -1.96059 -1.22015 0.11923 1.40008 1.99368 1.60863 0.43396 -0.95374 -1.87327 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.40008 -0.03976 -1.45576 -1.99842 -1.34220 0.11923 1.50913 1.99368 1.28219 -0.19851 -1.56011 -1.98578 -1.22015 0.27747 1.60863 1.97475 1.15618 -0.35600 -1.65461 -1.96059 -1.09039 0.43396 1.69797 1.94334 1.02287 -0.51123 -1.73864 -1.92301 -0.95374 0.58770 1.77657 1.89964 0.88309 -0.66324 -1.81168 -1.87327 -0.81105 0.73773 1.84393 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.28219 -0.35600 -1.73864 -1.87327 -0.66324 1.02287 1.97475 1.50913 -0.03976 -1.56011 -1.96059 -0.95374 0.73773 1.89964 1.69797 0.27747 -1.34220 -1.99842 -1.22015 0.43396 1.77657 1.84393 0.58770 -1.09039 -1.98578 -1.45576 0.11923 1.60863 1.94334 0.88309 -0.81105 -1.92301 -1.65461 -0.19851 1.40008 1.99368 1.15618 -0.51123 -1.81168 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.15618 -0.66324 -1.92301 -1.56011 0.11923 1.69797 1.84393 0.43396 -1.34220 -1.98578 -0.95374 0.88309 1.97475 1.40008 -0.35600 -1.81168 -1.73864 -0.19851 1.50913 1.94334 0.73773 -1.09039 -1.99842 -1.22015 0.58770 1.89964 1.60863 -0.03976 -1.65461 -1.87327 -0.51123 1.28219 1.99368 1.02287 -0.81105 -1.96059 -1.45576 0.27747 1.77657 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.02287 -0.95374 -1.99842 -1.09039 0.88309 1.99368 1.15618 -0.81105 -1.98578 -1.22015 0.73773 1.97475 1.28219 -0.66324 -1.96059 -1.34220 0.58770 1.94334 1.40008 -0.51123 -1.92301 -1.45576 0.43396 1.89964 1.50913 -0.35600 -1.87327 -1.56011 0.27747 1.84393 1.60863 -0.19851 -1.81168 -1.65461 0.11923 1.77657 1.69797 -0.03976 -1.73864 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 0.88309 -1.22015 -1.96059 -0.51123 1.50913 1.84393 0.11923 -1.73864 -1.65461 0.27747 1.89964 1.40008 -0.66324 -1.98578 -1.09039 1.02287 1.99368 0.73773 -1.34220 -1.92301 -0.35600 1.60863 1.77657 -0.03976 -1.81168 -1.56011 0.43396 1.94334 1.28219 -0.81105 -1.99842 -0.95374 1.15618 1.97475 0.58770 -1.45576 -1.87327 -0.19851 1.69797 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 0.73773 -1.45576 -1.81168 0.11923 1.89964 1.28219 -0.95374 -1.98578 -0.51123 1.60863 1.69797 -0.35600 -1.96059 -1.09039 1.15618 1.94334 0.27747 -1.73864 -1.56011 0.58770 1.99368 0.88309 -1.34220 -1.87327 -0.03976 1.84393 1.40008 -0.81105 -1.99842 -0.66324 1.50913 1.77657 -0.19851 -1.92301 -1.22015 1.02287 1.97475 0.43396 -1.65461 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 0.58770 -1.65461 -1.56011 0.73773 1.99368 0.43396 -1.73864 -1.45576 0.88309 1.97475 0.27747 -1.81168 -1.34220 1.02287 1.94334 0.11923 -1.87327 -1.22015 1.15618 1.89964 -0.03976 -1.92301 -1.09039 1.28219 1.84393 -0.19851 -1.96059 -0.95374 1.40008 1.77657 -0.35600 -1.98578 -0.81105 1.50913 1.69797 -0.51123 -1.99842 -0.66324 1.60863 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 0.43396 -1.81168 -1.22015 1.28219 1.77657 -0.51123 -1.99842 -0.35600 1.84393 1.15618 -1.34220 -1.73864 0.58770 1.99368 0.27747 -1.87327 -1.09039 1.40008 1.69797 -0.66324 -1.98578 -0.19851 1.89964 1.02287 -1.45576 -1.65461 0.73773 1.97475 0.11923 -1.92301 -0.95374 1.50913 1.60863 -0.81105 -1.96059 -0.03976 1.94334 0.88309 -1.56011 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.27747 -1.92301 -0.81105 1.69797 1.28219 -1.34220 -1.65461 0.88309 1.89964 -0.35600 -1.99842 -0.19851 1.94334 0.73773 -1.73864 -1.22015 1.40008 1.60863 -0.95374 -1.87327 0.43396 1.99368 0.11923 -1.96059 -0.66324 1.77657 1.15618 -1.45576 -1.56011 1.02287 1.84393 -0.51123 -1.98578 -0.03976 1.97475 0.58770 -1.81168 -1.09039 1.50913 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.11923 -1.98578 -0.35600 1.94334 0.58770 -1.87327 -0.81105 1.77657 1.02287 -1.65461 -1.22015 1.50913 1.40008 -1.34220 -1.56011 1.15618 1.69797 -0.95374 -1.81168 0.73773 1.89964 -0.51123 -1.96059 0.27747 1.99368 -0.03976 -1.99842 -0.19851 1.97475 0.43396 -1.92301 -0.66324 1.84393 0.88309 -1.73864 -1.09039 1.60863 1.28219 -1.45576 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 -0.03976 -1.99842 0.11923 1.99368 -0.19851 -1.98578 0.27747 1.97475 -0.35600 -1.96059 0.43396 1.94334 -0.51123 -1.92301 0.58770 1.89964 -0.66324 -1.87327 0.73773 1.84393 -0.81105 -1.81168 0.88309 1.77657 -0.95374 -1.73864 1.02287 1.69797 -1.09039 -1.65461 1.15618 1.60863 -1.22015 -1.56011 1.28219 1.50913 -1.34220 -1.45576 1.40008 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 -0.19851 -1.96059 0.58770 1.84393 -0.95374 -1.65461 1.28219 1.40008 -1.56011 -1.09039 1.77657 0.73773 -1.92301 -0.35600 1.99368 -0.03976 -1.98578 0.43396 1.89964 -0.81105 -1.73864 1.15618 1.50913 -1.45576 -1.22015 1.69797 0.88309 -1.87327 -0.51123 1.97475 0.11923 -1.99842 0.27747 1.94334 -0.66324 -1.81168 1.02287 1.60863 -1.34220 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 -0.35600 -1.87327 1.02287 1.50913 -1.56011 -0.95374 1.89964 0.27747 -1.99842 0.43396 1.84393 -1.09039 -1.45576 1.60863 0.88309 -1.92301 -0.19851 1.99368 -0.51123 -1.81168 1.15618 1.40008 -1.65461 -0.81105 1.94334 0.11923 -1.98578 0.58770 1.77657 -1.22015 -1.34220 1.69797 0.73773 -1.96059 -0.03976 1.97475 -0.66324 -1.73864 1.28219 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 -0.51123 -1.73864 1.40008 1.02287 -1.92301 -0.03976 1.94334 -0.95374 -1.45576 1.69797 0.58770 -1.99842 0.43396 1.77657 -1.34220 -1.09039 1.89964 0.11923 -1.96059 0.88309 1.50913 -1.65461 -0.66324 1.99368 -0.35600 -1.81168 1.28219 1.15618 -1.87327 -0.19851 1.97475 -0.81105 -1.56011 1.60863 0.73773 -1.98578 0.27747 1.84393 -1.22015 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 -0.66324 -1.56011 1.69797 0.43396 -1.98578 0.88309 1.40008 -1.81168 -0.19851 1.94334 -1.09039 -1.22015 1.89964 -0.03976 -1.87327 1.28219 1.02287 -1.96059 0.27747 1.77657 -1.45576 -0.81105 1.99368 -0.51123 -1.65461 1.60863 0.58770 -1.99842 0.73773 1.50913 -1.73864 -0.35600 1.97475 -0.95374 -1.34220 1.84393 0.11923 -1.92301 1.15618 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 -0.81105 -1.34220 1.89964 -0.19851 -1.73864 1.60863 0.43396 -1.96059 1.15618 1.02287 -1.98578 0.58770 1.50913 -1.81168 -0.03976 1.84393 -1.45576 -0.66324 1.99368 -0.95374 -1.22015 1.94334 -0.35600 -1.65461 1.69797 0.27747 -1.92301 1.28219 0.88309 -1.99842 0.73773 1.40008 -1.87327 0.11923 1.77657 -1.56011 -0.51123 1.97475 -1.09039 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.95374 -1.09039 1.99368 -0.81105 -1.22015 1.97475 -0.66324 -1.34220 1.94334 -0.51123 -1.45576 1.89964 -0.35600 -1.56011 1.84393 -0.19851 -1.65461 1.77657 -0.03976 -1.73864 1.69797 0.11923 -1.81168 1.60863 0.27747 -1.87327 1.50913 0.43396 -1.92301 1.40008 0.58770 -1.96059 1.28219 0.73773 -1.98578 1.15618 0.88309 -1.99842 1.02287 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 -1.09039 -0.81105 1.97475 -1.34220 -0.51123 1.89964 -1.56011 -0.19851 1.77657 -1.73864 0.11923 1.60863 -1.87327 0.43396 1.40008 -1.96059 0.73773 1.15618 -1.99842 1.02287 0.88309 -1.98578 1.28219 0.58770 -1.92301 1.50913 0.27747 -1.81168 1.69797 -0.03976 -1.65461 1.84393 -0.35600 -1.45576 1.94334 -0.66324 -1.22015 1.99368 -0.95374 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -1.22015 -0.51123 1.84393 -1.73864 0.27747 1.40008 -1.98578 1.02287 0.73773 -1.92301 1.60863 -0.03976 -1.56011 1.94334 -0.81105 -0.95374 1.97475 -1.45576 -0.19851 1.69797 -1.87327 0.58770 1.15618 -1.99842 1.28219 0.43396 -1.81168 1.77657 -0.35600 -1.34220 1.99368 -1.09039 -0.66324 1.89964 -1.65461 0.11923 1.50913 -1.96059 0.88309 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -1.34220 -0.19851 1.60863 -1.96059 1.02287 0.58770 -1.81168 1.84393 -0.66324 -0.95374 1.94334 -1.65461 0.27747 1.28219 -1.99842 1.40008 0.11923 -1.56011 1.97475 -1.09039 -0.51123 1.77657 -1.87327 0.73773 0.88309 -1.92301 1.69797 -0.35600 -1.22015 1.99368 -1.45576 -0.03976 1.50913 -1.98578 1.15618 0.43396 -1.73864 1.89964 -0.81105 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -1.45576 0.11923 1.28219 -1.98578 1.60863 -0.35600 -1.09039 1.94334 -1.73864 0.58770 0.88309 -1.87327 1.84393 -0.81105 -0.66324 1.77657 -1.92301 1.02287 0.43396 -1.65461 1.97475 -1.22015 -0.19851 1.50913 -1.99842 1.40008 -0.03976 -1.34220 1.99368 -1.56011 0.27747 1.15618 -1.96059 1.69797 -0.51123 -0.95374 1.89964 -1.81168 0.73773 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -1.56011 0.43396 0.88309 -1.81168 1.94334 -1.22015 -0.03976 1.28219 -1.96059 1.77657 -0.81105 -0.51123 1.60863 -1.99842 1.50913 -0.35600 -0.95374 1.84393 -1.92301 1.15618 0.11923 -1.34220 1.97475 -1.73864 0.73773 0.58770 -1.65461 1.99368 -1.45576 0.27747 1.02287 -1.87327 1.89964 -1.09039 -0.19851 1.40008 -1.98578 1.69797 -0.66324 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -1.65461 0.73773 0.43396 -1.45576 1.97475 -1.81168 1.02287 0.11923 -1.22015 1.89964 -1.92301 1.28219 -0.19851 -0.95374 1.77657 -1.98578 1.50913 -0.51123 -0.66324 1.60863 -1.99842 1.69797 -0.81105 -0.35600 1.40008 -1.96059 1.84393 -1.09039 -0.03976 1.15618 -1.87327 1.94334 -1.34220 0.27747 0.88309 -1.73864 1.99368 -1.56011 0.58770 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -1.73864 1.02287 -0.03976 -0.95374 1.69797 -1.99842 1.77657 -1.09039 0.11923 0.88309 -1.65461 1.99368 -1.81168 1.15618 -0.19851 -0.81105 1.60863 -1.98578 1.84393 -1.22015 0.27747 0.73773 -1.56011 1.97475 -1.87327 1.28219 -0.35600 -0.66324 1.50913 -1.96059 1.89964 -1.34220 0.43396 0.58770 -1.45576 1.94334 -1.92301 1.40008 -0.51123 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.81168 1.28219 -0.51123 -0.35600 1.15618 -1.73864 1.99368 -1.87327 1.40008 -0.66324 -0.19851 1.02287 -1.65461 1.97475 -1.92301 1.50913 -0.81105 -0.03976 0.88309 -1.56011 1.94334 -1.96059 1.60863 -0.95374 0.11923 0.73773 -1.45576 1.89964 -1.98578 1.69797 -1.09039 0.27747 0.58770 -1.34220 1.84393 -1.99842 1.77657 -1.22015 0.43396 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.87327 1.50913 -0.95374 0.27747 0.43396 -1.09039 1.60863 -1.92301 1.99368 -1.81168 1.40008 -0.81105 0.11923 0.58770 -1.22015 1.69797 -1.96059 1.97475 -1.73864 1.28219 -0.66324 -0.03976 0.73773 -1.34220 1.77657 -1.98578 1.94334 -1.65461 1.15618 -0.51123 -0.19851 0.88309 -1.45576 1.84393 -1.99842 1.89964 -1.56011 1.02287 -0.35600 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.92301 1.69797 -1.34220 0.88309 -0.35600 -0.19851 0.73773 -1.22015 1.60863 -1.87327 1.99368 -1.96059 1.77657 -1.45576 1.02287 -0.51123 -0.03976 0.58770 -1.09039 1.50913 -1.81168 1.97475 -1.98578 1.84393 -1.56011 1.15618 -0.66324 0.11923 0.43396 -0.95374 1.40008 -1.73864 1.94334 -1.99842 1.89964 -1.65461 1.28219 -0.81105 0.27747 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.96059 1.84393 -1.65461 1.40008 -1.09039 0.73773 -0.35600 -0.03976 0.43396 -0.81105 1.15618 -1.45576 1.69797 -1.87327 1.97475 -1.99842 1.94334 -1.81168 1.60863 -1.34220 1.02287 -0.66324 0.27747 0.11923 -0.51123 0.88309 -1.22015 1.50913 -1.73864 1.89964 -1.98578 1.99368 -1.92301 1.77657 -1.56011 1.28219 -0.95374 0.58770 -0.19851 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.98578 1.94334 -1.87327 1.77657 -1.65461 1.50913 -1.34220 1.15618 -0.95374 0.73773 -0.51123 0.27747 -0.03976 -0.19851 0.43396 -0.66324 0.88309 -1.09039 1.28219 -1.45576 1.60863 -1.73864 1.84393 -1.92301 1.97475 -1.99842 1.99368 -1.96059 1.89964 -1.81168 1.69797 -1.56011 1.40008 -1.22015 1.02287 -0.81105 0.58770 -0.35600 0.11923 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.99842 1.99368 -1.98578 1.97475 -1.96059 1.94334 -1.92301 1.89964 -1.87327 1.84393 -1.81168 1.77657 -1.73864 1.69797 -1.65461 1.60863 -1.56011 1.50913 -1.45576 1.40008 -1.34220 1.28219 -1.22015 1.15618 -1.09039 1.02287 -0.95374 0.88309 -0.81105 0.73773 -0.66324 0.58770 -0.51123 0.43396 -0.35600 0.27747 -0.19851 0.11923 -0.03976 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.993677678029 = 2*cos(2*π/79) 1.974750683873 = 2*cos(4*π/79) 1.943338680081 = 2*cos(6*π/79) 1.899640263456 = 2*cos(8*π/79) 1.843931709456 = 2*cos(10*π/79) 1.776565225498 = 2*cos(12*π/79) 1.697966724183 = 2*cos(14*π/79) 1.608633130542 = 2*cos(16*π/79) 1.509129240316 = 2*cos(18*π/79) 1.400084149139 = 2*cos(20*π/79) 1.282187275184 = 2*cos(22*π/79) 1.156184000450 = 2*cos(24*π/79) 1.022870958207 = 2*cos(26*π/79) 0.883090996432 = 2*cos(28*π/79) 0.737727849048 = 2*cos(30*π/79) 0.587700548676 = 2*cos(32*π/79) 0.433957616213 = 2*cos(34*π/79) 0.277471063978 = 2*cos(36*π/79) 0.119230250340 = 2*cos(38*π/79) -0.039764375330 = 2*cos(40*π/79) -0.198507597816 = 2*cos(42*π/79) -0.355995791355 = 2*cos(44*π/79) -0.511233264881 = 2*cos(46*π/79) -0.663238557104 = 2*cos(48*π/79) -0.811050641626 = 2*cos(50*π/79) -0.953735002857 = 2*cos(52*π/79) -1.090389544325 = 2*cos(54*π/79) -1.220150292021 = 2*cos(56*π/79) -1.342196856718 = 2*cos(58*π/79) -1.455757620739 = 2*cos(60*π/79) -1.560114616370 = 2*cos(62*π/79) -1.654608065086 = 2*cos(64*π/79) -1.738640548879 = 2*cos(66*π/79) -1.811680787331 = 2*cos(68*π/79) -1.873266996537 = 2*cos(70*π/79) -1.923009808655 = 2*cos(72*π/79) -1.960594733609 = 2*cos(74*π/79) -1.985784147404 = 2*cos(76*π/79) -1.998418794455 = 2*cos(78*π/79) 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 C79 point group is 79, and the order of the principal axis (C79) is 79. The group has 40 irreducible representations. β The C79 point group is generated by one single symmetry element, C79. Therefore, it is a cyclic group. γ The lowest nonvanishing multipole moment in C79 is 2 (dipole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C79 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 78 cases have been combined into 39 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 39 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 39 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 just 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.
| C77 | ||
| C78 | ||
| C79 | C79v C79h D79 D79h D79d | |
| C80 | ||
| C81 |
This Character Table for the C79 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.