Character Table for Point Group C136

Character table for the C₁₃₆ point group

C136 E 2 C136 2 C68 2 C136^3 2 C34 2 C136^5 2 C68^3 2 C136^7 2 C17 2 C136^9 2 C68^5 2 C136^11 2 C34^3 2 C136^13 2 C68^7 2 C136^15 2 C17^2 2 C8 2 C68^9 2 C136^19 2 C34^5 2 C136^21 2 C68^11 2 C136^23 2 C17^3 2 C136^25 2 C68^13 2 C136^27 2 C34^7 2 C136^29 2 C68^15 2 C136^31 2 C17^4 2 C136^33 2 C4 2 C136^35 2 C34^9 2 C136^37 2 C68^19 2 C136^39 2 C17^5 2 C136^41 2 C68^21 2 C136^43 2 C34^11 2 C136^45 2 C68^23 2 C136^47 2 C17^6 2 C136^49 2 C68^25 2 C8^3 2 C34^13 2 C136^53 2 C68^27 2 C136^55 2 C17^7 2 C136^57 2 C68^29 2 C136^59 2 C34^15 2 C136^61 2 C68^31 2 C136^63 2 C17^8 2 C136^65 2 C68^33 2 C136^67 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 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 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 1.99787 1.99147 1.98082 1.96595 1.94688 1.92365 1.89632 1.86494 1.82959 1.79033 1.74724 1.70043 1.64999 1.59603 1.53867 1.47802 1.41421 1.34739 1.27769 1.20527 1.13027 1.05286 0.97321 0.89148 0.80784 0.72248 0.63558 0.54733 0.45790 0.36750 0.27631 0.18454 0.09237 0.00000 -0.09237 -0.18454 -0.27631 -0.36750 -0.45790 -0.54733 -0.63558 -0.72248 -0.80784 -0.89148 -0.97321 -1.05286 -1.13027 -1.20527 -1.27769 -1.34739 -1.41421 -1.47802 -1.53867 -1.59603 -1.64999 -1.70043 -1.74724 -1.79033 -1.82959 -1.86494 -1.89632 -1.92365 -1.94688 -1.96595 -1.98082 -1.99147 -1.99787 -2.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.99147 1.96595 1.92365 1.86494 1.79033 1.70043 1.59603 1.47802 1.34739 1.20527 1.05286 0.89148 0.72248 0.54733 0.36750 0.18454 0.00000 -0.18454 -0.36750 -0.54733 -0.72248 -0.89148 -1.05286 -1.20527 -1.34739 -1.47802 -1.59603 -1.70043 -1.79033 -1.86494 -1.92365 -1.96595 -1.99147 -2.00000 -1.99147 -1.96595 -1.92365 -1.86494 -1.79033 -1.70043 -1.59603 -1.47802 -1.34739 -1.20527 -1.05286 -0.89148 -0.72248 -0.54733 -0.36750 -0.18454 0.00000 0.18454 0.36750 0.54733 0.72248 0.89148 1.05286 1.20527 1.34739 1.47802 1.59603 1.70043 1.79033 1.86494 1.92365 1.96595 1.99147 2.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.98082 1.92365 1.82959 1.70043 1.53867 1.34739 1.13027 0.89148 0.63558 0.36750 0.09237 -0.18454 -0.45790 -0.72248 -0.97321 -1.20527 -1.41421 -1.59603 -1.74724 -1.86494 -1.94688 -1.99147 -1.99787 -1.96595 -1.89632 -1.79033 -1.64999 -1.47802 -1.27769 -1.05286 -0.80784 -0.54733 -0.27631 0.00000 0.27631 0.54733 0.80784 1.05286 1.27769 1.47802 1.64999 1.79033 1.89632 1.96595 1.99787 1.99147 1.94688 1.86494 1.74724 1.59603 1.41421 1.20527 0.97321 0.72248 0.45790 0.18454 -0.09237 -0.36750 -0.63558 -0.89148 -1.13027 -1.34739 -1.53867 -1.70043 -1.82959 -1.92365 -1.98082 -2.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.96595 1.86494 1.70043 1.47802 1.20527 0.89148 0.54733 0.18454 -0.18454 -0.54733 -0.89148 -1.20527 -1.47802 -1.70043 -1.86494 -1.96595 -2.00000 -1.96595 -1.86494 -1.70043 -1.47802 -1.20527 -0.89148 -0.54733 -0.18454 0.18454 0.54733 0.89148 1.20527 1.47802 1.70043 1.86494 1.96595 2.00000 1.96595 1.86494 1.70043 1.47802 1.20527 0.89148 0.54733 0.18454 -0.18454 -0.54733 -0.89148 -1.20527 -1.47802 -1.70043 -1.86494 -1.96595 -2.00000 -1.96595 -1.86494 -1.70043 -1.47802 -1.20527 -0.89148 -0.54733 -0.18454 0.18454 0.54733 0.89148 1.20527 1.47802 1.70043 1.86494 1.96595 2.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.94688 1.79033 1.53867 1.20527 0.80784 0.36750 -0.09237 -0.54733 -0.97321 -1.34739 -1.64999 -1.86494 -1.98082 -1.99147 -1.89632 -1.70043 -1.41421 -1.05286 -0.63558 -0.18454 0.27631 0.72248 1.13027 1.47802 1.74724 1.92365 1.99787 1.96595 1.82959 1.59603 1.27769 0.89148 0.45790 0.00000 -0.45790 -0.89148 -1.27769 -1.59603 -1.82959 -1.96595 -1.99787 -1.92365 -1.74724 -1.47802 -1.13027 -0.72248 -0.27631 0.18454 0.63558 1.05286 1.41421 1.70043 1.89632 1.99147 1.98082 1.86494 1.64999 1.34739 0.97321 0.54733 0.09237 -0.36750 -0.80784 -1.20527 -1.53867 -1.79033 -1.94688 -2.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.92365 1.70043 1.34739 0.89148 0.36750 -0.18454 -0.72248 -1.20527 -1.59603 -1.86494 -1.99147 -1.96595 -1.79033 -1.47802 -1.05286 -0.54733 0.00000 0.54733 1.05286 1.47802 1.79033 1.96595 1.99147 1.86494 1.59603 1.20527 0.72248 0.18454 -0.36750 -0.89148 -1.34739 -1.70043 -1.92365 -2.00000 -1.92365 -1.70043 -1.34739 -0.89148 -0.36750 0.18454 0.72248 1.20527 1.59603 1.86494 1.99147 1.96595 1.79033 1.47802 1.05286 0.54733 0.00000 -0.54733 -1.05286 -1.47802 -1.79033 -1.96595 -1.99147 -1.86494 -1.59603 -1.20527 -0.72248 -0.18454 0.36750 0.89148 1.34739 1.70043 1.92365 2.00000 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.89632 1.59603 1.13027 0.54733 -0.09237 -0.72248 -1.27769 -1.70043 -1.94688 -1.99147 -1.82959 -1.47802 -0.97321 -0.36750 0.27631 0.89148 1.41421 1.79033 1.98082 1.96595 1.74724 1.34739 0.80784 0.18454 -0.45790 -1.05286 -1.53867 -1.86494 -1.99787 -1.92365 -1.64999 -1.20527 -0.63558 0.00000 0.63558 1.20527 1.64999 1.92365 1.99787 1.86494 1.53867 1.05286 0.45790 -0.18454 -0.80784 -1.34739 -1.74724 -1.96595 -1.98082 -1.79033 -1.41421 -0.89148 -0.27631 0.36750 0.97321 1.47802 1.82959 1.99147 1.94688 1.70043 1.27769 0.72248 0.09237 -0.54733 -1.13027 -1.59603 -1.89632 -2.00000 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.82959 1.34739 0.63558 -0.18454 -0.97321 -1.59603 -1.94688 -1.96595 -1.64999 -1.05286 -0.27631 0.54733 1.27769 1.79033 1.99787 1.86494 1.41421 0.72248 -0.09237 -0.89148 -1.53867 -1.92365 -1.98082 -1.70043 -1.13027 -0.36750 0.45790 1.20527 1.74724 1.99147 1.89632 1.47802 0.80784 0.00000 -0.80784 -1.47802 -1.89632 -1.99147 -1.74724 -1.20527 -0.45790 0.36750 1.13027 1.70043 1.98082 1.92365 1.53867 0.89148 0.09237 -0.72248 -1.41421 -1.86494 -1.99787 -1.79033 -1.27769 -0.54733 0.27631 1.05286 1.64999 1.96595 1.94688 1.59603 0.97321 0.18454 -0.63558 -1.34739 -1.82959 -2.00000 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.79033 1.20527 0.36750 -0.54733 -1.34739 -1.86494 -1.99147 -1.70043 -1.05286 -0.18454 0.72248 1.47802 1.92365 1.96595 1.59603 0.89148 0.00000 -0.89148 -1.59603 -1.96595 -1.92365 -1.47802 -0.72248 0.18454 1.05286 1.70043 1.99147 1.86494 1.34739 0.54733 -0.36750 -1.20527 -1.79033 -2.00000 -1.79033 -1.20527 -0.36750 0.54733 1.34739 1.86494 1.99147 1.70043 1.05286 0.18454 -0.72248 -1.47802 -1.92365 -1.96595 -1.59603 -0.89148 0.00000 0.89148 1.59603 1.96595 1.92365 1.47802 0.72248 -0.18454 -1.05286 -1.70043 -1.99147 -1.86494 -1.34739 -0.54733 0.36750 1.20527 1.79033 2.00000 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.74724 1.05286 0.09237 -0.89148 -1.64999 -1.99147 -1.82959 -1.20527 -0.27631 0.72248 1.53867 1.96595 1.89632 1.34739 0.45790 -0.54733 -1.41421 -1.92365 -1.94688 -1.47802 -0.63558 0.36750 1.27769 1.86494 1.98082 1.59603 0.80784 -0.18454 -1.13027 -1.79033 -1.99787 -1.70043 -0.97321 0.00000 0.97321 1.70043 1.99787 1.79033 1.13027 0.18454 -0.80784 -1.59603 -1.98082 -1.86494 -1.27769 -0.36750 0.63558 1.47802 1.94688 1.92365 1.41421 0.54733 -0.45790 -1.34739 -1.89632 -1.96595 -1.53867 -0.72248 0.27631 1.20527 1.82959 1.99147 1.64999 0.89148 -0.09237 -1.05286 -1.74724 -2.00000 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.70043 0.89148 -0.18454 -1.20527 -1.86494 -1.96595 -1.47802 -0.54733 0.54733 1.47802 1.96595 1.86494 1.20527 0.18454 -0.89148 -1.70043 -2.00000 -1.70043 -0.89148 0.18454 1.20527 1.86494 1.96595 1.47802 0.54733 -0.54733 -1.47802 -1.96595 -1.86494 -1.20527 -0.18454 0.89148 1.70043 2.00000 1.70043 0.89148 -0.18454 -1.20527 -1.86494 -1.96595 -1.47802 -0.54733 0.54733 1.47802 1.96595 1.86494 1.20527 0.18454 -0.89148 -1.70043 -2.00000 -1.70043 -0.89148 0.18454 1.20527 1.86494 1.96595 1.47802 0.54733 -0.54733 -1.47802 -1.96595 -1.86494 -1.20527 -0.18454 0.89148 1.70043 2.00000 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.64999 0.72248 -0.45790 -1.47802 -1.98082 -1.79033 -0.97321 0.18454 1.27769 1.92365 1.89632 1.20527 0.09237 -1.05286 -1.82959 -1.96595 -1.41421 -0.36750 0.80784 1.70043 1.99787 1.59603 0.63558 -0.54733 -1.53867 -1.99147 -1.74724 -0.89148 0.27631 1.34739 1.94688 1.86494 1.13027 0.00000 -1.13027 -1.86494 -1.94688 -1.34739 -0.27631 0.89148 1.74724 1.99147 1.53867 0.54733 -0.63558 -1.59603 -1.99787 -1.70043 -0.80784 0.36750 1.41421 1.96595 1.82959 1.05286 -0.09237 -1.20527 -1.89632 -1.92365 -1.27769 -0.18454 0.97321 1.79033 1.98082 1.47802 0.45790 -0.72248 -1.64999 -2.00000 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.59603 0.54733 -0.72248 -1.70043 -1.99147 -1.47802 -0.36750 0.89148 1.79033 1.96595 1.34739 0.18454 -1.05286 -1.86494 -1.92365 -1.20527 0.00000 1.20527 1.92365 1.86494 1.05286 -0.18454 -1.34739 -1.96595 -1.79033 -0.89148 0.36750 1.47802 1.99147 1.70043 0.72248 -0.54733 -1.59603 -2.00000 -1.59603 -0.54733 0.72248 1.70043 1.99147 1.47802 0.36750 -0.89148 -1.79033 -1.96595 -1.34739 -0.18454 1.05286 1.86494 1.92365 1.20527 0.00000 -1.20527 -1.92365 -1.86494 -1.05286 0.18454 1.34739 1.96595 1.79033 0.89148 -0.36750 -1.47802 -1.99147 -1.70043 -0.72248 0.54733 1.59603 2.00000 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.53867 0.36750 -0.97321 -1.86494 -1.89632 -1.05286 0.27631 1.47802 1.99787 1.59603 0.45790 -0.89148 -1.82959 -1.92365 -1.13027 0.18454 1.41421 1.99147 1.64999 0.54733 -0.80784 -1.79033 -1.94688 -1.20527 0.09237 1.34739 1.98082 1.70043 0.63558 -0.72248 -1.74724 -1.96595 -1.27769 0.00000 1.27769 1.96595 1.74724 0.72248 -0.63558 -1.70043 -1.98082 -1.34739 -0.09237 1.20527 1.94688 1.79033 0.80784 -0.54733 -1.64999 -1.99147 -1.41421 -0.18454 1.13027 1.92365 1.82959 0.89148 -0.45790 -1.59603 -1.99787 -1.47802 -0.27631 1.05286 1.89632 1.86494 0.97321 -0.36750 -1.53867 -2.00000 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 1.34739 -0.18454 -1.59603 -1.96595 -1.05286 0.54733 1.79033 1.86494 0.72248 -0.89148 -1.92365 -1.70043 -0.36750 1.20527 1.99147 1.47802 0.00000 -1.47802 -1.99147 -1.20527 0.36750 1.70043 1.92365 0.89148 -0.72248 -1.86494 -1.79033 -0.54733 1.05286 1.96595 1.59603 0.18454 -1.34739 -2.00000 -1.34739 0.18454 1.59603 1.96595 1.05286 -0.54733 -1.79033 -1.86494 -0.72248 0.89148 1.92365 1.70043 0.36750 -1.20527 -1.99147 -1.47802 0.00000 1.47802 1.99147 1.20527 -0.36750 -1.70043 -1.92365 -0.89148 0.72248 1.86494 1.79033 0.54733 -1.05286 -1.96595 -1.59603 -0.18454 1.34739 2.00000 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 1.27769 -0.36750 -1.74724 -1.86494 -0.63558 1.05286 1.98082 1.47802 -0.09237 -1.59603 -1.94688 -0.89148 0.80784 1.92365 1.64999 0.18454 -1.41421 -1.99147 -1.13027 0.54733 1.82959 1.79033 0.45790 -1.20527 -1.99787 -1.34739 0.27631 1.70043 1.89632 0.72248 -0.97321 -1.96595 -1.53867 0.00000 1.53867 1.96595 0.97321 -0.72248 -1.89632 -1.70043 -0.27631 1.34739 1.99787 1.20527 -0.45790 -1.79033 -1.82959 -0.54733 1.13027 1.99147 1.41421 -0.18454 -1.64999 -1.92365 -0.80784 0.89148 1.94688 1.59603 0.09237 -1.47802 -1.98082 -1.05286 0.63558 1.86494 1.74724 0.36750 -1.27769 -2.00000 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 1.20527 -0.54733 -1.86494 -1.70043 -0.18454 1.47802 1.96595 0.89148 -0.89148 -1.96595 -1.47802 0.18454 1.70043 1.86494 0.54733 -1.20527 -2.00000 -1.20527 0.54733 1.86494 1.70043 0.18454 -1.47802 -1.96595 -0.89148 0.89148 1.96595 1.47802 -0.18454 -1.70043 -1.86494 -0.54733 1.20527 2.00000 1.20527 -0.54733 -1.86494 -1.70043 -0.18454 1.47802 1.96595 0.89148 -0.89148 -1.96595 -1.47802 0.18454 1.70043 1.86494 0.54733 -1.20527 -2.00000 -1.20527 0.54733 1.86494 1.70043 0.18454 -1.47802 -1.96595 -0.89148 0.89148 1.96595 1.47802 -0.18454 -1.70043 -1.86494 -0.54733 1.20527 2.00000 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 1.13027 -0.72248 -1.94688 -1.47802 0.27631 1.79033 1.74724 0.18454 -1.53867 -1.92365 -0.63558 1.20527 1.99787 1.05286 -0.80784 -1.96595 -1.41421 0.36750 1.82959 1.70043 0.09237 -1.59603 -1.89632 -0.54733 1.27769 1.99147 0.97321 -0.89148 -1.98082 -1.34739 0.45790 1.86494 1.64999 0.00000 -1.64999 -1.86494 -0.45790 1.34739 1.98082 0.89148 -0.97321 -1.99147 -1.27769 0.54733 1.89632 1.59603 -0.09237 -1.70043 -1.82959 -0.36750 1.41421 1.96595 0.80784 -1.05286 -1.99787 -1.20527 0.63558 1.92365 1.53867 -0.18454 -1.74724 -1.79033 -0.27631 1.47802 1.94688 0.72248 -1.13027 -2.00000 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 1.05286 -0.89148 -1.99147 -1.20527 0.72248 1.96595 1.34739 -0.54733 -1.92365 -1.47802 0.36750 1.86494 1.59603 -0.18454 -1.79033 -1.70043 0.00000 1.70043 1.79033 0.18454 -1.59603 -1.86494 -0.36750 1.47802 1.92365 0.54733 -1.34739 -1.96595 -0.72248 1.20527 1.99147 0.89148 -1.05286 -2.00000 -1.05286 0.89148 1.99147 1.20527 -0.72248 -1.96595 -1.34739 0.54733 1.92365 1.47802 -0.36750 -1.86494 -1.59603 0.18454 1.79033 1.70043 0.00000 -1.70043 -1.79033 -0.18454 1.59603 1.86494 0.36750 -1.47802 -1.92365 -0.54733 1.34739 1.96595 0.72248 -1.20527 -1.99147 -0.89148 1.05286 2.00000 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.97321 -1.05286 -1.99787 -0.89148 1.13027 1.99147 0.80784 -1.20527 -1.98082 -0.72248 1.27769 1.96595 0.63558 -1.34739 -1.94688 -0.54733 1.41421 1.92365 0.45790 -1.47802 -1.89632 -0.36750 1.53867 1.86494 0.27631 -1.59603 -1.82959 -0.18454 1.64999 1.79033 0.09237 -1.70043 -1.74724 0.00000 1.74724 1.70043 -0.09237 -1.79033 -1.64999 0.18454 1.82959 1.59603 -0.27631 -1.86494 -1.53867 0.36750 1.89632 1.47802 -0.45790 -1.92365 -1.41421 0.54733 1.94688 1.34739 -0.63558 -1.96595 -1.27769 0.72248 1.98082 1.20527 -0.80784 -1.99147 -1.13027 0.89148 1.99787 1.05286 -0.97321 -2.00000 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 0.80784 -1.34739 -1.89632 -0.18454 1.74724 1.59603 -0.45790 -1.96595 -1.13027 1.05286 1.98082 0.54733 -1.53867 -1.79033 0.09237 1.86494 1.41421 -0.72248 -1.99787 -0.89148 1.27769 1.92365 0.27631 -1.70043 -1.64999 0.36750 1.94688 1.20527 -0.97321 -1.99147 -0.63558 1.47802 1.82959 0.00000 -1.82959 -1.47802 0.63558 1.99147 0.97321 -1.20527 -1.94688 -0.36750 1.64999 1.70043 -0.27631 -1.92365 -1.27769 0.89148 1.99787 0.72248 -1.41421 -1.86494 -0.09237 1.79033 1.53867 -0.54733 -1.98082 -1.05286 1.13027 1.96595 0.45790 -1.59603 -1.74724 0.18454 1.89632 1.34739 -0.80784 -2.00000 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 0.72248 -1.47802 -1.79033 0.18454 1.92365 1.20527 -1.05286 -1.96595 -0.36750 1.70043 1.59603 -0.54733 -1.99147 -0.89148 1.34739 1.86494 0.00000 -1.86494 -1.34739 0.89148 1.99147 0.54733 -1.59603 -1.70043 0.36750 1.96595 1.05286 -1.20527 -1.92365 -0.18454 1.79033 1.47802 -0.72248 -2.00000 -0.72248 1.47802 1.79033 -0.18454 -1.92365 -1.20527 1.05286 1.96595 0.36750 -1.70043 -1.59603 0.54733 1.99147 0.89148 -1.34739 -1.86494 0.00000 1.86494 1.34739 -0.89148 -1.99147 -0.54733 1.59603 1.70043 -0.36750 -1.96595 -1.05286 1.20527 1.92365 0.18454 -1.79033 -1.47802 0.72248 2.00000 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 0.63558 -1.59603 -1.64999 0.54733 1.99787 0.72248 -1.53867 -1.70043 0.45790 1.99147 0.80784 -1.47802 -1.74724 0.36750 1.98082 0.89148 -1.41421 -1.79033 0.27631 1.96595 0.97321 -1.34739 -1.82959 0.18454 1.94688 1.05286 -1.27769 -1.86494 0.09237 1.92365 1.13027 -1.20527 -1.89632 0.00000 1.89632 1.20527 -1.13027 -1.92365 -0.09237 1.86494 1.27769 -1.05286 -1.94688 -0.18454 1.82959 1.34739 -0.97321 -1.96595 -0.27631 1.79033 1.41421 -0.89148 -1.98082 -0.36750 1.74724 1.47802 -0.80784 -1.99147 -0.45790 1.70043 1.53867 -0.72248 -1.99787 -0.54733 1.64999 1.59603 -0.63558 -2.00000 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 0.54733 -1.70043 -1.47802 0.89148 1.96595 0.18454 -1.86494 -1.20527 1.20527 1.86494 -0.18454 -1.96595 -0.89148 1.47802 1.70043 -0.54733 -2.00000 -0.54733 1.70043 1.47802 -0.89148 -1.96595 -0.18454 1.86494 1.20527 -1.20527 -1.86494 0.18454 1.96595 0.89148 -1.47802 -1.70043 0.54733 2.00000 0.54733 -1.70043 -1.47802 0.89148 1.96595 0.18454 -1.86494 -1.20527 1.20527 1.86494 -0.18454 -1.96595 -0.89148 1.47802 1.70043 -0.54733 -2.00000 -0.54733 1.70043 1.47802 -0.89148 -1.96595 -0.18454 1.86494 1.20527 -1.20527 -1.86494 0.18454 1.96595 0.89148 -1.47802 -1.70043 0.54733 2.00000 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 0.45790 -1.79033 -1.27769 1.20527 1.82959 -0.36750 -1.99787 -0.54733 1.74724 1.34739 -1.13027 -1.86494 0.27631 1.99147 0.63558 -1.70043 -1.41421 1.05286 1.89632 -0.18454 -1.98082 -0.72248 1.64999 1.47802 -0.97321 -1.92365 0.09237 1.96595 0.80784 -1.59603 -1.53867 0.89148 1.94688 0.00000 -1.94688 -0.89148 1.53867 1.59603 -0.80784 -1.96595 -0.09237 1.92365 0.97321 -1.47802 -1.64999 0.72248 1.98082 0.18454 -1.89632 -1.05286 1.41421 1.70043 -0.63558 -1.99147 -0.27631 1.86494 1.13027 -1.34739 -1.74724 0.54733 1.99787 0.36750 -1.82959 -1.20527 1.27769 1.79033 -0.45790 -2.00000 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 0.36750 -1.86494 -1.05286 1.47802 1.59603 -0.89148 -1.92365 0.18454 1.99147 0.54733 -1.79033 -1.20527 1.34739 1.70043 -0.72248 -1.96595 0.00000 1.96595 0.72248 -1.70043 -1.34739 1.20527 1.79033 -0.54733 -1.99147 -0.18454 1.92365 0.89148 -1.59603 -1.47802 1.05286 1.86494 -0.36750 -2.00000 -0.36750 1.86494 1.05286 -1.47802 -1.59603 0.89148 1.92365 -0.18454 -1.99147 -0.54733 1.79033 1.20527 -1.34739 -1.70043 0.72248 1.96595 0.00000 -1.96595 -0.72248 1.70043 1.34739 -1.20527 -1.79033 0.54733 1.99147 0.18454 -1.92365 -0.89148 1.59603 1.47802 -1.05286 -1.86494 0.36750 2.00000 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 0.27631 -1.92365 -0.80784 1.70043 1.27769 -1.34739 -1.64999 0.89148 1.89632 -0.36750 -1.99787 -0.18454 1.94688 0.72248 -1.74724 -1.20527 1.41421 1.59603 -0.97321 -1.86494 0.45790 1.99147 0.09237 -1.96595 -0.63558 1.79033 1.13027 -1.47802 -1.53867 1.05286 1.82959 -0.54733 -1.98082 0.00000 1.98082 0.54733 -1.82959 -1.05286 1.53867 1.47802 -1.13027 -1.79033 0.63558 1.96595 -0.09237 -1.99147 -0.45790 1.86494 0.97321 -1.59603 -1.41421 1.20527 1.74724 -0.72248 -1.94688 0.18454 1.99787 0.36750 -1.89632 -0.89148 1.64999 1.34739 -1.27769 -1.70043 0.80784 1.92365 -0.27631 -2.00000 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 2.00000 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 0.09237 -1.99147 -0.27631 1.96595 0.45790 -1.92365 -0.63558 1.86494 0.80784 -1.79033 -0.97321 1.70043 1.13027 -1.59603 -1.27769 1.47802 1.41421 -1.34739 -1.53867 1.20527 1.64999 -1.05286 -1.74724 0.89148 1.82959 -0.72248 -1.89632 0.54733 1.94688 -0.36750 -1.98082 0.18454 1.99787 0.00000 -1.99787 -0.18454 1.98082 0.36750 -1.94688 -0.54733 1.89632 0.72248 -1.82959 -0.89148 1.74724 1.05286 -1.64999 -1.20527 1.53867 1.34739 -1.41421 -1.47802 1.27769 1.59603 -1.13027 -1.70043 0.97321 1.79033 -0.80784 -1.86494 0.63558 1.92365 -0.45790 -1.96595 0.27631 1.99147 -0.09237 -2.00000 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -0.09237 -1.99147 0.27631 1.96595 -0.45790 -1.92365 0.63558 1.86494 -0.80784 -1.79033 0.97321 1.70043 -1.13027 -1.59603 1.27769 1.47802 -1.41421 -1.34739 1.53867 1.20527 -1.64999 -1.05286 1.74724 0.89148 -1.82959 -0.72248 1.89632 0.54733 -1.94688 -0.36750 1.98082 0.18454 -1.99787 0.00000 1.99787 -0.18454 -1.98082 0.36750 1.94688 -0.54733 -1.89632 0.72248 1.82959 -0.89148 -1.74724 1.05286 1.64999 -1.20527 -1.53867 1.34739 1.41421 -1.47802 -1.27769 1.59603 1.13027 -1.70043 -0.97321 1.79033 0.80784 -1.86494 -0.63558 1.92365 0.45790 -1.96595 -0.27631 1.99147 0.09237 -2.00000 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -0.18454 -1.96595 0.54733 1.86494 -0.89148 -1.70043 1.20527 1.47802 -1.47802 -1.20527 1.70043 0.89148 -1.86494 -0.54733 1.96595 0.18454 -2.00000 0.18454 1.96595 -0.54733 -1.86494 0.89148 1.70043 -1.20527 -1.47802 1.47802 1.20527 -1.70043 -0.89148 1.86494 0.54733 -1.96595 -0.18454 2.00000 -0.18454 -1.96595 0.54733 1.86494 -0.89148 -1.70043 1.20527 1.47802 -1.47802 -1.20527 1.70043 0.89148 -1.86494 -0.54733 1.96595 0.18454 -2.00000 0.18454 1.96595 -0.54733 -1.86494 0.89148 1.70043 -1.20527 -1.47802 1.47802 1.20527 -1.70043 -0.89148 1.86494 0.54733 -1.96595 -0.18454 2.00000 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -0.27631 -1.92365 0.80784 1.70043 -1.27769 -1.34739 1.64999 0.89148 -1.89632 -0.36750 1.99787 -0.18454 -1.94688 0.72248 1.74724 -1.20527 -1.41421 1.59603 0.97321 -1.86494 -0.45790 1.99147 -0.09237 -1.96595 0.63558 1.79033 -1.13027 -1.47802 1.53867 1.05286 -1.82959 -0.54733 1.98082 0.00000 -1.98082 0.54733 1.82959 -1.05286 -1.53867 1.47802 1.13027 -1.79033 -0.63558 1.96595 0.09237 -1.99147 0.45790 1.86494 -0.97321 -1.59603 1.41421 1.20527 -1.74724 -0.72248 1.94688 0.18454 -1.99787 0.36750 1.89632 -0.89148 -1.64999 1.34739 1.27769 -1.70043 -0.80784 1.92365 0.27631 -2.00000 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -0.36750 -1.86494 1.05286 1.47802 -1.59603 -0.89148 1.92365 0.18454 -1.99147 0.54733 1.79033 -1.20527 -1.34739 1.70043 0.72248 -1.96595 0.00000 1.96595 -0.72248 -1.70043 1.34739 1.20527 -1.79033 -0.54733 1.99147 -0.18454 -1.92365 0.89148 1.59603 -1.47802 -1.05286 1.86494 0.36750 -2.00000 0.36750 1.86494 -1.05286 -1.47802 1.59603 0.89148 -1.92365 -0.18454 1.99147 -0.54733 -1.79033 1.20527 1.34739 -1.70043 -0.72248 1.96595 0.00000 -1.96595 0.72248 1.70043 -1.34739 -1.20527 1.79033 0.54733 -1.99147 0.18454 1.92365 -0.89148 -1.59603 1.47802 1.05286 -1.86494 -0.36750 2.00000 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -0.45790 -1.79033 1.27769 1.20527 -1.82959 -0.36750 1.99787 -0.54733 -1.74724 1.34739 1.13027 -1.86494 -0.27631 1.99147 -0.63558 -1.70043 1.41421 1.05286 -1.89632 -0.18454 1.98082 -0.72248 -1.64999 1.47802 0.97321 -1.92365 -0.09237 1.96595 -0.80784 -1.59603 1.53867 0.89148 -1.94688 0.00000 1.94688 -0.89148 -1.53867 1.59603 0.80784 -1.96595 0.09237 1.92365 -0.97321 -1.47802 1.64999 0.72248 -1.98082 0.18454 1.89632 -1.05286 -1.41421 1.70043 0.63558 -1.99147 0.27631 1.86494 -1.13027 -1.34739 1.74724 0.54733 -1.99787 0.36750 1.82959 -1.20527 -1.27769 1.79033 0.45790 -2.00000 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 2.00000 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -0.63558 -1.59603 1.64999 0.54733 -1.99787 0.72248 1.53867 -1.70043 -0.45790 1.99147 -0.80784 -1.47802 1.74724 0.36750 -1.98082 0.89148 1.41421 -1.79033 -0.27631 1.96595 -0.97321 -1.34739 1.82959 0.18454 -1.94688 1.05286 1.27769 -1.86494 -0.09237 1.92365 -1.13027 -1.20527 1.89632 0.00000 -1.89632 1.20527 1.13027 -1.92365 0.09237 1.86494 -1.27769 -1.05286 1.94688 -0.18454 -1.82959 1.34739 0.97321 -1.96595 0.27631 1.79033 -1.41421 -0.89148 1.98082 -0.36750 -1.74724 1.47802 0.80784 -1.99147 0.45790 1.70043 -1.53867 -0.72248 1.99787 -0.54733 -1.64999 1.59603 0.63558 -2.00000 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -0.72248 -1.47802 1.79033 0.18454 -1.92365 1.20527 1.05286 -1.96595 0.36750 1.70043 -1.59603 -0.54733 1.99147 -0.89148 -1.34739 1.86494 0.00000 -1.86494 1.34739 0.89148 -1.99147 0.54733 1.59603 -1.70043 -0.36750 1.96595 -1.05286 -1.20527 1.92365 -0.18454 -1.79033 1.47802 0.72248 -2.00000 0.72248 1.47802 -1.79033 -0.18454 1.92365 -1.20527 -1.05286 1.96595 -0.36750 -1.70043 1.59603 0.54733 -1.99147 0.89148 1.34739 -1.86494 0.00000 1.86494 -1.34739 -0.89148 1.99147 -0.54733 -1.59603 1.70043 0.36750 -1.96595 1.05286 1.20527 -1.92365 0.18454 1.79033 -1.47802 -0.72248 2.00000 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -0.80784 -1.34739 1.89632 -0.18454 -1.74724 1.59603 0.45790 -1.96595 1.13027 1.05286 -1.98082 0.54733 1.53867 -1.79033 -0.09237 1.86494 -1.41421 -0.72248 1.99787 -0.89148 -1.27769 1.92365 -0.27631 -1.70043 1.64999 0.36750 -1.94688 1.20527 0.97321 -1.99147 0.63558 1.47802 -1.82959 0.00000 1.82959 -1.47802 -0.63558 1.99147 -0.97321 -1.20527 1.94688 -0.36750 -1.64999 1.70043 0.27631 -1.92365 1.27769 0.89148 -1.99787 0.72248 1.41421 -1.86494 0.09237 1.79033 -1.53867 -0.54733 1.98082 -1.05286 -1.13027 1.96595 -0.45790 -1.59603 1.74724 0.18454 -1.89632 1.34739 0.80784 -2.00000 ... ... ..... ....... ......... ........... ............. E44 * 2.00000 -0.89148 -1.20527 1.96595 -0.54733 -1.47802 1.86494 -0.18454 -1.70043 1.70043 0.18454 -1.86494 1.47802 0.54733 -1.96595 1.20527 0.89148 -2.00000 0.89148 1.20527 -1.96595 0.54733 1.47802 -1.86494 0.18454 1.70043 -1.70043 -0.18454 1.86494 -1.47802 -0.54733 1.96595 -1.20527 -0.89148 2.00000 -0.89148 -1.20527 1.96595 -0.54733 -1.47802 1.86494 -0.18454 -1.70043 1.70043 0.18454 -1.86494 1.47802 0.54733 -1.96595 1.20527 0.89148 -2.00000 0.89148 1.20527 -1.96595 0.54733 1.47802 -1.86494 0.18454 1.70043 -1.70043 -0.18454 1.86494 -1.47802 -0.54733 1.96595 -1.20527 -0.89148 2.00000 ... ... ..... ....... ......... ........... ............. 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E46 * 2.00000 -1.05286 -0.89148 1.99147 -1.20527 -0.72248 1.96595 -1.34739 -0.54733 1.92365 -1.47802 -0.36750 1.86494 -1.59603 -0.18454 1.79033 -1.70043 0.00000 1.70043 -1.79033 0.18454 1.59603 -1.86494 0.36750 1.47802 -1.92365 0.54733 1.34739 -1.96595 0.72248 1.20527 -1.99147 0.89148 1.05286 -2.00000 1.05286 0.89148 -1.99147 1.20527 0.72248 -1.96595 1.34739 0.54733 -1.92365 1.47802 0.36750 -1.86494 1.59603 0.18454 -1.79033 1.70043 0.00000 -1.70043 1.79033 -0.18454 -1.59603 1.86494 -0.36750 -1.47802 1.92365 -0.54733 -1.34739 1.96595 -0.72248 -1.20527 1.99147 -0.89148 -1.05286 2.00000 ... ... ..... ....... ......... ........... ............. 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E48 * 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 2.00000 ... ... ..... ....... ......... ........... ............. E49 * 2.00000 -1.27769 -0.36750 1.74724 -1.86494 0.63558 1.05286 -1.98082 1.47802 0.09237 -1.59603 1.94688 -0.89148 -0.80784 1.92365 -1.64999 0.18454 1.41421 -1.99147 1.13027 0.54733 -1.82959 1.79033 -0.45790 -1.20527 1.99787 -1.34739 -0.27631 1.70043 -1.89632 0.72248 0.97321 -1.96595 1.53867 0.00000 -1.53867 1.96595 -0.97321 -0.72248 1.89632 -1.70043 0.27631 1.34739 -1.99787 1.20527 0.45790 -1.79033 1.82959 -0.54733 -1.13027 1.99147 -1.41421 -0.18454 1.64999 -1.92365 0.80784 0.89148 -1.94688 1.59603 -0.09237 -1.47802 1.98082 -1.05286 -0.63558 1.86494 -1.74724 0.36750 1.27769 -2.00000 ... ... ..... ....... ......... ........... ............. E50 * 2.00000 -1.34739 -0.18454 1.59603 -1.96595 1.05286 0.54733 -1.79033 1.86494 -0.72248 -0.89148 1.92365 -1.70043 0.36750 1.20527 -1.99147 1.47802 0.00000 -1.47802 1.99147 -1.20527 -0.36750 1.70043 -1.92365 0.89148 0.72248 -1.86494 1.79033 -0.54733 -1.05286 1.96595 -1.59603 0.18454 1.34739 -2.00000 1.34739 0.18454 -1.59603 1.96595 -1.05286 -0.54733 1.79033 -1.86494 0.72248 0.89148 -1.92365 1.70043 -0.36750 -1.20527 1.99147 -1.47802 0.00000 1.47802 -1.99147 1.20527 0.36750 -1.70043 1.92365 -0.89148 -0.72248 1.86494 -1.79033 0.54733 1.05286 -1.96595 1.59603 -0.18454 -1.34739 2.00000 ... ... ..... ....... ......... ........... ............. E51 * 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 ... ... ..... ....... ......... ........... ............. E52 * 2.00000 -1.47802 0.18454 1.20527 -1.96595 1.70043 -0.54733 -0.89148 1.86494 -1.86494 0.89148 0.54733 -1.70043 1.96595 -1.20527 -0.18454 1.47802 -2.00000 1.47802 -0.18454 -1.20527 1.96595 -1.70043 0.54733 0.89148 -1.86494 1.86494 -0.89148 -0.54733 1.70043 -1.96595 1.20527 0.18454 -1.47802 2.00000 -1.47802 0.18454 1.20527 -1.96595 1.70043 -0.54733 -0.89148 1.86494 -1.86494 0.89148 0.54733 -1.70043 1.96595 -1.20527 -0.18454 1.47802 -2.00000 1.47802 -0.18454 -1.20527 1.96595 -1.70043 0.54733 0.89148 -1.86494 1.86494 -0.89148 -0.54733 1.70043 -1.96595 1.20527 0.18454 -1.47802 2.00000 ... ... ..... ....... ......... ........... ............. E53 * 2.00000 -1.53867 0.36750 0.97321 -1.86494 1.89632 -1.05286 -0.27631 1.47802 -1.99787 1.59603 -0.45790 -0.89148 1.82959 -1.92365 1.13027 0.18454 -1.41421 1.99147 -1.64999 0.54733 0.80784 -1.79033 1.94688 -1.20527 -0.09237 1.34739 -1.98082 1.70043 -0.63558 -0.72248 1.74724 -1.96595 1.27769 0.00000 -1.27769 1.96595 -1.74724 0.72248 0.63558 -1.70043 1.98082 -1.34739 0.09237 1.20527 -1.94688 1.79033 -0.80784 -0.54733 1.64999 -1.99147 1.41421 -0.18454 -1.13027 1.92365 -1.82959 0.89148 0.45790 -1.59603 1.99787 -1.47802 0.27631 1.05286 -1.89632 1.86494 -0.97321 -0.36750 1.53867 -2.00000 ... ... ..... ....... ......... ........... ............. E54 * 2.00000 -1.59603 0.54733 0.72248 -1.70043 1.99147 -1.47802 0.36750 0.89148 -1.79033 1.96595 -1.34739 0.18454 1.05286 -1.86494 1.92365 -1.20527 0.00000 1.20527 -1.92365 1.86494 -1.05286 -0.18454 1.34739 -1.96595 1.79033 -0.89148 -0.36750 1.47802 -1.99147 1.70043 -0.72248 -0.54733 1.59603 -2.00000 1.59603 -0.54733 -0.72248 1.70043 -1.99147 1.47802 -0.36750 -0.89148 1.79033 -1.96595 1.34739 -0.18454 -1.05286 1.86494 -1.92365 1.20527 0.00000 -1.20527 1.92365 -1.86494 1.05286 0.18454 -1.34739 1.96595 -1.79033 0.89148 0.36750 -1.47802 1.99147 -1.70043 0.72248 0.54733 -1.59603 2.00000 ... ... ..... ....... ......... ........... ............. E55 * 2.00000 -1.64999 0.72248 0.45790 -1.47802 1.98082 -1.79033 0.97321 0.18454 -1.27769 1.92365 -1.89632 1.20527 -0.09237 -1.05286 1.82959 -1.96595 1.41421 -0.36750 -0.80784 1.70043 -1.99787 1.59603 -0.63558 -0.54733 1.53867 -1.99147 1.74724 -0.89148 -0.27631 1.34739 -1.94688 1.86494 -1.13027 0.00000 1.13027 -1.86494 1.94688 -1.34739 0.27631 0.89148 -1.74724 1.99147 -1.53867 0.54733 0.63558 -1.59603 1.99787 -1.70043 0.80784 0.36750 -1.41421 1.96595 -1.82959 1.05286 0.09237 -1.20527 1.89632 -1.92365 1.27769 -0.18454 -0.97321 1.79033 -1.98082 1.47802 -0.45790 -0.72248 1.64999 -2.00000 ... ... ..... ....... ......... ........... ............. E56 * 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 ... ... ..... ....... ......... ........... ............. E57 * 2.00000 -1.74724 1.05286 -0.09237 -0.89148 1.64999 -1.99147 1.82959 -1.20527 0.27631 0.72248 -1.53867 1.96595 -1.89632 1.34739 -0.45790 -0.54733 1.41421 -1.92365 1.94688 -1.47802 0.63558 0.36750 -1.27769 1.86494 -1.98082 1.59603 -0.80784 -0.18454 1.13027 -1.79033 1.99787 -1.70043 0.97321 0.00000 -0.97321 1.70043 -1.99787 1.79033 -1.13027 0.18454 0.80784 -1.59603 1.98082 -1.86494 1.27769 -0.36750 -0.63558 1.47802 -1.94688 1.92365 -1.41421 0.54733 0.45790 -1.34739 1.89632 -1.96595 1.53867 -0.72248 -0.27631 1.20527 -1.82959 1.99147 -1.64999 0.89148 0.09237 -1.05286 1.74724 -2.00000 ... ... ..... ....... ......... ........... ............. E58 * 2.00000 -1.79033 1.20527 -0.36750 -0.54733 1.34739 -1.86494 1.99147 -1.70043 1.05286 -0.18454 -0.72248 1.47802 -1.92365 1.96595 -1.59603 0.89148 0.00000 -0.89148 1.59603 -1.96595 1.92365 -1.47802 0.72248 0.18454 -1.05286 1.70043 -1.99147 1.86494 -1.34739 0.54733 0.36750 -1.20527 1.79033 -2.00000 1.79033 -1.20527 0.36750 0.54733 -1.34739 1.86494 -1.99147 1.70043 -1.05286 0.18454 0.72248 -1.47802 1.92365 -1.96595 1.59603 -0.89148 0.00000 0.89148 -1.59603 1.96595 -1.92365 1.47802 -0.72248 -0.18454 1.05286 -1.70043 1.99147 -1.86494 1.34739 -0.54733 -0.36750 1.20527 -1.79033 2.00000 ... ... ..... ....... ......... ........... ............. E59 * 2.00000 -1.82959 1.34739 -0.63558 -0.18454 0.97321 -1.59603 1.94688 -1.96595 1.64999 -1.05286 0.27631 0.54733 -1.27769 1.79033 -1.99787 1.86494 -1.41421 0.72248 0.09237 -0.89148 1.53867 -1.92365 1.98082 -1.70043 1.13027 -0.36750 -0.45790 1.20527 -1.74724 1.99147 -1.89632 1.47802 -0.80784 0.00000 0.80784 -1.47802 1.89632 -1.99147 1.74724 -1.20527 0.45790 0.36750 -1.13027 1.70043 -1.98082 1.92365 -1.53867 0.89148 -0.09237 -0.72248 1.41421 -1.86494 1.99787 -1.79033 1.27769 -0.54733 -0.27631 1.05286 -1.64999 1.96595 -1.94688 1.59603 -0.97321 0.18454 0.63558 -1.34739 1.82959 -2.00000 ... ... ..... ....... ......... ........... ............. E60 * 2.00000 -1.86494 1.47802 -0.89148 0.18454 0.54733 -1.20527 1.70043 -1.96595 1.96595 -1.70043 1.20527 -0.54733 -0.18454 0.89148 -1.47802 1.86494 -2.00000 1.86494 -1.47802 0.89148 -0.18454 -0.54733 1.20527 -1.70043 1.96595 -1.96595 1.70043 -1.20527 0.54733 0.18454 -0.89148 1.47802 -1.86494 2.00000 -1.86494 1.47802 -0.89148 0.18454 0.54733 -1.20527 1.70043 -1.96595 1.96595 -1.70043 1.20527 -0.54733 -0.18454 0.89148 -1.47802 1.86494 -2.00000 1.86494 -1.47802 0.89148 -0.18454 -0.54733 1.20527 -1.70043 1.96595 -1.96595 1.70043 -1.20527 0.54733 0.18454 -0.89148 1.47802 -1.86494 2.00000 ... ... ..... ....... ......... ........... ............. 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E65 * 2.00000 -1.98082 1.92365 -1.82959 1.70043 -1.53867 1.34739 -1.13027 0.89148 -0.63558 0.36750 -0.09237 -0.18454 0.45790 -0.72248 0.97321 -1.20527 1.41421 -1.59603 1.74724 -1.86494 1.94688 -1.99147 1.99787 -1.96595 1.89632 -1.79033 1.64999 -1.47802 1.27769 -1.05286 0.80784 -0.54733 0.27631 0.00000 -0.27631 0.54733 -0.80784 1.05286 -1.27769 1.47802 -1.64999 1.79033 -1.89632 1.96595 -1.99787 1.99147 -1.94688 1.86494 -1.74724 1.59603 -1.41421 1.20527 -0.97321 0.72248 -0.45790 0.18454 0.09237 -0.36750 0.63558 -0.89148 1.13027 -1.34739 1.53867 -1.70043 1.82959 -1.92365 1.98082 -2.00000 ... ... ..... ....... ......... ........... ............. E66 * 2.00000 -1.99147 1.96595 -1.92365 1.86494 -1.79033 1.70043 -1.59603 1.47802 -1.34739 1.20527 -1.05286 0.89148 -0.72248 0.54733 -0.36750 0.18454 0.00000 -0.18454 0.36750 -0.54733 0.72248 -0.89148 1.05286 -1.20527 1.34739 -1.47802 1.59603 -1.70043 1.79033 -1.86494 1.92365 -1.96595 1.99147 -2.00000 1.99147 -1.96595 1.92365 -1.86494 1.79033 -1.70043 1.59603 -1.47802 1.34739 -1.20527 1.05286 -0.89148 0.72248 -0.54733 0.36750 -0.18454 0.00000 0.18454 -0.36750 0.54733 -0.72248 0.89148 -1.05286 1.20527 -1.34739 1.47802 -1.59603 1.70043 -1.79033 1.86494 -1.92365 1.96595 -1.99147 2.00000 ... ... ..... ....... ......... ........... ............. E67 * 2.00000 -1.99787 1.99147 -1.98082 1.96595 -1.94688 1.92365 -1.89632 1.86494 -1.82959 1.79033 -1.74724 1.70043 -1.64999 1.59603 -1.53867 1.47802 -1.41421 1.34739 -1.27769 1.20527 -1.13027 1.05286 -0.97321 0.89148 -0.80784 0.72248 -0.63558 0.54733 -0.45790 0.36750 -0.27631 0.18454 -0.09237 0.00000 0.09237 -0.18454 0.27631 -0.36750 0.45790 -0.54733 0.63558 -0.72248 0.80784 -0.89148 0.97321 -1.05286 1.13027 -1.20527 1.27769 -1.34739 1.41421 -1.47802 1.53867 -1.59603 1.64999 -1.70043 1.74724 -1.79033 1.82959 -1.86494 1.89632 -1.92365 1.94688 -1.96595 1.98082 -1.99147 1.99787 -2.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.997865949605 = 2*cos(2*π/136) = 2*cos(π/68) = √8+√2*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/2 1.991468352590 = 2*cos(4*π/136) = 2*cos(π/34) = √2*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/4 1.980820861750 = 2*cos(6*π/136) = 2*cos(3*π/68) = √8+√2*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/2 1.965946199368 = 2*cos(8*π/136) = 2*cos(π/17) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 1.946876108721 = 2*cos(10*π/136) = 2*cos(5*π/68) = √8+√2*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/2 1.923651286346 = 2*cos(12*π/136) = 2*cos(3*π/34) = √2*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/4 1.896321295182 = 2*cos(14*π/136) = 2*cos(7*π/68) = √8+√2*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/2 1.864944458809 = 2*cos(16*π/136) = 2*cos(2*π/17) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 1.829587736976 = 2*cos(18*π/136) = 2*cos(9*π/68) = √8+√2*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/2 1.790326582710 = 2*cos(20*π/136) = 2*cos(5*π/34) = √2*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/4 1.747244781293 = 2*cos(22*π/136) = 2*cos(11*π/68) = √8+√2*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/2 1.700434271459 = 2*cos(24*π/136) = 2*cos(3*π/17) = (1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 1.649994949197 = 2*cos(26*π/136) = 2*cos(13*π/68) = √8+√2*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/2 1.596034454560 = 2*cos(28*π/136) = 2*cos(7*π/34) = √2*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/4 1.538667941966 = 2*cos(30*π/136) = 2*cos(15*π/68) = √8+√2*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/2 1.478017834441 = 2*cos(32*π/136) = 2*cos(4*π/17) = (−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 1.414213562373 = 2*cos(34*π/136) = 2*cos(π/4) = √2 1.347391287293 = 2*cos(36*π/136) = 2*cos(9*π/34) = √2*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/4 1.277693611304 = 2*cos(38*π/136) = 2*cos(19*π/68) = √8−√2*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/2 1.205269272759 = 2*cos(40*π/136) = 2*cos(5*π/17) = (1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 1.130272828845 = 2*cos(42*π/136) = 2*cos(21*π/68) = √8−√2*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/2 1.052864325755 = 2*cos(44*π/136) = 2*cos(11*π/34) = √2*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/4 0.973208957134 = 2*cos(46*π/136) = 2*cos(23*π/68) = √8−√2*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/2 0.891476711553 = 2*cos(48*π/136) = 2*cos(6*π/17) = (−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 0.807842009744 = 2*cos(50*π/136) = 2*cos(25*π/68) = √8−√2*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/2 0.722483332374 = 2*cos(52*π/136) = 2*cos(13*π/34) = √2*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/4 0.635582839164 = 2*cos(54*π/136) = 2*cos(27*π/68) = √8−√2*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/2 0.547325980144 = 2*cos(56*π/136) = 2*cos(7*π/17) = (1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 0.457901099900 = 2*cos(58*π/136) = 2*cos(29*π/68) = √8−√2*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/2 0.367499035633 = 2*cos(60*π/136) = 2*cos(15*π/34) = √2*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/4 0.276312709904 = 2*cos(62*π/136) = 2*cos(31*π/68) = √8−√2*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/2 0.184536718927 = 2*cos(64*π/136) = 2*cos(8*π/17) = (−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 0.092366917291 = 2*cos(66*π/136) = 2*cos(33*π/68) = √8−√2*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/2 Symmetry of Rotations and Cartesian products A R+p+d+f+g+h+i+j+k+l+m R_z, z, z², z³, z⁴, z⁵, z⁶ E1 R+p+d+f+g+h+i+j+k+l+m {R_x, R_y}, {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 C₁₃₆ point group is 136, and the order of the principal axis (C₁₃₆) is 136. The group has 69 irreducible representations. β The C₁₃₆ point group is isomorphic to S₁₃₆. γ The C₁₃₆ point group is generated by one single symmetry element, C₁₃₆. Therefore, it is a cyclic group. δ The lowest nonvanishing multipole moment in C₁₃₆ is 2 (dipole moment). ε This is an Abelian point group (the commutative law holds between all symmetry operations). The C₁₃₆ 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 134 cases have been combined into 67 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 67 pairs of left and right rotations have been combined into one two-membered pseudo-class each. η The 67 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. κ The point group corresponds to a constructible polygon, as the order of the principal axis is a product of any number of different Fermat primes (3,5,17,257,65537) times an arbitrary power of two. Therefore, all characters have an algebraic degree which is a power of two and can be expressed as radicals involving only square roots and integer numbers. λ That a regular 17-gon can be constructed with compass and ruler was unknown to mathematicians until Gauss proved it in 1796. The first actual construction was performed thirty years later by Johannes Erchinger in 1825. Regular polygons of order 34,68,136 etc are easily derived from the regular 17-gon by successive halving of angles.

This Character Table for the C₁₃₆ point group was created by Gernot Katzer.

For other groups and some explanations, see the Main Page.

	C₁₂₇
	C₁₂₈
	C₁₃₆	C_136v C_136h D₁₃₆ D_136h D_136d S₁₃₆
	C₁₄₄
	C₁₅₃

Character table for the C136 point group

Character table for the C₁₃₆ point group