Character Table for Point Group S122

Character table for the S₁₂₂ point group

S122 E 2 C61 2 C61^2 2 C61^3 2 C61^4 2 C61^5 2 C61^6 2 C61^7 2 C61^8 2 C61^9 2 C61^10 2 C61^11 2 C61^12 2 C61^13 2 C61^14 2 C61^15 2 C61^16 2 C61^17 2 C61^18 2 C61^19 2 C61^20 2 C61^21 2 C61^22 2 C61^23 2 C61^24 2 C61^25 2 C61^26 2 C61^27 2 C61^28 2 C61^29 2 C61^30 i 2 S122 2 S122^3 2 S122^5 2 S122^7 2 S122^9 2 S122^11 2 S122^13 2 S122^15 2 S122^17 2 S122^19 2 S122^21 2 S122^23 2 S122^25 2 S122^27 2 S122^29 2 S122^31 2 S122^33 2 S122^35 2 S122^37 2 S122^39 2 S122^41 2 S122^43 2 S122^45 2 S122^47 2 S122^49 2 S122^51 2 S122^53 2 S122^55 2 S122^57 2 S122^59 <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> Ag 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 E1g * 2.00000 1.98940 1.95771 1.90527 1.83263 1.74057 1.63006 1.50226 1.35855 1.20043 1.02959 0.84783 0.65708 0.45938 0.25680 0.05150 -0.15435 -0.35856 -0.55897 -0.75346 -0.93995 -1.11649 -1.28119 -1.43230 -1.56824 -1.68755 -1.78897 -1.87143 -1.93406 -1.97618 -1.99735 2.00000 -1.99735 -1.97618 -1.93406 -1.87143 -1.78897 -1.68755 -1.56824 -1.43230 -1.28119 -1.11649 -0.93995 -0.75346 -0.55897 -0.35856 -0.15435 0.05150 0.25680 0.45938 0.65708 0.84783 1.02959 1.20043 1.35855 1.50226 1.63006 1.74057 1.83263 1.90527 1.95771 1.98940 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g * 2.00000 1.95771 1.83263 1.63006 1.35855 1.02959 0.65708 0.25680 -0.15435 -0.55897 -0.93995 -1.28119 -1.56824 -1.78897 -1.93406 -1.99735 -1.97618 -1.87143 -1.68755 -1.43230 -1.11649 -0.75346 -0.35856 0.05150 0.45938 0.84783 1.20043 1.50226 1.74057 1.90527 1.98940 2.00000 1.98940 1.90527 1.74057 1.50226 1.20043 0.84783 0.45938 0.05150 -0.35856 -0.75346 -1.11649 -1.43230 -1.68755 -1.87143 -1.97618 -1.99735 -1.93406 -1.78897 -1.56824 -1.28119 -0.93995 -0.55897 -0.15435 0.25680 0.65708 1.02959 1.35855 1.63006 1.83263 1.95771 ... ... TT... ....... ....TT... ........... ........TT... E3g * 2.00000 1.90527 1.63006 1.20043 0.65708 0.05150 -0.55897 -1.11649 -1.56824 -1.87143 -1.99735 -1.93406 -1.68755 -1.28119 -0.75346 -0.15435 0.45938 1.02959 1.50226 1.83263 1.98940 1.95771 1.74057 1.35855 0.84783 0.25680 -0.35856 -0.93995 -1.43230 -1.78897 -1.97618 2.00000 -1.97618 -1.78897 -1.43230 -0.93995 -0.35856 0.25680 0.84783 1.35855 1.74057 1.95771 1.98940 1.83263 1.50226 1.02959 0.45938 -0.15435 -0.75346 -1.28119 -1.68755 -1.93406 -1.99735 -1.87143 -1.56824 -1.11649 -0.55897 0.05150 0.65708 1.20043 1.63006 1.90527 ... ... ..... ....... ..TT..... ........... ......TT..... E4g * 2.00000 1.83263 1.35855 0.65708 -0.15435 -0.93995 -1.56824 -1.93406 -1.97618 -1.68755 -1.11649 -0.35856 0.45938 1.20043 1.74057 1.98940 1.90527 1.50226 0.84783 0.05150 -0.75346 -1.43230 -1.87143 -1.99735 -1.78897 -1.28119 -0.55897 0.25680 1.02959 1.63006 1.95771 2.00000 1.95771 1.63006 1.02959 0.25680 -0.55897 -1.28119 -1.78897 -1.99735 -1.87143 -1.43230 -0.75346 0.05150 0.84783 1.50226 1.90527 1.98940 1.74057 1.20043 0.45938 -0.35856 -1.11649 -1.68755 -1.97618 -1.93406 -1.56824 -0.93995 -0.15435 0.65708 1.35855 1.83263 ... ... ..... ....... TT....... ........... ....TT....... E5g * 2.00000 1.74057 1.02959 0.05150 -0.93995 -1.68755 -1.99735 -1.78897 -1.11649 -0.15435 0.84783 1.63006 1.98940 1.83263 1.20043 0.25680 -0.75346 -1.56824 -1.97618 -1.87143 -1.28119 -0.35856 0.65708 1.50226 1.95771 1.90527 1.35855 0.45938 -0.55897 -1.43230 -1.93406 2.00000 -1.93406 -1.43230 -0.55897 0.45938 1.35855 1.90527 1.95771 1.50226 0.65708 -0.35856 -1.28119 -1.87143 -1.97618 -1.56824 -0.75346 0.25680 1.20043 1.83263 1.98940 1.63006 0.84783 -0.15435 -1.11649 -1.78897 -1.99735 -1.68755 -0.93995 0.05150 1.02959 1.74057 ... ... ..... ....... ......... ........... ..TT......... E6g * 2.00000 1.63006 0.65708 -0.55897 -1.56824 -1.99735 -1.68755 -0.75346 0.45938 1.50226 1.98940 1.74057 0.84783 -0.35856 -1.43230 -1.97618 -1.78897 -0.93995 0.25680 1.35855 1.95771 1.83263 1.02959 -0.15435 -1.28119 -1.93406 -1.87143 -1.11649 0.05150 1.20043 1.90527 2.00000 1.90527 1.20043 0.05150 -1.11649 -1.87143 -1.93406 -1.28119 -0.15435 1.02959 1.83263 1.95771 1.35855 0.25680 -0.93995 -1.78897 -1.97618 -1.43230 -0.35856 0.84783 1.74057 1.98940 1.50226 0.45938 -0.75346 -1.68755 -1.99735 -1.56824 -0.55897 0.65708 1.63006 ... ... ..... ....... ......... ........... TT........... E7g * 2.00000 1.50226 0.25680 -1.11649 -1.93406 -1.78897 -0.75346 0.65708 1.74057 1.95771 1.20043 -0.15435 -1.43230 -1.99735 -1.56824 -0.35856 1.02959 1.90527 1.83263 0.84783 -0.55897 -1.68755 -1.97618 -1.28119 0.05150 1.35855 1.98940 1.63006 0.45938 -0.93995 -1.87143 2.00000 -1.87143 -0.93995 0.45938 1.63006 1.98940 1.35855 0.05150 -1.28119 -1.97618 -1.68755 -0.55897 0.84783 1.83263 1.90527 1.02959 -0.35856 -1.56824 -1.99735 -1.43230 -0.15435 1.20043 1.95771 1.74057 0.65708 -0.75346 -1.78897 -1.93406 -1.11649 0.25680 1.50226 ... ... ..... ....... ......... ........... ............. E8g * 2.00000 1.35855 -0.15435 -1.56824 -1.97618 -1.11649 0.45938 1.74057 1.90527 0.84783 -0.75346 -1.87143 -1.78897 -0.55897 1.02959 1.95771 1.63006 0.25680 -1.28119 -1.99735 -1.43230 0.05150 1.50226 1.98940 1.20043 -0.35856 -1.68755 -1.93406 -0.93995 0.65708 1.83263 2.00000 1.83263 0.65708 -0.93995 -1.93406 -1.68755 -0.35856 1.20043 1.98940 1.50226 0.05150 -1.43230 -1.99735 -1.28119 0.25680 1.63006 1.95771 1.02959 -0.55897 -1.78897 -1.87143 -0.75346 0.84783 1.90527 1.74057 0.45938 -1.11649 -1.97618 -1.56824 -0.15435 1.35855 ... ... ..... ....... ......... ........... ............. E9g * 2.00000 1.20043 -0.55897 -1.87143 -1.68755 -0.15435 1.50226 1.95771 0.84783 -0.93995 -1.97618 -1.43230 0.25680 1.74057 1.83263 0.45938 -1.28119 -1.99735 -1.11649 0.65708 1.90527 1.63006 0.05150 -1.56824 -1.93406 -0.75346 1.02959 1.98940 1.35855 -0.35856 -1.78897 2.00000 -1.78897 -0.35856 1.35855 1.98940 1.02959 -0.75346 -1.93406 -1.56824 0.05150 1.63006 1.90527 0.65708 -1.11649 -1.99735 -1.28119 0.45938 1.83263 1.74057 0.25680 -1.43230 -1.97618 -0.93995 0.84783 1.95771 1.50226 -0.15435 -1.68755 -1.87143 -0.55897 1.20043 ... ... ..... ....... ......... ........... ............. E10g * 2.00000 1.02959 -0.93995 -1.99735 -1.11649 0.84783 1.98940 1.20043 -0.75346 -1.97618 -1.28119 0.65708 1.95771 1.35855 -0.55897 -1.93406 -1.43230 0.45938 1.90527 1.50226 -0.35856 -1.87143 -1.56824 0.25680 1.83263 1.63006 -0.15435 -1.78897 -1.68755 0.05150 1.74057 2.00000 1.74057 0.05150 -1.68755 -1.78897 -0.15435 1.63006 1.83263 0.25680 -1.56824 -1.87143 -0.35856 1.50226 1.90527 0.45938 -1.43230 -1.93406 -0.55897 1.35855 1.95771 0.65708 -1.28119 -1.97618 -0.75346 1.20043 1.98940 0.84783 -1.11649 -1.99735 -0.93995 1.02959 ... ... ..... ....... ......... ........... ............. E11g * 2.00000 0.84783 -1.28119 -1.93406 -0.35856 1.63006 1.74057 -0.15435 -1.87143 -1.43230 0.65708 1.98940 1.02959 -1.11649 -1.97618 -0.55897 1.50226 1.83263 0.05150 -1.78897 -1.56824 0.45938 1.95771 1.20043 -0.93995 -1.99735 -0.75346 1.35855 1.90527 0.25680 -1.68755 2.00000 -1.68755 0.25680 1.90527 1.35855 -0.75346 -1.99735 -0.93995 1.20043 1.95771 0.45938 -1.56824 -1.78897 0.05150 1.83263 1.50226 -0.55897 -1.97618 -1.11649 1.02959 1.98940 0.65708 -1.43230 -1.87143 -0.15435 1.74057 1.63006 -0.35856 -1.93406 -1.28119 0.84783 ... ... ..... ....... ......... ........... ............. E12g * 2.00000 0.65708 -1.56824 -1.68755 0.45938 1.98940 0.84783 -1.43230 -1.78897 0.25680 1.95771 1.02959 -1.28119 -1.87143 0.05150 1.90527 1.20043 -1.11649 -1.93406 -0.15435 1.83263 1.35855 -0.93995 -1.97618 -0.35856 1.74057 1.50226 -0.75346 -1.99735 -0.55897 1.63006 2.00000 1.63006 -0.55897 -1.99735 -0.75346 1.50226 1.74057 -0.35856 -1.97618 -0.93995 1.35855 1.83263 -0.15435 -1.93406 -1.11649 1.20043 1.90527 0.05150 -1.87143 -1.28119 1.02959 1.95771 0.25680 -1.78897 -1.43230 0.84783 1.98940 0.45938 -1.68755 -1.56824 0.65708 ... ... ..... ....... ......... ........... ............. E13g * 2.00000 0.45938 -1.78897 -1.28119 1.20043 1.83263 -0.35856 -1.99735 -0.55897 1.74057 1.35855 -1.11649 -1.87143 0.25680 1.98940 0.65708 -1.68755 -1.43230 1.02959 1.90527 -0.15435 -1.97618 -0.75346 1.63006 1.50226 -0.93995 -1.93406 0.05150 1.95771 0.84783 -1.56824 2.00000 -1.56824 0.84783 1.95771 0.05150 -1.93406 -0.93995 1.50226 1.63006 -0.75346 -1.97618 -0.15435 1.90527 1.02959 -1.43230 -1.68755 0.65708 1.98940 0.25680 -1.87143 -1.11649 1.35855 1.74057 -0.55897 -1.99735 -0.35856 1.83263 1.20043 -1.28119 -1.78897 0.45938 ... ... ..... ....... ......... ........... ............. E14g * 2.00000 0.25680 -1.93406 -0.75346 1.74057 1.20043 -1.43230 -1.56824 1.02959 1.83263 -0.55897 -1.97618 0.05150 1.98940 0.45938 -1.87143 -0.93995 1.63006 1.35855 -1.28119 -1.68755 0.84783 1.90527 -0.35856 -1.99735 -0.15435 1.95771 0.65708 -1.78897 -1.11649 1.50226 2.00000 1.50226 -1.11649 -1.78897 0.65708 1.95771 -0.15435 -1.99735 -0.35856 1.90527 0.84783 -1.68755 -1.28119 1.35855 1.63006 -0.93995 -1.87143 0.45938 1.98940 0.05150 -1.97618 -0.55897 1.83263 1.02959 -1.56824 -1.43230 1.20043 1.74057 -0.75346 -1.93406 0.25680 ... ... ..... ....... ......... ........... ............. E15g * 2.00000 0.05150 -1.99735 -0.15435 1.98940 0.25680 -1.97618 -0.35856 1.95771 0.45938 -1.93406 -0.55897 1.90527 0.65708 -1.87143 -0.75346 1.83263 0.84783 -1.78897 -0.93995 1.74057 1.02959 -1.68755 -1.11649 1.63006 1.20043 -1.56824 -1.28119 1.50226 1.35855 -1.43230 2.00000 -1.43230 1.35855 1.50226 -1.28119 -1.56824 1.20043 1.63006 -1.11649 -1.68755 1.02959 1.74057 -0.93995 -1.78897 0.84783 1.83263 -0.75346 -1.87143 0.65708 1.90527 -0.55897 -1.93406 0.45938 1.95771 -0.35856 -1.97618 0.25680 1.98940 -0.15435 -1.99735 0.05150 ... ... ..... ....... ......... ........... ............. E16g * 2.00000 -0.15435 -1.97618 0.45938 1.90527 -0.75346 -1.78897 1.02959 1.63006 -1.28119 -1.43230 1.50226 1.20043 -1.68755 -0.93995 1.83263 0.65708 -1.93406 -0.35856 1.98940 0.05150 -1.99735 0.25680 1.95771 -0.55897 -1.87143 0.84783 1.74057 -1.11649 -1.56824 1.35855 2.00000 1.35855 -1.56824 -1.11649 1.74057 0.84783 -1.87143 -0.55897 1.95771 0.25680 -1.99735 0.05150 1.98940 -0.35856 -1.93406 0.65708 1.83263 -0.93995 -1.68755 1.20043 1.50226 -1.43230 -1.28119 1.63006 1.02959 -1.78897 -0.75346 1.90527 0.45938 -1.97618 -0.15435 ... ... ..... ....... ......... ........... ............. E17g * 2.00000 -0.35856 -1.87143 1.02959 1.50226 -1.56824 -0.93995 1.90527 0.25680 -1.99735 0.45938 1.83263 -1.11649 -1.43230 1.63006 0.84783 -1.93406 -0.15435 1.98940 -0.55897 -1.78897 1.20043 1.35855 -1.68755 -0.75346 1.95771 0.05150 -1.97618 0.65708 1.74057 -1.28119 2.00000 -1.28119 1.74057 0.65708 -1.97618 0.05150 1.95771 -0.75346 -1.68755 1.35855 1.20043 -1.78897 -0.55897 1.98940 -0.15435 -1.93406 0.84783 1.63006 -1.43230 -1.11649 1.83263 0.45938 -1.99735 0.25680 1.90527 -0.93995 -1.56824 1.50226 1.02959 -1.87143 -0.35856 ... ... ..... ....... ......... ........... ............. E18g * 2.00000 -0.55897 -1.68755 1.50226 0.84783 -1.97618 0.25680 1.83263 -1.28119 -1.11649 1.90527 0.05150 -1.93406 1.02959 1.35855 -1.78897 -0.35856 1.98940 -0.75346 -1.56824 1.63006 0.65708 -1.99735 0.45938 1.74057 -1.43230 -0.93995 1.95771 -0.15435 -1.87143 1.20043 2.00000 1.20043 -1.87143 -0.15435 1.95771 -0.93995 -1.43230 1.74057 0.45938 -1.99735 0.65708 1.63006 -1.56824 -0.75346 1.98940 -0.35856 -1.78897 1.35855 1.02959 -1.93406 0.05150 1.90527 -1.11649 -1.28119 1.83263 0.25680 -1.97618 0.84783 1.50226 -1.68755 -0.55897 ... ... ..... ....... ......... ........... ............. E19g * 2.00000 -0.75346 -1.43230 1.83263 0.05150 -1.87143 1.35855 0.84783 -1.99735 0.65708 1.50226 -1.78897 -0.15435 1.90527 -1.28119 -0.93995 1.98940 -0.55897 -1.56824 1.74057 0.25680 -1.93406 1.20043 1.02959 -1.97618 0.45938 1.63006 -1.68755 -0.35856 1.95771 -1.11649 2.00000 -1.11649 1.95771 -0.35856 -1.68755 1.63006 0.45938 -1.97618 1.02959 1.20043 -1.93406 0.25680 1.74057 -1.56824 -0.55897 1.98940 -0.93995 -1.28119 1.90527 -0.15435 -1.78897 1.50226 0.65708 -1.99735 0.84783 1.35855 -1.87143 0.05150 1.83263 -1.43230 -0.75346 ... ... ..... ....... ......... ........... ............. E20g * 2.00000 -0.93995 -1.11649 1.98940 -0.75346 -1.28119 1.95771 -0.55897 -1.43230 1.90527 -0.35856 -1.56824 1.83263 -0.15435 -1.68755 1.74057 0.05150 -1.78897 1.63006 0.25680 -1.87143 1.50226 0.45938 -1.93406 1.35855 0.65708 -1.97618 1.20043 0.84783 -1.99735 1.02959 2.00000 1.02959 -1.99735 0.84783 1.20043 -1.97618 0.65708 1.35855 -1.93406 0.45938 1.50226 -1.87143 0.25680 1.63006 -1.78897 0.05150 1.74057 -1.68755 -0.15435 1.83263 -1.56824 -0.35856 1.90527 -1.43230 -0.55897 1.95771 -1.28119 -0.75346 1.98940 -1.11649 -0.93995 ... ... ..... ....... ......... ........... ............. E21g * 2.00000 -1.11649 -0.75346 1.95771 -1.43230 -0.35856 1.83263 -1.68755 0.05150 1.63006 -1.87143 0.45938 1.35855 -1.97618 0.84783 1.02959 -1.99735 1.20043 0.65708 -1.93406 1.50226 0.25680 -1.78897 1.74057 -0.15435 -1.56824 1.90527 -0.55897 -1.28119 1.98940 -0.93995 2.00000 -0.93995 1.98940 -1.28119 -0.55897 1.90527 -1.56824 -0.15435 1.74057 -1.78897 0.25680 1.50226 -1.93406 0.65708 1.20043 -1.99735 1.02959 0.84783 -1.97618 1.35855 0.45938 -1.87143 1.63006 0.05150 -1.68755 1.83263 -0.35856 -1.43230 1.95771 -0.75346 -1.11649 ... ... ..... ....... ......... ........... ............. E22g * 2.00000 -1.28119 -0.35856 1.74057 -1.87143 0.65708 1.02959 -1.97618 1.50226 0.05150 -1.56824 1.95771 -0.93995 -0.75346 1.90527 -1.68755 0.25680 1.35855 -1.99735 1.20043 0.45938 -1.78897 1.83263 -0.55897 -1.11649 1.98940 -1.43230 -0.15435 1.63006 -1.93406 0.84783 2.00000 0.84783 -1.93406 1.63006 -0.15435 -1.43230 1.98940 -1.11649 -0.55897 1.83263 -1.78897 0.45938 1.20043 -1.99735 1.35855 0.25680 -1.68755 1.90527 -0.75346 -0.93995 1.95771 -1.56824 0.05150 1.50226 -1.97618 1.02959 0.65708 -1.87143 1.74057 -0.35856 -1.28119 ... ... ..... ....... ......... ........... ............. E23g * 2.00000 -1.43230 0.05150 1.35855 -1.99735 1.50226 -0.15435 -1.28119 1.98940 -1.56824 0.25680 1.20043 -1.97618 1.63006 -0.35856 -1.11649 1.95771 -1.68755 0.45938 1.02959 -1.93406 1.74057 -0.55897 -0.93995 1.90527 -1.78897 0.65708 0.84783 -1.87143 1.83263 -0.75346 2.00000 -0.75346 1.83263 -1.87143 0.84783 0.65708 -1.78897 1.90527 -0.93995 -0.55897 1.74057 -1.93406 1.02959 0.45938 -1.68755 1.95771 -1.11649 -0.35856 1.63006 -1.97618 1.20043 0.25680 -1.56824 1.98940 -1.28119 -0.15435 1.50226 -1.99735 1.35855 0.05150 -1.43230 ... ... ..... ....... ......... ........... ............. E24g * 2.00000 -1.56824 0.45938 0.84783 -1.78897 1.95771 -1.28119 0.05150 1.20043 -1.93406 1.83263 -0.93995 -0.35856 1.50226 -1.99735 1.63006 -0.55897 -0.75346 1.74057 -1.97618 1.35855 -0.15435 -1.11649 1.90527 -1.87143 1.02959 0.25680 -1.43230 1.98940 -1.68755 0.65708 2.00000 0.65708 -1.68755 1.98940 -1.43230 0.25680 1.02959 -1.87143 1.90527 -1.11649 -0.15435 1.35855 -1.97618 1.74057 -0.75346 -0.55897 1.63006 -1.99735 1.50226 -0.35856 -0.93995 1.83263 -1.93406 1.20043 0.05150 -1.28119 1.95771 -1.78897 0.84783 0.45938 -1.56824 ... ... ..... ....... ......... ........... ............. E25g * 2.00000 -1.68755 0.84783 0.25680 -1.28119 1.90527 -1.93406 1.35855 -0.35856 -0.75346 1.63006 -1.99735 1.74057 -0.93995 -0.15435 1.20043 -1.87143 1.95771 -1.43230 0.45938 0.65708 -1.56824 1.98940 -1.78897 1.02959 0.05150 -1.11649 1.83263 -1.97618 1.50226 -0.55897 2.00000 -0.55897 1.50226 -1.97618 1.83263 -1.11649 0.05150 1.02959 -1.78897 1.98940 -1.56824 0.65708 0.45938 -1.43230 1.95771 -1.87143 1.20043 -0.15435 -0.93995 1.74057 -1.99735 1.63006 -0.75346 -0.35856 1.35855 -1.93406 1.90527 -1.28119 0.25680 0.84783 -1.68755 ... ... ..... ....... ......... ........... ............. E26g * 2.00000 -1.78897 1.20043 -0.35856 -0.55897 1.35855 -1.87143 1.98940 -1.68755 1.02959 -0.15435 -0.75346 1.50226 -1.93406 1.95771 -1.56824 0.84783 0.05150 -0.93995 1.63006 -1.97618 1.90527 -1.43230 0.65708 0.25680 -1.11649 1.74057 -1.99735 1.83263 -1.28119 0.45938 2.00000 0.45938 -1.28119 1.83263 -1.99735 1.74057 -1.11649 0.25680 0.65708 -1.43230 1.90527 -1.97618 1.63006 -0.93995 0.05150 0.84783 -1.56824 1.95771 -1.93406 1.50226 -0.75346 -0.15435 1.02959 -1.68755 1.98940 -1.87143 1.35855 -0.55897 -0.35856 1.20043 -1.78897 ... ... ..... ....... ......... ........... ............. E27g * 2.00000 -1.87143 1.50226 -0.93995 0.25680 0.45938 -1.11649 1.63006 -1.93406 1.98940 -1.78897 1.35855 -0.75346 0.05150 0.65708 -1.28119 1.74057 -1.97618 1.95771 -1.68755 1.20043 -0.55897 -0.15435 0.84783 -1.43230 1.83263 -1.99735 1.90527 -1.56824 1.02959 -0.35856 2.00000 -0.35856 1.02959 -1.56824 1.90527 -1.99735 1.83263 -1.43230 0.84783 -0.15435 -0.55897 1.20043 -1.68755 1.95771 -1.97618 1.74057 -1.28119 0.65708 0.05150 -0.75346 1.35855 -1.78897 1.98940 -1.93406 1.63006 -1.11649 0.45938 0.25680 -0.93995 1.50226 -1.87143 ... ... ..... ....... ......... ........... ............. E28g * 2.00000 -1.93406 1.74057 -1.43230 1.02959 -0.55897 0.05150 0.45938 -0.93995 1.35855 -1.68755 1.90527 -1.99735 1.95771 -1.78897 1.50226 -1.11649 0.65708 -0.15435 -0.35856 0.84783 -1.28119 1.63006 -1.87143 1.98940 -1.97618 1.83263 -1.56824 1.20043 -0.75346 0.25680 2.00000 0.25680 -0.75346 1.20043 -1.56824 1.83263 -1.97618 1.98940 -1.87143 1.63006 -1.28119 0.84783 -0.35856 -0.15435 0.65708 -1.11649 1.50226 -1.78897 1.95771 -1.99735 1.90527 -1.68755 1.35855 -0.93995 0.45938 0.05150 -0.55897 1.02959 -1.43230 1.74057 -1.93406 ... ... ..... ....... ......... ........... ............. E29g * 2.00000 -1.97618 1.90527 -1.78897 1.63006 -1.43230 1.20043 -0.93995 0.65708 -0.35856 0.05150 0.25680 -0.55897 0.84783 -1.11649 1.35855 -1.56824 1.74057 -1.87143 1.95771 -1.99735 1.98940 -1.93406 1.83263 -1.68755 1.50226 -1.28119 1.02959 -0.75346 0.45938 -0.15435 2.00000 -0.15435 0.45938 -0.75346 1.02959 -1.28119 1.50226 -1.68755 1.83263 -1.93406 1.98940 -1.99735 1.95771 -1.87143 1.74057 -1.56824 1.35855 -1.11649 0.84783 -0.55897 0.25680 0.05150 -0.35856 0.65708 -0.93995 1.20043 -1.43230 1.63006 -1.78897 1.90527 -1.97618 ... ... ..... ....... ......... ........... ............. E30g * 2.00000 -1.99735 1.98940 -1.97618 1.95771 -1.93406 1.90527 -1.87143 1.83263 -1.78897 1.74057 -1.68755 1.63006 -1.56824 1.50226 -1.43230 1.35855 -1.28119 1.20043 -1.11649 1.02959 -0.93995 0.84783 -0.75346 0.65708 -0.55897 0.45938 -0.35856 0.25680 -0.15435 0.05150 2.00000 0.05150 -0.15435 0.25680 -0.35856 0.45938 -0.55897 0.65708 -0.75346 0.84783 -0.93995 1.02959 -1.11649 1.20043 -1.28119 1.35855 -1.43230 1.50226 -1.56824 1.63006 -1.68755 1.74057 -1.78897 1.83263 -1.87143 1.90527 -1.93406 1.95771 -1.97618 1.98940 -1.99735 ... ... ..... ....... ......... ........... ............. Au 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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 ............. E1u * 2.00000 1.98940 1.95771 1.90527 1.83263 1.74057 1.63006 1.50226 1.35855 1.20043 1.02959 0.84783 0.65708 0.45938 0.25680 0.05150 -0.15435 -0.35856 -0.55897 -0.75346 -0.93995 -1.11649 -1.28119 -1.43230 -1.56824 -1.68755 -1.78897 -1.87143 -1.93406 -1.97618 -1.99735 -2.00000 1.99735 1.97618 1.93406 1.87143 1.78897 1.68755 1.56824 1.43230 1.28119 1.11649 0.93995 0.75346 0.55897 0.35856 0.15435 -0.05150 -0.25680 -0.45938 -0.65708 -0.84783 -1.02959 -1.20043 -1.35855 -1.50226 -1.63006 -1.74057 -1.83263 -1.90527 -1.95771 -1.98940 ... TT. ..... ....TT. ......... ........TT. ............. E2u * 2.00000 1.95771 1.83263 1.63006 1.35855 1.02959 0.65708 0.25680 -0.15435 -0.55897 -0.93995 -1.28119 -1.56824 -1.78897 -1.93406 -1.99735 -1.97618 -1.87143 -1.68755 -1.43230 -1.11649 -0.75346 -0.35856 0.05150 0.45938 0.84783 1.20043 1.50226 1.74057 1.90527 1.98940 -2.00000 -1.98940 -1.90527 -1.74057 -1.50226 -1.20043 -0.84783 -0.45938 -0.05150 0.35856 0.75346 1.11649 1.43230 1.68755 1.87143 1.97618 1.99735 1.93406 1.78897 1.56824 1.28119 0.93995 0.55897 0.15435 -0.25680 -0.65708 -1.02959 -1.35855 -1.63006 -1.83263 -1.95771 ... ... ..... ..TT... ......... ......TT... ............. E3u * 2.00000 1.90527 1.63006 1.20043 0.65708 0.05150 -0.55897 -1.11649 -1.56824 -1.87143 -1.99735 -1.93406 -1.68755 -1.28119 -0.75346 -0.15435 0.45938 1.02959 1.50226 1.83263 1.98940 1.95771 1.74057 1.35855 0.84783 0.25680 -0.35856 -0.93995 -1.43230 -1.78897 -1.97618 -2.00000 1.97618 1.78897 1.43230 0.93995 0.35856 -0.25680 -0.84783 -1.35855 -1.74057 -1.95771 -1.98940 -1.83263 -1.50226 -1.02959 -0.45938 0.15435 0.75346 1.28119 1.68755 1.93406 1.99735 1.87143 1.56824 1.11649 0.55897 -0.05150 -0.65708 -1.20043 -1.63006 -1.90527 ... ... ..... TT..... ......... ....TT..... ............. E4u * 2.00000 1.83263 1.35855 0.65708 -0.15435 -0.93995 -1.56824 -1.93406 -1.97618 -1.68755 -1.11649 -0.35856 0.45938 1.20043 1.74057 1.98940 1.90527 1.50226 0.84783 0.05150 -0.75346 -1.43230 -1.87143 -1.99735 -1.78897 -1.28119 -0.55897 0.25680 1.02959 1.63006 1.95771 -2.00000 -1.95771 -1.63006 -1.02959 -0.25680 0.55897 1.28119 1.78897 1.99735 1.87143 1.43230 0.75346 -0.05150 -0.84783 -1.50226 -1.90527 -1.98940 -1.74057 -1.20043 -0.45938 0.35856 1.11649 1.68755 1.97618 1.93406 1.56824 0.93995 0.15435 -0.65708 -1.35855 -1.83263 ... ... ..... ....... ......... ..TT....... ............. E5u * 2.00000 1.74057 1.02959 0.05150 -0.93995 -1.68755 -1.99735 -1.78897 -1.11649 -0.15435 0.84783 1.63006 1.98940 1.83263 1.20043 0.25680 -0.75346 -1.56824 -1.97618 -1.87143 -1.28119 -0.35856 0.65708 1.50226 1.95771 1.90527 1.35855 0.45938 -0.55897 -1.43230 -1.93406 -2.00000 1.93406 1.43230 0.55897 -0.45938 -1.35855 -1.90527 -1.95771 -1.50226 -0.65708 0.35856 1.28119 1.87143 1.97618 1.56824 0.75346 -0.25680 -1.20043 -1.83263 -1.98940 -1.63006 -0.84783 0.15435 1.11649 1.78897 1.99735 1.68755 0.93995 -0.05150 -1.02959 -1.74057 ... ... ..... ....... ......... TT......... ............. E6u * 2.00000 1.63006 0.65708 -0.55897 -1.56824 -1.99735 -1.68755 -0.75346 0.45938 1.50226 1.98940 1.74057 0.84783 -0.35856 -1.43230 -1.97618 -1.78897 -0.93995 0.25680 1.35855 1.95771 1.83263 1.02959 -0.15435 -1.28119 -1.93406 -1.87143 -1.11649 0.05150 1.20043 1.90527 -2.00000 -1.90527 -1.20043 -0.05150 1.11649 1.87143 1.93406 1.28119 0.15435 -1.02959 -1.83263 -1.95771 -1.35855 -0.25680 0.93995 1.78897 1.97618 1.43230 0.35856 -0.84783 -1.74057 -1.98940 -1.50226 -0.45938 0.75346 1.68755 1.99735 1.56824 0.55897 -0.65708 -1.63006 ... ... ..... ....... ......... ........... ............. E7u * 2.00000 1.50226 0.25680 -1.11649 -1.93406 -1.78897 -0.75346 0.65708 1.74057 1.95771 1.20043 -0.15435 -1.43230 -1.99735 -1.56824 -0.35856 1.02959 1.90527 1.83263 0.84783 -0.55897 -1.68755 -1.97618 -1.28119 0.05150 1.35855 1.98940 1.63006 0.45938 -0.93995 -1.87143 -2.00000 1.87143 0.93995 -0.45938 -1.63006 -1.98940 -1.35855 -0.05150 1.28119 1.97618 1.68755 0.55897 -0.84783 -1.83263 -1.90527 -1.02959 0.35856 1.56824 1.99735 1.43230 0.15435 -1.20043 -1.95771 -1.74057 -0.65708 0.75346 1.78897 1.93406 1.11649 -0.25680 -1.50226 ... ... ..... ....... ......... ........... ............. E8u * 2.00000 1.35855 -0.15435 -1.56824 -1.97618 -1.11649 0.45938 1.74057 1.90527 0.84783 -0.75346 -1.87143 -1.78897 -0.55897 1.02959 1.95771 1.63006 0.25680 -1.28119 -1.99735 -1.43230 0.05150 1.50226 1.98940 1.20043 -0.35856 -1.68755 -1.93406 -0.93995 0.65708 1.83263 -2.00000 -1.83263 -0.65708 0.93995 1.93406 1.68755 0.35856 -1.20043 -1.98940 -1.50226 -0.05150 1.43230 1.99735 1.28119 -0.25680 -1.63006 -1.95771 -1.02959 0.55897 1.78897 1.87143 0.75346 -0.84783 -1.90527 -1.74057 -0.45938 1.11649 1.97618 1.56824 0.15435 -1.35855 ... ... ..... ....... ......... ........... ............. E9u * 2.00000 1.20043 -0.55897 -1.87143 -1.68755 -0.15435 1.50226 1.95771 0.84783 -0.93995 -1.97618 -1.43230 0.25680 1.74057 1.83263 0.45938 -1.28119 -1.99735 -1.11649 0.65708 1.90527 1.63006 0.05150 -1.56824 -1.93406 -0.75346 1.02959 1.98940 1.35855 -0.35856 -1.78897 -2.00000 1.78897 0.35856 -1.35855 -1.98940 -1.02959 0.75346 1.93406 1.56824 -0.05150 -1.63006 -1.90527 -0.65708 1.11649 1.99735 1.28119 -0.45938 -1.83263 -1.74057 -0.25680 1.43230 1.97618 0.93995 -0.84783 -1.95771 -1.50226 0.15435 1.68755 1.87143 0.55897 -1.20043 ... ... ..... ....... ......... ........... ............. E10u * 2.00000 1.02959 -0.93995 -1.99735 -1.11649 0.84783 1.98940 1.20043 -0.75346 -1.97618 -1.28119 0.65708 1.95771 1.35855 -0.55897 -1.93406 -1.43230 0.45938 1.90527 1.50226 -0.35856 -1.87143 -1.56824 0.25680 1.83263 1.63006 -0.15435 -1.78897 -1.68755 0.05150 1.74057 -2.00000 -1.74057 -0.05150 1.68755 1.78897 0.15435 -1.63006 -1.83263 -0.25680 1.56824 1.87143 0.35856 -1.50226 -1.90527 -0.45938 1.43230 1.93406 0.55897 -1.35855 -1.95771 -0.65708 1.28119 1.97618 0.75346 -1.20043 -1.98940 -0.84783 1.11649 1.99735 0.93995 -1.02959 ... ... ..... ....... ......... ........... ............. E11u * 2.00000 0.84783 -1.28119 -1.93406 -0.35856 1.63006 1.74057 -0.15435 -1.87143 -1.43230 0.65708 1.98940 1.02959 -1.11649 -1.97618 -0.55897 1.50226 1.83263 0.05150 -1.78897 -1.56824 0.45938 1.95771 1.20043 -0.93995 -1.99735 -0.75346 1.35855 1.90527 0.25680 -1.68755 -2.00000 1.68755 -0.25680 -1.90527 -1.35855 0.75346 1.99735 0.93995 -1.20043 -1.95771 -0.45938 1.56824 1.78897 -0.05150 -1.83263 -1.50226 0.55897 1.97618 1.11649 -1.02959 -1.98940 -0.65708 1.43230 1.87143 0.15435 -1.74057 -1.63006 0.35856 1.93406 1.28119 -0.84783 ... ... ..... ....... ......... ........... ............. E12u * 2.00000 0.65708 -1.56824 -1.68755 0.45938 1.98940 0.84783 -1.43230 -1.78897 0.25680 1.95771 1.02959 -1.28119 -1.87143 0.05150 1.90527 1.20043 -1.11649 -1.93406 -0.15435 1.83263 1.35855 -0.93995 -1.97618 -0.35856 1.74057 1.50226 -0.75346 -1.99735 -0.55897 1.63006 -2.00000 -1.63006 0.55897 1.99735 0.75346 -1.50226 -1.74057 0.35856 1.97618 0.93995 -1.35855 -1.83263 0.15435 1.93406 1.11649 -1.20043 -1.90527 -0.05150 1.87143 1.28119 -1.02959 -1.95771 -0.25680 1.78897 1.43230 -0.84783 -1.98940 -0.45938 1.68755 1.56824 -0.65708 ... ... ..... ....... ......... ........... ............. E13u * 2.00000 0.45938 -1.78897 -1.28119 1.20043 1.83263 -0.35856 -1.99735 -0.55897 1.74057 1.35855 -1.11649 -1.87143 0.25680 1.98940 0.65708 -1.68755 -1.43230 1.02959 1.90527 -0.15435 -1.97618 -0.75346 1.63006 1.50226 -0.93995 -1.93406 0.05150 1.95771 0.84783 -1.56824 -2.00000 1.56824 -0.84783 -1.95771 -0.05150 1.93406 0.93995 -1.50226 -1.63006 0.75346 1.97618 0.15435 -1.90527 -1.02959 1.43230 1.68755 -0.65708 -1.98940 -0.25680 1.87143 1.11649 -1.35855 -1.74057 0.55897 1.99735 0.35856 -1.83263 -1.20043 1.28119 1.78897 -0.45938 ... ... ..... ....... ......... ........... ............. E14u * 2.00000 0.25680 -1.93406 -0.75346 1.74057 1.20043 -1.43230 -1.56824 1.02959 1.83263 -0.55897 -1.97618 0.05150 1.98940 0.45938 -1.87143 -0.93995 1.63006 1.35855 -1.28119 -1.68755 0.84783 1.90527 -0.35856 -1.99735 -0.15435 1.95771 0.65708 -1.78897 -1.11649 1.50226 -2.00000 -1.50226 1.11649 1.78897 -0.65708 -1.95771 0.15435 1.99735 0.35856 -1.90527 -0.84783 1.68755 1.28119 -1.35855 -1.63006 0.93995 1.87143 -0.45938 -1.98940 -0.05150 1.97618 0.55897 -1.83263 -1.02959 1.56824 1.43230 -1.20043 -1.74057 0.75346 1.93406 -0.25680 ... ... ..... ....... ......... ........... ............. E15u * 2.00000 0.05150 -1.99735 -0.15435 1.98940 0.25680 -1.97618 -0.35856 1.95771 0.45938 -1.93406 -0.55897 1.90527 0.65708 -1.87143 -0.75346 1.83263 0.84783 -1.78897 -0.93995 1.74057 1.02959 -1.68755 -1.11649 1.63006 1.20043 -1.56824 -1.28119 1.50226 1.35855 -1.43230 -2.00000 1.43230 -1.35855 -1.50226 1.28119 1.56824 -1.20043 -1.63006 1.11649 1.68755 -1.02959 -1.74057 0.93995 1.78897 -0.84783 -1.83263 0.75346 1.87143 -0.65708 -1.90527 0.55897 1.93406 -0.45938 -1.95771 0.35856 1.97618 -0.25680 -1.98940 0.15435 1.99735 -0.05150 ... ... ..... ....... ......... ........... ............. E16u * 2.00000 -0.15435 -1.97618 0.45938 1.90527 -0.75346 -1.78897 1.02959 1.63006 -1.28119 -1.43230 1.50226 1.20043 -1.68755 -0.93995 1.83263 0.65708 -1.93406 -0.35856 1.98940 0.05150 -1.99735 0.25680 1.95771 -0.55897 -1.87143 0.84783 1.74057 -1.11649 -1.56824 1.35855 -2.00000 -1.35855 1.56824 1.11649 -1.74057 -0.84783 1.87143 0.55897 -1.95771 -0.25680 1.99735 -0.05150 -1.98940 0.35856 1.93406 -0.65708 -1.83263 0.93995 1.68755 -1.20043 -1.50226 1.43230 1.28119 -1.63006 -1.02959 1.78897 0.75346 -1.90527 -0.45938 1.97618 0.15435 ... ... ..... ....... ......... ........... ............. E17u * 2.00000 -0.35856 -1.87143 1.02959 1.50226 -1.56824 -0.93995 1.90527 0.25680 -1.99735 0.45938 1.83263 -1.11649 -1.43230 1.63006 0.84783 -1.93406 -0.15435 1.98940 -0.55897 -1.78897 1.20043 1.35855 -1.68755 -0.75346 1.95771 0.05150 -1.97618 0.65708 1.74057 -1.28119 -2.00000 1.28119 -1.74057 -0.65708 1.97618 -0.05150 -1.95771 0.75346 1.68755 -1.35855 -1.20043 1.78897 0.55897 -1.98940 0.15435 1.93406 -0.84783 -1.63006 1.43230 1.11649 -1.83263 -0.45938 1.99735 -0.25680 -1.90527 0.93995 1.56824 -1.50226 -1.02959 1.87143 0.35856 ... ... ..... ....... ......... ........... ............. E18u * 2.00000 -0.55897 -1.68755 1.50226 0.84783 -1.97618 0.25680 1.83263 -1.28119 -1.11649 1.90527 0.05150 -1.93406 1.02959 1.35855 -1.78897 -0.35856 1.98940 -0.75346 -1.56824 1.63006 0.65708 -1.99735 0.45938 1.74057 -1.43230 -0.93995 1.95771 -0.15435 -1.87143 1.20043 -2.00000 -1.20043 1.87143 0.15435 -1.95771 0.93995 1.43230 -1.74057 -0.45938 1.99735 -0.65708 -1.63006 1.56824 0.75346 -1.98940 0.35856 1.78897 -1.35855 -1.02959 1.93406 -0.05150 -1.90527 1.11649 1.28119 -1.83263 -0.25680 1.97618 -0.84783 -1.50226 1.68755 0.55897 ... ... ..... ....... ......... ........... ............. E19u * 2.00000 -0.75346 -1.43230 1.83263 0.05150 -1.87143 1.35855 0.84783 -1.99735 0.65708 1.50226 -1.78897 -0.15435 1.90527 -1.28119 -0.93995 1.98940 -0.55897 -1.56824 1.74057 0.25680 -1.93406 1.20043 1.02959 -1.97618 0.45938 1.63006 -1.68755 -0.35856 1.95771 -1.11649 -2.00000 1.11649 -1.95771 0.35856 1.68755 -1.63006 -0.45938 1.97618 -1.02959 -1.20043 1.93406 -0.25680 -1.74057 1.56824 0.55897 -1.98940 0.93995 1.28119 -1.90527 0.15435 1.78897 -1.50226 -0.65708 1.99735 -0.84783 -1.35855 1.87143 -0.05150 -1.83263 1.43230 0.75346 ... ... ..... ....... ......... ........... ............. E20u * 2.00000 -0.93995 -1.11649 1.98940 -0.75346 -1.28119 1.95771 -0.55897 -1.43230 1.90527 -0.35856 -1.56824 1.83263 -0.15435 -1.68755 1.74057 0.05150 -1.78897 1.63006 0.25680 -1.87143 1.50226 0.45938 -1.93406 1.35855 0.65708 -1.97618 1.20043 0.84783 -1.99735 1.02959 -2.00000 -1.02959 1.99735 -0.84783 -1.20043 1.97618 -0.65708 -1.35855 1.93406 -0.45938 -1.50226 1.87143 -0.25680 -1.63006 1.78897 -0.05150 -1.74057 1.68755 0.15435 -1.83263 1.56824 0.35856 -1.90527 1.43230 0.55897 -1.95771 1.28119 0.75346 -1.98940 1.11649 0.93995 ... ... ..... ....... ......... ........... ............. E21u * 2.00000 -1.11649 -0.75346 1.95771 -1.43230 -0.35856 1.83263 -1.68755 0.05150 1.63006 -1.87143 0.45938 1.35855 -1.97618 0.84783 1.02959 -1.99735 1.20043 0.65708 -1.93406 1.50226 0.25680 -1.78897 1.74057 -0.15435 -1.56824 1.90527 -0.55897 -1.28119 1.98940 -0.93995 -2.00000 0.93995 -1.98940 1.28119 0.55897 -1.90527 1.56824 0.15435 -1.74057 1.78897 -0.25680 -1.50226 1.93406 -0.65708 -1.20043 1.99735 -1.02959 -0.84783 1.97618 -1.35855 -0.45938 1.87143 -1.63006 -0.05150 1.68755 -1.83263 0.35856 1.43230 -1.95771 0.75346 1.11649 ... ... ..... ....... ......... ........... ............. E22u * 2.00000 -1.28119 -0.35856 1.74057 -1.87143 0.65708 1.02959 -1.97618 1.50226 0.05150 -1.56824 1.95771 -0.93995 -0.75346 1.90527 -1.68755 0.25680 1.35855 -1.99735 1.20043 0.45938 -1.78897 1.83263 -0.55897 -1.11649 1.98940 -1.43230 -0.15435 1.63006 -1.93406 0.84783 -2.00000 -0.84783 1.93406 -1.63006 0.15435 1.43230 -1.98940 1.11649 0.55897 -1.83263 1.78897 -0.45938 -1.20043 1.99735 -1.35855 -0.25680 1.68755 -1.90527 0.75346 0.93995 -1.95771 1.56824 -0.05150 -1.50226 1.97618 -1.02959 -0.65708 1.87143 -1.74057 0.35856 1.28119 ... ... ..... ....... ......... ........... ............. E23u * 2.00000 -1.43230 0.05150 1.35855 -1.99735 1.50226 -0.15435 -1.28119 1.98940 -1.56824 0.25680 1.20043 -1.97618 1.63006 -0.35856 -1.11649 1.95771 -1.68755 0.45938 1.02959 -1.93406 1.74057 -0.55897 -0.93995 1.90527 -1.78897 0.65708 0.84783 -1.87143 1.83263 -0.75346 -2.00000 0.75346 -1.83263 1.87143 -0.84783 -0.65708 1.78897 -1.90527 0.93995 0.55897 -1.74057 1.93406 -1.02959 -0.45938 1.68755 -1.95771 1.11649 0.35856 -1.63006 1.97618 -1.20043 -0.25680 1.56824 -1.98940 1.28119 0.15435 -1.50226 1.99735 -1.35855 -0.05150 1.43230 ... ... ..... ....... ......... ........... ............. E24u * 2.00000 -1.56824 0.45938 0.84783 -1.78897 1.95771 -1.28119 0.05150 1.20043 -1.93406 1.83263 -0.93995 -0.35856 1.50226 -1.99735 1.63006 -0.55897 -0.75346 1.74057 -1.97618 1.35855 -0.15435 -1.11649 1.90527 -1.87143 1.02959 0.25680 -1.43230 1.98940 -1.68755 0.65708 -2.00000 -0.65708 1.68755 -1.98940 1.43230 -0.25680 -1.02959 1.87143 -1.90527 1.11649 0.15435 -1.35855 1.97618 -1.74057 0.75346 0.55897 -1.63006 1.99735 -1.50226 0.35856 0.93995 -1.83263 1.93406 -1.20043 -0.05150 1.28119 -1.95771 1.78897 -0.84783 -0.45938 1.56824 ... ... ..... ....... ......... ........... ............. E25u * 2.00000 -1.68755 0.84783 0.25680 -1.28119 1.90527 -1.93406 1.35855 -0.35856 -0.75346 1.63006 -1.99735 1.74057 -0.93995 -0.15435 1.20043 -1.87143 1.95771 -1.43230 0.45938 0.65708 -1.56824 1.98940 -1.78897 1.02959 0.05150 -1.11649 1.83263 -1.97618 1.50226 -0.55897 -2.00000 0.55897 -1.50226 1.97618 -1.83263 1.11649 -0.05150 -1.02959 1.78897 -1.98940 1.56824 -0.65708 -0.45938 1.43230 -1.95771 1.87143 -1.20043 0.15435 0.93995 -1.74057 1.99735 -1.63006 0.75346 0.35856 -1.35855 1.93406 -1.90527 1.28119 -0.25680 -0.84783 1.68755 ... ... ..... ....... ......... ........... ............. E26u * 2.00000 -1.78897 1.20043 -0.35856 -0.55897 1.35855 -1.87143 1.98940 -1.68755 1.02959 -0.15435 -0.75346 1.50226 -1.93406 1.95771 -1.56824 0.84783 0.05150 -0.93995 1.63006 -1.97618 1.90527 -1.43230 0.65708 0.25680 -1.11649 1.74057 -1.99735 1.83263 -1.28119 0.45938 -2.00000 -0.45938 1.28119 -1.83263 1.99735 -1.74057 1.11649 -0.25680 -0.65708 1.43230 -1.90527 1.97618 -1.63006 0.93995 -0.05150 -0.84783 1.56824 -1.95771 1.93406 -1.50226 0.75346 0.15435 -1.02959 1.68755 -1.98940 1.87143 -1.35855 0.55897 0.35856 -1.20043 1.78897 ... ... ..... ....... ......... ........... ............. E27u * 2.00000 -1.87143 1.50226 -0.93995 0.25680 0.45938 -1.11649 1.63006 -1.93406 1.98940 -1.78897 1.35855 -0.75346 0.05150 0.65708 -1.28119 1.74057 -1.97618 1.95771 -1.68755 1.20043 -0.55897 -0.15435 0.84783 -1.43230 1.83263 -1.99735 1.90527 -1.56824 1.02959 -0.35856 -2.00000 0.35856 -1.02959 1.56824 -1.90527 1.99735 -1.83263 1.43230 -0.84783 0.15435 0.55897 -1.20043 1.68755 -1.95771 1.97618 -1.74057 1.28119 -0.65708 -0.05150 0.75346 -1.35855 1.78897 -1.98940 1.93406 -1.63006 1.11649 -0.45938 -0.25680 0.93995 -1.50226 1.87143 ... ... ..... ....... ......... ........... ............. E28u * 2.00000 -1.93406 1.74057 -1.43230 1.02959 -0.55897 0.05150 0.45938 -0.93995 1.35855 -1.68755 1.90527 -1.99735 1.95771 -1.78897 1.50226 -1.11649 0.65708 -0.15435 -0.35856 0.84783 -1.28119 1.63006 -1.87143 1.98940 -1.97618 1.83263 -1.56824 1.20043 -0.75346 0.25680 -2.00000 -0.25680 0.75346 -1.20043 1.56824 -1.83263 1.97618 -1.98940 1.87143 -1.63006 1.28119 -0.84783 0.35856 0.15435 -0.65708 1.11649 -1.50226 1.78897 -1.95771 1.99735 -1.90527 1.68755 -1.35855 0.93995 -0.45938 -0.05150 0.55897 -1.02959 1.43230 -1.74057 1.93406 ... ... ..... ....... ......... ........... ............. E29u * 2.00000 -1.97618 1.90527 -1.78897 1.63006 -1.43230 1.20043 -0.93995 0.65708 -0.35856 0.05150 0.25680 -0.55897 0.84783 -1.11649 1.35855 -1.56824 1.74057 -1.87143 1.95771 -1.99735 1.98940 -1.93406 1.83263 -1.68755 1.50226 -1.28119 1.02959 -0.75346 0.45938 -0.15435 -2.00000 0.15435 -0.45938 0.75346 -1.02959 1.28119 -1.50226 1.68755 -1.83263 1.93406 -1.98940 1.99735 -1.95771 1.87143 -1.74057 1.56824 -1.35855 1.11649 -0.84783 0.55897 -0.25680 -0.05150 0.35856 -0.65708 0.93995 -1.20043 1.43230 -1.63006 1.78897 -1.90527 1.97618 ... ... ..... ....... ......... ........... ............. E30u * 2.00000 -1.99735 1.98940 -1.97618 1.95771 -1.93406 1.90527 -1.87143 1.83263 -1.78897 1.74057 -1.68755 1.63006 -1.56824 1.50226 -1.43230 1.35855 -1.28119 1.20043 -1.11649 1.02959 -0.93995 0.84783 -0.75346 0.65708 -0.55897 0.45938 -0.35856 0.25680 -0.15435 0.05150 -2.00000 -0.05150 0.15435 -0.25680 0.35856 -0.45938 0.55897 -0.65708 0.75346 -0.84783 0.93995 -1.02959 1.11649 -1.20043 1.28119 -1.35855 1.43230 -1.50226 1.56824 -1.63006 1.68755 -1.74057 1.78897 -1.83263 1.87143 -1.90527 1.93406 -1.95771 1.97618 -1.98940 1.99735 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.997348179770 = 2*cos(2*π/122) = 2*cos(π/61) 1.989399751229 = 2*cos(4*π/122) = 2*cos(2*π/61) 1.976175792182 = 2*cos(6*π/122) = 2*cos(3*π/61) 1.957711370191 = 2*cos(8*π/122) = 2*cos(4*π/61) 1.934055449583 = 2*cos(10*π/122) = 2*cos(5*π/61) 1.905270761607 = 2*cos(12*π/122) = 2*cos(6*π/61) 1.871433638081 = 2*cos(14*π/122) = 2*cos(7*π/61) 1.832633808974 = 2*cos(16*π/122) = 2*cos(8*π/61) 1.788974164458 = 2*cos(18*π/122) = 2*cos(9*π/61) 1.740570482060 = 2*cos(20*π/122) = 2*cos(10*π/61) 1.687551119646 = 2*cos(22*π/122) = 2*cos(11*π/61) 1.630056675034 = 2*cos(24*π/122) = 2*cos(12*π/61) 1.568239613153 = 2*cos(26*π/122) = 2*cos(13*π/61) 1.502263861741 = 2*cos(28*π/122) = 2*cos(14*π/61) 1.432304376629 = 2*cos(30*π/122) = 2*cos(15*π/61) 1.358546677795 = 2*cos(32*π/122) = 2*cos(16*π/61) 1.281186357396 = 2*cos(34*π/122) = 2*cos(17*π/61) 1.200428561097 = 2*cos(36*π/122) = 2*cos(18*π/61) 1.116487444054 = 2*cos(38*π/122) = 2*cos(19*π/61) 1.029585603020 = 2*cos(40*π/122) = 2*cos(20*π/61) 0.939953486055 = 2*cos(42*π/122) = 2*cos(21*π/61) 0.847828781420 = 2*cos(44*π/122) = 2*cos(22*π/61) 0.753455787270 = 2*cos(46*π/122) = 2*cos(23*π/61) 0.657084763822 = 2*cos(48*π/122) = 2*cos(24*π/61) 0.558971269703 = 2*cos(50*π/122) = 2*cos(25*π/61) 0.459375484263 = 2*cos(52*π/122) = 2*cos(26*π/61) 0.358561517621 = 2*cos(54*π/122) = 2*cos(27*π/61) 0.256796710293 = 2*cos(56*π/122) = 2*cos(28*π/61) 0.154350924253 = 2*cos(58*π/122) = 2*cos(29*π/61) 0.051495827310 = 2*cos(60*π/122) = 2*cos(30*π/61) Symmetry of Rotations and Cartesian products Ag R+d+g+i R_z, z², z⁴, z⁶ E1g R+d+g+i {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2g d+g+i {x²–y², xy}, {z²(x²–y²), xyz²}, {z⁴(x²–y²), xyz⁴} E3g g+i {xz(x²–3y²), yz(3x²–y²)}, {xz³(x²–3y²), yz³(3x²–y²)} E4g g+i {(x²–y²)²–2x²y², xy(x²–y²)}, {z²((x²–y²)²–4x²y²), xyz²(x²–y²)} E5g i {xz(x²–(5+2√5)y²)(x²–(5–2√5)y²), yz(y²–(5+2√5)x²)(y²–(5–2√5)x²)(y²–(5–2√5)x²)} E6g i {x²(x²–3y²)²–y²(3x²–y²)², xy(x²–3y²)(3x²–y²)} Au p+f+h z, z³, z⁵ E1u p+f+h {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2u f+h {z(x²–y²), xyz}, {z³(x²–y²), xyz³} E3u f+h {x(x²–3y²), y(3x²–y²)}, {xz²(x²–3y²), yz²(3x²–y²)} E4u h {z((x²–y²)²–4x²y²), xyz(x²–y²)} E5u h {x(x²–(5+2√5)y²)(x²–(5–2√5)y²), y(y²–(5+2√5)x²)(y²–(5–2√5)x²)(y²–(5–2√5)x²)} Notes: α The order of the S₁₂₂ point group is 122, and the order of the principal axis is 122. β The S₁₂₂ point group could also be named C_61i, because the S₁₂₂ axis is identical to a roto-inversion axis of order 61. γ This is an Abelian point group (the commutative law holds between all symmetry operations). The S₁₂₂ 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. δ Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 120 cases have been combined into 60 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 60 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ε The 60 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. ζ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree less than half the order of the principal axis (and often much less). For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the S₁₂₂ point group was created by Gernot Katzer.

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

	S₁₂₀
C₁₂₂ C_122v C_122h D₁₂₂ D_122h D_122d	S₁₂₂
	S₁₂₄

Character table for the S122 point group

Character table for the S₁₂₂ point group