C102 E 2 C102 2 C51 2 C34 2 C51^2 2 C102^5 2 C17 2 C102^7 2 C51^4 2 C34^3 2 C51^5 2 C102^11 2 C17^2 2 C102^13 2 C51^7 2 C34^5 2 C51^8 2 C6 2 C17^3 2 C102^19 2 C51^10 2 C34^7 2 C51^11 2 C102^23 2 C17^4 2 C102^25 2 C51^13 2 C34^9 2 C51^14 2 C102^29 2 C17^5 2 C102^31 2 C51^16 2 C34^11 2 C3 2 C102^35 2 C17^6 2 C102^37 2 C51^19 2 C34^13 2 C51^20 2 C102^41 2 C17^7 2 C102^43 2 C51^22 2 C34^15 2 C51^23 2 C102^47 2 C17^8 2 C102^49 2 C51^25 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 ..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 ... ... ..... ....... ......... ........... ............. E1 * 2.00000 1.99621 1.98484 1.96595 1.93959 1.90588 1.86494 1.81693 1.76202 1.70043 1.63239 1.55816 1.47802 1.39227 1.30124 1.20527 1.10473 1.00000 0.89148 0.77957 0.66471 0.54733 0.42787 0.30678 0.18454 0.06159 -0.06159 -0.18454 -0.30678 -0.42787 -0.54733 -0.66471 -0.77957 -0.89148 -1.00000 -1.10473 -1.20527 -1.30124 -1.39227 -1.47802 -1.55816 -1.63239 -1.70043 -1.76202 -1.81693 -1.86494 -1.90588 -1.93959 -1.96595 -1.98484 -1.99621 -2.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98484 1.93959 1.86494 1.76202 1.63239 1.47802 1.30124 1.10473 0.89148 0.66471 0.42787 0.18454 -0.06159 -0.30678 -0.54733 -0.77957 -1.00000 -1.20527 -1.39227 -1.55816 -1.70043 -1.81693 -1.90588 -1.96595 -1.99621 -1.99621 -1.96595 -1.90588 -1.81693 -1.70043 -1.55816 -1.39227 -1.20527 -1.00000 -0.77957 -0.54733 -0.30678 -0.06159 0.18454 0.42787 0.66471 0.89148 1.10473 1.30124 1.47802 1.63239 1.76202 1.86494 1.93959 1.98484 2.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 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..... ......TT..... E4 * 2.00000 1.93959 1.76202 1.47802 1.10473 0.66471 0.18454 -0.30678 -0.77957 -1.20527 -1.55816 -1.81693 -1.96595 -1.99621 -1.90588 -1.70043 -1.39227 -1.00000 -0.54733 -0.06159 0.42787 0.89148 1.30124 1.63239 1.86494 1.98484 1.98484 1.86494 1.63239 1.30124 0.89148 0.42787 -0.06159 -0.54733 -1.00000 -1.39227 -1.70043 -1.90588 -1.99621 -1.96595 -1.81693 -1.55816 -1.20527 -0.77957 -0.30678 0.18454 0.66471 1.10473 1.47802 1.76202 1.93959 2.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.90588 1.63239 1.20527 0.66471 0.06159 -0.54733 -1.10473 -1.55816 -1.86494 -1.99621 -1.93959 -1.70043 -1.30124 -0.77957 -0.18454 0.42787 1.00000 1.47802 1.81693 1.98484 1.96595 1.76202 1.39227 0.89148 0.30678 -0.30678 -0.89148 -1.39227 -1.76202 -1.96595 -1.98484 -1.81693 -1.47802 -1.00000 -0.42787 0.18454 0.77957 1.30124 1.70043 1.93959 1.99621 1.86494 1.55816 1.10473 0.54733 -0.06159 -0.66471 -1.20527 -1.63239 -1.90588 -2.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 * 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 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.81693 1.30124 0.54733 -0.30678 -1.10473 -1.70043 -1.98484 -1.90588 -1.47802 -0.77957 0.06159 0.89148 1.55816 1.93959 1.96595 1.63239 1.00000 0.18454 -0.66471 -1.39227 -1.86494 -1.99621 -1.76202 -1.20527 -0.42787 0.42787 1.20527 1.76202 1.99621 1.86494 1.39227 0.66471 -0.18454 -1.00000 -1.63239 -1.96595 -1.93959 -1.55816 -0.89148 -0.06159 0.77957 1.47802 1.90588 1.98484 1.70043 1.10473 0.30678 -0.54733 -1.30124 -1.81693 -2.00000 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.76202 1.10473 0.18454 -0.77957 -1.55816 -1.96595 -1.90588 -1.39227 -0.54733 0.42787 1.30124 1.86494 1.98484 1.63239 0.89148 -0.06159 -1.00000 -1.70043 -1.99621 -1.81693 -1.20527 -0.30678 0.66471 1.47802 1.93959 1.93959 1.47802 0.66471 -0.30678 -1.20527 -1.81693 -1.99621 -1.70043 -1.00000 -0.06159 0.89148 1.63239 1.98484 1.86494 1.30124 0.42787 -0.54733 -1.39227 -1.90588 -1.96595 -1.55816 -0.77957 0.18454 1.10473 1.76202 2.00000 ... ... ..... ....... ......... ........... ............. E9 * 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 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.63239 0.66471 -0.54733 -1.55816 -1.99621 -1.70043 -0.77957 0.42787 1.47802 1.98484 1.76202 0.89148 -0.30678 -1.39227 -1.96595 -1.81693 -1.00000 0.18454 1.30124 1.93959 1.86494 1.10473 -0.06159 -1.20527 -1.90588 -1.90588 -1.20527 -0.06159 1.10473 1.86494 1.93959 1.30124 0.18454 -1.00000 -1.81693 -1.96595 -1.39227 -0.30678 0.89148 1.76202 1.98484 1.47802 0.42787 -0.77957 -1.70043 -1.99621 -1.55816 -0.54733 0.66471 1.63239 2.00000 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.55816 0.42787 -0.89148 -1.81693 -1.93959 -1.20527 0.06159 1.30124 1.96595 1.76202 0.77957 -0.54733 -1.63239 -1.99621 -1.47802 -0.30678 1.00000 1.86494 1.90588 1.10473 -0.18454 -1.39227 -1.98484 -1.70043 -0.66471 0.66471 1.70043 1.98484 1.39227 0.18454 -1.10473 -1.90588 -1.86494 -1.00000 0.30678 1.47802 1.99621 1.63239 0.54733 -0.77957 -1.76202 -1.96595 -1.30124 -0.06159 1.20527 1.93959 1.81693 0.89148 -0.42787 -1.55816 -2.00000 ... ... ..... ....... ......... ........... ............. E12 * 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 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.39227 -0.06159 -1.47802 -1.99621 -1.30124 0.18454 1.55816 1.98484 1.20527 -0.30678 -1.63239 -1.96595 -1.10473 0.42787 1.70043 1.93959 1.00000 -0.54733 -1.76202 -1.90588 -0.89148 0.66471 1.81693 1.86494 0.77957 -0.77957 -1.86494 -1.81693 -0.66471 0.89148 1.90588 1.76202 0.54733 -1.00000 -1.93959 -1.70043 -0.42787 1.10473 1.96595 1.63239 0.30678 -1.20527 -1.98484 -1.55816 -0.18454 1.30124 1.99621 1.47802 0.06159 -1.39227 -2.00000 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.30124 -0.30678 -1.70043 -1.90588 -0.77957 0.89148 1.93959 1.63239 0.18454 -1.39227 -1.99621 -1.20527 0.42787 1.76202 1.86494 0.66471 -1.00000 -1.96595 -1.55816 -0.06159 1.47802 1.98484 1.10473 -0.54733 -1.81693 -1.81693 -0.54733 1.10473 1.98484 1.47802 -0.06159 -1.55816 -1.96595 -1.00000 0.66471 1.86494 1.76202 0.42787 -1.20527 -1.99621 -1.39227 0.18454 1.63239 1.93959 0.89148 -0.77957 -1.90588 -1.70043 -0.30678 1.30124 2.00000 ... ... ..... ....... ......... ........... ............. E15 * 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 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.10473 -0.77957 -1.96595 -1.39227 0.42787 1.86494 1.63239 -0.06159 -1.70043 -1.81693 -0.30678 1.47802 1.93959 0.66471 -1.20527 -1.99621 -1.00000 0.89148 1.98484 1.30124 -0.54733 -1.90588 -1.55816 0.18454 1.76202 1.76202 0.18454 -1.55816 -1.90588 -0.54733 1.30124 1.98484 0.89148 -1.00000 -1.99621 -1.20527 0.66471 1.93959 1.47802 -0.30678 -1.81693 -1.70043 -0.06159 1.63239 1.86494 0.42787 -1.39227 -1.96595 -0.77957 1.10473 2.00000 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 ... ... ..... ....... ......... ........... ............. E18 * 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 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.77957 -1.39227 -1.86494 -0.06159 1.81693 1.47802 -0.66471 -1.99621 -0.89148 1.30124 1.90588 0.18454 -1.76202 -1.55816 0.54733 1.98484 1.00000 -1.20527 -1.93959 -0.30678 1.70043 1.63239 -0.42787 -1.96595 -1.10473 1.10473 1.96595 0.42787 -1.63239 -1.70043 0.30678 1.93959 1.20527 -1.00000 -1.98484 -0.54733 1.55816 1.76202 -0.18454 -1.90588 -1.30124 0.89148 1.99621 0.66471 -1.47802 -1.81693 0.06159 1.86494 1.39227 -0.77957 -2.00000 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.66471 -1.55816 -1.70043 0.42787 1.98484 0.89148 -1.39227 -1.81693 0.18454 1.93959 1.10473 -1.20527 -1.90588 -0.06159 1.86494 1.30124 -1.00000 -1.96595 -0.30678 1.76202 1.47802 -0.77957 -1.99621 -0.54733 1.63239 1.63239 -0.54733 -1.99621 -0.77957 1.47802 1.76202 -0.30678 -1.96595 -1.00000 1.30124 1.86494 -0.06159 -1.90588 -1.20527 1.10473 1.93959 0.18454 -1.81693 -1.39227 0.89148 1.98484 0.42787 -1.70043 -1.55816 0.66471 2.00000 ... ... ..... ....... ......... ........... ............. E21 * 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 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.42787 -1.81693 -1.20527 1.30124 1.76202 -0.54733 -1.99621 -0.30678 1.86494 1.10473 -1.39227 -1.70043 0.66471 1.98484 0.18454 -1.90588 -1.00000 1.47802 1.63239 -0.77957 -1.96595 -0.06159 1.93959 0.89148 -1.55816 -1.55816 0.89148 1.93959 -0.06159 -1.96595 -0.77957 1.63239 1.47802 -1.00000 -1.90588 0.18454 1.98484 0.66471 -1.70043 -1.39227 1.10473 1.86494 -0.30678 -1.99621 -0.54733 1.76202 1.30124 -1.20527 -1.81693 0.42787 2.00000 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.30678 -1.90588 -0.89148 1.63239 1.39227 -1.20527 -1.76202 0.66471 1.96595 -0.06159 -1.98484 -0.54733 1.81693 1.10473 -1.47802 -1.55816 1.00000 1.86494 -0.42787 -1.99621 -0.18454 1.93959 0.77957 -1.70043 -1.30124 1.30124 1.70043 -0.77957 -1.93959 0.18454 1.99621 0.42787 -1.86494 -1.00000 1.55816 1.47802 -1.10473 -1.81693 0.54733 1.98484 0.06159 -1.96595 -0.66471 1.76202 1.20527 -1.39227 -1.63239 0.89148 1.90588 -0.30678 -2.00000 ... ... ..... ....... ......... ........... ............. E24 * 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 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 0.06159 -1.99621 -0.18454 1.98484 0.30678 -1.96595 -0.42787 1.93959 0.54733 -1.90588 -0.66471 1.86494 0.77957 -1.81693 -0.89148 1.76202 1.00000 -1.70043 -1.10473 1.63239 1.20527 -1.55816 -1.30124 1.47802 1.39227 -1.39227 -1.47802 1.30124 1.55816 -1.20527 -1.63239 1.10473 1.70043 -1.00000 -1.76202 0.89148 1.81693 -0.77957 -1.86494 0.66471 1.90588 -0.54733 -1.93959 0.42787 1.96595 -0.30678 -1.98484 0.18454 1.99621 -0.06159 -2.00000 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.06159 -1.99621 0.18454 1.98484 -0.30678 -1.96595 0.42787 1.93959 -0.54733 -1.90588 0.66471 1.86494 -0.77957 -1.81693 0.89148 1.76202 -1.00000 -1.70043 1.10473 1.63239 -1.20527 -1.55816 1.30124 1.47802 -1.39227 -1.39227 1.47802 1.30124 -1.55816 -1.20527 1.63239 1.10473 -1.70043 -1.00000 1.76202 0.89148 -1.81693 -0.77957 1.86494 0.66471 -1.90588 -0.54733 1.93959 0.42787 -1.96595 -0.30678 1.98484 0.18454 -1.99621 -0.06159 2.00000 ... ... ..... ....... ......... ........... ............. E27 * 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 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.30678 -1.90588 0.89148 1.63239 -1.39227 -1.20527 1.76202 0.66471 -1.96595 -0.06159 1.98484 -0.54733 -1.81693 1.10473 1.47802 -1.55816 -1.00000 1.86494 0.42787 -1.99621 0.18454 1.93959 -0.77957 -1.70043 1.30124 1.30124 -1.70043 -0.77957 1.93959 0.18454 -1.99621 0.42787 1.86494 -1.00000 -1.55816 1.47802 1.10473 -1.81693 -0.54733 1.98484 -0.06159 -1.96595 0.66471 1.76202 -1.20527 -1.39227 1.63239 0.89148 -1.90588 -0.30678 2.00000 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.42787 -1.81693 1.20527 1.30124 -1.76202 -0.54733 1.99621 -0.30678 -1.86494 1.10473 1.39227 -1.70043 -0.66471 1.98484 -0.18454 -1.90588 1.00000 1.47802 -1.63239 -0.77957 1.96595 -0.06159 -1.93959 0.89148 1.55816 -1.55816 -0.89148 1.93959 0.06159 -1.96595 0.77957 1.63239 -1.47802 -1.00000 1.90588 0.18454 -1.98484 0.66471 1.70043 -1.39227 -1.10473 1.86494 0.30678 -1.99621 0.54733 1.76202 -1.30124 -1.20527 1.81693 0.42787 -2.00000 ... ... ..... ....... ......... ........... ............. 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E32 * 2.00000 -0.77957 -1.39227 1.86494 -0.06159 -1.81693 1.47802 0.66471 -1.99621 0.89148 1.30124 -1.90588 0.18454 1.76202 -1.55816 -0.54733 1.98484 -1.00000 -1.20527 1.93959 -0.30678 -1.70043 1.63239 0.42787 -1.96595 1.10473 1.10473 -1.96595 0.42787 1.63239 -1.70043 -0.30678 1.93959 -1.20527 -1.00000 1.98484 -0.54733 -1.55816 1.76202 0.18454 -1.90588 1.30124 0.89148 -1.99621 0.66471 1.47802 -1.81693 -0.06159 1.86494 -1.39227 -0.77957 2.00000 ... ... ..... ....... ......... ........... ............. E33 * 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 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.10473 -0.77957 1.96595 -1.39227 -0.42787 1.86494 -1.63239 -0.06159 1.70043 -1.81693 0.30678 1.47802 -1.93959 0.66471 1.20527 -1.99621 1.00000 0.89148 -1.98484 1.30124 0.54733 -1.90588 1.55816 0.18454 -1.76202 1.76202 -0.18454 -1.55816 1.90588 -0.54733 -1.30124 1.98484 -0.89148 -1.00000 1.99621 -1.20527 -0.66471 1.93959 -1.47802 -0.30678 1.81693 -1.70043 0.06159 1.63239 -1.86494 0.42787 1.39227 -1.96595 0.77957 1.10473 -2.00000 ... ... ..... ....... ......... ........... ............. E36 * 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 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.30124 -0.30678 1.70043 -1.90588 0.77957 0.89148 -1.93959 1.63239 -0.18454 -1.39227 1.99621 -1.20527 -0.42787 1.76202 -1.86494 0.66471 1.00000 -1.96595 1.55816 -0.06159 -1.47802 1.98484 -1.10473 -0.54733 1.81693 -1.81693 0.54733 1.10473 -1.98484 1.47802 0.06159 -1.55816 1.96595 -1.00000 -0.66471 1.86494 -1.76202 0.42787 1.20527 -1.99621 1.39227 0.18454 -1.63239 1.93959 -0.89148 -0.77957 1.90588 -1.70043 0.30678 1.30124 -2.00000 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.39227 -0.06159 1.47802 -1.99621 1.30124 0.18454 -1.55816 1.98484 -1.20527 -0.30678 1.63239 -1.96595 1.10473 0.42787 -1.70043 1.93959 -1.00000 -0.54733 1.76202 -1.90588 0.89148 0.66471 -1.81693 1.86494 -0.77957 -0.77957 1.86494 -1.81693 0.66471 0.89148 -1.90588 1.76202 -0.54733 -1.00000 1.93959 -1.70043 0.42787 1.10473 -1.96595 1.63239 -0.30678 -1.20527 1.98484 -1.55816 0.18454 1.30124 -1.99621 1.47802 -0.06159 -1.39227 2.00000 ... ... ..... ....... ......... ........... ............. E39 * 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 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.55816 0.42787 0.89148 -1.81693 1.93959 -1.20527 -0.06159 1.30124 -1.96595 1.76202 -0.77957 -0.54733 1.63239 -1.99621 1.47802 -0.30678 -1.00000 1.86494 -1.90588 1.10473 0.18454 -1.39227 1.98484 -1.70043 0.66471 0.66471 -1.70043 1.98484 -1.39227 0.18454 1.10473 -1.90588 1.86494 -1.00000 -0.30678 1.47802 -1.99621 1.63239 -0.54733 -0.77957 1.76202 -1.96595 1.30124 -0.06159 -1.20527 1.93959 -1.81693 0.89148 0.42787 -1.55816 2.00000 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.63239 0.66471 0.54733 -1.55816 1.99621 -1.70043 0.77957 0.42787 -1.47802 1.98484 -1.76202 0.89148 0.30678 -1.39227 1.96595 -1.81693 1.00000 0.18454 -1.30124 1.93959 -1.86494 1.10473 0.06159 -1.20527 1.90588 -1.90588 1.20527 -0.06159 -1.10473 1.86494 -1.93959 1.30124 -0.18454 -1.00000 1.81693 -1.96595 1.39227 -0.30678 -0.89148 1.76202 -1.98484 1.47802 -0.42787 -0.77957 1.70043 -1.99621 1.55816 -0.54733 -0.66471 1.63239 -2.00000 ... ... ..... ....... ......... ........... ............. E42 * 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 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.76202 1.10473 -0.18454 -0.77957 1.55816 -1.96595 1.90588 -1.39227 0.54733 0.42787 -1.30124 1.86494 -1.98484 1.63239 -0.89148 -0.06159 1.00000 -1.70043 1.99621 -1.81693 1.20527 -0.30678 -0.66471 1.47802 -1.93959 1.93959 -1.47802 0.66471 0.30678 -1.20527 1.81693 -1.99621 1.70043 -1.00000 0.06159 0.89148 -1.63239 1.98484 -1.86494 1.30124 -0.42787 -0.54733 1.39227 -1.90588 1.96595 -1.55816 0.77957 0.18454 -1.10473 1.76202 -2.00000 ... ... ..... ....... ......... ........... ............. E44 * 2.00000 -1.81693 1.30124 -0.54733 -0.30678 1.10473 -1.70043 1.98484 -1.90588 1.47802 -0.77957 -0.06159 0.89148 -1.55816 1.93959 -1.96595 1.63239 -1.00000 0.18454 0.66471 -1.39227 1.86494 -1.99621 1.76202 -1.20527 0.42787 0.42787 -1.20527 1.76202 -1.99621 1.86494 -1.39227 0.66471 0.18454 -1.00000 1.63239 -1.96595 1.93959 -1.55816 0.89148 -0.06159 -0.77957 1.47802 -1.90588 1.98484 -1.70043 1.10473 -0.30678 -0.54733 1.30124 -1.81693 2.00000 ... ... ..... ....... ......... ........... ............. E45 * 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 ... ... ..... ....... ......... ........... ............. E46 * 2.00000 -1.90588 1.63239 -1.20527 0.66471 -0.06159 -0.54733 1.10473 -1.55816 1.86494 -1.99621 1.93959 -1.70043 1.30124 -0.77957 0.18454 0.42787 -1.00000 1.47802 -1.81693 1.98484 -1.96595 1.76202 -1.39227 0.89148 -0.30678 -0.30678 0.89148 -1.39227 1.76202 -1.96595 1.98484 -1.81693 1.47802 -1.00000 0.42787 0.18454 -0.77957 1.30124 -1.70043 1.93959 -1.99621 1.86494 -1.55816 1.10473 -0.54733 -0.06159 0.66471 -1.20527 1.63239 -1.90588 2.00000 ... ... ..... ....... ......... ........... ............. 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E49 * 2.00000 -1.98484 1.93959 -1.86494 1.76202 -1.63239 1.47802 -1.30124 1.10473 -0.89148 0.66471 -0.42787 0.18454 0.06159 -0.30678 0.54733 -0.77957 1.00000 -1.20527 1.39227 -1.55816 1.70043 -1.81693 1.90588 -1.96595 1.99621 -1.99621 1.96595 -1.90588 1.81693 -1.70043 1.55816 -1.39227 1.20527 -1.00000 0.77957 -0.54733 0.30678 -0.06159 -0.18454 0.42787 -0.66471 0.89148 -1.10473 1.30124 -1.47802 1.63239 -1.76202 1.86494 -1.93959 1.98484 -2.00000 ... ... ..... ....... ......... ........... ............. E50 * 2.00000 -1.99621 1.98484 -1.96595 1.93959 -1.90588 1.86494 -1.81693 1.76202 -1.70043 1.63239 -1.55816 1.47802 -1.39227 1.30124 -1.20527 1.10473 -1.00000 0.89148 -0.77957 0.66471 -0.54733 0.42787 -0.30678 0.18454 -0.06159 -0.06159 0.18454 -0.30678 0.42787 -0.54733 0.66471 -0.77957 0.89148 -1.00000 1.10473 -1.20527 1.30124 -1.39227 1.47802 -1.55816 1.63239 -1.70043 1.76202 -1.81693 1.86494 -1.90588 1.93959 -1.96595 1.98484 -1.99621 2.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.996206657474 = 2*cos(2*π/102) = 2*cos(π/51) = (−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/8 1.984841019344 = 2*cos(4*π/102) = 2*cos(2*π/51) = (1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/8 1.965946199368 = 2*cos(6*π/102) = 2*cos(π/17) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 1.939593872070 = 2*cos(8*π/102) = 2*cos(4*π/51) = (1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/8 1.905884000854 = 2*cos(10*π/102) = 2*cos(5*π/51) = (−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/8 1.864944458809 = 2*cos(12*π/102) = 2*cos(2*π/17) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 1.816930543639 = 2*cos(14*π/102) = 2*cos(7*π/51) = (−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/8 1.762024388572 = 2*cos(16*π/102) = 2*cos(8*π/51) = (1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/8 1.700434271459 = 2*cos(18*π/102) = 2*cos(3*π/17) = (1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 1.632393824712 = 2*cos(20*π/102) = 2*cos(10*π/51) = (1−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/8 1.558161149051 = 2*cos(22*π/102) = 2*cos(11*π/51) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/8 1.478017834441 = 2*cos(24*π/102) = 2*cos(4*π/17) = (−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 1.392267891926 = 2*cos(26*π/102) = 2*cos(13*π/51) = (−1−√17+√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/8 1.301236600408 = 2*cos(28*π/102) = 2*cos(14*π/51) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/8 1.205269272759 = 2*cos(30*π/102) = 2*cos(5*π/17) = (1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 1.104729945921 = 2*cos(32*π/102) = 2*cos(16*π/51) = (1+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/8 0.891476711553 = 2*cos(36*π/102) = 2*cos(6*π/17) = (−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 0.779571746585 = 2*cos(38*π/102) = 2*cos(19*π/51) = (−1−√17−√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/8 0.664709598959 = 2*cos(40*π/102) = 2*cos(20*π/51) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 − √6*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/8 0.547325980144 = 2*cos(42*π/102) = 2*cos(7*π/17) = (1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 0.427866166413 = 2*cos(44*π/102) = 2*cos(22*π/51) = (1−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/8 0.306783309757 = 2*cos(46*π/102) = 2*cos(23*π/51) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 − √6*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/8 0.184536718927 = 2*cos(48*π/102) = 2*cos(8*π/17) = (−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 0.061590117112 = 2*cos(50*π/102) = 2*cos(25*π/51) = (−1−√17−√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/8 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 C102 point group is 102, and the order of the principal axis (C102) is 102. The group has 52 irreducible representations. β The C102 point group is isomorphic to S102 and C51h. γ The C102 point group is generated by one single symmetry element, C102. Therefore, it is a cyclic group. δ The lowest nonvanishing multipole moment in C102 is 2 (dipole moment). ε This is an Abelian point group (the commutative law holds between all symmetry operations). The C102 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 100 cases have been combined into 50 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 50 pairs of left and right rotations have been combined into one two-membered pseudo-class each. η The 50 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. The regular 51-gon can be derived from the regular 17-gon by overlaying it with a equilateral triangle. Further halving of angles yields regular polygons of order 102,204,408 etc.
C100 | ||
C101 | ||
C102 | C102v C102h D102 D102h D102d S102 | |
C103 | ||
C104 |
This Character Table for the C102 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.