C109 E 2 C109 2 C109^2 2 C109^3 2 C109^4 2 C109^5 2 C109^6 2 C109^7 2 C109^8 2 C109^9 2 C109^10 2 C109^11 2 C109^12 2 C109^13 2 C109^14 2 C109^15 2 C109^16 2 C109^17 2 C109^18 2 C109^19 2 C109^20 2 C109^21 2 C109^22 2 C109^23 2 C109^24 2 C109^25 2 C109^26 2 C109^27 2 C109^28 2 C109^29 2 C109^30 2 C109^31 2 C109^32 2 C109^33 2 C109^34 2 C109^35 2 C109^36 2 C109^37 2 C109^38 2 C109^39 2 C109^40 2 C109^41 2 C109^42 2 C109^43 2 C109^44 2 C109^45 2 C109^46 2 C109^47 2 C109^48 2 C109^49 2 C109^50 2 C109^51 2 C109^52 2 C109^53 2 C109^54 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99668 1.98672 1.97017 1.94707 1.91750 1.88157 1.83938 1.79108 1.73683 1.67682 1.61123 1.54029 1.46424 1.38332 1.29780 1.20797 1.11413 1.01659 0.91568 0.81172 0.70506 0.59606 0.48509 0.37250 0.25867 0.14399 0.02882 -0.08644 -0.20141 -0.31572 -0.42897 -0.54080 -0.65083 -0.75870 -0.86406 -0.96654 -1.06581 -1.16154 -1.25341 -1.34111 -1.42437 -1.50289 -1.57642 -1.64471 -1.70754 -1.76469 -1.81598 -1.86125 -1.90032 -1.93309 -1.95943 -1.97927 -1.99253 -1.99917 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98672 1.94707 1.88157 1.79108 1.67682 1.54029 1.38332 1.20797 1.01659 0.81172 0.59606 0.37250 0.14399 -0.08644 -0.31572 -0.54080 -0.75870 -0.96654 -1.16154 -1.34111 -1.50289 -1.64471 -1.76469 -1.86125 -1.93309 -1.97927 -1.99917 -1.99253 -1.95943 -1.90032 -1.81598 -1.70754 -1.57642 -1.42437 -1.25341 -1.06581 -0.86406 -0.65083 -0.42897 -0.20141 0.02882 0.25867 0.48509 0.70506 0.91568 1.11413 1.29780 1.46424 1.61123 1.73683 1.83938 1.91750 1.97017 1.99668 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.97017 1.88157 1.73683 1.54029 1.29780 1.01659 0.70506 0.37250 0.02882 -0.31572 -0.65083 -0.96654 -1.25341 -1.50289 -1.70754 -1.86125 -1.95943 -1.99917 -1.97927 -1.90032 -1.76469 -1.57642 -1.34111 -1.06581 -0.75870 -0.42897 -0.08644 0.25867 0.59606 0.91568 1.20797 1.46424 1.67682 1.83938 1.94707 1.99668 1.98672 1.91750 1.79108 1.61123 1.38332 1.11413 0.81172 0.48509 0.14399 -0.20141 -0.54080 -0.86406 -1.16154 -1.42437 -1.64471 -1.81598 -1.93309 -1.99253 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.94707 1.79108 1.54029 1.20797 0.81172 0.37250 -0.08644 -0.54080 -0.96654 -1.34111 -1.64471 -1.86125 -1.97927 -1.99253 -1.90032 -1.70754 -1.42437 -1.06581 -0.65083 -0.20141 0.25867 0.70506 1.11413 1.46424 1.73683 1.91750 1.99668 1.97017 1.83938 1.61123 1.29780 0.91568 0.48509 0.02882 -0.42897 -0.86406 -1.25341 -1.57642 -1.81598 -1.95943 -1.99917 -1.93309 -1.76469 -1.50289 -1.16154 -0.75870 -0.31572 0.14399 0.59606 1.01659 1.38332 1.67682 1.88157 1.98672 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.91750 1.67682 1.29780 0.81172 0.25867 -0.31572 -0.86406 -1.34111 -1.70754 -1.93309 -1.99917 -1.90032 -1.64471 -1.25341 -0.75870 -0.20141 0.37250 0.91568 1.38332 1.73683 1.94707 1.99668 1.88157 1.61123 1.20797 0.70506 0.14399 -0.42897 -0.96654 -1.42437 -1.76469 -1.95943 -1.99253 -1.86125 -1.57642 -1.16154 -0.65083 -0.08644 0.48509 1.01659 1.46424 1.79108 1.97017 1.98672 1.83938 1.54029 1.11413 0.59606 0.02882 -0.54080 -1.06581 -1.50289 -1.81598 -1.97927 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.88157 1.54029 1.01659 0.37250 -0.31572 -0.96654 -1.50289 -1.86125 -1.99917 -1.90032 -1.57642 -1.06581 -0.42897 0.25867 0.91568 1.46424 1.83938 1.99668 1.91750 1.61123 1.11413 0.48509 -0.20141 -0.86406 -1.42437 -1.81598 -1.99253 -1.93309 -1.64471 -1.16154 -0.54080 0.14399 0.81172 1.38332 1.79108 1.98672 1.94707 1.67682 1.20797 0.59606 -0.08644 -0.75870 -1.34111 -1.76469 -1.97927 -1.95943 -1.70754 -1.25341 -0.65083 0.02882 0.70506 1.29780 1.73683 1.97017 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.83938 1.38332 0.70506 -0.08644 -0.86406 -1.50289 -1.90032 -1.99253 -1.76469 -1.25341 -0.54080 0.25867 1.01659 1.61123 1.94707 1.97017 1.67682 1.11413 0.37250 -0.42897 -1.16154 -1.70754 -1.97927 -1.93309 -1.57642 -0.96654 -0.20141 0.59606 1.29780 1.79108 1.99668 1.88157 1.46424 0.81172 0.02882 -0.75870 -1.42437 -1.86125 -1.99917 -1.81598 -1.34111 -0.65083 0.14399 0.91568 1.54029 1.91750 1.98672 1.73683 1.20797 0.48509 -0.31572 -1.06581 -1.64471 -1.95943 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.79108 1.20797 0.37250 -0.54080 -1.34111 -1.86125 -1.99253 -1.70754 -1.06581 -0.20141 0.70506 1.46424 1.91750 1.97017 1.61123 0.91568 0.02882 -0.86406 -1.57642 -1.95943 -1.93309 -1.50289 -0.75870 0.14399 1.01659 1.67682 1.98672 1.88157 1.38332 0.59606 -0.31572 -1.16154 -1.76469 -1.99917 -1.81598 -1.25341 -0.42897 0.48509 1.29780 1.83938 1.99668 1.73683 1.11413 0.25867 -0.65083 -1.42437 -1.90032 -1.97927 -1.64471 -0.96654 -0.08644 0.81172 1.54029 1.94707 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.73683 1.01659 0.02882 -0.96654 -1.70754 -1.99917 -1.76469 -1.06581 -0.08644 0.91568 1.67682 1.99668 1.79108 1.11413 0.14399 -0.86406 -1.64471 -1.99253 -1.81598 -1.16154 -0.20141 0.81172 1.61123 1.98672 1.83938 1.20797 0.25867 -0.75870 -1.57642 -1.97927 -1.86125 -1.25341 -0.31572 0.70506 1.54029 1.97017 1.88157 1.29780 0.37250 -0.65083 -1.50289 -1.95943 -1.90032 -1.34111 -0.42897 0.59606 1.46424 1.94707 1.91750 1.38332 0.48509 -0.54080 -1.42437 -1.93309 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.67682 0.81172 -0.31572 -1.34111 -1.93309 -1.90032 -1.25341 -0.20141 0.91568 1.73683 1.99668 1.61123 0.70506 -0.42897 -1.42437 -1.95943 -1.86125 -1.16154 -0.08644 1.01659 1.79108 1.98672 1.54029 0.59606 -0.54080 -1.50289 -1.97927 -1.81598 -1.06581 0.02882 1.11413 1.83938 1.97017 1.46424 0.48509 -0.65083 -1.57642 -1.99253 -1.76469 -0.96654 0.14399 1.20797 1.88157 1.94707 1.38332 0.37250 -0.75870 -1.64471 -1.99917 -1.70754 -0.86406 0.25867 1.29780 1.91750 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.61123 0.59606 -0.65083 -1.64471 -1.99917 -1.57642 -0.54080 0.70506 1.67682 1.99668 1.54029 0.48509 -0.75870 -1.70754 -1.99253 -1.50289 -0.42897 0.81172 1.73683 1.98672 1.46424 0.37250 -0.86406 -1.76469 -1.97927 -1.42437 -0.31572 0.91568 1.79108 1.97017 1.38332 0.25867 -0.96654 -1.81598 -1.95943 -1.34111 -0.20141 1.01659 1.83938 1.94707 1.29780 0.14399 -1.06581 -1.86125 -1.93309 -1.25341 -0.08644 1.11413 1.88157 1.91750 1.20797 0.02882 -1.16154 -1.90032 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.54029 0.37250 -0.96654 -1.86125 -1.90032 -1.06581 0.25867 1.46424 1.99668 1.61123 0.48509 -0.86406 -1.81598 -1.93309 -1.16154 0.14399 1.38332 1.98672 1.67682 0.59606 -0.75870 -1.76469 -1.95943 -1.25341 0.02882 1.29780 1.97017 1.73683 0.70506 -0.65083 -1.70754 -1.97927 -1.34111 -0.08644 1.20797 1.94707 1.79108 0.81172 -0.54080 -1.64471 -1.99253 -1.42437 -0.20141 1.11413 1.91750 1.83938 0.91568 -0.42897 -1.57642 -1.99917 -1.50289 -0.31572 1.01659 1.88157 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.46424 0.14399 -1.25341 -1.97927 -1.64471 -0.42897 1.01659 1.91750 1.79108 0.70506 -0.75870 -1.81598 -1.90032 -0.96654 0.48509 1.67682 1.97017 1.20797 -0.20141 -1.50289 -1.99917 -1.42437 -0.08644 1.29780 1.98672 1.61123 0.37250 -1.06581 -1.93309 -1.76469 -0.65083 0.81172 1.83938 1.88157 0.91568 -0.54080 -1.70754 -1.95943 -1.16154 0.25867 1.54029 1.99668 1.38332 0.02882 -1.34111 -1.99253 -1.57642 -0.31572 1.11413 1.94707 1.73683 0.59606 -0.86406 -1.86125 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.38332 -0.08644 -1.50289 -1.99253 -1.25341 0.25867 1.61123 1.97017 1.11413 -0.42897 -1.70754 -1.93309 -0.96654 0.59606 1.79108 1.88157 0.81172 -0.75870 -1.86125 -1.81598 -0.65083 0.91568 1.91750 1.73683 0.48509 -1.06581 -1.95943 -1.64471 -0.31572 1.20797 1.98672 1.54029 0.14399 -1.34111 -1.99917 -1.42437 0.02882 1.46424 1.99668 1.29780 -0.20141 -1.57642 -1.97927 -1.16154 0.37250 1.67682 1.94707 1.01659 -0.54080 -1.76469 -1.90032 -0.86406 0.70506 1.83938 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.29780 -0.31572 -1.70754 -1.90032 -0.75870 0.91568 1.94707 1.61123 0.14399 -1.42437 -1.99253 -1.16154 0.48509 1.79108 1.83938 0.59606 -1.06581 -1.97927 -1.50289 0.02882 1.54029 1.97017 1.01659 -0.65083 -1.86125 -1.76469 -0.42897 1.20797 1.99668 1.38332 -0.20141 -1.64471 -1.93309 -0.86406 0.81172 1.91750 1.67682 0.25867 -1.34111 -1.99917 -1.25341 0.37250 1.73683 1.88157 0.70506 -0.96654 -1.95943 -1.57642 -0.08644 1.46424 1.98672 1.11413 -0.54080 -1.81598 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.20797 -0.54080 -1.86125 -1.70754 -0.20141 1.46424 1.97017 0.91568 -0.86406 -1.95943 -1.50289 0.14399 1.67682 1.88157 0.59606 -1.16154 -1.99917 -1.25341 0.48509 1.83938 1.73683 0.25867 -1.42437 -1.97927 -0.96654 0.81172 1.94707 1.54029 -0.08644 -1.64471 -1.90032 -0.65083 1.11413 1.99668 1.29780 -0.42897 -1.81598 -1.76469 -0.31572 1.38332 1.98672 1.01659 -0.75870 -1.93309 -1.57642 0.02882 1.61123 1.91750 0.70506 -1.06581 -1.99253 -1.34111 0.37250 1.79108 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 1.11413 -0.75870 -1.95943 -1.42437 0.37250 1.83938 1.67682 0.02882 -1.64471 -1.86125 -0.42897 1.38332 1.97017 0.81172 -1.06581 -1.99917 -1.16154 0.70506 1.94707 1.46424 -0.31572 -1.81598 -1.70754 -0.08644 1.61123 1.88157 0.48509 -1.34111 -1.97927 -0.86406 1.01659 1.99668 1.20797 -0.65083 -1.93309 -1.50289 0.25867 1.79108 1.73683 0.14399 -1.57642 -1.90032 -0.54080 1.29780 1.98672 0.91568 -0.96654 -1.99253 -1.25341 0.59606 1.91750 1.54029 -0.20141 -1.76469 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 1.01659 -0.96654 -1.99917 -1.06581 0.91568 1.99668 1.11413 -0.86406 -1.99253 -1.16154 0.81172 1.98672 1.20797 -0.75870 -1.97927 -1.25341 0.70506 1.97017 1.29780 -0.65083 -1.95943 -1.34111 0.59606 1.94707 1.38332 -0.54080 -1.93309 -1.42437 0.48509 1.91750 1.46424 -0.42897 -1.90032 -1.50289 0.37250 1.88157 1.54029 -0.31572 -1.86125 -1.57642 0.25867 1.83938 1.61123 -0.20141 -1.81598 -1.64471 0.14399 1.79108 1.67682 -0.08644 -1.76469 -1.70754 0.02882 1.73683 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.91568 -1.16154 -1.97927 -0.65083 1.38332 1.91750 0.37250 -1.57642 -1.81598 -0.08644 1.73683 1.67682 -0.20141 -1.86125 -1.50289 0.48509 1.94707 1.29780 -0.75870 -1.99253 -1.06581 1.01659 1.99668 0.81172 -1.25341 -1.95943 -0.54080 1.46424 1.88157 0.25867 -1.64471 -1.76469 0.02882 1.79108 1.61123 -0.31572 -1.90032 -1.42437 0.59606 1.97017 1.20797 -0.86406 -1.99917 -0.96654 1.11413 1.98672 0.70506 -1.34111 -1.93309 -0.42897 1.54029 1.83938 0.14399 -1.70754 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.81172 -1.34111 -1.90032 -0.20141 1.73683 1.61123 -0.42897 -1.95943 -1.16154 1.01659 1.98672 0.59606 -1.50289 -1.81598 0.02882 1.83938 1.46424 -0.65083 -1.99253 -0.96654 1.20797 1.94707 0.37250 -1.64471 -1.70754 0.25867 1.91750 1.29780 -0.86406 -1.99917 -0.75870 1.38332 1.88157 0.14399 -1.76469 -1.57642 0.48509 1.97017 1.11413 -1.06581 -1.97927 -0.54080 1.54029 1.79108 -0.08644 -1.86125 -1.42437 0.70506 1.99668 0.91568 -1.25341 -1.93309 -0.31572 1.67682 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.70506 -1.50289 -1.76469 0.25867 1.94707 1.11413 -1.16154 -1.93309 -0.20141 1.79108 1.46424 -0.75870 -1.99917 -0.65083 1.54029 1.73683 -0.31572 -1.95943 -1.06581 1.20797 1.91750 0.14399 -1.81598 -1.42437 0.81172 1.99668 0.59606 -1.57642 -1.70754 0.37250 1.97017 1.01659 -1.25341 -1.90032 -0.08644 1.83938 1.38332 -0.86406 -1.99253 -0.54080 1.61123 1.67682 -0.42897 -1.97927 -0.96654 1.29780 1.88157 0.02882 -1.86125 -1.34111 0.91568 1.98672 0.48509 -1.64471 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.59606 -1.64471 -1.57642 0.70506 1.99668 0.48509 -1.70754 -1.50289 0.81172 1.98672 0.37250 -1.76469 -1.42437 0.91568 1.97017 0.25867 -1.81598 -1.34111 1.01659 1.94707 0.14399 -1.86125 -1.25341 1.11413 1.91750 0.02882 -1.90032 -1.16154 1.20797 1.88157 -0.08644 -1.93309 -1.06581 1.29780 1.83938 -0.20141 -1.95943 -0.96654 1.38332 1.79108 -0.31572 -1.97927 -0.86406 1.46424 1.73683 -0.42897 -1.99253 -0.75870 1.54029 1.67682 -0.54080 -1.99917 -0.65083 1.61123 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.48509 -1.76469 -1.34111 1.11413 1.88157 -0.20141 -1.97927 -0.75870 1.61123 1.54029 -0.86406 -1.95943 -0.08644 1.91750 1.01659 -1.42437 -1.70754 0.59606 1.99668 0.37250 -1.81598 -1.25341 1.20797 1.83938 -0.31572 -1.99253 -0.65083 1.67682 1.46424 -0.96654 -1.93309 0.02882 1.94707 0.91568 -1.50289 -1.64471 0.70506 1.98672 0.25867 -1.86125 -1.16154 1.29780 1.79108 -0.42897 -1.99917 -0.54080 1.73683 1.38332 -1.06581 -1.90032 0.14399 1.97017 0.81172 -1.57642 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 0.37250 -1.86125 -1.06581 1.46424 1.61123 -0.86406 -1.93309 0.14399 1.98672 0.59606 -1.76469 -1.25341 1.29780 1.73683 -0.65083 -1.97927 -0.08644 1.94707 0.81172 -1.64471 -1.42437 1.11413 1.83938 -0.42897 -1.99917 -0.31572 1.88157 1.01659 -1.50289 -1.57642 0.91568 1.91750 -0.20141 -1.99253 -0.54080 1.79108 1.20797 -1.34111 -1.70754 0.70506 1.97017 0.02882 -1.95943 -0.75870 1.67682 1.38332 -1.16154 -1.81598 0.48509 1.99668 0.25867 -1.90032 -0.96654 1.54029 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 0.25867 -1.93309 -0.75870 1.73683 1.20797 -1.42437 -1.57642 1.01659 1.83938 -0.54080 -1.97927 0.02882 1.98672 0.48509 -1.86125 -0.96654 1.61123 1.38332 -1.25341 -1.70754 0.81172 1.91750 -0.31572 -1.99917 -0.20141 1.94707 0.70506 -1.76469 -1.16154 1.46424 1.54029 -1.06581 -1.81598 0.59606 1.97017 -0.08644 -1.99253 -0.42897 1.88157 0.91568 -1.64471 -1.34111 1.29780 1.67682 -0.86406 -1.90032 0.37250 1.99668 0.14399 -1.95943 -0.65083 1.79108 1.11413 -1.50289 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 0.14399 -1.97927 -0.42897 1.91750 0.70506 -1.81598 -0.96654 1.67682 1.20797 -1.50289 -1.42437 1.29780 1.61123 -1.06581 -1.76469 0.81172 1.88157 -0.54080 -1.95943 0.25867 1.99668 0.02882 -1.99253 -0.31572 1.94707 0.59606 -1.86125 -0.86406 1.73683 1.11413 -1.57642 -1.34111 1.38332 1.54029 -1.16154 -1.70754 0.91568 1.83938 -0.65083 -1.93309 0.37250 1.98672 -0.08644 -1.99917 -0.20141 1.97017 0.48509 -1.90032 -0.75870 1.79108 1.01659 -1.64471 -1.25341 1.46424 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 0.02882 -1.99917 -0.08644 1.99668 0.14399 -1.99253 -0.20141 1.98672 0.25867 -1.97927 -0.31572 1.97017 0.37250 -1.95943 -0.42897 1.94707 0.48509 -1.93309 -0.54080 1.91750 0.59606 -1.90032 -0.65083 1.88157 0.70506 -1.86125 -0.75870 1.83938 0.81172 -1.81598 -0.86406 1.79108 0.91568 -1.76469 -0.96654 1.73683 1.01659 -1.70754 -1.06581 1.67682 1.11413 -1.64471 -1.16154 1.61123 1.20797 -1.57642 -1.25341 1.54029 1.29780 -1.50289 -1.34111 1.46424 1.38332 -1.42437 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.08644 -1.99253 0.25867 1.97017 -0.42897 -1.93309 0.59606 1.88157 -0.75870 -1.81598 0.91568 1.73683 -1.06581 -1.64471 1.20797 1.54029 -1.34111 -1.42437 1.46424 1.29780 -1.57642 -1.16154 1.67682 1.01659 -1.76469 -0.86406 1.83938 0.70506 -1.90032 -0.54080 1.94707 0.37250 -1.97927 -0.20141 1.99668 0.02882 -1.99917 0.14399 1.98672 -0.31572 -1.95943 0.48509 1.91750 -0.65083 -1.86125 0.81172 1.79108 -0.96654 -1.70754 1.11413 1.61123 -1.25341 -1.50289 1.38332 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.20141 -1.95943 0.59606 1.83938 -0.96654 -1.64471 1.29780 1.38332 -1.57642 -1.06581 1.79108 0.70506 -1.93309 -0.31572 1.99668 -0.08644 -1.97927 0.48509 1.88157 -0.86406 -1.70754 1.20797 1.46424 -1.50289 -1.16154 1.73683 0.81172 -1.90032 -0.42897 1.98672 0.02882 -1.99253 0.37250 1.91750 -0.75870 -1.76469 1.11413 1.54029 -1.42437 -1.25341 1.67682 0.91568 -1.86125 -0.54080 1.97017 0.14399 -1.99917 0.25867 1.94707 -0.65083 -1.81598 1.01659 1.61123 -1.34111 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -0.31572 -1.90032 0.91568 1.61123 -1.42437 -1.16154 1.79108 0.59606 -1.97927 0.02882 1.97017 -0.65083 -1.76469 1.20797 1.38332 -1.64471 -0.86406 1.91750 0.25867 -1.99917 0.37250 1.88157 -0.96654 -1.57642 1.46424 1.11413 -1.81598 -0.54080 1.98672 -0.08644 -1.95943 0.70506 1.73683 -1.25341 -1.34111 1.67682 0.81172 -1.93309 -0.20141 1.99668 -0.42897 -1.86125 1.01659 1.54029 -1.50289 -1.06581 1.83938 0.48509 -1.99253 0.14399 1.94707 -0.75870 -1.70754 1.29780 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -0.42897 -1.81598 1.20797 1.29780 -1.76469 -0.54080 1.99668 -0.31572 -1.86125 1.11413 1.38332 -1.70754 -0.65083 1.98672 -0.20141 -1.90032 1.01659 1.46424 -1.64471 -0.75870 1.97017 -0.08644 -1.93309 0.91568 1.54029 -1.57642 -0.86406 1.94707 0.02882 -1.95943 0.81172 1.61123 -1.50289 -0.96654 1.91750 0.14399 -1.97927 0.70506 1.67682 -1.42437 -1.06581 1.88157 0.25867 -1.99253 0.59606 1.73683 -1.34111 -1.16154 1.83938 0.37250 -1.99917 0.48509 1.79108 -1.25341 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -0.54080 -1.70754 1.46424 0.91568 -1.95943 0.14399 1.88157 -1.16154 -1.25341 1.83938 0.25867 -1.97927 0.81172 1.54029 -1.64471 -0.65083 1.99668 -0.42897 -1.76469 1.38332 1.01659 -1.93309 0.02882 1.91750 -1.06581 -1.34111 1.79108 0.37250 -1.99253 0.70506 1.61123 -1.57642 -0.75870 1.98672 -0.31572 -1.81598 1.29780 1.11413 -1.90032 -0.08644 1.94707 -0.96654 -1.42437 1.73683 0.48509 -1.99917 0.59606 1.67682 -1.50289 -0.86406 1.97017 -0.20141 -1.86125 1.20797 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -0.65083 -1.57642 1.67682 0.48509 -1.99253 0.81172 1.46424 -1.76469 -0.31572 1.97017 -0.96654 -1.34111 1.83938 0.14399 -1.93309 1.11413 1.20797 -1.90032 0.02882 1.88157 -1.25341 -1.06581 1.94707 -0.20141 -1.81598 1.38332 0.91568 -1.97927 0.37250 1.73683 -1.50289 -0.75870 1.99668 -0.54080 -1.64471 1.61123 0.59606 -1.99917 0.70506 1.54029 -1.70754 -0.42897 1.98672 -0.86406 -1.42437 1.79108 0.25867 -1.95943 1.01659 1.29780 -1.86125 -0.08644 1.91750 -1.16154 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -0.75870 -1.42437 1.83938 0.02882 -1.86125 1.38332 0.81172 -1.99917 0.70506 1.46424 -1.81598 -0.08644 1.88157 -1.34111 -0.86406 1.99668 -0.65083 -1.50289 1.79108 0.14399 -1.90032 1.29780 0.91568 -1.99253 0.59606 1.54029 -1.76469 -0.20141 1.91750 -1.25341 -0.96654 1.98672 -0.54080 -1.57642 1.73683 0.25867 -1.93309 1.20797 1.01659 -1.97927 0.48509 1.61123 -1.70754 -0.31572 1.94707 -1.16154 -1.06581 1.97017 -0.42897 -1.64471 1.67682 0.37250 -1.95943 1.11413 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -0.86406 -1.25341 1.94707 -0.42897 -1.57642 1.79108 0.02882 -1.81598 1.54029 0.48509 -1.95943 1.20797 0.91568 -1.99917 0.81172 1.29780 -1.93309 0.37250 1.61123 -1.76469 -0.08644 1.83938 -1.50289 -0.54080 1.97017 -1.16154 -0.96654 1.99668 -0.75870 -1.34111 1.91750 -0.31572 -1.64471 1.73683 0.14399 -1.86125 1.46424 0.59606 -1.97927 1.11413 1.01659 -1.99253 0.70506 1.38332 -1.90032 0.25867 1.67682 -1.70754 -0.20141 1.88157 -1.42437 -0.65083 1.98672 -1.06581 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -0.96654 -1.06581 1.99668 -0.86406 -1.16154 1.98672 -0.75870 -1.25341 1.97017 -0.65083 -1.34111 1.94707 -0.54080 -1.42437 1.91750 -0.42897 -1.50289 1.88157 -0.31572 -1.57642 1.83938 -0.20141 -1.64471 1.79108 -0.08644 -1.70754 1.73683 0.02882 -1.76469 1.67682 0.14399 -1.81598 1.61123 0.25867 -1.86125 1.54029 0.37250 -1.90032 1.46424 0.48509 -1.93309 1.38332 0.59606 -1.95943 1.29780 0.70506 -1.97927 1.20797 0.81172 -1.99253 1.11413 0.91568 -1.99917 1.01659 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.06581 -0.86406 1.98672 -1.25341 -0.65083 1.94707 -1.42437 -0.42897 1.88157 -1.57642 -0.20141 1.79108 -1.70754 0.02882 1.67682 -1.81598 0.25867 1.54029 -1.90032 0.48509 1.38332 -1.95943 0.70506 1.20797 -1.99253 0.91568 1.01659 -1.99917 1.11413 0.81172 -1.97927 1.29780 0.59606 -1.93309 1.46424 0.37250 -1.86125 1.61123 0.14399 -1.76469 1.73683 -0.08644 -1.64471 1.83938 -0.31572 -1.50289 1.91750 -0.54080 -1.34111 1.97017 -0.75870 -1.16154 1.99668 -0.96654 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.16154 -0.65083 1.91750 -1.57642 -0.08644 1.67682 -1.86125 0.48509 1.29780 -1.99253 1.01659 0.81172 -1.95943 1.46424 0.25867 -1.76469 1.79108 -0.31572 -1.42437 1.97017 -0.86406 -0.96654 1.98672 -1.34111 -0.42897 1.83938 -1.70754 0.14399 1.54029 -1.93309 0.70506 1.11413 -1.99917 1.20797 0.59606 -1.90032 1.61123 0.02882 -1.64471 1.88157 -0.54080 -1.25341 1.99668 -1.06581 -0.75870 1.94707 -1.50289 -0.20141 1.73683 -1.81598 0.37250 1.38332 -1.97927 0.91568 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.25341 -0.42897 1.79108 -1.81598 0.48509 1.20797 -1.99917 1.29780 0.37250 -1.76469 1.83938 -0.54080 -1.16154 1.99668 -1.34111 -0.31572 1.73683 -1.86125 0.59606 1.11413 -1.99253 1.38332 0.25867 -1.70754 1.88157 -0.65083 -1.06581 1.98672 -1.42437 -0.20141 1.67682 -1.90032 0.70506 1.01659 -1.97927 1.46424 0.14399 -1.64471 1.91750 -0.75870 -0.96654 1.97017 -1.50289 -0.08644 1.61123 -1.93309 0.81172 0.91568 -1.95943 1.54029 0.02882 -1.57642 1.94707 -0.86406 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.34111 -0.20141 1.61123 -1.95943 1.01659 0.59606 -1.81598 1.83938 -0.65083 -0.96654 1.94707 -1.64471 0.25867 1.29780 -1.99917 1.38332 0.14399 -1.57642 1.97017 -1.06581 -0.54080 1.79108 -1.86125 0.70506 0.91568 -1.93309 1.67682 -0.31572 -1.25341 1.99668 -1.42437 -0.08644 1.54029 -1.97927 1.11413 0.48509 -1.76469 1.88157 -0.75870 -0.86406 1.91750 -1.70754 0.37250 1.20797 -1.99253 1.46424 0.02882 -1.50289 1.98672 -1.16154 -0.42897 1.73683 -1.90032 0.81172 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.42437 0.02882 1.38332 -1.99917 1.46424 -0.08644 -1.34111 1.99668 -1.50289 0.14399 1.29780 -1.99253 1.54029 -0.20141 -1.25341 1.98672 -1.57642 0.25867 1.20797 -1.97927 1.61123 -0.31572 -1.16154 1.97017 -1.64471 0.37250 1.11413 -1.95943 1.67682 -0.42897 -1.06581 1.94707 -1.70754 0.48509 1.01659 -1.93309 1.73683 -0.54080 -0.96654 1.91750 -1.76469 0.59606 0.91568 -1.90032 1.79108 -0.65083 -0.86406 1.88157 -1.81598 0.70506 0.81172 -1.86125 1.83938 -0.75870 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.50289 0.25867 1.11413 -1.93309 1.79108 -0.75870 -0.65083 1.73683 -1.95943 1.20797 0.14399 -1.42437 1.99668 -1.57642 0.37250 1.01659 -1.90032 1.83938 -0.86406 -0.54080 1.67682 -1.97927 1.29780 0.02882 -1.34111 1.98672 -1.64471 0.48509 0.91568 -1.86125 1.88157 -0.96654 -0.42897 1.61123 -1.99253 1.38332 -0.08644 -1.25341 1.97017 -1.70754 0.59606 0.81172 -1.81598 1.91750 -1.06581 -0.31572 1.54029 -1.99917 1.46424 -0.20141 -1.16154 1.94707 -1.76469 0.70506 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.57642 0.48509 0.81172 -1.76469 1.97017 -1.34111 0.14399 1.11413 -1.90032 1.88157 -1.06581 -0.20141 1.38332 -1.97927 1.73683 -0.75870 -0.54080 1.61123 -1.99917 1.54029 -0.42897 -0.86406 1.79108 -1.95943 1.29780 -0.08644 -1.16154 1.91750 -1.86125 1.01659 0.25867 -1.42437 1.98672 -1.70754 0.70506 0.59606 -1.64471 1.99668 -1.50289 0.37250 0.91568 -1.81598 1.94707 -1.25341 0.02882 1.20797 -1.93309 1.83938 -0.96654 -0.31572 1.46424 -1.99253 1.67682 -0.65083 ... ... ..... ....... ......... ........... ............. E44 * 2.00000 -1.64471 0.70506 0.48509 -1.50289 1.98672 -1.76469 0.91568 0.25867 -1.34111 1.94707 -1.86125 1.11413 0.02882 -1.16154 1.88157 -1.93309 1.29780 -0.20141 -0.96654 1.79108 -1.97927 1.46424 -0.42897 -0.75870 1.67682 -1.99917 1.61123 -0.65083 -0.54080 1.54029 -1.99253 1.73683 -0.86406 -0.31572 1.38332 -1.95943 1.83938 -1.06581 -0.08644 1.20797 -1.90032 1.91750 -1.25341 0.14399 1.01659 -1.81598 1.97017 -1.42437 0.37250 0.81172 -1.70754 1.99668 -1.57642 0.59606 ... ... ..... ....... ......... ........... ............. E45 * 2.00000 -1.70754 0.91568 0.14399 -1.16154 1.83938 -1.97927 1.54029 -0.65083 -0.42897 1.38332 -1.93309 1.91750 -1.34111 0.37250 0.70506 -1.57642 1.98672 -1.81598 1.11413 -0.08644 -0.96654 1.73683 -1.99917 1.67682 -0.86406 -0.20141 1.20797 -1.86125 1.97017 -1.50289 0.59606 0.48509 -1.42437 1.94707 -1.90032 1.29780 -0.31572 -0.75870 1.61123 -1.99253 1.79108 -1.06581 0.02882 1.01659 -1.76469 1.99668 -1.64471 0.81172 0.25867 -1.25341 1.88157 -1.95943 1.46424 -0.54080 ... ... ..... ....... ......... ........... ............. E46 * 2.00000 -1.76469 1.11413 -0.20141 -0.75870 1.54029 -1.95943 1.91750 -1.42437 0.59606 0.37250 -1.25341 1.83938 -1.99253 1.67682 -0.96654 0.02882 0.91568 -1.64471 1.98672 -1.86125 1.29780 -0.42897 -0.54080 1.38332 -1.90032 1.97017 -1.57642 0.81172 0.14399 -1.06581 1.73683 -1.99917 1.79108 -1.16154 0.25867 0.70506 -1.50289 1.94707 -1.93309 1.46424 -0.65083 -0.31572 1.20797 -1.81598 1.99668 -1.70754 1.01659 -0.08644 -0.86406 1.61123 -1.97927 1.88157 -1.34111 0.48509 ... ... ..... ....... ......... ........... ............. E47 * 2.00000 -1.81598 1.29780 -0.54080 -0.31572 1.11413 -1.70754 1.98672 -1.90032 1.46424 -0.75870 -0.08644 0.91568 -1.57642 1.94707 -1.95943 1.61123 -0.96654 0.14399 0.70506 -1.42437 1.88157 -1.99253 1.73683 -1.16154 0.37250 0.48509 -1.25341 1.79108 -1.99917 1.83938 -1.34111 0.59606 0.25867 -1.06581 1.67682 -1.97927 1.91750 -1.50289 0.81172 0.02882 -0.86406 1.54029 -1.93309 1.97017 -1.64471 1.01659 -0.20141 -0.65083 1.38332 -1.86125 1.99668 -1.76469 1.20797 -0.42897 ... ... ..... ....... ......... ........... ............. E48 * 2.00000 -1.86125 1.46424 -0.86406 0.14399 0.59606 -1.25341 1.73683 -1.97927 1.94707 -1.64471 1.11413 -0.42897 -0.31572 1.01659 -1.57642 1.91750 -1.99253 1.79108 -1.34111 0.70506 0.02882 -0.75870 1.38332 -1.81598 1.99668 -1.90032 1.54029 -0.96654 0.25867 0.48509 -1.16154 1.67682 -1.95943 1.97017 -1.70754 1.20797 -0.54080 -0.20141 0.91568 -1.50289 1.88157 -1.99917 1.83938 -1.42437 0.81172 -0.08644 -0.65083 1.29780 -1.76469 1.98672 -1.93309 1.61123 -1.06581 0.37250 ... ... ..... ....... ......... ........... ............. E49 * 2.00000 -1.90032 1.61123 -1.16154 0.59606 0.02882 -0.65083 1.20797 -1.64471 1.91750 -1.99917 1.88157 -1.57642 1.11413 -0.54080 -0.08644 0.70506 -1.25341 1.67682 -1.93309 1.99668 -1.86125 1.54029 -1.06581 0.48509 0.14399 -0.75870 1.29780 -1.70754 1.94707 -1.99253 1.83938 -1.50289 1.01659 -0.42897 -0.20141 0.81172 -1.34111 1.73683 -1.95943 1.98672 -1.81598 1.46424 -0.96654 0.37250 0.25867 -0.86406 1.38332 -1.76469 1.97017 -1.97927 1.79108 -1.42437 0.91568 -0.31572 ... ... ..... ....... ......... ........... ............. E50 * 2.00000 -1.93309 1.73683 -1.42437 1.01659 -0.54080 0.02882 0.48509 -0.96654 1.38332 -1.70754 1.91750 -1.99917 1.94707 -1.76469 1.46424 -1.06581 0.59606 -0.08644 -0.42897 0.91568 -1.34111 1.67682 -1.90032 1.99668 -1.95943 1.79108 -1.50289 1.11413 -0.65083 0.14399 0.37250 -0.86406 1.29780 -1.64471 1.88157 -1.99253 1.97017 -1.81598 1.54029 -1.16154 0.70506 -0.20141 -0.31572 0.81172 -1.25341 1.61123 -1.86125 1.98672 -1.97927 1.83938 -1.57642 1.20797 -0.75870 0.25867 ... ... ..... ....... ......... ........... ............. E51 * 2.00000 -1.95943 1.83938 -1.64471 1.38332 -1.06581 0.70506 -0.31572 -0.08644 0.48509 -0.86406 1.20797 -1.50289 1.73683 -1.90032 1.98672 -1.99253 1.91750 -1.76469 1.54029 -1.25341 0.91568 -0.54080 0.14399 0.25867 -0.65083 1.01659 -1.34111 1.61123 -1.81598 1.94707 -1.99917 1.97017 -1.86125 1.67682 -1.42437 1.11413 -0.75870 0.37250 0.02882 -0.42897 0.81172 -1.16154 1.46424 -1.70754 1.88157 -1.97927 1.99668 -1.93309 1.79108 -1.57642 1.29780 -0.96654 0.59606 -0.20141 ... ... ..... ....... ......... ........... ............. E52 * 2.00000 -1.97927 1.91750 -1.81598 1.67682 -1.50289 1.29780 -1.06581 0.81172 -0.54080 0.25867 0.02882 -0.31572 0.59606 -0.86406 1.11413 -1.34111 1.54029 -1.70754 1.83938 -1.93309 1.98672 -1.99917 1.97017 -1.90032 1.79108 -1.64471 1.46424 -1.25341 1.01659 -0.75870 0.48509 -0.20141 -0.08644 0.37250 -0.65083 0.91568 -1.16154 1.38332 -1.57642 1.73683 -1.86125 1.94707 -1.99253 1.99668 -1.95943 1.88157 -1.76469 1.61123 -1.42437 1.20797 -0.96654 0.70506 -0.42897 0.14399 ... ... ..... ....... ......... ........... ............. E53 * 2.00000 -1.99253 1.97017 -1.93309 1.88157 -1.81598 1.73683 -1.64471 1.54029 -1.42437 1.29780 -1.16154 1.01659 -0.86406 0.70506 -0.54080 0.37250 -0.20141 0.02882 0.14399 -0.31572 0.48509 -0.65083 0.81172 -0.96654 1.11413 -1.25341 1.38332 -1.50289 1.61123 -1.70754 1.79108 -1.86125 1.91750 -1.95943 1.98672 -1.99917 1.99668 -1.97927 1.94707 -1.90032 1.83938 -1.76469 1.67682 -1.57642 1.46424 -1.34111 1.20797 -1.06581 0.91568 -0.75870 0.59606 -0.42897 0.25867 -0.08644 ... ... ..... ....... ......... ........... ............. E54 * 2.00000 -1.99917 1.99668 -1.99253 1.98672 -1.97927 1.97017 -1.95943 1.94707 -1.93309 1.91750 -1.90032 1.88157 -1.86125 1.83938 -1.81598 1.79108 -1.76469 1.73683 -1.70754 1.67682 -1.64471 1.61123 -1.57642 1.54029 -1.50289 1.46424 -1.42437 1.38332 -1.34111 1.29780 -1.25341 1.20797 -1.16154 1.11413 -1.06581 1.01659 -0.96654 0.91568 -0.86406 0.81172 -0.75870 0.70506 -0.65083 0.59606 -0.54080 0.48509 -0.42897 0.37250 -0.31572 0.25867 -0.20141 0.14399 -0.08644 0.02882 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.996678100566 = 2*cos(2*π/109) 1.986723437279 = 2*cos(4*π/109) 1.970169078530 = 2*cos(6*π/109) 1.947070016234 = 2*cos(8*π/109) 1.917502983153 = 2*cos(10*π/109) 1.881566197997 = 2*cos(12*π/109) 1.839379039153 = 2*cos(14*π/109) 1.791081648119 = 2*cos(16*π/109) 1.736834463972 = 2*cos(18*π/109) 1.676817690402 = 2*cos(20*π/109) 1.611230697094 = 2*cos(22*π/109) 1.540291357446 = 2*cos(24*π/109) 1.464235324809 = 2*cos(26*π/109) 1.383315249675 = 2*cos(28*π/109) 1.297799940396 = 2*cos(30*π/109) 1.207973470229 = 2*cos(32*π/109) 1.114134233675 = 2*cos(34*π/109) 1.016593955240 = 2*cos(36*π/109) 0.915676653921 = 2*cos(38*π/109) 0.811717566843 = 2*cos(40*π/109) 0.705062035640 = 2*cos(42*π/109) 0.596064359259 = 2*cos(44*π/109) 0.485086617020 = 2*cos(46*π/109) 0.372497465823 = 2*cos(48*π/109) 0.258670915504 = 2*cos(50*π/109) 0.143985086418 = 2*cos(52*π/109) 0.028820953355 = 2*cos(54*π/109) -0.086438920017 = 2*cos(56*π/109) -0.201411651989 = 2*cos(58*π/109) -0.315715314709 = 2*cos(60*π/109) -0.428970202903 = 2*cos(62*π/109) -0.540800095223 = 2*cos(64*π/109) -0.650833504013 = 2*cos(66*π/109) -0.758704909354 = 2*cos(68*π/109) -0.864055973286 = 2*cos(70*π/109) -0.966536730169 = 2*cos(72*π/109) -1.065806749235 = 2*cos(74*π/109) -1.161536265464 = 2*cos(76*π/109) -1.253407275030 = 2*cos(78*π/109) -1.341114591678 = 2*cos(80*π/109) -1.424366860523 = 2*cos(82*π/109) -1.502887525900 = 2*cos(84*π/109) -1.576415750055 = 2*cos(86*π/109) -1.644707279621 = 2*cos(88*π/109) -1.707535257007 = 2*cos(90*π/109) -1.764690973988 = 2*cos(92*π/109) -1.815984565021 = 2*cos(94*π/109) -1.861245637956 = 2*cos(96*π/109) -1.900323840058 = 2*cos(98*π/109) -1.933089357472 = 2*cos(100*π/109) -1.959433346443 = 2*cos(102*π/109) -1.979268294889 = 2*cos(104*π/109) -1.992528313106 = 2*cos(106*π/109) -1.999169352648 = 2*cos(108*π/109) 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 C109 point group is 109, and the order of the principal axis (C109) is 109. The group has 55 irreducible representations. β The C109 point group is generated by one single symmetry element, C109. Therefore, it is a cyclic group. γ The lowest nonvanishing multipole moment in C109 is 2 (dipole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C109 group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition). In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. ε Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 108 cases have been combined into 54 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 54 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 54 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. η The point group is chiral, as it does not contain any mirroring operation. θ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree just less than half the order of the principal axis. ι The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. All characters of this group can be expressed using complex numbers, elementary arithmetic operations, square roots and third roots.
C107 | ||
C108 | ||
C109 | C109v C109h D109 D109h D109d | |
C110 | ||
C111 |
This Character Table for the C109 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.