C98 E 2 C98 2 C49 2 C98^3 2 C49^2 2 C98^5 2 C49^3 2 C14 2 C49^4 2 C98^9 2 C49^5 2 C98^11 2 C49^6 2 C98^13 2 C7 2 C98^15 2 C49^8 2 C98^17 2 C49^9 2 C98^19 2 C49^10 2 C14^3 2 C49^11 2 C98^23 2 C49^12 2 C98^25 2 C49^13 2 C98^27 2 C7^2 2 C98^29 2 C49^15 2 C98^31 2 C49^16 2 C98^33 2 C49^17 2 C14^5 2 C49^18 2 C98^37 2 C49^19 2 C98^39 2 C49^20 2 C98^41 2 C7^3 2 C98^43 2 C49^22 2 C98^45 2 C49^23 2 C98^47 2 C49^24 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 ..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 ... ... ..... ....... ......... ........... ............. E1 * 2.00000 1.99589 1.98358 1.96312 1.93459 1.89811 1.85383 1.80194 1.74264 1.67618 1.60283 1.52289 1.43670 1.34460 1.24698 1.14423 1.03679 0.92508 0.80957 0.69073 0.56906 0.44504 0.31920 0.19205 0.06410 -0.06410 -0.19205 -0.31920 -0.44504 -0.56906 -0.69073 -0.80957 -0.92508 -1.03679 -1.14423 -1.24698 -1.34460 -1.43670 -1.52289 -1.60283 -1.67618 -1.74264 -1.80194 -1.85383 -1.89811 -1.93459 -1.96312 -1.98358 -1.99589 -2.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98358 1.93459 1.85383 1.74264 1.60283 1.43670 1.24698 1.03679 0.80957 0.56906 0.31920 0.06410 -0.19205 -0.44504 -0.69073 -0.92508 -1.14423 -1.34460 -1.52289 -1.67618 -1.80194 -1.89811 -1.96312 -1.99589 -1.99589 -1.96312 -1.89811 -1.80194 -1.67618 -1.52289 -1.34460 -1.14423 -0.92508 -0.69073 -0.44504 -0.19205 0.06410 0.31920 0.56906 0.80957 1.03679 1.24698 1.43670 1.60283 1.74264 1.85383 1.93459 1.98358 2.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.96312 1.85383 1.67618 1.43670 1.14423 0.80957 0.44504 0.06410 -0.31920 -0.69073 -1.03679 -1.34460 -1.60283 -1.80194 -1.93459 -1.99589 -1.98358 -1.89811 -1.74264 -1.52289 -1.24698 -0.92508 -0.56906 -0.19205 0.19205 0.56906 0.92508 1.24698 1.52289 1.74264 1.89811 1.98358 1.99589 1.93459 1.80194 1.60283 1.34460 1.03679 0.69073 0.31920 -0.06410 -0.44504 -0.80957 -1.14423 -1.43670 -1.67618 -1.85383 -1.96312 -2.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.93459 1.74264 1.43670 1.03679 0.56906 0.06410 -0.44504 -0.92508 -1.34460 -1.67618 -1.89811 -1.99589 -1.96312 -1.80194 -1.52289 -1.14423 -0.69073 -0.19205 0.31920 0.80957 1.24698 1.60283 1.85383 1.98358 1.98358 1.85383 1.60283 1.24698 0.80957 0.31920 -0.19205 -0.69073 -1.14423 -1.52289 -1.80194 -1.96312 -1.99589 -1.89811 -1.67618 -1.34460 -0.92508 -0.44504 0.06410 0.56906 1.03679 1.43670 1.74264 1.93459 2.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.89811 1.60283 1.14423 0.56906 -0.06410 -0.69073 -1.24698 -1.67618 -1.93459 -1.99589 -1.85383 -1.52289 -1.03679 -0.44504 0.19205 0.80957 1.34460 1.74264 1.96312 1.98358 1.80194 1.43670 0.92508 0.31920 -0.31920 -0.92508 -1.43670 -1.80194 -1.98358 -1.96312 -1.74264 -1.34460 -0.80957 -0.19205 0.44504 1.03679 1.52289 1.85383 1.99589 1.93459 1.67618 1.24698 0.69073 0.06410 -0.56906 -1.14423 -1.60283 -1.89811 -2.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.85383 1.43670 0.80957 0.06410 -0.69073 -1.34460 -1.80194 -1.99589 -1.89811 -1.52289 -0.92508 -0.19205 0.56906 1.24698 1.74264 1.98358 1.93459 1.60283 1.03679 0.31920 -0.44504 -1.14423 -1.67618 -1.96312 -1.96312 -1.67618 -1.14423 -0.44504 0.31920 1.03679 1.60283 1.93459 1.98358 1.74264 1.24698 0.56906 -0.19205 -0.92508 -1.52289 -1.89811 -1.99589 -1.80194 -1.34460 -0.69073 0.06410 0.80957 1.43670 1.85383 2.00000 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.74264 1.03679 0.06410 -0.92508 -1.67618 -1.99589 -1.80194 -1.14423 -0.19205 0.80957 1.60283 1.98358 1.85383 1.24698 0.31920 -0.69073 -1.52289 -1.96312 -1.89811 -1.34460 -0.44504 0.56906 1.43670 1.93459 1.93459 1.43670 0.56906 -0.44504 -1.34460 -1.89811 -1.96312 -1.52289 -0.69073 0.31920 1.24698 1.85383 1.98358 1.60283 0.80957 -0.19205 -1.14423 -1.80194 -1.99589 -1.67618 -0.92508 0.06410 1.03679 1.74264 2.00000 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.67618 0.80957 -0.31920 -1.34460 -1.93459 -1.89811 -1.24698 -0.19205 0.92508 1.74264 1.99589 1.60283 0.69073 -0.44504 -1.43670 -1.96312 -1.85383 -1.14423 -0.06410 1.03679 1.80194 1.98358 1.52289 0.56906 -0.56906 -1.52289 -1.98358 -1.80194 -1.03679 0.06410 1.14423 1.85383 1.96312 1.43670 0.44504 -0.69073 -1.60283 -1.99589 -1.74264 -0.92508 0.19205 1.24698 1.89811 1.93459 1.34460 0.31920 -0.80957 -1.67618 -2.00000 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.60283 0.56906 -0.69073 -1.67618 -1.99589 -1.52289 -0.44504 0.80957 1.74264 1.98358 1.43670 0.31920 -0.92508 -1.80194 -1.96312 -1.34460 -0.19205 1.03679 1.85383 1.93459 1.24698 0.06410 -1.14423 -1.89811 -1.89811 -1.14423 0.06410 1.24698 1.93459 1.85383 1.03679 -0.19205 -1.34460 -1.96312 -1.80194 -0.92508 0.31920 1.43670 1.98358 1.74264 0.80957 -0.44504 -1.52289 -1.99589 -1.67618 -0.69073 0.56906 1.60283 2.00000 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.52289 0.31920 -1.03679 -1.89811 -1.85383 -0.92508 0.44504 1.60283 1.99589 1.43670 0.19205 -1.14423 -1.93459 -1.80194 -0.80957 0.56906 1.67618 1.98358 1.34460 0.06410 -1.24698 -1.96312 -1.74264 -0.69073 0.69073 1.74264 1.96312 1.24698 -0.06410 -1.34460 -1.98358 -1.67618 -0.56906 0.80957 1.80194 1.93459 1.14423 -0.19205 -1.43670 -1.99589 -1.60283 -0.44504 0.92508 1.85383 1.89811 1.03679 -0.31920 -1.52289 -2.00000 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.43670 0.06410 -1.34460 -1.99589 -1.52289 -0.19205 1.24698 1.98358 1.60283 0.31920 -1.14423 -1.96312 -1.67618 -0.44504 1.03679 1.93459 1.74264 0.56906 -0.92508 -1.89811 -1.80194 -0.69073 0.80957 1.85383 1.85383 0.80957 -0.69073 -1.80194 -1.89811 -0.92508 0.56906 1.74264 1.93459 1.03679 -0.44504 -1.67618 -1.96312 -1.14423 0.31920 1.60283 1.98358 1.24698 -0.19205 -1.52289 -1.99589 -1.34460 0.06410 1.43670 2.00000 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.34460 -0.19205 -1.60283 -1.96312 -1.03679 0.56906 1.80194 1.85383 0.69073 -0.92508 -1.93459 -1.67618 -0.31920 1.24698 1.99589 1.43670 -0.06410 -1.52289 -1.98358 -1.14423 0.44504 1.74264 1.89811 0.80957 -0.80957 -1.89811 -1.74264 -0.44504 1.14423 1.98358 1.52289 0.06410 -1.43670 -1.99589 -1.24698 0.31920 1.67618 1.93459 0.92508 -0.69073 -1.85383 -1.80194 -0.56906 1.03679 1.96312 1.60283 0.19205 -1.34460 -2.00000 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.14423 -0.69073 -1.93459 -1.52289 0.19205 1.74264 1.80194 0.31920 -1.43670 -1.96312 -0.80957 1.03679 1.99589 1.24698 -0.56906 -1.89811 -1.60283 0.06410 1.67618 1.85383 0.44504 -1.34460 -1.98358 -0.92508 0.92508 1.98358 1.34460 -0.44504 -1.85383 -1.67618 -0.06410 1.60283 1.89811 0.56906 -1.24698 -1.99589 -1.03679 0.80957 1.96312 1.43670 -0.31920 -1.80194 -1.74264 -0.19205 1.52289 1.93459 0.69073 -1.14423 -2.00000 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.03679 -0.92508 -1.99589 -1.14423 0.80957 1.98358 1.24698 -0.69073 -1.96312 -1.34460 0.56906 1.93459 1.43670 -0.44504 -1.89811 -1.52289 0.31920 1.85383 1.60283 -0.19205 -1.80194 -1.67618 0.06410 1.74264 1.74264 0.06410 -1.67618 -1.80194 -0.19205 1.60283 1.85383 0.31920 -1.52289 -1.89811 -0.44504 1.43670 1.93459 0.56906 -1.34460 -1.96312 -0.69073 1.24698 1.98358 0.80957 -1.14423 -1.99589 -0.92508 1.03679 2.00000 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 0.92508 -1.14423 -1.98358 -0.69073 1.34460 1.93459 0.44504 -1.52289 -1.85383 -0.19205 1.67618 1.74264 -0.06410 -1.80194 -1.60283 0.31920 1.89811 1.43670 -0.56906 -1.96312 -1.24698 0.80957 1.99589 1.03679 -1.03679 -1.99589 -0.80957 1.24698 1.96312 0.56906 -1.43670 -1.89811 -0.31920 1.60283 1.80194 0.06410 -1.74264 -1.67618 0.19205 1.85383 1.52289 -0.44504 -1.93459 -1.34460 0.69073 1.98358 1.14423 -0.92508 -2.00000 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.80957 -1.34460 -1.89811 -0.19205 1.74264 1.60283 -0.44504 -1.96312 -1.14423 1.03679 1.98358 0.56906 -1.52289 -1.80194 0.06410 1.85383 1.43670 -0.69073 -1.99589 -0.92508 1.24698 1.93459 0.31920 -1.67618 -1.67618 0.31920 1.93459 1.24698 -0.92508 -1.99589 -0.69073 1.43670 1.85383 0.06410 -1.80194 -1.52289 0.56906 1.98358 1.03679 -1.14423 -1.96312 -0.44504 1.60283 1.74264 -0.19205 -1.89811 -1.34460 0.80957 2.00000 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.69073 -1.52289 -1.74264 0.31920 1.96312 1.03679 -1.24698 -1.89811 -0.06410 1.85383 1.34460 -0.92508 -1.98358 -0.44504 1.67618 1.60283 -0.56906 -1.99589 -0.80957 1.43670 1.80194 -0.19205 -1.93459 -1.14423 1.14423 1.93459 0.19205 -1.80194 -1.43670 0.80957 1.99589 0.56906 -1.60283 -1.67618 0.44504 1.98358 0.92508 -1.34460 -1.85383 0.06410 1.89811 1.24698 -1.03679 -1.96312 -0.31920 1.74264 1.52289 -0.69073 -2.00000 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.56906 -1.67618 -1.52289 0.80957 1.98358 0.31920 -1.80194 -1.34460 1.03679 1.93459 0.06410 -1.89811 -1.14423 1.24698 1.85383 -0.19205 -1.96312 -0.92508 1.43670 1.74264 -0.44504 -1.99589 -0.69073 1.60283 1.60283 -0.69073 -1.99589 -0.44504 1.74264 1.43670 -0.92508 -1.96312 -0.19205 1.85383 1.24698 -1.14423 -1.89811 0.06410 1.93459 1.03679 -1.34460 -1.80194 0.31920 1.98358 0.80957 -1.52289 -1.67618 0.56906 2.00000 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.31920 -1.89811 -0.92508 1.60283 1.43670 -1.14423 -1.80194 0.56906 1.98358 0.06410 -1.96312 -0.69073 1.74264 1.24698 -1.34460 -1.67618 0.80957 1.93459 -0.19205 -1.99589 -0.44504 1.85383 1.03679 -1.52289 -1.52289 1.03679 1.85383 -0.44504 -1.99589 -0.19205 1.93459 0.80957 -1.67618 -1.34460 1.24698 1.74264 -0.69073 -1.96312 0.06410 1.98358 0.56906 -1.80194 -1.14423 1.43670 1.60283 -0.92508 -1.89811 0.31920 2.00000 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.19205 -1.96312 -0.56906 1.85383 0.92508 -1.67618 -1.24698 1.43670 1.52289 -1.14423 -1.74264 0.80957 1.89811 -0.44504 -1.98358 0.06410 1.99589 0.31920 -1.93459 -0.69073 1.80194 1.03679 -1.60283 -1.34460 1.34460 1.60283 -1.03679 -1.80194 0.69073 1.93459 -0.31920 -1.99589 -0.06410 1.98358 0.44504 -1.89811 -0.80957 1.74264 1.14423 -1.52289 -1.43670 1.24698 1.67618 -0.92508 -1.85383 0.56906 1.96312 -0.19205 -2.00000 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 0.06410 -1.99589 -0.19205 1.98358 0.31920 -1.96312 -0.44504 1.93459 0.56906 -1.89811 -0.69073 1.85383 0.80957 -1.80194 -0.92508 1.74264 1.03679 -1.67618 -1.14423 1.60283 1.24698 -1.52289 -1.34460 1.43670 1.43670 -1.34460 -1.52289 1.24698 1.60283 -1.14423 -1.67618 1.03679 1.74264 -0.92508 -1.80194 0.80957 1.85383 -0.69073 -1.89811 0.56906 1.93459 -0.44504 -1.96312 0.31920 1.98358 -0.19205 -1.99589 0.06410 2.00000 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 -0.06410 -1.99589 0.19205 1.98358 -0.31920 -1.96312 0.44504 1.93459 -0.56906 -1.89811 0.69073 1.85383 -0.80957 -1.80194 0.92508 1.74264 -1.03679 -1.67618 1.14423 1.60283 -1.24698 -1.52289 1.34460 1.43670 -1.43670 -1.34460 1.52289 1.24698 -1.60283 -1.14423 1.67618 1.03679 -1.74264 -0.92508 1.80194 0.80957 -1.85383 -0.69073 1.89811 0.56906 -1.93459 -0.44504 1.96312 0.31920 -1.98358 -0.19205 1.99589 0.06410 -2.00000 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.19205 -1.96312 0.56906 1.85383 -0.92508 -1.67618 1.24698 1.43670 -1.52289 -1.14423 1.74264 0.80957 -1.89811 -0.44504 1.98358 0.06410 -1.99589 0.31920 1.93459 -0.69073 -1.80194 1.03679 1.60283 -1.34460 -1.34460 1.60283 1.03679 -1.80194 -0.69073 1.93459 0.31920 -1.99589 0.06410 1.98358 -0.44504 -1.89811 0.80957 1.74264 -1.14423 -1.52289 1.43670 1.24698 -1.67618 -0.92508 1.85383 0.56906 -1.96312 -0.19205 2.00000 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 -0.31920 -1.89811 0.92508 1.60283 -1.43670 -1.14423 1.80194 0.56906 -1.98358 0.06410 1.96312 -0.69073 -1.74264 1.24698 1.34460 -1.67618 -0.80957 1.93459 0.19205 -1.99589 0.44504 1.85383 -1.03679 -1.52289 1.52289 1.03679 -1.85383 -0.44504 1.99589 -0.19205 -1.93459 0.80957 1.67618 -1.34460 -1.24698 1.74264 0.69073 -1.96312 -0.06410 1.98358 -0.56906 -1.80194 1.14423 1.43670 -1.60283 -0.92508 1.89811 0.31920 -2.00000 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.56906 -1.67618 1.52289 0.80957 -1.98358 0.31920 1.80194 -1.34460 -1.03679 1.93459 -0.06410 -1.89811 1.14423 1.24698 -1.85383 -0.19205 1.96312 -0.92508 -1.43670 1.74264 0.44504 -1.99589 0.69073 1.60283 -1.60283 -0.69073 1.99589 -0.44504 -1.74264 1.43670 0.92508 -1.96312 0.19205 1.85383 -1.24698 -1.14423 1.89811 0.06410 -1.93459 1.03679 1.34460 -1.80194 -0.31920 1.98358 -0.80957 -1.52289 1.67618 0.56906 -2.00000 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -0.69073 -1.52289 1.74264 0.31920 -1.96312 1.03679 1.24698 -1.89811 0.06410 1.85383 -1.34460 -0.92508 1.98358 -0.44504 -1.67618 1.60283 0.56906 -1.99589 0.80957 1.43670 -1.80194 -0.19205 1.93459 -1.14423 -1.14423 1.93459 -0.19205 -1.80194 1.43670 0.80957 -1.99589 0.56906 1.60283 -1.67618 -0.44504 1.98358 -0.92508 -1.34460 1.85383 0.06410 -1.89811 1.24698 1.03679 -1.96312 0.31920 1.74264 -1.52289 -0.69073 2.00000 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -0.80957 -1.34460 1.89811 -0.19205 -1.74264 1.60283 0.44504 -1.96312 1.14423 1.03679 -1.98358 0.56906 1.52289 -1.80194 -0.06410 1.85383 -1.43670 -0.69073 1.99589 -0.92508 -1.24698 1.93459 -0.31920 -1.67618 1.67618 0.31920 -1.93459 1.24698 0.92508 -1.99589 0.69073 1.43670 -1.85383 0.06410 1.80194 -1.52289 -0.56906 1.98358 -1.03679 -1.14423 1.96312 -0.44504 -1.60283 1.74264 0.19205 -1.89811 1.34460 0.80957 -2.00000 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -0.92508 -1.14423 1.98358 -0.69073 -1.34460 1.93459 -0.44504 -1.52289 1.85383 -0.19205 -1.67618 1.74264 0.06410 -1.80194 1.60283 0.31920 -1.89811 1.43670 0.56906 -1.96312 1.24698 0.80957 -1.99589 1.03679 1.03679 -1.99589 0.80957 1.24698 -1.96312 0.56906 1.43670 -1.89811 0.31920 1.60283 -1.80194 0.06410 1.74264 -1.67618 -0.19205 1.85383 -1.52289 -0.44504 1.93459 -1.34460 -0.69073 1.98358 -1.14423 -0.92508 2.00000 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -1.03679 -0.92508 1.99589 -1.14423 -0.80957 1.98358 -1.24698 -0.69073 1.96312 -1.34460 -0.56906 1.93459 -1.43670 -0.44504 1.89811 -1.52289 -0.31920 1.85383 -1.60283 -0.19205 1.80194 -1.67618 -0.06410 1.74264 -1.74264 0.06410 1.67618 -1.80194 0.19205 1.60283 -1.85383 0.31920 1.52289 -1.89811 0.44504 1.43670 -1.93459 0.56906 1.34460 -1.96312 0.69073 1.24698 -1.98358 0.80957 1.14423 -1.99589 0.92508 1.03679 -2.00000 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.14423 -0.69073 1.93459 -1.52289 -0.19205 1.74264 -1.80194 0.31920 1.43670 -1.96312 0.80957 1.03679 -1.99589 1.24698 0.56906 -1.89811 1.60283 0.06410 -1.67618 1.85383 -0.44504 -1.34460 1.98358 -0.92508 -0.92508 1.98358 -1.34460 -0.44504 1.85383 -1.67618 0.06410 1.60283 -1.89811 0.56906 1.24698 -1.99589 1.03679 0.80957 -1.96312 1.43670 0.31920 -1.80194 1.74264 -0.19205 -1.52289 1.93459 -0.69073 -1.14423 2.00000 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.34460 -0.19205 1.60283 -1.96312 1.03679 0.56906 -1.80194 1.85383 -0.69073 -0.92508 1.93459 -1.67618 0.31920 1.24698 -1.99589 1.43670 0.06410 -1.52289 1.98358 -1.14423 -0.44504 1.74264 -1.89811 0.80957 0.80957 -1.89811 1.74264 -0.44504 -1.14423 1.98358 -1.52289 0.06410 1.43670 -1.99589 1.24698 0.31920 -1.67618 1.93459 -0.92508 -0.69073 1.85383 -1.80194 0.56906 1.03679 -1.96312 1.60283 -0.19205 -1.34460 2.00000 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.43670 0.06410 1.34460 -1.99589 1.52289 -0.19205 -1.24698 1.98358 -1.60283 0.31920 1.14423 -1.96312 1.67618 -0.44504 -1.03679 1.93459 -1.74264 0.56906 0.92508 -1.89811 1.80194 -0.69073 -0.80957 1.85383 -1.85383 0.80957 0.69073 -1.80194 1.89811 -0.92508 -0.56906 1.74264 -1.93459 1.03679 0.44504 -1.67618 1.96312 -1.14423 -0.31920 1.60283 -1.98358 1.24698 0.19205 -1.52289 1.99589 -1.34460 -0.06410 1.43670 -2.00000 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.52289 0.31920 1.03679 -1.89811 1.85383 -0.92508 -0.44504 1.60283 -1.99589 1.43670 -0.19205 -1.14423 1.93459 -1.80194 0.80957 0.56906 -1.67618 1.98358 -1.34460 0.06410 1.24698 -1.96312 1.74264 -0.69073 -0.69073 1.74264 -1.96312 1.24698 0.06410 -1.34460 1.98358 -1.67618 0.56906 0.80957 -1.80194 1.93459 -1.14423 -0.19205 1.43670 -1.99589 1.60283 -0.44504 -0.92508 1.85383 -1.89811 1.03679 0.31920 -1.52289 2.00000 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.60283 0.56906 0.69073 -1.67618 1.99589 -1.52289 0.44504 0.80957 -1.74264 1.98358 -1.43670 0.31920 0.92508 -1.80194 1.96312 -1.34460 0.19205 1.03679 -1.85383 1.93459 -1.24698 0.06410 1.14423 -1.89811 1.89811 -1.14423 -0.06410 1.24698 -1.93459 1.85383 -1.03679 -0.19205 1.34460 -1.96312 1.80194 -0.92508 -0.31920 1.43670 -1.98358 1.74264 -0.80957 -0.44504 1.52289 -1.99589 1.67618 -0.69073 -0.56906 1.60283 -2.00000 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.67618 0.80957 0.31920 -1.34460 1.93459 -1.89811 1.24698 -0.19205 -0.92508 1.74264 -1.99589 1.60283 -0.69073 -0.44504 1.43670 -1.96312 1.85383 -1.14423 0.06410 1.03679 -1.80194 1.98358 -1.52289 0.56906 0.56906 -1.52289 1.98358 -1.80194 1.03679 0.06410 -1.14423 1.85383 -1.96312 1.43670 -0.44504 -0.69073 1.60283 -1.99589 1.74264 -0.92508 -0.19205 1.24698 -1.89811 1.93459 -1.34460 0.31920 0.80957 -1.67618 2.00000 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.74264 1.03679 -0.06410 -0.92508 1.67618 -1.99589 1.80194 -1.14423 0.19205 0.80957 -1.60283 1.98358 -1.85383 1.24698 -0.31920 -0.69073 1.52289 -1.96312 1.89811 -1.34460 0.44504 0.56906 -1.43670 1.93459 -1.93459 1.43670 -0.56906 -0.44504 1.34460 -1.89811 1.96312 -1.52289 0.69073 0.31920 -1.24698 1.85383 -1.98358 1.60283 -0.80957 -0.19205 1.14423 -1.80194 1.99589 -1.67618 0.92508 0.06410 -1.03679 1.74264 -2.00000 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.85383 1.43670 -0.80957 0.06410 0.69073 -1.34460 1.80194 -1.99589 1.89811 -1.52289 0.92508 -0.19205 -0.56906 1.24698 -1.74264 1.98358 -1.93459 1.60283 -1.03679 0.31920 0.44504 -1.14423 1.67618 -1.96312 1.96312 -1.67618 1.14423 -0.44504 -0.31920 1.03679 -1.60283 1.93459 -1.98358 1.74264 -1.24698 0.56906 0.19205 -0.92508 1.52289 -1.89811 1.99589 -1.80194 1.34460 -0.69073 -0.06410 0.80957 -1.43670 1.85383 -2.00000 ... ... ..... ....... ......... ........... ............. E44 * 2.00000 -1.89811 1.60283 -1.14423 0.56906 0.06410 -0.69073 1.24698 -1.67618 1.93459 -1.99589 1.85383 -1.52289 1.03679 -0.44504 -0.19205 0.80957 -1.34460 1.74264 -1.96312 1.98358 -1.80194 1.43670 -0.92508 0.31920 0.31920 -0.92508 1.43670 -1.80194 1.98358 -1.96312 1.74264 -1.34460 0.80957 -0.19205 -0.44504 1.03679 -1.52289 1.85383 -1.99589 1.93459 -1.67618 1.24698 -0.69073 0.06410 0.56906 -1.14423 1.60283 -1.89811 2.00000 ... ... ..... ....... ......... ........... ............. E45 * 2.00000 -1.93459 1.74264 -1.43670 1.03679 -0.56906 0.06410 0.44504 -0.92508 1.34460 -1.67618 1.89811 -1.99589 1.96312 -1.80194 1.52289 -1.14423 0.69073 -0.19205 -0.31920 0.80957 -1.24698 1.60283 -1.85383 1.98358 -1.98358 1.85383 -1.60283 1.24698 -0.80957 0.31920 0.19205 -0.69073 1.14423 -1.52289 1.80194 -1.96312 1.99589 -1.89811 1.67618 -1.34460 0.92508 -0.44504 -0.06410 0.56906 -1.03679 1.43670 -1.74264 1.93459 -2.00000 ... ... ..... ....... ......... ........... ............. E46 * 2.00000 -1.96312 1.85383 -1.67618 1.43670 -1.14423 0.80957 -0.44504 0.06410 0.31920 -0.69073 1.03679 -1.34460 1.60283 -1.80194 1.93459 -1.99589 1.98358 -1.89811 1.74264 -1.52289 1.24698 -0.92508 0.56906 -0.19205 -0.19205 0.56906 -0.92508 1.24698 -1.52289 1.74264 -1.89811 1.98358 -1.99589 1.93459 -1.80194 1.60283 -1.34460 1.03679 -0.69073 0.31920 0.06410 -0.44504 0.80957 -1.14423 1.43670 -1.67618 1.85383 -1.96312 2.00000 ... ... ..... ....... ......... ........... ............. E47 * 2.00000 -1.98358 1.93459 -1.85383 1.74264 -1.60283 1.43670 -1.24698 1.03679 -0.80957 0.56906 -0.31920 0.06410 0.19205 -0.44504 0.69073 -0.92508 1.14423 -1.34460 1.52289 -1.67618 1.80194 -1.89811 1.96312 -1.99589 1.99589 -1.96312 1.89811 -1.80194 1.67618 -1.52289 1.34460 -1.14423 0.92508 -0.69073 0.44504 -0.19205 -0.06410 0.31920 -0.56906 0.80957 -1.03679 1.24698 -1.43670 1.60283 -1.74264 1.85383 -1.93459 1.98358 -2.00000 ... ... ..... ....... ......... ........... ............. E48 * 2.00000 -1.99589 1.98358 -1.96312 1.93459 -1.89811 1.85383 -1.80194 1.74264 -1.67618 1.60283 -1.52289 1.43670 -1.34460 1.24698 -1.14423 1.03679 -0.92508 0.80957 -0.69073 0.56906 -0.44504 0.31920 -0.19205 0.06410 0.06410 -0.19205 0.31920 -0.44504 0.56906 -0.69073 0.80957 -0.92508 1.03679 -1.14423 1.24698 -1.34460 1.43670 -1.52289 1.60283 -1.67618 1.74264 -1.80194 1.85383 -1.89811 1.93459 -1.96312 1.98358 -1.99589 2.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.995890785501 = 2*cos(2*π/98) = 2*cos(π/49) 1.983580027646 = 2*cos(4*π/98) = 2*cos(2*π/49) 1.963118313982 = 2*cos(6*π/98) = 2*cos(3*π/49) 1.934589726078 = 2*cos(8*π/98) = 2*cos(4*π/49) 1.898111494021 = 2*cos(10*π/98) = 2*cos(5*π/49) 1.853833514692 = 2*cos(12*π/98) = 2*cos(6*π/49) 1.801937735805 = 2*cos(14*π/98) = 2*cos(π/7) 1.742637408247 = 2*cos(16*π/98) = 2*cos(8*π/49) 1.676176209784 = 2*cos(18*π/98) = 2*cos(9*π/49) 1.602827243736 = 2*cos(20*π/98) = 2*cos(10*π/49) 1.522891916738 = 2*cos(22*π/98) = 2*cos(11*π/49) 1.436698700195 = 2*cos(24*π/98) = 2*cos(12*π/49) 1.344601780523 = 2*cos(26*π/98) = 2*cos(13*π/49) 1.246979603717 = 2*cos(28*π/98) = 2*cos(2*π/7) 1.144233320244 = 2*cos(30*π/98) = 2*cos(15*π/49) 1.036785136621 = 2*cos(32*π/98) = 2*cos(16*π/49) 0.925076580482 = 2*cos(34*π/98) = 2*cos(17*π/49) 0.809566686245 = 2*cos(36*π/98) = 2*cos(18*π/49) 0.690730108842 = 2*cos(38*π/98) = 2*cos(19*π/49) 0.569055173262 = 2*cos(40*π/98) = 2*cos(20*π/49) 0.445041867912 = 2*cos(42*π/98) = 2*cos(3*π/7) 0.319199790067 = 2*cos(44*π/98) = 2*cos(22*π/49) 0.192046051815 = 2*cos(46*π/98) = 2*cos(23*π/49) 0.064103155143 = 2*cos(48*π/98) = 2*cos(24*π/49) Symmetry of Rotations and Cartesian products A R+p+d+f+g+h+i z, Rz, z2, z3, z4, z5, z6 E1 R+p+d+f+g+h+i {x, y}, {Rx, Ry}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} E2 d+f+g+h+i {x2–y2, xy}, {z(x2–y2), xyz}, {z2(x2–y2), xyz2}, {z3(x2–y2), xyz3}, {z4(x2–y2), xyz4} E3 f+g+h+i {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 {(x2–y2)2–2x2y2, xy(x2–y2)}, {z((x2–y2)2–4x2y2), xyz(x2–y2)}, {z2((x2–y2)2–4x2y2), xyz2(x2–y2)} E5 h+i {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)}, {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)} E6 i {x2(x2–3y2)2–y2(3x2–y2)2, xy(x2–3y2)(3x2–y2)} Notes: α The order of the C98 point group is 98, and the order of the principal axis is 98. β This is an Abelian point group (the commutative law holds between all symmetry operations). The C98 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. γ Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 96 cases have been combined into 48 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 48 pairs of left and right rotations have been combined into one two-membered pseudo-class each. δ The 48 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. ε The point group is chiral, as it does not contain any mirroring operation. 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.
C97 | ||
C98 | C98v C98h D98 D98h D98d S98 | |
C99 |
This Character Table for the C98 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.