Character Table for Point Group D75d

Character table for the D_75d point group

D75d E 2 C75 2 C75^2 2 C25 2 C75^4 2 C15 2 C25^2 2 C75^7 2 C75^8 2 C25^3 2 C15^2 2 C75^11 2 C25^4 2 C75^13 2 C75^14 2 C5 2 C75^16 2 C75^17 2 C25^6 2 C75^19 2 C15^4 2 C25^7 2 C75^22 2 C75^23 2 C25^8 2 C3 2 C75^26 2 C25^9 2 C75^28 2 C75^29 2 C5^2 2 C75^31 2 C75^32 2 C25^11 2 C75^34 2 C15^7 2 C25^12 2 C75^37 75 C2' i 2 S150 2 S50 2 S30 2 S150^7 2 S50^3 2 S150^11 2 S150^13 2 S10 2 S150^17 2 S150^19 2 S50^7 2 S150^23 2 S6 2 S50^9 2 S150^29 2 S150^31 2 S50^11 2 S30^7 2 S150^37 2 S50^13 2 S150^41 2 S150^43 2 S10^3 2 S150^47 2 S150^49 2 S50^17 2 S150^53 2 S30^11 2 S50^19 2 S150^59 2 S150^61 2 S50^21 2 S30^13 2 S150^67 2 S50^23 2 S150^71 2 S150^73 75 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 A2g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 ... ..... ....... ......... ........... ............. E1g 2.00000 1.99299 1.97199 1.93717 1.88875 1.82709 1.75261 1.66584 1.56739 1.45794 1.33826 1.20920 1.07165 0.92659 0.77503 0.61803 0.45670 0.29217 0.12558 -0.04188 -0.20906 -0.37476 -0.53784 -0.69714 -0.85156 -1.00000 -1.14143 -1.27485 -1.39933 -1.51399 -1.61803 -1.71073 -1.79142 -1.85955 -1.91464 -1.95630 -1.98423 -1.99825 0.00000 2.00000 -1.99825 -1.98423 -1.95630 -1.91464 -1.85955 -1.79142 -1.71073 -1.61803 -1.51399 -1.39933 -1.27485 -1.14143 -1.00000 -0.85156 -0.69714 -0.53784 -0.37476 -0.20906 -0.04188 0.12558 0.29217 0.45670 0.61803 0.77503 0.92659 1.07165 1.20920 1.33826 1.45794 1.56739 1.66584 1.75261 1.82709 1.88875 1.93717 1.97199 1.99299 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.97199 1.88875 1.75261 1.56739 1.33826 1.07165 0.77503 0.45670 0.12558 -0.20906 -0.53784 -0.85156 -1.14143 -1.39933 -1.61803 -1.79142 -1.91464 -1.98423 -1.99825 -1.95630 -1.85955 -1.71073 -1.51399 -1.27485 -1.00000 -0.69714 -0.37476 -0.04188 0.29217 0.61803 0.92659 1.20920 1.45794 1.66584 1.82709 1.93717 1.99299 0.00000 2.00000 1.99299 1.93717 1.82709 1.66584 1.45794 1.20920 0.92659 0.61803 0.29217 -0.04188 -0.37476 -0.69714 -1.00000 -1.27485 -1.51399 -1.71073 -1.85955 -1.95630 -1.99825 -1.98423 -1.91464 -1.79142 -1.61803 -1.39933 -1.14143 -0.85156 -0.53784 -0.20906 0.12558 0.45670 0.77503 1.07165 1.33826 1.56739 1.75261 1.88875 1.97199 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 0.00000 2.00000 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g 2.00000 1.88875 1.56739 1.07165 0.45670 -0.20906 -0.85156 -1.39933 -1.79142 -1.98423 -1.95630 -1.71073 -1.27485 -0.69714 -0.04188 0.61803 1.20920 1.66584 1.93717 1.99299 1.82709 1.45794 0.92659 0.29217 -0.37476 -1.00000 -1.51399 -1.85955 -1.99825 -1.91464 -1.61803 -1.14143 -0.53784 0.12558 0.77503 1.33826 1.75261 1.97199 0.00000 2.00000 1.97199 1.75261 1.33826 0.77503 0.12558 -0.53784 -1.14143 -1.61803 -1.91464 -1.99825 -1.85955 -1.51399 -1.00000 -0.37476 0.29217 0.92659 1.45794 1.82709 1.99299 1.93717 1.66584 1.20920 0.61803 -0.04188 -0.69714 -1.27485 -1.71073 -1.95630 -1.98423 -1.79142 -1.39933 -0.85156 -0.20906 0.45670 1.07165 1.56739 1.88875 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 0.00000 2.00000 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 1.93717 1.45794 0.61803 -0.37476 -1.27485 -1.85955 -1.98423 -1.61803 -0.85156 0.12558 1.07165 1.75261 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 0.00000 2.00000 1.93717 1.45794 0.61803 -0.37476 -1.27485 -1.85955 -1.98423 -1.61803 -0.85156 0.12558 1.07165 1.75261 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 1.93717 1.45794 0.61803 -0.37476 -1.27485 -1.85955 -1.98423 -1.61803 -0.85156 0.12558 1.07165 1.75261 0.00000 ... ... ..... ....... ......... ........... TT........... E7g 2.00000 1.66584 0.77503 -0.37476 -1.39933 -1.95630 -1.85955 -1.14143 -0.04188 1.07165 1.82709 1.97199 1.45794 0.45670 -0.69714 -1.61803 -1.99825 -1.71073 -0.85156 0.29217 1.33826 1.93717 1.88875 1.20920 0.12558 -1.00000 -1.79142 -1.98423 -1.51399 -0.53784 0.61803 1.56739 1.99299 1.75261 0.92659 -0.20906 -1.27485 -1.91464 0.00000 2.00000 -1.91464 -1.27485 -0.20906 0.92659 1.75261 1.99299 1.56739 0.61803 -0.53784 -1.51399 -1.98423 -1.79142 -1.00000 0.12558 1.20920 1.88875 1.93717 1.33826 0.29217 -0.85156 -1.71073 -1.99825 -1.61803 -0.69714 0.45670 1.45794 1.97199 1.82709 1.07165 -0.04188 -1.14143 -1.85955 -1.95630 -1.39933 -0.37476 0.77503 1.66584 0.00000 ... ... ..... ....... ......... ........... ............. E8g 2.00000 1.56739 0.45670 -0.85156 -1.79142 -1.95630 -1.27485 -0.04188 1.20920 1.93717 1.82709 0.92659 -0.37476 -1.51399 -1.99825 -1.61803 -0.53784 0.77503 1.75261 1.97199 1.33826 0.12558 -1.14143 -1.91464 -1.85955 -1.00000 0.29217 1.45794 1.99299 1.66584 0.61803 -0.69714 -1.71073 -1.98423 -1.39933 -0.20906 1.07165 1.88875 0.00000 2.00000 1.88875 1.07165 -0.20906 -1.39933 -1.98423 -1.71073 -0.69714 0.61803 1.66584 1.99299 1.45794 0.29217 -1.00000 -1.85955 -1.91464 -1.14143 0.12558 1.33826 1.97199 1.75261 0.77503 -0.53784 -1.61803 -1.99825 -1.51399 -0.37476 0.92659 1.82709 1.93717 1.20920 -0.04188 -1.27485 -1.95630 -1.79142 -0.85156 0.45670 1.56739 0.00000 ... ... ..... ....... ......... ........... ............. E9g 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 -1.85955 -0.85156 0.61803 1.75261 1.93717 1.07165 -0.37476 -1.61803 -1.98423 -1.27485 0.12558 1.45794 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 0.00000 2.00000 -1.85955 -0.85156 0.61803 1.75261 1.93717 1.07165 -0.37476 -1.61803 -1.98423 -1.27485 0.12558 1.45794 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 -1.85955 -0.85156 0.61803 1.75261 1.93717 1.07165 -0.37476 -1.61803 -1.98423 -1.27485 0.12558 1.45794 0.00000 ... ... ..... ....... ......... ........... ............. E10g 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 0.00000 2.00000 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 1.20920 -0.53784 -1.85955 -1.71073 -0.20906 1.45794 1.97199 0.92659 -0.85156 -1.95630 -1.51399 0.12558 1.66584 1.88875 0.61803 -1.14143 -1.99825 -1.27485 0.45670 1.82709 1.75261 0.29217 -1.39933 -1.98423 -1.00000 0.77503 1.93717 1.56739 -0.04188 -1.61803 -1.91464 -0.69714 1.07165 1.99299 1.33826 -0.37476 -1.79142 0.00000 2.00000 -1.79142 -0.37476 1.33826 1.99299 1.07165 -0.69714 -1.91464 -1.61803 -0.04188 1.56739 1.93717 0.77503 -1.00000 -1.98423 -1.39933 0.29217 1.75261 1.82709 0.45670 -1.27485 -1.99825 -1.14143 0.61803 1.88875 1.66584 0.12558 -1.51399 -1.95630 -0.85156 0.92659 1.97199 1.45794 -0.20906 -1.71073 -1.85955 -0.53784 1.20920 0.00000 ... ... ..... ....... ......... ........... ............. E12g 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 1.75261 0.12558 -1.61803 -1.85955 -0.37476 1.45794 1.93717 0.61803 -1.27485 -1.98423 -0.85156 1.07165 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 0.00000 2.00000 1.75261 0.12558 -1.61803 -1.85955 -0.37476 1.45794 1.93717 0.61803 -1.27485 -1.98423 -0.85156 1.07165 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 1.75261 0.12558 -1.61803 -1.85955 -0.37476 1.45794 1.93717 0.61803 -1.27485 -1.98423 -0.85156 1.07165 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 0.92659 -1.14143 -1.98423 -0.69714 1.33826 1.93717 0.45670 -1.51399 -1.85955 -0.20906 1.66584 1.75261 -0.04188 -1.79142 -1.61803 0.29217 1.88875 1.45794 -0.53784 -1.95630 -1.27485 0.77503 1.99299 1.07165 -1.00000 -1.99825 -0.85156 1.20920 1.97199 0.61803 -1.39933 -1.91464 -0.37476 1.56739 1.82709 0.12558 -1.71073 0.00000 2.00000 -1.71073 0.12558 1.82709 1.56739 -0.37476 -1.91464 -1.39933 0.61803 1.97199 1.20920 -0.85156 -1.99825 -1.00000 1.07165 1.99299 0.77503 -1.27485 -1.95630 -0.53784 1.45794 1.88875 0.29217 -1.61803 -1.79142 -0.04188 1.75261 1.66584 -0.20906 -1.85955 -1.51399 0.45670 1.93717 1.33826 -0.69714 -1.98423 -1.14143 0.92659 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 0.77503 -1.39933 -1.85955 -0.04188 1.82709 1.45794 -0.69714 -1.99825 -0.85156 1.33826 1.88875 0.12558 -1.79142 -1.51399 0.61803 1.99299 0.92659 -1.27485 -1.91464 -0.20906 1.75261 1.56739 -0.53784 -1.98423 -1.00000 1.20920 1.93717 0.29217 -1.71073 -1.61803 0.45670 1.97199 1.07165 -1.14143 -1.95630 -0.37476 1.66584 0.00000 2.00000 1.66584 -0.37476 -1.95630 -1.14143 1.07165 1.97199 0.45670 -1.61803 -1.71073 0.29217 1.93717 1.20920 -1.00000 -1.98423 -0.53784 1.56739 1.75261 -0.20906 -1.91464 -1.27485 0.92659 1.99299 0.61803 -1.51399 -1.79142 0.12558 1.88875 1.33826 -0.85156 -1.99825 -0.69714 1.45794 1.82709 -0.04188 -1.85955 -1.39933 0.77503 0.00000 ... ... ..... ....... ......... ........... ............. E15g 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 0.00000 2.00000 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 0.00000 ... ... ..... ....... ......... ........... ............. E16g 2.00000 0.45670 -1.79142 -1.27485 1.20920 1.82709 -0.37476 -1.99825 -0.53784 1.75261 1.33826 -1.14143 -1.85955 0.29217 1.99299 0.61803 -1.71073 -1.39933 1.07165 1.88875 -0.20906 -1.98423 -0.69714 1.66584 1.45794 -1.00000 -1.91464 0.12558 1.97199 0.77503 -1.61803 -1.51399 0.92659 1.93717 -0.04188 -1.95630 -0.85156 1.56739 0.00000 2.00000 1.56739 -0.85156 -1.95630 -0.04188 1.93717 0.92659 -1.51399 -1.61803 0.77503 1.97199 0.12558 -1.91464 -1.00000 1.45794 1.66584 -0.69714 -1.98423 -0.20906 1.88875 1.07165 -1.39933 -1.71073 0.61803 1.99299 0.29217 -1.85955 -1.14143 1.33826 1.75261 -0.53784 -1.99825 -0.37476 1.82709 1.20920 -1.27485 -1.79142 0.45670 0.00000 ... ... ..... ....... ......... ........... ............. E17g 2.00000 0.29217 -1.91464 -0.85156 1.66584 1.33826 -1.27485 -1.71073 0.77503 1.93717 -0.20906 -1.99825 -0.37476 1.88875 0.92659 -1.61803 -1.39933 1.20920 1.75261 -0.69714 -1.95630 0.12558 1.99299 0.45670 -1.85955 -1.00000 1.56739 1.45794 -1.14143 -1.79142 0.61803 1.97199 -0.04188 -1.98423 -0.53784 1.82709 1.07165 -1.51399 0.00000 2.00000 -1.51399 1.07165 1.82709 -0.53784 -1.98423 -0.04188 1.97199 0.61803 -1.79142 -1.14143 1.45794 1.56739 -1.00000 -1.85955 0.45670 1.99299 0.12558 -1.95630 -0.69714 1.75261 1.20920 -1.39933 -1.61803 0.92659 1.88875 -0.37476 -1.99825 -0.20906 1.93717 0.77503 -1.71073 -1.27485 1.33826 1.66584 -0.85156 -1.91464 0.29217 0.00000 ... ... ..... ....... ......... ........... ............. E18g 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 1.45794 -1.27485 -1.61803 1.07165 1.75261 -0.85156 -1.85955 0.61803 1.93717 -0.37476 -1.98423 0.12558 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 0.00000 2.00000 1.45794 -1.27485 -1.61803 1.07165 1.75261 -0.85156 -1.85955 0.61803 1.93717 -0.37476 -1.98423 0.12558 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 1.45794 -1.27485 -1.61803 1.07165 1.75261 -0.85156 -1.85955 0.61803 1.93717 -0.37476 -1.98423 0.12558 0.00000 ... ... ..... ....... ......... ........... ............. E19g 2.00000 -0.04188 -1.99825 0.12558 1.99299 -0.20906 -1.98423 0.29217 1.97199 -0.37476 -1.95630 0.45670 1.93717 -0.53784 -1.91464 0.61803 1.88875 -0.69714 -1.85955 0.77503 1.82709 -0.85156 -1.79142 0.92659 1.75261 -1.00000 -1.71073 1.07165 1.66584 -1.14143 -1.61803 1.20920 1.56739 -1.27485 -1.51399 1.33826 1.45794 -1.39933 0.00000 2.00000 -1.39933 1.45794 1.33826 -1.51399 -1.27485 1.56739 1.20920 -1.61803 -1.14143 1.66584 1.07165 -1.71073 -1.00000 1.75261 0.92659 -1.79142 -0.85156 1.82709 0.77503 -1.85955 -0.69714 1.88875 0.61803 -1.91464 -0.53784 1.93717 0.45670 -1.95630 -0.37476 1.97199 0.29217 -1.98423 -0.20906 1.99299 0.12558 -1.99825 -0.04188 0.00000 ... ... ..... ....... ......... ........... ............. E20g 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 0.00000 2.00000 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 0.00000 ... ... ..... ....... ......... ........... ............. E21g 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 -1.27485 1.75261 0.61803 -1.98423 0.12558 1.93717 -0.85156 -1.61803 1.45794 1.07165 -1.85955 -0.37476 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 0.00000 2.00000 -1.27485 1.75261 0.61803 -1.98423 0.12558 1.93717 -0.85156 -1.61803 1.45794 1.07165 -1.85955 -0.37476 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 -1.27485 1.75261 0.61803 -1.98423 0.12558 1.93717 -0.85156 -1.61803 1.45794 1.07165 -1.85955 -0.37476 0.00000 ... ... ..... ....... ......... ........... ............. E22g 2.00000 -0.53784 -1.71073 1.45794 0.92659 -1.95630 0.12558 1.88875 -1.14143 -1.27485 1.82709 0.29217 -1.98423 0.77503 1.56739 -1.61803 -0.69714 1.99299 -0.37476 -1.79142 1.33826 1.07165 -1.91464 -0.04188 1.93717 -1.00000 -1.39933 1.75261 0.45670 -1.99825 0.61803 1.66584 -1.51399 -0.85156 1.97199 -0.20906 -1.85955 1.20920 0.00000 2.00000 1.20920 -1.85955 -0.20906 1.97199 -0.85156 -1.51399 1.66584 0.61803 -1.99825 0.45670 1.75261 -1.39933 -1.00000 1.93717 -0.04188 -1.91464 1.07165 1.33826 -1.79142 -0.37476 1.99299 -0.69714 -1.61803 1.56739 0.77503 -1.98423 0.29217 1.82709 -1.27485 -1.14143 1.88875 0.12558 -1.95630 0.92659 1.45794 -1.71073 -0.53784 0.00000 ... ... ..... ....... ......... ........... ............. E23g 2.00000 -0.69714 -1.51399 1.75261 0.29217 -1.95630 1.07165 1.20920 -1.91464 0.12558 1.82709 -1.39933 -0.85156 1.99299 -0.53784 -1.61803 1.66584 0.45670 -1.98423 0.92659 1.33826 -1.85955 -0.04188 1.88875 -1.27485 -1.00000 1.97199 -0.37476 -1.71073 1.56739 0.61803 -1.99825 0.77503 1.45794 -1.79142 -0.20906 1.93717 -1.14143 0.00000 2.00000 -1.14143 1.93717 -0.20906 -1.79142 1.45794 0.77503 -1.99825 0.61803 1.56739 -1.71073 -0.37476 1.97199 -1.00000 -1.27485 1.88875 -0.04188 -1.85955 1.33826 0.92659 -1.98423 0.45670 1.66584 -1.61803 -0.53784 1.99299 -0.85156 -1.39933 1.82709 0.12558 -1.91464 1.20920 1.07165 -1.95630 0.29217 1.75261 -1.51399 -0.69714 0.00000 ... ... ..... ....... ......... ........... ............. E24g 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 1.07165 -1.98423 0.61803 1.45794 -1.85955 0.12558 1.75261 -1.61803 -0.37476 1.93717 -1.27485 -0.85156 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 0.00000 2.00000 1.07165 -1.98423 0.61803 1.45794 -1.85955 0.12558 1.75261 -1.61803 -0.37476 1.93717 -1.27485 -0.85156 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 1.07165 -1.98423 0.61803 1.45794 -1.85955 0.12558 1.75261 -1.61803 -0.37476 1.93717 -1.27485 -0.85156 0.00000 ... ... ..... ....... ......... ........... ............. E25g 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 0.00000 2.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E26g 2.00000 -1.14143 -0.69714 1.93717 -1.51399 -0.20906 1.75261 -1.79142 0.29217 1.45794 -1.95630 0.77503 1.07165 -1.99825 1.20920 0.61803 -1.91464 1.56739 0.12558 -1.71073 1.82709 -0.37476 -1.39933 1.97199 -0.85156 -1.00000 1.99299 -1.27485 -0.53784 1.88875 -1.61803 -0.04188 1.66584 -1.85955 0.45670 1.33826 -1.98423 0.92659 0.00000 2.00000 0.92659 -1.98423 1.33826 0.45670 -1.85955 1.66584 -0.04188 -1.61803 1.88875 -0.53784 -1.27485 1.99299 -1.00000 -0.85156 1.97199 -1.39933 -0.37476 1.82709 -1.71073 0.12558 1.56739 -1.91464 0.61803 1.20920 -1.99825 1.07165 0.77503 -1.95630 1.45794 0.29217 -1.79142 1.75261 -0.20906 -1.51399 1.93717 -0.69714 -1.14143 0.00000 ... ... ..... ....... ......... ........... ............. E27g 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 -0.85156 1.93717 -1.61803 0.12558 1.45794 -1.98423 1.07165 0.61803 -1.85955 1.75261 -0.37476 -1.27485 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 0.00000 2.00000 -0.85156 1.93717 -1.61803 0.12558 1.45794 -1.98423 1.07165 0.61803 -1.85955 1.75261 -0.37476 -1.27485 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 -0.85156 1.93717 -1.61803 0.12558 1.45794 -1.98423 1.07165 0.61803 -1.85955 1.75261 -0.37476 -1.27485 0.00000 ... ... ..... ....... ......... ........... ............. E28g 2.00000 -1.39933 -0.04188 1.45794 -1.99825 1.33826 0.12558 -1.51399 1.99299 -1.27485 -0.20906 1.56739 -1.98423 1.20920 0.29217 -1.61803 1.97199 -1.14143 -0.37476 1.66584 -1.95630 1.07165 0.45670 -1.71073 1.93717 -1.00000 -0.53784 1.75261 -1.91464 0.92659 0.61803 -1.79142 1.88875 -0.85156 -0.69714 1.82709 -1.85955 0.77503 0.00000 2.00000 0.77503 -1.85955 1.82709 -0.69714 -0.85156 1.88875 -1.79142 0.61803 0.92659 -1.91464 1.75261 -0.53784 -1.00000 1.93717 -1.71073 0.45670 1.07165 -1.95630 1.66584 -0.37476 -1.14143 1.97199 -1.61803 0.29217 1.20920 -1.98423 1.56739 -0.20906 -1.27485 1.99299 -1.51399 0.12558 1.33826 -1.99825 1.45794 -0.04188 -1.39933 0.00000 ... ... ..... ....... ......... ........... ............. E29g 2.00000 -1.51399 0.29217 1.07165 -1.91464 1.82709 -0.85156 -0.53784 1.66584 -1.98423 1.33826 -0.04188 -1.27485 1.97199 -1.71073 0.61803 0.77503 -1.79142 1.93717 -1.14143 -0.20906 1.45794 -1.99825 1.56739 -0.37476 -1.00000 1.88875 -1.85955 0.92659 0.45670 -1.61803 1.99299 -1.39933 0.12558 1.20920 -1.95630 1.75261 -0.69714 0.00000 2.00000 -0.69714 1.75261 -1.95630 1.20920 0.12558 -1.39933 1.99299 -1.61803 0.45670 0.92659 -1.85955 1.88875 -1.00000 -0.37476 1.56739 -1.99825 1.45794 -0.20906 -1.14143 1.93717 -1.79142 0.77503 0.61803 -1.71073 1.97199 -1.27485 -0.04188 1.33826 -1.98423 1.66584 -0.53784 -0.85156 1.82709 -1.91464 1.07165 0.29217 -1.51399 0.00000 ... ... ..... ....... ......... ........... ............. E30g 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.00000 2.00000 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 0.00000 ... ... ..... ....... ......... ........... ............. E31g 2.00000 -1.71073 0.92659 0.12558 -1.14143 1.82709 -1.98423 1.56739 -0.69714 -0.37476 1.33826 -1.91464 1.93717 -1.39933 0.45670 0.61803 -1.51399 1.97199 -1.85955 1.20920 -0.20906 -0.85156 1.66584 -1.99825 1.75261 -1.00000 -0.04188 1.07165 -1.79142 1.99299 -1.61803 0.77503 0.29217 -1.27485 1.88875 -1.95630 1.45794 -0.53784 0.00000 2.00000 -0.53784 1.45794 -1.95630 1.88875 -1.27485 0.29217 0.77503 -1.61803 1.99299 -1.79142 1.07165 -0.04188 -1.00000 1.75261 -1.99825 1.66584 -0.85156 -0.20906 1.20920 -1.85955 1.97199 -1.51399 0.61803 0.45670 -1.39933 1.93717 -1.91464 1.33826 -0.37476 -0.69714 1.56739 -1.98423 1.82709 -1.14143 0.12558 0.92659 -1.71073 0.00000 ... ... ..... ....... ......... ........... ............. E32g 2.00000 -1.79142 1.20920 -0.37476 -0.53784 1.33826 -1.85955 1.99299 -1.71073 1.07165 -0.20906 -0.69714 1.45794 -1.91464 1.97199 -1.61803 0.92659 -0.04188 -0.85156 1.56739 -1.95630 1.93717 -1.51399 0.77503 0.12558 -1.00000 1.66584 -1.98423 1.88875 -1.39933 0.61803 0.29217 -1.14143 1.75261 -1.99825 1.82709 -1.27485 0.45670 0.00000 2.00000 0.45670 -1.27485 1.82709 -1.99825 1.75261 -1.14143 0.29217 0.61803 -1.39933 1.88875 -1.98423 1.66584 -1.00000 0.12558 0.77503 -1.51399 1.93717 -1.95630 1.56739 -0.85156 -0.04188 0.92659 -1.61803 1.97199 -1.91464 1.45794 -0.69714 -0.20906 1.07165 -1.71073 1.99299 -1.85955 1.33826 -0.53784 -0.37476 1.20920 -1.79142 0.00000 ... ... ..... ....... ......... ........... ............. E33g 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 -0.37476 1.07165 -1.61803 1.93717 -1.98423 1.75261 -1.27485 0.61803 0.12558 -0.85156 1.45794 -1.85955 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 0.00000 2.00000 -0.37476 1.07165 -1.61803 1.93717 -1.98423 1.75261 -1.27485 0.61803 0.12558 -0.85156 1.45794 -1.85955 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 -0.37476 1.07165 -1.61803 1.93717 -1.98423 1.75261 -1.27485 0.61803 0.12558 -0.85156 1.45794 -1.85955 0.00000 ... ... ..... ....... ......... ........... ............. E34g 2.00000 -1.91464 1.66584 -1.27485 0.77503 -0.20906 -0.37476 0.92659 -1.39933 1.75261 -1.95630 1.99299 -1.85955 1.56739 -1.14143 0.61803 -0.04188 -0.53784 1.07165 -1.51399 1.82709 -1.98423 1.97199 -1.79142 1.45794 -1.00000 0.45670 0.12558 -0.69714 1.20920 -1.61803 1.88875 -1.99825 1.93717 -1.71073 1.33826 -0.85156 0.29217 0.00000 2.00000 0.29217 -0.85156 1.33826 -1.71073 1.93717 -1.99825 1.88875 -1.61803 1.20920 -0.69714 0.12558 0.45670 -1.00000 1.45794 -1.79142 1.97199 -1.98423 1.82709 -1.51399 1.07165 -0.53784 -0.04188 0.61803 -1.14143 1.56739 -1.85955 1.99299 -1.95630 1.75261 -1.39933 0.92659 -0.37476 -0.20906 0.77503 -1.27485 1.66584 -1.91464 0.00000 ... ... ..... ....... ......... ........... ............. E35g 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 0.00000 2.00000 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 0.00000 ... ... ..... ....... ......... ........... ............. E36g 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 0.12558 -0.37476 0.61803 -0.85156 1.07165 -1.27485 1.45794 -1.61803 1.75261 -1.85955 1.93717 -1.98423 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 0.00000 2.00000 0.12558 -0.37476 0.61803 -0.85156 1.07165 -1.27485 1.45794 -1.61803 1.75261 -1.85955 1.93717 -1.98423 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 0.12558 -0.37476 0.61803 -0.85156 1.07165 -1.27485 1.45794 -1.61803 1.75261 -1.85955 1.93717 -1.98423 0.00000 ... ... ..... ....... ......... ........... ............. E37g 2.00000 -1.99825 1.99299 -1.98423 1.97199 -1.95630 1.93717 -1.91464 1.88875 -1.85955 1.82709 -1.79142 1.75261 -1.71073 1.66584 -1.61803 1.56739 -1.51399 1.45794 -1.39933 1.33826 -1.27485 1.20920 -1.14143 1.07165 -1.00000 0.92659 -0.85156 0.77503 -0.69714 0.61803 -0.53784 0.45670 -0.37476 0.29217 -0.20906 0.12558 -0.04188 0.00000 2.00000 -0.04188 0.12558 -0.20906 0.29217 -0.37476 0.45670 -0.53784 0.61803 -0.69714 0.77503 -0.85156 0.92659 -1.00000 1.07165 -1.14143 1.20920 -1.27485 1.33826 -1.39933 1.45794 -1.51399 1.56739 -1.61803 1.66584 -1.71073 1.75261 -1.79142 1.82709 -1.85955 1.88875 -1.91464 1.93717 -1.95630 1.97199 -1.98423 1.99299 -1.99825 0.00000 ... ... ..... ....... ......... ........... ............. A1u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. A2u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 1.00000 ... ..T ..... ......T ......... ..........T ............. E1u 2.00000 1.99299 1.97199 1.93717 1.88875 1.82709 1.75261 1.66584 1.56739 1.45794 1.33826 1.20920 1.07165 0.92659 0.77503 0.61803 0.45670 0.29217 0.12558 -0.04188 -0.20906 -0.37476 -0.53784 -0.69714 -0.85156 -1.00000 -1.14143 -1.27485 -1.39933 -1.51399 -1.61803 -1.71073 -1.79142 -1.85955 -1.91464 -1.95630 -1.98423 -1.99825 0.00000 -2.00000 1.99825 1.98423 1.95630 1.91464 1.85955 1.79142 1.71073 1.61803 1.51399 1.39933 1.27485 1.14143 1.00000 0.85156 0.69714 0.53784 0.37476 0.20906 0.04188 -0.12558 -0.29217 -0.45670 -0.61803 -0.77503 -0.92659 -1.07165 -1.20920 -1.33826 -1.45794 -1.56739 -1.66584 -1.75261 -1.82709 -1.88875 -1.93717 -1.97199 -1.99299 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.97199 1.88875 1.75261 1.56739 1.33826 1.07165 0.77503 0.45670 0.12558 -0.20906 -0.53784 -0.85156 -1.14143 -1.39933 -1.61803 -1.79142 -1.91464 -1.98423 -1.99825 -1.95630 -1.85955 -1.71073 -1.51399 -1.27485 -1.00000 -0.69714 -0.37476 -0.04188 0.29217 0.61803 0.92659 1.20920 1.45794 1.66584 1.82709 1.93717 1.99299 0.00000 -2.00000 -1.99299 -1.93717 -1.82709 -1.66584 -1.45794 -1.20920 -0.92659 -0.61803 -0.29217 0.04188 0.37476 0.69714 1.00000 1.27485 1.51399 1.71073 1.85955 1.95630 1.99825 1.98423 1.91464 1.79142 1.61803 1.39933 1.14143 0.85156 0.53784 0.20906 -0.12558 -0.45670 -0.77503 -1.07165 -1.33826 -1.56739 -1.75261 -1.88875 -1.97199 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 0.00000 -2.00000 1.98423 1.85955 1.61803 1.27485 0.85156 0.37476 -0.12558 -0.61803 -1.07165 -1.45794 -1.75261 -1.93717 -2.00000 -1.93717 -1.75261 -1.45794 -1.07165 -0.61803 -0.12558 0.37476 0.85156 1.27485 1.61803 1.85955 1.98423 1.98423 1.85955 1.61803 1.27485 0.85156 0.37476 -0.12558 -0.61803 -1.07165 -1.45794 -1.75261 -1.93717 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u 2.00000 1.88875 1.56739 1.07165 0.45670 -0.20906 -0.85156 -1.39933 -1.79142 -1.98423 -1.95630 -1.71073 -1.27485 -0.69714 -0.04188 0.61803 1.20920 1.66584 1.93717 1.99299 1.82709 1.45794 0.92659 0.29217 -0.37476 -1.00000 -1.51399 -1.85955 -1.99825 -1.91464 -1.61803 -1.14143 -0.53784 0.12558 0.77503 1.33826 1.75261 1.97199 0.00000 -2.00000 -1.97199 -1.75261 -1.33826 -0.77503 -0.12558 0.53784 1.14143 1.61803 1.91464 1.99825 1.85955 1.51399 1.00000 0.37476 -0.29217 -0.92659 -1.45794 -1.82709 -1.99299 -1.93717 -1.66584 -1.20920 -0.61803 0.04188 0.69714 1.27485 1.71073 1.95630 1.98423 1.79142 1.39933 0.85156 0.20906 -0.45670 -1.07165 -1.56739 -1.88875 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5u 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 0.00000 -2.00000 1.95630 1.61803 1.00000 0.20906 -0.61803 -1.33826 -1.82709 -2.00000 -1.82709 -1.33826 -0.61803 0.20906 1.00000 1.61803 1.95630 1.95630 1.61803 1.00000 0.20906 -0.61803 -1.33826 -1.82709 -2.00000 -1.82709 -1.33826 -0.61803 0.20906 1.00000 1.61803 1.95630 1.95630 1.61803 1.00000 0.20906 -0.61803 -1.33826 -1.82709 0.00000 ... ... ..... ....... ......... TT......... ............. E6u 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 1.93717 1.45794 0.61803 -0.37476 -1.27485 -1.85955 -1.98423 -1.61803 -0.85156 0.12558 1.07165 1.75261 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 0.00000 -2.00000 -1.93717 -1.45794 -0.61803 0.37476 1.27485 1.85955 1.98423 1.61803 0.85156 -0.12558 -1.07165 -1.75261 -2.00000 -1.75261 -1.07165 -0.12558 0.85156 1.61803 1.98423 1.85955 1.27485 0.37476 -0.61803 -1.45794 -1.93717 -1.93717 -1.45794 -0.61803 0.37476 1.27485 1.85955 1.98423 1.61803 0.85156 -0.12558 -1.07165 -1.75261 0.00000 ... ... ..... ....... ......... ........... ............. E7u 2.00000 1.66584 0.77503 -0.37476 -1.39933 -1.95630 -1.85955 -1.14143 -0.04188 1.07165 1.82709 1.97199 1.45794 0.45670 -0.69714 -1.61803 -1.99825 -1.71073 -0.85156 0.29217 1.33826 1.93717 1.88875 1.20920 0.12558 -1.00000 -1.79142 -1.98423 -1.51399 -0.53784 0.61803 1.56739 1.99299 1.75261 0.92659 -0.20906 -1.27485 -1.91464 0.00000 -2.00000 1.91464 1.27485 0.20906 -0.92659 -1.75261 -1.99299 -1.56739 -0.61803 0.53784 1.51399 1.98423 1.79142 1.00000 -0.12558 -1.20920 -1.88875 -1.93717 -1.33826 -0.29217 0.85156 1.71073 1.99825 1.61803 0.69714 -0.45670 -1.45794 -1.97199 -1.82709 -1.07165 0.04188 1.14143 1.85955 1.95630 1.39933 0.37476 -0.77503 -1.66584 0.00000 ... ... ..... ....... ......... ........... ............. E8u 2.00000 1.56739 0.45670 -0.85156 -1.79142 -1.95630 -1.27485 -0.04188 1.20920 1.93717 1.82709 0.92659 -0.37476 -1.51399 -1.99825 -1.61803 -0.53784 0.77503 1.75261 1.97199 1.33826 0.12558 -1.14143 -1.91464 -1.85955 -1.00000 0.29217 1.45794 1.99299 1.66584 0.61803 -0.69714 -1.71073 -1.98423 -1.39933 -0.20906 1.07165 1.88875 0.00000 -2.00000 -1.88875 -1.07165 0.20906 1.39933 1.98423 1.71073 0.69714 -0.61803 -1.66584 -1.99299 -1.45794 -0.29217 1.00000 1.85955 1.91464 1.14143 -0.12558 -1.33826 -1.97199 -1.75261 -0.77503 0.53784 1.61803 1.99825 1.51399 0.37476 -0.92659 -1.82709 -1.93717 -1.20920 0.04188 1.27485 1.95630 1.79142 0.85156 -0.45670 -1.56739 0.00000 ... ... ..... ....... ......... ........... ............. E9u 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 -1.85955 -0.85156 0.61803 1.75261 1.93717 1.07165 -0.37476 -1.61803 -1.98423 -1.27485 0.12558 1.45794 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 0.00000 -2.00000 1.85955 0.85156 -0.61803 -1.75261 -1.93717 -1.07165 0.37476 1.61803 1.98423 1.27485 -0.12558 -1.45794 -2.00000 -1.45794 -0.12558 1.27485 1.98423 1.61803 0.37476 -1.07165 -1.93717 -1.75261 -0.61803 0.85156 1.85955 1.85955 0.85156 -0.61803 -1.75261 -1.93717 -1.07165 0.37476 1.61803 1.98423 1.27485 -0.12558 -1.45794 0.00000 ... ... ..... ....... ......... ........... ............. E10u 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 0.00000 -2.00000 -1.82709 -0.61803 1.00000 1.95630 1.61803 0.20906 -1.33826 -2.00000 -1.33826 0.20906 1.61803 1.95630 1.00000 -0.61803 -1.82709 -1.82709 -0.61803 1.00000 1.95630 1.61803 0.20906 -1.33826 -2.00000 -1.33826 0.20906 1.61803 1.95630 1.00000 -0.61803 -1.82709 -1.82709 -0.61803 1.00000 1.95630 1.61803 0.20906 -1.33826 0.00000 ... ... ..... ....... ......... ........... ............. E11u 2.00000 1.20920 -0.53784 -1.85955 -1.71073 -0.20906 1.45794 1.97199 0.92659 -0.85156 -1.95630 -1.51399 0.12558 1.66584 1.88875 0.61803 -1.14143 -1.99825 -1.27485 0.45670 1.82709 1.75261 0.29217 -1.39933 -1.98423 -1.00000 0.77503 1.93717 1.56739 -0.04188 -1.61803 -1.91464 -0.69714 1.07165 1.99299 1.33826 -0.37476 -1.79142 0.00000 -2.00000 1.79142 0.37476 -1.33826 -1.99299 -1.07165 0.69714 1.91464 1.61803 0.04188 -1.56739 -1.93717 -0.77503 1.00000 1.98423 1.39933 -0.29217 -1.75261 -1.82709 -0.45670 1.27485 1.99825 1.14143 -0.61803 -1.88875 -1.66584 -0.12558 1.51399 1.95630 0.85156 -0.92659 -1.97199 -1.45794 0.20906 1.71073 1.85955 0.53784 -1.20920 0.00000 ... ... ..... ....... ......... ........... ............. E12u 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 1.75261 0.12558 -1.61803 -1.85955 -0.37476 1.45794 1.93717 0.61803 -1.27485 -1.98423 -0.85156 1.07165 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 0.00000 -2.00000 -1.75261 -0.12558 1.61803 1.85955 0.37476 -1.45794 -1.93717 -0.61803 1.27485 1.98423 0.85156 -1.07165 -2.00000 -1.07165 0.85156 1.98423 1.27485 -0.61803 -1.93717 -1.45794 0.37476 1.85955 1.61803 -0.12558 -1.75261 -1.75261 -0.12558 1.61803 1.85955 0.37476 -1.45794 -1.93717 -0.61803 1.27485 1.98423 0.85156 -1.07165 0.00000 ... ... ..... ....... ......... ........... ............. E13u 2.00000 0.92659 -1.14143 -1.98423 -0.69714 1.33826 1.93717 0.45670 -1.51399 -1.85955 -0.20906 1.66584 1.75261 -0.04188 -1.79142 -1.61803 0.29217 1.88875 1.45794 -0.53784 -1.95630 -1.27485 0.77503 1.99299 1.07165 -1.00000 -1.99825 -0.85156 1.20920 1.97199 0.61803 -1.39933 -1.91464 -0.37476 1.56739 1.82709 0.12558 -1.71073 0.00000 -2.00000 1.71073 -0.12558 -1.82709 -1.56739 0.37476 1.91464 1.39933 -0.61803 -1.97199 -1.20920 0.85156 1.99825 1.00000 -1.07165 -1.99299 -0.77503 1.27485 1.95630 0.53784 -1.45794 -1.88875 -0.29217 1.61803 1.79142 0.04188 -1.75261 -1.66584 0.20906 1.85955 1.51399 -0.45670 -1.93717 -1.33826 0.69714 1.98423 1.14143 -0.92659 0.00000 ... ... ..... ....... ......... ........... ............. E14u 2.00000 0.77503 -1.39933 -1.85955 -0.04188 1.82709 1.45794 -0.69714 -1.99825 -0.85156 1.33826 1.88875 0.12558 -1.79142 -1.51399 0.61803 1.99299 0.92659 -1.27485 -1.91464 -0.20906 1.75261 1.56739 -0.53784 -1.98423 -1.00000 1.20920 1.93717 0.29217 -1.71073 -1.61803 0.45670 1.97199 1.07165 -1.14143 -1.95630 -0.37476 1.66584 0.00000 -2.00000 -1.66584 0.37476 1.95630 1.14143 -1.07165 -1.97199 -0.45670 1.61803 1.71073 -0.29217 -1.93717 -1.20920 1.00000 1.98423 0.53784 -1.56739 -1.75261 0.20906 1.91464 1.27485 -0.92659 -1.99299 -0.61803 1.51399 1.79142 -0.12558 -1.88875 -1.33826 0.85156 1.99825 0.69714 -1.45794 -1.82709 0.04188 1.85955 1.39933 -0.77503 0.00000 ... ... ..... ....... ......... ........... ............. E15u 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 0.00000 -2.00000 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 0.00000 ... ... ..... ....... ......... ........... ............. E16u 2.00000 0.45670 -1.79142 -1.27485 1.20920 1.82709 -0.37476 -1.99825 -0.53784 1.75261 1.33826 -1.14143 -1.85955 0.29217 1.99299 0.61803 -1.71073 -1.39933 1.07165 1.88875 -0.20906 -1.98423 -0.69714 1.66584 1.45794 -1.00000 -1.91464 0.12558 1.97199 0.77503 -1.61803 -1.51399 0.92659 1.93717 -0.04188 -1.95630 -0.85156 1.56739 0.00000 -2.00000 -1.56739 0.85156 1.95630 0.04188 -1.93717 -0.92659 1.51399 1.61803 -0.77503 -1.97199 -0.12558 1.91464 1.00000 -1.45794 -1.66584 0.69714 1.98423 0.20906 -1.88875 -1.07165 1.39933 1.71073 -0.61803 -1.99299 -0.29217 1.85955 1.14143 -1.33826 -1.75261 0.53784 1.99825 0.37476 -1.82709 -1.20920 1.27485 1.79142 -0.45670 0.00000 ... ... ..... ....... ......... ........... ............. E17u 2.00000 0.29217 -1.91464 -0.85156 1.66584 1.33826 -1.27485 -1.71073 0.77503 1.93717 -0.20906 -1.99825 -0.37476 1.88875 0.92659 -1.61803 -1.39933 1.20920 1.75261 -0.69714 -1.95630 0.12558 1.99299 0.45670 -1.85955 -1.00000 1.56739 1.45794 -1.14143 -1.79142 0.61803 1.97199 -0.04188 -1.98423 -0.53784 1.82709 1.07165 -1.51399 0.00000 -2.00000 1.51399 -1.07165 -1.82709 0.53784 1.98423 0.04188 -1.97199 -0.61803 1.79142 1.14143 -1.45794 -1.56739 1.00000 1.85955 -0.45670 -1.99299 -0.12558 1.95630 0.69714 -1.75261 -1.20920 1.39933 1.61803 -0.92659 -1.88875 0.37476 1.99825 0.20906 -1.93717 -0.77503 1.71073 1.27485 -1.33826 -1.66584 0.85156 1.91464 -0.29217 0.00000 ... ... ..... ....... ......... ........... ............. E18u 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 1.45794 -1.27485 -1.61803 1.07165 1.75261 -0.85156 -1.85955 0.61803 1.93717 -0.37476 -1.98423 0.12558 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 0.00000 -2.00000 -1.45794 1.27485 1.61803 -1.07165 -1.75261 0.85156 1.85955 -0.61803 -1.93717 0.37476 1.98423 -0.12558 -2.00000 -0.12558 1.98423 0.37476 -1.93717 -0.61803 1.85955 0.85156 -1.75261 -1.07165 1.61803 1.27485 -1.45794 -1.45794 1.27485 1.61803 -1.07165 -1.75261 0.85156 1.85955 -0.61803 -1.93717 0.37476 1.98423 -0.12558 0.00000 ... ... ..... ....... ......... ........... ............. E19u 2.00000 -0.04188 -1.99825 0.12558 1.99299 -0.20906 -1.98423 0.29217 1.97199 -0.37476 -1.95630 0.45670 1.93717 -0.53784 -1.91464 0.61803 1.88875 -0.69714 -1.85955 0.77503 1.82709 -0.85156 -1.79142 0.92659 1.75261 -1.00000 -1.71073 1.07165 1.66584 -1.14143 -1.61803 1.20920 1.56739 -1.27485 -1.51399 1.33826 1.45794 -1.39933 0.00000 -2.00000 1.39933 -1.45794 -1.33826 1.51399 1.27485 -1.56739 -1.20920 1.61803 1.14143 -1.66584 -1.07165 1.71073 1.00000 -1.75261 -0.92659 1.79142 0.85156 -1.82709 -0.77503 1.85955 0.69714 -1.88875 -0.61803 1.91464 0.53784 -1.93717 -0.45670 1.95630 0.37476 -1.97199 -0.29217 1.98423 0.20906 -1.99299 -0.12558 1.99825 0.04188 0.00000 ... ... ..... ....... ......... ........... ............. E20u 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 0.00000 -2.00000 -1.33826 1.61803 1.00000 -1.82709 -0.61803 1.95630 0.20906 -2.00000 0.20906 1.95630 -0.61803 -1.82709 1.00000 1.61803 -1.33826 -1.33826 1.61803 1.00000 -1.82709 -0.61803 1.95630 0.20906 -2.00000 0.20906 1.95630 -0.61803 -1.82709 1.00000 1.61803 -1.33826 -1.33826 1.61803 1.00000 -1.82709 -0.61803 1.95630 0.20906 0.00000 ... ... ..... ....... ......... ........... ............. E21u 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 -1.27485 1.75261 0.61803 -1.98423 0.12558 1.93717 -0.85156 -1.61803 1.45794 1.07165 -1.85955 -0.37476 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 0.00000 -2.00000 1.27485 -1.75261 -0.61803 1.98423 -0.12558 -1.93717 0.85156 1.61803 -1.45794 -1.07165 1.85955 0.37476 -2.00000 0.37476 1.85955 -1.07165 -1.45794 1.61803 0.85156 -1.93717 -0.12558 1.98423 -0.61803 -1.75261 1.27485 1.27485 -1.75261 -0.61803 1.98423 -0.12558 -1.93717 0.85156 1.61803 -1.45794 -1.07165 1.85955 0.37476 0.00000 ... ... ..... ....... ......... ........... ............. E22u 2.00000 -0.53784 -1.71073 1.45794 0.92659 -1.95630 0.12558 1.88875 -1.14143 -1.27485 1.82709 0.29217 -1.98423 0.77503 1.56739 -1.61803 -0.69714 1.99299 -0.37476 -1.79142 1.33826 1.07165 -1.91464 -0.04188 1.93717 -1.00000 -1.39933 1.75261 0.45670 -1.99825 0.61803 1.66584 -1.51399 -0.85156 1.97199 -0.20906 -1.85955 1.20920 0.00000 -2.00000 -1.20920 1.85955 0.20906 -1.97199 0.85156 1.51399 -1.66584 -0.61803 1.99825 -0.45670 -1.75261 1.39933 1.00000 -1.93717 0.04188 1.91464 -1.07165 -1.33826 1.79142 0.37476 -1.99299 0.69714 1.61803 -1.56739 -0.77503 1.98423 -0.29217 -1.82709 1.27485 1.14143 -1.88875 -0.12558 1.95630 -0.92659 -1.45794 1.71073 0.53784 0.00000 ... ... ..... ....... ......... ........... ............. E23u 2.00000 -0.69714 -1.51399 1.75261 0.29217 -1.95630 1.07165 1.20920 -1.91464 0.12558 1.82709 -1.39933 -0.85156 1.99299 -0.53784 -1.61803 1.66584 0.45670 -1.98423 0.92659 1.33826 -1.85955 -0.04188 1.88875 -1.27485 -1.00000 1.97199 -0.37476 -1.71073 1.56739 0.61803 -1.99825 0.77503 1.45794 -1.79142 -0.20906 1.93717 -1.14143 0.00000 -2.00000 1.14143 -1.93717 0.20906 1.79142 -1.45794 -0.77503 1.99825 -0.61803 -1.56739 1.71073 0.37476 -1.97199 1.00000 1.27485 -1.88875 0.04188 1.85955 -1.33826 -0.92659 1.98423 -0.45670 -1.66584 1.61803 0.53784 -1.99299 0.85156 1.39933 -1.82709 -0.12558 1.91464 -1.20920 -1.07165 1.95630 -0.29217 -1.75261 1.51399 0.69714 0.00000 ... ... ..... ....... ......... ........... ............. E24u 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 1.07165 -1.98423 0.61803 1.45794 -1.85955 0.12558 1.75261 -1.61803 -0.37476 1.93717 -1.27485 -0.85156 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 0.00000 -2.00000 -1.07165 1.98423 -0.61803 -1.45794 1.85955 -0.12558 -1.75261 1.61803 0.37476 -1.93717 1.27485 0.85156 -2.00000 0.85156 1.27485 -1.93717 0.37476 1.61803 -1.75261 -0.12558 1.85955 -1.45794 -0.61803 1.98423 -1.07165 -1.07165 1.98423 -0.61803 -1.45794 1.85955 -0.12558 -1.75261 1.61803 0.37476 -1.93717 1.27485 0.85156 0.00000 ... ... ..... ....... ......... ........... ............. E25u 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 0.00000 -2.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E26u 2.00000 -1.14143 -0.69714 1.93717 -1.51399 -0.20906 1.75261 -1.79142 0.29217 1.45794 -1.95630 0.77503 1.07165 -1.99825 1.20920 0.61803 -1.91464 1.56739 0.12558 -1.71073 1.82709 -0.37476 -1.39933 1.97199 -0.85156 -1.00000 1.99299 -1.27485 -0.53784 1.88875 -1.61803 -0.04188 1.66584 -1.85955 0.45670 1.33826 -1.98423 0.92659 0.00000 -2.00000 -0.92659 1.98423 -1.33826 -0.45670 1.85955 -1.66584 0.04188 1.61803 -1.88875 0.53784 1.27485 -1.99299 1.00000 0.85156 -1.97199 1.39933 0.37476 -1.82709 1.71073 -0.12558 -1.56739 1.91464 -0.61803 -1.20920 1.99825 -1.07165 -0.77503 1.95630 -1.45794 -0.29217 1.79142 -1.75261 0.20906 1.51399 -1.93717 0.69714 1.14143 0.00000 ... ... ..... ....... ......... ........... ............. E27u 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 -0.85156 1.93717 -1.61803 0.12558 1.45794 -1.98423 1.07165 0.61803 -1.85955 1.75261 -0.37476 -1.27485 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 0.00000 -2.00000 0.85156 -1.93717 1.61803 -0.12558 -1.45794 1.98423 -1.07165 -0.61803 1.85955 -1.75261 0.37476 1.27485 -2.00000 1.27485 0.37476 -1.75261 1.85955 -0.61803 -1.07165 1.98423 -1.45794 -0.12558 1.61803 -1.93717 0.85156 0.85156 -1.93717 1.61803 -0.12558 -1.45794 1.98423 -1.07165 -0.61803 1.85955 -1.75261 0.37476 1.27485 0.00000 ... ... ..... ....... ......... ........... ............. E28u 2.00000 -1.39933 -0.04188 1.45794 -1.99825 1.33826 0.12558 -1.51399 1.99299 -1.27485 -0.20906 1.56739 -1.98423 1.20920 0.29217 -1.61803 1.97199 -1.14143 -0.37476 1.66584 -1.95630 1.07165 0.45670 -1.71073 1.93717 -1.00000 -0.53784 1.75261 -1.91464 0.92659 0.61803 -1.79142 1.88875 -0.85156 -0.69714 1.82709 -1.85955 0.77503 0.00000 -2.00000 -0.77503 1.85955 -1.82709 0.69714 0.85156 -1.88875 1.79142 -0.61803 -0.92659 1.91464 -1.75261 0.53784 1.00000 -1.93717 1.71073 -0.45670 -1.07165 1.95630 -1.66584 0.37476 1.14143 -1.97199 1.61803 -0.29217 -1.20920 1.98423 -1.56739 0.20906 1.27485 -1.99299 1.51399 -0.12558 -1.33826 1.99825 -1.45794 0.04188 1.39933 0.00000 ... ... ..... ....... ......... ........... ............. E29u 2.00000 -1.51399 0.29217 1.07165 -1.91464 1.82709 -0.85156 -0.53784 1.66584 -1.98423 1.33826 -0.04188 -1.27485 1.97199 -1.71073 0.61803 0.77503 -1.79142 1.93717 -1.14143 -0.20906 1.45794 -1.99825 1.56739 -0.37476 -1.00000 1.88875 -1.85955 0.92659 0.45670 -1.61803 1.99299 -1.39933 0.12558 1.20920 -1.95630 1.75261 -0.69714 0.00000 -2.00000 0.69714 -1.75261 1.95630 -1.20920 -0.12558 1.39933 -1.99299 1.61803 -0.45670 -0.92659 1.85955 -1.88875 1.00000 0.37476 -1.56739 1.99825 -1.45794 0.20906 1.14143 -1.93717 1.79142 -0.77503 -0.61803 1.71073 -1.97199 1.27485 0.04188 -1.33826 1.98423 -1.66584 0.53784 0.85156 -1.82709 1.91464 -1.07165 -0.29217 1.51399 0.00000 ... ... ..... ....... ......... ........... ............. E30u 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.00000 -2.00000 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 0.00000 ... ... ..... ....... ......... ........... ............. E31u 2.00000 -1.71073 0.92659 0.12558 -1.14143 1.82709 -1.98423 1.56739 -0.69714 -0.37476 1.33826 -1.91464 1.93717 -1.39933 0.45670 0.61803 -1.51399 1.97199 -1.85955 1.20920 -0.20906 -0.85156 1.66584 -1.99825 1.75261 -1.00000 -0.04188 1.07165 -1.79142 1.99299 -1.61803 0.77503 0.29217 -1.27485 1.88875 -1.95630 1.45794 -0.53784 0.00000 -2.00000 0.53784 -1.45794 1.95630 -1.88875 1.27485 -0.29217 -0.77503 1.61803 -1.99299 1.79142 -1.07165 0.04188 1.00000 -1.75261 1.99825 -1.66584 0.85156 0.20906 -1.20920 1.85955 -1.97199 1.51399 -0.61803 -0.45670 1.39933 -1.93717 1.91464 -1.33826 0.37476 0.69714 -1.56739 1.98423 -1.82709 1.14143 -0.12558 -0.92659 1.71073 0.00000 ... ... ..... ....... ......... ........... ............. E32u 2.00000 -1.79142 1.20920 -0.37476 -0.53784 1.33826 -1.85955 1.99299 -1.71073 1.07165 -0.20906 -0.69714 1.45794 -1.91464 1.97199 -1.61803 0.92659 -0.04188 -0.85156 1.56739 -1.95630 1.93717 -1.51399 0.77503 0.12558 -1.00000 1.66584 -1.98423 1.88875 -1.39933 0.61803 0.29217 -1.14143 1.75261 -1.99825 1.82709 -1.27485 0.45670 0.00000 -2.00000 -0.45670 1.27485 -1.82709 1.99825 -1.75261 1.14143 -0.29217 -0.61803 1.39933 -1.88875 1.98423 -1.66584 1.00000 -0.12558 -0.77503 1.51399 -1.93717 1.95630 -1.56739 0.85156 0.04188 -0.92659 1.61803 -1.97199 1.91464 -1.45794 0.69714 0.20906 -1.07165 1.71073 -1.99299 1.85955 -1.33826 0.53784 0.37476 -1.20920 1.79142 0.00000 ... ... ..... ....... ......... ........... ............. E33u 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 -0.37476 1.07165 -1.61803 1.93717 -1.98423 1.75261 -1.27485 0.61803 0.12558 -0.85156 1.45794 -1.85955 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 0.00000 -2.00000 0.37476 -1.07165 1.61803 -1.93717 1.98423 -1.75261 1.27485 -0.61803 -0.12558 0.85156 -1.45794 1.85955 -2.00000 1.85955 -1.45794 0.85156 -0.12558 -0.61803 1.27485 -1.75261 1.98423 -1.93717 1.61803 -1.07165 0.37476 0.37476 -1.07165 1.61803 -1.93717 1.98423 -1.75261 1.27485 -0.61803 -0.12558 0.85156 -1.45794 1.85955 0.00000 ... ... ..... ....... ......... ........... ............. E34u 2.00000 -1.91464 1.66584 -1.27485 0.77503 -0.20906 -0.37476 0.92659 -1.39933 1.75261 -1.95630 1.99299 -1.85955 1.56739 -1.14143 0.61803 -0.04188 -0.53784 1.07165 -1.51399 1.82709 -1.98423 1.97199 -1.79142 1.45794 -1.00000 0.45670 0.12558 -0.69714 1.20920 -1.61803 1.88875 -1.99825 1.93717 -1.71073 1.33826 -0.85156 0.29217 0.00000 -2.00000 -0.29217 0.85156 -1.33826 1.71073 -1.93717 1.99825 -1.88875 1.61803 -1.20920 0.69714 -0.12558 -0.45670 1.00000 -1.45794 1.79142 -1.97199 1.98423 -1.82709 1.51399 -1.07165 0.53784 0.04188 -0.61803 1.14143 -1.56739 1.85955 -1.99299 1.95630 -1.75261 1.39933 -0.92659 0.37476 0.20906 -0.77503 1.27485 -1.66584 1.91464 0.00000 ... ... ..... ....... ......... ........... ............. E35u 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 0.00000 -2.00000 0.20906 -0.61803 1.00000 -1.33826 1.61803 -1.82709 1.95630 -2.00000 1.95630 -1.82709 1.61803 -1.33826 1.00000 -0.61803 0.20906 0.20906 -0.61803 1.00000 -1.33826 1.61803 -1.82709 1.95630 -2.00000 1.95630 -1.82709 1.61803 -1.33826 1.00000 -0.61803 0.20906 0.20906 -0.61803 1.00000 -1.33826 1.61803 -1.82709 1.95630 0.00000 ... ... ..... ....... ......... ........... ............. E36u 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 0.12558 -0.37476 0.61803 -0.85156 1.07165 -1.27485 1.45794 -1.61803 1.75261 -1.85955 1.93717 -1.98423 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 0.00000 -2.00000 -0.12558 0.37476 -0.61803 0.85156 -1.07165 1.27485 -1.45794 1.61803 -1.75261 1.85955 -1.93717 1.98423 -2.00000 1.98423 -1.93717 1.85955 -1.75261 1.61803 -1.45794 1.27485 -1.07165 0.85156 -0.61803 0.37476 -0.12558 -0.12558 0.37476 -0.61803 0.85156 -1.07165 1.27485 -1.45794 1.61803 -1.75261 1.85955 -1.93717 1.98423 0.00000 ... ... ..... ....... ......... ........... ............. E37u 2.00000 -1.99825 1.99299 -1.98423 1.97199 -1.95630 1.93717 -1.91464 1.88875 -1.85955 1.82709 -1.79142 1.75261 -1.71073 1.66584 -1.61803 1.56739 -1.51399 1.45794 -1.39933 1.33826 -1.27485 1.20920 -1.14143 1.07165 -1.00000 0.92659 -0.85156 0.77503 -0.69714 0.61803 -0.53784 0.45670 -0.37476 0.29217 -0.20906 0.12558 -0.04188 0.00000 -2.00000 0.04188 -0.12558 0.20906 -0.29217 0.37476 -0.45670 0.53784 -0.61803 0.69714 -0.77503 0.85156 -0.92659 1.00000 -1.07165 1.14143 -1.20920 1.27485 -1.33826 1.39933 -1.45794 1.51399 -1.56739 1.61803 -1.66584 1.71073 -1.75261 1.79142 -1.82709 1.85955 -1.88875 1.91464 -1.93717 1.95630 -1.97199 1.98423 -1.99299 1.99825 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.998245660198 = 2*cos(2*π/150) = 2*cos(π/75) 1.992985718499 = 2*cos(4*π/150) = 2*cos(2*π/75) 1.984229402629 = 2*cos(6*π/150) = 2*cos(π/25) 1.971992074141 = 2*cos(8*π/150) = 2*cos(4*π/75) 1.956295201468 = 2*cos(10*π/150) = 2*cos(π/15) = (√5−1+√30+6*√5)/4 1.937166322257 = 2*cos(12*π/150) = 2*cos(2*π/25) 1.914638995064 = 2*cos(14*π/150) = 2*cos(7*π/75) 1.888752740475 = 2*cos(16*π/150) = 2*cos(8*π/75) 1.859552971777 = 2*cos(18*π/150) = 2*cos(3*π/25) 1.827090915285 = 2*cos(20*π/150) = 2*cos(2*π/15) = (1+√5+√30−6*√5)/4 1.791423520479 = 2*cos(22*π/150) = 2*cos(11*π/75) 1.752613360088 = 2*cos(24*π/150) = 2*cos(4*π/25) 1.710728520321 = 2*cos(26*π/150) = 2*cos(13*π/75) 1.665842481420 = 2*cos(28*π/150) = 2*cos(14*π/75) 1.618033988750 = 2*cos(30*π/150) = 2*cos(π/5) = (√5+1)/2 1.567386914652 = 2*cos(32*π/150) = 2*cos(16*π/75) 1.513990111304 = 2*cos(34*π/150) = 2*cos(17*π/75) 1.457937254843 = 2*cos(36*π/150) = 2*cos(6*π/25) 1.399326681027 = 2*cos(38*π/150) = 2*cos(19*π/75) 1.338261212718 = 2*cos(40*π/150) = 2*cos(4*π/15) = (1−√5+√30+6*√5)/4 1.274847979497 = 2*cos(42*π/150) = 2*cos(7*π/25) 1.209198229725 = 2*cos(44*π/150) = 2*cos(22*π/75) 1.141427135369 = 2*cos(46*π/150) = 2*cos(23*π/75) 1.071653589958 = 2*cos(48*π/150) = 2*cos(8*π/25) 0.926592070240 = 2*cos(52*π/150) = 2*cos(26*π/75) 0.851558583130 = 2*cos(54*π/150) = 2*cos(9*π/25) 0.775031172904 = 2*cos(56*π/150) = 2*cos(28*π/75) 0.697144094644 = 2*cos(58*π/150) = 2*cos(29*π/75) 0.618033988750 = 2*cos(60*π/150) = 2*cos(2*π/5) = (√5−1)/2 0.537839641231 = 2*cos(62*π/150) = 2*cos(31*π/75) 0.456701740221 = 2*cos(64*π/150) = 2*cos(32*π/75) 0.374762629171 = 2*cos(66*π/150) = 2*cos(11*π/25) 0.292166057125 = 2*cos(68*π/150) = 2*cos(34*π/75) 0.209056926535 = 2*cos(70*π/150) = 2*cos(7*π/15) = (√30−6*√5−√5−1)/4 0.125581039059 = 2*cos(72*π/150) = 2*cos(12*π/25) 0.041884839767 = 2*cos(74*π/150) = 2*cos(37*π/75) Symmetry of Rotations and Cartesian products A1g d+g+i+k+m z², z⁴, z⁶ A2g R R_z E1g R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2g d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E3g g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4g g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5g i+k+m {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6g i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7g k+m E8g k+m E9g m E10g m A2u p+f+h+j+l z, z³, z⁵ E1u p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2u f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3u f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E4u h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5u h+j+l {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)} E6u j+l E7u j+l E8u l E9u l Notes: α The order of the D_75d point group is 300, and the order of the principal axis (S₁₅₀) is 150. The group has 78 irreducible representations. β The D_75d point group is isomorphic to D_75h, C_150v and D₁₅₀. γ The D_75d point group is generated by two symmetry elements, S₁₅₀ and either a perpendicular C₂^′ or a vertical σ_d. Also, the group may be generated from a C₂^′ plus a σ_d (some pairs will yield smaller groups, though; choosing a minimum angle is safe). The canonical choice, however, is to use redundant generators: C₇₅, C₂^′ and i. δ The group contains one set of C₂^′ symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set. Reversely, the single set of symmetry planes denoted σ_d contains the yz plane but not the xz plane. ε The lowest nonvanishing multipole moment in D_75d is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. η 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. For this group, however, some of the irrational characters cannot be expressed by a closed algebraic form using real numbers only.

This Character Table for the D_75d point group was created by Gernot Katzer.

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

	D_73d
	D_74d
C₇₅ C_75v C_75h D₇₅ D_75h	D_75d
	D_76d
	D_77d

Character table for the D75d point group

Character table for the D_75d point group