Character Table for Point Group C65h

Character table for the C_65h point group

C65h E 2 C65 2 C65^2 2 C65^3 2 C65^4 2 C13 2 C65^6 2 C65^7 2 C65^8 2 C65^9 2 C13^2 2 C65^11 2 C65^12 2 C5 2 C65^14 2 C13^3 2 C65^16 2 C65^17 2 C65^18 2 C65^19 2 C13^4 2 C65^21 2 C65^22 2 C65^23 2 C65^24 2 C13^5 2 C5^2 2 C65^27 2 C65^28 2 C65^29 2 C13^6 2 C65^31 2 C65^32 sh 2 S65 2 S65^3 2 S13 2 S65^7 2 S65^9 2 S65^11 2 S5 2 S13^3 2 S65^17 2 S65^19 2 S65^21 2 S65^23 2 S13^5 2 S65^27 2 S65^29 2 S65^31 2 S65^33 2 S13^7 2 S65^37 2 S5^3 2 S65^41 2 S65^43 2 S13^9 2 S65^47 2 S65^49 2 S65^51 2 S65^53 2 S13^11 2 S65^57 2 S65^59 2 S65^61 2 S65^63 <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 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 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 -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 ............. E1' * 2.00000 1.99066 1.96274 1.91649 1.85235 1.77091 1.67294 1.55935 1.43120 1.28968 1.13613 0.97197 0.79873 0.61803 0.43157 0.24107 0.04833 -0.14487 -0.33671 -0.52541 -0.70921 -0.88638 -1.05528 -1.21433 -1.36203 -1.49702 -1.61803 -1.72394 -1.81375 -1.88662 -1.94188 -1.97901 -1.99766 2.00000 1.99066 1.91649 1.77091 1.55935 1.28968 0.97197 0.61803 0.24107 -0.14487 -0.52541 -0.88638 -1.21433 -1.49702 -1.72394 -1.88662 -1.97901 -1.99766 -1.94188 -1.81375 -1.61803 -1.36203 -1.05528 -0.70921 -0.33671 0.04833 0.43157 0.79873 1.13613 1.43120 1.67294 1.85235 1.96274 ... TT. ..... ....TT. ......... ........TT. ............. E1" * 2.00000 1.99066 1.96274 1.91649 1.85235 1.77091 1.67294 1.55935 1.43120 1.28968 1.13613 0.97197 0.79873 0.61803 0.43157 0.24107 0.04833 -0.14487 -0.33671 -0.52541 -0.70921 -0.88638 -1.05528 -1.21433 -1.36203 -1.49702 -1.61803 -1.72394 -1.81375 -1.88662 -1.94188 -1.97901 -1.99766 -2.00000 -1.99066 -1.91649 -1.77091 -1.55935 -1.28968 -0.97197 -0.61803 -0.24107 0.14487 0.52541 0.88638 1.21433 1.49702 1.72394 1.88662 1.97901 1.99766 1.94188 1.81375 1.61803 1.36203 1.05528 0.70921 0.33671 -0.04833 -0.43157 -0.79873 -1.13613 -1.43120 -1.67294 -1.85235 -1.96274 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2' * 2.00000 1.96274 1.85235 1.67294 1.43120 1.13613 0.79873 0.43157 0.04833 -0.33671 -0.70921 -1.05528 -1.36203 -1.61803 -1.81375 -1.94188 -1.99766 -1.97901 -1.88662 -1.72394 -1.49702 -1.21433 -0.88638 -0.52541 -0.14487 0.24107 0.61803 0.97197 1.28968 1.55935 1.77091 1.91649 1.99066 2.00000 1.96274 1.67294 1.13613 0.43157 -0.33671 -1.05528 -1.61803 -1.94188 -1.97901 -1.72394 -1.21433 -0.52541 0.24107 0.97197 1.55935 1.91649 1.99066 1.77091 1.28968 0.61803 -0.14487 -0.88638 -1.49702 -1.88662 -1.99766 -1.81375 -1.36203 -0.70921 0.04833 0.79873 1.43120 1.85235 ... ... TT... ....... ....TT... ........... ........TT... E2" * 2.00000 1.96274 1.85235 1.67294 1.43120 1.13613 0.79873 0.43157 0.04833 -0.33671 -0.70921 -1.05528 -1.36203 -1.61803 -1.81375 -1.94188 -1.99766 -1.97901 -1.88662 -1.72394 -1.49702 -1.21433 -0.88638 -0.52541 -0.14487 0.24107 0.61803 0.97197 1.28968 1.55935 1.77091 1.91649 1.99066 -2.00000 -1.96274 -1.67294 -1.13613 -0.43157 0.33671 1.05528 1.61803 1.94188 1.97901 1.72394 1.21433 0.52541 -0.24107 -0.97197 -1.55935 -1.91649 -1.99066 -1.77091 -1.28968 -0.61803 0.14487 0.88638 1.49702 1.88662 1.99766 1.81375 1.36203 0.70921 -0.04833 -0.79873 -1.43120 -1.85235 ... ... ..... ..TT... ......... ......TT... ............. E3' * 2.00000 1.91649 1.67294 1.28968 0.79873 0.24107 -0.33671 -0.88638 -1.36203 -1.72394 -1.94188 -1.99766 -1.88662 -1.61803 -1.21433 -0.70921 -0.14487 0.43157 0.97197 1.43120 1.77091 1.96274 1.99066 1.85235 1.55935 1.13613 0.61803 0.04833 -0.52541 -1.05528 -1.49702 -1.81375 -1.97901 2.00000 1.91649 1.28968 0.24107 -0.88638 -1.72394 -1.99766 -1.61803 -0.70921 0.43157 1.43120 1.96274 1.85235 1.13613 0.04833 -1.05528 -1.81375 -1.97901 -1.49702 -0.52541 0.61803 1.55935 1.99066 1.77091 0.97197 -0.14487 -1.21433 -1.88662 -1.94188 -1.36203 -0.33671 0.79873 1.67294 ... ... ..... TT..... ......... ....TT..... ............. E3" * 2.00000 1.91649 1.67294 1.28968 0.79873 0.24107 -0.33671 -0.88638 -1.36203 -1.72394 -1.94188 -1.99766 -1.88662 -1.61803 -1.21433 -0.70921 -0.14487 0.43157 0.97197 1.43120 1.77091 1.96274 1.99066 1.85235 1.55935 1.13613 0.61803 0.04833 -0.52541 -1.05528 -1.49702 -1.81375 -1.97901 -2.00000 -1.91649 -1.28968 -0.24107 0.88638 1.72394 1.99766 1.61803 0.70921 -0.43157 -1.43120 -1.96274 -1.85235 -1.13613 -0.04833 1.05528 1.81375 1.97901 1.49702 0.52541 -0.61803 -1.55935 -1.99066 -1.77091 -0.97197 0.14487 1.21433 1.88662 1.94188 1.36203 0.33671 -0.79873 -1.67294 ... ... ..... ....... ..TT..... ........... ......TT..... E4' * 2.00000 1.85235 1.43120 0.79873 0.04833 -0.70921 -1.36203 -1.81375 -1.99766 -1.88662 -1.49702 -0.88638 -0.14487 0.61803 1.28968 1.77091 1.99066 1.91649 1.55935 0.97197 0.24107 -0.52541 -1.21433 -1.72394 -1.97901 -1.94188 -1.61803 -1.05528 -0.33671 0.43157 1.13613 1.67294 1.96274 2.00000 1.85235 0.79873 -0.70921 -1.81375 -1.88662 -0.88638 0.61803 1.77091 1.91649 0.97197 -0.52541 -1.72394 -1.94188 -1.05528 0.43157 1.67294 1.96274 1.13613 -0.33671 -1.61803 -1.97901 -1.21433 0.24107 1.55935 1.99066 1.28968 -0.14487 -1.49702 -1.99766 -1.36203 0.04833 1.43120 ... ... ..... ....... TT....... ........... ....TT....... E4" * 2.00000 1.85235 1.43120 0.79873 0.04833 -0.70921 -1.36203 -1.81375 -1.99766 -1.88662 -1.49702 -0.88638 -0.14487 0.61803 1.28968 1.77091 1.99066 1.91649 1.55935 0.97197 0.24107 -0.52541 -1.21433 -1.72394 -1.97901 -1.94188 -1.61803 -1.05528 -0.33671 0.43157 1.13613 1.67294 1.96274 -2.00000 -1.85235 -0.79873 0.70921 1.81375 1.88662 0.88638 -0.61803 -1.77091 -1.91649 -0.97197 0.52541 1.72394 1.94188 1.05528 -0.43157 -1.67294 -1.96274 -1.13613 0.33671 1.61803 1.97901 1.21433 -0.24107 -1.55935 -1.99066 -1.28968 0.14487 1.49702 1.99766 1.36203 -0.04833 -1.43120 ... ... ..... ....... ......... ..TT....... ............. E5' * 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 2.00000 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 ... ... ..... ....... ......... TT......... ............. E5" * 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -2.00000 -1.77091 -0.24107 1.49702 1.94188 0.70921 -1.13613 -2.00000 -1.13613 0.70921 1.94188 1.49702 -0.24107 -1.77091 -1.77091 -0.24107 1.49702 1.94188 0.70921 -1.13613 -2.00000 -1.13613 0.70921 1.94188 1.49702 -0.24107 -1.77091 -1.77091 -0.24107 1.49702 1.94188 0.70921 -1.13613 ... ... ..... ....... ......... ........... ..TT......... E6' * 2.00000 1.67294 0.79873 -0.33671 -1.36203 -1.94188 -1.88662 -1.21433 -0.14487 0.97197 1.77091 1.99066 1.55935 0.61803 -0.52541 -1.49702 -1.97901 -1.81375 -1.05528 0.04833 1.13613 1.85235 1.96274 1.43120 0.43157 -0.70921 -1.61803 -1.99766 -1.72394 -0.88638 0.24107 1.28968 1.91649 2.00000 1.67294 -0.33671 -1.94188 -1.21433 0.97197 1.99066 0.61803 -1.49702 -1.81375 0.04833 1.85235 1.43120 -0.70921 -1.99766 -0.88638 1.28968 1.91649 0.24107 -1.72394 -1.61803 0.43157 1.96274 1.13613 -1.05528 -1.97901 -0.52541 1.55935 1.77091 -0.14487 -1.88662 -1.36203 0.79873 ... ... ..... ....... ......... ........... TT........... E6" * 2.00000 1.67294 0.79873 -0.33671 -1.36203 -1.94188 -1.88662 -1.21433 -0.14487 0.97197 1.77091 1.99066 1.55935 0.61803 -0.52541 -1.49702 -1.97901 -1.81375 -1.05528 0.04833 1.13613 1.85235 1.96274 1.43120 0.43157 -0.70921 -1.61803 -1.99766 -1.72394 -0.88638 0.24107 1.28968 1.91649 -2.00000 -1.67294 0.33671 1.94188 1.21433 -0.97197 -1.99066 -0.61803 1.49702 1.81375 -0.04833 -1.85235 -1.43120 0.70921 1.99766 0.88638 -1.28968 -1.91649 -0.24107 1.72394 1.61803 -0.43157 -1.96274 -1.13613 1.05528 1.97901 0.52541 -1.55935 -1.77091 0.14487 1.88662 1.36203 -0.79873 ... ... ..... ....... ......... ........... ............. E7' * 2.00000 1.55935 0.43157 -0.88638 -1.81375 -1.94188 -1.21433 0.04833 1.28968 1.96274 1.77091 0.79873 -0.52541 -1.61803 -1.99766 -1.49702 -0.33671 0.97197 1.85235 1.91649 1.13613 -0.14487 -1.36203 -1.97901 -1.72394 -0.70921 0.61803 1.67294 1.99066 1.43120 0.24107 -1.05528 -1.88662 2.00000 1.55935 -0.88638 -1.94188 0.04833 1.96274 0.79873 -1.61803 -1.49702 0.97197 1.91649 -0.14487 -1.97901 -0.70921 1.67294 1.43120 -1.05528 -1.88662 0.24107 1.99066 0.61803 -1.72394 -1.36203 1.13613 1.85235 -0.33671 -1.99766 -0.52541 1.77091 1.28968 -1.21433 -1.81375 0.43157 ... ... ..... ....... ......... ........... ............. E7" * 2.00000 1.55935 0.43157 -0.88638 -1.81375 -1.94188 -1.21433 0.04833 1.28968 1.96274 1.77091 0.79873 -0.52541 -1.61803 -1.99766 -1.49702 -0.33671 0.97197 1.85235 1.91649 1.13613 -0.14487 -1.36203 -1.97901 -1.72394 -0.70921 0.61803 1.67294 1.99066 1.43120 0.24107 -1.05528 -1.88662 -2.00000 -1.55935 0.88638 1.94188 -0.04833 -1.96274 -0.79873 1.61803 1.49702 -0.97197 -1.91649 0.14487 1.97901 0.70921 -1.67294 -1.43120 1.05528 1.88662 -0.24107 -1.99066 -0.61803 1.72394 1.36203 -1.13613 -1.85235 0.33671 1.99766 0.52541 -1.77091 -1.28968 1.21433 1.81375 -0.43157 ... ... ..... ....... ......... ........... ............. E8' * 2.00000 1.43120 0.04833 -1.36203 -1.99766 -1.49702 -0.14487 1.28968 1.99066 1.55935 0.24107 -1.21433 -1.97901 -1.61803 -0.33671 1.13613 1.96274 1.67294 0.43157 -1.05528 -1.94188 -1.72394 -0.52541 0.97197 1.91649 1.77091 0.61803 -0.88638 -1.88662 -1.81375 -0.70921 0.79873 1.85235 2.00000 1.43120 -1.36203 -1.49702 1.28968 1.55935 -1.21433 -1.61803 1.13613 1.67294 -1.05528 -1.72394 0.97197 1.77091 -0.88638 -1.81375 0.79873 1.85235 -0.70921 -1.88662 0.61803 1.91649 -0.52541 -1.94188 0.43157 1.96274 -0.33671 -1.97901 0.24107 1.99066 -0.14487 -1.99766 0.04833 ... ... ..... ....... ......... ........... ............. E8" * 2.00000 1.43120 0.04833 -1.36203 -1.99766 -1.49702 -0.14487 1.28968 1.99066 1.55935 0.24107 -1.21433 -1.97901 -1.61803 -0.33671 1.13613 1.96274 1.67294 0.43157 -1.05528 -1.94188 -1.72394 -0.52541 0.97197 1.91649 1.77091 0.61803 -0.88638 -1.88662 -1.81375 -0.70921 0.79873 1.85235 -2.00000 -1.43120 1.36203 1.49702 -1.28968 -1.55935 1.21433 1.61803 -1.13613 -1.67294 1.05528 1.72394 -0.97197 -1.77091 0.88638 1.81375 -0.79873 -1.85235 0.70921 1.88662 -0.61803 -1.91649 0.52541 1.94188 -0.43157 -1.96274 0.33671 1.97901 -0.24107 -1.99066 0.14487 1.99766 -0.04833 ... ... ..... ....... ......... ........... ............. E9' * 2.00000 1.28968 -0.33671 -1.72394 -1.88662 -0.70921 0.97197 1.96274 1.55935 0.04833 -1.49702 -1.97901 -1.05528 0.61803 1.85235 1.77091 0.43157 -1.21433 -1.99766 -1.36203 0.24107 1.67294 1.91649 0.79873 -0.88638 -1.94188 -1.61803 -0.14487 1.43120 1.99066 1.13613 -0.52541 -1.81375 2.00000 1.28968 -1.72394 -0.70921 1.96274 0.04833 -1.97901 0.61803 1.77091 -1.21433 -1.36203 1.67294 0.79873 -1.94188 -0.14487 1.99066 -0.52541 -1.81375 1.13613 1.43120 -1.61803 -0.88638 1.91649 0.24107 -1.99766 0.43157 1.85235 -1.05528 -1.49702 1.55935 0.97197 -1.88662 -0.33671 ... ... ..... ....... ......... ........... ............. E9" * 2.00000 1.28968 -0.33671 -1.72394 -1.88662 -0.70921 0.97197 1.96274 1.55935 0.04833 -1.49702 -1.97901 -1.05528 0.61803 1.85235 1.77091 0.43157 -1.21433 -1.99766 -1.36203 0.24107 1.67294 1.91649 0.79873 -0.88638 -1.94188 -1.61803 -0.14487 1.43120 1.99066 1.13613 -0.52541 -1.81375 -2.00000 -1.28968 1.72394 0.70921 -1.96274 -0.04833 1.97901 -0.61803 -1.77091 1.21433 1.36203 -1.67294 -0.79873 1.94188 0.14487 -1.99066 0.52541 1.81375 -1.13613 -1.43120 1.61803 0.88638 -1.91649 -0.24107 1.99766 -0.43157 -1.85235 1.05528 1.49702 -1.55935 -0.97197 1.88662 0.33671 ... ... ..... ....... ......... ........... ............. E10' * 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 2.00000 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 ... ... ..... ....... ......... ........... ............. E10" * 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 -2.00000 -1.13613 1.94188 -0.24107 -1.77091 1.49702 0.70921 -2.00000 0.70921 1.49702 -1.77091 -0.24107 1.94188 -1.13613 -1.13613 1.94188 -0.24107 -1.77091 1.49702 0.70921 -2.00000 0.70921 1.49702 -1.77091 -0.24107 1.94188 -1.13613 -1.13613 1.94188 -0.24107 -1.77091 1.49702 0.70921 ... ... ..... ....... ......... ........... ............. E11' * 2.00000 0.97197 -1.05528 -1.99766 -0.88638 1.13613 1.99066 0.79873 -1.21433 -1.97901 -0.70921 1.28968 1.96274 0.61803 -1.36203 -1.94188 -0.52541 1.43120 1.91649 0.43157 -1.49702 -1.88662 -0.33671 1.55935 1.85235 0.24107 -1.61803 -1.81375 -0.14487 1.67294 1.77091 0.04833 -1.72394 2.00000 0.97197 -1.99766 1.13613 0.79873 -1.97901 1.28968 0.61803 -1.94188 1.43120 0.43157 -1.88662 1.55935 0.24107 -1.81375 1.67294 0.04833 -1.72394 1.77091 -0.14487 -1.61803 1.85235 -0.33671 -1.49702 1.91649 -0.52541 -1.36203 1.96274 -0.70921 -1.21433 1.99066 -0.88638 -1.05528 ... ... ..... ....... ......... ........... ............. E11" * 2.00000 0.97197 -1.05528 -1.99766 -0.88638 1.13613 1.99066 0.79873 -1.21433 -1.97901 -0.70921 1.28968 1.96274 0.61803 -1.36203 -1.94188 -0.52541 1.43120 1.91649 0.43157 -1.49702 -1.88662 -0.33671 1.55935 1.85235 0.24107 -1.61803 -1.81375 -0.14487 1.67294 1.77091 0.04833 -1.72394 -2.00000 -0.97197 1.99766 -1.13613 -0.79873 1.97901 -1.28968 -0.61803 1.94188 -1.43120 -0.43157 1.88662 -1.55935 -0.24107 1.81375 -1.67294 -0.04833 1.72394 -1.77091 0.14487 1.61803 -1.85235 0.33671 1.49702 -1.91649 0.52541 1.36203 -1.96274 0.70921 1.21433 -1.99066 0.88638 1.05528 ... ... ..... ....... ......... ........... ............. E12' * 2.00000 0.79873 -1.36203 -1.88662 -0.14487 1.77091 1.55935 -0.52541 -1.97901 -1.05528 1.13613 1.96274 0.43157 -1.61803 -1.72394 0.24107 1.91649 1.28968 -0.88638 -1.99766 -0.70921 1.43120 1.85235 0.04833 -1.81375 -1.49702 0.61803 1.99066 0.97197 -1.21433 -1.94188 -0.33671 1.67294 2.00000 0.79873 -1.88662 1.77091 -0.52541 -1.05528 1.96274 -1.61803 0.24107 1.28968 -1.99766 1.43120 0.04833 -1.49702 1.99066 -1.21433 -0.33671 1.67294 -1.94188 0.97197 0.61803 -1.81375 1.85235 -0.70921 -0.88638 1.91649 -1.72394 0.43157 1.13613 -1.97901 1.55935 -0.14487 -1.36203 ... ... ..... ....... ......... ........... ............. E12" * 2.00000 0.79873 -1.36203 -1.88662 -0.14487 1.77091 1.55935 -0.52541 -1.97901 -1.05528 1.13613 1.96274 0.43157 -1.61803 -1.72394 0.24107 1.91649 1.28968 -0.88638 -1.99766 -0.70921 1.43120 1.85235 0.04833 -1.81375 -1.49702 0.61803 1.99066 0.97197 -1.21433 -1.94188 -0.33671 1.67294 -2.00000 -0.79873 1.88662 -1.77091 0.52541 1.05528 -1.96274 1.61803 -0.24107 -1.28968 1.99766 -1.43120 -0.04833 1.49702 -1.99066 1.21433 0.33671 -1.67294 1.94188 -0.97197 -0.61803 1.81375 -1.85235 0.70921 0.88638 -1.91649 1.72394 -0.43157 -1.13613 1.97901 -1.55935 0.14487 1.36203 ... ... ..... ....... ......... ........... ............. E13' * 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 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 ... ... ..... ....... ......... ........... ............. E13" * 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 -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 ... ... ..... ....... ......... ........... ............. E14' * 2.00000 0.43157 -1.81375 -1.21433 1.28968 1.77091 -0.52541 -1.99766 -0.33671 1.85235 1.13613 -1.36203 -1.72394 0.61803 1.99066 0.24107 -1.88662 -1.05528 1.43120 1.67294 -0.70921 -1.97901 -0.14487 1.91649 0.97197 -1.49702 -1.61803 0.79873 1.96274 0.04833 -1.94188 -0.88638 1.55935 2.00000 0.43157 -1.21433 1.77091 -1.99766 1.85235 -1.36203 0.61803 0.24107 -1.05528 1.67294 -1.97901 1.91649 -1.49702 0.79873 0.04833 -0.88638 1.55935 -1.94188 1.96274 -1.61803 0.97197 -0.14487 -0.70921 1.43120 -1.88662 1.99066 -1.72394 1.13613 -0.33671 -0.52541 1.28968 -1.81375 ... ... ..... ....... ......... ........... ............. E14" * 2.00000 0.43157 -1.81375 -1.21433 1.28968 1.77091 -0.52541 -1.99766 -0.33671 1.85235 1.13613 -1.36203 -1.72394 0.61803 1.99066 0.24107 -1.88662 -1.05528 1.43120 1.67294 -0.70921 -1.97901 -0.14487 1.91649 0.97197 -1.49702 -1.61803 0.79873 1.96274 0.04833 -1.94188 -0.88638 1.55935 -2.00000 -0.43157 1.21433 -1.77091 1.99766 -1.85235 1.36203 -0.61803 -0.24107 1.05528 -1.67294 1.97901 -1.91649 1.49702 -0.79873 -0.04833 0.88638 -1.55935 1.94188 -1.96274 1.61803 -0.97197 0.14487 0.70921 -1.43120 1.88662 -1.99066 1.72394 -1.13613 0.33671 0.52541 -1.28968 1.81375 ... ... ..... ....... ......... ........... ............. E15' * 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 2.00000 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 ... ... ..... ....... ......... ........... ............. E15" * 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -2.00000 -0.24107 0.70921 -1.13613 1.49702 -1.77091 1.94188 -2.00000 1.94188 -1.77091 1.49702 -1.13613 0.70921 -0.24107 -0.24107 0.70921 -1.13613 1.49702 -1.77091 1.94188 -2.00000 1.94188 -1.77091 1.49702 -1.13613 0.70921 -0.24107 -0.24107 0.70921 -1.13613 1.49702 -1.77091 1.94188 ... ... ..... ....... ......... ........... ............. E16' * 2.00000 0.04833 -1.99766 -0.14487 1.99066 0.24107 -1.97901 -0.33671 1.96274 0.43157 -1.94188 -0.52541 1.91649 0.61803 -1.88662 -0.70921 1.85235 0.79873 -1.81375 -0.88638 1.77091 0.97197 -1.72394 -1.05528 1.67294 1.13613 -1.61803 -1.21433 1.55935 1.28968 -1.49702 -1.36203 1.43120 2.00000 0.04833 -0.14487 0.24107 -0.33671 0.43157 -0.52541 0.61803 -0.70921 0.79873 -0.88638 0.97197 -1.05528 1.13613 -1.21433 1.28968 -1.36203 1.43120 -1.49702 1.55935 -1.61803 1.67294 -1.72394 1.77091 -1.81375 1.85235 -1.88662 1.91649 -1.94188 1.96274 -1.97901 1.99066 -1.99766 ... ... ..... ....... ......... ........... ............. E16" * 2.00000 0.04833 -1.99766 -0.14487 1.99066 0.24107 -1.97901 -0.33671 1.96274 0.43157 -1.94188 -0.52541 1.91649 0.61803 -1.88662 -0.70921 1.85235 0.79873 -1.81375 -0.88638 1.77091 0.97197 -1.72394 -1.05528 1.67294 1.13613 -1.61803 -1.21433 1.55935 1.28968 -1.49702 -1.36203 1.43120 -2.00000 -0.04833 0.14487 -0.24107 0.33671 -0.43157 0.52541 -0.61803 0.70921 -0.79873 0.88638 -0.97197 1.05528 -1.13613 1.21433 -1.28968 1.36203 -1.43120 1.49702 -1.55935 1.61803 -1.67294 1.72394 -1.77091 1.81375 -1.85235 1.88662 -1.91649 1.94188 -1.96274 1.97901 -1.99066 1.99766 ... ... ..... ....... ......... ........... ............. E17' * 2.00000 -0.14487 -1.97901 0.43157 1.91649 -0.70921 -1.81375 0.97197 1.67294 -1.21433 -1.49702 1.43120 1.28968 -1.61803 -1.05528 1.77091 0.79873 -1.88662 -0.52541 1.96274 0.24107 -1.99766 0.04833 1.99066 -0.33671 -1.94188 0.61803 1.85235 -0.88638 -1.72394 1.13613 1.55935 -1.36203 2.00000 -0.14487 0.43157 -0.70921 0.97197 -1.21433 1.43120 -1.61803 1.77091 -1.88662 1.96274 -1.99766 1.99066 -1.94188 1.85235 -1.72394 1.55935 -1.36203 1.13613 -0.88638 0.61803 -0.33671 0.04833 0.24107 -0.52541 0.79873 -1.05528 1.28968 -1.49702 1.67294 -1.81375 1.91649 -1.97901 ... ... ..... ....... ......... ........... ............. E17" * 2.00000 -0.14487 -1.97901 0.43157 1.91649 -0.70921 -1.81375 0.97197 1.67294 -1.21433 -1.49702 1.43120 1.28968 -1.61803 -1.05528 1.77091 0.79873 -1.88662 -0.52541 1.96274 0.24107 -1.99766 0.04833 1.99066 -0.33671 -1.94188 0.61803 1.85235 -0.88638 -1.72394 1.13613 1.55935 -1.36203 -2.00000 0.14487 -0.43157 0.70921 -0.97197 1.21433 -1.43120 1.61803 -1.77091 1.88662 -1.96274 1.99766 -1.99066 1.94188 -1.85235 1.72394 -1.55935 1.36203 -1.13613 0.88638 -0.61803 0.33671 -0.04833 -0.24107 0.52541 -0.79873 1.05528 -1.28968 1.49702 -1.67294 1.81375 -1.91649 1.97901 ... ... ..... ....... ......... ........... ............. E18' * 2.00000 -0.33671 -1.88662 0.97197 1.55935 -1.49702 -1.05528 1.85235 0.43157 -1.99766 0.24107 1.91649 -0.88638 -1.61803 1.43120 1.13613 -1.81375 -0.52541 1.99066 -0.14487 -1.94188 0.79873 1.67294 -1.36203 -1.21433 1.77091 0.61803 -1.97901 0.04833 1.96274 -0.70921 -1.72394 1.28968 2.00000 -0.33671 0.97197 -1.49702 1.85235 -1.99766 1.91649 -1.61803 1.13613 -0.52541 -0.14487 0.79873 -1.36203 1.77091 -1.97901 1.96274 -1.72394 1.28968 -0.70921 0.04833 0.61803 -1.21433 1.67294 -1.94188 1.99066 -1.81375 1.43120 -0.88638 0.24107 0.43157 -1.05528 1.55935 -1.88662 ... ... ..... ....... ......... ........... ............. E18" * 2.00000 -0.33671 -1.88662 0.97197 1.55935 -1.49702 -1.05528 1.85235 0.43157 -1.99766 0.24107 1.91649 -0.88638 -1.61803 1.43120 1.13613 -1.81375 -0.52541 1.99066 -0.14487 -1.94188 0.79873 1.67294 -1.36203 -1.21433 1.77091 0.61803 -1.97901 0.04833 1.96274 -0.70921 -1.72394 1.28968 -2.00000 0.33671 -0.97197 1.49702 -1.85235 1.99766 -1.91649 1.61803 -1.13613 0.52541 0.14487 -0.79873 1.36203 -1.77091 1.97901 -1.96274 1.72394 -1.28968 0.70921 -0.04833 -0.61803 1.21433 -1.67294 1.94188 -1.99066 1.81375 -1.43120 0.88638 -0.24107 -0.43157 1.05528 -1.55935 1.88662 ... ... ..... ....... ......... ........... ............. E19' * 2.00000 -0.52541 -1.72394 1.43120 0.97197 -1.94188 0.04833 1.91649 -1.05528 -1.36203 1.77091 0.43157 -1.99766 0.61803 1.67294 -1.49702 -0.88638 1.96274 -0.14487 -1.88662 1.13613 1.28968 -1.81375 -0.33671 1.99066 -0.70921 -1.61803 1.55935 0.79873 -1.97901 0.24107 1.85235 -1.21433 2.00000 -0.52541 1.43120 -1.94188 1.91649 -1.36203 0.43157 0.61803 -1.49702 1.96274 -1.88662 1.28968 -0.33671 -0.70921 1.55935 -1.97901 1.85235 -1.21433 0.24107 0.79873 -1.61803 1.99066 -1.81375 1.13613 -0.14487 -0.88638 1.67294 -1.99766 1.77091 -1.05528 0.04833 0.97197 -1.72394 ... ... ..... ....... ......... ........... ............. E19" * 2.00000 -0.52541 -1.72394 1.43120 0.97197 -1.94188 0.04833 1.91649 -1.05528 -1.36203 1.77091 0.43157 -1.99766 0.61803 1.67294 -1.49702 -0.88638 1.96274 -0.14487 -1.88662 1.13613 1.28968 -1.81375 -0.33671 1.99066 -0.70921 -1.61803 1.55935 0.79873 -1.97901 0.24107 1.85235 -1.21433 -2.00000 0.52541 -1.43120 1.94188 -1.91649 1.36203 -0.43157 -0.61803 1.49702 -1.96274 1.88662 -1.28968 0.33671 0.70921 -1.55935 1.97901 -1.85235 1.21433 -0.24107 -0.79873 1.61803 -1.99066 1.81375 -1.13613 0.14487 0.88638 -1.67294 1.99766 -1.77091 1.05528 -0.04833 -0.97197 1.72394 ... ... ..... ....... ......... ........... ............. E20' * 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 2.00000 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 ... ... ..... ....... ......... ........... ............. E20" * 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 -2.00000 0.70921 -1.77091 1.94188 -1.13613 -0.24107 1.49702 -2.00000 1.49702 -0.24107 -1.13613 1.94188 -1.77091 0.70921 0.70921 -1.77091 1.94188 -1.13613 -0.24107 1.49702 -2.00000 1.49702 -0.24107 -1.13613 1.94188 -1.77091 0.70921 0.70921 -1.77091 1.94188 -1.13613 -0.24107 1.49702 ... ... ..... ....... ......... ........... ............. E21' * 2.00000 -0.88638 -1.21433 1.96274 -0.52541 -1.49702 1.85235 -0.14487 -1.72394 1.67294 0.24107 -1.88662 1.43120 0.61803 -1.97901 1.13613 0.97197 -1.99766 0.79873 1.28968 -1.94188 0.43157 1.55935 -1.81375 0.04833 1.77091 -1.61803 -0.33671 1.91649 -1.36203 -0.70921 1.99066 -1.05528 2.00000 -0.88638 1.96274 -1.49702 -0.14487 1.67294 -1.88662 0.61803 1.13613 -1.99766 1.28968 0.43157 -1.81375 1.77091 -0.33671 -1.36203 1.99066 -1.05528 -0.70921 1.91649 -1.61803 0.04833 1.55935 -1.94188 0.79873 0.97197 -1.97901 1.43120 0.24107 -1.72394 1.85235 -0.52541 -1.21433 ... ... ..... ....... ......... ........... ............. E21" * 2.00000 -0.88638 -1.21433 1.96274 -0.52541 -1.49702 1.85235 -0.14487 -1.72394 1.67294 0.24107 -1.88662 1.43120 0.61803 -1.97901 1.13613 0.97197 -1.99766 0.79873 1.28968 -1.94188 0.43157 1.55935 -1.81375 0.04833 1.77091 -1.61803 -0.33671 1.91649 -1.36203 -0.70921 1.99066 -1.05528 -2.00000 0.88638 -1.96274 1.49702 0.14487 -1.67294 1.88662 -0.61803 -1.13613 1.99766 -1.28968 -0.43157 1.81375 -1.77091 0.33671 1.36203 -1.99066 1.05528 0.70921 -1.91649 1.61803 -0.04833 -1.55935 1.94188 -0.79873 -0.97197 1.97901 -1.43120 -0.24107 1.72394 -1.85235 0.52541 1.21433 ... ... ..... ....... ......... ........... ............. E22' * 2.00000 -1.05528 -0.88638 1.99066 -1.21433 -0.70921 1.96274 -1.36203 -0.52541 1.91649 -1.49702 -0.33671 1.85235 -1.61803 -0.14487 1.77091 -1.72394 0.04833 1.67294 -1.81375 0.24107 1.55935 -1.88662 0.43157 1.43120 -1.94188 0.61803 1.28968 -1.97901 0.79873 1.13613 -1.99766 0.97197 2.00000 -1.05528 1.99066 -0.70921 -1.36203 1.91649 -0.33671 -1.61803 1.77091 0.04833 -1.81375 1.55935 0.43157 -1.94188 1.28968 0.79873 -1.99766 0.97197 1.13613 -1.97901 0.61803 1.43120 -1.88662 0.24107 1.67294 -1.72394 -0.14487 1.85235 -1.49702 -0.52541 1.96274 -1.21433 -0.88638 ... ... ..... ....... ......... ........... ............. E22" * 2.00000 -1.05528 -0.88638 1.99066 -1.21433 -0.70921 1.96274 -1.36203 -0.52541 1.91649 -1.49702 -0.33671 1.85235 -1.61803 -0.14487 1.77091 -1.72394 0.04833 1.67294 -1.81375 0.24107 1.55935 -1.88662 0.43157 1.43120 -1.94188 0.61803 1.28968 -1.97901 0.79873 1.13613 -1.99766 0.97197 -2.00000 1.05528 -1.99066 0.70921 1.36203 -1.91649 0.33671 1.61803 -1.77091 -0.04833 1.81375 -1.55935 -0.43157 1.94188 -1.28968 -0.79873 1.99766 -0.97197 -1.13613 1.97901 -0.61803 -1.43120 1.88662 -0.24107 -1.67294 1.72394 0.14487 -1.85235 1.49702 0.52541 -1.96274 1.21433 0.88638 ... ... ..... ....... ......... ........... ............. E23' * 2.00000 -1.21433 -0.52541 1.85235 -1.72394 0.24107 1.43120 -1.97901 0.97197 0.79873 -1.94188 1.55935 0.04833 -1.61803 1.91649 -0.70921 -1.05528 1.99066 -1.36203 -0.33671 1.77091 -1.81375 0.43157 1.28968 -1.99766 1.13613 0.61803 -1.88662 1.67294 -0.14487 -1.49702 1.96274 -0.88638 2.00000 -1.21433 1.85235 0.24107 -1.97901 0.79873 1.55935 -1.61803 -0.70921 1.99066 -0.33671 -1.81375 1.28968 1.13613 -1.88662 -0.14487 1.96274 -0.88638 -1.49702 1.67294 0.61803 -1.99766 0.43157 1.77091 -1.36203 -1.05528 1.91649 0.04833 -1.94188 0.97197 1.43120 -1.72394 -0.52541 ... ... ..... ....... ......... ........... ............. E23" * 2.00000 -1.21433 -0.52541 1.85235 -1.72394 0.24107 1.43120 -1.97901 0.97197 0.79873 -1.94188 1.55935 0.04833 -1.61803 1.91649 -0.70921 -1.05528 1.99066 -1.36203 -0.33671 1.77091 -1.81375 0.43157 1.28968 -1.99766 1.13613 0.61803 -1.88662 1.67294 -0.14487 -1.49702 1.96274 -0.88638 -2.00000 1.21433 -1.85235 -0.24107 1.97901 -0.79873 -1.55935 1.61803 0.70921 -1.99066 0.33671 1.81375 -1.28968 -1.13613 1.88662 0.14487 -1.96274 0.88638 1.49702 -1.67294 -0.61803 1.99766 -0.43157 -1.77091 1.36203 1.05528 -1.91649 -0.04833 1.94188 -0.97197 -1.43120 1.72394 0.52541 ... ... ..... ....... ......... ........... ............. E24' * 2.00000 -1.36203 -0.14487 1.55935 -1.97901 1.13613 0.43157 -1.72394 1.91649 -0.88638 -0.70921 1.85235 -1.81375 0.61803 0.97197 -1.94188 1.67294 -0.33671 -1.21433 1.99066 -1.49702 0.04833 1.43120 -1.99766 1.28968 0.24107 -1.61803 1.96274 -1.05528 -0.52541 1.77091 -1.88662 0.79873 2.00000 -1.36203 1.55935 1.13613 -1.72394 -0.88638 1.85235 0.61803 -1.94188 -0.33671 1.99066 0.04833 -1.99766 0.24107 1.96274 -0.52541 -1.88662 0.79873 1.77091 -1.05528 -1.61803 1.28968 1.43120 -1.49702 -1.21433 1.67294 0.97197 -1.81375 -0.70921 1.91649 0.43157 -1.97901 -0.14487 ... ... ..... ....... ......... ........... ............. E24" * 2.00000 -1.36203 -0.14487 1.55935 -1.97901 1.13613 0.43157 -1.72394 1.91649 -0.88638 -0.70921 1.85235 -1.81375 0.61803 0.97197 -1.94188 1.67294 -0.33671 -1.21433 1.99066 -1.49702 0.04833 1.43120 -1.99766 1.28968 0.24107 -1.61803 1.96274 -1.05528 -0.52541 1.77091 -1.88662 0.79873 -2.00000 1.36203 -1.55935 -1.13613 1.72394 0.88638 -1.85235 -0.61803 1.94188 0.33671 -1.99066 -0.04833 1.99766 -0.24107 -1.96274 0.52541 1.88662 -0.79873 -1.77091 1.05528 1.61803 -1.28968 -1.43120 1.49702 1.21433 -1.67294 -0.97197 1.81375 0.70921 -1.91649 -0.43157 1.97901 0.14487 ... ... ..... ....... ......... ........... ............. E25' * 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 2.00000 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 ... ... ..... ....... ......... ........... ............. E25" * 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -2.00000 1.49702 -1.13613 -1.77091 0.70921 1.94188 -0.24107 -2.00000 -0.24107 1.94188 0.70921 -1.77091 -1.13613 1.49702 1.49702 -1.13613 -1.77091 0.70921 1.94188 -0.24107 -2.00000 -0.24107 1.94188 0.70921 -1.77091 -1.13613 1.49702 1.49702 -1.13613 -1.77091 0.70921 1.94188 -0.24107 ... ... ..... ....... ......... ........... ............. E26' * 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 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 ... ... ..... ....... ......... ........... ............. E26" * 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 -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 ... ... ..... ....... ......... ........... ............. E27' * 2.00000 -1.72394 0.97197 0.04833 -1.05528 1.77091 -1.99766 1.67294 -0.88638 -0.14487 1.13613 -1.81375 1.99066 -1.61803 0.79873 0.24107 -1.21433 1.85235 -1.97901 1.55935 -0.70921 -0.33671 1.28968 -1.88662 1.96274 -1.49702 0.61803 0.43157 -1.36203 1.91649 -1.94188 1.43120 -0.52541 2.00000 -1.72394 0.04833 1.77091 1.67294 -0.14487 -1.81375 -1.61803 0.24107 1.85235 1.55935 -0.33671 -1.88662 -1.49702 0.43157 1.91649 1.43120 -0.52541 -1.94188 -1.36203 0.61803 1.96274 1.28968 -0.70921 -1.97901 -1.21433 0.79873 1.99066 1.13613 -0.88638 -1.99766 -1.05528 0.97197 ... ... ..... ....... ......... ........... ............. E27" * 2.00000 -1.72394 0.97197 0.04833 -1.05528 1.77091 -1.99766 1.67294 -0.88638 -0.14487 1.13613 -1.81375 1.99066 -1.61803 0.79873 0.24107 -1.21433 1.85235 -1.97901 1.55935 -0.70921 -0.33671 1.28968 -1.88662 1.96274 -1.49702 0.61803 0.43157 -1.36203 1.91649 -1.94188 1.43120 -0.52541 -2.00000 1.72394 -0.04833 -1.77091 -1.67294 0.14487 1.81375 1.61803 -0.24107 -1.85235 -1.55935 0.33671 1.88662 1.49702 -0.43157 -1.91649 -1.43120 0.52541 1.94188 1.36203 -0.61803 -1.96274 -1.28968 0.70921 1.97901 1.21433 -0.79873 -1.99066 -1.13613 0.88638 1.99766 1.05528 -0.97197 ... ... ..... ....... ......... ........... ............. E28' * 2.00000 -1.81375 1.28968 -0.52541 -0.33671 1.13613 -1.72394 1.99066 -1.88662 1.43120 -0.70921 -0.14487 0.97197 -1.61803 1.96274 -1.94188 1.55935 -0.88638 0.04833 0.79873 -1.49702 1.91649 -1.97901 1.67294 -1.05528 0.24107 0.61803 -1.36203 1.85235 -1.99766 1.77091 -1.21433 0.43157 2.00000 -1.81375 -0.52541 1.13613 1.99066 1.43120 -0.14487 -1.61803 -1.94188 -0.88638 0.79873 1.91649 1.67294 0.24107 -1.36203 -1.99766 -1.21433 0.43157 1.77091 1.85235 0.61803 -1.05528 -1.97901 -1.49702 0.04833 1.55935 1.96274 0.97197 -0.70921 -1.88662 -1.72394 -0.33671 1.28968 ... ... ..... ....... ......... ........... ............. E28" * 2.00000 -1.81375 1.28968 -0.52541 -0.33671 1.13613 -1.72394 1.99066 -1.88662 1.43120 -0.70921 -0.14487 0.97197 -1.61803 1.96274 -1.94188 1.55935 -0.88638 0.04833 0.79873 -1.49702 1.91649 -1.97901 1.67294 -1.05528 0.24107 0.61803 -1.36203 1.85235 -1.99766 1.77091 -1.21433 0.43157 -2.00000 1.81375 0.52541 -1.13613 -1.99066 -1.43120 0.14487 1.61803 1.94188 0.88638 -0.79873 -1.91649 -1.67294 -0.24107 1.36203 1.99766 1.21433 -0.43157 -1.77091 -1.85235 -0.61803 1.05528 1.97901 1.49702 -0.04833 -1.55935 -1.96274 -0.97197 0.70921 1.88662 1.72394 0.33671 -1.28968 ... ... ..... ....... ......... ........... ............. E29' * 2.00000 -1.88662 1.55935 -1.05528 0.43157 0.24107 -0.88638 1.43120 -1.81375 1.99066 -1.94188 1.67294 -1.21433 0.61803 0.04833 -0.70921 1.28968 -1.72394 1.96274 -1.97901 1.77091 -1.36203 0.79873 -0.14487 -0.52541 1.13613 -1.61803 1.91649 -1.99766 1.85235 -1.49702 0.97197 -0.33671 2.00000 -1.88662 -1.05528 0.24107 1.43120 1.99066 1.67294 0.61803 -0.70921 -1.72394 -1.97901 -1.36203 -0.14487 1.13613 1.91649 1.85235 0.97197 -0.33671 -1.49702 -1.99766 -1.61803 -0.52541 0.79873 1.77091 1.96274 1.28968 0.04833 -1.21433 -1.94188 -1.81375 -0.88638 0.43157 1.55935 ... ... ..... ....... ......... ........... ............. E29" * 2.00000 -1.88662 1.55935 -1.05528 0.43157 0.24107 -0.88638 1.43120 -1.81375 1.99066 -1.94188 1.67294 -1.21433 0.61803 0.04833 -0.70921 1.28968 -1.72394 1.96274 -1.97901 1.77091 -1.36203 0.79873 -0.14487 -0.52541 1.13613 -1.61803 1.91649 -1.99766 1.85235 -1.49702 0.97197 -0.33671 -2.00000 1.88662 1.05528 -0.24107 -1.43120 -1.99066 -1.67294 -0.61803 0.70921 1.72394 1.97901 1.36203 0.14487 -1.13613 -1.91649 -1.85235 -0.97197 0.33671 1.49702 1.99766 1.61803 0.52541 -0.79873 -1.77091 -1.96274 -1.28968 -0.04833 1.21433 1.94188 1.81375 0.88638 -0.43157 -1.55935 ... ... ..... ....... ......... ........... ............. E30' * 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 2.00000 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 ... ... ..... ....... ......... ........... ............. E30" * 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 -2.00000 1.94188 1.49702 0.70921 -0.24107 -1.13613 -1.77091 -2.00000 -1.77091 -1.13613 -0.24107 0.70921 1.49702 1.94188 1.94188 1.49702 0.70921 -0.24107 -1.13613 -1.77091 -2.00000 -1.77091 -1.13613 -0.24107 0.70921 1.49702 1.94188 1.94188 1.49702 0.70921 -0.24107 -1.13613 -1.77091 ... ... ..... ....... ......... ........... ............. E31' * 2.00000 -1.97901 1.91649 -1.81375 1.67294 -1.49702 1.28968 -1.05528 0.79873 -0.52541 0.24107 0.04833 -0.33671 0.61803 -0.88638 1.13613 -1.36203 1.55935 -1.72394 1.85235 -1.94188 1.99066 -1.99766 1.96274 -1.88662 1.77091 -1.61803 1.43120 -1.21433 0.97197 -0.70921 0.43157 -0.14487 2.00000 -1.97901 -1.81375 -1.49702 -1.05528 -0.52541 0.04833 0.61803 1.13613 1.55935 1.85235 1.99066 1.96274 1.77091 1.43120 0.97197 0.43157 -0.14487 -0.70921 -1.21433 -1.61803 -1.88662 -1.99766 -1.94188 -1.72394 -1.36203 -0.88638 -0.33671 0.24107 0.79873 1.28968 1.67294 1.91649 ... ... ..... ....... ......... ........... ............. E31" * 2.00000 -1.97901 1.91649 -1.81375 1.67294 -1.49702 1.28968 -1.05528 0.79873 -0.52541 0.24107 0.04833 -0.33671 0.61803 -0.88638 1.13613 -1.36203 1.55935 -1.72394 1.85235 -1.94188 1.99066 -1.99766 1.96274 -1.88662 1.77091 -1.61803 1.43120 -1.21433 0.97197 -0.70921 0.43157 -0.14487 -2.00000 1.97901 1.81375 1.49702 1.05528 0.52541 -0.04833 -0.61803 -1.13613 -1.55935 -1.85235 -1.99066 -1.96274 -1.77091 -1.43120 -0.97197 -0.43157 0.14487 0.70921 1.21433 1.61803 1.88662 1.99766 1.94188 1.72394 1.36203 0.88638 0.33671 -0.24107 -0.79873 -1.28968 -1.67294 -1.91649 ... ... ..... ....... ......... ........... ............. E32' * 2.00000 -1.99766 1.99066 -1.97901 1.96274 -1.94188 1.91649 -1.88662 1.85235 -1.81375 1.77091 -1.72394 1.67294 -1.61803 1.55935 -1.49702 1.43120 -1.36203 1.28968 -1.21433 1.13613 -1.05528 0.97197 -0.88638 0.79873 -0.70921 0.61803 -0.52541 0.43157 -0.33671 0.24107 -0.14487 0.04833 2.00000 -1.99766 -1.97901 -1.94188 -1.88662 -1.81375 -1.72394 -1.61803 -1.49702 -1.36203 -1.21433 -1.05528 -0.88638 -0.70921 -0.52541 -0.33671 -0.14487 0.04833 0.24107 0.43157 0.61803 0.79873 0.97197 1.13613 1.28968 1.43120 1.55935 1.67294 1.77091 1.85235 1.91649 1.96274 1.99066 ... ... ..... ....... ......... ........... ............. E32" * 2.00000 -1.99766 1.99066 -1.97901 1.96274 -1.94188 1.91649 -1.88662 1.85235 -1.81375 1.77091 -1.72394 1.67294 -1.61803 1.55935 -1.49702 1.43120 -1.36203 1.28968 -1.21433 1.13613 -1.05528 0.97197 -0.88638 0.79873 -0.70921 0.61803 -0.52541 0.43157 -0.33671 0.24107 -0.14487 0.04833 -2.00000 1.99766 1.97901 1.94188 1.88662 1.81375 1.72394 1.61803 1.49702 1.36203 1.21433 1.05528 0.88638 0.70921 0.52541 0.33671 0.14487 -0.04833 -0.24107 -0.43157 -0.61803 -0.79873 -0.97197 -1.13613 -1.28968 -1.43120 -1.55935 -1.67294 -1.77091 -1.85235 -1.91649 -1.96274 -1.99066 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.997664453665 = 2*cos(2*π/130) = 2*cos(π/65) 1.990663269435 = 2*cos(4*π/130) = 2*cos(2*π/65) 1.979012798902 = 2*cos(6*π/130) = 2*cos(3*π/65) 1.962740252279 = 2*cos(8*π/130) = 2*cos(4*π/65) 1.941883634852 = 2*cos(10*π/130) = 2*cos(π/13) 1.916491658218 = 2*cos(12*π/130) = 2*cos(6*π/65) 1.886623626515 = 2*cos(14*π/130) = 2*cos(7*π/65) 1.852349297916 = 2*cos(16*π/130) = 2*cos(8*π/65) 1.813748721701 = 2*cos(18*π/130) = 2*cos(9*π/65) 1.770912051306 = 2*cos(20*π/130) = 2*cos(2*π/13) 1.723939333760 = 2*cos(22*π/130) = 2*cos(11*π/65) 1.672940276020 = 2*cos(24*π/130) = 2*cos(12*π/65) 1.618033988750 = 2*cos(26*π/130) = 2*cos(π/5) = (√5+1)/2 1.559348708126 = 2*cos(28*π/130) = 2*cos(14*π/65) 1.497021496342 = 2*cos(30*π/130) = 2*cos(3*π/13) 1.431197921488 = 2*cos(32*π/130) = 2*cos(16*π/65) 1.362031717574 = 2*cos(34*π/130) = 2*cos(17*π/65) 1.289684425472 = 2*cos(36*π/130) = 2*cos(18*π/65) 1.214325015637 = 2*cos(38*π/130) = 2*cos(19*π/65) 1.136129493462 = 2*cos(40*π/130) = 2*cos(4*π/13) 1.055280488212 = 2*cos(42*π/130) = 2*cos(21*π/65) 0.971966826485 = 2*cos(44*π/130) = 2*cos(22*π/65) 0.886383091198 = 2*cos(46*π/130) = 2*cos(23*π/65) 0.798729167131 = 2*cos(48*π/130) = 2*cos(24*π/65) 0.709209774085 = 2*cos(50*π/130) = 2*cos(5*π/13) 0.618033988750 = 2*cos(52*π/130) = 2*cos(2*π/5) = (√5−1)/2 0.525414756397 = 2*cos(54*π/130) = 2*cos(27*π/65) 0.431568393536 = 2*cos(56*π/130) = 2*cos(28*π/65) 0.336714082694 = 2*cos(58*π/130) = 2*cos(29*π/65) 0.241073360511 = 2*cos(60*π/130) = 2*cos(6*π/13) 0.144869600324 = 2*cos(62*π/130) = 2*cos(31*π/65) 0.048327490472 = 2*cos(64*π/130) = 2*cos(32*π/65) Symmetry of Rotations and Cartesian products A' R+d+g+i+k+m R_z, z², z⁴, z⁶ A" p+f+h+j+l z, z³, z⁵ E1' p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E1" R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2' d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E2" f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3' f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E3" g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4' g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E4" h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5' 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)} E5" 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)} E6' i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E6" j+l E7' j+l E7" k+m E8' k+m E8" l E9' l E9" m E10' m Notes: α The order of the C_65h point group is 130, and the order of the principal axis (S₆₅) is 130. The group has 66 irreducible representations. β The C_65h point group could also be named S₆₅, as it contains the S₆₅ axis as its only symmetry element. Another rare designation is C_130i because the S₆₅ axis is identical to a roto-inversion axis of order 130. γ The C_65h point group is isomorphic to C₁₃₀ and S₁₃₀. δ The C_65h point group is generated by one single symmetry element, S₆₅. Therefore, it is a cyclic group. The canonical choice, however, is to use redundant generators: C₆₅ and σ_h. ε The lowest nonvanishing multipole moment in C_65h is 4 (quadrupole moment). ζ This is an Abelian point group (the commutative law holds between all symmetry operations). The C_65h 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. η Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 128 cases have been combined into 64 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 64 pairs of left and right rotations have been combined into one two-membered pseudo-class each. θ The 64 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. ι Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. κ The point group corresponds to a 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. While some characters of this group can be expressed using real integers and square roots alone, others need complex numbers and third roots.

This Character Table for the C_65h point group was created by Gernot Katzer.

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

	C_63h
	C_64h
C₆₅ C_65v	C_65h	D₆₅ D_65h D_65d
	C_66h
	C_67h

Character table for the C65h point group

Character table for the C_65h point group