C111 E 2 C111 2 C111^2 2 C37 2 C111^4 2 C111^5 2 C37^2 2 C111^7 2 C111^8 2 C37^3 2 C111^10 2 C111^11 2 C37^4 2 C111^13 2 C111^14 2 C37^5 2 C111^16 2 C111^17 2 C37^6 2 C111^19 2 C111^20 2 C37^7 2 C111^22 2 C111^23 2 C37^8 2 C111^25 2 C111^26 2 C37^9 2 C111^28 2 C111^29 2 C37^10 2 C111^31 2 C111^32 2 C37^11 2 C111^34 2 C111^35 2 C37^12 2 C3 2 C111^38 2 C37^13 2 C111^40 2 C111^41 2 C37^14 2 C111^43 2 C111^44 2 C37^15 2 C111^46 2 C111^47 2 C37^16 2 C111^49 2 C111^50 2 C37^17 2 C111^52 2 C111^53 2 C37^18 2 C111^55 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99680 1.98720 1.97123 1.94895 1.92043 1.88575 1.84504 1.79841 1.74603 1.68805 1.62466 1.55607 1.48250 1.40417 1.32135 1.23429 1.14329 1.04861 0.95058 0.84951 0.74571 0.63953 0.53129 0.42136 0.31007 0.19779 0.08488 -0.02830 -0.14140 -0.25404 -0.36586 -0.47652 -0.58565 -0.69290 -0.79793 -0.90041 -1.00000 -1.09639 -1.18927 -1.27833 -1.36331 -1.44391 -1.51989 -1.59100 -1.65702 -1.71773 -1.77293 -1.82246 -1.86614 -1.90385 -1.93547 -1.96088 -1.98001 -1.99279 -1.99920 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98720 1.94895 1.88575 1.79841 1.68805 1.55607 1.40417 1.23429 1.04861 0.84951 0.63953 0.42136 0.19779 -0.02830 -0.25404 -0.47652 -0.69290 -0.90041 -1.09639 -1.27833 -1.44391 -1.59100 -1.71773 -1.82246 -1.90385 -1.96088 -1.99279 -1.99920 -1.98001 -1.93547 -1.86614 -1.77293 -1.65702 -1.51989 -1.36331 -1.18927 -1.00000 -0.79793 -0.58565 -0.36586 -0.14140 0.08488 0.31007 0.53129 0.74571 0.95058 1.14329 1.32135 1.48250 1.62466 1.74603 1.84504 1.92043 1.97123 1.99680 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.97123 1.88575 1.74603 1.55607 1.32135 1.04861 0.74571 0.42136 0.08488 -0.25404 -0.58565 -0.90041 -1.18927 -1.44391 -1.65702 -1.82246 -1.93547 -1.99279 -1.99279 -1.93547 -1.82246 -1.65702 -1.44391 -1.18927 -0.90041 -0.58565 -0.25404 0.08488 0.42136 0.74571 1.04861 1.32135 1.55607 1.74603 1.88575 1.97123 2.00000 1.97123 1.88575 1.74603 1.55607 1.32135 1.04861 0.74571 0.42136 0.08488 -0.25404 -0.58565 -0.90041 -1.18927 -1.44391 -1.65702 -1.82246 -1.93547 -1.99279 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.94895 1.79841 1.55607 1.23429 0.84951 0.42136 -0.02830 -0.47652 -0.90041 -1.27833 -1.59100 -1.82246 -1.96088 -1.99920 -1.93547 -1.77293 -1.51989 -1.18927 -0.79793 -0.36586 0.08488 0.53129 0.95058 1.32135 1.62466 1.84504 1.97123 1.99680 1.92043 1.74603 1.48250 1.14329 0.74571 0.31007 -0.14140 -0.58565 -1.00000 -1.36331 -1.65702 -1.86614 -1.98001 -1.99279 -1.90385 -1.71773 -1.44391 -1.09639 -0.69290 -0.25404 0.19779 0.63953 1.04861 1.40417 1.68805 1.88575 1.98720 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.92043 1.68805 1.32135 0.84951 0.31007 -0.25404 -0.79793 -1.27833 -1.65702 -1.90385 -1.99920 -1.93547 -1.71773 -1.36331 -0.90041 -0.36586 0.19779 0.74571 1.23429 1.62466 1.88575 1.99680 1.94895 1.74603 1.40417 0.95058 0.42136 -0.14140 -0.69290 -1.18927 -1.59100 -1.86614 -1.99279 -1.96088 -1.77293 -1.44391 -1.00000 -0.47652 0.08488 0.63953 1.14329 1.55607 1.84504 1.98720 1.97123 1.79841 1.48250 1.04861 0.53129 -0.02830 -0.58565 -1.09639 -1.51989 -1.82246 -1.98001 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.88575 1.55607 1.04861 0.42136 -0.25404 -0.90041 -1.44391 -1.82246 -1.99279 -1.93547 -1.65702 -1.18927 -0.58565 0.08488 0.74571 1.32135 1.74603 1.97123 1.97123 1.74603 1.32135 0.74571 0.08488 -0.58565 -1.18927 -1.65702 -1.93547 -1.99279 -1.82246 -1.44391 -0.90041 -0.25404 0.42136 1.04861 1.55607 1.88575 2.00000 1.88575 1.55607 1.04861 0.42136 -0.25404 -0.90041 -1.44391 -1.82246 -1.99279 -1.93547 -1.65702 -1.18927 -0.58565 0.08488 0.74571 1.32135 1.74603 1.97123 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.84504 1.40417 0.74571 -0.02830 -0.79793 -1.44391 -1.86614 -1.99920 -1.82246 -1.36331 -0.69290 0.08488 0.84951 1.48250 1.88575 1.99680 1.79841 1.32135 0.63953 -0.14140 -0.90041 -1.51989 -1.90385 -1.99279 -1.77293 -1.27833 -0.58565 0.19779 0.95058 1.55607 1.92043 1.98720 1.74603 1.23429 0.53129 -0.25404 -1.00000 -1.59100 -1.93547 -1.98001 -1.71773 -1.18927 -0.47652 0.31007 1.04861 1.62466 1.94895 1.97123 1.68805 1.14329 0.42136 -0.36586 -1.09639 -1.65702 -1.96088 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.79841 1.23429 0.42136 -0.47652 -1.27833 -1.82246 -1.99920 -1.77293 -1.18927 -0.36586 0.53129 1.32135 1.84504 1.99680 1.74603 1.14329 0.31007 -0.58565 -1.36331 -1.86614 -1.99279 -1.71773 -1.09639 -0.25404 0.63953 1.40417 1.88575 1.98720 1.68805 1.04861 0.19779 -0.69290 -1.44391 -1.90385 -1.98001 -1.65702 -1.00000 -0.14140 0.74571 1.48250 1.92043 1.97123 1.62466 0.95058 0.08488 -0.79793 -1.51989 -1.93547 -1.96088 -1.59100 -0.90041 -0.02830 0.84951 1.55607 1.94895 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.74603 1.04861 0.08488 -0.90041 -1.65702 -1.99279 -1.82246 -1.18927 -0.25404 0.74571 1.55607 1.97123 1.88575 1.32135 0.42136 -0.58565 -1.44391 -1.93547 -1.93547 -1.44391 -0.58565 0.42136 1.32135 1.88575 1.97123 1.55607 0.74571 -0.25404 -1.18927 -1.82246 -1.99279 -1.65702 -0.90041 0.08488 1.04861 1.74603 2.00000 1.74603 1.04861 0.08488 -0.90041 -1.65702 -1.99279 -1.82246 -1.18927 -0.25404 0.74571 1.55607 1.97123 1.88575 1.32135 0.42136 -0.58565 -1.44391 -1.93547 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.68805 0.84951 -0.25404 -1.27833 -1.90385 -1.93547 -1.36331 -0.36586 0.74571 1.62466 1.99680 1.74603 0.95058 -0.14140 -1.18927 -1.86614 -1.96088 -1.44391 -0.47652 0.63953 1.55607 1.98720 1.79841 1.04861 -0.02830 -1.09639 -1.82246 -1.98001 -1.51989 -0.58565 0.53129 1.48250 1.97123 1.84504 1.14329 0.08488 -1.00000 -1.77293 -1.99279 -1.59100 -0.69290 0.42136 1.40417 1.94895 1.88575 1.23429 0.19779 -0.90041 -1.71773 -1.99920 -1.65702 -0.79793 0.31007 1.32135 1.92043 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.62466 0.63953 -0.58565 -1.59100 -1.99920 -1.65702 -0.69290 0.53129 1.55607 1.99680 1.68805 0.74571 -0.47652 -1.51989 -1.99279 -1.71773 -0.79793 0.42136 1.48250 1.98720 1.74603 0.84951 -0.36586 -1.44391 -1.98001 -1.77293 -0.90041 0.31007 1.40417 1.97123 1.79841 0.95058 -0.25404 -1.36331 -1.96088 -1.82246 -1.00000 0.19779 1.32135 1.94895 1.84504 1.04861 -0.14140 -1.27833 -1.93547 -1.86614 -1.09639 0.08488 1.23429 1.92043 1.88575 1.14329 -0.02830 -1.18927 -1.90385 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.55607 0.42136 -0.90041 -1.82246 -1.93547 -1.18927 0.08488 1.32135 1.97123 1.74603 0.74571 -0.58565 -1.65702 -1.99279 -1.44391 -0.25404 1.04861 1.88575 1.88575 1.04861 -0.25404 -1.44391 -1.99279 -1.65702 -0.58565 0.74571 1.74603 1.97123 1.32135 0.08488 -1.18927 -1.93547 -1.82246 -0.90041 0.42136 1.55607 2.00000 1.55607 0.42136 -0.90041 -1.82246 -1.93547 -1.18927 0.08488 1.32135 1.97123 1.74603 0.74571 -0.58565 -1.65702 -1.99279 -1.44391 -0.25404 1.04861 1.88575 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.48250 0.19779 -1.18927 -1.96088 -1.71773 -0.58565 0.84951 1.84504 1.88575 0.95058 -0.47652 -1.65702 -1.98001 -1.27833 0.08488 1.40417 1.99680 1.55607 0.31007 -1.09639 -1.93547 -1.77293 -0.69290 0.74571 1.79841 1.92043 1.04861 -0.36586 -1.59100 -1.99279 -1.36331 -0.02830 1.32135 1.98720 1.62466 0.42136 -1.00000 -1.90385 -1.82246 -0.79793 0.63953 1.74603 1.94895 1.14329 -0.25404 -1.51989 -1.99920 -1.44391 -0.14140 1.23429 1.97123 1.68805 0.53129 -0.90041 -1.86614 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.40417 -0.02830 -1.44391 -1.99920 -1.36331 0.08488 1.48250 1.99680 1.32135 -0.14140 -1.51989 -1.99279 -1.27833 0.19779 1.55607 1.98720 1.23429 -0.25404 -1.59100 -1.98001 -1.18927 0.31007 1.62466 1.97123 1.14329 -0.36586 -1.65702 -1.96088 -1.09639 0.42136 1.68805 1.94895 1.04861 -0.47652 -1.71773 -1.93547 -1.00000 0.53129 1.74603 1.92043 0.95058 -0.58565 -1.77293 -1.90385 -0.90041 0.63953 1.79841 1.88575 0.84951 -0.69290 -1.82246 -1.86614 -0.79793 0.74571 1.84504 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.32135 -0.25404 -1.65702 -1.93547 -0.90041 0.74571 1.88575 1.74603 0.42136 -1.18927 -1.99279 -1.44391 0.08488 1.55607 1.97123 1.04861 -0.58565 -1.82246 -1.82246 -0.58565 1.04861 1.97123 1.55607 0.08488 -1.44391 -1.99279 -1.18927 0.42136 1.74603 1.88575 0.74571 -0.90041 -1.93547 -1.65702 -0.25404 1.32135 2.00000 1.32135 -0.25404 -1.65702 -1.93547 -0.90041 0.74571 1.88575 1.74603 0.42136 -1.18927 -1.99279 -1.44391 0.08488 1.55607 1.97123 1.04861 -0.58565 -1.82246 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 1.23429 -0.47652 -1.82246 -1.77293 -0.36586 1.32135 1.99680 1.14329 -0.58565 -1.86614 -1.71773 -0.25404 1.40417 1.98720 1.04861 -0.69290 -1.90385 -1.65702 -0.14140 1.48250 1.97123 0.95058 -0.79793 -1.93547 -1.59100 -0.02830 1.55607 1.94895 0.84951 -0.90041 -1.96088 -1.51989 0.08488 1.62466 1.92043 0.74571 -1.00000 -1.98001 -1.44391 0.19779 1.68805 1.88575 0.63953 -1.09639 -1.99279 -1.36331 0.31007 1.74603 1.84504 0.53129 -1.18927 -1.99920 -1.27833 0.42136 1.79841 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 1.14329 -0.69290 -1.93547 -1.51989 0.19779 1.74603 1.79841 0.31007 -1.44391 -1.96088 -0.79793 1.04861 1.99680 1.23429 -0.58565 -1.90385 -1.59100 0.08488 1.68805 1.84504 0.42136 -1.36331 -1.98001 -0.90041 0.95058 1.98720 1.32135 -0.47652 -1.86614 -1.65702 -0.02830 1.62466 1.88575 0.53129 -1.27833 -1.99279 -1.00000 0.84951 1.97123 1.40417 -0.36586 -1.82246 -1.71773 -0.14140 1.55607 1.92043 0.63953 -1.18927 -1.99920 -1.09639 0.74571 1.94895 1.48250 -0.25404 -1.77293 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 1.04861 -0.90041 -1.99279 -1.18927 0.74571 1.97123 1.32135 -0.58565 -1.93547 -1.44391 0.42136 1.88575 1.55607 -0.25404 -1.82246 -1.65702 0.08488 1.74603 1.74603 0.08488 -1.65702 -1.82246 -0.25404 1.55607 1.88575 0.42136 -1.44391 -1.93547 -0.58565 1.32135 1.97123 0.74571 -1.18927 -1.99279 -0.90041 1.04861 2.00000 1.04861 -0.90041 -1.99279 -1.18927 0.74571 1.97123 1.32135 -0.58565 -1.93547 -1.44391 0.42136 1.88575 1.55607 -0.25404 -1.82246 -1.65702 0.08488 1.74603 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.95058 -1.09639 -1.99279 -0.79793 1.23429 1.97123 0.63953 -1.36331 -1.93547 -0.47652 1.48250 1.88575 0.31007 -1.59100 -1.82246 -0.14140 1.68805 1.74603 -0.02830 -1.77293 -1.65702 0.19779 1.84504 1.55607 -0.36586 -1.90385 -1.44391 0.53129 1.94895 1.32135 -0.69290 -1.98001 -1.18927 0.84951 1.99680 1.04861 -1.00000 -1.99920 -0.90041 1.14329 1.98720 0.74571 -1.27833 -1.96088 -0.58565 1.40417 1.92043 0.42136 -1.51989 -1.86614 -0.25404 1.62466 1.79841 0.08488 -1.71773 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.84951 -1.27833 -1.93547 -0.36586 1.62466 1.74603 -0.14140 -1.86614 -1.44391 0.63953 1.98720 1.04861 -1.09639 -1.98001 -0.58565 1.48250 1.84504 0.08488 -1.77293 -1.59100 0.42136 1.94895 1.23429 -0.90041 -1.99920 -0.79793 1.32135 1.92043 0.31007 -1.65702 -1.71773 0.19779 1.88575 1.40417 -0.69290 -1.99279 -1.00000 1.14329 1.97123 0.53129 -1.51989 -1.82246 -0.02830 1.79841 1.55607 -0.47652 -1.96088 -1.18927 0.95058 1.99680 0.74571 -1.36331 -1.90385 -0.25404 1.68805 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.74571 -1.44391 -1.82246 0.08488 1.88575 1.32135 -0.90041 -1.99279 -0.58565 1.55607 1.74603 -0.25404 -1.93547 -1.18927 1.04861 1.97123 0.42136 -1.65702 -1.65702 0.42136 1.97123 1.04861 -1.18927 -1.93547 -0.25404 1.74603 1.55607 -0.58565 -1.99279 -0.90041 1.32135 1.88575 0.08488 -1.82246 -1.44391 0.74571 2.00000 0.74571 -1.44391 -1.82246 0.08488 1.88575 1.32135 -0.90041 -1.99279 -0.58565 1.55607 1.74603 -0.25404 -1.93547 -1.18927 1.04861 1.97123 0.42136 -1.65702 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.63953 -1.59100 -1.65702 0.53129 1.99680 0.74571 -1.51989 -1.71773 0.42136 1.98720 0.84951 -1.44391 -1.77293 0.31007 1.97123 0.95058 -1.36331 -1.82246 0.19779 1.94895 1.04861 -1.27833 -1.86614 0.08488 1.92043 1.14329 -1.18927 -1.90385 -0.02830 1.88575 1.23429 -1.09639 -1.93547 -0.14140 1.84504 1.32135 -1.00000 -1.96088 -0.25404 1.79841 1.40417 -0.90041 -1.98001 -0.36586 1.74603 1.48250 -0.79793 -1.99279 -0.47652 1.68805 1.55607 -0.69290 -1.99920 -0.58565 1.62466 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.53129 -1.71773 -1.44391 0.95058 1.94895 0.08488 -1.90385 -1.09639 1.32135 1.79841 -0.36586 -1.99279 -0.69290 1.62466 1.55607 -0.79793 -1.98001 -0.25404 1.84504 1.23429 -1.18927 -1.86614 0.19779 1.97123 0.84951 -1.51989 -1.65702 0.63953 1.99680 0.42136 -1.77293 -1.36331 1.04861 1.92043 -0.02830 -1.93547 -1.00000 1.40417 1.74603 -0.47652 -1.99920 -0.58565 1.68805 1.48250 -0.90041 -1.96088 -0.14140 1.88575 1.14329 -1.27833 -1.82246 0.31007 1.98720 0.74571 -1.59100 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 0.42136 -1.82246 -1.18927 1.32135 1.74603 -0.58565 -1.99279 -0.25404 1.88575 1.04861 -1.44391 -1.65702 0.74571 1.97123 0.08488 -1.93547 -0.90041 1.55607 1.55607 -0.90041 -1.93547 0.08488 1.97123 0.74571 -1.65702 -1.44391 1.04861 1.88575 -0.25404 -1.99279 -0.58565 1.74603 1.32135 -1.18927 -1.82246 0.42136 2.00000 0.42136 -1.82246 -1.18927 1.32135 1.74603 -0.58565 -1.99279 -0.25404 1.88575 1.04861 -1.44391 -1.65702 0.74571 1.97123 0.08488 -1.93547 -0.90041 1.55607 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 0.31007 -1.90385 -0.90041 1.62466 1.40417 -1.18927 -1.77293 0.63953 1.97123 -0.02830 -1.98001 -0.58565 1.79841 1.14329 -1.44391 -1.59100 0.95058 1.88575 -0.36586 -1.99920 -0.25404 1.92043 0.84951 -1.65702 -1.36331 1.23429 1.74603 -0.69290 -1.96088 0.08488 1.98720 0.53129 -1.82246 -1.09639 1.48250 1.55607 -1.00000 -1.86614 0.42136 1.99680 0.19779 -1.93547 -0.79793 1.68805 1.32135 -1.27833 -1.71773 0.74571 1.94895 -0.14140 -1.99279 -0.47652 1.84504 1.04861 -1.51989 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 0.19779 -1.96088 -0.58565 1.84504 0.95058 -1.65702 -1.27833 1.40417 1.55607 -1.09639 -1.77293 0.74571 1.92043 -0.36586 -1.99279 -0.02830 1.98720 0.42136 -1.90385 -0.79793 1.74603 1.14329 -1.51989 -1.44391 1.23429 1.68805 -0.90041 -1.86614 0.53129 1.97123 -0.14140 -1.99920 -0.25404 1.94895 0.63953 -1.82246 -1.00000 1.62466 1.32135 -1.36331 -1.59100 1.04861 1.79841 -0.69290 -1.93547 0.31007 1.99680 0.08488 -1.98001 -0.47652 1.88575 0.84951 -1.71773 -1.18927 1.48250 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 0.08488 -1.99279 -0.25404 1.97123 0.42136 -1.93547 -0.58565 1.88575 0.74571 -1.82246 -0.90041 1.74603 1.04861 -1.65702 -1.18927 1.55607 1.32135 -1.44391 -1.44391 1.32135 1.55607 -1.18927 -1.65702 1.04861 1.74603 -0.90041 -1.82246 0.74571 1.88575 -0.58565 -1.93547 0.42136 1.97123 -0.25404 -1.99279 0.08488 2.00000 0.08488 -1.99279 -0.25404 1.97123 0.42136 -1.93547 -0.58565 1.88575 0.74571 -1.82246 -0.90041 1.74603 1.04861 -1.65702 -1.18927 1.55607 1.32135 -1.44391 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.02830 -1.99920 0.08488 1.99680 -0.14140 -1.99279 0.19779 1.98720 -0.25404 -1.98001 0.31007 1.97123 -0.36586 -1.96088 0.42136 1.94895 -0.47652 -1.93547 0.53129 1.92043 -0.58565 -1.90385 0.63953 1.88575 -0.69290 -1.86614 0.74571 1.84504 -0.79793 -1.82246 0.84951 1.79841 -0.90041 -1.77293 0.95058 1.74603 -1.00000 -1.71773 1.04861 1.68805 -1.09639 -1.65702 1.14329 1.62466 -1.18927 -1.59100 1.23429 1.55607 -1.27833 -1.51989 1.32135 1.48250 -1.36331 -1.44391 1.40417 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.14140 -1.98001 0.42136 1.92043 -0.69290 -1.82246 0.95058 1.68805 -1.18927 -1.51989 1.40417 1.32135 -1.59100 -1.09639 1.74603 0.84951 -1.86614 -0.58565 1.94895 0.31007 -1.99279 -0.02830 1.99680 -0.25404 -1.96088 0.53129 1.88575 -0.79793 -1.77293 1.04861 1.62466 -1.27833 -1.44391 1.48250 1.23429 -1.65702 -1.00000 1.79841 0.74571 -1.90385 -0.47652 1.97123 0.19779 -1.99920 0.08488 1.98720 -0.36586 -1.93547 0.63953 1.84504 -0.90041 -1.71773 1.14329 1.55607 -1.36331 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -0.25404 -1.93547 0.74571 1.74603 -1.18927 -1.44391 1.55607 1.04861 -1.82246 -0.58565 1.97123 0.08488 -1.99279 0.42136 1.88575 -0.90041 -1.65702 1.32135 1.32135 -1.65702 -0.90041 1.88575 0.42136 -1.99279 0.08488 1.97123 -0.58565 -1.82246 1.04861 1.55607 -1.44391 -1.18927 1.74603 0.74571 -1.93547 -0.25404 2.00000 -0.25404 -1.93547 0.74571 1.74603 -1.18927 -1.44391 1.55607 1.04861 -1.82246 -0.58565 1.97123 0.08488 -1.99279 0.42136 1.88575 -0.90041 -1.65702 1.32135 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -0.36586 -1.86614 1.04861 1.48250 -1.59100 -0.90041 1.92043 0.19779 -1.99279 0.53129 1.79841 -1.18927 -1.36331 1.68805 0.74571 -1.96088 -0.02830 1.97123 -0.69290 -1.71773 1.32135 1.23429 -1.77293 -0.58565 1.98720 -0.14140 -1.93547 0.84951 1.62466 -1.44391 -1.09639 1.84504 0.42136 -1.99920 0.31007 1.88575 -1.00000 -1.51989 1.55607 0.95058 -1.90385 -0.25404 1.99680 -0.47652 -1.82246 1.14329 1.40417 -1.65702 -0.79793 1.94895 0.08488 -1.98001 0.63953 1.74603 -1.27833 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -0.47652 -1.77293 1.32135 1.14329 -1.86614 -0.25404 1.98720 -0.69290 -1.65702 1.48250 0.95058 -1.93547 -0.02830 1.94895 -0.90041 -1.51989 1.62466 0.74571 -1.98001 0.19779 1.88575 -1.09639 -1.36331 1.74603 0.53129 -1.99920 0.42136 1.79841 -1.27833 -1.18927 1.84504 0.31007 -1.99279 0.63953 1.68805 -1.44391 -1.00000 1.92043 0.08488 -1.96088 0.84951 1.55607 -1.59100 -0.79793 1.97123 -0.14140 -1.90385 1.04861 1.40417 -1.71773 -0.58565 1.99680 -0.36586 -1.82246 1.23429 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -0.58565 -1.65702 1.55607 0.74571 -1.99279 0.42136 1.74603 -1.44391 -0.90041 1.97123 -0.25404 -1.82246 1.32135 1.04861 -1.93547 0.08488 1.88575 -1.18927 -1.18927 1.88575 0.08488 -1.93547 1.04861 1.32135 -1.82246 -0.25404 1.97123 -0.90041 -1.44391 1.74603 0.42136 -1.99279 0.74571 1.55607 -1.65702 -0.58565 2.00000 -0.58565 -1.65702 1.55607 0.74571 -1.99279 0.42136 1.74603 -1.44391 -0.90041 1.97123 -0.25404 -1.82246 1.32135 1.04861 -1.93547 0.08488 1.88575 -1.18927 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -0.69290 -1.51989 1.74603 0.31007 -1.96088 1.04861 1.23429 -1.90385 0.08488 1.84504 -1.36331 -0.90041 1.98720 -0.47652 -1.65702 1.62466 0.53129 -1.99279 0.84951 1.40417 -1.82246 -0.14140 1.92043 -1.18927 -1.09639 1.94895 -0.25404 -1.77293 1.48250 0.74571 -1.99920 0.63953 1.55607 -1.71773 -0.36586 1.97123 -1.00000 -1.27833 1.88575 -0.02830 -1.86614 1.32135 0.95058 -1.98001 0.42136 1.68805 -1.59100 -0.58565 1.99680 -0.79793 -1.44391 1.79841 0.19779 -1.93547 1.14329 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -0.79793 -1.36331 1.88575 -0.14140 -1.77293 1.55607 0.53129 -1.98001 1.04861 1.14329 -1.96088 0.42136 1.62466 -1.71773 -0.25404 1.92043 -1.27833 -0.90041 1.99680 -0.69290 -1.44391 1.84504 -0.02830 -1.82246 1.48250 0.63953 -1.99279 0.95058 1.23429 -1.93547 0.31007 1.68805 -1.65702 -0.36586 1.94895 -1.18927 -1.00000 1.98720 -0.58565 -1.51989 1.79841 0.08488 -1.86614 1.40417 0.74571 -1.99920 0.84951 1.32135 -1.90385 0.19779 1.74603 -1.59100 -0.47652 1.97123 -1.09639 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -0.90041 -1.18927 1.97123 -0.58565 -1.44391 1.88575 -0.25404 -1.65702 1.74603 0.08488 -1.82246 1.55607 0.42136 -1.93547 1.32135 0.74571 -1.99279 1.04861 1.04861 -1.99279 0.74571 1.32135 -1.93547 0.42136 1.55607 -1.82246 0.08488 1.74603 -1.65702 -0.25404 1.88575 -1.44391 -0.58565 1.97123 -1.18927 -0.90041 2.00000 -0.90041 -1.18927 1.97123 -0.58565 -1.44391 1.88575 -0.25404 -1.65702 1.74603 0.08488 -1.82246 1.55607 0.42136 -1.93547 1.32135 0.74571 -1.99279 1.04861 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.09639 -0.79793 1.97123 -1.36331 -0.47652 1.88575 -1.59100 -0.14140 1.74603 -1.77293 0.19779 1.55607 -1.90385 0.53129 1.32135 -1.98001 0.84951 1.04861 -1.99920 1.14329 0.74571 -1.96088 1.40417 0.42136 -1.86614 1.62466 0.08488 -1.71773 1.79841 -0.25404 -1.51989 1.92043 -0.58565 -1.27833 1.98720 -0.90041 -1.00000 1.99680 -1.18927 -0.69290 1.94895 -1.44391 -0.36586 1.84504 -1.65702 -0.02830 1.68805 -1.82246 0.31007 1.48250 -1.93547 0.63953 1.23429 -1.99279 0.95058 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.18927 -0.58565 1.88575 -1.65702 0.08488 1.55607 -1.93547 0.74571 1.04861 -1.99279 1.32135 0.42136 -1.82246 1.74603 -0.25404 -1.44391 1.97123 -0.90041 -0.90041 1.97123 -1.44391 -0.25404 1.74603 -1.82246 0.42136 1.32135 -1.99279 1.04861 0.74571 -1.93547 1.55607 0.08488 -1.65702 1.88575 -0.58565 -1.18927 2.00000 -1.18927 -0.58565 1.88575 -1.65702 0.08488 1.55607 -1.93547 0.74571 1.04861 -1.99279 1.32135 0.42136 -1.82246 1.74603 -0.25404 -1.44391 1.97123 -0.90041 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.27833 -0.36586 1.74603 -1.86614 0.63953 1.04861 -1.98001 1.48250 0.08488 -1.59100 1.94895 -0.90041 -0.79793 1.92043 -1.65702 0.19779 1.40417 -1.99279 1.14329 0.53129 -1.82246 1.79841 -0.47652 -1.18927 1.99680 -1.36331 -0.25404 1.68805 -1.90385 0.74571 0.95058 -1.96088 1.55607 -0.02830 -1.51989 1.97123 -1.00000 -0.69290 1.88575 -1.71773 0.31007 1.32135 -1.99920 1.23429 0.42136 -1.77293 1.84504 -0.58565 -1.09639 1.98720 -1.44391 -0.14140 1.62466 -1.93547 0.84951 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.36331 -0.14140 1.55607 -1.98001 1.14329 0.42136 -1.71773 1.92043 -0.90041 -0.69290 1.84504 -1.82246 0.63953 0.95058 -1.93547 1.68805 -0.36586 -1.18927 1.98720 -1.51989 0.08488 1.40417 -1.99920 1.32135 0.19779 -1.59100 1.97123 -1.09639 -0.47652 1.74603 -1.90385 0.84951 0.74571 -1.86614 1.79841 -0.58565 -1.00000 1.94895 -1.65702 0.31007 1.23429 -1.99279 1.48250 -0.02830 -1.44391 1.99680 -1.27833 -0.25404 1.62466 -1.96088 1.04861 0.53129 -1.77293 1.88575 -0.79793 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.44391 0.08488 1.32135 -1.99279 1.55607 -0.25404 -1.18927 1.97123 -1.65702 0.42136 1.04861 -1.93547 1.74603 -0.58565 -0.90041 1.88575 -1.82246 0.74571 0.74571 -1.82246 1.88575 -0.90041 -0.58565 1.74603 -1.93547 1.04861 0.42136 -1.65702 1.97123 -1.18927 -0.25404 1.55607 -1.99279 1.32135 0.08488 -1.44391 2.00000 -1.44391 0.08488 1.32135 -1.99279 1.55607 -0.25404 -1.18927 1.97123 -1.65702 0.42136 1.04861 -1.93547 1.74603 -0.58565 -0.90041 1.88575 -1.82246 0.74571 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.51989 0.31007 1.04861 -1.90385 1.84504 -0.90041 -0.47652 1.62466 -1.99279 1.40417 -0.14140 -1.18927 1.94895 -1.77293 0.74571 0.63953 -1.71773 1.97123 -1.27833 -0.02830 1.32135 -1.98001 1.68805 -0.58565 -0.79793 1.79841 -1.93547 1.14329 0.19779 -1.44391 1.99680 -1.59100 0.42136 0.95058 -1.86614 1.88575 -1.00000 -0.36586 1.55607 -1.99920 1.48250 -0.25404 -1.09639 1.92043 -1.82246 0.84951 0.53129 -1.65702 1.98720 -1.36331 0.08488 1.23429 -1.96088 1.74603 -0.69290 ... ... ..... ....... ......... ........... ............. E44 * 2.00000 -1.59100 0.53129 0.74571 -1.71773 1.98720 -1.44391 0.31007 0.95058 -1.82246 1.94895 -1.27833 0.08488 1.14329 -1.90385 1.88575 -1.09639 -0.14140 1.32135 -1.96088 1.79841 -0.90041 -0.36586 1.48250 -1.99279 1.68805 -0.69290 -0.58565 1.62466 -1.99920 1.55607 -0.47652 -0.79793 1.74603 -1.98001 1.40417 -0.25404 -1.00000 1.84504 -1.93547 1.23429 -0.02830 -1.18927 1.92043 -1.86614 1.04861 0.19779 -1.36331 1.97123 -1.77293 0.84951 0.42136 -1.51989 1.99680 -1.65702 0.63953 ... ... ..... ....... ......... ........... ............. E45 * 2.00000 -1.65702 0.74571 0.42136 -1.44391 1.97123 -1.82246 1.04861 0.08488 -1.18927 1.88575 -1.93547 1.32135 -0.25404 -0.90041 1.74603 -1.99279 1.55607 -0.58565 -0.58565 1.55607 -1.99279 1.74603 -0.90041 -0.25404 1.32135 -1.93547 1.88575 -1.18927 0.08488 1.04861 -1.82246 1.97123 -1.44391 0.42136 0.74571 -1.65702 2.00000 -1.65702 0.74571 0.42136 -1.44391 1.97123 -1.82246 1.04861 0.08488 -1.18927 1.88575 -1.93547 1.32135 -0.25404 -0.90041 1.74603 -1.99279 1.55607 -0.58565 ... ... ..... ....... ......... ........... ............. E46 * 2.00000 -1.71773 0.95058 0.08488 -1.09639 1.79841 -1.99279 1.62466 -0.79793 -0.25404 1.23429 -1.86614 1.97123 -1.51989 0.63953 0.42136 -1.36331 1.92043 -1.93547 1.40417 -0.47652 -0.58565 1.48250 -1.96088 1.88575 -1.27833 0.31007 0.74571 -1.59100 1.98720 -1.82246 1.14329 -0.14140 -0.90041 1.68805 -1.99920 1.74603 -1.00000 -0.02830 1.04861 -1.77293 1.99680 -1.65702 0.84951 0.19779 -1.18927 1.84504 -1.98001 1.55607 -0.69290 -0.36586 1.32135 -1.90385 1.94895 -1.44391 0.53129 ... ... ..... ....... ......... ........... ............. E47 * 2.00000 -1.77293 1.14329 -0.25404 -0.69290 1.48250 -1.93547 1.94895 -1.51989 0.74571 0.19779 -1.09639 1.74603 -1.99920 1.79841 -1.18927 0.31007 0.63953 -1.44391 1.92043 -1.96088 1.55607 -0.79793 -0.14140 1.04861 -1.71773 1.99680 -1.82246 1.23429 -0.36586 -0.58565 1.40417 -1.90385 1.97123 -1.59100 0.84951 0.08488 -1.00000 1.68805 -1.99279 1.84504 -1.27833 0.42136 0.53129 -1.36331 1.88575 -1.98001 1.62466 -0.90041 -0.02830 0.95058 -1.65702 1.98720 -1.86614 1.32135 -0.47652 ... ... ..... ....... ......... ........... ............. E48 * 2.00000 -1.82246 1.32135 -0.58565 -0.25404 1.04861 -1.65702 1.97123 -1.93547 1.55607 -0.90041 0.08488 0.74571 -1.44391 1.88575 -1.99279 1.74603 -1.18927 0.42136 0.42136 -1.18927 1.74603 -1.99279 1.88575 -1.44391 0.74571 0.08488 -0.90041 1.55607 -1.93547 1.97123 -1.65702 1.04861 -0.25404 -0.58565 1.32135 -1.82246 2.00000 -1.82246 1.32135 -0.58565 -0.25404 1.04861 -1.65702 1.97123 -1.93547 1.55607 -0.90041 0.08488 0.74571 -1.44391 1.88575 -1.99279 1.74603 -1.18927 0.42136 ... ... ..... ....... ......... ........... ............. E49 * 2.00000 -1.86614 1.48250 -0.90041 0.19779 0.53129 -1.18927 1.68805 -1.96088 1.97123 -1.71773 1.23429 -0.58565 -0.14140 0.84951 -1.44391 1.84504 -1.99920 1.88575 -1.51989 0.95058 -0.25404 -0.47652 1.14329 -1.65702 1.94895 -1.98001 1.74603 -1.27833 0.63953 0.08488 -0.79793 1.40417 -1.82246 1.99680 -1.90385 1.55607 -1.00000 0.31007 0.42136 -1.09639 1.62466 -1.93547 1.98720 -1.77293 1.32135 -0.69290 -0.02830 0.74571 -1.36331 1.79841 -1.99279 1.92043 -1.59100 1.04861 -0.36586 ... ... ..... ....... ......... ........... ............. E50 * 2.00000 -1.90385 1.62466 -1.18927 0.63953 -0.02830 -0.58565 1.14329 -1.59100 1.88575 -1.99920 1.92043 -1.65702 1.23429 -0.69290 0.08488 0.53129 -1.09639 1.55607 -1.86614 1.99680 -1.93547 1.68805 -1.27833 0.74571 -0.14140 -0.47652 1.04861 -1.51989 1.84504 -1.99279 1.94895 -1.71773 1.32135 -0.79793 0.19779 0.42136 -1.00000 1.48250 -1.82246 1.98720 -1.96088 1.74603 -1.36331 0.84951 -0.25404 -0.36586 0.95058 -1.44391 1.79841 -1.98001 1.97123 -1.77293 1.40417 -0.90041 0.31007 ... ... ..... ....... ......... ........... ............. E51 * 2.00000 -1.93547 1.74603 -1.44391 1.04861 -0.58565 0.08488 0.42136 -0.90041 1.32135 -1.65702 1.88575 -1.99279 1.97123 -1.82246 1.55607 -1.18927 0.74571 -0.25404 -0.25404 0.74571 -1.18927 1.55607 -1.82246 1.97123 -1.99279 1.88575 -1.65702 1.32135 -0.90041 0.42136 0.08488 -0.58565 1.04861 -1.44391 1.74603 -1.93547 2.00000 -1.93547 1.74603 -1.44391 1.04861 -0.58565 0.08488 0.42136 -0.90041 1.32135 -1.65702 1.88575 -1.99279 1.97123 -1.82246 1.55607 -1.18927 0.74571 -0.25404 ... ... ..... ....... ......... ........... ............. E52 * 2.00000 -1.96088 1.84504 -1.65702 1.40417 -1.09639 0.74571 -0.36586 -0.02830 0.42136 -0.79793 1.14329 -1.44391 1.68805 -1.86614 1.97123 -1.99920 1.94895 -1.82246 1.62466 -1.36331 1.04861 -0.69290 0.31007 0.08488 -0.47652 0.84951 -1.18927 1.48250 -1.71773 1.88575 -1.98001 1.99680 -1.93547 1.79841 -1.59100 1.32135 -1.00000 0.63953 -0.25404 -0.14140 0.53129 -0.90041 1.23429 -1.51989 1.74603 -1.90385 1.98720 -1.99279 1.92043 -1.77293 1.55607 -1.27833 0.95058 -0.58565 0.19779 ... ... ..... ....... ......... ........... ............. E53 * 2.00000 -1.98001 1.92043 -1.82246 1.68805 -1.51989 1.32135 -1.09639 0.84951 -0.58565 0.31007 -0.02830 -0.25404 0.53129 -0.79793 1.04861 -1.27833 1.48250 -1.65702 1.79841 -1.90385 1.97123 -1.99920 1.98720 -1.93547 1.84504 -1.71773 1.55607 -1.36331 1.14329 -0.90041 0.63953 -0.36586 0.08488 0.19779 -0.47652 0.74571 -1.00000 1.23429 -1.44391 1.62466 -1.77293 1.88575 -1.96088 1.99680 -1.99279 1.94895 -1.86614 1.74603 -1.59100 1.40417 -1.18927 0.95058 -0.69290 0.42136 -0.14140 ... ... ..... ....... ......... ........... ............. E54 * 2.00000 -1.99279 1.97123 -1.93547 1.88575 -1.82246 1.74603 -1.65702 1.55607 -1.44391 1.32135 -1.18927 1.04861 -0.90041 0.74571 -0.58565 0.42136 -0.25404 0.08488 0.08488 -0.25404 0.42136 -0.58565 0.74571 -0.90041 1.04861 -1.18927 1.32135 -1.44391 1.55607 -1.65702 1.74603 -1.82246 1.88575 -1.93547 1.97123 -1.99279 2.00000 -1.99279 1.97123 -1.93547 1.88575 -1.82246 1.74603 -1.65702 1.55607 -1.44391 1.32135 -1.18927 1.04861 -0.90041 0.74571 -0.58565 0.42136 -0.25404 0.08488 ... ... ..... ....... ......... ........... ............. E55 * 2.00000 -1.99920 1.99680 -1.99279 1.98720 -1.98001 1.97123 -1.96088 1.94895 -1.93547 1.92043 -1.90385 1.88575 -1.86614 1.84504 -1.82246 1.79841 -1.77293 1.74603 -1.71773 1.68805 -1.65702 1.62466 -1.59100 1.55607 -1.51989 1.48250 -1.44391 1.40417 -1.36331 1.32135 -1.27833 1.23429 -1.18927 1.14329 -1.09639 1.04861 -1.00000 0.95058 -0.90041 0.84951 -0.79793 0.74571 -0.69290 0.63953 -0.58565 0.53129 -0.47652 0.42136 -0.36586 0.31007 -0.25404 0.19779 -0.14140 0.08488 -0.02830 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.996796698525 = 2*cos(2*π/111) 1.987197055239 = 2*cos(4*π/111) 1.971231820695 = 2*cos(6*π/111) = 2*cos(2*π/37) 1.948952136352 = 2*cos(8*π/111) 1.920429370755 = 2*cos(10*π/111) 1.885754890922 = 2*cos(12*π/111) = 2*cos(4*π/37) 1.845039769665 = 2*cos(14*π/111) 1.798414429792 = 2*cos(16*π/111) 1.746028226322 = 2*cos(18*π/111) = 2*cos(6*π/37) 1.688048968060 = 2*cos(20*π/111) 1.624662380048 = 2*cos(22*π/111) 1.556071508637 = 2*cos(24*π/111) = 2*cos(8*π/37) 1.482496071067 = 2*cos(26*π/111) 1.404171751645 = 2*cos(28*π/111) 1.321349446780 = 2*cos(30*π/111) = 2*cos(10*π/37) 1.234294461283 = 2*cos(32*π/111) 1.143285658517 = 2*cos(34*π/111) 1.048614567114 = 2*cos(36*π/111) = 2*cos(12*π/37) 0.950584447122 = 2*cos(38*π/111) 0.849509318568 = 2*cos(40*π/111) 0.745712955561 = 2*cos(42*π/111) = 2*cos(14*π/37) 0.639527849142 = 2*cos(44*π/111) 0.531294142222 = 2*cos(46*π/111) 0.421358539991 = 2*cos(48*π/111) = 2*cos(16*π/37) 0.310073199328 = 2*cos(50*π/111) 0.197794600728 = 2*cos(52*π/111) 0.084882406392 = 2*cos(54*π/111) = 2*cos(18*π/37) -0.028301691882 = 2*cos(56*π/111) -0.141395131304 = 2*cos(58*π/111) -0.254035639494 = 2*cos(60*π/111) = 2*cos(20*π/37) -0.365862394945 = 2*cos(62*π/111) -0.476517182846 = 2*cos(64*π/111) -0.585645542553 = 2*cos(66*π/111) = 2*cos(22*π/37) -0.692897903029 = 2*cos(68*π/111) -0.797930702631 = 2*cos(70*π/111) -0.900407489635 = 2*cos(72*π/111) = 2*cos(24*π/37) -1.096389208889 = 2*cos(76*π/111) -1.189266352609 = 2*cos(78*π/111) = 2*cos(26*π/37) -1.278333917666 = 2*cos(80*π/111) -1.363306593799 = 2*cos(82*π/111) -1.443912187909 = 2*cos(84*π/111) = 2*cos(28*π/37) -1.519892495977 = 2*cos(86*π/111) -1.591004130171 = 2*cos(88*π/111) -1.657019298488 = 2*cos(90*π/111) = 2*cos(30*π/37) -1.717726534441 = 2*cos(92*π/111) -1.772931374452 = 2*cos(94*π/111) -1.822456980776 = 2*cos(96*π/111) = 2*cos(32*π/37) -1.866144707965 = 2*cos(98*π/111) -1.903854611058 = 2*cos(100*π/111) -1.935465893867 = 2*cos(102*π/111) = 2*cos(34*π/37) -1.960877295923 = 2*cos(104*π/111) -1.980007416844 = 2*cos(106*π/111) -1.992794977085 = 2*cos(108*π/111) = 2*cos(36*π/37) -1.999199014237 = 2*cos(110*π/111) Symmetry of Rotations and Cartesian products A R+p+d+f+g+h+i+j+k+l+m Rz, z, z2, z3, z4, z5, z6 E1 R+p+d+f+g+h+i+j+k+l+m {Rx, Ry}, {x, y}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} E2 d+f+g+h+i+j+k+l+m {x2−y2, xy}, {z(x2−y2), xyz}, {z2(x2−y2), xyz2}, {z3(x2−y2), xyz3}, {z4(x2−y2), xyz4} E3 f+g+h+i+j+k+l+m {x(x2−3y2), y(3x2−y2)}, {xz(x2−3y2), yz(3x2−y2)}, {xz2(x2−3y2), yz2(3x2−y2)}, {xz3(x2−3y2), yz3(3x2−y2)} E4 g+h+i+j+k+l+m {(x2−y2)2−4x2y2, xy(x2−y2)}, {z((x2−y2)2−4x2y2), xyz(x2−y2)}, {z2((x2−y2)2−4x2y2), xyz2(x2−y2)} E5 h+i+j+k+l+m {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2−y2)((5−2√5)x2−y2)}, {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2−y2)((5−2√5)x2−y2)} E6 i+j+k+l+m {x2(x2−3y2)2−y2(3x2−y2)2, xy(x2−3y2)(3x2−y2)} E7 j+k+l+m E8 k+l+m E9 l+m E10 m Notes: α The order of the C111 point group is 111, and the order of the principal axis (C111) is 111. The group has 56 irreducible representations. β The C111 point group is generated by one single symmetry element, C111. Therefore, it is a cyclic group. γ The lowest nonvanishing multipole moment in C111 is 2 (dipole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C111 group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition). In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. ε Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 110 cases have been combined into 55 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 55 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 55 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. η The point group is chiral, as it does not contain any mirroring operation. θ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. ι The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. All characters of this group can be expressed using complex numbers, elementary arithmetic operations, square roots and third roots.
| C109 | ||
| C110 | ||
| C111 | C111v C111h D111 D111h D111d | |
| C112 | ||
| C113 |
This Character Table for the C111 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.