Character Table for Point Group D85d

Character table for the D_85d point group

D85d E 2 C85 2 C85^2 2 C85^3 2 C85^4 2 C17 2 C85^6 2 C85^7 2 C85^8 2 C85^9 2 C17^2 2 C85^11 2 C85^12 2 C85^13 2 C85^14 2 C17^3 2 C85^16 2 C5 2 C85^18 2 C85^19 2 C17^4 2 C85^21 2 C85^22 2 C85^23 2 C85^24 2 C17^5 2 C85^26 2 C85^27 2 C85^28 2 C85^29 2 C17^6 2 C85^31 2 C85^32 2 C85^33 2 C5^2 2 C17^7 2 C85^36 2 C85^37 2 C85^38 2 C85^39 2 C17^8 2 C85^41 2 C85^42 85 C2' i 2 S170 2 S170^3 2 S34 2 S170^7 2 S170^9 2 S170^11 2 S170^13 2 S34^3 2 S10 2 S170^19 2 S170^21 2 S170^23 2 S34^5 2 S170^27 2 S170^29 2 S170^31 2 S170^33 2 S34^7 2 S170^37 2 S170^39 2 S170^41 2 S170^43 2 S34^9 2 S170^47 2 S170^49 2 S10^3 2 S170^53 2 S34^11 2 S170^57 2 S170^59 2 S170^61 2 S170^63 2 S34^13 2 S170^67 2 S170^69 2 S170^71 2 S170^73 2 S34^15 2 S170^77 2 S170^79 2 S170^81 2 S170^83 85 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 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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. E1g 2.00000 1.99454 1.97818 1.95102 1.91321 1.86494 1.80649 1.73818 1.66037 1.57349 1.47802 1.37447 1.26342 1.14547 1.02126 0.89148 0.75682 0.61803 0.47587 0.33111 0.18454 0.03696 -0.11082 -0.25800 -0.40376 -0.54733 -0.68790 -0.82471 -0.95702 -1.08411 -1.20527 -1.31985 -1.42722 -1.52680 -1.61803 -1.70043 -1.77355 -1.83697 -1.89037 -1.93344 -1.96595 -1.98772 -1.99863 0.00000 2.00000 -1.99863 -1.98772 -1.96595 -1.93344 -1.89037 -1.83697 -1.77355 -1.70043 -1.61803 -1.52680 -1.42722 -1.31985 -1.20527 -1.08411 -0.95702 -0.82471 -0.68790 -0.54733 -0.40376 -0.25800 -0.11082 0.03696 0.18454 0.33111 0.47587 0.61803 0.75682 0.89148 1.02126 1.14547 1.26342 1.37447 1.47802 1.57349 1.66037 1.73818 1.80649 1.86494 1.91321 1.95102 1.97818 1.99454 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.97818 1.91321 1.80649 1.66037 1.47802 1.26342 1.02126 0.75682 0.47587 0.18454 -0.11082 -0.40376 -0.68790 -0.95702 -1.20527 -1.42722 -1.61803 -1.77355 -1.89037 -1.96595 -1.99863 -1.98772 -1.93344 -1.83697 -1.70043 -1.52680 -1.31985 -1.08411 -0.82471 -0.54733 -0.25800 0.03696 0.33111 0.61803 0.89148 1.14547 1.37447 1.57349 1.73818 1.86494 1.95102 1.99454 0.00000 2.00000 1.99454 1.95102 1.86494 1.73818 1.57349 1.37447 1.14547 0.89148 0.61803 0.33111 0.03696 -0.25800 -0.54733 -0.82471 -1.08411 -1.31985 -1.52680 -1.70043 -1.83697 -1.93344 -1.98772 -1.99863 -1.96595 -1.89037 -1.77355 -1.61803 -1.42722 -1.20527 -0.95702 -0.68790 -0.40376 -0.11082 0.18454 0.47587 0.75682 1.02126 1.26342 1.47802 1.66037 1.80649 1.91321 1.97818 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 2.00000 1.95102 1.80649 1.57349 1.26342 0.89148 0.47587 0.03696 -0.40376 -0.82471 -1.20527 -1.52680 -1.77355 -1.93344 -1.99863 -1.96595 -1.83697 -1.61803 -1.31985 -0.95702 -0.54733 -0.11082 0.33111 0.75682 1.14547 1.47802 1.73818 1.91321 1.99454 1.97818 1.86494 1.66037 1.37447 1.02126 0.61803 0.18454 -0.25800 -0.68790 -1.08411 -1.42722 -1.70043 -1.89037 -1.98772 0.00000 2.00000 -1.98772 -1.89037 -1.70043 -1.42722 -1.08411 -0.68790 -0.25800 0.18454 0.61803 1.02126 1.37447 1.66037 1.86494 1.97818 1.99454 1.91321 1.73818 1.47802 1.14547 0.75682 0.33111 -0.11082 -0.54733 -0.95702 -1.31985 -1.61803 -1.83697 -1.96595 -1.99863 -1.93344 -1.77355 -1.52680 -1.20527 -0.82471 -0.40376 0.03696 0.47587 0.89148 1.26342 1.57349 1.80649 1.95102 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g 2.00000 1.91321 1.66037 1.26342 0.75682 0.18454 -0.40376 -0.95702 -1.42722 -1.77355 -1.96595 -1.98772 -1.83697 -1.52680 -1.08411 -0.54733 0.03696 0.61803 1.14547 1.57349 1.86494 1.99454 1.95102 1.73818 1.37447 0.89148 0.33111 -0.25800 -0.82471 -1.31985 -1.70043 -1.93344 -1.99863 -1.89037 -1.61803 -1.20527 -0.68790 -0.11082 0.47587 1.02126 1.47802 1.80649 1.97818 0.00000 2.00000 1.97818 1.80649 1.47802 1.02126 0.47587 -0.11082 -0.68790 -1.20527 -1.61803 -1.89037 -1.99863 -1.93344 -1.70043 -1.31985 -0.82471 -0.25800 0.33111 0.89148 1.37447 1.73818 1.95102 1.99454 1.86494 1.57349 1.14547 0.61803 0.03696 -0.54733 -1.08411 -1.52680 -1.83697 -1.98772 -1.96595 -1.77355 -1.42722 -0.95702 -0.40376 0.18454 0.75682 1.26342 1.66037 1.91321 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 0.00000 2.00000 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 2.00000 1.80649 1.26342 0.47587 -0.40376 -1.20527 -1.77355 -1.99863 -1.83697 -1.31985 -0.54733 0.33111 1.14547 1.73818 1.99454 1.86494 1.37447 0.61803 -0.25800 -1.08411 -1.70043 -1.98772 -1.89037 -1.42722 -0.68790 0.18454 1.02126 1.66037 1.97818 1.91321 1.47802 0.75682 -0.11082 -0.95702 -1.61803 -1.96595 -1.93344 -1.52680 -0.82471 0.03696 0.89148 1.57349 1.95102 0.00000 2.00000 1.95102 1.57349 0.89148 0.03696 -0.82471 -1.52680 -1.93344 -1.96595 -1.61803 -0.95702 -0.11082 0.75682 1.47802 1.91321 1.97818 1.66037 1.02126 0.18454 -0.68790 -1.42722 -1.89037 -1.98772 -1.70043 -1.08411 -0.25800 0.61803 1.37447 1.86494 1.99454 1.73818 1.14547 0.33111 -0.54733 -1.31985 -1.83697 -1.99863 -1.77355 -1.20527 -0.40376 0.47587 1.26342 1.80649 0.00000 ... ... ..... ....... ......... ........... TT........... E7g 2.00000 1.73818 1.02126 0.03696 -0.95702 -1.70043 -1.99863 -1.77355 -1.08411 -0.11082 0.89148 1.66037 1.99454 1.80649 1.14547 0.18454 -0.82471 -1.61803 -1.98772 -1.83697 -1.20527 -0.25800 0.75682 1.57349 1.97818 1.86494 1.26342 0.33111 -0.68790 -1.52680 -1.96595 -1.89037 -1.31985 -0.40376 0.61803 1.47802 1.95102 1.91321 1.37447 0.47587 -0.54733 -1.42722 -1.93344 0.00000 2.00000 -1.93344 -1.42722 -0.54733 0.47587 1.37447 1.91321 1.95102 1.47802 0.61803 -0.40376 -1.31985 -1.89037 -1.96595 -1.52680 -0.68790 0.33111 1.26342 1.86494 1.97818 1.57349 0.75682 -0.25800 -1.20527 -1.83697 -1.98772 -1.61803 -0.82471 0.18454 1.14547 1.80649 1.99454 1.66037 0.89148 -0.11082 -1.08411 -1.77355 -1.99863 -1.70043 -0.95702 0.03696 1.02126 1.73818 0.00000 ... ... ..... ....... ......... ........... ............. E8g 2.00000 1.66037 0.75682 -0.40376 -1.42722 -1.96595 -1.83697 -1.08411 0.03696 1.14547 1.86494 1.95102 1.37447 0.33111 -0.82471 -1.70043 -1.99863 -1.61803 -0.68790 0.47587 1.47802 1.97818 1.80649 1.02126 -0.11082 -1.20527 -1.89037 -1.93344 -1.31985 -0.25800 0.89148 1.73818 1.99454 1.57349 0.61803 -0.54733 -1.52680 -1.98772 -1.77355 -0.95702 0.18454 1.26342 1.91321 0.00000 2.00000 1.91321 1.26342 0.18454 -0.95702 -1.77355 -1.98772 -1.52680 -0.54733 0.61803 1.57349 1.99454 1.73818 0.89148 -0.25800 -1.31985 -1.93344 -1.89037 -1.20527 -0.11082 1.02126 1.80649 1.97818 1.47802 0.47587 -0.68790 -1.61803 -1.99863 -1.70043 -0.82471 0.33111 1.37447 1.95102 1.86494 1.14547 0.03696 -1.08411 -1.83697 -1.96595 -1.42722 -0.40376 0.75682 1.66037 0.00000 ... ... ..... ....... ......... ........... ............. E9g 2.00000 1.57349 0.47587 -0.82471 -1.77355 -1.96595 -1.31985 -0.11082 1.14547 1.91321 1.86494 1.02126 -0.25800 -1.42722 -1.98772 -1.70043 -0.68790 0.61803 1.66037 1.99454 1.47802 0.33111 -0.95702 -1.83697 -1.93344 -1.20527 0.03696 1.26342 1.95102 1.80649 0.89148 -0.40376 -1.52680 -1.99863 -1.61803 -0.54733 0.75682 1.73818 1.97818 1.37447 0.18454 -1.08411 -1.89037 0.00000 2.00000 -1.89037 -1.08411 0.18454 1.37447 1.97818 1.73818 0.75682 -0.54733 -1.61803 -1.99863 -1.52680 -0.40376 0.89148 1.80649 1.95102 1.26342 0.03696 -1.20527 -1.93344 -1.83697 -0.95702 0.33111 1.47802 1.99454 1.66037 0.61803 -0.68790 -1.70043 -1.98772 -1.42722 -0.25800 1.02126 1.86494 1.91321 1.14547 -0.11082 -1.31985 -1.96595 -1.77355 -0.82471 0.47587 1.57349 0.00000 ... ... ..... ....... ......... ........... ............. E10g 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 0.00000 2.00000 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 1.37447 -0.11082 -1.52680 -1.98772 -1.20527 0.33111 1.66037 1.95102 1.02126 -0.54733 -1.77355 -1.89037 -0.82471 0.75682 1.86494 1.80649 0.61803 -0.95702 -1.93344 -1.70043 -0.40376 1.14547 1.97818 1.57349 0.18454 -1.31985 -1.99863 -1.42722 0.03696 1.47802 1.99454 1.26342 -0.25800 -1.61803 -1.96595 -1.08411 0.47587 1.73818 1.91321 0.89148 -0.68790 -1.83697 0.00000 2.00000 -1.83697 -0.68790 0.89148 1.91321 1.73818 0.47587 -1.08411 -1.96595 -1.61803 -0.25800 1.26342 1.99454 1.47802 0.03696 -1.42722 -1.99863 -1.31985 0.18454 1.57349 1.97818 1.14547 -0.40376 -1.70043 -1.93344 -0.95702 0.61803 1.80649 1.86494 0.75682 -0.82471 -1.89037 -1.77355 -0.54733 1.02126 1.95102 1.66037 0.33111 -1.20527 -1.98772 -1.52680 -0.11082 1.37447 0.00000 ... ... ..... ....... ......... ........... ............. E12g 2.00000 1.26342 -0.40376 -1.77355 -1.83697 -0.54733 1.14547 1.99454 1.37447 -0.25800 -1.70043 -1.89037 -0.68790 1.02126 1.97818 1.47802 -0.11082 -1.61803 -1.93344 -0.82471 0.89148 1.95102 1.57349 0.03696 -1.52680 -1.96595 -0.95702 0.75682 1.91321 1.66037 0.18454 -1.42722 -1.98772 -1.08411 0.61803 1.86494 1.73818 0.33111 -1.31985 -1.99863 -1.20527 0.47587 1.80649 0.00000 2.00000 1.80649 0.47587 -1.20527 -1.99863 -1.31985 0.33111 1.73818 1.86494 0.61803 -1.08411 -1.98772 -1.42722 0.18454 1.66037 1.91321 0.75682 -0.95702 -1.96595 -1.52680 0.03696 1.57349 1.95102 0.89148 -0.82471 -1.93344 -1.61803 -0.11082 1.47802 1.97818 1.02126 -0.68790 -1.89037 -1.70043 -0.25800 1.37447 1.99454 1.14547 -0.54733 -1.83697 -1.77355 -0.40376 1.26342 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 1.14547 -0.68790 -1.93344 -1.52680 0.18454 1.73818 1.80649 0.33111 -1.42722 -1.96595 -0.82471 1.02126 1.99454 1.26342 -0.54733 -1.89037 -1.61803 0.03696 1.66037 1.86494 0.47587 -1.31985 -1.98772 -0.95702 0.89148 1.97818 1.37447 -0.40376 -1.83697 -1.70043 -0.11082 1.57349 1.91321 0.61803 -1.20527 -1.99863 -1.08411 0.75682 1.95102 1.47802 -0.25800 -1.77355 0.00000 2.00000 -1.77355 -0.25800 1.47802 1.95102 0.75682 -1.08411 -1.99863 -1.20527 0.61803 1.91321 1.57349 -0.11082 -1.70043 -1.83697 -0.40376 1.37447 1.97818 0.89148 -0.95702 -1.98772 -1.31985 0.47587 1.86494 1.66037 0.03696 -1.61803 -1.89037 -0.54733 1.26342 1.99454 1.02126 -0.82471 -1.96595 -1.42722 0.33111 1.80649 1.73818 0.18454 -1.52680 -1.93344 -0.68790 1.14547 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 1.02126 -0.95702 -1.99863 -1.08411 0.89148 1.99454 1.14547 -0.82471 -1.98772 -1.20527 0.75682 1.97818 1.26342 -0.68790 -1.96595 -1.31985 0.61803 1.95102 1.37447 -0.54733 -1.93344 -1.42722 0.47587 1.91321 1.47802 -0.40376 -1.89037 -1.52680 0.33111 1.86494 1.57349 -0.25800 -1.83697 -1.61803 0.18454 1.80649 1.66037 -0.11082 -1.77355 -1.70043 0.03696 1.73818 0.00000 2.00000 1.73818 0.03696 -1.70043 -1.77355 -0.11082 1.66037 1.80649 0.18454 -1.61803 -1.83697 -0.25800 1.57349 1.86494 0.33111 -1.52680 -1.89037 -0.40376 1.47802 1.91321 0.47587 -1.42722 -1.93344 -0.54733 1.37447 1.95102 0.61803 -1.31985 -1.96595 -0.68790 1.26342 1.97818 0.75682 -1.20527 -1.98772 -0.82471 1.14547 1.99454 0.89148 -1.08411 -1.99863 -0.95702 1.02126 0.00000 ... ... ..... ....... ......... ........... ............. E15g 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 0.00000 2.00000 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 0.00000 ... ... ..... ....... ......... ........... ............. E16g 2.00000 0.75682 -1.42722 -1.83697 0.03696 1.86494 1.37447 -0.82471 -1.99863 -0.68790 1.47802 1.80649 -0.11082 -1.89037 -1.31985 0.89148 1.99454 0.61803 -1.52680 -1.77355 0.18454 1.91321 1.26342 -0.95702 -1.98772 -0.54733 1.57349 1.73818 -0.25800 -1.93344 -1.20527 1.02126 1.97818 0.47587 -1.61803 -1.70043 0.33111 1.95102 1.14547 -1.08411 -1.96595 -0.40376 1.66037 0.00000 2.00000 1.66037 -0.40376 -1.96595 -1.08411 1.14547 1.95102 0.33111 -1.70043 -1.61803 0.47587 1.97818 1.02126 -1.20527 -1.93344 -0.25800 1.73818 1.57349 -0.54733 -1.98772 -0.95702 1.26342 1.91321 0.18454 -1.77355 -1.52680 0.61803 1.99454 0.89148 -1.31985 -1.89037 -0.11082 1.80649 1.47802 -0.68790 -1.99863 -0.82471 1.37447 1.86494 0.03696 -1.83697 -1.42722 0.75682 0.00000 ... ... ..... ....... ......... ........... ............. E17g 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 -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 2.00000 0.61803 -1.61803 -1.61803 0.61803 0.00000 ... ... ..... ....... ......... ........... ............. E18g 2.00000 0.47587 -1.77355 -1.31985 1.14547 1.86494 -0.25800 -1.98772 -0.68790 1.66037 1.47802 -0.95702 -1.93344 0.03696 1.95102 0.89148 -1.52680 -1.61803 0.75682 1.97818 0.18454 -1.89037 -1.08411 1.37447 1.73818 -0.54733 -1.99863 -0.40376 1.80649 1.26342 -1.20527 -1.83697 0.33111 1.99454 0.61803 -1.70043 -1.42722 1.02126 1.91321 -0.11082 -1.96595 -0.82471 1.57349 0.00000 2.00000 1.57349 -0.82471 -1.96595 -0.11082 1.91321 1.02126 -1.42722 -1.70043 0.61803 1.99454 0.33111 -1.83697 -1.20527 1.26342 1.80649 -0.40376 -1.99863 -0.54733 1.73818 1.37447 -1.08411 -1.89037 0.18454 1.97818 0.75682 -1.61803 -1.52680 0.89148 1.95102 0.03696 -1.93344 -0.95702 1.47802 1.66037 -0.68790 -1.98772 -0.25800 1.86494 1.14547 -1.31985 -1.77355 0.47587 0.00000 ... ... ..... ....... ......... ........... ............. E19g 2.00000 0.33111 -1.89037 -0.95702 1.57349 1.47802 -1.08411 -1.83697 0.47587 1.99454 0.18454 -1.93344 -0.82471 1.66037 1.37447 -1.20527 -1.77355 0.61803 1.97818 0.03696 -1.96595 -0.68790 1.73818 1.26342 -1.31985 -1.70043 0.75682 1.95102 -0.11082 -1.98772 -0.54733 1.80649 1.14547 -1.42722 -1.61803 0.89148 1.91321 -0.25800 -1.99863 -0.40376 1.86494 1.02126 -1.52680 0.00000 2.00000 -1.52680 1.02126 1.86494 -0.40376 -1.99863 -0.25800 1.91321 0.89148 -1.61803 -1.42722 1.14547 1.80649 -0.54733 -1.98772 -0.11082 1.95102 0.75682 -1.70043 -1.31985 1.26342 1.73818 -0.68790 -1.96595 0.03696 1.97818 0.61803 -1.77355 -1.20527 1.37447 1.66037 -0.82471 -1.93344 0.18454 1.99454 0.47587 -1.83697 -1.08411 1.47802 1.57349 -0.95702 -1.89037 0.33111 0.00000 ... ... ..... ....... ......... ........... ............. E20g 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 0.00000 2.00000 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454 0.00000 ... ... ..... ....... ......... ........... ............. E21g 2.00000 0.03696 -1.99863 -0.11082 1.99454 0.18454 -1.98772 -0.25800 1.97818 0.33111 -1.96595 -0.40376 1.95102 0.47587 -1.93344 -0.54733 1.91321 0.61803 -1.89037 -0.68790 1.86494 0.75682 -1.83697 -0.82471 1.80649 0.89148 -1.77355 -0.95702 1.73818 1.02126 -1.70043 -1.08411 1.66037 1.14547 -1.61803 -1.20527 1.57349 1.26342 -1.52680 -1.31985 1.47802 1.37447 -1.42722 0.00000 2.00000 -1.42722 1.37447 1.47802 -1.31985 -1.52680 1.26342 1.57349 -1.20527 -1.61803 1.14547 1.66037 -1.08411 -1.70043 1.02126 1.73818 -0.95702 -1.77355 0.89148 1.80649 -0.82471 -1.83697 0.75682 1.86494 -0.68790 -1.89037 0.61803 1.91321 -0.54733 -1.93344 0.47587 1.95102 -0.40376 -1.96595 0.33111 1.97818 -0.25800 -1.98772 0.18454 1.99454 -0.11082 -1.99863 0.03696 0.00000 ... ... ..... ....... ......... ........... ............. E22g 2.00000 -0.11082 -1.98772 0.33111 1.95102 -0.54733 -1.89037 0.75682 1.80649 -0.95702 -1.70043 1.14547 1.57349 -1.31985 -1.42722 1.47802 1.26342 -1.61803 -1.08411 1.73818 0.89148 -1.83697 -0.68790 1.91321 0.47587 -1.96595 -0.25800 1.99454 0.03696 -1.99863 0.18454 1.97818 -0.40376 -1.93344 0.61803 1.86494 -0.82471 -1.77355 1.02126 1.66037 -1.20527 -1.52680 1.37447 0.00000 2.00000 1.37447 -1.52680 -1.20527 1.66037 1.02126 -1.77355 -0.82471 1.86494 0.61803 -1.93344 -0.40376 1.97818 0.18454 -1.99863 0.03696 1.99454 -0.25800 -1.96595 0.47587 1.91321 -0.68790 -1.83697 0.89148 1.73818 -1.08411 -1.61803 1.26342 1.47802 -1.42722 -1.31985 1.57349 1.14547 -1.70043 -0.95702 1.80649 0.75682 -1.89037 -0.54733 1.95102 0.33111 -1.98772 -0.11082 0.00000 ... ... ..... ....... ......... ........... ............. E23g 2.00000 -0.25800 -1.93344 0.75682 1.73818 -1.20527 -1.42722 1.57349 1.02126 -1.83697 -0.54733 1.97818 0.03696 -1.98772 0.47587 1.86494 -0.95702 -1.61803 1.37447 1.26342 -1.70043 -0.82471 1.91321 0.33111 -1.99863 0.18454 1.95102 -0.68790 -1.77355 1.14547 1.47802 -1.52680 -1.08411 1.80649 0.61803 -1.96595 -0.11082 1.99454 -0.40376 -1.89037 0.89148 1.66037 -1.31985 0.00000 2.00000 -1.31985 1.66037 0.89148 -1.89037 -0.40376 1.99454 -0.11082 -1.96595 0.61803 1.80649 -1.08411 -1.52680 1.47802 1.14547 -1.77355 -0.68790 1.95102 0.18454 -1.99863 0.33111 1.91321 -0.82471 -1.70043 1.26342 1.37447 -1.61803 -0.95702 1.86494 0.47587 -1.98772 0.03696 1.97818 -0.54733 -1.83697 1.02126 1.57349 -1.42722 -1.20527 1.73818 0.75682 -1.93344 -0.25800 0.00000 ... ... ..... ....... ......... ........... ............. E24g 2.00000 -0.40376 -1.83697 1.14547 1.37447 -1.70043 -0.68790 1.97818 -0.11082 -1.93344 0.89148 1.57349 -1.52680 -0.95702 1.91321 0.18454 -1.98772 0.61803 1.73818 -1.31985 -1.20527 1.80649 0.47587 -1.99863 0.33111 1.86494 -1.08411 -1.42722 1.66037 0.75682 -1.96595 0.03696 1.95102 -0.82471 -1.61803 1.47802 1.02126 -1.89037 -0.25800 1.99454 -0.54733 -1.77355 1.26342 0.00000 2.00000 1.26342 -1.77355 -0.54733 1.99454 -0.25800 -1.89037 1.02126 1.47802 -1.61803 -0.82471 1.95102 0.03696 -1.96595 0.75682 1.66037 -1.42722 -1.08411 1.86494 0.33111 -1.99863 0.47587 1.80649 -1.20527 -1.31985 1.73818 0.61803 -1.98772 0.18454 1.91321 -0.95702 -1.52680 1.57349 0.89148 -1.93344 -0.11082 1.97818 -0.68790 -1.70043 1.37447 1.14547 -1.83697 -0.40376 0.00000 ... ... ..... ....... ......... ........... ............. E25g 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 0.00000 2.00000 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733 0.00000 ... ... ..... ....... ......... ........... ............. E26g 2.00000 -0.68790 -1.52680 1.73818 0.33111 -1.96595 1.02126 1.26342 -1.89037 0.03696 1.86494 -1.31985 -0.95702 1.97818 -0.40376 -1.70043 1.57349 0.61803 -1.99863 0.75682 1.47802 -1.77355 -0.25800 1.95102 -1.08411 -1.20527 1.91321 -0.11082 -1.83697 1.37447 0.89148 -1.98772 0.47587 1.66037 -1.61803 -0.54733 1.99454 -0.82471 -1.42722 1.80649 0.18454 -1.93344 1.14547 0.00000 2.00000 1.14547 -1.93344 0.18454 1.80649 -1.42722 -0.82471 1.99454 -0.54733 -1.61803 1.66037 0.47587 -1.98772 0.89148 1.37447 -1.83697 -0.11082 1.91321 -1.20527 -1.08411 1.95102 -0.25800 -1.77355 1.47802 0.75682 -1.99863 0.61803 1.57349 -1.70043 -0.40376 1.97818 -0.95702 -1.31985 1.86494 0.03696 -1.89037 1.26342 1.02126 -1.96595 0.33111 1.73818 -1.52680 -0.68790 0.00000 ... ... ..... ....... ......... ........... ............. E27g 2.00000 -0.82471 -1.31985 1.91321 -0.25800 -1.70043 1.66037 0.33111 -1.93344 1.26342 0.89148 -1.99863 0.75682 1.37447 -1.89037 0.18454 1.73818 -1.61803 -0.40376 1.95102 -1.20527 -0.95702 1.99454 -0.68790 -1.42722 1.86494 -0.11082 -1.77355 1.57349 0.47587 -1.96595 1.14547 1.02126 -1.98772 0.61803 1.47802 -1.83697 0.03696 1.80649 -1.52680 -0.54733 1.97818 -1.08411 0.00000 2.00000 -1.08411 1.97818 -0.54733 -1.52680 1.80649 0.03696 -1.83697 1.47802 0.61803 -1.98772 1.02126 1.14547 -1.96595 0.47587 1.57349 -1.77355 -0.11082 1.86494 -1.42722 -0.68790 1.99454 -0.95702 -1.20527 1.95102 -0.40376 -1.61803 1.73818 0.18454 -1.89037 1.37447 0.75682 -1.99863 0.89148 1.26342 -1.93344 0.33111 1.66037 -1.70043 -0.25800 1.91321 -1.31985 -0.82471 0.00000 ... ... ..... ....... ......... ........... ............. E28g 2.00000 -0.95702 -1.08411 1.99454 -0.82471 -1.20527 1.97818 -0.68790 -1.31985 1.95102 -0.54733 -1.42722 1.91321 -0.40376 -1.52680 1.86494 -0.25800 -1.61803 1.80649 -0.11082 -1.70043 1.73818 0.03696 -1.77355 1.66037 0.18454 -1.83697 1.57349 0.33111 -1.89037 1.47802 0.47587 -1.93344 1.37447 0.61803 -1.96595 1.26342 0.75682 -1.98772 1.14547 0.89148 -1.99863 1.02126 0.00000 2.00000 1.02126 -1.99863 0.89148 1.14547 -1.98772 0.75682 1.26342 -1.96595 0.61803 1.37447 -1.93344 0.47587 1.47802 -1.89037 0.33111 1.57349 -1.83697 0.18454 1.66037 -1.77355 0.03696 1.73818 -1.70043 -0.11082 1.80649 -1.61803 -0.25800 1.86494 -1.52680 -0.40376 1.91321 -1.42722 -0.54733 1.95102 -1.31985 -0.68790 1.97818 -1.20527 -0.82471 1.99454 -1.08411 -0.95702 0.00000 ... ... ..... ....... ......... ........... ............. E29g 2.00000 -1.08411 -0.82471 1.97818 -1.31985 -0.54733 1.91321 -1.52680 -0.25800 1.80649 -1.70043 0.03696 1.66037 -1.83697 0.33111 1.47802 -1.93344 0.61803 1.26342 -1.98772 0.89148 1.02126 -1.99863 1.14547 0.75682 -1.96595 1.37447 0.47587 -1.89037 1.57349 0.18454 -1.77355 1.73818 -0.11082 -1.61803 1.86494 -0.40376 -1.42722 1.95102 -0.68790 -1.20527 1.99454 -0.95702 0.00000 2.00000 -0.95702 1.99454 -1.20527 -0.68790 1.95102 -1.42722 -0.40376 1.86494 -1.61803 -0.11082 1.73818 -1.77355 0.18454 1.57349 -1.89037 0.47587 1.37447 -1.96595 0.75682 1.14547 -1.99863 1.02126 0.89148 -1.98772 1.26342 0.61803 -1.93344 1.47802 0.33111 -1.83697 1.66037 0.03696 -1.70043 1.80649 -0.25800 -1.52680 1.91321 -0.54733 -1.31985 1.97818 -0.82471 -1.08411 0.00000 ... ... ..... ....... ......... ........... ............. E30g 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.00000 2.00000 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527 0.00000 ... ... ..... ....... ......... ........... ............. E31g 2.00000 -1.31985 -0.25800 1.66037 -1.93344 0.89148 0.75682 -1.89037 1.73818 -0.40376 -1.20527 1.99454 -1.42722 -0.11082 1.57349 -1.96595 1.02126 0.61803 -1.83697 1.80649 -0.54733 -1.08411 1.97818 -1.52680 0.03696 1.47802 -1.98772 1.14547 0.47587 -1.77355 1.86494 -0.68790 -0.95702 1.95102 -1.61803 0.18454 1.37447 -1.99863 1.26342 0.33111 -1.70043 1.91321 -0.82471 0.00000 2.00000 -0.82471 1.91321 -1.70043 0.33111 1.26342 -1.99863 1.37447 0.18454 -1.61803 1.95102 -0.95702 -0.68790 1.86494 -1.77355 0.47587 1.14547 -1.98772 1.47802 0.03696 -1.52680 1.97818 -1.08411 -0.54733 1.80649 -1.83697 0.61803 1.02126 -1.96595 1.57349 -0.11082 -1.42722 1.99454 -1.20527 -0.40376 1.73818 -1.89037 0.75682 0.89148 -1.93344 1.66037 -0.25800 -1.31985 0.00000 ... ... ..... ....... ......... ........... ............. E32g 2.00000 -1.42722 0.03696 1.37447 -1.99863 1.47802 -0.11082 -1.31985 1.99454 -1.52680 0.18454 1.26342 -1.98772 1.57349 -0.25800 -1.20527 1.97818 -1.61803 0.33111 1.14547 -1.96595 1.66037 -0.40376 -1.08411 1.95102 -1.70043 0.47587 1.02126 -1.93344 1.73818 -0.54733 -0.95702 1.91321 -1.77355 0.61803 0.89148 -1.89037 1.80649 -0.68790 -0.82471 1.86494 -1.83697 0.75682 0.00000 2.00000 0.75682 -1.83697 1.86494 -0.82471 -0.68790 1.80649 -1.89037 0.89148 0.61803 -1.77355 1.91321 -0.95702 -0.54733 1.73818 -1.93344 1.02126 0.47587 -1.70043 1.95102 -1.08411 -0.40376 1.66037 -1.96595 1.14547 0.33111 -1.61803 1.97818 -1.20527 -0.25800 1.57349 -1.98772 1.26342 0.18454 -1.52680 1.99454 -1.31985 -0.11082 1.47802 -1.99863 1.37447 0.03696 -1.42722 0.00000 ... ... ..... ....... ......... ........... ............. E33g 2.00000 -1.52680 0.33111 1.02126 -1.89037 1.86494 -0.95702 -0.40376 1.57349 -1.99863 1.47802 -0.25800 -1.08411 1.91321 -1.83697 0.89148 0.47587 -1.61803 1.99454 -1.42722 0.18454 1.14547 -1.93344 1.80649 -0.82471 -0.54733 1.66037 -1.98772 1.37447 -0.11082 -1.20527 1.95102 -1.77355 0.75682 0.61803 -1.70043 1.97818 -1.31985 0.03696 1.26342 -1.96595 1.73818 -0.68790 0.00000 2.00000 -0.68790 1.73818 -1.96595 1.26342 0.03696 -1.31985 1.97818 -1.70043 0.61803 0.75682 -1.77355 1.95102 -1.20527 -0.11082 1.37447 -1.98772 1.66037 -0.54733 -0.82471 1.80649 -1.93344 1.14547 0.18454 -1.42722 1.99454 -1.61803 0.47587 0.89148 -1.83697 1.91321 -1.08411 -0.25800 1.47802 -1.99863 1.57349 -0.40376 -0.95702 1.86494 -1.89037 1.02126 0.33111 -1.52680 0.00000 ... ... ..... ....... ......... ........... ............. E34g 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 0.61803 -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 2.00000 -1.61803 0.61803 0.61803 -1.61803 0.00000 ... ... ..... ....... ......... ........... ............. E35g 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 0.00000 2.00000 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 0.00000 ... ... ..... ....... ......... ........... ............. E36g 2.00000 -1.77355 1.14547 -0.25800 -0.68790 1.47802 -1.93344 1.95102 -1.52680 0.75682 0.18454 -1.08411 1.73818 -1.99863 1.80649 -1.20527 0.33111 0.61803 -1.42722 1.91321 -1.96595 1.57349 -0.82471 -0.11082 1.02126 -1.70043 1.99454 -1.83697 1.26342 -0.40376 -0.54733 1.37447 -1.89037 1.97818 -1.61803 0.89148 0.03696 -0.95702 1.66037 -1.98772 1.86494 -1.31985 0.47587 0.00000 2.00000 0.47587 -1.31985 1.86494 -1.98772 1.66037 -0.95702 0.03696 0.89148 -1.61803 1.97818 -1.89037 1.37447 -0.54733 -0.40376 1.26342 -1.83697 1.99454 -1.70043 1.02126 -0.11082 -0.82471 1.57349 -1.96595 1.91321 -1.42722 0.61803 0.33111 -1.20527 1.80649 -1.99863 1.73818 -1.08411 0.18454 0.75682 -1.52680 1.95102 -1.93344 1.47802 -0.68790 -0.25800 1.14547 -1.77355 0.00000 ... ... ..... ....... ......... ........... ............. E37g 2.00000 -1.83697 1.37447 -0.68790 -0.11082 0.89148 -1.52680 1.91321 -1.98772 1.73818 -1.20527 0.47587 0.33111 -1.08411 1.66037 -1.96595 1.95102 -1.61803 1.02126 -0.25800 -0.54733 1.26342 -1.77355 1.99454 -1.89037 1.47802 -0.82471 0.03696 0.75682 -1.42722 1.86494 -1.99863 1.80649 -1.31985 0.61803 0.18454 -0.95702 1.57349 -1.93344 1.97818 -1.70043 1.14547 -0.40376 0.00000 2.00000 -0.40376 1.14547 -1.70043 1.97818 -1.93344 1.57349 -0.95702 0.18454 0.61803 -1.31985 1.80649 -1.99863 1.86494 -1.42722 0.75682 0.03696 -0.82471 1.47802 -1.89037 1.99454 -1.77355 1.26342 -0.54733 -0.25800 1.02126 -1.61803 1.95102 -1.96595 1.66037 -1.08411 0.33111 0.47587 -1.20527 1.73818 -1.98772 1.91321 -1.52680 0.89148 -0.11082 -0.68790 1.37447 -1.83697 0.00000 ... ... ..... ....... ......... ........... ............. E38g 2.00000 -1.89037 1.57349 -1.08411 0.47587 0.18454 -0.82471 1.37447 -1.77355 1.97818 -1.96595 1.73818 -1.31985 0.75682 -0.11082 -0.54733 1.14547 -1.61803 1.91321 -1.99863 1.86494 -1.52680 1.02126 -0.40376 -0.25800 0.89148 -1.42722 1.80649 -1.98772 1.95102 -1.70043 1.26342 -0.68790 0.03696 0.61803 -1.20527 1.66037 -1.93344 1.99454 -1.83697 1.47802 -0.95702 0.33111 0.00000 2.00000 0.33111 -0.95702 1.47802 -1.83697 1.99454 -1.93344 1.66037 -1.20527 0.61803 0.03696 -0.68790 1.26342 -1.70043 1.95102 -1.98772 1.80649 -1.42722 0.89148 -0.25800 -0.40376 1.02126 -1.52680 1.86494 -1.99863 1.91321 -1.61803 1.14547 -0.54733 -0.11082 0.75682 -1.31985 1.73818 -1.96595 1.97818 -1.77355 1.37447 -0.82471 0.18454 0.47587 -1.08411 1.57349 -1.89037 0.00000 ... ... ..... ....... ......... ........... ............. E39g 2.00000 -1.93344 1.73818 -1.42722 1.02126 -0.54733 0.03696 0.47587 -0.95702 1.37447 -1.70043 1.91321 -1.99863 1.95102 -1.77355 1.47802 -1.08411 0.61803 -0.11082 -0.40376 0.89148 -1.31985 1.66037 -1.89037 1.99454 -1.96595 1.80649 -1.52680 1.14547 -0.68790 0.18454 0.33111 -0.82471 1.26342 -1.61803 1.86494 -1.98772 1.97818 -1.83697 1.57349 -1.20527 0.75682 -0.25800 0.00000 2.00000 -0.25800 0.75682 -1.20527 1.57349 -1.83697 1.97818 -1.98772 1.86494 -1.61803 1.26342 -0.82471 0.33111 0.18454 -0.68790 1.14547 -1.52680 1.80649 -1.96595 1.99454 -1.89037 1.66037 -1.31985 0.89148 -0.40376 -0.11082 0.61803 -1.08411 1.47802 -1.77355 1.95102 -1.99863 1.91321 -1.70043 1.37447 -0.95702 0.47587 0.03696 -0.54733 1.02126 -1.42722 1.73818 -1.93344 0.00000 ... ... ..... ....... ......... ........... ............. E40g 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.00000 2.00000 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 0.00000 ... ... ..... ....... ......... ........... ............. E41g 2.00000 -1.98772 1.95102 -1.89037 1.80649 -1.70043 1.57349 -1.42722 1.26342 -1.08411 0.89148 -0.68790 0.47587 -0.25800 0.03696 0.18454 -0.40376 0.61803 -0.82471 1.02126 -1.20527 1.37447 -1.52680 1.66037 -1.77355 1.86494 -1.93344 1.97818 -1.99863 1.99454 -1.96595 1.91321 -1.83697 1.73818 -1.61803 1.47802 -1.31985 1.14547 -0.95702 0.75682 -0.54733 0.33111 -0.11082 0.00000 2.00000 -0.11082 0.33111 -0.54733 0.75682 -0.95702 1.14547 -1.31985 1.47802 -1.61803 1.73818 -1.83697 1.91321 -1.96595 1.99454 -1.99863 1.97818 -1.93344 1.86494 -1.77355 1.66037 -1.52680 1.37447 -1.20527 1.02126 -0.82471 0.61803 -0.40376 0.18454 0.03696 -0.25800 0.47587 -0.68790 0.89148 -1.08411 1.26342 -1.42722 1.57349 -1.70043 1.80649 -1.89037 1.95102 -1.98772 0.00000 ... ... ..... ....... ......... ........... ............. E42g 2.00000 -1.99863 1.99454 -1.98772 1.97818 -1.96595 1.95102 -1.93344 1.91321 -1.89037 1.86494 -1.83697 1.80649 -1.77355 1.73818 -1.70043 1.66037 -1.61803 1.57349 -1.52680 1.47802 -1.42722 1.37447 -1.31985 1.26342 -1.20527 1.14547 -1.08411 1.02126 -0.95702 0.89148 -0.82471 0.75682 -0.68790 0.61803 -0.54733 0.47587 -0.40376 0.33111 -0.25800 0.18454 -0.11082 0.03696 0.00000 2.00000 0.03696 -0.11082 0.18454 -0.25800 0.33111 -0.40376 0.47587 -0.54733 0.61803 -0.68790 0.75682 -0.82471 0.89148 -0.95702 1.02126 -1.08411 1.14547 -1.20527 1.26342 -1.31985 1.37447 -1.42722 1.47802 -1.52680 1.57349 -1.61803 1.66037 -1.70043 1.73818 -1.77355 1.80649 -1.83697 1.86494 -1.89037 1.91321 -1.93344 1.95102 -1.96595 1.97818 -1.98772 1.99454 -1.99863 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 -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 -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 1.99454 1.97818 1.95102 1.91321 1.86494 1.80649 1.73818 1.66037 1.57349 1.47802 1.37447 1.26342 1.14547 1.02126 0.89148 0.75682 0.61803 0.47587 0.33111 0.18454 0.03696 -0.11082 -0.25800 -0.40376 -0.54733 -0.68790 -0.82471 -0.95702 -1.08411 -1.20527 -1.31985 -1.42722 -1.52680 -1.61803 -1.70043 -1.77355 -1.83697 -1.89037 -1.93344 -1.96595 -1.98772 -1.99863 0.00000 -2.00000 1.99863 1.98772 1.96595 1.93344 1.89037 1.83697 1.77355 1.70043 1.61803 1.52680 1.42722 1.31985 1.20527 1.08411 0.95702 0.82471 0.68790 0.54733 0.40376 0.25800 0.11082 -0.03696 -0.18454 -0.33111 -0.47587 -0.61803 -0.75682 -0.89148 -1.02126 -1.14547 -1.26342 -1.37447 -1.47802 -1.57349 -1.66037 -1.73818 -1.80649 -1.86494 -1.91321 -1.95102 -1.97818 -1.99454 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.97818 1.91321 1.80649 1.66037 1.47802 1.26342 1.02126 0.75682 0.47587 0.18454 -0.11082 -0.40376 -0.68790 -0.95702 -1.20527 -1.42722 -1.61803 -1.77355 -1.89037 -1.96595 -1.99863 -1.98772 -1.93344 -1.83697 -1.70043 -1.52680 -1.31985 -1.08411 -0.82471 -0.54733 -0.25800 0.03696 0.33111 0.61803 0.89148 1.14547 1.37447 1.57349 1.73818 1.86494 1.95102 1.99454 0.00000 -2.00000 -1.99454 -1.95102 -1.86494 -1.73818 -1.57349 -1.37447 -1.14547 -0.89148 -0.61803 -0.33111 -0.03696 0.25800 0.54733 0.82471 1.08411 1.31985 1.52680 1.70043 1.83697 1.93344 1.98772 1.99863 1.96595 1.89037 1.77355 1.61803 1.42722 1.20527 0.95702 0.68790 0.40376 0.11082 -0.18454 -0.47587 -0.75682 -1.02126 -1.26342 -1.47802 -1.66037 -1.80649 -1.91321 -1.97818 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u 2.00000 1.95102 1.80649 1.57349 1.26342 0.89148 0.47587 0.03696 -0.40376 -0.82471 -1.20527 -1.52680 -1.77355 -1.93344 -1.99863 -1.96595 -1.83697 -1.61803 -1.31985 -0.95702 -0.54733 -0.11082 0.33111 0.75682 1.14547 1.47802 1.73818 1.91321 1.99454 1.97818 1.86494 1.66037 1.37447 1.02126 0.61803 0.18454 -0.25800 -0.68790 -1.08411 -1.42722 -1.70043 -1.89037 -1.98772 0.00000 -2.00000 1.98772 1.89037 1.70043 1.42722 1.08411 0.68790 0.25800 -0.18454 -0.61803 -1.02126 -1.37447 -1.66037 -1.86494 -1.97818 -1.99454 -1.91321 -1.73818 -1.47802 -1.14547 -0.75682 -0.33111 0.11082 0.54733 0.95702 1.31985 1.61803 1.83697 1.96595 1.99863 1.93344 1.77355 1.52680 1.20527 0.82471 0.40376 -0.03696 -0.47587 -0.89148 -1.26342 -1.57349 -1.80649 -1.95102 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u 2.00000 1.91321 1.66037 1.26342 0.75682 0.18454 -0.40376 -0.95702 -1.42722 -1.77355 -1.96595 -1.98772 -1.83697 -1.52680 -1.08411 -0.54733 0.03696 0.61803 1.14547 1.57349 1.86494 1.99454 1.95102 1.73818 1.37447 0.89148 0.33111 -0.25800 -0.82471 -1.31985 -1.70043 -1.93344 -1.99863 -1.89037 -1.61803 -1.20527 -0.68790 -0.11082 0.47587 1.02126 1.47802 1.80649 1.97818 0.00000 -2.00000 -1.97818 -1.80649 -1.47802 -1.02126 -0.47587 0.11082 0.68790 1.20527 1.61803 1.89037 1.99863 1.93344 1.70043 1.31985 0.82471 0.25800 -0.33111 -0.89148 -1.37447 -1.73818 -1.95102 -1.99454 -1.86494 -1.57349 -1.14547 -0.61803 -0.03696 0.54733 1.08411 1.52680 1.83697 1.98772 1.96595 1.77355 1.42722 0.95702 0.40376 -0.18454 -0.75682 -1.26342 -1.66037 -1.91321 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5u 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 0.00000 -2.00000 1.96595 1.70043 1.20527 0.54733 -0.18454 -0.89148 -1.47802 -1.86494 -2.00000 -1.86494 -1.47802 -0.89148 -0.18454 0.54733 1.20527 1.70043 1.96595 1.96595 1.70043 1.20527 0.54733 -0.18454 -0.89148 -1.47802 -1.86494 -2.00000 -1.86494 -1.47802 -0.89148 -0.18454 0.54733 1.20527 1.70043 1.96595 1.96595 1.70043 1.20527 0.54733 -0.18454 -0.89148 -1.47802 -1.86494 0.00000 ... ... ..... ....... ......... TT......... ............. E6u 2.00000 1.80649 1.26342 0.47587 -0.40376 -1.20527 -1.77355 -1.99863 -1.83697 -1.31985 -0.54733 0.33111 1.14547 1.73818 1.99454 1.86494 1.37447 0.61803 -0.25800 -1.08411 -1.70043 -1.98772 -1.89037 -1.42722 -0.68790 0.18454 1.02126 1.66037 1.97818 1.91321 1.47802 0.75682 -0.11082 -0.95702 -1.61803 -1.96595 -1.93344 -1.52680 -0.82471 0.03696 0.89148 1.57349 1.95102 0.00000 -2.00000 -1.95102 -1.57349 -0.89148 -0.03696 0.82471 1.52680 1.93344 1.96595 1.61803 0.95702 0.11082 -0.75682 -1.47802 -1.91321 -1.97818 -1.66037 -1.02126 -0.18454 0.68790 1.42722 1.89037 1.98772 1.70043 1.08411 0.25800 -0.61803 -1.37447 -1.86494 -1.99454 -1.73818 -1.14547 -0.33111 0.54733 1.31985 1.83697 1.99863 1.77355 1.20527 0.40376 -0.47587 -1.26342 -1.80649 0.00000 ... ... ..... ....... ......... ........... ............. E7u 2.00000 1.73818 1.02126 0.03696 -0.95702 -1.70043 -1.99863 -1.77355 -1.08411 -0.11082 0.89148 1.66037 1.99454 1.80649 1.14547 0.18454 -0.82471 -1.61803 -1.98772 -1.83697 -1.20527 -0.25800 0.75682 1.57349 1.97818 1.86494 1.26342 0.33111 -0.68790 -1.52680 -1.96595 -1.89037 -1.31985 -0.40376 0.61803 1.47802 1.95102 1.91321 1.37447 0.47587 -0.54733 -1.42722 -1.93344 0.00000 -2.00000 1.93344 1.42722 0.54733 -0.47587 -1.37447 -1.91321 -1.95102 -1.47802 -0.61803 0.40376 1.31985 1.89037 1.96595 1.52680 0.68790 -0.33111 -1.26342 -1.86494 -1.97818 -1.57349 -0.75682 0.25800 1.20527 1.83697 1.98772 1.61803 0.82471 -0.18454 -1.14547 -1.80649 -1.99454 -1.66037 -0.89148 0.11082 1.08411 1.77355 1.99863 1.70043 0.95702 -0.03696 -1.02126 -1.73818 0.00000 ... ... ..... ....... ......... ........... ............. 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E40u 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.00000 -2.00000 -0.18454 0.54733 -0.89148 1.20527 -1.47802 1.70043 -1.86494 1.96595 -2.00000 1.96595 -1.86494 1.70043 -1.47802 1.20527 -0.89148 0.54733 -0.18454 -0.18454 0.54733 -0.89148 1.20527 -1.47802 1.70043 -1.86494 1.96595 -2.00000 1.96595 -1.86494 1.70043 -1.47802 1.20527 -0.89148 0.54733 -0.18454 -0.18454 0.54733 -0.89148 1.20527 -1.47802 1.70043 -1.86494 1.96595 0.00000 ... ... ..... ....... ......... ........... ............. E41u 2.00000 -1.98772 1.95102 -1.89037 1.80649 -1.70043 1.57349 -1.42722 1.26342 -1.08411 0.89148 -0.68790 0.47587 -0.25800 0.03696 0.18454 -0.40376 0.61803 -0.82471 1.02126 -1.20527 1.37447 -1.52680 1.66037 -1.77355 1.86494 -1.93344 1.97818 -1.99863 1.99454 -1.96595 1.91321 -1.83697 1.73818 -1.61803 1.47802 -1.31985 1.14547 -0.95702 0.75682 -0.54733 0.33111 -0.11082 0.00000 -2.00000 0.11082 -0.33111 0.54733 -0.75682 0.95702 -1.14547 1.31985 -1.47802 1.61803 -1.73818 1.83697 -1.91321 1.96595 -1.99454 1.99863 -1.97818 1.93344 -1.86494 1.77355 -1.66037 1.52680 -1.37447 1.20527 -1.02126 0.82471 -0.61803 0.40376 -0.18454 -0.03696 0.25800 -0.47587 0.68790 -0.89148 1.08411 -1.26342 1.42722 -1.57349 1.70043 -1.80649 1.89037 -1.95102 1.98772 0.00000 ... ... ..... ....... ......... ........... ............. E42u 2.00000 -1.99863 1.99454 -1.98772 1.97818 -1.96595 1.95102 -1.93344 1.91321 -1.89037 1.86494 -1.83697 1.80649 -1.77355 1.73818 -1.70043 1.66037 -1.61803 1.57349 -1.52680 1.47802 -1.42722 1.37447 -1.31985 1.26342 -1.20527 1.14547 -1.08411 1.02126 -0.95702 0.89148 -0.82471 0.75682 -0.68790 0.61803 -0.54733 0.47587 -0.40376 0.33111 -0.25800 0.18454 -0.11082 0.03696 0.00000 -2.00000 -0.03696 0.11082 -0.18454 0.25800 -0.33111 0.40376 -0.47587 0.54733 -0.61803 0.68790 -0.75682 0.82471 -0.89148 0.95702 -1.02126 1.08411 -1.14547 1.20527 -1.26342 1.31985 -1.37447 1.42722 -1.47802 1.52680 -1.57349 1.61803 -1.66037 1.70043 -1.73818 1.77355 -1.80649 1.83697 -1.86494 1.89037 -1.91321 1.93344 -1.95102 1.96595 -1.97818 1.98772 -1.99454 1.99863 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.998634120286 = 2*cos(2*π/170) = 2*cos(π/85) 1.994538346772 = 2*cos(4*π/170) = 2*cos(2*π/85) 1.987718273791 = 2*cos(6*π/170) = 2*cos(3*π/85) 1.978183216742 = 2*cos(8*π/170) = 2*cos(4*π/85) 1.965946199368 = 2*cos(10*π/170) = 2*cos(π/17) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 1.951023935961 = 2*cos(12*π/170) = 2*cos(6*π/85) 1.933436808538 = 2*cos(14*π/170) = 2*cos(7*π/85) 1.913208839001 = 2*cos(16*π/170) = 2*cos(8*π/85) 1.890367656322 = 2*cos(18*π/170) = 2*cos(9*π/85) 1.864944458809 = 2*cos(20*π/170) = 2*cos(2*π/17) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 1.836973971492 = 2*cos(22*π/170) = 2*cos(11*π/85) 1.806494398692 = 2*cos(24*π/170) = 2*cos(12*π/85) 1.773547371840 = 2*cos(26*π/170) = 2*cos(13*π/85) 1.738177892611 = 2*cos(28*π/170) = 2*cos(14*π/85) 1.700434271459 = 2*cos(30*π/170) = 2*cos(3*π/17) = (1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 1.660368061631 = 2*cos(32*π/170) = 2*cos(16*π/85) 1.618033988750 = 2*cos(34*π/170) = 2*cos(π/5) = (√5+1)/2 1.573489876067 = 2*cos(36*π/170) = 2*cos(18*π/85) 1.526796565482 = 2*cos(38*π/170) = 2*cos(19*π/85) 1.478017834441 = 2*cos(40*π/170) = 2*cos(4*π/17) = (−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 1.427220308824 = 2*cos(42*π/170) = 2*cos(21*π/85) 1.374473371939 = 2*cos(44*π/170) = 2*cos(22*π/85) 1.319849069757 = 2*cos(46*π/170) = 2*cos(23*π/85) 1.263422012507 = 2*cos(48*π/170) = 2*cos(24*π/85) 1.205269272759 = 2*cos(50*π/170) = 2*cos(5*π/17) = (1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 1.145470280161 = 2*cos(52*π/170) = 2*cos(26*π/85) 1.084106712945 = 2*cos(54*π/170) = 2*cos(27*π/85) 1.021262386362 = 2*cos(56*π/170) = 2*cos(28*π/85) 0.957023138203 = 2*cos(58*π/170) = 2*cos(29*π/85) 0.891476711553 = 2*cos(60*π/170) = 2*cos(6*π/17) = (−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 0.824712634948 = 2*cos(62*π/170) = 2*cos(31*π/85) 0.756822100085 = 2*cos(64*π/170) = 2*cos(32*π/85) 0.687897837268 = 2*cos(66*π/170) = 2*cos(33*π/85) 0.618033988750 = 2*cos(68*π/170) = 2*cos(2*π/5) = (√5−1)/2 0.547325980144 = 2*cos(70*π/170) = 2*cos(7*π/17) = (1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 0.475870390085 = 2*cos(72*π/170) = 2*cos(36*π/85) 0.403764818314 = 2*cos(74*π/170) = 2*cos(37*π/85) 0.331107752368 = 2*cos(76*π/170) = 2*cos(38*π/85) 0.257998433060 = 2*cos(78*π/170) = 2*cos(39*π/85) 0.184536718927 = 2*cos(80*π/170) = 2*cos(8*π/17) = (−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 0.110822949832 = 2*cos(82*π/170) = 2*cos(41*π/85) 0.036957809918 = 2*cos(84*π/170) = 2*cos(42*π/85) 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_85d point group is 340, and the order of the principal axis (S₁₇₀) is 170. The group has 88 irreducible representations. β The D_85d point group is isomorphic to D_85h, C_170v and D₁₇₀. γ The D_85d point group is generated by two symmetry elements, S₁₇₀ 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: C₈₅, 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_85d 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. θ The point group corresponds to a constructible polygon, as the order of the principal axis is a product of any number of different Fermat primes (3,5,17,257,65537) times an arbitrary power of two. Therefore, all characters have an algebraic degree which is a power of two and can be expressed as radicals involving only square roots and integer numbers. Some of these algebraic expressions, however, are too complicated to be included in the list above. ι The fact that the regular pentagon is constructible is known since antiquity; Eukleides already discovered a construction for it. The double cosine of 2π/5 is equal to the reciprocal of the Golden Ratio of (1+√5)/2 = 1.61803. κ That a regular 17-gon can be constructed with compass and ruler was unknown to mathematicians until Gauss proved it in 1796. The first actual construction was performed thirty years later by Johannes Erchinger in 1825. The regular 85-gon can be derived from the regular 17-gon by overlaying it with a regular pentagon.

This Character Table for the D_85d point group was created by Gernot Katzer.

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

	D_83d
	D_84d
C₈₅ C_85v C_85h D₈₅ D_85h	D_85d
	D_86d
	D_87d

Character table for the D85d point group

Character table for the D_85d point group