C93 E 2 C93 2 C93^2 2 C31 2 C93^4 2 C93^5 2 C31^2 2 C93^7 2 C93^8 2 C31^3 2 C93^10 2 C93^11 2 C31^4 2 C93^13 2 C93^14 2 C31^5 2 C93^16 2 C93^17 2 C31^6 2 C93^19 2 C93^20 2 C31^7 2 C93^22 2 C93^23 2 C31^8 2 C93^25 2 C93^26 2 C31^9 2 C93^28 2 C93^29 2 C31^10 2 C3 2 C93^32 2 C31^11 2 C93^34 2 C93^35 2 C31^12 2 C93^37 2 C93^38 2 C31^13 2 C93^40 2 C93^41 2 C31^14 2 C93^43 2 C93^44 2 C31^15 2 C93^46 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99544 1.98177 1.95906 1.92741 1.88697 1.83792 1.78048 1.71491 1.64153 1.56065 1.47265 1.37793 1.27693 1.17010 1.05793 0.94093 0.81964 0.69461 0.56641 0.43563 0.30286 0.16870 0.03378 -0.10130 -0.23591 -0.36945 -0.50131 -0.63087 -0.75756 -0.88079 -1.00000 -1.11465 -1.22421 -1.32819 -1.42611 -1.51752 -1.60200 -1.67918 -1.74869 -1.81023 -1.86351 -1.90828 -1.94434 -1.97154 -1.98974 -1.99886 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.98177 1.92741 1.83792 1.71491 1.56065 1.37793 1.17010 0.94093 0.69461 0.43563 0.16870 -0.10130 -0.36945 -0.63087 -0.88079 -1.11465 -1.32819 -1.51752 -1.67918 -1.81023 -1.90828 -1.97154 -1.99886 -1.98974 -1.94434 -1.86351 -1.74869 -1.60200 -1.42611 -1.22421 -1.00000 -0.75756 -0.50131 -0.23591 0.03378 0.30286 0.56641 0.81964 1.05793 1.27693 1.47265 1.64153 1.78048 1.88697 1.95906 1.99544 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.95906 1.83792 1.64153 1.37793 1.05793 0.69461 0.30286 -0.10130 -0.50131 -0.88079 -1.22421 -1.51752 -1.74869 -1.90828 -1.98974 -1.98974 -1.90828 -1.74869 -1.51752 -1.22421 -0.88079 -0.50131 -0.10130 0.30286 0.69461 1.05793 1.37793 1.64153 1.83792 1.95906 2.00000 1.95906 1.83792 1.64153 1.37793 1.05793 0.69461 0.30286 -0.10130 -0.50131 -0.88079 -1.22421 -1.51752 -1.74869 -1.90828 -1.98974 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.92741 1.71491 1.37793 0.94093 0.43563 -0.10130 -0.63087 -1.11465 -1.51752 -1.81023 -1.97154 -1.98974 -1.86351 -1.60200 -1.22421 -0.75756 -0.23591 0.30286 0.81964 1.27693 1.64153 1.88697 1.99544 1.95906 1.78048 1.47265 1.05793 0.56641 0.03378 -0.50131 -1.00000 -1.42611 -1.74869 -1.94434 -1.99886 -1.90828 -1.67918 -1.32819 -0.88079 -0.36945 0.16870 0.69461 1.17010 1.56065 1.83792 1.98177 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.88697 1.56065 1.05793 0.43563 -0.23591 -0.88079 -1.42611 -1.81023 -1.98974 -1.94434 -1.67918 -1.22421 -0.63087 0.03378 0.69461 1.27693 1.71491 1.95906 1.98177 1.78048 1.37793 0.81964 0.16870 -0.50131 -1.11465 -1.60200 -1.90828 -1.99886 -1.86351 -1.51752 -1.00000 -0.36945 0.30286 0.94093 1.47265 1.83792 1.99544 1.92741 1.64153 1.17010 0.56641 -0.10130 -0.75756 -1.32819 -1.74869 -1.97154 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.83792 1.37793 0.69461 -0.10130 -0.88079 -1.51752 -1.90828 -1.98974 -1.74869 -1.22421 -0.50131 0.30286 1.05793 1.64153 1.95906 1.95906 1.64153 1.05793 0.30286 -0.50131 -1.22421 -1.74869 -1.98974 -1.90828 -1.51752 -0.88079 -0.10130 0.69461 1.37793 1.83792 2.00000 1.83792 1.37793 0.69461 -0.10130 -0.88079 -1.51752 -1.90828 -1.98974 -1.74869 -1.22421 -0.50131 0.30286 1.05793 1.64153 1.95906 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.78048 1.17010 0.30286 -0.63087 -1.42611 -1.90828 -1.97154 -1.60200 -0.88079 0.03378 0.94093 1.64153 1.98177 1.88697 1.37793 0.56641 -0.36945 -1.22421 -1.81023 -1.99886 -1.74869 -1.11465 -0.23591 0.69461 1.47265 1.92741 1.95906 1.56065 0.81964 -0.10130 -1.00000 -1.67918 -1.98974 -1.86351 -1.32819 -0.50131 0.43563 1.27693 1.83792 1.99544 1.71491 1.05793 0.16870 -0.75756 -1.51752 -1.94434 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.71491 0.94093 -0.10130 -1.11465 -1.81023 -1.98974 -1.60200 -0.75756 0.30286 1.27693 1.88697 1.95906 1.47265 0.56641 -0.50131 -1.42611 -1.94434 -1.90828 -1.32819 -0.36945 0.69461 1.56065 1.98177 1.83792 1.17010 0.16870 -0.88079 -1.67918 -1.99886 -1.74869 -1.00000 0.03378 1.05793 1.78048 1.99544 1.64153 0.81964 -0.23591 -1.22421 -1.86351 -1.97154 -1.51752 -0.63087 0.43563 1.37793 1.92741 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.64153 0.69461 -0.50131 -1.51752 -1.98974 -1.74869 -0.88079 0.30286 1.37793 1.95906 1.83792 1.05793 -0.10130 -1.22421 -1.90828 -1.90828 -1.22421 -0.10130 1.05793 1.83792 1.95906 1.37793 0.30286 -0.88079 -1.74869 -1.98974 -1.51752 -0.50131 0.69461 1.64153 2.00000 1.64153 0.69461 -0.50131 -1.51752 -1.98974 -1.74869 -0.88079 0.30286 1.37793 1.95906 1.83792 1.05793 -0.10130 -1.22421 -1.90828 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.56065 0.43563 -0.88079 -1.81023 -1.94434 -1.22421 0.03378 1.27693 1.95906 1.78048 0.81964 -0.50131 -1.60200 -1.99886 -1.51752 -0.36945 0.94093 1.83792 1.92741 1.17010 -0.10130 -1.32819 -1.97154 -1.74869 -0.75756 0.56641 1.64153 1.99544 1.47265 0.30286 -1.00000 -1.86351 -1.90828 -1.11465 0.16870 1.37793 1.98177 1.71491 0.69461 -0.63087 -1.67918 -1.98974 -1.42611 -0.23591 1.05793 1.88697 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.47265 0.16870 -1.22421 -1.97154 -1.67918 -0.50131 0.94093 1.88697 1.83792 0.81964 -0.63087 -1.74869 -1.94434 -1.11465 0.30286 1.56065 1.99544 1.37793 0.03378 -1.32819 -1.98974 -1.60200 -0.36945 1.05793 1.92741 1.78048 0.69461 -0.75756 -1.81023 -1.90828 -1.00000 0.43563 1.64153 1.98177 1.27693 -0.10130 -1.42611 -1.99886 -1.51752 -0.23591 1.17010 1.95906 1.71491 0.56641 -0.88079 -1.86351 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.37793 -0.10130 -1.51752 -1.98974 -1.22421 0.30286 1.64153 1.95906 1.05793 -0.50131 -1.74869 -1.90828 -0.88079 0.69461 1.83792 1.83792 0.69461 -0.88079 -1.90828 -1.74869 -0.50131 1.05793 1.95906 1.64153 0.30286 -1.22421 -1.98974 -1.51752 -0.10130 1.37793 2.00000 1.37793 -0.10130 -1.51752 -1.98974 -1.22421 0.30286 1.64153 1.95906 1.05793 -0.50131 -1.74869 -1.90828 -0.88079 0.69461 1.83792 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.27693 -0.36945 -1.74869 -1.86351 -0.63087 1.05793 1.98177 1.47265 -0.10130 -1.60200 -1.94434 -0.88079 0.81964 1.92741 1.64153 0.16870 -1.42611 -1.98974 -1.11465 0.56641 1.83792 1.78048 0.43563 -1.22421 -1.99886 -1.32819 0.30286 1.71491 1.88697 0.69461 -1.00000 -1.97154 -1.51752 0.03378 1.56065 1.95906 0.94093 -0.75756 -1.90828 -1.67918 -0.23591 1.37793 1.99544 1.17010 -0.50131 -1.81023 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.17010 -0.63087 -1.90828 -1.60200 0.03378 1.64153 1.88697 0.56641 -1.22421 -1.99886 -1.11465 0.69461 1.92741 1.56065 -0.10130 -1.67918 -1.86351 -0.50131 1.27693 1.99544 1.05793 -0.75756 -1.94434 -1.51752 0.16870 1.71491 1.83792 0.43563 -1.32819 -1.98974 -1.00000 0.81964 1.95906 1.47265 -0.23591 -1.74869 -1.81023 -0.36945 1.37793 1.98177 0.94093 -0.88079 -1.97154 -1.42611 0.30286 1.78048 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 1.05793 -0.88079 -1.98974 -1.22421 0.69461 1.95906 1.37793 -0.50131 -1.90828 -1.51752 0.30286 1.83792 1.64153 -0.10130 -1.74869 -1.74869 -0.10130 1.64153 1.83792 0.30286 -1.51752 -1.90828 -0.50131 1.37793 1.95906 0.69461 -1.22421 -1.98974 -0.88079 1.05793 2.00000 1.05793 -0.88079 -1.98974 -1.22421 0.69461 1.95906 1.37793 -0.50131 -1.90828 -1.51752 0.30286 1.83792 1.64153 -0.10130 -1.74869 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 0.94093 -1.11465 -1.98974 -0.75756 1.27693 1.95906 0.56641 -1.42611 -1.90828 -0.36945 1.56065 1.83792 0.16870 -1.67918 -1.74869 0.03378 1.78048 1.64153 -0.23591 -1.86351 -1.51752 0.43563 1.92741 1.37793 -0.63087 -1.97154 -1.22421 0.81964 1.99544 1.05793 -1.00000 -1.99886 -0.88079 1.17010 1.98177 0.69461 -1.32819 -1.94434 -0.50131 1.47265 1.88697 0.30286 -1.60200 -1.81023 -0.10130 1.71491 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 0.81964 -1.32819 -1.90828 -0.23591 1.71491 1.64153 -0.36945 -1.94434 -1.22421 0.94093 1.99544 0.69461 -1.42611 -1.86351 -0.10130 1.78048 1.56065 -0.50131 -1.97154 -1.11465 1.05793 1.98177 0.56641 -1.51752 -1.81023 0.03378 1.83792 1.47265 -0.63087 -1.98974 -1.00000 1.17010 1.95906 0.43563 -1.60200 -1.74869 0.16870 1.88697 1.37793 -0.75756 -1.99886 -0.88079 1.27693 1.92741 0.30286 -1.67918 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.69461 -1.51752 -1.74869 0.30286 1.95906 1.05793 -1.22421 -1.90828 -0.10130 1.83792 1.37793 -0.88079 -1.98974 -0.50131 1.64153 1.64153 -0.50131 -1.98974 -0.88079 1.37793 1.83792 -0.10130 -1.90828 -1.22421 1.05793 1.95906 0.30286 -1.74869 -1.51752 0.69461 2.00000 0.69461 -1.51752 -1.74869 0.30286 1.95906 1.05793 -1.22421 -1.90828 -0.10130 1.83792 1.37793 -0.88079 -1.98974 -0.50131 1.64153 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.56641 -1.67918 -1.51752 0.81964 1.98177 0.30286 -1.81023 -1.32819 1.05793 1.92741 0.03378 -1.90828 -1.11465 1.27693 1.83792 -0.23591 -1.97154 -0.88079 1.47265 1.71491 -0.50131 -1.99886 -0.63087 1.64153 1.56065 -0.75756 -1.98974 -0.36945 1.78048 1.37793 -1.00000 -1.94434 -0.10130 1.88697 1.17010 -1.22421 -1.86351 0.16870 1.95906 0.94093 -1.42611 -1.74869 0.43563 1.99544 0.69461 -1.60200 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.43563 -1.81023 -1.22421 1.27693 1.78048 -0.50131 -1.99886 -0.36945 1.83792 1.17010 -1.32819 -1.74869 0.56641 1.99544 0.30286 -1.86351 -1.11465 1.37793 1.71491 -0.63087 -1.98974 -0.23591 1.88697 1.05793 -1.42611 -1.67918 0.69461 1.98177 0.16870 -1.90828 -1.00000 1.47265 1.64153 -0.75756 -1.97154 -0.10130 1.92741 0.94093 -1.51752 -1.60200 0.81964 1.95906 0.03378 -1.94434 -0.88079 1.56065 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.30286 -1.90828 -0.88079 1.64153 1.37793 -1.22421 -1.74869 0.69461 1.95906 -0.10130 -1.98974 -0.50131 1.83792 1.05793 -1.51752 -1.51752 1.05793 1.83792 -0.50131 -1.98974 -0.10130 1.95906 0.69461 -1.74869 -1.22421 1.37793 1.64153 -0.88079 -1.90828 0.30286 2.00000 0.30286 -1.90828 -0.88079 1.64153 1.37793 -1.22421 -1.74869 0.69461 1.95906 -0.10130 -1.98974 -0.50131 1.83792 1.05793 -1.51752 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 0.16870 -1.97154 -0.50131 1.88697 0.81964 -1.74869 -1.11465 1.56065 1.37793 -1.32819 -1.60200 1.05793 1.78048 -0.75756 -1.90828 0.43563 1.98177 -0.10130 -1.99886 -0.23591 1.95906 0.56641 -1.86351 -0.88079 1.71491 1.17010 -1.51752 -1.42611 1.27693 1.64153 -1.00000 -1.81023 0.69461 1.92741 -0.36945 -1.98974 0.03378 1.99544 0.30286 -1.94434 -0.63087 1.83792 0.94093 -1.67918 -1.22421 1.47265 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 0.03378 -1.99886 -0.10130 1.99544 0.16870 -1.98974 -0.23591 1.98177 0.30286 -1.97154 -0.36945 1.95906 0.43563 -1.94434 -0.50131 1.92741 0.56641 -1.90828 -0.63087 1.88697 0.69461 -1.86351 -0.75756 1.83792 0.81964 -1.81023 -0.88079 1.78048 0.94093 -1.74869 -1.00000 1.71491 1.05793 -1.67918 -1.11465 1.64153 1.17010 -1.60200 -1.22421 1.56065 1.27693 -1.51752 -1.32819 1.47265 1.37793 -1.42611 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 -0.10130 -1.98974 0.30286 1.95906 -0.50131 -1.90828 0.69461 1.83792 -0.88079 -1.74869 1.05793 1.64153 -1.22421 -1.51752 1.37793 1.37793 -1.51752 -1.22421 1.64153 1.05793 -1.74869 -0.88079 1.83792 0.69461 -1.90828 -0.50131 1.95906 0.30286 -1.98974 -0.10130 2.00000 -0.10130 -1.98974 0.30286 1.95906 -0.50131 -1.90828 0.69461 1.83792 -0.88079 -1.74869 1.05793 1.64153 -1.22421 -1.51752 1.37793 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 -0.23591 -1.94434 0.69461 1.78048 -1.11465 -1.51752 1.47265 1.17010 -1.74869 -0.75756 1.92741 0.30286 -1.99886 0.16870 1.95906 -0.63087 -1.81023 1.05793 1.56065 -1.42611 -1.22421 1.71491 0.81964 -1.90828 -0.36945 1.99544 -0.10130 -1.97154 0.56641 1.83792 -1.00000 -1.60200 1.37793 1.27693 -1.67918 -0.88079 1.88697 0.43563 -1.98974 0.03378 1.98177 -0.50131 -1.86351 0.94093 1.64153 -1.32819 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.36945 -1.86351 1.05793 1.47265 -1.60200 -0.88079 1.92741 0.16870 -1.98974 0.56641 1.78048 -1.22421 -1.32819 1.71491 0.69461 -1.97154 0.03378 1.95906 -0.75756 -1.67918 1.37793 1.17010 -1.81023 -0.50131 1.99544 -0.23591 -1.90828 0.94093 1.56065 -1.51752 -1.00000 1.88697 0.30286 -1.99886 0.43563 1.83792 -1.11465 -1.42611 1.64153 0.81964 -1.94434 -0.10130 1.98177 -0.63087 -1.74869 1.27693 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 -0.50131 -1.74869 1.37793 1.05793 -1.90828 -0.10130 1.95906 -0.88079 -1.51752 1.64153 0.69461 -1.98974 0.30286 1.83792 -1.22421 -1.22421 1.83792 0.30286 -1.98974 0.69461 1.64153 -1.51752 -0.88079 1.95906 -0.10130 -1.90828 1.05793 1.37793 -1.74869 -0.50131 2.00000 -0.50131 -1.74869 1.37793 1.05793 -1.90828 -0.10130 1.95906 -0.88079 -1.51752 1.64153 0.69461 -1.98974 0.30286 1.83792 -1.22421 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.63087 -1.60200 1.64153 0.56641 -1.99886 0.69461 1.56065 -1.67918 -0.50131 1.99544 -0.75756 -1.51752 1.71491 0.43563 -1.98974 0.81964 1.47265 -1.74869 -0.36945 1.98177 -0.88079 -1.42611 1.78048 0.30286 -1.97154 0.94093 1.37793 -1.81023 -0.23591 1.95906 -1.00000 -1.32819 1.83792 0.16870 -1.94434 1.05793 1.27693 -1.86351 -0.10130 1.92741 -1.11465 -1.22421 1.88697 0.03378 -1.90828 1.17010 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -0.75756 -1.42611 1.83792 0.03378 -1.86351 1.37793 0.81964 -1.99886 0.69461 1.47265 -1.81023 -0.10130 1.88697 -1.32819 -0.88079 1.99544 -0.63087 -1.51752 1.78048 0.16870 -1.90828 1.27693 0.94093 -1.98974 0.56641 1.56065 -1.74869 -0.23591 1.92741 -1.22421 -1.00000 1.98177 -0.50131 -1.60200 1.71491 0.30286 -1.94434 1.17010 1.05793 -1.97154 0.43563 1.64153 -1.67918 -0.36945 1.95906 -1.11465 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -0.88079 -1.22421 1.95906 -0.50131 -1.51752 1.83792 -0.10130 -1.74869 1.64153 0.30286 -1.90828 1.37793 0.69461 -1.98974 1.05793 1.05793 -1.98974 0.69461 1.37793 -1.90828 0.30286 1.64153 -1.74869 -0.10130 1.83792 -1.51752 -0.50131 1.95906 -1.22421 -0.88079 2.00000 -0.88079 -1.22421 1.95906 -0.50131 -1.51752 1.83792 -0.10130 -1.74869 1.64153 0.30286 -1.90828 1.37793 0.69461 -1.98974 1.05793 ... ... ..... ....... ......... ........... ............. E31 * 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 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -1.11465 -0.75756 1.95906 -1.42611 -0.36945 1.83792 -1.67918 0.03378 1.64153 -1.86351 0.43563 1.37793 -1.97154 0.81964 1.05793 -1.99886 1.17010 0.69461 -1.94434 1.47265 0.30286 -1.81023 1.71491 -0.10130 -1.60200 1.88697 -0.50131 -1.32819 1.98177 -0.88079 -1.00000 1.99544 -1.22421 -0.63087 1.92741 -1.51752 -0.23591 1.78048 -1.74869 0.16870 1.56065 -1.90828 0.56641 1.27693 -1.98974 0.94093 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -1.22421 -0.50131 1.83792 -1.74869 0.30286 1.37793 -1.98974 1.05793 0.69461 -1.90828 1.64153 -0.10130 -1.51752 1.95906 -0.88079 -0.88079 1.95906 -1.51752 -0.10130 1.64153 -1.90828 0.69461 1.05793 -1.98974 1.37793 0.30286 -1.74869 1.83792 -0.50131 -1.22421 2.00000 -1.22421 -0.50131 1.83792 -1.74869 0.30286 1.37793 -1.98974 1.05793 0.69461 -1.90828 1.64153 -0.10130 -1.51752 1.95906 -0.88079 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.32819 -0.23591 1.64153 -1.94434 0.94093 0.69461 -1.86351 1.78048 -0.50131 -1.11465 1.98177 -1.51752 0.03378 1.47265 -1.98974 1.17010 0.43563 -1.74869 1.88697 -0.75756 -0.88079 1.92741 -1.67918 0.30286 1.27693 -1.99886 1.37793 0.16870 -1.60200 1.95906 -1.00000 -0.63087 1.83792 -1.81023 0.56641 1.05793 -1.97154 1.56065 -0.10130 -1.42611 1.99544 -1.22421 -0.36945 1.71491 -1.90828 0.81964 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.42611 0.03378 1.37793 -1.99886 1.47265 -0.10130 -1.32819 1.99544 -1.51752 0.16870 1.27693 -1.98974 1.56065 -0.23591 -1.22421 1.98177 -1.60200 0.30286 1.17010 -1.97154 1.64153 -0.36945 -1.11465 1.95906 -1.67918 0.43563 1.05793 -1.94434 1.71491 -0.50131 -1.00000 1.92741 -1.74869 0.56641 0.94093 -1.90828 1.78048 -0.63087 -0.88079 1.88697 -1.81023 0.69461 0.81964 -1.86351 1.83792 -0.75756 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.51752 0.30286 1.05793 -1.90828 1.83792 -0.88079 -0.50131 1.64153 -1.98974 1.37793 -0.10130 -1.22421 1.95906 -1.74869 0.69461 0.69461 -1.74869 1.95906 -1.22421 -0.10130 1.37793 -1.98974 1.64153 -0.50131 -0.88079 1.83792 -1.90828 1.05793 0.30286 -1.51752 2.00000 -1.51752 0.30286 1.05793 -1.90828 1.83792 -0.88079 -0.50131 1.64153 -1.98974 1.37793 -0.10130 -1.22421 1.95906 -1.74869 0.69461 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.60200 0.56641 0.69461 -1.67918 1.99544 -1.51752 0.43563 0.81964 -1.74869 1.98177 -1.42611 0.30286 0.94093 -1.81023 1.95906 -1.32819 0.16870 1.05793 -1.86351 1.92741 -1.22421 0.03378 1.17010 -1.90828 1.88697 -1.11465 -0.10130 1.27693 -1.94434 1.83792 -1.00000 -0.23591 1.37793 -1.97154 1.78048 -0.88079 -0.36945 1.47265 -1.98974 1.71491 -0.75756 -0.50131 1.56065 -1.99886 1.64153 -0.63087 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.67918 0.81964 0.30286 -1.32819 1.92741 -1.90828 1.27693 -0.23591 -0.88079 1.71491 -1.99886 1.64153 -0.75756 -0.36945 1.37793 -1.94434 1.88697 -1.22421 0.16870 0.94093 -1.74869 1.99544 -1.60200 0.69461 0.43563 -1.42611 1.95906 -1.86351 1.17010 -0.10130 -1.00000 1.78048 -1.98974 1.56065 -0.63087 -0.50131 1.47265 -1.97154 1.83792 -1.11465 0.03378 1.05793 -1.81023 1.98177 -1.51752 0.56641 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.74869 1.05793 -0.10130 -0.88079 1.64153 -1.98974 1.83792 -1.22421 0.30286 0.69461 -1.51752 1.95906 -1.90828 1.37793 -0.50131 -0.50131 1.37793 -1.90828 1.95906 -1.51752 0.69461 0.30286 -1.22421 1.83792 -1.98974 1.64153 -0.88079 -0.10130 1.05793 -1.74869 2.00000 -1.74869 1.05793 -0.10130 -0.88079 1.64153 -1.98974 1.83792 -1.22421 0.30286 0.69461 -1.51752 1.95906 -1.90828 1.37793 -0.50131 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.81023 1.27693 -0.50131 -0.36945 1.17010 -1.74869 1.99544 -1.86351 1.37793 -0.63087 -0.23591 1.05793 -1.67918 1.98177 -1.90828 1.47265 -0.75756 -0.10130 0.94093 -1.60200 1.95906 -1.94434 1.56065 -0.88079 0.03378 0.81964 -1.51752 1.92741 -1.97154 1.64153 -1.00000 0.16870 0.69461 -1.42611 1.88697 -1.98974 1.71491 -1.11465 0.30286 0.56641 -1.32819 1.83792 -1.99886 1.78048 -1.22421 0.43563 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.86351 1.47265 -0.88079 0.16870 0.56641 -1.22421 1.71491 -1.97154 1.95906 -1.67918 1.17010 -0.50131 -0.23591 0.94093 -1.51752 1.88697 -1.99886 1.83792 -1.42611 0.81964 -0.10130 -0.63087 1.27693 -1.74869 1.98177 -1.94434 1.64153 -1.11465 0.43563 0.30286 -1.00000 1.56065 -1.90828 1.99544 -1.81023 1.37793 -0.75756 0.03378 0.69461 -1.32819 1.78048 -1.98974 1.92741 -1.60200 1.05793 -0.36945 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.90828 1.64153 -1.22421 0.69461 -0.10130 -0.50131 1.05793 -1.51752 1.83792 -1.98974 1.95906 -1.74869 1.37793 -0.88079 0.30286 0.30286 -0.88079 1.37793 -1.74869 1.95906 -1.98974 1.83792 -1.51752 1.05793 -0.50131 -0.10130 0.69461 -1.22421 1.64153 -1.90828 2.00000 -1.90828 1.64153 -1.22421 0.69461 -0.10130 -0.50131 1.05793 -1.51752 1.83792 -1.98974 1.95906 -1.74869 1.37793 -0.88079 0.30286 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.94434 1.78048 -1.51752 1.17010 -0.75756 0.30286 0.16870 -0.63087 1.05793 -1.42611 1.71491 -1.90828 1.99544 -1.97154 1.83792 -1.60200 1.27693 -0.88079 0.43563 0.03378 -0.50131 0.94093 -1.32819 1.64153 -1.86351 1.98177 -1.98974 1.88697 -1.67918 1.37793 -1.00000 0.56641 -0.10130 -0.36945 0.81964 -1.22421 1.56065 -1.81023 1.95906 -1.99886 1.92741 -1.74869 1.47265 -1.11465 0.69461 -0.23591 ... ... ..... ....... ......... ........... ............. E44 * 2.00000 -1.97154 1.88697 -1.74869 1.56065 -1.32819 1.05793 -0.75756 0.43563 -0.10130 -0.23591 0.56641 -0.88079 1.17010 -1.42611 1.64153 -1.81023 1.92741 -1.98974 1.99544 -1.94434 1.83792 -1.67918 1.47265 -1.22421 0.94093 -0.63087 0.30286 0.03378 -0.36945 0.69461 -1.00000 1.27693 -1.51752 1.71491 -1.86351 1.95906 -1.99886 1.98177 -1.90828 1.78048 -1.60200 1.37793 -1.11465 0.81964 -0.50131 0.16870 ... ... ..... ....... ......... ........... ............. E45 * 2.00000 -1.98974 1.95906 -1.90828 1.83792 -1.74869 1.64153 -1.51752 1.37793 -1.22421 1.05793 -0.88079 0.69461 -0.50131 0.30286 -0.10130 -0.10130 0.30286 -0.50131 0.69461 -0.88079 1.05793 -1.22421 1.37793 -1.51752 1.64153 -1.74869 1.83792 -1.90828 1.95906 -1.98974 2.00000 -1.98974 1.95906 -1.90828 1.83792 -1.74869 1.64153 -1.51752 1.37793 -1.22421 1.05793 -0.88079 0.69461 -0.50131 0.30286 -0.10130 ... ... ..... ....... ......... ........... ............. E46 * 2.00000 -1.99886 1.99544 -1.98974 1.98177 -1.97154 1.95906 -1.94434 1.92741 -1.90828 1.88697 -1.86351 1.83792 -1.81023 1.78048 -1.74869 1.71491 -1.67918 1.64153 -1.60200 1.56065 -1.51752 1.47265 -1.42611 1.37793 -1.32819 1.27693 -1.22421 1.17010 -1.11465 1.05793 -1.00000 0.94093 -0.88079 0.81964 -0.75756 0.69461 -0.63087 0.56641 -0.50131 0.43563 -0.36945 0.30286 -0.23591 0.16870 -0.10130 0.03378 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.995437229360 = 2*cos(2*π/93) 1.981769736316 = 2*cos(4*π/93) 1.959059882505 = 2*cos(6*π/93) = 2*cos(2*π/31) 1.927411287780 = 2*cos(8*π/93) 1.886968357420 = 2*cos(10*π/93) 1.837915623240 = 2*cos(12*π/93) = 2*cos(4*π/31) 1.780476901617 = 2*cos(14*π/93) 1.714914272261 = 2*cos(16*π/93) 1.641526882415 = 2*cos(18*π/93) = 2*cos(6*π/31) 1.560649581904 = 2*cos(20*π/93) 1.472651395302 = 2*cos(22*π/93) 1.377933838151 = 2*cos(24*π/93) = 2*cos(8*π/31) 1.276929084940 = 2*cos(26*π/93) 1.170097997191 = 2*cos(28*π/93) 1.057928020654 = 2*cos(30*π/93) = 2*cos(10*π/31) 0.940930961205 = 2*cos(32*π/93) 0.819640649593 = 2*cos(34*π/93) 0.694610505689 = 2*cos(36*π/93) = 2*cos(12*π/31) 0.566411013364 = 2*cos(38*π/93) 0.435627117498 = 2*cos(40*π/93) 0.302855555009 = 2*cos(42*π/93) = 2*cos(14*π/31) 0.168702132086 = 2*cos(44*π/93) 0.033778960028 = 2*cos(46*π/93) -0.101298337678 = 2*cos(48*π/93) = 2*cos(16*π/31) -0.235913434302 = 2*cos(50*π/93) -0.369452112035 = 2*cos(52*π/93) -0.501305064518 = 2*cos(54*π/93) = 2*cos(18*π/31) -0.630870676971 = 2*cos(56*π/93) -0.757557771221 = 2*cos(58*π/93) -0.880788303116 = 2*cos(60*π/93) = 2*cos(20*π/31) -1.114648926245 = 2*cos(64*π/93) -1.224211965096 = 2*cos(66*π/93) = 2*cos(22*π/31) -1.328189205535 = 2*cos(68*π/93) -1.426106223263 = 2*cos(70*π/93) -1.517516245386 = 2*cos(72*π/93) = 2*cos(24*π/31) -1.602002188939 = 2*cos(74*π/93) -1.679178563939 = 2*cos(76*π/93) -1.748693232289 = 2*cos(78*π/93) = 2*cos(26*π/31) -1.810229014501 = 2*cos(80*π/93) -1.863505136913 = 2*cos(82*π/93) -1.908278512800 = 2*cos(84*π/93) = 2*cos(28*π/31) -1.944344851516 = 2*cos(86*π/93) -1.971539590630 = 2*cos(88*π/93) -1.989738646784 = 2*cos(90*π/93) = 2*cos(30*π/31) -1.998858981859 = 2*cos(92*π/93) Symmetry of Rotations and Cartesian products A R+p+d+f+g+h+i z, Rz, z2, z3, z4, z5, z6 E1 R+p+d+f+g+h+i {x, y}, {Rx, Ry}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} E2 d+f+g+h+i {x2–y2, xy}, {z(x2–y2), xyz}, {z2(x2–y2), xyz2}, {z3(x2–y2), xyz3}, {z4(x2–y2), xyz4} E3 f+g+h+i {x(x2–3y2), y(3x2–y2)}, {xz(x2–3y2), yz(3x2–y2)}, {xz2(x2–3y2), yz2(3x2–y2)}, {xz3(x2–3y2), yz3(3x2–y2)} E4 g+h+i {(x2–y2)2–2x2y2, xy(x2–y2)}, {z((x2–y2)2–4x2y2), xyz(x2–y2)}, {z2((x2–y2)2–4x2y2), xyz2(x2–y2)} E5 h+i {x(x2–(5+2√5)y2)(x2–(5–2√5)y2), y(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)}, {xz(x2–(5+2√5)y2)(x2–(5–2√5)y2), yz(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)} E6 i {x2(x2–3y2)2–y2(3x2–y2)2, xy(x2–3y2)(3x2–y2)} Notes: α The order of the C93 point group is 93, and the order of the principal axis is 93. β This is an Abelian point group (the commutative law holds between all symmetry operations). The C93 group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition). In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. γ Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 92 cases have been combined into 46 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 46 pairs of left and right rotations have been combined into one two-membered pseudo-class each. δ The 46 reducible "E" representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into "irreducible" ones using the familiar projection formula. ε The point group is chiral, as it does not contain any mirroring operation. ζ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree less than half the order of the principal axis (and often much less). For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.
| C92 | ||
| C93 | C93v C93h D93 D93h D93d | |
| C94 |
This Character Table for the C93 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.