D93 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 93 C2' <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 A2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 ............. 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 0.00000 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 0.00000 ... ... 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 0.00000 ... ... ..... 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 0.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... 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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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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 0.00000 ... ... ..... ....... ......... ........... ............. 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) 0.940930961206 = 2*cos(32*π/93) 0.819640649593 = 2*cos(34*π/93) 0.694610505690 = 2*cos(36*π/93) = 2*cos(12*π/31) 0.566411013365 = 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) -0.101298337677 = 2*cos(48*π/93) = 2*cos(16*π/31) -0.235913434302 = 2*cos(50*π/93) -0.369452112034 = 2*cos(52*π/93) -0.501305064517 = 2*cos(54*π/93) = 2*cos(18*π/31) -0.630870676971 = 2*cos(56*π/93) -0.757557771221 = 2*cos(58*π/93) -0.880788303115 = 2*cos(60*π/93) = 2*cos(20*π/31) -1.114648926245 = 2*cos(64*π/93) -1.224211965095 = 2*cos(66*π/93) = 2*cos(22*π/31) -1.328189205534 = 2*cos(68*π/93) -1.426106223262 = 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 A1 d+g+i+k+m z2, z4, z6 A2 R+p+f+h+j+l Rz, z, z3, z5 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 D93 point group is 186, and the order of the principal axis (C93) is 93. The group has 48 irreducible representations. β The D93 point group is isomorphic to C93v. γ The D93 point group is generated by two symmetry elements, C93 and a perpendicular C2′. Also, the group may be generated from two C2′ axes (some pairs will yield smaller groups, though; choosing a minimum angle is safe). 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. ε The lowest nonvanishing multipole moment in D93 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 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. For this group, however, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.
| D91 | ||
| D92 | ||
| C93 C93v C93h | D93 | D93h D93d |
| D94 | ||
| D95 |
This Character Table for the D93 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.