C83 E 2 C83 2 C83^2 2 C83^3 2 C83^4 2 C83^5 2 C83^6 2 C83^7 2 C83^8 2 C83^9 2 C83^10 2 C83^11 2 C83^12 2 C83^13 2 C83^14 2 C83^15 2 C83^16 2 C83^17 2 C83^18 2 C83^19 2 C83^20 2 C83^21 2 C83^22 2 C83^23 2 C83^24 2 C83^25 2 C83^26 2 C83^27 2 C83^28 2 C83^29 2 C83^30 2 C83^31 2 C83^32 2 C83^33 2 C83^34 2 C83^35 2 C83^36 2 C83^37 2 C83^38 2 C83^39 2 C83^40 2 C83^41 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99427 1.97712 1.94865 1.90901 1.85844 1.79722 1.72571 1.64431 1.55350 1.45378 1.34575 1.23000 1.10720 0.97807 0.84333 0.70376 0.56016 0.41335 0.26418 0.11349 -0.03785 -0.18897 -0.33901 -0.48711 -0.63242 -0.77410 -0.91135 -1.04338 -1.16944 -1.28879 -1.40077 -1.50472 -1.60005 -1.68622 -1.76273 -1.82914 -1.88507 -1.93021 -1.96429 -1.98712 -1.99857 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.97712 1.90901 1.79722 1.64431 1.45378 1.23000 0.97807 0.70376 0.41335 0.11349 -0.18897 -0.48711 -0.77410 -1.04338 -1.28879 -1.50472 -1.68622 -1.82914 -1.93021 -1.98712 -1.99857 -1.96429 -1.88507 -1.76273 -1.60005 -1.40077 -1.16944 -0.91135 -0.63242 -0.33901 -0.03785 0.26418 0.56016 0.84333 1.10720 1.34575 1.55350 1.72571 1.85844 1.94865 1.99427 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.94865 1.79722 1.55350 1.23000 0.84333 0.41335 -0.03785 -0.48711 -0.91135 -1.28879 -1.60005 -1.82914 -1.96429 -1.99857 -1.93021 -1.76273 -1.50472 -1.16944 -0.77410 -0.33901 0.11349 0.56016 0.97807 1.34575 1.64431 1.85844 1.97712 1.99427 1.90901 1.72571 1.45378 1.10720 0.70376 0.26418 -0.18897 -0.63242 -1.04338 -1.40077 -1.68622 -1.88507 -1.98712 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.90901 1.64431 1.23000 0.70376 0.11349 -0.48711 -1.04338 -1.50472 -1.82914 -1.98712 -1.96429 -1.76273 -1.40077 -0.91135 -0.33901 0.26418 0.84333 1.34575 1.72571 1.94865 1.99427 1.85844 1.55350 1.10720 0.56016 -0.03785 -0.63242 -1.16944 -1.60005 -1.88507 -1.99857 -1.93021 -1.68622 -1.28879 -0.77410 -0.18897 0.41335 0.97807 1.45378 1.79722 1.97712 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.85844 1.45378 0.84333 0.11349 -0.63242 -1.28879 -1.76273 -1.98712 -1.93021 -1.60005 -1.04338 -0.33901 0.41335 1.10720 1.64431 1.94865 1.97712 1.72571 1.23000 0.56016 -0.18897 -0.91135 -1.50472 -1.88507 -1.99857 -1.82914 -1.40077 -0.77410 -0.03785 0.70376 1.34575 1.79722 1.99427 1.90901 1.55350 0.97807 0.26418 -0.48711 -1.16944 -1.68622 -1.96429 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.79722 1.23000 0.41335 -0.48711 -1.28879 -1.82914 -1.99857 -1.76273 -1.16944 -0.33901 0.56016 1.34575 1.85844 1.99427 1.72571 1.10720 0.26418 -0.63242 -1.40077 -1.88507 -1.98712 -1.68622 -1.04338 -0.18897 0.70376 1.45378 1.90901 1.97712 1.64431 0.97807 0.11349 -0.77410 -1.50472 -1.93021 -1.96429 -1.60005 -0.91135 -0.03785 0.84333 1.55350 1.94865 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.72571 0.97807 -0.03785 -1.04338 -1.76273 -1.99857 -1.68622 -0.91135 0.11349 1.10720 1.79722 1.99427 1.64431 0.84333 -0.18897 -1.16944 -1.82914 -1.98712 -1.60005 -0.77410 0.26418 1.23000 1.85844 1.97712 1.55350 0.70376 -0.33901 -1.28879 -1.88507 -1.96429 -1.50472 -0.63242 0.41335 1.34575 1.90901 1.94865 1.45378 0.56016 -0.48711 -1.40077 -1.93021 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.64431 0.70376 -0.48711 -1.50472 -1.98712 -1.76273 -0.91135 0.26418 1.34575 1.94865 1.85844 1.10720 -0.03785 -1.16944 -1.88507 -1.93021 -1.28879 -0.18897 0.97807 1.79722 1.97712 1.45378 0.41335 -0.77410 -1.68622 -1.99857 -1.60005 -0.63242 0.56016 1.55350 1.99427 1.72571 0.84333 -0.33901 -1.40077 -1.96429 -1.82914 -1.04338 0.11349 1.23000 1.90901 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.55350 0.41335 -0.91135 -1.82914 -1.93021 -1.16944 0.11349 1.34575 1.97712 1.72571 0.70376 -0.63242 -1.68622 -1.98712 -1.40077 -0.18897 1.10720 1.90901 1.85844 0.97807 -0.33901 -1.50472 -1.99857 -1.60005 -0.48711 0.84333 1.79722 1.94865 1.23000 -0.03785 -1.28879 -1.96429 -1.76273 -0.77410 0.56016 1.64431 1.99427 1.45378 0.26418 -1.04338 -1.88507 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.45378 0.11349 -1.28879 -1.98712 -1.60005 -0.33901 1.10720 1.94865 1.72571 0.56016 -0.91135 -1.88507 -1.82914 -0.77410 0.70376 1.79722 1.90901 0.97807 -0.48711 -1.68622 -1.96429 -1.16944 0.26418 1.55350 1.99427 1.34575 -0.03785 -1.40077 -1.99857 -1.50472 -0.18897 1.23000 1.97712 1.64431 0.41335 -1.04338 -1.93021 -1.76273 -0.63242 0.84333 1.85844 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.34575 -0.18897 -1.60005 -1.96429 -1.04338 0.56016 1.79722 1.85844 0.70376 -0.91135 -1.93021 -1.68622 -0.33901 1.23000 1.99427 1.45378 -0.03785 -1.50472 -1.98712 -1.16944 0.41335 1.72571 1.90901 0.84333 -0.77410 -1.88507 -1.76273 -0.48711 1.10720 1.97712 1.55350 0.11349 -1.40077 -1.99857 -1.28879 0.26418 1.64431 1.94865 0.97807 -0.63242 -1.82914 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.23000 -0.48711 -1.82914 -1.76273 -0.33901 1.34575 1.99427 1.10720 -0.63242 -1.88507 -1.68622 -0.18897 1.45378 1.97712 0.97807 -0.77410 -1.93021 -1.60005 -0.03785 1.55350 1.94865 0.84333 -0.91135 -1.96429 -1.50472 0.11349 1.64431 1.90901 0.70376 -1.04338 -1.98712 -1.40077 0.26418 1.72571 1.85844 0.56016 -1.16944 -1.99857 -1.28879 0.41335 1.79722 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.10720 -0.77410 -1.96429 -1.40077 0.41335 1.85844 1.64431 -0.03785 -1.68622 -1.82914 -0.33901 1.45378 1.94865 0.70376 -1.16944 -1.99857 -1.04338 0.84333 1.97712 1.34575 -0.48711 -1.88507 -1.60005 0.11349 1.72571 1.79722 0.26418 -1.50472 -1.93021 -0.63242 1.23000 1.99427 0.97807 -0.91135 -1.98712 -1.28879 0.56016 1.90901 1.55350 -0.18897 -1.76273 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 0.97807 -1.04338 -1.99857 -0.91135 1.10720 1.99427 0.84333 -1.16944 -1.98712 -0.77410 1.23000 1.97712 0.70376 -1.28879 -1.96429 -0.63242 1.34575 1.94865 0.56016 -1.40077 -1.93021 -0.48711 1.45378 1.90901 0.41335 -1.50472 -1.88507 -0.33901 1.55350 1.85844 0.26418 -1.60005 -1.82914 -0.18897 1.64431 1.79722 0.11349 -1.68622 -1.76273 -0.03785 1.72571 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 0.84333 -1.28879 -1.93021 -0.33901 1.64431 1.72571 -0.18897 -1.88507 -1.40077 0.70376 1.99427 0.97807 -1.16944 -1.96429 -0.48711 1.55350 1.79722 -0.03785 -1.82914 -1.50472 0.56016 1.97712 1.10720 -1.04338 -1.98712 -0.63242 1.45378 1.85844 0.11349 -1.76273 -1.60005 0.41335 1.94865 1.23000 -0.91135 -1.99857 -0.77410 1.34575 1.90901 0.26418 -1.68622 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 0.70376 -1.50472 -1.76273 0.26418 1.94865 1.10720 -1.16944 -1.93021 -0.18897 1.79722 1.45378 -0.77410 -1.99857 -0.63242 1.55350 1.72571 -0.33901 -1.96429 -1.04338 1.23000 1.90901 0.11349 -1.82914 -1.40077 0.84333 1.99427 0.56016 -1.60005 -1.68622 0.41335 1.97712 0.97807 -1.28879 -1.88507 -0.03785 1.85844 1.34575 -0.91135 -1.98712 -0.48711 1.64431 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 0.56016 -1.68622 -1.50472 0.84333 1.97712 0.26418 -1.82914 -1.28879 1.10720 1.90901 -0.03785 -1.93021 -1.04338 1.34575 1.79722 -0.33901 -1.98712 -0.77410 1.55350 1.64431 -0.63242 -1.99857 -0.48711 1.72571 1.45378 -0.91135 -1.96429 -0.18897 1.85844 1.23000 -1.16944 -1.88507 0.11349 1.94865 0.97807 -1.40077 -1.76273 0.41335 1.99427 0.70376 -1.60005 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.41335 -1.82914 -1.16944 1.34575 1.72571 -0.63242 -1.98712 -0.18897 1.90901 0.97807 -1.50472 -1.60005 0.84333 1.94865 -0.03785 -1.96429 -0.77410 1.64431 1.45378 -1.04338 -1.88507 0.26418 1.99427 0.56016 -1.76273 -1.28879 1.23000 1.79722 -0.48711 -1.99857 -0.33901 1.85844 1.10720 -1.40077 -1.68622 0.70376 1.97712 0.11349 -1.93021 -0.91135 1.55350 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.26418 -1.93021 -0.77410 1.72571 1.23000 -1.40077 -1.60005 0.97807 1.85844 -0.48711 -1.98712 -0.03785 1.97712 0.56016 -1.82914 -1.04338 1.55350 1.45378 -1.16944 -1.76273 0.70376 1.94865 -0.18897 -1.99857 -0.33901 1.90901 0.84333 -1.68622 -1.28879 1.34575 1.64431 -0.91135 -1.88507 0.41335 1.99427 0.11349 -1.96429 -0.63242 1.79722 1.10720 -1.50472 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.11349 -1.98712 -0.33901 1.94865 0.56016 -1.88507 -0.77410 1.79722 0.97807 -1.68622 -1.16944 1.55350 1.34575 -1.40077 -1.50472 1.23000 1.64431 -1.04338 -1.76273 0.84333 1.85844 -0.63242 -1.93021 0.41335 1.97712 -0.18897 -1.99857 -0.03785 1.99427 0.26418 -1.96429 -0.48711 1.90901 0.70376 -1.82914 -0.91135 1.72571 1.10720 -1.60005 -1.28879 1.45378 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 -0.03785 -1.99857 0.11349 1.99427 -0.18897 -1.98712 0.26418 1.97712 -0.33901 -1.96429 0.41335 1.94865 -0.48711 -1.93021 0.56016 1.90901 -0.63242 -1.88507 0.70376 1.85844 -0.77410 -1.82914 0.84333 1.79722 -0.91135 -1.76273 0.97807 1.72571 -1.04338 -1.68622 1.10720 1.64431 -1.16944 -1.60005 1.23000 1.55350 -1.28879 -1.50472 1.34575 1.45378 -1.40077 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 -0.18897 -1.96429 0.56016 1.85844 -0.91135 -1.68622 1.23000 1.45378 -1.50472 -1.16944 1.72571 0.84333 -1.88507 -0.48711 1.97712 0.11349 -1.99857 0.26418 1.94865 -0.63242 -1.82914 0.97807 1.64431 -1.28879 -1.40077 1.55350 1.10720 -1.76273 -0.77410 1.90901 0.41335 -1.98712 -0.03785 1.99427 -0.33901 -1.93021 0.70376 1.79722 -1.04338 -1.60005 1.34575 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 -0.33901 -1.88507 0.97807 1.55350 -1.50472 -1.04338 1.85844 0.41335 -1.99857 0.26418 1.90901 -0.91135 -1.60005 1.45378 1.10720 -1.82914 -0.48711 1.99427 -0.18897 -1.93021 0.84333 1.64431 -1.40077 -1.16944 1.79722 0.56016 -1.98712 0.11349 1.94865 -0.77410 -1.68622 1.34575 1.23000 -1.76273 -0.63242 1.97712 -0.03785 -1.96429 0.70376 1.72571 -1.28879 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 -0.48711 -1.76273 1.34575 1.10720 -1.88507 -0.18897 1.97712 -0.77410 -1.60005 1.55350 0.84333 -1.96429 0.11349 1.90901 -1.04338 -1.40077 1.72571 0.56016 -1.99857 0.41335 1.79722 -1.28879 -1.16944 1.85844 0.26418 -1.98712 0.70376 1.64431 -1.50472 -0.91135 1.94865 -0.03785 -1.93021 0.97807 1.45378 -1.68622 -0.63242 1.99427 -0.33901 -1.82914 1.23000 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 -0.63242 -1.60005 1.64431 0.56016 -1.99857 0.70376 1.55350 -1.68622 -0.48711 1.99427 -0.77410 -1.50472 1.72571 0.41335 -1.98712 0.84333 1.45378 -1.76273 -0.33901 1.97712 -0.91135 -1.40077 1.79722 0.26418 -1.96429 0.97807 1.34575 -1.82914 -0.18897 1.94865 -1.04338 -1.28879 1.85844 0.11349 -1.93021 1.10720 1.23000 -1.88507 -0.03785 1.90901 -1.16944 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.77410 -1.40077 1.85844 -0.03785 -1.82914 1.45378 0.70376 -1.99857 0.84333 1.34575 -1.88507 0.11349 1.79722 -1.50472 -0.63242 1.99427 -0.91135 -1.28879 1.90901 -0.18897 -1.76273 1.55350 0.56016 -1.98712 0.97807 1.23000 -1.93021 0.26418 1.72571 -1.60005 -0.48711 1.97712 -1.04338 -1.16944 1.94865 -0.33901 -1.68622 1.64431 0.41335 -1.96429 1.10720 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 -0.91135 -1.16944 1.97712 -0.63242 -1.40077 1.90901 -0.33901 -1.60005 1.79722 -0.03785 -1.76273 1.64431 0.26418 -1.88507 1.45378 0.56016 -1.96429 1.23000 0.84333 -1.99857 0.97807 1.10720 -1.98712 0.70376 1.34575 -1.93021 0.41335 1.55350 -1.82914 0.11349 1.72571 -1.68622 -0.18897 1.85844 -1.50472 -0.48711 1.94865 -1.28879 -0.77410 1.99427 -1.04338 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -1.04338 -0.91135 1.99427 -1.16944 -0.77410 1.97712 -1.28879 -0.63242 1.94865 -1.40077 -0.48711 1.90901 -1.50472 -0.33901 1.85844 -1.60005 -0.18897 1.79722 -1.68622 -0.03785 1.72571 -1.76273 0.11349 1.64431 -1.82914 0.26418 1.55350 -1.88507 0.41335 1.45378 -1.93021 0.56016 1.34575 -1.96429 0.70376 1.23000 -1.98712 0.84333 1.10720 -1.99857 0.97807 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -1.16944 -0.63242 1.90901 -1.60005 -0.03785 1.64431 -1.88507 0.56016 1.23000 -1.99857 1.10720 0.70376 -1.93021 1.55350 0.11349 -1.68622 1.85844 -0.48711 -1.28879 1.99427 -1.04338 -0.77410 1.94865 -1.50472 -0.18897 1.72571 -1.82914 0.41335 1.34575 -1.98712 0.97807 0.84333 -1.96429 1.45378 0.26418 -1.76273 1.79722 -0.33901 -1.40077 1.97712 -0.91135 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -1.28879 -0.33901 1.72571 -1.88507 0.70376 0.97807 -1.96429 1.55350 -0.03785 -1.50472 1.97712 -1.04338 -0.63242 1.85844 -1.76273 0.41335 1.23000 -1.99857 1.34575 0.26418 -1.68622 1.90901 -0.77410 -0.91135 1.94865 -1.60005 0.11349 1.45378 -1.98712 1.10720 0.56016 -1.82914 1.79722 -0.48711 -1.16944 1.99427 -1.40077 -0.18897 1.64431 -1.93021 0.84333 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -1.40077 -0.03785 1.45378 -1.99857 1.34575 0.11349 -1.50472 1.99427 -1.28879 -0.18897 1.55350 -1.98712 1.23000 0.26418 -1.60005 1.97712 -1.16944 -0.33901 1.64431 -1.96429 1.10720 0.41335 -1.68622 1.94865 -1.04338 -0.48711 1.72571 -1.93021 0.97807 0.56016 -1.76273 1.90901 -0.91135 -0.63242 1.79722 -1.88507 0.84333 0.70376 -1.82914 1.85844 -0.77410 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -1.50472 0.26418 1.10720 -1.93021 1.79722 -0.77410 -0.63242 1.72571 -1.96429 1.23000 0.11349 -1.40077 1.99427 -1.60005 0.41335 0.97807 -1.88507 1.85844 -0.91135 -0.48711 1.64431 -1.98712 1.34575 -0.03785 -1.28879 1.97712 -1.68622 0.56016 0.84333 -1.82914 1.90901 -1.04338 -0.33901 1.55350 -1.99857 1.45378 -0.18897 -1.16944 1.94865 -1.76273 0.70376 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -1.60005 0.56016 0.70376 -1.68622 1.99427 -1.50472 0.41335 0.84333 -1.76273 1.97712 -1.40077 0.26418 0.97807 -1.82914 1.94865 -1.28879 0.11349 1.10720 -1.88507 1.90901 -1.16944 -0.03785 1.23000 -1.93021 1.85844 -1.04338 -0.18897 1.34575 -1.96429 1.79722 -0.91135 -0.33901 1.45378 -1.98712 1.72571 -0.77410 -0.48711 1.55350 -1.99857 1.64431 -0.63242 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.68622 0.84333 0.26418 -1.28879 1.90901 -1.93021 1.34575 -0.33901 -0.77410 1.64431 -1.99857 1.72571 -0.91135 -0.18897 1.23000 -1.88507 1.94865 -1.40077 0.41335 0.70376 -1.60005 1.99427 -1.76273 0.97807 0.11349 -1.16944 1.85844 -1.96429 1.45378 -0.48711 -0.63242 1.55350 -1.98712 1.79722 -1.04338 -0.03785 1.10720 -1.82914 1.97712 -1.50472 0.56016 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.76273 1.10720 -0.18897 -0.77410 1.55350 -1.96429 1.90901 -1.40077 0.56016 0.41335 -1.28879 1.85844 -1.98712 1.64431 -0.91135 -0.03785 0.97807 -1.68622 1.99427 -1.82914 1.23000 -0.33901 -0.63242 1.45378 -1.93021 1.94865 -1.50472 0.70376 0.26418 -1.16944 1.79722 -1.99857 1.72571 -1.04338 0.11349 0.84333 -1.60005 1.97712 -1.88507 1.34575 -0.48711 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.82914 1.34575 -0.63242 -0.18897 0.97807 -1.60005 1.94865 -1.96429 1.64431 -1.04338 0.26418 0.56016 -1.28879 1.79722 -1.99857 1.85844 -1.40077 0.70376 0.11349 -0.91135 1.55350 -1.93021 1.97712 -1.68622 1.10720 -0.33901 -0.48711 1.23000 -1.76273 1.99427 -1.88507 1.45378 -0.77410 -0.03785 0.84333 -1.50472 1.90901 -1.98712 1.72571 -1.16944 0.41335 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.88507 1.55350 -1.04338 0.41335 0.26418 -0.91135 1.45378 -1.82914 1.99427 -1.93021 1.64431 -1.16944 0.56016 0.11349 -0.77410 1.34575 -1.76273 1.97712 -1.96429 1.72571 -1.28879 0.70376 -0.03785 -0.63242 1.23000 -1.68622 1.94865 -1.98712 1.79722 -1.40077 0.84333 -0.18897 -0.48711 1.10720 -1.60005 1.90901 -1.99857 1.85844 -1.50472 0.97807 -0.33901 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.93021 1.72571 -1.40077 0.97807 -0.48711 -0.03785 0.56016 -1.04338 1.45378 -1.76273 1.94865 -1.99857 1.90901 -1.68622 1.34575 -0.91135 0.41335 0.11349 -0.63242 1.10720 -1.50472 1.79722 -1.96429 1.99427 -1.88507 1.64431 -1.28879 0.84333 -0.33901 -0.18897 0.70376 -1.16944 1.55350 -1.82914 1.97712 -1.98712 1.85844 -1.60005 1.23000 -0.77410 0.26418 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.96429 1.85844 -1.68622 1.45378 -1.16944 0.84333 -0.48711 0.11349 0.26418 -0.63242 0.97807 -1.28879 1.55350 -1.76273 1.90901 -1.98712 1.99427 -1.93021 1.79722 -1.60005 1.34575 -1.04338 0.70376 -0.33901 -0.03785 0.41335 -0.77410 1.10720 -1.40077 1.64431 -1.82914 1.94865 -1.99857 1.97712 -1.88507 1.72571 -1.50472 1.23000 -0.91135 0.56016 -0.18897 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.98712 1.94865 -1.88507 1.79722 -1.68622 1.55350 -1.40077 1.23000 -1.04338 0.84333 -0.63242 0.41335 -0.18897 -0.03785 0.26418 -0.48711 0.70376 -0.91135 1.10720 -1.28879 1.45378 -1.60005 1.72571 -1.82914 1.90901 -1.96429 1.99427 -1.99857 1.97712 -1.93021 1.85844 -1.76273 1.64431 -1.50472 1.34575 -1.16944 0.97807 -0.77410 0.56016 -0.33901 0.11349 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.99857 1.99427 -1.98712 1.97712 -1.96429 1.94865 -1.93021 1.90901 -1.88507 1.85844 -1.82914 1.79722 -1.76273 1.72571 -1.68622 1.64431 -1.60005 1.55350 -1.50472 1.45378 -1.40077 1.34575 -1.28879 1.23000 -1.16944 1.10720 -1.04338 0.97807 -0.91135 0.84333 -0.77410 0.70376 -0.63242 0.56016 -0.48711 0.41335 -0.33901 0.26418 -0.18897 0.11349 -0.03785 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.994272090559 = 2*cos(2*π/83) 1.977121171184 = 2*cos(4*π/83) 1.948645480786 = 2*cos(6*π/83) 1.909008125543 = 2*cos(8*π/83) 1.858436144635 = 2*cos(10*π/83) 1.797219209789 = 2*cos(12*π/83) 1.725707966065 = 2*cos(14*π/83) 1.644312023390 = 2*cos(16*π/83) 1.553497610352 = 2*cos(18*π/83) 1.453784903686 = 2*cos(20*π/83) 1.345745048746 = 2*cos(22*π/83) 1.229996888036 = 2*cos(24*π/83) 1.107203416539 = 2*cos(26*π/83) 0.978067984140 = 2*cos(28*π/83) 0.843330266900 = 2*cos(30*π/83) 0.703762030264 = 2*cos(32*π/83) 0.560162708450 = 2*cos(34*π/83) 0.413354825370 = 2*cos(36*π/83) 0.264179283283 = 2*cos(38*π/83) 0.113490546186 = 2*cos(40*π/83) -0.037848254482 = 2*cos(42*π/83) -0.188970263776 = 2*cos(44*π/83) -0.339009868512 = 2*cos(46*π/83) -0.487107655422 = 2*cos(48*π/83) -0.632415333794 = 2*cos(50*π/83) -0.774100594404 = 2*cos(52*π/83) -0.911351876912 = 2*cos(54*π/83) -1.043383018401 = 2*cos(56*π/83) -1.169437756448 = 2*cos(58*π/83) -1.288794060930 = 2*cos(60*π/83) -1.400768269743 = 2*cos(62*π/83) -1.504719004759 = 2*cos(64*π/83) -1.600050845583 = 2*cos(66*π/83) -1.686217740062 = 2*cos(68*π/83) -1.762726132029 = 2*cos(70*π/83) -1.829137788343 = 2*cos(72*π/83) -1.885072309051 = 2*cos(74*π/83) -1.930209306284 = 2*cos(76*π/83) -1.964290239408 = 2*cos(78*π/83) -1.987119895926 = 2*cos(80*π/83) -1.998567509633 = 2*cos(82*π/83) Symmetry of Rotations and Cartesian products A R+p+d+f+g+h+i+j+k+l+m Rz, z, z2, z3, z4, z5, z6 E1 R+p+d+f+g+h+i+j+k+l+m {Rx, Ry}, {x, y}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} E2 d+f+g+h+i+j+k+l+m {x2−y2, xy}, {z(x2−y2), xyz}, {z2(x2−y2), xyz2}, {z3(x2−y2), xyz3}, {z4(x2−y2), xyz4} E3 f+g+h+i+j+k+l+m {x(x2−3y2), y(3x2−y2)}, {xz(x2−3y2), yz(3x2−y2)}, {xz2(x2−3y2), yz2(3x2−y2)}, {xz3(x2−3y2), yz3(3x2−y2)} E4 g+h+i+j+k+l+m {(x2−y2)2−4x2y2, xy(x2−y2)}, {z((x2−y2)2−4x2y2), xyz(x2−y2)}, {z2((x2−y2)2−4x2y2), xyz2(x2−y2)} E5 h+i+j+k+l+m {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2−y2)((5−2√5)x2−y2)}, {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2−y2)((5−2√5)x2−y2)} E6 i+j+k+l+m {x2(x2−3y2)2−y2(3x2−y2)2, xy(x2−3y2)(3x2−y2)} E7 j+k+l+m E8 k+l+m E9 l+m E10 m Notes: α The order of the C83 point group is 83, and the order of the principal axis (C83) is 83. The group has 42 irreducible representations. β The C83 point group is generated by one single symmetry element, C83. Therefore, it is a cyclic group. γ The lowest nonvanishing multipole moment in C83 is 2 (dipole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C83 group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition). In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. ε Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 82 cases have been combined into 41 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 41 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 41 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. η The point group is chiral, as it does not contain any mirroring operation. θ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree just 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.
| C81 | ||
| C82 | ||
| C83 | C83v C83h D83 D83h D83d | |
| C84 | ||
| C85 |
This Character Table for the C83 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.