Character table for the C83v point group

C83v    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 83 sv       <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     ... ..T ....T ......T ........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     ..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  0.00000     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  0.00000     ... ... 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  0.00000     ... ... ..... 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  0.00000     ... ... ..... ....... 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  0.00000     ... ... ..... ....... ......... 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  0.00000     ... ... ..... ....... ......... ........... 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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............
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  0.00000     ... ... ..... ....... ......... ........... .............

 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

A1   p+d+f+g+h+i+j+k+l+m    z, z2, z3, z4, z5, z6 
A2   R                      Rz 
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      {x2y2, xy}, {z(x2y2), xyz}, {z2(x2y2), xyz2}, {z3(x2y2), xyz3}, {z4(x2y2), xyz4} 
E3   f+g+h+i+j+k+l+m        {x(x2−3y2), y(3x2y2)}, {xz(x2−3y2), yz(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E4   g+h+i+j+k+l+m          {(x2y2)2−4x2y2, xy(x2y2)}, {z((x2y2)2−4x2y2), xyz(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E5   h+i+j+k+l+m            {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)}, {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E6   i+j+k+l+m              {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7   j+k+l+m 
E8   k+l+m 
E9   l+m 
E10  m 

 Notes:

    α  The order of the C83v point group is 166, and the order of the principal axis (C83) is 83. The group has 43 irreducible representations.

    β  The C83v point group is isomorphic to D83.

    γ  The C83v point group is generated by two symmetry elements, C83 and any σv.
       Also, the group may be generated from any two σv planes.

    δ  The group contains one set of symmetry planes σv intersecting in the principal (z) axis. The xz plane (but not the yz plane) is a member of that set.

    ε  The lowest nonvanishing multipole moment in C83v is 2 (dipole 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 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.

This Character Table for the C83v point group was created by Gernot Katzer.

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