Character table for the C97v point group

C97v    E        2 C97    2 C97^2  2 C97^3  2 C97^4  2 C97^5  2 C97^6  2 C97^7  2 C97^8  2 C97^9  2 C97^10 2 C97^11 2 C97^12 2 C97^13 2 C97^14 2 C97^15 2 C97^16 2 C97^17 2 C97^18 2 C97^19 2 C97^20 2 C97^21 2 C97^22 2 C97^23 2 C97^24 2 C97^25 2 C97^26 2 C97^27 2 C97^28 2 C97^29 2 C97^30 2 C97^31 2 C97^32 2 C97^33 2 C97^34 2 C97^35 2 C97^36 2 C97^37 2 C97^38 2 C97^39 2 C97^40 2 C97^41 2 C97^42 2 C97^43 2 C97^44 2 C97^45 2 C97^46 2 C97^47 2 C97^48 97 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  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  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000 -1.00000     ..T ... ..... ....... ......... ........... .............
E1      2.00000  1.99581  1.98324  1.96236  1.93324  1.89602  1.85084  1.79790  1.73742  1.66966  1.59489  1.51343  1.42562  1.33183  1.23246  1.12791  1.01864  0.90509  0.78775  0.66710  0.54366  0.41794  0.29046  0.16176  0.03239 -0.09712 -0.22623 -0.35438 -0.48105 -0.60570 -0.72781 -0.84687 -0.96237 -1.07384 -1.18080 -1.28282 -1.37945 -1.47029 -1.55497 -1.63313 -1.70443 -1.76859 -1.82533 -1.87441 -1.91563 -1.94882 -1.97383 -1.99057 -1.99895  0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2      2.00000  1.98324  1.93324  1.85084  1.73742  1.59489  1.42562  1.23246  1.01864  0.78775  0.54366  0.29046  0.03239 -0.22623 -0.48105 -0.72781 -0.96237 -1.18080 -1.37945 -1.55497 -1.70443 -1.82533 -1.91563 -1.97383 -1.99895 -1.99057 -1.94882 -1.87441 -1.76859 -1.63313 -1.47029 -1.28282 -1.07384 -0.84687 -0.60570 -0.35438 -0.09712  0.16176  0.41794  0.66710  0.90509  1.12791  1.33183  1.51343  1.66966  1.79790  1.89602  1.96236  1.99581  0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3      2.00000  1.96236  1.85084  1.66966  1.42562  1.12791  0.78775  0.41794  0.03239 -0.35438 -0.72781 -1.07384 -1.37945 -1.63313 -1.82533 -1.94882 -1.99895 -1.97383 -1.87441 -1.70443 -1.47029 -1.18080 -0.84687 -0.48105 -0.09712  0.29046  0.66710  1.01864  1.33183  1.59489  1.79790  1.93324  1.99581  1.98324  1.89602  1.73742  1.51343  1.23246  0.90509  0.54366  0.16176 -0.22623 -0.60570 -0.96237 -1.28282 -1.55497 -1.76859 -1.91563 -1.99057  0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4      2.00000  1.93324  1.73742  1.42562  1.01864  0.54366  0.03239 -0.48105 -0.96237 -1.37945 -1.70443 -1.91563 -1.99895 -1.94882 -1.76859 -1.47029 -1.07384 -0.60570 -0.09712  0.41794  0.90509  1.33183  1.66966  1.89602  1.99581  1.96236  1.79790  1.51343  1.12791  0.66710  0.16176 -0.35438 -0.84687 -1.28282 -1.63313 -1.87441 -1.99057 -1.97383 -1.82533 -1.55497 -1.18080 -0.72781 -0.22623  0.29046  0.78775  1.23246  1.59489  1.85084  1.98324  0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5      2.00000  1.89602  1.59489  1.12791  0.54366 -0.09712 -0.72781 -1.28282 -1.70443 -1.94882 -1.99057 -1.82533 -1.47029 -0.96237 -0.35438  0.29046  0.90509  1.42562  1.79790  1.98324  1.96236  1.73742  1.33183  0.78775  0.16176 -0.48105 -1.07384 -1.55497 -1.87441 -1.99895 -1.91563 -1.63313 -1.18080 -0.60570  0.03239  0.66710  1.23246  1.66966  1.93324  1.99581  1.85084  1.51343  1.01864  0.41794 -0.22623 -0.84687 -1.37945 -1.76859 -1.97383  0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6      2.00000  1.85084  1.42562  0.78775  0.03239 -0.72781 -1.37945 -1.82533 -1.99895 -1.87441 -1.47029 -0.84687 -0.09712  0.66710  1.33183  1.79790  1.99581  1.89602  1.51343  0.90509  0.16176 -0.60570 -1.28282 -1.76859 -1.99057 -1.91563 -1.55497 -0.96237 -0.22623  0.54366  1.23246  1.73742  1.98324  1.93324  1.59489  1.01864  0.29046 -0.48105 -1.18080 -1.70443 -1.97383 -1.94882 -1.63313 -1.07384 -0.35438  0.41794  1.12791  1.66966  1.96236  0.00000     ... ... ..... ....... ......... ........... TT...........
E7      2.00000  1.79790  1.23246  0.41794 -0.48105 -1.28282 -1.82533 -1.99895 -1.76859 -1.18080 -0.35438  0.54366  1.33183  1.85084  1.99581  1.73742  1.12791  0.29046 -0.60570 -1.37945 -1.87441 -1.99057 -1.70443 -1.07384 -0.22623  0.66710  1.42562  1.89602  1.98324  1.66966  1.01864  0.16176 -0.72781 -1.47029 -1.91563 -1.97383 -1.63313 -0.96237 -0.09712  0.78775  1.51343  1.93324  1.96236  1.59489  0.90509  0.03239 -0.84687 -1.55497 -1.94882  0.00000     ... ... ..... ....... ......... ........... .............
E8      2.00000  1.73742  1.01864  0.03239 -0.96237 -1.70443 -1.99895 -1.76859 -1.07384 -0.09712  0.90509  1.66966  1.99581  1.79790  1.12791  0.16176 -0.84687 -1.63313 -1.99057 -1.82533 -1.18080 -0.22623  0.78775  1.59489  1.98324  1.85084  1.23246  0.29046 -0.72781 -1.55497 -1.97383 -1.87441 -1.28282 -0.35438  0.66710  1.51343  1.96236  1.89602  1.33183  0.41794 -0.60570 -1.47029 -1.94882 -1.91563 -1.37945 -0.48105  0.54366  1.42562  1.93324  0.00000     ... ... ..... ....... ......... ........... .............
E9      2.00000  1.66966  0.78775 -0.35438 -1.37945 -1.94882 -1.87441 -1.18080 -0.09712  1.01864  1.79790  1.98324  1.51343  0.54366 -0.60570 -1.55497 -1.99057 -1.76859 -0.96237  0.16176  1.23246  1.89602  1.93324  1.33183  0.29046 -0.84687 -1.70443 -1.99895 -1.63313 -0.72781  0.41794  1.42562  1.96236  1.85084  1.12791  0.03239 -1.07384 -1.82533 -1.97383 -1.47029 -0.48105  0.66710  1.59489  1.99581  1.73742  0.90509 -0.22623 -1.28282 -1.91563  0.00000     ... ... ..... ....... ......... ........... .............
E10     2.00000  1.59489  0.54366 -0.72781 -1.70443 -1.99057 -1.47029 -0.35438  0.90509  1.79790  1.96236  1.33183  0.16176 -1.07384 -1.87441 -1.91563 -1.18080  0.03239  1.23246  1.93324  1.85084  1.01864 -0.22623 -1.37945 -1.97383 -1.76859 -0.84687  0.41794  1.51343  1.99581  1.66966  0.66710 -0.60570 -1.63313 -1.99895 -1.55497 -0.48105  0.78775  1.73742  1.98324  1.42562  0.29046 -0.96237 -1.82533 -1.94882 -1.28282 -0.09712  1.12791  1.89602  0.00000     ... ... ..... ....... ......... ........... .............
E11     2.00000  1.51343  0.29046 -1.07384 -1.91563 -1.82533 -0.84687  0.54366  1.66966  1.98324  1.33183  0.03239 -1.28282 -1.97383 -1.70443 -0.60570  0.78775  1.79790  1.93324  1.12791 -0.22623 -1.47029 -1.99895 -1.55497 -0.35438  1.01864  1.89602  1.85084  0.90509 -0.48105 -1.63313 -1.99057 -1.37945 -0.09712  1.23246  1.96236  1.73742  0.66710 -0.72781 -1.76859 -1.94882 -1.18080  0.16176  1.42562  1.99581  1.59489  0.41794 -0.96237 -1.87441  0.00000     ... ... ..... ....... ......... ........... .............
E12     2.00000  1.42562  0.03239 -1.37945 -1.99895 -1.47029 -0.09712  1.33183  1.99581  1.51343  0.16176 -1.28282 -1.99057 -1.55497 -0.22623  1.23246  1.98324  1.59489  0.29046 -1.18080 -1.97383 -1.63313 -0.35438  1.12791  1.96236  1.66966  0.41794 -1.07384 -1.94882 -1.70443 -0.48105  1.01864  1.93324  1.73742  0.54366 -0.96237 -1.91563 -1.76859 -0.60570  0.90509  1.89602  1.79790  0.66710 -0.84687 -1.87441 -1.82533 -0.72781  0.78775  1.85084  0.00000     ... ... ..... ....... ......... ........... .............
E13     2.00000  1.33183 -0.22623 -1.63313 -1.94882 -0.96237  0.66710  1.85084  1.79790  0.54366 -1.07384 -1.97383 -1.55497 -0.09712  1.42562  1.99581  1.23246 -0.35438 -1.70443 -1.91563 -0.84687  0.78775  1.89602  1.73742  0.41794 -1.18080 -1.99057 -1.47029  0.03239  1.51343  1.98324  1.12791 -0.48105 -1.76859 -1.87441 -0.72781  0.90509  1.93324  1.66966  0.29046 -1.28282 -1.99895 -1.37945  0.16176  1.59489  1.96236  1.01864 -0.60570 -1.82533  0.00000     ... ... ..... ....... ......... ........... .............
E14     2.00000  1.23246 -0.48105 -1.82533 -1.76859 -0.35438  1.33183  1.99581  1.12791 -0.60570 -1.87441 -1.70443 -0.22623  1.42562  1.98324  1.01864 -0.72781 -1.91563 -1.63313 -0.09712  1.51343  1.96236  0.90509 -0.84687 -1.94882 -1.55497  0.03239  1.59489  1.93324  0.78775 -0.96237 -1.97383 -1.47029  0.16176  1.66966  1.89602  0.66710 -1.07384 -1.99057 -1.37945  0.29046  1.73742  1.85084  0.54366 -1.18080 -1.99895 -1.28282  0.41794  1.79790  0.00000     ... ... ..... ....... ......... ........... .............
E15     2.00000  1.12791 -0.72781 -1.94882 -1.47029  0.29046  1.79790  1.73742  0.16176 -1.55497 -1.91563 -0.60570  1.23246  1.99581  1.01864 -0.84687 -1.97383 -1.37945  0.41794  1.85084  1.66966  0.03239 -1.63313 -1.87441 -0.48105  1.33183  1.98324  0.90509 -0.96237 -1.99057 -1.28282  0.54366  1.89602  1.59489 -0.09712 -1.70443 -1.82533 -0.35438  1.42562  1.96236  0.78775 -1.07384 -1.99895 -1.18080  0.66710  1.93324  1.51343 -0.22623 -1.76859  0.00000     ... ... ..... ....... ......... ........... .............
E16     2.00000  1.01864 -0.96237 -1.99895 -1.07384  0.90509  1.99581  1.12791 -0.84687 -1.99057 -1.18080  0.78775  1.98324  1.23246 -0.72781 -1.97383 -1.28282  0.66710  1.96236  1.33183 -0.60570 -1.94882 -1.37945  0.54366  1.93324  1.42562 -0.48105 -1.91563 -1.47029  0.41794  1.89602  1.51343 -0.35438 -1.87441 -1.55497  0.29046  1.85084  1.59489 -0.22623 -1.82533 -1.63313  0.16176  1.79790  1.66966 -0.09712 -1.76859 -1.70443  0.03239  1.73742  0.00000     ... ... ..... ....... ......... ........... .............
E17     2.00000  0.90509 -1.18080 -1.97383 -0.60570  1.42562  1.89602  0.29046 -1.63313 -1.76859  0.03239  1.79790  1.59489 -0.35438 -1.91563 -1.37945  0.66710  1.98324  1.12791 -0.96237 -1.99895 -0.84687  1.23246  1.96236  0.54366 -1.47029 -1.87441 -0.22623  1.66966  1.73742 -0.09712 -1.82533 -1.55497  0.41794  1.93324  1.33183 -0.72781 -1.99057 -1.07384  1.01864  1.99581  0.78775 -1.28282 -1.94882 -0.48105  1.51343  1.85084  0.16176 -1.70443  0.00000     ... ... ..... ....... ......... ........... .............
E18     2.00000  0.78775 -1.37945 -1.87441 -0.09712  1.79790  1.51343 -0.60570 -1.99057 -0.96237  1.23246  1.93324  0.29046 -1.70443 -1.63313  0.41794  1.96236  1.12791 -1.07384 -1.97383 -0.48105  1.59489  1.73742 -0.22623 -1.91563 -1.28282  0.90509  1.99581  0.66710 -1.47029 -1.82533  0.03239  1.85084  1.42562 -0.72781 -1.99895 -0.84687  1.33183  1.89602  0.16176 -1.76859 -1.55497  0.54366  1.98324  1.01864 -1.18080 -1.94882 -0.35438  1.66966  0.00000     ... ... ..... ....... ......... ........... .............
E19     2.00000  0.66710 -1.55497 -1.70443  0.41794  1.98324  0.90509 -1.37945 -1.82533  0.16176  1.93324  1.12791 -1.18080 -1.91563 -0.09712  1.85084  1.33183 -0.96237 -1.97383 -0.35438  1.73742  1.51343 -0.72781 -1.99895 -0.60570  1.59489  1.66966 -0.48105 -1.99057 -0.84687  1.42562  1.79790 -0.22623 -1.94882 -1.07384  1.23246  1.89602  0.03239 -1.87441 -1.28282  1.01864  1.96236  0.29046 -1.76859 -1.47029  0.78775  1.99581  0.54366 -1.63313  0.00000     ... ... ..... ....... ......... ........... .............
E20     2.00000  0.54366 -1.70443 -1.47029  0.90509  1.96236  0.16176 -1.87441 -1.18080  1.23246  1.85084 -0.22623 -1.97383 -0.84687  1.51343  1.66966 -0.60570 -1.99895 -0.48105  1.73742  1.42562 -0.96237 -1.94882 -0.09712  1.89602  1.12791 -1.28282 -1.82533  0.29046  1.98324  0.78775 -1.55497 -1.63313  0.66710  1.99581  0.41794 -1.76859 -1.37945  1.01864  1.93324  0.03239 -1.91563 -1.07384  1.33183  1.79790 -0.35438 -1.99057 -0.72781  1.59489  0.00000     ... ... ..... ....... ......... ........... .............
E21     2.00000  0.41794 -1.82533 -1.18080  1.33183  1.73742 -0.60570 -1.99057 -0.22623  1.89602  1.01864 -1.47029 -1.63313  0.78775  1.96236  0.03239 -1.94882 -0.84687  1.59489  1.51343 -0.96237 -1.91563  0.16176  1.98324  0.66710 -1.70443 -1.37945  1.12791  1.85084 -0.35438 -1.99895 -0.48105  1.79790  1.23246 -1.28282 -1.76859  0.54366  1.99581  0.29046 -1.87441 -1.07384  1.42562  1.66966 -0.72781 -1.97383 -0.09712  1.93324  0.90509 -1.55497  0.00000     ... ... ..... ....... ......... ........... .............
E22     2.00000  0.29046 -1.91563 -0.84687  1.66966  1.33183 -1.28282 -1.70443  0.78775  1.93324 -0.22623 -1.99895 -0.35438  1.89602  0.90509 -1.63313 -1.37945  1.23246  1.73742 -0.72781 -1.94882  0.16176  1.99581  0.41794 -1.87441 -0.96237  1.59489  1.42562 -1.18080 -1.76859  0.66710  1.96236 -0.09712 -1.99057 -0.48105  1.85084  1.01864 -1.55497 -1.47029  1.12791  1.79790 -0.60570 -1.97383  0.03239  1.98324  0.54366 -1.82533 -1.07384  1.51343  0.00000     ... ... ..... ....... ......... ........... .............
E23     2.00000  0.16176 -1.97383 -0.48105  1.89602  0.78775 -1.76859 -1.07384  1.59489  1.33183 -1.37945 -1.55497  1.12791  1.73742 -0.84687 -1.87441  0.54366  1.96236 -0.22623 -1.99895 -0.09712  1.98324  0.41794 -1.91563 -0.72781  1.79790  1.01864 -1.63313 -1.28282  1.42562  1.51343 -1.18080 -1.70443  0.90509  1.85084 -0.60570 -1.94882  0.29046  1.99581  0.03239 -1.99057 -0.35438  1.93324  0.66710 -1.82533 -0.96237  1.66966  1.23246 -1.47029  0.00000     ... ... ..... ....... ......... ........... .............
E24     2.00000  0.03239 -1.99895 -0.09712  1.99581  0.16176 -1.99057 -0.22623  1.98324  0.29046 -1.97383 -0.35438  1.96236  0.41794 -1.94882 -0.48105  1.93324  0.54366 -1.91563 -0.60570  1.89602  0.66710 -1.87441 -0.72781  1.85084  0.78775 -1.82533 -0.84687  1.79790  0.90509 -1.76859 -0.96237  1.73742  1.01864 -1.70443 -1.07384  1.66966  1.12791 -1.63313 -1.18080  1.59489  1.23246 -1.55497 -1.28282  1.51343  1.33183 -1.47029 -1.37945  1.42562  0.00000     ... ... ..... ....... ......... ........... .............
E25     2.00000 -0.09712 -1.99057  0.29046  1.96236 -0.48105 -1.91563  0.66710  1.85084 -0.84687 -1.76859  1.01864  1.66966 -1.18080 -1.55497  1.33183  1.42562 -1.47029 -1.28282  1.59489  1.12791 -1.70443 -0.96237  1.79790  0.78775 -1.87441 -0.60570  1.93324  0.41794 -1.97383 -0.22623  1.99581  0.03239 -1.99895  0.16176  1.98324 -0.35438 -1.94882  0.54366  1.89602 -0.72781 -1.82533  0.90509  1.73742 -1.07384 -1.63313  1.23246  1.51343 -1.37945  0.00000     ... ... ..... ....... ......... ........... .............
E26     2.00000 -0.22623 -1.94882  0.66710  1.79790 -1.07384 -1.55497  1.42562  1.23246 -1.70443 -0.84687  1.89602  0.41794 -1.99057  0.03239  1.98324 -0.48105 -1.87441  0.90509  1.66966 -1.28282 -1.37945  1.59489  1.01864 -1.82533 -0.60570  1.96236  0.16176 -1.99895  0.29046  1.93324 -0.72781 -1.76859  1.12791  1.51343 -1.47029 -1.18080  1.73742  0.78775 -1.91563 -0.35438  1.99581 -0.09712 -1.97383  0.54366  1.85084 -0.96237 -1.63313  1.33183  0.00000     ... ... ..... ....... ......... ........... .............
E27     2.00000 -0.35438 -1.87441  1.01864  1.51343 -1.55497 -0.96237  1.89602  0.29046 -1.99895  0.41794  1.85084 -1.07384 -1.47029  1.59489  0.90509 -1.91563 -0.22623  1.99581 -0.48105 -1.82533  1.12791  1.42562 -1.63313 -0.84687  1.93324  0.16176 -1.99057  0.54366  1.79790 -1.18080 -1.37945  1.66966  0.78775 -1.94882 -0.09712  1.98324 -0.60570 -1.76859  1.23246  1.33183 -1.70443 -0.72781  1.96236  0.03239 -1.97383  0.66710  1.73742 -1.28282  0.00000     ... ... ..... ....... ......... ........... .............
E28     2.00000 -0.48105 -1.76859  1.33183  1.12791 -1.87441 -0.22623  1.98324 -0.72781 -1.63313  1.51343  0.90509 -1.94882  0.03239  1.93324 -0.96237 -1.47029  1.66966  0.66710 -1.99057  0.29046  1.85084 -1.18080 -1.28282  1.79790  0.41794 -1.99895  0.54366  1.73742 -1.37945 -1.07384  1.89602  0.16176 -1.97383  0.78775  1.59489 -1.55497 -0.84687  1.96236 -0.09712 -1.91563  1.01864  1.42562 -1.70443 -0.60570  1.99581 -0.35438 -1.82533  1.23246  0.00000     ... ... ..... ....... ......... ........... .............
E29     2.00000 -0.60570 -1.63313  1.59489  0.66710 -1.99895  0.54366  1.66966 -1.55497 -0.72781  1.99581 -0.48105 -1.70443  1.51343  0.78775 -1.99057  0.41794  1.73742 -1.47029 -0.84687  1.98324 -0.35438 -1.76859  1.42562  0.90509 -1.97383  0.29046  1.79790 -1.37945 -0.96237  1.96236 -0.22623 -1.82533  1.33183  1.01864 -1.94882  0.16176  1.85084 -1.28282 -1.07384  1.93324 -0.09712 -1.87441  1.23246  1.12791 -1.91563  0.03239  1.89602 -1.18080  0.00000     ... ... ..... ....... ......... ........... .............
E30     2.00000 -0.72781 -1.47029  1.79790  0.16176 -1.91563  1.23246  1.01864 -1.97383  0.41794  1.66966 -1.63313 -0.48105  1.98324 -0.96237 -1.28282  1.89602 -0.09712 -1.82533  1.42562  0.78775 -1.99895  0.66710  1.51343 -1.76859 -0.22623  1.93324 -1.18080 -1.07384  1.96236 -0.35438 -1.70443  1.59489  0.54366 -1.99057  0.90509  1.33183 -1.87441  0.03239  1.85084 -1.37945 -0.84687  1.99581 -0.60570 -1.55497  1.73742  0.29046 -1.94882  1.12791  0.00000     ... ... ..... ....... ......... ........... .............
E31     2.00000 -0.84687 -1.28282  1.93324 -0.35438 -1.63313  1.73742  0.16176 -1.87441  1.42562  0.66710 -1.99057  1.01864  1.12791 -1.97383  0.54366  1.51343 -1.82533  0.03239  1.79790 -1.55497 -0.48105  1.96236 -1.18080 -0.96237  1.99581 -0.72781 -1.37945  1.89602 -0.22623 -1.70443  1.66966  0.29046 -1.91563  1.33183  0.78775 -1.99895  0.90509  1.23246 -1.94882  0.41794  1.59489 -1.76859 -0.09712  1.85084 -1.47029 -0.60570  1.98324 -1.07384  0.00000     ... ... ..... ....... ......... ........... .............
E32     2.00000 -0.96237 -1.07384  1.99581 -0.84687 -1.18080  1.98324 -0.72781 -1.28282  1.96236 -0.60570 -1.37945  1.93324 -0.48105 -1.47029  1.89602 -0.35438 -1.55497  1.85084 -0.22623 -1.63313  1.79790 -0.09712 -1.70443  1.73742  0.03239 -1.76859  1.66966  0.16176 -1.82533  1.59489  0.29046 -1.87441  1.51343  0.41794 -1.91563  1.42562  0.54366 -1.94882  1.33183  0.66710 -1.97383  1.23246  0.78775 -1.99057  1.12791  0.90509 -1.99895  1.01864  0.00000     ... ... ..... ....... ......... ........... .............
E33     2.00000 -1.07384 -0.84687  1.98324 -1.28282 -0.60570  1.93324 -1.47029 -0.35438  1.85084 -1.63313 -0.09712  1.73742 -1.76859  0.16176  1.59489 -1.87441  0.41794  1.42562 -1.94882  0.66710  1.23246 -1.99057  0.90509  1.01864 -1.99895  1.12791  0.78775 -1.97383  1.33183  0.54366 -1.91563  1.51343  0.29046 -1.82533  1.66966  0.03239 -1.70443  1.79790 -0.22623 -1.55497  1.89602 -0.48105 -1.37945  1.96236 -0.72781 -1.18080  1.99581 -0.96237  0.00000     ... ... ..... ....... ......... ........... .............
E34     2.00000 -1.18080 -0.60570  1.89602 -1.63313  0.03239  1.59489 -1.91563  0.66710  1.12791 -1.99895  1.23246  0.54366 -1.87441  1.66966 -0.09712 -1.55497  1.93324 -0.72781 -1.07384  1.99581 -1.28282 -0.48105  1.85084 -1.70443  0.16176  1.51343 -1.94882  0.78775  1.01864 -1.99057  1.33183  0.41794 -1.82533  1.73742 -0.22623 -1.47029  1.96236 -0.84687 -0.96237  1.98324 -1.37945 -0.35438  1.79790 -1.76859  0.29046  1.42562 -1.97383  0.90509  0.00000     ... ... ..... ....... ......... ........... .............
E35     2.00000 -1.28282 -0.35438  1.73742 -1.87441  0.66710  1.01864 -1.97383  1.51343  0.03239 -1.55497  1.96236 -0.96237 -0.72781  1.89602 -1.70443  0.29046  1.33183 -1.99895  1.23246  0.41794 -1.76859  1.85084 -0.60570 -1.07384  1.98324 -1.47029 -0.09712  1.59489 -1.94882  0.90509  0.78775 -1.91563  1.66966 -0.22623 -1.37945  1.99581 -1.18080 -0.48105  1.79790 -1.82533  0.54366  1.12791 -1.99057  1.42562  0.16176 -1.63313  1.93324 -0.84687  0.00000     ... ... ..... ....... ......... ........... .............
E36     2.00000 -1.37945 -0.09712  1.51343 -1.99057  1.23246  0.29046 -1.63313  1.96236 -1.07384 -0.48105  1.73742 -1.91563  0.90509  0.66710 -1.82533  1.85084 -0.72781 -0.84687  1.89602 -1.76859  0.54366  1.01864 -1.94882  1.66966 -0.35438 -1.18080  1.98324 -1.55497  0.16176  1.33183 -1.99895  1.42562  0.03239 -1.47029  1.99581 -1.28282 -0.22623  1.59489 -1.97383  1.12791  0.41794 -1.70443  1.93324 -0.96237 -0.60570  1.79790 -1.87441  0.78775  0.00000     ... ... ..... ....... ......... ........... .............
E37     2.00000 -1.47029  0.16176  1.23246 -1.97383  1.66966 -0.48105 -0.96237  1.89602 -1.82533  0.78775  0.66710 -1.76859  1.93324 -1.07384 -0.35438  1.59489 -1.99057  1.33183  0.03239 -1.37945  1.99581 -1.55497  0.29046  1.12791 -1.94882  1.73742 -0.60570 -0.84687  1.85084 -1.87441  0.90509  0.54366 -1.70443  1.96236 -1.18080 -0.22623  1.51343 -1.99895  1.42562 -0.09712 -1.28282  1.98324 -1.63313  0.41794  1.01864 -1.91563  1.79790 -0.72781  0.00000     ... ... ..... ....... ......... ........... .............
E38     2.00000 -1.55497  0.41794  0.90509 -1.82533  1.93324 -1.18080 -0.09712  1.33183 -1.97383  1.73742 -0.72781 -0.60570  1.66966 -1.99057  1.42562 -0.22623 -1.07384  1.89602 -1.87441  1.01864  0.29046 -1.47029  1.99581 -1.63313  0.54366  0.78775 -1.76859  1.96236 -1.28282  0.03239  1.23246 -1.94882  1.79790 -0.84687 -0.48105  1.59489 -1.99895  1.51343 -0.35438 -0.96237  1.85084 -1.91563  1.12791  0.16176 -1.37945  1.98324 -1.70443  0.66710  0.00000     ... ... ..... ....... ......... ........... .............
E39     2.00000 -1.63313  0.66710  0.54366 -1.55497  1.99581 -1.70443  0.78775  0.41794 -1.47029  1.98324 -1.76859  0.90509  0.29046 -1.37945  1.96236 -1.82533  1.01864  0.16176 -1.28282  1.93324 -1.87441  1.12791  0.03239 -1.18080  1.89602 -1.91563  1.23246 -0.09712 -1.07384  1.85084 -1.94882  1.33183 -0.22623 -0.96237  1.79790 -1.97383  1.42562 -0.35438 -0.84687  1.73742 -1.99057  1.51343 -0.48105 -0.72781  1.66966 -1.99895  1.59489 -0.60570  0.00000     ... ... ..... ....... ......... ........... .............
E40     2.00000 -1.70443  0.90509  0.16176 -1.18080  1.85084 -1.97383  1.51343 -0.60570 -0.48105  1.42562 -1.94882  1.89602 -1.28282  0.29046  0.78775 -1.63313  1.99581 -1.76859  1.01864  0.03239 -1.07384  1.79790 -1.99057  1.59489 -0.72781 -0.35438  1.33183 -1.91563  1.93324 -1.37945  0.41794  0.66710 -1.55497  1.98324 -1.82533  1.12791 -0.09712 -0.96237  1.73742 -1.99895  1.66966 -0.84687 -0.22623  1.23246 -1.87441  1.96236 -1.47029  0.54366  0.00000     ... ... ..... ....... ......... ........... .............
E41     2.00000 -1.76859  1.12791 -0.22623 -0.72781  1.51343 -1.94882  1.93324 -1.47029  0.66710  0.29046 -1.18080  1.79790 -1.99895  1.73742 -1.07384  0.16176  0.78775 -1.55497  1.96236 -1.91563  1.42562 -0.60570 -0.35438  1.23246 -1.82533  1.99581 -1.70443  1.01864 -0.09712 -0.84687  1.59489 -1.97383  1.89602 -1.37945  0.54366  0.41794 -1.28282  1.85084 -1.99057  1.66966 -0.96237  0.03239  0.90509 -1.63313  1.98324 -1.87441  1.33183 -0.48105  0.00000     ... ... ..... ....... ......... ........... .............
E42     2.00000 -1.82533  1.33183 -0.60570 -0.22623  1.01864 -1.63313  1.96236 -1.94882  1.59489 -0.96237  0.16176  0.66710 -1.37945  1.85084 -1.99895  1.79790 -1.28282  0.54366  0.29046 -1.07384  1.66966 -1.97383  1.93324 -1.55497  0.90509 -0.09712 -0.72781  1.42562 -1.87441  1.99581 -1.76859  1.23246 -0.48105 -0.35438  1.12791 -1.70443  1.98324 -1.91563  1.51343 -0.84687  0.03239  0.78775 -1.47029  1.89602 -1.99057  1.73742 -1.18080  0.41794  0.00000     ... ... ..... ....... ......... ........... .............
E43     2.00000 -1.87441  1.51343 -0.96237  0.29046  0.41794 -1.07384  1.59489 -1.91563  1.99581 -1.82533  1.42562 -0.84687  0.16176  0.54366 -1.18080  1.66966 -1.94882  1.98324 -1.76859  1.33183 -0.72781  0.03239  0.66710 -1.28282  1.73742 -1.97383  1.96236 -1.70443  1.23246 -0.60570 -0.09712  0.78775 -1.37945  1.79790 -1.99057  1.93324 -1.63313  1.12791 -0.48105 -0.22623  0.90509 -1.47029  1.85084 -1.99895  1.89602 -1.55497  1.01864 -0.35438  0.00000     ... ... ..... ....... ......... ........... .............
E44     2.00000 -1.91563  1.66966 -1.28282  0.78775 -0.22623 -0.35438  0.90509 -1.37945  1.73742 -1.94882  1.99581 -1.87441  1.59489 -1.18080  0.66710 -0.09712 -0.48105  1.01864 -1.47029  1.79790 -1.97383  1.98324 -1.82533  1.51343 -1.07384  0.54366  0.03239 -0.60570  1.12791 -1.55497  1.85084 -1.99057  1.96236 -1.76859  1.42562 -0.96237  0.41794  0.16176 -0.72781  1.23246 -1.63313  1.89602 -1.99895  1.93324 -1.70443  1.33183 -0.84687  0.29046  0.00000     ... ... ..... ....... ......... ........... .............
E45     2.00000 -1.94882  1.79790 -1.55497  1.23246 -0.84687  0.41794  0.03239 -0.48105  0.90509 -1.28282  1.59489 -1.82533  1.96236 -1.99895  1.93324 -1.76859  1.51343 -1.18080  0.78775 -0.35438 -0.09712  0.54366 -0.96237  1.33183 -1.63313  1.85084 -1.97383  1.99581 -1.91563  1.73742 -1.47029  1.12791 -0.72781  0.29046  0.16176 -0.60570  1.01864 -1.37945  1.66966 -1.87441  1.98324 -1.99057  1.89602 -1.70443  1.42562 -1.07384  0.66710 -0.22623  0.00000     ... ... ..... ....... ......... ........... .............
E46     2.00000 -1.97383  1.89602 -1.76859  1.59489 -1.37945  1.12791 -0.84687  0.54366 -0.22623 -0.09712  0.41794 -0.72781  1.01864 -1.28282  1.51343 -1.70443  1.85084 -1.94882  1.99581 -1.99057  1.93324 -1.82533  1.66966 -1.47029  1.23246 -0.96237  0.66710 -0.35438  0.03239  0.29046 -0.60570  0.90509 -1.18080  1.42562 -1.63313  1.79790 -1.91563  1.98324 -1.99895  1.96236 -1.87441  1.73742 -1.55497  1.33183 -1.07384  0.78775 -0.48105  0.16176  0.00000     ... ... ..... ....... ......... ........... .............
E47     2.00000 -1.99057  1.96236 -1.91563  1.85084 -1.76859  1.66966 -1.55497  1.42562 -1.28282  1.12791 -0.96237  0.78775 -0.60570  0.41794 -0.22623  0.03239  0.16176 -0.35438  0.54366 -0.72781  0.90509 -1.07384  1.23246 -1.37945  1.51343 -1.63313  1.73742 -1.82533  1.89602 -1.94882  1.98324 -1.99895  1.99581 -1.97383  1.93324 -1.87441  1.79790 -1.70443  1.59489 -1.47029  1.33183 -1.18080  1.01864 -0.84687  0.66710 -0.48105  0.29046 -0.09712  0.00000     ... ... ..... ....... ......... ........... .............
E48     2.00000 -1.99895  1.99581 -1.99057  1.98324 -1.97383  1.96236 -1.94882  1.93324 -1.91563  1.89602 -1.87441  1.85084 -1.82533  1.79790 -1.76859  1.73742 -1.70443  1.66966 -1.63313  1.59489 -1.55497  1.51343 -1.47029  1.42562 -1.37945  1.33183 -1.28282  1.23246 -1.18080  1.12791 -1.07384  1.01864 -0.96237  0.90509 -0.84687  0.78775 -0.72781  0.66710 -0.60570  0.54366 -0.48105  0.41794 -0.35438  0.29046 -0.22623  0.16176 -0.09712  0.03239  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.995805652475 = 2*cos(2*π/97)
                               1.983240202453 = 2*cos(4*π/97)
                               1.962356353796 = 2*cos(6*π/97)
                               1.933241700625 = 2*cos(8*π/97)
                               1.896018359913 = 2*cos(10*π/97)
                               1.850842459285 = 2*cos(12*π/97)
                               1.797903482171 = 2*cos(14*π/97)
                               1.737423473036 = 2*cos(16*π/97)
                               1.669656106059 = 2*cos(18*π/97)
                               1.594885621125 = 2*cos(20*π/97)
                               1.513425631635 = 2*cos(22*π/97)
                               1.425617809094 = 2*cos(24*π/97)
                               1.331830450023 = 2*cos(26*π/97)
                               1.232456931202 = 2*cos(28*π/97)
                               1.127914059702 = 2*cos(30*π/97)
                               1.018640324657 = 2*cos(32*π/97)
                               0.905094058089 = 2*cos(34*π/97)
                               0.787751512498 = 2*cos(36*π/97)
                               0.667104863301 = 2*cos(38*π/97)
                               0.543660144473 = 2*cos(40*π/97)
                               0.417935126062 = 2*cos(42*π/97)
                               0.290457142491 = 2*cos(44*π/97)
                               0.161760880723 = 2*cos(46*π/97)
                               0.032386137605 = 2*cos(48*π/97)
                              -0.097124444229 = 2*cos(50*π/97)
                              -0.226227652391 = 2*cos(52*π/97)
                              -0.354381983159 = 2*cos(54*π/97)
                              -0.481049912733 = 2*cos(56*π/97)
                              -0.605700151796 = 2*cos(58*π/97)
                              -0.727809873927 = 2*cos(60*π/97)
                              -0.846866908515 = 2*cos(62*π/97)
                              -0.962371888982 = 2*cos(64*π/97)
                              -1.073840347298 = 2*cos(66*π/97)
                              -1.180804746012 = 2*cos(68*π/97)
                              -1.282816439263 = 2*cos(70*π/97)
                              -1.379447554556 = 2*cos(72*π/97)
                              -1.470292787415 = 2*cos(74*π/97)
                              -1.554971101360 = 2*cos(76*π/97)
                              -1.633127326115 = 2*cos(78*π/97)
                              -1.704433647312 = 2*cos(80*π/97)
                              -1.768590981460 = 2*cos(82*π/97)
                              -1.825330230403 = 2*cos(84*π/97)
                              -1.874413410013 = 2*cos(86*π/97)
                              -1.915634648376 = 2*cos(88*π/97)
                              -1.948821049294 = 2*cos(90*π/97)
                              -1.973833417468 = 2*cos(92*π/97)
                              -1.990566842333 = 2*cos(94*π/97)
                              -1.998951138091 = 2*cos(96*π/97)



 Symmetry of Rotations and Cartesian products

A1   p+d+f+g+h+i    z, z2, z3, z4, z5, z6 
A2   R              Rz 
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      {x2y2, xy}, {z(x2y2), xyz}, {z2(x2y2), xyz2}, {z3(x2y2), xyz3}, {z4(x2y2), xyz4} 
E3   f+g+h+i        {x(x2–3y2), y(3x2y2)}, {xz(x2–3y2), yz(3x2y2)}, {xz2(x2–3y2), yz2(3x2y2)}, {xz3(x2–3y2), yz3(3x2y2)} 
E4   g+h+i          {(x2y2)2–2x2y2, xy(x2y2)}, {z((x2y2)2–4x2y2), xyz(x2y2)}, {z2((x2y2)2–4x2y2), xyz2(x2y2)} 
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)2y2(3x2y2)2, xy(x2–3y2)(3x2y2)} 

 Notes:

    α  The order of the C97v point group is 194, and the order of the principal axis is 97.

    β  This point group is non-Abelian (some symmetry operations are not commutative).
       Therefore, the character table contains multi-membered classes and degenerate irreducible representations.

    γ  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.

This Character Table for the C97v point group was created by Gernot Katzer.

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