C97 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 <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ..T ..T ....T ......T ........T ..........T ............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 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 ... ... 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 ... ... ..... 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 ... ... ..... ....... 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 ... ... ..... ....... ......... 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 ... ... ..... ....... ......... ........... 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. 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 A R+p+d+f+g+h+i z, Rz, z2, z3, z4, z5, z6 E1 R+p+d+f+g+h+i {x, y}, {Rx, Ry}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} E2 d+f+g+h+i {x2–y2, xy}, {z(x2–y2), xyz}, {z2(x2–y2), xyz2}, {z3(x2–y2), xyz3}, {z4(x2–y2), xyz4} E3 f+g+h+i {x(x2–3y2), y(3x2–y2)}, {xz(x2–3y2), yz(3x2–y2)}, {xz2(x2–3y2), yz2(3x2–y2)}, {xz3(x2–3y2), yz3(3x2–y2)} E4 g+h+i {(x2–y2)2–2x2y2, xy(x2–y2)}, {z((x2–y2)2–4x2y2), xyz(x2–y2)}, {z2((x2–y2)2–4x2y2), xyz2(x2–y2)} E5 h+i {x(x2–(5+2√5)y2)(x2–(5–2√5)y2), y(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)}, {xz(x2–(5+2√5)y2)(x2–(5–2√5)y2), yz(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)} E6 i {x2(x2–3y2)2–y2(3x2–y2)2, xy(x2–3y2)(3x2–y2)} Notes: α The order of the C97 point group is 97, and the order of the principal axis is 97. β This is an Abelian point group (the commutative law holds between all symmetry operations). The C97 group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition). In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. γ Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 96 cases have been combined into 48 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 48 pairs of left and right rotations have been combined into one two-membered pseudo-class each. δ The 48 reducible "E" representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into "irreducible" ones using the familiar projection formula. ε The point group is chiral, as it does not contain any mirroring operation. ζ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree less than half the order of the principal axis (and often much less). For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.
| C96 | ||
| C97 | C97v C97h D97 D97h D97d | |
| C98 |
This Character Table for the C97 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.