C87 E 2 C87 2 C87^2 2 C29 2 C87^4 2 C87^5 2 C29^2 2 C87^7 2 C87^8 2 C29^3 2 C87^10 2 C87^11 2 C29^4 2 C87^13 2 C87^14 2 C29^5 2 C87^16 2 C87^17 2 C29^6 2 C87^19 2 C87^20 2 C29^7 2 C87^22 2 C87^23 2 C29^8 2 C87^25 2 C87^26 2 C29^9 2 C87^28 2 C3 2 C29^10 2 C87^31 2 C87^32 2 C29^11 2 C87^34 2 C87^35 2 C29^12 2 C87^37 2 C87^38 2 C29^13 2 C87^40 2 C87^41 2 C29^14 2 C87^43 <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 ..T ..T ....T ......T ........T ..........T ............T E1 * 2.00000 1.99479 1.97917 1.95324 1.91713 1.87102 1.81515 1.74982 1.67537 1.59219 1.50070 1.40139 1.29477 1.18141 1.06188 0.93682 0.80687 0.67272 0.53506 0.39461 0.25210 0.10828 -0.03611 -0.18031 -0.32356 -0.46513 -0.60428 -0.74028 -0.87241 -1.00000 -1.12237 -1.23890 -1.34896 -1.45199 -1.54745 -1.63484 -1.71371 -1.78365 -1.84429 -1.89531 -1.93645 -1.96749 -1.98828 -1.99870 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 * 2.00000 1.97917 1.91713 1.81515 1.67537 1.50070 1.29477 1.06188 0.80687 0.53506 0.25210 -0.03611 -0.32356 -0.60428 -0.87241 -1.12237 -1.34896 -1.54745 -1.71371 -1.84429 -1.93645 -1.98828 -1.99870 -1.96749 -1.89531 -1.78365 -1.63484 -1.45199 -1.23890 -1.00000 -0.74028 -0.46513 -0.18031 0.10828 0.39461 0.67272 0.93682 1.18141 1.40139 1.59219 1.74982 1.87102 1.95324 1.99479 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 * 2.00000 1.95324 1.81515 1.59219 1.29477 0.93682 0.53506 0.10828 -0.32356 -0.74028 -1.12237 -1.45199 -1.71371 -1.89531 -1.98828 -1.98828 -1.89531 -1.71371 -1.45199 -1.12237 -0.74028 -0.32356 0.10828 0.53506 0.93682 1.29477 1.59219 1.81515 1.95324 2.00000 1.95324 1.81515 1.59219 1.29477 0.93682 0.53506 0.10828 -0.32356 -0.74028 -1.12237 -1.45199 -1.71371 -1.89531 -1.98828 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 * 2.00000 1.91713 1.67537 1.29477 0.80687 0.25210 -0.32356 -0.87241 -1.34896 -1.71371 -1.93645 -1.99870 -1.89531 -1.63484 -1.23890 -0.74028 -0.18031 0.39461 0.93682 1.40139 1.74982 1.95324 1.99479 1.87102 1.59219 1.18141 0.67272 0.10828 -0.46513 -1.00000 -1.45199 -1.78365 -1.96749 -1.98828 -1.84429 -1.54745 -1.12237 -0.60428 -0.03611 0.53506 1.06188 1.50070 1.81515 1.97917 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 * 2.00000 1.87102 1.50070 0.93682 0.25210 -0.46513 -1.12237 -1.63484 -1.93645 -1.98828 -1.78365 -1.34896 -0.74028 -0.03611 0.67272 1.29477 1.74982 1.97917 1.95324 1.67537 1.18141 0.53506 -0.18031 -0.87241 -1.45199 -1.84429 -1.99870 -1.89531 -1.54745 -1.00000 -0.32356 0.39461 1.06188 1.59219 1.91713 1.99479 1.81515 1.40139 0.80687 0.10828 -0.60428 -1.23890 -1.71371 -1.96749 ... ... ..... ....... ......... TT......... ..TT......... E6 * 2.00000 1.81515 1.29477 0.53506 -0.32356 -1.12237 -1.71371 -1.98828 -1.89531 -1.45199 -0.74028 0.10828 0.93682 1.59219 1.95324 1.95324 1.59219 0.93682 0.10828 -0.74028 -1.45199 -1.89531 -1.98828 -1.71371 -1.12237 -0.32356 0.53506 1.29477 1.81515 2.00000 1.81515 1.29477 0.53506 -0.32356 -1.12237 -1.71371 -1.98828 -1.89531 -1.45199 -0.74028 0.10828 0.93682 1.59219 1.95324 ... ... ..... ....... ......... ........... TT........... E7 * 2.00000 1.74982 1.06188 0.10828 -0.87241 -1.63484 -1.98828 -1.84429 -1.23890 -0.32356 0.67272 1.50070 1.95324 1.91713 1.40139 0.53506 -0.46513 -1.34896 -1.89531 -1.96749 -1.54745 -0.74028 0.25210 1.18141 1.81515 1.99479 1.67537 0.93682 -0.03611 -1.00000 -1.71371 -1.99870 -1.78365 -1.12237 -0.18031 0.80687 1.59219 1.97917 1.87102 1.29477 0.39461 -0.60428 -1.45199 -1.93645 ... ... ..... ....... ......... ........... ............. E8 * 2.00000 1.67537 0.80687 -0.32356 -1.34896 -1.93645 -1.89531 -1.23890 -0.18031 0.93682 1.74982 1.99479 1.59219 0.67272 -0.46513 -1.45199 -1.96749 -1.84429 -1.12237 -0.03611 1.06188 1.81515 1.97917 1.50070 0.53506 -0.60428 -1.54745 -1.98828 -1.78365 -1.00000 0.10828 1.18141 1.87102 1.95324 1.40139 0.39461 -0.74028 -1.63484 -1.99870 -1.71371 -0.87241 0.25210 1.29477 1.91713 ... ... ..... ....... ......... ........... ............. E9 * 2.00000 1.59219 0.53506 -0.74028 -1.71371 -1.98828 -1.45199 -0.32356 0.93682 1.81515 1.95324 1.29477 0.10828 -1.12237 -1.89531 -1.89531 -1.12237 0.10828 1.29477 1.95324 1.81515 0.93682 -0.32356 -1.45199 -1.98828 -1.71371 -0.74028 0.53506 1.59219 2.00000 1.59219 0.53506 -0.74028 -1.71371 -1.98828 -1.45199 -0.32356 0.93682 1.81515 1.95324 1.29477 0.10828 -1.12237 -1.89531 ... ... ..... ....... ......... ........... ............. E10 * 2.00000 1.50070 0.25210 -1.12237 -1.93645 -1.78365 -0.74028 0.67272 1.74982 1.95324 1.18141 -0.18031 -1.45199 -1.99870 -1.54745 -0.32356 1.06188 1.91713 1.81515 0.80687 -0.60428 -1.71371 -1.96749 -1.23890 0.10828 1.40139 1.99479 1.59219 0.39461 -1.00000 -1.89531 -1.84429 -0.87241 0.53506 1.67537 1.97917 1.29477 -0.03611 -1.34896 -1.98828 -1.63484 -0.46513 0.93682 1.87102 ... ... ..... ....... ......... ........... ............. E11 * 2.00000 1.40139 -0.03611 -1.45199 -1.99870 -1.34896 0.10828 1.50070 1.99479 1.29477 -0.18031 -1.54745 -1.98828 -1.23890 0.25210 1.59219 1.97917 1.18141 -0.32356 -1.63484 -1.96749 -1.12237 0.39461 1.67537 1.95324 1.06188 -0.46513 -1.71371 -1.93645 -1.00000 0.53506 1.74982 1.91713 0.93682 -0.60428 -1.78365 -1.89531 -0.87241 0.67272 1.81515 1.87102 0.80687 -0.74028 -1.84429 ... ... ..... ....... ......... ........... ............. E12 * 2.00000 1.29477 -0.32356 -1.71371 -1.89531 -0.74028 0.93682 1.95324 1.59219 0.10828 -1.45199 -1.98828 -1.12237 0.53506 1.81515 1.81515 0.53506 -1.12237 -1.98828 -1.45199 0.10828 1.59219 1.95324 0.93682 -0.74028 -1.89531 -1.71371 -0.32356 1.29477 2.00000 1.29477 -0.32356 -1.71371 -1.89531 -0.74028 0.93682 1.95324 1.59219 0.10828 -1.45199 -1.98828 -1.12237 0.53506 1.81515 ... ... ..... ....... ......... ........... ............. E13 * 2.00000 1.18141 -0.60428 -1.89531 -1.63484 -0.03611 1.59219 1.91713 0.67272 -1.12237 -1.99870 -1.23890 0.53506 1.87102 1.67537 0.10828 -1.54745 -1.93645 -0.74028 1.06188 1.99479 1.29477 -0.46513 -1.84429 -1.71371 -0.18031 1.50070 1.95324 0.80687 -1.00000 -1.98828 -1.34896 0.39461 1.81515 1.74982 0.25210 -1.45199 -1.96749 -0.87241 0.93682 1.97917 1.40139 -0.32356 -1.78365 ... ... ..... ....... ......... ........... ............. E14 * 2.00000 1.06188 -0.87241 -1.98828 -1.23890 0.67272 1.95324 1.40139 -0.46513 -1.89531 -1.54745 0.25210 1.81515 1.67537 -0.03611 -1.71371 -1.78365 -0.18031 1.59219 1.87102 0.39461 -1.45199 -1.93645 -0.60428 1.29477 1.97917 0.80687 -1.12237 -1.99870 -1.00000 0.93682 1.99479 1.18141 -0.74028 -1.96749 -1.34896 0.53506 1.91713 1.50070 -0.32356 -1.84429 -1.63484 0.10828 1.74982 ... ... ..... ....... ......... ........... ............. E15 * 2.00000 0.93682 -1.12237 -1.98828 -0.74028 1.29477 1.95324 0.53506 -1.45199 -1.89531 -0.32356 1.59219 1.81515 0.10828 -1.71371 -1.71371 0.10828 1.81515 1.59219 -0.32356 -1.89531 -1.45199 0.53506 1.95324 1.29477 -0.74028 -1.98828 -1.12237 0.93682 2.00000 0.93682 -1.12237 -1.98828 -0.74028 1.29477 1.95324 0.53506 -1.45199 -1.89531 -0.32356 1.59219 1.81515 0.10828 -1.71371 ... ... ..... ....... ......... ........... ............. E16 * 2.00000 0.80687 -1.34896 -1.89531 -0.18031 1.74982 1.59219 -0.46513 -1.96749 -1.12237 1.06188 1.97917 0.53506 -1.54745 -1.78365 0.10828 1.87102 1.40139 -0.74028 -1.99870 -0.87241 1.29477 1.91713 0.25210 -1.71371 -1.63484 0.39461 1.95324 1.18141 -1.00000 -1.98828 -0.60428 1.50070 1.81515 -0.03611 -1.84429 -1.45199 0.67272 1.99479 0.93682 -1.23890 -1.93645 -0.32356 1.67537 ... ... ..... ....... ......... ........... ............. E17 * 2.00000 0.67272 -1.54745 -1.71371 0.39461 1.97917 0.93682 -1.34896 -1.84429 0.10828 1.91713 1.18141 -1.12237 -1.93645 -0.18031 1.81515 1.40139 -0.87241 -1.98828 -0.46513 1.67537 1.59219 -0.60428 -1.99870 -0.74028 1.50070 1.74982 -0.32356 -1.96749 -1.00000 1.29477 1.87102 -0.03611 -1.89531 -1.23890 1.06188 1.95324 0.25210 -1.78365 -1.45199 0.80687 1.99479 0.53506 -1.63484 ... ... ..... ....... ......... ........... ............. E18 * 2.00000 0.53506 -1.71371 -1.45199 0.93682 1.95324 0.10828 -1.89531 -1.12237 1.29477 1.81515 -0.32356 -1.98828 -0.74028 1.59219 1.59219 -0.74028 -1.98828 -0.32356 1.81515 1.29477 -1.12237 -1.89531 0.10828 1.95324 0.93682 -1.45199 -1.71371 0.53506 2.00000 0.53506 -1.71371 -1.45199 0.93682 1.95324 0.10828 -1.89531 -1.12237 1.29477 1.81515 -0.32356 -1.98828 -0.74028 1.59219 ... ... ..... ....... ......... ........... ............. E19 * 2.00000 0.39461 -1.84429 -1.12237 1.40139 1.67537 -0.74028 -1.96749 -0.03611 1.95324 0.80687 -1.63484 -1.45199 1.06188 1.87102 -0.32356 -1.99870 -0.46513 1.81515 1.18141 -1.34896 -1.71371 0.67272 1.97917 0.10828 -1.93645 -0.87241 1.59219 1.50070 -1.00000 -1.89531 0.25210 1.99479 0.53506 -1.78365 -1.23890 1.29477 1.74982 -0.60428 -1.98828 -0.18031 1.91713 0.93682 -1.54745 ... ... ..... ....... ......... ........... ............. E20 * 2.00000 0.25210 -1.93645 -0.74028 1.74982 1.18141 -1.45199 -1.54745 1.06188 1.81515 -0.60428 -1.96749 0.10828 1.99479 0.39461 -1.89531 -0.87241 1.67537 1.29477 -1.34896 -1.63484 0.93682 1.87102 -0.46513 -1.98828 -0.03611 1.97917 0.53506 -1.84429 -1.00000 1.59219 1.40139 -1.23890 -1.71371 0.80687 1.91713 -0.32356 -1.99870 -0.18031 1.95324 0.67272 -1.78365 -1.12237 1.50070 ... ... ..... ....... ......... ........... ............. E21 * 2.00000 0.10828 -1.98828 -0.32356 1.95324 0.53506 -1.89531 -0.74028 1.81515 0.93682 -1.71371 -1.12237 1.59219 1.29477 -1.45199 -1.45199 1.29477 1.59219 -1.12237 -1.71371 0.93682 1.81515 -0.74028 -1.89531 0.53506 1.95324 -0.32356 -1.98828 0.10828 2.00000 0.10828 -1.98828 -0.32356 1.95324 0.53506 -1.89531 -0.74028 1.81515 0.93682 -1.71371 -1.12237 1.59219 1.29477 -1.45199 ... ... ..... ....... ......... ........... ............. E22 * 2.00000 -0.03611 -1.99870 0.10828 1.99479 -0.18031 -1.98828 0.25210 1.97917 -0.32356 -1.96749 0.39461 1.95324 -0.46513 -1.93645 0.53506 1.91713 -0.60428 -1.89531 0.67272 1.87102 -0.74028 -1.84429 0.80687 1.81515 -0.87241 -1.78365 0.93682 1.74982 -1.00000 -1.71371 1.06188 1.67537 -1.12237 -1.63484 1.18141 1.59219 -1.23890 -1.54745 1.29477 1.50070 -1.34896 -1.45199 1.40139 ... ... ..... ....... ......... ........... ............. E23 * 2.00000 -0.18031 -1.96749 0.53506 1.87102 -0.87241 -1.71371 1.18141 1.50070 -1.45199 -1.23890 1.67537 0.93682 -1.84429 -0.60428 1.95324 0.25210 -1.99870 0.10828 1.97917 -0.46513 -1.89531 0.80687 1.74982 -1.12237 -1.54745 1.40139 1.29477 -1.63484 -1.00000 1.81515 0.67272 -1.93645 -0.32356 1.99479 -0.03611 -1.98828 0.39461 1.91713 -0.74028 -1.78365 1.06188 1.59219 -1.34896 ... ... ..... ....... ......... ........... ............. E24 * 2.00000 -0.32356 -1.89531 0.93682 1.59219 -1.45199 -1.12237 1.81515 0.53506 -1.98828 0.10828 1.95324 -0.74028 -1.71371 1.29477 1.29477 -1.71371 -0.74028 1.95324 0.10828 -1.98828 0.53506 1.81515 -1.12237 -1.45199 1.59219 0.93682 -1.89531 -0.32356 2.00000 -0.32356 -1.89531 0.93682 1.59219 -1.45199 -1.12237 1.81515 0.53506 -1.98828 0.10828 1.95324 -0.74028 -1.71371 1.29477 ... ... ..... ....... ......... ........... ............. E25 * 2.00000 -0.46513 -1.78365 1.29477 1.18141 -1.84429 -0.32356 1.99479 -0.60428 -1.71371 1.40139 1.06188 -1.89531 -0.18031 1.97917 -0.74028 -1.63484 1.50070 0.93682 -1.93645 -0.03611 1.95324 -0.87241 -1.54745 1.59219 0.80687 -1.96749 0.10828 1.91713 -1.00000 -1.45199 1.67537 0.67272 -1.98828 0.25210 1.87102 -1.12237 -1.34896 1.74982 0.53506 -1.99870 0.39461 1.81515 -1.23890 ... ... ..... ....... ......... ........... ............. E26 * 2.00000 -0.60428 -1.63484 1.59219 0.67272 -1.99870 0.53506 1.67537 -1.54745 -0.74028 1.99479 -0.46513 -1.71371 1.50070 0.80687 -1.98828 0.39461 1.74982 -1.45199 -0.87241 1.97917 -0.32356 -1.78365 1.40139 0.93682 -1.96749 0.25210 1.81515 -1.34896 -1.00000 1.95324 -0.18031 -1.84429 1.29477 1.06188 -1.93645 0.10828 1.87102 -1.23890 -1.12237 1.91713 -0.03611 -1.89531 1.18141 ... ... ..... ....... ......... ........... ............. E27 * 2.00000 -0.74028 -1.45199 1.81515 0.10828 -1.89531 1.29477 0.93682 -1.98828 0.53506 1.59219 -1.71371 -0.32356 1.95324 -1.12237 -1.12237 1.95324 -0.32356 -1.71371 1.59219 0.53506 -1.98828 0.93682 1.29477 -1.89531 0.10828 1.81515 -1.45199 -0.74028 2.00000 -0.74028 -1.45199 1.81515 0.10828 -1.89531 1.29477 0.93682 -1.98828 0.53506 1.59219 -1.71371 -0.32356 1.95324 -1.12237 ... ... ..... ....... ......... ........... ............. E28 * 2.00000 -0.87241 -1.23890 1.95324 -0.46513 -1.54745 1.81515 -0.03611 -1.78365 1.59219 0.39461 -1.93645 1.29477 0.80687 -1.99870 0.93682 1.18141 -1.96749 0.53506 1.50070 -1.84429 0.10828 1.74982 -1.63484 -0.32356 1.91713 -1.34896 -0.74028 1.99479 -1.00000 -1.12237 1.97917 -0.60428 -1.45199 1.87102 -0.18031 -1.71371 1.67537 0.25210 -1.89531 1.40139 0.67272 -1.98828 1.06188 ... ... ..... ....... ......... ........... ............. E29 * 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E30 * 2.00000 -1.12237 -0.74028 1.95324 -1.45199 -0.32356 1.81515 -1.71371 0.10828 1.59219 -1.89531 0.53506 1.29477 -1.98828 0.93682 0.93682 -1.98828 1.29477 0.53506 -1.89531 1.59219 0.10828 -1.71371 1.81515 -0.32356 -1.45199 1.95324 -0.74028 -1.12237 2.00000 -1.12237 -0.74028 1.95324 -1.45199 -0.32356 1.81515 -1.71371 0.10828 1.59219 -1.89531 0.53506 1.29477 -1.98828 0.93682 ... ... ..... ....... ......... ........... ............. E31 * 2.00000 -1.23890 -0.46513 1.81515 -1.78365 0.39461 1.29477 -1.99870 1.18141 0.53506 -1.84429 1.74982 -0.32356 -1.34896 1.99479 -1.12237 -0.60428 1.87102 -1.71371 0.25210 1.40139 -1.98828 1.06188 0.67272 -1.89531 1.67537 -0.18031 -1.45199 1.97917 -1.00000 -0.74028 1.91713 -1.63484 0.10828 1.50070 -1.96749 0.93682 0.80687 -1.93645 1.59219 -0.03611 -1.54745 1.95324 -0.87241 ... ... ..... ....... ......... ........... ............. E32 * 2.00000 -1.34896 -0.18031 1.59219 -1.96749 1.06188 0.53506 -1.78365 1.87102 -0.74028 -0.87241 1.91713 -1.71371 0.39461 1.18141 -1.98828 1.50070 -0.03611 -1.45199 1.99479 -1.23890 -0.32356 1.67537 -1.93645 0.93682 0.67272 -1.84429 1.81515 -0.60428 -1.00000 1.95324 -1.63484 0.25210 1.29477 -1.99870 1.40139 0.10828 -1.54745 1.97917 -1.12237 -0.46513 1.74982 -1.89531 0.80687 ... ... ..... ....... ......... ........... ............. E33 * 2.00000 -1.45199 0.10828 1.29477 -1.98828 1.59219 -0.32356 -1.12237 1.95324 -1.71371 0.53506 0.93682 -1.89531 1.81515 -0.74028 -0.74028 1.81515 -1.89531 0.93682 0.53506 -1.71371 1.95324 -1.12237 -0.32356 1.59219 -1.98828 1.29477 0.10828 -1.45199 2.00000 -1.45199 0.10828 1.29477 -1.98828 1.59219 -0.32356 -1.12237 1.95324 -1.71371 0.53506 0.93682 -1.89531 1.81515 -0.74028 ... ... ..... ....... ......... ........... ............. E34 * 2.00000 -1.54745 0.39461 0.93682 -1.84429 1.91713 -1.12237 -0.18031 1.40139 -1.98828 1.67537 -0.60428 -0.74028 1.74982 -1.96749 1.29477 -0.03611 -1.23890 1.95324 -1.78365 0.80687 0.53506 -1.63484 1.99479 -1.45199 0.25210 1.06188 -1.89531 1.87102 -1.00000 -0.32356 1.50070 -1.99870 1.59219 -0.46513 -0.87241 1.81515 -1.93645 1.18141 0.10828 -1.34896 1.97917 -1.71371 0.67272 ... ... ..... ....... ......... ........... ............. E35 * 2.00000 -1.63484 0.67272 0.53506 -1.54745 1.99479 -1.71371 0.80687 0.39461 -1.45199 1.97917 -1.78365 0.93682 0.25210 -1.34896 1.95324 -1.84429 1.06188 0.10828 -1.23890 1.91713 -1.89531 1.18141 -0.03611 -1.12237 1.87102 -1.93645 1.29477 -0.18031 -1.00000 1.81515 -1.96749 1.40139 -0.32356 -0.87241 1.74982 -1.98828 1.50070 -0.46513 -0.74028 1.67537 -1.99870 1.59219 -0.60428 ... ... ..... ....... ......... ........... ............. E36 * 2.00000 -1.71371 0.93682 0.10828 -1.12237 1.81515 -1.98828 1.59219 -0.74028 -0.32356 1.29477 -1.89531 1.95324 -1.45199 0.53506 0.53506 -1.45199 1.95324 -1.89531 1.29477 -0.32356 -0.74028 1.59219 -1.98828 1.81515 -1.12237 0.10828 0.93682 -1.71371 2.00000 -1.71371 0.93682 0.10828 -1.12237 1.81515 -1.98828 1.59219 -0.74028 -0.32356 1.29477 -1.89531 1.95324 -1.45199 0.53506 ... ... ..... ....... ......... ........... ............. E37 * 2.00000 -1.78365 1.18141 -0.32356 -0.60428 1.40139 -1.89531 1.97917 -1.63484 0.93682 -0.03611 -0.87241 1.59219 -1.96749 1.91713 -1.45199 0.67272 0.25210 -1.12237 1.74982 -1.99870 1.81515 -1.23890 0.39461 0.53506 -1.34896 1.87102 -1.98828 1.67537 -1.00000 0.10828 0.80687 -1.54745 1.95324 -1.93645 1.50070 -0.74028 -0.18031 1.06188 -1.71371 1.99479 -1.84429 1.29477 -0.46513 ... ... ..... ....... ......... ........... ............. E38 * 2.00000 -1.84429 1.40139 -0.74028 -0.03611 0.80687 -1.45199 1.87102 -1.99870 1.81515 -1.34896 0.67272 0.10828 -0.87241 1.50070 -1.89531 1.99479 -1.78365 1.29477 -0.60428 -0.18031 0.93682 -1.54745 1.91713 -1.98828 1.74982 -1.23890 0.53506 0.25210 -1.00000 1.59219 -1.93645 1.97917 -1.71371 1.18141 -0.46513 -0.32356 1.06188 -1.63484 1.95324 -1.96749 1.67537 -1.12237 0.39461 ... ... ..... ....... ......... ........... ............. E39 * 2.00000 -1.89531 1.59219 -1.12237 0.53506 0.10828 -0.74028 1.29477 -1.71371 1.95324 -1.98828 1.81515 -1.45199 0.93682 -0.32356 -0.32356 0.93682 -1.45199 1.81515 -1.98828 1.95324 -1.71371 1.29477 -0.74028 0.10828 0.53506 -1.12237 1.59219 -1.89531 2.00000 -1.89531 1.59219 -1.12237 0.53506 0.10828 -0.74028 1.29477 -1.71371 1.95324 -1.98828 1.81515 -1.45199 0.93682 -0.32356 ... ... ..... ....... ......... ........... ............. E40 * 2.00000 -1.93645 1.74982 -1.45199 1.06188 -0.60428 0.10828 0.39461 -0.87241 1.29477 -1.63484 1.87102 -1.98828 1.97917 -1.84429 1.59219 -1.23890 0.80687 -0.32356 -0.18031 0.67272 -1.12237 1.50070 -1.78365 1.95324 -1.99870 1.91713 -1.71371 1.40139 -1.00000 0.53506 -0.03611 -0.46513 0.93682 -1.34896 1.67537 -1.89531 1.99479 -1.96749 1.81515 -1.54745 1.18141 -0.74028 0.25210 ... ... ..... ....... ......... ........... ............. E41 * 2.00000 -1.96749 1.87102 -1.71371 1.50070 -1.23890 0.93682 -0.60428 0.25210 0.10828 -0.46513 0.80687 -1.12237 1.40139 -1.63484 1.81515 -1.93645 1.99479 -1.98828 1.91713 -1.78365 1.59219 -1.34896 1.06188 -0.74028 0.39461 -0.03611 -0.32356 0.67272 -1.00000 1.29477 -1.54745 1.74982 -1.89531 1.97917 -1.99870 1.95324 -1.84429 1.67537 -1.45199 1.18141 -0.87241 0.53506 -0.18031 ... ... ..... ....... ......... ........... ............. E42 * 2.00000 -1.98828 1.95324 -1.89531 1.81515 -1.71371 1.59219 -1.45199 1.29477 -1.12237 0.93682 -0.74028 0.53506 -0.32356 0.10828 0.10828 -0.32356 0.53506 -0.74028 0.93682 -1.12237 1.29477 -1.45199 1.59219 -1.71371 1.81515 -1.89531 1.95324 -1.98828 2.00000 -1.98828 1.95324 -1.89531 1.81515 -1.71371 1.59219 -1.45199 1.29477 -1.12237 0.93682 -0.74028 0.53506 -0.32356 0.10828 ... ... ..... ....... ......... ........... ............. E43 * 2.00000 -1.99870 1.99479 -1.98828 1.97917 -1.96749 1.95324 -1.93645 1.91713 -1.89531 1.87102 -1.84429 1.81515 -1.78365 1.74982 -1.71371 1.67537 -1.63484 1.59219 -1.54745 1.50070 -1.45199 1.40139 -1.34896 1.29477 -1.23890 1.18141 -1.12237 1.06188 -1.00000 0.93682 -0.87241 0.80687 -0.74028 0.67272 -0.60428 0.53506 -0.46513 0.39461 -0.32356 0.25210 -0.18031 0.10828 -0.03611 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.994786463036 = 2*cos(2*π/87) 1.979173033111 = 2*cos(4*π/87) 1.953241111420 = 2*cos(6*π/87) = 2*cos(2*π/29) 1.917125894995 = 2*cos(8*π/87) 1.871015671851 = 2*cos(10*π/87) 1.815150839342 = 2*cos(12*π/87) = 2*cos(4*π/29) 1.749822650836 = 2*cos(14*π/87) 1.675371697260 = 2*cos(16*π/87) 1.592186131411 = 2*cos(18*π/87) = 2*cos(6*π/29) 1.500699644313 = 2*cos(20*π/87) 1.401389204147 = 2*cos(22*π/87) 1.294772569564 = 2*cos(24*π/87) = 2*cos(8*π/29) 1.181405590329 = 2*cos(26*π/87) 1.061879309380 = 2*cos(28*π/87) 0.936816881400 = 2*cos(30*π/87) = 2*cos(10*π/29) 0.806870323980 = 2*cos(32*π/87) 0.672717118300 = 2*cos(34*π/87) 0.535056677058 = 2*cos(36*π/87) = 2*cos(12*π/29) 0.394606698053 = 2*cos(38*π/87) 0.252099422441 = 2*cos(40*π/87) 0.108277817171 = 2*cos(42*π/87) = 2*cos(14*π/29) -0.036108298501 = 2*cos(44*π/87) -0.180306162224 = 2*cos(46*π/87) -0.323563993106 = 2*cos(48*π/87) = 2*cos(16*π/29) -0.465134911149 = 2*cos(50*π/87) -0.604280831139 = 2*cos(52*π/87) -0.740276310680 = 2*cos(54*π/87) = 2*cos(18*π/29) -0.872412332311 = 2*cos(56*π/87) -1.122374130725 = 2*cos(60*π/87) = 2*cos(20*π/29) -1.238896722431 = 2*cos(62*π/87) -1.348960280281 = 2*cos(64*π/87) -1.451990983846 = 2*cos(66*π/87) = 2*cos(22*π/29) -1.547451678746 = 2*cos(68*π/87) -1.634844677118 = 2*cos(70*π/87) -1.713714352335 = 2*cos(72*π/87) = 2*cos(24*π/29) -1.783649514431 = 2*cos(74*π/87) -1.844285553852 = 2*cos(76*π/87) -1.895306342366 = 2*cos(78*π/87) = 2*cos(26*π/29) -1.936445881205 = 2*cos(80*π/87) -1.967489687864 = 2*cos(82*π/87) -1.988275914309 = 2*cos(84*π/87) = 2*cos(28*π/29) -1.998696190779 = 2*cos(86*π/87) 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 C87 point group is 87, and the order of the principal axis (C87) is 87. The group has 44 irreducible representations. β The C87 point group is generated by one single symmetry element, C87. Therefore, it is a cyclic group. γ The lowest nonvanishing multipole moment in C87 is 2 (dipole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C87 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 86 cases have been combined into 43 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 43 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 43 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 much less than half the order of the principal axis. For this group, however, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.
| C85 | ||
| C86 | ||
| C87 | C87v C87h D87 D87h D87d | |
| C88 | ||
| C89 |
This Character Table for the C87 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.