Character table for the S114 point group

S114     E         2 C57     2 C57^2   2 C19     2 C57^4   2 C57^5   2 C19^2   2 C57^7   2 C57^8   2 C19^3   2 C57^10  2 C57^11  2 C19^4   2 C57^13  2 C57^14  2 C19^5   2 C57^16  2 C57^17  2 C19^6   2 C3      2 C57^20  2 C19^7   2 C57^22  2 C57^23  2 C19^8   2 C57^25  2 C57^26  2 C19^9   2 C57^28  i         2 S114    2 S38     2 S114^5  2 S114^7  2 S114^9  2 S114^11 2 S114^13 2 S114^15 2 S114^17 2 S6      2 S114^21 2 S114^23 2 S114^25 2 S114^27 2 S114^29 2 S114^31 2 S114^33 2 S114^35 2 S114^37 2 S114^39 2 S114^41 2 S114^43 2 S114^45 2 S114^47 2 S114^49 2 S114^51 2 S114^53 2 S114^55   <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
Ag       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   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000     ..T ... ....T ....... ........T ........... ............T
E1g  *   2.00000   1.98786   1.95159   1.89163   1.80871   1.70384   1.57828   1.43357   1.27145   1.09390   0.90307   0.70128   0.49097   0.27471   0.05511  -0.16516  -0.38342  -0.59703  -0.80339  -1.00000  -1.18447  -1.35456  -1.50821  -1.64356  -1.75895  -1.85299  -1.92454  -1.97272  -1.99696   2.00000  -1.99696  -1.97272  -1.92454  -1.85299  -1.75895  -1.64356  -1.50821  -1.35456  -1.18447  -1.00000  -0.80339  -0.59703  -0.38342  -0.16516   0.05511   0.27471   0.49097   0.70128   0.90307   1.09390   1.27145   1.43357   1.57828   1.70384   1.80871   1.89163   1.95159   1.98786     TT. ... ..TT. ....... ......TT. ........... ..........TT.
E2g  *   2.00000   1.95159   1.80871   1.57828   1.27145   0.90307   0.49097   0.05511  -0.38342  -0.80339  -1.18447  -1.50821  -1.75895  -1.92454  -1.99696  -1.97272  -1.85299  -1.64356  -1.35456  -1.00000  -0.59703  -0.16516   0.27471   0.70128   1.09390   1.43357   1.70384   1.89163   1.98786   2.00000   1.98786   1.89163   1.70384   1.43357   1.09390   0.70128   0.27471  -0.16516  -0.59703  -1.00000  -1.35456  -1.64356  -1.85299  -1.97272  -1.99696  -1.92454  -1.75895  -1.50821  -1.18447  -0.80339  -0.38342   0.05511   0.49097   0.90307   1.27145   1.57828   1.80871   1.95159     ... ... TT... ....... ....TT... ........... ........TT...
E3g  *   2.00000   1.89163   1.57828   1.09390   0.49097  -0.16516  -0.80339  -1.35456  -1.75895  -1.97272  -1.97272  -1.75895  -1.35456  -0.80339  -0.16516   0.49097   1.09390   1.57828   1.89163   2.00000   1.89163   1.57828   1.09390   0.49097  -0.16516  -0.80339  -1.35456  -1.75895  -1.97272   2.00000  -1.97272  -1.75895  -1.35456  -0.80339  -0.16516   0.49097   1.09390   1.57828   1.89163   2.00000   1.89163   1.57828   1.09390   0.49097  -0.16516  -0.80339  -1.35456  -1.75895  -1.97272  -1.97272  -1.75895  -1.35456  -0.80339  -0.16516   0.49097   1.09390   1.57828   1.89163     ... ... ..... ....... ..TT..... ........... ......TT.....
E4g  *   2.00000   1.80871   1.27145   0.49097  -0.38342  -1.18447  -1.75895  -1.99696  -1.85299  -1.35456  -0.59703   0.27471   1.09390   1.70384   1.98786   1.89163   1.43357   0.70128  -0.16516  -1.00000  -1.64356  -1.97272  -1.92454  -1.50821  -0.80339   0.05511   0.90307   1.57828   1.95159   2.00000   1.95159   1.57828   0.90307   0.05511  -0.80339  -1.50821  -1.92454  -1.97272  -1.64356  -1.00000  -0.16516   0.70128   1.43357   1.89163   1.98786   1.70384   1.09390   0.27471  -0.59703  -1.35456  -1.85299  -1.99696  -1.75895  -1.18447  -0.38342   0.49097   1.27145   1.80871     ... ... ..... ....... TT....... ........... ....TT.......
E5g  *   2.00000   1.70384   0.90307  -0.16516  -1.18447  -1.85299  -1.97272  -1.50821  -0.59703   0.49097   1.43357   1.95159   1.89163   1.27145   0.27471  -0.80339  -1.64356  -1.99696  -1.75895  -1.00000   0.05511   1.09390   1.80871   1.98786   1.57828   0.70128  -0.38342  -1.35456  -1.92454   2.00000  -1.92454  -1.35456  -0.38342   0.70128   1.57828   1.98786   1.80871   1.09390   0.05511  -1.00000  -1.75895  -1.99696  -1.64356  -0.80339   0.27471   1.27145   1.89163   1.95159   1.43357   0.49097  -0.59703  -1.50821  -1.97272  -1.85299  -1.18447  -0.16516   0.90307   1.70384     ... ... ..... ....... ......... ........... ..TT.........
E6g  *   2.00000   1.57828   0.49097  -0.80339  -1.75895  -1.97272  -1.35456  -0.16516   1.09390   1.89163   1.89163   1.09390  -0.16516  -1.35456  -1.97272  -1.75895  -0.80339   0.49097   1.57828   2.00000   1.57828   0.49097  -0.80339  -1.75895  -1.97272  -1.35456  -0.16516   1.09390   1.89163   2.00000   1.89163   1.09390  -0.16516  -1.35456  -1.97272  -1.75895  -0.80339   0.49097   1.57828   2.00000   1.57828   0.49097  -0.80339  -1.75895  -1.97272  -1.35456  -0.16516   1.09390   1.89163   1.89163   1.09390  -0.16516  -1.35456  -1.97272  -1.75895  -0.80339   0.49097   1.57828     ... ... ..... ....... ......... ........... TT...........
E7g  *   2.00000   1.43357   0.05511  -1.35456  -1.99696  -1.50821  -0.16516   1.27145   1.98786   1.57828   0.27471  -1.18447  -1.97272  -1.64356  -0.38342   1.09390   1.95159   1.70384   0.49097  -1.00000  -1.92454  -1.75895  -0.59703   0.90307   1.89163   1.80871   0.70128  -0.80339  -1.85299   2.00000  -1.85299  -0.80339   0.70128   1.80871   1.89163   0.90307  -0.59703  -1.75895  -1.92454  -1.00000   0.49097   1.70384   1.95159   1.09390  -0.38342  -1.64356  -1.97272  -1.18447   0.27471   1.57828   1.98786   1.27145  -0.16516  -1.50821  -1.99696  -1.35456   0.05511   1.43357     ... ... ..... ....... ......... ........... .............
E8g  *   2.00000   1.27145  -0.38342  -1.75895  -1.85299  -0.59703   1.09390   1.98786   1.43357  -0.16516  -1.64356  -1.92454  -0.80339   0.90307   1.95159   1.57828   0.05511  -1.50821  -1.97272  -1.00000   0.70128   1.89163   1.70384   0.27471  -1.35456  -1.99696  -1.18447   0.49097   1.80871   2.00000   1.80871   0.49097  -1.18447  -1.99696  -1.35456   0.27471   1.70384   1.89163   0.70128  -1.00000  -1.97272  -1.50821   0.05511   1.57828   1.95159   0.90307  -0.80339  -1.92454  -1.64356  -0.16516   1.43357   1.98786   1.09390  -0.59703  -1.85299  -1.75895  -0.38342   1.27145     ... ... ..... ....... ......... ........... .............
E9g  *   2.00000   1.09390  -0.80339  -1.97272  -1.35456   0.49097   1.89163   1.57828  -0.16516  -1.75895  -1.75895  -0.16516   1.57828   1.89163   0.49097  -1.35456  -1.97272  -0.80339   1.09390   2.00000   1.09390  -0.80339  -1.97272  -1.35456   0.49097   1.89163   1.57828  -0.16516  -1.75895   2.00000  -1.75895  -0.16516   1.57828   1.89163   0.49097  -1.35456  -1.97272  -0.80339   1.09390   2.00000   1.09390  -0.80339  -1.97272  -1.35456   0.49097   1.89163   1.57828  -0.16516  -1.75895  -1.75895  -0.16516   1.57828   1.89163   0.49097  -1.35456  -1.97272  -0.80339   1.09390     ... ... ..... ....... ......... ........... .............
E10g *   2.00000   0.90307  -1.18447  -1.97272  -0.59703   1.43357   1.89163   0.27471  -1.64356  -1.75895   0.05511   1.80871   1.57828  -0.38342  -1.92454  -1.35456   0.70128   1.98786   1.09390  -1.00000  -1.99696  -0.80339   1.27145   1.95159   0.49097  -1.50821  -1.85299  -0.16516   1.70384   2.00000   1.70384  -0.16516  -1.85299  -1.50821   0.49097   1.95159   1.27145  -0.80339  -1.99696  -1.00000   1.09390   1.98786   0.70128  -1.35456  -1.92454  -0.38342   1.57828   1.80871   0.05511  -1.75895  -1.64356   0.27471   1.89163   1.43357  -0.59703  -1.97272  -1.18447   0.90307     ... ... ..... ....... ......... ........... .............
E11g *   2.00000   0.70128  -1.50821  -1.75895   0.27471   1.95159   1.09390  -1.18447  -1.92454  -0.16516   1.80871   1.43357  -0.80339  -1.99696  -0.59703   1.57828   1.70384  -0.38342  -1.97272  -1.00000   1.27145   1.89163   0.05511  -1.85299  -1.35456   0.90307   1.98786   0.49097  -1.64356   2.00000  -1.64356   0.49097   1.98786   0.90307  -1.35456  -1.85299   0.05511   1.89163   1.27145  -1.00000  -1.97272  -0.38342   1.70384   1.57828  -0.59703  -1.99696  -0.80339   1.43357   1.80871  -0.16516  -1.92454  -1.18447   1.09390   1.95159   0.27471  -1.75895  -1.50821   0.70128     ... ... ..... ....... ......... ........... .............
E12g *   2.00000   0.49097  -1.75895  -1.35456   1.09390   1.89163  -0.16516  -1.97272  -0.80339   1.57828   1.57828  -0.80339  -1.97272  -0.16516   1.89163   1.09390  -1.35456  -1.75895   0.49097   2.00000   0.49097  -1.75895  -1.35456   1.09390   1.89163  -0.16516  -1.97272  -0.80339   1.57828   2.00000   1.57828  -0.80339  -1.97272  -0.16516   1.89163   1.09390  -1.35456  -1.75895   0.49097   2.00000   0.49097  -1.75895  -1.35456   1.09390   1.89163  -0.16516  -1.97272  -0.80339   1.57828   1.57828  -0.80339  -1.97272  -0.16516   1.89163   1.09390  -1.35456  -1.75895   0.49097     ... ... ..... ....... ......... ........... .............
E13g *   2.00000   0.27471  -1.92454  -0.80339   1.70384   1.27145  -1.35456  -1.64356   0.90307   1.89163  -0.38342  -1.99696  -0.16516   1.95159   0.70128  -1.75895  -1.18447   1.43357   1.57828  -1.00000  -1.85299   0.49097   1.98786   0.05511  -1.97272  -0.59703   1.80871   1.09390  -1.50821   2.00000  -1.50821   1.09390   1.80871  -0.59703  -1.97272   0.05511   1.98786   0.49097  -1.85299  -1.00000   1.57828   1.43357  -1.18447  -1.75895   0.70128   1.95159  -0.16516  -1.99696  -0.38342   1.89163   0.90307  -1.64356  -1.35456   1.27145   1.70384  -0.80339  -1.92454   0.27471     ... ... ..... ....... ......... ........... .............
E14g *   2.00000   0.05511  -1.99696  -0.16516   1.98786   0.27471  -1.97272  -0.38342   1.95159   0.49097  -1.92454  -0.59703   1.89163   0.70128  -1.85299  -0.80339   1.80871   0.90307  -1.75895  -1.00000   1.70384   1.09390  -1.64356  -1.18447   1.57828   1.27145  -1.50821  -1.35456   1.43357   2.00000   1.43357  -1.35456  -1.50821   1.27145   1.57828  -1.18447  -1.64356   1.09390   1.70384  -1.00000  -1.75895   0.90307   1.80871  -0.80339  -1.85299   0.70128   1.89163  -0.59703  -1.92454   0.49097   1.95159  -0.38342  -1.97272   0.27471   1.98786  -0.16516  -1.99696   0.05511     ... ... ..... ....... ......... ........... .............
E15g *   2.00000  -0.16516  -1.97272   0.49097   1.89163  -0.80339  -1.75895   1.09390   1.57828  -1.35456  -1.35456   1.57828   1.09390  -1.75895  -0.80339   1.89163   0.49097  -1.97272  -0.16516   2.00000  -0.16516  -1.97272   0.49097   1.89163  -0.80339  -1.75895   1.09390   1.57828  -1.35456   2.00000  -1.35456   1.57828   1.09390  -1.75895  -0.80339   1.89163   0.49097  -1.97272  -0.16516   2.00000  -0.16516  -1.97272   0.49097   1.89163  -0.80339  -1.75895   1.09390   1.57828  -1.35456  -1.35456   1.57828   1.09390  -1.75895  -0.80339   1.89163   0.49097  -1.97272  -0.16516     ... ... ..... ....... ......... ........... .............
E16g *   2.00000  -0.38342  -1.85299   1.09390   1.43357  -1.64356  -0.80339   1.95159   0.05511  -1.97272   0.70128   1.70384  -1.35456  -1.18447   1.80871   0.49097  -1.99696   0.27471   1.89163  -1.00000  -1.50821   1.57828   0.90307  -1.92454  -0.16516   1.98786  -0.59703  -1.75895   1.27145   2.00000   1.27145  -1.75895  -0.59703   1.98786  -0.16516  -1.92454   0.90307   1.57828  -1.50821  -1.00000   1.89163   0.27471  -1.99696   0.49097   1.80871  -1.18447  -1.35456   1.70384   0.70128  -1.97272   0.05511   1.95159  -0.80339  -1.64356   1.43357   1.09390  -1.85299  -0.38342     ... ... ..... ....... ......... ........... .............
E17g *   2.00000  -0.59703  -1.64356   1.57828   0.70128  -1.99696   0.49097   1.70384  -1.50821  -0.80339   1.98786  -0.38342  -1.75895   1.43357   0.90307  -1.97272   0.27471   1.80871  -1.35456  -1.00000   1.95159  -0.16516  -1.85299   1.27145   1.09390  -1.92454   0.05511   1.89163  -1.18447   2.00000  -1.18447   1.89163   0.05511  -1.92454   1.09390   1.27145  -1.85299  -0.16516   1.95159  -1.00000  -1.35456   1.80871   0.27471  -1.97272   0.90307   1.43357  -1.75895  -0.38342   1.98786  -0.80339  -1.50821   1.70384   0.49097  -1.99696   0.70128   1.57828  -1.64356  -0.59703     ... ... ..... ....... ......... ........... .............
E18g *   2.00000  -0.80339  -1.35456   1.89163  -0.16516  -1.75895   1.57828   0.49097  -1.97272   1.09390   1.09390  -1.97272   0.49097   1.57828  -1.75895  -0.16516   1.89163  -1.35456  -0.80339   2.00000  -0.80339  -1.35456   1.89163  -0.16516  -1.75895   1.57828   0.49097  -1.97272   1.09390   2.00000   1.09390  -1.97272   0.49097   1.57828  -1.75895  -0.16516   1.89163  -1.35456  -0.80339   2.00000  -0.80339  -1.35456   1.89163  -0.16516  -1.75895   1.57828   0.49097  -1.97272   1.09390   1.09390  -1.97272   0.49097   1.57828  -1.75895  -0.16516   1.89163  -1.35456  -0.80339     ... ... ..... ....... ......... ........... .............
E19g *   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   2.00000  -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     ... ... ..... ....... ......... ........... .............
E20g *   2.00000  -1.18447  -0.59703   1.89163  -1.64356   0.05511   1.57828  -1.92454   0.70128   1.09390  -1.99696   1.27145   0.49097  -1.85299   1.70384  -0.16516  -1.50821   1.95159  -0.80339  -1.00000   1.98786  -1.35456  -0.38342   1.80871  -1.75895   0.27471   1.43357  -1.97272   0.90307   2.00000   0.90307  -1.97272   1.43357   0.27471  -1.75895   1.80871  -0.38342  -1.35456   1.98786  -1.00000  -0.80339   1.95159  -1.50821  -0.16516   1.70384  -1.85299   0.49097   1.27145  -1.99696   1.09390   0.70128  -1.92454   1.57828   0.05511  -1.64356   1.89163  -0.59703  -1.18447     ... ... ..... ....... ......... ........... .............
E21g *   2.00000  -1.35456  -0.16516   1.57828  -1.97272   1.09390   0.49097  -1.75895   1.89163  -0.80339  -0.80339   1.89163  -1.75895   0.49097   1.09390  -1.97272   1.57828  -0.16516  -1.35456   2.00000  -1.35456  -0.16516   1.57828  -1.97272   1.09390   0.49097  -1.75895   1.89163  -0.80339   2.00000  -0.80339   1.89163  -1.75895   0.49097   1.09390  -1.97272   1.57828  -0.16516  -1.35456   2.00000  -1.35456  -0.16516   1.57828  -1.97272   1.09390   0.49097  -1.75895   1.89163  -0.80339  -0.80339   1.89163  -1.75895   0.49097   1.09390  -1.97272   1.57828  -0.16516  -1.35456     ... ... ..... ....... ......... ........... .............
E22g *   2.00000  -1.50821   0.27471   1.09390  -1.92454   1.80871  -0.80339  -0.59703   1.70384  -1.97272   1.27145   0.05511  -1.35456   1.98786  -1.64356   0.49097   0.90307  -1.85299   1.89163  -1.00000  -0.38342   1.57828  -1.99696   1.43357  -0.16516  -1.18447   1.95159  -1.75895   0.70128   2.00000   0.70128  -1.75895   1.95159  -1.18447  -0.16516   1.43357  -1.99696   1.57828  -0.38342  -1.00000   1.89163  -1.85299   0.90307   0.49097  -1.64356   1.98786  -1.35456   0.05511   1.27145  -1.97272   1.70384  -0.59703  -0.80339   1.80871  -1.92454   1.09390   0.27471  -1.50821     ... ... ..... ....... ......... ........... .............
E23g *   2.00000  -1.64356   0.70128   0.49097  -1.50821   1.98786  -1.75895   0.90307   0.27471  -1.35456   1.95159  -1.85299   1.09390   0.05511  -1.18447   1.89163  -1.92454   1.27145  -0.16516  -1.00000   1.80871  -1.97272   1.43357  -0.38342  -0.80339   1.70384  -1.99696   1.57828  -0.59703   2.00000  -0.59703   1.57828  -1.99696   1.70384  -0.80339  -0.38342   1.43357  -1.97272   1.80871  -1.00000  -0.16516   1.27145  -1.92454   1.89163  -1.18447   0.05511   1.09390  -1.85299   1.95159  -1.35456   0.27471   0.90307  -1.75895   1.98786  -1.50821   0.49097   0.70128  -1.64356     ... ... ..... ....... ......... ........... .............
E24g *   2.00000  -1.75895   1.09390  -0.16516  -0.80339   1.57828  -1.97272   1.89163  -1.35456   0.49097   0.49097  -1.35456   1.89163  -1.97272   1.57828  -0.80339  -0.16516   1.09390  -1.75895   2.00000  -1.75895   1.09390  -0.16516  -0.80339   1.57828  -1.97272   1.89163  -1.35456   0.49097   2.00000   0.49097  -1.35456   1.89163  -1.97272   1.57828  -0.80339  -0.16516   1.09390  -1.75895   2.00000  -1.75895   1.09390  -0.16516  -0.80339   1.57828  -1.97272   1.89163  -1.35456   0.49097   0.49097  -1.35456   1.89163  -1.97272   1.57828  -0.80339  -0.16516   1.09390  -1.75895     ... ... ..... ....... ......... ........... .............
E25g *   2.00000  -1.85299   1.43357  -0.80339   0.05511   0.70128  -1.35456   1.80871  -1.99696   1.89163  -1.50821   0.90307  -0.16516  -0.59703   1.27145  -1.75895   1.98786  -1.92454   1.57828  -1.00000   0.27471   0.49097  -1.18447   1.70384  -1.97272   1.95159  -1.64356   1.09390  -0.38342   2.00000  -0.38342   1.09390  -1.64356   1.95159  -1.97272   1.70384  -1.18447   0.49097   0.27471  -1.00000   1.57828  -1.92454   1.98786  -1.75895   1.27145  -0.59703  -0.16516   0.90307  -1.50821   1.89163  -1.99696   1.80871  -1.35456   0.70128   0.05511  -0.80339   1.43357  -1.85299     ... ... ..... ....... ......... ........... .............
E26g *   2.00000  -1.92454   1.70384  -1.35456   0.90307  -0.38342  -0.16516   0.70128  -1.18447   1.57828  -1.85299   1.98786  -1.97272   1.80871  -1.50821   1.09390  -0.59703   0.05511   0.49097  -1.00000   1.43357  -1.75895   1.95159  -1.99696   1.89163  -1.64356   1.27145  -0.80339   0.27471   2.00000   0.27471  -0.80339   1.27145  -1.64356   1.89163  -1.99696   1.95159  -1.75895   1.43357  -1.00000   0.49097   0.05511  -0.59703   1.09390  -1.50821   1.80871  -1.97272   1.98786  -1.85299   1.57828  -1.18447   0.70128  -0.16516  -0.38342   0.90307  -1.35456   1.70384  -1.92454     ... ... ..... ....... ......... ........... .............
E27g *   2.00000  -1.97272   1.89163  -1.75895   1.57828  -1.35456   1.09390  -0.80339   0.49097  -0.16516  -0.16516   0.49097  -0.80339   1.09390  -1.35456   1.57828  -1.75895   1.89163  -1.97272   2.00000  -1.97272   1.89163  -1.75895   1.57828  -1.35456   1.09390  -0.80339   0.49097  -0.16516   2.00000  -0.16516   0.49097  -0.80339   1.09390  -1.35456   1.57828  -1.75895   1.89163  -1.97272   2.00000  -1.97272   1.89163  -1.75895   1.57828  -1.35456   1.09390  -0.80339   0.49097  -0.16516  -0.16516   0.49097  -0.80339   1.09390  -1.35456   1.57828  -1.75895   1.89163  -1.97272     ... ... ..... ....... ......... ........... .............
E28g *   2.00000  -1.99696   1.98786  -1.97272   1.95159  -1.92454   1.89163  -1.85299   1.80871  -1.75895   1.70384  -1.64356   1.57828  -1.50821   1.43357  -1.35456   1.27145  -1.18447   1.09390  -1.00000   0.90307  -0.80339   0.70128  -0.59703   0.49097  -0.38342   0.27471  -0.16516   0.05511   2.00000   0.05511  -0.16516   0.27471  -0.38342   0.49097  -0.59703   0.70128  -0.80339   0.90307  -1.00000   1.09390  -1.18447   1.27145  -1.35456   1.43357  -1.50821   1.57828  -1.64356   1.70384  -1.75895   1.80871  -1.85299   1.89163  -1.92454   1.95159  -1.97272   1.98786  -1.99696     ... ... ..... ....... ......... ........... .............
Au       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  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000  -1.00000     ... ..T ..... ......T ......... ..........T .............
E1u  *   2.00000   1.98786   1.95159   1.89163   1.80871   1.70384   1.57828   1.43357   1.27145   1.09390   0.90307   0.70128   0.49097   0.27471   0.05511  -0.16516  -0.38342  -0.59703  -0.80339  -1.00000  -1.18447  -1.35456  -1.50821  -1.64356  -1.75895  -1.85299  -1.92454  -1.97272  -1.99696  -2.00000   1.99696   1.97272   1.92454   1.85299   1.75895   1.64356   1.50821   1.35456   1.18447   1.00000   0.80339   0.59703   0.38342   0.16516  -0.05511  -0.27471  -0.49097  -0.70128  -0.90307  -1.09390  -1.27145  -1.43357  -1.57828  -1.70384  -1.80871  -1.89163  -1.95159  -1.98786     ... TT. ..... ....TT. ......... ........TT. .............
E2u  *   2.00000   1.95159   1.80871   1.57828   1.27145   0.90307   0.49097   0.05511  -0.38342  -0.80339  -1.18447  -1.50821  -1.75895  -1.92454  -1.99696  -1.97272  -1.85299  -1.64356  -1.35456  -1.00000  -0.59703  -0.16516   0.27471   0.70128   1.09390   1.43357   1.70384   1.89163   1.98786  -2.00000  -1.98786  -1.89163  -1.70384  -1.43357  -1.09390  -0.70128  -0.27471   0.16516   0.59703   1.00000   1.35456   1.64356   1.85299   1.97272   1.99696   1.92454   1.75895   1.50821   1.18447   0.80339   0.38342  -0.05511  -0.49097  -0.90307  -1.27145  -1.57828  -1.80871  -1.95159     ... ... ..... ..TT... ......... ......TT... .............
E3u  *   2.00000   1.89163   1.57828   1.09390   0.49097  -0.16516  -0.80339  -1.35456  -1.75895  -1.97272  -1.97272  -1.75895  -1.35456  -0.80339  -0.16516   0.49097   1.09390   1.57828   1.89163   2.00000   1.89163   1.57828   1.09390   0.49097  -0.16516  -0.80339  -1.35456  -1.75895  -1.97272  -2.00000   1.97272   1.75895   1.35456   0.80339   0.16516  -0.49097  -1.09390  -1.57828  -1.89163  -2.00000  -1.89163  -1.57828  -1.09390  -0.49097   0.16516   0.80339   1.35456   1.75895   1.97272   1.97272   1.75895   1.35456   0.80339   0.16516  -0.49097  -1.09390  -1.57828  -1.89163     ... ... ..... TT..... ......... ....TT..... .............
E4u  *   2.00000   1.80871   1.27145   0.49097  -0.38342  -1.18447  -1.75895  -1.99696  -1.85299  -1.35456  -0.59703   0.27471   1.09390   1.70384   1.98786   1.89163   1.43357   0.70128  -0.16516  -1.00000  -1.64356  -1.97272  -1.92454  -1.50821  -0.80339   0.05511   0.90307   1.57828   1.95159  -2.00000  -1.95159  -1.57828  -0.90307  -0.05511   0.80339   1.50821   1.92454   1.97272   1.64356   1.00000   0.16516  -0.70128  -1.43357  -1.89163  -1.98786  -1.70384  -1.09390  -0.27471   0.59703   1.35456   1.85299   1.99696   1.75895   1.18447   0.38342  -0.49097  -1.27145  -1.80871     ... ... ..... ....... ......... ..TT....... .............
E5u  *   2.00000   1.70384   0.90307  -0.16516  -1.18447  -1.85299  -1.97272  -1.50821  -0.59703   0.49097   1.43357   1.95159   1.89163   1.27145   0.27471  -0.80339  -1.64356  -1.99696  -1.75895  -1.00000   0.05511   1.09390   1.80871   1.98786   1.57828   0.70128  -0.38342  -1.35456  -1.92454  -2.00000   1.92454   1.35456   0.38342  -0.70128  -1.57828  -1.98786  -1.80871  -1.09390  -0.05511   1.00000   1.75895   1.99696   1.64356   0.80339  -0.27471  -1.27145  -1.89163  -1.95159  -1.43357  -0.49097   0.59703   1.50821   1.97272   1.85299   1.18447   0.16516  -0.90307  -1.70384     ... ... ..... ....... ......... TT......... .............
E6u  *   2.00000   1.57828   0.49097  -0.80339  -1.75895  -1.97272  -1.35456  -0.16516   1.09390   1.89163   1.89163   1.09390  -0.16516  -1.35456  -1.97272  -1.75895  -0.80339   0.49097   1.57828   2.00000   1.57828   0.49097  -0.80339  -1.75895  -1.97272  -1.35456  -0.16516   1.09390   1.89163  -2.00000  -1.89163  -1.09390   0.16516   1.35456   1.97272   1.75895   0.80339  -0.49097  -1.57828  -2.00000  -1.57828  -0.49097   0.80339   1.75895   1.97272   1.35456   0.16516  -1.09390  -1.89163  -1.89163  -1.09390   0.16516   1.35456   1.97272   1.75895   0.80339  -0.49097  -1.57828     ... ... ..... ....... ......... ........... .............
E7u  *   2.00000   1.43357   0.05511  -1.35456  -1.99696  -1.50821  -0.16516   1.27145   1.98786   1.57828   0.27471  -1.18447  -1.97272  -1.64356  -0.38342   1.09390   1.95159   1.70384   0.49097  -1.00000  -1.92454  -1.75895  -0.59703   0.90307   1.89163   1.80871   0.70128  -0.80339  -1.85299  -2.00000   1.85299   0.80339  -0.70128  -1.80871  -1.89163  -0.90307   0.59703   1.75895   1.92454   1.00000  -0.49097  -1.70384  -1.95159  -1.09390   0.38342   1.64356   1.97272   1.18447  -0.27471  -1.57828  -1.98786  -1.27145   0.16516   1.50821   1.99696   1.35456  -0.05511  -1.43357     ... ... ..... ....... ......... ........... .............
E8u  *   2.00000   1.27145  -0.38342  -1.75895  -1.85299  -0.59703   1.09390   1.98786   1.43357  -0.16516  -1.64356  -1.92454  -0.80339   0.90307   1.95159   1.57828   0.05511  -1.50821  -1.97272  -1.00000   0.70128   1.89163   1.70384   0.27471  -1.35456  -1.99696  -1.18447   0.49097   1.80871  -2.00000  -1.80871  -0.49097   1.18447   1.99696   1.35456  -0.27471  -1.70384  -1.89163  -0.70128   1.00000   1.97272   1.50821  -0.05511  -1.57828  -1.95159  -0.90307   0.80339   1.92454   1.64356   0.16516  -1.43357  -1.98786  -1.09390   0.59703   1.85299   1.75895   0.38342  -1.27145     ... ... ..... ....... ......... ........... .............
E9u  *   2.00000   1.09390  -0.80339  -1.97272  -1.35456   0.49097   1.89163   1.57828  -0.16516  -1.75895  -1.75895  -0.16516   1.57828   1.89163   0.49097  -1.35456  -1.97272  -0.80339   1.09390   2.00000   1.09390  -0.80339  -1.97272  -1.35456   0.49097   1.89163   1.57828  -0.16516  -1.75895  -2.00000   1.75895   0.16516  -1.57828  -1.89163  -0.49097   1.35456   1.97272   0.80339  -1.09390  -2.00000  -1.09390   0.80339   1.97272   1.35456  -0.49097  -1.89163  -1.57828   0.16516   1.75895   1.75895   0.16516  -1.57828  -1.89163  -0.49097   1.35456   1.97272   0.80339  -1.09390     ... ... ..... ....... ......... ........... .............
E10u *   2.00000   0.90307  -1.18447  -1.97272  -0.59703   1.43357   1.89163   0.27471  -1.64356  -1.75895   0.05511   1.80871   1.57828  -0.38342  -1.92454  -1.35456   0.70128   1.98786   1.09390  -1.00000  -1.99696  -0.80339   1.27145   1.95159   0.49097  -1.50821  -1.85299  -0.16516   1.70384  -2.00000  -1.70384   0.16516   1.85299   1.50821  -0.49097  -1.95159  -1.27145   0.80339   1.99696   1.00000  -1.09390  -1.98786  -0.70128   1.35456   1.92454   0.38342  -1.57828  -1.80871  -0.05511   1.75895   1.64356  -0.27471  -1.89163  -1.43357   0.59703   1.97272   1.18447  -0.90307     ... ... ..... ....... ......... ........... .............
E11u *   2.00000   0.70128  -1.50821  -1.75895   0.27471   1.95159   1.09390  -1.18447  -1.92454  -0.16516   1.80871   1.43357  -0.80339  -1.99696  -0.59703   1.57828   1.70384  -0.38342  -1.97272  -1.00000   1.27145   1.89163   0.05511  -1.85299  -1.35456   0.90307   1.98786   0.49097  -1.64356  -2.00000   1.64356  -0.49097  -1.98786  -0.90307   1.35456   1.85299  -0.05511  -1.89163  -1.27145   1.00000   1.97272   0.38342  -1.70384  -1.57828   0.59703   1.99696   0.80339  -1.43357  -1.80871   0.16516   1.92454   1.18447  -1.09390  -1.95159  -0.27471   1.75895   1.50821  -0.70128     ... ... ..... ....... ......... ........... .............
E12u *   2.00000   0.49097  -1.75895  -1.35456   1.09390   1.89163  -0.16516  -1.97272  -0.80339   1.57828   1.57828  -0.80339  -1.97272  -0.16516   1.89163   1.09390  -1.35456  -1.75895   0.49097   2.00000   0.49097  -1.75895  -1.35456   1.09390   1.89163  -0.16516  -1.97272  -0.80339   1.57828  -2.00000  -1.57828   0.80339   1.97272   0.16516  -1.89163  -1.09390   1.35456   1.75895  -0.49097  -2.00000  -0.49097   1.75895   1.35456  -1.09390  -1.89163   0.16516   1.97272   0.80339  -1.57828  -1.57828   0.80339   1.97272   0.16516  -1.89163  -1.09390   1.35456   1.75895  -0.49097     ... ... ..... ....... ......... ........... .............
E13u *   2.00000   0.27471  -1.92454  -0.80339   1.70384   1.27145  -1.35456  -1.64356   0.90307   1.89163  -0.38342  -1.99696  -0.16516   1.95159   0.70128  -1.75895  -1.18447   1.43357   1.57828  -1.00000  -1.85299   0.49097   1.98786   0.05511  -1.97272  -0.59703   1.80871   1.09390  -1.50821  -2.00000   1.50821  -1.09390  -1.80871   0.59703   1.97272  -0.05511  -1.98786  -0.49097   1.85299   1.00000  -1.57828  -1.43357   1.18447   1.75895  -0.70128  -1.95159   0.16516   1.99696   0.38342  -1.89163  -0.90307   1.64356   1.35456  -1.27145  -1.70384   0.80339   1.92454  -0.27471     ... ... ..... ....... ......... ........... .............
E14u *   2.00000   0.05511  -1.99696  -0.16516   1.98786   0.27471  -1.97272  -0.38342   1.95159   0.49097  -1.92454  -0.59703   1.89163   0.70128  -1.85299  -0.80339   1.80871   0.90307  -1.75895  -1.00000   1.70384   1.09390  -1.64356  -1.18447   1.57828   1.27145  -1.50821  -1.35456   1.43357  -2.00000  -1.43357   1.35456   1.50821  -1.27145  -1.57828   1.18447   1.64356  -1.09390  -1.70384   1.00000   1.75895  -0.90307  -1.80871   0.80339   1.85299  -0.70128  -1.89163   0.59703   1.92454  -0.49097  -1.95159   0.38342   1.97272  -0.27471  -1.98786   0.16516   1.99696  -0.05511     ... ... ..... ....... ......... ........... .............
E15u *   2.00000  -0.16516  -1.97272   0.49097   1.89163  -0.80339  -1.75895   1.09390   1.57828  -1.35456  -1.35456   1.57828   1.09390  -1.75895  -0.80339   1.89163   0.49097  -1.97272  -0.16516   2.00000  -0.16516  -1.97272   0.49097   1.89163  -0.80339  -1.75895   1.09390   1.57828  -1.35456  -2.00000   1.35456  -1.57828  -1.09390   1.75895   0.80339  -1.89163  -0.49097   1.97272   0.16516  -2.00000   0.16516   1.97272  -0.49097  -1.89163   0.80339   1.75895  -1.09390  -1.57828   1.35456   1.35456  -1.57828  -1.09390   1.75895   0.80339  -1.89163  -0.49097   1.97272   0.16516     ... ... ..... ....... ......... ........... .............
E16u *   2.00000  -0.38342  -1.85299   1.09390   1.43357  -1.64356  -0.80339   1.95159   0.05511  -1.97272   0.70128   1.70384  -1.35456  -1.18447   1.80871   0.49097  -1.99696   0.27471   1.89163  -1.00000  -1.50821   1.57828   0.90307  -1.92454  -0.16516   1.98786  -0.59703  -1.75895   1.27145  -2.00000  -1.27145   1.75895   0.59703  -1.98786   0.16516   1.92454  -0.90307  -1.57828   1.50821   1.00000  -1.89163  -0.27471   1.99696  -0.49097  -1.80871   1.18447   1.35456  -1.70384  -0.70128   1.97272  -0.05511  -1.95159   0.80339   1.64356  -1.43357  -1.09390   1.85299   0.38342     ... ... ..... ....... ......... ........... .............
E17u *   2.00000  -0.59703  -1.64356   1.57828   0.70128  -1.99696   0.49097   1.70384  -1.50821  -0.80339   1.98786  -0.38342  -1.75895   1.43357   0.90307  -1.97272   0.27471   1.80871  -1.35456  -1.00000   1.95159  -0.16516  -1.85299   1.27145   1.09390  -1.92454   0.05511   1.89163  -1.18447  -2.00000   1.18447  -1.89163  -0.05511   1.92454  -1.09390  -1.27145   1.85299   0.16516  -1.95159   1.00000   1.35456  -1.80871  -0.27471   1.97272  -0.90307  -1.43357   1.75895   0.38342  -1.98786   0.80339   1.50821  -1.70384  -0.49097   1.99696  -0.70128  -1.57828   1.64356   0.59703     ... ... ..... ....... ......... ........... .............
E18u *   2.00000  -0.80339  -1.35456   1.89163  -0.16516  -1.75895   1.57828   0.49097  -1.97272   1.09390   1.09390  -1.97272   0.49097   1.57828  -1.75895  -0.16516   1.89163  -1.35456  -0.80339   2.00000  -0.80339  -1.35456   1.89163  -0.16516  -1.75895   1.57828   0.49097  -1.97272   1.09390  -2.00000  -1.09390   1.97272  -0.49097  -1.57828   1.75895   0.16516  -1.89163   1.35456   0.80339  -2.00000   0.80339   1.35456  -1.89163   0.16516   1.75895  -1.57828  -0.49097   1.97272  -1.09390  -1.09390   1.97272  -0.49097  -1.57828   1.75895   0.16516  -1.89163   1.35456   0.80339     ... ... ..... ....... ......... ........... .............
E19u *   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  -2.00000   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     ... ... ..... ....... ......... ........... .............
E20u *   2.00000  -1.18447  -0.59703   1.89163  -1.64356   0.05511   1.57828  -1.92454   0.70128   1.09390  -1.99696   1.27145   0.49097  -1.85299   1.70384  -0.16516  -1.50821   1.95159  -0.80339  -1.00000   1.98786  -1.35456  -0.38342   1.80871  -1.75895   0.27471   1.43357  -1.97272   0.90307  -2.00000  -0.90307   1.97272  -1.43357  -0.27471   1.75895  -1.80871   0.38342   1.35456  -1.98786   1.00000   0.80339  -1.95159   1.50821   0.16516  -1.70384   1.85299  -0.49097  -1.27145   1.99696  -1.09390  -0.70128   1.92454  -1.57828  -0.05511   1.64356  -1.89163   0.59703   1.18447     ... ... ..... ....... ......... ........... .............
E21u *   2.00000  -1.35456  -0.16516   1.57828  -1.97272   1.09390   0.49097  -1.75895   1.89163  -0.80339  -0.80339   1.89163  -1.75895   0.49097   1.09390  -1.97272   1.57828  -0.16516  -1.35456   2.00000  -1.35456  -0.16516   1.57828  -1.97272   1.09390   0.49097  -1.75895   1.89163  -0.80339  -2.00000   0.80339  -1.89163   1.75895  -0.49097  -1.09390   1.97272  -1.57828   0.16516   1.35456  -2.00000   1.35456   0.16516  -1.57828   1.97272  -1.09390  -0.49097   1.75895  -1.89163   0.80339   0.80339  -1.89163   1.75895  -0.49097  -1.09390   1.97272  -1.57828   0.16516   1.35456     ... ... ..... ....... ......... ........... .............
E22u *   2.00000  -1.50821   0.27471   1.09390  -1.92454   1.80871  -0.80339  -0.59703   1.70384  -1.97272   1.27145   0.05511  -1.35456   1.98786  -1.64356   0.49097   0.90307  -1.85299   1.89163  -1.00000  -0.38342   1.57828  -1.99696   1.43357  -0.16516  -1.18447   1.95159  -1.75895   0.70128  -2.00000  -0.70128   1.75895  -1.95159   1.18447   0.16516  -1.43357   1.99696  -1.57828   0.38342   1.00000  -1.89163   1.85299  -0.90307  -0.49097   1.64356  -1.98786   1.35456  -0.05511  -1.27145   1.97272  -1.70384   0.59703   0.80339  -1.80871   1.92454  -1.09390  -0.27471   1.50821     ... ... ..... ....... ......... ........... .............
E23u *   2.00000  -1.64356   0.70128   0.49097  -1.50821   1.98786  -1.75895   0.90307   0.27471  -1.35456   1.95159  -1.85299   1.09390   0.05511  -1.18447   1.89163  -1.92454   1.27145  -0.16516  -1.00000   1.80871  -1.97272   1.43357  -0.38342  -0.80339   1.70384  -1.99696   1.57828  -0.59703  -2.00000   0.59703  -1.57828   1.99696  -1.70384   0.80339   0.38342  -1.43357   1.97272  -1.80871   1.00000   0.16516  -1.27145   1.92454  -1.89163   1.18447  -0.05511  -1.09390   1.85299  -1.95159   1.35456  -0.27471  -0.90307   1.75895  -1.98786   1.50821  -0.49097  -0.70128   1.64356     ... ... ..... ....... ......... ........... .............
E24u *   2.00000  -1.75895   1.09390  -0.16516  -0.80339   1.57828  -1.97272   1.89163  -1.35456   0.49097   0.49097  -1.35456   1.89163  -1.97272   1.57828  -0.80339  -0.16516   1.09390  -1.75895   2.00000  -1.75895   1.09390  -0.16516  -0.80339   1.57828  -1.97272   1.89163  -1.35456   0.49097  -2.00000  -0.49097   1.35456  -1.89163   1.97272  -1.57828   0.80339   0.16516  -1.09390   1.75895  -2.00000   1.75895  -1.09390   0.16516   0.80339  -1.57828   1.97272  -1.89163   1.35456  -0.49097  -0.49097   1.35456  -1.89163   1.97272  -1.57828   0.80339   0.16516  -1.09390   1.75895     ... ... ..... ....... ......... ........... .............
E25u *   2.00000  -1.85299   1.43357  -0.80339   0.05511   0.70128  -1.35456   1.80871  -1.99696   1.89163  -1.50821   0.90307  -0.16516  -0.59703   1.27145  -1.75895   1.98786  -1.92454   1.57828  -1.00000   0.27471   0.49097  -1.18447   1.70384  -1.97272   1.95159  -1.64356   1.09390  -0.38342  -2.00000   0.38342  -1.09390   1.64356  -1.95159   1.97272  -1.70384   1.18447  -0.49097  -0.27471   1.00000  -1.57828   1.92454  -1.98786   1.75895  -1.27145   0.59703   0.16516  -0.90307   1.50821  -1.89163   1.99696  -1.80871   1.35456  -0.70128  -0.05511   0.80339  -1.43357   1.85299     ... ... ..... ....... ......... ........... .............
E26u *   2.00000  -1.92454   1.70384  -1.35456   0.90307  -0.38342  -0.16516   0.70128  -1.18447   1.57828  -1.85299   1.98786  -1.97272   1.80871  -1.50821   1.09390  -0.59703   0.05511   0.49097  -1.00000   1.43357  -1.75895   1.95159  -1.99696   1.89163  -1.64356   1.27145  -0.80339   0.27471  -2.00000  -0.27471   0.80339  -1.27145   1.64356  -1.89163   1.99696  -1.95159   1.75895  -1.43357   1.00000  -0.49097  -0.05511   0.59703  -1.09390   1.50821  -1.80871   1.97272  -1.98786   1.85299  -1.57828   1.18447  -0.70128   0.16516   0.38342  -0.90307   1.35456  -1.70384   1.92454     ... ... ..... ....... ......... ........... .............
E27u *   2.00000  -1.97272   1.89163  -1.75895   1.57828  -1.35456   1.09390  -0.80339   0.49097  -0.16516  -0.16516   0.49097  -0.80339   1.09390  -1.35456   1.57828  -1.75895   1.89163  -1.97272   2.00000  -1.97272   1.89163  -1.75895   1.57828  -1.35456   1.09390  -0.80339   0.49097  -0.16516  -2.00000   0.16516  -0.49097   0.80339  -1.09390   1.35456  -1.57828   1.75895  -1.89163   1.97272  -2.00000   1.97272  -1.89163   1.75895  -1.57828   1.35456  -1.09390   0.80339  -0.49097   0.16516   0.16516  -0.49097   0.80339  -1.09390   1.35456  -1.57828   1.75895  -1.89163   1.97272     ... ... ..... ....... ......... ........... .............
E28u *   2.00000  -1.99696   1.98786  -1.97272   1.95159  -1.92454   1.89163  -1.85299   1.80871  -1.75895   1.70384  -1.64356   1.57828  -1.50821   1.43357  -1.35456   1.27145  -1.18447   1.09390  -1.00000   0.90307  -0.80339   0.70128  -0.59703   0.49097  -0.38342   0.27471  -0.16516   0.05511  -2.00000  -0.05511   0.16516  -0.27471   0.38342  -0.49097   0.59703  -0.70128   0.80339  -0.90307   1.00000  -1.09390   1.18447  -1.27145   1.35456  -1.43357   1.50821  -1.57828   1.64356  -1.70384   1.75895  -1.80871   1.85299  -1.89163   1.92454  -1.95159   1.97272  -1.98786   1.99696     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.996963032867 = 2*cos(2*π/114) = 2*cos(π/57)
                               1.987861354636 = 2*cos(4*π/114) = 2*cos(2*π/57)
                               1.972722606805 = 2*cos(6*π/114) = 2*cos(π/19)
                               1.951592765255 = 2*cos(8*π/114) = 2*cos(4*π/57)
                               1.924536000618 = 2*cos(10*π/114) = 2*cos(5*π/57)
                               1.891634483401 = 2*cos(12*π/114) = 2*cos(2*π/19)
                               1.852988134430 = 2*cos(14*π/114) = 2*cos(7*π/57)
                               1.808714321395 = 2*cos(16*π/114) = 2*cos(8*π/57)
                               1.758947502413 = 2*cos(18*π/114) = 2*cos(3*π/19)
                               1.703838817677 = 2*cos(20*π/114) = 2*cos(10*π/57)
                               1.643555630450 = 2*cos(22*π/114) = 2*cos(11*π/57)
                               1.578281018793 = 2*cos(24*π/114) = 2*cos(4*π/19)
                               1.508213219554 = 2*cos(26*π/114) = 2*cos(13*π/57)
                               1.433565026337 = 2*cos(28*π/114) = 2*cos(14*π/57)
                               1.354563143251 = 2*cos(30*π/114) = 2*cos(5*π/19)
                               1.271447496420 = 2*cos(32*π/114) = 2*cos(16*π/57)
                               1.184470505330 = 2*cos(34*π/114) = 2*cos(17*π/57)
                               1.093896316245 = 2*cos(36*π/114) = 2*cos(6*π/19)
                               0.903066716622 = 2*cos(40*π/114) = 2*cos(20*π/57)
                               0.803390849306 = 2*cos(42*π/114) = 2*cos(7*π/19)
                               0.701275110385 = 2*cos(44*π/114) = 2*cos(22*π/57)
                               0.597029622003 = 2*cos(46*π/114) = 2*cos(23*π/57)
                               0.490970974281 = 2*cos(48*π/114) = 2*cos(8*π/19)
                               0.383421263847 = 2*cos(50*π/114) = 2*cos(25*π/57)
                               0.274707115637 = 2*cos(52*π/114) = 2*cos(26*π/57)
                               0.165158690944 = 2*cos(54*π/114) = 2*cos(9*π/19)
                               0.055108684736 = 2*cos(56*π/114) = 2*cos(28*π/57)



 Symmetry of Rotations and Cartesian products

Ag   R+d+g+i  Rz, z2, z4, z6 
E1g  R+d+g+i  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 
E2g  d+g+i    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E3g  g+i      {xz(x2–3y2), yz(3x2y2)}, {xz3(x2–3y2), yz3(3x2y2)} 
E4g  g+i      {(x2y2)2–2x2y2, xy(x2y2)}, {z2((x2y2)2–4x2y2), xyz2(x2y2)} 
E5g  i        {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)} 
E6g  i        {x2(x2–3y2)2y2(3x2y2)2, xy(x2–3y2)(3x2y2)} 
Au   p+f+h    z, z3, z5 
E1u  p+f+h    {x, y}, {xz2, yz2}, {xz4, yz4} 
E2u  f+h      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E3u  f+h      {x(x2–3y2), y(3x2y2)}, {xz2(x2–3y2), yz2(3x2y2)} 
E4u  h        {z((x2y2)2–4x2y2), xyz(x2y2)} 
E5u  h        {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)} 

 Notes:

    α  The order of the S114 point group is 114, and the order of the principal axis is 114.

    β  The S114 point group could also be named C57i, because the S114 axis is identical to a roto-inversion axis of order 57.

    γ  This is an Abelian point group (the commutative law holds between all symmetry operations).
       The S114 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.

    δ  Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters.
       These 112 cases have been combined into 56 two-dimensional representations that are no longer irreducible but have real-valued characters.
       Accordingly, 56 pairs of left and right rotations have been combined into one two-membered pseudo-class each.

    ε  The 56 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.

    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.

This Character Table for the S114 point group was created by Gernot Katzer.

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