Character Table for Point Group C57h

Character table for the C_57h point group

C57h 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 sh 2 S57 2 S19 2 S57^5 2 S57^7 2 S19^3 2 S57^11 2 S57^13 2 S19^5 2 S57^17 2 S3 2 S19^7 2 S57^23 2 S57^25 2 S19^9 2 S57^29 2 S57^31 2 S19^11 2 S57^35 2 S57^37 2 S19^13 2 S57^41 2 S57^43 2 S19^15 2 S57^47 2 S57^49 2 S19^17 2 S57^53 2 S57^55 <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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ..T ... ....T ....... ........T ........... ............T 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 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ..T ..... ......T ......... ..........T ............. E1' * 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 1.98786 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. ............. E1" * 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 -1.98786 -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. ........... ..........TT. E2' * 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 1.95159 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... ........... ........TT... E2" * 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 -1.95159 -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... ............. E3' * 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 1.89163 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..... ......... ....TT..... ............. E3" * 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 -1.89163 -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..... ........... ......TT..... E4' * 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 1.80871 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 ... ... ..... ....... TT....... ........... ....TT....... E4" * 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 -1.80871 -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 ... ... ..... ....... ......... ..TT....... ............. E5' * 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 1.70384 -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 ... ... ..... ....... ......... TT......... ............. E5" * 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 -1.70384 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 ... ... ..... ....... ......... ........... ..TT......... E6' * 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 1.57828 -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 ... ... ..... ....... ......... ........... TT........... E6" * 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 -1.57828 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 ... ... ..... ....... ......... ........... ............. E7' * 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 1.43357 -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 ... ... ..... ....... ......... ........... ............. E7" * 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 -1.43357 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 ... ... ..... ....... ......... ........... ............. E8' * 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 1.27145 -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 ... ... ..... ....... ......... ........... ............. E8" * 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 -1.27145 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 ... ... ..... ....... ......... ........... ............. E9' * 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 1.09390 -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 ... ... ..... ....... ......... ........... ............. E9" * 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 -1.09390 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 ... ... ..... ....... ......... ........... ............. E10' * 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 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 ... ... ..... ....... ......... ........... ............. E10" * 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 -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 ... ... ..... ....... ......... ........... ............. E11' * 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 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 ... ... ..... ....... ......... ........... ............. E11" * 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 -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 ... ... ..... ....... ......... ........... ............. E12' * 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 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 ... ... ..... ....... ......... ........... ............. E12" * 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 -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 ... ... ..... ....... ......... ........... ............. E13' * 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 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 ... ... ..... ....... ......... ........... ............. E13" * 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 -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 ... ... ..... ....... ......... ........... ............. E14' * 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 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 ... ... ..... ....... ......... ........... ............. E14" * 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 -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 ... ... ..... ....... ......... ........... ............. E15' * 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 -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 ... ... ..... ....... ......... ........... ............. E15" * 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 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 ... ... ..... ....... ......... ........... ............. E16' * 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 -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 ... ... ..... ....... ......... ........... ............. E16" * 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 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 ... ... ..... ....... ......... ........... ............. E17' * 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 -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 ... ... ..... ....... ......... ........... ............. E17" * 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 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 ... ... ..... ....... ......... ........... ............. E18' * 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 -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 ... ... ..... ....... ......... ........... ............. E18" * 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 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 ... ... ..... ....... ......... ........... ............. E19' * 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 ... ... ..... ....... ......... ........... ............. E19" * 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 ... ... ..... ....... ......... ........... ............. E20' * 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 -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 ... ... ..... ....... ......... ........... ............. E20" * 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 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 ... ... ..... ....... ......... ........... ............. E21' * 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 -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 ... ... ..... ....... ......... ........... ............. E21" * 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 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 ... ... ..... ....... ......... ........... ............. E22' * 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 -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 ... ... ..... ....... ......... ........... ............. E22" * 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 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 ... ... ..... ....... ......... ........... ............. E23' * 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 -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 ... ... ..... ....... ......... ........... ............. E23" * 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 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 ... ... ..... ....... ......... ........... ............. E24' * 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 -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 ... ... ..... ....... ......... ........... ............. E24" * 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 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 ... ... ..... ....... ......... ........... ............. E25' * 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 -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 ... ... ..... ....... ......... ........... ............. E25" * 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 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 ... ... ..... ....... ......... ........... ............. E26' * 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 -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 ... ... ..... ....... ......... ........... ............. E26" * 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 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 ... ... ..... ....... ......... ........... ............. E27' * 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 -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 ... ... ..... ....... ......... ........... ............. E27" * 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 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 ... ... ..... ....... ......... ........... ............. E28' * 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 -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 ... ... ..... ....... ......... ........... ............. E28" * 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 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 ... ... ..... ....... ......... ........... ............. 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) 1.924536000619 = 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) 0.701275110386 = 2*cos(44*π/114) = 2*cos(22*π/57) 0.597029622003 = 2*cos(46*π/114) = 2*cos(23*π/57) 0.490970974282 = 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) 0.165158690945 = 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 A' R+d+g+i+k+m R_z, z², z⁴, z⁶ A" p+f+h+j+l z, z³, z⁵ E1' p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E1" R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2' d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E2" f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3' f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E3" g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4' g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E4" h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5' h+j+l {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)} E5" i+k+m {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6' i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E6" j+l E7' j+l E7" k+m E8' k+m E8" l E9' l E9" m E10' m Notes: α The order of the C_57h point group is 114, and the order of the principal axis (S₅₇) is 114. The group has 58 irreducible representations. β The C_57h point group could also be named S₅₇, as it contains the S₅₇ axis as its only symmetry element. Another rare designation is C_114i because the S₅₇ axis is identical to a roto-inversion axis of order 114. γ The C_57h point group is isomorphic to C₁₁₄ and S₁₁₄. δ The C_57h point group is generated by one single symmetry element, S₅₇. Therefore, it is a cyclic group. The canonical choice, however, is to use redundant generators: C₅₇ and σ_h. ε The lowest nonvanishing multipole moment in C_57h is 4 (quadrupole moment). ζ This is an Abelian point group (the commutative law holds between all symmetry operations). The C_57h 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. η 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. θ 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. ι 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. κ The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. All characters of this group can be expressed using complex numbers, elementary arithmetic operations, square roots and third roots.

This Character Table for the C_57h point group was created by Gernot Katzer.

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

	C_55h
	C_56h
C₅₇ C_57v	C_57h	D₅₇ D_57h D_57d
	C_58h
	C_59h

Character table for the C57h point group

Character table for the C_57h point group