C47h E 2 C47 2 C47^2 2 C47^3 2 C47^4 2 C47^5 2 C47^6 2 C47^7 2 C47^8 2 C47^9 2 C47^10 2 C47^11 2 C47^12 2 C47^13 2 C47^14 2 C47^15 2 C47^16 2 C47^17 2 C47^18 2 C47^19 2 C47^20 2 C47^21 2 C47^22 2 C47^23 sh 2 S47 2 S47^3 2 S47^5 2 S47^7 2 S47^9 2 S47^11 2 S47^13 2 S47^15 2 S47^17 2 S47^19 2 S47^21 2 S47^23 2 S47^25 2 S47^27 2 S47^29 2 S47^31 2 S47^33 2 S47^35 2 S47^37 2 S47^39 2 S47^41 2 S47^43 2 S47^45 <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 ..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 ... ..T ..... ......T ......... ..........T ............. E1' * 2.00000 1.98215 1.92894 1.84130 1.72080 1.56960 1.39038 1.18636 0.96116 0.71882 0.46364 0.20019 -0.06683 -0.33266 -0.59255 -0.84187 -1.07616 -1.29126 -1.48330 -1.64888 -1.78504 -1.88934 -1.95992 -1.99553 2.00000 1.98215 1.84130 1.56960 1.18636 0.71882 0.20019 -0.33266 -0.84187 -1.29126 -1.64888 -1.88934 -1.99553 -1.95992 -1.78504 -1.48330 -1.07616 -0.59255 -0.06683 0.46364 0.96116 1.39038 1.72080 1.92894 ... TT. ..... ....TT. ......... ........TT. ............. E1" * 2.00000 1.98215 1.92894 1.84130 1.72080 1.56960 1.39038 1.18636 0.96116 0.71882 0.46364 0.20019 -0.06683 -0.33266 -0.59255 -0.84187 -1.07616 -1.29126 -1.48330 -1.64888 -1.78504 -1.88934 -1.95992 -1.99553 -2.00000 -1.98215 -1.84130 -1.56960 -1.18636 -0.71882 -0.20019 0.33266 0.84187 1.29126 1.64888 1.88934 1.99553 1.95992 1.78504 1.48330 1.07616 0.59255 0.06683 -0.46364 -0.96116 -1.39038 -1.72080 -1.92894 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2' * 2.00000 1.92894 1.72080 1.39038 0.96116 0.46364 -0.06683 -0.59255 -1.07616 -1.48330 -1.78504 -1.95992 -1.99553 -1.88934 -1.64888 -1.29126 -0.84187 -0.33266 0.20019 0.71882 1.18636 1.56960 1.84130 1.98215 2.00000 1.92894 1.39038 0.46364 -0.59255 -1.48330 -1.95992 -1.88934 -1.29126 -0.33266 0.71882 1.56960 1.98215 1.84130 1.18636 0.20019 -0.84187 -1.64888 -1.99553 -1.78504 -1.07616 -0.06683 0.96116 1.72080 ... ... TT... ....... ....TT... ........... ........TT... E2" * 2.00000 1.92894 1.72080 1.39038 0.96116 0.46364 -0.06683 -0.59255 -1.07616 -1.48330 -1.78504 -1.95992 -1.99553 -1.88934 -1.64888 -1.29126 -0.84187 -0.33266 0.20019 0.71882 1.18636 1.56960 1.84130 1.98215 -2.00000 -1.92894 -1.39038 -0.46364 0.59255 1.48330 1.95992 1.88934 1.29126 0.33266 -0.71882 -1.56960 -1.98215 -1.84130 -1.18636 -0.20019 0.84187 1.64888 1.99553 1.78504 1.07616 0.06683 -0.96116 -1.72080 ... ... ..... ..TT... ......... ......TT... ............. E3' * 2.00000 1.84130 1.39038 0.71882 -0.06683 -0.84187 -1.48330 -1.88934 -1.99553 -1.78504 -1.29126 -0.59255 0.20019 0.96116 1.56960 1.92894 1.98215 1.72080 1.18636 0.46364 -0.33266 -1.07616 -1.64888 -1.95992 2.00000 1.84130 0.71882 -0.84187 -1.88934 -1.78504 -0.59255 0.96116 1.92894 1.72080 0.46364 -1.07616 -1.95992 -1.64888 -0.33266 1.18636 1.98215 1.56960 0.20019 -1.29126 -1.99553 -1.48330 -0.06683 1.39038 ... ... ..... TT..... ......... ....TT..... ............. E3" * 2.00000 1.84130 1.39038 0.71882 -0.06683 -0.84187 -1.48330 -1.88934 -1.99553 -1.78504 -1.29126 -0.59255 0.20019 0.96116 1.56960 1.92894 1.98215 1.72080 1.18636 0.46364 -0.33266 -1.07616 -1.64888 -1.95992 -2.00000 -1.84130 -0.71882 0.84187 1.88934 1.78504 0.59255 -0.96116 -1.92894 -1.72080 -0.46364 1.07616 1.95992 1.64888 0.33266 -1.18636 -1.98215 -1.56960 -0.20019 1.29126 1.99553 1.48330 0.06683 -1.39038 ... ... ..... ....... ..TT..... ........... ......TT..... E4' * 2.00000 1.72080 0.96116 -0.06683 -1.07616 -1.78504 -1.99553 -1.64888 -0.84187 0.20019 1.18636 1.84130 1.98215 1.56960 0.71882 -0.33266 -1.29126 -1.88934 -1.95992 -1.48330 -0.59255 0.46364 1.39038 1.92894 2.00000 1.72080 -0.06683 -1.78504 -1.64888 0.20019 1.84130 1.56960 -0.33266 -1.88934 -1.48330 0.46364 1.92894 1.39038 -0.59255 -1.95992 -1.29126 0.71882 1.98215 1.18636 -0.84187 -1.99553 -1.07616 0.96116 ... ... ..... ....... TT....... ........... ....TT....... E4" * 2.00000 1.72080 0.96116 -0.06683 -1.07616 -1.78504 -1.99553 -1.64888 -0.84187 0.20019 1.18636 1.84130 1.98215 1.56960 0.71882 -0.33266 -1.29126 -1.88934 -1.95992 -1.48330 -0.59255 0.46364 1.39038 1.92894 -2.00000 -1.72080 0.06683 1.78504 1.64888 -0.20019 -1.84130 -1.56960 0.33266 1.88934 1.48330 -0.46364 -1.92894 -1.39038 0.59255 1.95992 1.29126 -0.71882 -1.98215 -1.18636 0.84187 1.99553 1.07616 -0.96116 ... ... ..... ....... ......... ..TT....... ............. E5' * 2.00000 1.56960 0.46364 -0.84187 -1.78504 -1.95992 -1.29126 -0.06683 1.18636 1.92894 1.84130 0.96116 -0.33266 -1.48330 -1.99553 -1.64888 -0.59255 0.71882 1.72080 1.98215 1.39038 0.20019 -1.07616 -1.88934 2.00000 1.56960 -0.84187 -1.95992 -0.06683 1.92894 0.96116 -1.48330 -1.64888 0.71882 1.98215 0.20019 -1.88934 -1.07616 1.39038 1.72080 -0.59255 -1.99553 -0.33266 1.84130 1.18636 -1.29126 -1.78504 0.46364 ... ... ..... ....... ......... TT......... ............. E5" * 2.00000 1.56960 0.46364 -0.84187 -1.78504 -1.95992 -1.29126 -0.06683 1.18636 1.92894 1.84130 0.96116 -0.33266 -1.48330 -1.99553 -1.64888 -0.59255 0.71882 1.72080 1.98215 1.39038 0.20019 -1.07616 -1.88934 -2.00000 -1.56960 0.84187 1.95992 0.06683 -1.92894 -0.96116 1.48330 1.64888 -0.71882 -1.98215 -0.20019 1.88934 1.07616 -1.39038 -1.72080 0.59255 1.99553 0.33266 -1.84130 -1.18636 1.29126 1.78504 -0.46364 ... ... ..... ....... ......... ........... ..TT......... E6' * 2.00000 1.39038 -0.06683 -1.48330 -1.99553 -1.29126 0.20019 1.56960 1.98215 1.18636 -0.33266 -1.64888 -1.95992 -1.07616 0.46364 1.72080 1.92894 0.96116 -0.59255 -1.78504 -1.88934 -0.84187 0.71882 1.84130 2.00000 1.39038 -1.48330 -1.29126 1.56960 1.18636 -1.64888 -1.07616 1.72080 0.96116 -1.78504 -0.84187 1.84130 0.71882 -1.88934 -0.59255 1.92894 0.46364 -1.95992 -0.33266 1.98215 0.20019 -1.99553 -0.06683 ... ... ..... ....... ......... ........... TT........... E6" * 2.00000 1.39038 -0.06683 -1.48330 -1.99553 -1.29126 0.20019 1.56960 1.98215 1.18636 -0.33266 -1.64888 -1.95992 -1.07616 0.46364 1.72080 1.92894 0.96116 -0.59255 -1.78504 -1.88934 -0.84187 0.71882 1.84130 -2.00000 -1.39038 1.48330 1.29126 -1.56960 -1.18636 1.64888 1.07616 -1.72080 -0.96116 1.78504 0.84187 -1.84130 -0.71882 1.88934 0.59255 -1.92894 -0.46364 1.95992 0.33266 -1.98215 -0.20019 1.99553 0.06683 ... ... ..... ....... ......... ........... ............. E7' * 2.00000 1.18636 -0.59255 -1.88934 -1.64888 -0.06683 1.56960 1.92894 0.71882 -1.07616 -1.99553 -1.29126 0.46364 1.84130 1.72080 0.20019 -1.48330 -1.95992 -0.84187 0.96116 1.98215 1.39038 -0.33266 -1.78504 2.00000 1.18636 -1.88934 -0.06683 1.92894 -1.07616 -1.29126 1.84130 0.20019 -1.95992 0.96116 1.39038 -1.78504 -0.33266 1.98215 -0.84187 -1.48330 1.72080 0.46364 -1.99553 0.71882 1.56960 -1.64888 -0.59255 ... ... ..... ....... ......... ........... ............. E7" * 2.00000 1.18636 -0.59255 -1.88934 -1.64888 -0.06683 1.56960 1.92894 0.71882 -1.07616 -1.99553 -1.29126 0.46364 1.84130 1.72080 0.20019 -1.48330 -1.95992 -0.84187 0.96116 1.98215 1.39038 -0.33266 -1.78504 -2.00000 -1.18636 1.88934 0.06683 -1.92894 1.07616 1.29126 -1.84130 -0.20019 1.95992 -0.96116 -1.39038 1.78504 0.33266 -1.98215 0.84187 1.48330 -1.72080 -0.46364 1.99553 -0.71882 -1.56960 1.64888 0.59255 ... ... ..... ....... ......... ........... ............. E8' * 2.00000 0.96116 -1.07616 -1.99553 -0.84187 1.18636 1.98215 0.71882 -1.29126 -1.95992 -0.59255 1.39038 1.92894 0.46364 -1.48330 -1.88934 -0.33266 1.56960 1.84130 0.20019 -1.64888 -1.78504 -0.06683 1.72080 2.00000 0.96116 -1.99553 1.18636 0.71882 -1.95992 1.39038 0.46364 -1.88934 1.56960 0.20019 -1.78504 1.72080 -0.06683 -1.64888 1.84130 -0.33266 -1.48330 1.92894 -0.59255 -1.29126 1.98215 -0.84187 -1.07616 ... ... ..... ....... ......... ........... ............. E8" * 2.00000 0.96116 -1.07616 -1.99553 -0.84187 1.18636 1.98215 0.71882 -1.29126 -1.95992 -0.59255 1.39038 1.92894 0.46364 -1.48330 -1.88934 -0.33266 1.56960 1.84130 0.20019 -1.64888 -1.78504 -0.06683 1.72080 -2.00000 -0.96116 1.99553 -1.18636 -0.71882 1.95992 -1.39038 -0.46364 1.88934 -1.56960 -0.20019 1.78504 -1.72080 0.06683 1.64888 -1.84130 0.33266 1.48330 -1.92894 0.59255 1.29126 -1.98215 0.84187 1.07616 ... ... ..... ....... ......... ........... ............. E9' * 2.00000 0.71882 -1.48330 -1.78504 0.20019 1.92894 1.18636 -1.07616 -1.95992 -0.33266 1.72080 1.56960 -0.59255 -1.99553 -0.84187 1.39038 1.84130 -0.06683 -1.88934 -1.29126 0.96116 1.98215 0.46364 -1.64888 2.00000 0.71882 -1.78504 1.92894 -1.07616 -0.33266 1.56960 -1.99553 1.39038 -0.06683 -1.29126 1.98215 -1.64888 0.46364 0.96116 -1.88934 1.84130 -0.84187 -0.59255 1.72080 -1.95992 1.18636 0.20019 -1.48330 ... ... ..... ....... ......... ........... ............. E9" * 2.00000 0.71882 -1.48330 -1.78504 0.20019 1.92894 1.18636 -1.07616 -1.95992 -0.33266 1.72080 1.56960 -0.59255 -1.99553 -0.84187 1.39038 1.84130 -0.06683 -1.88934 -1.29126 0.96116 1.98215 0.46364 -1.64888 -2.00000 -0.71882 1.78504 -1.92894 1.07616 0.33266 -1.56960 1.99553 -1.39038 0.06683 1.29126 -1.98215 1.64888 -0.46364 -0.96116 1.88934 -1.84130 0.84187 0.59255 -1.72080 1.95992 -1.18636 -0.20019 1.48330 ... ... ..... ....... ......... ........... ............. E10' * 2.00000 0.46364 -1.78504 -1.29126 1.18636 1.84130 -0.33266 -1.99553 -0.59255 1.72080 1.39038 -1.07616 -1.88934 0.20019 1.98215 0.71882 -1.64888 -1.48330 0.96116 1.92894 -0.06683 -1.95992 -0.84187 1.56960 2.00000 0.46364 -1.29126 1.84130 -1.99553 1.72080 -1.07616 0.20019 0.71882 -1.48330 1.92894 -1.95992 1.56960 -0.84187 -0.06683 0.96116 -1.64888 1.98215 -1.88934 1.39038 -0.59255 -0.33266 1.18636 -1.78504 ... ... ..... ....... ......... ........... ............. E10" * 2.00000 0.46364 -1.78504 -1.29126 1.18636 1.84130 -0.33266 -1.99553 -0.59255 1.72080 1.39038 -1.07616 -1.88934 0.20019 1.98215 0.71882 -1.64888 -1.48330 0.96116 1.92894 -0.06683 -1.95992 -0.84187 1.56960 -2.00000 -0.46364 1.29126 -1.84130 1.99553 -1.72080 1.07616 -0.20019 -0.71882 1.48330 -1.92894 1.95992 -1.56960 0.84187 0.06683 -0.96116 1.64888 -1.98215 1.88934 -1.39038 0.59255 0.33266 -1.18636 1.78504 ... ... ..... ....... ......... ........... ............. E11' * 2.00000 0.20019 -1.95992 -0.59255 1.84130 0.96116 -1.64888 -1.29126 1.39038 1.56960 -1.07616 -1.78504 0.71882 1.92894 -0.33266 -1.99553 -0.06683 1.98215 0.46364 -1.88934 -0.84187 1.72080 1.18636 -1.48330 2.00000 0.20019 -0.59255 0.96116 -1.29126 1.56960 -1.78504 1.92894 -1.99553 1.98215 -1.88934 1.72080 -1.48330 1.18636 -0.84187 0.46364 -0.06683 -0.33266 0.71882 -1.07616 1.39038 -1.64888 1.84130 -1.95992 ... ... ..... ....... ......... ........... ............. E11" * 2.00000 0.20019 -1.95992 -0.59255 1.84130 0.96116 -1.64888 -1.29126 1.39038 1.56960 -1.07616 -1.78504 0.71882 1.92894 -0.33266 -1.99553 -0.06683 1.98215 0.46364 -1.88934 -0.84187 1.72080 1.18636 -1.48330 -2.00000 -0.20019 0.59255 -0.96116 1.29126 -1.56960 1.78504 -1.92894 1.99553 -1.98215 1.88934 -1.72080 1.48330 -1.18636 0.84187 -0.46364 0.06683 0.33266 -0.71882 1.07616 -1.39038 1.64888 -1.84130 1.95992 ... ... ..... ....... ......... ........... ............. E12' * 2.00000 -0.06683 -1.99553 0.20019 1.98215 -0.33266 -1.95992 0.46364 1.92894 -0.59255 -1.88934 0.71882 1.84130 -0.84187 -1.78504 0.96116 1.72080 -1.07616 -1.64888 1.18636 1.56960 -1.29126 -1.48330 1.39038 2.00000 -0.06683 0.20019 -0.33266 0.46364 -0.59255 0.71882 -0.84187 0.96116 -1.07616 1.18636 -1.29126 1.39038 -1.48330 1.56960 -1.64888 1.72080 -1.78504 1.84130 -1.88934 1.92894 -1.95992 1.98215 -1.99553 ... ... ..... ....... ......... ........... ............. E12" * 2.00000 -0.06683 -1.99553 0.20019 1.98215 -0.33266 -1.95992 0.46364 1.92894 -0.59255 -1.88934 0.71882 1.84130 -0.84187 -1.78504 0.96116 1.72080 -1.07616 -1.64888 1.18636 1.56960 -1.29126 -1.48330 1.39038 -2.00000 0.06683 -0.20019 0.33266 -0.46364 0.59255 -0.71882 0.84187 -0.96116 1.07616 -1.18636 1.29126 -1.39038 1.48330 -1.56960 1.64888 -1.72080 1.78504 -1.84130 1.88934 -1.92894 1.95992 -1.98215 1.99553 ... ... ..... ....... ......... ........... ............. E13' * 2.00000 -0.33266 -1.88934 0.96116 1.56960 -1.48330 -1.07616 1.84130 0.46364 -1.99553 0.20019 1.92894 -0.84187 -1.64888 1.39038 1.18636 -1.78504 -0.59255 1.98215 -0.06683 -1.95992 0.71882 1.72080 -1.29126 2.00000 -0.33266 0.96116 -1.48330 1.84130 -1.99553 1.92894 -1.64888 1.18636 -0.59255 -0.06683 0.71882 -1.29126 1.72080 -1.95992 1.98215 -1.78504 1.39038 -0.84187 0.20019 0.46364 -1.07616 1.56960 -1.88934 ... ... ..... ....... ......... ........... ............. E13" * 2.00000 -0.33266 -1.88934 0.96116 1.56960 -1.48330 -1.07616 1.84130 0.46364 -1.99553 0.20019 1.92894 -0.84187 -1.64888 1.39038 1.18636 -1.78504 -0.59255 1.98215 -0.06683 -1.95992 0.71882 1.72080 -1.29126 -2.00000 0.33266 -0.96116 1.48330 -1.84130 1.99553 -1.92894 1.64888 -1.18636 0.59255 0.06683 -0.71882 1.29126 -1.72080 1.95992 -1.98215 1.78504 -1.39038 0.84187 -0.20019 -0.46364 1.07616 -1.56960 1.88934 ... ... ..... ....... ......... ........... ............. E14' * 2.00000 -0.59255 -1.64888 1.56960 0.71882 -1.99553 0.46364 1.72080 -1.48330 -0.84187 1.98215 -0.33266 -1.78504 1.39038 0.96116 -1.95992 0.20019 1.84130 -1.29126 -1.07616 1.92894 -0.06683 -1.88934 1.18636 2.00000 -0.59255 1.56960 -1.99553 1.72080 -0.84187 -0.33266 1.39038 -1.95992 1.84130 -1.07616 -0.06683 1.18636 -1.88934 1.92894 -1.29126 0.20019 0.96116 -1.78504 1.98215 -1.48330 0.46364 0.71882 -1.64888 ... ... ..... ....... ......... ........... ............. E14" * 2.00000 -0.59255 -1.64888 1.56960 0.71882 -1.99553 0.46364 1.72080 -1.48330 -0.84187 1.98215 -0.33266 -1.78504 1.39038 0.96116 -1.95992 0.20019 1.84130 -1.29126 -1.07616 1.92894 -0.06683 -1.88934 1.18636 -2.00000 0.59255 -1.56960 1.99553 -1.72080 0.84187 0.33266 -1.39038 1.95992 -1.84130 1.07616 0.06683 -1.18636 1.88934 -1.92894 1.29126 -0.20019 -0.96116 1.78504 -1.98215 1.48330 -0.46364 -0.71882 1.64888 ... ... ..... ....... ......... ........... ............. E15' * 2.00000 -0.84187 -1.29126 1.92894 -0.33266 -1.64888 1.72080 0.20019 -1.88934 1.39038 0.71882 -1.99553 0.96116 1.18636 -1.95992 0.46364 1.56960 -1.78504 -0.06683 1.84130 -1.48330 -0.59255 1.98215 -1.07616 2.00000 -0.84187 1.92894 -1.64888 0.20019 1.39038 -1.99553 1.18636 0.46364 -1.78504 1.84130 -0.59255 -1.07616 1.98215 -1.48330 -0.06683 1.56960 -1.95992 0.96116 0.71882 -1.88934 1.72080 -0.33266 -1.29126 ... ... ..... ....... ......... ........... ............. E15" * 2.00000 -0.84187 -1.29126 1.92894 -0.33266 -1.64888 1.72080 0.20019 -1.88934 1.39038 0.71882 -1.99553 0.96116 1.18636 -1.95992 0.46364 1.56960 -1.78504 -0.06683 1.84130 -1.48330 -0.59255 1.98215 -1.07616 -2.00000 0.84187 -1.92894 1.64888 -0.20019 -1.39038 1.99553 -1.18636 -0.46364 1.78504 -1.84130 0.59255 1.07616 -1.98215 1.48330 0.06683 -1.56960 1.95992 -0.96116 -0.71882 1.88934 -1.72080 0.33266 1.29126 ... ... ..... ....... ......... ........... ............. E16' * 2.00000 -1.07616 -0.84187 1.98215 -1.29126 -0.59255 1.92894 -1.48330 -0.33266 1.84130 -1.64888 -0.06683 1.72080 -1.78504 0.20019 1.56960 -1.88934 0.46364 1.39038 -1.95992 0.71882 1.18636 -1.99553 0.96116 2.00000 -1.07616 1.98215 -0.59255 -1.48330 1.84130 -0.06683 -1.78504 1.56960 0.46364 -1.95992 1.18636 0.96116 -1.99553 0.71882 1.39038 -1.88934 0.20019 1.72080 -1.64888 -0.33266 1.92894 -1.29126 -0.84187 ... ... ..... ....... ......... ........... ............. E16" * 2.00000 -1.07616 -0.84187 1.98215 -1.29126 -0.59255 1.92894 -1.48330 -0.33266 1.84130 -1.64888 -0.06683 1.72080 -1.78504 0.20019 1.56960 -1.88934 0.46364 1.39038 -1.95992 0.71882 1.18636 -1.99553 0.96116 -2.00000 1.07616 -1.98215 0.59255 1.48330 -1.84130 0.06683 1.78504 -1.56960 -0.46364 1.95992 -1.18636 -0.96116 1.99553 -0.71882 -1.39038 1.88934 -0.20019 -1.72080 1.64888 0.33266 -1.92894 1.29126 0.84187 ... ... ..... ....... ......... ........... ............. E17' * 2.00000 -1.29126 -0.33266 1.72080 -1.88934 0.71882 0.96116 -1.95992 1.56960 -0.06683 -1.48330 1.98215 -1.07616 -0.59255 1.84130 -1.78504 0.46364 1.18636 -1.99553 1.39038 0.20019 -1.64888 1.92894 -0.84187 2.00000 -1.29126 1.72080 0.71882 -1.95992 -0.06683 1.98215 -0.59255 -1.78504 1.18636 1.39038 -1.64888 -0.84187 1.92894 0.20019 -1.99553 0.46364 1.84130 -1.07616 -1.48330 1.56960 0.96116 -1.88934 -0.33266 ... ... ..... ....... ......... ........... ............. E17" * 2.00000 -1.29126 -0.33266 1.72080 -1.88934 0.71882 0.96116 -1.95992 1.56960 -0.06683 -1.48330 1.98215 -1.07616 -0.59255 1.84130 -1.78504 0.46364 1.18636 -1.99553 1.39038 0.20019 -1.64888 1.92894 -0.84187 -2.00000 1.29126 -1.72080 -0.71882 1.95992 0.06683 -1.98215 0.59255 1.78504 -1.18636 -1.39038 1.64888 0.84187 -1.92894 -0.20019 1.99553 -0.46364 -1.84130 1.07616 1.48330 -1.56960 -0.96116 1.88934 0.33266 ... ... ..... ....... ......... ........... ............. E18' * 2.00000 -1.48330 0.20019 1.18636 -1.95992 1.72080 -0.59255 -0.84187 1.84130 -1.88934 0.96116 0.46364 -1.64888 1.98215 -1.29126 -0.06683 1.39038 -1.99553 1.56960 -0.33266 -1.07616 1.92894 -1.78504 0.71882 2.00000 -1.48330 1.18636 1.72080 -0.84187 -1.88934 0.46364 1.98215 -0.06683 -1.99553 -0.33266 1.92894 0.71882 -1.78504 -1.07616 1.56960 1.39038 -1.29126 -1.64888 0.96116 1.84130 -0.59255 -1.95992 0.20019 ... ... ..... ....... ......... ........... ............. E18" * 2.00000 -1.48330 0.20019 1.18636 -1.95992 1.72080 -0.59255 -0.84187 1.84130 -1.88934 0.96116 0.46364 -1.64888 1.98215 -1.29126 -0.06683 1.39038 -1.99553 1.56960 -0.33266 -1.07616 1.92894 -1.78504 0.71882 -2.00000 1.48330 -1.18636 -1.72080 0.84187 1.88934 -0.46364 -1.98215 0.06683 1.99553 0.33266 -1.92894 -0.71882 1.78504 1.07616 -1.56960 -1.39038 1.29126 1.64888 -0.96116 -1.84130 0.59255 1.95992 -0.20019 ... ... ..... ....... ......... ........... ............. E19' * 2.00000 -1.64888 0.71882 0.46364 -1.48330 1.98215 -1.78504 0.96116 0.20019 -1.29126 1.92894 -1.88934 1.18636 -0.06683 -1.07616 1.84130 -1.95992 1.39038 -0.33266 -0.84187 1.72080 -1.99553 1.56960 -0.59255 2.00000 -1.64888 0.46364 1.98215 0.96116 -1.29126 -1.88934 -0.06683 1.84130 1.39038 -0.84187 -1.99553 -0.59255 1.56960 1.72080 -0.33266 -1.95992 -1.07616 1.18636 1.92894 0.20019 -1.78504 -1.48330 0.71882 ... ... ..... ....... ......... ........... ............. E19" * 2.00000 -1.64888 0.71882 0.46364 -1.48330 1.98215 -1.78504 0.96116 0.20019 -1.29126 1.92894 -1.88934 1.18636 -0.06683 -1.07616 1.84130 -1.95992 1.39038 -0.33266 -0.84187 1.72080 -1.99553 1.56960 -0.59255 -2.00000 1.64888 -0.46364 -1.98215 -0.96116 1.29126 1.88934 0.06683 -1.84130 -1.39038 0.84187 1.99553 0.59255 -1.56960 -1.72080 0.33266 1.95992 1.07616 -1.18636 -1.92894 -0.20019 1.78504 1.48330 -0.71882 ... ... ..... ....... ......... ........... ............. E20' * 2.00000 -1.78504 1.18636 -0.33266 -0.59255 1.39038 -1.88934 1.98215 -1.64888 0.96116 -0.06683 -0.84187 1.56960 -1.95992 1.92894 -1.48330 0.71882 0.20019 -1.07616 1.72080 -1.99553 1.84130 -1.29126 0.46364 2.00000 -1.78504 -0.33266 1.39038 1.98215 0.96116 -0.84187 -1.95992 -1.48330 0.20019 1.72080 1.84130 0.46364 -1.29126 -1.99553 -1.07616 0.71882 1.92894 1.56960 -0.06683 -1.64888 -1.88934 -0.59255 1.18636 ... ... ..... ....... ......... ........... ............. E20" * 2.00000 -1.78504 1.18636 -0.33266 -0.59255 1.39038 -1.88934 1.98215 -1.64888 0.96116 -0.06683 -0.84187 1.56960 -1.95992 1.92894 -1.48330 0.71882 0.20019 -1.07616 1.72080 -1.99553 1.84130 -1.29126 0.46364 -2.00000 1.78504 0.33266 -1.39038 -1.98215 -0.96116 0.84187 1.95992 1.48330 -0.20019 -1.72080 -1.84130 -0.46364 1.29126 1.99553 1.07616 -0.71882 -1.92894 -1.56960 0.06683 1.64888 1.88934 0.59255 -1.18636 ... ... ..... ....... ......... ........... ............. E21' * 2.00000 -1.88934 1.56960 -1.07616 0.46364 0.20019 -0.84187 1.39038 -1.78504 1.98215 -1.95992 1.72080 -1.29126 0.71882 -0.06683 -0.59255 1.18636 -1.64888 1.92894 -1.99553 1.84130 -1.48330 0.96116 -0.33266 2.00000 -1.88934 -1.07616 0.20019 1.39038 1.98215 1.72080 0.71882 -0.59255 -1.64888 -1.99553 -1.48330 -0.33266 0.96116 1.84130 1.92894 1.18636 -0.06683 -1.29126 -1.95992 -1.78504 -0.84187 0.46364 1.56960 ... ... ..... ....... ......... ........... ............. E21" * 2.00000 -1.88934 1.56960 -1.07616 0.46364 0.20019 -0.84187 1.39038 -1.78504 1.98215 -1.95992 1.72080 -1.29126 0.71882 -0.06683 -0.59255 1.18636 -1.64888 1.92894 -1.99553 1.84130 -1.48330 0.96116 -0.33266 -2.00000 1.88934 1.07616 -0.20019 -1.39038 -1.98215 -1.72080 -0.71882 0.59255 1.64888 1.99553 1.48330 0.33266 -0.96116 -1.84130 -1.92894 -1.18636 0.06683 1.29126 1.95992 1.78504 0.84187 -0.46364 -1.56960 ... ... ..... ....... ......... ........... ............. E22' * 2.00000 -1.95992 1.84130 -1.64888 1.39038 -1.07616 0.71882 -0.33266 -0.06683 0.46364 -0.84187 1.18636 -1.48330 1.72080 -1.88934 1.98215 -1.99553 1.92894 -1.78504 1.56960 -1.29126 0.96116 -0.59255 0.20019 2.00000 -1.95992 -1.64888 -1.07616 -0.33266 0.46364 1.18636 1.72080 1.98215 1.92894 1.56960 0.96116 0.20019 -0.59255 -1.29126 -1.78504 -1.99553 -1.88934 -1.48330 -0.84187 -0.06683 0.71882 1.39038 1.84130 ... ... ..... ....... ......... ........... ............. E22" * 2.00000 -1.95992 1.84130 -1.64888 1.39038 -1.07616 0.71882 -0.33266 -0.06683 0.46364 -0.84187 1.18636 -1.48330 1.72080 -1.88934 1.98215 -1.99553 1.92894 -1.78504 1.56960 -1.29126 0.96116 -0.59255 0.20019 -2.00000 1.95992 1.64888 1.07616 0.33266 -0.46364 -1.18636 -1.72080 -1.98215 -1.92894 -1.56960 -0.96116 -0.20019 0.59255 1.29126 1.78504 1.99553 1.88934 1.48330 0.84187 0.06683 -0.71882 -1.39038 -1.84130 ... ... ..... ....... ......... ........... ............. E23' * 2.00000 -1.99553 1.98215 -1.95992 1.92894 -1.88934 1.84130 -1.78504 1.72080 -1.64888 1.56960 -1.48330 1.39038 -1.29126 1.18636 -1.07616 0.96116 -0.84187 0.71882 -0.59255 0.46364 -0.33266 0.20019 -0.06683 2.00000 -1.99553 -1.95992 -1.88934 -1.78504 -1.64888 -1.48330 -1.29126 -1.07616 -0.84187 -0.59255 -0.33266 -0.06683 0.20019 0.46364 0.71882 0.96116 1.18636 1.39038 1.56960 1.72080 1.84130 1.92894 1.98215 ... ... ..... ....... ......... ........... ............. E23" * 2.00000 -1.99553 1.98215 -1.95992 1.92894 -1.88934 1.84130 -1.78504 1.72080 -1.64888 1.56960 -1.48330 1.39038 -1.29126 1.18636 -1.07616 0.96116 -0.84187 0.71882 -0.59255 0.46364 -0.33266 0.20019 -0.06683 -2.00000 1.99553 1.95992 1.88934 1.78504 1.64888 1.48330 1.29126 1.07616 0.84187 0.59255 0.33266 0.06683 -0.20019 -0.46364 -0.71882 -0.96116 -1.18636 -1.39038 -1.56960 -1.72080 -1.84130 -1.92894 -1.98215 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.995533757246 = 2*cos(2*π/94) = 2*cos(π/47) 1.982154976310 = 2*cos(4*π/94) = 2*cos(2*π/47) 1.959923410073 = 2*cos(6*π/94) = 2*cos(3*π/47) 1.928938350109 = 2*cos(8*π/94) = 2*cos(4*π/47) 1.889338183216 = 2*cos(10*π/94) = 2*cos(5*π/47) 1.841299773353 = 2*cos(12*π/94) = 2*cos(6*π/47) 1.785037671720 = 2*cos(14*π/94) = 2*cos(7*π/47) 1.720803158520 = 2*cos(16*π/94) = 2*cos(8*π/47) 1.648883120684 = 2*cos(18*π/94) = 2*cos(9*π/47) 1.569598770557 = 2*cos(20*π/94) = 2*cos(10*π/47) 1.483304211296 = 2*cos(22*π/94) = 2*cos(11*π/47) 1.390384855349 = 2*cos(24*π/94) = 2*cos(12*π/47) 1.291255703118 = 2*cos(26*π/94) = 2*cos(13*π/47) 1.186359489459 = 2*cos(28*π/94) = 2*cos(14*π/47) 1.076164706327 = 2*cos(30*π/94) = 2*cos(15*π/47) 0.961163510373 = 2*cos(32*π/94) = 2*cos(16*π/47) 0.841869524857 = 2*cos(34*π/94) = 2*cos(17*π/47) 0.718815545675 = 2*cos(36*π/94) = 2*cos(18*π/47) 0.592551161771 = 2*cos(38*π/94) = 2*cos(19*π/47) 0.463640300535 = 2*cos(40*π/94) = 2*cos(20*π/47) 0.332658709166 = 2*cos(42*π/94) = 2*cos(21*π/47) 0.200191383248 = 2*cos(44*π/94) = 2*cos(22*π/47) 0.066829954015 = 2*cos(46*π/94) = 2*cos(23*π/47) Symmetry of Rotations and Cartesian products A' R+d+g+i+k+m Rz, 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 {Rx, Ry}, {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 C47h point group is 94, and the order of the principal axis (S47) is 94. The group has 48 irreducible representations. β The C47h point group could also be named S47, as it contains the S47 axis as its only symmetry element. Another rare designation is C94i because the S47 axis is identical to a roto-inversion axis of order 94. γ The C47h point group is isomorphic to C94 and S94. δ The C47h point group is generated by one single symmetry element, S47. Therefore, it is a cyclic group. The canonical choice, however, is to use redundant generators: C47 and σh. ε The lowest nonvanishing multipole moment in C47h is 4 (quadrupole moment). ζ This is an Abelian point group (the commutative law holds between all symmetry operations). The C47h 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 92 cases have been combined into 46 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 46 pairs of left and right rotations have been combined into one two-membered pseudo-class each. θ The 46 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 just 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.
C45h | ||
C46h | ||
C47 C47v | C47h | D47 D47h D47d |
C48h | ||
C49h |
This Character Table for the C47h point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.