S86 E 2 C43 2 C43^2 2 C43^3 2 C43^4 2 C43^5 2 C43^6 2 C43^7 2 C43^8 2 C43^9 2 C43^10 2 C43^11 2 C43^12 2 C43^13 2 C43^14 2 C43^15 2 C43^16 2 C43^17 2 C43^18 2 C43^19 2 C43^20 2 C43^21 i 2 S86 2 S86^3 2 S86^5 2 S86^7 2 S86^9 2 S86^11 2 S86^13 2 S86^15 2 S86^17 2 S86^19 2 S86^21 2 S86^23 2 S86^25 2 S86^27 2 S86^29 2 S86^31 2 S86^33 2 S86^35 2 S86^37 2 S86^39 2 S86^41 <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 ..T ... ....T ....... ........T ........... ............T E1g * 2.00000 1.97869 1.91520 1.81090 1.66800 1.48954 1.27935 1.04188 0.78221 0.50587 0.21874 -0.07304 -0.36327 -0.64576 -0.91448 -1.16372 -1.38815 -1.58299 -1.74410 -1.86803 -1.95215 -1.99466 2.00000 -1.99466 -1.95215 -1.86803 -1.74410 -1.58299 -1.38815 -1.16372 -0.91448 -0.64576 -0.36327 -0.07304 0.21874 0.50587 0.78221 1.04188 1.27935 1.48954 1.66800 1.81090 1.91520 1.97869 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g * 2.00000 1.91520 1.66800 1.27935 0.78221 0.21874 -0.36327 -0.91448 -1.38815 -1.74410 -1.95215 -1.99466 -1.86803 -1.58299 -1.16372 -0.64576 -0.07304 0.50587 1.04188 1.48954 1.81090 1.97869 2.00000 1.97869 1.81090 1.48954 1.04188 0.50587 -0.07304 -0.64576 -1.16372 -1.58299 -1.86803 -1.99466 -1.95215 -1.74410 -1.38815 -0.91448 -0.36327 0.21874 0.78221 1.27935 1.66800 1.91520 ... ... TT... ....... ....TT... ........... ........TT... E3g * 2.00000 1.81090 1.27935 0.50587 -0.36327 -1.16372 -1.74410 -1.99466 -1.86803 -1.38815 -0.64576 0.21874 1.04188 1.66800 1.97869 1.91520 1.48954 0.78221 -0.07304 -0.91448 -1.58299 -1.95215 2.00000 -1.95215 -1.58299 -0.91448 -0.07304 0.78221 1.48954 1.91520 1.97869 1.66800 1.04188 0.21874 -0.64576 -1.38815 -1.86803 -1.99466 -1.74410 -1.16372 -0.36327 0.50587 1.27935 1.81090 ... ... ..... ....... ..TT..... ........... ......TT..... E4g * 2.00000 1.66800 0.78221 -0.36327 -1.38815 -1.95215 -1.86803 -1.16372 -0.07304 1.04188 1.81090 1.97869 1.48954 0.50587 -0.64576 -1.58299 -1.99466 -1.74410 -0.91448 0.21874 1.27935 1.91520 2.00000 1.91520 1.27935 0.21874 -0.91448 -1.74410 -1.99466 -1.58299 -0.64576 0.50587 1.48954 1.97869 1.81090 1.04188 -0.07304 -1.16372 -1.86803 -1.95215 -1.38815 -0.36327 0.78221 1.66800 ... ... ..... ....... TT....... ........... ....TT....... E5g * 2.00000 1.48954 0.21874 -1.16372 -1.95215 -1.74410 -0.64576 0.78221 1.81090 1.91520 1.04188 -0.36327 -1.58299 -1.99466 -1.38815 -0.07304 1.27935 1.97869 1.66800 0.50587 -0.91448 -1.86803 2.00000 -1.86803 -0.91448 0.50587 1.66800 1.97869 1.27935 -0.07304 -1.38815 -1.99466 -1.58299 -0.36327 1.04188 1.91520 1.81090 0.78221 -0.64576 -1.74410 -1.95215 -1.16372 0.21874 1.48954 ... ... ..... ....... ......... ........... ..TT......... E6g * 2.00000 1.27935 -0.36327 -1.74410 -1.86803 -0.64576 1.04188 1.97869 1.48954 -0.07304 -1.58299 -1.95215 -0.91448 0.78221 1.91520 1.66800 0.21874 -1.38815 -1.99466 -1.16372 0.50587 1.81090 2.00000 1.81090 0.50587 -1.16372 -1.99466 -1.38815 0.21874 1.66800 1.91520 0.78221 -0.91448 -1.95215 -1.58299 -0.07304 1.48954 1.97869 1.04188 -0.64576 -1.86803 -1.74410 -0.36327 1.27935 ... ... ..... ....... ......... ........... TT........... E7g * 2.00000 1.04188 -0.91448 -1.99466 -1.16372 0.78221 1.97869 1.27935 -0.64576 -1.95215 -1.38815 0.50587 1.91520 1.48954 -0.36327 -1.86803 -1.58299 0.21874 1.81090 1.66800 -0.07304 -1.74410 2.00000 -1.74410 -0.07304 1.66800 1.81090 0.21874 -1.58299 -1.86803 -0.36327 1.48954 1.91520 0.50587 -1.38815 -1.95215 -0.64576 1.27935 1.97869 0.78221 -1.16372 -1.99466 -0.91448 1.04188 ... ... ..... ....... ......... ........... ............. E8g * 2.00000 0.78221 -1.38815 -1.86803 -0.07304 1.81090 1.48954 -0.64576 -1.99466 -0.91448 1.27935 1.91520 0.21874 -1.74410 -1.58299 0.50587 1.97869 1.04188 -1.16372 -1.95215 -0.36327 1.66800 2.00000 1.66800 -0.36327 -1.95215 -1.16372 1.04188 1.97869 0.50587 -1.58299 -1.74410 0.21874 1.91520 1.27935 -0.91448 -1.99466 -0.64576 1.48954 1.81090 -0.07304 -1.86803 -1.38815 0.78221 ... ... ..... ....... ......... ........... ............. E9g * 2.00000 0.50587 -1.74410 -1.38815 1.04188 1.91520 -0.07304 -1.95215 -0.91448 1.48954 1.66800 -0.64576 -1.99466 -0.36327 1.81090 1.27935 -1.16372 -1.86803 0.21874 1.97869 0.78221 -1.58299 2.00000 -1.58299 0.78221 1.97869 0.21874 -1.86803 -1.16372 1.27935 1.81090 -0.36327 -1.99466 -0.64576 1.66800 1.48954 -0.91448 -1.95215 -0.07304 1.91520 1.04188 -1.38815 -1.74410 0.50587 ... ... ..... ....... ......... ........... ............. E10g * 2.00000 0.21874 -1.95215 -0.64576 1.81090 1.04188 -1.58299 -1.38815 1.27935 1.66800 -0.91448 -1.86803 0.50587 1.97869 -0.07304 -1.99466 -0.36327 1.91520 0.78221 -1.74410 -1.16372 1.48954 2.00000 1.48954 -1.16372 -1.74410 0.78221 1.91520 -0.36327 -1.99466 -0.07304 1.97869 0.50587 -1.86803 -0.91448 1.66800 1.27935 -1.38815 -1.58299 1.04188 1.81090 -0.64576 -1.95215 0.21874 ... ... ..... ....... ......... ........... ............. E11g * 2.00000 -0.07304 -1.99466 0.21874 1.97869 -0.36327 -1.95215 0.50587 1.91520 -0.64576 -1.86803 0.78221 1.81090 -0.91448 -1.74410 1.04188 1.66800 -1.16372 -1.58299 1.27935 1.48954 -1.38815 2.00000 -1.38815 1.48954 1.27935 -1.58299 -1.16372 1.66800 1.04188 -1.74410 -0.91448 1.81090 0.78221 -1.86803 -0.64576 1.91520 0.50587 -1.95215 -0.36327 1.97869 0.21874 -1.99466 -0.07304 ... ... ..... ....... ......... ........... ............. E12g * 2.00000 -0.36327 -1.86803 1.04188 1.48954 -1.58299 -0.91448 1.91520 0.21874 -1.99466 0.50587 1.81090 -1.16372 -1.38815 1.66800 0.78221 -1.95215 -0.07304 1.97869 -0.64576 -1.74410 1.27935 2.00000 1.27935 -1.74410 -0.64576 1.97869 -0.07304 -1.95215 0.78221 1.66800 -1.38815 -1.16372 1.81090 0.50587 -1.99466 0.21874 1.91520 -0.91448 -1.58299 1.48954 1.04188 -1.86803 -0.36327 ... ... ..... ....... ......... ........... ............. E13g * 2.00000 -0.64576 -1.58299 1.66800 0.50587 -1.99466 0.78221 1.48954 -1.74410 -0.36327 1.97869 -0.91448 -1.38815 1.81090 0.21874 -1.95215 1.04188 1.27935 -1.86803 -0.07304 1.91520 -1.16372 2.00000 -1.16372 1.91520 -0.07304 -1.86803 1.27935 1.04188 -1.95215 0.21874 1.81090 -1.38815 -0.91448 1.97869 -0.36327 -1.74410 1.48954 0.78221 -1.99466 0.50587 1.66800 -1.58299 -0.64576 ... ... ..... ....... ......... ........... ............. E14g * 2.00000 -0.91448 -1.16372 1.97869 -0.64576 -1.38815 1.91520 -0.36327 -1.58299 1.81090 -0.07304 -1.74410 1.66800 0.21874 -1.86803 1.48954 0.50587 -1.95215 1.27935 0.78221 -1.99466 1.04188 2.00000 1.04188 -1.99466 0.78221 1.27935 -1.95215 0.50587 1.48954 -1.86803 0.21874 1.66800 -1.74410 -0.07304 1.81090 -1.58299 -0.36327 1.91520 -1.38815 -0.64576 1.97869 -1.16372 -0.91448 ... ... ..... ....... ......... ........... ............. E15g * 2.00000 -1.16372 -0.64576 1.91520 -1.58299 -0.07304 1.66800 -1.86803 0.50587 1.27935 -1.99466 1.04188 0.78221 -1.95215 1.48954 0.21874 -1.74410 1.81090 -0.36327 -1.38815 1.97869 -0.91448 2.00000 -0.91448 1.97869 -1.38815 -0.36327 1.81090 -1.74410 0.21874 1.48954 -1.95215 0.78221 1.04188 -1.99466 1.27935 0.50587 -1.86803 1.66800 -0.07304 -1.58299 1.91520 -0.64576 -1.16372 ... ... ..... ....... ......... ........... ............. E16g * 2.00000 -1.38815 -0.07304 1.48954 -1.99466 1.27935 0.21874 -1.58299 1.97869 -1.16372 -0.36327 1.66800 -1.95215 1.04188 0.50587 -1.74410 1.91520 -0.91448 -0.64576 1.81090 -1.86803 0.78221 2.00000 0.78221 -1.86803 1.81090 -0.64576 -0.91448 1.91520 -1.74410 0.50587 1.04188 -1.95215 1.66800 -0.36327 -1.16372 1.97869 -1.58299 0.21874 1.27935 -1.99466 1.48954 -0.07304 -1.38815 ... ... ..... ....... ......... ........... ............. E17g * 2.00000 -1.58299 0.50587 0.78221 -1.74410 1.97869 -1.38815 0.21874 1.04188 -1.86803 1.91520 -1.16372 -0.07304 1.27935 -1.95215 1.81090 -0.91448 -0.36327 1.48954 -1.99466 1.66800 -0.64576 2.00000 -0.64576 1.66800 -1.99466 1.48954 -0.36327 -0.91448 1.81090 -1.95215 1.27935 -0.07304 -1.16372 1.91520 -1.86803 1.04188 0.21874 -1.38815 1.97869 -1.74410 0.78221 0.50587 -1.58299 ... ... ..... ....... ......... ........... ............. E18g * 2.00000 -1.74410 1.04188 -0.07304 -0.91448 1.66800 -1.99466 1.81090 -1.16372 0.21874 0.78221 -1.58299 1.97869 -1.86803 1.27935 -0.36327 -0.64576 1.48954 -1.95215 1.91520 -1.38815 0.50587 2.00000 0.50587 -1.38815 1.91520 -1.95215 1.48954 -0.64576 -0.36327 1.27935 -1.86803 1.97869 -1.58299 0.78221 0.21874 -1.16372 1.81090 -1.99466 1.66800 -0.91448 -0.07304 1.04188 -1.74410 ... ... ..... ....... ......... ........... ............. E19g * 2.00000 -1.86803 1.48954 -0.91448 0.21874 0.50587 -1.16372 1.66800 -1.95215 1.97869 -1.74410 1.27935 -0.64576 -0.07304 0.78221 -1.38815 1.81090 -1.99466 1.91520 -1.58299 1.04188 -0.36327 2.00000 -0.36327 1.04188 -1.58299 1.91520 -1.99466 1.81090 -1.38815 0.78221 -0.07304 -0.64576 1.27935 -1.74410 1.97869 -1.95215 1.66800 -1.16372 0.50587 0.21874 -0.91448 1.48954 -1.86803 ... ... ..... ....... ......... ........... ............. E20g * 2.00000 -1.95215 1.81090 -1.58299 1.27935 -0.91448 0.50587 -0.07304 -0.36327 0.78221 -1.16372 1.48954 -1.74410 1.91520 -1.99466 1.97869 -1.86803 1.66800 -1.38815 1.04188 -0.64576 0.21874 2.00000 0.21874 -0.64576 1.04188 -1.38815 1.66800 -1.86803 1.97869 -1.99466 1.91520 -1.74410 1.48954 -1.16372 0.78221 -0.36327 -0.07304 0.50587 -0.91448 1.27935 -1.58299 1.81090 -1.95215 ... ... ..... ....... ......... ........... ............. E21g * 2.00000 -1.99466 1.97869 -1.95215 1.91520 -1.86803 1.81090 -1.74410 1.66800 -1.58299 1.48954 -1.38815 1.27935 -1.16372 1.04188 -0.91448 0.78221 -0.64576 0.50587 -0.36327 0.21874 -0.07304 2.00000 -0.07304 0.21874 -0.36327 0.50587 -0.64576 0.78221 -0.91448 1.04188 -1.16372 1.27935 -1.38815 1.48954 -1.58299 1.66800 -1.74410 1.81090 -1.86803 1.91520 -1.95215 1.97869 -1.99466 ... ... ..... ....... ......... ........... ............. 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 ... ..T ..... ......T ......... ..........T ............. E1u * 2.00000 1.97869 1.91520 1.81090 1.66800 1.48954 1.27935 1.04188 0.78221 0.50587 0.21874 -0.07304 -0.36327 -0.64576 -0.91448 -1.16372 -1.38815 -1.58299 -1.74410 -1.86803 -1.95215 -1.99466 -2.00000 1.99466 1.95215 1.86803 1.74410 1.58299 1.38815 1.16372 0.91448 0.64576 0.36327 0.07304 -0.21874 -0.50587 -0.78221 -1.04188 -1.27935 -1.48954 -1.66800 -1.81090 -1.91520 -1.97869 ... TT. ..... ....TT. ......... ........TT. ............. E2u * 2.00000 1.91520 1.66800 1.27935 0.78221 0.21874 -0.36327 -0.91448 -1.38815 -1.74410 -1.95215 -1.99466 -1.86803 -1.58299 -1.16372 -0.64576 -0.07304 0.50587 1.04188 1.48954 1.81090 1.97869 -2.00000 -1.97869 -1.81090 -1.48954 -1.04188 -0.50587 0.07304 0.64576 1.16372 1.58299 1.86803 1.99466 1.95215 1.74410 1.38815 0.91448 0.36327 -0.21874 -0.78221 -1.27935 -1.66800 -1.91520 ... ... ..... ..TT... ......... ......TT... ............. E3u * 2.00000 1.81090 1.27935 0.50587 -0.36327 -1.16372 -1.74410 -1.99466 -1.86803 -1.38815 -0.64576 0.21874 1.04188 1.66800 1.97869 1.91520 1.48954 0.78221 -0.07304 -0.91448 -1.58299 -1.95215 -2.00000 1.95215 1.58299 0.91448 0.07304 -0.78221 -1.48954 -1.91520 -1.97869 -1.66800 -1.04188 -0.21874 0.64576 1.38815 1.86803 1.99466 1.74410 1.16372 0.36327 -0.50587 -1.27935 -1.81090 ... ... ..... TT..... ......... ....TT..... ............. E4u * 2.00000 1.66800 0.78221 -0.36327 -1.38815 -1.95215 -1.86803 -1.16372 -0.07304 1.04188 1.81090 1.97869 1.48954 0.50587 -0.64576 -1.58299 -1.99466 -1.74410 -0.91448 0.21874 1.27935 1.91520 -2.00000 -1.91520 -1.27935 -0.21874 0.91448 1.74410 1.99466 1.58299 0.64576 -0.50587 -1.48954 -1.97869 -1.81090 -1.04188 0.07304 1.16372 1.86803 1.95215 1.38815 0.36327 -0.78221 -1.66800 ... ... ..... ....... ......... ..TT....... ............. E5u * 2.00000 1.48954 0.21874 -1.16372 -1.95215 -1.74410 -0.64576 0.78221 1.81090 1.91520 1.04188 -0.36327 -1.58299 -1.99466 -1.38815 -0.07304 1.27935 1.97869 1.66800 0.50587 -0.91448 -1.86803 -2.00000 1.86803 0.91448 -0.50587 -1.66800 -1.97869 -1.27935 0.07304 1.38815 1.99466 1.58299 0.36327 -1.04188 -1.91520 -1.81090 -0.78221 0.64576 1.74410 1.95215 1.16372 -0.21874 -1.48954 ... ... ..... ....... ......... TT......... ............. E6u * 2.00000 1.27935 -0.36327 -1.74410 -1.86803 -0.64576 1.04188 1.97869 1.48954 -0.07304 -1.58299 -1.95215 -0.91448 0.78221 1.91520 1.66800 0.21874 -1.38815 -1.99466 -1.16372 0.50587 1.81090 -2.00000 -1.81090 -0.50587 1.16372 1.99466 1.38815 -0.21874 -1.66800 -1.91520 -0.78221 0.91448 1.95215 1.58299 0.07304 -1.48954 -1.97869 -1.04188 0.64576 1.86803 1.74410 0.36327 -1.27935 ... ... ..... ....... ......... ........... ............. E7u * 2.00000 1.04188 -0.91448 -1.99466 -1.16372 0.78221 1.97869 1.27935 -0.64576 -1.95215 -1.38815 0.50587 1.91520 1.48954 -0.36327 -1.86803 -1.58299 0.21874 1.81090 1.66800 -0.07304 -1.74410 -2.00000 1.74410 0.07304 -1.66800 -1.81090 -0.21874 1.58299 1.86803 0.36327 -1.48954 -1.91520 -0.50587 1.38815 1.95215 0.64576 -1.27935 -1.97869 -0.78221 1.16372 1.99466 0.91448 -1.04188 ... ... ..... ....... ......... ........... ............. E8u * 2.00000 0.78221 -1.38815 -1.86803 -0.07304 1.81090 1.48954 -0.64576 -1.99466 -0.91448 1.27935 1.91520 0.21874 -1.74410 -1.58299 0.50587 1.97869 1.04188 -1.16372 -1.95215 -0.36327 1.66800 -2.00000 -1.66800 0.36327 1.95215 1.16372 -1.04188 -1.97869 -0.50587 1.58299 1.74410 -0.21874 -1.91520 -1.27935 0.91448 1.99466 0.64576 -1.48954 -1.81090 0.07304 1.86803 1.38815 -0.78221 ... ... ..... ....... ......... ........... ............. E9u * 2.00000 0.50587 -1.74410 -1.38815 1.04188 1.91520 -0.07304 -1.95215 -0.91448 1.48954 1.66800 -0.64576 -1.99466 -0.36327 1.81090 1.27935 -1.16372 -1.86803 0.21874 1.97869 0.78221 -1.58299 -2.00000 1.58299 -0.78221 -1.97869 -0.21874 1.86803 1.16372 -1.27935 -1.81090 0.36327 1.99466 0.64576 -1.66800 -1.48954 0.91448 1.95215 0.07304 -1.91520 -1.04188 1.38815 1.74410 -0.50587 ... ... ..... ....... ......... ........... ............. E10u * 2.00000 0.21874 -1.95215 -0.64576 1.81090 1.04188 -1.58299 -1.38815 1.27935 1.66800 -0.91448 -1.86803 0.50587 1.97869 -0.07304 -1.99466 -0.36327 1.91520 0.78221 -1.74410 -1.16372 1.48954 -2.00000 -1.48954 1.16372 1.74410 -0.78221 -1.91520 0.36327 1.99466 0.07304 -1.97869 -0.50587 1.86803 0.91448 -1.66800 -1.27935 1.38815 1.58299 -1.04188 -1.81090 0.64576 1.95215 -0.21874 ... ... ..... ....... ......... ........... ............. E11u * 2.00000 -0.07304 -1.99466 0.21874 1.97869 -0.36327 -1.95215 0.50587 1.91520 -0.64576 -1.86803 0.78221 1.81090 -0.91448 -1.74410 1.04188 1.66800 -1.16372 -1.58299 1.27935 1.48954 -1.38815 -2.00000 1.38815 -1.48954 -1.27935 1.58299 1.16372 -1.66800 -1.04188 1.74410 0.91448 -1.81090 -0.78221 1.86803 0.64576 -1.91520 -0.50587 1.95215 0.36327 -1.97869 -0.21874 1.99466 0.07304 ... ... ..... ....... ......... ........... ............. E12u * 2.00000 -0.36327 -1.86803 1.04188 1.48954 -1.58299 -0.91448 1.91520 0.21874 -1.99466 0.50587 1.81090 -1.16372 -1.38815 1.66800 0.78221 -1.95215 -0.07304 1.97869 -0.64576 -1.74410 1.27935 -2.00000 -1.27935 1.74410 0.64576 -1.97869 0.07304 1.95215 -0.78221 -1.66800 1.38815 1.16372 -1.81090 -0.50587 1.99466 -0.21874 -1.91520 0.91448 1.58299 -1.48954 -1.04188 1.86803 0.36327 ... ... ..... ....... ......... ........... ............. E13u * 2.00000 -0.64576 -1.58299 1.66800 0.50587 -1.99466 0.78221 1.48954 -1.74410 -0.36327 1.97869 -0.91448 -1.38815 1.81090 0.21874 -1.95215 1.04188 1.27935 -1.86803 -0.07304 1.91520 -1.16372 -2.00000 1.16372 -1.91520 0.07304 1.86803 -1.27935 -1.04188 1.95215 -0.21874 -1.81090 1.38815 0.91448 -1.97869 0.36327 1.74410 -1.48954 -0.78221 1.99466 -0.50587 -1.66800 1.58299 0.64576 ... ... ..... ....... ......... ........... ............. E14u * 2.00000 -0.91448 -1.16372 1.97869 -0.64576 -1.38815 1.91520 -0.36327 -1.58299 1.81090 -0.07304 -1.74410 1.66800 0.21874 -1.86803 1.48954 0.50587 -1.95215 1.27935 0.78221 -1.99466 1.04188 -2.00000 -1.04188 1.99466 -0.78221 -1.27935 1.95215 -0.50587 -1.48954 1.86803 -0.21874 -1.66800 1.74410 0.07304 -1.81090 1.58299 0.36327 -1.91520 1.38815 0.64576 -1.97869 1.16372 0.91448 ... ... ..... ....... ......... ........... ............. E15u * 2.00000 -1.16372 -0.64576 1.91520 -1.58299 -0.07304 1.66800 -1.86803 0.50587 1.27935 -1.99466 1.04188 0.78221 -1.95215 1.48954 0.21874 -1.74410 1.81090 -0.36327 -1.38815 1.97869 -0.91448 -2.00000 0.91448 -1.97869 1.38815 0.36327 -1.81090 1.74410 -0.21874 -1.48954 1.95215 -0.78221 -1.04188 1.99466 -1.27935 -0.50587 1.86803 -1.66800 0.07304 1.58299 -1.91520 0.64576 1.16372 ... ... ..... ....... ......... ........... ............. E16u * 2.00000 -1.38815 -0.07304 1.48954 -1.99466 1.27935 0.21874 -1.58299 1.97869 -1.16372 -0.36327 1.66800 -1.95215 1.04188 0.50587 -1.74410 1.91520 -0.91448 -0.64576 1.81090 -1.86803 0.78221 -2.00000 -0.78221 1.86803 -1.81090 0.64576 0.91448 -1.91520 1.74410 -0.50587 -1.04188 1.95215 -1.66800 0.36327 1.16372 -1.97869 1.58299 -0.21874 -1.27935 1.99466 -1.48954 0.07304 1.38815 ... ... ..... ....... ......... ........... ............. E17u * 2.00000 -1.58299 0.50587 0.78221 -1.74410 1.97869 -1.38815 0.21874 1.04188 -1.86803 1.91520 -1.16372 -0.07304 1.27935 -1.95215 1.81090 -0.91448 -0.36327 1.48954 -1.99466 1.66800 -0.64576 -2.00000 0.64576 -1.66800 1.99466 -1.48954 0.36327 0.91448 -1.81090 1.95215 -1.27935 0.07304 1.16372 -1.91520 1.86803 -1.04188 -0.21874 1.38815 -1.97869 1.74410 -0.78221 -0.50587 1.58299 ... ... ..... ....... ......... ........... ............. E18u * 2.00000 -1.74410 1.04188 -0.07304 -0.91448 1.66800 -1.99466 1.81090 -1.16372 0.21874 0.78221 -1.58299 1.97869 -1.86803 1.27935 -0.36327 -0.64576 1.48954 -1.95215 1.91520 -1.38815 0.50587 -2.00000 -0.50587 1.38815 -1.91520 1.95215 -1.48954 0.64576 0.36327 -1.27935 1.86803 -1.97869 1.58299 -0.78221 -0.21874 1.16372 -1.81090 1.99466 -1.66800 0.91448 0.07304 -1.04188 1.74410 ... ... ..... ....... ......... ........... ............. E19u * 2.00000 -1.86803 1.48954 -0.91448 0.21874 0.50587 -1.16372 1.66800 -1.95215 1.97869 -1.74410 1.27935 -0.64576 -0.07304 0.78221 -1.38815 1.81090 -1.99466 1.91520 -1.58299 1.04188 -0.36327 -2.00000 0.36327 -1.04188 1.58299 -1.91520 1.99466 -1.81090 1.38815 -0.78221 0.07304 0.64576 -1.27935 1.74410 -1.97869 1.95215 -1.66800 1.16372 -0.50587 -0.21874 0.91448 -1.48954 1.86803 ... ... ..... ....... ......... ........... ............. E20u * 2.00000 -1.95215 1.81090 -1.58299 1.27935 -0.91448 0.50587 -0.07304 -0.36327 0.78221 -1.16372 1.48954 -1.74410 1.91520 -1.99466 1.97869 -1.86803 1.66800 -1.38815 1.04188 -0.64576 0.21874 -2.00000 -0.21874 0.64576 -1.04188 1.38815 -1.66800 1.86803 -1.97869 1.99466 -1.91520 1.74410 -1.48954 1.16372 -0.78221 0.36327 0.07304 -0.50587 0.91448 -1.27935 1.58299 -1.81090 1.95215 ... ... ..... ....... ......... ........... ............. E21u * 2.00000 -1.99466 1.97869 -1.95215 1.91520 -1.86803 1.81090 -1.74410 1.66800 -1.58299 1.48954 -1.38815 1.27935 -1.16372 1.04188 -0.91448 0.78221 -0.64576 0.50587 -0.36327 0.21874 -0.07304 -2.00000 0.07304 -0.21874 0.36327 -0.50587 0.64576 -0.78221 0.91448 -1.04188 1.16372 -1.27935 1.38815 -1.48954 1.58299 -1.66800 1.74410 -1.81090 1.86803 -1.91520 1.95215 -1.97869 1.99466 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.994664567327 = 2*cos(2*π/86) = 2*cos(π/43) 1.978686736150 = 2*cos(4*π/86) = 2*cos(2*π/43) 1.952151755112 = 2*cos(6*π/86) = 2*cos(3*π/43) 1.915201199817 = 2*cos(8*π/86) = 2*cos(4*π/43) 1.868032217465 = 2*cos(10*π/86) = 2*cos(5*π/43) 1.810896474986 = 2*cos(12*π/86) = 2*cos(6*π/43) 1.744098816288 = 2*cos(14*π/86) = 2*cos(7*π/43) 1.667995635780 = 2*cos(16*π/86) = 2*cos(8*π/43) 1.582992976859 = 2*cos(18*π/86) = 2*cos(9*π/43) 1.489544365488 = 2*cos(20*π/86) = 2*cos(10*π/43) 1.388148390441 = 2*cos(22*π/86) = 2*cos(11*π/43) 1.279346043118 = 2*cos(24*π/86) = 2*cos(12*π/43) 1.163717831116 = 2*cos(26*π/86) = 2*cos(13*π/43) 1.041880680976 = 2*cos(28*π/86) = 2*cos(14*π/43) 0.914484646609 = 2*cos(30*π/86) = 2*cos(15*π/43) 0.782209440980 = 2*cos(32*π/86) = 2*cos(16*π/43) 0.645760809543 = 2*cos(34*π/86) = 2*cos(17*π/43) 0.505866764783 = 2*cos(36*π/86) = 2*cos(18*π/43) 0.363273701959 = 2*cos(38*π/86) = 2*cos(19*π/43) 0.218742416756 = 2*cos(40*π/86) = 2*cos(20*π/43) 0.073044046115 = 2*cos(42*π/86) = 2*cos(21*π/43) Symmetry of Rotations and Cartesian products Ag R+d+g+i+k+m Rz, z2, z4, z6 E1g R+d+g+i+k+m {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} E2g d+g+i+k+m {x2−y2, xy}, {z2(x2−y2), xyz2}, {z4(x2−y2), xyz4} E3g g+i+k+m {xz(x2−3y2), yz(3x2−y2)}, {xz3(x2−3y2), yz3(3x2−y2)} E4g g+i+k+m {(x2−y2)2−4x2y2, xy(x2−y2)}, {z2((x2−y2)2−4x2y2), xyz2(x2−y2)} E5g 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)} E6g i+k+m {x2(x2−3y2)2−y2(3x2−y2)2, xy(x2−3y2)(3x2−y2)} E7g k+m E8g k+m E9g m E10g m Au p+f+h+j+l z, z3, z5 E1u p+f+h+j+l {x, y}, {xz2, yz2}, {xz4, yz4} E2u f+h+j+l {z(x2−y2), xyz}, {z3(x2−y2), xyz3} E3u f+h+j+l {x(x2−3y2), y(3x2−y2)}, {xz2(x2−3y2), yz2(3x2−y2)} E4u h+j+l {z((x2−y2)2−4x2y2), xyz(x2−y2)} E5u 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)} E6u j+l E7u j+l E8u l E9u l Notes: α The order of the S86 point group is 86, and the order of the principal axis (S86) is 86. The group has 44 irreducible representations. β The S86 point group could also be named C43i, because the S86 axis is identical to a roto-inversion axis of order 43. γ The S86 point group is isomorphic to C86 and C43h. δ The S86 point group is generated by one single symmetry element, S86. Therefore, it is a cyclic group. ε The lowest nonvanishing multipole moment in S86 is 4 (quadrupole moment). ζ This is an Abelian point group (the commutative law holds between all symmetry operations). The S86 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 84 cases have been combined into 42 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 42 pairs of left and right rotations have been combined into one two-membered pseudo-class each. θ The 42 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. For this group, however, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.
S82 | ||
S84 | ||
C86 C86v C86h D86 D86h D86d | S86 | |
S88 | ||
S90 |
This Character Table for the S86 point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.