D46h E 2 C46 2 C23 2 C46^3 2 C23^2 2 C46^5 2 C23^3 2 C46^7 2 C23^4 2 C46^9 2 C23^5 2 C46^11 2 C23^6 2 C46^13 2 C23^7 2 C46^15 2 C23^8 2 C46^17 2 C23^9 2 C46^19 2 C23^10 2 C46^21 2 C23^11 C2 23 C2' 23 C2" i 2 S46 2 S23 2 S46^3 2 S23^2 2 S46^5 2 S23^3 2 S46^7 2 S23^4 2 S46^9 2 S23^5 2 S46^11 2 S23^6 2 S46^13 2 S23^7 2 S46^15 2 S23^8 2 S46^17 2 S23^9 2 S46^19 2 S23^10 2 S46^21 2 S23^11 sh 23 sv 23 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 A2g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 ... ..... ....... ......... ........... ............. B1g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. B2g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E1g 2.00000 1.98137 1.92583 1.83442 1.70884 1.55142 1.36511 1.15336 0.92013 0.66976 0.40691 0.13648 -0.13648 -0.40691 -0.66976 -0.92013 -1.15336 -1.36511 -1.55142 -1.70884 -1.83442 -1.92583 -1.98137 -2.00000 0.00000 0.00000 2.00000 -1.98137 -1.92583 -1.83442 -1.70884 -1.55142 -1.36511 -1.15336 -0.92013 -0.66976 -0.40691 -0.13648 0.13648 0.40691 0.66976 0.92013 1.15336 1.36511 1.55142 1.70884 1.83442 1.92583 1.98137 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583 2.00000 0.00000 0.00000 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 2.00000 1.83442 1.36511 0.66976 -0.13648 -0.92013 -1.55142 -1.92583 -1.98137 -1.70884 -1.15336 -0.40691 0.40691 1.15336 1.70884 1.98137 1.92583 1.55142 0.92013 0.13648 -0.66976 -1.36511 -1.83442 -2.00000 0.00000 0.00000 2.00000 -1.83442 -1.36511 -0.66976 0.13648 0.92013 1.55142 1.92583 1.98137 1.70884 1.15336 0.40691 -0.40691 -1.15336 -1.70884 -1.98137 -1.92583 -1.55142 -0.92013 -0.13648 0.66976 1.36511 1.83442 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884 2.00000 0.00000 0.00000 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.55142 0.40691 -0.92013 -1.83442 -1.92583 -1.15336 0.13648 1.36511 1.98137 1.70884 0.66976 -0.66976 -1.70884 -1.98137 -1.36511 -0.13648 1.15336 1.92583 1.83442 0.92013 -0.40691 -1.55142 -2.00000 0.00000 0.00000 2.00000 -1.55142 -0.40691 0.92013 1.83442 1.92583 1.15336 -0.13648 -1.36511 -1.98137 -1.70884 -0.66976 0.66976 1.70884 1.98137 1.36511 0.13648 -1.15336 -1.92583 -1.83442 -0.92013 0.40691 1.55142 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511 2.00000 0.00000 0.00000 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7g 2.00000 1.15336 -0.66976 -1.92583 -1.55142 0.13648 1.70884 1.83442 0.40691 -1.36511 -1.98137 -0.92013 0.92013 1.98137 1.36511 -0.40691 -1.83442 -1.70884 -0.13648 1.55142 1.92583 0.66976 -1.15336 -2.00000 0.00000 0.00000 2.00000 -1.15336 0.66976 1.92583 1.55142 -0.13648 -1.70884 -1.83442 -0.40691 1.36511 1.98137 0.92013 -0.92013 -1.98137 -1.36511 0.40691 1.83442 1.70884 0.13648 -1.55142 -1.92583 -0.66976 1.15336 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8g 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013 2.00000 0.00000 0.00000 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9g 2.00000 0.66976 -1.55142 -1.70884 0.40691 1.98137 0.92013 -1.36511 -1.83442 0.13648 1.92583 1.15336 -1.15336 -1.92583 -0.13648 1.83442 1.36511 -0.92013 -1.98137 -0.40691 1.70884 1.55142 -0.66976 -2.00000 0.00000 0.00000 2.00000 -0.66976 1.55142 1.70884 -0.40691 -1.98137 -0.92013 1.36511 1.83442 -0.13648 -1.92583 -1.15336 1.15336 1.92583 0.13648 -1.83442 -1.36511 0.92013 1.98137 0.40691 -1.70884 -1.55142 0.66976 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10g 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 -1.55142 0.92013 1.92583 -0.13648 -1.98137 -0.66976 1.70884 1.36511 -1.15336 -1.83442 0.40691 2.00000 0.00000 0.00000 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 -1.55142 0.92013 1.92583 -0.13648 -1.98137 -0.66976 1.70884 1.36511 -1.15336 -1.83442 0.40691 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 0.13648 -1.98137 -0.40691 1.92583 0.66976 -1.83442 -0.92013 1.70884 1.15336 -1.55142 -1.36511 1.36511 1.55142 -1.15336 -1.70884 0.92013 1.83442 -0.66976 -1.92583 0.40691 1.98137 -0.13648 -2.00000 0.00000 0.00000 2.00000 -0.13648 1.98137 0.40691 -1.92583 -0.66976 1.83442 0.92013 -1.70884 -1.15336 1.55142 1.36511 -1.36511 -1.55142 1.15336 1.70884 -0.92013 -1.83442 0.66976 1.92583 -0.40691 -1.98137 0.13648 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12g 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648 2.00000 0.00000 0.00000 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 -0.40691 -1.83442 1.15336 1.36511 -1.70884 -0.66976 1.98137 -0.13648 -1.92583 0.92013 1.55142 -1.55142 -0.92013 1.92583 0.13648 -1.98137 0.66976 1.70884 -1.36511 -1.15336 1.83442 0.40691 -2.00000 0.00000 0.00000 2.00000 0.40691 1.83442 -1.15336 -1.36511 1.70884 0.66976 -1.98137 0.13648 1.92583 -0.92013 -1.55142 1.55142 0.92013 -1.92583 -0.13648 1.98137 -0.66976 -1.70884 1.36511 1.15336 -1.83442 -0.40691 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976 2.00000 0.00000 0.00000 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15g 2.00000 -0.92013 -1.15336 1.98137 -0.66976 -1.36511 1.92583 -0.40691 -1.55142 1.83442 -0.13648 -1.70884 1.70884 0.13648 -1.83442 1.55142 0.40691 -1.92583 1.36511 0.66976 -1.98137 1.15336 0.92013 -2.00000 0.00000 0.00000 2.00000 0.92013 1.15336 -1.98137 0.66976 1.36511 -1.92583 0.40691 1.55142 -1.83442 0.13648 1.70884 -1.70884 -0.13648 1.83442 -1.55142 -0.40691 1.92583 -1.36511 -0.66976 1.98137 -1.15336 -0.92013 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16g 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 0.92013 -1.98137 1.36511 0.40691 -1.83442 1.70884 -0.13648 -1.55142 1.92583 -0.66976 -1.15336 2.00000 0.00000 0.00000 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 0.92013 -1.98137 1.36511 0.40691 -1.83442 1.70884 -0.13648 -1.55142 1.92583 -0.66976 -1.15336 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17g 2.00000 -1.36511 -0.13648 1.55142 -1.98137 1.15336 0.40691 -1.70884 1.92583 -0.92013 -0.66976 1.83442 -1.83442 0.66976 0.92013 -1.92583 1.70884 -0.40691 -1.15336 1.98137 -1.55142 0.13648 1.36511 -2.00000 0.00000 0.00000 2.00000 1.36511 0.13648 -1.55142 1.98137 -1.15336 -0.40691 1.70884 -1.92583 0.92013 0.66976 -1.83442 1.83442 -0.66976 -0.92013 1.92583 -1.70884 0.40691 1.15336 -1.98137 1.55142 -0.13648 -1.36511 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18g 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 -0.66976 1.70884 -1.98137 1.36511 -0.13648 -1.15336 1.92583 -1.83442 0.92013 0.40691 -1.55142 2.00000 0.00000 0.00000 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 -0.66976 1.70884 -1.98137 1.36511 -0.13648 -1.15336 1.92583 -1.83442 0.92013 0.40691 -1.55142 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19g 2.00000 -1.70884 0.92013 0.13648 -1.15336 1.83442 -1.98137 1.55142 -0.66976 -0.40691 1.36511 -1.92583 1.92583 -1.36511 0.40691 0.66976 -1.55142 1.98137 -1.83442 1.15336 -0.13648 -0.92013 1.70884 -2.00000 0.00000 0.00000 2.00000 1.70884 -0.92013 -0.13648 1.15336 -1.83442 1.98137 -1.55142 0.66976 0.40691 -1.36511 1.92583 -1.92583 1.36511 -0.40691 -0.66976 1.55142 -1.98137 1.83442 -1.15336 0.13648 0.92013 -1.70884 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20g 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 0.40691 -1.15336 1.70884 -1.98137 1.92583 -1.55142 0.92013 -0.13648 -0.66976 1.36511 -1.83442 2.00000 0.00000 0.00000 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 0.40691 -1.15336 1.70884 -1.98137 1.92583 -1.55142 0.92013 -0.13648 -0.66976 1.36511 -1.83442 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21g 2.00000 -1.92583 1.70884 -1.36511 0.92013 -0.40691 -0.13648 0.66976 -1.15336 1.55142 -1.83442 1.98137 -1.98137 1.83442 -1.55142 1.15336 -0.66976 0.13648 0.40691 -0.92013 1.36511 -1.70884 1.92583 -2.00000 0.00000 0.00000 2.00000 1.92583 -1.70884 1.36511 -0.92013 0.40691 0.13648 -0.66976 1.15336 -1.55142 1.83442 -1.98137 1.98137 -1.83442 1.55142 -1.15336 0.66976 -0.13648 -0.40691 0.92013 -1.36511 1.70884 -1.92583 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E22g 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137 2.00000 0.00000 0.00000 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. A1u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. A2u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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 ............. B1u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. B2u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E1u 2.00000 1.98137 1.92583 1.83442 1.70884 1.55142 1.36511 1.15336 0.92013 0.66976 0.40691 0.13648 -0.13648 -0.40691 -0.66976 -0.92013 -1.15336 -1.36511 -1.55142 -1.70884 -1.83442 -1.92583 -1.98137 -2.00000 0.00000 0.00000 -2.00000 1.98137 1.92583 1.83442 1.70884 1.55142 1.36511 1.15336 0.92013 0.66976 0.40691 0.13648 -0.13648 -0.40691 -0.66976 -0.92013 -1.15336 -1.36511 -1.55142 -1.70884 -1.83442 -1.92583 -1.98137 2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583 2.00000 0.00000 0.00000 -2.00000 -1.92583 -1.70884 -1.36511 -0.92013 -0.40691 0.13648 0.66976 1.15336 1.55142 1.83442 1.98137 1.98137 1.83442 1.55142 1.15336 0.66976 0.13648 -0.40691 -0.92013 -1.36511 -1.70884 -1.92583 -2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u 2.00000 1.83442 1.36511 0.66976 -0.13648 -0.92013 -1.55142 -1.92583 -1.98137 -1.70884 -1.15336 -0.40691 0.40691 1.15336 1.70884 1.98137 1.92583 1.55142 0.92013 0.13648 -0.66976 -1.36511 -1.83442 -2.00000 0.00000 0.00000 -2.00000 1.83442 1.36511 0.66976 -0.13648 -0.92013 -1.55142 -1.92583 -1.98137 -1.70884 -1.15336 -0.40691 0.40691 1.15336 1.70884 1.98137 1.92583 1.55142 0.92013 0.13648 -0.66976 -1.36511 -1.83442 2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884 2.00000 0.00000 0.00000 -2.00000 -1.70884 -0.92013 0.13648 1.15336 1.83442 1.98137 1.55142 0.66976 -0.40691 -1.36511 -1.92583 -1.92583 -1.36511 -0.40691 0.66976 1.55142 1.98137 1.83442 1.15336 0.13648 -0.92013 -1.70884 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5u 2.00000 1.55142 0.40691 -0.92013 -1.83442 -1.92583 -1.15336 0.13648 1.36511 1.98137 1.70884 0.66976 -0.66976 -1.70884 -1.98137 -1.36511 -0.13648 1.15336 1.92583 1.83442 0.92013 -0.40691 -1.55142 -2.00000 0.00000 0.00000 -2.00000 1.55142 0.40691 -0.92013 -1.83442 -1.92583 -1.15336 0.13648 1.36511 1.98137 1.70884 0.66976 -0.66976 -1.70884 -1.98137 -1.36511 -0.13648 1.15336 1.92583 1.83442 0.92013 -0.40691 -1.55142 2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6u 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511 2.00000 0.00000 0.00000 -2.00000 -1.36511 0.13648 1.55142 1.98137 1.15336 -0.40691 -1.70884 -1.92583 -0.92013 0.66976 1.83442 1.83442 0.66976 -0.92013 -1.92583 -1.70884 -0.40691 1.15336 1.98137 1.55142 0.13648 -1.36511 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E7u 2.00000 1.15336 -0.66976 -1.92583 -1.55142 0.13648 1.70884 1.83442 0.40691 -1.36511 -1.98137 -0.92013 0.92013 1.98137 1.36511 -0.40691 -1.83442 -1.70884 -0.13648 1.55142 1.92583 0.66976 -1.15336 -2.00000 0.00000 0.00000 -2.00000 1.15336 -0.66976 -1.92583 -1.55142 0.13648 1.70884 1.83442 0.40691 -1.36511 -1.98137 -0.92013 0.92013 1.98137 1.36511 -0.40691 -1.83442 -1.70884 -0.13648 1.55142 1.92583 0.66976 -1.15336 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8u 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013 2.00000 0.00000 0.00000 -2.00000 -0.92013 1.15336 1.98137 0.66976 -1.36511 -1.92583 -0.40691 1.55142 1.83442 0.13648 -1.70884 -1.70884 0.13648 1.83442 1.55142 -0.40691 -1.92583 -1.36511 0.66976 1.98137 1.15336 -0.92013 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9u 2.00000 0.66976 -1.55142 -1.70884 0.40691 1.98137 0.92013 -1.36511 -1.83442 0.13648 1.92583 1.15336 -1.15336 -1.92583 -0.13648 1.83442 1.36511 -0.92013 -1.98137 -0.40691 1.70884 1.55142 -0.66976 -2.00000 0.00000 0.00000 -2.00000 0.66976 -1.55142 -1.70884 0.40691 1.98137 0.92013 -1.36511 -1.83442 0.13648 1.92583 1.15336 -1.15336 -1.92583 -0.13648 1.83442 1.36511 -0.92013 -1.98137 -0.40691 1.70884 1.55142 -0.66976 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10u 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 -1.55142 0.92013 1.92583 -0.13648 -1.98137 -0.66976 1.70884 1.36511 -1.15336 -1.83442 0.40691 2.00000 0.00000 0.00000 -2.00000 -0.40691 1.83442 1.15336 -1.36511 -1.70884 0.66976 1.98137 0.13648 -1.92583 -0.92013 1.55142 1.55142 -0.92013 -1.92583 0.13648 1.98137 0.66976 -1.70884 -1.36511 1.15336 1.83442 -0.40691 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11u 2.00000 0.13648 -1.98137 -0.40691 1.92583 0.66976 -1.83442 -0.92013 1.70884 1.15336 -1.55142 -1.36511 1.36511 1.55142 -1.15336 -1.70884 0.92013 1.83442 -0.66976 -1.92583 0.40691 1.98137 -0.13648 -2.00000 0.00000 0.00000 -2.00000 0.13648 -1.98137 -0.40691 1.92583 0.66976 -1.83442 -0.92013 1.70884 1.15336 -1.55142 -1.36511 1.36511 1.55142 -1.15336 -1.70884 0.92013 1.83442 -0.66976 -1.92583 0.40691 1.98137 -0.13648 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12u 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648 2.00000 0.00000 0.00000 -2.00000 0.13648 1.98137 -0.40691 -1.92583 0.66976 1.83442 -0.92013 -1.70884 1.15336 1.55142 -1.36511 -1.36511 1.55142 1.15336 -1.70884 -0.92013 1.83442 0.66976 -1.92583 -0.40691 1.98137 0.13648 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13u 2.00000 -0.40691 -1.83442 1.15336 1.36511 -1.70884 -0.66976 1.98137 -0.13648 -1.92583 0.92013 1.55142 -1.55142 -0.92013 1.92583 0.13648 -1.98137 0.66976 1.70884 -1.36511 -1.15336 1.83442 0.40691 -2.00000 0.00000 0.00000 -2.00000 -0.40691 -1.83442 1.15336 1.36511 -1.70884 -0.66976 1.98137 -0.13648 -1.92583 0.92013 1.55142 -1.55142 -0.92013 1.92583 0.13648 -1.98137 0.66976 1.70884 -1.36511 -1.15336 1.83442 0.40691 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14u 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976 2.00000 0.00000 0.00000 -2.00000 0.66976 1.55142 -1.70884 -0.40691 1.98137 -0.92013 -1.36511 1.83442 0.13648 -1.92583 1.15336 1.15336 -1.92583 0.13648 1.83442 -1.36511 -0.92013 1.98137 -0.40691 -1.70884 1.55142 0.66976 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15u 2.00000 -0.92013 -1.15336 1.98137 -0.66976 -1.36511 1.92583 -0.40691 -1.55142 1.83442 -0.13648 -1.70884 1.70884 0.13648 -1.83442 1.55142 0.40691 -1.92583 1.36511 0.66976 -1.98137 1.15336 0.92013 -2.00000 0.00000 0.00000 -2.00000 -0.92013 -1.15336 1.98137 -0.66976 -1.36511 1.92583 -0.40691 -1.55142 1.83442 -0.13648 -1.70884 1.70884 0.13648 -1.83442 1.55142 0.40691 -1.92583 1.36511 0.66976 -1.98137 1.15336 0.92013 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16u 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 0.92013 -1.98137 1.36511 0.40691 -1.83442 1.70884 -0.13648 -1.55142 1.92583 -0.66976 -1.15336 2.00000 0.00000 0.00000 -2.00000 1.15336 0.66976 -1.92583 1.55142 0.13648 -1.70884 1.83442 -0.40691 -1.36511 1.98137 -0.92013 -0.92013 1.98137 -1.36511 -0.40691 1.83442 -1.70884 0.13648 1.55142 -1.92583 0.66976 1.15336 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17u 2.00000 -1.36511 -0.13648 1.55142 -1.98137 1.15336 0.40691 -1.70884 1.92583 -0.92013 -0.66976 1.83442 -1.83442 0.66976 0.92013 -1.92583 1.70884 -0.40691 -1.15336 1.98137 -1.55142 0.13648 1.36511 -2.00000 0.00000 0.00000 -2.00000 -1.36511 -0.13648 1.55142 -1.98137 1.15336 0.40691 -1.70884 1.92583 -0.92013 -0.66976 1.83442 -1.83442 0.66976 0.92013 -1.92583 1.70884 -0.40691 -1.15336 1.98137 -1.55142 0.13648 1.36511 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18u 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 -0.66976 1.70884 -1.98137 1.36511 -0.13648 -1.15336 1.92583 -1.83442 0.92013 0.40691 -1.55142 2.00000 0.00000 0.00000 -2.00000 1.55142 -0.40691 -0.92013 1.83442 -1.92583 1.15336 0.13648 -1.36511 1.98137 -1.70884 0.66976 0.66976 -1.70884 1.98137 -1.36511 0.13648 1.15336 -1.92583 1.83442 -0.92013 -0.40691 1.55142 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19u 2.00000 -1.70884 0.92013 0.13648 -1.15336 1.83442 -1.98137 1.55142 -0.66976 -0.40691 1.36511 -1.92583 1.92583 -1.36511 0.40691 0.66976 -1.55142 1.98137 -1.83442 1.15336 -0.13648 -0.92013 1.70884 -2.00000 0.00000 0.00000 -2.00000 -1.70884 0.92013 0.13648 -1.15336 1.83442 -1.98137 1.55142 -0.66976 -0.40691 1.36511 -1.92583 1.92583 -1.36511 0.40691 0.66976 -1.55142 1.98137 -1.83442 1.15336 -0.13648 -0.92013 1.70884 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20u 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 0.40691 -1.15336 1.70884 -1.98137 1.92583 -1.55142 0.92013 -0.13648 -0.66976 1.36511 -1.83442 2.00000 0.00000 0.00000 -2.00000 1.83442 -1.36511 0.66976 0.13648 -0.92013 1.55142 -1.92583 1.98137 -1.70884 1.15336 -0.40691 -0.40691 1.15336 -1.70884 1.98137 -1.92583 1.55142 -0.92013 0.13648 0.66976 -1.36511 1.83442 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21u 2.00000 -1.92583 1.70884 -1.36511 0.92013 -0.40691 -0.13648 0.66976 -1.15336 1.55142 -1.83442 1.98137 -1.98137 1.83442 -1.55142 1.15336 -0.66976 0.13648 0.40691 -0.92013 1.36511 -1.70884 1.92583 -2.00000 0.00000 0.00000 -2.00000 -1.92583 1.70884 -1.36511 0.92013 -0.40691 -0.13648 0.66976 -1.15336 1.55142 -1.83442 1.98137 -1.98137 1.83442 -1.55142 1.15336 -0.66976 0.13648 0.40691 -0.92013 1.36511 -1.70884 1.92583 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E22u 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137 2.00000 0.00000 0.00000 -2.00000 1.98137 -1.92583 1.83442 -1.70884 1.55142 -1.36511 1.15336 -0.92013 0.66976 -0.40691 0.13648 0.13648 -0.40691 0.66976 -0.92013 1.15336 -1.36511 1.55142 -1.70884 1.83442 -1.92583 1.98137 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.981371892073 = 2*cos(2*π/46) = 2*cos(π/23) 1.925834574696 = 2*cos(4*π/46) = 2*cos(2*π/23) 1.834422603011 = 2*cos(6*π/46) = 2*cos(3*π/23) 1.708838809093 = 2*cos(8*π/46) = 2*cos(4*π/23) 1.551422581409 = 2*cos(10*π/46) = 2*cos(5*π/23) 1.365106286437 = 2*cos(12*π/46) = 2*cos(6*π/23) 1.153360644230 = 2*cos(14*π/46) = 2*cos(7*π/23) 0.920130075462 = 2*cos(16*π/46) = 2*cos(8*π/23) 0.669759224342 = 2*cos(18*π/46) = 2*cos(9*π/23) 0.406912026105 = 2*cos(20*π/46) = 2*cos(10*π/23) 0.136484826729 = 2*cos(22*π/46) = 2*cos(11*π/23) Symmetry of Rotations and Cartesian products A1g d+g+i+k+m z2, z4, z6 A2g R Rz 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 A2u 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 D46h point group is 184, and the order of the principal axis (C46) is 46. The group has 52 irreducible representations. β The D46h point group is generated by three symmetry elements that are canonically chosen C46, C2′ and i. Other choices include σh instead of i, or any of C2″, σv or σd instead of C2′. Also, some ternary combinations of C2′, C2″, σv and σd act as generators. Lastly, the S46 can be chosen, together with σh or C2 and any one of C2′, C2″, σv or σd. γ There are two different sets of twofold symmetry axes perpendicular to the principal axis (z axis in standard orientation). By convention, the set denoted as C2′ has the x axis as a member, while the y axis is a member of the C2″ set. δ There are two different sets of symmetry planes containing the principal axis (z axis in standard orientation). By convention, the set denoted as σv has the xz plane as a member, while the yz plane is a member of the σd set. ε The lowest nonvanishing multipole moment in D46h is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. η 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.
D44h | ||
D45h | ||
C46 C46v C46h D46 | D46h | D46d S46 |
D47h | ||
D48h |
This Character Table for the D46h point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.