Character Table for Point Group D69d

Character table for the D_69d point group

D69d E 2 C69 2 C69^2 2 C23 2 C69^4 2 C69^5 2 C23^2 2 C69^7 2 C69^8 2 C23^3 2 C69^10 2 C69^11 2 C23^4 2 C69^13 2 C69^14 2 C23^5 2 C69^16 2 C69^17 2 C23^6 2 C69^19 2 C69^20 2 C23^7 2 C69^22 2 C3 2 C23^8 2 C69^25 2 C69^26 2 C23^9 2 C69^28 2 C69^29 2 C23^10 2 C69^31 2 C69^32 2 C23^11 2 C69^34 69 C2' i 2 S138 2 S46 2 S138^5 2 S138^7 2 S46^3 2 S138^11 2 S138^13 2 S46^5 2 S138^17 2 S138^19 2 S46^7 2 S6 2 S138^25 2 S46^9 2 S138^29 2 S138^31 2 S46^11 2 S138^35 2 S138^37 2 S46^13 2 S138^41 2 S138^43 2 S46^15 2 S138^47 2 S138^49 2 S46^17 2 S138^53 2 S138^55 2 S46^19 2 S138^59 2 S138^61 2 S46^21 2 S138^65 2 S138^67 69 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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 ... ..... ....... ......... ........... ............. E1g 2.00000 1.99171 1.96692 1.92583 1.86879 1.79626 1.70884 1.60726 1.49237 1.36511 1.22653 1.07780 0.92013 0.75484 0.58329 0.40691 0.22716 0.04553 -0.13648 -0.31737 -0.49562 -0.66976 -0.83835 -1.00000 -1.15336 -1.29716 -1.43022 -1.55142 -1.65977 -1.75437 -1.83442 -1.89928 -1.94840 -1.98137 -1.99793 0.00000 2.00000 -1.99793 -1.98137 -1.94840 -1.89928 -1.83442 -1.75437 -1.65977 -1.55142 -1.43022 -1.29716 -1.15336 -1.00000 -0.83835 -0.66976 -0.49562 -0.31737 -0.13648 0.04553 0.22716 0.40691 0.58329 0.75484 0.92013 1.07780 1.22653 1.36511 1.49237 1.60726 1.70884 1.79626 1.86879 1.92583 1.96692 1.99171 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.96692 1.86879 1.70884 1.49237 1.22653 0.92013 0.58329 0.22716 -0.13648 -0.49562 -0.83835 -1.15336 -1.43022 -1.65977 -1.83442 -1.94840 -1.99793 -1.98137 -1.89928 -1.75437 -1.55142 -1.29716 -1.00000 -0.66976 -0.31737 0.04553 0.40691 0.75484 1.07780 1.36511 1.60726 1.79626 1.92583 1.99171 0.00000 2.00000 1.99171 1.92583 1.79626 1.60726 1.36511 1.07780 0.75484 0.40691 0.04553 -0.31737 -0.66976 -1.00000 -1.29716 -1.55142 -1.75437 -1.89928 -1.98137 -1.99793 -1.94840 -1.83442 -1.65977 -1.43022 -1.15336 -0.83835 -0.49562 -0.13648 0.22716 0.58329 0.92013 1.22653 1.49237 1.70884 1.86879 1.96692 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 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 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 0.00000 2.00000 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583 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 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g 2.00000 1.86879 1.49237 0.92013 0.22716 -0.49562 -1.15336 -1.65977 -1.94840 -1.98137 -1.75437 -1.29716 -0.66976 0.04553 0.75484 1.36511 1.79626 1.99171 1.92583 1.60726 1.07780 0.40691 -0.31737 -1.00000 -1.55142 -1.89928 -1.99793 -1.83442 -1.43022 -0.83835 -0.13648 0.58329 1.22653 1.70884 1.96692 0.00000 2.00000 1.96692 1.70884 1.22653 0.58329 -0.13648 -0.83835 -1.43022 -1.83442 -1.99793 -1.89928 -1.55142 -1.00000 -0.31737 0.40691 1.07780 1.60726 1.92583 1.99171 1.79626 1.36511 0.75484 0.04553 -0.66976 -1.29716 -1.75437 -1.98137 -1.94840 -1.65977 -1.15336 -0.49562 0.22716 0.92013 1.49237 1.86879 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.79626 1.22653 0.40691 -0.49562 -1.29716 -1.83442 -1.99793 -1.75437 -1.15336 -0.31737 0.58329 1.36511 1.86879 1.99171 1.70884 1.07780 0.22716 -0.66976 -1.43022 -1.89928 -1.98137 -1.65977 -1.00000 -0.13648 0.75484 1.49237 1.92583 1.96692 1.60726 0.92013 0.04553 -0.83835 -1.55142 -1.94840 0.00000 2.00000 -1.94840 -1.55142 -0.83835 0.04553 0.92013 1.60726 1.96692 1.92583 1.49237 0.75484 -0.13648 -1.00000 -1.65977 -1.98137 -1.89928 -1.43022 -0.66976 0.22716 1.07780 1.70884 1.99171 1.86879 1.36511 0.58329 -0.31737 -1.15336 -1.75437 -1.99793 -1.83442 -1.29716 -0.49562 0.40691 1.22653 1.79626 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 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 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 0.00000 2.00000 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884 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 0.00000 ... ... ..... ....... ......... ........... TT........... E7g 2.00000 1.60726 0.58329 -0.66976 -1.65977 -1.99793 -1.55142 -0.49562 0.75484 1.70884 1.99171 1.49237 0.40691 -0.83835 -1.75437 -1.98137 -1.43022 -0.31737 0.92013 1.79626 1.96692 1.36511 0.22716 -1.00000 -1.83442 -1.94840 -1.29716 -0.13648 1.07780 1.86879 1.92583 1.22653 0.04553 -1.15336 -1.89928 0.00000 2.00000 -1.89928 -1.15336 0.04553 1.22653 1.92583 1.86879 1.07780 -0.13648 -1.29716 -1.94840 -1.83442 -1.00000 0.22716 1.36511 1.96692 1.79626 0.92013 -0.31737 -1.43022 -1.98137 -1.75437 -0.83835 0.40691 1.49237 1.99171 1.70884 0.75484 -0.49562 -1.55142 -1.99793 -1.65977 -0.66976 0.58329 1.60726 0.00000 ... ... ..... ....... ......... ........... ............. E8g 2.00000 1.49237 0.22716 -1.15336 -1.94840 -1.75437 -0.66976 0.75484 1.79626 1.92583 1.07780 -0.31737 -1.55142 -1.99793 -1.43022 -0.13648 1.22653 1.96692 1.70884 0.58329 -0.83835 -1.83442 -1.89928 -1.00000 0.40691 1.60726 1.99171 1.36511 0.04553 -1.29716 -1.98137 -1.65977 -0.49562 0.92013 1.86879 0.00000 2.00000 1.86879 0.92013 -0.49562 -1.65977 -1.98137 -1.29716 0.04553 1.36511 1.99171 1.60726 0.40691 -1.00000 -1.89928 -1.83442 -0.83835 0.58329 1.70884 1.96692 1.22653 -0.13648 -1.43022 -1.99793 -1.55142 -0.31737 1.07780 1.92583 1.79626 0.75484 -0.66976 -1.75437 -1.94840 -1.15336 0.22716 1.49237 0.00000 ... ... ..... ....... ......... ........... ............. E9g 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 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 0.00000 2.00000 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511 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 0.00000 ... ... ..... ....... ......... ........... ............. E10g 2.00000 1.22653 -0.49562 -1.83442 -1.75437 -0.31737 1.36511 1.99171 1.07780 -0.66976 -1.89928 -1.65977 -0.13648 1.49237 1.96692 0.92013 -0.83835 -1.94840 -1.55142 0.04553 1.60726 1.92583 0.75484 -1.00000 -1.98137 -1.43022 0.22716 1.70884 1.86879 0.58329 -1.15336 -1.99793 -1.29716 0.40691 1.79626 0.00000 2.00000 1.79626 0.40691 -1.29716 -1.99793 -1.15336 0.58329 1.86879 1.70884 0.22716 -1.43022 -1.98137 -1.00000 0.75484 1.92583 1.60726 0.04553 -1.55142 -1.94840 -0.83835 0.92013 1.96692 1.49237 -0.13648 -1.65977 -1.89928 -0.66976 1.07780 1.99171 1.36511 -0.31737 -1.75437 -1.83442 -0.49562 1.22653 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 1.07780 -0.83835 -1.98137 -1.29716 0.58329 1.92583 1.49237 -0.31737 -1.83442 -1.65977 0.04553 1.70884 1.79626 0.22716 -1.55142 -1.89928 -0.49562 1.36511 1.96692 0.75484 -1.15336 -1.99793 -1.00000 0.92013 1.99171 1.22653 -0.66976 -1.94840 -1.43022 0.40691 1.86879 1.60726 -0.13648 -1.75437 0.00000 2.00000 -1.75437 -0.13648 1.60726 1.86879 0.40691 -1.43022 -1.94840 -0.66976 1.22653 1.99171 0.92013 -1.00000 -1.99793 -1.15336 0.75484 1.96692 1.36511 -0.49562 -1.89928 -1.55142 0.22716 1.79626 1.70884 0.04553 -1.65977 -1.83442 -0.31737 1.49237 1.92583 0.58329 -1.29716 -1.98137 -0.83835 1.07780 0.00000 ... ... ..... ....... ......... ........... ............. E12g 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 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 0.00000 2.00000 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013 2.00000 0.92013 -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 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 0.75484 -1.43022 -1.83442 0.04553 1.86879 1.36511 -0.83835 -1.99793 -0.66976 1.49237 1.79626 -0.13648 -1.89928 -1.29716 0.92013 1.99171 0.58329 -1.55142 -1.75437 0.22716 1.92583 1.22653 -1.00000 -1.98137 -0.49562 1.60726 1.70884 -0.31737 -1.94840 -1.15336 1.07780 1.96692 0.40691 -1.65977 0.00000 2.00000 -1.65977 0.40691 1.96692 1.07780 -1.15336 -1.94840 -0.31737 1.70884 1.60726 -0.49562 -1.98137 -1.00000 1.22653 1.92583 0.22716 -1.75437 -1.55142 0.58329 1.99171 0.92013 -1.29716 -1.89928 -0.13648 1.79626 1.49237 -0.66976 -1.99793 -0.83835 1.36511 1.86879 0.04553 -1.83442 -1.43022 0.75484 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 0.58329 -1.65977 -1.55142 0.75484 1.99171 0.40691 -1.75437 -1.43022 0.92013 1.96692 0.22716 -1.83442 -1.29716 1.07780 1.92583 0.04553 -1.89928 -1.15336 1.22653 1.86879 -0.13648 -1.94840 -1.00000 1.36511 1.79626 -0.31737 -1.98137 -0.83835 1.49237 1.70884 -0.49562 -1.99793 -0.66976 1.60726 0.00000 2.00000 1.60726 -0.66976 -1.99793 -0.49562 1.70884 1.49237 -0.83835 -1.98137 -0.31737 1.79626 1.36511 -1.00000 -1.94840 -0.13648 1.86879 1.22653 -1.15336 -1.89928 0.04553 1.92583 1.07780 -1.29716 -1.83442 0.22716 1.96692 0.92013 -1.43022 -1.75437 0.40691 1.99171 0.75484 -1.55142 -1.65977 0.58329 0.00000 ... ... ..... ....... ......... ........... ............. E15g 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 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 0.00000 2.00000 -1.55142 0.92013 1.92583 -0.13648 -1.98137 -0.66976 1.70884 1.36511 -1.15336 -1.83442 0.40691 2.00000 0.40691 -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 0.00000 ... ... ..... ....... ......... ........... ............. E16g 2.00000 0.22716 -1.94840 -0.66976 1.79626 1.07780 -1.55142 -1.43022 1.22653 1.70884 -0.83835 -1.89928 0.40691 1.99171 0.04553 -1.98137 -0.49562 1.86879 0.92013 -1.65977 -1.29716 1.36511 1.60726 -1.00000 -1.83442 0.58329 1.96692 -0.13648 -1.99793 -0.31737 1.92583 0.75484 -1.75437 -1.15336 1.49237 0.00000 2.00000 1.49237 -1.15336 -1.75437 0.75484 1.92583 -0.31737 -1.99793 -0.13648 1.96692 0.58329 -1.83442 -1.00000 1.60726 1.36511 -1.29716 -1.65977 0.92013 1.86879 -0.49562 -1.98137 0.04553 1.99171 0.40691 -1.89928 -0.83835 1.70884 1.22653 -1.43022 -1.55142 1.07780 1.79626 -0.66976 -1.94840 0.22716 0.00000 ... ... ..... ....... ......... ........... ............. E17g 2.00000 0.04553 -1.99793 -0.13648 1.99171 0.22716 -1.98137 -0.31737 1.96692 0.40691 -1.94840 -0.49562 1.92583 0.58329 -1.89928 -0.66976 1.86879 0.75484 -1.83442 -0.83835 1.79626 0.92013 -1.75437 -1.00000 1.70884 1.07780 -1.65977 -1.15336 1.60726 1.22653 -1.55142 -1.29716 1.49237 1.36511 -1.43022 0.00000 2.00000 -1.43022 1.36511 1.49237 -1.29716 -1.55142 1.22653 1.60726 -1.15336 -1.65977 1.07780 1.70884 -1.00000 -1.75437 0.92013 1.79626 -0.83835 -1.83442 0.75484 1.86879 -0.66976 -1.89928 0.58329 1.92583 -0.49562 -1.94840 0.40691 1.96692 -0.31737 -1.98137 0.22716 1.99171 -0.13648 -1.99793 0.04553 0.00000 ... ... ..... ....... ......... ........... ............. E18g 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 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 0.00000 2.00000 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648 2.00000 -0.13648 -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 0.00000 ... ... ..... ....... ......... ........... ............. E19g 2.00000 -0.31737 -1.89928 0.92013 1.60726 -1.43022 -1.15336 1.79626 0.58329 -1.98137 0.04553 1.96692 -0.66976 -1.75437 1.22653 1.36511 -1.65977 -0.83835 1.92583 0.22716 -1.99793 0.40691 1.86879 -1.00000 -1.55142 1.49237 1.07780 -1.83442 -0.49562 1.99171 -0.13648 -1.94840 0.75484 1.70884 -1.29716 0.00000 2.00000 -1.29716 1.70884 0.75484 -1.94840 -0.13648 1.99171 -0.49562 -1.83442 1.07780 1.49237 -1.55142 -1.00000 1.86879 0.40691 -1.99793 0.22716 1.92583 -0.83835 -1.65977 1.36511 1.22653 -1.75437 -0.66976 1.96692 0.04553 -1.98137 0.58329 1.79626 -1.15336 -1.43022 1.60726 0.92013 -1.89928 -0.31737 0.00000 ... ... ..... ....... ......... ........... ............. E20g 2.00000 -0.49562 -1.75437 1.36511 1.07780 -1.89928 -0.13648 1.96692 -0.83835 -1.55142 1.60726 0.75484 -1.98137 0.22716 1.86879 -1.15336 -1.29716 1.79626 0.40691 -1.99793 0.58329 1.70884 -1.43022 -1.00000 1.92583 0.04553 -1.94840 0.92013 1.49237 -1.65977 -0.66976 1.99171 -0.31737 -1.83442 1.22653 0.00000 2.00000 1.22653 -1.83442 -0.31737 1.99171 -0.66976 -1.65977 1.49237 0.92013 -1.94840 0.04553 1.92583 -1.00000 -1.43022 1.70884 0.58329 -1.99793 0.40691 1.79626 -1.29716 -1.15336 1.86879 0.22716 -1.98137 0.75484 1.60726 -1.55142 -0.83835 1.96692 -0.13648 -1.89928 1.07780 1.36511 -1.75437 -0.49562 0.00000 ... ... ..... ....... ......... ........... ............. E21g 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 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 0.00000 2.00000 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976 2.00000 -0.66976 -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 0.00000 ... ... ..... ....... ......... ........... ............. E22g 2.00000 -0.83835 -1.29716 1.92583 -0.31737 -1.65977 1.70884 0.22716 -1.89928 1.36511 0.75484 -1.99793 0.92013 1.22653 -1.94840 0.40691 1.60726 -1.75437 -0.13648 1.86879 -1.43022 -0.66976 1.99171 -1.00000 -1.15336 1.96692 -0.49562 -1.55142 1.79626 0.04553 -1.83442 1.49237 0.58329 -1.98137 1.07780 0.00000 2.00000 1.07780 -1.98137 0.58329 1.49237 -1.83442 0.04553 1.79626 -1.55142 -0.49562 1.96692 -1.15336 -1.00000 1.99171 -0.66976 -1.43022 1.86879 -0.13648 -1.75437 1.60726 0.40691 -1.94840 1.22653 0.92013 -1.99793 0.75484 1.36511 -1.89928 0.22716 1.70884 -1.65977 -0.31737 1.92583 -1.29716 -0.83835 0.00000 ... ... ..... ....... ......... ........... ............. E23g 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 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000 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 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 0.00000 ... ... ..... ....... ......... ........... ............. E24g 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 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 0.00000 2.00000 0.92013 -1.98137 1.36511 0.40691 -1.83442 1.70884 -0.13648 -1.55142 1.92583 -0.66976 -1.15336 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 0.00000 ... ... ..... ....... ......... ........... ............. E25g 2.00000 -1.29716 -0.31737 1.70884 -1.89928 0.75484 0.92013 -1.94840 1.60726 -0.13648 -1.43022 1.99171 -1.15336 -0.49562 1.79626 -1.83442 0.58329 1.07780 -1.98137 1.49237 0.04553 -1.55142 1.96692 -1.00000 -0.66976 1.86879 -1.75437 0.40691 1.22653 -1.99793 1.36511 0.22716 -1.65977 1.92583 -0.83835 0.00000 2.00000 -0.83835 1.92583 -1.65977 0.22716 1.36511 -1.99793 1.22653 0.40691 -1.75437 1.86879 -0.66976 -1.00000 1.96692 -1.55142 0.04553 1.49237 -1.98137 1.07780 0.58329 -1.83442 1.79626 -0.49562 -1.15336 1.99171 -1.43022 -0.13648 1.60726 -1.94840 0.92013 0.75484 -1.89928 1.70884 -0.31737 -1.29716 0.00000 ... ... ..... ....... ......... ........... ............. E26g 2.00000 -1.43022 0.04553 1.36511 -1.99793 1.49237 -0.13648 -1.29716 1.99171 -1.55142 0.22716 1.22653 -1.98137 1.60726 -0.31737 -1.15336 1.96692 -1.65977 0.40691 1.07780 -1.94840 1.70884 -0.49562 -1.00000 1.92583 -1.75437 0.58329 0.92013 -1.89928 1.79626 -0.66976 -0.83835 1.86879 -1.83442 0.75484 0.00000 2.00000 0.75484 -1.83442 1.86879 -0.83835 -0.66976 1.79626 -1.89928 0.92013 0.58329 -1.75437 1.92583 -1.00000 -0.49562 1.70884 -1.94840 1.07780 0.40691 -1.65977 1.96692 -1.15336 -0.31737 1.60726 -1.98137 1.22653 0.22716 -1.55142 1.99171 -1.29716 -0.13648 1.49237 -1.99793 1.36511 0.04553 -1.43022 0.00000 ... ... ..... ....... ......... ........... ............. E27g 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 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 0.00000 2.00000 -0.66976 1.70884 -1.98137 1.36511 -0.13648 -1.15336 1.92583 -1.83442 0.92013 0.40691 -1.55142 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 0.00000 ... ... ..... ....... ......... ........... ............. E28g 2.00000 -1.65977 0.75484 0.40691 -1.43022 1.96692 -1.83442 1.07780 0.04553 -1.15336 1.86879 -1.94840 1.36511 -0.31737 -0.83835 1.70884 -1.99793 1.60726 -0.66976 -0.49562 1.49237 -1.98137 1.79626 -1.00000 -0.13648 1.22653 -1.89928 1.92583 -1.29716 0.22716 0.92013 -1.75437 1.99171 -1.55142 0.58329 0.00000 2.00000 0.58329 -1.55142 1.99171 -1.75437 0.92013 0.22716 -1.29716 1.92583 -1.89928 1.22653 -0.13648 -1.00000 1.79626 -1.98137 1.49237 -0.49562 -0.66976 1.60726 -1.99793 1.70884 -0.83835 -0.31737 1.36511 -1.94840 1.86879 -1.15336 0.04553 1.07780 -1.83442 1.96692 -1.43022 0.40691 0.75484 -1.65977 0.00000 ... ... ..... ....... ......... ........... ............. E29g 2.00000 -1.75437 1.07780 -0.13648 -0.83835 1.60726 -1.98137 1.86879 -1.29716 0.40691 0.58329 -1.43022 1.92583 -1.94840 1.49237 -0.66976 -0.31737 1.22653 -1.83442 1.99171 -1.65977 0.92013 0.04553 -1.00000 1.70884 -1.99793 1.79626 -1.15336 0.22716 0.75484 -1.55142 1.96692 -1.89928 1.36511 -0.49562 0.00000 2.00000 -0.49562 1.36511 -1.89928 1.96692 -1.55142 0.75484 0.22716 -1.15336 1.79626 -1.99793 1.70884 -1.00000 0.04553 0.92013 -1.65977 1.99171 -1.83442 1.22653 -0.31737 -0.66976 1.49237 -1.94840 1.92583 -1.43022 0.58329 0.40691 -1.29716 1.86879 -1.98137 1.60726 -0.83835 -0.13648 1.07780 -1.75437 0.00000 ... ... ..... ....... ......... ........... ............. E30g 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 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 0.00000 2.00000 0.40691 -1.15336 1.70884 -1.98137 1.92583 -1.55142 0.92013 -0.13648 -0.66976 1.36511 -1.83442 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 0.00000 ... ... ..... ....... ......... ........... ............. E31g 2.00000 -1.89928 1.60726 -1.15336 0.58329 0.04553 -0.66976 1.22653 -1.65977 1.92583 -1.99793 1.86879 -1.55142 1.07780 -0.49562 -0.13648 0.75484 -1.29716 1.70884 -1.94840 1.99171 -1.83442 1.49237 -1.00000 0.40691 0.22716 -0.83835 1.36511 -1.75437 1.96692 -1.98137 1.79626 -1.43022 0.92013 -0.31737 0.00000 2.00000 -0.31737 0.92013 -1.43022 1.79626 -1.98137 1.96692 -1.75437 1.36511 -0.83835 0.22716 0.40691 -1.00000 1.49237 -1.83442 1.99171 -1.94840 1.70884 -1.29716 0.75484 -0.13648 -0.49562 1.07780 -1.55142 1.86879 -1.99793 1.92583 -1.65977 1.22653 -0.66976 0.04553 0.58329 -1.15336 1.60726 -1.89928 0.00000 ... ... ..... ....... ......... ........... ............. E32g 2.00000 -1.94840 1.79626 -1.55142 1.22653 -0.83835 0.40691 0.04553 -0.49562 0.92013 -1.29716 1.60726 -1.83442 1.96692 -1.99793 1.92583 -1.75437 1.49237 -1.15336 0.75484 -0.31737 -0.13648 0.58329 -1.00000 1.36511 -1.65977 1.86879 -1.98137 1.99171 -1.89928 1.70884 -1.43022 1.07780 -0.66976 0.22716 0.00000 2.00000 0.22716 -0.66976 1.07780 -1.43022 1.70884 -1.89928 1.99171 -1.98137 1.86879 -1.65977 1.36511 -1.00000 0.58329 -0.13648 -0.31737 0.75484 -1.15336 1.49237 -1.75437 1.92583 -1.99793 1.96692 -1.83442 1.60726 -1.29716 0.92013 -0.49562 0.04553 0.40691 -0.83835 1.22653 -1.55142 1.79626 -1.94840 0.00000 ... ... ..... ....... ......... ........... ............. E33g 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 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 0.00000 2.00000 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137 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 0.00000 ... ... ..... ....... ......... ........... ............. E34g 2.00000 -1.99793 1.99171 -1.98137 1.96692 -1.94840 1.92583 -1.89928 1.86879 -1.83442 1.79626 -1.75437 1.70884 -1.65977 1.60726 -1.55142 1.49237 -1.43022 1.36511 -1.29716 1.22653 -1.15336 1.07780 -1.00000 0.92013 -0.83835 0.75484 -0.66976 0.58329 -0.49562 0.40691 -0.31737 0.22716 -0.13648 0.04553 0.00000 2.00000 0.04553 -0.13648 0.22716 -0.31737 0.40691 -0.49562 0.58329 -0.66976 0.75484 -0.83835 0.92013 -1.00000 1.07780 -1.15336 1.22653 -1.29716 1.36511 -1.43022 1.49237 -1.55142 1.60726 -1.65977 1.70884 -1.75437 1.79626 -1.83442 1.86879 -1.89928 1.92583 -1.94840 1.96692 -1.98137 1.99171 -1.99793 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 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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 1.99171 1.96692 1.92583 1.86879 1.79626 1.70884 1.60726 1.49237 1.36511 1.22653 1.07780 0.92013 0.75484 0.58329 0.40691 0.22716 0.04553 -0.13648 -0.31737 -0.49562 -0.66976 -0.83835 -1.00000 -1.15336 -1.29716 -1.43022 -1.55142 -1.65977 -1.75437 -1.83442 -1.89928 -1.94840 -1.98137 -1.99793 0.00000 -2.00000 1.99793 1.98137 1.94840 1.89928 1.83442 1.75437 1.65977 1.55142 1.43022 1.29716 1.15336 1.00000 0.83835 0.66976 0.49562 0.31737 0.13648 -0.04553 -0.22716 -0.40691 -0.58329 -0.75484 -0.92013 -1.07780 -1.22653 -1.36511 -1.49237 -1.60726 -1.70884 -1.79626 -1.86879 -1.92583 -1.96692 -1.99171 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.96692 1.86879 1.70884 1.49237 1.22653 0.92013 0.58329 0.22716 -0.13648 -0.49562 -0.83835 -1.15336 -1.43022 -1.65977 -1.83442 -1.94840 -1.99793 -1.98137 -1.89928 -1.75437 -1.55142 -1.29716 -1.00000 -0.66976 -0.31737 0.04553 0.40691 0.75484 1.07780 1.36511 1.60726 1.79626 1.92583 1.99171 0.00000 -2.00000 -1.99171 -1.92583 -1.79626 -1.60726 -1.36511 -1.07780 -0.75484 -0.40691 -0.04553 0.31737 0.66976 1.00000 1.29716 1.55142 1.75437 1.89928 1.98137 1.99793 1.94840 1.83442 1.65977 1.43022 1.15336 0.83835 0.49562 0.13648 -0.22716 -0.58329 -0.92013 -1.22653 -1.49237 -1.70884 -1.86879 -1.96692 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u 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 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 0.00000 -2.00000 1.98137 1.83442 1.55142 1.15336 0.66976 0.13648 -0.40691 -0.92013 -1.36511 -1.70884 -1.92583 -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 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u 2.00000 1.86879 1.49237 0.92013 0.22716 -0.49562 -1.15336 -1.65977 -1.94840 -1.98137 -1.75437 -1.29716 -0.66976 0.04553 0.75484 1.36511 1.79626 1.99171 1.92583 1.60726 1.07780 0.40691 -0.31737 -1.00000 -1.55142 -1.89928 -1.99793 -1.83442 -1.43022 -0.83835 -0.13648 0.58329 1.22653 1.70884 1.96692 0.00000 -2.00000 -1.96692 -1.70884 -1.22653 -0.58329 0.13648 0.83835 1.43022 1.83442 1.99793 1.89928 1.55142 1.00000 0.31737 -0.40691 -1.07780 -1.60726 -1.92583 -1.99171 -1.79626 -1.36511 -0.75484 -0.04553 0.66976 1.29716 1.75437 1.98137 1.94840 1.65977 1.15336 0.49562 -0.22716 -0.92013 -1.49237 -1.86879 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5u 2.00000 1.79626 1.22653 0.40691 -0.49562 -1.29716 -1.83442 -1.99793 -1.75437 -1.15336 -0.31737 0.58329 1.36511 1.86879 1.99171 1.70884 1.07780 0.22716 -0.66976 -1.43022 -1.89928 -1.98137 -1.65977 -1.00000 -0.13648 0.75484 1.49237 1.92583 1.96692 1.60726 0.92013 0.04553 -0.83835 -1.55142 -1.94840 0.00000 -2.00000 1.94840 1.55142 0.83835 -0.04553 -0.92013 -1.60726 -1.96692 -1.92583 -1.49237 -0.75484 0.13648 1.00000 1.65977 1.98137 1.89928 1.43022 0.66976 -0.22716 -1.07780 -1.70884 -1.99171 -1.86879 -1.36511 -0.58329 0.31737 1.15336 1.75437 1.99793 1.83442 1.29716 0.49562 -0.40691 -1.22653 -1.79626 0.00000 ... ... ..... ....... ......... TT......... ............. E6u 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 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 0.00000 -2.00000 -1.92583 -1.36511 -0.40691 0.66976 1.55142 1.98137 1.83442 1.15336 0.13648 -0.92013 -1.70884 -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 0.00000 ... ... ..... ....... ......... ........... ............. E7u 2.00000 1.60726 0.58329 -0.66976 -1.65977 -1.99793 -1.55142 -0.49562 0.75484 1.70884 1.99171 1.49237 0.40691 -0.83835 -1.75437 -1.98137 -1.43022 -0.31737 0.92013 1.79626 1.96692 1.36511 0.22716 -1.00000 -1.83442 -1.94840 -1.29716 -0.13648 1.07780 1.86879 1.92583 1.22653 0.04553 -1.15336 -1.89928 0.00000 -2.00000 1.89928 1.15336 -0.04553 -1.22653 -1.92583 -1.86879 -1.07780 0.13648 1.29716 1.94840 1.83442 1.00000 -0.22716 -1.36511 -1.96692 -1.79626 -0.92013 0.31737 1.43022 1.98137 1.75437 0.83835 -0.40691 -1.49237 -1.99171 -1.70884 -0.75484 0.49562 1.55142 1.99793 1.65977 0.66976 -0.58329 -1.60726 0.00000 ... ... ..... ....... ......... ........... ............. E8u 2.00000 1.49237 0.22716 -1.15336 -1.94840 -1.75437 -0.66976 0.75484 1.79626 1.92583 1.07780 -0.31737 -1.55142 -1.99793 -1.43022 -0.13648 1.22653 1.96692 1.70884 0.58329 -0.83835 -1.83442 -1.89928 -1.00000 0.40691 1.60726 1.99171 1.36511 0.04553 -1.29716 -1.98137 -1.65977 -0.49562 0.92013 1.86879 0.00000 -2.00000 -1.86879 -0.92013 0.49562 1.65977 1.98137 1.29716 -0.04553 -1.36511 -1.99171 -1.60726 -0.40691 1.00000 1.89928 1.83442 0.83835 -0.58329 -1.70884 -1.96692 -1.22653 0.13648 1.43022 1.99793 1.55142 0.31737 -1.07780 -1.92583 -1.79626 -0.75484 0.66976 1.75437 1.94840 1.15336 -0.22716 -1.49237 0.00000 ... ... ..... ....... ......... ........... ............. E9u 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 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 0.00000 -2.00000 1.83442 0.66976 -0.92013 -1.92583 -1.70884 -0.40691 1.15336 1.98137 1.55142 0.13648 -1.36511 -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 0.00000 ... ... ..... ....... ......... ........... ............. E10u 2.00000 1.22653 -0.49562 -1.83442 -1.75437 -0.31737 1.36511 1.99171 1.07780 -0.66976 -1.89928 -1.65977 -0.13648 1.49237 1.96692 0.92013 -0.83835 -1.94840 -1.55142 0.04553 1.60726 1.92583 0.75484 -1.00000 -1.98137 -1.43022 0.22716 1.70884 1.86879 0.58329 -1.15336 -1.99793 -1.29716 0.40691 1.79626 0.00000 -2.00000 -1.79626 -0.40691 1.29716 1.99793 1.15336 -0.58329 -1.86879 -1.70884 -0.22716 1.43022 1.98137 1.00000 -0.75484 -1.92583 -1.60726 -0.04553 1.55142 1.94840 0.83835 -0.92013 -1.96692 -1.49237 0.13648 1.65977 1.89928 0.66976 -1.07780 -1.99171 -1.36511 0.31737 1.75437 1.83442 0.49562 -1.22653 0.00000 ... ... ..... ....... ......... ........... ............. E11u 2.00000 1.07780 -0.83835 -1.98137 -1.29716 0.58329 1.92583 1.49237 -0.31737 -1.83442 -1.65977 0.04553 1.70884 1.79626 0.22716 -1.55142 -1.89928 -0.49562 1.36511 1.96692 0.75484 -1.15336 -1.99793 -1.00000 0.92013 1.99171 1.22653 -0.66976 -1.94840 -1.43022 0.40691 1.86879 1.60726 -0.13648 -1.75437 0.00000 -2.00000 1.75437 0.13648 -1.60726 -1.86879 -0.40691 1.43022 1.94840 0.66976 -1.22653 -1.99171 -0.92013 1.00000 1.99793 1.15336 -0.75484 -1.96692 -1.36511 0.49562 1.89928 1.55142 -0.22716 -1.79626 -1.70884 -0.04553 1.65977 1.83442 0.31737 -1.49237 -1.92583 -0.58329 1.29716 1.98137 0.83835 -1.07780 0.00000 ... ... ..... ....... ......... ........... ............. E12u 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 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 0.00000 -2.00000 -1.70884 0.13648 1.83442 1.55142 -0.40691 -1.92583 -1.36511 0.66976 1.98137 1.15336 -0.92013 -2.00000 -0.92013 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 0.00000 ... ... ..... ....... ......... ........... ............. E13u 2.00000 0.75484 -1.43022 -1.83442 0.04553 1.86879 1.36511 -0.83835 -1.99793 -0.66976 1.49237 1.79626 -0.13648 -1.89928 -1.29716 0.92013 1.99171 0.58329 -1.55142 -1.75437 0.22716 1.92583 1.22653 -1.00000 -1.98137 -0.49562 1.60726 1.70884 -0.31737 -1.94840 -1.15336 1.07780 1.96692 0.40691 -1.65977 0.00000 -2.00000 1.65977 -0.40691 -1.96692 -1.07780 1.15336 1.94840 0.31737 -1.70884 -1.60726 0.49562 1.98137 1.00000 -1.22653 -1.92583 -0.22716 1.75437 1.55142 -0.58329 -1.99171 -0.92013 1.29716 1.89928 0.13648 -1.79626 -1.49237 0.66976 1.99793 0.83835 -1.36511 -1.86879 -0.04553 1.83442 1.43022 -0.75484 0.00000 ... ... ..... ....... ......... ........... ............. E14u 2.00000 0.58329 -1.65977 -1.55142 0.75484 1.99171 0.40691 -1.75437 -1.43022 0.92013 1.96692 0.22716 -1.83442 -1.29716 1.07780 1.92583 0.04553 -1.89928 -1.15336 1.22653 1.86879 -0.13648 -1.94840 -1.00000 1.36511 1.79626 -0.31737 -1.98137 -0.83835 1.49237 1.70884 -0.49562 -1.99793 -0.66976 1.60726 0.00000 -2.00000 -1.60726 0.66976 1.99793 0.49562 -1.70884 -1.49237 0.83835 1.98137 0.31737 -1.79626 -1.36511 1.00000 1.94840 0.13648 -1.86879 -1.22653 1.15336 1.89928 -0.04553 -1.92583 -1.07780 1.29716 1.83442 -0.22716 -1.96692 -0.92013 1.43022 1.75437 -0.40691 -1.99171 -0.75484 1.55142 1.65977 -0.58329 0.00000 ... ... ..... ....... ......... ........... ............. E15u 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 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 0.00000 -2.00000 1.55142 -0.92013 -1.92583 0.13648 1.98137 0.66976 -1.70884 -1.36511 1.15336 1.83442 -0.40691 -2.00000 -0.40691 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 0.00000 ... ... ..... ....... ......... ........... ............. E16u 2.00000 0.22716 -1.94840 -0.66976 1.79626 1.07780 -1.55142 -1.43022 1.22653 1.70884 -0.83835 -1.89928 0.40691 1.99171 0.04553 -1.98137 -0.49562 1.86879 0.92013 -1.65977 -1.29716 1.36511 1.60726 -1.00000 -1.83442 0.58329 1.96692 -0.13648 -1.99793 -0.31737 1.92583 0.75484 -1.75437 -1.15336 1.49237 0.00000 -2.00000 -1.49237 1.15336 1.75437 -0.75484 -1.92583 0.31737 1.99793 0.13648 -1.96692 -0.58329 1.83442 1.00000 -1.60726 -1.36511 1.29716 1.65977 -0.92013 -1.86879 0.49562 1.98137 -0.04553 -1.99171 -0.40691 1.89928 0.83835 -1.70884 -1.22653 1.43022 1.55142 -1.07780 -1.79626 0.66976 1.94840 -0.22716 0.00000 ... ... ..... ....... ......... ........... ............. E17u 2.00000 0.04553 -1.99793 -0.13648 1.99171 0.22716 -1.98137 -0.31737 1.96692 0.40691 -1.94840 -0.49562 1.92583 0.58329 -1.89928 -0.66976 1.86879 0.75484 -1.83442 -0.83835 1.79626 0.92013 -1.75437 -1.00000 1.70884 1.07780 -1.65977 -1.15336 1.60726 1.22653 -1.55142 -1.29716 1.49237 1.36511 -1.43022 0.00000 -2.00000 1.43022 -1.36511 -1.49237 1.29716 1.55142 -1.22653 -1.60726 1.15336 1.65977 -1.07780 -1.70884 1.00000 1.75437 -0.92013 -1.79626 0.83835 1.83442 -0.75484 -1.86879 0.66976 1.89928 -0.58329 -1.92583 0.49562 1.94840 -0.40691 -1.96692 0.31737 1.98137 -0.22716 -1.99171 0.13648 1.99793 -0.04553 0.00000 ... ... ..... ....... ......... ........... ............. E18u 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 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 0.00000 -2.00000 -1.36511 1.55142 1.15336 -1.70884 -0.92013 1.83442 0.66976 -1.92583 -0.40691 1.98137 0.13648 -2.00000 0.13648 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 0.00000 ... ... ..... ....... ......... ........... ............. E19u 2.00000 -0.31737 -1.89928 0.92013 1.60726 -1.43022 -1.15336 1.79626 0.58329 -1.98137 0.04553 1.96692 -0.66976 -1.75437 1.22653 1.36511 -1.65977 -0.83835 1.92583 0.22716 -1.99793 0.40691 1.86879 -1.00000 -1.55142 1.49237 1.07780 -1.83442 -0.49562 1.99171 -0.13648 -1.94840 0.75484 1.70884 -1.29716 0.00000 -2.00000 1.29716 -1.70884 -0.75484 1.94840 0.13648 -1.99171 0.49562 1.83442 -1.07780 -1.49237 1.55142 1.00000 -1.86879 -0.40691 1.99793 -0.22716 -1.92583 0.83835 1.65977 -1.36511 -1.22653 1.75437 0.66976 -1.96692 -0.04553 1.98137 -0.58329 -1.79626 1.15336 1.43022 -1.60726 -0.92013 1.89928 0.31737 0.00000 ... ... ..... ....... ......... ........... ............. E20u 2.00000 -0.49562 -1.75437 1.36511 1.07780 -1.89928 -0.13648 1.96692 -0.83835 -1.55142 1.60726 0.75484 -1.98137 0.22716 1.86879 -1.15336 -1.29716 1.79626 0.40691 -1.99793 0.58329 1.70884 -1.43022 -1.00000 1.92583 0.04553 -1.94840 0.92013 1.49237 -1.65977 -0.66976 1.99171 -0.31737 -1.83442 1.22653 0.00000 -2.00000 -1.22653 1.83442 0.31737 -1.99171 0.66976 1.65977 -1.49237 -0.92013 1.94840 -0.04553 -1.92583 1.00000 1.43022 -1.70884 -0.58329 1.99793 -0.40691 -1.79626 1.29716 1.15336 -1.86879 -0.22716 1.98137 -0.75484 -1.60726 1.55142 0.83835 -1.96692 0.13648 1.89928 -1.07780 -1.36511 1.75437 0.49562 0.00000 ... ... ..... ....... ......... ........... ............. E21u 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 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 0.00000 -2.00000 1.15336 -1.92583 0.13648 1.83442 -1.36511 -0.92013 1.98137 -0.40691 -1.70884 1.55142 0.66976 -2.00000 0.66976 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 0.00000 ... ... ..... ....... ......... ........... ............. E22u 2.00000 -0.83835 -1.29716 1.92583 -0.31737 -1.65977 1.70884 0.22716 -1.89928 1.36511 0.75484 -1.99793 0.92013 1.22653 -1.94840 0.40691 1.60726 -1.75437 -0.13648 1.86879 -1.43022 -0.66976 1.99171 -1.00000 -1.15336 1.96692 -0.49562 -1.55142 1.79626 0.04553 -1.83442 1.49237 0.58329 -1.98137 1.07780 0.00000 -2.00000 -1.07780 1.98137 -0.58329 -1.49237 1.83442 -0.04553 -1.79626 1.55142 0.49562 -1.96692 1.15336 1.00000 -1.99171 0.66976 1.43022 -1.86879 0.13648 1.75437 -1.60726 -0.40691 1.94840 -1.22653 -0.92013 1.99793 -0.75484 -1.36511 1.89928 -0.22716 -1.70884 1.65977 0.31737 -1.92583 1.29716 0.83835 0.00000 ... ... ..... ....... ......... ........... ............. E23u 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 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000 -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 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 0.00000 ... ... ..... ....... ......... ........... ............. E24u 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 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 0.00000 -2.00000 -0.92013 1.98137 -1.36511 -0.40691 1.83442 -1.70884 0.13648 1.55142 -1.92583 0.66976 1.15336 -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 0.00000 ... ... ..... ....... ......... ........... ............. E25u 2.00000 -1.29716 -0.31737 1.70884 -1.89928 0.75484 0.92013 -1.94840 1.60726 -0.13648 -1.43022 1.99171 -1.15336 -0.49562 1.79626 -1.83442 0.58329 1.07780 -1.98137 1.49237 0.04553 -1.55142 1.96692 -1.00000 -0.66976 1.86879 -1.75437 0.40691 1.22653 -1.99793 1.36511 0.22716 -1.65977 1.92583 -0.83835 0.00000 -2.00000 0.83835 -1.92583 1.65977 -0.22716 -1.36511 1.99793 -1.22653 -0.40691 1.75437 -1.86879 0.66976 1.00000 -1.96692 1.55142 -0.04553 -1.49237 1.98137 -1.07780 -0.58329 1.83442 -1.79626 0.49562 1.15336 -1.99171 1.43022 0.13648 -1.60726 1.94840 -0.92013 -0.75484 1.89928 -1.70884 0.31737 1.29716 0.00000 ... ... ..... ....... ......... ........... ............. E26u 2.00000 -1.43022 0.04553 1.36511 -1.99793 1.49237 -0.13648 -1.29716 1.99171 -1.55142 0.22716 1.22653 -1.98137 1.60726 -0.31737 -1.15336 1.96692 -1.65977 0.40691 1.07780 -1.94840 1.70884 -0.49562 -1.00000 1.92583 -1.75437 0.58329 0.92013 -1.89928 1.79626 -0.66976 -0.83835 1.86879 -1.83442 0.75484 0.00000 -2.00000 -0.75484 1.83442 -1.86879 0.83835 0.66976 -1.79626 1.89928 -0.92013 -0.58329 1.75437 -1.92583 1.00000 0.49562 -1.70884 1.94840 -1.07780 -0.40691 1.65977 -1.96692 1.15336 0.31737 -1.60726 1.98137 -1.22653 -0.22716 1.55142 -1.99171 1.29716 0.13648 -1.49237 1.99793 -1.36511 -0.04553 1.43022 0.00000 ... ... ..... ....... ......... ........... ............. E27u 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 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 0.00000 -2.00000 0.66976 -1.70884 1.98137 -1.36511 0.13648 1.15336 -1.92583 1.83442 -0.92013 -0.40691 1.55142 -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 0.00000 ... ... ..... ....... ......... ........... ............. E28u 2.00000 -1.65977 0.75484 0.40691 -1.43022 1.96692 -1.83442 1.07780 0.04553 -1.15336 1.86879 -1.94840 1.36511 -0.31737 -0.83835 1.70884 -1.99793 1.60726 -0.66976 -0.49562 1.49237 -1.98137 1.79626 -1.00000 -0.13648 1.22653 -1.89928 1.92583 -1.29716 0.22716 0.92013 -1.75437 1.99171 -1.55142 0.58329 0.00000 -2.00000 -0.58329 1.55142 -1.99171 1.75437 -0.92013 -0.22716 1.29716 -1.92583 1.89928 -1.22653 0.13648 1.00000 -1.79626 1.98137 -1.49237 0.49562 0.66976 -1.60726 1.99793 -1.70884 0.83835 0.31737 -1.36511 1.94840 -1.86879 1.15336 -0.04553 -1.07780 1.83442 -1.96692 1.43022 -0.40691 -0.75484 1.65977 0.00000 ... ... ..... ....... ......... ........... ............. E29u 2.00000 -1.75437 1.07780 -0.13648 -0.83835 1.60726 -1.98137 1.86879 -1.29716 0.40691 0.58329 -1.43022 1.92583 -1.94840 1.49237 -0.66976 -0.31737 1.22653 -1.83442 1.99171 -1.65977 0.92013 0.04553 -1.00000 1.70884 -1.99793 1.79626 -1.15336 0.22716 0.75484 -1.55142 1.96692 -1.89928 1.36511 -0.49562 0.00000 -2.00000 0.49562 -1.36511 1.89928 -1.96692 1.55142 -0.75484 -0.22716 1.15336 -1.79626 1.99793 -1.70884 1.00000 -0.04553 -0.92013 1.65977 -1.99171 1.83442 -1.22653 0.31737 0.66976 -1.49237 1.94840 -1.92583 1.43022 -0.58329 -0.40691 1.29716 -1.86879 1.98137 -1.60726 0.83835 0.13648 -1.07780 1.75437 0.00000 ... ... ..... ....... ......... ........... ............. E30u 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 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 0.00000 -2.00000 -0.40691 1.15336 -1.70884 1.98137 -1.92583 1.55142 -0.92013 0.13648 0.66976 -1.36511 1.83442 -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 0.00000 ... ... ..... ....... ......... ........... ............. E31u 2.00000 -1.89928 1.60726 -1.15336 0.58329 0.04553 -0.66976 1.22653 -1.65977 1.92583 -1.99793 1.86879 -1.55142 1.07780 -0.49562 -0.13648 0.75484 -1.29716 1.70884 -1.94840 1.99171 -1.83442 1.49237 -1.00000 0.40691 0.22716 -0.83835 1.36511 -1.75437 1.96692 -1.98137 1.79626 -1.43022 0.92013 -0.31737 0.00000 -2.00000 0.31737 -0.92013 1.43022 -1.79626 1.98137 -1.96692 1.75437 -1.36511 0.83835 -0.22716 -0.40691 1.00000 -1.49237 1.83442 -1.99171 1.94840 -1.70884 1.29716 -0.75484 0.13648 0.49562 -1.07780 1.55142 -1.86879 1.99793 -1.92583 1.65977 -1.22653 0.66976 -0.04553 -0.58329 1.15336 -1.60726 1.89928 0.00000 ... ... ..... ....... ......... ........... ............. E32u 2.00000 -1.94840 1.79626 -1.55142 1.22653 -0.83835 0.40691 0.04553 -0.49562 0.92013 -1.29716 1.60726 -1.83442 1.96692 -1.99793 1.92583 -1.75437 1.49237 -1.15336 0.75484 -0.31737 -0.13648 0.58329 -1.00000 1.36511 -1.65977 1.86879 -1.98137 1.99171 -1.89928 1.70884 -1.43022 1.07780 -0.66976 0.22716 0.00000 -2.00000 -0.22716 0.66976 -1.07780 1.43022 -1.70884 1.89928 -1.99171 1.98137 -1.86879 1.65977 -1.36511 1.00000 -0.58329 0.13648 0.31737 -0.75484 1.15336 -1.49237 1.75437 -1.92583 1.99793 -1.96692 1.83442 -1.60726 1.29716 -0.92013 0.49562 -0.04553 -0.40691 0.83835 -1.22653 1.55142 -1.79626 1.94840 0.00000 ... ... ..... ....... ......... ........... ............. E33u 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 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 0.00000 -2.00000 0.13648 -0.40691 0.66976 -0.92013 1.15336 -1.36511 1.55142 -1.70884 1.83442 -1.92583 1.98137 -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 0.00000 ... ... ..... ....... ......... ........... ............. E34u 2.00000 -1.99793 1.99171 -1.98137 1.96692 -1.94840 1.92583 -1.89928 1.86879 -1.83442 1.79626 -1.75437 1.70884 -1.65977 1.60726 -1.55142 1.49237 -1.43022 1.36511 -1.29716 1.22653 -1.15336 1.07780 -1.00000 0.92013 -0.83835 0.75484 -0.66976 0.58329 -0.49562 0.40691 -0.31737 0.22716 -0.13648 0.04553 0.00000 -2.00000 -0.04553 0.13648 -0.22716 0.31737 -0.40691 0.49562 -0.58329 0.66976 -0.75484 0.83835 -0.92013 1.00000 -1.07780 1.15336 -1.22653 1.29716 -1.36511 1.43022 -1.49237 1.55142 -1.60726 1.65977 -1.70884 1.75437 -1.79626 1.83442 -1.86879 1.89928 -1.92583 1.94840 -1.96692 1.98137 -1.99171 1.99793 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.997927347293 = 2*cos(2*π/138) = 2*cos(π/69) 1.991713685063 = 2*cos(4*π/138) = 2*cos(2*π/69) 1.981371892073 = 2*cos(6*π/138) = 2*cos(π/23) 1.966923403267 = 2*cos(8*π/138) = 2*cos(4*π/69) 1.948398165347 = 2*cos(10*π/138) = 2*cos(5*π/69) 1.925834574696 = 2*cos(12*π/138) = 2*cos(2*π/23) 1.899279397801 = 2*cos(14*π/138) = 2*cos(7*π/69) 1.868787674321 = 2*cos(16*π/138) = 2*cos(8*π/69) 1.834422603011 = 2*cos(18*π/138) = 2*cos(3*π/23) 1.796255410727 = 2*cos(20*π/138) = 2*cos(10*π/69) 1.754365204805 = 2*cos(22*π/138) = 2*cos(11*π/69) 1.708838809093 = 2*cos(24*π/138) = 2*cos(4*π/23) 1.659770583998 = 2*cos(26*π/138) = 2*cos(13*π/69) 1.607262230910 = 2*cos(28*π/138) = 2*cos(14*π/69) 1.551422581409 = 2*cos(30*π/138) = 2*cos(5*π/23) 1.492367371695 = 2*cos(32*π/138) = 2*cos(16*π/69) 1.430219002710 = 2*cos(34*π/138) = 2*cos(17*π/69) 1.365106286437 = 2*cos(36*π/138) = 2*cos(6*π/23) 1.297164178926 = 2*cos(38*π/138) = 2*cos(19*π/69) 1.226533500567 = 2*cos(40*π/138) = 2*cos(20*π/69) 1.153360644230 = 2*cos(42*π/138) = 2*cos(7*π/23) 1.077797271831 = 2*cos(44*π/138) = 2*cos(22*π/69) 0.920130075462 = 2*cos(48*π/138) = 2*cos(8*π/23) 0.838353040833 = 2*cos(50*π/138) = 2*cos(25*π/69) 0.754838391505 = 2*cos(52*π/138) = 2*cos(26*π/69) 0.669759224342 = 2*cos(54*π/138) = 2*cos(9*π/23) 0.583291878910 = 2*cos(56*π/138) = 2*cos(28*π/69) 0.495615571986 = 2*cos(58*π/138) = 2*cos(29*π/69) 0.406912026105 = 2*cos(60*π/138) = 2*cos(10*π/23) 0.317365092913 = 2*cos(62*π/138) = 2*cos(31*π/69) 0.227160372101 = 2*cos(64*π/138) = 2*cos(32*π/69) 0.136484826729 = 2*cos(66*π/138) = 2*cos(11*π/23) 0.045526395712 = 2*cos(68*π/138) = 2*cos(34*π/69) Symmetry of Rotations and Cartesian products A1g d+g+i+k+m z², z⁴, z⁶ A2g R R_z E1g R+d+g+i+k+m {R_x, R_y}, {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 D_69d point group is 276, and the order of the principal axis (S₁₃₈) is 138. The group has 72 irreducible representations. β The D_69d point group is isomorphic to D_69h, C_138v and D₁₃₈. γ The D_69d point group is generated by two symmetry elements, S₁₃₈ and either a perpendicular C₂^′ or a vertical σ_d. Also, the group may be generated from a C₂^′ plus a σ_d (some pairs will yield smaller groups, though; choosing a minimum angle is safe). The canonical choice, however, is to use redundant generators: C₆₉, C₂^′ and i. δ The group contains one set of C₂^′ symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set. Reversely, the single set of symmetry planes denoted σ_d contains the yz plane but not the xz plane. ε The lowest nonvanishing multipole moment in D_69d 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.

This Character Table for the D_69d point group was created by Gernot Katzer.

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

	D_67d
	D_68d
C₆₉ C_69v C_69h D₆₉ D_69h	D_69d
	D_70d
	D_71d

Character table for the D69d point group

Character table for the D_69d point group