Character table for the C69h point group

C69h     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 sh       2 S69    2 S23    2 S69^5  2 S69^7  2 S23^3  2 S69^11 2 S69^13 2 S23^5  2 S69^17 2 S69^19 2 S23^7  2 S3     2 S69^25 2 S23^9  2 S69^29 2 S69^31 2 S23^11 2 S69^35 2 S69^37 2 S23^13 2 S69^41 2 S69^43 2 S23^15 2 S69^47 2 S69^49 2 S23^17 2 S69^53 2 S69^55 2 S23^19 2 S69^59 2 S69^61 2 S23^21 2 S69^65 2 S69^67   <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A'      1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000     ..T ... ....T ....... ........T ........... ............T
A"      1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000     ... ..T ..... ......T ......... ..........T .............
E1'  *  2.00000  1.99171  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  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     ... TT. ..... ....TT. ......... ........TT. .............
E1"  *  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 -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     TT. ... ..TT. ....... ......TT. ........... ..........TT.
E2'  *  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  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     ... ... TT... ....... ....TT... ........... ........TT...
E2"  *  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 -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     ... ... ..... ..TT... ......... ......TT... .............
E3'  *  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  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     ... ... ..... TT..... ......... ....TT..... .............
E3"  *  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 -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     ... ... ..... ....... ..TT..... ........... ......TT.....
E4'  *  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  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     ... ... ..... ....... TT....... ........... ....TT.......
E4"  *  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 -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     ... ... ..... ....... ......... ..TT....... .............
E5'  *  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  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     ... ... ..... ....... ......... TT......... .............
E5"  *  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 -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     ... ... ..... ....... ......... ........... ..TT.........
E6'  *  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  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     ... ... ..... ....... ......... ........... TT...........
E6"  *  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 -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     ... ... ..... ....... ......... ........... .............
E7'  *  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  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     ... ... ..... ....... ......... ........... .............
E7"  *  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 -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     ... ... ..... ....... ......... ........... .............
E8'  *  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  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     ... ... ..... ....... ......... ........... .............
E8"  *  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 -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     ... ... ..... ....... ......... ........... .............
E9'  *  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  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     ... ... ..... ....... ......... ........... .............
E9"  *  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 -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     ... ... ..... ....... ......... ........... .............
E10' *  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  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     ... ... ..... ....... ......... ........... .............
E10" *  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 -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     ... ... ..... ....... ......... ........... .............
E11' *  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  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     ... ... ..... ....... ......... ........... .............
E11" *  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 -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     ... ... ..... ....... ......... ........... .............
E12' *  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  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     ... ... ..... ....... ......... ........... .............
E12" *  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 -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     ... ... ..... ....... ......... ........... .............
E13' *  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  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     ... ... ..... ....... ......... ........... .............
E13" *  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 -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     ... ... ..... ....... ......... ........... .............
E14' *  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  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     ... ... ..... ....... ......... ........... .............
E14" *  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 -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     ... ... ..... ....... ......... ........... .............
E15' *  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  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     ... ... ..... ....... ......... ........... .............
E15" *  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 -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     ... ... ..... ....... ......... ........... .............
E16' *  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  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     ... ... ..... ....... ......... ........... .............
E16" *  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 -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     ... ... ..... ....... ......... ........... .............
E17' *  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  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     ... ... ..... ....... ......... ........... .............
E17" *  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 -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     ... ... ..... ....... ......... ........... .............
E18' *  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  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     ... ... ..... ....... ......... ........... .............
E18" *  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 -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     ... ... ..... ....... ......... ........... .............
E19' *  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  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     ... ... ..... ....... ......... ........... .............
E19" *  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 -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     ... ... ..... ....... ......... ........... .............
E20' *  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  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     ... ... ..... ....... ......... ........... .............
E20" *  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 -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     ... ... ..... ....... ......... ........... .............
E21' *  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  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     ... ... ..... ....... ......... ........... .............
E21" *  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 -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     ... ... ..... ....... ......... ........... .............
E22' *  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  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     ... ... ..... ....... ......... ........... .............
E22" *  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 -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     ... ... ..... ....... ......... ........... .............
E23' *  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  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     ... ... ..... ....... ......... ........... .............
E23" *  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 -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     ... ... ..... ....... ......... ........... .............
E24' *  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  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     ... ... ..... ....... ......... ........... .............
E24" *  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 -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     ... ... ..... ....... ......... ........... .............
E25' *  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  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     ... ... ..... ....... ......... ........... .............
E25" *  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 -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     ... ... ..... ....... ......... ........... .............
E26' *  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  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     ... ... ..... ....... ......... ........... .............
E26" *  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 -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     ... ... ..... ....... ......... ........... .............
E27' *  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  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     ... ... ..... ....... ......... ........... .............
E27" *  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 -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     ... ... ..... ....... ......... ........... .............
E28' *  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  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     ... ... ..... ....... ......... ........... .............
E28" *  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 -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     ... ... ..... ....... ......... ........... .............
E29' *  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  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     ... ... ..... ....... ......... ........... .............
E29" *  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 -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     ... ... ..... ....... ......... ........... .............
E30' *  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  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     ... ... ..... ....... ......... ........... .............
E30" *  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 -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     ... ... ..... ....... ......... ........... .............
E31' *  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  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     ... ... ..... ....... ......... ........... .............
E31" *  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 -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     ... ... ..... ....... ......... ........... .............
E32' *  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  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     ... ... ..... ....... ......... ........... .............
E32" *  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 -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     ... ... ..... ....... ......... ........... .............
E33' *  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  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     ... ... ..... ....... ......... ........... .............
E33" *  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 -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     ... ... ..... ....... ......... ........... .............
E34' *  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  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     ... ... ..... ....... ......... ........... .............
E34" *  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 -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     ... ... ..... ....... ......... ........... .............

 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

A'   R+d+g+i+k+m  Rz, z2, z4, z6 
A"   p+f+h+j+l    z, z3, z5 
E1'  p+f+h+j+l    {x, y}, {xz2, yz2}, {xz4, yz4} 
E1"  R+d+g+i+k+m  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 
E2'  d+g+i+k+m    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E2"  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E3'  f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E3"  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E4'  g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E4"  h+j+l        {z((x2y2)2−4x2y2), xyz(x2y2)} 
E5'  h+j+l        {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)} 
E5"  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E6'  i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E6"  j+l 
E7'  j+l 
E7"  k+m 
E8'  k+m 
E8"  l 
E9'  l 
E9"  m 
E10' m 

 Notes:

    α  The order of the C69h point group is 138, and the order of the principal axis (S69) is 138. The group has 70 irreducible representations.

    β  The C69h point group could also be named S69, as it contains the S69 axis as its only symmetry element.
       Another rare designation is C138i because the S69 axis is identical to a roto-inversion axis of order 138.

    γ  The C69h point group is isomorphic to C138 and S138.

    δ  The C69h point group is generated by one single symmetry element, S69. Therefore, it is a cyclic group.
       The canonical choice, however, is to use redundant generators: C69 and σh.

    ε  The lowest nonvanishing multipole moment in C69h is 4 (quadrupole moment).

    ζ  This is an Abelian point group (the commutative law holds between all symmetry operations).
       The C69h 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 136 cases have been combined into 68 two-dimensional representations that are no longer irreducible but have real-valued characters.
       Accordingly, 68 pairs of left and right rotations have been combined into one two-membered pseudo-class each.

    θ  The 68 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.

This Character Table for the C69h point group was created by Gernot Katzer.

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