Character table for the S128 point group

S128    E         2 S128    2 C64     2 S128^3  2 C32     2 S128^5  2 C64^3   2 S128^7  2 C16     2 S128^9  2 C64^5   2 S128^11 2 C32^3   2 S128^13 2 C64^7   2 S128^15 2 C8      2 S128^17 2 C64^9   2 S128^19 2 C32^5   2 S128^21 2 C64^11  2 S128^23 2 C16^3   2 S128^25 2 C64^13  2 S128^27 2 C32^7   2 S128^29 2 C64^15  2 S128^31 2 C4      2 S128^33 2 C64^17  2 S128^35 2 C32^9   2 S128^37 2 C64^19  2 S128^39 2 C16^5   2 S128^41 2 C64^21  2 S128^43 2 C32^11  2 S128^45 2 C64^23  2 S128^47 2 C8^3    2 S128^49 2 C64^25  2 S128^51 2 C32^13  2 S128^53 2 C64^27  2 S128^55 2 C16^7   2 S128^57 2 C64^29  2 S128^59 2 C32^15  2 S128^61 2 C64^31  2 S128^63 C2           <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     ..T ... ....T ....... ........T ........... ............T
B        1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -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   1.99759   1.99037   1.97835   1.96157   1.94006   1.91388   1.88309   1.84776   1.80798   1.76384   1.71546   1.66294   1.60642   1.54602   1.48190   1.41421   1.34312   1.26879   1.19140   1.11114   1.02821   0.94279   0.85511   0.76537   0.67378   0.58057   0.48596   0.39018   0.29346   0.19603   0.09814   0.00000  -0.09814  -0.19603  -0.29346  -0.39018  -0.48596  -0.58057  -0.67378  -0.76537  -0.85511  -0.94279  -1.02821  -1.11114  -1.19140  -1.26879  -1.34312  -1.41421  -1.48190  -1.54602  -1.60642  -1.66294  -1.71546  -1.76384  -1.80798  -1.84776  -1.88309  -1.91388  -1.94006  -1.96157  -1.97835  -1.99037  -1.99759  -2.00000     ... TT. ..... ....TT. ......... ........TT. .............
E2  *    2.00000   1.99037   1.96157   1.91388   1.84776   1.76384   1.66294   1.54602   1.41421   1.26879   1.11114   0.94279   0.76537   0.58057   0.39018   0.19603   0.00000  -0.19603  -0.39018  -0.58057  -0.76537  -0.94279  -1.11114  -1.26879  -1.41421  -1.54602  -1.66294  -1.76384  -1.84776  -1.91388  -1.96157  -1.99037  -2.00000  -1.99037  -1.96157  -1.91388  -1.84776  -1.76384  -1.66294  -1.54602  -1.41421  -1.26879  -1.11114  -0.94279  -0.76537  -0.58057  -0.39018  -0.19603   0.00000   0.19603   0.39018   0.58057   0.76537   0.94279   1.11114   1.26879   1.41421   1.54602   1.66294   1.76384   1.84776   1.91388   1.96157   1.99037   2.00000     ... ... TT... ....... ....TT... ........... ........TT...
E3  *    2.00000   1.97835   1.91388   1.80798   1.66294   1.48190   1.26879   1.02821   0.76537   0.48596   0.19603  -0.09814  -0.39018  -0.67378  -0.94279  -1.19140  -1.41421  -1.60642  -1.76384  -1.88309  -1.96157  -1.99759  -1.99037  -1.94006  -1.84776  -1.71546  -1.54602  -1.34312  -1.11114  -0.85511  -0.58057  -0.29346   0.00000   0.29346   0.58057   0.85511   1.11114   1.34312   1.54602   1.71546   1.84776   1.94006   1.99037   1.99759   1.96157   1.88309   1.76384   1.60642   1.41421   1.19140   0.94279   0.67378   0.39018   0.09814  -0.19603  -0.48596  -0.76537  -1.02821  -1.26879  -1.48190  -1.66294  -1.80798  -1.91388  -1.97835  -2.00000     ... ... ..... TT..... ......... ....TT..... .............
E4  *    2.00000   1.96157   1.84776   1.66294   1.41421   1.11114   0.76537   0.39018   0.00000  -0.39018  -0.76537  -1.11114  -1.41421  -1.66294  -1.84776  -1.96157  -2.00000  -1.96157  -1.84776  -1.66294  -1.41421  -1.11114  -0.76537  -0.39018   0.00000   0.39018   0.76537   1.11114   1.41421   1.66294   1.84776   1.96157   2.00000   1.96157   1.84776   1.66294   1.41421   1.11114   0.76537   0.39018   0.00000  -0.39018  -0.76537  -1.11114  -1.41421  -1.66294  -1.84776  -1.96157  -2.00000  -1.96157  -1.84776  -1.66294  -1.41421  -1.11114  -0.76537  -0.39018   0.00000   0.39018   0.76537   1.11114   1.41421   1.66294   1.84776   1.96157   2.00000     ... ... ..... ....... TT....... ........... ....TT.......
E5  *    2.00000   1.94006   1.76384   1.48190   1.11114   0.67378   0.19603  -0.29346  -0.76537  -1.19140  -1.54602  -1.80798  -1.96157  -1.99759  -1.91388  -1.71546  -1.41421  -1.02821  -0.58057  -0.09814   0.39018   0.85511   1.26879   1.60642   1.84776   1.97835   1.99037   1.88309   1.66294   1.34312   0.94279   0.48596   0.00000  -0.48596  -0.94279  -1.34312  -1.66294  -1.88309  -1.99037  -1.97835  -1.84776  -1.60642  -1.26879  -0.85511  -0.39018   0.09814   0.58057   1.02821   1.41421   1.71546   1.91388   1.99759   1.96157   1.80798   1.54602   1.19140   0.76537   0.29346  -0.19603  -0.67378  -1.11114  -1.48190  -1.76384  -1.94006  -2.00000     ... ... ..... ....... ......... TT......... .............
E6  *    2.00000   1.91388   1.66294   1.26879   0.76537   0.19603  -0.39018  -0.94279  -1.41421  -1.76384  -1.96157  -1.99037  -1.84776  -1.54602  -1.11114  -0.58057   0.00000   0.58057   1.11114   1.54602   1.84776   1.99037   1.96157   1.76384   1.41421   0.94279   0.39018  -0.19603  -0.76537  -1.26879  -1.66294  -1.91388  -2.00000  -1.91388  -1.66294  -1.26879  -0.76537  -0.19603   0.39018   0.94279   1.41421   1.76384   1.96157   1.99037   1.84776   1.54602   1.11114   0.58057   0.00000  -0.58057  -1.11114  -1.54602  -1.84776  -1.99037  -1.96157  -1.76384  -1.41421  -0.94279  -0.39018   0.19603   0.76537   1.26879   1.66294   1.91388   2.00000     ... ... ..... ....... ......... ........... TT...........
E7  *    2.00000   1.88309   1.54602   1.02821   0.39018  -0.29346  -0.94279  -1.48190  -1.84776  -1.99759  -1.91388  -1.60642  -1.11114  -0.48596   0.19603   0.85511   1.41421   1.80798   1.99037   1.94006   1.66294   1.19140   0.58057  -0.09814  -0.76537  -1.34312  -1.76384  -1.97835  -1.96157  -1.71546  -1.26879  -0.67378   0.00000   0.67378   1.26879   1.71546   1.96157   1.97835   1.76384   1.34312   0.76537   0.09814  -0.58057  -1.19140  -1.66294  -1.94006  -1.99037  -1.80798  -1.41421  -0.85511  -0.19603   0.48596   1.11114   1.60642   1.91388   1.99759   1.84776   1.48190   0.94279   0.29346  -0.39018  -1.02821  -1.54602  -1.88309  -2.00000     ... ... ..... ....... ......... ........... .............
E8  *    2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000   1.84776   1.41421   0.76537   0.00000  -0.76537  -1.41421  -1.84776  -2.00000  -1.84776  -1.41421  -0.76537   0.00000   0.76537   1.41421   1.84776   2.00000     ... ... ..... ....... ......... ........... .............
E9  *    2.00000   1.80798   1.26879   0.48596  -0.39018  -1.19140  -1.76384  -1.99759  -1.84776  -1.34312  -0.58057   0.29346   1.11114   1.71546   1.99037   1.88309   1.41421   0.67378  -0.19603  -1.02821  -1.66294  -1.97835  -1.91388  -1.48190  -0.76537   0.09814   0.94279   1.60642   1.96157   1.94006   1.54602   0.85511   0.00000  -0.85511  -1.54602  -1.94006  -1.96157  -1.60642  -0.94279  -0.09814   0.76537   1.48190   1.91388   1.97835   1.66294   1.02821   0.19603  -0.67378  -1.41421  -1.88309  -1.99037  -1.71546  -1.11114  -0.29346   0.58057   1.34312   1.84776   1.99759   1.76384   1.19140   0.39018  -0.48596  -1.26879  -1.80798  -2.00000     ... ... ..... ....... ......... ........... .............
E10 *    2.00000   1.76384   1.11114   0.19603  -0.76537  -1.54602  -1.96157  -1.91388  -1.41421  -0.58057   0.39018   1.26879   1.84776   1.99037   1.66294   0.94279   0.00000  -0.94279  -1.66294  -1.99037  -1.84776  -1.26879  -0.39018   0.58057   1.41421   1.91388   1.96157   1.54602   0.76537  -0.19603  -1.11114  -1.76384  -2.00000  -1.76384  -1.11114  -0.19603   0.76537   1.54602   1.96157   1.91388   1.41421   0.58057  -0.39018  -1.26879  -1.84776  -1.99037  -1.66294  -0.94279   0.00000   0.94279   1.66294   1.99037   1.84776   1.26879   0.39018  -0.58057  -1.41421  -1.91388  -1.96157  -1.54602  -0.76537   0.19603   1.11114   1.76384   2.00000     ... ... ..... ....... ......... ........... .............
E11 *    2.00000   1.71546   0.94279  -0.09814  -1.11114  -1.80798  -1.99037  -1.60642  -0.76537   0.29346   1.26879   1.88309   1.96157   1.48190   0.58057  -0.48596  -1.41421  -1.94006  -1.91388  -1.34312  -0.39018   0.67378   1.54602   1.97835   1.84776   1.19140   0.19603  -0.85511  -1.66294  -1.99759  -1.76384  -1.02821   0.00000   1.02821   1.76384   1.99759   1.66294   0.85511  -0.19603  -1.19140  -1.84776  -1.97835  -1.54602  -0.67378   0.39018   1.34312   1.91388   1.94006   1.41421   0.48596  -0.58057  -1.48190  -1.96157  -1.88309  -1.26879  -0.29346   0.76537   1.60642   1.99037   1.80798   1.11114   0.09814  -0.94279  -1.71546  -2.00000     ... ... ..... ....... ......... ........... .............
E12 *    2.00000   1.66294   0.76537  -0.39018  -1.41421  -1.96157  -1.84776  -1.11114   0.00000   1.11114   1.84776   1.96157   1.41421   0.39018  -0.76537  -1.66294  -2.00000  -1.66294  -0.76537   0.39018   1.41421   1.96157   1.84776   1.11114   0.00000  -1.11114  -1.84776  -1.96157  -1.41421  -0.39018   0.76537   1.66294   2.00000   1.66294   0.76537  -0.39018  -1.41421  -1.96157  -1.84776  -1.11114   0.00000   1.11114   1.84776   1.96157   1.41421   0.39018  -0.76537  -1.66294  -2.00000  -1.66294  -0.76537   0.39018   1.41421   1.96157   1.84776   1.11114   0.00000  -1.11114  -1.84776  -1.96157  -1.41421  -0.39018   0.76537   1.66294   2.00000     ... ... ..... ....... ......... ........... .............
E13 *    2.00000   1.60642   0.58057  -0.67378  -1.66294  -1.99759  -1.54602  -0.48596   0.76537   1.71546   1.99037   1.48190   0.39018  -0.85511  -1.76384  -1.97835  -1.41421  -0.29346   0.94279   1.80798   1.96157   1.34312   0.19603  -1.02821  -1.84776  -1.94006  -1.26879  -0.09814   1.11114   1.88309   1.91388   1.19140   0.00000  -1.19140  -1.91388  -1.88309  -1.11114   0.09814   1.26879   1.94006   1.84776   1.02821  -0.19603  -1.34312  -1.96157  -1.80798  -0.94279   0.29346   1.41421   1.97835   1.76384   0.85511  -0.39018  -1.48190  -1.99037  -1.71546  -0.76537   0.48596   1.54602   1.99759   1.66294   0.67378  -0.58057  -1.60642  -2.00000     ... ... ..... ....... ......... ........... .............
E14 *    2.00000   1.54602   0.39018  -0.94279  -1.84776  -1.91388  -1.11114   0.19603   1.41421   1.99037   1.66294   0.58057  -0.76537  -1.76384  -1.96157  -1.26879   0.00000   1.26879   1.96157   1.76384   0.76537  -0.58057  -1.66294  -1.99037  -1.41421  -0.19603   1.11114   1.91388   1.84776   0.94279  -0.39018  -1.54602  -2.00000  -1.54602  -0.39018   0.94279   1.84776   1.91388   1.11114  -0.19603  -1.41421  -1.99037  -1.66294  -0.58057   0.76537   1.76384   1.96157   1.26879   0.00000  -1.26879  -1.96157  -1.76384  -0.76537   0.58057   1.66294   1.99037   1.41421   0.19603  -1.11114  -1.91388  -1.84776  -0.94279   0.39018   1.54602   2.00000     ... ... ..... ....... ......... ........... .............
E15 *    2.00000   1.48190   0.19603  -1.19140  -1.96157  -1.71546  -0.58057   0.85511   1.84776   1.88309   0.94279  -0.48596  -1.66294  -1.97835  -1.26879   0.09814   1.41421   1.99759   1.54602   0.29346  -1.11114  -1.94006  -1.76384  -0.67378   0.76537   1.80798   1.91388   1.02821  -0.39018  -1.60642  -1.99037  -1.34312   0.00000   1.34312   1.99037   1.60642   0.39018  -1.02821  -1.91388  -1.80798  -0.76537   0.67378   1.76384   1.94006   1.11114  -0.29346  -1.54602  -1.99759  -1.41421  -0.09814   1.26879   1.97835   1.66294   0.48596  -0.94279  -1.88309  -1.84776  -0.85511   0.58057   1.71546   1.96157   1.19140  -0.19603  -1.48190  -2.00000     ... ... ..... ....... ......... ........... .............
E16 *    2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000   1.41421   0.00000  -1.41421  -2.00000  -1.41421   0.00000   1.41421   2.00000     ... ... ..... ....... ......... ........... .............
E17 *    2.00000   1.34312  -0.19603  -1.60642  -1.96157  -1.02821   0.58057   1.80798   1.84776   0.67378  -0.94279  -1.94006  -1.66294  -0.29346   1.26879   1.99759   1.41421  -0.09814  -1.54602  -1.97835  -1.11114   0.48596   1.76384   1.88309   0.76537  -0.85511  -1.91388  -1.71546  -0.39018   1.19140   1.99037   1.48190   0.00000  -1.48190  -1.99037  -1.19140   0.39018   1.71546   1.91388   0.85511  -0.76537  -1.88309  -1.76384  -0.48596   1.11114   1.97835   1.54602   0.09814  -1.41421  -1.99759  -1.26879   0.29346   1.66294   1.94006   0.94279  -0.67378  -1.84776  -1.80798  -0.58057   1.02821   1.96157   1.60642   0.19603  -1.34312  -2.00000     ... ... ..... ....... ......... ........... .............
E18 *    2.00000   1.26879  -0.39018  -1.76384  -1.84776  -0.58057   1.11114   1.99037   1.41421  -0.19603  -1.66294  -1.91388  -0.76537   0.94279   1.96157   1.54602   0.00000  -1.54602  -1.96157  -0.94279   0.76537   1.91388   1.66294   0.19603  -1.41421  -1.99037  -1.11114   0.58057   1.84776   1.76384   0.39018  -1.26879  -2.00000  -1.26879   0.39018   1.76384   1.84776   0.58057  -1.11114  -1.99037  -1.41421   0.19603   1.66294   1.91388   0.76537  -0.94279  -1.96157  -1.54602   0.00000   1.54602   1.96157   0.94279  -0.76537  -1.91388  -1.66294  -0.19603   1.41421   1.99037   1.11114  -0.58057  -1.84776  -1.76384  -0.39018   1.26879   2.00000     ... ... ..... ....... ......... ........... .............
E19 *    2.00000   1.19140  -0.58057  -1.88309  -1.66294  -0.09814   1.54602   1.94006   0.76537  -1.02821  -1.99037  -1.34312   0.39018   1.80798   1.76384   0.29346  -1.41421  -1.97835  -0.94279   0.85511   1.96157   1.48190  -0.19603  -1.71546  -1.84776  -0.48596   1.26879   1.99759   1.11114  -0.67378  -1.91388  -1.60642   0.00000   1.60642   1.91388   0.67378  -1.11114  -1.99759  -1.26879   0.48596   1.84776   1.71546   0.19603  -1.48190  -1.96157  -0.85511   0.94279   1.97835   1.41421  -0.29346  -1.76384  -1.80798  -0.39018   1.34312   1.99037   1.02821  -0.76537  -1.94006  -1.54602   0.09814   1.66294   1.88309   0.58057  -1.19140  -2.00000     ... ... ..... ....... ......... ........... .............
E20 *    2.00000   1.11114  -0.76537  -1.96157  -1.41421   0.39018   1.84776   1.66294   0.00000  -1.66294  -1.84776  -0.39018   1.41421   1.96157   0.76537  -1.11114  -2.00000  -1.11114   0.76537   1.96157   1.41421  -0.39018  -1.84776  -1.66294   0.00000   1.66294   1.84776   0.39018  -1.41421  -1.96157  -0.76537   1.11114   2.00000   1.11114  -0.76537  -1.96157  -1.41421   0.39018   1.84776   1.66294   0.00000  -1.66294  -1.84776  -0.39018   1.41421   1.96157   0.76537  -1.11114  -2.00000  -1.11114   0.76537   1.96157   1.41421  -0.39018  -1.84776  -1.66294   0.00000   1.66294   1.84776   0.39018  -1.41421  -1.96157  -0.76537   1.11114   2.00000     ... ... ..... ....... ......... ........... .............
E21 *    2.00000   1.02821  -0.94279  -1.99759  -1.11114   0.85511   1.99037   1.19140  -0.76537  -1.97835  -1.26879   0.67378   1.96157   1.34312  -0.58057  -1.94006  -1.41421   0.48596   1.91388   1.48190  -0.39018  -1.88309  -1.54602   0.29346   1.84776   1.60642  -0.19603  -1.80798  -1.66294   0.09814   1.76384   1.71546   0.00000  -1.71546  -1.76384  -0.09814   1.66294   1.80798   0.19603  -1.60642  -1.84776  -0.29346   1.54602   1.88309   0.39018  -1.48190  -1.91388  -0.48596   1.41421   1.94006   0.58057  -1.34312  -1.96157  -0.67378   1.26879   1.97835   0.76537  -1.19140  -1.99037  -0.85511   1.11114   1.99759   0.94279  -1.02821  -2.00000     ... ... ..... ....... ......... ........... .............
E22 *    2.00000   0.94279  -1.11114  -1.99037  -0.76537   1.26879   1.96157   0.58057  -1.41421  -1.91388  -0.39018   1.54602   1.84776   0.19603  -1.66294  -1.76384   0.00000   1.76384   1.66294  -0.19603  -1.84776  -1.54602   0.39018   1.91388   1.41421  -0.58057  -1.96157  -1.26879   0.76537   1.99037   1.11114  -0.94279  -2.00000  -0.94279   1.11114   1.99037   0.76537  -1.26879  -1.96157  -0.58057   1.41421   1.91388   0.39018  -1.54602  -1.84776  -0.19603   1.66294   1.76384   0.00000  -1.76384  -1.66294   0.19603   1.84776   1.54602  -0.39018  -1.91388  -1.41421   0.58057   1.96157   1.26879  -0.76537  -1.99037  -1.11114   0.94279   2.00000     ... ... ..... ....... ......... ........... .............
E23 *    2.00000   0.85511  -1.26879  -1.94006  -0.39018   1.60642   1.76384  -0.09814  -1.84776  -1.48190   0.58057   1.97835   1.11114  -1.02821  -1.99037  -0.67378   1.41421   1.88309   0.19603  -1.71546  -1.66294   0.29346   1.91388   1.34312  -0.76537  -1.99759  -0.94279   1.19140   1.96157   0.48596  -1.54602  -1.80798   0.00000   1.80798   1.54602  -0.48596  -1.96157  -1.19140   0.94279   1.99759   0.76537  -1.34312  -1.91388  -0.29346   1.66294   1.71546  -0.19603  -1.88309  -1.41421   0.67378   1.99037   1.02821  -1.11114  -1.97835  -0.58057   1.48190   1.84776   0.09814  -1.76384  -1.60642   0.39018   1.94006   1.26879  -0.85511  -2.00000     ... ... ..... ....... ......... ........... .............
E24 *    2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000   0.76537  -1.41421  -1.84776   0.00000   1.84776   1.41421  -0.76537  -2.00000  -0.76537   1.41421   1.84776   0.00000  -1.84776  -1.41421   0.76537   2.00000     ... ... ..... ....... ......... ........... .............
E25 *    2.00000   0.67378  -1.54602  -1.71546   0.39018   1.97835   0.94279  -1.34312  -1.84776   0.09814   1.91388   1.19140  -1.11114  -1.94006  -0.19603   1.80798   1.41421  -0.85511  -1.99037  -0.48596   1.66294   1.60642  -0.58057  -1.99759  -0.76537   1.48190   1.76384  -0.29346  -1.96157  -1.02821   1.26879   1.88309   0.00000  -1.88309  -1.26879   1.02821   1.96157   0.29346  -1.76384  -1.48190   0.76537   1.99759   0.58057  -1.60642  -1.66294   0.48596   1.99037   0.85511  -1.41421  -1.80798   0.19603   1.94006   1.11114  -1.19140  -1.91388  -0.09814   1.84776   1.34312  -0.94279  -1.97835  -0.39018   1.71546   1.54602  -0.67378  -2.00000     ... ... ..... ....... ......... ........... .............
E26 *    2.00000   0.58057  -1.66294  -1.54602   0.76537   1.99037   0.39018  -1.76384  -1.41421   0.94279   1.96157   0.19603  -1.84776  -1.26879   1.11114   1.91388   0.00000  -1.91388  -1.11114   1.26879   1.84776  -0.19603  -1.96157  -0.94279   1.41421   1.76384  -0.39018  -1.99037  -0.76537   1.54602   1.66294  -0.58057  -2.00000  -0.58057   1.66294   1.54602  -0.76537  -1.99037  -0.39018   1.76384   1.41421  -0.94279  -1.96157  -0.19603   1.84776   1.26879  -1.11114  -1.91388   0.00000   1.91388   1.11114  -1.26879  -1.84776   0.19603   1.96157   0.94279  -1.41421  -1.76384   0.39018   1.99037   0.76537  -1.54602  -1.66294   0.58057   2.00000     ... ... ..... ....... ......... ........... .............
E27 *    2.00000   0.48596  -1.76384  -1.34312   1.11114   1.88309  -0.19603  -1.97835  -0.76537   1.60642   1.54602  -0.85511  -1.96157  -0.09814   1.91388   1.02821  -1.41421  -1.71546   0.58057   1.99759   0.39018  -1.80798  -1.26879   1.19140   1.84776  -0.29346  -1.99037  -0.67378   1.66294   1.48190  -0.94279  -1.94006   0.00000   1.94006   0.94279  -1.48190  -1.66294   0.67378   1.99037   0.29346  -1.84776  -1.19140   1.26879   1.80798  -0.39018  -1.99759  -0.58057   1.71546   1.41421  -1.02821  -1.91388   0.09814   1.96157   0.85511  -1.54602  -1.60642   0.76537   1.97835   0.19603  -1.88309  -1.11114   1.34312   1.76384  -0.48596  -2.00000     ... ... ..... ....... ......... ........... .............
E28 *    2.00000   0.39018  -1.84776  -1.11114   1.41421   1.66294  -0.76537  -1.96157   0.00000   1.96157   0.76537  -1.66294  -1.41421   1.11114   1.84776  -0.39018  -2.00000  -0.39018   1.84776   1.11114  -1.41421  -1.66294   0.76537   1.96157   0.00000  -1.96157  -0.76537   1.66294   1.41421  -1.11114  -1.84776   0.39018   2.00000   0.39018  -1.84776  -1.11114   1.41421   1.66294  -0.76537  -1.96157   0.00000   1.96157   0.76537  -1.66294  -1.41421   1.11114   1.84776  -0.39018  -2.00000  -0.39018   1.84776   1.11114  -1.41421  -1.66294   0.76537   1.96157   0.00000  -1.96157  -0.76537   1.66294   1.41421  -1.11114  -1.84776   0.39018   2.00000     ... ... ..... ....... ......... ........... .............
E29 *    2.00000   0.29346  -1.91388  -0.85511   1.66294   1.34312  -1.26879  -1.71546   0.76537   1.94006  -0.19603  -1.99759  -0.39018   1.88309   0.94279  -1.60642  -1.41421   1.19140   1.76384  -0.67378  -1.96157   0.09814   1.99037   0.48596  -1.84776  -1.02821   1.54602   1.48190  -1.11114  -1.80798   0.58057   1.97835   0.00000  -1.97835  -0.58057   1.80798   1.11114  -1.48190  -1.54602   1.02821   1.84776  -0.48596  -1.99037  -0.09814   1.96157   0.67378  -1.76384  -1.19140   1.41421   1.60642  -0.94279  -1.88309   0.39018   1.99759   0.19603  -1.94006  -0.76537   1.71546   1.26879  -1.34312  -1.66294   0.85511   1.91388  -0.29346  -2.00000     ... ... ..... ....... ......... ........... .............
E30 *    2.00000   0.19603  -1.96157  -0.58057   1.84776   0.94279  -1.66294  -1.26879   1.41421   1.54602  -1.11114  -1.76384   0.76537   1.91388  -0.39018  -1.99037   0.00000   1.99037   0.39018  -1.91388  -0.76537   1.76384   1.11114  -1.54602  -1.41421   1.26879   1.66294  -0.94279  -1.84776   0.58057   1.96157  -0.19603  -2.00000  -0.19603   1.96157   0.58057  -1.84776  -0.94279   1.66294   1.26879  -1.41421  -1.54602   1.11114   1.76384  -0.76537  -1.91388   0.39018   1.99037   0.00000  -1.99037  -0.39018   1.91388   0.76537  -1.76384  -1.11114   1.54602   1.41421  -1.26879  -1.66294   0.94279   1.84776  -0.58057  -1.96157   0.19603   2.00000     ... ... ..... ....... ......... ........... .............
E31 *    2.00000   0.09814  -1.99037  -0.29346   1.96157   0.48596  -1.91388  -0.67378   1.84776   0.85511  -1.76384  -1.02821   1.66294   1.19140  -1.54602  -1.34312   1.41421   1.48190  -1.26879  -1.60642   1.11114   1.71546  -0.94279  -1.80798   0.76537   1.88309  -0.58057  -1.94006   0.39018   1.97835  -0.19603  -1.99759   0.00000   1.99759   0.19603  -1.97835  -0.39018   1.94006   0.58057  -1.88309  -0.76537   1.80798   0.94279  -1.71546  -1.11114   1.60642   1.26879  -1.48190  -1.41421   1.34312   1.54602  -1.19140  -1.66294   1.02821   1.76384  -0.85511  -1.84776   0.67378   1.91388  -0.48596  -1.96157   0.29346   1.99037  -0.09814  -2.00000     ... ... ..... ....... ......... ........... .............
E32 *    2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000     ... ... ..... ....... ......... ........... .............
E33 *    2.00000  -0.09814  -1.99037   0.29346   1.96157  -0.48596  -1.91388   0.67378   1.84776  -0.85511  -1.76384   1.02821   1.66294  -1.19140  -1.54602   1.34312   1.41421  -1.48190  -1.26879   1.60642   1.11114  -1.71546  -0.94279   1.80798   0.76537  -1.88309  -0.58057   1.94006   0.39018  -1.97835  -0.19603   1.99759   0.00000  -1.99759   0.19603   1.97835  -0.39018  -1.94006   0.58057   1.88309  -0.76537  -1.80798   0.94279   1.71546  -1.11114  -1.60642   1.26879   1.48190  -1.41421  -1.34312   1.54602   1.19140  -1.66294  -1.02821   1.76384   0.85511  -1.84776  -0.67378   1.91388   0.48596  -1.96157  -0.29346   1.99037   0.09814  -2.00000     ... ... ..... ....... ......... ........... .............
E34 *    2.00000  -0.19603  -1.96157   0.58057   1.84776  -0.94279  -1.66294   1.26879   1.41421  -1.54602  -1.11114   1.76384   0.76537  -1.91388  -0.39018   1.99037   0.00000  -1.99037   0.39018   1.91388  -0.76537  -1.76384   1.11114   1.54602  -1.41421  -1.26879   1.66294   0.94279  -1.84776  -0.58057   1.96157   0.19603  -2.00000   0.19603   1.96157  -0.58057  -1.84776   0.94279   1.66294  -1.26879  -1.41421   1.54602   1.11114  -1.76384  -0.76537   1.91388   0.39018  -1.99037   0.00000   1.99037  -0.39018  -1.91388   0.76537   1.76384  -1.11114  -1.54602   1.41421   1.26879  -1.66294  -0.94279   1.84776   0.58057  -1.96157  -0.19603   2.00000     ... ... ..... ....... ......... ........... .............
E35 *    2.00000  -0.29346  -1.91388   0.85511   1.66294  -1.34312  -1.26879   1.71546   0.76537  -1.94006  -0.19603   1.99759  -0.39018  -1.88309   0.94279   1.60642  -1.41421  -1.19140   1.76384   0.67378  -1.96157  -0.09814   1.99037  -0.48596  -1.84776   1.02821   1.54602  -1.48190  -1.11114   1.80798   0.58057  -1.97835   0.00000   1.97835  -0.58057  -1.80798   1.11114   1.48190  -1.54602  -1.02821   1.84776   0.48596  -1.99037   0.09814   1.96157  -0.67378  -1.76384   1.19140   1.41421  -1.60642  -0.94279   1.88309   0.39018  -1.99759   0.19603   1.94006  -0.76537  -1.71546   1.26879   1.34312  -1.66294  -0.85511   1.91388   0.29346  -2.00000     ... ... ..... ....... ......... ........... .............
E36 *    2.00000  -0.39018  -1.84776   1.11114   1.41421  -1.66294  -0.76537   1.96157   0.00000  -1.96157   0.76537   1.66294  -1.41421  -1.11114   1.84776   0.39018  -2.00000   0.39018   1.84776  -1.11114  -1.41421   1.66294   0.76537  -1.96157   0.00000   1.96157  -0.76537  -1.66294   1.41421   1.11114  -1.84776  -0.39018   2.00000  -0.39018  -1.84776   1.11114   1.41421  -1.66294  -0.76537   1.96157   0.00000  -1.96157   0.76537   1.66294  -1.41421  -1.11114   1.84776   0.39018  -2.00000   0.39018   1.84776  -1.11114  -1.41421   1.66294   0.76537  -1.96157   0.00000   1.96157  -0.76537  -1.66294   1.41421   1.11114  -1.84776  -0.39018   2.00000     ... ... ..... ....... ......... ........... .............
E37 *    2.00000  -0.48596  -1.76384   1.34312   1.11114  -1.88309  -0.19603   1.97835  -0.76537  -1.60642   1.54602   0.85511  -1.96157   0.09814   1.91388  -1.02821  -1.41421   1.71546   0.58057  -1.99759   0.39018   1.80798  -1.26879  -1.19140   1.84776   0.29346  -1.99037   0.67378   1.66294  -1.48190  -0.94279   1.94006   0.00000  -1.94006   0.94279   1.48190  -1.66294  -0.67378   1.99037  -0.29346  -1.84776   1.19140   1.26879  -1.80798  -0.39018   1.99759  -0.58057  -1.71546   1.41421   1.02821  -1.91388  -0.09814   1.96157  -0.85511  -1.54602   1.60642   0.76537  -1.97835   0.19603   1.88309  -1.11114  -1.34312   1.76384   0.48596  -2.00000     ... ... ..... ....... ......... ........... .............
E38 *    2.00000  -0.58057  -1.66294   1.54602   0.76537  -1.99037   0.39018   1.76384  -1.41421  -0.94279   1.96157  -0.19603  -1.84776   1.26879   1.11114  -1.91388   0.00000   1.91388  -1.11114  -1.26879   1.84776   0.19603  -1.96157   0.94279   1.41421  -1.76384  -0.39018   1.99037  -0.76537  -1.54602   1.66294   0.58057  -2.00000   0.58057   1.66294  -1.54602  -0.76537   1.99037  -0.39018  -1.76384   1.41421   0.94279  -1.96157   0.19603   1.84776  -1.26879  -1.11114   1.91388   0.00000  -1.91388   1.11114   1.26879  -1.84776  -0.19603   1.96157  -0.94279  -1.41421   1.76384   0.39018  -1.99037   0.76537   1.54602  -1.66294  -0.58057   2.00000     ... ... ..... ....... ......... ........... .............
E39 *    2.00000  -0.67378  -1.54602   1.71546   0.39018  -1.97835   0.94279   1.34312  -1.84776  -0.09814   1.91388  -1.19140  -1.11114   1.94006  -0.19603  -1.80798   1.41421   0.85511  -1.99037   0.48596   1.66294  -1.60642  -0.58057   1.99759  -0.76537  -1.48190   1.76384   0.29346  -1.96157   1.02821   1.26879  -1.88309   0.00000   1.88309  -1.26879  -1.02821   1.96157  -0.29346  -1.76384   1.48190   0.76537  -1.99759   0.58057   1.60642  -1.66294  -0.48596   1.99037  -0.85511  -1.41421   1.80798   0.19603  -1.94006   1.11114   1.19140  -1.91388   0.09814   1.84776  -1.34312  -0.94279   1.97835  -0.39018  -1.71546   1.54602   0.67378  -2.00000     ... ... ..... ....... ......... ........... .............
E40 *    2.00000  -0.76537  -1.41421   1.84776   0.00000  -1.84776   1.41421   0.76537  -2.00000   0.76537   1.41421  -1.84776   0.00000   1.84776  -1.41421  -0.76537   2.00000  -0.76537  -1.41421   1.84776   0.00000  -1.84776   1.41421   0.76537  -2.00000   0.76537   1.41421  -1.84776   0.00000   1.84776  -1.41421  -0.76537   2.00000  -0.76537  -1.41421   1.84776   0.00000  -1.84776   1.41421   0.76537  -2.00000   0.76537   1.41421  -1.84776   0.00000   1.84776  -1.41421  -0.76537   2.00000  -0.76537  -1.41421   1.84776   0.00000  -1.84776   1.41421   0.76537  -2.00000   0.76537   1.41421  -1.84776   0.00000   1.84776  -1.41421  -0.76537   2.00000     ... ... ..... ....... ......... ........... .............
E41 *    2.00000  -0.85511  -1.26879   1.94006  -0.39018  -1.60642   1.76384   0.09814  -1.84776   1.48190   0.58057  -1.97835   1.11114   1.02821  -1.99037   0.67378   1.41421  -1.88309   0.19603   1.71546  -1.66294  -0.29346   1.91388  -1.34312  -0.76537   1.99759  -0.94279  -1.19140   1.96157  -0.48596  -1.54602   1.80798   0.00000  -1.80798   1.54602   0.48596  -1.96157   1.19140   0.94279  -1.99759   0.76537   1.34312  -1.91388   0.29346   1.66294  -1.71546  -0.19603   1.88309  -1.41421  -0.67378   1.99037  -1.02821  -1.11114   1.97835  -0.58057  -1.48190   1.84776  -0.09814  -1.76384   1.60642   0.39018  -1.94006   1.26879   0.85511  -2.00000     ... ... ..... ....... ......... ........... .............
E42 *    2.00000  -0.94279  -1.11114   1.99037  -0.76537  -1.26879   1.96157  -0.58057  -1.41421   1.91388  -0.39018  -1.54602   1.84776  -0.19603  -1.66294   1.76384   0.00000  -1.76384   1.66294   0.19603  -1.84776   1.54602   0.39018  -1.91388   1.41421   0.58057  -1.96157   1.26879   0.76537  -1.99037   1.11114   0.94279  -2.00000   0.94279   1.11114  -1.99037   0.76537   1.26879  -1.96157   0.58057   1.41421  -1.91388   0.39018   1.54602  -1.84776   0.19603   1.66294  -1.76384   0.00000   1.76384  -1.66294  -0.19603   1.84776  -1.54602  -0.39018   1.91388  -1.41421  -0.58057   1.96157  -1.26879  -0.76537   1.99037  -1.11114  -0.94279   2.00000     ... ... ..... ....... ......... ........... .............
E43 *    2.00000  -1.02821  -0.94279   1.99759  -1.11114  -0.85511   1.99037  -1.19140  -0.76537   1.97835  -1.26879  -0.67378   1.96157  -1.34312  -0.58057   1.94006  -1.41421  -0.48596   1.91388  -1.48190  -0.39018   1.88309  -1.54602  -0.29346   1.84776  -1.60642  -0.19603   1.80798  -1.66294  -0.09814   1.76384  -1.71546   0.00000   1.71546  -1.76384   0.09814   1.66294  -1.80798   0.19603   1.60642  -1.84776   0.29346   1.54602  -1.88309   0.39018   1.48190  -1.91388   0.48596   1.41421  -1.94006   0.58057   1.34312  -1.96157   0.67378   1.26879  -1.97835   0.76537   1.19140  -1.99037   0.85511   1.11114  -1.99759   0.94279   1.02821  -2.00000     ... ... ..... ....... ......... ........... .............
E44 *    2.00000  -1.11114  -0.76537   1.96157  -1.41421  -0.39018   1.84776  -1.66294   0.00000   1.66294  -1.84776   0.39018   1.41421  -1.96157   0.76537   1.11114  -2.00000   1.11114   0.76537  -1.96157   1.41421   0.39018  -1.84776   1.66294   0.00000  -1.66294   1.84776  -0.39018  -1.41421   1.96157  -0.76537  -1.11114   2.00000  -1.11114  -0.76537   1.96157  -1.41421  -0.39018   1.84776  -1.66294   0.00000   1.66294  -1.84776   0.39018   1.41421  -1.96157   0.76537   1.11114  -2.00000   1.11114   0.76537  -1.96157   1.41421   0.39018  -1.84776   1.66294   0.00000  -1.66294   1.84776  -0.39018  -1.41421   1.96157  -0.76537  -1.11114   2.00000     ... ... ..... ....... ......... ........... .............
E45 *    2.00000  -1.19140  -0.58057   1.88309  -1.66294   0.09814   1.54602  -1.94006   0.76537   1.02821  -1.99037   1.34312   0.39018  -1.80798   1.76384  -0.29346  -1.41421   1.97835  -0.94279  -0.85511   1.96157  -1.48190  -0.19603   1.71546  -1.84776   0.48596   1.26879  -1.99759   1.11114   0.67378  -1.91388   1.60642   0.00000  -1.60642   1.91388  -0.67378  -1.11114   1.99759  -1.26879  -0.48596   1.84776  -1.71546   0.19603   1.48190  -1.96157   0.85511   0.94279  -1.97835   1.41421   0.29346  -1.76384   1.80798  -0.39018  -1.34312   1.99037  -1.02821  -0.76537   1.94006  -1.54602  -0.09814   1.66294  -1.88309   0.58057   1.19140  -2.00000     ... ... ..... ....... ......... ........... .............
E46 *    2.00000  -1.26879  -0.39018   1.76384  -1.84776   0.58057   1.11114  -1.99037   1.41421   0.19603  -1.66294   1.91388  -0.76537  -0.94279   1.96157  -1.54602   0.00000   1.54602  -1.96157   0.94279   0.76537  -1.91388   1.66294  -0.19603  -1.41421   1.99037  -1.11114  -0.58057   1.84776  -1.76384   0.39018   1.26879  -2.00000   1.26879   0.39018  -1.76384   1.84776  -0.58057  -1.11114   1.99037  -1.41421  -0.19603   1.66294  -1.91388   0.76537   0.94279  -1.96157   1.54602   0.00000  -1.54602   1.96157  -0.94279  -0.76537   1.91388  -1.66294   0.19603   1.41421  -1.99037   1.11114   0.58057  -1.84776   1.76384  -0.39018  -1.26879   2.00000     ... ... ..... ....... ......... ........... .............
E47 *    2.00000  -1.34312  -0.19603   1.60642  -1.96157   1.02821   0.58057  -1.80798   1.84776  -0.67378  -0.94279   1.94006  -1.66294   0.29346   1.26879  -1.99759   1.41421   0.09814  -1.54602   1.97835  -1.11114  -0.48596   1.76384  -1.88309   0.76537   0.85511  -1.91388   1.71546  -0.39018  -1.19140   1.99037  -1.48190   0.00000   1.48190  -1.99037   1.19140   0.39018  -1.71546   1.91388  -0.85511  -0.76537   1.88309  -1.76384   0.48596   1.11114  -1.97835   1.54602  -0.09814  -1.41421   1.99759  -1.26879  -0.29346   1.66294  -1.94006   0.94279   0.67378  -1.84776   1.80798  -0.58057  -1.02821   1.96157  -1.60642   0.19603   1.34312  -2.00000     ... ... ..... ....... ......... ........... .............
E48 *    2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000  -1.41421   0.00000   1.41421  -2.00000   1.41421   0.00000  -1.41421   2.00000     ... ... ..... ....... ......... ........... .............
E49 *    2.00000  -1.48190   0.19603   1.19140  -1.96157   1.71546  -0.58057  -0.85511   1.84776  -1.88309   0.94279   0.48596  -1.66294   1.97835  -1.26879  -0.09814   1.41421  -1.99759   1.54602  -0.29346  -1.11114   1.94006  -1.76384   0.67378   0.76537  -1.80798   1.91388  -1.02821  -0.39018   1.60642  -1.99037   1.34312   0.00000  -1.34312   1.99037  -1.60642   0.39018   1.02821  -1.91388   1.80798  -0.76537  -0.67378   1.76384  -1.94006   1.11114   0.29346  -1.54602   1.99759  -1.41421   0.09814   1.26879  -1.97835   1.66294  -0.48596  -0.94279   1.88309  -1.84776   0.85511   0.58057  -1.71546   1.96157  -1.19140  -0.19603   1.48190  -2.00000     ... ... ..... ....... ......... ........... .............
E50 *    2.00000  -1.54602   0.39018   0.94279  -1.84776   1.91388  -1.11114  -0.19603   1.41421  -1.99037   1.66294  -0.58057  -0.76537   1.76384  -1.96157   1.26879   0.00000  -1.26879   1.96157  -1.76384   0.76537   0.58057  -1.66294   1.99037  -1.41421   0.19603   1.11114  -1.91388   1.84776  -0.94279  -0.39018   1.54602  -2.00000   1.54602  -0.39018  -0.94279   1.84776  -1.91388   1.11114   0.19603  -1.41421   1.99037  -1.66294   0.58057   0.76537  -1.76384   1.96157  -1.26879   0.00000   1.26879  -1.96157   1.76384  -0.76537  -0.58057   1.66294  -1.99037   1.41421  -0.19603  -1.11114   1.91388  -1.84776   0.94279   0.39018  -1.54602   2.00000     ... ... ..... ....... ......... ........... .............
E51 *    2.00000  -1.60642   0.58057   0.67378  -1.66294   1.99759  -1.54602   0.48596   0.76537  -1.71546   1.99037  -1.48190   0.39018   0.85511  -1.76384   1.97835  -1.41421   0.29346   0.94279  -1.80798   1.96157  -1.34312   0.19603   1.02821  -1.84776   1.94006  -1.26879   0.09814   1.11114  -1.88309   1.91388  -1.19140   0.00000   1.19140  -1.91388   1.88309  -1.11114  -0.09814   1.26879  -1.94006   1.84776  -1.02821  -0.19603   1.34312  -1.96157   1.80798  -0.94279  -0.29346   1.41421  -1.97835   1.76384  -0.85511  -0.39018   1.48190  -1.99037   1.71546  -0.76537  -0.48596   1.54602  -1.99759   1.66294  -0.67378  -0.58057   1.60642  -2.00000     ... ... ..... ....... ......... ........... .............
E52 *    2.00000  -1.66294   0.76537   0.39018  -1.41421   1.96157  -1.84776   1.11114   0.00000  -1.11114   1.84776  -1.96157   1.41421  -0.39018  -0.76537   1.66294  -2.00000   1.66294  -0.76537  -0.39018   1.41421  -1.96157   1.84776  -1.11114   0.00000   1.11114  -1.84776   1.96157  -1.41421   0.39018   0.76537  -1.66294   2.00000  -1.66294   0.76537   0.39018  -1.41421   1.96157  -1.84776   1.11114   0.00000  -1.11114   1.84776  -1.96157   1.41421  -0.39018  -0.76537   1.66294  -2.00000   1.66294  -0.76537  -0.39018   1.41421  -1.96157   1.84776  -1.11114   0.00000   1.11114  -1.84776   1.96157  -1.41421   0.39018   0.76537  -1.66294   2.00000     ... ... ..... ....... ......... ........... .............
E53 *    2.00000  -1.71546   0.94279   0.09814  -1.11114   1.80798  -1.99037   1.60642  -0.76537  -0.29346   1.26879  -1.88309   1.96157  -1.48190   0.58057   0.48596  -1.41421   1.94006  -1.91388   1.34312  -0.39018  -0.67378   1.54602  -1.97835   1.84776  -1.19140   0.19603   0.85511  -1.66294   1.99759  -1.76384   1.02821   0.00000  -1.02821   1.76384  -1.99759   1.66294  -0.85511  -0.19603   1.19140  -1.84776   1.97835  -1.54602   0.67378   0.39018  -1.34312   1.91388  -1.94006   1.41421  -0.48596  -0.58057   1.48190  -1.96157   1.88309  -1.26879   0.29346   0.76537  -1.60642   1.99037  -1.80798   1.11114  -0.09814  -0.94279   1.71546  -2.00000     ... ... ..... ....... ......... ........... .............
E54 *    2.00000  -1.76384   1.11114  -0.19603  -0.76537   1.54602  -1.96157   1.91388  -1.41421   0.58057   0.39018  -1.26879   1.84776  -1.99037   1.66294  -0.94279   0.00000   0.94279  -1.66294   1.99037  -1.84776   1.26879  -0.39018  -0.58057   1.41421  -1.91388   1.96157  -1.54602   0.76537   0.19603  -1.11114   1.76384  -2.00000   1.76384  -1.11114   0.19603   0.76537  -1.54602   1.96157  -1.91388   1.41421  -0.58057  -0.39018   1.26879  -1.84776   1.99037  -1.66294   0.94279   0.00000  -0.94279   1.66294  -1.99037   1.84776  -1.26879   0.39018   0.58057  -1.41421   1.91388  -1.96157   1.54602  -0.76537  -0.19603   1.11114  -1.76384   2.00000     ... ... ..... ....... ......... ........... .............
E55 *    2.00000  -1.80798   1.26879  -0.48596  -0.39018   1.19140  -1.76384   1.99759  -1.84776   1.34312  -0.58057  -0.29346   1.11114  -1.71546   1.99037  -1.88309   1.41421  -0.67378  -0.19603   1.02821  -1.66294   1.97835  -1.91388   1.48190  -0.76537  -0.09814   0.94279  -1.60642   1.96157  -1.94006   1.54602  -0.85511   0.00000   0.85511  -1.54602   1.94006  -1.96157   1.60642  -0.94279   0.09814   0.76537  -1.48190   1.91388  -1.97835   1.66294  -1.02821   0.19603   0.67378  -1.41421   1.88309  -1.99037   1.71546  -1.11114   0.29346   0.58057  -1.34312   1.84776  -1.99759   1.76384  -1.19140   0.39018   0.48596  -1.26879   1.80798  -2.00000     ... ... ..... ....... ......... ........... .............
E56 *    2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000  -1.84776   1.41421  -0.76537   0.00000   0.76537  -1.41421   1.84776  -2.00000   1.84776  -1.41421   0.76537   0.00000  -0.76537   1.41421  -1.84776   2.00000     ... ... ..... ....... ......... ........... .............
E57 *    2.00000  -1.88309   1.54602  -1.02821   0.39018   0.29346  -0.94279   1.48190  -1.84776   1.99759  -1.91388   1.60642  -1.11114   0.48596   0.19603  -0.85511   1.41421  -1.80798   1.99037  -1.94006   1.66294  -1.19140   0.58057   0.09814  -0.76537   1.34312  -1.76384   1.97835  -1.96157   1.71546  -1.26879   0.67378   0.00000  -0.67378   1.26879  -1.71546   1.96157  -1.97835   1.76384  -1.34312   0.76537  -0.09814  -0.58057   1.19140  -1.66294   1.94006  -1.99037   1.80798  -1.41421   0.85511  -0.19603  -0.48596   1.11114  -1.60642   1.91388  -1.99759   1.84776  -1.48190   0.94279  -0.29346  -0.39018   1.02821  -1.54602   1.88309  -2.00000     ... ... ..... ....... ......... ........... .............
E58 *    2.00000  -1.91388   1.66294  -1.26879   0.76537  -0.19603  -0.39018   0.94279  -1.41421   1.76384  -1.96157   1.99037  -1.84776   1.54602  -1.11114   0.58057   0.00000  -0.58057   1.11114  -1.54602   1.84776  -1.99037   1.96157  -1.76384   1.41421  -0.94279   0.39018   0.19603  -0.76537   1.26879  -1.66294   1.91388  -2.00000   1.91388  -1.66294   1.26879  -0.76537   0.19603   0.39018  -0.94279   1.41421  -1.76384   1.96157  -1.99037   1.84776  -1.54602   1.11114  -0.58057   0.00000   0.58057  -1.11114   1.54602  -1.84776   1.99037  -1.96157   1.76384  -1.41421   0.94279  -0.39018  -0.19603   0.76537  -1.26879   1.66294  -1.91388   2.00000     ... ... ..... ....... ......... ........... .............
E59 *    2.00000  -1.94006   1.76384  -1.48190   1.11114  -0.67378   0.19603   0.29346  -0.76537   1.19140  -1.54602   1.80798  -1.96157   1.99759  -1.91388   1.71546  -1.41421   1.02821  -0.58057   0.09814   0.39018  -0.85511   1.26879  -1.60642   1.84776  -1.97835   1.99037  -1.88309   1.66294  -1.34312   0.94279  -0.48596   0.00000   0.48596  -0.94279   1.34312  -1.66294   1.88309  -1.99037   1.97835  -1.84776   1.60642  -1.26879   0.85511  -0.39018  -0.09814   0.58057  -1.02821   1.41421  -1.71546   1.91388  -1.99759   1.96157  -1.80798   1.54602  -1.19140   0.76537  -0.29346  -0.19603   0.67378  -1.11114   1.48190  -1.76384   1.94006  -2.00000     ... ... ..... ....... ......... ........... ..TT.........
E60 *    2.00000  -1.96157   1.84776  -1.66294   1.41421  -1.11114   0.76537  -0.39018   0.00000   0.39018  -0.76537   1.11114  -1.41421   1.66294  -1.84776   1.96157  -2.00000   1.96157  -1.84776   1.66294  -1.41421   1.11114  -0.76537   0.39018   0.00000  -0.39018   0.76537  -1.11114   1.41421  -1.66294   1.84776  -1.96157   2.00000  -1.96157   1.84776  -1.66294   1.41421  -1.11114   0.76537  -0.39018   0.00000   0.39018  -0.76537   1.11114  -1.41421   1.66294  -1.84776   1.96157  -2.00000   1.96157  -1.84776   1.66294  -1.41421   1.11114  -0.76537   0.39018   0.00000  -0.39018   0.76537  -1.11114   1.41421  -1.66294   1.84776  -1.96157   2.00000     ... ... ..... ....... ......... ..TT....... .............
E61 *    2.00000  -1.97835   1.91388  -1.80798   1.66294  -1.48190   1.26879  -1.02821   0.76537  -0.48596   0.19603   0.09814  -0.39018   0.67378  -0.94279   1.19140  -1.41421   1.60642  -1.76384   1.88309  -1.96157   1.99759  -1.99037   1.94006  -1.84776   1.71546  -1.54602   1.34312  -1.11114   0.85511  -0.58057   0.29346   0.00000  -0.29346   0.58057  -0.85511   1.11114  -1.34312   1.54602  -1.71546   1.84776  -1.94006   1.99037  -1.99759   1.96157  -1.88309   1.76384  -1.60642   1.41421  -1.19140   0.94279  -0.67378   0.39018  -0.09814  -0.19603   0.48596  -0.76537   1.02821  -1.26879   1.48190  -1.66294   1.80798  -1.91388   1.97835  -2.00000     ... ... ..... ....... ..TT..... ........... ......TT.....
E62 *    2.00000  -1.99037   1.96157  -1.91388   1.84776  -1.76384   1.66294  -1.54602   1.41421  -1.26879   1.11114  -0.94279   0.76537  -0.58057   0.39018  -0.19603   0.00000   0.19603  -0.39018   0.58057  -0.76537   0.94279  -1.11114   1.26879  -1.41421   1.54602  -1.66294   1.76384  -1.84776   1.91388  -1.96157   1.99037  -2.00000   1.99037  -1.96157   1.91388  -1.84776   1.76384  -1.66294   1.54602  -1.41421   1.26879  -1.11114   0.94279  -0.76537   0.58057  -0.39018   0.19603   0.00000  -0.19603   0.39018  -0.58057   0.76537  -0.94279   1.11114  -1.26879   1.41421  -1.54602   1.66294  -1.76384   1.84776  -1.91388   1.96157  -1.99037   2.00000     ... ... ..... ..TT... ......... ......TT... .............
E63 *    2.00000  -1.99759   1.99037  -1.97835   1.96157  -1.94006   1.91388  -1.88309   1.84776  -1.80798   1.76384  -1.71546   1.66294  -1.60642   1.54602  -1.48190   1.41421  -1.34312   1.26879  -1.19140   1.11114  -1.02821   0.94279  -0.85511   0.76537  -0.67378   0.58057  -0.48596   0.39018  -0.29346   0.19603  -0.09814   0.00000   0.09814  -0.19603   0.29346  -0.39018   0.48596  -0.58057   0.67378  -0.76537   0.85511  -0.94279   1.02821  -1.11114   1.19140  -1.26879   1.34312  -1.41421   1.48190  -1.54602   1.60642  -1.66294   1.71546  -1.76384   1.80798  -1.84776   1.88309  -1.91388   1.94006  -1.96157   1.97835  -1.99037   1.99759  -2.00000     TT. ... ..TT. ....... ......TT. ........... ..........TT.

 Irrational character values:  1.997590912410 = 2*cos(2*π/128) = 2*cos(π/64) = √2+√2+√2+√2+√2
                               1.990369453344 = 2*cos(4*π/128) = 2*cos(π/32) = √2+√2+√2+√2
                               1.978353019930 = 2*cos(6*π/128) = 2*cos(3*π/64) = √2+√2+√2+√2−√2
                               1.961570560806 = 2*cos(8*π/128) = 2*cos(π/16) = √2+√2+√2
                               1.940062506389 = 2*cos(10*π/128) = 2*cos(5*π/64) = √2+√2+√2−√2−√2
                               1.913880671464 = 2*cos(12*π/128) = 2*cos(3*π/32) = √2+√2+√2−√2
                               1.883088130366 = 2*cos(14*π/128) = 2*cos(7*π/64) = √2+√2+√2−√2+√2
                               1.847759065023 = 2*cos(16*π/128) = 2*cos(π/8) = √2+√2
                               1.807978586247 = 2*cos(18*π/128) = 2*cos(9*π/64) = √2+√2−√2−√2+√2
                               1.763842528697 = 2*cos(20*π/128) = 2*cos(5*π/32) = √2+√2−√2−√2
                               1.715457220001 = 2*cos(22*π/128) = 2*cos(11*π/64) = √2+√2−√2−√2−√2
                               1.662939224605 = 2*cos(24*π/128) = 2*cos(3*π/16) = √2+√2−√2
                               1.606415062961 = 2*cos(26*π/128) = 2*cos(13*π/64) = √2+√2−√2+√2−√2
                               1.546020906725 = 2*cos(28*π/128) = 2*cos(7*π/32) = √2+√2−√2+√2
                               1.481902250710 = 2*cos(30*π/128) = 2*cos(15*π/64) = √2+√2−√2+√2+√2
                               1.414213562373 = 2*cos(32*π/128) = 2*cos(π/4) = √2
                               1.343117909694 = 2*cos(34*π/128) = 2*cos(17*π/64) = √2−√2−√2+√2+√2
                               1.268786568327 = 2*cos(36*π/128) = 2*cos(9*π/32) = √2−√2−√2+√2
                               1.191398608985 = 2*cos(38*π/128) = 2*cos(19*π/64) = √2−√2−√2+√2−√2
                               1.111140466039 = 2*cos(40*π/128) = 2*cos(5*π/16) = √2−√2−√2
                               1.028205488386 = 2*cos(42*π/128) = 2*cos(21*π/64) = √2−√2−√2−√2−√2
                               0.942793473652 = 2*cos(44*π/128) = 2*cos(11*π/32) = √2−√2−√2−√2
                               0.855110186861 = 2*cos(46*π/128) = 2*cos(23*π/64) = √2−√2−√2−√2+√2
                               0.765366864730 = 2*cos(48*π/128) = 2*cos(3*π/8) = √2−√2
                               0.673779706784 = 2*cos(50*π/128) = 2*cos(25*π/64) = √2−√2+√2−√2+√2
                               0.580569354509 = 2*cos(52*π/128) = 2*cos(13*π/32) = √2−√2+√2−√2
                               0.485960359807 = 2*cos(54*π/128) = 2*cos(27*π/64) = √2−√2+√2−√2−√2
                               0.390180644032 = 2*cos(56*π/128) = 2*cos(7*π/16) = √2−√2+√2
                               0.293460948911 = 2*cos(58*π/128) = 2*cos(29*π/64) = √2−√2+√2+√2−√2
                               0.196034280659 = 2*cos(60*π/128) = 2*cos(15*π/32) = √2−√2+√2+√2
                               0.098135348655 = 2*cos(62*π/128) = 2*cos(31*π/64) = √2−√2+√2+√2+√2



 Symmetry of Rotations and Cartesian products

A    R+d+g+i+k+m  Rz, z2, z4, z6 
B    p+f+h+j+l    z, z3, z5 
E1   p+f+h+j+l    {x, y}, {xz2, yz2}, {xz4, yz4} 
E2   d+g+i+k+m    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E3   f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E4   g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(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)} 
E6   i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7   j+l 
E8   k+m 
E9   l 
E10  m 
E55  m 
E56  l 
E57  k+m 
E58  j+l 
E59  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E60  h+j+l        {z((x2y2)2−4x2y2), xyz(x2y2)} 
E61  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E62  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E63  R+d+g+i+k+m  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 

 Notes:

    α  The order of the S128 point group is 128, and the order of the principal axis (S128) is 128. The group has 65 irreducible representations.

    β  The S128 point group could also be named C128i, because the S128 axis is identical to a roto-inversion axis of order 128.

    γ  The S128 point group is isomorphic to C128.

    δ  The S128 point group is generated by one single symmetry element, S128. Therefore, it is a cyclic group.

    ε  The lowest nonvanishing multipole moment in S128 is 4 (quadrupole moment).

    ζ  This is an Abelian point group (the commutative law holds between all symmetry operations).
       The S128 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 126 cases have been combined into 63 two-dimensional representations that are no longer irreducible but have real-valued characters.
       Accordingly, 63 pairs of left and right rotations have been combined into one two-membered pseudo-class each.

    θ  The 63 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.

    κ  The point group corresponds to a constructible polygon, as the order of the principal axis is a product of any number
       of different Fermat primes (3,5,17,257,65537) times an arbitrary power of two. Therefore, all characters have an
       algebraic degree which is a power of two and can be expressed as radicals involving only square roots and integer numbers.

This Character Table for the S128 point group was created by Gernot Katzer.

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