G 2(5) | VerlindeDB

\(\operatorname{G}_{2}(5)\): \( G_{2} \) at level \(5\)

Fusion Ring

\[ \begin{array}{llllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1 \oplus 2 \oplus 3 \oplus 6} & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{2 \oplus 6 \oplus 11} & \htmlTitle{3\otimes 3}{1 \oplus 3 \oplus 6 \oplus 10 \oplus 5} & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{9 \oplus 8 \oplus 4} & \htmlTitle{4\otimes 3}{12 \oplus 9 \oplus 8} & \htmlTitle{4\otimes 4}{1 \oplus 2 \oplus 6 \oplus 10 \oplus 9 \oplus 4} & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{11 \oplus 12 \oplus 7} & \htmlTitle{5\otimes 3}{3 \oplus 10 \oplus 5 \oplus 12 \oplus 8} & \htmlTitle{5\otimes 4}{11 \oplus 10 \oplus 5 \oplus 12 \oplus 7} & \htmlTitle{5\otimes 5}{1 \oplus 3 \oplus 6 \oplus 10 \oplus 5 \oplus 12 \oplus 9 \oplus 8 \oplus 4} & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{2 \oplus 3 \oplus 6 \oplus 11 \oplus 10} & \htmlTitle{6\otimes 3}{2 \oplus 3 \oplus 6 \oplus 11 \oplus 10 \oplus 12} & \htmlTitle{6\otimes 4}{10 \oplus 12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{6\otimes 5}{6 \oplus 11 \oplus 10 \oplus 5 \oplus 12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{6\otimes 6}{1 \oplus 2 \oplus 3 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 10 \oplus 5 \oplus 12 \oplus 9} & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{5 \oplus 12 \oplus 7 \oplus 8} & \htmlTitle{7\otimes 3}{11 \oplus 12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{7\otimes 4}{6 \oplus 11 \oplus 10 \oplus 5 \oplus 12 \oplus 7} & \htmlTitle{7\otimes 5}{2 \oplus 6 \oplus 11 \oplus 10 \oplus 12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{7\otimes 6}{11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{7\otimes 7}{1 \oplus 2 \oplus 3 \oplus 6 \oplus 11 \oplus 10 \oplus 5 \oplus 12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{8\otimes 3}{10 \oplus 5 \oplus 12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{8\otimes 4}{2 \oplus 3 \oplus 6 \oplus 11 \oplus 10 \oplus 12 \oplus 9 \oplus 8} & \htmlTitle{8\otimes 5}{3 \oplus 6 \oplus 11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{8\otimes 6}{11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{8\otimes 7}{2 \oplus 3 \oplus 6 \oplus 2\cdot11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{8\otimes 8}{1 \oplus 2 \oplus 3 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{10 \oplus 12 \oplus 9 \oplus 8 \oplus 4} & \htmlTitle{9\otimes 3}{11 \oplus 10 \oplus 12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{9\otimes 4}{2 \oplus 3 \oplus 6 \oplus 11 \oplus 10 \oplus 12 \oplus 9 \oplus 8 \oplus 4} & \htmlTitle{9\otimes 5}{6 \oplus 2\cdot11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{9\otimes 6}{6 \oplus 11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{9\otimes 7}{3 \oplus 6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{9\otimes 8}{2 \oplus 3 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{9\otimes 9}{1 \oplus 2 \oplus 3 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 2\cdot8 \oplus 4} & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{6 \oplus 11 \oplus 10 \oplus 12 \oplus 9} & \htmlTitle{10\otimes 3}{3 \oplus 6 \oplus 11 \oplus 10 \oplus 5 \oplus 12 \oplus 9 \oplus 8} & \htmlTitle{10\otimes 4}{6 \oplus 11 \oplus 10 \oplus 5 \oplus 12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{10\otimes 5}{3 \oplus 6 \oplus 11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{10\otimes 6}{2 \oplus 3 \oplus 6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{10\otimes 7}{6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{10\otimes 8}{3 \oplus 6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{10\otimes 9}{2 \oplus 3 \oplus 6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 2\cdot7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{10\otimes 10}{1 \oplus 2 \oplus 3 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 2\cdot5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 2\cdot7 \oplus 2\cdot8 \oplus 4} & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{3 \oplus 6 \oplus 11 \oplus 10 \oplus 5 \oplus 12} & \htmlTitle{11\otimes 3}{2 \oplus 6 \oplus 2\cdot11 \oplus 10 \oplus 12 \oplus 9 \oplus 7} & \htmlTitle{11\otimes 4}{11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{11\otimes 5}{2 \oplus 6 \oplus 2\cdot11 \oplus 10 \oplus 2\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{11\otimes 6}{2 \oplus 3 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{11\otimes 7}{3 \oplus 6 \oplus 11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{11\otimes 8}{6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 2\cdot7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{11\otimes 9}{3 \oplus 6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 2\cdot5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 2\cdot7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{11\otimes 10}{2 \oplus 3 \oplus 2\cdot6 \oplus 3\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 2\cdot7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{11\otimes 11}{1 \oplus 2 \oplus 2\cdot3 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 3\cdot10 \oplus 2\cdot5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 2\cdot8 \oplus 4} & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{11 \oplus 10 \oplus 5 \oplus 12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{12\otimes 3}{6 \oplus 11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{12\otimes 4}{3 \oplus 6 \oplus 2\cdot11 \oplus 10 \oplus 5 \oplus 2\cdot12 \oplus 9 \oplus 7 \oplus 8} & \htmlTitle{12\otimes 5}{2 \oplus 3 \oplus 6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{12\otimes 6}{3 \oplus 6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 2\cdot7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{12\otimes 7}{2 \oplus 3 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{12\otimes 8}{2 \oplus 3 \oplus 2\cdot6 \oplus 3\cdot11 \oplus 3\cdot10 \oplus 2\cdot5 \oplus 3\cdot12 \oplus 2\cdot9 \oplus 2\cdot7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{12\otimes 9}{2 \oplus 3 \oplus 2\cdot6 \oplus 3\cdot11 \oplus 3\cdot10 \oplus 2\cdot5 \oplus 4\cdot12 \oplus 2\cdot9 \oplus 2\cdot7 \oplus 2\cdot8 \oplus 4} & \htmlTitle{12\otimes 10}{2 \oplus 3 \oplus 2\cdot6 \oplus 3\cdot11 \oplus 3\cdot10 \oplus 2\cdot5 \oplus 4\cdot12 \oplus 3\cdot9 \oplus 2\cdot7 \oplus 3\cdot8 \oplus 4} & \htmlTitle{12\otimes 11}{2 \oplus 3 \oplus 2\cdot6 \oplus 3\cdot11 \oplus 3\cdot10 \oplus 2\cdot5 \oplus 4\cdot12 \oplus 3\cdot9 \oplus 2\cdot7 \oplus 3\cdot8 \oplus 2\cdot4} & \htmlTitle{12\otimes 12}{1 \oplus 2 \oplus 2\cdot3 \oplus 3\cdot6 \oplus 4\cdot11 \oplus 4\cdot10 \oplus 2\cdot5 \oplus 5\cdot12 \oplus 4\cdot9 \oplus 3\cdot7 \oplus 3\cdot8 \oplus 2\cdot4} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(4.933\)\( \cos{\left(\frac{11 \pi}{27} \right)} + \cos{\left(\frac{10 \pi}{27} \right)} + \cos{\left(\frac{8 \pi}{27} \right)} + \cos{\left(\frac{7 \pi}{27} \right)} + \cos{\left(\frac{2 \pi}{27} \right)} + \cos{\left(\frac{\pi}{27} \right)} + 1 \)
\( 3\)\(6.812\)\( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{11 \pi}{27} \right)} + \cos{\left(\frac{10 \pi}{27} \right)} + \cos{\left(\frac{8 \pi}{27} \right)} + \cos{\left(\frac{7 \pi}{27} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{2 \pi}{27} \right)} + \cos{\left(\frac{\pi}{27} \right)} + 1 \)
\( 4\)\(7.562\)\( - \cos{\left(\frac{11 \pi}{27} \right)} - \cos{\left(\frac{4 \pi}{9} \right)} - \cos{\left(\frac{13 \pi}{27} \right)} + \cos{\left(\frac{10 \pi}{27} \right)} + \cos{\left(\frac{8 \pi}{27} \right)} + \cos{\left(\frac{7 \pi}{27} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{5 \pi}{27} \right)} + \cos{\left(\frac{4 \pi}{27} \right)} + \cos{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{2 \pi}{27} \right)} + \cos{\left(\frac{\pi}{27} \right)} + 1 \)
\( 5\)\(10.270\)\( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{11 \pi}{27} \right)} + \cos{\left(\frac{10 \pi}{27} \right)} + \cos{\left(\frac{8 \pi}{27} \right)} + \cos{\left(\frac{7 \pi}{27} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{2 \pi}{27} \right)} + \cos{\left(\frac{\pi}{27} \right)} + 1 + 2 \cos{\left(\frac{5 \pi}{27} \right)} + 2 \cos{\left(\frac{4 \pi}{27} \right)} \)
\( 6\)\(11.586\)\( \cos{\left(\frac{13 \pi}{27} \right)} + \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{11 \pi}{27} \right)} + \cos{\left(\frac{7 \pi}{27} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{10 \pi}{27} \right)} + \cos{\left(\frac{5 \pi}{27} \right)} + \cos{\left(\frac{4 \pi}{27} \right)} + \cos{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{2 \pi}{27} \right)} + 2 \cos{\left(\frac{8 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{27} \right)} + 2 \)
\( 7\)\(11.802\)\( \cos{\left(\frac{11 \pi}{27} \right)} + \cos{\left(\frac{10 \pi}{27} \right)} + \cos{\left(\frac{8 \pi}{27} \right)} + \cos{\left(\frac{7 \pi}{27} \right)} + \cos{\left(\frac{2 \pi}{27} \right)} + \cos{\left(\frac{\pi}{27} \right)} + 1 + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{5 \pi}{27} \right)} + 2 \cos{\left(\frac{4 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} \)
\( 8\)\(14.369\)\( 1 + 2 \cos{\left(\frac{8 \pi}{27} \right)} + 2 \cos{\left(\frac{7 \pi}{27} \right)} + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{5 \pi}{27} \right)} + 2 \cos{\left(\frac{4 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \cos{\left(\frac{2 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{27} \right)} \)
\( 9\)\(15.369\)\( 2 \cos{\left(\frac{8 \pi}{27} \right)} + 2 \cos{\left(\frac{7 \pi}{27} \right)} + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{5 \pi}{27} \right)} + 2 \cos{\left(\frac{4 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \cos{\left(\frac{2 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{27} \right)} + 2 \)
\( 10\)\(16.735\)\( 2 \cos{\left(\frac{11 \pi}{27} \right)} + 2 \cos{\left(\frac{10 \pi}{27} \right)} + 2 \cos{\left(\frac{8 \pi}{27} \right)} + 2 \cos{\left(\frac{7 \pi}{27} \right)} + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{5 \pi}{27} \right)} + 2 \cos{\left(\frac{4 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \cos{\left(\frac{2 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{27} \right)} + 2 \)
\( 11\)\(17.082\)\( 2 \cos{\left(\frac{4 \pi}{9} \right)} + 2 \cos{\left(\frac{11 \pi}{27} \right)} + 2 \cos{\left(\frac{10 \pi}{27} \right)} + 2 \cos{\left(\frac{8 \pi}{27} \right)} + 2 \cos{\left(\frac{7 \pi}{27} \right)} + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{5 \pi}{27} \right)} + 2 \cos{\left(\frac{4 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \cos{\left(\frac{2 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{27} \right)} + 2 \)
\( 12\)\(21.774\)\( \cos{\left(\frac{13 \pi}{27} \right)} + \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{11 \pi}{27} \right)} + 2 \cos{\left(\frac{10 \pi}{27} \right)} + 2 \cos{\left(\frac{8 \pi}{27} \right)} + 2 \cos{\left(\frac{\pi}{27} \right)} + 2 + 3 \cos{\left(\frac{7 \pi}{27} \right)} + 3 \cos{\left(\frac{2 \pi}{9} \right)} + 3 \cos{\left(\frac{5 \pi}{27} \right)} + 3 \cos{\left(\frac{4 \pi}{27} \right)} + 3 \cos{\left(\frac{\pi}{9} \right)} + 3 \cos{\left(\frac{2 \pi}{27} \right)} \)
\( D^2\)1996.556\(27 \cos{\left(\frac{13 \pi}{27} \right)} + 81 \cos{\left(\frac{4 \pi}{9} \right)} + 135 \cos{\left(\frac{11 \pi}{27} \right)} + 189 \cos{\left(\frac{10 \pi}{27} \right)} + 243 \cos{\left(\frac{8 \pi}{27} \right)} + 243 \cos{\left(\frac{7 \pi}{27} \right)} + 243 \cos{\left(\frac{2 \pi}{9} \right)} + 243 \cos{\left(\frac{5 \pi}{27} \right)} + 243 \cos{\left(\frac{4 \pi}{27} \right)} + 243 \cos{\left(\frac{\pi}{9} \right)} + 243 \cos{\left(\frac{2 \pi}{27} \right)} + 243 \cos{\left(\frac{\pi}{27} \right)} + 243\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{4}{9}} & \htmlTitle{\theta_{3}}{\frac{8}{9}} & \htmlTitle{\theta_{4}}{\frac{46}{27}} & \htmlTitle{\theta_{5}}{\frac{2}{9}} & \htmlTitle{\theta_{6}}{\frac{28}{27}} & \htmlTitle{\theta_{7}}{\frac{10}{9}} & \htmlTitle{\theta_{8}}{\frac{4}{3}} & \htmlTitle{\theta_{9}}{\frac{2}{3}} & \htmlTitle{\theta_{10}}{\frac{16}{9}} & \htmlTitle{\theta_{11}}{\frac{14}{9}} & \htmlTitle{\theta_{12}}{\frac{10}{27}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{llllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{-\zeta_{108}^{34} - \zeta_{108}^{32} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{2; 2}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{3; 2}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} - \zeta_{108}^{20} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{3; 3}}{-\zeta_{108}^{34} - \zeta_{108}^{32} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{108}^{34} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{4; 2}}{2 \zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} - 2 \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{4; 3}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - 2 \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + 2 \zeta_{108}^{16} + 3 \zeta_{108}^{14} + 3 \zeta_{108}^{12} + 3 \zeta_{108}^{10} + 3 \zeta_{108}^{8} + 3 \zeta_{108}^{6} + 3 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{4; 4}}{0} & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{5; 2}}{-1} & \htmlTitle{S_{5; 3}}{2 \zeta_{108}^{34} + 2 \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} - 2 \zeta_{108}^{16} - 2 \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - 2 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{5; 4}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - 2 \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + 2 \zeta_{108}^{16} + 3 \zeta_{108}^{14} + 3 \zeta_{108}^{12} + 3 \zeta_{108}^{10} + 3 \zeta_{108}^{8} + 3 \zeta_{108}^{6} + 3 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{5; 5}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} + \zeta_{108}^{16} + \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & & & & & & & \\ \htmlTitle{S_{6; 1}}{-2 \zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} + 2 \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{6; 2}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - 2 \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + 2 \zeta_{108}^{16} + 3 \zeta_{108}^{14} + 3 \zeta_{108}^{12} + 3 \zeta_{108}^{10} + 3 \zeta_{108}^{8} + 3 \zeta_{108}^{6} + 3 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{6; 3}}{-\zeta_{108}^{34} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{6; 4}}{0} & \htmlTitle{S_{6; 5}}{-\zeta_{108}^{34} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{6; 6}}{0} & & & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} + \zeta_{108}^{16} + \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{7; 2}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{7; 3}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} + \zeta_{108}^{20} - 2 \zeta_{108}^{16} - 2 \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - 2 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 1} & \htmlTitle{S_{7; 4}}{2 \zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} - 2 \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{7; 5}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} - \zeta_{108}^{20} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{7; 6}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - 2 \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + 2 \zeta_{108}^{16} + 3 \zeta_{108}^{14} + 3 \zeta_{108}^{12} + 3 \zeta_{108}^{10} + 3 \zeta_{108}^{8} + 3 \zeta_{108}^{6} + 3 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{7; 7}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & & & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} - \zeta_{108}^{20} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 1} & \htmlTitle{S_{8; 2}}{2 \zeta_{108}^{34} + 2 \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} - 2 \zeta_{108}^{16} - 2 \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - 2 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{8; 3}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{8; 4}}{-\zeta_{108}^{34} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{8; 5}}{2 \zeta_{108}^{34} + 2 \zeta_{108}^{32} + 2 \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} - 2 \zeta_{108}^{16} - 2 \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - 2 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{8; 6}}{-2 \zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} + 2 \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{8; 7}}{-\zeta_{108}^{34} - \zeta_{108}^{32} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{8; 8}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} + \zeta_{108}^{20} - 2 \zeta_{108}^{16} - 2 \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - 2 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & & & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} - \zeta_{108}^{20} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{9; 2}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} - \zeta_{108}^{16} - \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{9; 3}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{9; 4}}{\zeta_{108}^{34} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{9; 5}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{9; 6}}{2 \zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} - 2 \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{9; 7}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{9; 8}}{-1} & \htmlTitle{S_{9; 9}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} - \zeta_{108}^{20} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 1} & & & \\ \htmlTitle{S_{10; 1}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{10; 2}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{10; 3}}{1} & \htmlTitle{S_{10; 4}}{-2 \zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} + 2 \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{10; 5}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} - \zeta_{108}^{20} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 1} & \htmlTitle{S_{10; 6}}{2 \zeta_{108}^{34} + 2 \zeta_{108}^{32} + 2 \zeta_{108}^{30} + 2 \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} - 2 \zeta_{108}^{16} - 3 \zeta_{108}^{14} - 3 \zeta_{108}^{12} - 3 \zeta_{108}^{10} - 3 \zeta_{108}^{8} - 3 \zeta_{108}^{6} - 3 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{10; 7}}{2 \zeta_{108}^{34} + 2 \zeta_{108}^{32} + 2 \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} - 2 \zeta_{108}^{16} - 2 \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - 2 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{10; 8}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} - \zeta_{108}^{16} - \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{10; 9}}{-\zeta_{108}^{34} - \zeta_{108}^{32} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{10; 10}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & & \\ \htmlTitle{S_{11; 1}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{11; 2}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} - \zeta_{108}^{20} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 1} & \htmlTitle{S_{11; 3}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} - \zeta_{108}^{16} - \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{11; 4}}{2 \zeta_{108}^{34} + 2 \zeta_{108}^{32} + 2 \zeta_{108}^{30} + 2 \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} - 2 \zeta_{108}^{16} - 3 \zeta_{108}^{14} - 3 \zeta_{108}^{12} - 3 \zeta_{108}^{10} - 3 \zeta_{108}^{8} - 3 \zeta_{108}^{6} - 3 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{11; 5}}{\zeta_{108}^{34} + \zeta_{108}^{32} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{11; 6}}{\zeta_{108}^{34} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{11; 7}}{1} & \htmlTitle{S_{11; 8}}{\zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{11; 9}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{11; 10}}{-\zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} - \zeta_{108}^{20} + 2 \zeta_{108}^{16} + 2 \zeta_{108}^{14} + 2 \zeta_{108}^{12} + 2 \zeta_{108}^{10} + 2 \zeta_{108}^{8} + 2 \zeta_{108}^{6} + 2 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{11; 11}}{2 \zeta_{108}^{34} + 2 \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} - 2 \zeta_{108}^{16} - 2 \zeta_{108}^{14} - 2 \zeta_{108}^{12} - 2 \zeta_{108}^{10} - 2 \zeta_{108}^{8} - 2 \zeta_{108}^{6} - 2 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \\ \htmlTitle{S_{12; 1}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - 2 \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + 2 \zeta_{108}^{16} + 3 \zeta_{108}^{14} + 3 \zeta_{108}^{12} + 3 \zeta_{108}^{10} + 3 \zeta_{108}^{8} + 3 \zeta_{108}^{6} + 3 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{12; 2}}{\zeta_{108}^{34} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{12; 3}}{2 \zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} - 2 \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{12; 4}}{0} & \htmlTitle{S_{12; 5}}{2 \zeta_{108}^{34} + \zeta_{108}^{32} + \zeta_{108}^{30} + \zeta_{108}^{28} - 2 \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{12; 6}}{0} & \htmlTitle{S_{12; 7}}{\zeta_{108}^{34} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} - \zeta_{108}^{16} - \zeta_{108}^{14} - \zeta_{108}^{12} - \zeta_{108}^{10} - \zeta_{108}^{8} - \zeta_{108}^{6} - \zeta_{108}^{4} - \zeta_{108}^{2} - 1} & \htmlTitle{S_{12; 8}}{-2 \zeta_{108}^{34} - 2 \zeta_{108}^{32} - 2 \zeta_{108}^{30} - 2 \zeta_{108}^{28} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + 2 \zeta_{108}^{16} + 3 \zeta_{108}^{14} + 3 \zeta_{108}^{12} + 3 \zeta_{108}^{10} + 3 \zeta_{108}^{8} + 3 \zeta_{108}^{6} + 3 \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{12; 9}}{2 \zeta_{108}^{34} + 2 \zeta_{108}^{32} + 2 \zeta_{108}^{30} + 2 \zeta_{108}^{28} + \zeta_{108}^{26} + \zeta_{108}^{24} + \zeta_{108}^{22} - 2 \zeta_{108}^{16} - 3 \zeta_{108}^{14} - 3 \zeta_{108}^{12} - 3 \zeta_{108}^{10} - 3 \zeta_{108}^{8} - 3 \zeta_{108}^{6} - 3 \zeta_{108}^{4} - 2 \zeta_{108}^{2} - 2} & \htmlTitle{S_{12; 10}}{-\zeta_{108}^{34} - \zeta_{108}^{26} - \zeta_{108}^{24} - \zeta_{108}^{22} + \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + \zeta_{108}^{2} + 1} & \htmlTitle{S_{12; 11}}{-2 \zeta_{108}^{34} - \zeta_{108}^{32} - \zeta_{108}^{30} - \zeta_{108}^{28} + 2 \zeta_{108}^{16} + \zeta_{108}^{14} + \zeta_{108}^{12} + \zeta_{108}^{10} + \zeta_{108}^{8} + \zeta_{108}^{6} + \zeta_{108}^{4} + 2 \zeta_{108}^{2} + 2} & \htmlTitle{S_{12; 12}}{0}\end{array}\right) \]

Central Charge

\[c = \frac{70}{9} \]