Fusion Ring
\[ \begin{array}{lllllllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{3} & & & & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{1} & \htmlTitle{3\otimes 3}{2} & & & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{8} & \htmlTitle{4\otimes 3}{7} & \htmlTitle{4\otimes 4}{5 \oplus 10} & & & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{6} & \htmlTitle{5\otimes 3}{9} & \htmlTitle{5\otimes 4}{1 \oplus 13} & \htmlTitle{5\otimes 5}{4 \oplus 11} & & & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{9} & \htmlTitle{6\otimes 3}{5} & \htmlTitle{6\otimes 4}{14 \oplus 2} & \htmlTitle{6\otimes 5}{10 \oplus 8} & \htmlTitle{6\otimes 6}{7 \oplus 12} & & & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{4} & \htmlTitle{7\otimes 3}{8} & \htmlTitle{7\otimes 4}{11 \oplus 9} & \htmlTitle{7\otimes 5}{15 \oplus 3} & \htmlTitle{7\otimes 6}{1 \oplus 13} & \htmlTitle{7\otimes 7}{6 \oplus 12} & & & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{7} & \htmlTitle{8\otimes 3}{4} & \htmlTitle{8\otimes 4}{6 \oplus 12} & \htmlTitle{8\otimes 5}{14 \oplus 2} & \htmlTitle{8\otimes 6}{15 \oplus 3} & \htmlTitle{8\otimes 7}{5 \oplus 10} & \htmlTitle{8\otimes 8}{11 \oplus 9} & & & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{5} & \htmlTitle{9\otimes 3}{6} & \htmlTitle{9\otimes 4}{15 \oplus 3} & \htmlTitle{9\otimes 5}{7 \oplus 12} & \htmlTitle{9\otimes 6}{4 \oplus 11} & \htmlTitle{9\otimes 7}{14 \oplus 2} & \htmlTitle{9\otimes 8}{1 \oplus 13} & \htmlTitle{9\otimes 9}{10 \oplus 8} & & & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{12} & \htmlTitle{10\otimes 3}{11} & \htmlTitle{10\otimes 4}{13 \oplus 6} & \htmlTitle{10\otimes 5}{4 \oplus 14} & \htmlTitle{10\otimes 6}{15 \oplus 8} & \htmlTitle{10\otimes 7}{5 \oplus 15} & \htmlTitle{10\otimes 8}{14 \oplus 9} & \htmlTitle{10\otimes 9}{7 \oplus 13} & \htmlTitle{10\otimes 10}{11 \oplus 14 \oplus 2} & & & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{10} & \htmlTitle{11\otimes 3}{12} & \htmlTitle{11\otimes 4}{5 \oplus 15} & \htmlTitle{11\otimes 5}{7 \oplus 13} & \htmlTitle{11\otimes 6}{4 \oplus 14} & \htmlTitle{11\otimes 7}{14 \oplus 9} & \htmlTitle{11\otimes 8}{13 \oplus 6} & \htmlTitle{11\otimes 9}{15 \oplus 8} & \htmlTitle{11\otimes 10}{1 \oplus 13 \oplus 12} & \htmlTitle{11\otimes 11}{10 \oplus 15 \oplus 3} & & & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{11} & \htmlTitle{12\otimes 3}{10} & \htmlTitle{12\otimes 4}{14 \oplus 9} & \htmlTitle{12\otimes 5}{15 \oplus 8} & \htmlTitle{12\otimes 6}{7 \oplus 13} & \htmlTitle{12\otimes 7}{13 \oplus 6} & \htmlTitle{12\otimes 8}{5 \oplus 15} & \htmlTitle{12\otimes 9}{4 \oplus 14} & \htmlTitle{12\otimes 10}{10 \oplus 15 \oplus 3} & \htmlTitle{12\otimes 11}{11 \oplus 14 \oplus 2} & \htmlTitle{12\otimes 12}{1 \oplus 13 \oplus 12} & & & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{14} & \htmlTitle{13\otimes 3}{15} & \htmlTitle{13\otimes 4}{4 \oplus 11 \oplus 14} & \htmlTitle{13\otimes 5}{5 \oplus 10 \oplus 15} & \htmlTitle{13\otimes 6}{13 \oplus 6 \oplus 12} & \htmlTitle{13\otimes 7}{7 \oplus 13 \oplus 12} & \htmlTitle{13\otimes 8}{10 \oplus 15 \oplus 8} & \htmlTitle{13\otimes 9}{11 \oplus 14 \oplus 9} & \htmlTitle{13\otimes 10}{5 \oplus 10 \oplus 15 \oplus 8} & \htmlTitle{13\otimes 11}{4 \oplus 11 \oplus 14 \oplus 9} & \htmlTitle{13\otimes 12}{7 \oplus 13 \oplus 6 \oplus 12} & \htmlTitle{13\otimes 13}{1 \oplus 7 \oplus 2\cdot13 \oplus 6 \oplus 12} & & \\ \htmlTitle{14\otimes 1}{14} & \htmlTitle{14\otimes 2}{15} & \htmlTitle{14\otimes 3}{13} & \htmlTitle{14\otimes 4}{10 \oplus 15 \oplus 8} & \htmlTitle{14\otimes 5}{13 \oplus 6 \oplus 12} & \htmlTitle{14\otimes 6}{11 \oplus 14 \oplus 9} & \htmlTitle{14\otimes 7}{4 \oplus 11 \oplus 14} & \htmlTitle{14\otimes 8}{7 \oplus 13 \oplus 12} & \htmlTitle{14\otimes 9}{5 \oplus 10 \oplus 15} & \htmlTitle{14\otimes 10}{7 \oplus 13 \oplus 6 \oplus 12} & \htmlTitle{14\otimes 11}{5 \oplus 10 \oplus 15 \oplus 8} & \htmlTitle{14\otimes 12}{4 \oplus 11 \oplus 14 \oplus 9} & \htmlTitle{14\otimes 13}{4 \oplus 11 \oplus 2\cdot14 \oplus 9 \oplus 2} & \htmlTitle{14\otimes 14}{5 \oplus 10 \oplus 2\cdot15 \oplus 3 \oplus 8} & \\ \htmlTitle{15\otimes 1}{15} & \htmlTitle{15\otimes 2}{13} & \htmlTitle{15\otimes 3}{14} & \htmlTitle{15\otimes 4}{7 \oplus 13 \oplus 12} & \htmlTitle{15\otimes 5}{11 \oplus 14 \oplus 9} & \htmlTitle{15\otimes 6}{5 \oplus 10 \oplus 15} & \htmlTitle{15\otimes 7}{10 \oplus 15 \oplus 8} & \htmlTitle{15\otimes 8}{4 \oplus 11 \oplus 14} & \htmlTitle{15\otimes 9}{13 \oplus 6 \oplus 12} & \htmlTitle{15\otimes 10}{4 \oplus 11 \oplus 14 \oplus 9} & \htmlTitle{15\otimes 11}{7 \oplus 13 \oplus 6 \oplus 12} & \htmlTitle{15\otimes 12}{5 \oplus 10 \oplus 15 \oplus 8} & \htmlTitle{15\otimes 13}{5 \oplus 10 \oplus 2\cdot15 \oplus 3 \oplus 8} & \htmlTitle{15\otimes 14}{1 \oplus 7 \oplus 2\cdot13 \oplus 6 \oplus 12} & \htmlTitle{15\otimes 15}{4 \oplus 11 \oplus 2\cdot14 \oplus 9 \oplus 2} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.000\) | \( 1 \) |
| \( 4\) | \(2.247\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( 5\) | \(2.247\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( 6\) | \(2.247\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( 7\) | \(2.247\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( 8\) | \(2.247\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( 9\) | \(2.247\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( 10\) | \(2.802\) | \( \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{4 \pi}{21} \right)} + \cos{\left(\frac{\pi}{7} \right)} + 1 \) |
| \( 11\) | \(2.802\) | \( \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{4 \pi}{21} \right)} + \cos{\left(\frac{\pi}{7} \right)} + 1 \) |
| \( 12\) | \(2.802\) | \( \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{4 \pi}{21} \right)} + \cos{\left(\frac{\pi}{7} \right)} + 1 \) |
| \( 13\) | \(4.049\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{4 \pi}{21} \right)} + \cos{\left(\frac{\pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( 14\) | \(4.049\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{4 \pi}{21} \right)} + \cos{\left(\frac{\pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( 15\) | \(4.049\) | \( - \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{4 \pi}{21} \right)} + \cos{\left(\frac{\pi}{7} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 1 \) |
| \( D^2\) | 106.027 | \(- 21 \cos{\left(\frac{8 \pi}{21} \right)} + 21 \cos{\left(\frac{10 \pi}{21} \right)} + 21 \cos{\left(\frac{2 \pi}{7} \right)} + 21 \cos{\left(\frac{4 \pi}{21} \right)} + 21 \cos{\left(\frac{\pi}{7} \right)} + 21 \cos{\left(\frac{\pi}{21} \right)} + 42\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{2}{3}} & \htmlTitle{\theta_{3}}{\frac{2}{3}} & \htmlTitle{\theta_{4}}{\frac{8}{21}} & \htmlTitle{\theta_{5}}{\frac{8}{21}} & \htmlTitle{\theta_{6}}{\frac{12}{7}} & \htmlTitle{\theta_{7}}{\frac{12}{7}} & \htmlTitle{\theta_{8}}{\frac{8}{21}} & \htmlTitle{\theta_{9}}{\frac{8}{21}} & \htmlTitle{\theta_{10}}{\frac{20}{21}} & \htmlTitle{\theta_{11}}{\frac{20}{21}} & \htmlTitle{\theta_{12}}{\frac{2}{7}} & \htmlTitle{\theta_{13}}{\frac{6}{7}} & \htmlTitle{\theta_{14}}{\frac{32}{21}} & \htmlTitle{\theta_{15}}{\frac{32}{21}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{\zeta_{84}^{14} - 1} & & & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{1} & \htmlTitle{S_{3; 2}}{-\zeta_{84}^{14}} & \htmlTitle{S_{3; 3}}{\zeta_{84}^{14} - 1} & & & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{4; 2}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{4; 3}}{-\zeta_{84}^{22} - \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{4; 4}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + 2 \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{10} + 2 \zeta_{84}^{6} + 2 \zeta_{84}^{4} - 1} & & & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{84}^{22} - \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{5; 3}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{5; 4}}{-\zeta_{84}^{20} - \zeta_{84}^{18} + \zeta_{84}^{14} + \zeta_{84}^{4} + 2 \zeta_{84}^{2}} & \htmlTitle{S_{5; 5}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + 2 \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{10} + 2 \zeta_{84}^{6} + 2 \zeta_{84}^{4} - 1} & & & & & & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{6; 2}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{6; 3}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{6; 4}}{\zeta_{84}^{18} + 2 \zeta_{84}^{16} + \zeta_{84}^{6} - 2 \zeta_{84}^{2} - 1} & \htmlTitle{S_{6; 5}}{-\zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{6} + \zeta_{84}^{2}} & \htmlTitle{S_{6; 6}}{-\zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{6} + \zeta_{84}^{2}} & & & & & & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{7; 2}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{7; 3}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{7; 4}}{-\zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{6} + \zeta_{84}^{2}} & \htmlTitle{S_{7; 5}}{\zeta_{84}^{18} + 2 \zeta_{84}^{16} + \zeta_{84}^{6} - 2 \zeta_{84}^{2} - 1} & \htmlTitle{S_{7; 6}}{\zeta_{84}^{18} + 2 \zeta_{84}^{16} + \zeta_{84}^{6} - 2 \zeta_{84}^{2} - 1} & \htmlTitle{S_{7; 7}}{-\zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{6} + \zeta_{84}^{2}} & & & & & & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{8; 2}}{-\zeta_{84}^{22} - \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{8; 3}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{8; 4}}{\zeta_{84}^{22} + 2 \zeta_{84}^{20} + \zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{14} + \zeta_{84}^{12} + \zeta_{84}^{10} - \zeta_{84}^{6} - 2 \zeta_{84}^{4} - \zeta_{84}^{2} + 1} & \htmlTitle{S_{8; 5}}{\zeta_{84}^{20} - 2 \zeta_{84}^{16} - \zeta_{84}^{14} - \zeta_{84}^{6} - \zeta_{84}^{4} + 1} & \htmlTitle{S_{8; 6}}{\zeta_{84}^{18} + 2 \zeta_{84}^{16} + \zeta_{84}^{6} - 2 \zeta_{84}^{2} - 1} & \htmlTitle{S_{8; 7}}{-\zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{6} + \zeta_{84}^{2}} & \htmlTitle{S_{8; 8}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + 2 \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{10} + 2 \zeta_{84}^{6} + 2 \zeta_{84}^{4} - 1} & & & & & & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{9; 2}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{9; 3}}{-\zeta_{84}^{22} - \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{9; 4}}{\zeta_{84}^{20} - 2 \zeta_{84}^{16} - \zeta_{84}^{14} - \zeta_{84}^{6} - \zeta_{84}^{4} + 1} & \htmlTitle{S_{9; 5}}{\zeta_{84}^{22} + 2 \zeta_{84}^{20} + \zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{14} + \zeta_{84}^{12} + \zeta_{84}^{10} - \zeta_{84}^{6} - 2 \zeta_{84}^{4} - \zeta_{84}^{2} + 1} & \htmlTitle{S_{9; 6}}{-\zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{6} + \zeta_{84}^{2}} & \htmlTitle{S_{9; 7}}{\zeta_{84}^{18} + 2 \zeta_{84}^{16} + \zeta_{84}^{6} - 2 \zeta_{84}^{2} - 1} & \htmlTitle{S_{9; 8}}{-\zeta_{84}^{20} - \zeta_{84}^{18} + \zeta_{84}^{14} + \zeta_{84}^{4} + 2 \zeta_{84}^{2}} & \htmlTitle{S_{9; 9}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + 2 \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{10} + 2 \zeta_{84}^{6} + 2 \zeta_{84}^{4} - 1} & & & & & & \\ \htmlTitle{S_{10; 1}}{-\zeta_{84}^{22} + \zeta_{84}^{8} + \zeta_{84}^{6} + 1} & \htmlTitle{S_{10; 2}}{-\zeta_{84}^{20} - \zeta_{84}^{14} - \zeta_{84}^{8}} & \htmlTitle{S_{10; 3}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{14} - \zeta_{84}^{6} - 1} & \htmlTitle{S_{10; 4}}{\zeta_{84}^{22} + \zeta_{84}^{20} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{10; 5}}{-\zeta_{84}^{22} - \zeta_{84}^{20} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4}} & \htmlTitle{S_{10; 6}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{10; 7}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{10; 8}}{-\zeta_{84}^{22} - \zeta_{84}^{20} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4}} & \htmlTitle{S_{10; 9}}{\zeta_{84}^{22} + \zeta_{84}^{20} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{10; 10}}{2 \zeta_{84}^{22} + 2 \zeta_{84}^{20} + \zeta_{84}^{10} - 2 \zeta_{84}^{6} - \zeta_{84}^{4}} & & & & & \\ \htmlTitle{S_{11; 1}}{-\zeta_{84}^{22} + \zeta_{84}^{8} + \zeta_{84}^{6} + 1} & \htmlTitle{S_{11; 2}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{14} - \zeta_{84}^{6} - 1} & \htmlTitle{S_{11; 3}}{-\zeta_{84}^{20} - \zeta_{84}^{14} - \zeta_{84}^{8}} & \htmlTitle{S_{11; 4}}{-\zeta_{84}^{22} - \zeta_{84}^{20} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4}} & \htmlTitle{S_{11; 5}}{\zeta_{84}^{22} + \zeta_{84}^{20} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{11; 6}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{11; 7}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{11; 8}}{\zeta_{84}^{22} + \zeta_{84}^{20} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{11; 9}}{-\zeta_{84}^{22} - \zeta_{84}^{20} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4}} & \htmlTitle{S_{11; 10}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} - \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{11; 11}}{2 \zeta_{84}^{22} + 2 \zeta_{84}^{20} + \zeta_{84}^{10} - 2 \zeta_{84}^{6} - \zeta_{84}^{4}} & & & & \\ \htmlTitle{S_{12; 1}}{-\zeta_{84}^{22} + \zeta_{84}^{8} + \zeta_{84}^{6} + 1} & \htmlTitle{S_{12; 2}}{-\zeta_{84}^{22} + \zeta_{84}^{8} + \zeta_{84}^{6} + 1} & \htmlTitle{S_{12; 3}}{-\zeta_{84}^{22} + \zeta_{84}^{8} + \zeta_{84}^{6} + 1} & \htmlTitle{S_{12; 4}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{12; 5}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{12; 6}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{12; 7}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{12; 8}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{12; 9}}{\zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{12; 10}}{-\zeta_{84}^{22} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{12; 11}}{-\zeta_{84}^{22} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{12; 12}}{-\zeta_{84}^{22} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{2} + 1} & & & \\ \htmlTitle{S_{13; 1}}{-\zeta_{84}^{22} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 2}}{-\zeta_{84}^{22} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 3}}{-\zeta_{84}^{22} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 4}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 5}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 6}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 7}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 8}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 9}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{13; 10}}{-1} & \htmlTitle{S_{13; 11}}{-1} & \htmlTitle{S_{13; 12}}{-1} & \htmlTitle{S_{13; 13}}{\zeta_{84}^{22} - \zeta_{84}^{8} - \zeta_{84}^{6} - 1} & & \\ \htmlTitle{S_{14; 1}}{-\zeta_{84}^{22} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{14; 2}}{2 \zeta_{84}^{22} + 2 \zeta_{84}^{20} + \zeta_{84}^{10} - 2 \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{14; 3}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} - \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{14; 4}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{14; 5}}{-\zeta_{84}^{22} - \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{14; 6}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{14; 7}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{14; 8}}{-\zeta_{84}^{22} - \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{14; 9}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{14; 10}}{\zeta_{84}^{14}} & \htmlTitle{S_{14; 11}}{-\zeta_{84}^{14} + 1} & \htmlTitle{S_{14; 12}}{-1} & \htmlTitle{S_{14; 13}}{\zeta_{84}^{22} - \zeta_{84}^{8} - \zeta_{84}^{6} - 1} & \htmlTitle{S_{14; 14}}{-\zeta_{84}^{22} - \zeta_{84}^{20} - \zeta_{84}^{14} + \zeta_{84}^{6} + 1} & \\ \htmlTitle{S_{15; 1}}{-\zeta_{84}^{22} - \zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{15; 2}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} - \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{15; 3}}{2 \zeta_{84}^{22} + 2 \zeta_{84}^{20} + \zeta_{84}^{10} - 2 \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{15; 4}}{-\zeta_{84}^{22} - \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{15; 5}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{15; 6}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{15; 7}}{-\zeta_{84}^{16} + \zeta_{84}^{12} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{15; 8}}{\zeta_{84}^{22} + \zeta_{84}^{20} + \zeta_{84}^{10} - \zeta_{84}^{6} - \zeta_{84}^{4}} & \htmlTitle{S_{15; 9}}{-\zeta_{84}^{22} - \zeta_{84}^{20} + \zeta_{84}^{16} - \zeta_{84}^{12} - \zeta_{84}^{10} + \zeta_{84}^{6} + \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{15; 10}}{-\zeta_{84}^{14} + 1} & \htmlTitle{S_{15; 11}}{\zeta_{84}^{14}} & \htmlTitle{S_{15; 12}}{-1} & \htmlTitle{S_{15; 13}}{\zeta_{84}^{22} - \zeta_{84}^{8} - \zeta_{84}^{6} - 1} & \htmlTitle{S_{15; 14}}{\zeta_{84}^{20} + \zeta_{84}^{14} + \zeta_{84}^{8}} & \htmlTitle{S_{15; 15}}{-\zeta_{84}^{22} - \zeta_{84}^{20} - \zeta_{84}^{14} + \zeta_{84}^{6} + 1}\end{array}\right) \]
Central Charge
\[c = \frac{32}{7} \]