Fusion Ring
\[ \begin{array}{llllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{7} & \htmlTitle{3\otimes 3}{1 \oplus 4 \oplus 11 \oplus 3} & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{5} & \htmlTitle{4\otimes 3}{10 \oplus 11 \oplus 3} & \htmlTitle{4\otimes 4}{1 \oplus 4 \oplus 11 \oplus 8} & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{4} & \htmlTitle{5\otimes 3}{9 \oplus 7 \oplus 12} & \htmlTitle{5\otimes 4}{5 \oplus 12 \oplus 6 \oplus 2} & \htmlTitle{5\otimes 5}{1 \oplus 4 \oplus 11 \oplus 8} & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{8} & \htmlTitle{6\otimes 3}{9 \oplus 12 \oplus 6} & \htmlTitle{6\otimes 4}{9 \oplus 5 \oplus 12} & \htmlTitle{6\otimes 5}{4 \oplus 10 \oplus 11} & \htmlTitle{6\otimes 6}{1 \oplus 11 \oplus 8 \oplus 3} & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{3} & \htmlTitle{7\otimes 3}{5 \oplus 7 \oplus 12 \oplus 2} & \htmlTitle{7\otimes 4}{9 \oplus 7 \oplus 12} & \htmlTitle{7\otimes 5}{10 \oplus 11 \oplus 3} & \htmlTitle{7\otimes 6}{10 \oplus 11 \oplus 8} & \htmlTitle{7\otimes 7}{1 \oplus 4 \oplus 11 \oplus 3} & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{6} & \htmlTitle{8\otimes 3}{10 \oplus 11 \oplus 8} & \htmlTitle{8\otimes 4}{4 \oplus 10 \oplus 11} & \htmlTitle{8\otimes 5}{9 \oplus 5 \oplus 12} & \htmlTitle{8\otimes 6}{7 \oplus 12 \oplus 6 \oplus 2} & \htmlTitle{8\otimes 7}{9 \oplus 12 \oplus 6} & \htmlTitle{8\otimes 8}{1 \oplus 11 \oplus 8 \oplus 3} & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{10} & \htmlTitle{9\otimes 3}{9 \oplus 5 \oplus 12 \oplus 6} & \htmlTitle{9\otimes 4}{9 \oplus 7 \oplus 12 \oplus 6} & \htmlTitle{9\otimes 5}{10 \oplus 11 \oplus 8 \oplus 3} & \htmlTitle{9\otimes 6}{4 \oplus 10 \oplus 11 \oplus 3} & \htmlTitle{9\otimes 7}{4 \oplus 10 \oplus 11 \oplus 8} & \htmlTitle{9\otimes 8}{9 \oplus 5 \oplus 7 \oplus 12} & \htmlTitle{9\otimes 9}{1 \oplus 4 \oplus 10 \oplus 11 \oplus 8 \oplus 3} & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{9} & \htmlTitle{10\otimes 3}{4 \oplus 10 \oplus 11 \oplus 8} & \htmlTitle{10\otimes 4}{10 \oplus 11 \oplus 8 \oplus 3} & \htmlTitle{10\otimes 5}{9 \oplus 7 \oplus 12 \oplus 6} & \htmlTitle{10\otimes 6}{9 \oplus 5 \oplus 7 \oplus 12} & \htmlTitle{10\otimes 7}{9 \oplus 5 \oplus 12 \oplus 6} & \htmlTitle{10\otimes 8}{4 \oplus 10 \oplus 11 \oplus 3} & \htmlTitle{10\otimes 9}{9 \oplus 5 \oplus 7 \oplus 12 \oplus 6 \oplus 2} & \htmlTitle{10\otimes 10}{1 \oplus 4 \oplus 10 \oplus 11 \oplus 8 \oplus 3} & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{12} & \htmlTitle{11\otimes 3}{4 \oplus 10 \oplus 11 \oplus 8 \oplus 3} & \htmlTitle{11\otimes 4}{4 \oplus 10 \oplus 11 \oplus 8 \oplus 3} & \htmlTitle{11\otimes 5}{9 \oplus 5 \oplus 7 \oplus 12 \oplus 6} & \htmlTitle{11\otimes 6}{9 \oplus 5 \oplus 7 \oplus 12 \oplus 6} & \htmlTitle{11\otimes 7}{9 \oplus 5 \oplus 7 \oplus 12 \oplus 6} & \htmlTitle{11\otimes 8}{4 \oplus 10 \oplus 11 \oplus 8 \oplus 3} & \htmlTitle{11\otimes 9}{9 \oplus 5 \oplus 7 \oplus 2\cdot12 \oplus 6} & \htmlTitle{11\otimes 10}{4 \oplus 10 \oplus 2\cdot11 \oplus 8 \oplus 3} & \htmlTitle{11\otimes 11}{1 \oplus 4 \oplus 2\cdot10 \oplus 2\cdot11 \oplus 8 \oplus 3} & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{11} & \htmlTitle{12\otimes 3}{9 \oplus 5 \oplus 7 \oplus 12 \oplus 6} & \htmlTitle{12\otimes 4}{9 \oplus 5 \oplus 7 \oplus 12 \oplus 6} & \htmlTitle{12\otimes 5}{4 \oplus 10 \oplus 11 \oplus 8 \oplus 3} & \htmlTitle{12\otimes 6}{4 \oplus 10 \oplus 11 \oplus 8 \oplus 3} & \htmlTitle{12\otimes 7}{4 \oplus 10 \oplus 11 \oplus 8 \oplus 3} & \htmlTitle{12\otimes 8}{9 \oplus 5 \oplus 7 \oplus 12 \oplus 6} & \htmlTitle{12\otimes 9}{4 \oplus 10 \oplus 2\cdot11 \oplus 8 \oplus 3} & \htmlTitle{12\otimes 10}{9 \oplus 5 \oplus 7 \oplus 2\cdot12 \oplus 6} & \htmlTitle{12\otimes 11}{2\cdot9 \oplus 5 \oplus 7 \oplus 2\cdot12 \oplus 6 \oplus 2} & \htmlTitle{12\otimes 12}{1 \oplus 4 \oplus 2\cdot10 \oplus 2\cdot11 \oplus 8 \oplus 3} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 4\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 5\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 6\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 7\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 8\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 9\) | \(4.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 2 \cos{\left(\frac{2 \pi}{21} \right)} + \frac{5}{2} \) |
| \( 10\) | \(4.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 2 \cos{\left(\frac{2 \pi}{21} \right)} + \frac{5}{2} \) |
| \( 11\) | \(5.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 2 \cos{\left(\frac{2 \pi}{21} \right)} + \frac{7}{2} \) |
| \( 12\) | \(5.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 2 \cos{\left(\frac{2 \pi}{21} \right)} + \frac{7}{2} \) |
| \( D^2\) | 201.234 | \(- 42 \cos{\left(\frac{4 \pi}{21} \right)} - 42 \cos{\left(\frac{3 \pi}{7} \right)} + 42 \cos{\left(\frac{10 \pi}{21} \right)} + 42 \cos{\left(\frac{8 \pi}{21} \right)} + 42 \cos{\left(\frac{\pi}{21} \right)} + 84 \cos{\left(\frac{2 \pi}{21} \right)} + 105\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{1}{2}} & \htmlTitle{\theta_{3}}{\frac{12}{7}} & \htmlTitle{\theta_{4}}{\frac{10}{7}} & \htmlTitle{\theta_{5}}{\frac{27}{14}} & \htmlTitle{\theta_{6}}{\frac{19}{14}} & \htmlTitle{\theta_{7}}{\frac{3}{14}} & \htmlTitle{\theta_{8}}{\frac{6}{7}} & \htmlTitle{\theta_{9}}{\frac{1}{2}} & \htmlTitle{\theta_{10}}{0} & \htmlTitle{\theta_{11}}{\frac{2}{3}} & \htmlTitle{\theta_{12}}{\frac{7}{6}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{-1} & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{3; 2}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{3; 3}}{-\zeta_{168}^{44} - 2 \zeta_{168}^{40} + \zeta_{168}^{36} + 2 \zeta_{168}^{32} + 2 \zeta_{168}^{28} - 3 \zeta_{168}^{20} - \zeta_{168}^{16} + \zeta_{168}^{12} + \zeta_{168}^{8} + 2 \zeta_{168}^{4} - 1} & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{4; 2}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{4; 3}}{3 \zeta_{168}^{40} - \zeta_{168}^{28} - \zeta_{168}^{24} + \zeta_{168}^{20} - \zeta_{168}^{16} - 2 \zeta_{168}^{12} - \zeta_{168}^{8} - 2 \zeta_{168}^{4} + 1} & \htmlTitle{S_{4; 4}}{-\zeta_{168}^{40} - 2 \zeta_{168}^{36} - \zeta_{168}^{32} + \zeta_{168}^{24} + 2 \zeta_{168}^{20} + \zeta_{168}^{16} + \zeta_{168}^{12} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{5; 2}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{5; 3}}{3 \zeta_{168}^{40} - \zeta_{168}^{28} - \zeta_{168}^{24} + \zeta_{168}^{20} - \zeta_{168}^{16} - 2 \zeta_{168}^{12} - \zeta_{168}^{8} - 2 \zeta_{168}^{4} + 1} & \htmlTitle{S_{5; 4}}{-\zeta_{168}^{40} - 2 \zeta_{168}^{36} - \zeta_{168}^{32} + \zeta_{168}^{24} + 2 \zeta_{168}^{20} + \zeta_{168}^{16} + \zeta_{168}^{12} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{5; 5}}{\zeta_{168}^{40} + 2 \zeta_{168}^{36} + \zeta_{168}^{32} - \zeta_{168}^{24} - 2 \zeta_{168}^{20} - \zeta_{168}^{16} - \zeta_{168}^{12} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & & & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{6; 2}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{6; 3}}{-\zeta_{168}^{40} - 2 \zeta_{168}^{36} - \zeta_{168}^{32} + \zeta_{168}^{24} + 2 \zeta_{168}^{20} + \zeta_{168}^{16} + \zeta_{168}^{12} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{6; 4}}{-\zeta_{168}^{44} - 2 \zeta_{168}^{40} + \zeta_{168}^{36} + 2 \zeta_{168}^{32} + 2 \zeta_{168}^{28} - 3 \zeta_{168}^{20} - \zeta_{168}^{16} + \zeta_{168}^{12} + \zeta_{168}^{8} + 2 \zeta_{168}^{4} - 1} & \htmlTitle{S_{6; 5}}{\zeta_{168}^{44} + 2 \zeta_{168}^{40} - \zeta_{168}^{36} - 2 \zeta_{168}^{32} - 2 \zeta_{168}^{28} + 3 \zeta_{168}^{20} + \zeta_{168}^{16} - \zeta_{168}^{12} - \zeta_{168}^{8} - 2 \zeta_{168}^{4} + 1} & \htmlTitle{S_{6; 6}}{-3 \zeta_{168}^{40} + \zeta_{168}^{28} + \zeta_{168}^{24} - \zeta_{168}^{20} + \zeta_{168}^{16} + 2 \zeta_{168}^{12} + \zeta_{168}^{8} + 2 \zeta_{168}^{4} - 1} & & & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{7; 2}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{7; 3}}{-\zeta_{168}^{44} - 2 \zeta_{168}^{40} + \zeta_{168}^{36} + 2 \zeta_{168}^{32} + 2 \zeta_{168}^{28} - 3 \zeta_{168}^{20} - \zeta_{168}^{16} + \zeta_{168}^{12} + \zeta_{168}^{8} + 2 \zeta_{168}^{4} - 1} & \htmlTitle{S_{7; 4}}{3 \zeta_{168}^{40} - \zeta_{168}^{28} - \zeta_{168}^{24} + \zeta_{168}^{20} - \zeta_{168}^{16} - 2 \zeta_{168}^{12} - \zeta_{168}^{8} - 2 \zeta_{168}^{4} + 1} & \htmlTitle{S_{7; 5}}{-3 \zeta_{168}^{40} + \zeta_{168}^{28} + \zeta_{168}^{24} - \zeta_{168}^{20} + \zeta_{168}^{16} + 2 \zeta_{168}^{12} + \zeta_{168}^{8} + 2 \zeta_{168}^{4} - 1} & \htmlTitle{S_{7; 6}}{\zeta_{168}^{40} + 2 \zeta_{168}^{36} + \zeta_{168}^{32} - \zeta_{168}^{24} - 2 \zeta_{168}^{20} - \zeta_{168}^{16} - \zeta_{168}^{12} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{7; 7}}{\zeta_{168}^{44} + 2 \zeta_{168}^{40} - \zeta_{168}^{36} - 2 \zeta_{168}^{32} - 2 \zeta_{168}^{28} + 3 \zeta_{168}^{20} + \zeta_{168}^{16} - \zeta_{168}^{12} - \zeta_{168}^{8} - 2 \zeta_{168}^{4} + 1} & & & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{8; 2}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{8; 3}}{-\zeta_{168}^{40} - 2 \zeta_{168}^{36} - \zeta_{168}^{32} + \zeta_{168}^{24} + 2 \zeta_{168}^{20} + \zeta_{168}^{16} + \zeta_{168}^{12} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{8; 4}}{-\zeta_{168}^{44} - 2 \zeta_{168}^{40} + \zeta_{168}^{36} + 2 \zeta_{168}^{32} + 2 \zeta_{168}^{28} - 3 \zeta_{168}^{20} - \zeta_{168}^{16} + \zeta_{168}^{12} + \zeta_{168}^{8} + 2 \zeta_{168}^{4} - 1} & \htmlTitle{S_{8; 5}}{-\zeta_{168}^{44} - 2 \zeta_{168}^{40} + \zeta_{168}^{36} + 2 \zeta_{168}^{32} + 2 \zeta_{168}^{28} - 3 \zeta_{168}^{20} - \zeta_{168}^{16} + \zeta_{168}^{12} + \zeta_{168}^{8} + 2 \zeta_{168}^{4} - 1} & \htmlTitle{S_{8; 6}}{3 \zeta_{168}^{40} - \zeta_{168}^{28} - \zeta_{168}^{24} + \zeta_{168}^{20} - \zeta_{168}^{16} - 2 \zeta_{168}^{12} - \zeta_{168}^{8} - 2 \zeta_{168}^{4} + 1} & \htmlTitle{S_{8; 7}}{-\zeta_{168}^{40} - 2 \zeta_{168}^{36} - \zeta_{168}^{32} + \zeta_{168}^{24} + 2 \zeta_{168}^{20} + \zeta_{168}^{16} + \zeta_{168}^{12} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{8; 8}}{3 \zeta_{168}^{40} - \zeta_{168}^{28} - \zeta_{168}^{24} + \zeta_{168}^{20} - \zeta_{168}^{16} - 2 \zeta_{168}^{12} - \zeta_{168}^{8} - 2 \zeta_{168}^{4} + 1} & & & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 2} & \htmlTitle{S_{9; 2}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 2} & \htmlTitle{S_{9; 3}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{9; 4}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{9; 5}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{9; 6}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{9; 7}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 1} & \htmlTitle{S_{9; 8}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{9; 9}}{-1} & & & \\ \htmlTitle{S_{10; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 2} & \htmlTitle{S_{10; 2}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 2} & \htmlTitle{S_{10; 3}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{10; 4}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{10; 5}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{10; 6}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{10; 7}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{10; 8}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 1} & \htmlTitle{S_{10; 9}}{1} & \htmlTitle{S_{10; 10}}{1} & & \\ \htmlTitle{S_{11; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 3} & \htmlTitle{S_{11; 2}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 3} & \htmlTitle{S_{11; 3}}{0} & \htmlTitle{S_{11; 4}}{0} & \htmlTitle{S_{11; 5}}{0} & \htmlTitle{S_{11; 6}}{0} & \htmlTitle{S_{11; 7}}{0} & \htmlTitle{S_{11; 8}}{0} & \htmlTitle{S_{11; 9}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 3} & \htmlTitle{S_{11; 10}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 3} & \htmlTitle{S_{11; 11}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 3} & \\ \htmlTitle{S_{12; 1}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 3} & \htmlTitle{S_{12; 2}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 3} & \htmlTitle{S_{12; 3}}{0} & \htmlTitle{S_{12; 4}}{0} & \htmlTitle{S_{12; 5}}{0} & \htmlTitle{S_{12; 6}}{0} & \htmlTitle{S_{12; 7}}{0} & \htmlTitle{S_{12; 8}}{0} & \htmlTitle{S_{12; 9}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 3} & \htmlTitle{S_{12; 10}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 3} & \htmlTitle{S_{12; 11}}{\zeta_{168}^{44} + \zeta_{168}^{36} - \zeta_{168}^{32} - \zeta_{168}^{28} + \zeta_{168}^{16} - 2 \zeta_{168}^{8} - \zeta_{168}^{4} - 3} & \htmlTitle{S_{12; 12}}{-\zeta_{168}^{44} - \zeta_{168}^{36} + \zeta_{168}^{32} + \zeta_{168}^{28} - \zeta_{168}^{16} + 2 \zeta_{168}^{8} + \zeta_{168}^{4} + 3}\end{array}\right) \]
Central Charge
\[c = 19 \]