Fusion Ring
\[ \begin{array}{lllllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{3} & \htmlTitle{3\otimes 3}{1 \oplus 4 \oplus 5 \oplus 2} & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{5} & \htmlTitle{4\otimes 3}{12 \oplus 3} & \htmlTitle{4\otimes 4}{1 \oplus 8 \oplus 5} & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{4} & \htmlTitle{5\otimes 3}{12 \oplus 3} & \htmlTitle{5\otimes 4}{4 \oplus 9 \oplus 2} & \htmlTitle{5\otimes 5}{1 \oplus 8 \oplus 5} & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{7} & \htmlTitle{6\otimes 3}{10 \oplus 11} & \htmlTitle{6\otimes 4}{6 \oplus 13} & \htmlTitle{6\otimes 5}{13 \oplus 7} & \htmlTitle{6\otimes 6}{1 \oplus 4 \oplus 8 \oplus 10} & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{6} & \htmlTitle{7\otimes 3}{10 \oplus 11} & \htmlTitle{7\otimes 4}{13 \oplus 7} & \htmlTitle{7\otimes 5}{6 \oplus 13} & \htmlTitle{7\otimes 6}{5 \oplus 9 \oplus 11 \oplus 2} & \htmlTitle{7\otimes 7}{1 \oplus 4 \oplus 8 \oplus 10} & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{9} & \htmlTitle{8\otimes 3}{13 \oplus 12} & \htmlTitle{8\otimes 4}{4 \oplus 10 \oplus 9} & \htmlTitle{8\otimes 5}{8 \oplus 5 \oplus 11} & \htmlTitle{8\otimes 6}{6 \oplus 13 \oplus 12} & \htmlTitle{8\otimes 7}{13 \oplus 12 \oplus 7} & \htmlTitle{8\otimes 8}{1 \oplus 8 \oplus 10 \oplus 5 \oplus 11} & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{8} & \htmlTitle{9\otimes 3}{13 \oplus 12} & \htmlTitle{9\otimes 4}{8 \oplus 5 \oplus 11} & \htmlTitle{9\otimes 5}{4 \oplus 10 \oplus 9} & \htmlTitle{9\otimes 6}{13 \oplus 12 \oplus 7} & \htmlTitle{9\otimes 7}{6 \oplus 13 \oplus 12} & \htmlTitle{9\otimes 8}{4 \oplus 10 \oplus 9 \oplus 11 \oplus 2} & \htmlTitle{9\otimes 9}{1 \oplus 8 \oplus 10 \oplus 5 \oplus 11} & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{11} & \htmlTitle{10\otimes 3}{6 \oplus 13 \oplus 7} & \htmlTitle{10\otimes 4}{8 \oplus 10 \oplus 11} & \htmlTitle{10\otimes 5}{10 \oplus 9 \oplus 11} & \htmlTitle{10\otimes 6}{6 \oplus 13 \oplus 12 \oplus 3} & \htmlTitle{10\otimes 7}{13 \oplus 12 \oplus 3 \oplus 7} & \htmlTitle{10\otimes 8}{4 \oplus 8 \oplus 10 \oplus 9 \oplus 11} & \htmlTitle{10\otimes 9}{8 \oplus 10 \oplus 5 \oplus 9 \oplus 11} & \htmlTitle{10\otimes 10}{1 \oplus 4 \oplus 8 \oplus 10 \oplus 5 \oplus 9 \oplus 11} & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{10} & \htmlTitle{11\otimes 3}{6 \oplus 13 \oplus 7} & \htmlTitle{11\otimes 4}{10 \oplus 9 \oplus 11} & \htmlTitle{11\otimes 5}{8 \oplus 10 \oplus 11} & \htmlTitle{11\otimes 6}{13 \oplus 12 \oplus 3 \oplus 7} & \htmlTitle{11\otimes 7}{6 \oplus 13 \oplus 12 \oplus 3} & \htmlTitle{11\otimes 8}{8 \oplus 10 \oplus 5 \oplus 9 \oplus 11} & \htmlTitle{11\otimes 9}{4 \oplus 8 \oplus 10 \oplus 9 \oplus 11} & \htmlTitle{11\otimes 10}{4 \oplus 8 \oplus 10 \oplus 5 \oplus 9 \oplus 11 \oplus 2} & \htmlTitle{11\otimes 11}{1 \oplus 4 \oplus 8 \oplus 10 \oplus 5 \oplus 9 \oplus 11} & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{12} & \htmlTitle{12\otimes 3}{4 \oplus 8 \oplus 5 \oplus 9} & \htmlTitle{12\otimes 4}{13 \oplus 12 \oplus 3} & \htmlTitle{12\otimes 5}{13 \oplus 12 \oplus 3} & \htmlTitle{12\otimes 6}{8 \oplus 10 \oplus 9 \oplus 11} & \htmlTitle{12\otimes 7}{8 \oplus 10 \oplus 9 \oplus 11} & \htmlTitle{12\otimes 8}{6 \oplus 13 \oplus 12 \oplus 3 \oplus 7} & \htmlTitle{12\otimes 9}{6 \oplus 13 \oplus 12 \oplus 3 \oplus 7} & \htmlTitle{12\otimes 10}{6 \oplus 2\cdot13 \oplus 12 \oplus 7} & \htmlTitle{12\otimes 11}{6 \oplus 2\cdot13 \oplus 12 \oplus 7} & \htmlTitle{12\otimes 12}{1 \oplus 4 \oplus 8 \oplus 10 \oplus 5 \oplus 9 \oplus 11 \oplus 2} & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{13} & \htmlTitle{13\otimes 3}{8 \oplus 10 \oplus 9 \oplus 11} & \htmlTitle{13\otimes 4}{6 \oplus 13 \oplus 12 \oplus 7} & \htmlTitle{13\otimes 5}{6 \oplus 13 \oplus 12 \oplus 7} & \htmlTitle{13\otimes 6}{4 \oplus 8 \oplus 10 \oplus 5 \oplus 9 \oplus 11} & \htmlTitle{13\otimes 7}{4 \oplus 8 \oplus 10 \oplus 5 \oplus 9 \oplus 11} & \htmlTitle{13\otimes 8}{6 \oplus 2\cdot13 \oplus 12 \oplus 3 \oplus 7} & \htmlTitle{13\otimes 9}{6 \oplus 2\cdot13 \oplus 12 \oplus 3 \oplus 7} & \htmlTitle{13\otimes 10}{6 \oplus 2\cdot13 \oplus 2\cdot12 \oplus 3 \oplus 7} & \htmlTitle{13\otimes 11}{6 \oplus 2\cdot13 \oplus 2\cdot12 \oplus 3 \oplus 7} & \htmlTitle{13\otimes 12}{4 \oplus 8 \oplus 2\cdot10 \oplus 5 \oplus 9 \oplus 2\cdot11} & \htmlTitle{13\otimes 13}{1 \oplus 4 \oplus 2\cdot8 \oplus 2\cdot10 \oplus 5 \oplus 2\cdot9 \oplus 2\cdot11 \oplus 2} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(2.774\) | \( 2 \cos{\left(\frac{5 \pi}{16} \right)} + 2 \cos{\left(\frac{3 \pi}{16} \right)} \) |
| \( 4\) | \(2.848\) | \( 1 + \sqrt{\sqrt{2} + 2} \) |
| \( 5\) | \(2.848\) | \( 1 + \sqrt{\sqrt{2} + 2} \) |
| \( 6\) | \(3.625\) | \( 2 \cos{\left(\frac{3 \pi}{16} \right)} + 2 \cos{\left(\frac{\pi}{16} \right)} \) |
| \( 7\) | \(3.625\) | \( 2 \cos{\left(\frac{3 \pi}{16} \right)} + 2 \cos{\left(\frac{\pi}{16} \right)} \) |
| \( 8\) | \(4.262\) | \( 1 + \sqrt{2} + \sqrt{\sqrt{2} + 2} \) |
| \( 9\) | \(4.262\) | \( 1 + \sqrt{2} + \sqrt{\sqrt{2} + 2} \) |
| \( 10\) | \(5.027\) | \( \sqrt{2 - \sqrt{2}} + 1 + \sqrt{2} + \sqrt{\sqrt{2} + 2} \) |
| \( 11\) | \(5.027\) | \( \sqrt{2 - \sqrt{2}} + 1 + \sqrt{2} + \sqrt{\sqrt{2} + 2} \) |
| \( 12\) | \(5.126\) | \( 2 \cos{\left(\frac{7 \pi}{16} \right)} + 2 \cos{\left(\frac{5 \pi}{16} \right)} + 2 \cos{\left(\frac{3 \pi}{16} \right)} + 2 \cos{\left(\frac{\pi}{16} \right)} \) |
| \( 13\) | \(6.697\) | \( 2 \cos{\left(\frac{5 \pi}{16} \right)} + 2 \cos{\left(\frac{3 \pi}{16} \right)} + 4 \cos{\left(\frac{\pi}{16} \right)} \) |
| \( D^2\) | 210.193 | \(16 \sqrt{2 - \sqrt{2}} + 32 \sqrt{2} + 64 + 48 \sqrt{\sqrt{2} + 2}\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{1} & \htmlTitle{\theta_{3}}{\frac{17}{32}} & \htmlTitle{\theta_{4}}{\frac{3}{4}} & \htmlTitle{\theta_{5}}{\frac{7}{4}} & \htmlTitle{\theta_{6}}{\frac{21}{32}} & \htmlTitle{\theta_{7}}{\frac{21}{32}} & \htmlTitle{\theta_{8}}{\frac{5}{4}} & \htmlTitle{\theta_{9}}{\frac{1}{4}} & \htmlTitle{\theta_{10}}{\frac{3}{2}} & \htmlTitle{\theta_{11}}{\frac{1}{2}} & \htmlTitle{\theta_{12}}{\frac{5}{32}} & \htmlTitle{\theta_{13}}{\frac{49}{32}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{64}^{26} - \zeta_{64}^{22} + \zeta_{64}^{10} + \zeta_{64}^{6}} & \htmlTitle{S_{3; 2}}{\zeta_{64}^{26} + \zeta_{64}^{22} - \zeta_{64}^{10} - \zeta_{64}^{6}} & \htmlTitle{S_{3; 3}}{0} & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{64}^{28} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{4; 2}}{-\zeta_{64}^{28} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{4; 3}}{2 \zeta_{64}^{30} + \zeta_{64}^{26} + \zeta_{64}^{22} - \zeta_{64}^{10} - \zeta_{64}^{6} - 2 \zeta_{64}^{2}} & \htmlTitle{S_{4; 4}}{-\zeta_{64}^{28} - \zeta_{64}^{24} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{64}^{28} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{64}^{28} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{5; 3}}{-2 \zeta_{64}^{30} - \zeta_{64}^{26} - \zeta_{64}^{22} + \zeta_{64}^{10} + \zeta_{64}^{6} + 2 \zeta_{64}^{2}} & \htmlTitle{S_{5; 4}}{-\zeta_{64}^{28} - \zeta_{64}^{24} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{5; 5}}{-\zeta_{64}^{28} - \zeta_{64}^{24} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & & & & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{64}^{30} - \zeta_{64}^{26} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{6; 2}}{\zeta_{64}^{30} + \zeta_{64}^{26} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{6; 3}}{0} & \htmlTitle{S_{6; 4}}{-\zeta_{64}^{30} - \zeta_{64}^{26} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{6; 5}}{\zeta_{64}^{30} + \zeta_{64}^{26} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{6; 6}}{-2 \zeta_{64}^{30} - 2 \zeta_{64}^{26} + 2 \zeta_{64}^{6} + 2 \zeta_{64}^{2}} & & & & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{64}^{30} - \zeta_{64}^{26} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{7; 2}}{\zeta_{64}^{30} + \zeta_{64}^{26} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{7; 3}}{0} & \htmlTitle{S_{7; 4}}{-\zeta_{64}^{30} - \zeta_{64}^{26} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{7; 5}}{\zeta_{64}^{30} + \zeta_{64}^{26} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{7; 6}}{2 \zeta_{64}^{30} + 2 \zeta_{64}^{26} - 2 \zeta_{64}^{6} - 2 \zeta_{64}^{2}} & \htmlTitle{S_{7; 7}}{-2 \zeta_{64}^{30} - 2 \zeta_{64}^{26} + 2 \zeta_{64}^{6} + 2 \zeta_{64}^{2}} & & & & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{64}^{28} - \zeta_{64}^{24} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{8; 2}}{-\zeta_{64}^{28} - \zeta_{64}^{24} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{8; 3}}{-2 \zeta_{64}^{30} - \zeta_{64}^{26} - \zeta_{64}^{22} + \zeta_{64}^{10} + \zeta_{64}^{6} + 2 \zeta_{64}^{2}} & \htmlTitle{S_{8; 4}}{1} & \htmlTitle{S_{8; 5}}{1} & \htmlTitle{S_{8; 6}}{-\zeta_{64}^{30} - \zeta_{64}^{26} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{8; 7}}{-\zeta_{64}^{30} - \zeta_{64}^{26} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{8; 8}}{\zeta_{64}^{28} + \zeta_{64}^{24} + \zeta_{64}^{20} - \zeta_{64}^{12} - \zeta_{64}^{8} - \zeta_{64}^{4} - 1} & & & & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{64}^{28} - \zeta_{64}^{24} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{9; 2}}{-\zeta_{64}^{28} - \zeta_{64}^{24} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{9; 3}}{2 \zeta_{64}^{30} + \zeta_{64}^{26} + \zeta_{64}^{22} - \zeta_{64}^{10} - \zeta_{64}^{6} - 2 \zeta_{64}^{2}} & \htmlTitle{S_{9; 4}}{1} & \htmlTitle{S_{9; 5}}{1} & \htmlTitle{S_{9; 6}}{\zeta_{64}^{30} + \zeta_{64}^{26} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{9; 7}}{\zeta_{64}^{30} + \zeta_{64}^{26} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{9; 8}}{\zeta_{64}^{28} + \zeta_{64}^{24} + \zeta_{64}^{20} - \zeta_{64}^{12} - \zeta_{64}^{8} - \zeta_{64}^{4} - 1} & \htmlTitle{S_{9; 9}}{\zeta_{64}^{28} + \zeta_{64}^{24} + \zeta_{64}^{20} - \zeta_{64}^{12} - \zeta_{64}^{8} - \zeta_{64}^{4} - 1} & & & & \\ \htmlTitle{S_{10; 1}}{-\zeta_{64}^{28} - \zeta_{64}^{24} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{10; 2}}{-\zeta_{64}^{28} - \zeta_{64}^{24} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{10; 3}}{\zeta_{64}^{26} + \zeta_{64}^{22} - \zeta_{64}^{10} - \zeta_{64}^{6}} & \htmlTitle{S_{10; 4}}{\zeta_{64}^{28} + \zeta_{64}^{24} - \zeta_{64}^{8} - \zeta_{64}^{4} - 1} & \htmlTitle{S_{10; 5}}{\zeta_{64}^{28} + \zeta_{64}^{24} - \zeta_{64}^{8} - \zeta_{64}^{4} - 1} & \htmlTitle{S_{10; 6}}{-\zeta_{64}^{30} - \zeta_{64}^{26} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{10; 7}}{-\zeta_{64}^{30} - \zeta_{64}^{26} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{10; 8}}{-\zeta_{64}^{28} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{10; 9}}{-\zeta_{64}^{28} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{10; 10}}{-1} & & & \\ \htmlTitle{S_{11; 1}}{-\zeta_{64}^{28} - \zeta_{64}^{24} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{11; 2}}{-\zeta_{64}^{28} - \zeta_{64}^{24} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{8} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{11; 3}}{-\zeta_{64}^{26} - \zeta_{64}^{22} + \zeta_{64}^{10} + \zeta_{64}^{6}} & \htmlTitle{S_{11; 4}}{\zeta_{64}^{28} + \zeta_{64}^{24} - \zeta_{64}^{8} - \zeta_{64}^{4} - 1} & \htmlTitle{S_{11; 5}}{\zeta_{64}^{28} + \zeta_{64}^{24} - \zeta_{64}^{8} - \zeta_{64}^{4} - 1} & \htmlTitle{S_{11; 6}}{\zeta_{64}^{30} + \zeta_{64}^{26} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{11; 7}}{\zeta_{64}^{30} + \zeta_{64}^{26} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{11; 8}}{-\zeta_{64}^{28} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{11; 9}}{-\zeta_{64}^{28} + \zeta_{64}^{4} + 1} & \htmlTitle{S_{11; 10}}{-1} & \htmlTitle{S_{11; 11}}{-1} & & \\ \htmlTitle{S_{12; 1}}{-\zeta_{64}^{30} - \zeta_{64}^{26} - \zeta_{64}^{22} - \zeta_{64}^{18} + \zeta_{64}^{14} + \zeta_{64}^{10} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{12; 2}}{\zeta_{64}^{30} + \zeta_{64}^{26} + \zeta_{64}^{22} + \zeta_{64}^{18} - \zeta_{64}^{14} - \zeta_{64}^{10} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{12; 3}}{0} & \htmlTitle{S_{12; 4}}{\zeta_{64}^{30} + \zeta_{64}^{26} + \zeta_{64}^{22} + \zeta_{64}^{18} - \zeta_{64}^{14} - \zeta_{64}^{10} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{12; 5}}{-\zeta_{64}^{30} - \zeta_{64}^{26} - \zeta_{64}^{22} - \zeta_{64}^{18} + \zeta_{64}^{14} + \zeta_{64}^{10} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{12; 6}}{0} & \htmlTitle{S_{12; 7}}{0} & \htmlTitle{S_{12; 8}}{\zeta_{64}^{30} + \zeta_{64}^{26} + \zeta_{64}^{22} + \zeta_{64}^{18} - \zeta_{64}^{14} - \zeta_{64}^{10} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{12; 9}}{-\zeta_{64}^{30} - \zeta_{64}^{26} - \zeta_{64}^{22} - \zeta_{64}^{18} + \zeta_{64}^{14} + \zeta_{64}^{10} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{12; 10}}{-\zeta_{64}^{30} - \zeta_{64}^{26} - \zeta_{64}^{22} - \zeta_{64}^{18} + \zeta_{64}^{14} + \zeta_{64}^{10} + \zeta_{64}^{6} + \zeta_{64}^{2}} & \htmlTitle{S_{12; 11}}{\zeta_{64}^{30} + \zeta_{64}^{26} + \zeta_{64}^{22} + \zeta_{64}^{18} - \zeta_{64}^{14} - \zeta_{64}^{10} - \zeta_{64}^{6} - \zeta_{64}^{2}} & \htmlTitle{S_{12; 12}}{0} & \\ \htmlTitle{S_{13; 1}}{-2 \zeta_{64}^{30} - \zeta_{64}^{26} - \zeta_{64}^{22} + \zeta_{64}^{10} + \zeta_{64}^{6} + 2 \zeta_{64}^{2}} & \htmlTitle{S_{13; 2}}{2 \zeta_{64}^{30} + \zeta_{64}^{26} + \zeta_{64}^{22} - \zeta_{64}^{10} - \zeta_{64}^{6} - 2 \zeta_{64}^{2}} & \htmlTitle{S_{13; 3}}{0} & \htmlTitle{S_{13; 4}}{-\zeta_{64}^{26} - \zeta_{64}^{22} + \zeta_{64}^{10} + \zeta_{64}^{6}} & \htmlTitle{S_{13; 5}}{\zeta_{64}^{26} + \zeta_{64}^{22} - \zeta_{64}^{10} - \zeta_{64}^{6}} & \htmlTitle{S_{13; 6}}{0} & \htmlTitle{S_{13; 7}}{0} & \htmlTitle{S_{13; 8}}{\zeta_{64}^{26} + \zeta_{64}^{22} - \zeta_{64}^{10} - \zeta_{64}^{6}} & \htmlTitle{S_{13; 9}}{-\zeta_{64}^{26} - \zeta_{64}^{22} + \zeta_{64}^{10} + \zeta_{64}^{6}} & \htmlTitle{S_{13; 10}}{2 \zeta_{64}^{30} + \zeta_{64}^{26} + \zeta_{64}^{22} - \zeta_{64}^{10} - \zeta_{64}^{6} - 2 \zeta_{64}^{2}} & \htmlTitle{S_{13; 11}}{-2 \zeta_{64}^{30} - \zeta_{64}^{26} - \zeta_{64}^{22} + \zeta_{64}^{10} + \zeta_{64}^{6} + 2 \zeta_{64}^{2}} & \htmlTitle{S_{13; 12}}{0} & \htmlTitle{S_{13; 13}}{0}\end{array}\right) \]
Central Charge
\[c = \frac{63}{8} \]