Fusion Ring
\[ \begin{array}{llllllllll} \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 2} & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{4} & \htmlTitle{4\otimes 3}{3 \oplus 5} & \htmlTitle{4\otimes 4}{1 \oplus 6 \oplus 2} & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5} & \htmlTitle{5\otimes 3}{4 \oplus 6} & \htmlTitle{5\otimes 4}{3 \oplus 7} & \htmlTitle{5\otimes 5}{1 \oplus 8 \oplus 2} & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{6} & \htmlTitle{6\otimes 3}{5 \oplus 7} & \htmlTitle{6\otimes 4}{4 \oplus 8} & \htmlTitle{6\otimes 5}{3 \oplus 8} & \htmlTitle{6\otimes 6}{1 \oplus 7 \oplus 2} & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{7} & \htmlTitle{7\otimes 3}{6 \oplus 8} & \htmlTitle{7\otimes 4}{5 \oplus 8} & \htmlTitle{7\otimes 5}{4 \oplus 7} & \htmlTitle{7\otimes 6}{3 \oplus 6} & \htmlTitle{7\otimes 7}{1 \oplus 5 \oplus 2} & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{8} & \htmlTitle{8\otimes 3}{7 \oplus 8} & \htmlTitle{8\otimes 4}{6 \oplus 7} & \htmlTitle{8\otimes 5}{5 \oplus 6} & \htmlTitle{8\otimes 6}{4 \oplus 5} & \htmlTitle{8\otimes 7}{3 \oplus 4} & \htmlTitle{8\otimes 8}{1 \oplus 3 \oplus 2} & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{10} & \htmlTitle{9\otimes 3}{9 \oplus 10} & \htmlTitle{9\otimes 4}{9 \oplus 10} & \htmlTitle{9\otimes 5}{9 \oplus 10} & \htmlTitle{9\otimes 6}{9 \oplus 10} & \htmlTitle{9\otimes 7}{9 \oplus 10} & \htmlTitle{9\otimes 8}{9 \oplus 10} & \htmlTitle{9\otimes 9}{1 \oplus 3 \oplus 4 \oplus 5 \oplus 6 \oplus 7 \oplus 8} & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{9} & \htmlTitle{10\otimes 3}{9 \oplus 10} & \htmlTitle{10\otimes 4}{9 \oplus 10} & \htmlTitle{10\otimes 5}{9 \oplus 10} & \htmlTitle{10\otimes 6}{9 \oplus 10} & \htmlTitle{10\otimes 7}{9 \oplus 10} & \htmlTitle{10\otimes 8}{9 \oplus 10} & \htmlTitle{10\otimes 9}{3 \oplus 4 \oplus 5 \oplus 6 \oplus 7 \oplus 8 \oplus 2} & \htmlTitle{10\otimes 10}{1 \oplus 3 \oplus 4 \oplus 5 \oplus 6 \oplus 7 \oplus 8} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(2.000\) | \( 2 \) |
| \( 4\) | \(2.000\) | \( 2 \) |
| \( 5\) | \(2.000\) | \( 2 \) |
| \( 6\) | \(2.000\) | \( 2 \) |
| \( 7\) | \(2.000\) | \( 2 \) |
| \( 8\) | \(2.000\) | \( 2 \) |
| \( 9\) | \(3.606\) | \( - 4 \cos{\left(\frac{5 \pi}{13} \right)} + 4 \cos{\left(\frac{6 \pi}{13} \right)} + 1 + 4 \cos{\left(\frac{2 \pi}{13} \right)} \) |
| \( 10\) | \(3.606\) | \( - 4 \cos{\left(\frac{5 \pi}{13} \right)} + 4 \cos{\left(\frac{6 \pi}{13} \right)} + 1 + 4 \cos{\left(\frac{2 \pi}{13} \right)} \) |
| \( D^2\) | 52.000 | \(52\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{12}{13}} & \htmlTitle{\theta_{4}}{\frac{22}{13}} & \htmlTitle{\theta_{5}}{\frac{4}{13}} & \htmlTitle{\theta_{6}}{\frac{10}{13}} & \htmlTitle{\theta_{7}}{\frac{14}{13}} & \htmlTitle{\theta_{8}}{\frac{16}{13}} & \htmlTitle{\theta_{9}}{\frac{3}{2}} & \htmlTitle{\theta_{10}}{\frac{1}{2}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & \\ \htmlTitle{S_{3; 1}}{2} & \htmlTitle{S_{3; 2}}{2} & \htmlTitle{S_{3; 3}}{-2 \zeta_{104}^{44} + 2 \zeta_{104}^{8}} & & & & & & & \\ \htmlTitle{S_{4; 1}}{2} & \htmlTitle{S_{4; 2}}{2} & \htmlTitle{S_{4; 3}}{-2 \zeta_{104}^{36} + 2 \zeta_{104}^{16}} & \htmlTitle{S_{4; 4}}{2 \zeta_{104}^{32} - 2 \zeta_{104}^{20}} & & & & & & \\ \htmlTitle{S_{5; 1}}{2} & \htmlTitle{S_{5; 2}}{2} & \htmlTitle{S_{5; 3}}{-2 \zeta_{104}^{28} + 2 \zeta_{104}^{24}} & \htmlTitle{S_{5; 4}}{2 \zeta_{104}^{44} - 2 \zeta_{104}^{40} + 2 \zeta_{104}^{36} - 2 \zeta_{104}^{32} + 2 \zeta_{104}^{28} - 2 \zeta_{104}^{24} + 2 \zeta_{104}^{20} - 2 \zeta_{104}^{16} + 2 \zeta_{104}^{12} - 2 \zeta_{104}^{8} - 2} & \htmlTitle{S_{5; 5}}{2 \zeta_{104}^{32} - 2 \zeta_{104}^{20}} & & & & & \\ \htmlTitle{S_{6; 1}}{2} & \htmlTitle{S_{6; 2}}{2} & \htmlTitle{S_{6; 3}}{2 \zeta_{104}^{32} - 2 \zeta_{104}^{20}} & \htmlTitle{S_{6; 4}}{2 \zeta_{104}^{40} - 2 \zeta_{104}^{12}} & \htmlTitle{S_{6; 5}}{-2 \zeta_{104}^{44} + 2 \zeta_{104}^{8}} & \htmlTitle{S_{6; 6}}{-2 \zeta_{104}^{28} + 2 \zeta_{104}^{24}} & & & & \\ \htmlTitle{S_{7; 1}}{2} & \htmlTitle{S_{7; 2}}{2} & \htmlTitle{S_{7; 3}}{2 \zeta_{104}^{40} - 2 \zeta_{104}^{12}} & \htmlTitle{S_{7; 4}}{-2 \zeta_{104}^{28} + 2 \zeta_{104}^{24}} & \htmlTitle{S_{7; 5}}{-2 \zeta_{104}^{36} + 2 \zeta_{104}^{16}} & \htmlTitle{S_{7; 6}}{2 \zeta_{104}^{44} - 2 \zeta_{104}^{40} + 2 \zeta_{104}^{36} - 2 \zeta_{104}^{32} + 2 \zeta_{104}^{28} - 2 \zeta_{104}^{24} + 2 \zeta_{104}^{20} - 2 \zeta_{104}^{16} + 2 \zeta_{104}^{12} - 2 \zeta_{104}^{8} - 2} & \htmlTitle{S_{7; 7}}{-2 \zeta_{104}^{44} + 2 \zeta_{104}^{8}} & & & \\ \htmlTitle{S_{8; 1}}{2} & \htmlTitle{S_{8; 2}}{2} & \htmlTitle{S_{8; 3}}{2 \zeta_{104}^{44} - 2 \zeta_{104}^{40} + 2 \zeta_{104}^{36} - 2 \zeta_{104}^{32} + 2 \zeta_{104}^{28} - 2 \zeta_{104}^{24} + 2 \zeta_{104}^{20} - 2 \zeta_{104}^{16} + 2 \zeta_{104}^{12} - 2 \zeta_{104}^{8} - 2} & \htmlTitle{S_{8; 4}}{-2 \zeta_{104}^{44} + 2 \zeta_{104}^{8}} & \htmlTitle{S_{8; 5}}{2 \zeta_{104}^{40} - 2 \zeta_{104}^{12}} & \htmlTitle{S_{8; 6}}{-2 \zeta_{104}^{36} + 2 \zeta_{104}^{16}} & \htmlTitle{S_{8; 7}}{2 \zeta_{104}^{32} - 2 \zeta_{104}^{20}} & \htmlTitle{S_{8; 8}}{-2 \zeta_{104}^{28} + 2 \zeta_{104}^{24}} & & \\ \htmlTitle{S_{9; 1}}{-2 \zeta_{104}^{44} + 2 \zeta_{104}^{32} - 2 \zeta_{104}^{28} + 2 \zeta_{104}^{24} - 2 \zeta_{104}^{20} + 2 \zeta_{104}^{8} + 1} & \htmlTitle{S_{9; 2}}{2 \zeta_{104}^{44} - 2 \zeta_{104}^{32} + 2 \zeta_{104}^{28} - 2 \zeta_{104}^{24} + 2 \zeta_{104}^{20} - 2 \zeta_{104}^{8} - 1} & \htmlTitle{S_{9; 3}}{0} & \htmlTitle{S_{9; 4}}{0} & \htmlTitle{S_{9; 5}}{0} & \htmlTitle{S_{9; 6}}{0} & \htmlTitle{S_{9; 7}}{0} & \htmlTitle{S_{9; 8}}{0} & \htmlTitle{S_{9; 9}}{-2 \zeta_{104}^{44} + 2 \zeta_{104}^{32} - 2 \zeta_{104}^{28} + 2 \zeta_{104}^{24} - 2 \zeta_{104}^{20} + 2 \zeta_{104}^{8} + 1} & \\ \htmlTitle{S_{10; 1}}{-2 \zeta_{104}^{44} + 2 \zeta_{104}^{32} - 2 \zeta_{104}^{28} + 2 \zeta_{104}^{24} - 2 \zeta_{104}^{20} + 2 \zeta_{104}^{8} + 1} & \htmlTitle{S_{10; 2}}{2 \zeta_{104}^{44} - 2 \zeta_{104}^{32} + 2 \zeta_{104}^{28} - 2 \zeta_{104}^{24} + 2 \zeta_{104}^{20} - 2 \zeta_{104}^{8} - 1} & \htmlTitle{S_{10; 3}}{0} & \htmlTitle{S_{10; 4}}{0} & \htmlTitle{S_{10; 5}}{0} & \htmlTitle{S_{10; 6}}{0} & \htmlTitle{S_{10; 7}}{0} & \htmlTitle{S_{10; 8}}{0} & \htmlTitle{S_{10; 9}}{2 \zeta_{104}^{44} - 2 \zeta_{104}^{32} + 2 \zeta_{104}^{28} - 2 \zeta_{104}^{24} + 2 \zeta_{104}^{20} - 2 \zeta_{104}^{8} - 1} & \htmlTitle{S_{10; 10}}{-2 \zeta_{104}^{44} + 2 \zeta_{104}^{32} - 2 \zeta_{104}^{28} + 2 \zeta_{104}^{24} - 2 \zeta_{104}^{20} + 2 \zeta_{104}^{8} + 1}\end{array}\right) \]
Central Charge
\[c = 12 \]