Fusion Ring
\[ \begin{array}{lllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1 \oplus 2 \oplus 7 \oplus 4} & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{6 \oplus 9} & \htmlTitle{3\otimes 3}{1 \oplus 5 \oplus 7 \oplus 3} & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{2 \oplus 7 \oplus 9} & \htmlTitle{4\otimes 3}{8 \oplus 6 \oplus 4} & \htmlTitle{4\otimes 4}{1 \oplus 8 \oplus 7 \oplus 4 \oplus 3} & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5 \oplus 8 \oplus 6} & \htmlTitle{5\otimes 3}{7 \oplus 9 \oplus 3} & \htmlTitle{5\otimes 4}{8 \oplus 6 \oplus 9} & \htmlTitle{5\otimes 5}{1 \oplus 5 \oplus 2 \oplus 8 \oplus 7} & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{5 \oplus 8 \oplus 6 \oplus 9 \oplus 3} & \htmlTitle{6\otimes 3}{2 \oplus 8 \oplus 6 \oplus 4 \oplus 9} & \htmlTitle{6\otimes 4}{5 \oplus 8 \oplus 7 \oplus 6 \oplus 9 \oplus 3} & \htmlTitle{6\otimes 5}{2 \oplus 8 \oplus 7 \oplus 6 \oplus 4 \oplus 9} & \htmlTitle{6\otimes 6}{1 \oplus 5 \oplus 2 \oplus 8 \oplus 2\cdot7 \oplus 6 \oplus 4 \oplus 2\cdot9 \oplus 3} & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{2 \oplus 8 \oplus 7 \oplus 4 \oplus 9} & \htmlTitle{7\otimes 3}{5 \oplus 8 \oplus 7 \oplus 9 \oplus 3} & \htmlTitle{7\otimes 4}{2 \oplus 8 \oplus 7 \oplus 6 \oplus 4 \oplus 9} & \htmlTitle{7\otimes 5}{5 \oplus 8 \oplus 7 \oplus 6 \oplus 9 \oplus 3} & \htmlTitle{7\otimes 6}{5 \oplus 2\cdot8 \oplus 7 \oplus 2\cdot6 \oplus 4 \oplus 2\cdot9} & \htmlTitle{7\otimes 7}{1 \oplus 5 \oplus 2 \oplus 8 \oplus 2\cdot7 \oplus 6 \oplus 4 \oplus 2\cdot9 \oplus 3} & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{5 \oplus 8 \oplus 7 \oplus 6 \oplus 9} & \htmlTitle{8\otimes 3}{8 \oplus 7 \oplus 6 \oplus 4 \oplus 9} & \htmlTitle{8\otimes 4}{5 \oplus 8 \oplus 7 \oplus 6 \oplus 4 \oplus 9 \oplus 3} & \htmlTitle{8\otimes 5}{5 \oplus 2 \oplus 8 \oplus 7 \oplus 6 \oplus 4 \oplus 9} & \htmlTitle{8\otimes 6}{5 \oplus 2 \oplus 2\cdot8 \oplus 2\cdot7 \oplus 6 \oplus 4 \oplus 2\cdot9 \oplus 3} & \htmlTitle{8\otimes 7}{5 \oplus 2 \oplus 2\cdot8 \oplus 7 \oplus 2\cdot6 \oplus 4 \oplus 2\cdot9 \oplus 3} & \htmlTitle{8\otimes 8}{1 \oplus 5 \oplus 2 \oplus 2\cdot8 \oplus 2\cdot7 \oplus 2\cdot6 \oplus 4 \oplus 2\cdot9 \oplus 3} & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{8 \oplus 7 \oplus 6 \oplus 4 \oplus 9 \oplus 3} & \htmlTitle{9\otimes 3}{5 \oplus 2 \oplus 8 \oplus 7 \oplus 6 \oplus 9} & \htmlTitle{9\otimes 4}{5 \oplus 2 \oplus 8 \oplus 7 \oplus 6 \oplus 2\cdot9} & \htmlTitle{9\otimes 5}{8 \oplus 7 \oplus 6 \oplus 4 \oplus 2\cdot9 \oplus 3} & \htmlTitle{9\otimes 6}{5 \oplus 2 \oplus 2\cdot8 \oplus 2\cdot7 \oplus 2\cdot6 \oplus 4 \oplus 2\cdot9 \oplus 3} & \htmlTitle{9\otimes 7}{5 \oplus 2 \oplus 2\cdot8 \oplus 2\cdot7 \oplus 2\cdot6 \oplus 4 \oplus 2\cdot9 \oplus 3} & \htmlTitle{9\otimes 8}{5 \oplus 2 \oplus 2\cdot8 \oplus 2\cdot7 \oplus 2\cdot6 \oplus 4 \oplus 3\cdot9 \oplus 3} & \htmlTitle{9\otimes 9}{1 \oplus 2\cdot5 \oplus 2 \oplus 3\cdot8 \oplus 2\cdot7 \oplus 2\cdot6 \oplus 2\cdot4 \oplus 2\cdot9 \oplus 3} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(4.449\) | \( 2 + \sqrt{6} \) |
| \( 3\) | \(4.449\) | \( 2 + \sqrt{6} \) |
| \( 4\) | \(5.449\) | \( \sqrt{6} + 3 \) |
| \( 5\) | \(5.449\) | \( \sqrt{6} + 3 \) |
| \( 6\) | \(8.899\) | \( 4 + 2 \sqrt{6} \) |
| \( 7\) | \(8.899\) | \( 4 + 2 \sqrt{6} \) |
| \( 8\) | \(9.899\) | \( 2 \sqrt{6} + 5 \) |
| \( 9\) | \(10.899\) | \( 2 \sqrt{6} + 6 \) |
| \( D^2\) | 475.151 | \(96 \sqrt{6} + 240\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{3}{2}} & \htmlTitle{\theta_{3}}{\frac{3}{2}} & \htmlTitle{\theta_{4}}{1} & \htmlTitle{\theta_{5}}{1} & \htmlTitle{\theta_{6}}{\frac{2}{3}} & \htmlTitle{\theta_{7}}{\frac{1}{6}} & \htmlTitle{\theta_{8}}{0} & \htmlTitle{\theta_{9}}{\frac{5}{4}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & \\ \htmlTitle{S_{2; 1}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{2; 2}}{-2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + 4 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 4 \zeta_{96}^{8} - 2 \zeta_{96}^{4} + 2} & & & & & & & \\ \htmlTitle{S_{3; 1}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{3; 2}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{24} - 2 \zeta_{96}^{20} + 4 \zeta_{96}^{12} + 4 \zeta_{96}^{8} + 4 \zeta_{96}^{4} + 2} & \htmlTitle{S_{3; 3}}{-2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + 4 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 4 \zeta_{96}^{8} - 2 \zeta_{96}^{4} + 2} & & & & & & \\ \htmlTitle{S_{4; 1}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 3} & \htmlTitle{S_{4; 2}}{2 \zeta_{96}^{24} + 3 \zeta_{96}^{20} - 3 \zeta_{96}^{12} - 4 \zeta_{96}^{8} - 3 \zeta_{96}^{4}} & \htmlTitle{S_{4; 3}}{-2 \zeta_{96}^{24} - 3 \zeta_{96}^{20} + 3 \zeta_{96}^{12} + 4 \zeta_{96}^{8} + 3 \zeta_{96}^{4}} & \htmlTitle{S_{4; 4}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{24} - 2 \zeta_{96}^{20} + 4 \zeta_{96}^{12} + 4 \zeta_{96}^{8} + 4 \zeta_{96}^{4} + 3} & & & & & \\ \htmlTitle{S_{5; 1}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 3} & \htmlTitle{S_{5; 2}}{-2 \zeta_{96}^{24} - 3 \zeta_{96}^{20} + 3 \zeta_{96}^{12} + 4 \zeta_{96}^{8} + 3 \zeta_{96}^{4}} & \htmlTitle{S_{5; 3}}{2 \zeta_{96}^{24} + 3 \zeta_{96}^{20} - 3 \zeta_{96}^{12} - 4 \zeta_{96}^{8} - 3 \zeta_{96}^{4}} & \htmlTitle{S_{5; 4}}{-2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + 4 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 4 \zeta_{96}^{8} - 2 \zeta_{96}^{4} + 3} & \htmlTitle{S_{5; 5}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{24} - 2 \zeta_{96}^{20} + 4 \zeta_{96}^{12} + 4 \zeta_{96}^{8} + 4 \zeta_{96}^{4} + 3} & & & & \\ \htmlTitle{S_{6; 1}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 4} & \htmlTitle{S_{6; 2}}{4 \zeta_{96}^{28} - 2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 4} & \htmlTitle{S_{6; 3}}{4 \zeta_{96}^{28} - 2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 4} & \htmlTitle{S_{6; 4}}{0} & \htmlTitle{S_{6; 5}}{0} & \htmlTitle{S_{6; 6}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 4} & & & \\ \htmlTitle{S_{7; 1}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 4} & \htmlTitle{S_{7; 2}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 4} & \htmlTitle{S_{7; 3}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 4} & \htmlTitle{S_{7; 4}}{0} & \htmlTitle{S_{7; 5}}{0} & \htmlTitle{S_{7; 6}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 4} & \htmlTitle{S_{7; 7}}{4 \zeta_{96}^{28} - 2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 4} & & \\ \htmlTitle{S_{8; 1}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 5} & \htmlTitle{S_{8; 2}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4} - 2} & \htmlTitle{S_{8; 3}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4} - 2} & \htmlTitle{S_{8; 4}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 3} & \htmlTitle{S_{8; 5}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 3} & \htmlTitle{S_{8; 6}}{4 \zeta_{96}^{28} - 2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 4} & \htmlTitle{S_{8; 7}}{4 \zeta_{96}^{28} - 2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 4} & \htmlTitle{S_{8; 8}}{1} & \\ \htmlTitle{S_{9; 1}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 6} & \htmlTitle{S_{9; 2}}{0} & \htmlTitle{S_{9; 3}}{0} & \htmlTitle{S_{9; 4}}{4 \zeta_{96}^{28} - 2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 6} & \htmlTitle{S_{9; 5}}{4 \zeta_{96}^{28} - 2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 6} & \htmlTitle{S_{9; 6}}{0} & \htmlTitle{S_{9; 7}}{0} & \htmlTitle{S_{9; 8}}{-4 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 6} & \htmlTitle{S_{9; 9}}{0}\end{array}\right) \]
Central Charge
\[c = 13 \]