Fusion Ring
\[ \begin{array}{lllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{1 \oplus 5} & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{6 \oplus 2} & \htmlTitle{4\otimes 4}{1 \oplus 5} & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{6} & \htmlTitle{5\otimes 3}{3 \oplus 7} & \htmlTitle{5\otimes 4}{8 \oplus 4} & \htmlTitle{5\otimes 5}{1 \oplus 5 \oplus 9} & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{5} & \htmlTitle{6\otimes 3}{8 \oplus 4} & \htmlTitle{6\otimes 4}{3 \oplus 7} & \htmlTitle{6\otimes 5}{9 \oplus 6 \oplus 2} & \htmlTitle{6\otimes 6}{1 \oplus 5 \oplus 9} & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{8} & \htmlTitle{7\otimes 3}{5 \oplus 9} & \htmlTitle{7\otimes 4}{9 \oplus 6} & \htmlTitle{7\otimes 5}{3 \oplus 7 \oplus 8} & \htmlTitle{7\otimes 6}{7 \oplus 8 \oplus 4} & \htmlTitle{7\otimes 7}{1 \oplus 5 \oplus 9 \oplus 6} & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{7} & \htmlTitle{8\otimes 3}{9 \oplus 6} & \htmlTitle{8\otimes 4}{5 \oplus 9} & \htmlTitle{8\otimes 5}{7 \oplus 8 \oplus 4} & \htmlTitle{8\otimes 6}{3 \oplus 7 \oplus 8} & \htmlTitle{8\otimes 7}{5 \oplus 9 \oplus 6 \oplus 2} & \htmlTitle{8\otimes 8}{1 \oplus 5 \oplus 9 \oplus 6} & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{9} & \htmlTitle{9\otimes 3}{7 \oplus 8} & \htmlTitle{9\otimes 4}{7 \oplus 8} & \htmlTitle{9\otimes 5}{5 \oplus 9 \oplus 6} & \htmlTitle{9\otimes 6}{5 \oplus 9 \oplus 6} & \htmlTitle{9\otimes 7}{3 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{9\otimes 8}{3 \oplus 7 \oplus 8 \oplus 4} & \htmlTitle{9\otimes 9}{1 \oplus 5 \oplus 9 \oplus 6 \oplus 2} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.902\) | \( \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 4\) | \(1.902\) | \( \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 5\) | \(2.618\) | \( \frac{\sqrt{5}}{2} + \frac{3}{2} \) |
| \( 6\) | \(2.618\) | \( \frac{\sqrt{5}}{2} + \frac{3}{2} \) |
| \( 7\) | \(3.078\) | \( \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 8\) | \(3.078\) | \( \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 9\) | \(3.236\) | \( 1 + \sqrt{5} \) |
| \( D^2\) | 52.361 | \(10 \sqrt{5} + 30\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{3}{20}} & \htmlTitle{\theta_{4}}{\frac{23}{20}} & \htmlTitle{\theta_{5}}{\frac{2}{5}} & \htmlTitle{\theta_{6}}{\frac{2}{5}} & \htmlTitle{\theta_{7}}{\frac{3}{4}} & \htmlTitle{\theta_{8}}{\frac{7}{4}} & \htmlTitle{\theta_{9}}{\frac{6}{5}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{3; 2}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{3; 3}}{-2 \zeta_{80}^{28} + \zeta_{80}^{20} + 2 \zeta_{80}^{4}} & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{4; 2}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{4; 3}}{2 \zeta_{80}^{28} - \zeta_{80}^{20} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{4; 4}}{-2 \zeta_{80}^{28} + \zeta_{80}^{20} + 2 \zeta_{80}^{4}} & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{80}^{24} + \zeta_{80}^{16} + 2} & \htmlTitle{S_{5; 2}}{-\zeta_{80}^{24} + \zeta_{80}^{16} + 2} & \htmlTitle{S_{5; 3}}{-2 \zeta_{80}^{28} + \zeta_{80}^{20} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{5; 4}}{-2 \zeta_{80}^{28} + \zeta_{80}^{20} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{5; 5}}{1} & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{80}^{24} + \zeta_{80}^{16} + 2} & \htmlTitle{S_{6; 2}}{-\zeta_{80}^{24} + \zeta_{80}^{16} + 2} & \htmlTitle{S_{6; 3}}{2 \zeta_{80}^{28} - \zeta_{80}^{20} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{6; 4}}{2 \zeta_{80}^{28} - \zeta_{80}^{20} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{6; 5}}{1} & \htmlTitle{S_{6; 6}}{1} & & & \\ \htmlTitle{S_{7; 1}}{-2 \zeta_{80}^{28} + \zeta_{80}^{20} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{7; 2}}{2 \zeta_{80}^{28} - \zeta_{80}^{20} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{7; 3}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{7; 4}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{7; 5}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{7; 6}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{7; 7}}{2 \zeta_{80}^{28} - \zeta_{80}^{20} - 2 \zeta_{80}^{4}} & & \\ \htmlTitle{S_{8; 1}}{-2 \zeta_{80}^{28} + \zeta_{80}^{20} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{8; 2}}{2 \zeta_{80}^{28} - \zeta_{80}^{20} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{8; 3}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{8; 4}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{8; 5}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4}} & \htmlTitle{S_{8; 6}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{8; 7}}{-2 \zeta_{80}^{28} + \zeta_{80}^{20} + 2 \zeta_{80}^{4}} & \htmlTitle{S_{8; 8}}{2 \zeta_{80}^{28} - \zeta_{80}^{20} - 2 \zeta_{80}^{4}} & \\ \htmlTitle{S_{9; 1}}{-2 \zeta_{80}^{24} + 2 \zeta_{80}^{16} + 2} & \htmlTitle{S_{9; 2}}{-2 \zeta_{80}^{24} + 2 \zeta_{80}^{16} + 2} & \htmlTitle{S_{9; 3}}{0} & \htmlTitle{S_{9; 4}}{0} & \htmlTitle{S_{9; 5}}{2 \zeta_{80}^{24} - 2 \zeta_{80}^{16} - 2} & \htmlTitle{S_{9; 6}}{2 \zeta_{80}^{24} - 2 \zeta_{80}^{16} - 2} & \htmlTitle{S_{9; 7}}{0} & \htmlTitle{S_{9; 8}}{0} & \htmlTitle{S_{9; 9}}{-2 \zeta_{80}^{24} + 2 \zeta_{80}^{16} + 2}\end{array}\right) \]
Central Charge
\[c = \frac{12}{5} \]