Fusion Ring
\[ \begin{array}{lllll} \htmlTitle{1\otimes 1}{1} & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1 \oplus 3} & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{2 \oplus 4} & \htmlTitle{3\otimes 3}{1 \oplus 3 \oplus 5} & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3 \oplus 5} & \htmlTitle{4\otimes 3}{2 \oplus 4 \oplus 5} & \htmlTitle{4\otimes 4}{1 \oplus 3 \oplus 4 \oplus 5} & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{4 \oplus 5} & \htmlTitle{5\otimes 3}{3 \oplus 4 \oplus 5} & \htmlTitle{5\otimes 4}{2 \oplus 3 \oplus 4 \oplus 5} & \htmlTitle{5\otimes 5}{1 \oplus 2 \oplus 3 \oplus 4 \oplus 5} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.919\) | \( \cos{\left(\frac{14 \pi}{33} \right)} + \cos{\left(\frac{8 \pi}{33} \right)} + \cos{\left(\frac{\pi}{11} \right)} \) |
| \( 3\) | \(2.683\) | \( - \cos{\left(\frac{16 \pi}{33} \right)} + \cos{\left(\frac{2 \pi}{11} \right)} + \cos{\left(\frac{5 \pi}{33} \right)} + 1 \) |
| \( 4\) | \(3.229\) | \( - \cos{\left(\frac{13 \pi}{33} \right)} + \cos{\left(\frac{14 \pi}{33} \right)} + \cos{\left(\frac{3 \pi}{11} \right)} + \cos{\left(\frac{8 \pi}{33} \right)} + \cos{\left(\frac{\pi}{11} \right)} + \cos{\left(\frac{2 \pi}{33} \right)} \) |
| \( 5\) | \(3.513\) | \( - \cos{\left(\frac{13 \pi}{33} \right)} + \cos{\left(\frac{14 \pi}{33} \right)} + 2 \cos{\left(\frac{5 \pi}{11} \right)} + \cos{\left(\frac{3 \pi}{11} \right)} + \cos{\left(\frac{8 \pi}{33} \right)} + \cos{\left(\frac{\pi}{11} \right)} + \cos{\left(\frac{2 \pi}{33} \right)} \) |
| \( D^2\) | 34.646 | \(- 5 \cos{\left(\frac{13 \pi}{33} \right)} - 4 \cos{\left(\frac{16 \pi}{33} \right)} + 6 \cos{\left(\frac{5 \pi}{11} \right)} + 6 \cos{\left(\frac{14 \pi}{33} \right)} + 5 \cos{\left(\frac{3 \pi}{11} \right)} + 4 \cos{\left(\frac{2 \pi}{11} \right)} + 4 \cos{\left(\frac{5 \pi}{33} \right)} + 6 \cos{\left(\frac{8 \pi}{33} \right)} + 5 \cos{\left(\frac{2 \pi}{33} \right)} + 6 \cos{\left(\frac{\pi}{11} \right)} + 9\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{4}{11}} & \htmlTitle{\theta_{3}}{\frac{18}{11}} & \htmlTitle{\theta_{4}}{\frac{20}{11}} & \htmlTitle{\theta_{5}}{\frac{10}{11}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllll} \htmlTitle{S_{1; 1}}{1} & & & & \\ \htmlTitle{S_{2; 1}}{-\zeta_{132}^{38} + \zeta_{132}^{16} + \zeta_{132}^{6}} & \htmlTitle{S_{2; 2}}{\zeta_{132}^{38} + \zeta_{132}^{26} - \zeta_{132}^{18} - \zeta_{132}^{16} - \zeta_{132}^{6} - \zeta_{132}^{4}} & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{132}^{32} + \zeta_{132}^{12} + \zeta_{132}^{10} + 1} & \htmlTitle{S_{3; 2}}{-\zeta_{132}^{38} - \zeta_{132}^{36} + \zeta_{132}^{30} - \zeta_{132}^{26} + \zeta_{132}^{18} + \zeta_{132}^{16} + \zeta_{132}^{6} + \zeta_{132}^{4}} & \htmlTitle{S_{3; 3}}{-\zeta_{132}^{38} + \zeta_{132}^{16} + \zeta_{132}^{6}} & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{132}^{38} - \zeta_{132}^{26} + \zeta_{132}^{18} + \zeta_{132}^{16} + \zeta_{132}^{6} + \zeta_{132}^{4}} & \htmlTitle{S_{4; 2}}{\zeta_{132}^{32} - \zeta_{132}^{12} - \zeta_{132}^{10} - 1} & \htmlTitle{S_{4; 3}}{-1} & \htmlTitle{S_{4; 4}}{-\zeta_{132}^{38} - \zeta_{132}^{36} + \zeta_{132}^{30} - \zeta_{132}^{26} + \zeta_{132}^{18} + \zeta_{132}^{16} + \zeta_{132}^{6} + \zeta_{132}^{4}} & \\ \htmlTitle{S_{5; 1}}{-\zeta_{132}^{38} - \zeta_{132}^{36} + \zeta_{132}^{30} - \zeta_{132}^{26} + \zeta_{132}^{18} + \zeta_{132}^{16} + \zeta_{132}^{6} + \zeta_{132}^{4}} & \htmlTitle{S_{5; 2}}{1} & \htmlTitle{S_{5; 3}}{\zeta_{132}^{38} + \zeta_{132}^{26} - \zeta_{132}^{18} - \zeta_{132}^{16} - \zeta_{132}^{6} - \zeta_{132}^{4}} & \htmlTitle{S_{5; 4}}{\zeta_{132}^{38} - \zeta_{132}^{16} - \zeta_{132}^{6}} & \htmlTitle{S_{5; 5}}{-\zeta_{132}^{32} + \zeta_{132}^{12} + \zeta_{132}^{10} + 1}\end{array}\right) \]
Central Charge
\[c = \frac{248}{11} \]