Fusion Ring
\[ \begin{array}{llllll} \htmlTitle{1\otimes 1}{1} & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1 \oplus 2 \oplus 3 \oplus 6} & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{2 \oplus 6 \oplus 5} & \htmlTitle{3\otimes 3}{1 \oplus 3 \oplus 6 \oplus 4} & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{6 \oplus 5 \oplus 4} & \htmlTitle{4\otimes 3}{3 \oplus 6 \oplus 5} & \htmlTitle{4\otimes 4}{1 \oplus 2 \oplus 6 \oplus 4} & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{3 \oplus 6 \oplus 5 \oplus 4} & \htmlTitle{5\otimes 3}{2 \oplus 6 \oplus 5 \oplus 4} & \htmlTitle{5\otimes 4}{2 \oplus 3 \oplus 6 \oplus 5} & \htmlTitle{5\otimes 5}{1 \oplus 2 \oplus 3 \oplus 6 \oplus 5 \oplus 4} & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{2 \oplus 3 \oplus 6 \oplus 5 \oplus 4} & \htmlTitle{6\otimes 3}{2 \oplus 3 \oplus 6 \oplus 5 \oplus 4} & \htmlTitle{6\otimes 4}{2 \oplus 3 \oplus 6 \oplus 5 \oplus 4} & \htmlTitle{6\otimes 5}{2 \oplus 3 \oplus 2\cdot6 \oplus 5 \oplus 4} & \htmlTitle{6\otimes 6}{1 \oplus 2 \oplus 3 \oplus 2\cdot6 \oplus 2\cdot5 \oplus 4} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 3\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 4\) | \(3.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + \frac{3}{2} + 2 \cos{\left(\frac{2 \pi}{21} \right)} \) |
| \( 5\) | \(4.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 2 \cos{\left(\frac{2 \pi}{21} \right)} + \frac{5}{2} \) |
| \( 6\) | \(5.791\) | \( - \cos{\left(\frac{4 \pi}{21} \right)} - \cos{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{10 \pi}{21} \right)} + \cos{\left(\frac{8 \pi}{21} \right)} + \cos{\left(\frac{\pi}{21} \right)} + 2 \cos{\left(\frac{2 \pi}{21} \right)} + \frac{7}{2} \) |
| \( D^2\) | 100.617 | \(- 21 \cos{\left(\frac{4 \pi}{21} \right)} - 21 \cos{\left(\frac{3 \pi}{7} \right)} + 21 \cos{\left(\frac{10 \pi}{21} \right)} + 21 \cos{\left(\frac{8 \pi}{21} \right)} + 21 \cos{\left(\frac{\pi}{21} \right)} + 42 \cos{\left(\frac{2 \pi}{21} \right)} + \frac{105}{2}\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{4}{7}} & \htmlTitle{\theta_{3}}{\frac{8}{7}} & \htmlTitle{\theta_{4}}{\frac{2}{7}} & \htmlTitle{\theta_{5}}{0} & \htmlTitle{\theta_{6}}{\frac{4}{3}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllll} \htmlTitle{S_{1; 1}}{1} & & & & & \\ \htmlTitle{S_{2; 1}}{-\zeta_{84}^{22} - \zeta_{84}^{18} + \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{8} + 2 \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{2; 2}}{-\zeta_{84}^{20} - 2 \zeta_{84}^{18} - \zeta_{84}^{16} + \zeta_{84}^{12} + 2 \zeta_{84}^{10} + \zeta_{84}^{8} + \zeta_{84}^{6} + 2 \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{84}^{22} - \zeta_{84}^{18} + \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{8} + 2 \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{3; 2}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + \zeta_{84}^{18} + 2 \zeta_{84}^{16} + 2 \zeta_{84}^{14} - 3 \zeta_{84}^{10} - \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{4} + 2 \zeta_{84}^{2} - 1} & \htmlTitle{S_{3; 3}}{3 \zeta_{84}^{20} - \zeta_{84}^{14} - \zeta_{84}^{12} + \zeta_{84}^{10} - \zeta_{84}^{8} - 2 \zeta_{84}^{6} - \zeta_{84}^{4} - 2 \zeta_{84}^{2} + 1} & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{84}^{22} - \zeta_{84}^{18} + \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{8} + 2 \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{4; 2}}{3 \zeta_{84}^{20} - \zeta_{84}^{14} - \zeta_{84}^{12} + \zeta_{84}^{10} - \zeta_{84}^{8} - 2 \zeta_{84}^{6} - \zeta_{84}^{4} - 2 \zeta_{84}^{2} + 1} & \htmlTitle{S_{4; 3}}{-\zeta_{84}^{20} - 2 \zeta_{84}^{18} - \zeta_{84}^{16} + \zeta_{84}^{12} + 2 \zeta_{84}^{10} + \zeta_{84}^{8} + \zeta_{84}^{6} + 2 \zeta_{84}^{4} + \zeta_{84}^{2} + 1} & \htmlTitle{S_{4; 4}}{-\zeta_{84}^{22} - 2 \zeta_{84}^{20} + \zeta_{84}^{18} + 2 \zeta_{84}^{16} + 2 \zeta_{84}^{14} - 3 \zeta_{84}^{10} - \zeta_{84}^{8} + \zeta_{84}^{6} + \zeta_{84}^{4} + 2 \zeta_{84}^{2} - 1} & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{84}^{22} - \zeta_{84}^{18} + \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{8} + 2 \zeta_{84}^{4} + \zeta_{84}^{2} + 2} & \htmlTitle{S_{5; 2}}{\zeta_{84}^{22} + \zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{14} + \zeta_{84}^{8} - 2 \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{5; 3}}{\zeta_{84}^{22} + \zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{14} + \zeta_{84}^{8} - 2 \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{5; 4}}{\zeta_{84}^{22} + \zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{14} + \zeta_{84}^{8} - 2 \zeta_{84}^{4} - \zeta_{84}^{2} - 1} & \htmlTitle{S_{5; 5}}{1} & \\ \htmlTitle{S_{6; 1}}{-\zeta_{84}^{22} - \zeta_{84}^{18} + \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{8} + 2 \zeta_{84}^{4} + \zeta_{84}^{2} + 3} & \htmlTitle{S_{6; 2}}{0} & \htmlTitle{S_{6; 3}}{0} & \htmlTitle{S_{6; 4}}{0} & \htmlTitle{S_{6; 5}}{-\zeta_{84}^{22} - \zeta_{84}^{18} + \zeta_{84}^{16} + \zeta_{84}^{14} - \zeta_{84}^{8} + 2 \zeta_{84}^{4} + \zeta_{84}^{2} + 3} & \htmlTitle{S_{6; 6}}{\zeta_{84}^{22} + \zeta_{84}^{18} - \zeta_{84}^{16} - \zeta_{84}^{14} + \zeta_{84}^{8} - 2 \zeta_{84}^{4} - \zeta_{84}^{2} - 3}\end{array}\right) \]
Central Charge
\[c = 6 \]