Fusion Ring
\[ \begin{array}{llllllllllllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{3} & & & & & & & & & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{1} & \htmlTitle{3\otimes 3}{2} & & & & & & & & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{8} & \htmlTitle{4\otimes 3}{7} & \htmlTitle{4\otimes 4}{14 \oplus 5 \oplus 6} & & & & & & & & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{6} & \htmlTitle{5\otimes 3}{9} & \htmlTitle{5\otimes 4}{1 \oplus 10 \oplus 20} & \htmlTitle{5\otimes 5}{15 \oplus 7 \oplus 4} & & & & & & & & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{9} & \htmlTitle{6\otimes 3}{5} & \htmlTitle{6\otimes 4}{11 \oplus 20 \oplus 2} & \htmlTitle{6\otimes 5}{16 \oplus 8 \oplus 4} & \htmlTitle{6\otimes 6}{19 \oplus 8 \oplus 7} & & & & & & & & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{4} & \htmlTitle{7\otimes 3}{8} & \htmlTitle{7\otimes 4}{18 \oplus 5 \oplus 9} & \htmlTitle{7\otimes 5}{12 \oplus 20 \oplus 3} & \htmlTitle{7\otimes 6}{1 \oplus 10 \oplus 20} & \htmlTitle{7\otimes 7}{17 \oplus 9 \oplus 6} & & & & & & & & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{7} & \htmlTitle{8\otimes 3}{4} & \htmlTitle{8\otimes 4}{17 \oplus 9 \oplus 6} & \htmlTitle{8\otimes 5}{11 \oplus 20 \oplus 2} & \htmlTitle{8\otimes 6}{12 \oplus 20 \oplus 3} & \htmlTitle{8\otimes 7}{14 \oplus 5 \oplus 6} & \htmlTitle{8\otimes 8}{18 \oplus 5 \oplus 9} & & & & & & & & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{5} & \htmlTitle{9\otimes 3}{6} & \htmlTitle{9\otimes 4}{12 \oplus 20 \oplus 3} & \htmlTitle{9\otimes 5}{19 \oplus 8 \oplus 7} & \htmlTitle{9\otimes 6}{15 \oplus 7 \oplus 4} & \htmlTitle{9\otimes 7}{11 \oplus 20 \oplus 2} & \htmlTitle{9\otimes 8}{1 \oplus 10 \oplus 20} & \htmlTitle{9\otimes 9}{16 \oplus 8 \oplus 4} & & & & & & & & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{11} & \htmlTitle{10\otimes 3}{12} & \htmlTitle{10\otimes 4}{16 \oplus 15 \oplus 4} & \htmlTitle{10\otimes 5}{14 \oplus 18 \oplus 5} & \htmlTitle{10\otimes 6}{14 \oplus 17 \oplus 6} & \htmlTitle{10\otimes 7}{19 \oplus 15 \oplus 7} & \htmlTitle{10\otimes 8}{19 \oplus 16 \oplus 8} & \htmlTitle{10\otimes 9}{18 \oplus 17 \oplus 9} & \htmlTitle{10\otimes 10}{1 \oplus 10 \oplus 13 \oplus 20} & & & & & & & & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{12} & \htmlTitle{11\otimes 3}{10} & \htmlTitle{11\otimes 4}{19 \oplus 16 \oplus 8} & \htmlTitle{11\otimes 5}{14 \oplus 17 \oplus 6} & \htmlTitle{11\otimes 6}{18 \oplus 17 \oplus 9} & \htmlTitle{11\otimes 7}{16 \oplus 15 \oplus 4} & \htmlTitle{11\otimes 8}{19 \oplus 15 \oplus 7} & \htmlTitle{11\otimes 9}{14 \oplus 18 \oplus 5} & \htmlTitle{11\otimes 10}{11 \oplus 13 \oplus 20 \oplus 2} & \htmlTitle{11\otimes 11}{13 \oplus 12 \oplus 20 \oplus 3} & & & & & & & & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{10} & \htmlTitle{12\otimes 3}{11} & \htmlTitle{12\otimes 4}{19 \oplus 15 \oplus 7} & \htmlTitle{12\otimes 5}{18 \oplus 17 \oplus 9} & \htmlTitle{12\otimes 6}{14 \oplus 18 \oplus 5} & \htmlTitle{12\otimes 7}{19 \oplus 16 \oplus 8} & \htmlTitle{12\otimes 8}{16 \oplus 15 \oplus 4} & \htmlTitle{12\otimes 9}{14 \oplus 17 \oplus 6} & \htmlTitle{12\otimes 10}{13 \oplus 12 \oplus 20 \oplus 3} & \htmlTitle{12\otimes 11}{1 \oplus 10 \oplus 13 \oplus 20} & \htmlTitle{12\otimes 12}{11 \oplus 13 \oplus 20 \oplus 2} & & & & & & & & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{13} & \htmlTitle{13\otimes 3}{13} & \htmlTitle{13\otimes 4}{19 \oplus 16 \oplus 15} & \htmlTitle{13\otimes 5}{14 \oplus 18 \oplus 17} & \htmlTitle{13\otimes 6}{14 \oplus 18 \oplus 17} & \htmlTitle{13\otimes 7}{19 \oplus 16 \oplus 15} & \htmlTitle{13\otimes 8}{19 \oplus 16 \oplus 15} & \htmlTitle{13\otimes 9}{14 \oplus 18 \oplus 17} & \htmlTitle{13\otimes 10}{11 \oplus 10 \oplus 12 \oplus 20} & \htmlTitle{13\otimes 11}{11 \oplus 10 \oplus 12 \oplus 20} & \htmlTitle{13\otimes 12}{11 \oplus 10 \oplus 12 \oplus 20} & \htmlTitle{13\otimes 13}{1 \oplus 13 \oplus 2\cdot20 \oplus 3 \oplus 2} & & & & & & & \\ \htmlTitle{14\otimes 1}{14} & \htmlTitle{14\otimes 2}{17} & \htmlTitle{14\otimes 3}{18} & \htmlTitle{14\otimes 4}{11 \oplus 10 \oplus 13 \oplus 20} & \htmlTitle{14\otimes 5}{19 \oplus 16 \oplus 15 \oplus 4} & \htmlTitle{14\otimes 6}{19 \oplus 16 \oplus 15 \oplus 8} & \htmlTitle{14\otimes 7}{10 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{14\otimes 8}{11 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{14\otimes 9}{19 \oplus 16 \oplus 15 \oplus 7} & \htmlTitle{14\otimes 10}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 6} & \htmlTitle{14\otimes 11}{14 \oplus 18 \oplus 17 \oplus 9 \oplus 6} & \htmlTitle{14\otimes 12}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9} & \htmlTitle{14\otimes 13}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{14\otimes 14}{19 \oplus 2\cdot16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & & & & & & \\ \htmlTitle{15\otimes 1}{15} & \htmlTitle{15\otimes 2}{16} & \htmlTitle{15\otimes 3}{19} & \htmlTitle{15\otimes 4}{14 \oplus 18 \oplus 17 \oplus 5} & \htmlTitle{15\otimes 5}{10 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{15\otimes 6}{11 \oplus 10 \oplus 13 \oplus 20} & \htmlTitle{15\otimes 7}{14 \oplus 18 \oplus 17 \oplus 9} & \htmlTitle{15\otimes 8}{14 \oplus 18 \oplus 17 \oplus 6} & \htmlTitle{15\otimes 9}{11 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{15\otimes 10}{19 \oplus 16 \oplus 15 \oplus 7 \oplus 4} & \htmlTitle{15\otimes 11}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 4} & \htmlTitle{15\otimes 12}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7} & \htmlTitle{15\otimes 13}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{15\otimes 14}{1 \oplus 11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20} & \htmlTitle{15\otimes 15}{14 \oplus 2\cdot18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & & & & & \\ \htmlTitle{16\otimes 1}{16} & \htmlTitle{16\otimes 2}{19} & \htmlTitle{16\otimes 3}{15} & \htmlTitle{16\otimes 4}{14 \oplus 18 \oplus 17 \oplus 6} & \htmlTitle{16\otimes 5}{11 \oplus 10 \oplus 13 \oplus 20} & \htmlTitle{16\otimes 6}{11 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{16\otimes 7}{14 \oplus 18 \oplus 17 \oplus 5} & \htmlTitle{16\otimes 8}{14 \oplus 18 \oplus 17 \oplus 9} & \htmlTitle{16\otimes 9}{10 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{16\otimes 10}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 4} & \htmlTitle{16\otimes 11}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7} & \htmlTitle{16\otimes 12}{19 \oplus 16 \oplus 15 \oplus 7 \oplus 4} & \htmlTitle{16\otimes 13}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{16\otimes 14}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20 \oplus 2} & \htmlTitle{16\otimes 15}{2\cdot14 \oplus 18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{16\otimes 16}{14 \oplus 18 \oplus 2\cdot17 \oplus 5 \oplus 9 \oplus 6} & & & & \\ \htmlTitle{17\otimes 1}{17} & \htmlTitle{17\otimes 2}{18} & \htmlTitle{17\otimes 3}{14} & \htmlTitle{17\otimes 4}{11 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{17\otimes 5}{19 \oplus 16 \oplus 15 \oplus 8} & \htmlTitle{17\otimes 6}{19 \oplus 16 \oplus 15 \oplus 7} & \htmlTitle{17\otimes 7}{11 \oplus 10 \oplus 13 \oplus 20} & \htmlTitle{17\otimes 8}{10 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{17\otimes 9}{19 \oplus 16 \oplus 15 \oplus 4} & \htmlTitle{17\otimes 10}{14 \oplus 18 \oplus 17 \oplus 9 \oplus 6} & \htmlTitle{17\otimes 11}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9} & \htmlTitle{17\otimes 12}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 6} & \htmlTitle{17\otimes 13}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{17\otimes 14}{2\cdot19 \oplus 16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{17\otimes 15}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20 \oplus 2} & \htmlTitle{17\otimes 16}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20 \oplus 3} & \htmlTitle{17\otimes 17}{19 \oplus 16 \oplus 2\cdot15 \oplus 8 \oplus 7 \oplus 4} & & & \\ \htmlTitle{18\otimes 1}{18} & \htmlTitle{18\otimes 2}{14} & \htmlTitle{18\otimes 3}{17} & \htmlTitle{18\otimes 4}{10 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{18\otimes 5}{19 \oplus 16 \oplus 15 \oplus 7} & \htmlTitle{18\otimes 6}{19 \oplus 16 \oplus 15 \oplus 4} & \htmlTitle{18\otimes 7}{11 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{18\otimes 8}{11 \oplus 10 \oplus 13 \oplus 20} & \htmlTitle{18\otimes 9}{19 \oplus 16 \oplus 15 \oplus 8} & \htmlTitle{18\otimes 10}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9} & \htmlTitle{18\otimes 11}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 6} & \htmlTitle{18\otimes 12}{14 \oplus 18 \oplus 17 \oplus 9 \oplus 6} & \htmlTitle{18\otimes 13}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{18\otimes 14}{19 \oplus 16 \oplus 2\cdot15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{18\otimes 15}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20 \oplus 3} & \htmlTitle{18\otimes 16}{1 \oplus 11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20} & \htmlTitle{18\otimes 17}{19 \oplus 2\cdot16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{18\otimes 18}{2\cdot19 \oplus 16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & & \\ \htmlTitle{19\otimes 1}{19} & \htmlTitle{19\otimes 2}{15} & \htmlTitle{19\otimes 3}{16} & \htmlTitle{19\otimes 4}{14 \oplus 18 \oplus 17 \oplus 9} & \htmlTitle{19\otimes 5}{11 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{19\otimes 6}{10 \oplus 13 \oplus 12 \oplus 20} & \htmlTitle{19\otimes 7}{14 \oplus 18 \oplus 17 \oplus 6} & \htmlTitle{19\otimes 8}{14 \oplus 18 \oplus 17 \oplus 5} & \htmlTitle{19\otimes 9}{11 \oplus 10 \oplus 13 \oplus 20} & \htmlTitle{19\otimes 10}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7} & \htmlTitle{19\otimes 11}{19 \oplus 16 \oplus 15 \oplus 7 \oplus 4} & \htmlTitle{19\otimes 12}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 4} & \htmlTitle{19\otimes 13}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{19\otimes 14}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20 \oplus 3} & \htmlTitle{19\otimes 15}{14 \oplus 18 \oplus 2\cdot17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{19\otimes 16}{14 \oplus 2\cdot18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{19\otimes 17}{1 \oplus 11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20} & \htmlTitle{19\otimes 18}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20 \oplus 2} & \htmlTitle{19\otimes 19}{2\cdot14 \oplus 18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \\ \htmlTitle{20\otimes 1}{20} & \htmlTitle{20\otimes 2}{20} & \htmlTitle{20\otimes 3}{20} & \htmlTitle{20\otimes 4}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{20\otimes 5}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{20\otimes 6}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{20\otimes 7}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{20\otimes 8}{19 \oplus 16 \oplus 15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{20\otimes 9}{14 \oplus 18 \oplus 17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{20\otimes 10}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20} & \htmlTitle{20\otimes 11}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20} & \htmlTitle{20\otimes 12}{11 \oplus 10 \oplus 13 \oplus 12 \oplus 2\cdot20} & \htmlTitle{20\otimes 13}{11 \oplus 10 \oplus 2\cdot13 \oplus 12 \oplus 2\cdot20} & \htmlTitle{20\otimes 14}{2\cdot14 \oplus 2\cdot18 \oplus 2\cdot17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{20\otimes 15}{2\cdot19 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{20\otimes 16}{2\cdot19 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{20\otimes 17}{2\cdot14 \oplus 2\cdot18 \oplus 2\cdot17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{20\otimes 18}{2\cdot14 \oplus 2\cdot18 \oplus 2\cdot17 \oplus 5 \oplus 9 \oplus 6} & \htmlTitle{20\otimes 19}{2\cdot19 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 8 \oplus 7 \oplus 4} & \htmlTitle{20\otimes 20}{1 \oplus 2\cdot11 \oplus 2\cdot10 \oplus 2\cdot13 \oplus 2\cdot12 \oplus 3\cdot20 \oplus 3 \oplus 2} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.000\) | \( 1 \) |
| \( 4\) | \(3.618\) | \( \frac{\sqrt{5}}{2} + \frac{5}{2} \) |
| \( 5\) | \(3.618\) | \( \frac{\sqrt{5}}{2} + \frac{5}{2} \) |
| \( 6\) | \(3.618\) | \( \frac{\sqrt{5}}{2} + \frac{5}{2} \) |
| \( 7\) | \(3.618\) | \( \frac{\sqrt{5}}{2} + \frac{5}{2} \) |
| \( 8\) | \(3.618\) | \( \frac{\sqrt{5}}{2} + \frac{5}{2} \) |
| \( 9\) | \(3.618\) | \( \frac{\sqrt{5}}{2} + \frac{5}{2} \) |
| \( 10\) | \(4.236\) | \( 2 + \sqrt{5} \) |
| \( 11\) | \(4.236\) | \( 2 + \sqrt{5} \) |
| \( 12\) | \(4.236\) | \( 2 + \sqrt{5} \) |
| \( 13\) | \(4.854\) | \( \frac{3}{2} + \frac{3 \sqrt{5}}{2} \) |
| \( 14\) | \(5.854\) | \( \frac{5}{2} + \frac{3 \sqrt{5}}{2} \) |
| \( 15\) | \(5.854\) | \( \frac{5}{2} + \frac{3 \sqrt{5}}{2} \) |
| \( 16\) | \(5.854\) | \( \frac{5}{2} + \frac{3 \sqrt{5}}{2} \) |
| \( 17\) | \(5.854\) | \( \frac{5}{2} + \frac{3 \sqrt{5}}{2} \) |
| \( 18\) | \(5.854\) | \( \frac{5}{2} + \frac{3 \sqrt{5}}{2} \) |
| \( 19\) | \(5.854\) | \( \frac{5}{2} + \frac{3 \sqrt{5}}{2} \) |
| \( 20\) | \(7.854\) | \( \frac{3 \sqrt{5}}{2} + \frac{9}{2} \) |
| \( D^2\) | 426.246 | \(90 \sqrt{5} + 225\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{0} & \htmlTitle{\theta_{4}}{\frac{52}{45}} & \htmlTitle{\theta_{5}}{\frac{52}{45}} & \htmlTitle{\theta_{6}}{\frac{22}{45}} & \htmlTitle{\theta_{7}}{\frac{22}{45}} & \htmlTitle{\theta_{8}}{\frac{82}{45}} & \htmlTitle{\theta_{9}}{\frac{82}{45}} & \htmlTitle{\theta_{10}}{\frac{8}{5}} & \htmlTitle{\theta_{11}}{\frac{8}{5}} & \htmlTitle{\theta_{12}}{\frac{8}{5}} & \htmlTitle{\theta_{13}}{\frac{6}{5}} & \htmlTitle{\theta_{14}}{\frac{2}{9}} & \htmlTitle{\theta_{15}}{\frac{2}{9}} & \htmlTitle{\theta_{16}}{\frac{8}{9}} & \htmlTitle{\theta_{17}}{\frac{14}{9}} & \htmlTitle{\theta_{18}}{\frac{8}{9}} & \htmlTitle{\theta_{19}}{\frac{14}{9}} & \htmlTitle{\theta_{20}}{\frac{2}{5}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllllllllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{1} & \htmlTitle{S_{3; 2}}{1} & \htmlTitle{S_{3; 3}}{1} & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{180}^{42} + \zeta_{180}^{18} + \zeta_{180}^{12} + 2} & \htmlTitle{S_{4; 2}}{\zeta_{180}^{42} - 3 \zeta_{180}^{30} - \zeta_{180}^{24} - \zeta_{180}^{18} - \zeta_{180}^{12} + \zeta_{180}^{6} + 1} & \htmlTitle{S_{4; 3}}{3 \zeta_{180}^{30} + \zeta_{180}^{24} - \zeta_{180}^{6} - 3} & \htmlTitle{S_{4; 4}}{\zeta_{180}^{44} - 4 \zeta_{180}^{32} - \zeta_{180}^{26} + 4 \zeta_{180}^{8} + 4 \zeta_{180}^{2}} & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{180}^{42} + \zeta_{180}^{18} + \zeta_{180}^{12} + 2} & \htmlTitle{S_{5; 2}}{3 \zeta_{180}^{30} + \zeta_{180}^{24} - \zeta_{180}^{6} - 3} & \htmlTitle{S_{5; 3}}{\zeta_{180}^{42} - 3 \zeta_{180}^{30} - \zeta_{180}^{24} - \zeta_{180}^{18} - \zeta_{180}^{12} + \zeta_{180}^{6} + 1} & \htmlTitle{S_{5; 4}}{3 \zeta_{180}^{46} - 3 \zeta_{180}^{34} + 4 \zeta_{180}^{10} + 3 \zeta_{180}^{4}} & \htmlTitle{S_{5; 5}}{\zeta_{180}^{44} - 4 \zeta_{180}^{32} - \zeta_{180}^{26} + 4 \zeta_{180}^{8} + 4 \zeta_{180}^{2}} & & & & & & & & & & & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{180}^{42} + \zeta_{180}^{18} + \zeta_{180}^{12} + 2} & \htmlTitle{S_{6; 2}}{3 \zeta_{180}^{30} + \zeta_{180}^{24} - \zeta_{180}^{6} - 3} & \htmlTitle{S_{6; 3}}{\zeta_{180}^{42} - 3 \zeta_{180}^{30} - \zeta_{180}^{24} - \zeta_{180}^{18} - \zeta_{180}^{12} + \zeta_{180}^{6} + 1} & \htmlTitle{S_{6; 4}}{-3 \zeta_{180}^{46} - 4 \zeta_{180}^{40} + 3 \zeta_{180}^{16} - 3 \zeta_{180}^{4}} & \htmlTitle{S_{6; 5}}{-\zeta_{180}^{44} + 3 \zeta_{180}^{38} + 4 \zeta_{180}^{32} + \zeta_{180}^{26} + \zeta_{180}^{20} - 4 \zeta_{180}^{8} - \zeta_{180}^{2}} & \htmlTitle{S_{6; 6}}{-3 \zeta_{180}^{38} - \zeta_{180}^{20} - 3 \zeta_{180}^{2}} & & & & & & & & & & & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{180}^{42} + \zeta_{180}^{18} + \zeta_{180}^{12} + 2} & \htmlTitle{S_{7; 2}}{\zeta_{180}^{42} - 3 \zeta_{180}^{30} - \zeta_{180}^{24} - \zeta_{180}^{18} - \zeta_{180}^{12} + \zeta_{180}^{6} + 1} & \htmlTitle{S_{7; 3}}{3 \zeta_{180}^{30} + \zeta_{180}^{24} - \zeta_{180}^{6} - 3} & \htmlTitle{S_{7; 4}}{-\zeta_{180}^{44} + 3 \zeta_{180}^{38} + 4 \zeta_{180}^{32} + \zeta_{180}^{26} + \zeta_{180}^{20} - 4 \zeta_{180}^{8} - \zeta_{180}^{2}} & \htmlTitle{S_{7; 5}}{-3 \zeta_{180}^{46} - 4 \zeta_{180}^{40} + 3 \zeta_{180}^{16} - 3 \zeta_{180}^{4}} & \htmlTitle{S_{7; 6}}{4 \zeta_{180}^{40} + 3 \zeta_{180}^{34} - 3 \zeta_{180}^{16} - 4 \zeta_{180}^{10}} & \htmlTitle{S_{7; 7}}{-3 \zeta_{180}^{38} - \zeta_{180}^{20} - 3 \zeta_{180}^{2}} & & & & & & & & & & & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{180}^{42} + \zeta_{180}^{18} + \zeta_{180}^{12} + 2} & \htmlTitle{S_{8; 2}}{\zeta_{180}^{42} - 3 \zeta_{180}^{30} - \zeta_{180}^{24} - \zeta_{180}^{18} - \zeta_{180}^{12} + \zeta_{180}^{6} + 1} & \htmlTitle{S_{8; 3}}{3 \zeta_{180}^{30} + \zeta_{180}^{24} - \zeta_{180}^{6} - 3} & \htmlTitle{S_{8; 4}}{-3 \zeta_{180}^{38} - \zeta_{180}^{20} - 3 \zeta_{180}^{2}} & \htmlTitle{S_{8; 5}}{4 \zeta_{180}^{40} + 3 \zeta_{180}^{34} - 3 \zeta_{180}^{16} - 4 \zeta_{180}^{10}} & \htmlTitle{S_{8; 6}}{3 \zeta_{180}^{46} - 3 \zeta_{180}^{34} + 4 \zeta_{180}^{10} + 3 \zeta_{180}^{4}} & \htmlTitle{S_{8; 7}}{\zeta_{180}^{44} - 4 \zeta_{180}^{32} - \zeta_{180}^{26} + 4 \zeta_{180}^{8} + 4 \zeta_{180}^{2}} & \htmlTitle{S_{8; 8}}{-\zeta_{180}^{44} + 3 \zeta_{180}^{38} + 4 \zeta_{180}^{32} + \zeta_{180}^{26} + \zeta_{180}^{20} - 4 \zeta_{180}^{8} - \zeta_{180}^{2}} & & & & & & & & & & & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{180}^{42} + \zeta_{180}^{18} + \zeta_{180}^{12} + 2} & \htmlTitle{S_{9; 2}}{3 \zeta_{180}^{30} + \zeta_{180}^{24} - \zeta_{180}^{6} - 3} & \htmlTitle{S_{9; 3}}{\zeta_{180}^{42} - 3 \zeta_{180}^{30} - \zeta_{180}^{24} - \zeta_{180}^{18} - \zeta_{180}^{12} + \zeta_{180}^{6} + 1} & \htmlTitle{S_{9; 4}}{4 \zeta_{180}^{40} + 3 \zeta_{180}^{34} - 3 \zeta_{180}^{16} - 4 \zeta_{180}^{10}} & \htmlTitle{S_{9; 5}}{-3 \zeta_{180}^{38} - \zeta_{180}^{20} - 3 \zeta_{180}^{2}} & \htmlTitle{S_{9; 6}}{\zeta_{180}^{44} - 4 \zeta_{180}^{32} - \zeta_{180}^{26} + 4 \zeta_{180}^{8} + 4 \zeta_{180}^{2}} & \htmlTitle{S_{9; 7}}{3 \zeta_{180}^{46} - 3 \zeta_{180}^{34} + 4 \zeta_{180}^{10} + 3 \zeta_{180}^{4}} & \htmlTitle{S_{9; 8}}{-3 \zeta_{180}^{46} - 4 \zeta_{180}^{40} + 3 \zeta_{180}^{16} - 3 \zeta_{180}^{4}} & \htmlTitle{S_{9; 9}}{-\zeta_{180}^{44} + 3 \zeta_{180}^{38} + 4 \zeta_{180}^{32} + \zeta_{180}^{26} + \zeta_{180}^{20} - 4 \zeta_{180}^{8} - \zeta_{180}^{2}} & & & & & & & & & & & \\ \htmlTitle{S_{10; 1}}{-2 \zeta_{180}^{42} + 2 \zeta_{180}^{18} + 2 \zeta_{180}^{12} + 1} & \htmlTitle{S_{10; 2}}{-2 \zeta_{180}^{42} + 2 \zeta_{180}^{18} + 2 \zeta_{180}^{12} + 1} & \htmlTitle{S_{10; 3}}{-2 \zeta_{180}^{42} + 2 \zeta_{180}^{18} + 2 \zeta_{180}^{12} + 1} & \htmlTitle{S_{10; 4}}{-3 \zeta_{180}^{42} + 3 \zeta_{180}^{18} + 3 \zeta_{180}^{12} + 1} & \htmlTitle{S_{10; 5}}{-3 \zeta_{180}^{42} + 3 \zeta_{180}^{18} + 3 \zeta_{180}^{12} + 1} & \htmlTitle{S_{10; 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Central Charge
\[c = \frac{78}{5} \]