Fusion Ring
\[ \begin{array}{llllllllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{3} & \htmlTitle{3\otimes 3}{1 \oplus 4 \oplus 5 \oplus 2} & & & & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{5} & \htmlTitle{4\otimes 3}{10 \oplus 3} & \htmlTitle{4\otimes 4}{1 \oplus 6 \oplus 5} & & & & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{4} & \htmlTitle{5\otimes 3}{10 \oplus 3} & \htmlTitle{5\otimes 4}{4 \oplus 8 \oplus 2} & \htmlTitle{5\otimes 5}{1 \oplus 6 \oplus 5} & & & & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{8} & \htmlTitle{6\otimes 3}{15 \oplus 10} & \htmlTitle{6\otimes 4}{4 \oplus 11 \oplus 8} & \htmlTitle{6\otimes 5}{6 \oplus 5 \oplus 12} & \htmlTitle{6\otimes 6}{1 \oplus 6 \oplus 13 \oplus 5 \oplus 12} & & & & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{9} & \htmlTitle{7\otimes 3}{13 \oplus 14} & \htmlTitle{7\otimes 4}{7 \oplus 16} & \htmlTitle{7\otimes 5}{16 \oplus 9} & \htmlTitle{7\otimes 6}{7 \oplus 16 \oplus 15} & \htmlTitle{7\otimes 7}{1 \oplus 4 \oplus 6 \oplus 11 \oplus 13} & & & & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{6} & \htmlTitle{8\otimes 3}{15 \oplus 10} & \htmlTitle{8\otimes 4}{6 \oplus 5 \oplus 12} & \htmlTitle{8\otimes 5}{4 \oplus 11 \oplus 8} & \htmlTitle{8\otimes 6}{4 \oplus 11 \oplus 8 \oplus 14 \oplus 2} & \htmlTitle{8\otimes 7}{16 \oplus 15 \oplus 9} & \htmlTitle{8\otimes 8}{1 \oplus 6 \oplus 13 \oplus 5 \oplus 12} & & & & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{7} & \htmlTitle{9\otimes 3}{13 \oplus 14} & \htmlTitle{9\otimes 4}{16 \oplus 9} & \htmlTitle{9\otimes 5}{7 \oplus 16} & \htmlTitle{9\otimes 6}{16 \oplus 15 \oplus 9} & \htmlTitle{9\otimes 7}{5 \oplus 8 \oplus 12 \oplus 14 \oplus 2} & \htmlTitle{9\otimes 8}{7 \oplus 16 \oplus 15} & \htmlTitle{9\otimes 9}{1 \oplus 4 \oplus 6 \oplus 11 \oplus 13} & & & & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{10} & \htmlTitle{10\otimes 3}{4 \oplus 6 \oplus 5 \oplus 8} & \htmlTitle{10\otimes 4}{15 \oplus 10 \oplus 3} & \htmlTitle{10\otimes 5}{15 \oplus 10 \oplus 3} & \htmlTitle{10\otimes 6}{16 \oplus 15 \oplus 10 \oplus 3} & \htmlTitle{10\otimes 7}{11 \oplus 13 \oplus 12 \oplus 14} & \htmlTitle{10\otimes 8}{16 \oplus 15 \oplus 10 \oplus 3} & \htmlTitle{10\otimes 9}{11 \oplus 13 \oplus 12 \oplus 14} & \htmlTitle{10\otimes 10}{1 \oplus 4 \oplus 6 \oplus 11 \oplus 5 \oplus 8 \oplus 12 \oplus 2} & & & & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{12} & \htmlTitle{11\otimes 3}{16 \oplus 15} & \htmlTitle{11\otimes 4}{6 \oplus 13 \oplus 12} & \htmlTitle{11\otimes 5}{11 \oplus 8 \oplus 14} & \htmlTitle{11\otimes 6}{4 \oplus 11 \oplus 13 \oplus 8 \oplus 14} & \htmlTitle{11\otimes 7}{7 \oplus 16 \oplus 15 \oplus 10} & \htmlTitle{11\otimes 8}{6 \oplus 13 \oplus 5 \oplus 12 \oplus 14} & \htmlTitle{11\otimes 9}{16 \oplus 15 \oplus 10 \oplus 9} & \htmlTitle{11\otimes 10}{7 \oplus 16 \oplus 15 \oplus 10 \oplus 9} & \htmlTitle{11\otimes 11}{1 \oplus 6 \oplus 11 \oplus 13 \oplus 5 \oplus 12 \oplus 14} & & & & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{11} & \htmlTitle{12\otimes 3}{16 \oplus 15} & \htmlTitle{12\otimes 4}{11 \oplus 8 \oplus 14} & \htmlTitle{12\otimes 5}{6 \oplus 13 \oplus 12} & \htmlTitle{12\otimes 6}{6 \oplus 13 \oplus 5 \oplus 12 \oplus 14} & \htmlTitle{12\otimes 7}{16 \oplus 15 \oplus 10 \oplus 9} & \htmlTitle{12\otimes 8}{4 \oplus 11 \oplus 13 \oplus 8 \oplus 14} & \htmlTitle{12\otimes 9}{7 \oplus 16 \oplus 15 \oplus 10} & \htmlTitle{12\otimes 10}{7 \oplus 16 \oplus 15 \oplus 10 \oplus 9} & \htmlTitle{12\otimes 11}{4 \oplus 11 \oplus 13 \oplus 8 \oplus 12 \oplus 14 \oplus 2} & \htmlTitle{12\otimes 12}{1 \oplus 6 \oplus 11 \oplus 13 \oplus 5 \oplus 12 \oplus 14} & & & & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{14} & \htmlTitle{13\otimes 3}{7 \oplus 16 \oplus 9} & \htmlTitle{13\otimes 4}{11 \oplus 13 \oplus 14} & \htmlTitle{13\otimes 5}{13 \oplus 12 \oplus 14} & \htmlTitle{13\otimes 6}{6 \oplus 11 \oplus 13 \oplus 12 \oplus 14} & \htmlTitle{13\otimes 7}{7 \oplus 16 \oplus 15 \oplus 10 \oplus 3} & \htmlTitle{13\otimes 8}{11 \oplus 13 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{13\otimes 9}{16 \oplus 15 \oplus 10 \oplus 3 \oplus 9} & \htmlTitle{13\otimes 10}{7 \oplus 2\cdot16 \oplus 15 \oplus 9} & \htmlTitle{13\otimes 11}{4 \oplus 6 \oplus 11 \oplus 13 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{13\otimes 12}{6 \oplus 11 \oplus 13 \oplus 5 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{13\otimes 13}{1 \oplus 4 \oplus 6 \oplus 11 \oplus 13 \oplus 5 \oplus 8 \oplus 12 \oplus 14} & & & \\ \htmlTitle{14\otimes 1}{14} & \htmlTitle{14\otimes 2}{13} & \htmlTitle{14\otimes 3}{7 \oplus 16 \oplus 9} & \htmlTitle{14\otimes 4}{13 \oplus 12 \oplus 14} & \htmlTitle{14\otimes 5}{11 \oplus 13 \oplus 14} & \htmlTitle{14\otimes 6}{11 \oplus 13 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{14\otimes 7}{16 \oplus 15 \oplus 10 \oplus 3 \oplus 9} & \htmlTitle{14\otimes 8}{6 \oplus 11 \oplus 13 \oplus 12 \oplus 14} & \htmlTitle{14\otimes 9}{7 \oplus 16 \oplus 15 \oplus 10 \oplus 3} & \htmlTitle{14\otimes 10}{7 \oplus 2\cdot16 \oplus 15 \oplus 9} & \htmlTitle{14\otimes 11}{6 \oplus 11 \oplus 13 \oplus 5 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{14\otimes 12}{4 \oplus 6 \oplus 11 \oplus 13 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{14\otimes 13}{4 \oplus 6 \oplus 11 \oplus 13 \oplus 5 \oplus 8 \oplus 12 \oplus 14 \oplus 2} & \htmlTitle{14\otimes 14}{1 \oplus 4 \oplus 6 \oplus 11 \oplus 13 \oplus 5 \oplus 8 \oplus 12 \oplus 14} & & \\ \htmlTitle{15\otimes 1}{15} & \htmlTitle{15\otimes 2}{15} & \htmlTitle{15\otimes 3}{6 \oplus 11 \oplus 8 \oplus 12} & \htmlTitle{15\otimes 4}{16 \oplus 15 \oplus 10} & \htmlTitle{15\otimes 5}{16 \oplus 15 \oplus 10} & \htmlTitle{15\otimes 6}{7 \oplus 16 \oplus 15 \oplus 10 \oplus 3 \oplus 9} & \htmlTitle{15\otimes 7}{6 \oplus 11 \oplus 13 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{15\otimes 8}{7 \oplus 16 \oplus 15 \oplus 10 \oplus 3 \oplus 9} & \htmlTitle{15\otimes 9}{6 \oplus 11 \oplus 13 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{15\otimes 10}{4 \oplus 6 \oplus 11 \oplus 13 \oplus 5 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{15\otimes 11}{7 \oplus 2\cdot16 \oplus 15 \oplus 10 \oplus 3 \oplus 9} & \htmlTitle{15\otimes 12}{7 \oplus 2\cdot16 \oplus 15 \oplus 10 \oplus 3 \oplus 9} & \htmlTitle{15\otimes 13}{7 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 10 \oplus 9} & \htmlTitle{15\otimes 14}{7 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 10 \oplus 9} & \htmlTitle{15\otimes 15}{1 \oplus 4 \oplus 6 \oplus 11 \oplus 2\cdot13 \oplus 5 \oplus 8 \oplus 12 \oplus 2\cdot14 \oplus 2} & \\ \htmlTitle{16\otimes 1}{16} & \htmlTitle{16\otimes 2}{16} & \htmlTitle{16\otimes 3}{11 \oplus 13 \oplus 12 \oplus 14} & \htmlTitle{16\otimes 4}{7 \oplus 16 \oplus 15 \oplus 9} & \htmlTitle{16\otimes 5}{7 \oplus 16 \oplus 15 \oplus 9} & \htmlTitle{16\otimes 6}{7 \oplus 2\cdot16 \oplus 15 \oplus 10 \oplus 9} & \htmlTitle{16\otimes 7}{4 \oplus 6 \oplus 11 \oplus 13 \oplus 5 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{16\otimes 8}{7 \oplus 2\cdot16 \oplus 15 \oplus 10 \oplus 9} & \htmlTitle{16\otimes 9}{4 \oplus 6 \oplus 11 \oplus 13 \oplus 5 \oplus 8 \oplus 12 \oplus 14} & \htmlTitle{16\otimes 10}{6 \oplus 11 \oplus 2\cdot13 \oplus 8 \oplus 12 \oplus 2\cdot14} & \htmlTitle{16\otimes 11}{7 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 10 \oplus 3 \oplus 9} & \htmlTitle{16\otimes 12}{7 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 10 \oplus 3 \oplus 9} & \htmlTitle{16\otimes 13}{7 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 2\cdot10 \oplus 3 \oplus 9} & \htmlTitle{16\otimes 14}{7 \oplus 2\cdot16 \oplus 2\cdot15 \oplus 2\cdot10 \oplus 3 \oplus 9} & \htmlTitle{16\otimes 15}{4 \oplus 6 \oplus 2\cdot11 \oplus 2\cdot13 \oplus 5 \oplus 8 \oplus 2\cdot12 \oplus 2\cdot14} & \htmlTitle{16\otimes 16}{1 \oplus 4 \oplus 2\cdot6 \oplus 2\cdot11 \oplus 2\cdot13 \oplus 5 \oplus 2\cdot8 \oplus 2\cdot12 \oplus 2\cdot14 \oplus 2} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(2.794\) | \( \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{10 - 2 \sqrt{5}}}{2} \) |
| \( 4\) | \(2.902\) | \( 1 + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 5\) | \(2.902\) | \( 1 + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 6\) | \(4.520\) | \( \frac{\sqrt{5}}{2} + \frac{3}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 7\) | \(4.520\) | \( \frac{\sqrt{5}}{2} + \frac{3}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 8\) | \(4.520\) | \( \frac{\sqrt{5}}{2} + \frac{3}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 9\) | \(4.520\) | \( \frac{\sqrt{5}}{2} + \frac{3}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 10\) | \(5.314\) | \( \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} + \sqrt{5} \) |
| \( 11\) | \(5.696\) | \( \frac{\sqrt{5}}{2} + \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{3}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 12\) | \(5.696\) | \( \frac{\sqrt{5}}{2} + \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{3}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} \) |
| \( 13\) | \(6.314\) | \( 1 + \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} + \sqrt{5} \) |
| \( 14\) | \(6.314\) | \( 1 + \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} + \sqrt{5} \) |
| \( 15\) | \(7.314\) | \( \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{\sqrt{2 \sqrt{5} + 10}}{2} + 2 + \sqrt{5} \) |
| \( 16\) | \(8.598\) | \( \frac{\sqrt{5}}{2} + \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \frac{5}{2} + \sqrt{2 \sqrt{5} + 10} \) |
| \( D^2\) | 408.635 | \(20 \sqrt{10 - 2 \sqrt{5}} + 40 \sqrt{5} + 120 + 40 \sqrt{2 \sqrt{5} + 10}\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{1} & \htmlTitle{\theta_{3}}{\frac{13}{10}} & \htmlTitle{\theta_{4}}{\frac{4}{5}} & \htmlTitle{\theta_{5}}{\frac{9}{5}} & \htmlTitle{\theta_{6}}{\frac{7}{5}} & \htmlTitle{\theta_{7}}{\frac{9}{10}} & \htmlTitle{\theta_{8}}{\frac{2}{5}} & \htmlTitle{\theta_{9}}{\frac{9}{10}} & \htmlTitle{\theta_{10}}{1} & \htmlTitle{\theta_{11}}{\frac{9}{5}} & \htmlTitle{\theta_{12}}{\frac{4}{5}} & \htmlTitle{\theta_{13}}{0} & \htmlTitle{\theta_{14}}{1} & \htmlTitle{\theta_{15}}{\frac{1}{2}} & \htmlTitle{\theta_{16}}{\frac{9}{5}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{16} + \zeta_{80}^{12} + 1} & \htmlTitle{S_{3; 2}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{16} - \zeta_{80}^{12} - 1} & \htmlTitle{S_{3; 3}}{0} & & & & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 1} & \htmlTitle{S_{4; 2}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 1} & \htmlTitle{S_{4; 3}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - \zeta_{80}^{20} - 2 \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 3} & \htmlTitle{S_{4; 4}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & & & & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{80}^{28} + \zeta_{80}^{20} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 1} & \htmlTitle{S_{5; 3}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 3} & \htmlTitle{S_{5; 4}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{5; 5}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & & & & & & & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{6; 2}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{6; 3}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + 2 \zeta_{80}^{20} + 2 \zeta_{80}^{16} - 2 \zeta_{80}^{12} + 4 \zeta_{80}^{4} + 4} & \htmlTitle{S_{6; 4}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{6; 5}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{6; 6}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & & & & & & & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{7; 2}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{7; 3}}{0} & \htmlTitle{S_{7; 4}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{7; 5}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{7; 6}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{7; 7}}{-3 \zeta_{80}^{28} - 3 \zeta_{80}^{24} + \zeta_{80}^{20} + 3 \zeta_{80}^{16} + \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 4} & & & & & & & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{8; 2}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{8; 3}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - 2 \zeta_{80}^{20} - 2 \zeta_{80}^{16} + 2 \zeta_{80}^{12} - 4 \zeta_{80}^{4} - 4} & \htmlTitle{S_{8; 4}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{8; 5}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{8; 6}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{8; 7}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{8; 8}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & & & & & & & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{9; 2}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{9; 3}}{0} & \htmlTitle{S_{9; 4}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{9; 5}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{9; 6}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{9; 7}}{3 \zeta_{80}^{28} + 3 \zeta_{80}^{24} - \zeta_{80}^{20} - 3 \zeta_{80}^{16} - \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 4} & \htmlTitle{S_{9; 8}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{9; 9}}{-3 \zeta_{80}^{28} - 3 \zeta_{80}^{24} + \zeta_{80}^{20} + 3 \zeta_{80}^{16} + \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 4} & & & & & & & \\ \htmlTitle{S_{10; 1}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 1} & \htmlTitle{S_{10; 2}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - \zeta_{80}^{20} - 2 \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 1} & \htmlTitle{S_{10; 3}}{0} & \htmlTitle{S_{10; 4}}{3 \zeta_{80}^{28} + \zeta_{80}^{24} - 2 \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 4 \zeta_{80}^{4} - 3} & \htmlTitle{S_{10; 5}}{-3 \zeta_{80}^{28} - \zeta_{80}^{24} + 2 \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 4 \zeta_{80}^{4} + 3} & \htmlTitle{S_{10; 6}}{0} & \htmlTitle{S_{10; 7}}{0} & \htmlTitle{S_{10; 8}}{0} & \htmlTitle{S_{10; 9}}{0} & \htmlTitle{S_{10; 10}}{0} & & & & & & \\ \htmlTitle{S_{11; 1}}{-2 \zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{11; 2}}{-2 \zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{11; 3}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - \zeta_{80}^{20} - 2 \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 3} & \htmlTitle{S_{11; 4}}{-1} & \htmlTitle{S_{11; 5}}{-1} & \htmlTitle{S_{11; 6}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{11; 7}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{11; 8}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{11; 9}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{11; 10}}{-3 \zeta_{80}^{28} - \zeta_{80}^{24} + 2 \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 4 \zeta_{80}^{4} + 3} & \htmlTitle{S_{11; 11}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & & & & & \\ \htmlTitle{S_{12; 1}}{-2 \zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{12; 2}}{-2 \zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{12; 3}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 3} & \htmlTitle{S_{12; 4}}{-1} & \htmlTitle{S_{12; 5}}{-1} & \htmlTitle{S_{12; 6}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{12; 7}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{12; 8}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{12; 9}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{12; 10}}{3 \zeta_{80}^{28} + \zeta_{80}^{24} - 2 \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 4 \zeta_{80}^{4} - 3} & \htmlTitle{S_{12; 11}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{12; 12}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & & & & \\ \htmlTitle{S_{13; 1}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{13; 2}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{13; 3}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{16} + \zeta_{80}^{12} + 1} & \htmlTitle{S_{13; 4}}{2 \zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{13; 5}}{2 \zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{13; 6}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{13; 7}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{13; 8}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{13; 9}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{13; 10}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - \zeta_{80}^{20} - 2 \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 1} & \htmlTitle{S_{13; 11}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 1} & \htmlTitle{S_{13; 12}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 1} & \htmlTitle{S_{13; 13}}{1} & & & \\ \htmlTitle{S_{14; 1}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{14; 2}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{14; 3}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{16} - \zeta_{80}^{12} - 1} & \htmlTitle{S_{14; 4}}{2 \zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{14; 5}}{2 \zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{14; 6}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{14; 7}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{14; 8}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 2 \zeta_{80}^{4} + 2} & \htmlTitle{S_{14; 9}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 2} & \htmlTitle{S_{14; 10}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 1} & \htmlTitle{S_{14; 11}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 1} & \htmlTitle{S_{14; 12}}{\zeta_{80}^{28} - \zeta_{80}^{20} + \zeta_{80}^{12} - 2 \zeta_{80}^{4} - 1} & \htmlTitle{S_{14; 13}}{1} & \htmlTitle{S_{14; 14}}{1} & & \\ \htmlTitle{S_{15; 1}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 3} & \htmlTitle{S_{15; 2}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - \zeta_{80}^{20} - 2 \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 3} & \htmlTitle{S_{15; 3}}{0} & \htmlTitle{S_{15; 4}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{16} - \zeta_{80}^{12} - 1} & \htmlTitle{S_{15; 5}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{16} + \zeta_{80}^{12} + 1} & \htmlTitle{S_{15; 6}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - 2 \zeta_{80}^{20} - 2 \zeta_{80}^{16} + 2 \zeta_{80}^{12} - 4 \zeta_{80}^{4} - 4} & \htmlTitle{S_{15; 7}}{0} & \htmlTitle{S_{15; 8}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + 2 \zeta_{80}^{20} + 2 \zeta_{80}^{16} - 2 \zeta_{80}^{12} + 4 \zeta_{80}^{4} + 4} & \htmlTitle{S_{15; 9}}{0} & \htmlTitle{S_{15; 10}}{0} & \htmlTitle{S_{15; 11}}{\zeta_{80}^{28} + \zeta_{80}^{24} - \zeta_{80}^{16} - \zeta_{80}^{12} - 1} & \htmlTitle{S_{15; 12}}{-\zeta_{80}^{28} - \zeta_{80}^{24} + \zeta_{80}^{16} + \zeta_{80}^{12} + 1} & \htmlTitle{S_{15; 13}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 3} & \htmlTitle{S_{15; 14}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - \zeta_{80}^{20} - 2 \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 3} & \htmlTitle{S_{15; 15}}{0} & \\ \htmlTitle{S_{16; 1}}{-3 \zeta_{80}^{28} - \zeta_{80}^{24} + 2 \zeta_{80}^{20} + \zeta_{80}^{16} - \zeta_{80}^{12} + 4 \zeta_{80}^{4} + 3} & \htmlTitle{S_{16; 2}}{3 \zeta_{80}^{28} + \zeta_{80}^{24} - 2 \zeta_{80}^{20} - \zeta_{80}^{16} + \zeta_{80}^{12} - 4 \zeta_{80}^{4} - 3} & \htmlTitle{S_{16; 3}}{0} & \htmlTitle{S_{16; 4}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 1} & \htmlTitle{S_{16; 5}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - \zeta_{80}^{20} - 2 \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 1} & \htmlTitle{S_{16; 6}}{0} & \htmlTitle{S_{16; 7}}{0} & \htmlTitle{S_{16; 8}}{0} & \htmlTitle{S_{16; 9}}{0} & \htmlTitle{S_{16; 10}}{0} & \htmlTitle{S_{16; 11}}{2 \zeta_{80}^{28} + 2 \zeta_{80}^{24} - \zeta_{80}^{20} - 2 \zeta_{80}^{16} - 2 \zeta_{80}^{4} - 1} & \htmlTitle{S_{16; 12}}{-2 \zeta_{80}^{28} - 2 \zeta_{80}^{24} + \zeta_{80}^{20} + 2 \zeta_{80}^{16} + 2 \zeta_{80}^{4} + 1} & \htmlTitle{S_{16; 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Central Charge
\[c = \frac{54}{5} \]