Fusion Ring
\[ \begin{array}{llllllllllllllllllllllll} \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} & & & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{2} & \htmlTitle{4\otimes 4}{1} & & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{8} & \htmlTitle{5\otimes 3}{15} & \htmlTitle{5\otimes 4}{16} & \htmlTitle{5\otimes 5}{1 \oplus 17 \oplus 8} & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{12} & \htmlTitle{6\otimes 3}{9} & \htmlTitle{6\otimes 4}{14} & \htmlTitle{6\otimes 5}{7 \oplus 21} & \htmlTitle{6\otimes 6}{1 \oplus 17 \oplus 9} & & & & & & & & & & & & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{11} & \htmlTitle{7\otimes 3}{13} & \htmlTitle{7\otimes 4}{10} & \htmlTitle{7\otimes 5}{6 \oplus 22} & \htmlTitle{7\otimes 6}{5 \oplus 23} & \htmlTitle{7\otimes 7}{1 \oplus 17 \oplus 10} & & & & & & & & & & & & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{5} & \htmlTitle{8\otimes 3}{16} & \htmlTitle{8\otimes 4}{15} & \htmlTitle{8\otimes 5}{5 \oplus 18 \oplus 2} & \htmlTitle{8\otimes 6}{22 \oplus 11} & \htmlTitle{8\otimes 7}{21 \oplus 12} & \htmlTitle{8\otimes 8}{1 \oplus 17 \oplus 8} & & & & & & & & & & & & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{14} & \htmlTitle{9\otimes 3}{6} & \htmlTitle{9\otimes 4}{12} & \htmlTitle{9\otimes 5}{23 \oplus 13} & \htmlTitle{9\otimes 6}{6 \oplus 19 \oplus 3} & \htmlTitle{9\otimes 7}{21 \oplus 15} & \htmlTitle{9\otimes 8}{10 \oplus 24} & \htmlTitle{9\otimes 9}{1 \oplus 17 \oplus 9} & & & & & & & & & & & & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{13} & \htmlTitle{10\otimes 3}{11} & \htmlTitle{10\otimes 4}{7} & \htmlTitle{10\otimes 5}{23 \oplus 14} & \htmlTitle{10\otimes 6}{22 \oplus 16} & \htmlTitle{10\otimes 7}{7 \oplus 20 \oplus 4} & \htmlTitle{10\otimes 8}{9 \oplus 24} & \htmlTitle{10\otimes 9}{8 \oplus 24} & \htmlTitle{10\otimes 10}{1 \oplus 17 \oplus 10} & & & & & & & & & & & & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{7} & \htmlTitle{11\otimes 3}{10} & \htmlTitle{11\otimes 4}{13} & \htmlTitle{11\otimes 5}{21 \oplus 12} & \htmlTitle{11\otimes 6}{8 \oplus 24} & \htmlTitle{11\otimes 7}{18 \oplus 13 \oplus 2} & \htmlTitle{11\otimes 8}{6 \oplus 22} & \htmlTitle{11\otimes 9}{22 \oplus 16} & \htmlTitle{11\otimes 10}{19 \oplus 3 \oplus 11} & \htmlTitle{11\otimes 11}{1 \oplus 17 \oplus 10} & & & & & & & & & & & & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{6} & \htmlTitle{12\otimes 3}{14} & \htmlTitle{12\otimes 4}{9} & \htmlTitle{12\otimes 5}{22 \oplus 11} & \htmlTitle{12\otimes 6}{18 \oplus 14 \oplus 2} & \htmlTitle{12\otimes 7}{8 \oplus 24} & \htmlTitle{12\otimes 8}{7 \oplus 21} & \htmlTitle{12\otimes 9}{20 \oplus 4 \oplus 12} & \htmlTitle{12\otimes 10}{21 \oplus 15} & \htmlTitle{12\otimes 11}{5 \oplus 23} & \htmlTitle{12\otimes 12}{1 \oplus 17 \oplus 9} & & & & & & & & & & & & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{10} & \htmlTitle{13\otimes 3}{7} & \htmlTitle{13\otimes 4}{11} & \htmlTitle{13\otimes 5}{9 \oplus 24} & \htmlTitle{13\otimes 6}{21 \oplus 15} & \htmlTitle{13\otimes 7}{19 \oplus 3 \oplus 11} & \htmlTitle{13\otimes 8}{23 \oplus 14} & \htmlTitle{13\otimes 9}{5 \oplus 23} & \htmlTitle{13\otimes 10}{18 \oplus 13 \oplus 2} & \htmlTitle{13\otimes 11}{7 \oplus 20 \oplus 4} & \htmlTitle{13\otimes 12}{22 \oplus 16} & \htmlTitle{13\otimes 13}{1 \oplus 17 \oplus 10} & & & & & & & & & & & \\ \htmlTitle{14\otimes 1}{14} & \htmlTitle{14\otimes 2}{9} & \htmlTitle{14\otimes 3}{12} & \htmlTitle{14\otimes 4}{6} & \htmlTitle{14\otimes 5}{10 \oplus 24} & \htmlTitle{14\otimes 6}{20 \oplus 4 \oplus 12} & \htmlTitle{14\otimes 7}{22 \oplus 16} & \htmlTitle{14\otimes 8}{23 \oplus 13} & \htmlTitle{14\otimes 9}{18 \oplus 14 \oplus 2} & \htmlTitle{14\otimes 10}{5 \oplus 23} & \htmlTitle{14\otimes 11}{21 \oplus 15} & \htmlTitle{14\otimes 12}{6 \oplus 19 \oplus 3} & \htmlTitle{14\otimes 13}{8 \oplus 24} & \htmlTitle{14\otimes 14}{1 \oplus 17 \oplus 9} & & & & & & & & & & \\ \htmlTitle{15\otimes 1}{15} & \htmlTitle{15\otimes 2}{16} & \htmlTitle{15\otimes 3}{5} & \htmlTitle{15\otimes 4}{8} & \htmlTitle{15\otimes 5}{19 \oplus 3 \oplus 16} & \htmlTitle{15\otimes 6}{23 \oplus 13} & \htmlTitle{15\otimes 7}{9 \oplus 24} & \htmlTitle{15\otimes 8}{20 \oplus 15 \oplus 4} & \htmlTitle{15\otimes 9}{7 \oplus 21} & \htmlTitle{15\otimes 10}{21 \oplus 12} & \htmlTitle{15\otimes 11}{23 \oplus 14} & \htmlTitle{15\otimes 12}{10 \oplus 24} & \htmlTitle{15\otimes 13}{6 \oplus 22} & \htmlTitle{15\otimes 14}{22 \oplus 11} & \htmlTitle{15\otimes 15}{1 \oplus 17 \oplus 8} & & & & & & & & & \\ \htmlTitle{16\otimes 1}{16} & \htmlTitle{16\otimes 2}{15} & \htmlTitle{16\otimes 3}{8} & \htmlTitle{16\otimes 4}{5} & \htmlTitle{16\otimes 5}{20 \oplus 15 \oplus 4} & \htmlTitle{16\otimes 6}{10 \oplus 24} & \htmlTitle{16\otimes 7}{23 \oplus 14} & \htmlTitle{16\otimes 8}{19 \oplus 3 \oplus 16} & \htmlTitle{16\otimes 9}{22 \oplus 11} & \htmlTitle{16\otimes 10}{6 \oplus 22} & \htmlTitle{16\otimes 11}{9 \oplus 24} & \htmlTitle{16\otimes 12}{23 \oplus 13} & \htmlTitle{16\otimes 13}{21 \oplus 12} & \htmlTitle{16\otimes 14}{7 \oplus 21} & \htmlTitle{16\otimes 15}{5 \oplus 18 \oplus 2} & \htmlTitle{16\otimes 16}{1 \oplus 17 \oplus 8} & & & & & & & & \\ \htmlTitle{17\otimes 1}{17} & \htmlTitle{17\otimes 2}{18} & \htmlTitle{17\otimes 3}{19} & \htmlTitle{17\otimes 4}{20} & \htmlTitle{17\otimes 5}{5 \oplus 23 \oplus 18} & \htmlTitle{17\otimes 6}{6 \oplus 22 \oplus 19} & \htmlTitle{17\otimes 7}{7 \oplus 21 \oplus 20} & \htmlTitle{17\otimes 8}{17 \oplus 8 \oplus 24} & \htmlTitle{17\otimes 9}{17 \oplus 9 \oplus 24} & \htmlTitle{17\otimes 10}{17 \oplus 10 \oplus 24} & \htmlTitle{17\otimes 11}{22 \oplus 19 \oplus 11} & \htmlTitle{17\otimes 12}{21 \oplus 20 \oplus 12} & \htmlTitle{17\otimes 13}{23 \oplus 18 \oplus 13} & \htmlTitle{17\otimes 14}{23 \oplus 18 \oplus 14} & \htmlTitle{17\otimes 15}{21 \oplus 20 \oplus 15} & \htmlTitle{17\otimes 16}{22 \oplus 19 \oplus 16} & \htmlTitle{17\otimes 17}{1 \oplus 17 \oplus 9 \oplus 10 \oplus 8 \oplus 24} & & & & & & & \\ \htmlTitle{18\otimes 1}{18} & \htmlTitle{18\otimes 2}{17} & \htmlTitle{18\otimes 3}{20} & \htmlTitle{18\otimes 4}{19} & \htmlTitle{18\otimes 5}{17 \oplus 8 \oplus 24} & \htmlTitle{18\otimes 6}{21 \oplus 20 \oplus 12} & \htmlTitle{18\otimes 7}{22 \oplus 19 \oplus 11} & \htmlTitle{18\otimes 8}{5 \oplus 23 \oplus 18} & \htmlTitle{18\otimes 9}{23 \oplus 18 \oplus 14} & \htmlTitle{18\otimes 10}{23 \oplus 18 \oplus 13} & \htmlTitle{18\otimes 11}{7 \oplus 21 \oplus 20} & \htmlTitle{18\otimes 12}{6 \oplus 22 \oplus 19} & \htmlTitle{18\otimes 13}{17 \oplus 10 \oplus 24} & \htmlTitle{18\otimes 14}{17 \oplus 9 \oplus 24} & \htmlTitle{18\otimes 15}{22 \oplus 19 \oplus 16} & \htmlTitle{18\otimes 16}{21 \oplus 20 \oplus 15} & \htmlTitle{18\otimes 17}{5 \oplus 23 \oplus 18 \oplus 13 \oplus 14 \oplus 2} & \htmlTitle{18\otimes 18}{1 \oplus 17 \oplus 9 \oplus 10 \oplus 8 \oplus 24} & & & & & & \\ \htmlTitle{19\otimes 1}{19} & \htmlTitle{19\otimes 2}{20} & \htmlTitle{19\otimes 3}{17} & \htmlTitle{19\otimes 4}{18} & \htmlTitle{19\otimes 5}{21 \oplus 20 \oplus 15} & \htmlTitle{19\otimes 6}{17 \oplus 9 \oplus 24} & \htmlTitle{19\otimes 7}{23 \oplus 18 \oplus 13} & \htmlTitle{19\otimes 8}{22 \oplus 19 \oplus 16} & \htmlTitle{19\otimes 9}{6 \oplus 22 \oplus 19} & \htmlTitle{19\otimes 10}{22 \oplus 19 \oplus 11} & \htmlTitle{19\otimes 11}{17 \oplus 10 \oplus 24} & \htmlTitle{19\otimes 12}{23 \oplus 18 \oplus 14} & \htmlTitle{19\otimes 13}{7 \oplus 21 \oplus 20} & \htmlTitle{19\otimes 14}{21 \oplus 20 \oplus 12} & \htmlTitle{19\otimes 15}{5 \oplus 23 \oplus 18} & \htmlTitle{19\otimes 16}{17 \oplus 8 \oplus 24} & \htmlTitle{19\otimes 17}{6 \oplus 22 \oplus 19 \oplus 3 \oplus 16 \oplus 11} & \htmlTitle{19\otimes 18}{7 \oplus 21 \oplus 20 \oplus 15 \oplus 4 \oplus 12} & \htmlTitle{19\otimes 19}{1 \oplus 17 \oplus 9 \oplus 10 \oplus 8 \oplus 24} & & & & & \\ \htmlTitle{20\otimes 1}{20} & \htmlTitle{20\otimes 2}{19} & \htmlTitle{20\otimes 3}{18} & \htmlTitle{20\otimes 4}{17} & \htmlTitle{20\otimes 5}{22 \oplus 19 \oplus 16} & \htmlTitle{20\otimes 6}{23 \oplus 18 \oplus 14} & \htmlTitle{20\otimes 7}{17 \oplus 10 \oplus 24} & \htmlTitle{20\otimes 8}{21 \oplus 20 \oplus 15} & \htmlTitle{20\otimes 9}{21 \oplus 20 \oplus 12} & \htmlTitle{20\otimes 10}{7 \oplus 21 \oplus 20} & \htmlTitle{20\otimes 11}{23 \oplus 18 \oplus 13} & \htmlTitle{20\otimes 12}{17 \oplus 9 \oplus 24} & \htmlTitle{20\otimes 13}{22 \oplus 19 \oplus 11} & \htmlTitle{20\otimes 14}{6 \oplus 22 \oplus 19} & \htmlTitle{20\otimes 15}{17 \oplus 8 \oplus 24} & \htmlTitle{20\otimes 16}{5 \oplus 23 \oplus 18} & \htmlTitle{20\otimes 17}{7 \oplus 21 \oplus 20 \oplus 15 \oplus 4 \oplus 12} & \htmlTitle{20\otimes 18}{6 \oplus 22 \oplus 19 \oplus 3 \oplus 16 \oplus 11} & \htmlTitle{20\otimes 19}{5 \oplus 23 \oplus 18 \oplus 13 \oplus 14 \oplus 2} & \htmlTitle{20\otimes 20}{1 \oplus 17 \oplus 9 \oplus 10 \oplus 8 \oplus 24} & & & & \\ \htmlTitle{21\otimes 1}{21} & \htmlTitle{21\otimes 2}{22} & \htmlTitle{21\otimes 3}{23} & \htmlTitle{21\otimes 4}{24} & \htmlTitle{21\otimes 5}{6 \oplus 22 \oplus 19 \oplus 11} & \htmlTitle{21\otimes 6}{5 \oplus 23 \oplus 18 \oplus 13} & \htmlTitle{21\otimes 7}{17 \oplus 9 \oplus 8 \oplus 24} & \htmlTitle{21\otimes 8}{7 \oplus 21 \oplus 20 \oplus 12} & \htmlTitle{21\otimes 9}{7 \oplus 21 \oplus 20 \oplus 15} & \htmlTitle{21\otimes 10}{21 \oplus 20 \oplus 15 \oplus 12} & \htmlTitle{21\otimes 11}{5 \oplus 23 \oplus 18 \oplus 14} & \htmlTitle{21\otimes 12}{17 \oplus 10 \oplus 8 \oplus 24} & \htmlTitle{21\otimes 13}{6 \oplus 22 \oplus 19 \oplus 16} & \htmlTitle{21\otimes 14}{22 \oplus 19 \oplus 16 \oplus 11} & \htmlTitle{21\otimes 15}{17 \oplus 9 \oplus 10 \oplus 24} & \htmlTitle{21\otimes 16}{23 \oplus 18 \oplus 13 \oplus 14} & \htmlTitle{21\otimes 17}{7 \oplus 2\cdot21 \oplus 20 \oplus 15 \oplus 12} & \htmlTitle{21\otimes 18}{6 \oplus 2\cdot22 \oplus 19 \oplus 16 \oplus 11} & \htmlTitle{21\otimes 19}{5 \oplus 2\cdot23 \oplus 18 \oplus 13 \oplus 14} & \htmlTitle{21\otimes 20}{17 \oplus 9 \oplus 10 \oplus 8 \oplus 2\cdot24} & \htmlTitle{21\otimes 21}{1 \oplus 2\cdot17 \oplus 9 \oplus 10 \oplus 8 \oplus 2\cdot24} & & & \\ \htmlTitle{22\otimes 1}{22} & \htmlTitle{22\otimes 2}{21} & \htmlTitle{22\otimes 3}{24} & \htmlTitle{22\otimes 4}{23} & \htmlTitle{22\otimes 5}{7 \oplus 21 \oplus 20 \oplus 12} & \htmlTitle{22\otimes 6}{17 \oplus 10 \oplus 8 \oplus 24} & \htmlTitle{22\otimes 7}{5 \oplus 23 \oplus 18 \oplus 14} & \htmlTitle{22\otimes 8}{6 \oplus 22 \oplus 19 \oplus 11} & \htmlTitle{22\otimes 9}{22 \oplus 19 \oplus 16 \oplus 11} & \htmlTitle{22\otimes 10}{6 \oplus 22 \oplus 19 \oplus 16} & \htmlTitle{22\otimes 11}{17 \oplus 9 \oplus 8 \oplus 24} & \htmlTitle{22\otimes 12}{5 \oplus 23 \oplus 18 \oplus 13} & \htmlTitle{22\otimes 13}{21 \oplus 20 \oplus 15 \oplus 12} & \htmlTitle{22\otimes 14}{7 \oplus 21 \oplus 20 \oplus 15} & \htmlTitle{22\otimes 15}{23 \oplus 18 \oplus 13 \oplus 14} & \htmlTitle{22\otimes 16}{17 \oplus 9 \oplus 10 \oplus 24} & \htmlTitle{22\otimes 17}{6 \oplus 2\cdot22 \oplus 19 \oplus 16 \oplus 11} & \htmlTitle{22\otimes 18}{7 \oplus 2\cdot21 \oplus 20 \oplus 15 \oplus 12} & \htmlTitle{22\otimes 19}{17 \oplus 9 \oplus 10 \oplus 8 \oplus 2\cdot24} & \htmlTitle{22\otimes 20}{5 \oplus 2\cdot23 \oplus 18 \oplus 13 \oplus 14} & \htmlTitle{22\otimes 21}{5 \oplus 2\cdot23 \oplus 2\cdot18 \oplus 13 \oplus 14 \oplus 2} & \htmlTitle{22\otimes 22}{1 \oplus 2\cdot17 \oplus 9 \oplus 10 \oplus 8 \oplus 2\cdot24} & & \\ \htmlTitle{23\otimes 1}{23} & \htmlTitle{23\otimes 2}{24} & \htmlTitle{23\otimes 3}{21} & \htmlTitle{23\otimes 4}{22} & \htmlTitle{23\otimes 5}{17 \oplus 9 \oplus 10 \oplus 24} & \htmlTitle{23\otimes 6}{7 \oplus 21 \oplus 20 \oplus 15} & \htmlTitle{23\otimes 7}{6 \oplus 22 \oplus 19 \oplus 16} & \htmlTitle{23\otimes 8}{23 \oplus 18 \oplus 13 \oplus 14} & \htmlTitle{23\otimes 9}{5 \oplus 23 \oplus 18 \oplus 13} & \htmlTitle{23\otimes 10}{5 \oplus 23 \oplus 18 \oplus 14} & \htmlTitle{23\otimes 11}{21 \oplus 20 \oplus 15 \oplus 12} & \htmlTitle{23\otimes 12}{22 \oplus 19 \oplus 16 \oplus 11} & \htmlTitle{23\otimes 13}{17 \oplus 9 \oplus 8 \oplus 24} & \htmlTitle{23\otimes 14}{17 \oplus 10 \oplus 8 \oplus 24} & \htmlTitle{23\otimes 15}{6 \oplus 22 \oplus 19 \oplus 11} & \htmlTitle{23\otimes 16}{7 \oplus 21 \oplus 20 \oplus 12} & \htmlTitle{23\otimes 17}{5 \oplus 2\cdot23 \oplus 18 \oplus 13 \oplus 14} & \htmlTitle{23\otimes 18}{17 \oplus 9 \oplus 10 \oplus 8 \oplus 2\cdot24} & \htmlTitle{23\otimes 19}{7 \oplus 2\cdot21 \oplus 20 \oplus 15 \oplus 12} & \htmlTitle{23\otimes 20}{6 \oplus 2\cdot22 \oplus 19 \oplus 16 \oplus 11} & \htmlTitle{23\otimes 21}{6 \oplus 2\cdot22 \oplus 2\cdot19 \oplus 3 \oplus 16 \oplus 11} & \htmlTitle{23\otimes 22}{7 \oplus 2\cdot21 \oplus 2\cdot20 \oplus 15 \oplus 4 \oplus 12} & \htmlTitle{23\otimes 23}{1 \oplus 2\cdot17 \oplus 9 \oplus 10 \oplus 8 \oplus 2\cdot24} & \\ \htmlTitle{24\otimes 1}{24} & \htmlTitle{24\otimes 2}{23} & \htmlTitle{24\otimes 3}{22} & \htmlTitle{24\otimes 4}{21} & \htmlTitle{24\otimes 5}{23 \oplus 18 \oplus 13 \oplus 14} & \htmlTitle{24\otimes 6}{22 \oplus 19 \oplus 16 \oplus 11} & \htmlTitle{24\otimes 7}{21 \oplus 20 \oplus 15 \oplus 12} & \htmlTitle{24\otimes 8}{17 \oplus 9 \oplus 10 \oplus 24} & \htmlTitle{24\otimes 9}{17 \oplus 10 \oplus 8 \oplus 24} & \htmlTitle{24\otimes 10}{17 \oplus 9 \oplus 8 \oplus 24} & \htmlTitle{24\otimes 11}{6 \oplus 22 \oplus 19 \oplus 16} & \htmlTitle{24\otimes 12}{7 \oplus 21 \oplus 20 \oplus 15} & \htmlTitle{24\otimes 13}{5 \oplus 23 \oplus 18 \oplus 14} & \htmlTitle{24\otimes 14}{5 \oplus 23 \oplus 18 \oplus 13} & \htmlTitle{24\otimes 15}{7 \oplus 21 \oplus 20 \oplus 12} & \htmlTitle{24\otimes 16}{6 \oplus 22 \oplus 19 \oplus 11} & \htmlTitle{24\otimes 17}{17 \oplus 9 \oplus 10 \oplus 8 \oplus 2\cdot24} & \htmlTitle{24\otimes 18}{5 \oplus 2\cdot23 \oplus 18 \oplus 13 \oplus 14} & \htmlTitle{24\otimes 19}{6 \oplus 2\cdot22 \oplus 19 \oplus 16 \oplus 11} & \htmlTitle{24\otimes 20}{7 \oplus 2\cdot21 \oplus 20 \oplus 15 \oplus 12} & \htmlTitle{24\otimes 21}{7 \oplus 2\cdot21 \oplus 2\cdot20 \oplus 15 \oplus 4 \oplus 12} & \htmlTitle{24\otimes 22}{6 \oplus 2\cdot22 \oplus 2\cdot19 \oplus 3 \oplus 16 \oplus 11} & \htmlTitle{24\otimes 23}{5 \oplus 2\cdot23 \oplus 2\cdot18 \oplus 13 \oplus 14 \oplus 2} & \htmlTitle{24\otimes 24}{1 \oplus 2\cdot17 \oplus 9 \oplus 10 \oplus 8 \oplus 2\cdot24} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.000\) | \( 1 \) |
| \( 4\) | \(1.000\) | \( 1 \) |
| \( 5\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 6\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 7\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 8\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 9\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 10\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 11\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 12\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 13\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 14\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 15\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 16\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 17\) | \(4.411\) | \( 1 + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} \) |
| \( 18\) | \(4.411\) | \( 1 + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} \) |
| \( 19\) | \(4.411\) | \( 1 + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} \) |
| \( 20\) | \(4.411\) | \( 1 + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} \) |
| \( 21\) | \(5.411\) | \( 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \) |
| \( 22\) | \(5.411\) | \( 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \) |
| \( 23\) | \(5.411\) | \( 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \) |
| \( 24\) | \(5.411\) | \( 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \) |
| \( D^2\) | 298.471 | \(36 \cos{\left(\frac{4 \pi}{9} \right)} + 108 \cos{\left(\frac{2 \pi}{9} \right)} + 108 \cos{\left(\frac{\pi}{9} \right)} + 108\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{1} & \htmlTitle{\theta_{3}}{1} & \htmlTitle{\theta_{4}}{1} & \htmlTitle{\theta_{5}}{\frac{7}{9}} & \htmlTitle{\theta_{6}}{\frac{7}{9}} & \htmlTitle{\theta_{7}}{\frac{7}{9}} & \htmlTitle{\theta_{8}}{\frac{16}{9}} & \htmlTitle{\theta_{9}}{\frac{16}{9}} & \htmlTitle{\theta_{10}}{\frac{16}{9}} & \htmlTitle{\theta_{11}}{\frac{7}{9}} & \htmlTitle{\theta_{12}}{\frac{7}{9}} & \htmlTitle{\theta_{13}}{\frac{7}{9}} & \htmlTitle{\theta_{14}}{\frac{7}{9}} & \htmlTitle{\theta_{15}}{\frac{7}{9}} & \htmlTitle{\theta_{16}}{\frac{7}{9}} & \htmlTitle{\theta_{17}}{\frac{4}{3}} & \htmlTitle{\theta_{18}}{\frac{1}{3}} & \htmlTitle{\theta_{19}}{\frac{1}{3}} & \htmlTitle{\theta_{20}}{\frac{1}{3}} & \htmlTitle{\theta_{21}}{\frac{5}{3}} & \htmlTitle{\theta_{22}}{\frac{5}{3}} & \htmlTitle{\theta_{23}}{\frac{5}{3}} & \htmlTitle{\theta_{24}}{\frac{2}{3}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllllllllllllllllllllll} \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}}{1} & \htmlTitle{S_{4; 2}}{-1} & \htmlTitle{S_{4; 3}}{-1} & \htmlTitle{S_{4; 4}}{1} & & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{5; 3}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{5; 4}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{5; 5}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{6; 2}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{6; 3}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{6; 4}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{6; 5}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{6; 6}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{7; 2}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{7; 3}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{7; 4}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{7; 5}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{7; 6}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{7; 7}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{8; 2}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{8; 3}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{8; 4}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{8; 5}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{8; 6}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{8; 7}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{8; 8}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{9; 2}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{9; 3}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{9; 4}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{9; 5}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{9; 6}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{9; 7}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{9; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{9; 9}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & & & & & \\ \htmlTitle{S_{10; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{10; 2}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{10; 3}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{10; 4}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{10; 5}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{10; 6}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{10; 7}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{10; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{10; 9}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{10; 10}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & & & & \\ \htmlTitle{S_{11; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{11; 2}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{11; 3}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{11; 4}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{11; 5}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{11; 6}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{11; 7}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{11; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{11; 9}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{11; 10}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{11; 11}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & & & \\ \htmlTitle{S_{12; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{12; 2}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{12; 3}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{12; 4}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{12; 5}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{12; 6}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{12; 7}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{12; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{12; 9}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{12; 10}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{12; 11}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{12; 12}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & & \\ \htmlTitle{S_{13; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{13; 2}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{13; 3}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{13; 4}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{13; 5}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{13; 6}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{13; 7}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{13; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{13; 9}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{13; 10}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{13; 11}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{13; 12}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{13; 13}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & & \\ \htmlTitle{S_{14; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{14; 2}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{14; 3}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{14; 4}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{14; 5}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{14; 6}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{14; 7}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{14; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{14; 9}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{14; 10}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{14; 11}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{14; 12}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{14; 13}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{14; 14}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & & \\ \htmlTitle{S_{15; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{15; 2}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{15; 3}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{15; 4}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{15; 5}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{15; 6}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{15; 7}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{15; 8}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{15; 9}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{15; 10}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{15; 11}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{15; 12}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{15; 13}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{15; 14}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{15; 15}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & & \\ \htmlTitle{S_{16; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{16; 2}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{16; 3}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{16; 4}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{16; 5}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{16; 6}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{16; 7}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{16; 8}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{16; 9}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{16; 10}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{16; 11}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{16; 12}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{16; 13}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{16; 14}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{16; 15}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{16; 16}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & & & & & & & & \\ \htmlTitle{S_{17; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 2}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 3}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 4}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 5}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 6}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 7}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 8}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 9}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 10}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 11}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 12}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 13}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 14}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 15}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 16}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{17; 17}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & & & & & & & \\ \htmlTitle{S_{18; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{18; 2}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{18; 3}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 1} & \htmlTitle{S_{18; 4}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 1} & \htmlTitle{S_{18; 5}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{18; 6}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{18; 7}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{18; 8}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{18; 9}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{18; 10}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{18; 11}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{18; 12}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{18; 13}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{18; 14}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{18; 15}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{18; 16}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{18; 17}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{18; 18}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & & & & & & \\ \htmlTitle{S_{19; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{19; 2}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 1} & \htmlTitle{S_{19; 3}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{19; 4}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 1} & \htmlTitle{S_{19; 5}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{19; 6}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{19; 7}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{19; 8}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{19; 9}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{19; 10}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{19; 11}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{19; 12}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{19; 13}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{19; 14}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{19; 15}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{19; 16}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{19; 17}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{19; 18}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{19; 19}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & & & & & \\ \htmlTitle{S_{20; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{20; 2}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 1} & \htmlTitle{S_{20; 3}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 1} & \htmlTitle{S_{20; 4}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & \htmlTitle{S_{20; 5}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{20; 6}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{20; 7}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{20; 8}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{20; 9}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{20; 10}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{20; 11}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{20; 12}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{20; 13}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{20; 14}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{20; 15}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{20; 16}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{20; 17}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{20; 18}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{20; 19}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{20; 20}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & & & & \\ \htmlTitle{S_{21; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{21; 2}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{21; 3}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{21; 4}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{21; 5}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{21; 6}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{21; 7}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{21; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{21; 9}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{21; 10}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{21; 11}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{21; 12}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{21; 13}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{21; 14}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{21; 15}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{21; 16}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{21; 17}}{-1} & \htmlTitle{S_{21; 18}}{1} & \htmlTitle{S_{21; 19}}{1} & \htmlTitle{S_{21; 20}}{-1} & \htmlTitle{S_{21; 21}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & & & \\ \htmlTitle{S_{22; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{22; 2}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{22; 3}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{22; 4}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{22; 5}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{22; 6}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{22; 7}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{22; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{22; 9}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{22; 10}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{22; 11}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{22; 12}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{22; 13}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{22; 14}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{22; 15}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{22; 16}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{22; 17}}{-1} & \htmlTitle{S_{22; 18}}{1} & \htmlTitle{S_{22; 19}}{-1} & \htmlTitle{S_{22; 20}}{1} & \htmlTitle{S_{22; 21}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 1} & \htmlTitle{S_{22; 22}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 1} & & \\ \htmlTitle{S_{23; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{23; 2}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{23; 3}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{23; 4}}{\zeta_{72}^{20} + \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{23; 5}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{23; 6}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{23; 7}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{23; 8}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{23; 9}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{23; 10}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{23; 11}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{23; 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Central Charge
\[c = \frac{28}{3} \]