SO(7) 4 | VerlindeDB

\(\operatorname{SO}(7)_{4}\): \( B_{3} \) at level \(4\)

Fusion Ring

\[ \begin{array}{llllllllllllllllllllll} \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 \oplus 10 \oplus 8} & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{8 \oplus 11 \oplus 2} & \htmlTitle{4\otimes 4}{1 \oplus 10 \oplus 8} & & & & & & & & & & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5} & \htmlTitle{5\otimes 3}{16 \oplus 5} & \htmlTitle{5\otimes 4}{16 \oplus 5} & \htmlTitle{5\otimes 5}{1 \oplus 3 \oplus 8 \oplus 4 \oplus 2} & & & & & & & & & & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{7} & \htmlTitle{6\otimes 3}{6 \oplus 18} & \htmlTitle{6\otimes 4}{19 \oplus 7} & \htmlTitle{6\otimes 5}{12 \oplus 13} & \htmlTitle{6\otimes 6}{1 \oplus 3 \oplus 10 \oplus 14} & & & & & & & & & & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{6} & \htmlTitle{7\otimes 3}{19 \oplus 7} & \htmlTitle{7\otimes 4}{6 \oplus 18} & \htmlTitle{7\otimes 5}{12 \oplus 13} & \htmlTitle{7\otimes 6}{4 \oplus 11 \oplus 15 \oplus 2} & \htmlTitle{7\otimes 7}{1 \oplus 3 \oplus 10 \oplus 14} & & & & & & & & & & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{8} & \htmlTitle{8\otimes 3}{3 \oplus 17 \oplus 4} & \htmlTitle{8\otimes 4}{3 \oplus 17 \oplus 4} & \htmlTitle{8\otimes 5}{9 \oplus 16 \oplus 5} & \htmlTitle{8\otimes 6}{18 \oplus 19} & \htmlTitle{8\otimes 7}{18 \oplus 19} & \htmlTitle{8\otimes 8}{1 \oplus 10 \oplus 8 \oplus 9 \oplus 11 \oplus 2} & & & & & & & & & & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{9} & \htmlTitle{9\otimes 3}{17 \oplus 16} & \htmlTitle{9\otimes 4}{17 \oplus 16} & \htmlTitle{9\otimes 5}{8 \oplus 17 \oplus 9} & \htmlTitle{9\otimes 6}{20 \oplus 21} & \htmlTitle{9\otimes 7}{20 \oplus 21} & \htmlTitle{9\otimes 8}{8 \oplus 22 \oplus 9 \oplus 5} & \htmlTitle{9\otimes 9}{1 \oplus 14 \oplus 8 \oplus 9 \oplus 5 \oplus 15 \oplus 2} & & & & & & & & & & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{11} & \htmlTitle{10\otimes 3}{3 \oplus 14 \oplus 17} & \htmlTitle{10\otimes 4}{17 \oplus 4 \oplus 15} & \htmlTitle{10\otimes 5}{22 \oplus 16} & \htmlTitle{10\otimes 6}{6 \oplus 18 \oplus 20} & \htmlTitle{10\otimes 7}{19 \oplus 21 \oplus 7} & \htmlTitle{10\otimes 8}{10 \oplus 8 \oplus 22 \oplus 11} & \htmlTitle{10\otimes 9}{10 \oplus 22 \oplus 16 \oplus 11} & \htmlTitle{10\otimes 10}{1 \oplus 10 \oplus 14 \oplus 8 \oplus 22 \oplus 9} & & & & & & & & & & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{10} & \htmlTitle{11\otimes 3}{17 \oplus 4 \oplus 15} & \htmlTitle{11\otimes 4}{3 \oplus 14 \oplus 17} & \htmlTitle{11\otimes 5}{22 \oplus 16} & \htmlTitle{11\otimes 6}{19 \oplus 21 \oplus 7} & \htmlTitle{11\otimes 7}{6 \oplus 18 \oplus 20} & \htmlTitle{11\otimes 8}{10 \oplus 8 \oplus 22 \oplus 11} & \htmlTitle{11\otimes 9}{10 \oplus 22 \oplus 16 \oplus 11} & \htmlTitle{11\otimes 10}{8 \oplus 22 \oplus 9 \oplus 11 \oplus 15 \oplus 2} & \htmlTitle{11\otimes 11}{1 \oplus 10 \oplus 14 \oplus 8 \oplus 22 \oplus 9} & & & & & & & & & & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{13} & \htmlTitle{12\otimes 3}{20 \oplus 12 \oplus 13} & \htmlTitle{12\otimes 4}{12 \oplus 21 \oplus 13} & \htmlTitle{12\otimes 5}{6 \oplus 18 \oplus 19 \oplus 7} & \htmlTitle{12\otimes 6}{14 \oplus 22 \oplus 16 \oplus 5} & \htmlTitle{12\otimes 7}{22 \oplus 16 \oplus 5 \oplus 15} & \htmlTitle{12\otimes 8}{20 \oplus 12 \oplus 21 \oplus 13} & \htmlTitle{12\otimes 9}{18 \oplus 20 \oplus 19 \oplus 21} & \htmlTitle{12\otimes 10}{18 \oplus 20 \oplus 12 \oplus 21 \oplus 13} & \htmlTitle{12\otimes 11}{20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{12\otimes 12}{1 \oplus 3 \oplus 10 \oplus 14 \oplus 8 \oplus 17 \oplus 22 \oplus 4 \oplus 11 \oplus 15} & & & & & & & & & & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{12} & \htmlTitle{13\otimes 3}{12 \oplus 21 \oplus 13} & \htmlTitle{13\otimes 4}{20 \oplus 12 \oplus 13} & \htmlTitle{13\otimes 5}{6 \oplus 18 \oplus 19 \oplus 7} & \htmlTitle{13\otimes 6}{22 \oplus 16 \oplus 5 \oplus 15} & \htmlTitle{13\otimes 7}{14 \oplus 22 \oplus 16 \oplus 5} & \htmlTitle{13\otimes 8}{20 \oplus 12 \oplus 21 \oplus 13} & \htmlTitle{13\otimes 9}{18 \oplus 20 \oplus 19 \oplus 21} & \htmlTitle{13\otimes 10}{20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{13\otimes 11}{18 \oplus 20 \oplus 12 \oplus 21 \oplus 13} & \htmlTitle{13\otimes 12}{3 \oplus 10 \oplus 14 \oplus 8 \oplus 17 \oplus 22 \oplus 4 \oplus 11 \oplus 15 \oplus 2} & \htmlTitle{13\otimes 13}{1 \oplus 3 \oplus 10 \oplus 14 \oplus 8 \oplus 17 \oplus 22 \oplus 4 \oplus 11 \oplus 15} & & & & & & & & & \\ \htmlTitle{14\otimes 1}{14} & \htmlTitle{14\otimes 2}{15} & \htmlTitle{14\otimes 3}{10 \oplus 14 \oplus 22} & \htmlTitle{14\otimes 4}{22 \oplus 11 \oplus 15} & \htmlTitle{14\otimes 5}{14 \oplus 22 \oplus 15} & \htmlTitle{14\otimes 6}{6 \oplus 18 \oplus 20 \oplus 12} & \htmlTitle{14\otimes 7}{19 \oplus 21 \oplus 13 \oplus 7} & \htmlTitle{14\otimes 8}{14 \oplus 17 \oplus 22 \oplus 15} & \htmlTitle{14\otimes 9}{14 \oplus 17 \oplus 22 \oplus 9 \oplus 15} & \htmlTitle{14\otimes 10}{3 \oplus 10 \oplus 14 \oplus 17 \oplus 22 \oplus 16} & \htmlTitle{14\otimes 11}{17 \oplus 22 \oplus 16 \oplus 4 \oplus 11 \oplus 15} & \htmlTitle{14\otimes 12}{6 \oplus 18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{14\otimes 13}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13 \oplus 7} & \htmlTitle{14\otimes 14}{1 \oplus 3 \oplus 10 \oplus 14 \oplus 8 \oplus 17 \oplus 22 \oplus 9 \oplus 16 \oplus 5} & & & & & & & & \\ \htmlTitle{15\otimes 1}{15} & \htmlTitle{15\otimes 2}{14} & \htmlTitle{15\otimes 3}{22 \oplus 11 \oplus 15} & \htmlTitle{15\otimes 4}{10 \oplus 14 \oplus 22} & \htmlTitle{15\otimes 5}{14 \oplus 22 \oplus 15} & \htmlTitle{15\otimes 6}{19 \oplus 21 \oplus 13 \oplus 7} & \htmlTitle{15\otimes 7}{6 \oplus 18 \oplus 20 \oplus 12} & \htmlTitle{15\otimes 8}{14 \oplus 17 \oplus 22 \oplus 15} & \htmlTitle{15\otimes 9}{14 \oplus 17 \oplus 22 \oplus 9 \oplus 15} & \htmlTitle{15\otimes 10}{17 \oplus 22 \oplus 16 \oplus 4 \oplus 11 \oplus 15} & \htmlTitle{15\otimes 11}{3 \oplus 10 \oplus 14 \oplus 17 \oplus 22 \oplus 16} & \htmlTitle{15\otimes 12}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13 \oplus 7} & \htmlTitle{15\otimes 13}{6 \oplus 18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{15\otimes 14}{8 \oplus 17 \oplus 22 \oplus 9 \oplus 16 \oplus 5 \oplus 4 \oplus 11 \oplus 15 \oplus 2} & \htmlTitle{15\otimes 15}{1 \oplus 3 \oplus 10 \oplus 14 \oplus 8 \oplus 17 \oplus 22 \oplus 9 \oplus 16 \oplus 5} & & & & & & & \\ \htmlTitle{16\otimes 1}{16} & \htmlTitle{16\otimes 2}{16} & \htmlTitle{16\otimes 3}{22 \oplus 9 \oplus 16 \oplus 5} & \htmlTitle{16\otimes 4}{22 \oplus 9 \oplus 16 \oplus 5} & \htmlTitle{16\otimes 5}{3 \oplus 10 \oplus 8 \oplus 17 \oplus 4 \oplus 11} & \htmlTitle{16\otimes 6}{20 \oplus 12 \oplus 21 \oplus 13} & \htmlTitle{16\otimes 7}{20 \oplus 12 \oplus 21 \oplus 13} & \htmlTitle{16\otimes 8}{17 \oplus 22 \oplus 2\cdot16 \oplus 5} & \htmlTitle{16\otimes 9}{3 \oplus 10 \oplus 17 \oplus 22 \oplus 16 \oplus 4 \oplus 11} & \htmlTitle{16\otimes 10}{14 \oplus 17 \oplus 22 \oplus 9 \oplus 16 \oplus 5 \oplus 15} & \htmlTitle{16\otimes 11}{14 \oplus 17 \oplus 22 \oplus 9 \oplus 16 \oplus 5 \oplus 15} & \htmlTitle{16\otimes 12}{6 \oplus 2\cdot18 \oplus 20 \oplus 2\cdot19 \oplus 21 \oplus 7} & \htmlTitle{16\otimes 13}{6 \oplus 2\cdot18 \oplus 20 \oplus 2\cdot19 \oplus 21 \oplus 7} & \htmlTitle{16\otimes 14}{10 \oplus 14 \oplus 17 \oplus 2\cdot22 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{16\otimes 15}{10 \oplus 14 \oplus 17 \oplus 2\cdot22 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{16\otimes 16}{1 \oplus 3 \oplus 10 \oplus 14 \oplus 2\cdot8 \oplus 2\cdot17 \oplus 22 \oplus 9 \oplus 4 \oplus 11 \oplus 15 \oplus 2} & & & & & & \\ \htmlTitle{17\otimes 1}{17} & \htmlTitle{17\otimes 2}{17} & \htmlTitle{17\otimes 3}{10 \oplus 8 \oplus 22 \oplus 9 \oplus 11} & \htmlTitle{17\otimes 4}{10 \oplus 8 \oplus 22 \oplus 9 \oplus 11} & \htmlTitle{17\otimes 5}{17 \oplus 22 \oplus 9 \oplus 16} & \htmlTitle{17\otimes 6}{18 \oplus 20 \oplus 19 \oplus 21} & \htmlTitle{17\otimes 7}{18 \oplus 20 \oplus 19 \oplus 21} & \htmlTitle{17\otimes 8}{3 \oplus 14 \oplus 2\cdot17 \oplus 16 \oplus 4 \oplus 15} & \htmlTitle{17\otimes 9}{3 \oplus 14 \oplus 17 \oplus 22 \oplus 16 \oplus 5 \oplus 4 \oplus 15} & \htmlTitle{17\otimes 10}{3 \oplus 14 \oplus 2\cdot17 \oplus 22 \oplus 16 \oplus 4 \oplus 15} & \htmlTitle{17\otimes 11}{3 \oplus 14 \oplus 2\cdot17 \oplus 22 \oplus 16 \oplus 4 \oplus 15} & \htmlTitle{17\otimes 12}{18 \oplus 2\cdot20 \oplus 12 \oplus 19 \oplus 2\cdot21 \oplus 13} & \htmlTitle{17\otimes 13}{18 \oplus 2\cdot20 \oplus 12 \oplus 19 \oplus 2\cdot21 \oplus 13} & \htmlTitle{17\otimes 14}{10 \oplus 14 \oplus 8 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{17\otimes 15}{10 \oplus 14 \oplus 8 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{17\otimes 16}{10 \oplus 14 \oplus 8 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 11 \oplus 15} & \htmlTitle{17\otimes 17}{1 \oplus 2\cdot10 \oplus 14 \oplus 2\cdot8 \oplus 3\cdot22 \oplus 9 \oplus 16 \oplus 5 \oplus 2\cdot11 \oplus 15 \oplus 2} & & & & & \\ \htmlTitle{18\otimes 1}{18} & \htmlTitle{18\otimes 2}{19} & \htmlTitle{18\otimes 3}{6 \oplus 18 \oplus 20 \oplus 19} & \htmlTitle{18\otimes 4}{18 \oplus 19 \oplus 21 \oplus 7} & \htmlTitle{18\otimes 5}{20 \oplus 12 \oplus 21 \oplus 13} & \htmlTitle{18\otimes 6}{3 \oplus 10 \oplus 14 \oplus 8 \oplus 17 \oplus 22} & \htmlTitle{18\otimes 7}{8 \oplus 17 \oplus 22 \oplus 4 \oplus 11 \oplus 15} & \htmlTitle{18\otimes 8}{6 \oplus 18 \oplus 20 \oplus 19 \oplus 21 \oplus 7} & \htmlTitle{18\otimes 9}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{18\otimes 10}{6 \oplus 2\cdot18 \oplus 20 \oplus 12 \oplus 19 \oplus 21} & \htmlTitle{18\otimes 11}{18 \oplus 20 \oplus 2\cdot19 \oplus 21 \oplus 13 \oplus 7} & \htmlTitle{18\otimes 12}{10 \oplus 14 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 15} & \htmlTitle{18\otimes 13}{14 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 11 \oplus 15} & \htmlTitle{18\otimes 14}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{18\otimes 15}{18 \oplus 20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{18\otimes 16}{18 \oplus 2\cdot20 \oplus 2\cdot12 \oplus 19 \oplus 2\cdot21 \oplus 2\cdot13} & \htmlTitle{18\otimes 17}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{18\otimes 18}{1 \oplus 3 \oplus 2\cdot10 \oplus 2\cdot14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 4 \oplus 11 \oplus 15} & & & & \\ \htmlTitle{19\otimes 1}{19} & \htmlTitle{19\otimes 2}{18} & \htmlTitle{19\otimes 3}{18 \oplus 19 \oplus 21 \oplus 7} & \htmlTitle{19\otimes 4}{6 \oplus 18 \oplus 20 \oplus 19} & \htmlTitle{19\otimes 5}{20 \oplus 12 \oplus 21 \oplus 13} & \htmlTitle{19\otimes 6}{8 \oplus 17 \oplus 22 \oplus 4 \oplus 11 \oplus 15} & \htmlTitle{19\otimes 7}{3 \oplus 10 \oplus 14 \oplus 8 \oplus 17 \oplus 22} & \htmlTitle{19\otimes 8}{6 \oplus 18 \oplus 20 \oplus 19 \oplus 21 \oplus 7} & \htmlTitle{19\otimes 9}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{19\otimes 10}{18 \oplus 20 \oplus 2\cdot19 \oplus 21 \oplus 13 \oplus 7} & \htmlTitle{19\otimes 11}{6 \oplus 2\cdot18 \oplus 20 \oplus 12 \oplus 19 \oplus 21} & \htmlTitle{19\otimes 12}{14 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 11 \oplus 15} & \htmlTitle{19\otimes 13}{10 \oplus 14 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 15} & \htmlTitle{19\otimes 14}{18 \oplus 20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{19\otimes 15}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{19\otimes 16}{18 \oplus 2\cdot20 \oplus 2\cdot12 \oplus 19 \oplus 2\cdot21 \oplus 2\cdot13} & \htmlTitle{19\otimes 17}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{19\otimes 18}{3 \oplus 10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 4 \oplus 2\cdot11 \oplus 2\cdot15 \oplus 2} & \htmlTitle{19\otimes 19}{1 \oplus 3 \oplus 2\cdot10 \oplus 2\cdot14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 4 \oplus 11 \oplus 15} & & & \\ \htmlTitle{20\otimes 1}{20} & \htmlTitle{20\otimes 2}{21} & \htmlTitle{20\otimes 3}{18 \oplus 20 \oplus 12 \oplus 21} & \htmlTitle{20\otimes 4}{20 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{20\otimes 5}{18 \oplus 20 \oplus 19 \oplus 21} & \htmlTitle{20\otimes 6}{10 \oplus 14 \oplus 17 \oplus 22 \oplus 9 \oplus 16} & \htmlTitle{20\otimes 7}{17 \oplus 22 \oplus 9 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{20\otimes 8}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{20\otimes 9}{6 \oplus 18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13 \oplus 7} & \htmlTitle{20\otimes 10}{6 \oplus 18 \oplus 2\cdot20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{20\otimes 11}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{20\otimes 12}{3 \oplus 10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{20\otimes 13}{10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 4 \oplus 11 \oplus 15} & \htmlTitle{20\otimes 14}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 19 \oplus 2\cdot21 \oplus 13} & \htmlTitle{20\otimes 15}{18 \oplus 2\cdot20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{20\otimes 16}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{20\otimes 17}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 2\cdot12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 2\cdot13 \oplus 7} & \htmlTitle{20\otimes 18}{3 \oplus 10 \oplus 2\cdot14 \oplus 8 \oplus 2\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 11 \oplus 15} & \htmlTitle{20\otimes 19}{10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 4 \oplus 11 \oplus 2\cdot15} & \htmlTitle{20\otimes 20}{1 \oplus 3 \oplus 2\cdot10 \oplus 2\cdot14 \oplus 8 \oplus 2\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 4 \oplus 11 \oplus 2\cdot15} & & \\ \htmlTitle{21\otimes 1}{21} & \htmlTitle{21\otimes 2}{20} & \htmlTitle{21\otimes 3}{20 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{21\otimes 4}{18 \oplus 20 \oplus 12 \oplus 21} & \htmlTitle{21\otimes 5}{18 \oplus 20 \oplus 19 \oplus 21} & \htmlTitle{21\otimes 6}{17 \oplus 22 \oplus 9 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{21\otimes 7}{10 \oplus 14 \oplus 17 \oplus 22 \oplus 9 \oplus 16} & \htmlTitle{21\otimes 8}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{21\otimes 9}{6 \oplus 18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13 \oplus 7} & \htmlTitle{21\otimes 10}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{21\otimes 11}{6 \oplus 18 \oplus 2\cdot20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{21\otimes 12}{10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 4 \oplus 11 \oplus 15} & \htmlTitle{21\otimes 13}{3 \oplus 10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{21\otimes 14}{18 \oplus 2\cdot20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{21\otimes 15}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 19 \oplus 2\cdot21 \oplus 13} & \htmlTitle{21\otimes 16}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{21\otimes 17}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 2\cdot12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 2\cdot13 \oplus 7} & \htmlTitle{21\otimes 18}{10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 4 \oplus 11 \oplus 2\cdot15} & \htmlTitle{21\otimes 19}{3 \oplus 10 \oplus 2\cdot14 \oplus 8 \oplus 2\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 11 \oplus 15} & \htmlTitle{21\otimes 20}{3 \oplus 10 \oplus 2\cdot14 \oplus 8 \oplus 2\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 4 \oplus 2\cdot11 \oplus 2\cdot15 \oplus 2} & \htmlTitle{21\otimes 21}{1 \oplus 3 \oplus 2\cdot10 \oplus 2\cdot14 \oplus 8 \oplus 2\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 4 \oplus 11 \oplus 2\cdot15} & \\ \htmlTitle{22\otimes 1}{22} & \htmlTitle{22\otimes 2}{22} & \htmlTitle{22\otimes 3}{14 \oplus 17 \oplus 22 \oplus 16 \oplus 15} & \htmlTitle{22\otimes 4}{14 \oplus 17 \oplus 22 \oplus 16 \oplus 15} & \htmlTitle{22\otimes 5}{10 \oplus 14 \oplus 17 \oplus 22 \oplus 11 \oplus 15} & \htmlTitle{22\otimes 6}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{22\otimes 7}{18 \oplus 20 \oplus 12 \oplus 19 \oplus 21 \oplus 13} & \htmlTitle{22\otimes 8}{10 \oplus 14 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{22\otimes 9}{10 \oplus 14 \oplus 8 \oplus 17 \oplus 2\cdot22 \oplus 16 \oplus 11 \oplus 15} & \htmlTitle{22\otimes 10}{10 \oplus 14 \oplus 8 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 5 \oplus 11 \oplus 15} & \htmlTitle{22\otimes 11}{10 \oplus 14 \oplus 8 \oplus 17 \oplus 2\cdot22 \oplus 9 \oplus 16 \oplus 5 \oplus 11 \oplus 15} & \htmlTitle{22\otimes 12}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{22\otimes 13}{6 \oplus 2\cdot18 \oplus 2\cdot20 \oplus 12 \oplus 2\cdot19 \oplus 2\cdot21 \oplus 13 \oplus 7} & \htmlTitle{22\otimes 14}{3 \oplus 10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 4 \oplus 11 \oplus 15} & \htmlTitle{22\otimes 15}{3 \oplus 10 \oplus 14 \oplus 8 \oplus 2\cdot17 \oplus 2\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 4 \oplus 11 \oplus 15} & \htmlTitle{22\otimes 16}{3 \oplus 10 \oplus 2\cdot14 \oplus 8 \oplus 2\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 16 \oplus 4 \oplus 11 \oplus 2\cdot15} & \htmlTitle{22\otimes 17}{3 \oplus 10 \oplus 2\cdot14 \oplus 3\cdot17 \oplus 3\cdot22 \oplus 9 \oplus 2\cdot16 \oplus 5 \oplus 4 \oplus 11 \oplus 2\cdot15} & \htmlTitle{22\otimes 18}{6 \oplus 2\cdot18 \oplus 3\cdot20 \oplus 2\cdot12 \oplus 2\cdot19 \oplus 3\cdot21 \oplus 2\cdot13 \oplus 7} & \htmlTitle{22\otimes 19}{6 \oplus 2\cdot18 \oplus 3\cdot20 \oplus 2\cdot12 \oplus 2\cdot19 \oplus 3\cdot21 \oplus 2\cdot13 \oplus 7} & \htmlTitle{22\otimes 20}{6 \oplus 3\cdot18 \oplus 3\cdot20 \oplus 2\cdot12 \oplus 3\cdot19 \oplus 3\cdot21 \oplus 2\cdot13 \oplus 7} & \htmlTitle{22\otimes 21}{6 \oplus 3\cdot18 \oplus 3\cdot20 \oplus 2\cdot12 \oplus 3\cdot19 \oplus 3\cdot21 \oplus 2\cdot13 \oplus 7} & \htmlTitle{22\otimes 22}{1 \oplus 3 \oplus 2\cdot10 \oplus 2\cdot14 \oplus 2\cdot8 \oplus 3\cdot17 \oplus 4\cdot22 \oplus 2\cdot9 \oplus 3\cdot16 \oplus 5 \oplus 4 \oplus 2\cdot11 \oplus 2\cdot15 \oplus 2} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(3.532\)\( - \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 2 \)
\( 4\)\(3.532\)\( - \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 2 \)
\( 5\)\(3.759\)\( 2 \cos{\left(\frac{4 \pi}{9} \right)} + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} \)
\( 6\)\(4.386\)\( \cos{\left(\frac{5 \pi}{18} \right)} + \cos{\left(\frac{\pi}{18} \right)} + 3 \cos{\left(\frac{7 \pi}{18} \right)} + \sqrt{3} \)
\( 7\)\(4.386\)\( \cos{\left(\frac{5 \pi}{18} \right)} + \cos{\left(\frac{\pi}{18} \right)} + 3 \cos{\left(\frac{7 \pi}{18} \right)} + \sqrt{3} \)
\( 8\)\(5.064\)\( - 2 \cos{\left(\frac{4 \pi}{9} \right)} + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \)
\( 9\)\(5.759\)\( 2 \cos{\left(\frac{4 \pi}{9} \right)} + 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 2 \)
\( 10\)\(6.411\)\( 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 3 \)
\( 11\)\(6.411\)\( 2 \cos{\left(\frac{2 \pi}{9} \right)} + 2 \cos{\left(\frac{\pi}{9} \right)} + 3 \)
\( 12\)\(8.242\)\( \sqrt{3} + 4 \cos{\left(\frac{5 \pi}{18} \right)} + 4 \cos{\left(\frac{\pi}{18} \right)} \)
\( 13\)\(8.242\)\( \sqrt{3} + 4 \cos{\left(\frac{5 \pi}{18} \right)} + 4 \cos{\left(\frac{\pi}{18} \right)} \)
\( 14\)\(8.291\)\( \cos{\left(\frac{4 \pi}{9} \right)} + 3 \cos{\left(\frac{2 \pi}{9} \right)} + 3 \cos{\left(\frac{\pi}{9} \right)} + 3 \)
\( 15\)\(8.291\)\( \cos{\left(\frac{4 \pi}{9} \right)} + 3 \cos{\left(\frac{2 \pi}{9} \right)} + 3 \cos{\left(\frac{\pi}{9} \right)} + 3 \)
\( 16\)\(9.518\)\( 4 \cos{\left(\frac{4 \pi}{9} \right)} + 2 + 4 \cos{\left(\frac{2 \pi}{9} \right)} + 4 \cos{\left(\frac{\pi}{9} \right)} \)
\( 17\)\(10.823\)\( 4 \cos{\left(\frac{2 \pi}{9} \right)} + 4 \cos{\left(\frac{\pi}{9} \right)} + 4 \)
\( 18\)\(11.105\)\( 3 \cos{\left(\frac{7 \pi}{18} \right)} + 3 \cos{\left(\frac{5 \pi}{18} \right)} + 3 \cos{\left(\frac{\pi}{18} \right)} + 3 \sqrt{3} \)
\( 19\)\(11.105\)\( 3 \cos{\left(\frac{7 \pi}{18} \right)} + 3 \cos{\left(\frac{5 \pi}{18} \right)} + 3 \cos{\left(\frac{\pi}{18} \right)} + 3 \sqrt{3} \)
\( 20\)\(12.628\)\( 3 \cos{\left(\frac{7 \pi}{18} \right)} + 5 \cos{\left(\frac{5 \pi}{18} \right)} + 2 \sqrt{3} + 5 \cos{\left(\frac{\pi}{18} \right)} \)
\( 21\)\(12.628\)\( 3 \cos{\left(\frac{7 \pi}{18} \right)} + 5 \cos{\left(\frac{5 \pi}{18} \right)} + 2 \sqrt{3} + 5 \cos{\left(\frac{\pi}{18} \right)} \)
\( 22\)\(14.582\)\( 2 \cos{\left(\frac{4 \pi}{9} \right)} + 4 + 6 \cos{\left(\frac{2 \pi}{9} \right)} + 6 \cos{\left(\frac{\pi}{9} \right)} \)
\( D^2\)1479.852\(108 \cos{\left(\frac{4 \pi}{9} \right)} + 540 \cos{\left(\frac{2 \pi}{9} \right)} + 540 \cos{\left(\frac{\pi}{9} \right)} + 540\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{2}{3}} & \htmlTitle{\theta_{4}}{\frac{2}{3}} & \htmlTitle{\theta_{5}}{\frac{4}{3}} & \htmlTitle{\theta_{6}}{\frac{7}{12}} & \htmlTitle{\theta_{7}}{\frac{19}{12}} & \htmlTitle{\theta_{8}}{\frac{14}{9}} & \htmlTitle{\theta_{9}}{\frac{2}{3}} & \htmlTitle{\theta_{10}}{\frac{10}{9}} & \htmlTitle{\theta_{11}}{\frac{10}{9}} & \htmlTitle{\theta_{12}}{\frac{1}{4}} & \htmlTitle{\theta_{13}}{\frac{5}{4}} & \htmlTitle{\theta_{14}}{\frac{4}{3}} & \htmlTitle{\theta_{15}}{\frac{4}{3}} & \htmlTitle{\theta_{16}}{\frac{8}{9}} & \htmlTitle{\theta_{17}}{0} & \htmlTitle{\theta_{18}}{\frac{49}{36}} & \htmlTitle{\theta_{19}}{\frac{13}{36}} & \htmlTitle{\theta_{20}}{\frac{23}{12}} & \htmlTitle{\theta_{21}}{\frac{11}{12}} & \htmlTitle{\theta_{22}}{\frac{2}{9}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{llllllllllllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 2} & \htmlTitle{S_{3; 2}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 2} & \htmlTitle{S_{3; 3}}{-2 \zeta_{72}^{20} - \zeta_{72}^{16} + 3 \zeta_{72}^{8} + 3 \zeta_{72}^{4} + 3} & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 2} & \htmlTitle{S_{4; 2}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 2} & \htmlTitle{S_{4; 3}}{-2 \zeta_{72}^{20} - \zeta_{72}^{16} + 3 \zeta_{72}^{8} + 3 \zeta_{72}^{4} + 3} & \htmlTitle{S_{4; 4}}{-2 \zeta_{72}^{20} - \zeta_{72}^{16} + 3 \zeta_{72}^{8} + 3 \zeta_{72}^{4} + 3} & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4}} & \htmlTitle{S_{5; 2}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4}} & \htmlTitle{S_{5; 3}}{2 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 4 \zeta_{72}^{8} - 4 \zeta_{72}^{4} - 4} & \htmlTitle{S_{5; 4}}{2 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 4 \zeta_{72}^{8} - 4 \zeta_{72}^{4} - 4} & \htmlTitle{S_{5; 5}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 2} & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{6; 1}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} + \zeta_{72}^{14} + \zeta_{72}^{10} + 2 \zeta_{72}^{6} + \zeta_{72}^{2}} & \htmlTitle{S_{6; 2}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} - \zeta_{72}^{14} - \zeta_{72}^{10} - 2 \zeta_{72}^{6} - \zeta_{72}^{2}} & \htmlTitle{S_{6; 3}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} - 2 \zeta_{72}^{14} + 4 \zeta_{72}^{10} + 2 \zeta_{72}^{6} + 4 \zeta_{72}^{2}} & \htmlTitle{S_{6; 4}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} + 2 \zeta_{72}^{14} - 4 \zeta_{72}^{10} - 2 \zeta_{72}^{6} - 4 \zeta_{72}^{2}} & \htmlTitle{S_{6; 5}}{0} & \htmlTitle{S_{6; 6}}{-4 \zeta_{72}^{22} - 2 \zeta_{72}^{18} - \zeta_{72}^{14} + 5 \zeta_{72}^{10} + 4 \zeta_{72}^{6} + 5 \zeta_{72}^{2}} & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{7; 1}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} + \zeta_{72}^{14} + \zeta_{72}^{10} + 2 \zeta_{72}^{6} + \zeta_{72}^{2}} & \htmlTitle{S_{7; 2}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} - \zeta_{72}^{14} - \zeta_{72}^{10} - 2 \zeta_{72}^{6} - \zeta_{72}^{2}} & \htmlTitle{S_{7; 3}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} - 2 \zeta_{72}^{14} + 4 \zeta_{72}^{10} + 2 \zeta_{72}^{6} + 4 \zeta_{72}^{2}} & \htmlTitle{S_{7; 4}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} + 2 \zeta_{72}^{14} - 4 \zeta_{72}^{10} - 2 \zeta_{72}^{6} - 4 \zeta_{72}^{2}} & \htmlTitle{S_{7; 5}}{0} & \htmlTitle{S_{7; 6}}{4 \zeta_{72}^{22} + 2 \zeta_{72}^{18} + \zeta_{72}^{14} - 5 \zeta_{72}^{10} - 4 \zeta_{72}^{6} - 5 \zeta_{72}^{2}} & \htmlTitle{S_{7; 7}}{-4 \zeta_{72}^{22} - 2 \zeta_{72}^{18} - \zeta_{72}^{14} + 5 \zeta_{72}^{10} + 4 \zeta_{72}^{6} + 5 \zeta_{72}^{2}} & & & & & & & & & & & & & & & \\ \htmlTitle{S_{8; 1}}{-2 \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{8; 2}}{-2 \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{8; 3}}{-4 \zeta_{72}^{20} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 2} & \htmlTitle{S_{8; 4}}{-4 \zeta_{72}^{20} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 2} & \htmlTitle{S_{8; 5}}{-4 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 6 \zeta_{72}^{8} + 6 \zeta_{72}^{4} + 4} & \htmlTitle{S_{8; 6}}{0} & \htmlTitle{S_{8; 7}}{0} & \htmlTitle{S_{8; 8}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 6} & & & & & & & & & & & & & & \\ \htmlTitle{S_{9; 1}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{9; 2}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{9; 3}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4}} & \htmlTitle{S_{9; 4}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4}} & \htmlTitle{S_{9; 5}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 2} & \htmlTitle{S_{9; 6}}{0} & \htmlTitle{S_{9; 7}}{0} & \htmlTitle{S_{9; 8}}{-4 \zeta_{72}^{20} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 2} & \htmlTitle{S_{9; 9}}{-6 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 8 \zeta_{72}^{8} + 8 \zeta_{72}^{4} + 6} & & & & & & & & & & & & & \\ \htmlTitle{S_{10; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{10; 2}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{10; 3}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{10; 4}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{10; 5}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 6} & \htmlTitle{S_{10; 6}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{10; 7}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{10; 8}}{0} & \htmlTitle{S_{10; 9}}{2 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 4 \zeta_{72}^{8} - 4 \zeta_{72}^{4} - 6} & \htmlTitle{S_{10; 10}}{0} & & & & & & & & & & & & \\ \htmlTitle{S_{11; 1}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{11; 2}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{11; 3}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{11; 4}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{11; 5}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 6} & \htmlTitle{S_{11; 6}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{11; 7}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{11; 8}}{0} & \htmlTitle{S_{11; 9}}{2 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 4 \zeta_{72}^{8} - 4 \zeta_{72}^{4} - 6} & \htmlTitle{S_{11; 10}}{0} & \htmlTitle{S_{11; 11}}{0} & & & & & & & & & & & \\ \htmlTitle{S_{12; 1}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} - 2 \zeta_{72}^{14} + 4 \zeta_{72}^{10} + 2 \zeta_{72}^{6} + 4 \zeta_{72}^{2}} & \htmlTitle{S_{12; 2}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} + 2 \zeta_{72}^{14} - 4 \zeta_{72}^{10} - 2 \zeta_{72}^{6} - 4 \zeta_{72}^{2}} & \htmlTitle{S_{12; 3}}{4 \zeta_{72}^{22} + 2 \zeta_{72}^{18} + \zeta_{72}^{14} - 5 \zeta_{72}^{10} - 4 \zeta_{72}^{6} - 5 \zeta_{72}^{2}} & \htmlTitle{S_{12; 4}}{-4 \zeta_{72}^{22} - 2 \zeta_{72}^{18} - \zeta_{72}^{14} + 5 \zeta_{72}^{10} + 4 \zeta_{72}^{6} + 5 \zeta_{72}^{2}} & \htmlTitle{S_{12; 5}}{0} & \htmlTitle{S_{12; 6}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} + \zeta_{72}^{14} + \zeta_{72}^{10} + 2 \zeta_{72}^{6} + \zeta_{72}^{2}} & \htmlTitle{S_{12; 7}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} - \zeta_{72}^{14} - \zeta_{72}^{10} - 2 \zeta_{72}^{6} - \zeta_{72}^{2}} & \htmlTitle{S_{12; 8}}{0} & \htmlTitle{S_{12; 9}}{0} & \htmlTitle{S_{12; 10}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{12; 11}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{12; 12}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} + 2 \zeta_{72}^{14} - 4 \zeta_{72}^{10} - 2 \zeta_{72}^{6} - 4 \zeta_{72}^{2}} & & & & & & & & & & \\ \htmlTitle{S_{13; 1}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} - 2 \zeta_{72}^{14} + 4 \zeta_{72}^{10} + 2 \zeta_{72}^{6} + 4 \zeta_{72}^{2}} & \htmlTitle{S_{13; 2}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} + 2 \zeta_{72}^{14} - 4 \zeta_{72}^{10} - 2 \zeta_{72}^{6} - 4 \zeta_{72}^{2}} & \htmlTitle{S_{13; 3}}{4 \zeta_{72}^{22} + 2 \zeta_{72}^{18} + \zeta_{72}^{14} - 5 \zeta_{72}^{10} - 4 \zeta_{72}^{6} - 5 \zeta_{72}^{2}} & \htmlTitle{S_{13; 4}}{-4 \zeta_{72}^{22} - 2 \zeta_{72}^{18} - \zeta_{72}^{14} + 5 \zeta_{72}^{10} + 4 \zeta_{72}^{6} + 5 \zeta_{72}^{2}} & \htmlTitle{S_{13; 5}}{0} & \htmlTitle{S_{13; 6}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} - \zeta_{72}^{14} - \zeta_{72}^{10} - 2 \zeta_{72}^{6} - \zeta_{72}^{2}} & \htmlTitle{S_{13; 7}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} + \zeta_{72}^{14} + \zeta_{72}^{10} + 2 \zeta_{72}^{6} + \zeta_{72}^{2}} & \htmlTitle{S_{13; 8}}{0} & \htmlTitle{S_{13; 9}}{0} & \htmlTitle{S_{13; 10}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{13; 11}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{13; 12}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} - 2 \zeta_{72}^{14} + 4 \zeta_{72}^{10} + 2 \zeta_{72}^{6} + 4 \zeta_{72}^{2}} & \htmlTitle{S_{13; 13}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} + 2 \zeta_{72}^{14} - 4 \zeta_{72}^{10} - 2 \zeta_{72}^{6} - 4 \zeta_{72}^{2}} & & & & & & & & & \\ \htmlTitle{S_{14; 1}}{-2 \zeta_{72}^{20} - \zeta_{72}^{16} + 3 \zeta_{72}^{8} + 3 \zeta_{72}^{4} + 3} & \htmlTitle{S_{14; 2}}{-2 \zeta_{72}^{20} - \zeta_{72}^{16} + 3 \zeta_{72}^{8} + 3 \zeta_{72}^{4} + 3} & \htmlTitle{S_{14; 3}}{1} & \htmlTitle{S_{14; 4}}{1} & \htmlTitle{S_{14; 5}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{14; 6}}{-4 \zeta_{72}^{22} - 2 \zeta_{72}^{18} - \zeta_{72}^{14} + 5 \zeta_{72}^{10} + 4 \zeta_{72}^{6} + 5 \zeta_{72}^{2}} & \htmlTitle{S_{14; 7}}{-4 \zeta_{72}^{22} - 2 \zeta_{72}^{18} - \zeta_{72}^{14} + 5 \zeta_{72}^{10} + 4 \zeta_{72}^{6} + 5 \zeta_{72}^{2}} & \htmlTitle{S_{14; 8}}{4 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 6 \zeta_{72}^{8} - 6 \zeta_{72}^{4} - 4} & \htmlTitle{S_{14; 9}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 4} & \htmlTitle{S_{14; 10}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{14; 11}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{14; 12}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} - \zeta_{72}^{14} - \zeta_{72}^{10} - 2 \zeta_{72}^{6} - \zeta_{72}^{2}} & \htmlTitle{S_{14; 13}}{2 \zeta_{72}^{22} + \zeta_{72}^{18} - \zeta_{72}^{14} - \zeta_{72}^{10} - 2 \zeta_{72}^{6} - \zeta_{72}^{2}} & \htmlTitle{S_{14; 14}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 2} & & & & & & & & \\ \htmlTitle{S_{15; 1}}{-2 \zeta_{72}^{20} - \zeta_{72}^{16} + 3 \zeta_{72}^{8} + 3 \zeta_{72}^{4} + 3} & \htmlTitle{S_{15; 2}}{-2 \zeta_{72}^{20} - \zeta_{72}^{16} + 3 \zeta_{72}^{8} + 3 \zeta_{72}^{4} + 3} & \htmlTitle{S_{15; 3}}{1} & \htmlTitle{S_{15; 4}}{1} & \htmlTitle{S_{15; 5}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{15; 6}}{4 \zeta_{72}^{22} + 2 \zeta_{72}^{18} + \zeta_{72}^{14} - 5 \zeta_{72}^{10} - 4 \zeta_{72}^{6} - 5 \zeta_{72}^{2}} & \htmlTitle{S_{15; 7}}{4 \zeta_{72}^{22} + 2 \zeta_{72}^{18} + \zeta_{72}^{14} - 5 \zeta_{72}^{10} - 4 \zeta_{72}^{6} - 5 \zeta_{72}^{2}} & \htmlTitle{S_{15; 8}}{4 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 6 \zeta_{72}^{8} - 6 \zeta_{72}^{4} - 4} & \htmlTitle{S_{15; 9}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 4} & \htmlTitle{S_{15; 10}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{15; 11}}{-\zeta_{72}^{20} - \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 3} & \htmlTitle{S_{15; 12}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} + \zeta_{72}^{14} + \zeta_{72}^{10} + 2 \zeta_{72}^{6} + \zeta_{72}^{2}} & \htmlTitle{S_{15; 13}}{-2 \zeta_{72}^{22} - \zeta_{72}^{18} + \zeta_{72}^{14} + \zeta_{72}^{10} + 2 \zeta_{72}^{6} + \zeta_{72}^{2}} & \htmlTitle{S_{15; 14}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 2} & \htmlTitle{S_{15; 15}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 2} & & & & & & & \\ \htmlTitle{S_{16; 1}}{-4 \zeta_{72}^{20} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 2} & \htmlTitle{S_{16; 2}}{-4 \zeta_{72}^{20} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 2} & \htmlTitle{S_{16; 3}}{4 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 6 \zeta_{72}^{8} - 6 \zeta_{72}^{4} - 4} & \htmlTitle{S_{16; 4}}{4 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 6 \zeta_{72}^{8} - 6 \zeta_{72}^{4} - 4} & \htmlTitle{S_{16; 5}}{2 \zeta_{72}^{16} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4} - 2} & \htmlTitle{S_{16; 6}}{0} & \htmlTitle{S_{16; 7}}{0} & \htmlTitle{S_{16; 8}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 6} & \htmlTitle{S_{16; 9}}{4 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 6 \zeta_{72}^{8} - 6 \zeta_{72}^{4} - 4} & \htmlTitle{S_{16; 10}}{0} & \htmlTitle{S_{16; 11}}{0} & \htmlTitle{S_{16; 12}}{0} & \htmlTitle{S_{16; 13}}{0} & \htmlTitle{S_{16; 14}}{-2 \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{16; 15}}{-2 \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{16; 16}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 6} & & & & & & \\ \htmlTitle{S_{17; 1}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 4} & \htmlTitle{S_{17; 2}}{-2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 4} & \htmlTitle{S_{17; 3}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{17; 4}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{17; 5}}{6 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 8 \zeta_{72}^{8} - 8 \zeta_{72}^{4} - 6} & \htmlTitle{S_{17; 6}}{0} & \htmlTitle{S_{17; 7}}{0} & \htmlTitle{S_{17; 8}}{-2 \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4} + 2} & \htmlTitle{S_{17; 9}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{16} + 2} & \htmlTitle{S_{17; 10}}{2 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 4 \zeta_{72}^{8} - 4 \zeta_{72}^{4} - 6} & \htmlTitle{S_{17; 11}}{2 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 4 \zeta_{72}^{8} - 4 \zeta_{72}^{4} - 6} & \htmlTitle{S_{17; 12}}{0} & \htmlTitle{S_{17; 13}}{0} & \htmlTitle{S_{17; 14}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4}} & \htmlTitle{S_{17; 15}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4}} & \htmlTitle{S_{17; 16}}{-4 \zeta_{72}^{20} + 4 \zeta_{72}^{8} + 4 \zeta_{72}^{4} + 2} & \htmlTitle{S_{17; 17}}{2 \zeta_{72}^{20} + 2 \zeta_{72}^{16} - 4 \zeta_{72}^{8} - 4 \zeta_{72}^{4} - 2} & & & & & \\ \htmlTitle{S_{18; 1}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 2}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 3}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 4}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 5}}{0} & \htmlTitle{S_{18; 6}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 7}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 8}}{0} & \htmlTitle{S_{18; 9}}{0} & \htmlTitle{S_{18; 10}}{0} & \htmlTitle{S_{18; 11}}{0} & \htmlTitle{S_{18; 12}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 13}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 14}}{3 \zeta_{72}^{22} + 3 \zeta_{72}^{18} - 3 \zeta_{72}^{10} - 6 \zeta_{72}^{6} - 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 15}}{-3 \zeta_{72}^{22} - 3 \zeta_{72}^{18} + 3 \zeta_{72}^{10} + 6 \zeta_{72}^{6} + 3 \zeta_{72}^{2}} & \htmlTitle{S_{18; 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Central Charge

\[c = \frac{28}{3} \]