SU(3) 5 | VerlindeDB

\(\operatorname{SU}(3)_{5}\): \( A_{2} \) at level \(5\)

Fusion Ring

\[ \begin{array}{lllllllllllllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{3} & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{1} & \htmlTitle{3\otimes 3}{2} & & & & & & & & & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{8} & \htmlTitle{4\otimes 3}{7} & \htmlTitle{4\otimes 4}{5 \oplus 10} & & & & & & & & & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{6} & \htmlTitle{5\otimes 3}{9} & \htmlTitle{5\otimes 4}{1 \oplus 16} & \htmlTitle{5\otimes 5}{4 \oplus 11} & & & & & & & & & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{9} & \htmlTitle{6\otimes 3}{5} & \htmlTitle{6\otimes 4}{17 \oplus 2} & \htmlTitle{6\otimes 5}{12 \oplus 8} & \htmlTitle{6\otimes 6}{7 \oplus 15} & & & & & & & & & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{4} & \htmlTitle{7\otimes 3}{8} & \htmlTitle{7\otimes 4}{13 \oplus 9} & \htmlTitle{7\otimes 5}{18 \oplus 3} & \htmlTitle{7\otimes 6}{1 \oplus 16} & \htmlTitle{7\otimes 7}{6 \oplus 14} & & & & & & & & & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{7} & \htmlTitle{8\otimes 3}{4} & \htmlTitle{8\otimes 4}{6 \oplus 14} & \htmlTitle{8\otimes 5}{17 \oplus 2} & \htmlTitle{8\otimes 6}{18 \oplus 3} & \htmlTitle{8\otimes 7}{5 \oplus 10} & \htmlTitle{8\otimes 8}{13 \oplus 9} & & & & & & & & & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{5} & \htmlTitle{9\otimes 3}{6} & \htmlTitle{9\otimes 4}{18 \oplus 3} & \htmlTitle{9\otimes 5}{7 \oplus 15} & \htmlTitle{9\otimes 6}{4 \oplus 11} & \htmlTitle{9\otimes 7}{17 \oplus 2} & \htmlTitle{9\otimes 8}{1 \oplus 16} & \htmlTitle{9\otimes 9}{12 \oplus 8} & & & & & & & & & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{14} & \htmlTitle{10\otimes 3}{13} & \htmlTitle{10\otimes 4}{16 \oplus 12} & \htmlTitle{10\otimes 5}{4 \oplus 19} & \htmlTitle{10\otimes 6}{21 \oplus 8} & \htmlTitle{10\otimes 7}{11 \oplus 18} & \htmlTitle{10\otimes 8}{17 \oplus 15} & \htmlTitle{10\otimes 9}{20 \oplus 7} & \htmlTitle{10\otimes 10}{11 \oplus 19 \oplus 6} & & & & & & & & & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{12} & \htmlTitle{11\otimes 3}{15} & \htmlTitle{11\otimes 4}{5 \oplus 20} & \htmlTitle{11\otimes 5}{13 \oplus 16} & \htmlTitle{11\otimes 6}{10 \oplus 17} & \htmlTitle{11\otimes 7}{9 \oplus 21} & \htmlTitle{11\otimes 8}{19 \oplus 6} & \htmlTitle{11\otimes 9}{18 \oplus 14} & \htmlTitle{11\otimes 10}{1 \oplus 16 \oplus 21} & \htmlTitle{11\otimes 11}{10 \oplus 20 \oplus 7} & & & & & & & & & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{15} & \htmlTitle{12\otimes 3}{11} & \htmlTitle{12\otimes 4}{19 \oplus 6} & \htmlTitle{12\otimes 5}{10 \oplus 17} & \htmlTitle{12\otimes 6}{18 \oplus 14} & \htmlTitle{12\otimes 7}{5 \oplus 20} & \htmlTitle{12\otimes 8}{9 \oplus 21} & \htmlTitle{12\otimes 9}{13 \oplus 16} & \htmlTitle{12\otimes 10}{20 \oplus 17 \oplus 2} & \htmlTitle{12\otimes 11}{4 \oplus 19 \oplus 14} & \htmlTitle{12\otimes 12}{13 \oplus 21 \oplus 8} & & & & & & & & & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{10} & \htmlTitle{13\otimes 3}{14} & \htmlTitle{13\otimes 4}{11 \oplus 18} & \htmlTitle{13\otimes 5}{20 \oplus 7} & \htmlTitle{13\otimes 6}{4 \oplus 19} & \htmlTitle{13\otimes 7}{17 \oplus 15} & \htmlTitle{13\otimes 8}{16 \oplus 12} & \htmlTitle{13\otimes 9}{21 \oplus 8} & \htmlTitle{13\otimes 10}{5 \oplus 20 \oplus 15} & \htmlTitle{13\otimes 11}{19 \oplus 18 \oplus 3} & \htmlTitle{13\otimes 12}{1 \oplus 16 \oplus 21} & \htmlTitle{13\otimes 13}{12 \oplus 9 \oplus 21} & & & & & & & & \\ \htmlTitle{14\otimes 1}{14} & \htmlTitle{14\otimes 2}{13} & \htmlTitle{14\otimes 3}{10} & \htmlTitle{14\otimes 4}{17 \oplus 15} & \htmlTitle{14\otimes 5}{21 \oplus 8} & \htmlTitle{14\otimes 6}{20 \oplus 7} & \htmlTitle{14\otimes 7}{16 \oplus 12} & \htmlTitle{14\otimes 8}{11 \oplus 18} & \htmlTitle{14\otimes 9}{4 \oplus 19} & \htmlTitle{14\otimes 10}{12 \oplus 9 \oplus 21} & \htmlTitle{14\otimes 11}{20 \oplus 17 \oplus 2} & \htmlTitle{14\otimes 12}{19 \oplus 18 \oplus 3} & \htmlTitle{14\otimes 13}{11 \oplus 19 \oplus 6} & \htmlTitle{14\otimes 14}{5 \oplus 20 \oplus 15} & & & & & & & \\ \htmlTitle{15\otimes 1}{15} & \htmlTitle{15\otimes 2}{11} & \htmlTitle{15\otimes 3}{12} & \htmlTitle{15\otimes 4}{9 \oplus 21} & \htmlTitle{15\otimes 5}{18 \oplus 14} & \htmlTitle{15\otimes 6}{13 \oplus 16} & \htmlTitle{15\otimes 7}{19 \oplus 6} & \htmlTitle{15\otimes 8}{5 \oplus 20} & \htmlTitle{15\otimes 9}{10 \oplus 17} & \htmlTitle{15\otimes 10}{19 \oplus 18 \oplus 3} & \htmlTitle{15\otimes 11}{13 \oplus 21 \oplus 8} & \htmlTitle{15\otimes 12}{10 \oplus 20 \oplus 7} & \htmlTitle{15\otimes 13}{20 \oplus 17 \oplus 2} & \htmlTitle{15\otimes 14}{1 \oplus 16 \oplus 21} & \htmlTitle{15\otimes 15}{4 \oplus 19 \oplus 14} & & & & & & \\ \htmlTitle{16\otimes 1}{16} & \htmlTitle{16\otimes 2}{17} & \htmlTitle{16\otimes 3}{18} & \htmlTitle{16\otimes 4}{4 \oplus 11 \oplus 19} & \htmlTitle{16\otimes 5}{5 \oplus 10 \oplus 20} & \htmlTitle{16\otimes 6}{19 \oplus 6 \oplus 14} & \htmlTitle{16\otimes 7}{20 \oplus 7 \oplus 15} & \htmlTitle{16\otimes 8}{12 \oplus 21 \oplus 8} & \htmlTitle{16\otimes 9}{13 \oplus 9 \oplus 21} & \htmlTitle{16\otimes 10}{5 \oplus 10 \oplus 20 \oplus 17} & \htmlTitle{16\otimes 11}{4 \oplus 11 \oplus 19 \oplus 18} & \htmlTitle{16\otimes 12}{16 \oplus 12 \oplus 21 \oplus 8} & \htmlTitle{16\otimes 13}{13 \oplus 16 \oplus 9 \oplus 21} & \htmlTitle{16\otimes 14}{19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{16\otimes 15}{20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{16\otimes 16}{1 \oplus 13 \oplus 2\cdot16 \oplus 12 \oplus 21} & & & & & \\ \htmlTitle{17\otimes 1}{17} & \htmlTitle{17\otimes 2}{18} & \htmlTitle{17\otimes 3}{16} & \htmlTitle{17\otimes 4}{12 \oplus 21 \oplus 8} & \htmlTitle{17\otimes 5}{19 \oplus 6 \oplus 14} & \htmlTitle{17\otimes 6}{13 \oplus 9 \oplus 21} & \htmlTitle{17\otimes 7}{4 \oplus 11 \oplus 19} & \htmlTitle{17\otimes 8}{20 \oplus 7 \oplus 15} & \htmlTitle{17\otimes 9}{5 \oplus 10 \oplus 20} & \htmlTitle{17\otimes 10}{19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{17\otimes 11}{16 \oplus 12 \oplus 21 \oplus 8} & \htmlTitle{17\otimes 12}{20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{17\otimes 13}{5 \oplus 10 \oplus 20 \oplus 17} & \htmlTitle{17\otimes 14}{13 \oplus 16 \oplus 9 \oplus 21} & \htmlTitle{17\otimes 15}{4 \oplus 11 \oplus 19 \oplus 18} & \htmlTitle{17\otimes 16}{10 \oplus 20 \oplus 2\cdot17 \oplus 15 \oplus 2} & \htmlTitle{17\otimes 17}{11 \oplus 19 \oplus 2\cdot18 \oplus 3 \oplus 14} & & & & \\ \htmlTitle{18\otimes 1}{18} & \htmlTitle{18\otimes 2}{16} & \htmlTitle{18\otimes 3}{17} & \htmlTitle{18\otimes 4}{20 \oplus 7 \oplus 15} & \htmlTitle{18\otimes 5}{13 \oplus 9 \oplus 21} & \htmlTitle{18\otimes 6}{5 \oplus 10 \oplus 20} & \htmlTitle{18\otimes 7}{12 \oplus 21 \oplus 8} & \htmlTitle{18\otimes 8}{4 \oplus 11 \oplus 19} & \htmlTitle{18\otimes 9}{19 \oplus 6 \oplus 14} & \htmlTitle{18\otimes 10}{13 \oplus 16 \oplus 9 \oplus 21} & \htmlTitle{18\otimes 11}{20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{18\otimes 12}{4 \oplus 11 \oplus 19 \oplus 18} & \htmlTitle{18\otimes 13}{19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{18\otimes 14}{5 \oplus 10 \oplus 20 \oplus 17} & \htmlTitle{18\otimes 15}{16 \oplus 12 \oplus 21 \oplus 8} & \htmlTitle{18\otimes 16}{11 \oplus 19 \oplus 2\cdot18 \oplus 3 \oplus 14} & \htmlTitle{18\otimes 17}{1 \oplus 13 \oplus 2\cdot16 \oplus 12 \oplus 21} & \htmlTitle{18\otimes 18}{10 \oplus 20 \oplus 2\cdot17 \oplus 15 \oplus 2} & & & \\ \htmlTitle{19\otimes 1}{19} & \htmlTitle{19\otimes 2}{21} & \htmlTitle{19\otimes 3}{20} & \htmlTitle{19\otimes 4}{10 \oplus 20 \oplus 17} & \htmlTitle{19\otimes 5}{16 \oplus 12 \oplus 21} & \htmlTitle{19\otimes 6}{20 \oplus 17 \oplus 15} & \htmlTitle{19\otimes 7}{13 \oplus 16 \oplus 21} & \htmlTitle{19\otimes 8}{19 \oplus 18 \oplus 14} & \htmlTitle{19\otimes 9}{11 \oplus 19 \oplus 18} & \htmlTitle{19\otimes 10}{13 \oplus 16 \oplus 12 \oplus 21 \oplus 8} & \htmlTitle{19\otimes 11}{5 \oplus 10 \oplus 20 \oplus 17 \oplus 15} & \htmlTitle{19\otimes 12}{11 \oplus 19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{19\otimes 13}{4 \oplus 11 \oplus 19 \oplus 18 \oplus 14} & \htmlTitle{19\otimes 14}{10 \oplus 20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{19\otimes 15}{13 \oplus 16 \oplus 12 \oplus 9 \oplus 21} & \htmlTitle{19\otimes 16}{4 \oplus 11 \oplus 2\cdot19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{19\otimes 17}{13 \oplus 16 \oplus 12 \oplus 9 \oplus 2\cdot21 \oplus 8} & \htmlTitle{19\otimes 18}{5 \oplus 10 \oplus 2\cdot20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{19\otimes 19}{5 \oplus 10 \oplus 2\cdot20 \oplus 7 \oplus 2\cdot17 \oplus 15 \oplus 2} & & \\ \htmlTitle{20\otimes 1}{20} & \htmlTitle{20\otimes 2}{19} & \htmlTitle{20\otimes 3}{21} & \htmlTitle{20\otimes 4}{13 \oplus 16 \oplus 21} & \htmlTitle{20\otimes 5}{11 \oplus 19 \oplus 18} & \htmlTitle{20\otimes 6}{16 \oplus 12 \oplus 21} & \htmlTitle{20\otimes 7}{19 \oplus 18 \oplus 14} & \htmlTitle{20\otimes 8}{10 \oplus 20 \oplus 17} & \htmlTitle{20\otimes 9}{20 \oplus 17 \oplus 15} & \htmlTitle{20\otimes 10}{4 \oplus 11 \oplus 19 \oplus 18 \oplus 14} & \htmlTitle{20\otimes 11}{13 \oplus 16 \oplus 12 \oplus 9 \oplus 21} & \htmlTitle{20\otimes 12}{5 \oplus 10 \oplus 20 \oplus 17 \oplus 15} & \htmlTitle{20\otimes 13}{10 \oplus 20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{20\otimes 14}{13 \oplus 16 \oplus 12 \oplus 21 \oplus 8} & \htmlTitle{20\otimes 15}{11 \oplus 19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{20\otimes 16}{5 \oplus 10 \oplus 2\cdot20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{20\otimes 17}{4 \oplus 11 \oplus 2\cdot19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{20\otimes 18}{13 \oplus 16 \oplus 12 \oplus 9 \oplus 2\cdot21 \oplus 8} & \htmlTitle{20\otimes 19}{1 \oplus 13 \oplus 2\cdot16 \oplus 12 \oplus 9 \oplus 2\cdot21 \oplus 8} & \htmlTitle{20\otimes 20}{4 \oplus 11 \oplus 2\cdot19 \oplus 2\cdot18 \oplus 3 \oplus 6 \oplus 14} & \\ \htmlTitle{21\otimes 1}{21} & \htmlTitle{21\otimes 2}{20} & \htmlTitle{21\otimes 3}{19} & \htmlTitle{21\otimes 4}{19 \oplus 18 \oplus 14} & \htmlTitle{21\otimes 5}{20 \oplus 17 \oplus 15} & \htmlTitle{21\otimes 6}{11 \oplus 19 \oplus 18} & \htmlTitle{21\otimes 7}{10 \oplus 20 \oplus 17} & \htmlTitle{21\otimes 8}{13 \oplus 16 \oplus 21} & \htmlTitle{21\otimes 9}{16 \oplus 12 \oplus 21} & \htmlTitle{21\otimes 10}{10 \oplus 20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{21\otimes 11}{11 \oplus 19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{21\otimes 12}{13 \oplus 16 \oplus 12 \oplus 9 \oplus 21} & \htmlTitle{21\otimes 13}{13 \oplus 16 \oplus 12 \oplus 21 \oplus 8} & \htmlTitle{21\otimes 14}{4 \oplus 11 \oplus 19 \oplus 18 \oplus 14} & \htmlTitle{21\otimes 15}{5 \oplus 10 \oplus 20 \oplus 17 \oplus 15} & \htmlTitle{21\otimes 16}{13 \oplus 16 \oplus 12 \oplus 9 \oplus 2\cdot21 \oplus 8} & \htmlTitle{21\otimes 17}{5 \oplus 10 \oplus 2\cdot20 \oplus 7 \oplus 17 \oplus 15} & \htmlTitle{21\otimes 18}{4 \oplus 11 \oplus 2\cdot19 \oplus 18 \oplus 6 \oplus 14} & \htmlTitle{21\otimes 19}{4 \oplus 11 \oplus 2\cdot19 \oplus 2\cdot18 \oplus 3 \oplus 6 \oplus 14} & \htmlTitle{21\otimes 20}{5 \oplus 10 \oplus 2\cdot20 \oplus 7 \oplus 2\cdot17 \oplus 15 \oplus 2} & \htmlTitle{21\otimes 21}{1 \oplus 13 \oplus 2\cdot16 \oplus 12 \oplus 9 \oplus 2\cdot21 \oplus 8} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(1.000\)\( 1 \)
\( 4\)\(2.414\)\( 1 + \sqrt{2} \)
\( 5\)\(2.414\)\( 1 + \sqrt{2} \)
\( 6\)\(2.414\)\( 1 + \sqrt{2} \)
\( 7\)\(2.414\)\( 1 + \sqrt{2} \)
\( 8\)\(2.414\)\( 1 + \sqrt{2} \)
\( 9\)\(2.414\)\( 1 + \sqrt{2} \)
\( 10\)\(3.414\)\( \sqrt{2} + 2 \)
\( 11\)\(3.414\)\( \sqrt{2} + 2 \)
\( 12\)\(3.414\)\( \sqrt{2} + 2 \)
\( 13\)\(3.414\)\( \sqrt{2} + 2 \)
\( 14\)\(3.414\)\( \sqrt{2} + 2 \)
\( 15\)\(3.414\)\( \sqrt{2} + 2 \)
\( 16\)\(4.828\)\( 2 + 2 \sqrt{2} \)
\( 17\)\(4.828\)\( 2 + 2 \sqrt{2} \)
\( 18\)\(4.828\)\( 2 + 2 \sqrt{2} \)
\( 19\)\(5.828\)\( 2 \sqrt{2} + 3 \)
\( 20\)\(5.828\)\( 2 \sqrt{2} + 3 \)
\( 21\)\(5.828\)\( 2 \sqrt{2} + 3 \)
\( D^2\)279.765\(96 \sqrt{2} + 144\)

Modular Data

Twist Factors

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

S Matrix

\[ \left(\begin{array}{lllllllllllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{-\zeta_{96}^{16}} & & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{1} & \htmlTitle{S_{3; 2}}{\zeta_{96}^{16} - 1} & \htmlTitle{S_{3; 3}}{-\zeta_{96}^{16}} & & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{4; 2}}{\zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{16} - \zeta_{96}^{12} - 1} & \htmlTitle{S_{4; 3}}{-\zeta_{96}^{28} - \zeta_{96}^{16} - \zeta_{96}^{4}} & \htmlTitle{S_{4; 4}}{-2 \zeta_{96}^{24} + \zeta_{96}^{16} + 2 \zeta_{96}^{8} + 2 \zeta_{96}^{4}} & & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{96}^{28} - \zeta_{96}^{16} - \zeta_{96}^{4}} & \htmlTitle{S_{5; 3}}{\zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{16} - \zeta_{96}^{12} - 1} & \htmlTitle{S_{5; 4}}{-2 \zeta_{96}^{28} - \zeta_{96}^{16} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{8} + 1} & \htmlTitle{S_{5; 5}}{-2 \zeta_{96}^{24} + \zeta_{96}^{16} + 2 \zeta_{96}^{8} + 2 \zeta_{96}^{4}} & & & & & & & & & & & & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{6; 2}}{\zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{16} - \zeta_{96}^{12} - 1} & \htmlTitle{S_{6; 3}}{-\zeta_{96}^{28} - \zeta_{96}^{16} - \zeta_{96}^{4}} & \htmlTitle{S_{6; 4}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + \zeta_{96}^{16} - 2 \zeta_{96}^{8}} & \htmlTitle{S_{6; 5}}{-2 \zeta_{96}^{20} - \zeta_{96}^{16} - 2 \zeta_{96}^{8} + 1} & \htmlTitle{S_{6; 6}}{-2 \zeta_{96}^{24} + \zeta_{96}^{16} + 2 \zeta_{96}^{8} + 2 \zeta_{96}^{4}} & & & & & & & & & & & & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{7; 2}}{-\zeta_{96}^{28} - \zeta_{96}^{16} - \zeta_{96}^{4}} & \htmlTitle{S_{7; 3}}{\zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{16} - \zeta_{96}^{12} - 1} & \htmlTitle{S_{7; 4}}{-2 \zeta_{96}^{20} - \zeta_{96}^{16} - 2 \zeta_{96}^{8} + 1} & \htmlTitle{S_{7; 5}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + \zeta_{96}^{16} - 2 \zeta_{96}^{8}} & \htmlTitle{S_{7; 6}}{-2 \zeta_{96}^{28} - \zeta_{96}^{16} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{8} + 1} & \htmlTitle{S_{7; 7}}{-2 \zeta_{96}^{24} + \zeta_{96}^{16} + 2 \zeta_{96}^{8} + 2 \zeta_{96}^{4}} & & & & & & & & & & & & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{8; 2}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{8; 3}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{8; 4}}{2 \zeta_{96}^{24} + 2 \zeta_{96}^{20} - 2 \zeta_{96}^{4} - 1} & \htmlTitle{S_{8; 5}}{-2 \zeta_{96}^{24} - 2 \zeta_{96}^{12} - 1} & \htmlTitle{S_{8; 6}}{-2 \zeta_{96}^{24} - 2 \zeta_{96}^{12} - 1} & \htmlTitle{S_{8; 7}}{2 \zeta_{96}^{24} + 2 \zeta_{96}^{20} - 2 \zeta_{96}^{4} - 1} & \htmlTitle{S_{8; 8}}{2 \zeta_{96}^{24} + 2 \zeta_{96}^{20} - 2 \zeta_{96}^{4} - 1} & & & & & & & & & & & & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{9; 2}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{9; 3}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 1} & \htmlTitle{S_{9; 4}}{-2 \zeta_{96}^{24} - 2 \zeta_{96}^{12} - 1} & \htmlTitle{S_{9; 5}}{2 \zeta_{96}^{24} + 2 \zeta_{96}^{20} - 2 \zeta_{96}^{4} - 1} & \htmlTitle{S_{9; 6}}{2 \zeta_{96}^{24} + 2 \zeta_{96}^{20} - 2 \zeta_{96}^{4} - 1} & \htmlTitle{S_{9; 7}}{-2 \zeta_{96}^{24} - 2 \zeta_{96}^{12} - 1} & \htmlTitle{S_{9; 8}}{-2 \zeta_{96}^{24} - 2 \zeta_{96}^{12} - 1} & \htmlTitle{S_{9; 9}}{2 \zeta_{96}^{24} + 2 \zeta_{96}^{20} - 2 \zeta_{96}^{4} - 1} & & & & & & & & & & & & \\ \htmlTitle{S_{10; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{10; 2}}{-\zeta_{96}^{28} - 2 \zeta_{96}^{16} - \zeta_{96}^{4}} & \htmlTitle{S_{10; 3}}{\zeta_{96}^{28} + \zeta_{96}^{20} + 2 \zeta_{96}^{16} - \zeta_{96}^{12} - 2} & \htmlTitle{S_{10; 4}}{-\zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + 2 \zeta_{96}^{8}} & \htmlTitle{S_{10; 5}}{-\zeta_{96}^{28} - 2 \zeta_{96}^{24} + 2 \zeta_{96}^{8} + \zeta_{96}^{4}} & \htmlTitle{S_{10; 6}}{\zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - 2 \zeta_{96}^{8}} & \htmlTitle{S_{10; 7}}{\zeta_{96}^{28} + 2 \zeta_{96}^{24} - 2 \zeta_{96}^{8} - \zeta_{96}^{4}} & \htmlTitle{S_{10; 8}}{-2 \zeta_{96}^{24} - \zeta_{96}^{20} - \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{10; 9}}{2 \zeta_{96}^{24} + \zeta_{96}^{20} + \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{10; 10}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{8}} & & & & & & & & & & & \\ \htmlTitle{S_{11; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{11; 2}}{\zeta_{96}^{28} + \zeta_{96}^{20} + 2 \zeta_{96}^{16} - \zeta_{96}^{12} - 2} & \htmlTitle{S_{11; 3}}{-\zeta_{96}^{28} - 2 \zeta_{96}^{16} - \zeta_{96}^{4}} & \htmlTitle{S_{11; 4}}{-\zeta_{96}^{28} - 2 \zeta_{96}^{24} + 2 \zeta_{96}^{8} + \zeta_{96}^{4}} & \htmlTitle{S_{11; 5}}{-\zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + 2 \zeta_{96}^{8}} & \htmlTitle{S_{11; 6}}{\zeta_{96}^{28} + 2 \zeta_{96}^{24} - 2 \zeta_{96}^{8} - \zeta_{96}^{4}} & \htmlTitle{S_{11; 7}}{\zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - 2 \zeta_{96}^{8}} & \htmlTitle{S_{11; 8}}{2 \zeta_{96}^{24} + \zeta_{96}^{20} + \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{11; 9}}{-2 \zeta_{96}^{24} - \zeta_{96}^{20} - \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{11; 10}}{-2 \zeta_{96}^{20} - 2 \zeta_{96}^{16} - 2 \zeta_{96}^{8} + 2} & \htmlTitle{S_{11; 11}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{8}} & & & & & & & & & & \\ \htmlTitle{S_{12; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{12; 2}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{12; 3}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{12; 4}}{2 \zeta_{96}^{24} + \zeta_{96}^{20} + \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{12; 5}}{-2 \zeta_{96}^{24} - \zeta_{96}^{20} - \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{12; 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5}}{\zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - 2 \zeta_{96}^{8}} & \htmlTitle{S_{14; 6}}{-\zeta_{96}^{28} - 2 \zeta_{96}^{24} + 2 \zeta_{96}^{8} + \zeta_{96}^{4}} & \htmlTitle{S_{14; 7}}{-\zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + 2 \zeta_{96}^{8}} & \htmlTitle{S_{14; 8}}{-2 \zeta_{96}^{24} - \zeta_{96}^{20} - \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{14; 9}}{2 \zeta_{96}^{24} + \zeta_{96}^{20} + \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{14; 10}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{16} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{8} + 2} & \htmlTitle{S_{14; 11}}{-2 \zeta_{96}^{24} + 2 \zeta_{96}^{16} + 2 \zeta_{96}^{8} + 2 \zeta_{96}^{4}} & \htmlTitle{S_{14; 12}}{2 \zeta_{96}^{24} + 2 \zeta_{96}^{20} - 2 \zeta_{96}^{4} - 2} & \htmlTitle{S_{14; 13}}{-2 \zeta_{96}^{24} - 2 \zeta_{96}^{12} - 2} & \htmlTitle{S_{14; 14}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{8}} & & & & & & & \\ \htmlTitle{S_{15; 1}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{15; 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13}}{2 \zeta_{96}^{24} + 2 \zeta_{96}^{20} - 2 \zeta_{96}^{4} - 2} & \htmlTitle{S_{15; 14}}{-2 \zeta_{96}^{20} - 2 \zeta_{96}^{16} - 2 \zeta_{96}^{8} + 2} & \htmlTitle{S_{15; 15}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{24} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{8}} & & & & & & \\ \htmlTitle{S_{16; 1}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 2}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 3}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 4}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 5}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 6}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 7}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 8}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 9}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{16; 10}}{0} & \htmlTitle{S_{16; 11}}{0} & \htmlTitle{S_{16; 12}}{0} & \htmlTitle{S_{16; 13}}{0} & \htmlTitle{S_{16; 14}}{0} & \htmlTitle{S_{16; 15}}{0} & \htmlTitle{S_{16; 16}}{0} & & & & & \\ \htmlTitle{S_{17; 1}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{17; 2}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{16} - 2 \zeta_{96}^{4}} & \htmlTitle{S_{17; 3}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{12} - 2} & \htmlTitle{S_{17; 4}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{12} - 2} & \htmlTitle{S_{17; 5}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{16} - 2 \zeta_{96}^{4}} & \htmlTitle{S_{17; 6}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{12} - 2} & \htmlTitle{S_{17; 7}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{16} - 2 \zeta_{96}^{4}} & \htmlTitle{S_{17; 8}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{17; 9}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{17; 10}}{0} & \htmlTitle{S_{17; 11}}{0} & \htmlTitle{S_{17; 12}}{0} & \htmlTitle{S_{17; 13}}{0} & \htmlTitle{S_{17; 14}}{0} & \htmlTitle{S_{17; 15}}{0} & \htmlTitle{S_{17; 16}}{0} & \htmlTitle{S_{17; 17}}{0} & & & & \\ \htmlTitle{S_{18; 1}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{18; 2}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{12} - 2} & \htmlTitle{S_{18; 3}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{16} - 2 \zeta_{96}^{4}} & \htmlTitle{S_{18; 4}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{16} - 2 \zeta_{96}^{4}} & \htmlTitle{S_{18; 5}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{12} - 2} & \htmlTitle{S_{18; 6}}{-2 \zeta_{96}^{28} - 2 \zeta_{96}^{16} - 2 \zeta_{96}^{4}} & \htmlTitle{S_{18; 7}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 2 \zeta_{96}^{16} - 2 \zeta_{96}^{12} - 2} & \htmlTitle{S_{18; 8}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{18; 9}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 2} & \htmlTitle{S_{18; 10}}{0} & \htmlTitle{S_{18; 11}}{0} & \htmlTitle{S_{18; 12}}{0} & \htmlTitle{S_{18; 13}}{0} & \htmlTitle{S_{18; 14}}{0} & \htmlTitle{S_{18; 15}}{0} & \htmlTitle{S_{18; 16}}{0} & \htmlTitle{S_{18; 17}}{0} & \htmlTitle{S_{18; 18}}{0} & & & \\ \htmlTitle{S_{19; 1}}{-2 \zeta_{96}^{20} + 2 \zeta_{96}^{12} + 2 \zeta_{96}^{4} + 3} & \htmlTitle{S_{19; 2}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 3 \zeta_{96}^{16} - 2 \zeta_{96}^{12} - 3} & \htmlTitle{S_{19; 3}}{-2 \zeta_{96}^{28} - 3 \zeta_{96}^{16} - 2 \zeta_{96}^{4}} & \htmlTitle{S_{19; 4}}{\zeta_{96}^{28} + \zeta_{96}^{16} + \zeta_{96}^{4}} & \htmlTitle{S_{19; 5}}{-\zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{16} + \zeta_{96}^{12} + 1} & \htmlTitle{S_{19; 6}}{\zeta_{96}^{28} + \zeta_{96}^{16} + \zeta_{96}^{4}} & \htmlTitle{S_{19; 7}}{-\zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{16} + \zeta_{96}^{12} + 1} & \htmlTitle{S_{19; 8}}{\zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4} - 1} & \htmlTitle{S_{19; 9}}{\zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4} - 1} & \htmlTitle{S_{19; 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3}}{2 \zeta_{96}^{28} + 2 \zeta_{96}^{20} + 3 \zeta_{96}^{16} - 2 \zeta_{96}^{12} - 3} & \htmlTitle{S_{20; 4}}{-\zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{16} + \zeta_{96}^{12} + 1} & \htmlTitle{S_{20; 5}}{\zeta_{96}^{28} + \zeta_{96}^{16} + \zeta_{96}^{4}} & \htmlTitle{S_{20; 6}}{-\zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{16} + \zeta_{96}^{12} + 1} & \htmlTitle{S_{20; 7}}{\zeta_{96}^{28} + \zeta_{96}^{16} + \zeta_{96}^{4}} & \htmlTitle{S_{20; 8}}{\zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4} - 1} & \htmlTitle{S_{20; 9}}{\zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4} - 1} & \htmlTitle{S_{20; 10}}{-\zeta_{96}^{28} - 2 \zeta_{96}^{16} - \zeta_{96}^{4}} & \htmlTitle{S_{20; 11}}{\zeta_{96}^{28} + \zeta_{96}^{20} + 2 \zeta_{96}^{16} - \zeta_{96}^{12} - 2} & \htmlTitle{S_{20; 12}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{20; 13}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{20; 14}}{\zeta_{96}^{28} + \zeta_{96}^{20} + 2 \zeta_{96}^{16} - \zeta_{96}^{12} - 2} & \htmlTitle{S_{20; 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8}}{\zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4} - 1} & \htmlTitle{S_{21; 9}}{\zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4} - 1} & \htmlTitle{S_{21; 10}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{21; 11}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{21; 12}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{21; 13}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{21; 14}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{21; 15}}{-\zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4} + 2} & \htmlTitle{S_{21; 16}}{2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 2} & \htmlTitle{S_{21; 17}}{2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 2} & \htmlTitle{S_{21; 18}}{2 \zeta_{96}^{20} - 2 \zeta_{96}^{12} - 2 \zeta_{96}^{4} - 2} & \htmlTitle{S_{21; 19}}{1} & \htmlTitle{S_{21; 20}}{1} & \htmlTitle{S_{21; 21}}{1}\end{array}\right) \]

Central Charge

\[c = 5 \]