AnyonWiki

\(\text{FR}^{9,0}_{19}\)

Fusion Rules

\[\begin{array}{|lllllllll|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{9} \\ \mathbf{2} & \mathbf{1} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{9} & \mathbf{8} \\ \mathbf{3} & \mathbf{3} & \mathbf{1}+\mathbf{2}+\mathbf{7} & \mathbf{6}+\mathbf{7} & \mathbf{5}+\mathbf{6} & \mathbf{4}+\mathbf{5} & \mathbf{3}+\mathbf{4} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} \\ \mathbf{4} & \mathbf{4} & \mathbf{6}+\mathbf{7} & \mathbf{1}+\mathbf{2}+\mathbf{5} & \mathbf{4}+\mathbf{7} & \mathbf{3}+\mathbf{6} & \mathbf{3}+\mathbf{5} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} \\ \mathbf{5} & \mathbf{5} & \mathbf{5}+\mathbf{6} & \mathbf{4}+\mathbf{7} & \mathbf{1}+\mathbf{2}+\mathbf{3} & \mathbf{3}+\mathbf{7} & \mathbf{4}+\mathbf{6} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} \\ \mathbf{6} & \mathbf{6} & \mathbf{4}+\mathbf{5} & \mathbf{3}+\mathbf{6} & \mathbf{3}+\mathbf{7} & \mathbf{1}+\mathbf{2}+\mathbf{4} & \mathbf{5}+\mathbf{7} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} \\ \mathbf{7} & \mathbf{7} & \mathbf{3}+\mathbf{4} & \mathbf{3}+\mathbf{5} & \mathbf{4}+\mathbf{6} & \mathbf{5}+\mathbf{7} & \mathbf{1}+\mathbf{2}+\mathbf{6} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} \\ \mathbf{8} & \mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{1}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7} & \mathbf{2}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7} \\ \mathbf{9} & \mathbf{8} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{2}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7} & \mathbf{1}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7} \\ \hline \end{array}\]

The fusion rules are invariant under the group generated by the following permutations:

\[\{(\mathbf{8} \ \mathbf{9}), (\mathbf{3} \ \mathbf{4} \ \mathbf{7} \ \mathbf{5} \ \mathbf{6}), (\mathbf{3} \ \mathbf{5} \ \mathbf{4} \ \mathbf{6} \ \mathbf{7})\}\]

The following particles form non-trivial sub fusion rings

Particles SubRing
\(\{\mathbf{1},\mathbf{2}\}\) \(\mathbb{Z}_2:\ \text{FR}^{2,0}_{1}\)
\(\{\mathbf{1},\mathbf{2},\mathbf{3},\mathbf{4},\mathbf{5},\mathbf{6},\mathbf{7}\}\) \(\text{FR}^{7,0}_{6}\)

Quantum Dimensions

Particle Numeric Symbolic
\(\mathbf{1}\) \(1.\) \(1\)
\(\mathbf{2}\) \(1.\) \(1\)
\(\mathbf{3}\) \(2.\) \(2\)
\(\mathbf{4}\) \(2.\) \(2\)
\(\mathbf{5}\) \(2.\) \(2\)
\(\mathbf{6}\) \(2.\) \(2\)
\(\mathbf{7}\) \(2.\) \(2\)
\(\mathbf{8}\) \(3.31662\) \(\sqrt{11}\)
\(\mathbf{9}\) \(3.31662\) \(\sqrt{11}\)
\(\mathcal{D}_{FP}^2\) \(44.\) \(44\)

Characters

The symbolic character table is the following

\[\begin{array}{|ccccccccc|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{9} \\ \hline 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 1 & 1 & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,4\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,1\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,5\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,3\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,2\right] & 0 & 0 \\ 1 & 1 & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,3\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,4\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,2\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,5\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,1\right] & 0 & 0 \\ 1 & 1 & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,5\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,3\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,1\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,2\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,4\right] & 0 & 0 \\ 1 & 1 & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,1\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,2\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,3\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,4\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,5\right] & 0 & 0 \\ 1 & 1 & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,2\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,5\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,4\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,1\right] & \text{Root}\left[x^5+x^4-4 x^3-3 x^2+3 x+1,3\right] & 0 & 0 \\ 1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ \hline \end{array}\]

The numeric character table is the following

\[\begin{array}{|rrrrrrrrr|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{9} \\ \hline 1.000 & 1.000 & 2.000 & 2.000 & 2.000 & 2.000 & 2.000 & 3.317 & 3.317 \\ 1.000 & 1.000 & 2.000 & 2.000 & 2.000 & 2.000 & 2.000 & -3.317 & -3.317 \\ 1.000 & 1.000 & 0.8308 & -1.919 & 1.683 & -0.2846 & -1.310 & 0 & 0 \\ 1.000 & 1.000 & -0.2846 & 0.8308 & -1.310 & 1.683 & -1.919 & 0 & 0 \\ 1.000 & 1.000 & 1.683 & -0.2846 & -1.919 & -1.310 & 0.8308 & 0 & 0 \\ 1.000 & 1.000 & -1.919 & -1.310 & -0.2846 & 0.8308 & 1.683 & 0 & 0 \\ 1.000 & 1.000 & -1.310 & 1.683 & 0.8308 & -1.919 & -0.2846 & 0 & 0 \\ 1.000 & -1.000 & 0 & 0 & 0 & 0 & 0 & 1.000 & -1.000 \\ 1.000 & -1.000 & 0 & 0 & 0 & 0 & 0 & -1.000 & 1.000 \\ \hline \end{array}\]

Modular Data

The matching \(S\)-matrices and twist factors are the following

\(S\)-matrix Twist factors
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,\frac{5}{11},\frac{1}{11},\frac{4}{11},\frac{3}{11},-\frac{2}{11},-\frac{3}{8},\frac{1}{8}\right) \\\left(0,0,\frac{5}{11},\frac{1}{11},\frac{4}{11},\frac{3}{11},-\frac{2}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,-\frac{5}{11},-\frac{1}{11},-\frac{4}{11},-\frac{3}{11},\frac{2}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,-\frac{5}{11},-\frac{1}{11},-\frac{4}{11},-\frac{3}{11},\frac{2}{11},-\frac{1}{8},\frac{3}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,\frac{5}{11},\frac{1}{11},\frac{4}{11},\frac{3}{11},-\frac{2}{11},-\frac{1}{8},\frac{3}{8}\right) \\\left(0,0,\frac{5}{11},\frac{1}{11},\frac{4}{11},\frac{3}{11},-\frac{2}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,-\frac{5}{11},-\frac{1}{11},-\frac{4}{11},-\frac{3}{11},\frac{2}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,-\frac{5}{11},-\frac{1}{11},-\frac{4}{11},-\frac{3}{11},\frac{2}{11},-\frac{3}{8},\frac{1}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,\frac{4}{11},\frac{3}{11},\frac{1}{11},-\frac{2}{11},\frac{5}{11},-\frac{3}{8},\frac{1}{8}\right) \\\left(0,0,\frac{4}{11},\frac{3}{11},\frac{1}{11},-\frac{2}{11},\frac{5}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,-\frac{4}{11},-\frac{3}{11},-\frac{1}{11},\frac{2}{11},-\frac{5}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,-\frac{4}{11},-\frac{3}{11},-\frac{1}{11},\frac{2}{11},-\frac{5}{11},-\frac{1}{8},\frac{3}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,\frac{4}{11},\frac{3}{11},\frac{1}{11},-\frac{2}{11},\frac{5}{11},-\frac{1}{8},\frac{3}{8}\right) \\\left(0,0,\frac{4}{11},\frac{3}{11},\frac{1}{11},-\frac{2}{11},\frac{5}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,-\frac{4}{11},-\frac{3}{11},-\frac{1}{11},\frac{2}{11},-\frac{5}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,-\frac{4}{11},-\frac{3}{11},-\frac{1}{11},\frac{2}{11},-\frac{5}{11},-\frac{3}{8},\frac{1}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,-\frac{2}{11},\frac{4}{11},\frac{5}{11},\frac{1}{11},\frac{3}{11},-\frac{3}{8},\frac{1}{8}\right) \\\left(0,0,-\frac{2}{11},\frac{4}{11},\frac{5}{11},\frac{1}{11},\frac{3}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,\frac{2}{11},-\frac{4}{11},-\frac{5}{11},-\frac{1}{11},-\frac{3}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,\frac{2}{11},-\frac{4}{11},-\frac{5}{11},-\frac{1}{11},-\frac{3}{11},-\frac{1}{8},\frac{3}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,-\frac{2}{11},\frac{4}{11},\frac{5}{11},\frac{1}{11},\frac{3}{11},-\frac{1}{8},\frac{3}{8}\right) \\\left(0,0,-\frac{2}{11},\frac{4}{11},\frac{5}{11},\frac{1}{11},\frac{3}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,\frac{2}{11},-\frac{4}{11},-\frac{5}{11},-\frac{1}{11},-\frac{3}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,\frac{2}{11},-\frac{4}{11},-\frac{5}{11},-\frac{1}{11},-\frac{3}{11},-\frac{3}{8},\frac{1}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,\frac{1}{11},-\frac{2}{11},\frac{3}{11},\frac{5}{11},\frac{4}{11},-\frac{3}{8},\frac{1}{8}\right) \\\left(0,0,\frac{1}{11},-\frac{2}{11},\frac{3}{11},\frac{5}{11},\frac{4}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,-\frac{1}{11},\frac{2}{11},-\frac{3}{11},-\frac{5}{11},-\frac{4}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,-\frac{1}{11},\frac{2}{11},-\frac{3}{11},-\frac{5}{11},-\frac{4}{11},-\frac{1}{8},\frac{3}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,\frac{1}{11},-\frac{2}{11},\frac{3}{11},\frac{5}{11},\frac{4}{11},-\frac{1}{8},\frac{3}{8}\right) \\\left(0,0,\frac{1}{11},-\frac{2}{11},\frac{3}{11},\frac{5}{11},\frac{4}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,-\frac{1}{11},\frac{2}{11},-\frac{3}{11},-\frac{5}{11},-\frac{4}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,-\frac{1}{11},\frac{2}{11},-\frac{3}{11},-\frac{5}{11},-\frac{4}{11},-\frac{3}{8},\frac{1}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,\frac{3}{11},\frac{5}{11},-\frac{2}{11},\frac{4}{11},\frac{1}{11},-\frac{3}{8},\frac{1}{8}\right) \\\left(0,0,\frac{3}{11},\frac{5}{11},-\frac{2}{11},\frac{4}{11},\frac{1}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,-\frac{3}{11},-\frac{5}{11},\frac{2}{11},-\frac{4}{11},-\frac{1}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,-\frac{3}{11},-\frac{5}{11},\frac{2}{11},-\frac{4}{11},-\frac{1}{11},-\frac{1}{8},\frac{3}{8}\right)\end{array}\)
\(\frac{1}{2 \sqrt{11}}\left(\begin{array}{ccccccccc} 1 & 1 & 2 & 2 & 2 & 2 & 2 & \sqrt{11} & \sqrt{11} \\ 1 & 1 & 2 & 2 & 2 & 2 & 2 & -\sqrt{11} & -\sqrt{11} \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 0 & 0 \\ 2 & 2 & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,9\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,5\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,1\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,3\right] & 2 \sqrt{11} \text{Root}\left[161051 x^{10}-131769 x^8+37268 x^6-4235 x^4+165 x^2-1,7\right] & 0 & 0 \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & -\sqrt{11} & \sqrt{11} \\ \sqrt{11} & -\sqrt{11} & 0 & 0 & 0 & 0 & 0 & \sqrt{11} & -\sqrt{11} \\\end{array}\right)\) \(\begin{array}{l}\left(0,0,\frac{3}{11},\frac{5}{11},-\frac{2}{11},\frac{4}{11},\frac{1}{11},-\frac{1}{8},\frac{3}{8}\right) \\\left(0,0,\frac{3}{11},\frac{5}{11},-\frac{2}{11},\frac{4}{11},\frac{1}{11},\frac{3}{8},-\frac{1}{8}\right) \\\left(0,0,-\frac{3}{11},-\frac{5}{11},\frac{2}{11},-\frac{4}{11},-\frac{1}{11},\frac{1}{8},-\frac{3}{8}\right) \\\left(0,0,-\frac{3}{11},-\frac{5}{11},\frac{2}{11},-\frac{4}{11},-\frac{1}{11},-\frac{3}{8},\frac{1}{8}\right)\end{array}\)

Adjoint Subring

Particles \(\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}\), form the adjoint subring \(\text{FR}^{7,0}_{6}\) .

The upper central series is the following: \(\text{FR}^{9,0}_{19} \underset{ \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7} }{\supset} \text{FR}^{7,0}_{6}\)

Universal grading

Each particle can be graded as follows: \(\text{deg}(\mathbf{1}) = \mathbf{1}', \text{deg}(\mathbf{2}) = \mathbf{1}', \text{deg}(\mathbf{3}) = \mathbf{1}', \text{deg}(\mathbf{4}) = \mathbf{1}', \text{deg}(\mathbf{5}) = \mathbf{1}', \text{deg}(\mathbf{6}) = \mathbf{1}', \text{deg}(\mathbf{7}) = \mathbf{1}', \text{deg}(\mathbf{8}) = \mathbf{2}', \text{deg}(\mathbf{9}) = \mathbf{2}'\), where the degrees form the group \(\mathbb{Z}_2\) with multiplication table:

\[\begin{array}{|ll|} \hline \mathbf{1}' & \mathbf{2}' \\ \mathbf{2}' & \mathbf{1}' \\ \hline \end{array}\]

Categorifications

Data

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