\(\text{PSU}(2)_5\times \text{PSU}(2)_5:\ \text{FR}^{9,0}_{34}\)

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

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

\[\{(\mathbf{2} \ \mathbf{3}) (\mathbf{4} \ \mathbf{5}) (\mathbf{7} \ \mathbf{8})\}\]

The following particles form non-trivial sub fusion rings

Particles	SubRing
\(\{\mathbf{1},\mathbf{3},\mathbf{4}\}\)	\(\text{PSU}(2)_5:\ \text{FR}^{3,0}_{3}\)
\(\{\mathbf{1},\mathbf{2},\mathbf{5}\}\)	\(\text{PSU}(2)_5:\ \text{FR}^{3,0}_{3}\)

Quantum Dimensions

Particle	Numeric	Symbolic
\(\mathbf{1}\)	\(1.\)	\(1\)
\(\mathbf{2}\)	\(1.80194\)	\(\text{Root}\left[x^3-x^2-2 x+1,3\right]\)
\(\mathbf{3}\)	\(1.80194\)	\(\text{Root}\left[x^3-x^2-2 x+1,3\right]\)
\(\mathbf{4}\)	\(2.24698\)	\(\text{Root}\left[x^3-2 x^2-x+1,3\right]\)
\(\mathbf{5}\)	\(2.24698\)	\(\text{Root}\left[x^3-2 x^2-x+1,3\right]\)
\(\mathbf{6}\)	\(3.24698\)	\(\text{Root}\left[x^3-5 x^2+6 x-1,3\right]\)
\(\mathbf{7}\)	\(4.04892\)	\(\text{Root}\left[x^3-3 x^2-4 x-1,3\right]\)
\(\mathbf{8}\)	\(4.04892\)	\(\text{Root}\left[x^3-3 x^2-4 x-1,3\right]\)
\(\mathbf{9}\)	\(5.04892\)	\(\text{Root}\left[x^3-6 x^2+5 x-1,3\right]\)
\(\mathcal{D}_{FP}^2\)	\(86.4137\)	\(2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1\)

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 & \text{Root}\left[x^3-x^2-2 x+1,3\right] & \text{Root}\left[x^3-x^2-2 x+1,3\right] & \text{Root}\left[x^3-2 x^2-x+1,3\right] & \text{Root}\left[x^3-2 x^2-x+1,3\right] & \text{Root}\left[x^3-5 x^2+6 x-1,3\right] & \text{Root}\left[x^3-3 x^2-4 x-1,3\right] & \text{Root}\left[x^3-3 x^2-4 x-1,3\right] & \text{Root}\left[x^3-6 x^2+5 x-1,3\right] \\ 1 & \text{Root}\left[x^3-x^2-2 x+1,2\right] & \text{Root}\left[x^3-x^2-2 x+1,3\right] & \text{Root}\left[x^3-2 x^2-x+1,3\right] & \text{Root}\left[x^3-2 x^2-x+1,1\right] & \text{Root}\left[x^3+2 x^2-x-1,3\right] & \text{Root}\left[x^3+4 x^2+3 x-1,2\right] & 1 & \text{Root}\left[x^3+x^2-2 x-1,1\right] \\ 1 & \text{Root}\left[x^3-x^2-2 x+1,3\right] & \text{Root}\left[x^3-x^2-2 x+1,2\right] & \text{Root}\left[x^3-2 x^2-x+1,1\right] & \text{Root}\left[x^3-2 x^2-x+1,3\right] & \text{Root}\left[x^3+2 x^2-x-1,3\right] & 1 & \text{Root}\left[x^3+4 x^2+3 x-1,2\right] & \text{Root}\left[x^3+x^2-2 x-1,1\right] \\ 1 & \text{Root}\left[x^3-x^2-2 x+1,1\right] & \text{Root}\left[x^3-x^2-2 x+1,3\right] & \text{Root}\left[x^3-2 x^2-x+1,3\right] & \text{Root}\left[x^3-2 x^2-x+1,2\right] & \text{Root}\left[x^3+2 x^2-x-1,1\right] & 1 & \text{Root}\left[x^3+4 x^2+3 x-1,1\right] & \text{Root}\left[x^3+x^2-2 x-1,3\right] \\ 1 & \text{Root}\left[x^3-x^2-2 x+1,3\right] & \text{Root}\left[x^3-x^2-2 x+1,1\right] & \text{Root}\left[x^3-2 x^2-x+1,2\right] & \text{Root}\left[x^3-2 x^2-x+1,3\right] & \text{Root}\left[x^3+2 x^2-x-1,1\right] & \text{Root}\left[x^3+4 x^2+3 x-1,1\right] & 1 & \text{Root}\left[x^3+x^2-2 x-1,3\right] \\ 1 & \text{Root}\left[x^3-x^2-2 x+1,2\right] & \text{Root}\left[x^3-x^2-2 x+1,2\right] & \text{Root}\left[x^3-2 x^2-x+1,1\right] & \text{Root}\left[x^3-2 x^2-x+1,1\right] & \text{Root}\left[x^3-5 x^2+6 x-1,1\right] & \text{Root}\left[x^3-3 x^2-4 x-1,2\right] & \text{Root}\left[x^3-3 x^2-4 x-1,2\right] & \text{Root}\left[x^3-6 x^2+5 x-1,2\right] \\ 1 & \text{Root}\left[x^3-x^2-2 x+1,1\right] & \text{Root}\left[x^3-x^2-2 x+1,2\right] & \text{Root}\left[x^3-2 x^2-x+1,1\right] & \text{Root}\left[x^3-2 x^2-x+1,2\right] & \text{Root}\left[x^3+2 x^2-x-1,2\right] & \text{Root}\left[x^3+4 x^2+3 x-1,3\right] & 1 & \text{Root}\left[x^3+x^2-2 x-1,2\right] \\ 1 & \text{Root}\left[x^3-x^2-2 x+1,2\right] & \text{Root}\left[x^3-x^2-2 x+1,1\right] & \text{Root}\left[x^3-2 x^2-x+1,2\right] & \text{Root}\left[x^3-2 x^2-x+1,1\right] & \text{Root}\left[x^3+2 x^2-x-1,2\right] & 1 & \text{Root}\left[x^3+4 x^2+3 x-1,3\right] & \text{Root}\left[x^3+x^2-2 x-1,2\right] \\ 1 & \text{Root}\left[x^3-x^2-2 x+1,1\right] & \text{Root}\left[x^3-x^2-2 x+1,1\right] & \text{Root}\left[x^3-2 x^2-x+1,2\right] & \text{Root}\left[x^3-2 x^2-x+1,2\right] & \text{Root}\left[x^3-5 x^2+6 x-1,2\right] & \text{Root}\left[x^3-3 x^2-4 x-1,1\right] & \text{Root}\left[x^3-3 x^2-4 x-1,1\right] & \text{Root}\left[x^3-6 x^2+5 x-1,1\right] \\ \hline \end{array}\]

The numeric character table is the following

\[\begin{array}{|rrrrrrrrr|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{9} \\ \hline 1.000 & 1.802 & 1.802 & 2.247 & 2.247 & 3.247 & 4.049 & 4.049 & 5.049 \\ 1.000 & 0.4450 & 1.802 & 2.247 & -0.8019 & 0.8019 & -1.445 & 1.000 & -1.802 \\ 1.000 & 1.802 & 0.4450 & -0.8019 & 2.247 & 0.8019 & 1.000 & -1.445 & -1.802 \\ 1.000 & -1.247 & 1.802 & 2.247 & 0.5550 & -2.247 & 1.000 & -2.802 & 1.247 \\ 1.000 & 1.802 & -1.247 & 0.5550 & 2.247 & -2.247 & -2.802 & 1.000 & 1.247 \\ 1.000 & 0.4450 & 0.4450 & -0.8019 & -0.8019 & 0.1981 & -0.3569 & -0.3569 & 0.6431 \\ 1.000 & -1.247 & 0.4450 & -0.8019 & 0.5550 & -0.5550 & 0.2470 & 1.000 & -0.4450 \\ 1.000 & 0.4450 & -1.247 & 0.5550 & -0.8019 & -0.5550 & 1.000 & 0.2470 & -0.4450 \\ 1.000 & -1.247 & -1.247 & 0.5550 & 0.5550 & 1.555 & -0.6920 & -0.6920 & 0.3080 \\ \hline \end{array}\]

Modular Data

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

\(S\)-matrix	Twist factors
\(\frac{1}{\sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1}}\left(\begin{array}{ccccccccc} \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\\end{array}\right)\)	\(\begin{array}{l}\left(0,\frac{1}{7},\frac{1}{7},-\frac{2}{7},-\frac{2}{7},\frac{2}{7},-\frac{1}{7},-\frac{1}{7},\frac{3}{7}\right) \\\left(0,\frac{1}{7},-\frac{1}{7},\frac{2}{7},-\frac{2}{7},0,-\frac{3}{7},\frac{3}{7},0\right) \\\left(0,-\frac{1}{7},\frac{1}{7},-\frac{2}{7},\frac{2}{7},0,\frac{3}{7},-\frac{3}{7},0\right) \\\left(0,-\frac{1}{7},-\frac{1}{7},\frac{2}{7},\frac{2}{7},-\frac{2}{7},\frac{1}{7},\frac{1}{7},-\frac{3}{7}\right)\end{array}\)

\(S\)-matrix

Twist factors

\(\frac{1}{\sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1}}\left(\begin{array}{ccccccccc} \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3+49 x^2+14 x+1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\ \text{Root}\left[49 x^3-49 x^2+14 x-1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,3\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x+1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,1\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-7 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} & \text{Root}\left[49 x^3-49 x^2+14 x-1,2\right] \sqrt{2 \text{Root}\left[x^3-x^2-2 x+1,3\right]^2+2 \text{Root}\left[x^3-2 x^2-x+1,3\right]^2+\text{Root}\left[x^3-5 x^2+6 x-1,3\right]^2+2 \text{Root}\left[x^3-3 x^2-4 x-1,3\right]^2+\text{Root}\left[x^3-6 x^2+5 x-1,3\right]^2+1} \\\end{array}\right)\)

\(\begin{array}{l}\left(0,\frac{1}{7},\frac{1}{7},-\frac{2}{7},-\frac{2}{7},\frac{2}{7},-\frac{1}{7},-\frac{1}{7},\frac{3}{7}\right) \\\left(0,\frac{1}{7},-\frac{1}{7},\frac{2}{7},-\frac{2}{7},0,-\frac{3}{7},\frac{3}{7},0\right) \\\left(0,-\frac{1}{7},\frac{1}{7},-\frac{2}{7},\frac{2}{7},0,\frac{3}{7},-\frac{3}{7},0\right) \\\left(0,-\frac{1}{7},-\frac{1}{7},\frac{2}{7},\frac{2}{7},-\frac{2}{7},\frac{1}{7},\frac{1}{7},-\frac{3}{7}\right)\end{array}\)

Adjoint Subring

The adjoint subring is the ring itself.

The upper central series is trivial.

Universal grading

This fusion ring allows only the trivial grading.

Categorifications

Data

Download links for numeric data:

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