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\(\text{Ising×\times }\text{PSU}(2)_5:\ \text{FR}^{9,0}_{14}\)

Fusion Rules

123456789213547689331+288994+56+74581+62+74+65+73+98+95482+71+65+74+63+98+96794+65+71+4+62+5+78+93+8+97695+74+62+5+71+4+68+93+8+9884+53+93+98+98+91+2+6+74+5+6+7996+78+98+93+8+93+8+94+5+6+71+2+4+5+6+7\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{5} & \mathbf{4} & \mathbf{7} & \mathbf{6} & \mathbf{8} & \mathbf{9} \\ \mathbf{3} & \mathbf{3} & \mathbf{1}+\mathbf{2} & \mathbf{8} & \mathbf{8} & \mathbf{9} & \mathbf{9} & \mathbf{4}+\mathbf{5} & \mathbf{6}+\mathbf{7} \\ \mathbf{4} & \mathbf{5} & \mathbf{8} & \mathbf{1}+\mathbf{6} & \mathbf{2}+\mathbf{7} & \mathbf{4}+\mathbf{6} & \mathbf{5}+\mathbf{7} & \mathbf{3}+\mathbf{9} & \mathbf{8}+\mathbf{9} \\ \mathbf{5} & \mathbf{4} & \mathbf{8} & \mathbf{2}+\mathbf{7} & \mathbf{1}+\mathbf{6} & \mathbf{5}+\mathbf{7} & \mathbf{4}+\mathbf{6} & \mathbf{3}+\mathbf{9} & \mathbf{8}+\mathbf{9} \\ \mathbf{6} & \mathbf{7} & \mathbf{9} & \mathbf{4}+\mathbf{6} & \mathbf{5}+\mathbf{7} & \mathbf{1}+\mathbf{4}+\mathbf{6} & \mathbf{2}+\mathbf{5}+\mathbf{7} & \mathbf{8}+\mathbf{9} & \mathbf{3}+\mathbf{8}+\mathbf{9} \\ \mathbf{7} & \mathbf{6} & \mathbf{9} & \mathbf{5}+\mathbf{7} & \mathbf{4}+\mathbf{6} & \mathbf{2}+\mathbf{5}+\mathbf{7} & \mathbf{1}+\mathbf{4}+\mathbf{6} & \mathbf{8}+\mathbf{9} & \mathbf{3}+\mathbf{8}+\mathbf{9} \\ \mathbf{8} & \mathbf{8} & \mathbf{4}+\mathbf{5} & \mathbf{3}+\mathbf{9} & \mathbf{3}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{1}+\mathbf{2}+\mathbf{6}+\mathbf{7} & \mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7} \\ \mathbf{9} & \mathbf{9} & \mathbf{6}+\mathbf{7} & \mathbf{8}+\mathbf{9} & \mathbf{8}+\mathbf{9} & \mathbf{3}+\mathbf{8}+\mathbf{9} & \mathbf{3}+\mathbf{8}+\mathbf{9} & \mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7} & \mathbf{1}+\mathbf{2}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7} \\ \hline \end{array}

The following particles form non-trivial sub fusion rings

Particles SubRing
{1,2}\{\mathbf{1},\mathbf{2}\} Z2: FR12,0\mathbb{Z}_2:\ \text{FR}^{2,0}_{1}
{1,2,3}\{\mathbf{1},\mathbf{2},\mathbf{3}\} Ising: FR13,0\text{Ising}:\ \text{FR}^{3,0}_{1}
{1,4,6}\{\mathbf{1},\mathbf{4},\mathbf{6}\} PSU(2)5: FR33,0\text{PSU}(2)_5:\ \text{FR}^{3,0}_{3}
{1,2,4,5,6,7}\{\mathbf{1},\mathbf{2},\mathbf{4},\mathbf{5},\mathbf{6},\mathbf{7}\} SU(2)5: FR66,0\text{SU(2})_5:\ \text{FR}^{6,0}_{6}

Quantum Dimensions

Particle Numeric Symbolic
1\mathbf{1} 1.1. 11
2\mathbf{2} 1.1. 11
3\mathbf{3} 1.414211.41421 2\sqrt{2}
4\mathbf{4} 1.801941.80194 Root[x3−x2−2x+1,3]\text{Root}\left[x^3-x^2-2 x+1,3\right]
5\mathbf{5} 1.801941.80194 Root[x3−x2−2x+1,3]\text{Root}\left[x^3-x^2-2 x+1,3\right]
6\mathbf{6} 2.246982.24698 Root[x3−2x2−x+1,3]\text{Root}\left[x^3-2 x^2-x+1,3\right]
7\mathbf{7} 2.246982.24698 Root[x3−2x2−x+1,3]\text{Root}\left[x^3-2 x^2-x+1,3\right]
8\mathbf{8} 2.548322.54832 Root[x3−10x2+24x−8,3]\sqrt{\text{Root}\left[x^3-10 x^2+24 x-8,3\right]}
9\mathbf{9} 3.177713.17771 Root[x3−12x2+20x−8,3]\sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]}
DFP2\mathcal{D}_{FP}^2 37.183637.1836 Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4

Characters

The symbolic character table is the following

123546789112Root[x3−x2−2x+1,3]Root[x3−x2−2x+1,3]Root[x3−2x2−x+1,3]Root[x3−2x2−x+1,3]Root[x6−10x4+24x2−8,6]Root[x6−12x4+20x2−8,6]11−2Root[x3−x2−2x+1,3]Root[x3−x2−2x+1,3]Root[x3−2x2−x+1,3]Root[x3−2x2−x+1,3]Root[x6−10x4+24x2−8,1]Root[x6−12x4+20x2−8,1]112Root[x3−x2−2x+1,2]Root[x3−x2−2x+1,2]Root[x3−2x2−x+1,1]Root[x3−2x2−x+1,1]Root[x6−10x4+24x2−8,4]Root[x6−12x4+20x2−8,2]112Root[x3−x2−2x+1,1]Root[x3−x2−2x+1,1]Root[x3−2x2−x+1,2]Root[x3−2x2−x+1,2]Root[x6−10x4+24x2−8,2]Root[x6−12x4+20x2−8,4]11−2Root[x3−x2−2x+1,2]Root[x3−x2−2x+1,2]Root[x3−2x2−x+1,1]Root[x3−2x2−x+1,1]Root[x6−10x4+24x2−8,3]Root[x6−12x4+20x2−8,5]11−2Root[x3−x2−2x+1,1]Root[x3−x2−2x+1,1]Root[x3−2x2−x+1,2]Root[x3−2x2−x+1,2]Root[x6−10x4+24x2−8,5]Root[x6−12x4+20x2−8,3]1−10Root[x3+x2−2x−1,3]Root[x3−x2−2x+1,1]Root[x3−2x2−x+1,2]Root[x3+2x2−x−1,2]001−10Root[x3+x2−2x−1,1]Root[x3−x2−2x+1,3]Root[x3−2x2−x+1,3]Root[x3+2x2−x−1,1]001−10Root[x3+x2−2x−1,2]Root[x3−x2−2x+1,2]Root[x3−2x2−x+1,1]Root[x3+2x2−x−1,3]00\begin{array}{|ccccccccc|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{5} & \mathbf{4} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{9} \\ \hline 1 & 1 & \sqrt{2} & \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^6-10 x^4+24 x^2-8,6\right] & \text{Root}\left[x^6-12 x^4+20 x^2-8,6\right] \\ 1 & 1 & -\sqrt{2} & \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^6-10 x^4+24 x^2-8,1\right] & \text{Root}\left[x^6-12 x^4+20 x^2-8,1\right] \\ 1 & 1 & \sqrt{2} & \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^6-10 x^4+24 x^2-8,4\right] & \text{Root}\left[x^6-12 x^4+20 x^2-8,2\right] \\ 1 & 1 & \sqrt{2} & \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^6-10 x^4+24 x^2-8,2\right] & \text{Root}\left[x^6-12 x^4+20 x^2-8,4\right] \\ 1 & 1 & -\sqrt{2} & \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^6-10 x^4+24 x^2-8,3\right] & \text{Root}\left[x^6-12 x^4+20 x^2-8,5\right] \\ 1 & 1 & -\sqrt{2} & \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^6-10 x^4+24 x^2-8,5\right] & \text{Root}\left[x^6-12 x^4+20 x^2-8,3\right] \\ 1 & -1 & 0 & \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-1,2\right] & 0 & 0 \\ 1 & -1 & 0 & \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-1,1\right] & 0 & 0 \\ 1 & -1 & 0 & \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-1,3\right] & 0 & 0 \\ \hline \end{array}

The numeric character table is the following

1235467891.0001.0001.4141.8021.8022.2472.2472.5483.1781.0001.000−1.4141.8021.8022.2472.247−2.548−3.1781.0001.0001.4140.44500.4450−0.8019−0.80190.6294−1.1341.0001.0001.414−1.247−1.2470.55500.5550−1.7630.78481.0001.000−1.4140.44500.4450−0.8019−0.8019−0.62941.1341.0001.000−1.414−1.247−1.2470.55500.55501.763−0.78481.000−1.00001.247−1.2470.5550−0.5550001.000−1.0000−1.8021.8022.247−2.247001.000−1.0000−0.44500.4450−0.80190.801900\begin{array}{|rrrrrrrrr|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{5} & \mathbf{4} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{9} \\ \hline 1.000 & 1.000 & 1.414 & 1.802 & 1.802 & 2.247 & 2.247 & 2.548 & 3.178 \\ 1.000 & 1.000 & -1.414 & 1.802 & 1.802 & 2.247 & 2.247 & -2.548 & -3.178 \\ 1.000 & 1.000 & 1.414 & 0.4450 & 0.4450 & -0.8019 & -0.8019 & 0.6294 & -1.134 \\ 1.000 & 1.000 & 1.414 & -1.247 & -1.247 & 0.5550 & 0.5550 & -1.763 & 0.7848 \\ 1.000 & 1.000 & -1.414 & 0.4450 & 0.4450 & -0.8019 & -0.8019 & -0.6294 & 1.134 \\ 1.000 & 1.000 & -1.414 & -1.247 & -1.247 & 0.5550 & 0.5550 & 1.763 & -0.7848 \\ 1.000 & -1.000 & 0 & 1.247 & -1.247 & 0.5550 & -0.5550 & 0 & 0 \\ 1.000 & -1.000 & 0 & -1.802 & 1.802 & 2.247 & -2.247 & 0 & 0 \\ 1.000 & -1.000 & 0 & -0.4450 & 0.4450 & -0.8019 & 0.8019 & 0 & 0 \\ \hline \end{array}

Modular Data

The matching SS-matrices and twist factors are the following

SS-matrix Twist factors
1Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4(Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,4]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,5]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,6]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,4]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+40Root[392x6−196x4+28x2−1,5]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,6]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+400Root[56x3−28x2+1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,5]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,4]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,6]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,6]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,4]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3−28x2+1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[56x3+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,5]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,5]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+40Root[392x6−196x4+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,6]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,4]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+400Root[392x6−196x4+28x2−1,6]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,1]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+40Root[392x6−196x4+28x2−1,4]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,3]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,2]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+4Root[392x6−196x4+28x2−1,5]Root[x3−12x2+20x−8,3]+2Root[x3−x2−2x+1,3]2+2Root[x3−2x2−x+1,3]2+Root[x3−10x2+24x−8,3]+400)\frac{1}{\sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4}}\left(\begin{array}{ccccccccc} \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,4\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,5\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,6\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} \\ \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} \\ \text{Root}\left[392 x^6-196 x^4+28 x^2-1,4\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & 0 & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,5\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,6\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & 0 & 0 \\ \text{Root}\left[56 x^3-28 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,5\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,4\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} \\ \text{Root}\left[56 x^3-28 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,6\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} \\ \text{Root}\left[56 x^3-28 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,6\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,4\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} \\ \text{Root}\left[56 x^3-28 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3-28 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[56 x^3+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,5\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} \\ \text{Root}\left[392 x^6-196 x^4+28 x^2-1,5\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & 0 & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,6\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,4\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & 0 & 0 \\ \text{Root}\left[392 x^6-196 x^4+28 x^2-1,6\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,1\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & 0 & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,4\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,3\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,2\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & \text{Root}\left[392 x^6-196 x^4+28 x^2-1,5\right] \sqrt{\text{Root}\left[x^3-12 x^2+20 x-8,3\right]+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^3-10 x^2+24 x-8,3\right]+4} & 0 & 0 \\\end{array}\right) (0,12,−716,17,−514,−27,314,−33112,31112)(0,12,116,−17,514,27,−314,−9112,39112)(0,12,316,17,−514,−27,314,37112,−11112)(0,12,−516,−17,514,27,−314,−51112,−3112)(0,12,−316,17,−514,−27,314,−5112,−53112)(0,12,516,−17,514,27,−314,19112,−45112)(0,12,716,17,−514,−27,314,−47112,17112)(0,12,−116,−17,514,27,−314,−23112,25112)(0,12,116,17,−514,−27,314,23112,−25112)(0,12,−716,−17,514,27,−314,47112,−17112)(0,12,−516,17,−514,−27,314,−19112,45112)(0,12,316,−17,514,27,−314,5112,53112)(0,12,516,17,−514,−27,314,51112,3112)(0,12,−316,−17,514,27,−314,−37112,11112)(0,12,−116,17,−514,−27,314,9112,−39112)(0,12,716,−17,514,27,−314,33112,−31112)\begin{array}{l}\left(0,\frac{1}{2},-\frac{7}{16},\frac{1}{7},-\frac{5}{14},-\frac{2}{7},\frac{3}{14},-\frac{33}{112},\frac{31}{112}\right) \\\left(0,\frac{1}{2},\frac{1}{16},-\frac{1}{7},\frac{5}{14},\frac{2}{7},-\frac{3}{14},-\frac{9}{112},\frac{39}{112}\right) \\\left(0,\frac{1}{2},\frac{3}{16},\frac{1}{7},-\frac{5}{14},-\frac{2}{7},\frac{3}{14},\frac{37}{112},-\frac{11}{112}\right) \\\left(0,\frac{1}{2},-\frac{5}{16},-\frac{1}{7},\frac{5}{14},\frac{2}{7},-\frac{3}{14},-\frac{51}{112},-\frac{3}{112}\right) \\\left(0,\frac{1}{2},-\frac{3}{16},\frac{1}{7},-\frac{5}{14},-\frac{2}{7},\frac{3}{14},-\frac{5}{112},-\frac{53}{112}\right) \\\left(0,\frac{1}{2},\frac{5}{16},-\frac{1}{7},\frac{5}{14},\frac{2}{7},-\frac{3}{14},\frac{19}{112},-\frac{45}{112}\right) \\\left(0,\frac{1}{2},\frac{7}{16},\frac{1}{7},-\frac{5}{14},-\frac{2}{7},\frac{3}{14},-\frac{47}{112},\frac{17}{112}\right) \\\left(0,\frac{1}{2},-\frac{1}{16},-\frac{1}{7},\frac{5}{14},\frac{2}{7},-\frac{3}{14},-\frac{23}{112},\frac{25}{112}\right) \\\left(0,\frac{1}{2},\frac{1}{16},\frac{1}{7},-\frac{5}{14},-\frac{2}{7},\frac{3}{14},\frac{23}{112},-\frac{25}{112}\right) \\\left(0,\frac{1}{2},-\frac{7}{16},-\frac{1}{7},\frac{5}{14},\frac{2}{7},-\frac{3}{14},\frac{47}{112},-\frac{17}{112}\right) \\\left(0,\frac{1}{2},-\frac{5}{16},\frac{1}{7},-\frac{5}{14},-\frac{2}{7},\frac{3}{14},-\frac{19}{112},\frac{45}{112}\right) \\\left(0,\frac{1}{2},\frac{3}{16},-\frac{1}{7},\frac{5}{14},\frac{2}{7},-\frac{3}{14},\frac{5}{112},\frac{53}{112}\right) \\\left(0,\frac{1}{2},\frac{5}{16},\frac{1}{7},-\frac{5}{14},-\frac{2}{7},\frac{3}{14},\frac{51}{112},\frac{3}{112}\right) \\\left(0,\frac{1}{2},-\frac{3}{16},-\frac{1}{7},\frac{5}{14},\frac{2}{7},-\frac{3}{14},-\frac{37}{112},\frac{11}{112}\right) \\\left(0,\frac{1}{2},-\frac{1}{16},\frac{1}{7},-\frac{5}{14},-\frac{2}{7},\frac{3}{14},\frac{9}{112},-\frac{39}{112}\right) \\\left(0,\frac{1}{2},\frac{7}{16},-\frac{1}{7},\frac{5}{14},\frac{2}{7},-\frac{3}{14},\frac{33}{112},-\frac{31}{112}\right)\end{array}

Adjoint Subring

Particles 1,2,4,5,6,7\mathbf{1}, \mathbf{2}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}, form the adjoint subring SU(2)5: FR66,0\text{SU(2})_5:\ \text{FR}^{6,0}_{6} .

The upper central series is the following: \(\text{Ising×\times }\text{PSU}(2)_5 \underset{ \mathbf{1}, \mathbf{2}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7} }{\supset} \text{SU(2})_5 \underset{ \mathbf{1}, \mathbf{3}, \mathbf{4} }{\supset} \text{PSU}(2)_5\)

Universal grading

Each particle can be graded as follows: deg(1)=1′,deg(2)=1′,deg(3)=2′,deg(4)=1′,deg(5)=1′,deg(6)=1′,deg(7)=1′,deg(8)=2′,deg(9)=2′\text{deg}(\mathbf{1}) = \mathbf{1}', \text{deg}(\mathbf{2}) = \mathbf{1}', \text{deg}(\mathbf{3}) = \mathbf{2}', \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 Z2\mathbb{Z}_2 with multiplication table:

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

Categorifications

Data

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