\(\text{Fib$\times $}\text{PSU}(2)_7:\ \text{FR}^{8,0}_{27}\)
Fusion Rules
\[\begin{array}{|llllllll|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} \\ \mathbf{2} & \mathbf{1}+\mathbf{2} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{3}+\mathbf{6} & \mathbf{4}+\mathbf{7} & \mathbf{5}+\mathbf{8} \\ \mathbf{3} & \mathbf{6} & \mathbf{1}+\mathbf{4} & \mathbf{3}+\mathbf{5} & \mathbf{4}+\mathbf{5} & \mathbf{2}+\mathbf{7} & \mathbf{6}+\mathbf{8} & \mathbf{7}+\mathbf{8} \\ \mathbf{4} & \mathbf{7} & \mathbf{3}+\mathbf{5} & \mathbf{1}+\mathbf{4}+\mathbf{5} & \mathbf{3}+\mathbf{4}+\mathbf{5} & \mathbf{6}+\mathbf{8} & \mathbf{2}+\mathbf{7}+\mathbf{8} & \mathbf{6}+\mathbf{7}+\mathbf{8} \\ \mathbf{5} & \mathbf{8} & \mathbf{4}+\mathbf{5} & \mathbf{3}+\mathbf{4}+\mathbf{5} & \mathbf{1}+\mathbf{3}+\mathbf{4}+\mathbf{5} & \mathbf{7}+\mathbf{8} & \mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{2}+\mathbf{6}+\mathbf{7}+\mathbf{8} \\ \mathbf{6} & \mathbf{3}+\mathbf{6} & \mathbf{2}+\mathbf{7} & \mathbf{6}+\mathbf{8} & \mathbf{7}+\mathbf{8} & \mathbf{1}+\mathbf{2}+\mathbf{4}+\mathbf{7} & \mathbf{3}+\mathbf{5}+\mathbf{6}+\mathbf{8} & \mathbf{4}+\mathbf{5}+\mathbf{7}+\mathbf{8} \\ \mathbf{7} & \mathbf{4}+\mathbf{7} & \mathbf{6}+\mathbf{8} & \mathbf{2}+\mathbf{7}+\mathbf{8} & \mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{3}+\mathbf{5}+\mathbf{6}+\mathbf{8} & \mathbf{1}+\mathbf{2}+\mathbf{4}+\mathbf{5}+\mathbf{7}+\mathbf{8} & \mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} \\ \mathbf{8} & \mathbf{5}+\mathbf{8} & \mathbf{7}+\mathbf{8} & \mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{2}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{4}+\mathbf{5}+\mathbf{7}+\mathbf{8} & \mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{1}+\mathbf{2}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} \\ \hline \end{array}\]The following particles form non-trivial sub fusion rings
| Particles | SubRing |
|---|---|
| \(\{\mathbf{1},\mathbf{2}\}\) | \(\text{Fib}:\ \text{FR}^{2,0}_{2}\) |
| \(\{\mathbf{1},\mathbf{3},\mathbf{4},\mathbf{5}\}\) | \(\text{PSU(2})_7:\ \text{FR}^{4,0}_{6}\) |
Quantum Dimensions
| Particle | Numeric | Symbolic |
|---|---|---|
| \(\mathbf{1}\) | \(1.\) | \(1\) |
| \(\mathbf{2}\) | \(1.61803\) | \(\frac{1}{2} \left(1+\sqrt{5}\right)\) |
| \(\mathbf{3}\) | \(1.87939\) | \(\text{Root}\left[x^3-3 x-1,3\right]\) |
| \(\mathbf{4}\) | \(2.53209\) | \(\text{Root}\left[x^3-3 x^2+3,3\right]\) |
| \(\mathbf{5}\) | \(2.87939\) | \(\text{Root}\left[x^3-3 x^2+1,3\right]\) |
| \(\mathbf{6}\) | \(3.04091\) | \(\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]\) |
| \(\mathbf{7}\) | \(4.09701\) | \(\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]\) |
| \(\mathbf{8}\) | \(4.65894\) | \(\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]\) |
| \(\mathcal{D}_{FP}^2\) | \(69.5908\) | \(\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2\) |
Characters
The symbolic character table is the following
\[\begin{array}{|cccccccc|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} \\ \hline 1 & \frac{1}{2} \left(1+\sqrt{5}\right) & \text{Root}\left[x^3-3 x-1,3\right] & \text{Root}\left[x^3-3 x^2+3,3\right] & \text{Root}\left[x^3-3 x^2+1,3\right] & \text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right] & \text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right] & \text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right] \\ 1 & \frac{1}{2} \left(1-\sqrt{5}\right) & \text{Root}\left[x^3-3 x-1,3\right] & \text{Root}\left[x^3-3 x^2+3,3\right] & \text{Root}\left[x^3-3 x^2+1,3\right] & \text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,2\right] & \text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,1\right] & \text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,1\right] \\ 1 & \frac{1}{2} \left(1+\sqrt{5}\right) & 1 & 0 & -1 & \frac{1}{2} \left(1+\sqrt{5}\right) & 0 & \frac{1}{2} \left(-1-\sqrt{5}\right) \\ 1 & \frac{1}{2} \left(1+\sqrt{5}\right) & \text{Root}\left[x^3-3 x-1,2\right] & \text{Root}\left[x^3-3 x^2+3,1\right] & \text{Root}\left[x^3-3 x^2+1,2\right] & \text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,3\right] & \text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,2\right] & \text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,5\right] \\ 1 & \frac{1}{2} \left(1+\sqrt{5}\right) & \text{Root}\left[x^3-3 x-1,1\right] & \text{Root}\left[x^3-3 x^2+3,2\right] & \text{Root}\left[x^3-3 x^2+1,1\right] & \text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,1\right] & \text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,5\right] & \text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,2\right] \\ 1 & \frac{1}{2} \left(1-\sqrt{5}\right) & 1 & 0 & -1 & \frac{1}{2} \left(1-\sqrt{5}\right) & 0 & \frac{1}{2} \left(\sqrt{5}-1\right) \\ 1 & \frac{1}{2} \left(1-\sqrt{5}\right) & \text{Root}\left[x^3-3 x-1,2\right] & \text{Root}\left[x^3-3 x^2+3,1\right] & \text{Root}\left[x^3-3 x^2+1,2\right] & \text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,4\right] & \text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,4\right] & \text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,3\right] \\ 1 & \frac{1}{2} \left(1-\sqrt{5}\right) & \text{Root}\left[x^3-3 x-1,1\right] & \text{Root}\left[x^3-3 x^2+3,2\right] & \text{Root}\left[x^3-3 x^2+1,1\right] & \text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,5\right] & \text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,3\right] & \text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,4\right] \\ \hline \end{array}\]The numeric character table is the following
\[\begin{array}{|rrrrrrrr|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} \\ \hline 1.000 & 1.618 & 1.879 & 2.532 & 2.879 & 3.041 & 4.097 & 4.659 \\ 1.000 & -0.6180 & 1.879 & 2.532 & 2.879 & -1.162 & -1.565 & -1.780 \\ 1.000 & 1.618 & 1.000 & 0 & -1.000 & 1.618 & 0 & -1.618 \\ 1.000 & 1.618 & -0.3473 & -0.8794 & 0.6527 & -0.5619 & -1.423 & 1.056 \\ 1.000 & 1.618 & -1.532 & 1.347 & -0.5321 & -2.479 & 2.180 & -0.8609 \\ 1.000 & -0.6180 & 1.000 & 0 & -1.000 & -0.6180 & 0 & 0.6180 \\ 1.000 & -0.6180 & -0.3473 & -0.8794 & 0.6527 & 0.2146 & 0.5435 & -0.4034 \\ 1.000 & -0.6180 & -1.532 & 1.347 & -0.5321 & 0.9469 & -0.8327 & 0.3288 \\ \hline \end{array}\]Modular Data
The matching \(S\)-matrices and twist factors are the following
| \(S\)-matrix | Twist factors |
|---|---|
| \(\frac{1}{\sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2}}\left(\begin{array}{cccccccc} \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,7\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,8\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,9\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,10\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,11\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,12\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} \\ \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,8\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,6\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,11\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,12\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} \\ \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,9\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,11\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,6\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,1\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,5\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} \\ \text{Root}\left[45 x^4-15 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & 0 & \text{Root}\left[45 x^4-15 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & 0 & \text{Root}\left[45 x^4-15 x^2+1,1\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} \\ \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,10\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,12\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,6\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,9\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,5\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,1\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,11\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} \\ \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,11\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,1\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,5\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,10\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,7\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} \\ \text{Root}\left[45 x^4-15 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & 0 & \text{Root}\left[45 x^4-15 x^2+1,1\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,2\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & 0 & \text{Root}\left[45 x^4-15 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} \\ \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,12\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,5\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,1\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,11\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,7\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[45 x^4-15 x^2+1,3\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} & \text{Root}\left[7381125 x^{12}-4920750 x^{10}+1148175 x^8-121500 x^6+6075 x^4-135 x^2+1,4\right] \sqrt{\text{Root}\left[x^3-3 x-1,3\right]^2+\text{Root}\left[x^3-3 x^2+3,3\right]^2+\text{Root}\left[x^3-3 x^2+1,3\right]^2+\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]^2+\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]^2+1+\frac{1}{4} \left(1+\sqrt{5}\right)^2} \\\end{array}\right)\) | \(\begin{array}{l}\left(0,\frac{2}{5},-\frac{1}{3},-\frac{2}{9},\frac{1}{3},\frac{1}{15},\frac{8}{45},-\frac{4}{15}\right) \\\left(0,-\frac{2}{5},-\frac{1}{3},-\frac{2}{9},\frac{1}{3},\frac{4}{15},\frac{17}{45},-\frac{1}{15}\right) \\\left(0,\frac{2}{5},\frac{1}{3},\frac{2}{9},-\frac{1}{3},-\frac{4}{15},-\frac{17}{45},\frac{1}{15}\right) \\\left(0,-\frac{2}{5},\frac{1}{3},\frac{2}{9},-\frac{1}{3},-\frac{1}{15},-\frac{8}{45},\frac{4}{15}\right)\end{array}\) |
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: