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\(\text{Fib×\times }\text{PSU}(2)_7:\ \text{FR}^{8,0}_{27}\)

Fusion Rules

1234567821+26783+64+75+8361+43+54+52+76+87+8473+51+4+53+4+56+82+7+86+7+8584+53+4+51+3+4+57+86+7+82+6+7+863+62+76+87+81+2+4+73+5+6+84+5+7+874+76+82+7+86+7+83+5+6+81+2+4+5+7+83+4+5+6+7+885+87+86+7+82+6+7+84+5+7+83+4+5+6+7+81+2+3+4+5+6+7+8\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 elements form non-trivial sub fusion rings

Elements SubRing
{1,2}\{\mathbf{1},\mathbf{2}\} Fib: FR22,0\text{Fib}:\ \text{FR}^{2,0}_{2}
{1,3,4,5}\{\mathbf{1},\mathbf{3},\mathbf{4},\mathbf{5}\} PSU(2)7: FR64,0\text{PSU(2})_7:\ \text{FR}^{4,0}_{6}

Frobenius-Perron Dimensions

Particle Numeric Symbolic
1\mathbf{1} 1.1. 11
2\mathbf{2} 1.618031.61803 12(1+5)\frac{1}{2} \left(1+\sqrt{5}\right)
3\mathbf{3} 1.879391.87939 Root[x3−3x−1,3]\text{Root}\left[x^3-3 x-1,3\right]
4\mathbf{4} 2.532092.53209 Root[x3−3x2+3,3]\text{Root}\left[x^3-3 x^2+3,3\right]
5\mathbf{5} 2.879392.87939 Root[x3−3x2+1,3]\text{Root}\left[x^3-3 x^2+1,3\right]
6\mathbf{6} 3.040913.04091 Root[x6−9x4−4x3+9x2+3x−1,6]\text{Root}\left[x^6-9 x^4-4 x^3+9 x^2+3 x-1,6\right]
7\mathbf{7} 4.097014.09701 Root[x6−3x5−9x4+12x3+27x2−9,6]\text{Root}\left[x^6-3 x^5-9 x^4+12 x^3+27 x^2-9,6\right]
8\mathbf{8} 4.658944.65894 Root[x6−3x5−9x4+4x3+9x2−1,6]\text{Root}\left[x^6-3 x^5-9 x^4+4 x^3+9 x^2-1,6\right]
DFP2\mathcal{D}_{FP}^2 69.590869.5908 Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2\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

12345678112(1+5)Root[x3−3x−1,3]Root[x3−3x2+3,3]Root[x3−3x2+1,3]Root[x6−9x4−4x3+9x2+3x−1,6]Root[x6−3x5−9x4+12x3+27x2−9,6]Root[x6−3x5−9x4+4x3+9x2−1,6]112(1−5)Root[x3−3x−1,3]Root[x3−3x2+3,3]Root[x3−3x2+1,3]Root[x6−9x4−4x3+9x2+3x−1,2]Root[x6−3x5−9x4+12x3+27x2−9,1]Root[x6−3x5−9x4+4x3+9x2−1,1]112(1+5)10−112(1+5)012(−1−5)112(1+5)Root[x3−3x−1,2]Root[x3−3x2+3,1]Root[x3−3x2+1,2]Root[x6−9x4−4x3+9x2+3x−1,3]Root[x6−3x5−9x4+12x3+27x2−9,2]Root[x6−3x5−9x4+4x3+9x2−1,5]112(1+5)Root[x3−3x−1,1]Root[x3−3x2+3,2]Root[x3−3x2+1,1]Root[x6−9x4−4x3+9x2+3x−1,1]Root[x6−3x5−9x4+12x3+27x2−9,5]Root[x6−3x5−9x4+4x3+9x2−1,2]112(1−5)10−112(1−5)012(5−1)112(1−5)Root[x3−3x−1,2]Root[x3−3x2+3,1]Root[x3−3x2+1,2]Root[x6−9x4−4x3+9x2+3x−1,4]Root[x6−3x5−9x4+12x3+27x2−9,4]Root[x6−3x5−9x4+4x3+9x2−1,3]112(1−5)Root[x3−3x−1,1]Root[x3−3x2+3,2]Root[x3−3x2+1,1]Root[x6−9x4−4x3+9x2+3x−1,5]Root[x6−3x5−9x4+12x3+27x2−9,3]Root[x6−3x5−9x4+4x3+9x2−1,4]\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

123456781.0001.6181.8792.5322.8793.0414.0974.6591.000−0.61801.8792.5322.879−1.162−1.565−1.7801.0001.6181.0000−1.0001.6180−1.6181.0001.618−0.3473−0.87940.6527−0.5619−1.4231.0561.0001.618−1.5321.347−0.5321−2.4792.180−0.86091.000−0.61801.0000−1.000−0.618000.61801.000−0.6180−0.3473−0.87940.65270.21460.5435−0.40341.000−0.6180−1.5321.347−0.53210.9469−0.83270.3288\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}

Representations of SL2(Z)SL_2(\mathbb{Z})

The matching SS-matrices and twist factors are the following

SS-matrix Twist factors
1Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2(Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,7]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,8]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,9]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,10]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,11]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,12]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,8]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,6]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,11]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,12]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,2]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,9]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,11]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,6]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,1]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,5]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)20Root[45x4−15x2+1,2]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)20Root[45x4−15x2+1,1]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,10]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,12]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,6]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,2]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,9]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,5]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,1]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,11]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,11]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,1]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,5]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,10]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,2]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,7]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,2]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)20Root[45x4−15x2+1,1]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,2]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)20Root[45x4−15x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,12]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,5]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,1]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,11]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,7]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[45x4−15x2+1,3]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2Root[7381125x12−4920750x10+1148175x8−121500x6+6075x4−135x2+1,4]Root[x3−3x−1,3]2+Root[x3−3x2+3,3]2+Root[x3−3x2+1,3]2+Root[x6−9x4−4x3+9x2+3x−1,6]2+Root[x6−3x5−9x4+12x3+27x2−9,6]2+Root[x6−3x5−9x4+4x3+9x2−1,6]2+1+14(1+5)2)\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) (0,25,−13,−29,13,115,845,−415)(0,−25,−13,−29,13,415,1745,−115)(0,25,13,29,−13,−415,−1745,115)(0,−25,13,29,−13,−115,−845,415)\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

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