$\text{PSU}(2)_{15}:\ \text{FR}^{8,0}_{36}$

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{3} & \mathbf{2}+\mathbf{4} & \mathbf{3}+\mathbf{5} & \mathbf{4}+\mathbf{6} & \mathbf{5}+\mathbf{7} & \mathbf{6}+\mathbf{8} & \mathbf{7}+\mathbf{8} \\ \mathbf{3} & \mathbf{2}+\mathbf{4} & \mathbf{1}+\mathbf{3}+\mathbf{5} & \mathbf{2}+\mathbf{4}+\mathbf{6} & \mathbf{3}+\mathbf{5}+\mathbf{7} & \mathbf{4}+\mathbf{6}+\mathbf{8} & \mathbf{5}+\mathbf{7}+\mathbf{8} & \mathbf{6}+\mathbf{7}+\mathbf{8} \\ \mathbf{4} & \mathbf{3}+\mathbf{5} & \mathbf{2}+\mathbf{4}+\mathbf{6} & \mathbf{1}+\mathbf{3}+\mathbf{5}+\mathbf{7} & \mathbf{2}+\mathbf{4}+\mathbf{6}+\mathbf{8} & \mathbf{3}+\mathbf{5}+\mathbf{7}+\mathbf{8} & \mathbf{4}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} \\ \mathbf{5} & \mathbf{4}+\mathbf{6} & \mathbf{3}+\mathbf{5}+\mathbf{7} & \mathbf{2}+\mathbf{4}+\mathbf{6}+\mathbf{8} & \mathbf{1}+\mathbf{3}+\mathbf{5}+\mathbf{7}+\mathbf{8} & \mathbf{2}+\mathbf{4}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{3}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} \\ \mathbf{6} & \mathbf{5}+\mathbf{7} & \mathbf{4}+\mathbf{6}+\mathbf{8} & \mathbf{3}+\mathbf{5}+\mathbf{7}+\mathbf{8} & \mathbf{2}+\mathbf{4}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{1}+\mathbf{3}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{2}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} \\ \mathbf{7} & \mathbf{6}+\mathbf{8} & \mathbf{5}+\mathbf{7}+\mathbf{8} & \mathbf{4}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{3}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{2}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{1}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{2}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} \\ \mathbf{8} & \mathbf{7}+\mathbf{8} & \mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{3}+\mathbf{4}+\mathbf{5}+\mathbf{6}+\mathbf{7}+\mathbf{8} & \mathbf{2}+\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}\]

Quantum Dimensions

Particle	Numeric	Symbolic
$\mathbf{1}$	$1.$	$ 1 $
$\mathbf{2}$	$1.96595$	$ \sin( 3\pi/17)/\sin(\pi/17) $
$\mathbf{3}$	$2.86494$	$ \sin( 5\pi/17)/\sin(\pi/17) $
$\mathbf{4}$	$3.66638$	$ \sin( 7\pi/17)/\sin(\pi/17) $
$\mathbf{5}$	$4.34296$	$ \sin( 9\pi/17)/\sin(\pi/17) $
$\mathbf{6}$	$4.87165$	$ \sin( 11\pi/17)/\sin(\pi/17) $
$\mathbf{7}$	$5.23444$	$ \sin( 13\pi/17)/\sin(\pi/17) $
$\mathbf{8}$	$5.41898$	$ \sin( 15\pi/17)/\sin(\pi/17) $
$\mathcal{D}_{FP}^2$	$125.874$	$ \frac{\sum\limits_{k = 1}^7 \sin( (2k - 1)\pi/17 )^2}{\sin(\pi/17)^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 & \text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right] & \text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right] & \text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right] & \text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right] & \text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right] & \text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right] & \text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right] \\ 1 & \text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,7\right] & \text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,6\right] & \text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,7\right] & \text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,5\right] & \text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,5\right] & \text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,2\right] & \text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,1\right] \\ 1 & \text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,6\right] & \text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,4\right] & \text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,3\right] & \text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,1\right] & \text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,2\right] & \text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,4\right] & \text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,7\right] \\ 1 & \text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,5\right] & \text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,2\right] & \text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,2\right] & \text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,4\right] & \text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,6\right] & \text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,5\right] & \text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,2\right] \\ 1 & \text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,4\right] & \text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,1\right] & \text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,5\right] & \text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,6\right] & \text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,3\right] & \text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,3\right] & \text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,6\right] \\ 1 & \text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,3\right] & \text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,3\right] & \text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,6\right] & \text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,3\right] & \text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,4\right] & \text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,6\right] & \text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,3\right] \\ 1 & \text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,2\right] & \text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,5\right] & \text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,4\right] & \text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,2\right] & \text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,7\right] & \text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,1\right] & \text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,5\right] \\ 1 & \text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,1\right] & \text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,7\right] & \text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,1\right] & \text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,7\right] & \text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,1\right] & \text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,7\right] & \text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,4\right] \\ \hline \end{array}\]

The numeric character table is the following

\[\begin{array}{|rrrrrrrr|} \hline \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} \\ \hline 1.000 & 1.966 & 2.865 & 3.666 & 4.343 & 4.872 & 5.234 & 5.419 \\ 1.000 & 1.700 & 1.891 & 1.516 & 0.6862 & -0.3490 & -1.280 & -1.827 \\ 1.000 & 1.205 & 0.4527 & -0.6597 & -1.248 & -0.8442 & 0.2303 & 1.122 \\ 1.000 & 0.5473 & -0.7004 & -0.9307 & 0.1910 & 1.035 & 0.3756 & -0.8297 \\ 1.000 & -0.1845 & -0.9659 & 0.3628 & 0.8990 & -0.5287 & -0.8014 & 0.6766 \\ 1.000 & -0.8915 & -0.2053 & 1.074 & -0.7526 & -0.4035 & 1.112 & -0.5881 \\ 1.000 & -1.478 & 1.185 & -0.2727 & -0.7814 & 1.428 & -1.329 & 0.5362 \\ 1.000 & -1.865 & 2.478 & -2.756 & 2.663 & -2.209 & 1.457 & -0.5087 \\ \hline \end{array}\]

Modular Data

The matching $S$-matrices and twist factors are the following

\(S\)-matrix	Twist factors
\(\frac{1}{\sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1}}\left(\begin{array}{cccccccc} \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,9\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,11\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,12\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,13\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,1\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,4\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,11\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,11\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,13\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,2\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,12\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,1\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,13\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,6\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,3\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,13\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,6\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,1\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,9\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,4\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,7\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,6\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,11\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,3\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,9\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,4\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,2\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,6\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,4\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,12\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\\end{array}\right)\)	\(\begin{array}{l}\left(0,\frac{5}{17},\frac{2}{17},\frac{8}{17},\frac{6}{17},-\frac{4}{17},-\frac{5}{17},\frac{3}{17}\right) \\\left(0,-\frac{5}{17},-\frac{2}{17},-\frac{8}{17},-\frac{6}{17},\frac{4}{17},\frac{5}{17},-\frac{3}{17}\right)\end{array}\)

$S$-matrix

Twist factors

\(\frac{1}{\sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1}}\left(\begin{array}{cccccccc} \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,9\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,11\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,12\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,13\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,1\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,4\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,11\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,11\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,13\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,2\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,12\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,1\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,13\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,6\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,3\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,13\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,6\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,1\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,9\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,4\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,7\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,6\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,15\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,11\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,5\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,3\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,9\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,4\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\ \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,16\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,8\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,2\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,10\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,14\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,6\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,4\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} & \text{Root}\left[410338673 x^{16}-410338673 x^{14}+168962983 x^{12}-36916282 x^{10}+4593655 x^8-324258 x^6+12138 x^4-204 x^2+1,12\right] \sqrt{\text{Root}\left[x^8-x^7-7 x^6+6 x^5+15 x^4-10 x^3-10 x^2+4 x+1,8\right]^2+\text{Root}\left[x^8-7 x^7+14 x^6+x^5-25 x^4+9 x^3+12 x^2-3 x-1,8\right]^2+\text{Root}\left[x^8-2 x^7-11 x^6+14 x^5+19 x^4-14 x^3-11 x^2+2 x+1,8\right]^2+\text{Root}\left[x^8-6 x^7+3 x^6+21 x^5-8 x^4-19 x^3+5 x^2+5 x-1,8\right]^2+\text{Root}\left[x^8-3 x^7-12 x^6+9 x^5+25 x^4+x^3-14 x^2-7 x-1,8\right]^2+\text{Root}\left[x^8-5 x^7-5 x^6+19 x^5+8 x^4-21 x^3-3 x^2+6 x-1,8\right]^2+\text{Root}\left[x^8-4 x^7-10 x^6+10 x^5+15 x^4-6 x^3-7 x^2+x+1,8\right]^2+1} \\\end{array}\right)\)

$\begin{array}{l}\left(0,\frac{5}{17},\frac{2}{17},\frac{8}{17},\frac{6}{17},-\frac{4}{17},-\frac{5}{17},\frac{3}{17}\right) \\\left(0,-\frac{5}{17},-\frac{2}{17},-\frac{8}{17},-\frac{6}{17},\frac{4}{17},\frac{5}{17},-\frac{3}{17}\right)\end{array}$

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:

Particle	Numeric	Symbolic
\(\mathbf{1}\)	\(1.\)	$ 1 $
\(\mathbf{2}\)	\(1.96595\)	$ \sin( 3\pi/17)/\sin(\pi/17) $
\(\mathbf{3}\)	\(2.86494\)	$ \sin( 5\pi/17)/\sin(\pi/17) $
\(\mathbf{4}\)	\(3.66638\)	$ \sin( 7\pi/17)/\sin(\pi/17) $
\(\mathbf{5}\)	\(4.34296\)	$ \sin( 9\pi/17)/\sin(\pi/17) $
\(\mathbf{6}\)	\(4.87165\)	$ \sin( 11\pi/17)/\sin(\pi/17) $
\(\mathbf{7}\)	\(5.23444\)	$ \sin( 13\pi/17)/\sin(\pi/17) $
\(\mathbf{8}\)	\(5.41898\)	$ \sin( 15\pi/17)/\sin(\pi/17) $
\(\mathcal{D}_{FP}^2\)	\(125.874\)	$ \frac{\sum\limits_{k = 1}^7 \sin( (2k - 1)\pi/17 )^2}{\sin(\pi/17)^2} $

AnyonWiki

\(\text{PSU}(2)_{15}:\ \text{FR}^{8,0}_{36}\)