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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.2.4.18a2.3 $( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $4$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,3,\frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 10\right) x^{2} + 8 t x + 6$ $[6, 2, 0]$ $[1, 1]$ $z^2 + t,t z + t$ $[1, 3, 7]$
2.2.4.18a2.4 $( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{3} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $4$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,3,\frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 2\right) x^{2} + 8 t x + 6$ $[6, 2, 0]$ $[1, 1]$ $z^2 + t,t z + t$ $[1, 3, 7]$
2.2.4.18a2.11 $( x^{2} + x + 1 )^{4} + 6 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $4$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,3,\frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 10\right) x^{2} + 6$ $[6, 2, 0]$ $[1, 1]$ $z^2 + t,t z + t$ $[1, 3, 7]$
2.2.4.18a2.12 $( x^{2} + x + 1 )^{4} + 6 ( x^{2} + x + 1 )^{3} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $4$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,3,\frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(2 t + 8\right) x^{2} + 8 x + 6$ $[6, 2, 0]$ $[1, 1]$ $z^2 + t,t z + t$ $[1, 3, 7]$
2.2.4.18a2.19 $( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 6$ $2$ $2$ $4$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,3,\frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(2 t + 10\right) x^{2} + \left(8 t + 8\right) x + 2$ $[6, 2, 0]$ $[1, 1]$ $z^2 + t,t z + t$ $[1, 3, 7]$
2.2.4.18a2.20 $( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{3} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 6$ $2$ $2$ $4$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,3,\frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(2 t + 2\right) x^{2} + \left(8 t + 8\right) x + 2$ $[6, 2, 0]$ $[1, 1]$ $z^2 + t,t z + t$ $[1, 3, 7]$
2.2.4.18a2.25 $( x^{2} + x + 1 )^{4} + 6 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 6$ $2$ $2$ $4$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,3,\frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(2 t + 10\right) x^{2} + 8 x + 2$ $[6, 2, 0]$ $[1, 1]$ $z^2 + t,t z + t$ $[1, 3, 7]$
2.2.4.18a2.26 $( x^{2} + x + 1 )^{4} + 6 ( x^{2} + x + 1 )^{3} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{2} + 6$ $2$ $2$ $4$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,3,\frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(2 t + 2\right) x^{2} + 8 x + 2$ $[6, 2, 0]$ $[1, 1]$ $z^2 + t,t z + t$ $[1, 3, 7]$
2.2.4.20a2.5 $( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 8 x + 2$ $2$ $2$ $4$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,2,\frac{7}{2}]$ $[1,1,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + 8 x^{2} + 8 x + 8 t + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + t$ $[1, 3, 7]$
2.2.4.20a2.6 $( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 x + 2$ $2$ $2$ $4$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,2,\frac{7}{2}]$ $[1,1,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + 8 t + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + t$ $[1, 3, 7]$
2.2.4.20a2.7 $( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $4$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,2,\frac{7}{2}]$ $[1,1,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + 8 x^{2} + 8 x + 8 t + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + t$ $[1, 3, 7]$
2.2.4.20a2.8 $( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $4$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,2,\frac{7}{2}]$ $[1,1,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + 8 x + 8 t + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + t$ $[1, 3, 7]$
2.2.4.20a2.17 $( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $4$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,2,\frac{7}{2}]$ $[1,1,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + 12 x^{2} + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + t$ $[1, 3, 7]$
2.2.4.20a2.18 $( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $4$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,2,\frac{7}{2}]$ $[1,1,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + 4 x^{2} + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + t$ $[1, 3, 7]$
2.2.4.20a2.19 $( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $4$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,2,\frac{7}{2}]$ $[1,1,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + 12 x^{2} + 8 x + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + t$ $[1, 3, 7]$
2.2.4.20a2.20 $( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $4$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ $[2,2,\frac{7}{2}]$ $[1,1,\frac{5}{2}]$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + 4 x^{2} + 8 x + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + t$ $[1, 3, 7]$
2.1.8.27a1.81 $x^{8} + 2 x^{4} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 2 x^{4} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.82 $x^{8} + 2 x^{4} + 16 x^{3} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 2 x^{4} + 16 x^{3} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.83 $x^{8} + 2 x^{4} + 16 x + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 2 x^{4} + 16 x + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.89 $x^{8} + 10 x^{4} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 10 x^{4} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.90 $x^{8} + 10 x^{4} + 16 x + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 10 x^{4} + 16 x + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.91 $x^{8} + 10 x^{4} + 16 x^{3} + 16 x + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 10 x^{4} + 16 x^{3} + 16 x + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.101 $x^{8} + 8 x^{7} + 2 x^{4} + 8 x^{2} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 2 x^{4} + 8 x^{2} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.102 $x^{8} + 8 x^{7} + 2 x^{4} + 16 x^{3} + 8 x^{2} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 2 x^{4} + 16 x^{3} + 8 x^{2} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.107 $x^{8} + 8 x^{7} + 10 x^{4} + 8 x^{2} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 10 x^{4} + 8 x^{2} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.108 $x^{8} + 8 x^{7} + 10 x^{4} + 16 x^{3} + 8 x^{2} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 10 x^{4} + 16 x^{3} + 8 x^{2} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.118 $x^{8} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.126 $x^{8} + 4 x^{6} + 8 x^{5} + 10 x^{4} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 10 x^{4} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.137 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 8 x^{2} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 8 x^{2} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.138 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x^{3} + 8 x^{2} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x^{3} + 8 x^{2} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.143 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 10 x^{4} + 8 x^{2} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 10 x^{4} + 8 x^{2} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.27a1.144 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 10 x^{4} + 16 x^{3} + 8 x^{2} + 6$ $2$ $1$ $8$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ $[3,4]^{2}$ $[2,3]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 10 x^{4} + 16 x^{3} + 8 x^{2} + 6$ $[20, 12, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 16]$
2.1.8.28a1.1 $x^{8} + 4 x^{6} + 8 x^{5} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.2 $x^{8} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.3 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.4 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.7 $x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.8 $x^{8} + 4 x^{6} + 8 x^{5} + 24 x^{4} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 24 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.9 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.10 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 24 x^{4} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 24 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.17 $x^{8} + 4 x^{6} + 8 x^{5} + 10$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 10$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.18 $x^{8} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 10$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 10$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.19 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 10$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 10$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.20 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 10$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 10$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.23 $x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 10$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 10$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.24 $x^{8} + 4 x^{6} + 8 x^{5} + 24 x^{4} + 10$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 24 x^{4} + 10$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.25 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 10$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 10$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.26 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 24 x^{4} + 10$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 24 x^{4} + 10$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.33 $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.1.8.28a1.34 $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 2$ $2$ $1$ $8$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
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