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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
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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
2.2.8.56a1.569 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.570 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.571 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 8 t x^{2} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.572 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 8 t x^{2} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.665 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.666 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.667 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.668 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.685 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.686 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.687 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.688 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.697 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.698 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.699 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.700 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1197 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + \left(12 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1198 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + \left(28 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1199 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + \left(12 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1200 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + \left(28 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1233 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 8 t x^{2} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1234 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 8 t x^{2} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1235 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1236 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1257 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1258 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1259 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1260 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1285 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + \left(12 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1286 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + \left(28 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1287 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + \left(12 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.1288 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + \left(28 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $(C_2\times C_4^3).D_4$ (as 16T1108) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ $[1,1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ $[2,2,2,3,4]_{2}$ $[1,1,1,2,3]_{2}$ $t^{2} + t + 1$ $x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
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