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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
2.2.8.56a1.29 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $C_2\times D_8$ (as 16T29) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.30 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T44) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.31 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T45) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 16 x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.32 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T38) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 t x^{3} + 16 x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.129 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $C_2\times D_8$ (as 16T29) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 8 t x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.130 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T44) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 8 t x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.131 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T45) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.132 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T38) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.145 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T44) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(8 t + 8\right) x^{2} + 16 t x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.146 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $C_2\times \SD_{16}$ (as 16T48) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + \left(8 t + 8\right) x^{2} + 16 t x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.147 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T38) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 t x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.148 $( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $Q_{16}:C_2$ (as 16T32) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 t x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.155 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T38) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.156 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $8$ $56$ $Q_{16}:C_2$ (as 16T32) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 8 x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.157 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T44) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 8 x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.158 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $8$ $56$ $C_2\times \SD_{16}$ (as 16T48) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.715 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 2$ $2$ $2$ $8$ $56$ $C_2\times \SD_{16}$ (as 16T48) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.716 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T44) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 4\right) x^{4} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.717 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T38) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 t x^{3} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.718 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ $2$ $2$ $8$ $56$ $Q_{16}:C_2$ (as 16T32) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 4\right) x^{4} + 16 t x^{3} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.767 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T38) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 8 t x^{2} + 16 x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.768 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $Q_{16}:C_2$ (as 16T32) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 4\right) x^{4} + 8 t x^{2} + 16 x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.769 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $C_2\times \SD_{16}$ (as 16T48) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.770 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T44) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 4\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.845 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T38) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.846 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T45) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 4\right) x^{4} + 8 x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.847 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $8$ $56$ $C_2\times D_8$ (as 16T29) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 t x^{3} + 8 x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.848 $( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T44) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 4\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.871 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $C_2\times D_8$ (as 16T29) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + \left(8 t + 8\right) x^{2} + 16 t x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.872 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T44) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 4\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 t x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.873 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T38) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 t x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.56a1.874 $( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ $2$ $2$ $8$ $56$ $D_8:C_2$ (as 16T45) $2$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 3, \frac{7}{2}, \frac{9}{2}]^{2}$ $[1,2,\frac{5}{2},\frac{7}{2}]^{2}$ $[2]$ $[1]$ $t^{2} + t + 1$ $x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 4\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 t x + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
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