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Properties

Label 2.1.4.8b1.4-1.4.20c
Base 2.1.4.8b1.4
Degree \(4\)
e \(4\)
f \(1\)
c \(20\)

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Defining polynomial

$x^{4} + \left(b_{27} \pi^{7} + b_{23} \pi^{6} + b_{19} \pi^{5}\right) x^{3} + \left(b_{10} \pi^{3} + a_{6} \pi^{2}\right) x^{2} + \left(b_{25} \pi^{7} + b_{21} \pi^{6} + a_{17} \pi^{5}\right) x + c_{28} \pi^{8} + c_{12} \pi^{4} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.8b1.4
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $20$
Absolute Artin slopes: $[2,3,3,4]$
Swan slopes: $[3,7]$
Means: $\langle\frac{3}{2},\frac{17}{4}\rangle$
Rams: $(3,11)$
Field count: $80$ (complete)
Ambiguity: $4$
Mass: $64$
Absolute Mass: $32$

Diagrams

Varying

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group: $C_4^2:C_4$ (show 2), $C_2^2.Q_{16}$ (show 8), $C_4^2:C_4$ (show 2), $C_2^4.D_4$ (show 8), $C_2^4.D_4$ (show 4), $C_4^2.D_4$ (show 4), $C_4^2.D_4$ (show 8), $C_4^2.(C_2\times D_4)$ (show 8), $C_4^2.(C_2\times D_4)$ (show 4), $C_2^5.(C_2\times D_4)$ (show 16), $D_4:C_2^3.D_4$ (show 16)
Hidden Artin slopes: $[2,2,3]^{4}$ (show 16), $[2,2,\frac{7}{2}]^{4}$ (show 16), $[\ ]^{4}$ (show 12), $[2]^{4}$ (show 12), $[2,\frac{7}{2}]^{4}$ (show 12), $[\frac{7}{2}]^{4}$ (show 12)
Indices of inseparability: $[37,26,24,8,0]$
Associated inertia: $[1,2,1]$
Jump Set: $[1,2,4,8,32]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 80

Next   displayed columns for results
Label Polynomial $/ \Q_p$ Galois group $/ \Q_p$ Galois degree $/ \Q_p$ $\#\Aut(K/\Q_p)$ Artin slope content $/ \Q_p$ Swan slope content $/ \Q_p$ Hidden Artin slopes $/ \Q_p$ Hidden Swan slopes $/ \Q_p$ Ind. of Insep. $/ \Q_p$ Assoc. Inertia $/ \Q_p$ Resid. Poly Jump Set
2.1.16.52k1.169 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,2,2,2,3]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.170 $x^{16} + 8 x^{15} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,2,2,2,3]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.171 $x^{16} + 8 x^{13} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,2,2,2,3]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.172 $x^{16} + 8 x^{13} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 22$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,2,2,2,3]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.173 $x^{16} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_2^2.Q_{16}$ (as 16T161) $64$ $4$ $[2, 3, 3, 4]^{4}$ $[1,2,2,3]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.174 $x^{16} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 22$ $C_2^2.Q_{16}$ (as 16T161) $64$ $4$ $[2, 3, 3, 4]^{4}$ $[1,2,2,3]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.175 $x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_2^2.Q_{16}$ (as 16T161) $64$ $4$ $[2, 3, 3, 4]^{4}$ $[1,2,2,3]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.176 $x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 22$ $C_2^2.Q_{16}$ (as 16T161) $64$ $4$ $[2, 3, 3, 4]^{4}$ $[1,2,2,3]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.177 $x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_2^4.D_4$ (as 16T297) $128$ $2$ $[2, 2, 3, 3, 4]^{4}$ $[1,1,2,2,3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.178 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_2^4.D_4$ (as 16T297) $128$ $2$ $[2, 2, 3, 3, 4]^{4}$ $[1,1,2,2,3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.179 $x^{16} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,2,2,2,3]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.180 $x^{16} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 22$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,2,2,2,3]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.181 $x^{16} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,2,2,2,3]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.182 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,2,2,2,3]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.183 $x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 6$ $C_4^2:C_4$ (as 16T143) $64$ $2$ $[2, 3, 3, 4]^{4}$ $[1,2,2,3]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.184 $x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 6$ $C_4^2:C_4$ (as 16T143) $64$ $2$ $[2, 3, 3, 4]^{4}$ $[1,2,2,3]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.185 $x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 6$ $C_2^4.D_4$ (as 16T254) $128$ $4$ $[2, 2, 3, 3, 4]^{4}$ $[1,1,2,2,3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.186 $x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 22$ $C_2^4.D_4$ (as 16T254) $128$ $4$ $[2, 2, 3, 3, 4]^{4}$ $[1,1,2,2,3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.187 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 6$ $C_2^4.D_4$ (as 16T254) $128$ $4$ $[2, 2, 3, 3, 4]^{4}$ $[1,1,2,2,3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.188 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 22$ $C_2^4.D_4$ (as 16T254) $128$ $4$ $[2, 2, 3, 3, 4]^{4}$ $[1,1,2,2,3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.189 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.190 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 22$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.191 $x^{16} + 8 x^{13} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.192 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.193 $x^{16} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $C_4^2.D_4$ (as 16T387) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.194 $x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $C_4^2.D_4$ (as 16T387) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.195 $x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $C_4^2.D_4$ (as 16T398) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.196 $x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 22$ $C_4^2.D_4$ (as 16T398) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.197 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $C_4^2.D_4$ (as 16T398) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.198 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 22$ $C_4^2.D_4$ (as 16T398) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.199 $x^{16} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.200 $x^{16} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 22$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.201 $x^{16} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.202 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.203 $x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $C_4^2.D_4$ (as 16T387) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.204 $x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $C_4^2.D_4$ (as 16T387) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.205 $x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $C_4^2.D_4$ (as 16T398) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.206 $x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 22$ $C_4^2.D_4$ (as 16T398) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.207 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 6$ $C_4^2.D_4$ (as 16T398) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.208 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 22$ $C_4^2.D_4$ (as 16T398) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,2,2,\frac{5}{2},3]^{4}$ $[\frac{7}{2}]^{4}$ $[\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.297 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.298 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 22$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.299 $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.300 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $D_4:C_2^3.D_4$ (as 16T918) $512$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,2,\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.301 $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_4^2.(C_2\times D_4)$ (as 16T504) $256$ $4$ $[2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,2,\frac{5}{2},3]^{4}$ $[2,\frac{7}{2}]^{4}$ $[1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.302 $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 22$ $C_4^2.(C_2\times D_4)$ (as 16T504) $256$ $4$ $[2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,2,\frac{5}{2},3]^{4}$ $[2,\frac{7}{2}]^{4}$ $[1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.303 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_4^2.(C_2\times D_4)$ (as 16T504) $256$ $4$ $[2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,2,\frac{5}{2},3]^{4}$ $[2,\frac{7}{2}]^{4}$ $[1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.304 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 22$ $C_4^2.(C_2\times D_4)$ (as 16T504) $256$ $4$ $[2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,2,\frac{5}{2},3]^{4}$ $[2,\frac{7}{2}]^{4}$ $[1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.305 $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_4^2.(C_2\times D_4)$ (as 16T655) $256$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,2,\frac{5}{2},3]^{4}$ $[2,\frac{7}{2}]^{4}$ $[1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.52k1.306 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 6$ $C_4^2.(C_2\times D_4)$ (as 16T655) $256$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,2,\frac{5}{2},3]^{4}$ $[2,\frac{7}{2}]^{4}$ $[1,\frac{5}{2}]^{4}$ $[37, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
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