Properties

Label 2.1.2.3a1.3-1.8.36g
Base 2.1.2.3a1.3
Degree \(8\)
e \(8\)
f \(1\)
c \(36\)

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Defining polynomial

$x^{8} + \left(b_{39} \pi^{5} + b_{31} \pi^{4}\right) x^{7} + \left(b_{30} \pi^{4} + b_{22} \pi^{3}\right) x^{6} + \left(b_{37} \pi^{5} + a_{29} \pi^{4}\right) x^{5} + a_{4} \pi x^{4} + b_{35} \pi^{5} x^{3} + \left(b_{26} \pi^{4} + a_{18} \pi^{3}\right) x^{2} + b_{33} \pi^{5} x + c_{40} \pi^{6} + c_{32} \pi^{5} + c_{8} \pi^{2} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $8$
Base field: $\Q_{2}(\sqrt{2})$
Ramification index $e$: $8$
Residue field degree $f$: $1$
Discriminant exponent $c$: $36$
Absolute Artin slopes: $[2,3,4,\frac{9}{2}]$
Swan slopes: $[1,4,5]$
Means: $\langle\frac{1}{2},\frac{9}{4},\frac{29}{8}\rangle$
Rams: $(1,7,11)$
Field count: $256$ (complete)
Ambiguity: $8$
Mass: $256$
Absolute Mass: $128$

Diagrams

Varying

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

Galois group: $C_2^5.(C_2\times D_4)$ (show 16), $C_2^3\wr C_2:C_4$ (show 16), $C_2^6.D_4$ (show 16), $(D_4\times C_2^3).C_2^3$ (show 16), $C_2^6.(C_2\times C_4)$ (show 16), $C_2^4.(C_4\times D_4)$ (show 16), $C_2^4.(C_4\times D_4)$ (show 16), $(D_4\times C_2^3).C_2^3$ (show 16), $C_2^5.(C_2\times D_4)$ (show 16), $C_2^6.Q_8$ (show 16), $(C_2^2\times C_4^2):Q_8$ (show 16), $(D_4\times C_2^3).C_2^3$ (show 16), $(D_4\times C_2^3).C_2^3$ (show 32), $(D_4\times C_2^3).C_2^3$ (show 32)
Hidden Artin slopes: $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$
Indices of inseparability: $[45,34,20,8,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,2,4,8,32]$ (show 128), $[1,2,29,45,61]$ (show 32), $[1,11,27,43,59]$ (show 64), $[1,13,26,42,58]$ (show 8), $[1,13,31,47,63]$ (show 16), $[1,13,32,48,64]$ (show 8)

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 256

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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
2.1.16.60l1.1 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.2 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.3 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.4 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.5 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.6 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.7 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.8 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.9 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.10 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.11 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.12 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.13 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.14 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.15 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.16 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.17 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.18 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.19 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.20 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.21 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.22 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.23 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.24 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$ $C_2^5.(C_2\times D_4)$ (as 16T953) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.25 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.26 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.27 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.28 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.29 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.30 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.31 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.32 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T916) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 29, 45, 61]$
2.1.16.60l1.33 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $C_2^6.(C_2\times C_4)$ (as 16T854) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 26, 42, 58]$
2.1.16.60l1.34 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $C_2^6.(C_2\times C_4)$ (as 16T854) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 26, 42, 58]$
2.1.16.60l1.35 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $C_2^6.(C_2\times C_4)$ (as 16T854) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 26, 42, 58]$
2.1.16.60l1.36 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $C_2^6.(C_2\times C_4)$ (as 16T854) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 26, 42, 58]$
2.1.16.60l1.37 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^6.(C_2\times C_4)$ (as 16T854) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 32, 48, 64]$
2.1.16.60l1.38 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^6.(C_2\times C_4)$ (as 16T854) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 32, 48, 64]$
2.1.16.60l1.39 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^6.(C_2\times C_4)$ (as 16T854) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 32, 48, 64]$
2.1.16.60l1.40 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^6.(C_2\times C_4)$ (as 16T854) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 32, 48, 64]$
2.1.16.60l1.41 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.42 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.43 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.44 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.45 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.46 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.47 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.48 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.49 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
2.1.16.60l1.50 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $(D_4\times C_2^3).C_2^3$ (as 16T1010) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 31, 47, 63]$
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