Properties

Label 2.1.2.3a1.3-1.8.34h
Base 2.1.2.3a1.3
Degree \(8\)
e \(8\)
f \(1\)
c \(34\)

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Defining polynomial

$x^{8} + b_{31} \pi^{4} x^{7} + \left(b_{30} \pi^{4} + b_{22} \pi^{3}\right) x^{6} + b_{29} \pi^{4} x^{5} + \left(c_{36} \pi^{5} + a_{4} \pi\right) x^{4} + \left(b_{35} \pi^{5} + a_{27} \pi^{4}\right) x^{3} + \left(b_{26} \pi^{4} + a_{18} \pi^{3}\right) x^{2} + b_{33} \pi^{5} x + c_{32} \pi^{5} + c_{8} \pi^{2} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $8$
Base field: $\Q_{2}(\sqrt{2})$
Ramification index $e$: $8$
Residue field degree $f$: $1$
Discriminant exponent $c$: $34$
Absolute Artin slopes: $[2,3,4,\frac{17}{4}]$
Swan slopes: $[1,4,\frac{9}{2}]$
Means: $\langle\frac{1}{2},\frac{9}{4},\frac{27}{8}\rangle$
Rams: $(1,7,9)$
Field count: $224$ (complete)
Ambiguity: $8$
Mass: $128$
Absolute Mass: $64$

Diagrams

Varying

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

Galois group: $C_2^3:C_4$ (show 8), $C_2^3:C_4$ (show 8), $C_2^4:C_4$ (show 4), $C_2^4:C_4$ (show 4), $C_2^4:C_4$ (show 4), $C_2^4:C_4$ (show 4), $C_2^3.C_2^3$ (show 4), $C_2^3.C_2^3$ (show 4), $C_2\wr C_2^2$ (show 8), $C_2\wr C_2^2$ (show 4), $C_2\wr C_2^2$ (show 16), $C_2\wr C_2^2$ (show 4), $C_2^3.D_4$ (show 4), $C_2^3.D_4$ (show 4), $C_2^4.D_4$ (show 8), $C_2^4.D_4$ (show 8), $C_2^4.C_2^3$ (show 4), $C_2^4.C_2^3$ (show 4), $C_2^4.D_4$ (show 24), $C_2^4.D_4$ (show 8), $C_2^4.D_4$ (show 16), $C_2^4.D_4$ (show 4), $C_2^4.D_4$ (show 4), $C_2^4:Q_8$ (show 8), $C_2^4:Q_8$ (show 8), $C_2^4:D_4$ (show 8), $C_2^4:Q_8$ (show 4), $C_2^4:Q_8$ (show 4), $C_2^4:D_4$ (show 8), $C_2^4.C_2^3$ (show 16), $C_2^4:Q_8$ (show 8)
Hidden Artin slopes: $[\frac{7}{2}]$ (show 16), $[\frac{7}{2}]^{2}$ (show 64), $[3,\frac{7}{2}]^{2}$ (show 96), $[2,\frac{7}{2}]^{2}$ (show 48)
Indices of inseparability: $[43,34,20,8,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,2,4,8,32]$ (show 112), $[1,2,27,43,59]$ (show 28), $[1,11,22,38,54]$ (show 8), $[1,11,29,45,61]$ (show 28), $[1,11,31,47,63]$ (show 12), $[1,11,32,48,64]$ (show 8), $[1,13,27,43,59]$ (show 28)

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 224

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
2.1.16.58n1.1 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.2 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.3 $x^{16} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.4 $x^{16} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.5 $x^{16} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.6 $x^{16} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.7 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.8 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 2$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.9 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 2$ $C_2^4:C_4$ (as 16T102) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.10 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 2$ $C_2^3:C_4$ (as 16T33) $32$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.11 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$ $C_2^3:C_4$ (as 16T33) $32$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.12 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 2$ $C_2^3:C_4$ (as 16T33) $32$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.13 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$ $C_2^4:C_4$ (as 16T102) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.14 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$ $C_2^4:C_4$ (as 16T102) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.15 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^3:C_4$ (as 16T33) $32$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.16 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^3:C_4$ (as 16T33) $32$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.17 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^3:C_4$ (as 16T33) $32$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.18 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^4:C_4$ (as 16T102) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.19 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.20 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.21 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.22 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.23 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.24 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.25 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.26 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.27 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 2$ $C_2^3:C_4$ (as 16T33) $32$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.28 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^3:C_4$ (as 16T33) $32$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 27, 43, 59]$
2.1.16.58n1.29 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 2$ $C_2^3.D_4$ (as 16T177) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.30 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$ $C_2\wr C_2^2$ (as 16T150) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.31 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^3.D_4$ (as 16T177) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.32 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2\wr C_2^2$ (as 16T150) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.33 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^4:Q_8$ (as 16T384) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.34 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^4:Q_8$ (as 16T384) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.35 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$ $C_2^4:Q_8$ (as 16T384) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.36 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^4:Q_8$ (as 16T384) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.37 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 2$ $C_2\wr C_2^2$ (as 16T150) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.38 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 2$ $C_2^3.D_4$ (as 16T177) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.39 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$ $C_2\wr C_2^2$ (as 16T150) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.40 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^3.D_4$ (as 16T177) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.41 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^4.D_4$ (as 16T274) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.42 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$ $C_2^4.D_4$ (as 16T274) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.43 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 18$ $C_2^4.D_4$ (as 16T274) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.44 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$ $C_2^4.D_4$ (as 16T274) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.45 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.46 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.47 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.48 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.49 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
2.1.16.58n1.50 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$ $C_2^4.D_4$ (as 16T237) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 13, 27, 43, 59]$
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