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Properties

Label 2.1.4.8b1.5-1.4.26a
Base 2.1.4.8b1.5
Degree \(4\)
e \(4\)
f \(1\)
c \(26\)

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Defining polynomial

$x^{4} + \left(b_{27} \pi^{7} + a_{23} \pi^{6}\right) x^{3} + \left(b_{30} \pi^{8} + b_{26} \pi^{7} + b_{22} \pi^{6} + b_{18} \pi^{5}\right) x^{2} + \left(b_{29} \pi^{8} + b_{25} \pi^{7}\right) x + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.8b1.5
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $26$
Absolute Artin slopes: $[2,3,\frac{25}{6},\frac{25}{6}]$
Swan slopes: $[\frac{23}{3},\frac{23}{3}]$
Means: $\langle\frac{23}{6},\frac{23}{4}\rangle$
Rams: $(\frac{23}{3},\frac{23}{3})$
Field count: $32$ (complete)
Ambiguity: $1$
Mass: $128$
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: $C_2^6.(C_2^2\times S_4)$
Hidden Artin slopes: $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$
Indices of inseparability: $[43,36,20,8,0]$
Associated inertia: $[1,1,1]$
Jump Set: $[1,2,4,8,32]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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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
2.1.16.58j1.193 $x^{16} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.194 $x^{16} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.195 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.196 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.197 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.198 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.199 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.200 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.201 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.202 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.203 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.204 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.205 $x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.206 $x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.207 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.208 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.209 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.210 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.211 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.212 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.213 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.214 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.215 $x^{16} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.216 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.217 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.218 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.219 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.220 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.221 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.222 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.223 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58j1.224 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{2} + 6$ $C_2^6.(C_2^2\times S_4)$ (as 16T1668) $6144$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{10}{3}, \frac{10}{3}, \frac{23}{6}, \frac{23}{6}, \frac{25}{6}, \frac{25}{6}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6},\frac{19}{6},\frac{19}{6}]_{3}^{2}$ $[\frac{8}{3},\frac{8}{3},\frac{10}{3},\frac{10}{3},\frac{23}{6},\frac{23}{6}]^{2}_{3}$ $[\frac{5}{3},\frac{5}{3},\frac{7}{3},\frac{7}{3},\frac{17}{6},\frac{17}{6}]^{2}_{3}$ $[43, 36, 20, 8, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 2, 4, 8, 32]$
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