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Properties

Label 2.1.4.10a1.3-1.4.22a
Base 2.1.4.10a1.3
Degree \(4\)
e \(4\)
f \(1\)
c \(22\)

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Defining polynomial

$x^{4} + \left(b_{23} \pi^{6} + a_{19} \pi^{5}\right) x^{3} + \left(b_{22} \pi^{6} + b_{18} \pi^{5} + b_{14} \pi^{4}\right) x^{2} + \left(b_{25} \pi^{7} + b_{21} \pi^{6}\right) x + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.10a1.3
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $22$
Absolute Artin slopes: $[3,\frac{7}{2},\frac{13}{3},\frac{13}{3}]$
Swan slopes: $[\frac{19}{3},\frac{19}{3}]$
Means: $\langle\frac{19}{6},\frac{19}{4}\rangle$
Rams: $(\frac{19}{3},\frac{19}{3})$
Field count: $32$ (complete)
Ambiguity: $1$
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: $C_2^6.(D_4\times S_4)$
Hidden Artin slopes: $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$
Indices of inseparability: $[47,42,28,16,0]$ (show 16), $[47,44,28,16,0]$ (show 16)
Associated inertia: $[1,1,1]$
Jump Set: $[1,3,7,15,31]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing all 32

  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
2.1.16.62f1.65 $x^{16} + 8 x^{15} + 4 x^{12} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.66 $x^{16} + 8 x^{15} + 4 x^{12} + 16 x^{5} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.67 $x^{16} + 8 x^{15} + 4 x^{12} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.68 $x^{16} + 8 x^{15} + 4 x^{12} + 16 x^{5} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.69 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.70 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{5} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.71 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.72 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{5} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.73 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.74 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.75 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.76 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.77 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.78 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.79 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.80 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.113 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{8} + 8 x^{4} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.114 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{8} + 16 x^{5} + 8 x^{4} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.115 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{8} + 8 x^{4} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.116 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{8} + 16 x^{5} + 8 x^{4} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.117 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{8} + 8 x^{4} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.118 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{8} + 16 x^{5} + 8 x^{4} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.119 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{8} + 8 x^{4} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.120 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{8} + 16 x^{5} + 8 x^{4} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.121 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{4} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.122 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{5} + 8 x^{4} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.123 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.124 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.125 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{4} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.126 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{5} + 8 x^{4} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.127 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62f1.128 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{7}{2}, \frac{43}{12}, \frac{43}{12}, \frac{13}{3}, \frac{13}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{5}{2},\frac{31}{12},\frac{31}{12},\frac{10}{3},\frac{10}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{43}{12},\frac{43}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{31}{12},\frac{31}{12}]^{2}_{3}$ $[47, 42, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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