Properties

Label 2.1.4.11a1.19-1.4.22a
Base 2.1.4.11a1.19
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: 2.1.4.11a1.19
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $22$
Absolute Artin slopes: $[3,4,\frac{55}{12},\frac{55}{12}]$
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: $C_2^6.(D_4\times S_4)$ (incomplete)
Hidden Artin slopes: $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ (show 12), $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ (show 8), not computed (show 12) (incomplete)
Indices of inseparability: $[51,46,32,16,0]$ (show 16), $[51,48,32,16,0]$ (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

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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
2.1.16.66d1.449 $x^{16} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.450 $x^{16} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.451 $x^{16} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.452 $x^{16} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.453 $x^{16} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.454 $x^{16} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.455 $x^{16} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.456 $x^{16} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.465 $x^{16} + 8 x^{14} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ $[\frac{13}{6},\frac{13}{6},1,\frac{1}{3},\frac{1}{3},\frac{37}{12},\frac{37}{12}]_{2}^{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.466 $x^{16} + 8 x^{14} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ $[\frac{13}{6},\frac{13}{6},1,\frac{1}{3},\frac{1}{3},\frac{37}{12},\frac{37}{12}]_{2}^{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.467 $x^{16} + 8 x^{14} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ $[\frac{13}{6},\frac{13}{6},1,\frac{1}{3},\frac{1}{3},\frac{37}{12},\frac{37}{12}]_{2}^{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.468 $x^{16} + 8 x^{14} + 8 x^{12} + 4 x^{8} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ $[\frac{13}{6},\frac{13}{6},1,\frac{1}{3},\frac{1}{3},\frac{37}{12},\frac{37}{12}]_{2}^{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.469 $x^{16} + 8 x^{14} + 8 x^{12} + 4 x^{8} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.470 $x^{16} + 8 x^{14} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.471 $x^{16} + 8 x^{14} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.472 $x^{16} + 8 x^{14} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.481 $x^{16} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.482 $x^{16} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.483 $x^{16} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.484 $x^{16} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.485 $x^{16} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.486 $x^{16} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.487 $x^{16} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.488 $x^{16} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 16 x^{2} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 48, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.497 $x^{16} + 8 x^{14} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.498 $x^{16} + 8 x^{14} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.499 $x^{16} + 8 x^{14} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.500 $x^{16} + 8 x^{14} + 8 x^{12} + 4 x^{8} + 16 x^{6} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.501 $x^{16} + 8 x^{14} + 8 x^{12} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ $[\frac{13}{6},\frac{13}{6},1,\frac{1}{3},\frac{1}{3},\frac{37}{12},\frac{37}{12}]_{2}^{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.502 $x^{16} + 8 x^{14} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ $[\frac{13}{6},\frac{13}{6},1,\frac{1}{3},\frac{1}{3},\frac{37}{12},\frac{37}{12}]_{2}^{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.503 $x^{16} + 8 x^{14} + 8 x^{12} + 4 x^{8} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ $[\frac{13}{6},\frac{13}{6},1,\frac{1}{3},\frac{1}{3},\frac{37}{12},\frac{37}{12}]_{2}^{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66d1.504 $x^{16} + 8 x^{14} + 8 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{6} + 16 x^{5} + 8 x^{4} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}, \frac{55}{12}, \frac{55}{12}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12},\frac{43}{12},\frac{43}{12}]_{3}^{2}$ $[\frac{19}{6}, \frac{19}{6}, 2, \frac{4}{3}, \frac{4}{3}, \frac{49}{12}, \frac{49}{12}]_{2}^{3}$ $[\frac{13}{6},\frac{13}{6},1,\frac{1}{3},\frac{1}{3},\frac{37}{12},\frac{37}{12}]_{2}^{3}$ $[51, 46, 32, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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