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Properties

Label 2.1.16.62g
Base 2.1.1.0a1.1
Degree \(16\)
e \(16\)
f \(1\)
c \(62\)

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Defining polynomial

$x^{16} + 8 a_{47} x^{15} + 8 b_{46} x^{14} + 8 b_{44} x^{12} + 8 b_{42} x^{10} + 4 b_{24} x^{8} + \left(8 b_{36} + 16 c_{52}\right) x^{4} + 16 b_{51} x^{3} + 16 b_{50} x^{2} + 16 b_{49} x + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic: $2$
Degree: $16$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $1$
Discriminant exponent $c$: $62$
Artin slopes: $[3,4,\frac{17}{4},\frac{17}{4}]$
Swan slopes: $[2,3,\frac{13}{4},\frac{13}{4}]$
Means: $\langle1,2,\frac{21}{8},\frac{47}{16}\rangle$
Rams: $(2,4,5,5)$
Field count: $384$ (complete)
Ambiguity: $8$
Mass: $256$
Absolute Mass: $256$

Diagrams

Varying

Indices of inseparability: $[47,42,32,16,0]$ (show 128), $[47,46,32,16,0]$ (show 128), $[47,47,32,16,0]$ (show 128)
Associated inertia: $[1,1,2]$ (show 256), $[1,1,3]$ (show 128)
Jump Set: $[1,3,7,15,31]$

Galois groups and Hidden Artin slopes

Select desired size of Galois group. Note that the following data has not all been computed for fields in this family, so the tables below are incomplete.

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 128

Next   displayed columns for results
Label Packet size Polynomial Galois group Galois degree $\#\Aut(K/\Q_p)$ Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.1.16.62g1.9 64 $x^{16} + 8 x^{15} + 8 x^{14} + 2$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.10 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{4} + 2$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.11 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{2} + 2$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.12 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{4} + 16 x^{2} + 2$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.13 64 $x^{16} + 8 x^{15} + 8 x^{14} + 18$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.14 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{4} + 18$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.15 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{2} + 18$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.16 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{4} + 16 x^{2} + 18$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.25 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 2$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.26 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{4} + 2$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.27 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{2} + 2$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.28 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{4} + 16 x^{2} + 2$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.29 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 18$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.30 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{4} + 18$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.31 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{2} + 18$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.32 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{4} + 16 x^{2} + 18$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.41 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{4} + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.42 64 $x^{16} + 8 x^{15} + 8 x^{14} + 24 x^{4} + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.43 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{4} + 16 x^{2} + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.44 64 $x^{16} + 8 x^{15} + 8 x^{14} + 24 x^{4} + 16 x^{2} + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.45 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{4} + 16 x + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.46 64 $x^{16} + 8 x^{15} + 8 x^{14} + 24 x^{4} + 16 x + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.47 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{4} + 16 x^{2} + 16 x + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.48 64 $x^{16} + 8 x^{15} + 8 x^{14} + 24 x^{4} + 16 x^{2} + 16 x + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.57 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{4} + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.58 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 24 x^{4} + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.59 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{4} + 16 x^{2} + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.60 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 24 x^{4} + 16 x^{2} + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.61 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{4} + 16 x + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.62 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 24 x^{4} + 16 x + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.63 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{4} + 16 x^{2} + 16 x + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.64 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 24 x^{4} + 16 x^{2} + 16 x + 2$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.73 64 $x^{16} + 8 x^{15} + 8 x^{14} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.74 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{4} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.75 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{2} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.76 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{4} + 16 x^{2} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.77 64 $x^{16} + 8 x^{15} + 8 x^{14} + 26$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.78 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{4} + 26$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.79 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{2} + 26$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.80 64 $x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{4} + 16 x^{2} + 26$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.89 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.90 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{4} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.91 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{2} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.92 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{4} + 16 x^{2} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.93 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 26$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.94 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{4} + 26$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.95 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{2} + 26$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.96 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{12} + 16 x^{4} + 16 x^{2} + 26$ $C_2^4.(C_4\times D_4)$ (as 16T824) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.105 64 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{4} + 10$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
2.1.16.62g1.106 64 $x^{16} + 8 x^{15} + 8 x^{14} + 24 x^{4} + 10$ $C_2^6:D_4$ (as 16T960) $512$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2}]^{2}$ $[47, 46, 32, 16, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 3, 7, 15, 31]$
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