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Properties

Label 2.1.8.28b1.7-1.2.16a
Base 2.1.8.28b1.7
Degree \(2\)
e \(2\)
f \(1\)
c \(16\)

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Defining polynomial

$x^{2} + \left(b_{29} \pi^{15} + b_{27} \pi^{14} + b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9} + a_{15} \pi^{8}\right) x + c_{30} \pi^{16} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.1.8.28b1.7
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $16$
Absolute Artin slopes: $[3,4,\frac{17}{4},\frac{11}{2}]$
Swan slopes: $[15]$
Means: $\langle\frac{15}{2}\rangle$
Rams: $(15)$
Field count: $128$ (complete)
Ambiguity: $2$
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: $C_2^6.C_2\wr D_4$ (incomplete)
Hidden Artin slopes: $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ (show 32), not computed (show 96) (incomplete)
Indices of inseparability: $[57,42,32,16,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,3,7,15,31]$

Fields

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

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
2.1.16.72c1.769 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.770 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.771 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.772 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.773 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.774 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.775 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.776 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.777 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{41}{8}, \frac{11}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8},\frac{9}{2}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8}]^{2}$ $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.778 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{41}{8}, \frac{11}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8},\frac{9}{2}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8}]^{2}$ $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.779 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{41}{8}, \frac{11}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8},\frac{9}{2}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8}]^{2}$ $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.780 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{41}{8}, \frac{11}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8},\frac{9}{2}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8}]^{2}$ $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.781 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{41}{8}, \frac{11}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8},\frac{9}{2}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8}]^{2}$ $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.782 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{41}{8}, \frac{11}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8},\frac{9}{2}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8}]^{2}$ $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.783 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{41}{8}, \frac{11}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8},\frac{9}{2}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8}]^{2}$ $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.784 $x^{16} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{41}{8}, \frac{11}{2}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8},\frac{9}{2}]^{2}$ $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2},\frac{19}{4},\frac{39}{8},\frac{41}{8}]^{2}$ $[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{33}{8}]^{2}$ $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.785 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.786 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.787 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.788 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.789 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.790 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.791 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.792 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.793 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.794 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.795 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.796 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.797 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.798 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.799 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.800 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.801 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.802 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.803 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.804 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.805 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.806 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.807 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.808 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{5} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.809 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.810 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.811 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.812 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.813 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.814 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.815 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{7} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.816 $x^{16} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 32 x^{7} + 32 x^{5} + 32 x^{3} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.817 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.818 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{12} + 8 x^{10} + 16 x^{9} + 32 x^{8} + 2$ $C_2^6.C_2\wr D_4$ (as 16T1739) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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