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Properties

Label 2.1.16.64j
Base 2.1.1.0a1.1
Degree \(16\)
e \(16\)
f \(1\)
c \(64\)

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Defining polynomial

$x^{16} + 8 b_{46} x^{14} + \left(4 b_{28} + 16 c_{60}\right) x^{12} + 16 b_{59} x^{11} + 8 b_{42} x^{10} + 16 b_{57} x^{9} + \left(2 a_{8} + 8 c_{40}\right) x^{8} + 16 b_{55} x^{7} + 8 a_{38} x^{6} + 16 b_{53} x^{5} + \left(8 b_{36} + 16 c_{52}\right) x^{4} + 16 b_{51} x^{3} + 16 b_{50} x^{2} + 16 a_{49} x + 4 c_{16} + 2$

Invariants

Residue field characteristic: $2$
Degree: $16$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $1$
Discriminant exponent $c$: $64$
Artin slopes: $[2,\frac{7}{2},\frac{17}{4},\frac{19}{4}]$
Swan slopes: $[1,\frac{5}{2},\frac{13}{4},\frac{15}{4}]$
Means: $\langle\frac{1}{2},\frac{3}{2},\frac{19}{8},\frac{49}{16}\rangle$
Rams: $(1,4,7,11)$
Field count: $2048$ (complete)
Ambiguity: $16$
Mass: $1024$
Absolute Mass: $1024$

Diagrams

Varying

Indices of inseparability: $[49,38,24,8,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,2,4,8,32]$ (show 1024), $[1,5,13,29,45]$ (show 1024)

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 at least 1000

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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
2.1.16.64j1.1 $x^{16} + 2 x^{8} + 8 x^{6} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.2 $x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.3 $x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.4 $x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.5 $x^{16} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.6 $x^{16} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.7 $x^{16} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.8 $x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.9 $x^{16} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.10 $x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.11 $x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.12 $x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.13 $x^{16} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.14 $x^{16} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.15 $x^{16} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.16 $x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.17 $x^{16} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.18 $x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.19 $x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.20 $x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.21 $x^{16} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.22 $x^{16} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.23 $x^{16} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.24 $x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.25 $x^{16} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.26 $x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.27 $x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.28 $x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.29 $x^{16} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.30 $x^{16} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.31 $x^{16} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.32 $x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x + 2$ $C_2^6:C_4\wr C_2$ (as 16T1361) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{4}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.33 $x^{16} + 8 x^{14} + 2 x^{8} + 8 x^{6} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.34 $x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.35 $x^{16} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.36 $x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.37 $x^{16} + 8 x^{14} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.38 $x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.39 $x^{16} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.40 $x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.41 $x^{16} + 8 x^{14} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.42 $x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.43 $x^{16} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.44 $x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.45 $x^{16} + 8 x^{14} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.46 $x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.47 $x^{16} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.48 $x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 2$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.49 $x^{16} + 8 x^{14} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
2.1.16.64j1.50 $x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 2$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 38, 24, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 5, 13, 29, 45]$
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