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Properties

Label 2.1.2.3a1.1-1.8.50c
Base 2.1.2.3a1.1
Degree \(8\)
e \(8\)
f \(1\)
c \(50\)

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Defining polynomial

$x^{8} + b_{47} \pi^{6} x^{7} + \left(c_{54} \pi^{7} + b_{46} \pi^{6} + b_{38} \pi^{5}\right) x^{6} + \left(b_{53} \pi^{7} + b_{45} \pi^{6}\right) x^{5} + \left(b_{28} \pi^{4} + b_{20} \pi^{3}\right) x^{4} + \left(b_{51} \pi^{7} + a_{43} \pi^{6}\right) x^{3} + \left(b_{42} \pi^{6} + b_{34} \pi^{5}\right) x^{2} + b_{49} \pi^{7} x + c_{48} \pi^{7} + c_{32} \pi^{5} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $8$
Base field: $\Q_{2}(\sqrt{-2})$
Ramification index $e$: $8$
Residue field degree $f$: $1$
Discriminant exponent $c$: $50$
Absolute Artin slopes: $[3,4,5,\frac{43}{8}]$
Swan slopes: $[4,6,\frac{27}{4}]$
Means: $\langle2,4,\frac{43}{8}\rangle$
Rams: $(4,8,11)$
Field count: $2048$ (complete)
Ambiguity: $8$
Mass: $2048$
Absolute Mass: $1024$

Diagrams

Varying

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group: $C_2^6:D_8$ (show 192), $C_2^6:\SD_{16}$ (show 64), $C_2^6:\SD_{16}$ (show 64), $(C_2^2\times C_4^2):\SD_{16}$ (show 64), $(C_2^2\times C_4^2):\SD_{16}$ (show 64), $C_2^6:D_8$ (show 192), $(C_2^2\times C_4^2):D_8$ (show 192), $(C_2^2\times C_4^2):D_8$ (show 192), $C_2^6:C_4\wr C_2$ (show 256), $C_2^6:C_4\wr C_2$ (show 256), $C_2^4.C_2\wr D_4$ (show 256), $C_2^4.C_2\wr D_4$ (show 256) (incomplete)
Hidden Artin slopes: $[2,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ (show 524), $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ (show 280), $[2,2,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ (show 280), not computed (show 464), $[\frac{17}{4},\frac{19}{4},2,\frac{41}{8},\frac{7}{2}]_{2}$ (show 500) (incomplete)
Indices of inseparability: $[59,48,32,16,0]$
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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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
2.1.16.74c1.1 $x^{16} + 16 x^{11} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.2 $x^{16} + 16 x^{11} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.3 $x^{16} + 16 x^{11} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.4 $x^{16} + 16 x^{11} + 32 x^{6} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.5 $x^{16} + 16 x^{15} + 16 x^{11} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.6 $x^{16} + 16 x^{15} + 16 x^{11} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.7 $x^{16} + 16 x^{15} + 16 x^{11} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.8 $x^{16} + 16 x^{15} + 16 x^{11} + 32 x^{6} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.9 $x^{16} + 16 x^{14} + 16 x^{11} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.10 $x^{16} + 16 x^{14} + 16 x^{11} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.11 $x^{16} + 16 x^{14} + 16 x^{11} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.12 $x^{16} + 16 x^{14} + 16 x^{11} + 32 x^{6} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.13 $x^{16} + 16 x^{15} + 16 x^{14} + 16 x^{11} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.14 $x^{16} + 16 x^{15} + 16 x^{14} + 16 x^{11} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.15 $x^{16} + 16 x^{15} + 16 x^{14} + 16 x^{11} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.16 $x^{16} + 16 x^{15} + 16 x^{14} + 16 x^{11} + 32 x^{6} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.17 $x^{16} + 16 x^{13} + 16 x^{11} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.18 $x^{16} + 16 x^{13} + 16 x^{11} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.19 $x^{16} + 16 x^{13} + 16 x^{11} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.20 $x^{16} + 16 x^{13} + 16 x^{11} + 32 x^{6} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.21 $x^{16} + 16 x^{15} + 16 x^{13} + 16 x^{11} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.22 $x^{16} + 16 x^{15} + 16 x^{13} + 16 x^{11} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.23 $x^{16} + 16 x^{15} + 16 x^{13} + 16 x^{11} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.24 $x^{16} + 16 x^{15} + 16 x^{13} + 16 x^{11} + 32 x^{6} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.25 $x^{16} + 16 x^{14} + 16 x^{13} + 16 x^{11} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.26 $x^{16} + 16 x^{14} + 16 x^{13} + 16 x^{11} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.27 $x^{16} + 16 x^{14} + 16 x^{13} + 16 x^{11} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.28 $x^{16} + 16 x^{14} + 16 x^{13} + 16 x^{11} + 32 x^{6} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.29 $x^{16} + 16 x^{15} + 16 x^{14} + 16 x^{13} + 16 x^{11} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.30 $x^{16} + 16 x^{15} + 16 x^{14} + 16 x^{13} + 16 x^{11} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.31 $x^{16} + 16 x^{15} + 16 x^{14} + 16 x^{13} + 16 x^{11} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.32 $x^{16} + 16 x^{15} + 16 x^{14} + 16 x^{13} + 16 x^{11} + 32 x^{6} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.33 $x^{16} + 16 x^{11} + 16 x^{10} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.34 $x^{16} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.35 $x^{16} + 16 x^{11} + 16 x^{10} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.36 $x^{16} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.37 $x^{16} + 16 x^{11} + 16 x^{10} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.38 $x^{16} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.39 $x^{16} + 16 x^{11} + 16 x^{10} + 32 x^{5} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.40 $x^{16} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 32 x^{5} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.41 $x^{16} + 16 x^{15} + 16 x^{11} + 16 x^{10} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.42 $x^{16} + 16 x^{15} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.43 $x^{16} + 16 x^{15} + 16 x^{11} + 16 x^{10} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.44 $x^{16} + 16 x^{15} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 32 x^{5} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.45 $x^{16} + 16 x^{15} + 16 x^{11} + 16 x^{10} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.46 $x^{16} + 16 x^{15} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.47 $x^{16} + 16 x^{15} + 16 x^{11} + 16 x^{10} + 32 x^{5} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.48 $x^{16} + 16 x^{15} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 32 x^{5} + 34$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.49 $x^{16} + 16 x^{14} + 16 x^{11} + 16 x^{10} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.74c1.50 $x^{16} + 16 x^{14} + 16 x^{11} + 16 x^{10} + 32 x^{6} + 2$ $C_2^6:C_4\wr C_2$ (as 16T1429) $2048$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}, 5, \frac{41}{8}, \frac{43}{8}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4},4,\frac{33}{8},\frac{35}{8}]^{2}$ $[2,3,\frac{7}{2},\frac{17}{4},\frac{19}{4},\frac{41}{8}]^{2}$ $[1,2,\frac{5}{2},\frac{13}{4},\frac{15}{4},\frac{33}{8}]^{2}$ $[59, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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