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Properties

Label 2.1.4.11a1.5-1.4.24b
Base 2.1.4.11a1.5
Degree \(4\)
e \(4\)
f \(1\)
c \(24\)

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Defining polynomial

$x^{4} + \left(b_{35} \pi^{9} + b_{31} \pi^{8} + b_{27} \pi^{7} + b_{23} \pi^{6}\right) x^{3} + \left(b_{10} \pi^{3} + a_{6} \pi^{2}\right) x^{2} + \left(b_{33} \pi^{9} + b_{29} \pi^{8} + b_{25} \pi^{7} + a_{21} \pi^{6}\right) x + c_{36} \pi^{10} + c_{12} \pi^{4} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.11a1.5
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $24$
Absolute Artin slopes: $[3,\frac{7}{2},4,\frac{21}{4}]$
Swan slopes: $[3,9]$
Means: $\langle\frac{3}{2},\frac{21}{4}\rangle$
Rams: $(3,15)$
Field count: $256$ (complete)
Ambiguity: $4$
Mass: $256$
Absolute Mass: $128$

Diagrams

Varying

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

Galois group: $C_2^6:\SD_{16}$ (show 32), $(C_2^2\times C_4^2):\SD_{16}$ (show 32), $C_2^6:D_8$ (show 32), $(C_2^2\times C_4^2):D_8$ (show 32), $C_2^4.C_2\wr D_4$ (show 128) (incomplete)
Hidden Artin slopes: $[2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ (show 32), $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ (show 16), $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ (show 96), not computed (show 112) (incomplete)
Indices of inseparability: $[53,38,28,16,0]$
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
2.1.16.68e1.3073 $x^{16} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3074 $x^{16} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3075 $x^{16} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3076 $x^{16} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3077 $x^{16} + 16 x^{15} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3078 $x^{16} + 16 x^{15} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3079 $x^{16} + 16 x^{15} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3080 $x^{16} + 16 x^{15} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3081 $x^{16} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3082 $x^{16} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3083 $x^{16} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3084 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3085 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3086 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3087 $x^{16} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3088 $x^{16} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3089 $x^{16} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3090 $x^{16} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3091 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3092 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3093 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3094 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3095 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3096 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3097 $x^{16} + 4 x^{12} + 16 x^{9} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3098 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{9} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3099 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3100 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3101 $x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3102 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3103 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3104 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 4 x^{8} + 8 x^{6} + 16 x^{5} + 32 x + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1271) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3105 $x^{16} + 4 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3106 $x^{16} + 4 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3107 $x^{16} + 16 x^{15} + 4 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3108 $x^{16} + 16 x^{15} + 4 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3109 $x^{16} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3110 $x^{16} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3111 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3112 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3113 $x^{16} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3114 $x^{16} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3115 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3116 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3117 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3118 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3119 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3120 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3121 $x^{16} + 4 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.3122 $x^{16} + 4 x^{12} + 16 x^{9} + 4 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1265) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[\frac{17}{4},\frac{19}{4},2,\frac{39}{8},\frac{9}{2}]_{2}$ $[\frac{13}{4},\frac{15}{4},1,\frac{31}{8},\frac{7}{2}]_{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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