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Properties

Label 2.1.4.10a1.3-1.4.28a
Base 2.1.4.10a1.3
Degree \(4\)
e \(4\)
f \(1\)
c \(28\)

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Defining polynomial

$x^{4} + \left(b_{39} \pi^{10} + b_{35} \pi^{9} + b_{31} \pi^{8} + b_{27} \pi^{7}\right) x^{3} + \left(b_{18} \pi^{5} + b_{14} \pi^{4} + a_{10} \pi^{3}\right) x^{2} + \left(b_{37} \pi^{10} + b_{33} \pi^{9} + b_{29} \pi^{8} + a_{25} \pi^{7}\right) x + c_{40} \pi^{11} + c_{20} \pi^{6} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.10a1.3
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $28$
Absolute Artin slopes: $[3,\frac{7}{2},4,\frac{21}{4}]$
Swan slopes: $[5,10]$
Means: $\langle\frac{5}{2},\frac{25}{4}\rangle$
Rams: $(5,15)$
Field count: $512$ (complete)
Ambiguity: $4$
Mass: $512$
Absolute Mass: $256$

Diagrams

Varying

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

Galois group: $C_2^5.D_8$ (show 64), $C_2^5.\SD_{16}$ (show 64), $C_2^5.C_2\wr C_4$ (show 128), $(C_2\times C_4^3):D_8$ (show 64), $(C_2\times C_4^3):\SD_{16}$ (show 64), $C_2^7:\SD_{16}$ (show 64), $C_2^7.D_8$ (show 64) (incomplete)
Hidden Artin slopes: $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ (show 128), not computed (show 256), $[2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]$ (show 128) (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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Showing 1-50 of 512

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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
2.1.16.68e1.1025 $x^{16} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1026 $x^{16} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1027 $x^{16} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1028 $x^{16} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1029 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1030 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1031 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1032 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1033 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1034 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1035 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1036 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1037 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1038 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1039 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1040 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1041 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1042 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1043 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1044 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1045 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1046 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1047 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1048 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1049 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1050 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1051 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1052 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1053 $x^{16} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1054 $x^{16} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1055 $x^{16} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1056 $x^{16} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1057 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1058 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1059 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1060 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1061 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1062 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1063 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1064 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1065 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1066 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1067 $x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1068 $x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1069 $x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1070 $x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1071 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1072 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1073 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68e1.1074 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 32 x^{3} + 10$ $C_2^7.D_8$ (as 16T1459) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,\frac{17}{4},\frac{9}{2},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ $[53, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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