$p$-adic family 2.1.16.66i

• Label: 2.1.16.66i
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(16\)
• f: \(1\)
• c: \(66\)

Defining polynomial

$x^{16} + 8 b_{46} x^{14} + \left(4 a_{28} + 16 c_{60}\right) x^{12} + 16 b_{59} x^{11} + 8 a_{42} x^{10} + 16 b_{57} x^{9} + \left(4 b_{24} + 8 c_{40} + 16 c_{56}\right) x^{8} + 16 b_{55} x^{7} + 16 b_{54} x^{6} + 16 b_{53} x^{5} + 8 b_{36} x^{4} + 16 a_{51} x^{3} + 16 b_{50} x^{2} + 8 c_{32} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$66$
Artin slopes:	$[3,\frac{7}{2},\frac{9}{2},\frac{19}{4}]$
Swan slopes:	$[2,\frac{5}{2},\frac{7}{2},\frac{15}{4}]$
Means:	$\langle1,\frac{7}{4},\frac{21}{8},\frac{51}{16}\rangle$
Rams:	$(2,3,7,9)$
Field count:	$1536$ (complete)
Ambiguity:	$16$
Mass:	$512$
Absolute Mass:	$512$

Diagrams

Varying

Indices of inseparability:	$[51,42,28,16,0]$
Associated inertia:	$[1,1,1,1]$
Jump Set:	$[1,3,7,15,31]$

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

		Galois groups of order 128
		$C_2^3.D_8$ (as 16T330)	$C_2^3.D_8$ (as 16T339)	Total
hidden slopes	$[2,4,\frac{17}{4}]$	64	64	128

		Galois groups of order 256
		$C_2^5.D_4$ (as 16T633)	$C_2^4:D_8$ (as 16T689)	$C_2^4:\SD_{16}$ (as 16T700)	$C_2^4:D_8$ (as 16T701)	$C_2^4:\SD_{16}$ (as 16T707)	Total
hidden slopes	$[2,4,\frac{17}{4}]^{2}$	128	64	64	64	64	384

		Galois groups of order 512
		$C_2^6.D_4$ (as 16T940)	$C_2^5:D_8$ (as 16T962)	$C_2^5:\SD_{16}$ (as 16T993)	$C_2^5.(C_2\times D_4)$ (as 16T995)	$C_2^5.(C_2\times D_4)$ (as 16T1009)	$C_2^5:\SD_{16}$ (as 16T1016)	$C_2^5:D_8$ (as 16T1017)	$C_2^6.D_4$ (as 16T1025)	Total
hidden slopes	$[2,2,4,\frac{17}{4}]^{2}$	256	64	64	128	128	64	64	256	1024

Fields

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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
2.1.16.66i1.1	128	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.2	128	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.3	128	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.4	128	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.5	128	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.6	128	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.7	128	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.8	128	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.9	128	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{6} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.10	128	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{6} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.11	128	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.12	128	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.13	128	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{6} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.14	128	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{6} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.15	128	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{6} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.16	128	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{6} + 16 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T995)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.17	64	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.18	64	$x^{16} + 20 x^{12} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.19	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.20	64	$x^{16} + 20 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.21	64	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.22	64	$x^{16} + 20 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.23	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.24	64	$x^{16} + 20 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.25	64	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.26	64	$x^{16} + 20 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.27	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.28	64	$x^{16} + 20 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.29	64	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.30	64	$x^{16} + 20 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.31	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.32	64	$x^{16} + 20 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.33	64	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.34	64	$x^{16} + 20 x^{12} + 8 x^{10} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.35	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.36	64	$x^{16} + 20 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.37	64	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.38	64	$x^{16} + 20 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.39	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.40	64	$x^{16} + 20 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.41	64	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.42	64	$x^{16} + 20 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.43	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.44	64	$x^{16} + 20 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.45	64	$x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.46	64	$x^{16} + 20 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.47	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.48	64	$x^{16} + 20 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_2^3.D_8$ (as 16T339)	$128$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]$	$[2,4,\frac{17}{4}]$	$[1,3,\frac{13}{4}]$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.49	256	$x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{3} + 2$	$C_2^6.D_4$ (as 16T940)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66i1.50	256	$x^{16} + 8 x^{14} + 20 x^{12} + 8 x^{10} + 16 x^{3} + 2$	$C_2^6.D_4$ (as 16T940)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4}]^{2}$	$[2,2,4,\frac{17}{4}]^{2}$	$[1,1,3,\frac{13}{4}]^{2}$	$[51, 42, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$

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