$p$-adic family 2.1.16.66j

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

Defining polynomial

$x^{16} + 8 b_{46} x^{14} + \left(8 b_{44} + 16 c_{60}\right) x^{12} + 16 b_{59} x^{11} + 8 a_{42} x^{10} + 16 b_{57} x^{9} + 4 b_{24} x^{8} + 16 b_{55} x^{7} + 16 b_{53} x^{5} + \left(8 b_{36} + 16 c_{52}\right) x^{4} + 16 a_{51} x^{3} + 16 b_{50} x^{2} + 8 c_{32} + 16 c_{48} + 2$

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:	$[3,4,\frac{17}{4},\frac{19}{4}]$
Swan slopes:	$[2,3,\frac{13}{4},\frac{15}{4}]$
Means:	$\langle1,2,\frac{21}{8},\frac{51}{16}\rangle$
Rams:	$(2,4,5,9)$
Field count:	$1280$ (complete)
Ambiguity:	$16$
Mass:	$512$
Absolute Mass:	$512$

Diagrams

Varying

Indices of inseparability:	$[51,42,32,16,0]$
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 64
		$C_4^2:C_4$ (as 16T143)	$C_2\wr C_4$ (as 16T157)	$C_2\wr C_4$ (as 16T159)	$C_4^2:C_4$ (as 16T176)	Total
hidden slopes	$[2,\frac{7}{2}]$	16	32	32	16	96

		Galois groups of order 128
		$C_2^5:C_4$ (as 16T259)	$C_2^4.D_4$ (as 16T297)	$C_4^2:D_4$ (as 16T341)	$C_4^2:D_4$ (as 16T365)	$C_2\wr D_4$ (as 16T395)	$C_4^2:D_4$ (as 16T399)	Total
hidden slopes	$[2,\frac{7}{2}]^{2}$	64	32	32	32	32	32	224

		Galois groups of order 512
		$C_2^4.(C_4\times D_4)$ (as 16T824)	$C_2^6:(C_2\times C_4)$ (as 16T863)	$C_2^4.(C_4\times D_4)$ (as 16T867)	$C_2^5.(C_2\times D_4)$ (as 16T874)	$C_2^6.D_4$ (as 16T893)	$C_2^6.(C_2\times C_4)$ (as 16T910)	$C_2^6.D_4$ (as 16T938)	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$C_2^6:D_4$ (as 16T956)	$C_2^6:D_4$ (as 16T969)	$C_2^5.(C_2\times D_4)$ (as 16T971)	Total
hidden slopes	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	64	64							64	128		320
		$[2,3,\frac{7}{2},4]^{2}$		64	64	64	128	64	128	64			64	640
	Total		64	128	64	64	128	64	128	64	64	128	64	960

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
2.1.16.66j1.1	64	$x^{16} + 8 x^{10} + 16 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T867)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.2	64	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T867)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.3	64	$x^{16} + 8 x^{10} + 16 x^{9} + 16 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T867)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.4	64	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T867)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.5	64	$x^{16} + 8 x^{10} + 16 x^{7} + 16 x^{3} + 2$	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.6	64	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{7} + 16 x^{3} + 2$	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.7	64	$x^{16} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{3} + 2$	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.8	64	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{3} + 2$	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.9	128	$x^{16} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.10	128	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.11	128	$x^{16} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.12	128	$x^{16} + 16 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.13	128	$x^{16} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.14	128	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.15	128	$x^{16} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.16	128	$x^{16} + 16 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.17	32	$x^{16} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 2$	$C_2\wr D_4$ (as 16T395)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.18	32	$x^{16} + 16 x^{11} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 2$	$C_2\wr D_4$ (as 16T395)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.19	32	$x^{16} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 2$	$C_4^2:D_4$ (as 16T365)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.20	32	$x^{16} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 2$	$C_4^2:D_4$ (as 16T365)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.21	64	$x^{16} + 8 x^{10} + 16 x^{4} + 16 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T867)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.22	64	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{4} + 16 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T867)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.23	64	$x^{16} + 8 x^{10} + 16 x^{9} + 16 x^{4} + 16 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T867)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.24	64	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{4} + 16 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T867)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.25	64	$x^{16} + 8 x^{10} + 16 x^{7} + 16 x^{4} + 16 x^{3} + 2$	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.26	64	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{7} + 16 x^{4} + 16 x^{3} + 2$	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.27	64	$x^{16} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{4} + 16 x^{3} + 2$	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.28	64	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{4} + 16 x^{3} + 2$	$(C_2^2\times C_4^2):Q_8$ (as 16T950)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,3,\frac{7}{2},4]^{2}$	$[1,2,\frac{5}{2},3]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.29	128	$x^{16} + 8 x^{10} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.30	128	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.31	128	$x^{16} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.32	128	$x^{16} + 16 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.33	128	$x^{16} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.34	128	$x^{16} + 16 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.35	128	$x^{16} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.36	128	$x^{16} + 16 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.37	32	$x^{16} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_4^2:D_4$ (as 16T399)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.38	32	$x^{16} + 16 x^{11} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_4^2:D_4$ (as 16T399)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.39	32	$x^{16} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_4^2:D_4$ (as 16T341)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.40	32	$x^{16} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 16 x^{4} + 16 x^{3} + 2$	$C_4^2:D_4$ (as 16T341)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.41	128	$x^{16} + 8 x^{14} + 8 x^{10} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.42	128	$x^{16} + 8 x^{14} + 16 x^{12} + 8 x^{10} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.43	128	$x^{16} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.44	128	$x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.45	128	$x^{16} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.46	128	$x^{16} + 8 x^{14} + 16 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.47	128	$x^{16} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.48	128	$x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{3} + 2$	$C_2^6:D_4$ (as 16T969)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,2,\frac{7}{2},\frac{7}{2}]^{2}$	$[1,1,\frac{5}{2},\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.49	32	$x^{16} + 8 x^{14} + 8 x^{10} + 16 x^{7} + 16 x^{3} + 2$	$C_4^2:D_4$ (as 16T365)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66j1.50	32	$x^{16} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{7} + 16 x^{3} + 2$	$C_4^2:D_4$ (as 16T365)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[51, 42, 32, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$

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