$p$-adic family 2.1.16.66h

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

Defining polynomial

$x^{16} + 16 b_{63} x^{15} + 8 b_{46} x^{14} + 16 b_{61} x^{13} + 4 a_{28} x^{12} + 16 b_{59} x^{11} + 8 b_{42} x^{10} + 16 b_{57} x^{9} + \left(4 b_{24} + 8 c_{40}\right) x^{8} + 16 b_{55} x^{7} + 8 a_{38} x^{6} + 16 b_{53} x^{5} + 8 b_{36} x^{4} + 16 a_{51} x^{3} + 8 c_{32} + 16 c_{48} + 32 c_{64} + 2$

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:	$[3,\frac{7}{2},4,5]$
Swan slopes:	$[2,\frac{5}{2},3,4]$
Means:	$\langle1,\frac{7}{4},\frac{19}{8},\frac{51}{16}\rangle$
Rams:	$(2,3,5,13)$
Field count:	$3072$ (complete)
Ambiguity:	$16$
Mass:	$1024$
Absolute Mass:	$1024$

Diagrams

Varying

Indices of inseparability:	$[51,38,28,16,0]$
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 32
		$C_2^2:C_8$ (as 16T24)	$D_4:C_4$ (as 16T26)	$C_4\wr C_2$ (as 16T28)	$\OD_{16}:C_2$ (as 16T41)	Total
hidden slopes	$[2]$	32	16	16	16	80

		Galois groups of order 64
		$\OD_{16}:C_2^2$ (as 16T72)	$C_2^3.D_4$ (as 16T75)	$C_2^2:\OD_{16}$ (as 16T95)	$C_4^2:C_2^2$ (as 16T122)	$D_4:D_4$ (as 16T126)	$C_2\wr C_4$ (as 16T130)	$C_4^2.C_4$ (as 16T131)	$D_4:D_4$ (as 16T135)	$C_4^2.C_4$ (as 16T139)	$C_4^2:C_2^2$ (as 16T145)	$C_4^2.C_4$ (as 16T151)	$C_2^3.D_4$ (as 16T153)	$C_2^2:\SD_{16}$ (as 16T155)	$C_2\wr C_4$ (as 16T158)	$C_2\wr C_4$ (as 16T172)	Total
hidden slopes	$[2,\frac{17}{4}]$						16	16		32		32	16		32	16	160
		$[2]^{2}$	16	16	32	16	32			16		16			32			176
	Total		16	16	32	16	32	16	16	16	32	16	32	16	32	32	16	336

		Galois groups of order 128
		$(C_2\times C_8):D_4$ (as 16T209)	$C_4^2:D_4$ (as 16T211)	$(C_2^2\times D_4):C_4$ (as 16T213)	$\OD_{16}:D_4$ (as 16T216)	$C_2^4.D_4$ (as 16T219)	$C_4^2.D_4$ (as 16T221)	$C_4^2:D_4$ (as 16T222)	$C_4^2.D_4$ (as 16T225)	$C_4^2.(C_2\times C_4)$ (as 16T226)	$C_2^5:C_4$ (as 16T227)	$(C_2\times D_4).D_4$ (as 16T233)	$C_2^4.D_4$ (as 16T236)	$(C_2\times C_8):D_4$ (as 16T238)	$(C_2^3\times C_4):C_4$ (as 16T243)	$C_2^5:C_4$ (as 16T273)	$C_4^2:D_4$ (as 16T276)	$C_4^2.(C_2\times C_4)$ (as 16T285)	$\OD_{16}:D_4$ (as 16T299)	$(C_2\times C_4^2).C_4$ (as 16T300)	$C_2^4.D_4$ (as 16T302)	$(C_2\times C_4^2):C_4$ (as 16T314)	$(C_2\times C_4^2).C_4$ (as 16T327)	$C_4^2.D_4$ (as 16T337)	$C_4^2.D_4$ (as 16T338)	$C_4^2.D_4$ (as 16T349)	$C_4^2:D_4$ (as 16T352)	$C_4^2.D_4$ (as 16T357)	$C_4^2:D_4$ (as 16T366)	$\OD_{16}:D_4$ (as 16T367)	$Q_8\wr C_2$ (as 16T370)	$C_2\wr D_4$ (as 16T376)	$C_4^2.D_4$ (as 16T380)	$C_4^2:D_4$ (as 16T381)	$C_4^2:D_4$ (as 16T382)	$C_4^2:D_4$ (as 16T386)	$C_2\wr D_4$ (as 16T388)	$C_2\wr D_4$ (as 16T390)	$C_2\wr D_4$ (as 16T391)	$C_4^2.D_4$ (as 16T404)	$C_4^2.D_4$ (as 16T407)	$C_4^2:D_4$ (as 16T408)	$C_4^2:D_4$ (as 16T410)	Total
hidden slopes	$[2,\frac{17}{4}]^{2}$			16		16				32	32		16		32	32		16		64			32	96		16	16	8	16		32	32	16	8		8	32	32	32	24	48		32	736
		$[2,2]^{2}$	32			16									16					32											32					32							32		192
	$[2,3]^{2}$		32	64		16		16	16	32			32					16				32	64			128																			448
		Total	64	64	16	32	16	16	16	32	32	32	32	16	16	32	32	16	16	32	64	32	64	32	96	128	16	16	8	16	32	32	32	16	8	32	8	32	32	32	24	48	32	32	1376

		Galois groups of order 256
		$C_4^2.(C_2\times D_4)$ (as 16T662)	$(C_4\times C_8).D_4$ (as 16T669)	$C_4^2.(C_2\times D_4)$ (as 16T672)	$Q_8^2:C_2^2$ (as 16T674)	$(C_4\times C_8).D_4$ (as 16T677)	$D_4^2:C_2^2$ (as 16T696)	Total
hidden slopes	$[2,2,\frac{17}{4}]^{2}$	64	32	64	32	32	32	256

		Galois groups of order 512
		$Q_8^2:(C_2\times C_4)$ (as 16T851)	$C_4^3:D_4$ (as 16T871)	$C_4^3.D_4$ (as 16T873)	$D_4^2:(C_2\times C_4)$ (as 16T882)	$C_4^3:D_4$ (as 16T890)	$C_4^3.D_4$ (as 16T899)	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$(C_4\times \OD_{16}).D_4$ (as 16T945)	$(C_4\times \OD_{16}):D_4$ (as 16T946)	$D_4^2:Q_8$ (as 16T961)	$C_4^3.D_4$ (as 16T974)	$Q_8^2:D_4$ (as 16T980)	$Q_8^2:Q_8$ (as 16T986)	$D_4^2:D_4$ (as 16T987)	Total
hidden slopes	$[2,2,\frac{17}{4}]^{4}$		64	128		128	64									384
		$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	32	32	64	32	64	32	64	32	32	64	64	32	64	32	640
	Total		32	96	192	32	192	96	64	32	32	64	64	32	64	32	1024

Fields

Showing 1-50 of

  To download results, . Download displayed columns for results to

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
2.1.16.66h1.1	32	$x^{16} + 4 x^{12} + 8 x^{6} + 16 x^{3} + 2$	$D_4^2:(C_2\times C_4)$ (as 16T882)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.2	32	$x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{6} + 16 x^{3} + 2$	$D_4^2:(C_2\times C_4)$ (as 16T882)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.3	32	$x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{3} + 2$	$D_4^2:(C_2\times C_4)$ (as 16T882)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.4	32	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{3} + 2$	$D_4^2:(C_2\times C_4)$ (as 16T882)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.5	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.6	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{3} + 34$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.7	64	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.8	64	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{3} + 34$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.9	64	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.10	64	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{3} + 34$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.11	64	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.12	64	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{3} + 34$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.13	32	$x^{16} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3.D_4$ (as 16T899)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.14	32	$x^{16} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{3} + 34$	$C_4^3.D_4$ (as 16T899)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.15	32	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3.D_4$ (as 16T899)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.16	32	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{3} + 34$	$C_4^3.D_4$ (as 16T899)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.17	64	$x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{3} + 2$	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.18	64	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{3} + 2$	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.19	64	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{3} + 2$	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.20	64	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{3} + 2$	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.21	32	$x^{16} + 4 x^{12} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T871)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.22	32	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T871)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.23	64	$x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.24	64	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.25	64	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.26	64	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.27	32	$x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$Q_8^2:(C_2\times C_4)$ (as 16T851)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.28	32	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$Q_8^2:(C_2\times C_4)$ (as 16T851)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.29	32	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$Q_8^2:(C_2\times C_4)$ (as 16T851)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.30	32	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$Q_8^2:(C_2\times C_4)$ (as 16T851)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.31	64	$x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3.D_4$ (as 16T873)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.32	64	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3.D_4$ (as 16T873)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.33	64	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3.D_4$ (as 16T873)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.34	64	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$C_4^3.D_4$ (as 16T873)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, 5]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,4]^{2}$	$[2,2,\frac{7}{2},\frac{15}{4}]^{2}$	$[1,1,\frac{5}{2},\frac{11}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.35	64	$x^{16} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T871)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{4}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{4}$	$[2,2,\frac{17}{4}]^{4}$	$[1,1,\frac{13}{4}]^{4}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.36	64	$x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T871)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{4}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{4}$	$[2,2,\frac{17}{4}]^{4}$	$[1,1,\frac{13}{4}]^{4}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.37	64	$x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^2.(C_2\times D_4)$ (as 16T662)	$256$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,2,\frac{17}{4}]^{2}$	$[1,1,\frac{13}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.38	64	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^2.(C_2\times D_4)$ (as 16T662)	$256$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,2,\frac{17}{4}]^{2}$	$[1,1,\frac{13}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.39	64	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^2.(C_2\times D_4)$ (as 16T662)	$256$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,2,\frac{17}{4}]^{2}$	$[1,1,\frac{13}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.40	64	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^2.(C_2\times D_4)$ (as 16T662)	$256$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,2,\frac{17}{4}]^{2}$	$[1,1,\frac{13}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.41	32	$x^{16} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$D_4^2:C_2^2$ (as 16T696)	$256$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,2,\frac{17}{4}]^{2}$	$[1,1,\frac{13}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.42	32	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$D_4^2:C_2^2$ (as 16T696)	$256$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,2,\frac{17}{4}]^{2}$	$[1,1,\frac{13}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.43	32	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$D_4^2:C_2^2$ (as 16T696)	$256$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,2,\frac{17}{4}]^{2}$	$[1,1,\frac{13}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.44	32	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$D_4^2:C_2^2$ (as 16T696)	$256$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,2,\frac{17}{4}]^{2}$	$[1,1,\frac{13}{4}]^{2}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.45	128	$x^{16} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{4}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{4}$	$[2,2,\frac{17}{4}]^{4}$	$[1,1,\frac{13}{4}]^{4}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.46	128	$x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{4}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{4}$	$[2,2,\frac{17}{4}]^{4}$	$[1,1,\frac{13}{4}]^{4}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.47	128	$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{4}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{4}$	$[2,2,\frac{17}{4}]^{4}$	$[1,1,\frac{13}{4}]^{4}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.48	128	$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^3:D_4$ (as 16T890)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{4}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{4}$	$[2,2,\frac{17}{4}]^{4}$	$[1,1,\frac{13}{4}]^{4}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.49	128	$x^{16} + 4 x^{12} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$C_4^3.D_4$ (as 16T873)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{4}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{4}$	$[2,2,\frac{17}{4}]^{4}$	$[1,1,\frac{13}{4}]^{4}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.66h1.50	128	$x^{16} + 4 x^{12} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 34$	$C_4^3.D_4$ (as 16T873)	$512$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{4}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4},4]^{4}$	$[2,2,\frac{17}{4}]^{4}$	$[1,1,\frac{13}{4}]^{4}$	$[51, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$

  To download results, . Download displayed columns for results to