$p$-adic family 2.1.16.62h

• Label: 2.1.16.62h
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(16\)
• f: \(1\)
• c: \(62\)

Defining polynomial

$x^{16} + 8 a_{47} x^{15} + 8 b_{46} x^{14} + \left(4 b_{28} + 16 c_{60}\right) x^{12} + 16 b_{59} x^{11} + 8 b_{42} x^{10} + 16 b_{57} x^{9} + 2 a_{8} x^{8} + 16 b_{55} x^{7} + 8 b_{38} x^{6} + 16 b_{53} x^{5} + 4 a_{20} x^{4} + 16 b_{51} x^{3} + 8 a_{34} x^{2} + 16 b_{49} x + 4 c_{16} + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$62$
Artin slopes:	$[2,3,4,\frac{19}{4}]$
Swan slopes:	$[1,2,3,\frac{15}{4}]$
Means:	$\langle\frac{1}{2},\frac{5}{4},\frac{17}{8},\frac{47}{16}\rangle$
Rams:	$(1,3,7,13)$
Field count:	$2176$ (complete)
Ambiguity:	$16$
Mass:	$1024$
Absolute Mass:	$1024$

Diagrams

Varying

Indices of inseparability:	$[47,34,20,8,0]$
Associated inertia:	$[1,1,1,1]$
Jump Set:	$[1,2,4,8,32]$ (show 1088), $[1,2,4,32,48]$ (show 288), $[1,2,31,47,63]$ (show 32), $[1,7,15,31,47]$ (show 512), $[1,11,27,43,59]$ (show 144), $[1,13,29,45,61]$ (show 72), $[1,15,30,46,62]$ (show 20), $[1,15,32,48,64]$ (show 20)

Galois groups and Hidden Artin slopes

Select desired size of Galois group. Note that the following data has not all been computed for fields in this family, so the tables below are incomplete.

		Galois groups of order 64
		$C_2^3.D_4$ (as 16T140)	$C_4^2:C_4$ (as 16T167)	$C_2\wr C_4$ (as 16T170)	$C_4^2:C_4$ (as 16T174)	Total
hidden slopes	$[\frac{7}{2},\frac{17}{4}]$	16	16	16	16	64

		Galois groups of order 128
		$(C_2^2\times D_4):C_4$ (as 16T244)	$C_2^4.D_4$ (as 16T248)	$C_2^4.D_4$ (as 16T250)	$C_2^5:C_4$ (as 16T261)	$C_2^4.D_4$ (as 16T266)	$(C_2^3\times C_4):C_4$ (as 16T292)	$(C_2\times C_4^2):C_4$ (as 16T293)	$C_2^4.D_4$ (as 16T310)	$(C_2^2\times D_4):C_4$ (as 16T315)	$C_2^4.D_4$ (as 16T317)	$C_4^2:D_4$ (as 16T336)	$C_4^2:D_4$ (as 16T340)	$C_4^2:D_4$ (as 16T342)	$C_4^2.D_4$ (as 16T344)	$C_4^2:D_4$ (as 16T345)	$C_4^2:D_4$ (as 16T359)	$C_2\wr D_4$ (as 16T393)	$C_4^2:D_4$ (as 16T394)	$C_2\wr D_4$ (as 16T396)	$C_4^2:D_4$ (as 16T400)	$C_2\wr D_4$ (as 16T401)	$C_4^2:D_4$ (as 16T402)	Total
hidden slopes	$[\frac{7}{2},\frac{17}{4}]^{2}$	8	16	8	16	16	16	16	16	8	8	8	8	16	16	32	16	16	8	16	16	32	8	320

		Galois groups of order 512
		$C_2^6:(C_2\times C_4)$ (as 16T815)	$C_2^5.(C_2\times D_4)$ (as 16T833)	$C_2^6.D_4$ (as 16T848)	$C_2^6.(C_2\times C_4)$ (as 16T854)	$C_2^4.(C_4\times D_4)$ (as 16T884)	$C_2^4.(C_4\times D_4)$ (as 16T896)	$C_2^4.(C_4\times D_4)$ (as 16T915)	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$C_2^4.(C_4\times D_4)$ (as 16T920)	$C_2^4.(C_4\times D_4)$ (as 16T926)	$C_2^6:Q_8$ (as 16T958)	$C_2^5.(C_2\times D_4)$ (as 16T963)	$C_2^6.D_4$ (as 16T966)	$C_2^6.Q_8$ (as 16T968)	$(C_2^2\times C_4^2):Q_8$ (as 16T991)	$C_2^6:D_4$ (as 16T996)	$(C_2^2\times C_4^2):Q_8$ (as 16T1008)	$(D_4\times C_2^3).C_2^3$ (as 16T1015)	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	Total
hidden slopes	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$			64				32		32			64	32			32				256
		$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	32	64		32	32	32		32		32	32			32	32		32	64	64	512
	Total		32	64	64	32	32	32	32	32	32	32	32	64	32	32	32	32	32	64	64	768

		Galois groups of order 1024
		$C_2^6.\SD_{16}$ (as 16T1248)	$C_2^6:D_8$ (as 16T1253)	$(C_2^2\times C_4^2).D_8$ (as 16T1257)	$(D_4\times C_2^3).Q_{16}$ (as 16T1258)	$C_2^6:\SD_{16}$ (as 16T1267)	$C_2^6.D_8$ (as 16T1272)	$(C_2^2\times C_4^2):\SD_{16}$ (as 16T1273)	$(C_2^2\times C_4^2):D_8$ (as 16T1282)	Total
hidden slopes	$[\frac{17}{4},\frac{17}{4},2,\frac{7}{2},\frac{7}{2}]_{2}$	64	16	32	64	24	32	40	16	288
		$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4}]^{2}$		48	32		40	32	24	48	224

		Galois groups of order 2048
		$(C_2^2\times D_4^2).D_4$ (as 16T1355)	$(C_2^2\times D_4^2).D_4$ (as 16T1374)	$C_2^6:C_4\wr C_2$ (as 16T1429)	Total
hidden slopes	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4}]^{4}$	32	32	136	200

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
2.1.16.62h1.1		$x^{16} + 8 x^{15} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.2		$x^{16} + 8 x^{15} + 16 x^{12} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.3		$x^{16} + 8 x^{15} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.4		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.5		$x^{16} + 8 x^{15} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.6		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.7		$x^{16} + 8 x^{15} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.8		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.9		$x^{16} + 8 x^{15} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.10		$x^{16} + 8 x^{15} + 16 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.11		$x^{16} + 8 x^{15} + 16 x^{11} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.12		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.13		$x^{16} + 8 x^{15} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.14		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.15		$x^{16} + 8 x^{15} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.16		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^6.D_4$ (as 16T848)	$512$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[2,\frac{7}{2},\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.17		$x^{16} + 8 x^{15} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.18		$x^{16} + 8 x^{15} + 16 x^{12} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.19		$x^{16} + 8 x^{15} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.20		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.21		$x^{16} + 8 x^{15} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.22		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.23		$x^{16} + 8 x^{15} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.24		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.25		$x^{16} + 8 x^{15} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.26		$x^{16} + 8 x^{15} + 16 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.27		$x^{16} + 8 x^{15} + 16 x^{11} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.28		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.29		$x^{16} + 8 x^{15} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.30		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.31		$x^{16} + 8 x^{15} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.32		$x^{16} + 8 x^{15} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 31, 47, 63]$
2.1.16.62h1.33		$x^{16} + 8 x^{15} + 8 x^{14} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^4.D_4$ (as 16T266)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[\frac{7}{2},\frac{17}{4}]^{2}$	$[\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.34		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^3.D_4$ (as 16T140)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$	$[\frac{7}{2},\frac{17}{4}]$	$[\frac{5}{2},\frac{13}{4}]$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.35		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^3.D_4$ (as 16T140)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$	$[\frac{7}{2},\frac{17}{4}]$	$[\frac{5}{2},\frac{13}{4}]$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.36		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2\wr C_4$ (as 16T170)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$	$[\frac{7}{2},\frac{17}{4}]$	$[\frac{5}{2},\frac{13}{4}]$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.37		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2\wr C_4$ (as 16T170)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$	$[\frac{7}{2},\frac{17}{4}]$	$[\frac{5}{2},\frac{13}{4}]$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.38		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 2$	$C_2^4.D_4$ (as 16T266)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[\frac{7}{2},\frac{17}{4}]^{2}$	$[\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.39		$x^{16} + 8 x^{15} + 8 x^{14} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^3.D_4$ (as 16T140)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$	$[\frac{7}{2},\frac{17}{4}]$	$[\frac{5}{2},\frac{13}{4}]$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.40		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^3.D_4$ (as 16T140)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$	$[\frac{7}{2},\frac{17}{4}]$	$[\frac{5}{2},\frac{13}{4}]$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.41		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^4.D_4$ (as 16T266)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[\frac{7}{2},\frac{17}{4}]^{2}$	$[\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.42		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2^4.D_4$ (as 16T266)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$	$[\frac{7}{2},\frac{17}{4}]^{2}$	$[\frac{5}{2},\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.43		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2\wr C_4$ (as 16T170)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$	$[\frac{7}{2},\frac{17}{4}]$	$[\frac{5}{2},\frac{13}{4}]$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.44		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 2$	$C_2\wr C_4$ (as 16T170)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$	$[\frac{7}{2},\frac{17}{4}]$	$[\frac{5}{2},\frac{13}{4}]$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.45		$x^{16} + 8 x^{15} + 8 x^{14} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.46		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.47		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.48		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.49		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$
2.1.16.62h1.50		$x^{16} + 8 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[47, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 15, 30, 46, 62]$

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