$p$-adic family 2.1.16.60l

• Label: 2.1.16.60l
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(16\)
• f: \(1\)
• c: \(60\)

Defining polynomial

$x^{16} + 8 b_{47} x^{15} + 8 b_{46} x^{14} + 8 a_{45} x^{13} + 4 b_{28} x^{12} + 8 b_{42} x^{10} + \left(2 a_{8} + 16 c_{56}\right) x^{8} + 16 b_{55} x^{7} + 8 b_{38} x^{6} + 16 b_{53} x^{5} + 4 a_{20} x^{4} + 16 b_{51} x^{3} + 8 a_{34} x^{2} + 16 b_{49} x + 4 c_{16} + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$60$
Artin slopes:	$[2,3,4,\frac{9}{2}]$
Swan slopes:	$[1,2,3,\frac{7}{2}]$
Means:	$\langle\frac{1}{2},\frac{5}{4},\frac{17}{8},\frac{45}{16}\rangle$
Rams:	$(1,3,7,11)$
Field count:	$1024$ (complete)
Ambiguity:	$16$
Mass:	$512$
Absolute Mass:	$512$

Diagrams

Varying

Indices of inseparability:	$[45,34,20,8,0]$
Associated inertia:	$[1,1,1,1]$
Jump Set:	$[1,2,4,8,32]$ (show 512), $[1,2,4,32,48]$ (show 128), $[1,2,29,45,61]$ (show 32), $[1,7,15,31,47]$ (show 256), $[1,11,27,43,59]$ (show 64), $[1,13,26,42,58]$ (show 8), $[1,13,31,47,63]$ (show 16), $[1,13,32,48,64]$ (show 8)

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 512
		$C_2^5.(C_2\times D_4)$ (as 16T813)	$C_2^3\wr C_2:C_4$ (as 16T820)	$C_2^6.D_4$ (as 16T835)	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$C_2^6.(C_2\times C_4)$ (as 16T854)	$C_2^4.(C_4\times D_4)$ (as 16T869)	$C_2^4.(C_4\times D_4)$ (as 16T881)	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$C_2^5.(C_2\times D_4)$ (as 16T953)	$C_2^6.Q_8$ (as 16T968)	$(C_2^2\times C_4^2):Q_8$ (as 16T1008)	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$(D_4\times C_2^3).C_2^3$ (as 16T1015)	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	Total
hidden slopes	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	32	32	32	32	32	32	32	32	32	32	32	32	64	64	512

		Galois groups of order 1024
		$C_2^6.\SD_{16}$ (as 16T1248)	$(C_2^2\times C_4^2).D_8$ (as 16T1257)	$(D_4\times C_2^3).Q_{16}$ (as 16T1258)	$C_2^6.D_8$ (as 16T1272)	Total
hidden slopes	$[\frac{17}{4},3,4,\frac{7}{2}]_{4}$	64	32	64	32	192
		$[3,\frac{7}{2},4,\frac{17}{4}]^{4}$		32		32	64

		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)	Total
hidden slopes	$[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$	48	48	96

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
2.1.16.60l1.1		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.2		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.3		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.4		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.5		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.6		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.7		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.8		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.9		$x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.10		$x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.11		$x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.12		$x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.13		$x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.14		$x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.15		$x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.16		$x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.17		$x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.18		$x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.19		$x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.20		$x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.21		$x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.22		$x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.23		$x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.24		$x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T953)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.25		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.26		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.27		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.28		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.29		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.30		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.31		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.32		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T916)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 29, 45, 61]$
2.1.16.60l1.33		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 26, 42, 58]$
2.1.16.60l1.34		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 26, 42, 58]$
2.1.16.60l1.35		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 26, 42, 58]$
2.1.16.60l1.36		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 26, 42, 58]$
2.1.16.60l1.37		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 32, 48, 64]$
2.1.16.60l1.38		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 32, 48, 64]$
2.1.16.60l1.39		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 32, 48, 64]$
2.1.16.60l1.40		$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^6.(C_2\times C_4)$ (as 16T854)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 32, 48, 64]$
2.1.16.60l1.41		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.42		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.43		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.44		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.45		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.46		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.47		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.48		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.49		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$
2.1.16.60l1.50		$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T1010)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,\frac{7}{2},4,\frac{17}{4}]^{2}$	$[2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[45, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 31, 47, 63]$

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