$p$-adic family 2.1.16.42b

• Label: 2.1.16.42b
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(16\)
• f: \(1\)
• c: \(42\)

Defining polynomial

$x^{16} + 4 b_{31} x^{15} + 2 a_{14} x^{14} + 4 b_{29} x^{13} + 2 b_{12} x^{12} + 4 a_{27} x^{11} + \left(2 b_{8} + 8 c_{40}\right) x^{8} + 8 b_{39} x^{7} + 8 b_{37} x^{5} + 8 b_{35} x^{3} + 8 b_{33} x + 4 c_{16} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$42$
Artin slopes:	$[2,2,2,\frac{7}{2}]$
Swan slopes:	$[1,1,1,\frac{5}{2}]$
Means:	$\langle\frac{1}{2},\frac{3}{4},\frac{7}{8},\frac{27}{16}\rangle$
Rams:	$(1,1,1,13)$
Field count:	$544$ (complete)
Ambiguity:	$4$
Mass:	$256$
Absolute Mass:	$256$

Diagrams

Varying

Indices of inseparability:	$[27,14,12,8,0]$ (show 144), $[27,14,12,12,0]$ (show 128), $[27,14,14,8,0]$ (show 128), $[27,14,14,14,0]$ (show 144)
Associated inertia:	$[3,1]$ (show 144), $[4,1]$ (show 144), $[7,1]$ (show 256)
Jump Set:	$[1,2,4,15,31]$ (show 128), $[1,2,7,14,32]$ (show 72), $[1,2,7,23,39]$ (show 72), $[1,3,6,15,31]$ (show 128), $[1,3,7,14,32]$ (show 72), $[1,3,7,23,39]$ (show 72)

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 96
		$D_4\times A_4$ (as 16T179)	$D_4.A_4$ (as 16T180)	Total
hidden slopes	$[3]^{3}$	8	8	16

		Galois groups of order 128
		$C_2^4.D_4$ (as 16T230)	$C_2^4.D_4$ (as 16T254)	$C_2^4.D_4$ (as 16T297)	$C_2^4.D_4$ (as 16T319)	$C_4^2.D_4$ (as 16T361)	$C_4^2.D_4$ (as 16T387)	$C_4^2.D_4$ (as 16T397)	$C_4^2.D_4$ (as 16T398)	Total
hidden slopes	$[3]^{4}$	8	8	4	4	4	4	8	8	48

		Galois groups of order 192
		$(C_2^2\times C_4):A_4$ (as 16T426)	$C_2\wr A_4$ (as 16T427)	Total
hidden slopes	$[3,3]^{3}$	8	8	16

		Galois groups of order 384
		$C_2^4:(C_2\times A_4)$ (as 16T716)	$(C_2^3\times C_4):A_4$ (as 16T717)	$(C_2^2\times D_4):A_4$ (as 16T720)	$C_2^4:(C_2\times A_4)$ (as 16T721)	$C_2^5:A_4$ (as 16T722)	Total
hidden slopes	$[3,3]^{6}$	8	8	4	4	8	32

		Galois groups of order 512
		$C_2^5.(C_2\times D_4)$ (as 16T874)	$D_4:C_2^3.D_4$ (as 16T918)	Total
hidden slopes	$[3,3,3]^{4}$	16	16	32

		Galois groups of order 768
		$(D_4\times C_2^3):A_4$ (as 16T1037)
hidden slopes	$[2,2,3]^{6}$	16

		Galois groups of order 896
		$C_2^4.F_8$ (as 16T1076)
hidden slopes	$[3,3,3]^{7}$	128

		Galois groups of order 1024
		$(D_4\times C_2^3).Q_{16}$ (as 16T1255)	$C_2^6.\SD_{16}$ (as 16T1284)	Total
hidden slopes	$[2,3,3,3]_{4}$	16	16	32
		$[2,3,\frac{5}{2},\frac{5}{2}]_{4}$	16	16	32
	Total		32	32	64

		Galois groups of order 6144
		$C_2\wr C_2^3:C_3$ (as 16T1658)
hidden slopes	$[2,2,2,\frac{5}{2},3,3]^{6}$	24
		$[2,2,2,\frac{5}{2},\frac{5}{2},3]^{6}$	32
	Total		56

Fields

Showing 1-50 of 72

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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
2.1.16.42b1.1		$x^{16} + 2 x^{14} + 4 x^{11} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.2		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.3		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.4		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.5		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{5} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.6		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.7		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.8		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.9		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x + 2$	$C_2^5:A_4$ (as 16T722)	$384$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.10		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x + 2$	$C_2^5:A_4$ (as 16T722)	$384$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.11		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x + 2$	$(C_2^2\times D_4):A_4$ (as 16T720)	$384$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.12		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{5} + 8 x + 2$	$C_2^4:(C_2\times A_4)$ (as 16T716)	$384$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.13		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x + 2$	$(C_2^2\times C_4):A_4$ (as 16T426)	$192$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,2,\frac{5}{2}]^{3}$	$[3,3]^{3}$	$[2,2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.14		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 2$	$(C_2^2\times C_4):A_4$ (as 16T426)	$192$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,2,\frac{5}{2}]^{3}$	$[3,3]^{3}$	$[2,2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.15		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{3} + 8 x + 2$	$C_2\wr A_4$ (as 16T427)	$192$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,2,\frac{5}{2}]^{3}$	$[3,3]^{3}$	$[2,2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.16		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{3} + 8 x + 2$	$C_2\wr A_4$ (as 16T427)	$192$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,2,\frac{5}{2}]^{3}$	$[3,3]^{3}$	$[2,2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.17		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{3} + 8 x + 2$	$C_2^4:(C_2\times A_4)$ (as 16T716)	$384$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.18		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 8 x + 2$	$C_2^4:(C_2\times A_4)$ (as 16T721)	$384$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.19		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 2$	$(C_2^3\times C_4):A_4$ (as 16T717)	$384$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.20		$x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 2$	$(C_2^3\times C_4):A_4$ (as 16T717)	$384$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.21		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.22		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.23		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.24		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.25		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{5} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.26		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.27		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.28		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 2$	$C_2\wr C_2^3:C_3$ (as 16T1658)	$6144$	$2$	$[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{5}{2}]^{6}$	$[2,2,2,\frac{5}{2},3,3]^{6}$	$[1,1,1,\frac{3}{2},2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.29		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x + 2$	$(C_2^3\times C_4):A_4$ (as 16T717)	$384$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.30		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x + 2$	$(C_2^3\times C_4):A_4$ (as 16T717)	$384$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.31		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x + 2$	$C_2^4:(C_2\times A_4)$ (as 16T721)	$384$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.32		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{5} + 8 x + 2$	$C_2^4:(C_2\times A_4)$ (as 16T716)	$384$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.33		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x + 2$	$C_2\wr A_4$ (as 16T427)	$192$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,2,\frac{5}{2}]^{3}$	$[3,3]^{3}$	$[2,2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.34		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 2$	$C_2\wr A_4$ (as 16T427)	$192$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,2,\frac{5}{2}]^{3}$	$[3,3]^{3}$	$[2,2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.35		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{3} + 8 x + 2$	$(C_2^2\times C_4):A_4$ (as 16T426)	$192$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,2,\frac{5}{2}]^{3}$	$[3,3]^{3}$	$[2,2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.36		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{3} + 8 x + 2$	$(C_2^2\times C_4):A_4$ (as 16T426)	$192$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,2,\frac{5}{2}]^{3}$	$[3,3]^{3}$	$[2,2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.37		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{3} + 8 x + 2$	$C_2^4:(C_2\times A_4)$ (as 16T716)	$384$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.38		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 8 x + 2$	$(C_2^2\times D_4):A_4$ (as 16T720)	$384$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.39		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 2$	$C_2^5:A_4$ (as 16T722)	$384$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.40		$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 2$	$C_2^5:A_4$ (as 16T722)	$384$	$4$	$[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$	$[1,1,1,2,2,\frac{5}{2}]^{6}$	$[3,3]^{6}$	$[2,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.41		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2$	$D_4.A_4$ (as 16T180)	$96$	$2$	$[2, 2, 2, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,\frac{5}{2}]^{3}$	$[3]^{3}$	$[2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.42		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{7} + 2$	$D_4.A_4$ (as 16T180)	$96$	$2$	$[2, 2, 2, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,\frac{5}{2}]^{3}$	$[3]^{3}$	$[2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.43		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 2$	$D_4.A_4$ (as 16T180)	$96$	$2$	$[2, 2, 2, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,\frac{5}{2}]^{3}$	$[3]^{3}$	$[2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.44		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 2$	$(D_4\times C_2^3):A_4$ (as 16T1037)	$768$	$2$	$[2, 2, 2, 2, 2, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,2,\frac{5}{2}]^{6}$	$[2,2,3]^{6}$	$[1,1,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.45		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 2$	$(D_4\times C_2^3):A_4$ (as 16T1037)	$768$	$2$	$[2, 2, 2, 2, 2, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,2,\frac{5}{2}]^{6}$	$[2,2,3]^{6}$	$[1,1,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.46		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 2$	$(D_4\times C_2^3):A_4$ (as 16T1037)	$768$	$2$	$[2, 2, 2, 2, 2, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,2,\frac{5}{2}]^{6}$	$[2,2,3]^{6}$	$[1,1,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.47		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{3} + 2$	$(D_4\times C_2^3):A_4$ (as 16T1037)	$768$	$2$	$[2, 2, 2, 2, 2, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,2,\frac{5}{2}]^{6}$	$[2,2,3]^{6}$	$[1,1,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.48		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{3} + 2$	$(D_4\times C_2^3):A_4$ (as 16T1037)	$768$	$2$	$[2, 2, 2, 2, 2, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,2,\frac{5}{2}]^{6}$	$[2,2,3]^{6}$	$[1,1,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.49		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{7} + 8 x^{3} + 2$	$(D_4\times C_2^3):A_4$ (as 16T1037)	$768$	$2$	$[2, 2, 2, 2, 2, 3, \frac{7}{2}]^{6}$	$[1,1,1,1,1,2,\frac{5}{2}]^{6}$	$[2,2,3]^{6}$	$[1,1,2]^{6}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$
2.1.16.42b1.50		$x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 2$	$D_4\times A_4$ (as 16T179)	$96$	$2$	$[2, 2, 2, 3, \frac{7}{2}]^{3}$	$[1,1,1,2,\frac{5}{2}]^{3}$	$[3]^{3}$	$[2]^{3}$	$[27, 14, 14, 14, 0]$	$[3, 1]$	$z^{14} + 1,z + 1$	$[1, 3, 7, 23, 39]$

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