$p$-adic family 2.1.16.58n

• Label: 2.1.16.58n
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(16\)
• f: \(1\)
• c: \(58\)

Defining polynomial

$x^{16} + 8 b_{47} x^{15} + 8 b_{46} x^{14} + 8 b_{45} x^{13} + 4 b_{28} x^{12} + 8 a_{43} x^{11} + 8 b_{42} x^{10} + 2 a_{8} x^{8} + 8 b_{38} x^{6} + \left(4 a_{20} + 16 c_{52}\right) x^{4} + 16 b_{51} x^{3} + 8 a_{34} x^{2} + 16 b_{49} x + 4 c_{16} + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$58$
Artin slopes:	$[2,3,4,\frac{17}{4}]$
Swan slopes:	$[1,2,3,\frac{13}{4}]$
Means:	$\langle\frac{1}{2},\frac{5}{4},\frac{17}{8},\frac{43}{16}\rangle$
Rams:	$(1,3,7,9)$
Field count:	$832$ (complete)
Ambiguity:	$16$
Mass:	$256$
Absolute Mass:	$256$

Diagrams

Varying

Indices of inseparability:	$[43,34,20,8,0]$
Associated inertia:	$[1,1,1,1]$
Jump Set:	$[1,2,4,8,32]$ (show 416), $[1,2,4,32,48]$ (show 112), $[1,2,27,43,59]$ (show 28), $[1,7,15,31,47]$ (show 192), $[1,11,22,38,54]$ (show 8), $[1,11,29,45,61]$ (show 28), $[1,11,31,47,63]$ (show 12), $[1,11,32,48,64]$ (show 8), $[1,13,27,43,59]$ (show 28)

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

		Galois groups of order 32
		$C_2^3:C_4$ (as 16T33)	$C_2^3:C_4$ (as 16T53)	Total
hidden slopes	$[\frac{7}{2}]$	16	16	32

		Galois groups of order 64
		$C_2^4:C_4$ (as 16T76)	$C_2^4:C_4$ (as 16T78)	$C_2^4:C_4$ (as 16T94)	$C_2^4:C_4$ (as 16T102)	$C_2^3.C_2^3$ (as 16T112)	$C_2^3.C_2^3$ (as 16T120)	$C_2\wr C_2^2$ (as 16T128)	$C_2\wr C_2^2$ (as 16T129)	$C_2\wr C_2^2$ (as 16T149)	$C_2\wr C_2^2$ (as 16T150)	$C_2^3.D_4$ (as 16T165)	$C_2^3.D_4$ (as 16T177)	Total
hidden slopes	$[\frac{7}{2}]^{2}$	8	8	8	8	8	8	16	8	32	8	8	8	128

		Galois groups of order 128
		$C_2^4.D_4$ (as 16T208)	$C_2^4.D_4$ (as 16T217)	$C_2^4.C_2^3$ (as 16T229)	$C_2^4.C_2^3$ (as 16T231)	$C_2^4.D_4$ (as 16T237)	$C_2^4.D_4$ (as 16T249)	$C_2^4.D_4$ (as 16T274)	$C_2^4.D_4$ (as 16T304)	$C_2^4.D_4$ (as 16T318)	$C_2^4:Q_8$ (as 16T333)	$C_2^4:Q_8$ (as 16T347)	$C_2^4:D_4$ (as 16T350)	$C_2^4:Q_8$ (as 16T354)	$C_2^4:Q_8$ (as 16T368)	$C_2^4:D_4$ (as 16T373)	$C_2^4.C_2^3$ (as 16T383)	$C_2^4:Q_8$ (as 16T384)	Total
hidden slopes	$[2,\frac{7}{2}]^{2}$					32			8	8			16			16		16	96
		$[3,\frac{7}{2}]^{2}$	16	16	8	8	16	16	32			16	16		8	8		32		192
	Total		16	16	8	8	48	16	32	8	8	16	16	16	8	8	16	32	16	288

		Galois groups of order 256
		$C_2^4.D_8$ (as 16T686)	$C_2^4:D_8$ (as 16T689)	$C_2^4.Q_{16}$ (as 16T691)	$C_2^4.Q_{16}$ (as 16T698)	$C_2^4:\SD_{16}$ (as 16T700)	$C_2^4:D_8$ (as 16T701)	$C_2^4.D_8$ (as 16T705)	$C_2^4:\SD_{16}$ (as 16T707)	Total
hidden slopes	$[2,\frac{7}{2},\frac{7}{2}]^{2}$	16	32	16	16	32	32	16	32	192

		Galois groups of order 512
		$C_2^6.D_4$ (as 16T876)	$C_2^6.D_4$ (as 16T900)	$C_2^6.D_4$ (as 16T921)	Total
hidden slopes	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	128	32	32	192

Fields

Showing 1-50 of 832

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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
2.1.16.58n1.1	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^4.C_2^3$ (as 16T383)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.2	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^4.C_2^3$ (as 16T383)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.3	8	$x^{16} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^4.C_2^3$ (as 16T229)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.4	8	$x^{16} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^4.C_2^3$ (as 16T229)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.5	8	$x^{16} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^4.C_2^3$ (as 16T229)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.6	8	$x^{16} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$	$C_2^4.C_2^3$ (as 16T229)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.7	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$	$C_2^4.C_2^3$ (as 16T383)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.8	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^4.C_2^3$ (as 16T383)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.9	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 2$	$C_2^4:C_4$ (as 16T102)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.10	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 2$	$C_2^3:C_4$ (as 16T33)	$32$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4}]$	$[\frac{7}{2}]$	$[\frac{5}{2}]$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.11	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^3:C_4$ (as 16T33)	$32$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4}]$	$[\frac{7}{2}]$	$[\frac{5}{2}]$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.12	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^3:C_4$ (as 16T33)	$32$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4}]$	$[\frac{7}{2}]$	$[\frac{5}{2}]$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.13	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$	$C_2^4:C_4$ (as 16T102)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.14	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$	$C_2^4:C_4$ (as 16T102)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.15	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^3:C_4$ (as 16T33)	$32$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4}]$	$[\frac{7}{2}]$	$[\frac{5}{2}]$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.16	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^3:C_4$ (as 16T33)	$32$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4}]$	$[\frac{7}{2}]$	$[\frac{5}{2}]$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.17	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^3:C_4$ (as 16T33)	$32$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4}]$	$[\frac{7}{2}]$	$[\frac{5}{2}]$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.18	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^4:C_4$ (as 16T102)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.19	32	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.20	32	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.21	32	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.22	32	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.23	32	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.24	32	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.25	32	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.26	32	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.27	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 2$	$C_2^3:C_4$ (as 16T33)	$32$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4}]$	$[\frac{7}{2}]$	$[\frac{5}{2}]$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.28	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^3:C_4$ (as 16T33)	$32$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$	$[1,2,\frac{5}{2},3,\frac{13}{4}]$	$[\frac{7}{2}]$	$[\frac{5}{2}]$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 27, 43, 59]$
2.1.16.58n1.29	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 2$	$C_2^3.D_4$ (as 16T177)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.30	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$	$C_2\wr C_2^2$ (as 16T150)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.31	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^3.D_4$ (as 16T177)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.32	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2\wr C_2^2$ (as 16T150)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.33	16	$x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^4:Q_8$ (as 16T384)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.34	16	$x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^4:Q_8$ (as 16T384)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.35	16	$x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$	$C_2^4:Q_8$ (as 16T384)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.36	16	$x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^4:Q_8$ (as 16T384)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[2,\frac{7}{2}]^{2}$	$[1,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.37	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 2$	$C_2\wr C_2^2$ (as 16T150)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.38	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 2$	$C_2^3.D_4$ (as 16T177)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.39	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$	$C_2\wr C_2^2$ (as 16T150)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.40	8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^3.D_4$ (as 16T177)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.41	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^4.D_4$ (as 16T274)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.42	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 18$	$C_2^4.D_4$ (as 16T274)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.43	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 18$	$C_2^4.D_4$ (as 16T274)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.44	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 18$	$C_2^4.D_4$ (as 16T274)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.45	16	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.46	16	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.47	16	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.48	16	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 18$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.49	16	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$
2.1.16.58n1.50	16	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 2$	$C_2^4.D_4$ (as 16T237)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$	$[3,\frac{7}{2}]^{2}$	$[2,\frac{5}{2}]^{2}$	$[43, 34, 20, 8, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 13, 27, 43, 59]$

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