$p$-adic family 2.1.16.50h

• Label: 2.1.16.50h
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(16\)
• f: \(1\)
• c: \(50\)

Defining polynomial

$x^{16} + 8 b_{47} x^{15} + 4 b_{30} x^{14} + 8 b_{45} x^{13} + 2 a_{12} x^{12} + 8 b_{43} x^{11} + 4 b_{26} x^{10} + 8 b_{41} x^{9} + 2 b_{8} x^{8} + 8 b_{39} x^{7} + 4 a_{22} x^{6} + 8 b_{37} x^{5} + 8 a_{35} x^{3} + 4 c_{16} + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$50$
Artin slopes:	$[2,2,3,4]$
Swan slopes:	$[1,1,2,3]$
Means:	$\langle\frac{1}{2},\frac{3}{4},\frac{11}{8},\frac{35}{16}\rangle$
Rams:	$(1,1,5,13)$
Field count:	$1312$ (complete)
Ambiguity:	$8$
Mass:	$512$
Absolute Mass:	$512$

Diagrams

Varying

Indices of inseparability:	$[35,22,12,8,0]$ (show 640), $[35,22,12,12,0]$ (show 672)
Associated inertia:	$[2,1,1]$ (show 672), $[3,1,1]$ (show 640)
Jump Set:	$[1,2,7,15,31]$ (show 640), $[1,3,6,12,24]$ (show 1), $[1,3,6,12,32]$ (show 336), $[1,3,6,32,48]$ (show 48), $[1,3,13,29,45]$ (show 160), $[1,3,15,31,47]$ (show 80), $[1,3,21,37,53]$ (show 20), $[1,3,23,39,55]$ (show 14), $[1,3,25,41,57]$ (show 4), $[1,3,27,43,59]$ (show 4), $[1,3,29,45,61]$ (show 3), $[1,3,31,47,63]$ (show 1), $[1,3,32,48,64]$ (show 1)

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 32
		$C_4\times D_4$ (as 16T19)	$C_2\times D_8$ (as 16T29)	$C_4^2:C_2$ (as 16T30)	$C_2^2:Q_8$ (as 16T31)	$Q_{16}:C_2$ (as 16T32)	$C_4:D_4$ (as 16T34)	$D_8:C_2$ (as 16T38)	$C_4:D_4$ (as 16T43)	$D_8:C_2$ (as 16T44)	$D_8:C_2$ (as 16T45)	$C_2\times \SD_{16}$ (as 16T48)	$C_4:D_4$ (as 16T51)	Total
hidden slopes	$[\ ]^{2}$	8	2	2	4	2	4	4	4	4	2	2	2	40

		Galois groups of order 48
		$C_4\times A_4$ (as 16T57)	$\SL(2,3):C_2$ (as 16T60)	Total
hidden slopes	$[\ ]^{3}$	8	8	16

		Galois groups of order 64
		$C_4^2:C_2^2$ (as 16T107)	$C_4^2:C_2^2$ (as 16T111)	$C_2^3.C_2^3$ (as 16T120)	Total
hidden slopes	$[\ ]^{4}$	8	16	16	40

		Galois groups of order 96
		$D_4\times A_4$ (as 16T179)	$D_4.A_4$ (as 16T180)	Total
hidden slopes	$[2]^{3}$	8	8	16
		$[\ ]^{6}$	4	4	8
	Total		12	12	24

		Galois groups of order 128
		$C_4^2:D_4$ (as 16T336)	$C_4^2.D_4$ (as 16T344)	$C_4^2:D_4$ (as 16T345)	$C_4^2:D_4$ (as 16T359)	$C_2^3.\SD_{16}$ (as 16T374)	Total
hidden slopes	$[\frac{5}{2},3]^{2}$					16	16
		$[\frac{7}{2},\frac{7}{2}]^{2}$	8	16	16	8		48
	Total		8	16	16	8	16	64

		Galois groups of order 192
		$(C_2^2\times C_4):A_4$ (as 16T426)
hidden slopes	$[\frac{7}{2},\frac{7}{2}]^{3}$	16

		Galois groups of order 256
		$C_4^2.(C_2\times D_4)$ (as 16T504)	$C_8^2:C_2^2$ (as 16T568)	$C_4^2.(C_2\times D_4)$ (as 16T605)	$C_4^2.(C_2\times D_4)$ (as 16T627)	$C_4^2.(C_2\times D_4)$ (as 16T655)	$C_2^4.\SD_{16}$ (as 16T670)	$C_2^4.\SD_{16}$ (as 16T673)	$C_4^2.Q_{16}$ (as 16T697)	Total
hidden slopes	$[2,2]^{4}$	16		8	16	8				48
		$[\frac{5}{2},3]^{4}$		32					32	16	80
	$[\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$							16	32		48
		Total	16	32	8	16	8	16	64	16	176

		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)	Total
hidden slopes	$[2,2]^{6}$		16	8		24
		$[2,3,3]^{3}$		32	16		48
	$[2,\frac{7}{2},\frac{7}{2}]^{3}$		16	32		16	64
		$[\frac{7}{2},\frac{7}{2}]^{6}$	8	16		8	32
	Total		24	96	24	24	168

		Galois groups of order 512
		$C_2^5.(C_2\times D_4)$ (as 16T813)	$C_2^4.(C_4\times D_4)$ (as 16T822)	$C_2^4.(C_4\times D_4)$ (as 16T824)	$(C_2^2\times C_4^2).D_4$ (as 16T831)	$(C_2^2\times C_4^2).D_4$ (as 16T845)	$C_2^5.(C_2\times D_4)$ (as 16T874)	$\OD_{16}\wr C_2$ (as 16T883)	$(C_2^2\times C_4^2).D_4$ (as 16T885)	$C_2^4.(C_4\times D_4)$ (as 16T915)	$C_2^4.(C_4\times D_4)$ (as 16T930)	Total
hidden slopes	$[2,3,3]^{4}$	32					32					64
		$[2,\frac{7}{2},\frac{7}{2}]^{4}$		16	16	16	32				16	16	112
	$[\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$								32	16			48
		Total	32	16	16	16	32	32	32	16	16	16	224

		Galois groups of order 768
		$(D_4\times C_2^3):A_4$ (as 16T1037)
hidden slopes	$[2,2,2]^{6}$	16
		$[2,3,3]^{6}$	32
	$[2,\frac{7}{2},\frac{7}{2}]^{6}$		48
		Total	96

		Galois groups of order 1024
		$C_2^6.\SD_{16}$ (as 16T1250)	$C_2^6.\SD_{16}$ (as 16T1264)	Total
hidden slopes	$[2,2,3,3]_{4}$	32	32	64
		$[2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]_{4}$	32	32	64
	Total		64	64	128

		Galois groups of order 1536
		$C_4^3.(C_2\times A_4)$ (as 16T1302)
hidden slopes	$[2,2,3,3]^{6}$	16

		Galois groups of order 3072
		$C_4\wr A_4$ (as 16T1517)	$C_4^3.(C_2^2\times A_4)$ (as 16T1518)	Total
hidden slopes	$[2,2,2,3,3]^{6}$	32		32
		$[2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{6}$	32	16	48
	Total		64	16	80

		Galois groups of order 6144
		$C_4^4:(C_2\times A_4)$ (as 16T1657)
hidden slopes	$[2,2,2,2,3,3]^{6}$	40
		$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{6}$	40
	Total		80

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
2.1.16.50h1.1	32	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 4 x^{6} + 8 x^{3} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.2	32	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 4 x^{6} + 8 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.3	32	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{6} + 8 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.4	32	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{6} + 8 x^{3} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.5	2	$x^{16} + 2 x^{12} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 18$	$C_4^2:C_2$ (as 16T30)	$32$	$4$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.6	16	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 18$	$C_2^3.C_2^3$ (as 16T120)	$64$	$4$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.7	2	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 18$	$C_2\times D_8$ (as 16T29)	$32$	$4$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.8	8	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 18$	$C_4^2:C_2^2$ (as 16T107)	$64$	$4$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.9	16	$x^{16} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 18$	$C_2^3.C_2^3$ (as 16T120)	$64$	$4$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.10	4	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 2$	$C_4:D_4$ (as 16T43)	$32$	$8$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.11	4	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 18$	$C_4:D_4$ (as 16T43)	$32$	$8$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.12	16	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 2$	$C_4^2:C_2^2$ (as 16T111)	$64$	$8$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.13	16	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 18$	$C_4^2:C_2^2$ (as 16T111)	$64$	$8$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.14	2	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 4 x^{6} + 8 x^{3} + 18$	$Q_{16}:C_2$ (as 16T32)	$32$	$4$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 23, 39, 55]$
2.1.16.50h1.15	32	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 25, 41, 57]$
2.1.16.50h1.16	32	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 25, 41, 57]$
2.1.16.50h1.17	32	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 25, 41, 57]$
2.1.16.50h1.18	32	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 25, 41, 57]$
2.1.16.50h1.19	16	$x^{16} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$	$C_4^2:C_2^2$ (as 16T111)	$64$	$8$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 29, 45, 61]$
2.1.16.50h1.20	16	$x^{16} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$C_4^2:C_2^2$ (as 16T111)	$64$	$8$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 29, 45, 61]$
2.1.16.50h1.21	4	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$D_8:C_2$ (as 16T44)	$32$	$4$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 29, 45, 61]$
2.1.16.50h1.22	16	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$C_2^3.C_2^3$ (as 16T120)	$64$	$4$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 31, 47, 63]$
2.1.16.50h1.23	8	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$	$C_4 \times D_4$ (as 16T19)	$32$	$8$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 24]$
2.1.16.50h1.24	8	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$C_4 \times D_4$ (as 16T19)	$32$	$8$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 32, 48, 64]$
2.1.16.50h1.25	4	$x^{16} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$D_8:C_2$ (as 16T38)	$32$	$4$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 27, 43, 59]$
2.1.16.50h1.26	8	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$C_4^2:C_2^2$ (as 16T107)	$64$	$4$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 27, 43, 59]$
2.1.16.50h1.27	4	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$C_4:D_4$ (as 16T34)	$32$	$4$	$[2, 2, 3, 4]^{2}$	$[1,1,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 27, 43, 59]$
2.1.16.50h1.28	16	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$C_2^3.C_2^3$ (as 16T120)	$64$	$4$	$[2, 2, 3, 4]^{4}$	$[1,1,2,3]^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 27, 43, 59]$
2.1.16.50h1.29	8	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_4^2:D_4$ (as 16T359)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.30	8	$x^{16} + 2 x^{12} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_4^2:D_4$ (as 16T359)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.31	8	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_4^2:D_4$ (as 16T336)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.32	8	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_4^2:D_4$ (as 16T336)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.33	16	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$	$C_4^2:D_4$ (as 16T345)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.34	16	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_4^2:D_4$ (as 16T345)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.35	16	$x^{16} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_4^2:D_4$ (as 16T345)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.36	16	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_4^2.D_4$ (as 16T344)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.37	16	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$	$C_4^2.D_4$ (as 16T344)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.38	16	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_4^2.D_4$ (as 16T344)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.39	16	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T822)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	$[1,\frac{5}{2},\frac{5}{2}]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.40	16	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_2^4.(C_4\times D_4)$ (as 16T822)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	$[1,\frac{5}{2},\frac{5}{2}]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.41	16	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_2^4.(C_4\times D_4)$ (as 16T915)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	$[1,\frac{5}{2},\frac{5}{2}]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.42	16	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T915)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	$[1,\frac{5}{2},\frac{5}{2}]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.43	16	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T822)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	$[1,\frac{5}{2},\frac{5}{2}]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.44	16	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_2^4.(C_4\times D_4)$ (as 16T915)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	$[1,\frac{5}{2},\frac{5}{2}]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.45	16	$x^{16} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$	$C_4^2:D_4$ (as 16T345)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.46	16	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$	$C_4^2.D_4$ (as 16T344)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$	$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$	$[\frac{7}{2},\frac{7}{2}]^{2}$	$[\frac{5}{2},\frac{5}{2}]^{2}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.47	16	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$	$C_2^4.(C_4\times D_4)$ (as 16T822)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	$[1,\frac{5}{2},\frac{5}{2}]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.48	16	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$	$C_2^4.(C_4\times D_4)$ (as 16T915)	$512$	$2$	$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,\frac{7}{2},\frac{7}{2}]^{4}$	$[1,\frac{5}{2},\frac{5}{2}]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 21, 37, 53]$
2.1.16.50h1.49	32	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 4 x^{6} + 8 x^{3} + 10$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 32, 48]$
2.1.16.50h1.50	32	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 4 x^{6} + 8 x^{3} + 26$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,3,3]^{4}$	$[1,2,2]^{4}$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 32, 48]$

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