$p$-adic family 2.1.16.52k

• Label: 2.1.16.52k
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(16\)
• f: \(1\)
• c: \(52\)

Defining polynomial

$x^{16} + 8 b_{47} x^{15} + 4 b_{30} x^{14} + 8 b_{45} x^{13} + 4 b_{28} x^{12} + 8 b_{43} x^{11} + 4 a_{26} x^{10} + 8 b_{41} x^{9} + 2 a_{8} x^{8} + 8 b_{39} x^{7} + 8 a_{37} x^{5} + 4 b_{20} x^{4} + 4 c_{16} + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$52$
Artin slopes:	$[2,3,3,4]$
Swan slopes:	$[1,2,2,3]$
Means:	$\langle\frac{1}{2},\frac{5}{4},\frac{13}{8},\frac{37}{16}\rangle$
Rams:	$(1,3,3,11)$
Field count:	$592$ (complete)
Ambiguity:	$8$
Mass:	$256$
Absolute Mass:	$256$

Diagrams

Varying

Indices of inseparability:	$[37,26,20,8,0]$ (show 256), $[37,26,24,8,0]$ (show 336)
Associated inertia:	$[1,2,1]$ (show 336), $[1,3,1]$ (show 256)
Jump Set:	$[1,2,4,8,32]$ (show 296), $[1,2,13,29,45]$ (show 128), $[1,5,10,20,36]$ (show 2), $[1,5,10,32,48]$ (show 44), $[1,5,15,31,47]$ (show 80), $[1,5,23,39,55]$ (show 20), $[1,5,25,41,57]$ (show 12), $[1,5,27,43,59]$ (show 4), $[1,5,29,45,61]$ (show 2), $[1,5,31,47,63]$ (show 2), $[1,5,32,48,64]$ (show 2)

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
		$C_4^2:C_2$ (as 16T17)	$C_4\times D_4$ (as 16T19)	$C_4^2:C_2$ (as 16T27)	$C_4^2:C_2$ (as 16T30)	$C_2^2:Q_8$ (as 16T31)	$C_2^2.D_4$ (as 16T37)	$C_2^2.D_4$ (as 16T54)	Total
hidden slopes	$[\ ]^{2}$	8	8	8	4	8	4	8	48

		Galois groups of order 64
		$C_8.D_4$ (as 16T133)	$C_4^2:C_4$ (as 16T143)	$C_2^2.Q_{16}$ (as 16T161)	$C_2^2.D_8$ (as 16T163)	$C_4^2:C_4$ (as 16T176)	Total
hidden slopes	$[\frac{7}{2}]^{2}$	8					8
		$[\ ]^{4}$		4	8	8	4	24
	Total		8	4	8	8	4	32

		Galois groups of order 128
		$C_2^4.C_2^3$ (as 16T229)	$C_2^4.D_4$ (as 16T254)	$C_2^4.D_4$ (as 16T297)	$C_4^2.D_4$ (as 16T321)	$C_4^2.D_4$ (as 16T360)	$C_4^2.D_4$ (as 16T387)	$C_4^2.D_4$ (as 16T398)	$\OD_{16}.D_4$ (as 16T411)	Total
hidden slopes	$[2,\frac{7}{2}]^{2}$					16			8	24
		$[2]^{4}$	16	16	8						40
	$[\frac{7}{2}]^{4}$					16		8	16		40
		Total	16	16	8	16	16	8	16	8	104

		Galois groups of order 256
		$C_4^2.(C_2\times D_4)$ (as 16T504)	$C_4^2.(C_2\times D_4)$ (as 16T655)	Total
hidden slopes	$[2,\frac{7}{2}]^{4}$	16	8	24

		Galois groups of order 384
		$C_2.C_2\wr A_4$ (as 16T727)	$Q_8^2:C_6$ (as 16T730)	$C_2.C_2\wr A_4$ (as 16T734)	Total
hidden slopes	$[2,2,\frac{7}{2}]^{3}$	64	32	32	128

		Galois groups of order 512
		$C_2^5.(C_2\times D_4)$ (as 16T833)	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$C_2^5.(C_2\times D_4)$ (as 16T874)	$D_4:C_2^3.D_4$ (as 16T918)	Total
hidden slopes	$[2,2,3]^{4}$	32		32		64
		$[2,2,\frac{7}{2}]^{4}$		32		32	64
	Total		32	32	32	32	128

		Galois groups of order 12288
		$C_2^4.C_2^6:A_4$ (as 16T1755)
hidden slopes	$[\frac{13}{4}, 2, 2, 2, 2, 3, 3]_{6}$	24

Fields

Showing 1-50 of 592

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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
2.1.16.52k1.1	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T833)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 25, 41, 57]$
2.1.16.52k1.2	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T833)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 25, 41, 57]$
2.1.16.52k1.3	16	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 18$	$C_2^4.C_2^3$ (as 16T229)	$128$	$2$	$[2, 2, 3, 3, 4]^{4}$	$[1,1,2,2,3]^{4}$	$[2]^{4}$	$[1]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 25, 41, 57]$
2.1.16.52k1.4	8	$x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 18$	$C_4^2:C_2$ (as 16T27)	$32$	$4$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 25, 41, 57]$
2.1.16.52k1.5	8	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 2$	$C_2^2.D_4$ (as 16T54)	$32$	$8$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 25, 41, 57]$
2.1.16.52k1.6	8	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 18$	$C_2^2.D_4$ (as 16T54)	$32$	$8$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 25, 41, 57]$
2.1.16.52k1.7	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T833)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 27, 43, 59]$
2.1.16.52k1.8	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 18$	$C_2^5.(C_2\times D_4)$ (as 16T833)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 27, 43, 59]$
2.1.16.52k1.9	8	$x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 2$	$C_4^2:C_2$ (as 16T17)	$32$	$8$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 20, 36]$
2.1.16.52k1.10	8	$x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 18$	$C_4^2:C_2$ (as 16T17)	$32$	$8$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 32, 48, 64]$
2.1.16.52k1.11	4	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 18$	$C_4^2:C_2$ (as 16T30)	$32$	$4$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 31, 47, 63]$
2.1.16.52k1.12	16	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 18$	$C_2^4.C_2^3$ (as 16T229)	$128$	$2$	$[2, 2, 3, 3, 4]^{4}$	$[1,1,2,2,3]^{4}$	$[2]^{4}$	$[1]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 29, 45, 61]$
2.1.16.52k1.13	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.14	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.15	32	$x^{16} + 8 x^{15} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.16	16	$x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$	$C_4^2.D_4$ (as 16T321)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.17	16	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 2$	$C_4^2.D_4$ (as 16T321)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.18	16	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$	$C_4^2.D_4$ (as 16T321)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.19	8	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$	$C_8.D_4$ (as 16T133)	$64$	$2$	$[2, 3, 3, \frac{7}{2}, 4]^{2}$	$[1,2,2,\frac{5}{2},3]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.20	8	$x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$	$C_8.D_4$ (as 16T133)	$64$	$2$	$[2, 3, 3, \frac{7}{2}, 4]^{2}$	$[1,2,2,\frac{5}{2},3]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.21	32	$x^{16} + 8 x^{15} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 2$	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.22	16	$x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 2$	$C_4^2.D_4$ (as 16T321)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 23, 39, 55]$
2.1.16.52k1.23	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 26$	$C_2^5.(C_2\times D_4)$ (as 16T833)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.24	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 10$	$C_2^5.(C_2\times D_4)$ (as 16T833)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.25	16	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 26$	$C_2^4.C_2^3$ (as 16T229)	$128$	$2$	$[2, 2, 3, 3, 4]^{4}$	$[1,1,2,2,3]^{4}$	$[2]^{4}$	$[1]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.26	8	$x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 10$	$C_2^2.D_4$ (as 16T54)	$32$	$8$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.27	8	$x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 26$	$C_2^2.D_4$ (as 16T54)	$32$	$8$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.28	8	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 26$	$C_4^2:C_2$ (as 16T27)	$32$	$4$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.29	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 26$	$C_2^5.(C_2\times D_4)$ (as 16T833)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.30	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 10$	$C_2^5.(C_2\times D_4)$ (as 16T833)	$512$	$2$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.31	4	$x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 26$	$C_4^2:C_2$ (as 16T30)	$32$	$4$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.32	8	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 10$	$C_4^2:C_2$ (as 16T17)	$32$	$8$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.33	8	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 26$	$C_4^2:C_2$ (as 16T17)	$32$	$8$	$[2, 3, 3, 4]^{2}$	$[1,2,2,3]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.34	16	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 26$	$C_2^4.C_2^3$ (as 16T229)	$128$	$2$	$[2, 2, 3, 3, 4]^{4}$	$[1,1,2,2,3]^{4}$	$[2]^{4}$	$[1]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.35	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.36	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 10$	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.37	32	$x^{16} + 8 x^{15} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 10$	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.38	16	$x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 10$	$C_4^2.D_4$ (as 16T321)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.39	16	$x^{16} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$	$C_4^2.D_4$ (as 16T321)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.40	16	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$	$C_4^2.D_4$ (as 16T321)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.41	8	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$	$C_8.D_4$ (as 16T133)	$64$	$2$	$[2, 3, 3, \frac{7}{2}, 4]^{2}$	$[1,2,2,\frac{5}{2},3]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.42	8	$x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$	$C_8.D_4$ (as 16T133)	$64$	$2$	$[2, 3, 3, \frac{7}{2}, 4]^{2}$	$[1,2,2,\frac{5}{2},3]^{2}$	$[\frac{7}{2}]^{2}$	$[\frac{5}{2}]^{2}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.43	32	$x^{16} + 8 x^{15} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$	$(D_4\times C_2^3).C_2^3$ (as 16T853)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.44	16	$x^{16} + 8 x^{15} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 10$	$C_4^2.D_4$ (as 16T321)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 10, 32, 48]$
2.1.16.52k1.45	32	$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 10$	$D_4:C_2^3.D_4$ (as 16T918)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 15, 31, 47]$
2.1.16.52k1.46	32	$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 26$	$D_4:C_2^3.D_4$ (as 16T918)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 15, 31, 47]$
2.1.16.52k1.47	32	$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 26$	$D_4:C_2^3.D_4$ (as 16T918)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 15, 31, 47]$
2.1.16.52k1.48	32	$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 10$	$D_4:C_2^3.D_4$ (as 16T918)	$512$	$2$	$[2, 2, 2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,1,1,2,2,\frac{5}{2},3]^{4}$	$[2,2,\frac{7}{2}]^{4}$	$[1,1,\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 15, 31, 47]$
2.1.16.52k1.49	8	$x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 26$	$C_4^2.D_4$ (as 16T387)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 15, 31, 47]$
2.1.16.52k1.50	8	$x^{16} + 4 x^{14} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 26$	$C_4^2.D_4$ (as 16T387)	$128$	$2$	$[2, 3, 3, \frac{7}{2}, 4]^{4}$	$[1,2,2,\frac{5}{2},3]^{4}$	$[\frac{7}{2}]^{4}$	$[\frac{5}{2}]^{4}$	$[37, 26, 24, 8, 0]$	$[1, 2, 1]$	$z^8 + 1,z^6 + 1,z + 1$	$[1, 5, 15, 31, 47]$

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