$p$-adic family 2.2.8.54a

• Label: 2.2.8.54a
• Base: 2.1.1.0a1.1
• Degree: \(16\)
• e: \(8\)
• f: \(2\)
• c: \(54\)

Defining polynomial over unramified subextension

$x^{8} + 8 b_{23} x^{7} + 4 b_{14} x^{6} + 8 b_{21} x^{5} + \left(2 a_{4} + 8 c_{20} + 16 c_{28}\right) x^{4} + 16 b_{27} x^{3} + 8 b_{18} x^{2} + 16 b_{25} x + 4 c_{8} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$8$
Residue field degree $f$:	$2$
Discriminant exponent $c$:	$54$
Artin slopes:	$[2,\frac{7}{2},\frac{9}{2}]$
Swan slopes:	$[1,\frac{5}{2},\frac{7}{2}]$
Means:	$\langle\frac{1}{2},\frac{3}{2},\frac{5}{2}\rangle$
Rams:	$(1,4,8)$
Field count:	$12744$ (complete)
Ambiguity:	$16$
Mass:	$12288$
Absolute Mass:	$6144$

Diagrams

Varying

Indices of inseparability:	$[20,12,4,0]$
Associated inertia:	$[1,1,1]$
Jump Set:	$[1,2,4,16]$ (show 2048), $[1,3,7,15]$ (show 8448), $[1,5,13,21]$ (show 2248)

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
		$C_2\times D_8$ (as 16T29)	$Q_{16}:C_2$ (as 16T32)	$D_8:C_2$ (as 16T38)	$D_8:C_2$ (as 16T44)	$D_8:C_2$ (as 16T45)	$C_2\times \SD_{16}$ (as 16T48)	Total
hidden slopes	$[3]$	4	4	8	8	4	4	32

		Galois groups of order 64
		$C_4^2:C_2^2$ (as 16T107)	$C_4^2:C_2^2$ (as 16T111)	$D_8:C_4$ (as 16T113)	$D_8:C_4$ (as 16T114)	$D_4.D_4$ (as 16T137)	$C_4^2:C_2^2$ (as 16T138)	$D_4:D_4$ (as 16T141)	$D_4.D_4$ (as 16T164)	Total
hidden slopes	$[3,4]$	8	16	8	16	8	4	8	4	72

		Galois groups of order 128
		$\OD_{16}.D_4$ (as 16T215)	$C_4^2.D_4$ (as 16T307)	$C_4^2.D_4$ (as 16T311)	$C_4^2.D_4$ (as 16T321)	$C_4^2.D_4$ (as 16T335)	$C_4^2:D_4$ (as 16T336)	$C_4^2:D_4$ (as 16T340)	$C_4^2.D_4$ (as 16T343)	$C_4^2.D_4$ (as 16T344)	$C_4^2.D_4$ (as 16T353)	$C_4^2.D_4$ (as 16T360)	$(C_4\times C_8):C_4$ (as 16T363)	$C_4^2.(C_2\times C_4)$ (as 16T375)	$(C_4\times C_8):C_4$ (as 16T377)	$C_2\wr D_4$ (as 16T393)	$\OD_{16}.D_4$ (as 16T411)	$(C_2\times C_8).D_4$ (as 16T412)	Total
hidden slopes	$[2,3,3]$																16	16	32
		$[2,3,4]$			16	16	8	8	8	8	16	16	16				16			128
	$[2,3,\frac{7}{2}]$						8	8	8	8	16			8	16	8	16			96
		$[2,3]^{2}$		16																16
	$[3,4]^{2}$		16																	16
		Total	16	16	16	16	16	16	16	16	32	16	16	8	16	8	32	16	16	288

		Galois groups of order 256
		$C_4^2.Q_{16}$ (as 16T555)	$(C_4\times \OD_{16}):C_4$ (as 16T557)	$(C_4\times \OD_{16}):C_4$ (as 16T558)	$C_4^2.(C_2\times D_4)$ (as 16T567)	$(C_4\times C_8).D_4$ (as 16T658)	$C_4^2.(C_2\times D_4)$ (as 16T662)	$D_4^2:C_4$ (as 16T663)	$C_8^2:C_4$ (as 16T664)	$C_8:C_8:C_4$ (as 16T668)	$(C_4\times C_8).D_4$ (as 16T669)	$D_4^2.C_4$ (as 16T671)	$C_4^2.(C_2\times D_4)$ (as 16T672)	$Q_8^2:C_2^2$ (as 16T674)	$(C_4\times C_8).D_4$ (as 16T677)	$D_8:D_8$ (as 16T679)	$C_2^2.C_2\wr C_4$ (as 16T680)	$C_2^2.C_2\wr C_4$ (as 16T681)	$(C_4\times C_8).D_4$ (as 16T683)	$D_4^2:C_4$ (as 16T685)	$C_8^2:C_2^2$ (as 16T687)	$D_4^2:C_4$ (as 16T688)	$C_8:C_8:C_4$ (as 16T690)	$D_4^2.C_4$ (as 16T692)	$D_8:D_8$ (as 16T693)	$C_8^2:C_4$ (as 16T694)	$D_4^2:C_2^2$ (as 16T696)	$Q_8^2:C_4$ (as 16T704)	$D_8:\SD_{16}$ (as 16T706)	Total
hidden slopes	$[2,3,4]^{2}$				16																									16
		$[2,3,\frac{7}{2},\frac{9}{2}]$					16	32		16	16	16		32	16	16	16	32	32	16		16	16	16		16	16	16	16	16	384
	$[2,3,\frac{7}{2}]^{2}$			16	16	16																									48
		$[2,\frac{5}{2},3,4]$	64																												64
	$[3,3,4]^{2}$								16				16								16				16						64
		Total	64	16	16	32	16	32	16	16	16	16	16	32	16	16	16	32	32	16	16	16	16	16	16	16	16	16	16	16	576

		Galois groups of order 512
		$C_2^5.(C_2\times D_4)$ (as 16T813)	$C_8^2:(C_2\times C_4)$ (as 16T814)	$C_8^2:(C_2\times C_4)$ (as 16T816)	$C_2^5.(C_2\times D_4)$ (as 16T833)	$Q_8^2:(C_2\times C_4)$ (as 16T851)	$(C_2^2\times C_4^2).D_4$ (as 16T855)	$(C_2\times D_4^2):C_4$ (as 16T858)	$(C_2\times D_4^2).C_4$ (as 16T859)	$C_4^3:D_4$ (as 16T871)	$C_4^3.D_4$ (as 16T873)	$C_2^4.(C_4\times D_4)$ (as 16T881)	$D_4^2:(C_2\times C_4)$ (as 16T882)	$C_4^3:D_4$ (as 16T890)	$C_8^2:(C_2\times C_4)$ (as 16T892)	$C_4^3.D_4$ (as 16T894)	$C_4^3.D_4$ (as 16T899)	$(C_4\times \OD_{16}).D_4$ (as 16T906)	$C_2^4.(C_4\times D_4)$ (as 16T915)	$C_2^4.(C_4\times D_4)$ (as 16T926)	$Q_8^2:C_8$ (as 16T929)	$C_4^3.D_4$ (as 16T936)	$(C_4\times \OD_{16}).D_4$ (as 16T937)	$D_4^2:C_8$ (as 16T941)	$Q_8^2:(C_2\times C_4)$ (as 16T942)	$D_4^2:(C_2\times C_4)$ (as 16T943)	$C_4^3.D_4$ (as 16T947)	$Q_8^2:D_4$ (as 16T951)	$C_2^5.(C_2\times D_4)$ (as 16T953)	$C_4^3.D_4$ (as 16T957)	$D_4^2:Q_8$ (as 16T961)	$C_2^5.(C_2\times D_4)$ (as 16T963)	$C_4^3.D_4$ (as 16T974)	$C_4^3.D_4$ (as 16T975)	$Q_8^2:Q_8$ (as 16T986)	$C_4^3.D_4$ (as 16T989)	$C_4^3:D_4$ (as 16T997)	$C_4^3:D_4$ (as 16T998)	$C_4^3.(C_2\times C_4)$ (as 16T1004)	$C_4^3.D_4$ (as 16T1011)	$(D_4\times C_2^3).C_2^3$ (as 16T1015)	$C_4^3.(C_2\times C_4)$ (as 16T1018)	$(D_4\times C_2^3).C_2^3$ (as 16T1024)	Total
hidden slopes	$[2,2,3,4]^{2}$						32					32																																64
		$[2,3,3,4]^{2}$							32	32																																			64
	$[2,3,3,\frac{7}{2}]^{2}$							32					32																																64
		$[2,3,\frac{7}{2},4,\frac{9}{2}]$									32	64			64			32				64	64		64			32	32		32	32		32	32	32	32	32	32		64				768
	$[2,3,\frac{7}{2},\frac{9}{2}]^{2}$			32	32		32							32		64			64					64		32	32																		384
		$[2,\frac{5}{2},3,4]^{2}$															64																												64
	$[3,3,4,4,\frac{17}{4}]$		32			32														32	32									32			32									32		32	256
		$[3,3,4,4]^{2}$																																						32			32		64
	Total		32	32	32	32	32	64	32	32	32	64	64	32	64	64	64	32	64	32	32	64	64	64	64	32	32	32	32	32	32	32	32	32	32	32	32	32	32	32	64	32	32	32	1728

		Galois groups of order 1024
		$(C_2\times C_4^3).D_4$ (as 16T1108)	$(C_2\times C_4^3).D_4$ (as 16T1112)	$D_4^2:\OD_{16}$ (as 16T1120)	$C_4^3.(C_2^2\times C_4)$ (as 16T1186)	$C_2^4.C_2\wr C_4$ (as 16T1251)	$C_2^4.C_2\wr C_4$ (as 16T1269)	Total
hidden slopes	$[\frac{17}{4},3,3,4,4]_{2}$					64	128	192
		$[2,3,3,4,4]^{2}$				64			64
	$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$		32	40	96				168
		$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$	32	24	32				88
	$[3,3,4,4,\frac{17}{4}]^{2}$						64		64
		Total	64	64	128	64	128	128	576

		Galois groups of order 2048
		$C_2^5.C_2\wr C_4$ (as 16T1354)	$C_2^5.C_2\wr C_4$ (as 16T1376)	$(C_2^2\times D_4^2).D_4$ (as 16T1383)	$C_4^4:(C_2\times C_4)$ (as 16T1388)	$\OD_{16}^2:(C_2\times C_4)$ (as 16T1397)	$\OD_{16}^2:(C_2\times C_4)$ (as 16T1409)	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$(C_2^2\times D_4^2).D_4$ (as 16T1424)	$(C_2^2\times D_4^2).D_4$ (as 16T1431)	$\OD_{16}^2:(C_2\times C_4)$ (as 16T1434)	$C_2^5.C_2\wr C_2^2$ (as 16T1444)	$C_2^5.C_2\wr C_2^2$ (as 16T1455)	Total
hidden slopes	$[2,2,3,\frac{7}{2},\frac{15}{4},4]^{2}$			40						8				48
		$[2,2,3,\frac{7}{2},\frac{7}{2},\frac{15}{4}]^{2}$			8						24				32
	$[2,3,3,3,4,4]^{2}$		32												32
		$[2,3,3,3,\frac{7}{2},4]^{2}$				64									64
	$[2,3,3,3,\frac{7}{2},\frac{9}{2}]^{2}$						64					32			96
		$[2,3,3,4,4,\frac{17}{4}]^{2}$		128	72				64	32	40				336
	$[2,3,3,\frac{7}{2},4,4,\frac{9}{2}]$												144	192	336
		$[2,3,3,\frac{7}{2},4,\frac{9}{2}]^{2}$						56				32			88
	Total		32	128	120	64	64	56	64	32	72	64	144	192	1032

		Galois groups of order 4096
		$C_4^4:\OD_{16}$ (as 16T1582)	$C_2^6.C_2\wr C_4$ (as 16T1585)	$C_2^6.C_2\wr C_4$ (as 16T1622)	$C_2^6.C_2\wr C_4$ (as 16T1628)	Total
hidden slopes	$[2,2,3,3,4,4,\frac{17}{4}]^{2}$	256				256
		$[2,2,3,3,\frac{7}{2},4,4]^{2}$		64			64
	$[2,2,3,3,\frac{7}{2},\frac{7}{2},4]^{2}$			64			64
		$[2,3,3,\frac{7}{2},4,4,\frac{9}{2}]^{2}$			320	128	448
	Total		256	128	320	128	832

		Galois groups of order 8192
		$C_2^7.D_4:D_4$ (as 16T1713)
hidden slopes	$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$	32
		$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$	32
	Total		64

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
2.2.8.54a1.1		$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 2$	$C_4^2:C_2^2$ (as 16T111)	$64$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[3,4]$	$[2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.2		$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$	$C_4^2:C_2^2$ (as 16T111)	$64$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[3,4]$	$[2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.3		$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$C_4^2.D_4$ (as 16T311)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.4		$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$C_4^2.D_4$ (as 16T311)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.5		$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$C_4^2:C_2^2$ (as 16T111)	$64$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[3,4]$	$[2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.6		$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$C_4^2:C_2^2$ (as 16T111)	$64$	$8$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[3,4]$	$[2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.7		$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2:C_2^2$ (as 16T107)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[3,4]$	$[2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.8		$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2:C_2^2$ (as 16T107)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[3,4]$	$[2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.9		$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2.D_4$ (as 16T311)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.10		$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2.D_4$ (as 16T311)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.11		$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2:C_2^2$ (as 16T107)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[3,4]$	$[2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.12		$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2:C_2^2$ (as 16T107)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[3,4]$	$[2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.13		$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2.D_4$ (as 16T311)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.14		$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2.D_4$ (as 16T311)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.15		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	not computed	not computed	not computed	not computed	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.16		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	not computed	not computed	not computed	not computed	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.17		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	not computed	not computed	not computed	not computed	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.18		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	not computed	not computed	not computed	not computed	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.19		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	not computed	not computed	not computed	not computed	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.20		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	not computed	not computed	not computed	not computed	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.21		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	not computed	not computed	not computed	not computed	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.22		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	not computed	not computed	not computed	not computed	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.23		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 2$	$C_2\wr D_4$ (as 16T393)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.24		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$	$C_4^2.D_4$ (as 16T344)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.25		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$C_4^2.D_4$ (as 16T344)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.26		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$C_2\wr D_4$ (as 16T393)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.27		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2:D_4$ (as 16T340)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.28		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2:D_4$ (as 16T336)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.29		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2:D_4$ (as 16T336)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.30		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$	$C_4^2:D_4$ (as 16T340)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.31		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$C_2\wr D_4$ (as 16T393)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.32		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$C_4^2.D_4$ (as 16T344)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.33		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$C_4^2.D_4$ (as 16T344)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.34		$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$C_2\wr D_4$ (as 16T393)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3,4]$	$[1,2,3]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.35		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.36		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.37		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.38		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.39		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.40		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.41		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.42		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.43		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.44		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.45		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.46		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$	$C_2^5.(C_2\times D_4)$ (as 16T813)	$512$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$	$[3,3,4,4,\frac{17}{4}]$	$[2,2,3,3,\frac{13}{4}]$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.47		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$	$[2,3,3,4,4,\frac{17}{4}]^{2}$	$[1,2,2,3,3,\frac{13}{4}]^{2}$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.48		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$	$[2,3,3,4,4,\frac{17}{4}]^{2}$	$[1,2,2,3,3,\frac{13}{4}]^{2}$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.49		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$	$[2,3,3,4,4,\frac{17}{4}]^{2}$	$[1,2,2,3,3,\frac{13}{4}]^{2}$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$
2.2.8.54a1.50		$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$	$(C_2^2\times D_4^2).D_4$ (as 16T1414)	$2048$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$	$[2,3,3,4,4,\frac{17}{4}]^{2}$	$[1,2,2,3,3,\frac{13}{4}]^{2}$	$[20, 12, 4, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 5, 13, 21]$

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