$p$-adic family 3.1.9.26a

• Label: 3.1.9.26a
• Base: 3.1.1.0a1.1
• Degree: \(9\)
• e: \(9\)
• f: \(1\)
• c: \(26\)

Defining polynomial

$x^{9} + 27 b_{22} x^{4} + 9 b_{12} x^{3} + 27 b_{20} x^{2} + 27 b_{19} x + 3$

Invariants

Residue field characteristic:	$3$
Degree:	$9$
Base field:	$\Q_{3}$
Ramification index $e$:	$9$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$26$
Artin slopes:	$[\frac{5}{2},\frac{7}{2}]$
Swan slopes:	$[\frac{3}{2},\frac{5}{2}]$
Means:	$\langle1,2\rangle$
Rams:	$(\frac{3}{2},\frac{9}{2})$
Field count:	$81$ (complete)
Ambiguity:	$1$
Mass:	$81$
Absolute Mass:	$81$

Diagrams

Varying

Indices of inseparability:	$[18,9,0]$
Associated inertia:	$[1,1]$
Jump Set:	undefined

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

		Galois groups of order 18
		$D_9$ (as 9T3)
hidden slopes	$[\ ]_{2}$	3

		Galois groups of order 54
		$C_9:C_6$ (as 9T10)
hidden slopes	$[2]_{2}$	18
		$[\ ]^{3}_{2}$	6
	Total		24

		Galois groups of order 162
		$C_3^3:S_3$ (as 9T21)
hidden slopes	$[\frac{3}{2},\frac{8}{3}]_{2}$	54

Fields

Showing 1-50 of 81

  Download displayed columns for results to

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
3.1.9.26a1.1	18	$x^{9} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.2	18	$x^{9} + 27 x^{4} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.3	18	$x^{9} + 54 x^{4} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.4	18	$x^{9} + 27 x^{2} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.5	18	$x^{9} + 27 x^{4} + 27 x^{2} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.6	18	$x^{9} + 54 x^{4} + 27 x^{2} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.7	3	$x^{9} + 54 x^{2} + 3$	$D_{9}$ (as 9T3)	$18$	$1$	$[\frac{5}{2}, \frac{7}{2}]_{2}$	$[\frac{3}{2},\frac{5}{2}]_{2}$	$[\ ]_{2}$	$[\ ]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.8	3	$x^{9} + 27 x^{4} + 54 x^{2} + 3$	$D_{9}$ (as 9T3)	$18$	$1$	$[\frac{5}{2}, \frac{7}{2}]_{2}$	$[\frac{3}{2},\frac{5}{2}]_{2}$	$[\ ]_{2}$	$[\ ]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.9	3	$x^{9} + 54 x^{4} + 54 x^{2} + 3$	$D_{9}$ (as 9T3)	$18$	$1$	$[\frac{5}{2}, \frac{7}{2}]_{2}$	$[\frac{3}{2},\frac{5}{2}]_{2}$	$[\ ]_{2}$	$[\ ]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.10	54	$x^{9} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.11	54	$x^{9} + 27 x^{4} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.12	54	$x^{9} + 54 x^{4} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.13	54	$x^{9} + 27 x^{2} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.14	54	$x^{9} + 27 x^{4} + 27 x^{2} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.15	54	$x^{9} + 54 x^{4} + 27 x^{2} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.16	54	$x^{9} + 54 x^{2} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.17	54	$x^{9} + 27 x^{4} + 54 x^{2} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.18	54	$x^{9} + 54 x^{4} + 54 x^{2} + 27 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.19	54	$x^{9} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.20	54	$x^{9} + 27 x^{4} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.21	54	$x^{9} + 54 x^{4} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.22	54	$x^{9} + 27 x^{2} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.23	54	$x^{9} + 27 x^{4} + 27 x^{2} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.24	54	$x^{9} + 54 x^{4} + 27 x^{2} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.25	54	$x^{9} + 54 x^{2} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.26	54	$x^{9} + 27 x^{4} + 54 x^{2} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.27	54	$x^{9} + 54 x^{4} + 54 x^{2} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.28	54	$x^{9} + 9 x^{3} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.29	54	$x^{9} + 27 x^{4} + 9 x^{3} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.30	54	$x^{9} + 54 x^{4} + 9 x^{3} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.31	54	$x^{9} + 9 x^{3} + 27 x^{2} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.32	54	$x^{9} + 27 x^{4} + 9 x^{3} + 27 x^{2} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.33	54	$x^{9} + 54 x^{4} + 9 x^{3} + 27 x^{2} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.34	54	$x^{9} + 9 x^{3} + 54 x^{2} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.35	54	$x^{9} + 27 x^{4} + 9 x^{3} + 54 x^{2} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.36	54	$x^{9} + 54 x^{4} + 9 x^{3} + 54 x^{2} + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.37	18	$x^{9} + 9 x^{3} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.38	18	$x^{9} + 27 x^{4} + 9 x^{3} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.39	18	$x^{9} + 54 x^{4} + 9 x^{3} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.40	18	$x^{9} + 9 x^{3} + 27 x^{2} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.41	18	$x^{9} + 27 x^{4} + 9 x^{3} + 27 x^{2} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.42	18	$x^{9} + 54 x^{4} + 9 x^{3} + 27 x^{2} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, \frac{5}{2}, \frac{7}{2}]_{2}$	$[1,\frac{3}{2},\frac{5}{2}]_{2}$	$[2]_{2}$	$[1]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.43	6	$x^{9} + 9 x^{3} + 54 x^{2} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[\frac{5}{2}, \frac{7}{2}]_{2}^{3}$	$[\frac{3}{2},\frac{5}{2}]_{2}^{3}$	$[\ ]^{3}_{2}$	$[\ ]^{3}_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.44	6	$x^{9} + 27 x^{4} + 9 x^{3} + 54 x^{2} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[\frac{5}{2}, \frac{7}{2}]_{2}^{3}$	$[\frac{3}{2},\frac{5}{2}]_{2}^{3}$	$[\ ]^{3}_{2}$	$[\ ]^{3}_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.45	6	$x^{9} + 54 x^{4} + 9 x^{3} + 54 x^{2} + 27 x + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[\frac{5}{2}, \frac{7}{2}]_{2}^{3}$	$[\frac{3}{2},\frac{5}{2}]_{2}^{3}$	$[\ ]^{3}_{2}$	$[\ ]^{3}_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.46	54	$x^{9} + 9 x^{3} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.47	54	$x^{9} + 27 x^{4} + 9 x^{3} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.48	54	$x^{9} + 54 x^{4} + 9 x^{3} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.49	54	$x^{9} + 9 x^{3} + 27 x^{2} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined
3.1.9.26a1.50	54	$x^{9} + 27 x^{4} + 9 x^{3} + 27 x^{2} + 54 x + 3$	$(C_3^3:C_3):C_2$ (as 9T21)	$162$	$1$	$[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{7}{2}]_{2}$	$[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{5}{2}]_{2}$	$[\frac{3}{2},\frac{8}{3}]_{2}$	$[\frac{1}{2},\frac{5}{3}]_{2}$	$[18, 9, 0]$	$[1, 1]$	$z^3 + 1,z + 1$	undefined

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