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Properties

Label 3.1.9.24a
Base 3.1.1.0a1.1
Degree \(9\)
e \(9\)
f \(1\)
c \(24\)

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Defining polynomial

$x^{9} + 9 b_{17} x^{8} + 9 a_{16} x^{7} + 9 b_{12} x^{3} + 27 b_{19} x + 3$

Invariants

Residue field characteristic: $3$
Degree: $9$
Base field: $\Q_{3}$
Ramification index $e$: $9$
Residue field degree $f$: $1$
Discriminant exponent $c$: $24$
Artin slopes: $[\frac{5}{2},\frac{19}{6}]$
Swan slopes: $[\frac{3}{2},\frac{13}{6}]$
Means: $\langle1,\frac{16}{9}\rangle$
Rams: $(\frac{3}{2},\frac{7}{2})$
Field count: $54$ (complete)
Ambiguity: $1$
Mass: $54$
Absolute Mass: $54$

Diagrams

Varying

Indices of inseparability: $[16,9,0]$
Associated inertia: $[1,1]$
Jump Set: undefined

Galois groups and Hidden Artin slopes

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Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set Fields per packet
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Showing 1-50 of 54

Next   displayed columns for results
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
3.1.9.24a1.1 27 $x^{9} + 9 x^{7} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.2 27 $x^{9} + 9 x^{7} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.3 27 $x^{9} + 9 x^{7} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.4 27 $x^{9} + 9 x^{8} + 9 x^{7} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.5 27 $x^{9} + 9 x^{8} + 9 x^{7} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.6 27 $x^{9} + 9 x^{8} + 9 x^{7} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.7 27 $x^{9} + 18 x^{8} + 9 x^{7} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.8 27 $x^{9} + 18 x^{8} + 9 x^{7} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.9 27 $x^{9} + 18 x^{8} + 9 x^{7} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.10 27 $x^{9} + 9 x^{7} + 9 x^{3} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.11 27 $x^{9} + 9 x^{7} + 9 x^{3} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.12 27 $x^{9} + 9 x^{7} + 9 x^{3} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.13 27 $x^{9} + 9 x^{8} + 9 x^{7} + 9 x^{3} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.14 27 $x^{9} + 9 x^{8} + 9 x^{7} + 9 x^{3} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.15 27 $x^{9} + 9 x^{8} + 9 x^{7} + 9 x^{3} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.16 27 $x^{9} + 18 x^{8} + 9 x^{7} + 9 x^{3} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.17 27 $x^{9} + 18 x^{8} + 9 x^{7} + 9 x^{3} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.18 27 $x^{9} + 18 x^{8} + 9 x^{7} + 9 x^{3} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.19 27 $x^{9} + 9 x^{7} + 18 x^{3} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.20 27 $x^{9} + 9 x^{7} + 18 x^{3} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.21 27 $x^{9} + 9 x^{7} + 18 x^{3} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.22 27 $x^{9} + 9 x^{8} + 9 x^{7} + 18 x^{3} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.23 27 $x^{9} + 9 x^{8} + 9 x^{7} + 18 x^{3} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.24 27 $x^{9} + 9 x^{8} + 9 x^{7} + 18 x^{3} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.25 27 $x^{9} + 18 x^{8} + 9 x^{7} + 18 x^{3} + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.26 27 $x^{9} + 18 x^{8} + 9 x^{7} + 18 x^{3} + 27 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a1.27 27 $x^{9} + 18 x^{8} + 9 x^{7} + 18 x^{3} + 54 x + 3$ $(C_3^3:C_3):C_2$ (as 9T21) $162$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}$ $[\frac{3}{2},\frac{8}{3}]_{2}$ $[\frac{1}{2},\frac{5}{3}]_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 1$ undefined
3.1.9.24a2.1 27 $x^{9} + 18 x^{7} + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.2 27 $x^{9} + 18 x^{7} + 27 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.3 27 $x^{9} + 18 x^{7} + 54 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.4 27 $x^{9} + 9 x^{8} + 18 x^{7} + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.5 27 $x^{9} + 9 x^{8} + 18 x^{7} + 27 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.6 27 $x^{9} + 9 x^{8} + 18 x^{7} + 54 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.7 27 $x^{9} + 18 x^{8} + 18 x^{7} + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.8 27 $x^{9} + 18 x^{8} + 18 x^{7} + 27 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.9 27 $x^{9} + 18 x^{8} + 18 x^{7} + 54 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.10 27 $x^{9} + 18 x^{7} + 9 x^{3} + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.11 27 $x^{9} + 18 x^{7} + 9 x^{3} + 27 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.12 27 $x^{9} + 18 x^{7} + 9 x^{3} + 54 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.13 27 $x^{9} + 9 x^{8} + 18 x^{7} + 9 x^{3} + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.14 27 $x^{9} + 9 x^{8} + 18 x^{7} + 9 x^{3} + 27 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.15 27 $x^{9} + 9 x^{8} + 18 x^{7} + 9 x^{3} + 54 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.16 27 $x^{9} + 18 x^{8} + 18 x^{7} + 9 x^{3} + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.17 27 $x^{9} + 18 x^{8} + 18 x^{7} + 9 x^{3} + 27 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.18 27 $x^{9} + 18 x^{8} + 18 x^{7} + 9 x^{3} + 54 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.19 27 $x^{9} + 18 x^{7} + 18 x^{3} + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.20 27 $x^{9} + 18 x^{7} + 18 x^{3} + 27 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.21 27 $x^{9} + 18 x^{7} + 18 x^{3} + 54 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.22 27 $x^{9} + 9 x^{8} + 18 x^{7} + 18 x^{3} + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
3.1.9.24a2.23 27 $x^{9} + 9 x^{8} + 18 x^{7} + 18 x^{3} + 27 x + 3$ $((C_3^3:C_3):C_2):C_2$ (as 9T24) $324$ $1$ $[\frac{3}{2}, \frac{5}{2}, \frac{8}{3}, \frac{19}{6}]_{2}^{2}$ $[\frac{1}{2},\frac{3}{2},\frac{5}{3},\frac{13}{6}]_{2}^{2}$ $[\frac{3}{2},\frac{8}{3}]^{2}_{2}$ $[\frac{1}{2},\frac{5}{3}]^{2}_{2}$ $[16, 9, 0]$ $[1, 1]$ $z^3 + 1,z + 2$ undefined
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