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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
3.3.1.0a1.1 $x^{3} + 2 x + 1$ $3$ $3$ $1$ $0$ $C_3$ (as 3T1) $3$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{3}$ $[\ ]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + 2 t + 1$ $x - 3$ $[0]$ $[\ ]$ undefined
3.1.3.3a1.1 $x^{3} + 3 x + 3$ $3$ $1$ $3$ $3$ $S_3$ (as 3T2) $1$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}]_{2}$ $[\frac{1}{2}]_{2}$ $[\ ]_{2}$ $[\ ]_{2}$ $t + 1$ $x^{3} + 3 x + 3$ $[1, 0]$ $[1]$ $z + 2$ undefined
3.1.3.3a1.2 $x^{3} + 6 x + 3$ $3$ $1$ $3$ $3$ $S_3$ (as 3T2) $1$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}]_{2}$ $[\frac{1}{2}]_{2}$ $[\ ]_{2}$ $[\ ]_{2}$ $t + 1$ $x^{3} + 6 x + 3$ $[1, 0]$ $[1]$ $z + 1$ undefined
3.1.3.4a1.1 $x^{3} + 3 x^{2} + 3$ $3$ $1$ $3$ $4$ $S_3$ (as 3T2) $2$ $1$ $[2]$ $[1]$ $[2]^{2}$ $[1]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{3} + 3 x^{2} + 3$ $[2, 0]$ $[2]$ $z^{2} + 1$ undefined
3.1.3.4a2.1 $x^{3} + 6 x^{2} + 3$ $3$ $1$ $3$ $4$ $C_3$ (as 3T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{3} + 6 x^{2} + 3$ $[2, 0]$ $[1]$ $z^{2} + 2$ undefined
3.1.3.4a2.2 $x^{3} + 6 x^{2} + 12$ $3$ $1$ $3$ $4$ $C_3$ (as 3T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{3} + 6 x^{2} + 12$ $[2, 0]$ $[1]$ $z^{2} + 2$ undefined
3.1.3.4a2.3 $x^{3} + 6 x^{2} + 21$ $3$ $1$ $3$ $4$ $C_3$ (as 3T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{3} + 6 x^{2} + 21$ $[2, 0]$ $[1]$ $z^{2} + 2$ undefined
3.1.3.5a1.1 $x^{3} + 3$ $3$ $1$ $3$ $5$ $S_3$ (as 3T2) $1$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{5}{2}]_{2}$ $[\frac{3}{2}]_{2}$ $[\ ]_{2}$ $[\ ]_{2}$ $t + 1$ $x^{3} + 3$ $[3, 0]$ $[1]$ $z + 2$ undefined
3.1.3.5a1.2 $x^{3} + 9 x + 3$ $3$ $1$ $3$ $5$ $S_3$ (as 3T2) $1$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{5}{2}]_{2}$ $[\frac{3}{2}]_{2}$ $[\ ]_{2}$ $[\ ]_{2}$ $t + 1$ $x^{3} + 9 x + 3$ $[3, 0]$ $[1]$ $z + 2$ undefined
3.1.3.5a1.3 $x^{3} + 18 x + 3$ $3$ $1$ $3$ $5$ $S_3$ (as 3T2) $1$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{5}{2}]_{2}$ $[\frac{3}{2}]_{2}$ $[\ ]_{2}$ $[\ ]_{2}$ $t + 1$ $x^{3} + 18 x + 3$ $[3, 0]$ $[1]$ $z + 2$ undefined
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