$p$-adic field search results

Degree	Residue characteristic	Galois group	Galois unramified degree
Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree
Residue field degree	Top slope	Wild inertia subgroup

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
5.13.0.1	$13$	x^13 + x^2 - 2x + 2	$5$	$1$	$13$	$0$	$C_{13}$ (as 13T1)	$13$	$1$	$[\ ]^{13}$
5.13.12.1	$13$	x^13 - 5	$5$	$13$	$1$	$12$	$C_{13}:C_4$ (as 13T4)	$4$	$13$	$[\ ]_{13}^{4}$