Alexander polynomial, Dijkgraaf-Witten invariant, and Seifert fibred surgery

We apply Dijkgraaf-Witten invariant over an semiproduct of abelian groups to show that, if the $k\mathrm{/}\mathrm{\ell }$-surgery along a knot $K$ results in a small Seifert 3-manifold with multiplicities $a_1,a_2,a_3$, then many constraints on $k,a_1,a_2,a_3$ can be read off from the Alexander polynomial of $K$.