Adjoint Reidemeister torsions of some 3-manifolds obtained by Dehn surgeries

We determine the adjoint Reidemeister torsion of a $3$-manifold obtained by some Dehn surgery along $K$, where $K$ is either the figure-eight knot or the $5_2$-knot. As in a vanishing conjecture, we consider a similar conjecture and show that the conjecture holds for the 3-manifold.