The prism manifold realization problem II

The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in S^3. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds (also known as the prism manifolds) as the only remaining case. Every prism manifold can be parametrized as P(p,q), for a pair of relatively prime integers p>1 and q. We determine a complete list of prism manifolds P(p,q) that can be realized by positive integral surgeries on knots in S^3 when q<0. The methodology undertaken to obtain the classification is similar to that of Greene for lens spaces.