  We prove that there are exactly $6$ Nil Seifert fibred spaces which can be
obtained by Dehn surgeries on non-trefoil knots in $S^3$, with $\{60, 144, 156,
288, 300\}$ as the exact set of all such surgery slopes up to taking the mirror
images of the knots. We conjecture that there are exactly $4$ specific
hyperbolic knots in $S^3$ which admit Nil Seifert fibred surgery. We also give
some more general results and a more general conjecture concerning Seifert
fibred surgeries on hyperbolic knots in $S^3$.
