I have constructed a list of surgery coefficients which yield spherical space forms. For instance, there are two knots with different Alexander polynomials on which 29surgery will give a small Seifert fibered space of $S^2(2,3,5)$type. Now I am just wondering does anyone know any knot on which 58 or 83 surgery will give a spherical space form. I would appreciate any help very much.
Lens spaces of orders 58 and 83 may be obtained by integral surgeries on torus knot; see Moser's "Elementary surgeries on torus knots" which gives the classification up to homeomorphism. (Mind Moser's conventions.) More specifically: 58/1 surgery on the (3,19)torus knot yields the lens space L(58,9), and 83/1 surgery on the (2,41)torus knot yields the lens space L(83,4). Here I'm using the convention that p/q surgery on the unknot yields the lens space L(p,q) so that +5/1 surgery on (2,3)torus knot yields L(5,4). Edit: Of course any nonzero surgery on unknot is spherical, but I reckon you were looking for something less trivial. 

