  We derive new obstructions to periodicity of classical knots by employing the
Heegaard Floer correction terms of the finite cyclic branched covers of the
knots. Applying our results to two fold covers, we demonstrate through numerous
examples that our obstructions are successful where many existing periodicity
obstructions fail. A combination of previously known periodicity obstructions
and the results presented here, leads to a nearly complete (with the exception
of a single knot) classification of alternating, periodic, 12-crossing knots
with odd prime periods. For the case of alternating knots with 13, 14 and 15
crossings, we give a complete listing of all periodic knots with odd prime
periods greater than 3.
