  We prove uniform Hausdorff and packing dimension results for the inverse
images of a large class of real-valued symmetric L\'evy processes. Our main
result for the Hausdorff dimension extends that of Kaufman (1985) for Brownian
motion and that of Song, Xiao, and Yang (2018) for $\alpha$-stable L\'evy
processes with $1<\alpha<2$. Along the way, we also prove an upper bound for
the uniform modulus of continuity of the local times of these processes.
