  We study a method to compute a topological phase factor of partition function
for pure Chern-Simons theory incorporating the supersymmetric localization. We
develop a regularization preserving supersymmetry and the topological phase
appears as a result of the supersymmetric regularization. Applying this method
to pure Chern-Simons theory on lens space we compute the background dependent
phase factor coming from the Chern-Simons term. We confirm that the partition
function computed in this method enjoys a couple of level rank dualities
including the one recently proposed in arXiv:1607.07457 for all ranks and
levels within our numerical calculation. We also present a phase factor with
which the lens space partition function exhibits the perfect match between any
level rank dual pair including the total phase.
