  We compare the low eigenvalue spectra of the Overlap Dirac operator on two
sets of configurations at $\mu_I/\mu_I^c$ = 0.5 and 1.5 generated with
dynamical staggered fermions at these isospin chemical potential on $24^3
\times 6$ lattices. We find very small changes in the number of zero modes and
low lying modes which is in stark contrast with those across the corresponding
finite temperature phases where one sees a drop across the phase transition.
Possible consequences are discussed.
