  The spectral properties of a variety of improved staggered operators are
studied in quenched QCD. The systematic dependence of the infrared eigenvalue
spectrum on i) improvement in the staggered operator, ii) improvement in the
gauge field action, iii) lattice spacing and iv) lattice volume, is analyzed.
It is observed that eigenmodes with small eigenvalues and large chirality
appear as the level of improvement increases or as one approaches the continuum
limit. These eigenmodes can be identified as the ``zero modes'' which
contribute to the chirality associated, via the index theorem, with the
topology of the background gauge field. This gives evidence that staggered
fermions are sensitive to gauge field topology. After successfully identifying
these would-be chiral zero modes, the distribution of the remaining non-chiral
modes is compared with the predictions of Random Matrix Theory in different
topological sectors. Satisfactory agreement is obtained.
