Using a dimensional reduction formula for the lattice fermion determinant we study canonical determinants on quenched SU(3) gauge configurations. The canonical determinants decribe a fixed quark number and we analyze their properties below and above the transition temperature. We find that above $T_c$ the signatures of center symmetry breaking are very strongly manifest in the distribution of the canonical determinants in the complex plane, and we discuss possible physical implications of this finding. We furthermore analyze the relative weight of the different quark sectors below and above the transition temperature.
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