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Strongly correlated Fermi systems with pairing interactions become superfluid below a critical temperature T_c. The extent to which such pairing correlations alter the behavior of the liquid at temperatures TT_c is a subtle issue that remains an area of debate, in particular regarding the appearance of the so-called pseudogap in the BCS-BEC crossover of unpolarized spin-1/2 nonrelativistic matter. To shed light on this, we extract several quantities of crucial importance at and around the unitary limit, namely, the odd-even stagger