  We define an enrichment of the logarithmic derivative of the zeta function of
a variety over a finite field to a power series with coefficients in the
Grothendieck--Witt group. We show that this enrichment is related to the
topology of the real points of a lift. For cellular schemes over a field, we
prove a rationality result for this enriched logarithmic derivative of the zeta
function as an analogue of part of the Weil conjectures. We also compute
several examples, including toric varieties, and show that the enrichment is a
motivic measure.
