  We give an anecdotal discussion of the problem of searching for polynomials
with all roots on the unit circle, whose coefficients are rational numbers
subject to certain congruence conditions. We illustrate with an example from a
calculation in p-adic cohomology made by Abbott, Kedlaya, and Roe, in which
(using an implementation developed with Andre Wibisono) we recover the zeta
function of a surface over a finite field.
