  We show that a Frobenius-semisimple Weil representation over a local field K
is determined by its Euler factors over the extensions of K. The construction
is explicit, and we illustrate it for l-adic representations attached to
elliptic and genus 2 curves. As an application, we construct an absolutely
simple 2-dimensional abelian variety over Q all of whose quadratic twists must
have positive rank, according to the Birch-Swinnerton-Dyer conjecture.
