  Let F be a non-archimedean local field of characteristic zero. Jacquet and
Shalika attached a family of zeta integrals to unitary irreducible generic
representations $\pi$ of GL_n(F). In this paper, we show that Jacquet-Shalika
integral attains a certain L-function, so called the formal exterior square
L-function, when the Whittaker function is associated to a newform for $\pi$.
By consideration on the Galois side, formal exterior square L-functions are
equal to exterior square L-functions for some principal series representations.
