  Katz showed that the L-functions of all Dirichlet characters of F_q(t), with
conductor a fixed power of a degree one prime, are equidistributed in the limit
as q goes to infinity. We generalize this statement to the L-functions of
twists of an arbitrary Galois representation by Dirichlet characters, including
independence of the L-functions of twists of different representations by the
same Dirichlet character. A similar generalization, without the independence
statement, for characters with squarefree conductor, was proven by Hall,
Keating, and Roditty-Gershon.
