  Let A and A' be abelian varieties defined over a number field k such that
Hom(A,A') = 0. Under the Generalized Riemann hypothesis for motivic L-functions
attached to A and A', we show that there exists a prime p of k of good
reduction for A and A' at which the Frobenius traces of A and A' are nonzero
and differ by sign, and such that the norm Nm(p) is O(log(2NN')^2), where N and
N' respectively denote the absolute conductors of A and A'. Our method extends
that of Chen, Park, and Swaminathan who considered the case in which A and A'
are elliptic curves.
