  Based on the Lagarias-Odlyzko effectivization of the Chebotarev density
theorem, Kumar Murty gave an effective version of the Sato-Tate conjecture for
an elliptic curve conditional on analytic continuation and Riemann hypothesis
for the symmetric power $L$-functions. We use Murty's analysis to give a
similar conditional effectivization of the generalized Sato-Tate conjecture for
an arbitrary motive. As an application, we give a conditional upper bound of
the form $O((\log N)^2 (\log \log 2N)^2)$ for the smallest prime at which two
given rational elliptic curves with conductor at most $N$ have Frobenius traces
of opposite sign.
