  We consider the question of the correlation of Fourier coefficients of
modular forms with functions of algebraic origin. We establish the absence of
correlation in considerable generality (with a power saving of Burgess type)
and a corresponding equidistribution property for twisted Hecke orbits. This is
done by exploiting the amplification method and the Riemann Hypothesis over
finite fields, relying in particular on the ell-adic Fourier transform
introduced by Deligne and studied by Katz and Laumon.
