  We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of
automorphic forms on $SL_3(\Zz)$ do not correlate with $q$-periodic functions
with bounded Fourier transform. This generalizes the earlier results of Munshi
and Holowinsky--Nelson, corresponding to multiplicative Dirichlet characters,
and applies in particular to trace functions of small conductor modulo primes.
