  Let $\nu_{f}(n)$ be the $n$-th nomalized Fourier coefficient of a
Hecke--Maass cusp form $f$ for ${\rm SL}(2,\Z)$ and let $\alpha$ be a real
number. We prove strong oscillations of the argument of $\nu_{f}(n)\mu (n) \exp
(2\pi i n \alpha)$ as $n$ takes consecutive integral values.
