  Let $f$ be a normalized Hecke-Maass cusp form of weight zero for the group
$SL_2(\mathbb Z)$. This article presents several quantitative results about the
distribution of Hecke eigenvalues of $f$. Applications to the
$\Omega_{\pm}$-results for the Hecke eigenvalues of $f$ and its symmetric
square sym$^2(f)$ are also given.
