  In this paper, we study the one level density of low-lying zeros of a family
of quadratic Hecke $L$-functions to prime moduli over the Gaussian field under
the generalized Riemann hypothesis (GRH) and the ratios conjecture. As a
corollary, we deduce that at least $75 \%$ of the members of this family do not
vanish at the central point under GRH.
