  In this paper, we apply the ratio conjecture of $L$-functions to derive the
lower order terms of the $1$-level density of the low-lying zeros of a family
quadratic Hecke $L$-functions in the Gaussian field. Up to the first lower
order term, we show that our result is consistent with that obtained from
previous work under the generalized Riemann hypothesis, when the Fourier
transforms of the test functions are supported in $(-2, 2)$.
