  In this paper, we study lower order terms of the $1$-level density of
low-lying zeros of quadratic Hecke L-functions in the Gaussian field. Assuming
the Generalized Riemann Hypothesis, our result is valid for even test functions
whose Fourier transforms are supported in $(-2, 2)$. Moreover, we apply the
ratios conjecture of $L$-functions to derive these lower order terms as well.
Up to the first lower order term, we show that our results is consistent with
each other, when the Fourier transforms of the test functions are supported in
$(-2, 2)$.
