  We develope the $L$-functions ratios conjecture with one shift in the
numerator and denominator in certain ranges for the family of quadratic Hecke
$L$-functions in the Gaussian field using multiple Dirichlet series under the
generalized Riemann hypothesis. We also obtain an asymptotical formula for the
first moment of central values of the same family of $L$-functions, obtaining
an error term of size $O(X^{1/2+\varepsilon})$.
