Are there any results on the proportion of nonzero central L-values of Maass cusp forms? More precisely, I am looking for lower bounds for

\begin{equation} \frac{\#\{\phi_j : \, L(1/2, \phi_j) \neq 0, \, \lambda_j \leq T\}}{\#\{\phi_j : \, \lambda_j \leq T\}} \end{equation}

as $T \rightarrow \infty$, where $\phi_j$ (with eigenvalue $\lambda_j$) is an orthonormal basis of Maass cusp forms for a congruence subgroup of $\mathrm{SL}_2(\mathbb{Z})$.

I ask this question as I found results of this kind for L-functions of holomorphic cusp forms in Iwaniec-Sarnak's work ''The non-vanishing of central values of automorphic L-functions and Landau-Siegel zeros'' and for Rankin-Selberg L-functions of Maass forms and a fixed holomorphic cusp form in Luo's work ''Nonvanishing of L-Values and the Weyl Law''.