Evaluating the integral $\int_{a}^{\infty} rH_{0}^{(1)}(kr)J_{0}(qr)dr$

Question

I am interested in computing integrals of the form $$ f(q,k,a) \equiv \int_{a}^{\infty} rH_{0}^{(1)}(kr)J_{0}(qr)dr $$ where $a\geq 0$ is a real number but $k\in\mathbb{C}$ is complex. $H_{0}^{(1)}$ is a Hankel function of the first kind of order 0 while $J_{0}$ is a Bessel function of the first kind of order 0. Any suggestions/references on how to evaluate such integrals for complex $k$? These type of integrals seem related to Hankel transforms, but I am unsure whether complex $k$ makes things more difficult. I can always do things numerically but I was hoping there would be semi-analytic results as well.