Confluent Heun function $H(\gamma, \delta, \epsilon, \alpha, q, z) = 0$

Question

I have the Heun Confluent differential equation $$ {\frac {d^{2}w}{dz^{2}}}+\left[{\frac {\gamma }{z}}+{\frac {\delta }{z-1}}+\epsilon \right]{\frac {dw}{dz}}+{\frac {\alpha z-q}{z(z-1)}}w=0 \, ,$$ where in my case $\alpha =0$. The Confluen Heun function reads $H(\gamma,\delta,\epsilon,0,q, z)$. I am looking for zeroes of the function at some $z=z_0 \in \mathbb{R}$. Is there a way to find values for $q$ in terms of the other parameters such that $H(\gamma, \delta,\epsilon,0,q, z_0)=0$? Is there some expansion around a point $z_0$ I could use? Or maybe some asympotic formulas for big arguments $\gamma, \delta, \epsilon$? Every expansion I can find is either at $z_0 = 0$ or $z_0 = \infty$. Any help is appreciated.