Integral of squared absolute of Bessel function of first kind

Question

As shown in the post on Integral of squared Bessel function the integral of the squared Bessel function can be solved yielding a function including the gamma function $\Gamma$ and the generalized hypergeometric function$\, _2F_3$:$$\int J_n(x)^2 \,dx = \int J_n(x) J_n(x) \,dz = \frac{2^{-2 n-1} x^{2 n+1} \, _2F_3\left(n+\frac{1}{2},n+\frac{1}{2};n+1,n+\frac{3}{2},2 n+1;-x^2\right)}{\left(n+\frac{1}{2}\right) \Gamma (n+1)^2}$$ I'm interested if the absolute squared Bessel function $$\int |J_n(z)|^2 \,dz = \int J_n(z) J_n(z)^\ast \,dz, z\in\mathbb{C}$$can be solved as well. I would especially need a solution for the definite integral $$\int_{z_1}^{z_2} |J_0(z)|^2 \,dz$$