$L^{2}(\mathbb R)$- norm of entire function

Let $f(z)$ be an entire function defined by $$f(z)=\prod_{n=1}^{\infty}\bigg(1-\frac{z^{2}}{a_{n}^{2}}\bigg),\qquad z\in \mathbb C$$ where $\{a_{n}\}_{n=1}^{\infty}$ is a sequence of positive real numbers, determined so that the infinite product above defines an entire function. How can we compute the integral $$\int_{-\infty}^{\infty}|f(x)|^{2}dx$$ where $x$ is real. Or at least finding an upper bound for it (if it is finite)?

I searched infinite products, http://mathworld.wolfram.com/InfiniteProduct.html. Consider $$cos(x)=\prod_{n=1}^\infty \left(1-\frac{4x^2}{\pi^2(2n-1)^2}\right).$$ Then $$\int_{-\infty}^\infty |cos(x)|^2 dx=\infty.$$ So I don't think an upper bound can be found.