I would like to know if it in the literature an approximation for
$$\sum_{\rho}\frac{1}{|\rho|^2}\tag{1}$$
where the sum is over all of the non-trivial zeros of the Ramanujan's zeta function (also known as Ramanujan $\tau$-Dirichlet series). I know a similar series as **Lemma 3.3** from [1], and that there are similar series involving non-trivial zeros of the Riemann zeta function in the literature. If isn't in the literature I would like how get and justify an approximation of $(1)$.

Question.Please refer the literature where is approximated $$\sum_{\rho}\frac{1}{|\rho|^2}$$ where the sum runs over all the non-trivial zeros of the Ramanujan's zeta function, and I try to search and read from the literature how was it computed. In case that it is unknown, please add your approach to calculate and justify an approximation.Many thanks.

Feel free if you want to add an optional comment/remark mentioning what convergent series involving non-trivial zeros (or convergent series involving the imaginary parts of those) of the Ramanujan's zeta function can be approximated, and that are similar to those series that are in the literature involving non-trivial zeros of the Riemann zeta function.

As reference for the Ramanujan's zeta function we know from Internet the article *Tau Dirichlet Series* of the encyclopedia Wolfram MathWorld, and the book [2].

## References:

[1] Kevin Ford, *Zero-free Regions for the Riemann Zeta Function*, Number Theory for the Millenium II, A K Peters (2002).

[2] G. H. Hardy, *Ramanujan: Twelve lectures on subjects suggested by his life and work*, AMS Chelsea Publishing (2002).