# How could I get access to more than the first 2 mln non-trivial zeros of $\zeta(s)$?

I would like to test whether or not the following product (or its complement)

$$\displaystyle \displaystyle \prod_{n=1}^\infty \left(1- \frac{s}{\frac12+ (-1)^n\, \gamma_n \, i} \right)$$

converges to fractions of known constants for e.g. $s=2n$. Note that $\gamma_n$ is the imaginary part of the n-th non-trivial zero of $\zeta(s)$.

I am aware of Andrew Odlyzko's tables of non-trivial zeros and using those I could calculate the product up to $n=2,001,052$. However convergence of the product is very slow and I am keen to get access to a table with couple of million zeros more (with $\gamma_n$ at 9 digits).

Grateful for any hints/tips on where I might to find these and/or for a fast tool/program (e.g. using the Riemann-Siegel formula) to generate them.

Thanks!

This solves my problem, however I did not find a nice relation to known constants (actually the product is complex). The only 'interesting' fact I found, is that the absolute value of the 'flipping' product of zeros is the square root of the Riemann $\xi(s)$ function.