Tables of zeros of $\zeta(s)$ Is there a table somewhere of the $n$th zero of $\zeta(s)$ for $n = 10^k$ for $k = 0,1,2,\ldots$?  I need the values for $k$ up to as large as is known (e.g., $k = 22$).  Same question for $n = 2^k$, or for other powers of a fixed integer.  This is not found at http://www.dtc.umn.edu/~odlyzko/zeta_tables/, nor at https://www.lmfdb.org.  Mathematica goes only to $10^8$.  I need out to $10^{22}$.
EDIT: The context for this is that I'm doing some computations that require the zeros to some (not super-high) accuracy, and the values I'm asking for would be most useful.  People have computed $\pi(n)$ for powers $n$ of a fixed integer $a>1$, so it shouldn't be too much to ask that we do the same for the $n$th zero of $\zeta(s)$.

Existing calculations of the zeros of $\zeta(s)$ are summarized well on the Wikipedia page for the Riemann hypothesis (and citations to the literature are included). The first $1.2\times10^{13}$ or so zeros have been tabulated, and there have also been calculations of a relatively small number of zeros of very large height (around $10^{24}$, for instance, which is around the $8.3\times10^{24}$th zero). The Odlyzko–Schönhage algorithm is well suited for calculating specific zeros, so that might be where you can start to develop your own calculations if desired.
If you only want approximations to the zeros, the number of zeros of $\zeta(s)$ has an extremely good error term: for example, you could use this formula to find the $10^{22}$nd zero (which has size about $1.4\times10^{21}$) with an error of less than $10$; that's 20 significant figures, using an almost trivial calculation.
