Let $Z(t)$ denote the rotated zeta function.
We have $Z(t) = \zeta(1/2 + it)$, and $Z'(t_j) =
\zeta'(1/2+it_j)$ where $t_j$ is a real zero ordinate.
The goal of these computations is to collect data sets spanning several hundred million
zeta zeros near $T = \ldots,10^{24}, 10^{25}, 10^{26}, 10^{27},
10^{28}$.
In addition, the derivative and max of $Z(t)$ are computed.
The computations were carried out using
this
amortized complexity algorithm for
zeta. The main advantages of this algorithm are it is
simple to implement, it does not use the fast Fourier transform or
large amounts of memory, and its error terms are easy to control.
(A basic version of this algorithm will be available in
lcalc.)
The table below contains links to some of the data, in case it's of interest.
Remarks:

This is meant as sample data, possibly useful in initial experiments.
Substantially more data has been computed; e.g. approx $4\times 10^8$ zeros near
$T = 10^{28}$.

The linked files are zipped text files, about 110 megabytes in size.
Each unzipped "zeros file" is about 400 megabytes. Each unzipped "max file" or
"derivatives file" is about 250 megabytes.

The data files have a trailing "1" on the last line, which is convenient for some purposes.
 Pointwise evaluations of $\zeta(1/2
+ iT + it)$, $T> 10^{15}$, are typically accuarate (i.e. in
the rootmeansquare sense) to within $\pm 5 \times 10^{11}$, which is
sufficient for my current purposes.
 Zero ordinates are typically
accurate (i.e. in the rootmeansquare sense) to within $\pm 5 \times
10^{12}$, for
$T > 10^{15}$. The ordinates are listed with the integer and fractional parts separated. The integer part is offset by $T$ (itself an integer).
 The "derivative at
zeros" files contain the derivative of the rotated zeta function $Z'(T+t_j)$,
where $t_j$ is a real zero ordinate.
The derivative was computed using a numerical differentiation formula. The
values of the derivative may not be accurate to more than $\pm 10^{5}$.
 The max of $Z(T +t)$ between consecutive zero ordinates was computed to within $\pm 10^{9}$ typical precision.
 To test the computational
correctness of the data, it was ensured that it agreed with some of Andrew Odlyzko's data (from near $T = 10^{15}, 10^{19}$, and $10^{22}$) to the expected accuracy. Another, less strong, check was to ensure that the data obtained by running the algorithm with different parameter choices agreed to the expected accuracy. Also, no counter examples to the RH were found, which is a further check of the validity of the computations.
 Computing the above data near $T = 10^{28}$ took about
8.20028e+07 cpu seconds to finish @2.27GHz processor speed (about 75% of the
time was spent performing the $T^{1/2+o(1)}$ precomputation). Thanks to the riemann
machine at U. Waterloo, where 14 nodes each having 8 cores @2.27GHz were typically available,
this took roughly 100 hours in real time.
 Memory requirements of the
algorithm are moderate, requiring about 1.5GB of RAM for each node on the riemann machine.