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.
$T$ | sample data for $Z(t)$: using $10^7$ zeros near each height $T$ | ||
---|---|---|---|
1e12 | zero ordinates | max between consecutive zeros | derivative at zeros |
1e13 | __ | __ | __ |
1e14 | __ | __ | __ |
1e15 | __ | __ | __ |
1e16 | __ | __ | __ |
1e17 | __ | __ | __ |
1e18 | __ | __ | __ |
1e19 | __ | __ | __ |
1e20 | __ | __ | __ |
1e21 | __ | __ | __ |
1e22 | __ | __ | __ |
1e23 | __ | __ | __ |
1e24 | __ | __ | __ |
1e25 | __ | __ | __ |
1e26 | __ | __ | __ |
1e27 | __ | __ | __ |
1e28 | __ | __ | __ |