Notes on the Phase Statistics of the Riemann Zeros

We numerically investigate, for zeros \(\rho=1/2+i\gamma\), the statistics of the imaginary part of \(\log(\zeta^\prime(1/2+i\gamma))\), computed by continuous variation along a vertical line from \(\sigma=4\) to \(4+i\gamma\) and then along a horizontal line to \(1/2+i\gamma\).