Discrete moments of the Riemann zeta function were studied by Gonek ,  and Hejhal  in the 1980s. They independently formulated a conjecture concerning the size of these moments. In 1999 Hughes, Keating, and O'Connell , by employing a random matrix model, made this conjecture more precise. Subject to the Riemann hypothesis, we establish upper and lower bounds of the correct order of magnitude in the case of the fourth moment.
Nathan Ng. "The fourth moment of ζ′(ρ)." Duke Math. J. 125 (2) 243 - 266, 1 November 2004. https://doi.org/10.1215/S0012-7094-04-12522-9