Array plot comparison between zeta zeros and random numbers.

(*Set nn=2000 for comparison to the Random case:*)
nn = 200;
Monitor[A =
   Table[Table[(Re[
       k^(0 + Pi*N[n]*I*
           Im[ZetaZero[n]]/(2*Pi*Exp[1]*
              Exp[ProductLog[(N[n] - 11/8)/Exp[1]]]))]), {k, 1,
      nn}], {n, 1, nn}];, Floor[n]]; g1 =
 ArrayPlot[
  A]
(*Replace Im[ZetaZero[n]] with the precomputed Odlyzko zeros*) \
(*for faster computation.*)

bb = RandomReal[{1 - 1/100, 1 + 1/100}, 2000]; Monitor[
 A = Table[
    Table[(Re[k^(0 + Pi*N[n]*I*bb[[n]])]), {k, 1, 2000}], {n, 1,
     2000}];, Floor[n]]; g1 = ArrayPlot[A]