Histogram of pushing the first Dirichlet Eta zero towards

(*start*)
nn = 300
Monitor[DirichletEtaRootList =
   Table[k /.
     FindRoot[
      Re[Zeta[1/2 + I*k]*
        Total[Table[
          Total[MoebiusMu[Divisors[n]]/Divisors[n]^(1/2 + I*k - 1)]/
           n, {n, 1, scale}]]], {k, 14.25}], {scale, 2, nn}];, scale]
Show[ListLinePlot[DirichletEtaRootList, PlotRange -> {14.1, 14.2}],
 Plot[Im[ZetaZero[1]], {scale, 2, nn}, PlotRange -> {14.1, 14.2}]]
ListPlot[Sort[DirichletEtaRootList, Greater]]
DirichletEtaRootList - Im[ZetaZero[1]];
Count[%, N[0]]
Histogram[DirichletEtaRootList]
(*aa=100000 first Riemnann zeta zeros, imaginary parts*)
(*Histogram[Abs[Differences[aa]]]*)
(*end*)