von Mangoldt function Fourier transform Dirichlet series

    scale = 10000;
    Print["Counting to 60"]
    Monitor[g1 =
      ListLinePlot[
       Table[Re[
         Zeta[1/2 + I*t]*
          Total[Table[
            1/N[Log[scale]]*1/n*
             Total[1/Divisors[n]^(1/2 + I*t - 1)*
               MoebiusMu[Divisors[n]]], {n, 1, scale}]]], {t, 0, 60,
         N[1/6]}], DataRange -> {0, 60}, PlotRange -> {-0.02, 1.6}],
     Floor[t]]

    Clear[f]
    f = ConstantArray[0, scale];
    f[[1]] = N@HarmonicNumber[scale];
    Monitor[Do[
      f[[i]] = N@MangoldtLambda[i] + f[[i - 1]], {i, 2, scale}], i]
    xres = .002;
    x = Exp[Range[0, Log[scale], xres]];
    tmax = 60;
    tres = N[1/6];
    Monitor[errList =
       Table[t*(x^(-1/2 + I t).(f[[Floor[x]]] - x)), {t,
         Range[0, 60, tres]}];, t]
    g2 = ListLinePlot[Im[errList]/Length[x], DataRange -> {0, 60},
      PlotRange -> {-.02, 1.6}, PlotStyle -> Black]

    scale = 600;
    Print["Counting to 60"]
    Monitor[g3 =
      ListLinePlot[
       Accumulate[+1.3 -
         Table[Re[
           Zeta[1/2 + I*t]*
            Total[Table[
              1/2/Pi*1/n*
               Total[1/Divisors[n]^(1/2 + I*t - 1)*
                 MoebiusMu[Divisors[n]]], {n, 1, scale}]]], {t, 0, 60,
           N[1/6]}]], DataRange -> {0, 60}, PlotRange -> {0, 80}],
     Floor[t]]