Fourier transform of the von Mangoldt function with first term equal to a harmonic number

(*Mathematica 8*)

Clear[f]
scale = 100000;
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;
xlist = Exp[Range[0, Log[scale], xres]];
tmax = 60;
tres = .015;
Monitor[errList =
Table[(xlist^(-1/2 + I t).(f[[Floor[xlist]]] - xlist)), {t,
Range[0, 60, tres]}];, t]
ListLinePlot[Im[errList]/Length[xlist], DataRange -> {0, 60},
PlotRange -> {-.02, .15}, Frame -> True, Axes -> False]

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