(*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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