Fourier transform symmetric around the x-axis

Mathematica 8:


Clear[n, d];
Clear[f]
scale = 1000000;
f = ConstantArray[0, scale];
f[[1]] = Sum[d*MoebiusMu@d, {d, Divisors[1]}];
Monitor[Do[
f[[i]] = Sum[d*MoebiusMu@d, {d, Divisors[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]]] - 0*xlist)), {t,
Range[0, tmax, tres]}];, t]
g = ListLinePlot[Im[errList]/Length[xlist], DataRange -> {0, tmax},
PlotRange -> {-5000, 5000}, Frame -> True, Axes -> False];
Show[g]

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