Zeta zero spectrum with spikes of similar heights

Mathematica


Clear[f]
scale = 1000000;
f = Range[scale];

f[[1]] = N@MangoldtLambda[1];
Monitor[Do[
f[[i]] = N@MangoldtLambda[i] + f[[i - 1]], {i, 2, scale}], i]

xres = .004;
xlist = Exp[Range[0, Log[scale - 1], xres]];
tmax = 60;
tres = .015;
s = 1/2;
Monitor[errList1 =
Table[(Total[(xlist^(-1/2 + I t)*(f[[Floor[xlist]]] -
xlist))])*(-1/2 + I t), {t, 0, tmax, tres}];, t]

Print["Variant of the Fourier transform of the von Mangoldt function"]
g1 = ListLinePlot[Re[errList1]/Length[xlist], DataRange -> {0, tmax},
PlotRange -> {-.3, 1.3}, Axes -> True, Filling -> Axis];
g2 = Graphics[Line[{{0, 1}, {tmax, 1}}]];
Show[g1, g2, ImageSize -> Large]

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