Local minima of Fourier transform of natural numbers close to imaginary parts of Riemann zeta zeros

Posted to math stackexchange:
What are the exact values of the local minima in this spectrum?

Apply this program, originally written by Heike and here modified:

(*Mathematica 8 start*)
Clear[f]
scale = 1000000;
f = Range[scale] - 1;
xres = .002;
xlist = Exp[Range[0, Log[scale], xres]];
tmax = 100;
tres = .015;
ymin = -0.025;
ymax = 0.015;
zz = N[Im[ZetaZero[1]]];
Monitor[errList =
Table[(xlist^(-1/2 + I t).(f[[Floor[xlist]]] - xlist)), {t,
Range[0, tmax, tres]}];, t]
g1 = ListLinePlot[Im[errList]/Length[xlist], DataRange -> {0, tmax},
PlotRange -> {ymin, ymax}, Frame -> True, Axes -> False];
g2 = Graphics[
Line[{{N[Im[ZetaZero[1]]], ymin}, {N[Im[ZetaZero[1]]], ymax}}]];
g3 = Graphics[
Line[{{N[Im[ZetaZero[2]]], ymin}, {N[Im[ZetaZero[2]]], ymax}}]];
g4 = Graphics[
Line[{{N[Im[ZetaZero[3]]], ymin}, {N[Im[ZetaZero[3]]], ymax}}]];
g5 = Graphics[
Line[{{N[Im[ZetaZero[4]]], ymin}, {N[Im[ZetaZero[4]]], ymax}}]];
g6 = Graphics[
Line[{{N[Im[ZetaZero[5]]], ymin}, {N[Im[ZetaZero[5]]], ymax}}]];
g7 = Graphics[
Line[{{N[Im[ZetaZero[6]]], ymin}, {N[Im[ZetaZero[6]]], ymax}}]];
g8 = Graphics[
Line[{{N[Im[ZetaZero[7]]], ymin}, {N[Im[ZetaZero[7]]], ymax}}]];
g9 = Graphics[
Line[{{N[Im[ZetaZero[8]]], ymin}, {N[Im[ZetaZero[8]]], ymax}}]];
g10 = Graphics[
Line[{{N[Im[ZetaZero[9]]], ymin}, {N[Im[ZetaZero[9]]], ymax}}]];
g11 = Graphics[
Line[{{N[Im[ZetaZero[10]]], ymin}, {N[Im[ZetaZero[10]]], ymax}}]];
g12 = Graphics[
Line[{{N[Im[ZetaZero[11]]], ymin}, {N[Im[ZetaZero[11]]], ymax}}]];
g13 = Graphics[
Line[{{N[Im[ZetaZero[12]]], ymin}, {N[Im[ZetaZero[12]]], ymax}}]];
g14 = Graphics[
Line[{{N[Im[ZetaZero[13]]], ymin}, {N[Im[ZetaZero[13]]], ymax}}]];
g15 = Graphics[
Line[{{N[Im[ZetaZero[14]]], ymin}, {N[Im[ZetaZero[14]]], ymax}}]];
g16 = Graphics[
Line[{{N[Im[ZetaZero[15]]], ymin}, {N[Im[ZetaZero[15]]], ymax}}]];
g17 = Graphics[
Line[{{N[Im[ZetaZero[16]]], ymin}, {N[Im[ZetaZero[16]]], ymax}}]];
g18 = Graphics[
Line[{{N[Im[ZetaZero[17]]], ymin}, {N[Im[ZetaZero[17]]], ymax}}]];
g19 = Graphics[
Line[{{N[Im[ZetaZero[18]]], ymin}, {N[Im[ZetaZero[18]]], ymax}}]];
g20 = Graphics[
Line[{{N[Im[ZetaZero[19]]], ymin}, {N[Im[ZetaZero[19]]], ymax}}]];
g21 = Graphics[
Line[{{N[Im[ZetaZero[20]]], ymin}, {N[Im[ZetaZero[20]]], ymax}}]];
g22 = Graphics[
Line[{{N[Im[ZetaZero[21]]], ymin}, {N[Im[ZetaZero[21]]], ymax}}]];
g23 = Graphics[
Line[{{N[Im[ZetaZero[22]]], ymin}, {N[Im[ZetaZero[22]]], ymax}}]];
g24 = Graphics[
Line[{{N[Im[ZetaZero[23]]], ymin}, {N[Im[ZetaZero[23]]], ymax}}]];
g25 = Graphics[
Line[{{N[Im[ZetaZero[24]]], ymin}, {N[Im[ZetaZero[24]]], ymax}}]];
g26 = Graphics[
Line[{{N[Im[ZetaZero[25]]], ymin}, {N[Im[ZetaZero[25]]], ymax}}]];
g27 = Graphics[
Line[{{N[Im[ZetaZero[26]]], ymin}, {N[Im[ZetaZero[26]]], ymax}}]];
g28 = Graphics[
Line[{{N[Im[ZetaZero[27]]], ymin}, {N[Im[ZetaZero[27]]], ymax}}]];
g29 = Graphics[
Line[{{N[Im[ZetaZero[28]]], ymin}, {N[Im[ZetaZero[28]]], ymax}}]];
g30 = Graphics[
Line[{{N[Im[ZetaZero[29]]], ymin}, {N[Im[ZetaZero[29]]], ymax}}]];
gw = Show[g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, g11, g12, g13, g14,
g15, g16, g17, g18, g19, g20, g21, g22, g23, g24, g25, g26, g27,
g28, g29, g30, ImageSize -> Large]
(*Mathematica 8 end*)

The result is a plot with local minima that are close to the imaginary part of the Riemann zeta zeros:

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