Riemann zeta function on the critical line as a Fourier transform of exponential sawtooth function plus minus one

The code does not work when copy pasted in this blogging platform,

so here is a link to Pastebin with some working code:

http://pastebin.com/TC1wcuzF

Mathematica:

scale = 1000000;

xres = .00001;

x = Exp[Range[0, Log[scale], xres]];

RealPart = Log[x]*FourierDST[-(SawtoothWave[x] – 1)*x^(-1/2)];

ImaginaryPart = Log[x]*FourierDCT[-(SawtoothWave[x] + 1)*x^(-1/2)];

datapointsdisplayed = 300;

ymin = -15;

ymax = 15;

g1 = ListLinePlot[

Sqrt[scale]*{RealPart[[1 ;; datapointsdisplayed]],

ImaginaryPart[[1 ;; datapointsdisplayed]]},

PlotRange -> {ymin, ymax}, DataRange -> {0, 68.00226987379779},

Filling -> Axis];

Show[Flatten[{g1,

Table[Graphics[{PointSize[0.013],

Point[{N[Im[ZetaZero[n]]], 0}]}], {n, 1, 16}]}],

ImageSize -> Large]

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