Fourier series like graph

(*Edit 9.11.2018:*)

    (*Mathematica divergent sum start*)
    nn = 500;
    f[t_] = D[RiemannSiegelTheta[t], t];
    g2 = Plot[
      Sign[RiemannSiegelZ[t]]*
       Abs[Zeta[1/2 + I*t]*
          Total[Table[
            Total[MoebiusMu[Divisors[n]]/Divisors[n]^(1/2 + I*t - 1)]/
             n, {n, 1, nn}]]]/(f[t] + HarmonicNumber[nn]), {t, 0, 60},
      PlotStyle -> Thickness[0.004], ImageSize -> Large,
      PlotRange -> {-4, 4}]
    (*end*)

    (*Mathematica analytic continuation start*)
    f[t_] = D[RiemannSiegelTheta[t], t];
    epsilon = 1/40;
    g3 = Monitor[
      Plot[Sign[RiemannSiegelZ[t]]*
        Abs[Zeta[1/2 + I*t]/Zeta[1/2 + I*t + (1 + epsilon) - 1]*
           Zeta[(1 + epsilon)]]/(f[t] + 1/epsilon + EulerGamma), {t, 0,
        60}, PlotStyle -> {Red, Thickness[0.004]}, ImageSize -> Large,
       PlotRange -> {-4, 4}], n]

    Show[{g2, g3}, ImageSize -> 1000]
    (*code line: "Show[{g2, g3}, ImageSize -> 1000]" added by Roger L. Bagula*)
    (*end*)