Mistake about Riemann zeta zero counting function

(*Integral*)(*start*)
Clear[k, n, s, i, d, r, q, f, a, b, integral, c, nn, n, k];
nn = 120;
delta = 1/10;
k = 16;
q = 10;
c = 1;
rr = 60;
f[s_, d_] =
  N[-I*MoebiusMu[
     d]*(If[d == 1, 0, -((d^(1 - s) 1^-s)/(Log[d] + Log[1]))] +
      Sum[-((d^(1 - s) n^-s)/(Log[d] + Log[n])), {n, 2, k}] +
      ExpIntegralEi[-(-1 + s) Log[d] - (-1 + s) Log[
          k]] + (d^(1 - s) k^-s)/(2 (Log[d] + Log[k])) +
      Sum[Sum[-(BernoulliB[2*(n + 1)]/((2*(n + 1))!))*(Abs[
           StirlingS1[2*n + 1, i]]) d k^(-2*n - 1) Gamma[1 + i,
          s Log[k*d]] Log[k*d]^(-1 - i), {i, 0, 2*n + 1}], {n, 0,
        q - 1}])];
integral[a_, b_, d_] = f[b, d] - f[a, d];
Print["Counting to ", nn];
rrr = N[Table[RiemannSiegelTheta[t]/Pi, {t, 0, rr, delta}]];
Monitor[iii =
   Table[Table[
     Re[Sum[integral[1/2 + I*0, 1/2 + I*t, d]/n^c, {d, Divisors[n]}]]/
      Pi, {t, 0, rr, delta}], {n, 1, nn}];, n]
Monitor[Table[
  Export[StringJoin["image", ToString[i], ".gif"],
   Show[Plot[(RiemannSiegelTheta[t] + Im[Log[Zeta[1/2 + I*t]]])/Pi +
      1, {t, 0, 60}, PlotStyle -> {Red, Thickness[0.004]},
     ImageSize -> Large],
    ListLinePlot[rrr - Sum[iii[[j]], {j, 1, i}],
     PlotStyle -> Thickness[0.004], DataRange -> {0, rr},
     ImageSize -> Large],
    Graphics[
     Text[Style["Counting Riemann zeta zeros using", Large], {21,
       12}]], Graphics[
     Text[Style[
       StringJoin[ToString[i],
        " terms of the von Mangoldt function."], Large], {23,
       10}]]]], {i, 1, nn}], i]
(*end*)