First Riemann zeta zero as an integral

(*start*)
(*Mathematica*)
Clear[k, n, s, i, d, r, q, f, a, b, integral, c, nn, n, k];
nn = 1000;
k = 15;
q = 10;
c = 1;
g[s_, d_] = -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}]);
f[s_, d_] = -I*MoebiusMu[d]*(If[d == 1, 0, d^(1 - s)/Log[d]^2] + \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 2\), \(k\)]
\*FractionBox[\(
\*SuperscriptBox[\(d\), \(1 - s\)]\
\*SuperscriptBox[\(n\), \(-s\)]\),
SuperscriptBox[\((Log[d] + Log[n])\), \(2\)]]\) + (-1 +
        s) ExpIntegralEi[-(-1 + s) (Log[d] + Log[k])] + (
     d E^(-s (Log[d] + Log[k])) k)/(Log[d] + Log[k]) - (
     d^(1 - s) k^-s)/(2 (Log[d] + Log[k])^2) +
     Sum[Sum[-(1/(2 (1 + n))!)
        Abs[StirlingS1[1 + 2 n, i]] BernoulliB[
          2 (1 + n)] (-d k^(-1 - 2 n)
             Gamma[2 + i, s Log[d k]] Log[d k]^(-2 - i) +
           d k^(-1 - 2 n)
             s Gamma[1 + i, s Log[d k]] Log[d k]^(-1 - i)), {i, 0,
        2*n + 1}], {n, 0, q - 1}]);
L = N[(Im[ZetaZero[1]] + Im[ZetaZero[2]])/2];
(L - (-I*2*(I*(-((L \[Pi])/2) +
           1/4 ((2 Catalan)/\[Pi] - L^2 Log[\[Pi]] +
              Log[2 Glaisher^9 \[Pi]] -
              4 PolyGamma[-2, 1/4 - (I L)/2] -
              4 PolyGamma[-2, 1/4 + (I L)/2])) -
        Sum[Sum[If[
           Mod[n, d] ==
            0, (f[1/2 + I*L, d] - f[1/2 + I*0, d] -
              I*L*g[1/2 + I*0, d])/n^c, 0], {d, 1, n}], {n, 1, nn}])/
      Pi))/2
(*end*)