Tautological

Do[
 Print[Show[
   Plot[Re[Zeta[x + I*Im[ZetaZero[n]]]], {x, 1, 0}, PlotStyle -> Red],
   Plot[Im[Zeta[x + I*Im[ZetaZero[n]]]], {x, 1, 0}]]], {n, 1, 12}]

Clear[n]
Do[Clear[x, a, b, c, d];
 b = 10;
 (*Andre LeClaire*)
 c = N[2*Pi*Exp[1]*(n - 11/8)/Exp[1]/LambertW[(n - 11/8)/Exp[1]], 10];
 a = Normal[InverseSeries[Series[(Zeta[1/2 + I*x]), {x, c, b}], x]];
 x = 0;
 d = N[Re[a]];
 Clear[a, x];
 a = Normal[InverseSeries[Series[(Zeta[1/2 + I*x]), {x, d, b}], x]];
 x = 0;
 Print[{N[Re[a]], N[Im[ZetaZero[n]]]}], {n, 1, 20}]

(*intressant 5 1 2014*)
Clear[n]
 Do[
 Clear[x, a, b, c, d];
 b = 20;
 (*c=N[2*Pi*Exp[1]*(n-11/8)/Exp[1]/LambertW[(n-11/8)/Exp[1]],20];*)
 d = N[Im[ZetaZero[n]], 20];
 (*d=c;*)
 Clear[a, x];
 a = Normal[InverseSeries[Series[(2*x*Zeta[x + I*d]), {x, 1, b}], x]];
 x = 0;
 Print[N[Re[a], 20]], {n, 1, 50}]


FindRoot[2*x*Zeta[x + I*Im[ZetaZero[1]]], {x, 1}]


(*intressant 5 1 2014*)
Clear[n]
 Do[
 Clear[x, a, b, c, d];
 b = 20;
 (*c=N[2*Pi*Exp[1]*(n-11/8)/Exp[1]/LambertW[(n-11/8)/Exp[1]],20];*)
 d = N[Im[ZetaZero[n]], 20];
 (*d=c;*)
 Clear[a, x];
 a = Normal[
   InverseSeries[Series[(2*x*Zeta[x + I*d]), {x, 1/2, b}], x]];
 x = 0;
 Print[N[Re[a], 20]], {n, 1, 50}]


(*intressant 5 1 2014*)
Clear[n]
 Do[
 Clear[x, a, b, c, d];
 b = 20;
 (*c=N[2*Pi*Exp[1]*(n-11/8)/Exp[1]/LambertW[(n-11/8)/Exp[1]],20];*)
 d = N[Im[ZetaZero[n]], 20];
 (*d=c;*)
 Clear[a, x];
 a = Normal[InverseSeries[Series[(Zeta[x + I*d]), {x, 0, b}], x]];
 x = 0;
 Print[N[Re[a], 20]], {n, 1, 50}]