(*Definition:*)
FrancaLeClair[n_] = 2*Pi*Exp[1]*Exp[ProductLog[(n - 11/8)/Exp[1]]];
f = Table[Sign[Im[ZetaZero[n]] - FrancaLeClair[n]], {n, 1, 90}];
Flatten[Position[(1 + f)/2, 0]]
(*Program 1:*)
a = Table[
   Floor[Im[ZetaZero[n]]/(2*Pi)*Log[Im[ZetaZero[n]]/(2*Pi*Exp[1])] + 
     11/8 - n + 1], {n, 1, 90}];
Flatten[Position[a, 0]]
(*Program 2:*)
Flatten[Position[
  Table[(1 - 
      Sign[Im[Zeta[1/2 + I*2*Pi*E*Exp[LambertW[(n - 11/8)/E]]]]])/
    2, {n, 1, 90}]
  , 0]]
(*Program 3:*)
Flatten[Position[
  Table[Floor[
    2*(RiemannSiegelTheta[Im[ZetaZero[n]]]/Pi - 
       Floor[RiemannSiegelTheta[Im[ZetaZero[n]]]/Pi])], {n, 1, 90}]
  , 0]]
(*Program 4:*)
(*For n>1:*)
Flatten[Position[
  Floor[2*FractionalPart[
     N[RiemannSiegelTheta[Im[ZetaZero[Range[90]]]]/Pi, 30]]], 0]]
(*Program 5:*)
Clear[nn, n, k, t, FrancaLeclair, NumberOfZetaZeros];
nn = 90;
FrancaLeclair[n_] = 2*Pi*Exp[1]*Exp[ProductLog[(n - 11/8)/Exp[1]]];
NumberOfZetaZeros[t_] = 
  RiemannSiegelTheta[t]/Pi + Im[Log[Zeta[1/2 + I*t]]]/Pi;
b = N[Table[n - 1 - NumberOfZetaZeros[FrancaLeclair[n]], {n, 1, nn}]];
Flatten[Position[Round[b], 0]]
(*End*)