Clear[x, n, d, c, numberOfIterations, i, t];
numberOfIterations = 100;
(*Interesting values of c are:c=0,c=1/2,c=1/4,c=3/4*)
(*c=0 gives Gram points*)
(*c=1/2 gives Franca-LeClair points*)
(*c=1/4 gives non-zero self \
intersections:Re[Zeta[1/2+I*t]]=Im[Zeta[1/2+I*t]]*)
(*c=3/4 gives:Re[Zeta[1/2+I*t]]=-Im[Zeta[1/2+I*t]]*)
c = 1/2;
dd = Infinity; (* Let this number dd approach 1 from above. dd = 3 is a \
good first choice. *)
t = Table[x = 1;
  Do[x = N[
      Round[2*Pi*E*
        E^LambertW[((x/(2*Pi))*Log[x/(2*Pi*E)] + 
             Arg[Limit[Zeta[d]/Zeta[1/2 + I*x + d - 1], d -> dd]]/
              Pi - 1/2 + n - 1 - RiemannSiegelTheta[x]/Pi)/E], 
       10^-20], 20];, {i, 1, numberOfIterations}]; x, {n, 1, 40}]
Zeta[1/2 + I*t]
Zeta[1/2 + I*t]*Zeta[dd]/Zeta[1/2 + I*t + dd - 1]