Generalized Dirichlet generating function for the Riemann zeta zero spectrum

(*start*)
Clear[nn, s, c, z, x];
nn = 60;
s = 8;
c = 9;
z = N[ZetaZero[1], 20];
x = N[ZetaZero[-1], 20];

Table[Limit[
  Zeta[ss] Total[1/Divisors[n]^(ss - z - x)*MoebiusMu[Divisors[n]]]/
    n^c, ss -> s], {n, 1, nn}]

A = Table[
   Table[If[Mod[n, k] == 0, MoebiusMu[k]*k^z/n^s, 0], {k, 1, nn}], {n,
     1, nn}];
B = Table[
   Table[If[Mod[k, n] == 0, n^x/k^c, 0], {k, 1, nn}], {n, 1, nn}];

MatrixForm[T = A.B];

"Double sum:"
Sum[Sum[N[T, 20][[n, k]], {k, 1, nn}], {n, 1, nn}]

"Generating function for the double sum:"
N[Zeta[s]*Zeta[c]/Zeta[s + c - z - x], 20]

Plot[Re[Zeta[1/2 + I*t]*
   Zeta[1 + 1/1000]/Zeta[1/2 + I*t + 1 + 1/1000 - z - x]], {t, 0, 60}]
(*end*)

(*start Feb 12 2022*)
Clear[s, c];
Limit[Zeta[s]*Zeta[c]/Zeta[s + c - 1] - Zeta[c], c -> 1]
Limit[Zeta[s - 1]*Zeta[c]/Zeta[s + c - 2] - Zeta[c], c -> 1]
(*end*)