Riemann zeta zeros 9 digits in common

Mathematica 8:

Clear[a, b, c]
a = Sin[N[Im[ZetaZero[1]], 30]]
b = 7 + Times @@ Exp[2*Pi/N[Im[ZetaZero[Range[8]]], 30]]^-1;
c = 6 + Exp[2*Pi/N[Im[ZetaZero[8]], 30]];
b/c

Output:

0.9999970188092790189088067450271
0.9999970144615309213084306406440

Which has 9 digits in common

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