Riemann zeta zero experimenting, four decimals in common

Mathematica 8:
Times @@ Exp[2*Pi/N[Im[ZetaZero[Range[8]]], 30]]^-1
Exp[2*Pi/N[Im[ZetaZero[8]], 30]]

Which outputs:
0.156038475339216033023505727944
1.156059840031155475145914537558

Where we see four decimals in common.

Or comparing several cases:
Do[
Print[Times @@ Exp[2*Pi/N[Im[ZetaZero[Range[i]]], 30]]^-1]
Print[Exp[2*Pi/N[Im[ZetaZero[i]], 30]]], {i, 1, 32}]

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