# How did Riemann calculate the first few non-trivial zeros of Zeta?

Does anyone know how Riemann calculated the first few non-trivial zeros of the Zeta function? I am wondering if he approximated the integral, $\frac{1}{2 \pi i} \int_{R} \frac{{\xi}^\prime(z)}{\xi (z)} dz$ over appropriate rectangle(s) in the critical strip. This still seems difficult, however, without a computer.

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see store.doverpublications.com/0486417409.html especially reproduction on page 156 and discussion of Riemann's hand calculations from about 155-162 –  Will Jagy Sep 19 '13 at 4:32
Thanks Will. I found your reference very helpful. –  Mustafa Said Sep 19 '13 at 6:04