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

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.

In searching through the Riemann Nachlass in Gottingen (including those folders not listed as connected with $$\zeta(s))$$ there is no evidence -- at least that has been saved -- that Riemann computed anything more than the first few zeros (I think up to ordinate about 80).