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

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).
The method he used was the expansion that is now called the Riemann-Siegel formula. I did not see any use, e.g., of an approach based on Euler-Maclaurin. The limited accuracy Riemann obtained reflects that of the error term in the R-S formula.

"Know" is hard for those of us without a ouija board, but I think people believe that the Riemann-Siegel formula was used.