John Derbyshire in his book PRIME OBSESSION in page 344 in secondary term in column totals at the end says that: The periodic terms to find π(1000000) are equals -29.37378... How many zeta zeros needed to find it?

John Derbyshire in his book PRIME OBSESSION says on page 343:

"I’ll round off with a complete calculation of $\pi(1,000,000)$, the number of primes up to one million, using Riemann’s formula -- not for the fun of it, though it is of course great fun, but to make some important points about the error term."

He finds that secondary terms contribute an error of -29.37378.
My question: How many zeta zeros are needed to find it?