Where are the zeros of zeta of s?

Tom Apostol's number theory song, which exists in various copies all over the web. It begins:

Where Are The Zeros of zeta of s?
G.F.B. Riemann has made a good guess:
"They're all on the critical line", stated he,
"And their density is one over two pi log T."

This is, of course, the Riemann hypothesis; the rest of the song goes on to give a lot of the history of this problem.

I was reminded of this because I checked out Tom Apostol's book Introduction to Analytic Number Theory; I keep saying that I should learn some analytic number theory and this was recommended to me as a good place to start. About a month ago I wrote about probabilities of relative primality, which was inspired by some things I thought about while reading Mark Dominus' post on a similar topic; Mark gave a picture of a quilt which tabulates the GCD for integers. Apostol's book has a similar picture on the cover.