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Today we know that the first 10 trillion zeros of ζ(s) are all on the critical line and that at least 41% of all of the complex zeros are on the critical line. Source.

I tried searching, the best I could find is something like

1/2 + 23453567232...i (note I made the number up just for this example)

If someone wants to see a list of exact numbers, where can he find something like that?

And what kind of computer calculators available for the public are capable of crunching those big numbers? Is Wolfram Alpha capable of that? If I write a python program and run it on my pc, will it be precise enough?

mvw
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Lynob
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  • I don't think we can express the exact numbers other than saying they're a nontrivial zero of the zeta function (and some blabbering around it to show which one you mean). –  Apr 02 '17 at 18:43
  • @vrugtehagel so it can't be computed? – Lynob Apr 02 '17 at 18:52
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    It can be computed to arbitrary precision, but you can't get all of the digits because there are infinitely many, and there's unlikely to be a simple way to describe them (they won't repeat, for example). – Matt Samuel Apr 02 '17 at 19:01
  • See this, we can only compute an approximation of the imaginary part of the zeros of $\zeta(s)$ on the critical line. – reuns Apr 03 '17 at 22:48
  • http://oeis.org/A058303 gives the digits to the right of the decimal point in the imaginary part of the first nontrivial zero. http://oeis.org/A002410 gives the imaginary parts (rounded) of a lot of the nontrivial zeroes. – Jonathan Apr 10 '17 at 23:05

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