Pi starts out...............3.1415.................3 fives add up to 15..........the 1st zero.............the imaginary part is between 14 and 15.................14 is also half of 28..........the 2nd perfect number..............1 and 2.................like 1/2..................???????????
The above plot shows for between 0 and 60. As can be seen, the first few nontrivial zeros occur at the values given in the following table (Wagon 1991, pp. 361-362 and 367-368; Havil 2003, p. 196; Odlyzko), where the corresponding negative values are also roots. The integers closest to these values are 14, 21, 25, 30, 33, 38, 41, 43, 48, 50, ... (OEIS A002410). The numbers of nontrivial zeros less than 10, , , ... are 0, 29, 649, 10142, 138069, 1747146, ... (OEIS A072080; Odlyzko).
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