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# Tables of zeros of the Riemann-Zeta function

`sage.databases.odlyzko.``zeta_zeros`()

  List of the imaginary parts of the first 100,000 nontrivial zeros of the Riemann zeta function. Andrew Odlyzko computed these to precision within \(3\cdot 10^{-9}\).

  In order to use `zeta_zeros()`, you will need to install the optional Odlyzko database package: `sage -i database_odlyzko_zeta`. You can see a list of all available optional packages with `sage --optional`.

  REFERENCES:

  - http://www.dtc.umn.edu/~odlyzko/zeta_tables/

  EXAMPLES:

  The following example prints the imaginary part of the 13th nontrivial zero of the Riemann zeta function. Note that only the first 9 digits after the decimal come from the database. Subsequent digits are the result of the inherent imprecision of a binary representation of decimal numbers.

      sage: zz = zeta_zeros() # optional - database_odlyzko_zeta
      sage: zz[12]            # optional - database_odlyzko_zeta
      59.347044003...

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