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Zeros of the Zeta Function
Mathematica 6 can efficiently find zeros of the zeta function on the critical line.
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Click for copyable input
Plot[Im[Zeta[1/2 + I t]], {t, 0, 80}, 

 Epilog -> {PointSize[.02], Red, 

   Point[Table[{Im[ZetaZero[n]], 0}, {n, 20}]]}]
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