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Riemann zeta function for nonnegative even integers. The Riemann zeta function for negative even integers is 0 (those are the trivial zeros of the Riemann zeta function). The Riemann zeta function for nonnegative even integers is given by (note that is the only rational number for nonnegative even integers) where are the Bernoulli numbers.
Hardy proved in 1915 that an infinite number of the zeros do occur on the critical line and in 1989 Conrey showed that over 40% of the zeros in the critical strip are on the critical line [ Conrey89 ]. However, there is still a chance that the Riemann hypothesis is false. From August of 2001 through 2005, Sebastian Wedeniwski ran ZetaGrid which verified that the first 100 billion zeros were on the critical line.