Experiments with zeta zeros and Perrons formula

Of what use are the zeros of the Riemann zeta function? We can use sums involving zeta zeros to count the primes up to $x$. Perrons formula leads to sums over zeta zeros that can count the squarefree integers up to $x$, or tally Eulers $phi$ function and other arithmetical functions. This is largely a presentation of experimental results.