  The motion in the complex plane of the zeros to various zeta functions is
investigated numerically. First the Hurwitz zeta function is considered and an
accurate formula for the distribution of its zeros is suggested. Then functions
which are linear combinations of different Hurwitz zeta functions, and have a
symmetric distribution of their zeros with respect to the critical line, are
examined. Finally the existence of the hypothetical non-trivial Riemann zeros
with $Re(s)\neq 1/2$ is discussed.
