  This article considers linear relations between the non-trivial zeroes of the
Riemann zeta-function. The main application is an alternative disproof to
Mertens' conjecture. We show that $\limsup M(x)x^{-1/2} \geq 1.6383$ and that
$\liminf M(x)x^{-1/2}\leq -1.6383$.
