  We numerically obtain a class of soliton solutions for Einstein gravity in
$(n+1)$ dimensions coupled to massive abelian gauge fields and with a negative
cosmological constant with Lifshitz asymptotic behaviour. We find that for all
$n\geq3$, a discrete set of magic values for the charge density at the origin
(guaranteeing an asymptotically Lifshitz geometry) exists when the critical
exponent associated with the Lifshitz scaling is $z=2$; moreover, in all cases,
a single magic value is obtained for essentially every $1<z<2$, yet none when
$z>2$ sufficiently.
