  We have performed powder inelastic neutron scattering measurements on the
unconventional superconductor $\beta$-FeSe ($T_{\rm c} \simeq 8\,\mathrm{K}$).
The spectra reveal highly dispersive paramagnetic fluctuations emerging from
the square-lattice wave vector $(\pi,0)$ extending beyond 80 meV in energy.
Measurements as a function of temperature at an energy of $\sim
13\,\mathrm{meV}$ did not show any variation from $T_{\rm c}$ to
$104\,\mathrm{K}$. The results show that FeSe is close to an instability
towards $(\pi,0)$ antiferromagnetism characteristic of the parent phases of the
high-$T_{\rm c}$ iron arsenide superconductors, and that the iron paramagnetic
moment is neither affected by the orthorhombic-to-tetragonal structural
transition at $T_{\rm s} \simeq 90\,\mathrm{K}$ nor does it undergo a change in
spin state over the temperature range studied.
