  We compute dispersion relations of non-hydrodynamic and hydrodynamic modes in
a non-relativistic strongly coupled two-dimensional quantum field theory. This
is achieved by numerically computing quasinormal modes (QNMs) of a particular
analytically known black brane solution to 3+1-dimensional Ho\v{r}ava Gravity.
Ho\v{r}ava Gravity is distinguished from Einstein Gravity by the presence of a
scalar field, termed the khronon, defining a preferred time-foliation.
Surprisingly, for this black brane solution, the khronon fluctuation
numerically decouples from all others, having its own set of purely imaginary
eigenfrequencies, for which we provide an analytic expression. All other
Ho\v{r}ava Gravity QNMs are expressed analytically in terms of QNMs of Einstein
Gravity, in units involving the khronon coupling constants and various
horizons. Our numerical computation reproduces the analytically known momentum
diffusion mode, and extends the analytic expression for the sound modes to a
wide range of khronon coupling values. In the eikonal limit (large momentum
limit), the analytically known dispersion of QNM frequencies with the momentum
is reproduced by our numerics. We provide a parametrization of all QNM
frequencies to fourth order in the momentum. We demonstrate perturbative
stability in a wide range of coupling constants and momenta.
