  Using first-principles calculation within Quantum Chromodynamics, we are able
to determine a pattern of strangeness=1 resonances which appear as complex
singularities within coupled $\pi K$, $\eta K$ scattering amplitudes. We make
use of numerical computation in the lattice discretized approach to the quantum
field theory with light quark masses corresponding to $m_\pi \sim 400\,
\textrm{MeV}$ and at a single lattice spacing. The energy dependence of
scattering amplitudes is extracted through their relationship to the discrete
spectrum in a finite-volume, which we map out in unprecedented detail.
