  In this work we present a determination of the mass, width and coupling of
the resonances that appear in kaon-pion scattering below 1.8 GeV. These are:
the much debated scalar $\kappa$-meson, nowdays known as $K_0^*(800)$, the
scalar $K_0^*(1430)$, the $K^*(892)$ and $K_1^*(1410)$ vectors, the spin-two
$K_2^*(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters will be
determined from the pole associated to each resonance by means of an analytic
continuation of the $K\pi$ scattering amplitudes obtained in a recent and
precise data analysis constrained with dispersion relations, which were not
well satisfied in previous analyses. This analytic continuation will be
performed by means of Pad\'e approximants, thus avoiding a particular model for
the pole parameterization. We also pay particular attention to the evaluation
of uncertainties.
