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 κ-meson, nowadays 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 π 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 Padé approximants, thus avoiding a particular model for the pole parameterization. We also pay particular attention to the evaluation of uncertainties.