  In this work, we present a precise and model--independent method to extract
resonance pole parameters from phase-shift scattering data. These parameters
are defined from the associated poles in the second Riemann sheet, unfolded by
the analytic continuation to the complex pole using Pad\'e approximants.
Precise theoretical parameterizations of pion-pion scattering phase shifts
based on once-- and twice-- subtracted dispersion relations are used as input,
whose functional form allows us to show the benefit and accuracy of the method.
In particular, we extract from these parametrization the pole positions of the
$f_0(500)$ at $\sqrt{s}=(453\pm 15) - i(297 \pm 15)$ MeV, the $\rho(770)$ at
$\sqrt{s}=(761.4\pm 1.2)-i(71.8 \pm 1.0)$ MeV, and the pole of the $f_2(1270)$,
located at $\sqrt{s}=(1267.3\pm 1.7)-i(95.0\pm 2.3)$ MeV. The couplings of the
resonances to two pions are also determined with high precision, obtaining
respectively, $3.8\pm 0.4$ GeV, $5.92\pm 0.15$ and $4.41\pm 0.23$ GeV$^{-1}$.
Special attention is dedicated to the systematic treatment of the theoretical
and statistical uncertainties, together with their comparison with previous
determinations.
