  We provide global parameterizations of $\pi\pi$ scattering $S0$ and $P$
partial waves up to roughly 2 GeV for phenomenological use. These
parameterizations describe the output and uncertainties of previous
partial-wave dispersive analyses of $\pi\pi$, both in the real axis up to 1.12
GeV and in the complex plane within their applicability region, while also
fulfilling forward dispersion relations up to 1.43 GeV. Above that energy we
just describe the available experimental data. Moreover, the analytic
continuations of these global parameterizations also describe accurately the
dispersive determinations of the $\sigma/f_0(500)$, $f_0(980)$ and $\rho(770)$
pole parameters.
