  Working in two space dimensions, we show that the orientational order
emerging from self-propelled polar particles aligning nematically is
quasi-long-ranged beyond $\ell_{\rm r}$, the scale associated to induced
velocity reversals, which is typically extremely large and often cannot even be
measured. Below $\ell_{\rm r}$, nematic order is long-range. We construct and
study a hydrodynamic theory for this de facto phase and show that its structure
and symmetries differ from conventional descriptions of active nematics. We
check numerically our theoretical predictions, in particular the presence of
$\pi$-symmetric propagative sound modes, and provide estimates of all scaling
exponents governing long-range space-time correlations.
