ALMA Band 3 polarimetric follow-up of a complete sample of faint PACO sources.

We present Atacama Large Millimeter/submillimiter Array (ALMA) high sensitivity ($\sigma_P \simeq 0.4\,$mJy) polarimetric observations at $97.5\,$GHz (Band 3) of a complete sample of $32$ extragalactic radio sources drawn from the faint Planck-ATCA Co-eval Observations (PACO) sample ($b<-75^\circ$, compact sources brighter than $200\,$mJy at $20\,$GHz). We achieved a detection rate of $~97\%$ at $3\,\sigma$ (only $1$ non-detection). We complement these observations with new Australia Telescope Compact Array (ATCA) data between $2.1$ and $35\,$GHz obtained within a few months and with data published in earlier papers from our collaboration. Adding the co-eval GaLactic and Extragalactic All-sky Murchison widefield array (GLEAM) survey detections between $70\,$ and $230\,$MHz for our sources, we present spectra over more than $3$ decades in frequency in total intensity and over about $1.7$ decades in polarization. The spectra of our sources are smooth over the whole frequency range, with no sign of dust emission from the host galaxy at mm wavelengths nor of a sharp high frequency decline due, for example, to electron ageing. We do however find indications of multiple emitting components and present a classification based on the number of detected components. We analyze the polarization fraction behaviour and distributions up to $97\,$GHz for different source classes. Source counts in polarization are presented at $95\,$GHz.