Result of the joint analysis of the four HLS sources with spectroscopic redshifts derived in Sect. 4.2, using only the 31 GHz NOEMA spectral scans observed in 2018. The first row shows the likelihood from the SED fittings and the joint log-likelihood of photometric and spectroscopic data, using the SED-fitting outputs with the Béthermin et al. (2015a) templates and MMPZ. The comparison of the observed spectra and the model spectra predicted by the IR luminosities from the two SED-fitting results are shown in the second and third row.