Spatially integrated rest-frame spectra around the emission lines of interest. The bottom and top x-axes show the rest-frame wavelength and frequency ranges for the Paα and CO(1–0) emission lines, respectively. For each galaxy, the solid green curve shows the CO(1–0) spectrum convoluted by the SINFONI LSF. From HATLAS090750, we also detect the Br_δ, H₂(1–0)S(3), H₂(1–0)S(2), H₂(1–0)S(1), and He I near-IR emission lines using as an aperture an encircled zone given by the PSF FWHM and centred at the Paα luminosity peak. In the case of the HATLAS114625 galaxy observation, we also detect the H₂(1–0)S(3) emission. These detections are shown in the sub-plots (blue-shaded area) in each panel (see also Appendix C). The CO(1–0) and Paα emission lines are clearly detected.