Rotation diagrams for sources with detected 7₋₁ → 6₀ − E methanol transition (indicated with an arrow). The shaded red and blue regions represent the uncertainty level at 1 and 3σ, respectively. Methanol lines in the J₋₁ → (J− 1)₀ − E line series, prone to be masers, are in red, thermal lines are in green, and quasi-thermal emission (those out of LTE best fit, positive optical depths and strong presence of a non-LTE component in our models) are in blue. These quasi-thermal transitions correspond to the 7₋₁→6₋₁ − E and 7₀→6₀ − A⁺ transition lines at 338.344588 and 338.408698 GHz, respectively. Only unblended lines were used for the fit. Best fit results (total column densities (N_tot) and excitation temperatures (T_ex) plus 1σ uncertainties) are labeled in the bottom left corner of each subplot. Transitions detected in each source are listed in Table B.1.