\begin{table}%tC.3 \caption{\label{Table: line widths}Line widths in the linear phase for a perturbation corresponding to the Odin beam at a number of redshifts.} %\centering \par \begin{tabular}{ccccccc } \hline \hline \noalign{\smallskip} Redshift & Temp & Size\tablefootmark{a} & Mass\tablefootmark{a} & Fract. width & Line width\tablefootmark{b} & Width at 500~GHz \\ $z$ & $T$ & $L$ & $M$ &$\Delta \nu/\nu$& $\Delta \upsilon_{\rm Linear}$& $\Delta \nu$ \\ &[K] & [kpc] & [$M_\odot$] && [\kms] &[GHz] ]\\ \hline \noalign{\smallskip} 10 & 30 & 540 & 4 $\times$ 10$^{12}$ & 2 $\times$ 10$^{-3}$ & 720 & 1.3 \\ 20 & 57 & 320 & 6~$\times$ 10$^{12}$ & 4~$\times$ 10$^{-3}$ & 1100 & 2.1 \\ 50 & 139 & 150 & 9~$\times$ 10$^{12}$ & 7~$\times$ 10$^{-3}$ &2000 & 3.7 \\ 75 & 207 & 100 & 9~$\times$ 10$^{12}$ & 8~$\times$ 10$^{-3}$ &2500 & 4.5 \\ 100 & 275 & 79 & 1~$\times$ 10$^{13}$ & 1~$\times$ 10$^{-2}$ &2900 & 5.3 \\ 150 & 411 & 54 & 1~$\times$ 10$^{13}$ & 1~$\times$ 10$^{-2}$ &3600 & 6.6 \\ 200 & 547 & 41 & 1~$\times$ 10$^{13}$ & 1~$\times$ 10$^{-2}$ &4200 & 7.7 \\ \hline \end{tabular} \tablefoot {\tablefoottext{a}{For an angular size of the Odin beam, 2$\farcm$1~calculated with Eqs.~(\ref{angular size})$-$(\ref{mass within perturbation});} \tablefoottext{b}{the line width during the linear evolution, Eq.~(\ref{fraction of resolution}).}} \end{table}