\begin{table}%t1
      \caption{The periods and the growth rates of the LmSG model.
      \label{table1}}
      $$ \begin{array}{ccccccc} \hline\hline
         & \multicolumn{2}{c}{\mbox{$f=f_{\rm osc}$}} &
         \multicolumn{2}{c}{\mbox{$f=f_{\rm eq}$}} &
         \multicolumn{2}{c}{\mbox{$f=1/3$}}
         \\ \hline
         {\rm Mode} & \mbox{Periods}^{{a}} & 
         \mbox{Growth rates}^{{b}} &
         \mbox{Periods} & \mbox{Growth rates}  &
         \mbox{Periods} & \mbox{Growth rates} \\
         \hline
          0 & 20.3298 & -2.4272 & 24.4097 & -2.0248 & 20.1065 & -2.3242 \\
          1 & 14.0599 & -1.5140 & 14.2388 & -1.3763 & 12.1421 & -1.2191 \\ 
          2 & 8.1076 & -0.9907 & 8.7434 & -0.8230 & 8.2988 & -0.8334 \\
          3 & 3.0924 & 2.6378 &  6.1597 & 0.6374 & 6.7517 & 2.2026 \\
          4 & 6.1649 & -0.8164 & 6.6140 & -1.0804 & 6.1661 & -1.7044 \\
          5 & 5.0212 & -0.3508 & 5.5270 & -0.7063 & 5.6073 & -1.0007 \\
          \hline
        \end{array}  $$ 
\par
        \smallskip
$^{{a}}$  Units of days. $^{{b}}$  $-4 \pi \omega _{\rm I}/\omega _ {\rm R}$.
   \end{table}