\begin{table}%t1
\caption{\label{tab:first_tests}Description of the ``observed'' frequencies and parameters/results from the mode identification scheme.}
%\centerline
 {\small \begin{tabular}{ccccccc}
\hline \hline\noalign{\smallskip}
&
\multicolumn{3}{c}{\dotfill ``Observed'' frequencies \dotfill} &
\multicolumn{3}{c}{\dotfill Mode identification \dotfill} \\
Case &
Type &
$\displaystyle \frac{\delta \omega}{\Delta_{\tilde{n}}}$ &
$\tilde{n}$ &
$\tilde{n}$ &
Average success &
$\displaystyle \frac{\delta \omega}{\Delta_{\tilde{n}}}$ \\
\noalign{\smallskip}\hline\noalign{\smallskip}
1 & Asymptotic &                    0 & 10--25 & 10--25 & 77.4 \% & $3.7 \times 10^{-3}$ \\
2 & Numerical  & $2.4 \times 10^{-2}$ & 15--20 & 10--25 & 17.5 \% & $1.2 \times 10^{-2}$ \\
3 & Random     &         --   &  -- & 10--25 & --& $2.1 \times 10^{-2}$ \\
4 & Numerical  & $2.8 \times 10^{-3}$ & 45--50 & 40--55 & 65.9 \% & $5.4 \times 10^{-3}$ \\
5 & Numerical  & $7.9 \times 10^{-3}$ & 40--55 & 35--60 &  73.9 \% & $7.3 \times 10^{-3}$ \\
\hline
\end{tabular}}
\medskip
Characteristics of the ``observed'' frequency spectra (Cols.~2--4), of
the $\tilde{n}$ values used in the mode identification scheme (Col.~5) and of the results (Cols.~6--7).  The observed frequencies from cases~2, 4 and 5 come from a $25~M_\odot$ model, uniformly rotating at $60\%$ of the critical rotation rate.
%\vspace*{3mm}
\end{table}