\begin{table}%t1
\caption{Coefficients for Eq.~(\ref{eq:asymptotic}), for $N=3$~polytropes.}
\label{tab:delta}
%\centering
\small
\begin{tabular}{*{7}{c}}
\hline
\hline
&&&&&& \\[-8pt]
$\frac{\Omega}{\Omega_{K}}$ &
$\frac{\Omega}{\Omega_{\star}}$ &
$\frac{\Delta_n}{\Omega_{\star}}$ &
$\frac{\Delta_\l}{\Omega_{\star}}$ &
$\frac{\Delta_m}{\Omega_{\star}}$ &
$\frac{\alpha^+}{\Omega_{\star}}$ &
$\frac{\alpha^-}{\Omega_{\star}}$ \\
&&&&&& \\[-8pt]
\hline
0.000 &   0.000 &   1.248 &   0.543 &   0.000 &   1.758 &   1.761 \\
0.037 &   0.037 &   1.246 &   0.545 &  --0.007 &   1.757 &   1.764 \\
0.111 &   0.110 &   1.239 &   0.515 &  --0.031 &   1.770 &   1.843 \\
0.186 &   0.181 &   1.234 &   0.395 &  --0.031 &   1.727 &   1.942 \\
0.262 &   0.249 &   1.229 &   0.279 &  --0.036 &   1.680 &   2.006 \\
0.339 &   0.311 &   1.220 &   0.191 &  --0.064 &   1.614 &   2.020 \\
0.419 &   0.368 &   1.194 &   0.189 &  --0.142 &   1.666 &   2.068 \\
0.502 &   0.419 &   1.154 &   0.201 &  --0.182 &   1.661 &   2.036 \\
0.589 &   0.461 &   1.102 &   0.194 &  --0.185 &   1.598 &   1.953 \\
\hline  
0.589 &   0.461 &   1.102 &   0.194 &  --0.185 &   1.587 &   1.943 \\
\hline
\end{tabular}
\end{table}