\begin{table}%T9
\caption{\label{tab9}Periods and  relative rates of period change 
($\ell= 1$ modes) 
for selected models with~$M_*= 0.85~M_{\odot}$ and 
$M_{\rm He}= 8 \times  10^{-3}~M_*$.}
{{%\centerline
{
\begin{tabular}{c|cc|cc|cc|cc|cc|cc|cc}
\hline
\hline
\multicolumn{1}{c|}{} & 
\multicolumn{2}{c|}{$T_{\rm eff}= 27~968$ K} & 
\multicolumn{2}{c|}{27~040 K} &
\multicolumn{2}{c|}{26~010 K} & 
\multicolumn{2}{c|}{25~003 K} &
\multicolumn{2}{c|}{24~014 K} & 
\multicolumn{2}{c|}{23~038 K} &
\multicolumn{2}{c}{21~960 K}\\
\hline
$k$ &~$P$ [s] &~$\dot{P}/P$ &~$P$ [s] &~$\dot{P}/P$ &~$P$ [s] &~$\dot{P}/P$ 
&~$P$ [s] &~$\dot{P}/P$ &~$P$ [s] &~$\dot{P}/P$ &~$P$ [s] &~$\dot{P}/P$ &~$P$ [s] &~$\dot{P}/P$\\
 1&        110.97&          1.11&        114.43&          0.99&        118.52&          0.87&        122.70&          0.77&        126.95&          0.68&        131.23&          0.60&        136.07&          0.53\\
 2&        138.36&          0.89&        141.68&          0.74&        145.34&          0.61&        148.88&          0.53&        152.39&          0.47&        155.97&          0.43&        160.18&          0.40\\
 3&        157.44&          0.69&        160.61&          0.66&        164.70&          0.65&        169.33&          0.64&        174.42&          0.61&        179.87&          0.57&        186.28&          0.52\\
 4&        197.77&          0.97&        203.09&          0.84&        209.16&          0.71&        215.00&          0.59&        220.48&          0.49&        225.60&          0.41&        231.07&          0.34\\
 5&        218.20&          0.96&        223.92&          0.82&        230.50&          0.72&        237.27&          0.65&        244.43&          0.61&        252.06&          0.58&        261.21&          0.53\\
 6&        250.83&          0.53&        254.69&          0.51&        259.78&          0.52&        265.70&          0.53&        272.30&          0.51&        279.35&          0.48&        287.60&          0.43\\
 7&        272.95&          0.97&        280.58&          0.89&        289.71&          0.79&        298.95&          0.69&        308.06&          0.59&        316.93&          0.51&        326.78&          0.45\\
 8&        305.06&          0.72&        310.74&          0.56&        316.74&          0.46&        322.75&          0.43&        329.28&          0.42&        336.65&          0.43&        346.15&          0.43\\
 9&        343.00&          0.72&        349.43&          0.58&        356.75&          0.52&        364.30&          0.47&        371.99&          0.42&        379.78&          0.38&        389.45&          0.40\\
10&        356.75&          0.90&        366.63&          0.92&        379.39&          0.87&        392.95&          0.78&        406.73&          0.68&        419.94&          0.56&        434.29&          0.50\\
11&        394.17&          0.67&        401.17&          0.55&        408.87&          0.46&        416.67&          0.43&        425.18&          0.43&        435.31&          0.48&        450.50&          0.56\\
12&        425.26&          0.91&        435.47&          0.73&        446.45&          0.60&        457.01&          0.51&        467.35&          0.45&        477.68&          0.41&        492.31&          0.51\\
13&        446.89&          0.67&        456.16&          0.71&        468.92&          0.72&        483.14&          0.68&        497.84&          0.60&        512.53&          0.53&        531.22&          0.57\\
14&        481.73&          0.78&        491.86&          0.65&        502.81&          0.53&        513.53&          0.47&        524.89&          0.46&        537.71&          0.48&        557.25&          0.59\\
15&        507.76&          0.90&        520.29&          0.77&        534.50&          0.66&        548.43&          0.56&        562.03&          0.49&        575.61&          0.45&        596.25&          0.59\\
16&        534.22&          0.72&        545.23&          0.68&        559.60&          0.68&        575.86&          0.66&        593.21&          0.60&        610.84&          0.54&        635.62&          0.65\\
17&        563.02&          0.75&        575.07&          0.69&        589.20&          0.60&        603.37&          0.53&        618.17&          0.50&        634.77&          0.53&        660.20&          0.63\\
18&        599.01&          0.78&        611.48&          0.64&        625.34&          0.55&        639.44&          0.50&        654.11&          0.47&        669.82&          0.47&        696.61&          0.67\\
19&        625.97&          0.92&        641.62&          0.78&        659.54&          0.68&        677.42&          0.59&        694.88&          0.50&        712.38&          0.48&        742.25&          0.70\\
20&        651.11&          0.71&        665.00&          0.72&        683.43&          0.70&        703.55&          0.66&        724.56&          0.60&        746.35&          0.56&        778.67&          0.69\\
21&        684.35&          0.78&        699.15&          0.68&        716.09&          0.59&        733.41&          0.54&        752.23&          0.53&        773.39&          0.55&        807.38&          0.71\\
22&        714.41&          0.84&        730.59&          0.70&        748.78&          0.61&        767.61&          0.56&        787.18&          0.51&        807.93&          0.52&        843.11&          0.71\\
23&        744.68&          0.75&        760.36&          0.68&        780.00&          0.65&        800.68&          0.58&        821.42&          0.51&        843.04&          0.51&        879.78&          0.71\\
24&        775.02&          0.82&        792.77&          0.73&        813.23&          0.62&        833.46&          0.55&        854.48&          0.51&        877.27&          0.52&        916.02&          0.72\\
25&        799.37&          0.88&        819.63&          0.81&        843.63&          0.71&        867.58&          0.61&        890.98&          0.53&        914.71&          0.52&        956.48&          0.75\\
26&        831.80&          0.73&        848.10&          0.62&        868.29&          0.62&        892.12&          0.64&        919.11&          0.62&        948.18&          0.60&        991.63&          0.71\\
27&        869.63&          0.71&        886.65&          0.63&        906.96&          0.56&        927.36&          0.50&        948.68&          0.47&        973.21&          0.53&       1017.88&          0.75\\
28&        896.10&          0.93&        919.68&          0.82&        945.10&          0.63&        968.17&          0.52&        990.78&          0.47&       1014.94&          0.49&       1062.17&          0.77\\
29&        922.59&          0.80&        943.71&          0.74&        970.29&          0.72&        999.84&          0.67&       1028.90&          0.55&       1056.64&          0.52&       1105.71&          0.76\\
30&        955.46&          0.80&        975.90&          0.67&       1000.25&          0.63&       1026.53&          0.59&       1055.53&          0.59&       1088.05&          0.59&       1139.19&          0.74\\
31&        986.08&          0.75&       1007.39&          0.71&       1033.53&          0.63&       1060.00&          0.56&       1087.32&          0.52&       1117.51&          0.56&       1170.46&          0.76\\
\hline
\end{tabular}}}}
\smallskip
Note -- All~$\dot{P}/P$ values are in units of~$10^{-16}$ s$^{-1}$.
\end{table}