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\noindent 
{\bf Table 9.} Fundamental Nonlinear Survey for $M=0.75M_{\odot}$ \\

\noindent 
\begin{tabular}{ccccccccccc}  \hline

  Model &  $T_e$ & NP &  Period &  $\Delta R/R_{ph}$ &  $\Delta u$ &  $\Delta M_{bol}$ &  $\Delta {\log{g_s}}$ &  $\Delta {\log{g_{eff}}}$ &  $\Delta T$ &  $\Delta T_{e}$   \\
    Number & ($^\circ${\em K}) &  &  ({\em days}) &   &  ({\em km/sec})& ({\em mag.})  &   &   &  ($^\circ${\em K})&  ($^\circ${\em K}) \\
\hline
 & & & & & & & & & & \vspace*{-2.0mm}\\
  \multicolumn{11}{c}{$log L / L_{\odot} = 1.91$} \vspace*{-2.0mm}\\
 & & & & & & & & & & \\ 
1.30 (--)   &7100&  1600& .5906&   .001&  .46&   .011&    .00&  .00&  0&  0 \\  
1.33 (+)  &7000&  3000& .6204&   .195&  117.76&   1.742&  .07& 1.95&  2650&  3300 \\
1.36 (+)  &6900&  1250& .6520&   .197&  119.56&  1.720&  .17& 1.86&  2600&  3200 \\
1.40 (+)   &6800&   1000& .6862&   .190&  123.53&  1.609&  .17& 1.88&  2350&  2900 \\
1.53 (+)  &6400&   1000& .8478&   .184&   92.92&  0.894&  .16& 1.58&  1050&  1300 \\
1.66 (+)  &6000&  1000& 1.0629&   .110&   60.48&  .269&   .10&  .90&   450&   550 \\
1.70 (+)   &5900&  2000& 1.1255&   .077&   36.19&  .184&   .07&  .52&   300&   350 \\
1.73 (+)  &5800&  6000& 1.1883&   .021&    8.47&   .037&   .01&  .09&    50&   100 \\
1.76 (--)  &5700&  2000& 0.8224&   .000&     .00&   .000&   .00&  .04&     0&     0 \\
 & & & & & & & & & & \vspace*{-2.0mm}\\
  \multicolumn{11}{c}{$log L / L_{\odot} = 1.81$} \vspace*{-2.0mm}\\
 & & & & & & & & & & \\ 
2.33 ($\ast$)  &7000&  9000&  .3839&   .070& 66.29&   .692&    .06&  .87&  1000&  1250 \\
2.36 (+)  &6900&   1000&  .5394&   .181& 131.88&  1.655&   .16&  1.76& 2600&  3150 \\
2.40 (+)   &6800&   1000&  .5673&   .187& 131.50&  1.556&   .17&  1.71& 2350&  2950 \\
2.43 (+)  &6700&   600&   .5971&   .198& 132.02&  1.393&   .17&  1.63& 2100&  2600 \\
2.53 (+)  &6400&   400&   .7093&   .191& 95.50&   .834&    .17&  1.43& 1200&  1450 \\
2.63 (+)  &6100&   1000&   .8257&   .144& 70.09&   .450&    .13&  1.14&  600&   750 \\
2.70 (+)   &5900&   7000&   .9233&   .035& 14.74&   .064&    .03&  .16&   100&   150 \\
2.73 (--)  &5800&   2000&  .0060&   .000&  .00&    .000&    .00&  .00&     0&     0 \\
 & & & & & & & & & & \vspace*{-2.0mm}\\
  \multicolumn{11}{c}{$log L / L_{\odot} = 1.72$} \vspace*{-2.0mm}\\
 & & & & & & & & & & \\ 
3.33 ($\ast$) &7000&   3000&  .3259&  .095&   77.14&  1.008&  .08&   1.28&  1450&  1800 \\
3.36 (+) &6900&   2000&  .4542&  .158&  132.67&  1.607&  .14&   1.78&  2450&  3000 \\
3.40 (+) &6800&   2000&   .4776&   .168&  131.92&  1.469&  .15&   1.66&  2200&  2700 \\
3.53 (+) &6400&   1000&  .5880&   .194&  107.41&  .753&   .17&   1.52&  1200&  1500 \\
3.60 (+) &6200&   1000&   .6550&   .172&   91.17&  .559&   .16&   1.41&   900&  1100 \\
3.66 (+) &6000&  7000&   .7321&   .065&   29.61&  .137&   .06&   .34&    300&   300 \\
3.70 (--)  &5900&  2000&  .7713&   .000&    .09&   .000&   .00&   .03&      0&     0  \\
 & & & & & & & & & & \vspace*{-2.0mm}\\
  \multicolumn{11}{c}{$log L / L_{\odot} = 1.61$} \vspace*{-2.0mm}\\
 & & & & & & & & & & \\ 
35.26 ($\ast$)  &7200&   3200&  .2437&   .095& 94.06&   1.272&   .08&  1.34&  2500&  2500
\\
35.30 (+)  &7100&   2600&  .3346&   .091& 80.52&   .8750&   .08&  1.13&  1250&  1500
\\
35.33 (\#)  &7000&   10500&  .3509&   .089& 68.77&   .720&   .08&  1.11&  850&  1100
\\
35.36 ($\ast$)  &6900&   4000&  .2792&   .101& 96.38&   .913&   .09&  1.33&  1300& 1600 \\
35.40 ($\ast$)   &6800&   2000&  .2926&   .100& 93.22&   .741&   .09&  1.36&  1000& 1250 \\
35.43 ($\ast$)  &6700&   3000& .3100&   .096& 79.91&   .546&   .08&  1.16&   750&  900  \\
35.46 (+)  &6600&   2500&  .4279&   .155&  114.88&  .867&   .14&  1.38&  1150& 1400 \\  
35.56 (+)  &6300&   1600&  .5010&   .156& 92.90&   .593&   .13&  1.25&   950& 1150 \\
35.60 (+)  &6200&    2000& .5289&   .148& 83.48&   .423&   .13& 1.08&    700&  900 \\
35.63 (+) &6100&    12300& .5587&   .057& 28.66&   .124&   .05&  .31&    250&  350 \\
35.66 (--)  &6000&   2000& .5889&   .0006&  .298&   .001&  .00&  .02&    0&  0  \\
\hline
\end{tabular}
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