\begin{table}%t3
\par
\caption{The field recognition for M~31.} \label{tab:m31r}
\small%\centerline
{
\begin{tabular}{ccccccc}
 \hline \hline\noalign{\smallskip}
  $N$  & temp. & $p'$ & $q'$ & $\phi_0'$ & $B'$ & $\chi^2$  \\ 
  \hline
  & {ASS} & {--8~$\pm$~31} & -- & -- & {0.4~$\pm$~0.2} & {5.3~$\pm$~1.2} \\
  & {BSS} & {12~$\pm$~16} & -- & {46~$\pm$~121} & {2.2~$\pm$~2.6} & {5.0~$\pm$~1.1} \\
 22 & {QSS} & {3~$\pm$~45} & -- & {--10~$\pm$~53} & {1.7~$\pm$~2.1} & {5.0~$\pm$~1.2} \\
  & {A+B} & {6~$\pm$~16} & {0.1~$\pm$~0.1} & {--51~$\pm$~115} & {2.7~$\pm$~1.9} & {5.7~$\pm$~1.4} \\
  & {A+Q} & {44~$\pm$~34} & {0.3~$\pm$~0.1} & {--39~$\pm$~38} & {2.6~$\pm$~1.7} & {5.1~$\pm$~1.2} \\
 \hline
  & {ASS} & {--16~$\pm$~22} & -- & -- & {0.4~$\pm$~0.2} & {4.6~$\pm$~1.2} \\
  & {BSS} & {1~$\pm$~21} & -- & {85~$\pm$~92} & {3.7~$\pm$~3.6} & {5.8~$\pm$~1.3} \\
 20 & {QSS} & {9~$\pm$~36} & -- & {--12~$\pm$~52} & {2.4~$\pm$~2.7} & {5.1~$\pm$~1.2} \\
  & {A+B} & {--17~$\pm$~17} & {0.4~$\pm$~0.2} & {34~$\pm$~89} & {2.~$\pm$~1.5} & {6.3~$\pm$~1.7} \\
  & {A+Q} & {8~$\pm$~32} & {0.2~$\pm$~0.2} & {--28~$\pm$~50} & {2.8~$\pm$~2.1} & {6.4~$\pm$~1.6} \\
  \hline
  & {ASS} & {--3~$\pm$~17} & -- & -- & {0.5~$\pm$~0.2} & {\bf  2.8~$\pm$~0.9} \\
  & {BSS} & {8~$\pm$~15} & -- & {17~$\pm$~120} & {2.8~$\pm$~2.4} & {3.3~$\pm$~1.2} \\
 {$\tilde{20}$} & {QSS} & {28~$\pm$~39} & -- & {--12~$\pm$~42} & {2.6~$\pm$~3.1} & {3.3~$\pm$~1.1} \\
  & {A+B} & {3~$\pm$~19} & {0.3~$\pm$~0.2} & {9~$\pm$~114} & {3.1~$\pm$~2.3} & {3.8~$\pm$~1.4} \\
  & {A+Q} & {19~$\pm$~34} & {0.3~$\pm$~0.1} & {--21~$\pm$~49} & {3.6~$\pm$~2.1} & {3.7~$\pm$~1.2}
 \\ \hline
\end{tabular}}
\smallskip
{Parameters of fitted pitch angles $p'$, field amplitudes $B'$,
azimuthal phases $\phi_0'$, amplitude ratios $q'$ (in case of a
superposition), and $\chi^2$ of the best fit, using 22 and 20 $\RM$
values observed in the M~31 regime by \cite{han98}. For 22 and 20~values (8 and 6.5 effective points), models with $\chi^2>2.7$ and
$\chi^2>3.1$, respectively, are rejected at the 98\% significance
level.}
\end{table}