\begin{table}%t1
\caption{\label{table: pq_coeff}Numerical values of the coefficients used to regularize $g$ as a function of $n$ for the Vesta family ($s$-intervals between $-$42.89 and $-$45.00$''$/yr, and between $-$45.00 and $-$47.64$''$/yr).}
\par
%\centering
\small
\begin{tabular}{ccc}
\hline \hline
  Coefficient & Vesta                       & Vesta                 \\
              & $-42.89 < s < -45.00$ $''$/yr & $-45.00 < s < -47.64$ \\
\hline
 $p(1)$ [$\rm ''/degrees$] & --0.4073              &     --0.4624           \\
 $p(2)$ [$\rm ''/yr$] &      79.2635              &     83.7082           \\
 $q(1)$ [$\rm ''{yr}^2/{degrees}^3$] & --26.1652   &     --7.1026           \\
 $q(2)$ [$\rm '' yr/{degrees}^2$] & 7.2563 $\times$ $10^3$ & 1.9738 $\times$ $10^3$\\
 $q(3)$ [$\rm ''/degrees$] & --6.7080 $\times$ $10^5$  & --1.8284 $\times$ $10^5$   \\
 $q(4)$ [$\rm ''/yr$] & 2.0670 $\times$ $10^6$        &  5.6457 $\times$ $10^6$  \\
\hline
\end{tabular}
\end{table}