\begin{table}%t1
\caption{\label{tbl:scargle_comp_th_emp}Comparison between errors derived using theoretical formulas with correlation correction (input) and empirically derived estimates of the parameters and errors (estimators).}
%\centering
\small
\begin{tabular}{llllllll}
\hline\hline
Set                    & Type & Frequency $f$                & $\sigma(f)$       & Amplitude $A$             & $\sigma(A)$           & Phase $\phi$                 & $\sigma(\phi)$\\
\hline
Monoperiodic High $S/N$  &estimator& $5.4800000\pm 0.0000004$  & $0.000007$        & $2.0000 \pm 0.0002$       & $0.004$               & $+0.31703 \pm 0.00003$       & $0.0006$            \\
                       &    input& $5.4800000$               & $0.000007$        & $2.0000$                  & $0.004$               & $+0.31700$                   & $0.002$             \\
Monoperiodic Low $S/N$   &estimator& $5.47998  \pm 0.00002$    & $0.0008 $         & $0.2153 \pm 0.0001$       & $0.003$               & $+0.319   \pm 0.002$         & $0.06$              \\
                       &    input& $5.48000$                 & $0.0007$          & $0.0200$                  & $0.004$               & $+0.317$                     & $0.2$               \\
Multiperiodic          &estimator& $5.4868899\pm 0.0000003$  & $0.000007$        & $34~912  \pm 3$            & $66$                  & $-0.03552\pm 0.00003$        & $0.0006$            \\
                       &    input& $5.4868900$               & $0.00001$         & $34~918$                   & $98$                  & $-0.03551$                   & $0.003$             \\
\hline
\end{tabular}
\end{table}