\begin{table}%tB.1
\caption{Non-linear fitting coefficients for the non-resonant $n{\rm
s}\rightarrow 1{\rm s}$ emission spectra within the frequency range
$10^{-3}\leq y\leq 0.999$ for $n\leq 20$.}
\label{tab:two}
%\centering
\small
\begin{tabular}{lrrrrr}
\hline
\hline
 & 2s  & 3s  & 4s  & 5s  & 6s 
 \\ 
 \hline 
 $a_0$ & $\pot{-1.3974426528}{1}$ & $\pot{-2.0848318929}{1}$ & $\pot{-2.5412664413}{1}$ & $\pot{-2.8856705303}{1}$ & $\pot{-3.1567507558}{1}$ 
 \\ 
 $\beta$ & $\pot{2.5591291935}{-1}$ & $\pot{5.5198239644}{-1}$ & $\pot{8.0397418838}{-1}$ & $\pot{4.8110524091}{-1}$ & $\pot{2.5266888083}{-1}$ 
 \\ 
 $b_0$ & $\pot{6.6487585307}{0}$ & $\pot{4.6179953215}{2}$ & $\pot{7.6795669026}{2}$ & $\pot{8.3598144011}{2}$ & $\pot{5.6902488765}{2}$ 
 \\ 
 $b_1$ & $\pot{-5.1211954644}{1}$ & $\pot{-9.8891531378}{1}$ & $\pot{-4.2588083735}{2}$ & $\pot{5.1404483119}{1}$ & $\pot{4.5519082179}{1}$ 
 \\ 
 $b_2$ & $\pot{3.4686628383}{1}$ & $\pot{1.0769127960}{2}$ & $\pot{7.0510361599}{2}$ & $\pot{-7.2853184204}{1}$ & $\pot{-6.7551149725}{1}$ 
 \\ 
 $b_3$ & $\pot{3.8515432953}{1}$ & $\pot{6.1301937755}{1}$ & $\pot{-3.6120946105}{1}$ & $\pot{-4.9378611706}{1}$ & $\pot{-3.8327617310}{1}$ 
 \\ 
 $b_4$ & $\pot{6.7503966084}{0}$ & $\pot{-4.1466090643}{1}$ & $\pot{-4.4049919721}{2}$ & $\pot{4.7383284338}{1}$ & $\pot{4.4401360958}{1}$ 
 \\ 
 $b_5$ & $\pot{-3.1431622488}{1}$ & $\pot{-8.4016250015}{1}$ & $\pot{2.4657329140}{2}$ & $\pot{9.9191282175}{1}$ & $\pot{7.4195208626}{1}$ 
 \\ 
 $b_6$ & $\pot{-1.3697636757}{1}$ & $\pot{7.1191755771}{1}$ & $\pot{-6.5900037717}{1}$ & $\pot{-1.0379836854}{2}$ & $\pot{-7.9312304169}{1}$ 
 \\ 
 $b_7$ & $\pot{2.4016413274}{1}$ & $\pot{-1.8695504961}{1}$ & $\pot{1.8226732411}{1}$ & $\pot{2.9602921680}{1}$ & $\pot{2.1866188936}{1}$ 
 \\ 
 $b_8$ & $\pot{-9.5149995633}{0}$ & $\pot{2.2794449683}{0}$ & $\pot{-2.8692508508}{0}$ & $\pot{-2.8636914451}{0}$ & $\pot{-1.9806370670}{0}$ 
 \\ 
 $b_9$ & $\pot{2.6555412799}{0}$ & $\pot{-4.3875761781}{-1}$ & $\pot{4.4042663362}{-1}$ & $\pot{3.8579054257}{-1}$ & $\pot{2.6143991878}{-1}$ 
 \\ 
 $\phi^{\rm nr}(1/2)$ & $\pot{2.1303295046}{1}$ & $\pot{2.5955835234}{1}$ & $\pot{3.0008781647}{1}$ & $\pot{3.5729374807}{1}$ & $\pot{4.2778194752}{1}$ 
\\
%\end{tabular} 
%\begin{tabular}{lrrrrr}
%\hline
 & 7s  & 8s  & 9s  & 10s  & 11s 
 \\ 
 \hline 
  $a_0$ & $\pot{-3.3720076517}{1}$ & $\pot{-3.5420358274}{1}$ & $\pot{-3.6749872667}{1}$ & $\pot{-3.7779791307}{1}$ & $\pot{-3.8573952826}{1}$ 
 \\ 
 $\beta$ & $\pot{8.5151589950}{-2}$ & $\pot{-4.2719713121}{-2}$ & $\pot{-1.3118006971}{-1}$ & $\pot{-2.1932912263}{-1}$ & $\pot{-2.9226372396}{-1}$ 
 \\ 
 $b_0$ & $\pot{3.7656038819}{2}$ & $\pot{2.7408956380}{2}$ & $\pot{2.8136510570}{2}$ & $\pot{1.5264948382}{2}$ & $\pot{8.6437136666}{1}$ 
 \\ 
 $b_1$ & $\pot{2.7980511952}{1}$ & $\pot{7.4703207553}{0}$ & $\pot{-1.8981579892}{1}$ & $\pot{-1.9235840320}{1}$ & $\pot{-1.9681933480}{1}$ 
 \\ 
 $b_2$ & $\pot{-4.9359948916}{1}$ & $\pot{-2.6259765669}{1}$ & $\pot{6.6356770418}{0}$ & $\pot{7.1592304894}{0}$ & $\pot{7.8432338862}{0}$ 
 \\ 
 $b_3$ & $\pot{-2.0507457345}{1}$ & $\pot{-3.3913231244}{0}$ & $\pot{1.3837014244}{1}$ & $\pot{1.3979846789}{1}$ & $\pot{1.4343371719}{1}$ 
 \\ 
 $b_4$ & $\pot{3.6291414100}{1}$ & $\pot{2.5464049259}{1}$ & $\pot{7.8618686503}{0}$ & $\pot{7.3730033289}{0}$ & $\pot{6.8679571684}{0}$ 
 \\ 
 $b_5$ & $\pot{4.3713955958}{1}$ & $\pot{1.6166653183}{1}$ & $\pot{-8.0358407914}{0}$ & $\pot{-8.6532015972}{0}$ & $\pot{-9.6695240617}{0}$ 
 \\ 
 $b_6$ & $\pot{-5.2721158916}{1}$ & $\pot{-2.8335792233}{1}$ & $\pot{-4.8006902023}{0}$ & $\pot{-3.6779369765}{0}$ & $\pot{-2.2948815920}{0}$ 
 \\ 
 $b_7$ & $\pot{1.4831730999}{1}$ & $\pot{8.6649789093}{0}$ & $\pot{2.8424870765}{0}$ & $\pot{2.4362978935}{0}$ & $\pot{2.0390764869}{0}$ 
 \\ 
 $b_8$ & $\pot{-1.3230829528}{0}$ & $\pot{-7.9156543417}{-1}$ & $\pot{-3.2207517000}{-1}$ & $\pot{-2.7645228408}{-1}$ & $\pot{-2.3641043114}{-1}$ 
 \\ 
 $b_9$ & $\pot{1.7474071394}{-1}$ & $\pot{1.0596166967}{-1}$ & $\pot{4.6227764509}{-2}$ & $\pot{3.9732841793}{-2}$ & $\pot{3.4157538873}{-2}$ 
 \\ 
 $\phi^{\rm nr}(1/2)$ & $\pot{5.0793294231}{1}$ & $\pot{5.9525977879}{1}$ & $\pot{6.8805689403}{1}$ & $\pot{7.8512293219}{1}$ & $\pot{8.8558644431}{1}$ 
\\[1mm]
%\end{tabular} 
%\begin{tabular}{lrrrrr}
%\hline
 & 12s  & 13s  & 14s  & 15s  & 16s 
 \\ 
 \hline 
 $a_0$ & $\pot{-3.9188326323}{1}$ & $\pot{-3.9670102478}{1}$ & $\pot{-4.0057506143}{1}$ & $\pot{-4.0380409686}{1}$ & $\pot{-4.0661454371}{1}$ 
 \\ 
 $\beta$ & $\pot{-3.5484078761}{-1}$ & $\pot{-4.0844617686}{-1}$ & $\pot{-4.5428570381}{-1}$ & $\pot{-4.6335483910}{-1}$ & $\pot{-4.9050805652}{-1}$ 
 \\ 
 $b_0$ & $\pot{4.9431541043}{1}$ & $\pot{2.9197464029}{1}$ & $\pot{1.7971514946}{1}$ & $\pot{1.5982980641}{1}$ & $\pot{1.1724743879}{1}$ 
 \\ 
 $b_1$ & $\pot{-1.9750664049}{1}$ & $\pot{-1.9723076238}{1}$ & $\pot{-1.9651279272}{1}$ & $\pot{-2.0606406024}{1}$ & $\pot{-2.1081283167}{1}$ 
 \\ 
 $b_2$ & $\pot{8.1838767684}{0}$ & $\pot{8.3673624537}{0}$ & $\pot{8.4788048970}{0}$ & $\pot{9.3338234414}{0}$ & $\pot{9.8388495127}{0}$ 
 \\ 
 $b_3$ & $\pot{1.4326519992}{1}$ & $\pot{1.4291867041}{1}$ & $\pot{1.4206704409}{1}$ & $\pot{1.4985604253}{1}$ & $\pot{1.5395638329}{1}$ 
 \\ 
 $b_4$ & $\pot{6.4270125576}{0}$ & $\pot{6.0967371906}{0}$ & $\pot{5.8366404588}{0}$ & $\pot{5.7371156374}{0}$ & $\pot{5.5633379574}{0}$ 
 \\ 
 $b_5$ & $\pot{-1.0032296167}{1}$ & $\pot{-1.0363858125}{1}$ & $\pot{-1.0518387038}{1}$ & $\pot{-1.1546724399}{1}$ & $\pot{-1.2242342508}{1}$ 
 \\ 
 $b_6$ & $\pot{-1.4087194335}{0}$ & $\pot{-6.8184121010}{-1}$ & $\pot{-2.9722754662}{-1}$ & $\pot{1.1575092351}{-1}$ & $\pot{4.8942663430}{-1}$ 
 \\ 
 $b_7$ & $\pot{1.8482968593}{0}$ & $\pot{1.8529967851}{0}$ & $\pot{2.1519310722}{0}$ & $\pot{2.2891230659}{0}$ & $\pot{2.6782065008}{0}$ 
 \\ 
 $b_8$ & $\pot{-2.1185600113}{-1}$ & $\pot{-1.9498101086}{-1}$ & $\pot{-1.8067549402}{-1}$ & $\pot{-2.0119354736}{-1}$ & $\pot{-1.8223251218}{-1}$ 
 \\ 
 $b_9$ & $\pot{3.0555243512}{-2}$ & $\pot{2.7915669075}{-2}$ & $\pot{2.5650331467}{-2}$ & $\pot{3.2820939449}{-2}$ & $\pot{3.0707648484}{-2}$ 
 \\ 
 $\phi^{\rm nr}(1/2)$ & $\pot{9.8879969305}{1}$ & $\pot{1.0942707459}{2}$ & $\pot{1.2016192323}{2}$ & $\pot{1.3105436054}{2}$ & $\pot{1.4208118814}{2}$ 
\\[1mm]
%\end{tabular} 
%\begin{tabular}{lrrrrr}
%\hline
 & 17s  & 18s  & 19s  & 20s 
 \\ 
 \hline
 $a_0$ & $\pot{-4.0917355907}{1}$ & $\pot{-4.1160166944}{1}$ & $\pot{-4.1398378313}{1}$ & $\pot{-4.1637819958}{1}$ 
 \\ 
 $\beta$ & $\pot{-4.7538949275}{-1}$ & $\pot{-4.4937224788}{-1}$ & $\pot{-4.4703263317}{-1}$ & $\pot{-4.8244405309}{-1}$ 
 \\ 
 $b_0$ & $\pot{1.2547183851}{1}$ & $\pot{1.4317441971}{1}$ & $\pot{1.3339226887}{1}$ & $\pot{9.1516183240}{0}$ 
 \\ 
 $b_1$ & $\pot{-2.1972421315}{1}$ & $\pot{-2.2875778234}{1}$ & $\pot{-2.3839004652}{1}$ & $\pot{-2.3934619536}{1}$ 
 \\ 
 $b_2$ & $\pot{1.0636513367}{1}$ & $\pot{1.1277442747}{1}$ & $\pot{1.2219984677}{1}$ & $\pot{1.2479746639}{1}$ 
 \\ 
 $b_3$ & $\pot{1.5943304131}{1}$ & $\pot{1.6640858983}{1}$ & $\pot{1.7332324934}{1}$ & $\pot{1.7384969031}{1}$ 
 \\ 
 $b_4$ & $\pot{5.4874376556}{0}$ & $\pot{5.6104613925}{0}$ & $\pot{5.3841616235}{0}$ & $\pot{5.1298737644}{0}$ 
 \\ 
 $b_5$ & $\pot{-1.2655779187}{1}$ & $\pot{-1.3260181912}{1}$ & $\pot{-1.4146776145}{1}$ & $\pot{-1.4462821999}{1}$ 
 \\ 
 $b_6$ & $\pot{4.9579530934}{-1}$ & $\pot{5.2627269447}{-1}$ & $\pot{1.0461078949}{0}$ & $\pot{1.3716208664}{0}$ 
 \\ 
 $b_7$ & $\pot{2.5916598871}{0}$ & $\pot{2.4342837775}{0}$ & $\pot{2.3937323753}{0}$ & $\pot{2.8470359883}{0}$ 
 \\ 
 $b_8$ & $\pot{-2.2938505101}{-1}$ & $\pot{-2.7807376757}{-1}$ & $\pot{-2.8519500457}{-1}$ & $\pot{-2.4816096711}{-1}$ 
 \\ 
 $b_9$ & $\pot{4.2155577449}{-2}$ & $\pot{5.4040208750}{-2}$ & $\pot{5.6731652666}{-2}$ & $\pot{4.9205565009}{-2}$ 
 \\ 
 $\phi^{\rm nr}(1/2)$ & $\pot{1.5322255378}{2}$ & $\pot{1.6446312975}{2}$ & $\pot{1.7579037822}{2}$ & $\pot{1.8719377215}{2}$ 
\\[1mm]
\hline
\end{tabular} 
\end{table}