Table B.2: Non-linear fitting coefficients for the non-resonant $n{\rm d}\rightarrow 1{\rm s}$ emission spectra within the frequency range $10^{-3}\leq y\leq 0.999$ for $n\leq 20$.
  3d 4d 5d 6d 7d
a0 $-1.0484392971 \times 10^{1}$ $-1.4527047719 \times 10^{1}$ $-1.7350074013 \times 10^{1}$ $-1.9527421713 \times 10^{1}$ $-2.1271595034 \times 10^{1}$
$\beta $ $2.6115596268 \times 10^{-1}$ $8.1050542323 \times 10^{-1}$ $4.6206291704 \times 10^{-1}$ $2.3419462081 \times 10^{-1}$ $6.7999906938 \times 10^{-2}$
b0 $5.3546036998 \times 10^{1}$ $1.7065087104 \times 10^{2}$ $2.0902445563 \times 10^{2}$ $1.4535416639 \times 10^{2}$ $1.1921878150 \times 10^{2}$
b1 $-9.7319568527 \times 10^{1}$ $-4.2936500531 \times 10^{2}$ $5.8562543507 \times 10^{1}$ $5.9612688683 \times 10^{1}$ $3.0991642200 \times 10^{1}$
b2 $1.0624929126 \times 10^{2}$ $7.1072286522 \times 10^{2}$ $-7.8501054392 \times 10^{1}$ $-8.0969461685 \times 10^{1}$ $-5.2470184998 \times 10^{1}$
b3 $6.0569007312 \times 10^{1}$ $-3.6472867939 \times 10^{1}$ $-5.8200368181 \times 10^{1}$ $-5.3437128442 \times 10^{1}$ $-2.3362093646 \times 10^{1}$
b4 $-4.1091307521 \times 10^{1}$ $-4.4275350080 \times 10^{2}$ $4.8846690629 \times 10^{1}$ $4.9735078265 \times 10^{1}$ $3.7636220223 \times 10^{1}$
b5 $-8.3346792794 \times 10^{1}$ $2.4703670467 \times 10^{2}$ $1.1281858951 \times 10^{2}$ $9.8247844915 \times 10^{1}$ $4.8276486304 \times 10^{1}$
b6 $6.9608223453 \times 10^{1}$ $-6.6433743910 \times 10^{1}$ $-1.1364879196 \times 10^{2}$ $-9.8596391243 \times 10^{1}$ $-5.6611227459 \times 10^{1}$
b7 $-1.7046798510 \times 10^{1}$ $1.8959198585 \times 10^{1}$ $3.1841053645 \times 10^{1}$ $2.6560347162 \times 10^{1}$ $1.5852011862 \times 10^{1}$
b8 $1.6052249571 \times 10^{0}$ $-3.1192847294 \times 10^{0}$ $-3.0563352329 \times 10^{0}$ $-2.3898992832 \times 10^{0}$ $-1.4245686402 \times 10^{0}$
b9 $-2.2422235582 \times 10^{-1}$ $5.0786391006 \times 10^{-1}$ $4.1302480839 \times 10^{-1}$ $3.1693775497 \times 10^{-1}$ $1.8991428606 \times 10^{-1}$
$\phi ^{\rm nr}(1/2)$ $2.0915177571 \times 10^{1}$ $3.4902680010 \times 10^{1}$ $4.4901877444 \times 10^{1}$ $5.2879363207 \times 10^{1}$ $5.9763238933 \times 10^{1}$
  8d 9d 10d 11d 12d
a0 $-2.2687581599 \times 10^{1}$ $-2.3840999089 \times 10^{1}$ $-2.4781138994 \times 10^{1}$ $-2.5548956191 \times 10^{1}$ $-2.6179506753 \times 10^{1}$
$\beta $ $-4.0416246997 \times 10^{-2}$ $-1.4739834639 \times 10^{-1}$ $-2.3472013799 \times 10^{-1}$ $-3.0648469505 \times 10^{-1}$ $-3.6629270128 \times 10^{-1}$
b0 $1.8805941117 \times 10^{2}$ $1.0632962733 \times 10^{2}$ $6.0922960536 \times 10^{1}$ $3.6160368635 \times 10^{1}$ $2.2144091289 \times 10^{1}$
b1 $-1.8483714555 \times 10^{1}$ $-1.8910499138 \times 10^{1}$ $-1.9083232938 \times 10^{1}$ $-1.9357145527 \times 10^{1}$ $-1.9508239494 \times 10^{1}$
b2 $5.8156915967 \times 10^{0}$ $6.5026790075 \times 10^{0}$ $6.8739045830 \times 10^{0}$ $7.3456517995 \times 10^{0}$ $7.6357892226 \times 10^{0}$
b3 $1.3504738304 \times 10^{1}$ $1.3795221365 \times 10^{1}$ $1.3924013399 \times 10^{1}$ $1.4140788681 \times 10^{1}$ $1.4314213871 \times 10^{1}$
b4 $8.5177417832 \times 10^{0}$ $8.0023959097 \times 10^{0}$ $7.6277097156 \times 10^{0}$ $7.2310576094 \times 10^{0}$ $6.9389854602 \times 10^{0}$
b5 $-7.0817594819 \times 10^{0}$ $-7.9116375657 \times 10^{0}$ $-8.4667321100 \times 10^{0}$ $-9.1736549163 \times 10^{0}$ $-9.8020559467 \times 10^{0}$
b6 $-6.3232881999 \times 10^{0}$ $-5.0886630492 \times 10^{0}$ $-4.1097110628 \times 10^{0}$ $-3.0436236228 \times 10^{0}$ $-2.1203514774 \times 10^{0}$
b7 $3.4340616701 \times 10^{0}$ $2.9768149183 \times 10^{0}$ $2.6171546155 \times 10^{0}$ $2.2949189350 \times 10^{0}$ $2.0887633671 \times 10^{0}$
b8 $-3.9664209528 \times 10^{-1}$ $-3.4089403622 \times 10^{-1}$ $-2.9766246686 \times 10^{-1}$ $-2.6063687833 \times 10^{-1}$ $-2.3211600328 \times 10^{-1}$
b9 $5.7497854559 \times 10^{-2}$ $4.9213789949 \times 10^{-2}$ $4.2727779792 \times 10^{-2}$ $3.7171055385 \times 10^{-2}$ $3.2750870685 \times 10^{-2}$
$\phi ^{\rm nr}(1/2)$ $6.6011443629 \times 10^{1}$ $7.1866675229 \times 10^{1}$ $7.7466332091 \times 10^{1}$ $8.2892729834 \times 10^{1}$ $8.8197557986 \times 10^{1}$
  13d 14d 15d 16d 17d
a0 $-2.6702542838 \times 10^{1}$ $-2.7142749615 \times 10^{1}$ $-2.7520108750 \times 10^{1}$ $-2.7850443691 \times 10^{1}$ $-2.8146062687 \times 10^{1}$
$\beta $ $-4.1655350067 \times 10^{-1}$ $-4.5817894101 \times 10^{-1}$ $-4.9230994423 \times 10^{-1}$ $-4.8799319840 \times 10^{-1}$ $-5.1046103153 \times 10^{-1}$
b0 $1.4031825050 \times 10^{1}$ $9.3536034158 \times 10^{0}$ $6.5800387184 \times 10^{0}$ $6.5003185806 \times 10^{0}$ $5.0269776925 \times 10^{0}$
b1 $-1.9675880116 \times 10^{1}$ $-1.9851518345 \times 10^{1}$ $-2.0183574589 \times 10^{1}$ $-2.0542531107 \times 10^{1}$ $-2.0953818322 \times 10^{1}$
b2 $8.0418685007 \times 10^{0}$ $8.3266612119 \times 10^{0}$ $8.8233502592 \times 10^{0}$ $8.8786234533 \times 10^{0}$ $9.3483218939 \times 10^{0}$
b3 $1.4344987353 \times 10^{1}$ $1.4507266322 \times 10^{1}$ $1.4666068986 \times 10^{1}$ $1.5088704084 \times 10^{1}$ $1.5370738183 \times 10^{1}$
b4 $6.5426767345 \times 10^{0}$ $6.3117201027 \times 10^{0}$ $6.0075843919 \times 10^{0}$ $6.3138200610 \times 10^{0}$ $6.1350437791 \times 10^{0}$
b5 $-1.0108197620 \times 10^{1}$ $-1.0587100158 \times 10^{1}$ $-1.0920565892 \times 10^{1}$ $-1.1277066540 \times 10^{1}$ $-1.1714497606 \times 10^{1}$
b6 $-1.4725216928 \times 10^{0}$ $-9.1174802515 \times 10^{-1}$ $-6.0110879243 \times 10^{-1}$ $-8.1971758897 \times 10^{-1}$ $-6.0125221865 \times 10^{-1}$
b7 $2.0501069105 \times 10^{0}$ $2.1660824963 \times 10^{0}$ $2.4592074550 \times 10^{0}$ $2.6330961336 \times 10^{0}$ $2.9489602434 \times 10^{0}$
b8 $-2.0980025116 \times 10^{-1}$ $-1.8682379725 \times 10^{-1}$ $-1.5933095829 \times 10^{-1}$ $-2.0505355745 \times 10^{-1}$ $-1.7710483631 \times 10^{-1}$
b9 $2.9129276734 \times 10^{-2}$ $2.5589737997 \times 10^{-2}$ $2.1812553698 \times 10^{-2}$ $3.3518563369 \times 10^{-2}$ $2.9819941280 \times 10^{-2}$
$\phi ^{\rm nr}(1/2)$ $9.3414593519 \times 10^{1}$ $9.8566665797 \times 10^{1}$ $1.0366966228 \times 10^{2}$ $1.0873478648 \times 10^{2}$ $1.1377060842 \times 10^{2}$
  18d 19d 20d    
a0 $-2.8416405767 \times 10^{1}$ $-2.8668633507 \times 10^{1}$ $-2.8908128993 \times 10^{1}$    
$\beta $ $-5.2741247590 \times 10^{-1}$ $-4.8873340484 \times 10^{-1}$ $-4.7794020321 \times 10^{-1}$    
b0 $4.1457341691 \times 10^{0}$ $5.2856466775 \times 10^{0}$ $5.2735742805 \times 10^{0}$    
b1 $-2.1898431473 \times 10^{1}$ $-2.2963670035 \times 10^{1}$ $-2.3833638246 \times 10^{1}$    
b2 $1.0391335216 \times 10^{1}$ $1.1284085887 \times 10^{1}$ $1.2121030366 \times 10^{1}$    
b3 $1.6037472635 \times 10^{1}$ $1.6719978965 \times 10^{1}$ $1.7273259137 \times 10^{1}$    
b4 $5.7762172996 \times 10^{0}$ $5.7383329948 \times 10^{0}$ $5.5675791948 \times 10^{0}$    
b5 $-1.2705538272 \times 10^{1}$ $-1.3194456779 \times 10^{1}$ $-1.3752468820 \times 10^{1}$    
b6 $-1.8363323426 \times 10^{-2}$ $7.2380465060 \times 10^{-2}$ $3.0584919862 \times 10^{-1}$    
b7 $3.1624501247 \times 10^{0}$ $2.7857591072 \times 10^{0}$ $2.7454079863 \times 10^{0}$    
b8 $-1.4050292467 \times 10^{-1}$ $-2.4398422587 \times 10^{-1}$ $-2.7060311659 \times 10^{-1}$    
b9 $2.5244597061 \times 10^{-2}$ $4.6094366553 \times 10^{-2}$ $5.2504979483 \times 10^{-2}$    
$\phi ^{\rm nr}(1/2)$ $1.1878311140 \times 10^{2}$ $1.2377675855 \times 10^{2}$ $1.2875544820 \times 10^{2}$    

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