Table B.1: 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 $n\leq 20$.
  2s 3s 4s 5s 6s
a0 $-1.3974426528 \times 10^{1}$ $-2.0848318929 \times 10^{1}$ $-2.5412664413 \times 10^{1}$ $-2.8856705303 \times 10^{1}$ $-3.1567507558 \times 10^{1}$
$\beta $ $2.5591291935 \times 10^{-1}$ $5.5198239644 \times 10^{-1}$ $8.0397418838 \times 10^{-1}$ $4.8110524091 \times 10^{-1}$ $2.5266888083 \times 10^{-1}$
b0 $6.6487585307 \times 10^{0}$ $4.6179953215 \times 10^{2}$ $7.6795669026 \times 10^{2}$ $8.3598144011 \times 10^{2}$ $5.6902488765 \times 10^{2}$
b1 $-5.1211954644 \times 10^{1}$ $-9.8891531378 \times 10^{1}$ $-4.2588083735 \times 10^{2}$ $5.1404483119 \times 10^{1}$ $4.5519082179 \times 10^{1}$
b2 $3.4686628383 \times 10^{1}$ $1.0769127960 \times 10^{2}$ $7.0510361599 \times 10^{2}$ $-7.2853184204 \times 10^{1}$ $-6.7551149725 \times 10^{1}$
b3 $3.8515432953 \times 10^{1}$ $6.1301937755 \times 10^{1}$ $-3.6120946105 \times 10^{1}$ $-4.9378611706 \times 10^{1}$ $-3.8327617310 \times 10^{1}$
b4 $6.7503966084 \times 10^{0}$ $-4.1466090643 \times 10^{1}$ $-4.4049919721 \times 10^{2}$ $4.7383284338 \times 10^{1}$ $4.4401360958 \times 10^{1}$
b5 $-3.1431622488 \times 10^{1}$ $-8.4016250015 \times 10^{1}$ $2.4657329140 \times 10^{2}$ $9.9191282175 \times 10^{1}$ $7.4195208626 \times 10^{1}$
b6 $-1.3697636757 \times 10^{1}$ $7.1191755771 \times 10^{1}$ $-6.5900037717 \times 10^{1}$ $-1.0379836854 \times 10^{2}$ $-7.9312304169 \times 10^{1}$
b7 $2.4016413274 \times 10^{1}$ $-1.8695504961 \times 10^{1}$ $1.8226732411 \times 10^{1}$ $2.9602921680 \times 10^{1}$ $2.1866188936 \times 10^{1}$
b8 $-9.5149995633 \times 10^{0}$ $2.2794449683 \times 10^{0}$ $-2.8692508508 \times 10^{0}$ $-2.8636914451 \times 10^{0}$ $-1.9806370670 \times 10^{0}$
b9 $2.6555412799 \times 10^{0}$ $-4.3875761781 \times 10^{-1}$ $4.4042663362 \times 10^{-1}$ $3.8579054257 \times 10^{-1}$ $2.6143991878 \times 10^{-1}$
$\phi ^{\rm nr}(1/2)$ $2.1303295046 \times 10^{1}$ $2.5955835234 \times 10^{1}$ $3.0008781647 \times 10^{1}$ $3.5729374807 \times 10^{1}$ $4.2778194752 \times 10^{1}$
  7s 8s 9s 10s 11s
a0 $-3.3720076517 \times 10^{1}$ $-3.5420358274 \times 10^{1}$ $-3.6749872667 \times 10^{1}$ $-3.7779791307 \times 10^{1}$ $-3.8573952826 \times 10^{1}$
$\beta $ $8.5151589950 \times 10^{-2}$ $-4.2719713121 \times 10^{-2}$ $-1.3118006971 \times 10^{-1}$ $-2.1932912263 \times 10^{-1}$ $-2.9226372396 \times 10^{-1}$
b0 $3.7656038819 \times 10^{2}$ $2.7408956380 \times 10^{2}$ $2.8136510570 \times 10^{2}$ $1.5264948382 \times 10^{2}$ $8.6437136666 \times 10^{1}$
b1 $2.7980511952 \times 10^{1}$ $7.4703207553 \times 10^{0}$ $-1.8981579892 \times 10^{1}$ $-1.9235840320 \times 10^{1}$ $-1.9681933480 \times 10^{1}$
b2 $-4.9359948916 \times 10^{1}$ $-2.6259765669 \times 10^{1}$ $6.6356770418 \times 10^{0}$ $7.1592304894 \times 10^{0}$ $7.8432338862 \times 10^{0}$
b3 $-2.0507457345 \times 10^{1}$ $-3.3913231244 \times 10^{0}$ $1.3837014244 \times 10^{1}$ $1.3979846789 \times 10^{1}$ $1.4343371719 \times 10^{1}$
b4 $3.6291414100 \times 10^{1}$ $2.5464049259 \times 10^{1}$ $7.8618686503 \times 10^{0}$ $7.3730033289 \times 10^{0}$ $6.8679571684 \times 10^{0}$
b5 $4.3713955958 \times 10^{1}$ $1.6166653183 \times 10^{1}$ $-8.0358407914 \times 10^{0}$ $-8.6532015972 \times 10^{0}$ $-9.6695240617 \times 10^{0}$
b6 $-5.2721158916 \times 10^{1}$ $-2.8335792233 \times 10^{1}$ $-4.8006902023 \times 10^{0}$ $-3.6779369765 \times 10^{0}$ $-2.2948815920 \times 10^{0}$
b7 $1.4831730999 \times 10^{1}$ $8.6649789093 \times 10^{0}$ $2.8424870765 \times 10^{0}$ $2.4362978935 \times 10^{0}$ $2.0390764869 \times 10^{0}$
b8 $-1.3230829528 \times 10^{0}$ $-7.9156543417 \times 10^{-1}$ $-3.2207517000 \times 10^{-1}$ $-2.7645228408 \times 10^{-1}$ $-2.3641043114 \times 10^{-1}$
b9 $1.7474071394 \times 10^{-1}$ $1.0596166967 \times 10^{-1}$ $4.6227764509 \times 10^{-2}$ $3.9732841793 \times 10^{-2}$ $3.4157538873 \times 10^{-2}$
$\phi ^{\rm nr}(1/2)$ $5.0793294231 \times 10^{1}$ $5.9525977879 \times 10^{1}$ $6.8805689403 \times 10^{1}$ $7.8512293219 \times 10^{1}$ $8.8558644431 \times 10^{1}$
  12s 13s 14s 15s 16s
a0 $-3.9188326323 \times 10^{1}$ $-3.9670102478 \times 10^{1}$ $-4.0057506143 \times 10^{1}$ $-4.0380409686 \times 10^{1}$ $-4.0661454371 \times 10^{1}$
$\beta $ $-3.5484078761 \times 10^{-1}$ $-4.0844617686 \times 10^{-1}$ $-4.5428570381 \times 10^{-1}$ $-4.6335483910 \times 10^{-1}$ $-4.9050805652 \times 10^{-1}$
b0 $4.9431541043 \times 10^{1}$ $2.9197464029 \times 10^{1}$ $1.7971514946 \times 10^{1}$ $1.5982980641 \times 10^{1}$ $1.1724743879 \times 10^{1}$
b1 $-1.9750664049 \times 10^{1}$ $-1.9723076238 \times 10^{1}$ $-1.9651279272 \times 10^{1}$ $-2.0606406024 \times 10^{1}$ $-2.1081283167 \times 10^{1}$
b2 $8.1838767684 \times 10^{0}$ $8.3673624537 \times 10^{0}$ $8.4788048970 \times 10^{0}$ $9.3338234414 \times 10^{0}$ $9.8388495127 \times 10^{0}$
b3 $1.4326519992 \times 10^{1}$ $1.4291867041 \times 10^{1}$ $1.4206704409 \times 10^{1}$ $1.4985604253 \times 10^{1}$ $1.5395638329 \times 10^{1}$
b4 $6.4270125576 \times 10^{0}$ $6.0967371906 \times 10^{0}$ $5.8366404588 \times 10^{0}$ $5.7371156374 \times 10^{0}$ $5.5633379574 \times 10^{0}$
b5 $-1.0032296167 \times 10^{1}$ $-1.0363858125 \times 10^{1}$ $-1.0518387038 \times 10^{1}$ $-1.1546724399 \times 10^{1}$ $-1.2242342508 \times 10^{1}$
b6 $-1.4087194335 \times 10^{0}$ $-6.8184121010 \times 10^{-1}$ $-2.9722754662 \times 10^{-1}$ $1.1575092351 \times 10^{-1}$ $4.8942663430 \times 10^{-1}$
b7 $1.8482968593 \times 10^{0}$ $1.8529967851 \times 10^{0}$ $2.1519310722 \times 10^{0}$ $2.2891230659 \times 10^{0}$ $2.6782065008 \times 10^{0}$
b8 $-2.1185600113 \times 10^{-1}$ $-1.9498101086 \times 10^{-1}$ $-1.8067549402 \times 10^{-1}$ $-2.0119354736 \times 10^{-1}$ $-1.8223251218 \times 10^{-1}$
b9 $3.0555243512 \times 10^{-2}$ $2.7915669075 \times 10^{-2}$ $2.5650331467 \times 10^{-2}$ $3.2820939449 \times 10^{-2}$ $3.0707648484 \times 10^{-2}$
$\phi ^{\rm nr}(1/2)$ $9.8879969305 \times 10^{1}$ $1.0942707459 \times 10^{2}$ $1.2016192323 \times 10^{2}$ $1.3105436054 \times 10^{2}$ $1.4208118814 \times 10^{2}$
  17s 18s 19s 20s  
a0 $-4.0917355907 \times 10^{1}$ $-4.1160166944 \times 10^{1}$ $-4.1398378313 \times 10^{1}$ $-4.1637819958 \times 10^{1}$  
$\beta $ $-4.7538949275 \times 10^{-1}$ $-4.4937224788 \times 10^{-1}$ $-4.4703263317 \times 10^{-1}$ $-4.8244405309 \times 10^{-1}$  
b0 $1.2547183851 \times 10^{1}$ $1.4317441971 \times 10^{1}$ $1.3339226887 \times 10^{1}$ $9.1516183240 \times 10^{0}$  
b1 $-2.1972421315 \times 10^{1}$ $-2.2875778234 \times 10^{1}$ $-2.3839004652 \times 10^{1}$ $-2.3934619536 \times 10^{1}$  
b2 $1.0636513367 \times 10^{1}$ $1.1277442747 \times 10^{1}$ $1.2219984677 \times 10^{1}$ $1.2479746639 \times 10^{1}$  
b3 $1.5943304131 \times 10^{1}$ $1.6640858983 \times 10^{1}$ $1.7332324934 \times 10^{1}$ $1.7384969031 \times 10^{1}$  
b4 $5.4874376556 \times 10^{0}$ $5.6104613925 \times 10^{0}$ $5.3841616235 \times 10^{0}$ $5.1298737644 \times 10^{0}$  
b5 $-1.2655779187 \times 10^{1}$ $-1.3260181912 \times 10^{1}$ $-1.4146776145 \times 10^{1}$ $-1.4462821999 \times 10^{1}$  
b6 $4.9579530934 \times 10^{-1}$ $5.2627269447 \times 10^{-1}$ $1.0461078949 \times 10^{0}$ $1.3716208664 \times 10^{0}$  
b7 $2.5916598871 \times 10^{0}$ $2.4342837775 \times 10^{0}$ $2.3937323753 \times 10^{0}$ $2.8470359883 \times 10^{0}$  
b8 $-2.2938505101 \times 10^{-1}$ $-2.7807376757 \times 10^{-1}$ $-2.8519500457 \times 10^{-1}$ $-2.4816096711 \times 10^{-1}$  
b9 $4.2155577449 \times 10^{-2}$ $5.4040208750 \times 10^{-2}$ $5.6731652666 \times 10^{-2}$ $4.9205565009 \times 10^{-2}$  
$\phi ^{\rm nr}(1/2)$ $1.5322255378 \times 10^{2}$ $1.6446312975 \times 10^{2}$ $1.7579037822 \times 10^{2}$ $1.8719377215 \times 10^{2}$  

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