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Here is the k<=40 table in >>38 format. Increasing the group order by one means that one generator level is eliminated.
1 69 7 0
2 5764 13 0
3 526334 20 1
4 50874761 26 2
5 5028514748 33 2
6 500918449417 39 2
7 50029364025646 46 2
8 5000934571821489 53 3
9 500029664631299282 59 3
10 50000940106333921296 66 3
11 5000029765607020319048 73 3
12 500000941936492050650505 79 3
13 50000029798618763894670256 86 3
14 5000000942529842698007077786 93 3
15 500000029809255627825531266625 99 4
16 50000000942720152238624116795401 106 4
17 5000000029812655507343465281696595 112 4
18 500000000942780823112495107784753816 119 4
19 50000000029813737262126730811322149673 126 4
20 5000000000942800098290022420982686040347 132 4
21 500000000029814080548392288266955229183571 139 4
22 50000000000942806209878293665994446398371544 146 4
23 5000000000029814189323670710814676032031444555 152 4
24 500000000000942808145472258657037814775197247031 159 4
25 50000000000029814223760934912839828327249688721190 166 4
26 5000000000000942808758091081952084125868709915711089 172 4
27 500000000000029814234658067055252766458087914346630413 179 4
28 50000000000000942808951913512756782469229223199209677641 186 4
29 5000000000000029814238105320163714566005337846445873165675 192 4
30 500000000000000942809013222649956573426148951590151576716407 199 5
31 50000000000000029814239195666197369782628797813806672178028303 205 5
32 5000000000000000942809032613363227344483520545074111347580106666 212 5
33 500000000000000029814239540504829346639521751526121067855028048469 219 5
34 50000000000000000942809038745792444395013325500575549841178605176222 225 5
35 5000000000000000029814239649559693010895101002840721426848127286038482 232 5
36 500000000000000000942809040685134541874198687080125967207639651015633313 239 5
37 50000000000000000029814239684047173947897406203055196803310606765583116781 245 5
38 5000000000000000000942809041298425788194699108125613517442497904284636150437 252 5
39 500000000000000000029814239694953305682145634502486118475654808671411192582303 259 5
40 50000000000000000000942809041492368615124254362375085779982992292343853681977675 265 5Please verify the value of R(10^40) with other implementations.