Magma V2.27-4 Wed May 15 2024 12:43:33 on socrates [Seed = 637830345] +-------------------------------------------------------------------+ | This copy of Magma has been made available through a | | generous initiative of the | | | | Simons Foundation | | | | covering U.S. Colleges, Universities, Nonprofit Research entities,| | and their students, faculty, and staff | +-------------------------------------------------------------------+ Type ? for help. Type -D to quit. Loading file "classical-bounds.mag" Loading "find-invariants.mag" Loading "classical-bounds-linear-no-aut.mag" 7 2 1.21513888095147379330611889427 PSL(2,7) deg 7 8 2 1.10245262288875058682378310863 Schmidt 11 2 1.28452325786651290201168984776 PSL(2,11) deg 11 13 2 1.45254607840512580763230121430 PSL(2,13) invariants; {* 1, 2, 3^^2, 4^^4, 5^^6 *} 16 2 1.11937592031470471366031620603 PSL(2,16) invariants; {* 1, 2, 3, 4^^3, 5^^4, 6^^7 *} 17 2 1.33394593769983135435398554164 PSL(2,17) invariants; {* 1, 2, 3^^2, 4^^4, 5^^10 *} 19 2 1.36797113611353879394223343156 PSL(2,19) invariants; {* 1, 2, 3, 4^^5, 5^^8, 6^^4 *} 23 2 1.29615068090684705987841201867 PSL(2,23) invariants; {* 1, 2, 3, 4^^5, 5^^9, 6^^7 *} 25 2 1.12095426380314979310466696150 PSL(2,25) invariants; {* 1, 2, 3^^2, 4^^7, 5^^15 *} 27 2 1.18019368870416471870124473662 PSL(2,27) invariants; {* 1, 2, 3, 4^^6, 5^^13, 6^^6 *} 29 2 1.06919855503180596387858270856 PSL(2,29) invariants; {* 1, 2, 3^^2, 4^^6, 5^^20 *} 31 2 1.06571698314892355418648233508 PSL(2,31) invariants; {* 1, 2, 3, 4^^8, 5^^18, 6^^3 *} 32 2 0.820755208879740102531076632063 PSL(2,32) invariants; {* 1, 2, 3, 4^^5, 5^^11, 6^^14 *} 37 2 0.949178810392598700658312565121 PSL(2,37) invariants; {* 1, 2, 3^^2, 4^^9, 5^^25 *} 41 2 0.910657635276601955319413623635 PSL(2,41) invariants; {* 1, 2, 3^^2, 4^^9, 5^^29 *} 43 2 0.898013400822045100910220614637 PSL(2,43) invariants; {* 1, 2, 3, 4^^10, 5^^31 *} 47 2 1.40919653530500623088475398752 Better invariants. 49 2 0.833033959830745745934628954725 PSL(2,49) invariants; {* 1, 2, 3^^2, 4^^12, 5^^34 *} 53 2 1.29772231713302178902665543985 Better invariants. 59 2 1.20784257821387765705780866252 Better invariants. 61 2 1.18157605820150269383982373258 Better invariants. 64 2 0.553778541546097718532627472189 PSL(2,64) invariants; {* 1, 2, 3, 4^^11, 5^^40, 6^^11 *} 67 2 1.11154856545795804987133890483 Better invariants. 71 2 1.07094892013448677833400063336 Better invariants. 73 2 1.05217854113365578349832988973 Better invariants. 79 2 1.00107253421524996445931340522 Better invariants. 81 2 0.985562750697071463747332984467 Better invariants. 83 2 0.970726175043234022458460022521 Better invariants. 89 2 0.929814857404446443126368387327 Better invariants. 97 2 0.882321244079729007044940764282 Better invariants. 3 3 0.650520624833166479775718033431 Schmidt 4 3 0.850436468820569806119053441911 Schmidt 5 3 0.419318643754364921512604395688 Schmidt 7 3 0.613686785323791669701160909039 Schmidt 8 3 0.337138559531098551012356006328 Schmidt 9 3 0.272333806495803651557443012167 Easy invariants 11 3 0.177942947913780587829931676951 Easy invariants 13 3 0.217100333820689794569346229503 Easy invariants 16 3 0.140987584031725790745744187080 Easy invariants 17 3 0.0718082233672509225713476415203 Easy invariants 19 3 0.0988871413039360534290030383547 Easy invariants 23 3 0.0385724408125479421795169395101 Easy invariants 25 3 0.0563349358746417674485803403734 Easy invariants 27 3 0.0277961432526950608325250036825 Easy invariants 29 3 0.0240285759581633154153534170559 Easy invariants 31 3 0.0363354947788856191297268112137 Easy invariants 32 3 0.0196665632759554019627441268121 Easy invariants 37 3 0.0253656153405193123798337171392 Easy invariants 41 3 0.0118936958531293839297713260064 Easy invariants 43 3 0.0187064868804054271405049405232 Easy invariants 47 3 0.00902142522187462438091696218845 Easy invariants 49 3 0.0143630454505266351173056846995 Easy invariants 53 3 0.00707670769632302271511661684984 Easy invariants 59 3 0.00569922678048139117610960846763 Easy invariants 61 3 0.00922935947576030852476593019236 Easy invariants 64 3 0.00837774057483697512518980621433 Easy invariants 67 3 0.00763878272134256918106736135229 Easy invariants 71 3 0.00392392498666598112631298874076 Easy invariants 73 3 0.00642658233619732490679655608812 Easy invariants 79 3 0.00548160706166102431872357468560 Easy invariants 81 3 0.00300948578334850025730309533582 Easy invariants 83 3 0.00286532447851968584890180926552 Easy invariants 89 3 0.00248994090787485825722726004381 Easy invariants 97 3 0.00362723015570887812730676979152 Easy invariants 2 4 0.448988197824524431801984736413 Schmidt 3 4 0.170539059309700125084451777328 Schmidt 4 4 0.0588453592493370011037132589535 Schmidt 5 4 0.0448747360491832973159211315360 Easy invariants 7 4 0.00643735798137946580017772805081 Easy invariants 8 4 0.00243805956405387518534910508086 Easy invariants 9 4 0.00281980970714699175058474188918 Easy invariants 11 4 0.000788419072325157782713480499047 Easy invariants 13 4 0.000517122066012311368876157117446 Easy invariants 16 4 9.98974691997149358830659331774E-5 Easy invariants 17 4 0.000151460418720467624866611683129 Easy invariants 19 4 6.44767768286918633851677395530E-5 Easy invariants 23 4 2.70171119311640034144988892243E-5 Easy invariants 25 4 2.61550686196044350342470004049E-5 Easy invariants 27 4 1.30389691583796450874726118255E-5 Easy invariants 29 4 1.33325127466089072255388253413E-5 Easy invariants 31 4 6.96669873328907639803363086190E-6 Easy invariants 32 4 4.26577601182918452061245447118E-6 Easy invariants 37 4 4.41926852941537898279136547440E-6 Easy invariants 41 4 2.77667391178500762005857625128E-6 Easy invariants 43 4 1.58275005425447613295388803678E-6 Easy invariants 47 4 1.05847625089823581665493805150E-6 Easy invariants 49 4 1.23982625757006791312476243294E-6 Easy invariants 53 4 8.69572790064617816686252671892E-7 Easy invariants 59 4 3.78734158932555761346397039033E-7 Easy invariants 61 4 4.60733417416875846024957430950E-7 Easy invariants 64 4 1.85459661302252600033394941484E-7 Easy invariants 67 4 2.13267376729283434532192849539E-7 Easy invariants 71 4 1.64143050522883484350840869725E-7 Easy invariants 73 4 2.04774029234474348195172683183E-7 Easy invariants 79 4 1.01374071924765352532147573929E-7 Easy invariants 81 4 1.28068413545111586609914065480E-7 Easy invariants 83 4 8.11196008128177538162234168688E-8 Easy invariants 89 4 8.37290386938812519188405814030E-8 Easy invariants 97 4 5.67867602550563272452688054352E-8 Easy invariants Largest value for linear groups without a graph automorphism: 1.45254607840512580763230121430 2 13 PSL(2,13) invariants; {* 1, 2, 3^^2, 4^^4, 5^^6 *} Loading "classical-bounds-linear-graph-aut.mag" 3 3 0.919975090242484047371254450725 Schmidt 3 4 1.20269878814273360021862228707 Schmidt 3 5 0.593006112953315178555183399473 Schmidt 3 7 0.867884174854052241673337769247 Schmidt 3 8 0.476785923287808658921408946776 Schmidt 3 9 0.385138162639055614946559846913 Easy invariants 3 11 0.251649330268317746837229850251 Easy invariants 3 13 0.307026236484945843316656559181 Easy invariants 3 16 0.199386553463883021082554446944 Easy invariants 3 17 0.101552163375882853958978794819 Easy invariants 3 19 0.139847536376331033550704211576 Easy invariants 3 23 0.0545496689309387862928225188184 Easy invariants 3 25 0.0796696303493370050668219300814 Easy invariants 3 27 0.0393096827696267515031348653847 Easy invariants 3 29 0.0339815380045466479910224919847 Easy invariants 3 31 0.0513861495118368270177881296820 Easy invariants 3 32 0.0278127205101247753480782428369 Easy invariants 3 37 0.0358723972325014451838312550816 Easy invariants 3 41 0.0168202259822362139289432150991 Easy invariants 3 43 0.0264549674506237247560579791160 Easy invariants 3 47 0.0127582219007098019465647204328 Easy invariants 3 49 0.0203124136731159485684242683391 Easy invariants 3 53 0.0100079760010900808598669063087 Easy invariants 3 59 0.00805992380799673358367693464401 Easy invariants 3 61 0.0130522853426368669010453119225 Easy invariants 3 64 0.0118479143429778196897167607522 Easy invariants 3 67 0.0108028701245439201959934985074 Easy invariants 3 71 0.00554926793387769665726217373868 Easy invariants 3 73 0.00908855989955762644166368726242 Easy invariants 3 79 0.00775216305020115129253279124930 Easy invariants 3 81 0.00425605561058046708144492409091 Easy invariants 3 83 0.00405218073812215578764239695601 Easy invariants 3 89 0.00352130820142420177073536703932 Easy invariants 3 97 0.00512967808005216878340155724846 Easy invariants 4 2 0.634965198708896621233434126712 Schmidt 4 3 0.241178650590127553703274754753 Schmidt 4 4 0.0832199051331294386501645527485 Schmidt 4 5 0.0634624603286678599242868053061 Easy invariants 4 7 0.00910379896311753039314323722611 Easy invariants 4 8 0.00344793690135842593780807260824 Easy invariants 4 9 0.00398781313115858110147854588682 Easy invariants 4 11 0.00111499294491585226236859017676 Easy invariants 4 13 0.000731321039157005679286739502059 Easy invariants 4 16 0.000141276355788985400006025129064 Easy invariants 4 17 0.000214197378317193134382327760203 Easy invariants 4 19 9.11839322492393501158318304244E-5 Easy invariants 4 23 3.82079661092040947694369571207E-5 Easy invariants 4 25 3.69888527666435377038228764539E-5 Easy invariants 4 27 1.84398870231449948619198117829E-5 Easy invariants 4 29 1.88550203467664806022019867682E-5 Easy invariants 4 31 9.85239983358487351243642187305E-6 Easy invariants 4 32 6.03271828997464508576108435446E-6 Easy invariants 4 37 6.24978949006783209648331165322E-6 Easy invariants 4 41 3.92680990433391269318398511854E-6 Easy invariants 4 43 2.23834659257343215516165283102E-6 Easy invariants 4 47 1.49691146947011202227186467702E-6 Easy invariants 4 49 1.75337910844186824607579641277E-6 Easy invariants 4 53 1.22976163317999467525030763564E-6 Easy invariants 4 59 5.35610984096387640527118497669E-7 Easy invariants 4 61 6.51575447549450185974436704714E-7 Easy invariants 4 64 2.62279568286766289501297374728E-7 Easy invariants 4 67 3.01605616582284837985986390596E-7 Easy invariants 4 71 2.32133328218753974360067195523E-7 Easy invariants 4 73 2.89594209365178277589278071932E-7 Easy invariants 4 79 1.43364587388988769530670372017E-7 Easy invariants 4 81 1.81116087347102995588646335694E-7 Easy invariants 4 83 1.14720439643778412305312159917E-7 Easy invariants 4 89 1.18410742085348522658774982737E-7 Easy invariants 4 97 8.03086065159300961528192830191E-8 Easy invariants Largest value for linear groups with a graph automorphism: 1.20269878814273360021862228707 3 4 Schmidt Loading "classical-bounds-symplectic-no-aut.mag" Largest value for symplectic groups without a graph automorphism: 1.25500919395958088856649817195 4 5 Better version of easy invariants. Loading "classical-bounds-symplectic-graph-aut.mag" Largest value for symplectic groups with a graph automorphism: 2.24734604280495955648274642156 4 4 Easy invariants Loading "classical-bounds-unitary3.mag" Loading "find-invariants.mag" Largest value for unitary groups PSU(3,q): 2.07509345206943115432850171785 3 8 Base of size 3. Loading "classical-bounds-unitary4.mag" Largest value for unitary groups PSU(4,q): 0.840533452582844416255848748127 4 3 Base of size 4 for PSU(4,3). Loading "classical-bounds-unitary-odd.mag" Largest value for unitary groups PSU(2m+1,q): 1.27114280726373672594906807852 5 2 Easy invariants Loading "classical-bounds-unitary-even.mag" Largest value for unitary groups PSU(2m,q): 0.213174942345100226265011460370 6 2 Easy invariants Loading "classical-bounds-orthogonal-plus.mag" Largest value for groups POmegaPlus(2m,q) with no graph automorphism: 0.373357171575643214822463666453 8 2 Easy invariants Loading "classical-bounds-orthogonal-4-triality.mag" Largest value for groups POmegaPlus(8,q) with a graph automorphism: 0.646673590539224709062336886213 8 2 Easy invariants Loading "classical-bounds-orthogonal-minus.mag" Largest value for groups POmegaMinus(2m,q) with no graph automorphism: 0.408358624474904061362715849262 8 2 Easy invariants Loading "classical-bounds-orthogonal-odd.mag" Largest value for unitary groups POmega(2m+1,q): 0.196204029807769256504474365523 7 3 Easy invariants Total time: 4290.420 seconds, Total memory usage: 23640.69MB