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Residues of Dedekind zeta functions of cubic fields
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Numbers
$D$
$k$ 
$\kappa_K$
-23
1:
0.3684093207158268211118684666288852698579339813036019804462113447742746935929528961568565975478835671
comment: $a^3-a^2+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.23.1; $\kappa_K=2\pi\log\rho/\sqrt{23}$ with $\rho$ the plastic number, $\rho^3=\rho+1$
-31
1:
0.4313610545599581555372627480952355366768142911083023715858501514940768580115117152533056207861428990
comment: $a^3+a-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.31.1
-44
1:
0.5772184494905310366224202207956216412227228439768616419772027080546084041397331135918168232651370685
comment: $a^3-a^2+a+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.44.1
49
1:
0.3002598183557556504793291688276140054520314548638827343243710128116063196314271960457637792240897043
comment: $a^3-a^2-2a+1=0$; $C_3$, conductor $7$; $h_K=1$; LMFDB 3.3.49.1; $K=\mathbb{Q}(\zeta_7)^+$; $\kappa_K=|L(1,\chi)|^2$ for $\chi=\chi_{7}(2,\cdot)$
-59
1:
0.6470271520998537745990518121621722621533197203476464769148236152771774158404751186866284481270419714
comment: $a^3+2a-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.59.1
-76
1:
0.7341304809928935003234851832724360125000668793340409564814073604617193617585393133281014028806047975
comment: $a^3-2a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.76.1
81
1:
0.3774610891760855682865608910833096605399089687606127157193052614239225737788488880139275052381814984
comment: $a^3-3a-1=0$; $C_3$, conductor $9$; $h_K=1$; LMFDB 3.3.81.1; $K=\mathbb{Q}(\zeta_9)^+$; $\kappa_K=|L(1,\chi)|^2$ for $\chi=\chi_{9}(4,\cdot)$
-83
1:
0.7177336175375079251375039078238607082796779917341081358170245536926595882776619367172915347551570051
comment: $a^3-a^2+a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.83.1
-87
1:
0.6297378250199123346241987088836037855282082977616603445557656299644145063458664496232837141889558967
comment: $a^3-a^2+2a+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.87.1
-104
1:
0.9710515157102734167712177287699375748377224944825589029622420007202954843397192277806434972444032581
comment: $a^3-a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.104.1
-107
1:
0.7629520273566409964741121769982360646869151011032844253356760993668635961672765134715091281289261961
comment: $a^3-a^2+3a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.107.1
-108
1:
0.8146240592611410570739926789866319953599077927852219753156967742444325271232469925504817810110772818
comment: $a^3-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.108.1; $K=\mathbb{Q}(\sqrt[3]{2})$, a pure cubic field
-116
1:
1.001971004159106015228724286116803300161672535494983117393964477567088007380923802506658878601305150
comment: $a^3-a^2-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.116.1
-135
1:
0.6124919412243018724087404893788990697438779258926846634493616798282544366651596464334639652730514965
comment: $a^3+3a-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.135.1
-139
1:
0.8865629197832667947142141189008662515341082080585500047521169328726650190082177553456056513009840585
comment: $a^3-a^2+a+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.139.1
-140
1:
0.7825576714796405317116253002361996592611454737051990506924688250569269000165876000729552367645337459
comment: $a^3+2a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.140.1
148
1:
0.5465728811499063615707124804121002761808253226723008798032396239055832265693914755356998494983307824
comment: $a^3-a^2-3a+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.148.1
-152
1:
1.085848633304247222867418257556340249448396823897205522870899497603050621493847325058604822739516140
comment: $a^3-a^2-2a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.152.1
169
1:
0.4200153438751946448107950168621510600506197068193908293902131358909976856036448465185585546325709631
comment: $a^3-a^2-4a-1=0$; $C_3$, conductor $13$; $h_K=1$; LMFDB 3.3.169.1; the cubic subfield of $\mathbb{Q}(\zeta_{13})$; $\kappa_K=|L(1,\chi)|^2$ for $\chi=\chi_{13}(3,\cdot)$
-172
1:
0.9016217862132160098195912633582721363658965962374223178374167437699211878552010610200888668330964833
comment: $a^3-a^2-a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.172.1
-175
1:
0.6119944195128886488010472774453733369438958403279010259238814389759965710011520530472495665939007182
comment: $a^3-a^2+2a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.175.1
-199
1:
0.5953516474094782437920509904459608954583343741914104664559927361826815486090430180110078945052049715
comment: $a^3-a^2+4a-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.199.1
-200
1:
1.157104169212456226383007935559650580409981790827923335029785804917488383331386125452946755869846242
comment: $a^3-a^2+2a+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.200.1
-204
1:
1.035833567053636394919182505159491255252815746367362514097902839101430807332026282468018238411721331
comment: $a^3-a^2+a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.204.1
-211
1:
0.9678932793052480651986571534191354626627293121727990956373939370993230414861268476404794346356088113
comment: $a^3-2a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.211.1
-212
1:
1.170638233081550225637401022701724149546143843201312476193876704209525012422878252757061516218759753
comment: $a^3-a^2+4a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.212.1
-216
1:
1.292629422927715041422654698958441247592690878728905148413624804609980020322113960350305287192569556
comment: $a^3+3a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.216.1
229
1:
0.6226112824629684971082312273209196133059406862141911392330432408329321306250384437372277632935583582
comment: $a^3-4a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.229.1
-231
1:
0.7215912812053140029664420379808503430033548954822905005524047946702726952258974959896605006702386131
comment: $a^3-a^2+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.231.1
-239
1:
0.8520880797835939394661222868185036502271568659270750733999575029601533758101740028875378639128574873
comment: $a^3-a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.239.1
-243
1:
1.017614561500059518387922892417083450939824535282566020169153219266082033139229482163319075184064576
comment: $a^3-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.243.1; $K=\mathbb{Q}(\sqrt[3]{3})$, a pure cubic field
-244
1:
1.328467277167303022615869709763069402277958420153563311296314788405645947343065169076996384902071468
comment: $a^3+a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.244.1
-247
1:
0.6174878031644330541507415989310388572342783464380557958521359978019470111064200225144712508245230141
comment: $a^3+a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.247.1
-255
1:
0.7841606687673446547818875119809262172254174091377736500222274028698898785760204487932894462931856368
comment: $a^3-a^2-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.255.1
257
1:
0.4926871260472981080996767058544169321634351556298413816973362045965694203994237060322052966645018324
comment: $a^3-a^2-4a+3=0$; $S_3$; $h_K=1$; LMFDB 3.3.257.1
-268
1:
0.9676660674535819201863598797920616713578323510148869306087908441201659367236663406536088617698486436
comment: $a^3-a^2-3a+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.268.1
-283
1:
1.046793184260792898507994186225918664740451631844374088296536156097523703189319376356843942676746891
comment: $a^3+4a-1=0$; $S_3$; $h_K=2$; LMFDB 3.1.283.1
-300
1:
1.142167443719363681986380794964268341568869988789280304969448303177033050679312186025044950020079624
comment: $a^3-a^2-3a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.300.1; $K=\mathbb{Q}(\sqrt[3]{10})$, a pure cubic field
-307
1:
1.060792931344966901756911088759888368494724357201385596812079724566880651019338494924997171982858523
comment: $a^3-a^2+3a+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.307.1
316
1:
0.8805969600507206389464484032332011462813730062822064174910888819820739170190915475025718328761343593
comment: $a^3-a^2-4a+2=0$; $S_3$; $h_K=1$; LMFDB 3.3.316.1
321
1:
0.5736083657044567353481203398536192296958732842179540466249605058383088333230472186585179414484002901
comment: $a^3-a^2-4a+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.321.1
-324
1:
1.412893501353160525880591814327645268254046003747612500968799940204734037162734080540510823251211048
comment: $a^3-3a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.324.1
-327
1:
0.7639247207913900848742880072539412301548778331457433170019950482119115666443665447188961812469237859
comment: $a^3-a^2-2a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.327.1
-331
1:
1.038035775517224772528051410982638256227429180848107053903672556423579120876753294041560005630673116
comment: $a^3-a^2+3a-4=0$; $S_3$; $h_K=2$; LMFDB 3.1.331.1
-335
1:
0.4997343475257837170771967847656081589310406053220345393575683745305578110720139152421733309455591823
comment: $a^3-a^2+4a+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.335.1
-339
1:
1.210184883855170678796263711723634134148071385585024050131219435781436840117745633809632857303765519
comment: $a^3-a^2-a+4=0$; $S_3$; $h_K=1$; LMFDB 3.1.339.1
-351
1:
0.5708948464602133537021660449577483486115654172284489132164699274040320675400114593845105814447267508
comment: $a^3+3a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.351.1
-356
1:
1.250515566526270172654706911208333079460250445679492745032482416263316024622766006406625584739508830
comment: $a^3-a^2+a+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.356.1
361
1:
0.4109803571594346699175620709613890802408076611301325053766180110815579267614312062939962143881548773
comment: $a^3-a^2-6a+7=0$; $C_3$, conductor $19$; $h_K=1$; LMFDB 3.3.361.1; the cubic subfield of $\mathbb{Q}(\zeta_{19})$; $\kappa_K=|L(1,\chi)|^2$ for $\chi=\chi_{19}(7,\cdot)$
-364
1:
0.9669654430449658673755168451088623602280960064023368759490728789244405018680075360110426887188237139
comment: $a^3+4a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.364.1
-367
1:
0.6087948783474462805796726296862737909846594934519265785818425337838818930391060621426157203648784009
comment: $a^3-a^2+2a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.367.1
-379
1:
1.056225247002252433832540585493530202346770025491229374774170417278248749948982010398208605146694708
comment: $a^3-a^2+a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.379.1
404
1:
0.7482439113954884145060409826105879717372772109392398454933463011527509731708086698086128903702750209
comment: $a^3-a^2-5a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.404.1
-411
1:
1.248549201542750358786988468913918816797591864732884558078891614574034982749535121601044627254543067
comment: $a^3-a^2+5a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.411.1
-419
1:
1.026688138596539129282838490448334864244052228734373531843738139593298290941083471976308609822261461
comment: $a^3-4a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.419.1
-424
1:
1.482529983258733135931330717740615017529656940047030643273324268692215651969415151505252306960884997
comment: $a^3-a^2+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.424.1
-431
1:
1.862716965220339612183771505339685062399169254870386071954738568141682827494760903532658573010317743
comment: $a^3-a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.431.1
-436
1:
1.488934501155397371372278323944733673812835494595924553999013152942803286029092376764611512874258298
comment: $a^3+a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.436.1
-439
1:
0.7287345520672687559105295014218168678265031579219033488922645727282086261137360375789883590133028194
comment: $a^3-a^2-2a+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.439.1
-440
1:
1.358209318295501142560363280776656092711512649301485316732795811811225619957816527408214877221151410
comment: $a^3+2a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.440.1
-451
1:
1.057929719694696019805088388121274377274987127059138570881514995288753128532343937173338277785437857
comment: $a^3-a^2-5a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.451.1
-459
1:
1.076152261841048414843673436036494066246706522627234176706623387016682552485337949767836372603101849
comment: $a^3+3a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.459.1
-460
1:
1.075359649059708156529202004398628957006950453214151164018563761660598701605148983145957536038633399
comment: $a^3-a^2+5a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.460.1
469
1:
0.7116280126004024387792801539799854716710061303967816207657551483576709122207416778096152338821855920
comment: $a^3-a^2-5a+4=0$; $S_3$; $h_K=1$; LMFDB 3.3.469.1
-472
1:
1.556069931612638148318048972659782500859018621157784113156549550160727800727277647171884292281613449
comment: $a^3-5a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.472.1
473
1:
0.5229273082964934146705821621896118220067078808330366110345878459758622459584112203664760427199253672
comment: $a^3-5a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.473.1
-484
1:
1.514443483008047476357694745375595727216729612225256550769759459797583191549319026915117530177411263
comment: $a^3-a^2+4a+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.484.1
-491
1:
1.072446042480841962228046676213461661886685607014053285190167267430976313652865514840709895659830277
comment: $a^3-a^2+a+4=0$; $S_3$; $h_K=2$; LMFDB 3.1.491.1
-492
1:
1.252249097129449014227957443040969707434484011750844995252237932226070321557383110070843935300231926
comment: $a^3-a^2+3a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.492.1
-499
1:
1.089600365337339242299672205496143931809622448299922387615994150298364055792020633721346786290046656
comment: $a^3+4a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.499.1
-503
1:
1.968734998797822533754935930276042606097958971800484335131428465462944882680808205865026724578272309
comment: $a^3-a^2+2a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.503.1
-515
1:
1.009416879722814846874115181793014351357684520626546917179787461797978111510392799167956327709722428
comment: $a^3-a^2-a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.515.1
-516
1:
1.766124073130257317523352582935843629131722786874261216187346956581094186415465410775716237883366263
comment: $a^3-a^2+a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.516.1
-519
1:
0.7393072445583079565681140114176058243485640545048704589731467940372677488667301455129071586062029342
comment: $a^3-a^2-4a+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.519.1
-524
1:
0.9393809056035119889130232705314327067974995668519155747719542641078910815989860030942567406347813736
comment: $a^3-a^2+3a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.524.1
-527
1:
0.4426499868230105982832204351191442514041834007998706392313907108211143243083039651350128038630994023
comment: $a^3+5a-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.527.1
-543
1:
0.8123920075025341512151154988676082111431725312488782540889969176323867345811143393784500601722229450
comment: $a^3-a^2+2a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.543.1
-547
1:
1.173202957471195349785402256270730553535772671317524529141517869511057297883408525574305106333295036
comment: $a^3-a^2-3a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.547.1
-563
1:
0.9197959083964123511639492560091811372412765351877916517521907432392704785174749010203045856717343510
comment: $a^3-a^2+5a-4=0$; $S_3$; $h_K=2$; LMFDB 3.1.563.1
564
1:
0.9099869062860827828011600279225957234151350211512667106989202784219612696202884240610853825140927168
comment: $a^3-a^2-5a+3=0$; $S_3$; $h_K=1$; LMFDB 3.3.564.1
-567
1:
0.6501785486330719128966193371398582472927210898256796509415310379787745877717160675489258041625353550
comment: $a^3-3a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.567.1
568
1:
1.021684993986789083120881746703885217567535904235053240336018220906168392318242684342798127928958929
comment: $a^3-a^2-6a-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.568.1
-588
1:
1.285727899439781234066138963981611432565949010587873210297563181612481924126164788202531431359330437
comment: $a^3-a^2+5a+1=0$; $S_3$; $h_K=3$; LMFDB 3.1.588.1; $K=\mathbb{Q}(\sqrt[3]{28})$, a pure cubic field
-620
1:
0.8965379313134157860892543107304422812665160629672009505891627670788038425604145819967223884456783686
comment: $a^3-a^2-5a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.620.1
621
1:
0.8667304378112817084507820255847887137052357819506802629359518235519949633480678931465573022097938737
comment: $a^3-6a-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.621.1
-628
1:
1.628157175774727629504672798417893578166182463622100383942595855604791235313566964419486322381425126
comment: $a^3-a^2+4a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.628.1
-643
1:
1.168855064908177787171926747868484941830279907624918251099630846634047432932774156367300998554378012
comment: $a^3-2a-5=0$; $S_3$; $h_K=2$; LMFDB 3.1.643.1
-648
1:
1.653898929860607333411982019605941024748376910167668481910690782300985451899295722795967960147981591
comment: $a^3-3a-10=0$; $S_3$; $h_K=3$; LMFDB 3.1.648.1
-652
1:
1.063138844038298218657728130755097523616615417054836777595697415927955648035229022743361927384034995
comment: $a^3-a^2+7a+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.652.1
-655
1:
0.7133423455337915389905535251489257216021108671313156817837274274257471248875000738550648360438412995
comment: $a^3-a^2+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.655.1
-671
1:
0.5688228474563830749657914076262833692297340590088372845917335575516250432729715952394365411456381530
comment: $a^3-a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.671.1
-675
1:
1.163730416808703737249532757065157778962103075923547750110376715696620209498552518173846511947870397
comment: $a^3-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.675.1; $K=\mathbb{Q}(\sqrt[3]{5})$, a pure cubic field
-676
1:
1.584871647326182780372559370195208753691884966077030006616451486358282341852328116380638583521940929
comment: $a^3-a^2-4a+12=0$; $S_3$; $h_K=3$; LMFDB 3.1.676.1
-679
1:
0.8302603204426874093588326719543422557868289770633710782676559038236986129794162574697331403741779132
comment: $a^3+a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.679.1
-680
1:
1.462732717699784048356286861133082331368053217851957152540324626325822697965145416541911906506219143
comment: $a^3-a^2-6a+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.680.1
-687
1:
0.8281909422851150994960026292154260746701186786244783338181639350875393501037492041931078388072607097
comment: $a^3-a^2+4a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.687.1
-695
1:
0.5127082097158632688502014593369465423972374954854152877245447960810657071750723224690516504484307382
comment: $a^3-a^2-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.695.1
-696
1:
1.860041505680633735993520677762326060086712665035991729224228421146768350088330482717502241318101857
comment: $a^3-a^2-2a+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.696.1
697
1:
0.4108745217951735699889131130306171931166733205953022350043302410392708765604152962104113589814357925
comment: $a^3-7a-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.697.1
-707
1:
0.9893772465249515689782634317300810830943255633772518860101409860054899925641694739018268856942960733
comment: $a^3+2a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.707.1
-716
1:
1.504066564479973965817579191873594943857375085090978020089203247139751592629139646137005213448324652
comment: $a^3-4a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.716.1
-728
1:
1.409366250599083918717462783338577933639586124470194684645589436003535808768967761460248435205523885
comment: $a^3-a^2+6a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.728.1
-731
1:
0.9354608669916707632642282882502355403257457360871604052193768297630082786015920328640992936019250518
comment: $a^3-a^2+3a+4=0$; $S_3$; $h_K=2$; LMFDB 3.1.731.1
733
1:
0.7843819835282986224736501483056073990072678790592056734355580044218845048825113033569376616517909250
comment: $a^3-a^2-7a+8=0$; $S_3$; $h_K=1$; LMFDB 3.3.733.1
-743
1:
1.050111587460262640472881000216597851570494491689870037822027930450561959094158199737809352399220773
comment: $a^3+5a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.743.1
-744
1:
1.910614649048782617831893670639920473161909553408454212182900080277552454138409312749236838076290814
comment: $a^3-a^2-6a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.744.1
-748
1:
1.041115436718788598605019069373737972998685482689884703480337374603512063950251515706590383179784007
comment: $a^3-a^2+a+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.748.1
-751
1:
0.8106690819804506686357682977199784809570776307127941114412805113641470960707738870970485717243575768
comment: $a^3-a^2+6a-1=0$; $S_3$; $h_K=2$; LMFDB 3.1.751.1
-755
1:
1.121392919107630338764082907269921776474782782499790350985879687350565715286235258368983842406076948
comment: $a^3-a^2+5a+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.755.1
-756
1:
1.624177071899878460913114508699086331075187534211594546755460417017825933699599777594439224932698437
comment: $a^3-6a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.756.1
756
1:
0.8280231880470821640241000097875709854971924293113926192179027459350813901794490150910684779513951867
comment: $a^3-6a-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.756.1
-759
1:
0.7155455543758229774385352799519656044819442119777271866569330200568868423683177030755948474211012785
comment: $a^3-a^2+6a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.759.1
761
1:
0.5113102760036285565045360812320222065630840824921327767648166262557684302778364822506002809856232993
comment: $a^3-a^2-6a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.761.1
-771
1:
1.389313952546271187001457271873441798482747282369320686120530911939965003586622409256825562650353657
comment: $a^3-a^2+3a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.771.1
-780
1:
1.385662218948574080089864078091312864133585881596386221164560364035019418420493273090582432305851194
comment: $a^3-a^2-a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.780.1
785
1:
0.5850935476357672015170915463983467528866671453513742634270985342494273588282526656457555258010071997
comment: $a^3-a^2-6a+5=0$; $S_3$; $h_K=1$; LMFDB 3.3.785.1
788
1:
0.8530474851495875998619083079174517756429553239149552942593835008059265990612191802380281423204574371
comment: $a^3-a^2-7a-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.788.1
-804
1:
1.899363143203612486284315024502117286358516743687506782785930278590437062068200803970566767655848404
comment: $a^3-a^2+4a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.804.1
-808
1:
1.685462078127346524692601687330270601726746552257446190400675908045393682384400548381632610421591366
comment: $a^3-a^2+2a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.808.1
-812
1:
0.8476373128237877814730430017838278452491591339278596030243466051417556158767012126347194045787977159
comment: $a^3-a^2-7a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.812.1
-815
1:
1.114448607179145916000886889268382261812307067625839462703670381140784756582762264152622241675041835
comment: $a^3-7a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.815.1
-823
1:
0.6424505918514098123911722568050849200766185576605839303853180091935712366210705336185925033241588767
comment: $a^3-5a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.823.1
-835
1:
1.333208413960400310964226478950964926604022036144145353749254701936593518526402450918532377152841451
comment: $a^3-a^2-a+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.835.1
837
1:
0.9403588875117748460106446359426108911724063907830856947671796339190700794744226785901112235217336322
comment: $a^3-6a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.837.1
-839
1:
0.6954205820130348763129580468659519682715746459162267954868389092925481316873336549269870204290498579
comment: $a^3-a^2-2a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.839.1
-843
1:
1.457670115558886461685397482295770080642373285555751450441110918442342609227282054833649697083283678
comment: $a^3-a^2-2a+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.843.1
-856
1:
1.628321683713180490846160355293562910852966614710747370776297439160262604056803990904225446035332690
comment: $a^3-a^2+a+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.856.1
-863
1:
0.4323028664519562153642182269582371914001438531252833504745539801908696715417893176722559180877544518
comment: $a^3-a^2+2a+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.863.1
-867
1:
1.467960883315759822554790096609544841493709719444463945443037320338935009418239709780244286198896776
comment: $a^3-a^2+6a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.867.1; $K=\mathbb{Q}(\sqrt[3]{17})$, a pure cubic field
-876
1:
1.262687424555783085897976623940056875999036685213453573329067837754106644345460289728867456273686398
comment: $a^3-a^2-a-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.876.1
-883
1:
1.246913763240385956482095267701033968839094233802369130854820459599846530614338206320500421967742369
comment: $a^3-a^2+2a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.883.1
-888
1:
2.032890098275175861734513094283107803111212361941322666350042439713505292463332833135821286573542951
comment: $a^3-a^2+9a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.888.1
-891
1:
1.134357500152468174874580892199351168759053214050168011080630749132297625217673093331904058140365137
comment: $a^3+6a-1=0$; $S_3$; $h_K=3$; LMFDB 3.1.891.1
892
1:
1.114725308607885386176718141535507032740821851162761454587793650019638623200042806237214765087258061
comment: $a^3-a^2-8a+10=0$; $S_3$; $h_K=1$; LMFDB 3.3.892.1
-907
1:
1.251002109205188386749483302408639455892378484258409559862926232891821147079905473942994935088858212
comment: $a^3-a^2-7a+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.907.1
-908
1:
1.608811193020107343466594974240846467706821110977865314052293968693564205545571501318604764135198142
comment: $a^3-4a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.908.1
-931
1:
1.140975833327764349413196852377300359539403762720478865245038583104644488518539780736129447490444587
comment: $a^3-a^2+5a-6=0$; $S_3$; $h_K=3$; LMFDB 3.1.931.1
-932
1:
1.411805676146372545840060983995949255260613216906888243404404925298031263759582987323237325785224414
comment: $a^3+5a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.932.1
-940
1:
1.196380882156706433443325646192099897886833977684080627777774742010052064330475865336409050987791976
comment: $a^3-2a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.940.1
940
1:
1.162212068451935364166472191971955572497556922140736387351541569667482696674952624546867693432631822
comment: $a^3-7a-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.940.1
-948
1:
2.052652682647235001581285729588192150883081088417444679917409153540953753070477093165692424368248243
comment: $a^3-a^2+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.948.1
-959
1:
0.3697892673978084890825730432356926393554867601554180751532759772428208605493142689001545134521150519
comment: $a^3-a^2+6a+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.959.1
961
1:
1.573649279043335784582533614280749907049378688992380043103464702332361140794223041569321238347667622
comment: $a^3-a^2-10a+8=0$; $C_3$, conductor $31$; $h_K=1$; LMFDB 3.3.961.1; the cubic subfield of $\mathbb{Q}(\zeta_{31})$; $\kappa_K=|L(1,\chi)|^2$ for $\chi=\chi_{31}(5,\cdot)$
-964
1:
1.616488667631960793236179077345486379304922661772809587157989001482566192755766570616440098105881086
comment: $a^3-2a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.964.1
-971
1:
1.699426553777631833728775655985524632710979847382670311067143433893554970282117216071870749566346627
comment: $a^3-a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.971.1
-972
1:
1.028995684175976725333974068156413889861952697326763381218947938894053096823015249625772902615114878
comment: $a^3-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.972.1; $K=\mathbb{Q}(\sqrt[3]{12})$, a pure cubic field
-972
2:
1.166863915410888211007328976143866303247506035041573637370232976191583768347423519523036128361741375
comment: $a^3-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.972.2; $K=\mathbb{Q}(\sqrt[3]{6})$, a pure cubic field
-980
1:
1.526073964721646531745291208836370646956485230669893589198430063186808095403675566684669369746777466
comment: $a^3-a^2+5a-13=0$; $S_3$; $h_K=3$; LMFDB 3.1.980.1
-983
1:
0.3819245909249189282862763475545971867659895354115036073059407527633252700514206961631264100766486003
comment: $a^3-a^2+6a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.983.1
-984
1:
1.998839746493294475789055914042547319782730627062207413649481698405592699979816863290795682632465888
comment: $a^3-a^2-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.984.1
985
1:
0.4746481585273399408117436824769623967993748822874521828890127169558480320813785507421754989589412733
comment: $a^3-a^2-6a+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.985.1
993
1:
0.7050851916000282219545039342249782091984711937694230314049131554314950883915032691261433081365699728
comment: $a^3-a^2-6a+3=0$; $S_3$; $h_K=1$; LMFDB 3.3.993.1
-996
1:
1.996610487413031049886875354845199027209597384581207385820769500325970584336873106389497245996823148
comment: $a^3-a^2-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.996.1
-999
1:
2.486992766726557376620164658818088475784070145156136894254582426966495842629817358273962469112741326
comment: $a^3+3a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.999.1
-1004
1:
1.534162262746097792379341306830811180335585611391885736527867497831449383481861332904541372285226902
comment: $a^3+2a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1004.1
-1007
1:
0.5151337867303164909422180421713245060523577976072110171457633907589470281419502330590227427625888475
comment: $a^3-a^2-2a+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1007.1
-1011
1:
1.402045623250473750258760431207558710716463328685121477941504679023379739386293056395985239979171262
comment: $a^3-a^2-5a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1011.1
1016
1:
1.271090818310435421784740191876159192547820977914188689832205870039704035308357428023477221498509297
comment: $a^3-a^2-6a+2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1016.1
-1036
1:
1.021243555167014698596199714470476327822094944249629549515782850117723522043084476403977640668051250
comment: $a^3+4a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1036.1
-1048
1:
1.737067639993670844748725952711236151411163889096184709832545325236096182342593096846968186120894926
comment: $a^3-a^2+8a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1048.1
-1055
1:
2.336039366957959999064859092774690427078428160462454175515673272683315914017051873163526525348844598
comment: $a^3-a^2-6a+16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1055.1
-1059
1:
1.443981336207916030366810389394466463625631337274281930643963059809481365081142497201857374868323196
comment: $a^3-a^2+a+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1059.1
-1067
1:
1.079616754783463402863912254161184660887860371795986657695040387319331029367291356081488398236970330
comment: $a^3-4a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1067.1
-1068
1:
1.378401879205442563353247080510627362478453257988157134986850447335668448839397447247708483116745309
comment: $a^3-a^2-a+13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1068.1
-1075
1:
1.261598199869839613822039631491252303532819034891667015804198864204238431105057146924615424347132754
comment: $a^3-a^2+2a+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1075.1
1076
1:
0.8453428443228883740046561515484004840492657235494263213984232203716197623860797004941534273124021856
comment: $a^3-8a-6=0$; $S_3$; $h_K=1$; LMFDB 3.3.1076.1
-1080
1:
1.890812813990096071273198050285591452606886219119447943717334375083672959875446919236197146526267356
comment: $a^3+3a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1080.1
-1083
1:
1.505877114677266571072545520669845679705770199601259248714019033907012033562518094778555437419776456
comment: $a^3-a^2-6a-12=0$; $S_3$; $h_K=3$; LMFDB 3.1.1083.1; $K=\mathbb{Q}(\sqrt[3]{19})$, a pure cubic field
-1087
1:
0.6530338674540356294361112164961424372797099905746474308819496966020648163141499654584982330525552676
comment: $a^3-a^2+4a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1087.1
-1096
1:
1.666130444602738696865905193846985666040091441108650490430094610004277323804948004760427079319922233
comment: $a^3-a^2+a-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1096.1
-1099
1:
1.206017998653386726331766073170431938706836337252075338342586348067321199266329788508990667460645943
comment: $a^3-a^2-a-6=0$; $S_3$; $h_K=2$; LMFDB 3.1.1099.1
1101
1:
1.107123935223925523648293031054560340821164392483851851586191310731739031717277693812512064538858610
comment: $a^3-a^2-9a+12=0$; $S_3$; $h_K=1$; LMFDB 3.3.1101.1
-1107
1:
1.243261794029301885167648082495291979971719548583913017604816974930444083790521693339242766797995100
comment: $a^3+6a-3=0$; $S_3$; $h_K=2$; LMFDB 3.1.1107.1
-1108
1:
1.788343634144408279132977404429600618787029436432616247707017949333821184958018906732397554268705886
comment: $a^3-a^2-8a+14=0$; $S_3$; $h_K=1$; LMFDB 3.1.1108.1
1129
1:
0.8008849803408968615359593442904127194519298850946430358675207938982177695298676173885782206107469687
comment: $a^3-7a-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.1129.1
-1135
1:
0.7752268016330520917121146263389123605307467169672538378405763773859897941521848488511101852553418394
comment: $a^3-a^2-6a+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1135.1
-1144
1:
1.633921797075778171608263680198474118397124557014608343487847259860767888661200736741244476876880728
comment: $a^3-a^2+6a+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1144.1
-1147
1:
1.225166886379692158562423389223987977690440147346574002757456532503592227141066881381800423179275218
comment: $a^3-a^2-3a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1147.1
-1164
1:
1.267482199079368771853922046179472985026464465045769334607162169972424276035564729221158820486139371
comment: $a^3-a^2-a+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1164.1
-1172
1:
1.381015770378547251330958781752146013925535002209451454600805849200924892973424994495545512271389508
comment: $a^3-a^2+5a+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1172.1
-1175
1:
0.3723288740798184873388299245754291470790416295838970618125590421580441734863601032755938823691898069
comment: $a^3+5a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1175.1
-1176
1:
2.039583462851885393666139415551718145969705272604264625747890899713302443217962613801357891426817075
comment: $a^3-a^2-2a-6=0$; $S_3$; $h_K=3$; LMFDB 3.1.1176.1
-1187
1:
0.9892550476449419890049252279561359740893242032406994193286122357838601819809634303477840713247246722
comment: $a^3-a^2+7a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1187.1
-1188
1:
1.743972123632277259536395878392837082810226819174036432079581999617784278035074719509134396850515591
comment: $a^3+6a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1188.1
-1191
1:
0.7547276880488274661583787893330266467675522762057701087248445460498172132993414313541950022296881955
comment: $a^3-a^2-10a-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1191.1
-1192
1:
1.816073122443011009368740359601215134821006115064002227213932089849781477326355328462330404758221193
comment: $a^3-a^2+2a+6=0$; $S_3$; $h_K=2$; LMFDB 3.1.1192.1
-1196
1:
0.7838630112659529552503653282472948640380450661704989802405384928546644820049066049187069357536930668
comment: $a^3-a^2+5a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1196.1
-1203
1:
1.528679834238898654382986248432082830335269277754029595563290656653648511096105219046665400196952009
comment: $a^3-a^2-3a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1203.1
-1207
1:
0.7522803794523176660832714074006315214598012309059273486863321235116931999638110054741358110573557558
comment: $a^3-a^2-6a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1207.1
-1208
1:
1.428262133793110844807401831320821421466868090312979530615027361572922691874778824931963686311997509
comment: $a^3-a^2+8a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1208.1
-1219
1:
1.164480174794187841134892032226642384692015200907370193867917551820958706208173883246371965234535020
comment: $a^3-8a-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1219.1
-1228
1:
1.212969492167461695721005096078406636534198170734127307791717826774857931955264540803371782388602370
comment: $a^3-a^2+a-7=0$; $S_3$; $h_K=3$; LMFDB 3.1.1228.1
-1228
2:
1.037069655374242938806871716910068307326252524185529384803820121880583928747656662382913479256403456
comment: $a^3-a^2+7a-1=0$; $S_3$; $h_K=3$; LMFDB 3.1.1228.2
-1228
3:
1.078218294996386531750209988226479612716095819806740247178263836129776513552785671678157606618751014
comment: $a^3+4a-6=0$; $S_3$; $h_K=3$; LMFDB 3.1.1228.3
1229
1:
0.9392585080707858405010068595784502872198241538252648977320754137022100827143010877862777288038808889
comment: $a^3-a^2-7a+6=0$; $S_3$; $h_K=1$; LMFDB 3.3.1229.1
-1231
1:
0.8297408695601356649735286330093747331774687358309316183293720789922928660452603620259188067273329489
comment: $a^3-a^2-4a+9=0$; $S_3$; $h_K=1$; LMFDB 3.1.1231.1
-1235
1:
1.035757073103577064507826154527243158208987570190686916281009246812900815025080357260853856577512668
comment: $a^3-a^2-5a+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.1235.1
-1236
1:
2.059849397055059789902186438045308761432323226854784899433765383280038972787343394155579399170846246
comment: $a^3-a^2+4a+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1236.1
-1255
1:
0.7610269431118826275543482001784638071830276229591790915439799963991824807425659123803232154579798010
comment: $a^3-a^2+4a+5=0$; $S_3$; $h_K=2$; LMFDB 3.1.1255.1
1257
1:
0.6991432562258760546042203903734607591298423415405265915527799837342445859542157813257897774918505393
comment: $a^3-a^2-8a+9=0$; $S_3$; $h_K=1$; LMFDB 3.3.1257.1
-1259
1:
0.9668194987653197449134444866943970565848151540481276591780344935746867249325834410459599622579539616
comment: $a^3-a^2-9a+16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1259.1
-1267
1:
1.343369785563429219051696570329200254924515576439369873684003673938986164121813755880634659736281405
comment: $a^3-a^2+7a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.1267.1
-1272
1:
2.143336046851459912358741789060960977079903780946347232183594807329378813254334838322434773711908152
comment: $a^3-a^2-3a+15=0$; $S_3$; $h_K=1$; LMFDB 3.1.1272.1
-1291
1:
1.289710440103613380633101185578871414707168227195368056657332548970609805838761704334934790198572695
comment: $a^3-2a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1291.1
-1292
1:
0.7925738616666260214022473860367050757648051938865988900798446268629333399547398730522811050017733915
comment: $a^3-10a-14=0$; $S_3$; $h_K=1$; LMFDB 3.1.1292.1
-1295
1:
0.6158588728936857956055742778055095819698082771674705382009784924806120891308263207806743518061368238
comment: $a^3-a^2+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1295.1
-1300
1:
1.767015180897481360524969209225442330628080953741840226906009648312031212066873188247996243443890572
comment: $a^3-a^2-3a-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1300.1
1300
1:
0.7266578634333542215010747633128913369553015939933876910600685905071024017465575861649175095460801833
comment: $a^3-10a-10=0$; $S_3$; $h_K=1$; LMFDB 3.3.1300.1
1304
1:
1.321099682749909884341160645205910917224334961826541703181008522248791292459530529201964573934690130
comment: $a^3-11a-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1304.1
-1315
1:
1.352506939898543636257367165912875952855337491975308106042949976485775600330420255932348034470521718
comment: $a^3+7a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1315.1
-1316
1:
1.341668861853682004997911052353052029812165192430784676414813888205613770640031341440551971390647734
comment: $a^3-a^2+9a+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1316.1
-1319
1:
0.4229577650096286111886362815043655778748719893913483513561728126328379261533963392218461996233264795
comment: $a^3-a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1319.1
-1323
1:
1.265024764014699236046046767126675320316850443209426677661025305976835048670704634554177103837078305
comment: $a^3-7=0$; $S_3$; $h_K=3$; LMFDB 3.1.1323.1; $K=\mathbb{Q}(\sqrt[3]{7})$, a pure cubic field
-1327
1:
0.6374426183723695698970897917745176078454312193783081488432838730904720809062337842923717126732848606
comment: $a^3+a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1327.1
-1336
1:
1.644756695090981733054935639806126810556496528968329581488471077596760015363172541475209793292326479
comment: $a^3-a^2+9a-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1336.1
1345
1:
0.5368924450560727465059338857791600107625834619025711466063996647817014577427325719779926902361084316
comment: $a^3-7a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.1345.1
-1347
1:
1.546484307357525406723918211967794847606386810100008603579726682853094204139378681356573305459471097
comment: $a^3-a^2-7a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1347.1
-1351
1:
0.6041276705756111379166153448621608181835053047530704092425318175629382619206379016496371382059103878
comment: $a^3-a^2-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1351.1
-1355
1:
1.094728801351111527911236793686281550037426349546731477601351948563550303400127261423637868275807218
comment: $a^3+2a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1355.1
-1356
1:
1.393043072447469712939617584815954208595524732369205231848607160772251682066304884720679951083840028
comment: $a^3-a^2+a+21=0$; $S_3$; $h_K=3$; LMFDB 3.1.1356.1
-1356
2:
1.600143717597090310182629763813830761740956657765358792368572219603868424446325903663923508944441801
comment: $a^3-a^2+3a-15=0$; $S_3$; $h_K=3$; LMFDB 3.1.1356.3
-1356
3:
1.231993966321399598111472981108677256947695879414265194796192901073056874392295477807005741760107176
comment: $a^3-a^2+11a+1=0$; $S_3$; $h_K=3$; LMFDB 3.1.1356.2
-1363
1:
1.227952631874290203240016960682158168730838483201361372587547907770553087334934102260204138966417730
comment: $a^3-a^2-9a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.1363.1
1369
1:
0.3379708314502688694228188230765245504939444656831449572341793086260741227449926657844415937244825171
comment: $a^3-a^2-12a-11=0$; $C_3$, conductor $37$; $h_K=1$; LMFDB 3.3.1369.1; the cubic subfield of $\mathbb{Q}(\zeta_{37})$; $\kappa_K=|L(1,\chi)|^2$ for $\chi=\chi_{37}(10,\cdot)$
-1371
1:
1.451432203572405954657834353952462864036010543974713995877244454820906578681852894197054196078528601
comment: $a^3-a^2+3a+6=0$; $S_3$; $h_K=4$; LMFDB 3.1.1371.1
1373
1:
1.017170759842542986094592638585872314782178730534013690591442272619320219805239419339066528666627414
comment: $a^3-8a-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.1373.1
-1383
1:
0.8467249805598354249100273900031630711725026321809421585281404371710863661685533407950266892079828522
comment: $a^3-a^2+6a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.1383.1
1384
1:
1.116337027917748954961024247609400744490120865311734676438917329908451557072226911013554543085727311
comment: $a^3-a^2-10a+14=0$; $S_3$; $h_K=1$; LMFDB 3.3.1384.1
-1388
1:
0.7883203863443698965415054843382395360193302472331172089549374654984166925067746189197680524110190411
comment: $a^3-a^2+7a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1388.1
1396
1:
0.8721404564276296665760663791455561566484582471666998893186626648382324352286660409982524687238043863
comment: $a^3-a^2-7a+5=0$; $S_3$; $h_K=1$; LMFDB 3.3.1396.1
-1399
1:
0.6547406395950409818984163274392858748143186957545640164293289142138980079200497698085332202375483510
comment: $a^3+7a-1=0$; $S_3$; $h_K=2$; LMFDB 3.1.1399.1
-1407
1:
0.8996228126250860806692720373507433440443632813656891760924934078496719995953123525341939157209838548
comment: $a^3-a^2-8a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.1407.1
-1419
1:
1.437689162290735276644635779145096033861162324329320474959677762219067929222395786969210292936269624
comment: $a^3-a^2+10a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1419.1
-1420
1:
1.177247429746818306653062339527002231111305391997919311600909051749003979335541003405481334458686515
comment: $a^3-a^2-5a+17=0$; $S_3$; $h_K=1$; LMFDB 3.1.1420.1
-1423
1:
0.6618929543841479324350008651258970495199143148697048898492180853616704958719872000486797986388559867
comment: $a^3-a^2+6a-7=0$; $S_3$; $h_K=2$; LMFDB 3.1.1423.1
1425
1:
0.7074342133922592274401449328535800903692495462432864305375145919772664896812766567810147092336960427
comment: $a^3-a^2-8a-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.1425.1
-1427
1:
0.9031277932352451413149187351045060859012227640367675278247213900137084900501895413579487625728037275
comment: $a^3-a^2+3a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1427.1
-1431
1:
0.6312814169634788620370005742412422159616573949816296512091480552526379386829553115816078986930069067
comment: $a^3+3a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1431.1
-1432
1:
1.844339723647503442696649447475901540301387752306349617026106911546029379810603854260932778967556144
comment: $a^3+10a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1432.1
1436
1:
1.340565548776665245012133453154112233068120288771334661121918648138825902328297102324261422191296792
comment: $a^3-11a-12=0$; $S_3$; $h_K=1$; LMFDB 3.3.1436.1
-1439
1:
2.188892915859507692876731305261915497341585454270529700241960254043856385078140508955808493186478509
comment: $a^3+11a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.1439.1
-1448
1:
1.555179931488601298666612212780187561898487076670330481761920589684653242870995414935454141471450617
comment: $a^3+5a-14=0$; $S_3$; $h_K=1$; LMFDB 3.1.1448.1
-1452
1:
1.367900052140011056757359684795594525570175550206150886741092819877866956182204894541052234799775657
comment: $a^3-a^2-7a+13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1452.1; $K=\mathbb{Q}(\sqrt[3]{44})$, a pure cubic field
-1464
1:
2.108059252095943589206984077437224448559219308949305262564930291353235437606698984997722859541658154
comment: $a^3-a^2-7a+19=0$; $S_3$; $h_K=1$; LMFDB 3.1.1464.1
-1480
1:
1.936417755674055725521736254681390059854344512382627806408182247103464041777982199614841314564485465
comment: $a^3+7a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1480.1
-1484
1:
1.693488474994623250008751132152595154178185216029743709470876916344709922886349855705441208609913266
comment: $a^3+8a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1484.1
1489
1:
0.3483654634187193645398162198092278551987718866748233731853070369895004603712559098925891080502181419
comment: $a^3-a^2-10a-7=0$; $S_3$; $h_K=1$; LMFDB 3.3.1489.1
-1491
1:
1.531143789817210806496500599678459451111274190705567655652561425943156521514197883438604521522682372
comment: $a^3-a^2+6a+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1491.1
1492
1:
0.7918278919172364719365593758278549947448022364746582238469134513447265880938730019381243287379586796
comment: $a^3-a^2-9a-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.1492.1
1509
1:
1.163126411462310178883866413219878027052832181008161382959950699042561420133433738182961216733043298
comment: $a^3-a^2-7a+4=0$; $S_3$; $h_K=1$; LMFDB 3.3.1509.1
-1512
1:
1.902191400099689236614394260785727530846402541747987296449946300618974954926722569482484268427848076
comment: $a^3-6a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1512.1
-1515
1:
1.684043217456981506660744359904307956965955440432185889739402777127663773190399371410611715171927218
comment: $a^3-a^2+5a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1515.1
1524
1:
1.070695019946056095853518211804210348194605201875782965079029955533007034765201203962236083937376064
comment: $a^3-a^2-7a+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.1524.1
-1539
1:
1.467658423905250204397723046231261141707465354861441652490234739016200904715249491836009451186858336
comment: $a^3+6a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1539.1
-1547
1:
1.032222849478243441627577637604301486133511455075766997396364285577984199029914599203745082352858734
comment: $a^3-a^2-a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1547.1
1556
1:
0.8493443896044726374754877190280822695144177721436312650608253431382196769111009702653917200199253868
comment: $a^3-a^2-9a+11=0$; $S_3$; $h_K=1$; LMFDB 3.3.1556.1
-1559
1:
2.323658778345661322162173288473346707740995568206429117411753089225026728075654894350319092412274732
comment: $a^3-a^2-2a+16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1559.1
-1563
1:
1.628084477914089102969134607958578806441196374132144678489015260830830916006131404751371708109141713
comment: $a^3-a^2+7a-6=0$; $S_3$; $h_K=5$; LMFDB 3.1.1563.1
-1567
1:
0.7897506827570646734333264956956352170333726591008722910723904304326952276973253437925312420106015595
comment: $a^3-a^2-2a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1567.1
-1572
1:
2.263607449486914209793432678264062347361362121481039817046359518291862192805819292596582816198996698
comment: $a^3-a^2+a+15=0$; $S_3$; $h_K=5$; LMFDB 3.1.1572.1
1573
1:
0.8517110177284526236660247145369574353755071708104993957700813560660001326968950494808921005378675773
comment: $a^3-a^2-7a+2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1573.1
-1579
1:
1.167165996100363552174112406234216687903680517401820274717346660115787465819886527728705948837770778
comment: $a^3+4a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1579.1
-1580
1:
0.8319830289555173971799977172936094217720479809839650066509171571062060597654584963462501507911699356
comment: $a^3-a^2+5a+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1580.1
-1583
1:
0.4516527107662877565155871052199915779728242788604744378079882819448916744385937601686839652826172026
comment: $a^3-a^2-4a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1583.1
-1588
1:
1.808090491158188139670481488672015023547112128049718689445285710028746956748661921691976055960662041
comment: $a^3-11a-16=0$; $S_3$; $h_K=2$; LMFDB 3.1.1588.1
1593
1:
0.6344688524050503958122851254588016486876337604093717194926252693550781183137121173855226340631244869
comment: $a^3-9a-7=0$; $S_3$; $h_K=1$; LMFDB 3.3.1593.1
-1599
1:
0.7014104475100152645444138289279628764050028224178570678558569269826380887150565730929239368057763961
comment: $a^3+3a-23=0$; $S_3$; $h_K=1$; LMFDB 3.1.1599.1
-1603
1:
1.367108902931706779048167114834021981408683567940442402216767509161463595447441691540052959896568663
comment: $a^3-5a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1603.1
-1607
1:
2.378617902000089715850506381915046948759253722245254651684173097552567597454713958451934948377447739
comment: $a^3-a^2+2a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1607.1
-1612
1:
1.115310431324501980697857436144700886758821683552885923061143021551182103052703509204316438229237744
comment: $a^3-a^2-3a-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1612.1
-1615
1:
0.7038656307945527708968859479826832034700815744936812979848848420094745531685826780438965004990342702
comment: $a^3+7a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.1615.1
-1619
1:
0.8787256879957525422269723982902410599940052585655278192813527080324201483862596596855869209140876511
comment: $a^3-a^2+a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1619.1
-1620
1:
1.938538786300611769016145123363900616178546155352287845126473541969403677739335638702738790164638702
comment: $a^3-3a-8=0$; $S_3$; $h_K=3$; LMFDB 3.1.1620.1
1620
1:
1.010498282982043444920394632970033106355549219297730564339644655305870782120159016627412757309913442
comment: $a^3-12a-14=0$; $S_3$; $h_K=1$; LMFDB 3.3.1620.1
-1647
1:
0.6265233617216422627856783939270569207964867054156966938183235676698348297666964882717159520211424447
comment: $a^3-9a-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1647.1
-1668
1:
2.279642264152196327653170168951579340329127344629403823896984380062017554416636184917015733730829189
comment: $a^3-a^2-4a+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.1668.1
-1675
1:
1.329385210663093484284448906083049687335686278323057587716193288978740155147742156535808603393100041
comment: $a^3-a^2+7a+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1675.1
-1687
1:
0.7517065424774998311926480785099898519935888298577957798111876861889939812156237353781467035247007446
comment: $a^3-5a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.1687.1
-1691
1:
1.868300927953679677731331239952740291332150737638679267499942258631999532330369013713426516472608888
comment: $a^3-a^2+a-24=0$; $S_3$; $h_K=1$; LMFDB 3.1.1691.1
-1700
1:
1.389238778198465696116351542925415996573006079011800407660975540984578024753964573013757540218182002
comment: $a^3-a^2+12a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1700.1
-1704
1:
2.070113181698032471025894376011516846238702971999583451525757167569303698360713941711553976747372704
comment: $a^3-a^2+5a-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.1704.1
-1708
1:
1.199224727849914119279497990081692322240897337513800423591872756886896836236797663615920594621037715
comment: $a^3-a^2-5a+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1708.1
1708
1:
1.245936631862243645685124641044704684316360220183257043820082245176851840863086102472454690192458135
comment: $a^3-a^2-8a-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1708.1
-1720
1:
1.979751427494764903209298645976471323660433095099991339450865033342016989457741146750318339762381717
comment: $a^3-2a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1720.1
-1727
1:
2.331866877626148819706985319957933992293153714161205722391842755065287449564091993128230157277696227
comment: $a^3-a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1727.1
-1732
1:
1.808433165223247916556529540620954519677726354681781317744966668460207995522253090793887391876328214
comment: $a^3+a-8=0$; $S_3$; $h_K=2$; LMFDB 3.1.1732.1
-1736
1:
1.358137788716954118778892877878836430474977826695305906259480763236683212407217599481640916682013512
comment: $a^3+2a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1736.1
-1740
1:
1.561984829782057093747609922598321948749944289727407997580409500533419668048456763134387961916065885
comment: $a^3-a^2-5a-15=0$; $S_3$; $h_K=1$; LMFDB 3.1.1740.1
-1743
1:
0.9243485894122902560248869234666043307895164658847167169519715455629868596492127698131643701592254659
comment: $a^3-a^2-8a+15=0$; $S_3$; $h_K=1$; LMFDB 3.1.1743.1
-1751
1:
0.9991461164246579740752918033494376171754933919068899764506273674440894948789558336274110423335142634
comment: $a^3-a^2-4a-23=0$; $S_3$; $h_K=1$; LMFDB 3.1.1751.1
-1755
1:
1.352266747613905489478961440181359737370330636180771736924096036815555770324256835630362894396471483
comment: $a^3+3a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1755.1
-1759
1:
2.767707226512934246488235728294235155435857719137449441450300770668521660708306026004088860179817936
comment: $a^3-a^2+10a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1759.1
-1763
1:
0.9006462746977786960751922470613307890112607575325592303396316799666301408873756032624812983503978457
comment: $a^3+11a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1763.1
1765
1:
0.8992646162333769505491071487639878497181469696096244791788733603675961173886753195061976789015562068
comment: $a^3-a^2-11a+16=0$; $S_3$; $h_K=1$; LMFDB 3.3.1765.1
-1772
1:
0.7741887936109046094985087400868751836597572481714497150897860525266966409949174321209449120497346239
comment: $a^3-a^2+3a+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1772.1
1772
1:
1.460630109661248023374824925734911001093875296919916846464776850945547568033012173251277978840675904
comment: $a^3-a^2-12a+8=0$; $S_3$; $h_K=1$; LMFDB 3.3.1772.1
-1807
1:
0.6804633988326187150805394419865463106040929517910455278108569537925943878722427139980189319253181800
comment: $a^3-a^2+8a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.1807.1
-1812
1:
2.233619602283713061379388332954894818259173678623356553090122514596953182638213567401609242107553770
comment: $a^3-a^2+8a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1812.1
-1815
1:
0.9928827624062163646724864147161662077723103806420025487496352093763798948285939874299409666428547085
comment: $a^3-a^2+4a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.1815.1
-1823
1:
0.6254140926957309633862728373479133147329718051327414631967609480038046459581790888857490384613980944
comment: $a^3+5a-7=0$; $S_3$; $h_K=2$; LMFDB 3.1.1823.1
1825
1:
0.4202313684002098994747187358508986115327985040397945716280406985293857838693926305357304533350162333
comment: $a^3-a^2-8a+7=0$; $S_3$; $h_K=1$; LMFDB 3.3.1825.1
-1836
1:
1.348077462673608726945531215410765132863160157325291509200776945851528474512911068413479391019124092
comment: $a^3-6a-10=0$; $S_3$; $h_K=3$; LMFDB 3.1.1836.1
-1836
2:
0.9500067809808678959123558492924832998589584265446962833675610465072209373647943807323391175561050794
comment: $a^3+6a-6=0$; $S_3$; $h_K=3$; LMFDB 3.1.1836.2
-1843
1:
1.307495688334854812953019845066025252450601649956811766721808516030689754511024142701924892904389327
comment: $a^3-a^2+a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1843.1
-1844
1:
2.564302542312973403677776056262952627783076228945647078201885697519939758422459149840319541039235945
comment: $a^3-7a-18=0$; $S_3$; $h_K=1$; LMFDB 3.1.1844.1
1849
1:
1.760173430970984430085834430411721431524791833395546426490500402713280032105492236659430809876946647
comment: $a^3-a^2-14a-8=0$; $C_3$, conductor $43$; $h_K=1$; LMFDB 3.3.1849.1; the cubic subfield of $\mathbb{Q}(\zeta_{43})$; $\kappa_K=|L(1,\chi)|^2$ for $\chi=\chi_{43}(6,\cdot)$
-1868
1:
0.7253320496938908707007071842873921038098495106479052889195059383825712379714547263592811993677861111
comment: $a^3-a^2+7a+13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1868.1
-1871
1:
0.3000337238615706780179364512877169717464212378364316395923458817025572106894309868046252975794489012
comment: $a^3-a^2+8a-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.1871.1
-1879
1:
2.731373413523486866062330660171870747816048491769226321970576554408624070890601625894835496637059061
comment: $a^3-a^2-2a-16=0$; $S_3$; $h_K=4$; LMFDB 3.1.1879.1
-1892
1:
1.464914272355977141484226701014742329017636994825047395312851594075176428207691185495668138159541957
comment: $a^3-a^2+a-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.1892.1
-1895
1:
0.4531196231914058219640350586571802700624094666576648545563026554652954807549815360789510494807077713
comment: $a^3-7a-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1895.1
1901
1:
0.9780511147327767852991978941862189003706855463887002055526502879528910798585351216332977808157004527
comment: $a^3-a^2-9a-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.1901.1
-1915
1:
1.481023582144235944330773099449077421018316994521592720877178972903592237292380679615040718156562161
comment: $a^3-a^2-6a+20=0$; $S_3$; $h_K=1$; LMFDB 3.1.1915.1
-1927
1:
0.6727335995190008600793242998160763148311878561986389900871871182394404569193956097230266763525665236
comment: $a^3-a^2+2a-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.1927.1
1929
1:
0.7484088226262983713012102486436122636102581459683080416190870979079944907726837046010291411309673873
comment: $a^3-a^2-10a+13=0$; $S_3$; $h_K=1$; LMFDB 3.3.1929.1
-1931
1:
1.834546232124302956045644395583915585469852678094877527870349798777220452887670170760911694415283344
comment: $a^3-4a-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.1931.1
-1932
1:
1.499354622811037195518788146772769127112245591146376888064262256365515930282433718831004585332474216
comment: $a^3-a^2+7a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.1932.1
1937
1:
0.5945958055853421654380643175904264599394174119374016091473741844622031663862705579497139642996195181
comment: $a^3-a^2-8a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.1937.1
1940
1:
1.006846225509569398886371375455153029413837251384489511842611057842863089434563560417414932642872432
comment: $a^3-8a-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1940.1
1944
1:
1.415307290959754407080901651737754542067354991293929859873261874295565268111565307203292803136361667
comment: $a^3-9a-6=0$; $S_3$; $h_K=1$; LMFDB 3.3.1944.1
-1951
1:
2.738222728104622272394739717932213147390676274745485185682827417102789270388592601806873465833765479
comment: $a^3-a^2-6a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1951.1
-1955
1:
1.092627175928928703324881909618140178753301933799504902318479065667655009265805190843315937322300815
comment: $a^3-a^2-5a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1955.1
1957
1:
0.8230844949917018420919581976598605628166428236582681098885450674169541602807145930724896517154743698
comment: $a^3-a^2-9a+10=0$; $S_3$; $h_K=2$; LMFDB 3.3.1957.1
-1959
1:
1.074768179069786414588922326818208855528204343781961087830884795052096861104432988800546871588163494
comment: $a^3-a^2+8a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1959.1
-1960
1:
2.069434300353847261034014199614935879386996942552927557783500715927052468574335901129383648621296570
comment: $a^3-a^2+5a+15=0$; $S_3$; $h_K=3$; LMFDB 3.1.1960.1
-1963
1:
1.282641965359856377310268732276427253389965708487838490428386861461141173767553995161133313232155464
comment: $a^3-a^2+5a+6=0$; $S_3$; $h_K=4$; LMFDB 3.1.1963.1
-1967
1:
1.217900191948593499749689988876834482158509328316141833215917034555661322577147793117431972570871303
comment: $a^3-a^2+2a+25=0$; $S_3$; $h_K=1$; LMFDB 3.1.1967.1
-1971
1:
1.573483000577272275956500861099382561801836644888528859145710257646564124235963490755669074281725306
comment: $a^3-9a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.1971.1
-1972
1:
1.827112978547127366663462018919657799083916431077644149211614446479200985719991159344539405493078199
comment: $a^3+10a-12=0$; $S_3$; $h_K=5$; LMFDB 3.1.1972.1
-1988
1:
1.502541976847634001136649228680524827710834562033231715212170937005228875953067794499271317927035797
comment: $a^3-a^2+9a-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.1988.1
-1999
1:
2.814153958618229898023139094615796512415967282478686871911078061024010829824044783088845739438429086
comment: $a^3-a^2+10a-16=0$; $S_3$; $h_K=5$; LMFDB 3.1.1999.1
-2003
1:
0.9625774334737917143053085748080889528736860736268838697154441224726161929154157004170256957635039823
comment: $a^3-a^2-3a+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2003.1
2021
1:
1.024868938166870864250419403526343203202749016716191549045655779019798309498225461331344179638326629
comment: $a^3-8a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.2021.1
-2023
1:
0.7930111572067430989424776178383461352680009199473829478272852581346016193708135191596730471029625365
comment: $a^3-a^2+6a+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.2023.1
2024
1:
1.402211318199005239575768655260017848819481775331560227133177357265737869734859959806188708032076257
comment: $a^3-a^2-10a-6=0$; $S_3$; $h_K=1$; LMFDB 3.3.2024.1
-2028
1:
1.374291853861159551472842642285417132714659995937393318172064766125566456572352340408220006893256022
comment: $a^3-26=0$; $S_3$; $h_K=3$; LMFDB 3.1.2028.1; $K=\mathbb{Q}(\sqrt[3]{26})$, a pure cubic field
-2036
1:
1.707406864643103726347017888744189674646746861265994991027355360595007859413333523501934004103966129
comment: $a^3-a^2+13a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.2036.1
-2039
1:
0.3123059373583041923039034134352824645958988456631118570763408964632128811327573729241804498368457416
comment: $a^3-a^2+4a+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.2039.1
-2047
1:
0.5997350710832906062814629290725284807619077498760193392984373753037183662426162022418141968695237805
comment: $a^3+7a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.2047.1
-2051
1:
0.8998648315509516406206165992534937642074427752648679830797534958792599239282720043776566498245074896
comment: $a^3-a^2-7a+14=0$; $S_3$; $h_K=2$; LMFDB 3.1.2051.1
-2052
1:
1.863978751298919545063098047763889659117495759115073399760046600960179844564803234868628052631510206
comment: $a^3+9a-14=0$; $S_3$; $h_K=1$; LMFDB 3.1.2052.1
2057
1:
0.5981756586325515067094512347985348001795348468542880614656999871605397129416139601065782955469915879
comment: $a^3-11a-11=0$; $S_3$; $h_K=1$; LMFDB 3.3.2057.1
-2063
1:
1.103011087207689075821965195124884550245025740479921067876603768482062626863284527047016784955934709
comment: $a^3-a^2-2a+27=0$; $S_3$; $h_K=1$; LMFDB 3.1.2063.1
-2068
1:
1.857705555237813524058383695295316894071961069173341601425225942677838477168206971747120198803352643
comment: $a^3-a^2-8a-10=0$; $S_3$; $h_K=4$; LMFDB 3.1.2068.1
-2071
1:
2.751215929953094761771242926014752935327072120296849277683814507652279361104752502303285382063674483
comment: $a^3+7a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.2071.1
-2075
1:
1.185500886588901767822172453636144672746889212620490405414094233171034851467652957057513474621261248
comment: $a^3-a^2-3a-8=0$; $S_3$; $h_K=3$; LMFDB 3.1.2075.3
-2075
2:
0.8735548455558771102866934875495216370828188016166360136695767274476816844994210469017338040590998283
comment: $a^3-a^2+7a-8=0$; $S_3$; $h_K=3$; LMFDB 3.1.2075.2
-2075
3:
2.008332178550057498412349894298340224546653924341519778791366896858616879639302238152651709006148029
comment: $a^3-10a-15=0$; $S_3$; $h_K=3$; LMFDB 3.1.2075.1
2089
1:
1.817000239944131994202377299651362040559635099404021256680330078208613067113107745089519537020016897
comment: $a^3-13a-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.2089.1
-2091
1:
1.455694595951183149055133313313409587849858442839943059130446406256970740696712183201641902582394908
comment: $a^3-a^2-a-26=0$; $S_3$; $h_K=1$; LMFDB 3.1.2091.1
-2092
1:
1.334892678637986472757142879462254659247974063952040693985486405849038060344921775684820720244721354
comment: $a^3-a^2+11a-15=0$; $S_3$; $h_K=2$; LMFDB 3.1.2092.1
2101
1:
0.7454865366021705769298258825235105405581754601700692510632720159291589106998377117617307005660957372
comment: $a^3-a^2-11a-8=0$; $S_3$; $h_K=1$; LMFDB 3.3.2101.1
-2104
1:
1.752962967363014516505335540812985449103295010902028660461555976208321436054981567912789033490401596
comment: $a^3-a^2+13a-1=0$; $S_3$; $h_K=5$; LMFDB 3.1.2104.1
-2116
1:
1.747943702912442563538883142055564568958865740904724491277553199487880255920422808417602785301342117
comment: $a^3-a^2+8a-6=0$; $S_3$; $h_K=2$; LMFDB 3.1.2116.1
-2132
1:
1.460118265270674281177584382735840987971306165480308378209676034965155879820506159331693292400557348
comment: $a^3-a^2-3a+19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2132.1
-2148
1:
2.284231373201790735142096106226556466198281741565499198034675974860338821399305387419545906363618534
comment: $a^3-a^2-7a-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.2148.1
-2155
1:
1.430229822244817152562263876106268783099608013351175028716776249186008316577640553461879002365301859
comment: $a^3-2a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2155.1
-2159
1:
0.4927261294893014102892108566139947752897845400442054634456710022070092090356019637582997965437740366
comment: $a^3-a^2-4a+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2159.1
-2167
1:
0.6790249291452101289497858101196594001131598315638857757537178185602789618840715976068124417527564647
comment: $a^3-a^2-12a+23=0$; $S_3$; $h_K=1$; LMFDB 3.1.2167.1
-2168
1:
1.347781013534641399428134855956507419915709693790969499926384275353176214255196090899346666860918701
comment: $a^3-a^2-3a-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.2168.1
2177
1:
0.6445185520951996736987637255976735617834657688289080235118959983784015610144428624738584824889214991
comment: $a^3-a^2-8a+5=0$; $S_3$; $h_K=1$; LMFDB 3.3.2177.1
-2183
1:
1.083756448058461215140115889265211935071273865180509804231560459453498823716960453852293384410605058
comment: $a^3-a-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2183.1
-2184
1:
2.278501383182768072844636699235117388565910104016107301315104781539592000538178189238121999627073070
comment: $a^3-a^2+13a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2184.1
-2188
1:
1.178545685957916266385969887827375279863583909030609344524569019718194833442855969735926749580130571
comment: $a^3-a^2+3a+17=0$; $S_3$; $h_K=3$; LMFDB 3.1.2188.1
-2188
2:
1.100054871365582615523748835713590166674385896694354690029915608251625692485093849849935958950413526
comment: $a^3-a^2+7a-19=0$; $S_3$; $h_K=3$; LMFDB 3.1.2188.3
-2188
3:
1.143180519436793284393117384128758125184762068172076105042286188306954013336227735773935685507553023
comment: $a^3-8a-20=0$; $S_3$; $h_K=3$; LMFDB 3.1.2188.2
-2191
1:
0.6786596230371450003744592716105127098943243455638857207212965667630277034052835376298569321992769227
comment: $a^3+a-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2191.1
-2199
1:
0.7221401971327709467601389803609144993849950118235997344558864442126736446559568479302639384259885150
comment: $a^3+3a-27=0$; $S_3$; $h_K=1$; LMFDB 3.1.2199.1
-2200
1:
1.961462335472812364196651004328333485980917964191095233202284945078487802163185019864895126988651089
comment: $a^3-5a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2200.1
-2207
1:
0.4252911326519268712778652934746449479238570312300140424153776634217391930961661945130037915587034652
comment: $a^3-a^2-6a+13=0$; $S_3$; $h_K=1$; LMFDB 3.1.2207.1
2213
1:
1.078242957053658414993676981294298864341499852916890972951599611431550621919811104401652537875906369
comment: $a^3-a^2-13a-12=0$; $S_3$; $h_K=1$; LMFDB 3.3.2213.1
-2219
1:
2.001191323007922581225737676145203503986871993871797343395451325721042174456953912296560789118283695
comment: $a^3+2a-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2219.1
-2220
1:
1.607056635335077393971303258471852120204201852180495516681055450629780415705406979614792955509021712
comment: $a^3-a^2-11a+21=0$; $S_3$; $h_K=1$; LMFDB 3.1.2220.1
-2227
1:
1.353126616533456729958545716162770569088828871340336271926508048632532676794404523829913643347795879
comment: $a^3-a^2+3a+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.2227.1
-2228
1:
1.427139277408158191863729686902197790127727667204861554934028522681910591364811260794674448609993679
comment: $a^3+5a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.2228.1
2228
1:
0.9401496500377762916465922972837533723819318323570238868528564171169637332641663261005625988228103676
comment: $a^3-a^2-13a+9=0$; $S_3$; $h_K=1$; LMFDB 3.3.2228.1
2233
1:
0.4674714340750901614485600484042384828776690264720562219225923255284701197566929680847028587231938531
comment: $a^3-a^2-8a+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.2233.1
-2235
1:
1.818639734766666788107951176561260889551067738890933033094064413262348252012672763878855035030635916
comment: $a^3-a^2-5a+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.2235.1
2241
1:
0.6982379368808923925881175291552413911263047996508077734365537631790782492885126492541994709255748284
comment: $a^3-9a-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.2241.1
-2243
1:
0.9444422878341164144310422230272954609898022458326385998188600257435525768556083274089301373483848414
comment: $a^3-a^2+7a+4=0$; $S_3$; $h_K=2$; LMFDB 3.1.2243.1
-2260
1:
2.044723215394111321034296288229248330541535001920425945118445091203821318700869693894951092413438698
comment: $a^3-a^2+4a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2260.1
-2264
1:
1.717750673929042880779569117448228943148813027333073202324053309979463793513005487024733682160819163
comment: $a^3-a^2-2a+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2264.1
-2283
1:
1.678182051330826739885757772426950003320711288401580346228233950918291024445922646101023635783220887
comment: $a^3-a^2-a+28=0$; $S_3$; $h_K=1$; LMFDB 3.1.2283.1
-2284
1:
1.407405419387610204490647874871353873985846843117788734255862075411759508509277603211185244981858594
comment: $a^3-a^2+11a+9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2284.1
-2291
1:
1.951360868796527745677781461709391211254180062038661301092386004514224062728214871729460241060487553
comment: $a^3+8a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.2291.1
2292
1:
1.199985215175982489477614505221675244651833923574537745081567844203906182281609243423006082219292105
comment: $a^3-a^2-13a+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.2292.1
2296
1:
1.190865184237733290733552082612994190890419108887014294942661806452426657948798862840695918787459579
comment: $a^3-a^2-14a-14=0$; $S_3$; $h_K=1$; LMFDB 3.3.2296.1
2300
1:
1.510918021613389378788527127572976240237322226179755230160481535303266380806723309045292277975425257
comment: $a^3-a^2-8a+2=0$; $S_3$; $h_K=1$; LMFDB 3.3.2300.1
-2303
1:
1.171723845117313134744976094951230202533814839510455446741279142097876790161886592029102423851447348
comment: $a^3-a^2-2a-27=0$; $S_3$; $h_K=3$; LMFDB 3.1.2303.1
-2315
1:
1.019779911534487397162149208689948447493465527914122001222570265758568151345804514172925317089392986
comment: $a^3-a^2+5a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2315.1
-2316
1:
1.672992894707495651096858376316350360136764524957305885560742489439134745501740559258564514660570250
comment: $a^3-a^2+a+9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2316.1
-2319
1:
1.136243689175994953321621847819042125936063536753250558219858264743300496360154304551367043180312604
comment: $a^3-a^2-12a-15=0$; $S_3$; $h_K=2$; LMFDB 3.1.2319.1
-2327
1:
0.5660925531065187942807440602623745804001982084953724867049392769966299155469008149572421176214259292
comment: $a^3-a^2+8a-7=0$; $S_3$; $h_K=2$; LMFDB 3.1.2327.1
-2344
1:
1.942338050347892715215632243571194757906102010381643657912374772308109658577084500843617800298764694
comment: $a^3+7a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.2344.1
-2348
1:
1.791299079450182367419536926211094363907337044399764299261045583764314787291235856339543641657605722
comment: $a^3-a^2+3a+27=0$; $S_3$; $h_K=1$; LMFDB 3.1.2348.1
2349
1:
0.9837591127689327397372706735498441594159678382060357363169287449000184701638910378120300799156518666
comment: $a^3-12a-13=0$; $S_3$; $h_K=1$; LMFDB 3.3.2349.1
-2351
1:
2.199316760510768038822282910049078417043070592451137742303375994958683972110900896531374258610412981
comment: $a^3-a^2+6a+16=0$; $S_3$; $h_K=1$; LMFDB 3.1.2351.1
-2355
1:
1.788610633054883392660483149249445431015087602217823291810852905283132346650481639387659426982830958
comment: $a^3+12a-23=0$; $S_3$; $h_K=1$; LMFDB 3.1.2355.1
-2372
1:
1.405323695165299773897377752757896820980763351059068038371809879517873110483223284691701617459291510
comment: $a^3-a^2+8a+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.2372.1
-2376
1:
1.920703172415603027071022421478826952035724465394065391676748499512146097076976010328429361292739283
comment: $a^3-9a-14=0$; $S_3$; $h_K=1$; LMFDB 3.1.2376.1
-2380
1:
1.376408167976147389275021225677432091775427088464210513451636044769697020592304035811973408782879429
comment: $a^3-a^2-a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2380.1
-2387
1:
1.087768655792590083201852279824608397803961124548839779997797889167192441767022758137095685786958131
comment: $a^3-a^2+6a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2387.1
-2388
1:
2.400715047668510290951561656407975074160143488786806425522366351297167200102908722459477736889480839
comment: $a^3-a^2+13a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.2388.1
-2403
1:
1.320073751891656593538416274296208033726962346880650187710527182027651070669424606362326183205316076
comment: $a^3-6a-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2403.1
-2408
1:
1.550724727861710931410557749605631944505648203955749110747173326732372623315030195875385106735755870
comment: $a^3-a^2+2a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2408.1
-2420
1:
1.537800371800105646321570004202944648537358318373404131090829551127377027242196557610973942718682060
comment: $a^3-a^2+4a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2420.1
-2423
1:
1.170759942495099075099319323003794240527959247269474394107077899014064372967380758194186470692975446
comment: $a^3-a^2+2a-29=0$; $S_3$; $h_K=1$; LMFDB 3.1.2423.1
-2424
1:
2.222290499093915446729390417903447709740356093151155272176420998155887077271820255643043957194122887
comment: $a^3-a^2+6a+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.2424.1
2429
1:
1.077706940522866564840713422166744331933336502428759562681499665599871629815412727798954044705080831
comment: $a^3-a^2-14a-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.2429.1
-2440
1:
2.143505384711960534057896416243785650612873981438592525808181340109687809954634258070237657424149847
comment: $a^3+13a-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.2440.1
-2443
1:
1.443367387678974027687838966578859762717486844363234633246531557314111958401937749184495237616678636
comment: $a^3+4a-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2443.1
-2444
1:
1.052310500380654801309715800878998937312945957692832778443289011599377236472713754479565207925458624
comment: $a^3-4a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2444.1
-2468
1:
1.450225570217557822051842656752538283246456795534375743299638312178446349332268926272287181292556559
comment: $a^3-a^2-7a+23=0$; $S_3$; $h_K=1$; LMFDB 3.1.2468.1
-2472
1:
2.403091539756233501983085004757144442980699755930592541356206296385225137555892443068158344670057417
comment: $a^3-a^2-8a+24=0$; $S_3$; $h_K=1$; LMFDB 3.1.2472.1
-2476
1:
1.164694386166163157150872059083047329938656212787930097384131721376179984530959995332198452491452490
comment: $a^3-a^2-9a-19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2476.1
-2479
1:
0.5379535930643875953921225270864692871647256745802392590493559042395372003645519501872278578496690297
comment: $a^3-11a-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.2479.1
-2484
1:
2.189415920981461384181277868225012571593018677271562694954780638980045913601268569511180377928787305
comment: $a^3-6a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2484.1
-2488
1:
1.843616098791287158495938985133138474200433569573570265408165218162431999220108706815429702192899811
comment: $a^3-a^2+6a-10=0$; $S_3$; $h_K=4$; LMFDB 3.1.2488.1
-2491
1:
1.601258467777830614117295523037831018841542864664762691704832441168042346743194361696684837688266973
comment: $a^3-a^2-2a+20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2491.1
-2503
1:
0.7483407338288180402301835078834523773455698847874148301448540254454986354249297002738777301807976139
comment: $a^3-a^2+2a+9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2503.1
-2504
1:
1.702879295112995064034925922404484181921057055267549087908743421086700798847655623677109113910509278
comment: $a^3-a^2+a+19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2504.1
2505
1:
0.8536734907663845595606985477712098169046586274581249987956655151329376845305134018902040137993969072
comment: $a^3-a^2-10a-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.2505.1
-2508
1:
1.480403336670979108838669800004472128157919618917038042692276918786140535586844065432103064408972533
comment: $a^3-a^2-5a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2508.1
-2515
1:
1.500720787524391191650664648206639637568095076488295910995601994402778639666315430280298738994333348
comment: $a^3-8a-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.2515.1
-2516
1:
2.663642438775223843605585835495444264362906132848212826121219290035635987357027624364602255580735242
comment: $a^3-7a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.2516.1
-2540
1:
0.8021984615583924767220544500610093276649257063291052892997780669695812350784217090273905030985117226
comment: $a^3-a^2-a-19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2540.1
-2548
1:
1.953129234471297153958288952464040891622203394271243818269401742460723806834507469857445139281263063
comment: $a^3-a^2+12a+8=0$; $S_3$; $h_K=3$; LMFDB 3.1.2548.1
-2555
1:
1.213716114449430523310597308210160779706258744444141274454085826912266718265206662186719339114301842
comment: $a^3-a^2+14a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.2555.1
2557
1:
0.8482222729439344353299684835715870891073708487463065594372584399306186582087837697895427874566620110
comment: $a^3-a^2-9a-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.2557.1
-2563
1:
1.404795784477116892719531019435999768171432965177863955901546205015422037264525897795318151049623132
comment: $a^3-a^2+a-10=0$; $S_3$; $h_K=2$; LMFDB 3.1.2563.1
-2575
1:
3.047677192026674360085190181027275842417388861696694217117434985320708141642344426463061090256153756
comment: $a^3-5a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2575.1
-2579
1:
1.185563250102574621650983923618970170787206222270224560513924982150021024090101406542695087719023299
comment: $a^3-a^2-7a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2579.1
2589
1:
1.280738753992885539958497986449431490253815141925416664534949997217652798791633274029072571721604736
comment: $a^3-a^2-14a+12=0$; $S_3$; $h_K=1$; LMFDB 3.3.2589.1
-2591
1:
1.083952248043903956454498841144828191080991977806486722356253145769059905363087741436407277221729586
comment: $a^3-a^2-4a+31=0$; $S_3$; $h_K=1$; LMFDB 3.1.2591.1
-2595
1:
1.782627692431261485150485114055650355516872528172057601353303227453520955674636165939820187020769703
comment: $a^3-a^2-10a-20=0$; $S_3$; $h_K=5$; LMFDB 3.1.2595.1
2597
1:
1.129337086932545457833708031335414489214739868531886154609624132271216070610487063365605515284620600
comment: $a^3-a^2-9a+8=0$; $S_3$; $h_K=3$; LMFDB 3.3.2597.1
-2599
1:
0.5881586065158244148966866131219884133948055832013254288091296664826336816466376425083227072750118521
comment: $a^3-a^2-4a-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2599.1
-2604
1:
1.438618452299368597826723260854182416425002608085625809190293811239899979733667331881977153446088390
comment: $a^3-a^2+9a-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.2604.1
-2619
1:
1.156131626735513824022114223587516941500523350176358075080365869242328781332866799449919666847453478
comment: $a^3+6a-29=0$; $S_3$; $h_K=2$; LMFDB 3.1.2619.1
-2627
1:
1.007989672545051570683270845332853246819425701549155453981914234562225265685999858610543004966583857
comment: $a^3-a^2+9a-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.2627.1
-2631
1:
3.423378736588850364126352976155452223759108302430909859687442219508827220337548280133280431259098469
comment: $a^3-a^2+14a-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.2631.1
-2635
1:
1.403749361347907477754267092880204598857599984251598944157385895986431375076921478007549670083395782
comment: $a^3-a^2+9a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.2635.1
-2636
1:
1.024408675964842960111442802986829223044012554795438010250369798138658496332337982714020401829582854
comment: $a^3-4a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2636.1
2636
1:
1.431910762286212720929146466059172830770347273052881712710956713284734436036590566016218696985524862
comment: $a^3-14a-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.2636.1
-2644
1:
1.980949794460784971099618190804801534639758411517799015414700895443798247307141903605537863456627825
comment: $a^3-a^2+5a-21=0$; $S_3$; $h_K=1$; LMFDB 3.1.2644.1
-2647
1:
0.7422311181782899578154100402230895697694073198560953592779170362923445156061941840557480485515503823
comment: $a^3-a^2+8a+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.2647.1
-2660
1:
1.747815982600499269326362443031348193850273693641909400040111717709352017279332240297809388241521817
comment: $a^3-a^2+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2660.1
-2668
1:
1.185341638008804445913572768809948387944369863605962062972390279447654353839512190747232921577269241
comment: $a^3-2a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2668.1
2673
1:
0.6003824396838432951366281984205046255920821599960078068355120589152869294510018132470110515815821629
comment: $a^3-9a-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.2673.1
-2676
1:
2.241269587268470184021782496900932388875641314282885624334524049250156656972186282879953650107614777
comment: $a^3-a^2-11a-21=0$; $S_3$; $h_K=1$; LMFDB 3.1.2676.1
2677
1:
0.8626657499662461949109775507640026405125642656563469997023869036335138896043168600562956512962358045
comment: $a^3-10a-7=0$; $S_3$; $h_K=1$; LMFDB 3.3.2677.1
-2680
1:
2.052358961619674456810349403537380777572297017499945558827678209718746151078188408048467344922264936
comment: $a^3-a^2+20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2680.1
-2687
1:
1.098475208021528482845802008321981845069600340573822754592918117555819979751469399464730873058598458
comment: $a^3+5a-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2687.1
-2692
1:
1.940148564614244282163158186311173685513470011804972730556294155507367148247752159218535033838585349
comment: $a^3-2a-20=0$; $S_3$; $h_K=5$; LMFDB 3.1.2692.1
-2695
1:
0.8250524081707096532215701198864309866403339652246057618891588962704133126927809475859847458623501963
comment: $a^3+7a-7=0$; $S_3$; $h_K=3$; LMFDB 3.1.2695.1
-2696
1:
1.844241089943186256715865625441145422280562548855855687364599084870578574380828265443702515272295487
comment: $a^3-a-10=0$; $S_3$; $h_K=4$; LMFDB 3.1.2696.1
-2699
1:
1.273850710227135155445821050080832759183050989877592087431319460956719544556177820626007191163769079
comment: $a^3-a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2699.1
-2700
1:
1.267399350953519232707181631957971904515709549793027327847259772705094580520055018553391448198458488
comment: $a^3-20=0$; $S_3$; $h_K=3$; LMFDB 3.1.2700.1; $K=\mathbb{Q}(\sqrt[3]{20})$, a pure cubic field
2700
1:
1.568033693393829479737247986992953273056495657589591656238433741906929878859441038197777074968802645
comment: $a^3-15a-20=0$; $S_3$; $h_K=1$; LMFDB 3.3.2700.1
-2708
1:
1.348689372150755125141122369414402921668717798891718922079417056315493180896622789550649808946053550
comment: $a^3+2a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2708.1
2708
1:
0.9954525259078663940264180797892421140950131311522793913870649408615095971099358504605774834319051280
comment: $a^3-a^2-11a-7=0$; $S_3$; $h_K=1$; LMFDB 3.3.2708.1
2713
1:
0.9473207187170228435901375600004790889998217283541118734649119614899992738146552211875300049010093208
comment: $a^3-13a-15=0$; $S_3$; $h_K=1$; LMFDB 3.3.2713.1
-2723
1:
1.029612137037430592554296569830848187414173165783056073520584011318722017541617750055203136287504535
comment: $a^3+8a-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.2723.1
-2727
1:
3.097957180444527546786446029560702842428325861582293359257577241267559346203742990232139187336698946
comment: $a^3+3a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2727.1
-2728
1:
1.908325032633760502727286377255938558662305818049200403289896368137765138182053542951898375295003512
comment: $a^3+10a-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.2728.1
-2732
1:
0.7613273463179758956280808890730541383794435741888210055016769311059391015384146382789621203670011512
comment: $a^3+2a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2732.1
-2740
1:
2.070703807260719049555870797328831916077724894538735597408892925971608999323065204692233146340414582
comment: $a^3-a^2-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2740.1
-2747
1:
2.054580127766741388699795132671513430431965069983966115303774636611027811242606014987543728103718959
comment: $a^3-a^2+a+30=0$; $S_3$; $h_K=1$; LMFDB 3.1.2747.1
-2759
1:
0.2929366405209947288516269490423186422329232082576403095127942085663447023855832762921937366658004561
comment: $a^3-a^2+4a-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2759.1
-2764
1:
1.386797596990069648214124869148280274302405945573908329332910549369019868552782256393712735162454923
comment: $a^3+4a-20=0$; $S_3$; $h_K=2$; LMFDB 3.1.2764.1
-2767
1:
0.7338842568075294100780542583457745802057827389235306479179370587343795016466902477733688442115328426
comment: $a^3-5a-11=0$; $S_3$; $h_K=2$; LMFDB 3.1.2767.1
2777
1:
0.5995057621929815318220416591388507113007172453907155967858276818154384081434818059976103142555734044
comment: $a^3-a^2-14a+23=0$; $S_3$; $h_K=2$; LMFDB 3.3.2777.1
-2787
1:
1.731425286753967808594161015345581718000688532913447180367363427737868901355879926122011216076641993
comment: $a^3-6a-31=0$; $S_3$; $h_K=2$; LMFDB 3.1.2787.1
-2791
1:
0.5272531054991820254727015911987072540023826577728607703291425743095337001131782866763749288469661435
comment: $a^3-a^2-2a+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2791.1
-2795
1:
1.146386202211984154111337703535966977748688589096687258710522314447645660145571840424149961643475134
comment: $a^3-a^2+10a-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2795.1
-2796
1:
1.253624854062747600896392907431153453192568044666549475644572267652011146445897577647414848127285886
comment: $a^3-a^2+5a-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2796.1
-2803
1:
1.294582806999299098009779167968159170350558025576458122947012848292027020907992335153937389019021106
comment: $a^3-a^2+7a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2803.1
2804
1:
1.151217568779174209280912376562642246691355154497384368493192132087242186775511788804309309819593655
comment: $a^3-a^2-9a-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.2804.1
-2808
1:
1.950902495369064001071716804436014065672109096358101348277030286580074134296234426646242575071031610
comment: $a^3+3a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2808.1
2808
1:
1.533318696294487330679124338981102646213042057665037336623967642538641050869498029364899368942919878
comment: $a^3-9a-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.2808.1
-2819
1:
1.920724391184137734396936067807601358284982009026156656326596546364750735019294624337351159509044329
comment: $a^3-a^2+5a-32=0$; $S_3$; $h_K=5$; LMFDB 3.1.2819.1
-2820
1:
2.553336078946957101223238851330096322889798422949653079573458710397505449739396348616847301858564120
comment: $a^3-a^2+9a+15=0$; $S_3$; $h_K=1$; LMFDB 3.1.2820.1
-2824
1:
1.949481185013945749164582550586534427563245324450065841713551838729404266841047889889924472123124421
comment: $a^3-a^2-6a+14=0$; $S_3$; $h_K=2$; LMFDB 3.1.2824.1
-2835
1:
1.528277738096774796876124409410778967165872280304459306315313443159410066400047451934490169725120026
comment: $a^3-12a-19=0$; $S_3$; $h_K=3$; LMFDB 3.1.2835.1
2836
1:
0.7279611160614317914019609608145177307916148061424246427970305551221276393703792665570035609014633413
comment: $a^3-a^2-9a+7=0$; $S_3$; $h_K=1$; LMFDB 3.3.2836.1
-2843
1:
0.9409265344131128598346926241830918421642418050181758493595564605190496035462792757573986465260593065
comment: $a^3-a^2+a+10=0$; $S_3$; $h_K=2$; LMFDB 3.1.2843.1
-2852
1:
1.344658825924501955006444123545469817091815590231945910880167722942780401146397988614495972352926931
comment: $a^3+14a-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.2852.1
-2855
1:
0.4102902458958640540214833647945397592488388815613531702337404383198356959061508097283406934785491012
comment: $a^3-a^2-10a-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.2855.1
-2856
1:
2.317285749417317419750511517860841464119647741441317278312481667691781290633000091616111708579838464
comment: $a^3-a^2+9a-21=0$; $S_3$; $h_K=7$; LMFDB 3.1.2856.1
2857
1:
0.3644138359966921726930749921680642282954076476355914703202732940527293035267682327780810719626210962
comment: $a^3-a^2-10a+11=0$; $S_3$; $h_K=1$; LMFDB 3.3.2857.1
-2859
1:
1.479514482353750795586672065804690381126727406074491746091869232849871542370701105858581656142223501
comment: $a^3-a^2+9a-6=0$; $S_3$; $h_K=2$; LMFDB 3.1.2859.1
-2860
1:
1.362466956960227769331470999240253249480790753789660657802698675966029290779408607310068667121580510
comment: $a^3-a^2-a+21=0$; $S_3$; $h_K=1$; LMFDB 3.1.2860.1
-2867
1:
1.046499254647667055122660176747428025637485509122180185268799488380006457709527065730268176935593567
comment: $a^3-a^2+2a+20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2867.1
-2872
1:
1.977181060598621884263441390040182263452770485949342418849563740169133913062567299608360267362246195
comment: $a^3+13a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2872.1
-2879
1:
0.2768174544226209865165101165796177668564614298969537592480097109839097733499631566805555518673657903
comment: $a^3-a^2+6a+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.2879.1
-2888
1:
1.430716654802887658591400986030680914284924119913867327315151159619030980655944579532195589260971989
comment: $a^3-a^2+13a+7=0$; $S_3$; $h_K=3$; LMFDB 3.1.2888.1
-2891
1:
2.012300581049410179242732787059973223465925333830755734857717119290885593660331823046977170083056883
comment: $a^3-a^2-9a+36=0$; $S_3$; $h_K=3$; LMFDB 3.1.2891.2
-2891
2:
1.272788590112189740626466920349838119958543134481503208247852084320389803772330105900540941837333737
comment: $a^3-a^2-2a-20=0$; $S_3$; $h_K=3$; LMFDB 3.1.2891.3
-2891
3:
0.8207719924815180012046710604266000078183582357274778508280374731840341089102121642289733727375824476
comment: $a^3-a^2+5a+8=0$; $S_3$; $h_K=3$; LMFDB 3.1.2891.1
-2892
1:
1.463202938794020506417163574385928118382544034253896520091341106013578013715856988627554271401920021
comment: $a^3-a^2-13a-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.2892.1
-2895
1:
0.9619142570600047936568386045402863427180082444266404900900087977416192684641732176700952683226858854
comment: $a^3+3a-31=0$; $S_3$; $h_K=1$; LMFDB 3.1.2895.1
-2911
1:
0.5175948898827861761072144996659980295398426532389466345931360141974530708004692454380125519276256045
comment: $a^3-a^2+8a-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2911.1
-2915
1:
1.062328830094462244258109996362522389500295594139745691154455494107010483983995084283471940997811150
comment: $a^3-a^2-a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2915.1
2917
1:
0.8837947827199977634950683774106347047151307228360058432188669673055586013748302734167538224924580694
comment: $a^3-a^2-13a+20=0$; $S_3$; $h_K=1$; LMFDB 3.3.2917.1
-2920
1:
2.203865092259272708488593837504065806424794139873523224514297073415834375103138519173004542331309656
comment: $a^3-a^2-6a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2920.1
2920
1:
1.328095786305953965437749271686030075548624799458586667541015702298263111559033633597926836960722397
comment: $a^3-a^2-15a-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.2920.1
-2923
1:
1.346612021277998450025628150725586967316261966113298512374755900835195140120184925134755795644477979
comment: $a^3-a^2+14a-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.2923.1
2941
1:
1.011793999910440308154331417956952956785145843649327533086468582894249728702649599799807812461153626
comment: $a^3-a^2-14a+4=0$; $S_3$; $h_K=1$; LMFDB 3.3.2941.1
-2951
1:
0.6601078376371643474578119515072779605461502942242462419873357578960793558463406963562649166039117006
comment: $a^3-a^2+6a-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2951.1
-2955
1:
1.872473440454431272089369670196626954747112618144967206910031574930388893984248427503991947751682146
comment: $a^3-a^2-5a-30=0$; $S_3$; $h_K=1$; LMFDB 3.1.2955.1
-2956
1:
1.441912901136177211042009929343738886072448032807089748849931590496812355769718945548568423592713470
comment: $a^3+4a-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2956.1
-2964
1:
2.169030905040397510139012513027451327221200030010391319050840717316716667234694881289455699794736746
comment: $a^3-a^2+5a+19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2964.1
2981
1:
1.071722694449655351622965987445108493664418708954519816427079619960620672178890991460167529659965933
comment: $a^3-a^2-11a+14=0$; $S_3$; $h_K=1$; LMFDB 3.3.2981.1
-2991
1:
3.581907301937602057180334076676349074909209319765416086370011666646133964502069832520002739457554595
comment: $a^3-a^2-6a+24=0$; $S_3$; $h_K=1$; LMFDB 3.1.2991.1
2993
1:
0.5493921355945401862746806086609322493690922063535711513803539981856628679597784349747867884307657621
comment: $a^3-a^2-12a+17=0$; $S_3$; $h_K=1$; LMFDB 3.3.2993.1
Definition
Let $K$ be a cubic field [3] of discriminant $D$ and $\zeta_K(s)=\sum_{\mathfrak{a}}N(\mathfrak{a})^{-s}$ its Dedekind zeta function [2], summed over the nonzero ideals of $\mathcal{O}_K$. Listed is $\kappa_K=\lim_{s\to 1}(s-1)\zeta_K(s)$, the residue of $\zeta_K$ at its pole $s=1$.
Parameters
$D$
—   discriminant of $K$ ($D$ the discriminant of a cubic field)
$k$
—   index of $K$ among the cubic fields of discriminant $D$ ($k\geq 1$)
Formulas
(1)
$\kappa_K=\frac{2\pi\,h_KR_K}{\sqrt{|D|}}$ for $D<0$ and $\kappa_K=\frac{4\,h_KR_K}{\sqrt{D}}$ for $D>0$, where $h_K$ is the class number and $R_K$ the regulator of $K$, held in the table of regulators of cubic fields. Both are the class number formula [4] [5] $\kappa_K=\frac{2^{r_1}(2\pi)^{r_2}h_KR_K}{w_K\sqrt{|D|}}$ with $w_K=2$ and signature $(r_1,r_2)=(1,1)$ for $D<0$, $(3,0)$ for $D>0$.
(2)
$\kappa_K=L(1,\chi)L(1,\bar\chi)=|L(1,\chi)|^2$ for a cyclic cubic field, where $\chi$ is either cubic Dirichlet character of conductor $\sqrt{D}$, since $\zeta_K(s)=\zeta(s)L(s,\chi)L(s,\bar\chi)$ and $\zeta$ has residue $1$. For $D=49$ and $\chi=\chi_7(2,\cdot)$ in Conrey's notation, $L(1,\chi)=0.5377\ldots-0.1052\ldots i$ and $\kappa_K=|L(1,\chi)|^2=0.3002598183\ldots$.
(3)
$\zeta_K(s)=\zeta(s)\,L(s,\rho)$ and so $\kappa_K=L(1,\rho)$ for a cubic field with Galois closure $L$ and $\mathrm{Gal}(L/\mathbb{Q})=S_3$, where $\rho$ is the irreducible two-dimensional representation of $S_3$, because the permutation representation of $S_3$ on the three embeddings of $K$ is $1\oplus\rho$. The Dedekind zeta function of the closure is $\zeta_L(s)=\zeta(s)\,L(s,\chi_d)\,L(s,\rho)^2$, with $\chi_d$ the Kronecker character of the quadratic subfield of $L$, of discriminant $d$ with $D=df^2$.
Comments
(4)
Non-isomorphic cubic fields can share a discriminant, which quadratic fields never do. The fields of discriminant $D$ are numbered $k=1,2,\ldots$ in lexicographic order of the coefficient vectors $(a_2,a_1,a_0)$ of their reduced defining polynomials $x^3+a_2x^2+a_1x+a_0$, the polynomial PARI's polredabs returns for the field and the LMFDB displays as its defining polynomial; this is the index of the table of regulators of cubic fields, which holds the same 515 fields. Seven discriminants with $|D|\leq 3000$ carry more than one field: $D=-972$ and $-1836$ two each, and $D=-1228$, $-1356$, $-2075$, $-2188$ and $-2891$ three each; so for $D=-1228$, $k=1$ is $x^3-x^2+x-7$, $k=2$ is $x^3-x^2+7x-1$ and $k=3$ is $x^3+4x-6$. Every other negative $D$ here, and every positive one, carries a single field, with $k=1$. The LMFDB's own index for fields sharing a discriminant is not this order (for $D=-2891$ its first field is $k=3$ here), and its label knowl states no rule for it; the label in each entry's comment was read from that field's LMFDB page.
(5)
The comment on each entry gives the reduced polynomial $f$, so that $K=\mathbb{Q}(a)$ with $f(a)=0$; the Galois group of the Galois closure, $C_3$ or $S_3$; the class number $h_K$; and the LMFDB label. The fundamental units and the regulator $R_K$, the other factor of the class number formula (1), are in the entry of the same $D$ and $k$ in the table of regulators.
(6)
$\kappa_K$ is the constant in the ideal count of $K$: the number of nonzero ideals of $\mathcal{O}_K$ of norm at most $x$ is asymptotically $\kappa_K\,x$. For $D=-23$ there are $11045$ ideals of norm at most $30000$, and $11045/30000=0.3681\ldots$ against $\kappa_K=0.3684\ldots$.
(7)
$D$ is a perfect square exactly for the cyclic cubic fields, those with Galois group $C_3$, and $\sqrt{D}$ is then the conductor: the seven cyclic fields here have conductors $7$, $9$, $13$, $19$, $31$, $37$ and $43$, and each is the cubic subfield of the cyclotomic field of that conductor, for $7$ and $9$ its maximal real subfield. For a cyclic field $\zeta_K(s)=\zeta(s)L(s,\chi)L(s,\bar\chi)$ with $\chi$ a cubic Dirichlet character of that conductor, so $\kappa_K=|L(1,\chi)|^2$, formula (2); the comment on each of the seven names such a $\chi$ by its Conrey label, and $L(1,\chi)$ itself is held in the table of Dirichlet $L$-values for conductors up to $29$, that is for $D=49$, $81$, $169$ and $361$. The other 508 fields have Galois group $S_3$, and for them $\kappa_K$ is the value at $1$ of the Artin $L$-function of the two-dimensional representation of $S_3$, formula (3); the Galois closure contains the quadratic field of discriminant $d$, where $D=df^2$ with $d$ a fundamental discriminant [3], and the pure cubic fields $\mathbb{Q}(\sqrt[3]{m})$ are those with $d=-3$.
(8)
$h_K=1$ for 423 of the 515 fields, $h_K=2$ for 41, $h_K=3$ for 36, $h_K=4$ for 6, $h_K=5$ for 8, and $h_K=7$ for one, the field of $x^3-x^2+9x-21$ with $D=-2856$. The three fields of $D=-1228$ all have $h_K=3$.
(9)
The smallest residue here is $\kappa_K=0.2768\ldots$ for $D=-2879$ and the largest $3.5819\ldots$ for $D=-2991$, whose fundamental unit has coefficients of thirteen digits and regulator $15.37\ldots$; 184 of the 515 values are less than $1$. For every cubic field $w_K=2$, since a cubic field contains no root of unity other than $\pm1$, which is why $w_K$ does not appear in the two cases of the class number formula (1).
(10)
A few entries are constants a reader may hold under another name. For $D=-23$, the cubic field of smallest $|D|$, $h_K=1$ and the fundamental unit is the plastic number $\rho=1.3247\ldots$, the real root of $x^3-x-1$ (OEIS A060006 [10]), so $\kappa_K=2\pi\log\rho/\sqrt{23}$. For $D=49$, $K=\mathbb{Q}(\zeta_7)^+$ and $\kappa_K=|L(1,\chi)|^2$ for the cubic character $\chi=\chi_7(2,\cdot)$ of conductor $7$ in Conrey's notation. The thirteen pure cubic fields here, those with $D=-3f^2$, are named $\mathbb{Q}(\sqrt[3]{m})$ in their comments with the least $m$ for which that holds; $\mathbb{Q}(\sqrt[3]{2})$ is $D=-108$.
(11)
The residue is that of $\zeta_K$ itself. The completed function $\Lambda_K(s)$, which carries the Gamma factors and a power of $|D|$, has a different residue at $s=1$.
(12)
The residues for quadratic fields are in the table for degree two, where $\kappa_K=L(1,\chi_D)$ is a single Dirichlet $L$-value; for a cubic field the corresponding $L$-function has degree two, formula (3), and only splits into Dirichlet $L$-functions when the field is cyclic.
Programs
(P1)
PARI/GP
default(realprecision, 60);
bnf = bnfinit(x^3 - x^2 + 1, 1); 2*Pi*bnf.no*bnf.reg/sqrt(abs(bnf.disc))   \\ D = -23: 0.368409320715826821111868466628885269857933981303601980446211
lfun(lfuncreate(x^3 - x^2 + 1), 1)   \\ the polar part 0.3684093207...*x^-1 + O(x^0), from the L-function alone
(P2)
Sage
K.<a> = NumberField(x^3 - x^2 + 1)                                # D = -23
(2*pi*K.class_number()*K.regulator(proof=True)/sqrt(23)).n()    # 0.368409320715827, the regulator being a 53-bit float
References
[1]
H. Cohen, A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics 138, Springer, 1993; Theorem 6.4.2 (Hunter)
Links
Similar tables
Residues of Dedekind zeta functions of quadratic fields —   the same residue for degree two, $\kappa_K=L(1,\chi_D)$; its entry comments carry $h_K$ the same way
Regulators of cubic fields —   the other factor of the class number formula, for the same 515 fields under the same $D$ and $k$; its entry comments carry the fundamental units
Values of Dirichlet $L$-functions at positive integers —   $\kappa_K=|L(1,\chi)|^2$ for the seven cyclic fields, $\chi$ a cubic character of conductor $\sqrt{D}$
Values of the Riemann zeta function at rational numbers —   the factor $\zeta(s)$ of $\zeta_K(s)=\zeta(s)L(s,\rho)$, whose residue $1$ is why $\kappa_K=L(1,\rho)$
Data properties
Entries are of type: real number
How well the digits are known: proven
Table is complete: no (it holds every cubic field with $|D|\leq 3000$, the 419 complex and the 96 totally real ones)
How they were obtained:

Each value is a real ball from the class number formula $\kappa_K=2^{r_1}(2\pi)^{r_2}h_KR_K/(2\sqrt{|D|})$ at 461 bits, with $\pi$ and the square root arb's.

more

The class number and the fundamental units are PARI's, from bnfinit and certified by bnfcertify on every field, which removes the generalised Riemann hypothesis that bnfinit assumes; the regulator is computed as the table of regulators computes it, each unit taken exactly as a polynomial in $a$, checked to be an algebraic integer of norm $\pm1$, and evaluated by Horner's rule in balls at the real roots of the reduced polynomial isolated in interval arithmetic, the logarithms and the determinant being arb's. Each value is written to 100 significant digits, fewer than any ball supports (the worst, $D=1772$, supports 133). The generator refuses a value unless it agrees to 50 digits with the residue that PARI's lfunrootres computes from the Dirichlet coefficients and functional equation of $\zeta_K$, a computation sharing nothing with bnfinit; all 515 do. The enumeration rests on Hunter's theorem [1]: every cubic field with $|D|\leq 3000$ is generated by an algebraic integer of trace $0$ or $1$ whose minimal polynomial $x^3+a_2x^2+a_1x+a_0$ has $|a_1|\leq 18$ and $|a_0|\leq 43$, and the fields found in that box, 419 complex and 96 totally real, are exactly the terms of OEIS A023679 [8] and A006832 [9] up to 3000 counted with multiplicity. Outside the generator, when this was written, every value was compared with the class number formula evaluated from the regulator stored in the table of regulators; with lfunrootres at 70 digits; with the eleven digits of the analytic class number formula on 21 LMFDB field pages [6] [7]; for the seven cyclic fields with $|L(1,\chi)|^2$ from a digamma sum in ball arithmetic, and for the four of conductor at most $29$ with the $L(1,\chi)$ stored in the table of Dirichlet $L$-values for both cubic characters; and for $D=-23$ with $2\pi\log\rho/\sqrt{23}$. The controls that must fail failed.



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