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Values of Dedekind zeta functions of cubic fields at 2
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Numbers
$D$
$k$ 
$\zeta_K(2)$
-23
1:
1.110001006025015392937222256059538537476870758569780969349895906056886507495835397424141962916320245
comment: $x^3-x^2+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.23.1; the Weeks manifold has volume $3\cdot 23^{3/2}\zeta_K(2)/(4\pi^4)=0.9427\ldots$
-31
1:
1.191303238150987861270892143311632382612737183285875874385666418539144753537612339027019640664553766
comment: $x^3+x-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.31.1
-44
1:
1.413892909939682335612278054101757761912592494026457682926192772784808624281775972526243405966164415
comment: $x^3-x^2+x+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.44.1
49
1:
1.067765312869975773461301617273269358730770543474715108639262737730494419372317327223902717369891141
comment: $x^3-x^2-2x+1=0$; $C_3$, conductor $7$; $h_K=1$; LMFDB 3.3.49.1; $\zeta_K(-1)=-1/21$; $K=\mathbb{Q}(\zeta_7)^+$; $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$ for $\chi=\chi_{7}(2,\cdot)$
-59
1:
1.472479780199296743105735080391972764062731401270990532559355487740216268531842224279486377800103342
comment: $x^3+2x-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.59.1
-76
1:
1.556574900954933586121902537700925720468061316048571412792473326143767425325258588453913415682832839
comment: $x^3-2x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.76.1
81
1:
1.172247149611710942880926009635628591821024268350613157678495579922687288940527618959574954003250402
comment: $x^3-3x-1=0$; $C_3$, conductor $9$; $h_K=1$; LMFDB 3.3.81.1; $\zeta_K(-1)=-1/9$; $K=\mathbb{Q}(\zeta_9)^+$; $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$ for $\chi=\chi_{9}(4,\cdot)$
-83
1:
1.516751720642021315916016557693482880989345994781057375180937990559034154631429816073230703247288119
comment: $x^3-x^2+x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.83.1
-87
1:
1.361263304536882944454385025693933951612360764220187663918957206401085970599393130761012398026919232
comment: $x^3-x^2+2x+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.87.1
-104
1:
1.841207016617393876740526044612320286500932347991763405727666676167193340063194548593946980464827787
comment: $x^3-x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.104.1
-107
1:
1.537621450500642326222529349360718274028498865790934364540016972310765892807560324728646462454596464
comment: $x^3-x^2+3x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.107.1
-108
1:
1.602663261900440599007507227865098958403245496306594517203819838388165893011079671833379955576198751
comment: $x^3-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.108.1; $K=\mathbb{Q}(\sqrt[3]{2})$, a pure cubic field
-116
1:
1.856519522118669205536315808505942859842543646991693247518635238985903878752485726942066101673437552
comment: $x^3-x^2-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.116.1
-135
1:
1.294549466093607874666883488624514902356660052987457744087081788922110978072231524362069564041406264
comment: $x^3+3x-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.135.1
-139
1:
1.647967051621593106827156322509119437666128889164915404995799576304207460047550126643338797352601170
comment: $x^3-x^2+x+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.139.1
-140
1:
1.528100252461759308199157109942790155524766692999881346284336529126299746648728736611122751574952078
comment: $x^3+2x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.140.1
148
1:
1.423886575045893291752093458380157280340190847046204341592766595699465954359558186269187727148320188
comment: $x^3-x^2-3x+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.148.1; $\zeta_K(-1)=-1/3$
-152
1:
1.899391115885789043674995353554745826539076694793662616994963750902263077782929812308813619009707792
comment: $x^3-x^2-2x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.152.1
169
1:
1.166911477560679031443143005495275252759481144689481554775999013787399681799241648914242341558993459
comment: $x^3-x^2-4x-1=0$; $C_3$, conductor $13$; $h_K=1$; LMFDB 3.3.169.1; $\zeta_K(-1)=-1/3$; the cubic subfield of $\mathbb{Q}(\zeta_{13})$; $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$ for $\chi=\chi_{13}(3,\cdot)$
-172
1:
1.636032990259343322234681355967772287252767075142079904197164824377075099951625495390476148921132640
comment: $x^3-x^2-x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.172.1
-175
1:
1.279496538086186315693882009666480691644257295834694671297770928301153839662098926592870730346184425
comment: $x^3-x^2+2x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.175.1
-199
1:
1.259094014097368319077054762382195685787127526349454545326619208874865555664260081010387786473032086
comment: $x^3-x^2+4x-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.199.1
-200
1:
1.925682086173639643233763967535078628888312663037544385050766258479032484819015605473776640409688229
comment: $x^3-x^2+2x+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.200.1
-204
1:
1.753114747405701540801568362224998987261070634703073147828547927909774245333726395989126333368114805
comment: $x^3-x^2+x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.204.1
-211
1:
1.676731336151351610767890747981083455761475031752929204738520711460158261402801760111468658119461584
comment: $x^3-2x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.211.1
-212
1:
1.929699788154696144240603326456894260760276223306852351206114849579931630964788611160558281350559946
comment: $x^3-x^2+4x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.212.1
-216
1:
2.048276392192361767327636573364804657166233772868798680391104223956278979526245892301145900928887678
comment: $x^3+3x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.216.1
229
1:
1.479601423909356780877654997242169007283999787295628091994011482947299586133968405009451271269378483
comment: $x^3-4x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.229.1; $\zeta_K(-1)=-2/3$
-231
1:
1.378111851622184467981894376080549796412725053144822253710221686642897245445620637140221243389295769
comment: $x^3-x^2+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.231.1
-239
1:
1.502415917431084306357946713474120947493282428387329925743926116056920025653253903371267455521286128
comment: $x^3-x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.239.1
-243
1:
1.704535916539279798685775324606324889224006844530708034163159313818660071852369521354896917358548304
comment: $x^3-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.243.1; $K=\mathbb{Q}(\sqrt[3]{3})$, a pure cubic field
-244
1:
2.059736640384412572440108152737617393654144653726583883120099088373854097439979901275941662625494523
comment: $x^3+x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.244.1
-247
1:
1.271497340978601459079752382274652273915704615221485515054219343301471732041997681510862841879382125
comment: $x^3+x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.247.1
-255
1:
1.424135801517708521343079880305274638410891861201998761546922049892906646481519050674993345965407048
comment: $x^3-x^2-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.255.1
257
1:
1.244509680380567400790397276099614642817507785378430655287879537016767628214113382937669162485070341
comment: $x^3-x^2-4x+3=0$; $S_3$; $h_K=1$; LMFDB 3.3.257.1; $\zeta_K(-1)=-2/3$
-268
1:
1.652088106218549174042896964066760969612543917627538737032737715425099781478116666856075207058783218
comment: $x^3-x^2-3x+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.268.1
-283
1:
1.712872047327151030069391689456636074823629574246216066828589366067537033573554229293870918671768245
comment: $x^3+4x-1=0$; $S_3$; $h_K=2$; LMFDB 3.1.283.1
-300
1:
1.797273237191832962355195153773360254599069487333816345311471156176254912539800667590689872512207015
comment: $x^3-x^2-3x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.300.1; $K=\mathbb{Q}(\sqrt[3]{10})$, a pure cubic field
-307
1:
1.716135616543061287951955632081859699280555460972717030056346256516795672684006960262531946460751345
comment: $x^3-x^2+3x+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.307.1
316
1:
1.825565147295531031646230470249195232800109626979846421425769581106530652349037372317406128047894251
comment: $x^3-x^2-4x+2=0$; $S_3$; $h_K=1$; LMFDB 3.3.316.1; $\zeta_K(-1)=-4/3$
321
1:
1.337308714122056099862755089109129219613978061214270008553099052326638733089242525316453589977995064
comment: $x^3-x^2-4x+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.321.1; $\zeta_K(-1)=-1$
-324
1:
2.085818104357753990993479337532755105923418645560229463736709799491372319688005569492116787303027508
comment: $x^3-3x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.324.1
-327
1:
1.395541634369134371515519573389310074454493416032009182251233944715782331714385380724315683427923086
comment: $x^3-x^2-2x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.327.1
-331
1:
1.692633312486623817212420443189252978409007525851605302276276878045846849205413214568742235150836986
comment: $x^3-x^2+3x-4=0$; $S_3$; $h_K=2$; LMFDB 3.1.331.1
-335
1:
1.155805527453403309999109823784941951972784541420412936585407495602280709854188174643858896966192094
comment: $x^3-x^2+4x+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.335.1
-339
1:
1.838837846209719948753481125813081394782248503381650280874311478408711570483782023879842118355139803
comment: $x^3-x^2-x+4=0$; $S_3$; $h_K=1$; LMFDB 3.1.339.1
-351
1:
1.230166794437598716862579428967459921926247050753899529235622598365847945373434373763339206167583693
comment: $x^3+3x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.351.1
-356
1:
1.934835702665283643921470677547065953296955337798473265448990922746180991548839053126999634268588405
comment: $x^3-x^2+x+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.356.1
361
1:
1.121317035807324026278139021609470650377276603681057432210032001730974092832599753315901920573746303
comment: $x^3-x^2-6x+7=0$; $C_3$, conductor $19$; $h_K=1$; LMFDB 3.3.361.1; $\zeta_K(-1)=-1$; the cubic subfield of $\mathbb{Q}(\zeta_{19})$; $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$ for $\chi=\chi_{19}(7,\cdot)$
-364
1:
1.630698341617059606423394178139104067759590997234755857529249153679903336825970671031413363132938801
comment: $x^3+4x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.364.1
-367
1:
1.257075033416344969245587883797087187013769706516914766482478041356984480834883695401255716010154014
comment: $x^3-x^2+2x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.367.1
-379
1:
1.695664356820336062802816195270626510853593404138990692546540894697997142257167401181588375507607873
comment: $x^3-x^2+x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.379.1
404
1:
1.578577560847224861739099396043640753613705712964880359081649768669216063088749694317771437011867567
comment: $x^3-x^2-5x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.404.1; $\zeta_K(-1)=-5/3$
-411
1:
1.846754244907915592797873549753775281271166746465271632100456894254514363004320903789595560247495090
comment: $x^3-x^2+5x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.411.1
-419
1:
1.643654709101332444243606297233302645120103781086826271239464008545602931263920478243722108403230725
comment: $x^3-4x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.419.1
-424
1:
2.102101047924586814810461685049407895254766492568621558141565305915605672987019560331589605175227343
comment: $x^3-x^2+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.424.1
-431
1:
2.467232073699768176069102325634392601636479569892905714619898450712158862091492050733269867719510173
comment: $x^3-x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.431.1
-436
1:
2.103274703080055485015080642549409906166165261297970548750408291485142172287319125957970988039805794
comment: $x^3+x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.436.1
-439
1:
1.333966382687206969953015040136891473373759887521089381443881880113824959725856242652957531850696581
comment: $x^3-x^2-2x+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.439.1
-440
1:
1.990729962312811833196580244748684442289984347198741197249454887383480475943760369188984760189087928
comment: $x^3+2x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.440.1
-451
1:
1.686755590283627847087624856950438113166368565248981000432976982300184676611454194333055183185404815
comment: $x^3-x^2-5x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.451.1
-459
1:
1.696825861438881794079136960514359599081772245858396761367064938749968526631056302392219960049265858
comment: $x^3+3x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.459.1
-460
1:
1.691371165684596440817514816217142748789995156142967453600905968964572384516593121501040722173499027
comment: $x^3-x^2+5x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.460.1
469
1:
1.514467488852502461518926916109607302174534862301531423200025537718622569145155993427193720341560129
comment: $x^3-x^2-5x+4=0$; $S_3$; $h_K=1$; LMFDB 3.3.469.1; $\zeta_K(-1)=-2$
-472
1:
2.138650077817706572167014164890495014796621189906388326783936716379522335739971957053857329357337229
comment: $x^3-5x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.472.1
473
1:
1.246080964519482317214434211829219426085428273010644069838074294618213585768565068696677187945210534
comment: $x^3-5x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.473.1; $\zeta_K(-1)=-5/3$
-484
1:
2.108513260095292735305968908960853417155736648257746023725435358118535296944846587266092437499036717
comment: $x^3-x^2+4x+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.484.1
-491
1:
1.661421584110706937731170512894899128860683371394548235172644850434954277551162075854254403029658746
comment: $x^3-x^2+x+4=0$; $S_3$; $h_K=2$; LMFDB 3.1.491.1
-492
1:
1.827215171741018270264103954088224717732752296276351607320123560857283999205067890148026099667857790
comment: $x^3-x^2+3x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.492.1
-499
1:
1.700219701206939198455733964135695243024956100558929300810328840209748070811364874432940582070673020
comment: $x^3+4x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.499.1
-503
1:
2.512188061560284142489684395237957693728112017451553757552177170303982531325060762052753476400956411
comment: $x^3-x^2+2x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.503.1
-515
1:
1.619029556305371369410489432586949011088399158165226479037973995258621845105610377143662807061819689
comment: $x^3-x^2-x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.515.1
-516
1:
2.288365412549146362281455110991358958557967550288398439994674539669991984294628894555495474617480085
comment: $x^3-x^2+x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.516.1
-519
1:
1.364392626251736847707347622601857171787383341291817471131756562935233385583871804084652769599390052
comment: $x^3-x^2-4x+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.519.1
-524
1:
1.569609691080116380637667005727634934961959879517840961616751887642577548125811535494539342959255504
comment: $x^3-x^2+3x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.524.1
-527
1:
1.118696582787073924433116897049257791287175846825198116357717813213389360897021136462242090760134617
comment: $x^3+5x-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.527.1
-543
1:
1.408264165360580360466345558001350577271014848080303656522755634120033017805919688380768432666464248
comment: $x^3-x^2+2x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.543.1
-547
1:
1.746166405598178939389953762712484312157701756850128055391794074561083063499857318483625412669660266
comment: $x^3-x^2-3x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.547.1
-563
1:
1.561536679207199595009958903153341149940342613274758338258727857734163129621098004748042420748949033
comment: $x^3-x^2+5x-4=0$; $S_3$; $h_K=2$; LMFDB 3.1.563.1
564
1:
1.722629268642625728101792342654392774371309993718679685379564927351787730325206627546783868758201921
comment: $x^3-x^2-5x+3=0$; $S_3$; $h_K=1$; LMFDB 3.3.564.1; $\zeta_K(-1)=-3$
-567
1:
1.275688036403392944852029088890581349383222583458905769983542767807605229051031692204646718006475468
comment: $x^3-3x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.567.1
568
1:
1.893849505437282932667688189299957593761456082889828468062692289816907322245831825954221483075861398
comment: $x^3-x^2-6x-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.568.1; $\zeta_K(-1)=-10/3$
-588
1:
1.833621116824598902892770860182854933355553748945789405694445796903512704109232425560458547795966621
comment: $x^3-x^2+5x+1=0$; $S_3$; $h_K=3$; LMFDB 3.1.588.1; $K=\mathbb{Q}(\sqrt[3]{28})$, a pure cubic field
-620
1:
1.537042399350863767333552511497423937618678207383473470700342839265475731257412922848942144649643122
comment: $x^3-x^2-5x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.620.1
621
1:
1.656649249826483838122491769658044690090650159901092256478706649290042859291324577109843256090334604
comment: $x^3-6x-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.621.1; $\zeta_K(-1)=-10/3$
-628
1:
2.152152052874459795428031727037674352109252470698263708752899602575571125440522914521130353940428286
comment: $x^3-x^2+4x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.628.1
-643
1:
1.734870797152218556132166969632710207836593395824082490539098179467976648358170801948183034117459093
comment: $x^3-2x-5=0$; $S_3$; $h_K=2$; LMFDB 3.1.643.1
-648
1:
2.163304510831309940362844249508360865443070425347136353303778652119959648065301226817573850598645891
comment: $x^3-3x-10=0$; $S_3$; $h_K=3$; LMFDB 3.1.648.1
-652
1:
1.664600985270675046161170934684868678947026141564865011378995480879170163601804655320447622475790552
comment: $x^3-x^2+7x+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.652.1
-655
1:
1.310957889199449065695565758077241528435507452660204307290186278897100184409655636397334801349676291
comment: $x^3-x^2+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.655.1
-671
1:
1.194585712587370953542757536285080719503746756528429536886391177509983894695848564119289005059039329
comment: $x^3-x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.671.1
-675
1:
1.730134550769024186669171514598931943227522503960939771828067341126638247190179147593076858662558685
comment: $x^3-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.675.1; $K=\mathbb{Q}(\sqrt[3]{5})$, a pure cubic field
-676
1:
2.119406307558528932572086854138686893197296072566951662715669081351714857912274278230385595033920604
comment: $x^3-x^2-4x+12=0$; $S_3$; $h_K=3$; LMFDB 3.1.676.1
-679
1:
1.375088732066892424993724979480559767367473607268990862413752337252472932852006734647352113232055253
comment: $x^3+x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.679.1
-680
1:
2.016798762211161485480976743921484739502880809833459125731327746138128637253626494864269556162682437
comment: $x^3-x^2-6x+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.680.1
-687
1:
1.410253557078522394878843641346689173325349843924809444178958993052275355167487951013280494357532261
comment: $x^3-x^2+4x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.687.1
-695
1:
1.161164567967825548863224727625439565096834430038289848431432138376798179406208463802711173554524143
comment: $x^3-x^2-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.695.1
-696
1:
2.306364312134909253169742076518342966028770609894303405948764173397084749703711620864442208404235707
comment: $x^3-x^2-2x+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.696.1
697
1:
1.114573692957134216560333960532293961329368743867197074902357619623535859906934371162293497951859177
comment: $x^3-7x-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.697.1; $\zeta_K(-1)=-8/3$
-707
1:
1.591613848557608508628322116611024747920933364613569954156212178309184657350205720146862021551268436
comment: $x^3+2x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.707.1
-716
1:
1.975102984319427887265682360609406614569869536308715454390549324626836795316143741247630918797238748
comment: $x^3-4x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.716.1
-728
1:
1.981131846994278801538120842906433422000767056855948616624622069725750971701956291977822828593545961
comment: $x^3-x^2+6x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.728.1
-731
1:
1.558763791757315225594068554961146545782672030890762351869156100187466620948067539234516077673281319
comment: $x^3-x^2+3x+4=0$; $S_3$; $h_K=2$; LMFDB 3.1.731.1
733
1:
1.550219703478615861175057066207603542311676959174685600878880935173627103582906251926600635588293679
comment: $x^3-x^2-7x+8=0$; $S_3$; $h_K=1$; LMFDB 3.3.733.1; $\zeta_K(-1)=-4$
-743
1:
1.566269101443148955656190237593222654625650926617039906188412176554055786309706708655637079592781613
comment: $x^3+5x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.743.1
-744
1:
2.325271830079581437910200309528098894229155009634443092933292735273885650270765251310001250370530671
comment: $x^3-x^2-6x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.744.1
-748
1:
1.648753244054363151317928765605997324748976747562648400184799738450417983857142740669963515476223221
comment: $x^3-x^2+x+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.748.1
-751
1:
1.361568603641598097679677415935155941706425740308521267669014628536159225056776311023728586031041247
comment: $x^3-x^2+6x-1=0$; $S_3$; $h_K=2$; LMFDB 3.1.751.1
-755
1:
1.659985092670984692941376650656406234436822817478084597978643714891829211998532786220058196890033193
comment: $x^3-x^2+5x+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.755.1
-756
1:
2.131570080779124153896773578776530138493456750344380520646860443955727915505535519941731633300459654
comment: $x^3-6x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.756.1
756
1:
1.603351075678956614422175638765671128366119166227632299529744865713725065624308663132750704242854613
comment: $x^3-6x-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.756.1; $\zeta_K(-1)=-13/3$
-759
1:
1.346815989216567895056887607805853503301702368044117841486510541190822491473375044626219445662016687
comment: $x^3-x^2+6x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.759.1
761
1:
1.221211775393580239373446381113298909030396381561659371563141829213656830666085385037977668358311114
comment: $x^3-x^2-6x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.761.1; $\zeta_K(-1)=-10/3$
-771
1:
1.879992710843955726648375794330640294863539355527121705127854440438026234483725302634723104722970963
comment: $x^3-x^2+3x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.771.1
-780
1:
1.871831555860338972410044293828817741071202850007441487262917406166236321667671301891201663616181155
comment: $x^3-x^2-x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.780.1
785
1:
1.282201168933376514808024333478695913971729563053133876445296607058991878752987808163757819904638106
comment: $x^3-x^2-6x+5=0$; $S_3$; $h_K=1$; LMFDB 3.3.785.1; $\zeta_K(-1)=-11/3$
788
1:
1.622582089771475419916979097705640921662465623683704169152908362834563961083624801468538578367103962
comment: $x^3-x^2-7x-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.788.1; $\zeta_K(-1)=-14/3$
-804
1:
2.312053096831630101692671656018792141331902049988772489348623638117266962065598422180437679230525393
comment: $x^3-x^2+4x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.804.1
-808
1:
2.160830935058594920263495588989604674615739186750375516812132185535366318554940320975330790262596321
comment: $x^3-x^2+2x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.808.1
-812
1:
1.502545134315979086912629692771394111962664845178647105128184765694448849958315326722042726282192216
comment: $x^3-x^2-7x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.812.1
-815
1:
1.598863299374306438871303652229379000954818312098134759736938903471414332242291162991088282989384633
comment: $x^3-7x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.815.1
-823
1:
1.266857205847112133604371434618376427983115196050597229388411490401900019094717009039948888568431613
comment: $x^3-5x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.823.1
-835
1:
1.807756255603240273385298853944794810837442350858957170971147371382689102886364474094817167279600261
comment: $x^3-x^2-x+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.835.1
837
1:
1.693946789557930279694938981939307087381885180737312612679040367644598584654265323106663705469586378
comment: $x^3-6x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.837.1; $\zeta_K(-1)=-16/3$
-839
1:
1.252974327052892517332688582795032988077722178302373202398360224353004307104088080429235684420899382
comment: $x^3-x^2-2x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.839.1
-843
1:
1.912943852077880896327775378470766540158764633307748477800853919838727149773196841326100560039727208
comment: $x^3-x^2-2x+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.843.1
-856
1:
2.124528623785953853899809176399555087077605642072377274250794973654470645106159768179829075766537275
comment: $x^3-x^2+x+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.856.1
-863
1:
1.116379679077291616897100565915705669110344527590250413171637992555279274130937062337961026569704347
comment: $x^3-x^2+2x+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.863.1
-867
1:
1.915848163675572646080116952091486495682601891095065943589703471736447694474284330355397726612186984
comment: $x^3-x^2+6x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.867.1; $K=\mathbb{Q}(\sqrt[3]{17})$, a pure cubic field
-876
1:
1.795590785403444840771138040802101928587051059435924816883791784865991399448095455060688120743449424
comment: $x^3-x^2-x-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.876.1
-883
1:
1.758327962706469765322316299458043866237690374616423745511507260465636029231286252688761480291690266
comment: $x^3-x^2+2x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.883.1
-888
1:
2.371201621789598268649496420133866682795183331591960920424626639188342330751154562136150783801395003
comment: $x^3-x^2+9x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.888.1
-891
1:
1.699967144658901605320187965918750886487880940870462153049145382616177298611581904795591372746713520
comment: $x^3+6x-1=0$; $S_3$; $h_K=3$; LMFDB 3.1.891.1
892
1:
1.924645207175375514611788820013861752059791147785495112191849421524969800373036051249062178671282188
comment: $x^3-x^2-8x+10=0$; $S_3$; $h_K=1$; LMFDB 3.3.892.1; $\zeta_K(-1)=-20/3$
-907
1:
1.758963940131322675657599891220266871924247957140180896282914809516953399403749403895862572815327197
comment: $x^3-x^2-7x+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.907.1
-908
1:
2.013805623518930448669629158142483743513898050002381760264183727333249949117623994503352150025217454
comment: $x^3-4x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.908.1
-931
1:
1.701812286431204439978502951877667072553917941916639183177363671108542501923467317372396798176215570
comment: $x^3-x^2+5x-6=0$; $S_3$; $h_K=3$; LMFDB 3.1.931.1
-932
1:
1.969742674670679936487668045028930387802787979376112953649950890636639513194752684215538784883733420
comment: $x^3+5x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.932.1
-940
1:
1.720345094699754217498042799289884009622949916226762460157013965296648371226289953690529510729431464
comment: $x^3-2x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.940.1
940
1:
1.957036244281756547908490907686950019282852601002203625453605038003938971866590257001792249609293428
comment: $x^3-7x-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.940.1; $\zeta_K(-1)=-22/3$
-948
1:
2.373913545728532984938634865868180146352033693108688608234645134185303918934990705456623330246376804
comment: $x^3-x^2+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.948.1
-959
1:
1.082733221688343005592452653395420125470125633701046626101292334582509592377185808710235058682668328
comment: $x^3-x^2+6x+1=0$; $S_3$; $h_K=1$; LMFDB 3.1.959.1
961
1:
2.409577605774318797564915079253712612827774901705822138350520470348282327735294192024723301780505577
comment: $x^3-x^2-10x+8=0$; $C_3$, conductor $31$; $h_K=1$; LMFDB 3.3.961.1; $\zeta_K(-1)=-28/3$; the cubic subfield of $\mathbb{Q}(\zeta_{31})$; $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$ for $\chi=\chi_{31}(5,\cdot)$
-964
1:
2.111427540933566749023282200104225346607279101583603716180806575106174619028268634636225140925769304
comment: $x^3-2x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.964.1
-971
1:
2.061659123204625342466484775018157765202018034904043624792578408819154367279091418272935560096290588
comment: $x^3-x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.971.1
-972
1:
1.637667305701474075609922190562257160872785407810687665599266459472186888157020637761205686403157480
comment: $x^3-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.972.1; $K=\mathbb{Q}(\sqrt[3]{12})$, a pure cubic field
-972
2:
1.700167424475893219550978749492600103533359222111008482886101445237942052396643637584024516007392354
comment: $x^3-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.972.2; $K=\mathbb{Q}(\sqrt[3]{6})$, a pure cubic field
-980
1:
2.025246873336751422308715020709382780651046852392426370292429992646446149193664720772924702310498151
comment: $x^3-x^2+5x-13=0$; $S_3$; $h_K=3$; LMFDB 3.1.980.1
-983
1:
1.094397015261434471642213491746106757239794164387391917788674043349008924028035580943652459421275889
comment: $x^3-x^2+6x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.983.1
-984
1:
2.340154050129696212896469006293432641744319828414301347613137464108178833034417693315807117961748756
comment: $x^3-x^2-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.984.1
985
1:
1.161025232576859278260746635212535285539708212734379525624349192825405082226673824244384453595447152
comment: $x^3-x^2-6x+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.985.1; $\zeta_K(-1)=-14/3$
993
1:
1.392813658733913920686716107147353012134217826257075773792656105962117874929336840486318313424287911
comment: $x^3-x^2-6x+3=0$; $S_3$; $h_K=1$; LMFDB 3.3.993.1; $\zeta_K(-1)=-17/3$
-996
1:
2.338291261800421737510642717885497792019103981495138245212657304790431882699379892722067123336632210
comment: $x^3-x^2-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.996.1
-999
1:
2.734511782338550732488435292749129427094102476031378744584680983706216666207301475212824290863411448
comment: $x^3+3x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.999.1
-1004
1:
1.966879931284543912349534677761672063355856417730950539772502886733637150844321862873297329924008029
comment: $x^3+2x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1004.1
-1007
1:
1.154734331878906235335929145272072742025281398785563951190245487403639701596252444507919618703426761
comment: $x^3-x^2-2x+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1007.1
-1011
1:
1.870693718284181589282371355641910432832738724390643010549446412049341894918430054982009899349425567
comment: $x^3-x^2-5x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1011.1
1016
1:
2.058262466293157227008399302221575924702148865707215011616111544029635024423033800247377204920348917
comment: $x^3-x^2-6x+2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1016.1; $\zeta_K(-1)=-26/3$
-1036
1:
1.627186097934483981939763922228747483389979117260080580532370741527943082560505831898354369541285880
comment: $x^3+4x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1036.1
-1048
1:
2.166776369711439278131467475451584348942413022242086251175105064363093900911518420789713114160821159
comment: $x^3-x^2+8x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1048.1
-1055
1:
2.613391723858723170640425396859315112128720865247165820700638069489318747182558904743535309588386064
comment: $x^3-x^2-6x+16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1055.1
-1059
1:
1.887552211602397200994233944869256124508379475477488257427799068455114306793560693606852855014882824
comment: $x^3-x^2+x+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1059.1
-1067
1:
1.620119352571078751341149010996925890115079793016843378737300470750392473369783223443365947995487152
comment: $x^3-4x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1067.1
-1068
1:
1.845988686331764798829260754356338834232739922845519939186896914744518603863711093693811115442442612
comment: $x^3-x^2-x+13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1068.1
-1075
1:
1.757042721977802346832314207544272130146354525877018271041025038912977595271733028220244521224913093
comment: $x^3-x^2+2x+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1075.1
1076
1:
1.597983321824580344057738626797667541618153005019835144015668097305334692838805478997179949711193817
comment: $x^3-8x-6=0$; $S_3$; $h_K=1$; LMFDB 3.3.1076.1; $\zeta_K(-1)=-22/3$
-1080
1:
2.238888937558721694922385871732915648225837123303716792636744892636567787872559501866747964343807200
comment: $x^3+3x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1080.1
-1083
1:
1.920108442545196094760182065813047598141666488527028217404735879598125389993450501984010007954620373
comment: $x^3-x^2-6x-12=0$; $S_3$; $h_K=3$; LMFDB 3.1.1083.1; $K=\mathbb{Q}(\sqrt[3]{19})$, a pure cubic field
-1087
1:
1.268996766075547595008646084694395453069213190045936166813995422002540198584573990324882442901714337
comment: $x^3-x^2+4x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1087.1
-1096
1:
2.127213618757188014173615952791439527872000754473440305849586615152023298991049849737981918674511264
comment: $x^3-x^2+x-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1096.1
-1099
1:
1.725290619788296627020251800358054309086730487002481651762659354191755087860618581479563960881653651
comment: $x^3-x^2-x-6=0$; $S_3$; $h_K=2$; LMFDB 3.1.1099.1
1101
1:
1.824569193925960536840555300747042224199678410982587861345288657634295151915854679153984741937313669
comment: $x^3-x^2-9x+12=0$; $S_3$; $h_K=1$; LMFDB 3.3.1101.1; $\zeta_K(-1)=-26/3$
-1107
1:
1.748554432475229626560453432299118533081912139076136187844408175332761324181464246243257580758146871
comment: $x^3+6x-3=0$; $S_3$; $h_K=2$; LMFDB 3.1.1107.1
-1108
1:
2.186038057926191913787143764839314158533016379421411639567227124526067765081332775455802906495888458
comment: $x^3-x^2-8x+14=0$; $S_3$; $h_K=1$; LMFDB 3.1.1108.1
1129
1:
1.486790359324168127031929521243896052303043170632108385769333795685800162693418995342899862922079255
comment: $x^3-7x-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.1129.1; $\zeta_K(-1)=-22/3$
-1135
1:
1.327380009439044417300860767062456946855838643645552367300436740758310408876614997416130489939382051
comment: $x^3-x^2-6x+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1135.1
-1144
1:
2.110573604046767128723318956697443046810736797541650104205605787301058838697211940336866899130973160
comment: $x^3-x^2+6x+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1144.1
-1147
1:
1.738581552073691527963388349103682319747494449705134891838624273851082711467451926605698688285459317
comment: $x^3-x^2-3x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1147.1
-1164
1:
1.788545328000622009093581443202786971867785329563738703592494128581376305809588664049166832742871720
comment: $x^3-x^2-x+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1164.1
-1172
1:
1.948017563577497012348043945980355350158196920999982271458141925139337627100137037956120942941261951
comment: $x^3-x^2+5x+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1172.1
-1175
1:
1.092415520508682938931216618942579059795512303164673268381189155726546217850234005204749727966086509
comment: $x^3+5x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1175.1
-1176
1:
2.343283100649102667421323299929479427663123415584037098706834829461110013948439140426577752792254010
comment: $x^3-x^2-2x-6=0$; $S_3$; $h_K=3$; LMFDB 3.1.1176.1
-1187
1:
1.578220953277234355105720227437717789318916478164495780643656041923132516182992574273633065124651027
comment: $x^3-x^2+7x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1187.1
-1188
1:
2.162598193347788252897200546906195766054832642608814252853240625202374010701711334270525972478860445
comment: $x^3+6x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1188.1
-1191
1:
1.361611989184428806997526607918199805539849548731747311513937779402598396068385156177025843116317934
comment: $x^3-x^2-10x-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1191.1
-1192
1:
2.192474631895982008612730606912198073430734671542716582364452695340921698057043464764408716293449650
comment: $x^3-x^2+2x+6=0$; $S_3$; $h_K=2$; LMFDB 3.1.1192.1
-1196
1:
1.464879061970303885209596308300244450803274560809300649659480401305067770542346611756026980958934179
comment: $x^3-x^2+5x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1196.1
-1203
1:
1.923953887510739403316812678888640456600728778813752496588598557947325271782118366382987951254593300
comment: $x^3-x^2-3x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.1203.1
-1207
1:
1.310602056309311004704699446897564952839033668312743817227666481593194455122148303422163858846327942
comment: $x^3-x^2-6x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1207.1
-1208
1:
1.967343581081594345407273416144834487120291954399870499975897573063473335496893627214862973003942817
comment: $x^3-x^2+8x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1208.1
-1219
1:
1.704409537194949616008575756393335058832131597625661477495947583650239121075742000889343551755523088
comment: $x^3-8x-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1219.1
-1228
1:
1.711034658221187313756132026482454718402877845625253654386276560591577802588795945259728399052095276
comment: $x^3-x^2+x-7=0$; $S_3$; $h_K=3$; LMFDB 3.1.1228.1
-1228
2:
1.637887348556204192435922648762317273495208441300123988678168941671391800036678475916864884220686925
comment: $x^3-x^2+7x-1=0$; $S_3$; $h_K=3$; LMFDB 3.1.1228.2
-1228
3:
1.653116668064054862482343195575214109323483596420919984882060986446291127272995917182068452971704108
comment: $x^3+4x-6=0$; $S_3$; $h_K=3$; LMFDB 3.1.1228.3
1229
1:
1.666088917108660661098699157739754607918282321561714276085059537222177465553864233033857266014613654
comment: $x^3-x^2-7x+6=0$; $S_3$; $h_K=1$; LMFDB 3.3.1229.1; $\zeta_K(-1)=-28/3$
-1231
1:
1.356075660813048269112201866103955798791950280494445568516953121870907243207070672554174077225761425
comment: $x^3-x^2-4x+9=0$; $S_3$; $h_K=1$; LMFDB 3.1.1231.1
-1235
1:
1.604849226506698402257412301627354658931597498207937527971718124987491415646487537336903801735226998
comment: $x^3-x^2-5x+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.1235.1
-1236
1:
2.347585991231709317555470768857989618078856151708826752359265209098287918433188657950045860615078963
comment: $x^3-x^2+4x+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1236.1
-1255
1:
1.320431385473475460387586823034843777980095131039428003686414629319046115022060988149960976016176752
comment: $x^3-x^2+4x+5=0$; $S_3$; $h_K=2$; LMFDB 3.1.1255.1
1257
1:
1.380626781529906895111907543842276075950545668831907495391305169742614394513549912274518853175868771
comment: $x^3-x^2-8x+9=0$; $S_3$; $h_K=1$; LMFDB 3.3.1257.1; $\zeta_K(-1)=-8$
-1259
1:
1.561498387873360876072306356147904618450337556484508812253980447791496515554295703115666690946190458
comment: $x^3-x^2-9x+16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1259.1
-1267
1:
1.784689169413476532214940866530594705286858622928156849078201788792301194828743216696442834673553539
comment: $x^3-x^2+7x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.1267.1
-1272
1:
2.386579930355129021707808181188397597313414361994971501491079829959605008831686082278960337731484217
comment: $x^3-x^2-3x+15=0$; $S_3$; $h_K=1$; LMFDB 3.1.1272.1
-1291
1:
1.754232029110656744959811714993208468043099520382220277688561724289319858632726709120676491083346310
comment: $x^3-2x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1291.1
-1292
1:
1.475471232509373471819839121878931814934616361771571009723691408991201804280207494324216222685739359
comment: $x^3-10x-14=0$; $S_3$; $h_K=1$; LMFDB 3.1.1292.1
-1295
1:
1.200314326754070773690699764234002822410747413224437923383291171731911251676367770556053457406455456
comment: $x^3-x^2+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1295.1
-1300
1:
2.167236573403619968589970967323235662760703687973826159811606249003945092598226005186195593907328545
comment: $x^3-x^2-3x-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1300.1
1300
1:
1.476783067361638585755377871384997009305793903185354187794086649612310000071055597980547672275637184
comment: $x^3-10x-10=0$; $S_3$; $h_K=1$; LMFDB 3.3.1300.1; $\zeta_K(-1)=-9$
1304
1:
2.068879412555196000674363486502551678370412387327212137562857434075397192222683711787293793933074030
comment: $x^3-11x-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1304.1; $\zeta_K(-1)=-38/3$
-1315
1:
1.794265653494247064233051904714188632312319669567691036050142748277058320508347389280056679958702973
comment: $x^3+7x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1315.1
-1316
1:
1.922982324800633292582010333349363155857792103023193270558519836473613734048644134262266930799004280
comment: $x^3-x^2+9x+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1316.1
-1319
1:
1.107163836552983745988856166674447271974538777874793094365544158779946352143375702619341897986561318
comment: $x^3-x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1319.1
-1323
1:
1.751674481802537846577392199782165250481385723450431241729527324394626786938413668117997540495111474
comment: $x^3-7=0$; $S_3$; $h_K=3$; LMFDB 3.1.1323.1; $K=\mathbb{Q}(\sqrt[3]{7})$, a pure cubic field
-1327
1:
1.262130866358217233320249123628861632238596621079697478104164383600439807773494672888036127972677970
comment: $x^3+x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1327.1
-1336
1:
2.108536228882395467908422657794794487745982603519313500188753944818317492476367472377231346654146485
comment: $x^3-x^2+9x-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1336.1
1345
1:
1.195397595545392772598312341732212713325890079145819202787826370874837072042403514473127889312895646
comment: $x^3-7x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.1345.1; $\zeta_K(-1)=-23/3$
-1347
1:
1.925632652191709413198107376465119084224760810467829392010794105743090280372896419699707027187941999
comment: $x^3-x^2-7x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1347.1
-1351
1:
1.239825637730720669304909742795228743897546185988886829071559802015783055203302984838656924536712083
comment: $x^3-x^2-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1351.1
-1355
1:
1.627192510041005415619194555094599590637073417259419338113219211701359869672966246099591774966367126
comment: $x^3+2x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1355.1
-1356
1:
1.835580815578457056028643263685004778645907101400605778777125453348302751416471762262736556724985881
comment: $x^3-x^2+x+21=0$; $S_3$; $h_K=3$; LMFDB 3.1.1356.1
-1356
2:
1.941020278628793910457790536133647303210347866302455805040582812193226645659602172224058037919545022
comment: $x^3-x^2+3x-15=0$; $S_3$; $h_K=3$; LMFDB 3.1.1356.3
-1356
3:
1.769079622875090110191685153179925193785052142065418293327973469686207006291164067214012701894613455
comment: $x^3-x^2+11x+1=0$; $S_3$; $h_K=3$; LMFDB 3.1.1356.2
-1363
1:
1.735238999215173579567815930075910263705587187042176025209506318321151463181019766112536734083061812
comment: $x^3-x^2-9x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.1363.1
1369
1:
1.062874752536217962878650600054004981670664749818147207326323544491131011374876353936714487049282002
comment: $x^3-x^2-12x-11=0$; $C_3$, conductor $37$; $h_K=1$; LMFDB 3.3.1369.1; $\zeta_K(-1)=-7$; the cubic subfield of $\mathbb{Q}(\zeta_{37})$; $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$ for $\chi=\chi_{37}(10,\cdot)$
-1371
1:
1.877561756394889167324362132821575591531124657321405131013276202502249866987983509913422445769272449
comment: $x^3-x^2+3x+6=0$; $S_3$; $h_K=4$; LMFDB 3.1.1371.1
1373
1:
1.713330237811166972518745865493396090541400066145568397201469018760811215983126000300719021360450206
comment: $x^3-8x-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.1373.1; $\zeta_K(-1)=-34/3$
-1383
1:
1.406718817239709883149927027551237415110254150152289994977541412681407786400677064544571015526789903
comment: $x^3-x^2+6x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.1383.1
1384
1:
1.892114569628189566133684310756107678672961270124387591024482993365415322103999534734448998901033804
comment: $x^3-x^2-10x+14=0$; $S_3$; $h_K=1$; LMFDB 3.3.1384.1; $\zeta_K(-1)=-38/3$
-1388
1:
1.473767860064543618362682605516587856166986558475588439139599224182432854094998010349868204390089608
comment: $x^3-x^2+7x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1388.1
1396
1:
1.572859099878156298556469401375279009091110024446840350062772793827442830096003655057256372804326252
comment: $x^3-x^2-7x+5=0$; $S_3$; $h_K=1$; LMFDB 3.3.1396.1; $\zeta_K(-1)=-32/3$
-1399
1:
1.260515029271509758582724851022042956435989705936601201610197970947645209444300691970197052129887732
comment: $x^3+7x-1=0$; $S_3$; $h_K=2$; LMFDB 3.1.1399.1
-1407
1:
1.428265911471020661010929427415015133082975204448868669939378762939558938997139003051605075704961829
comment: $x^3-x^2-8x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.1407.1
-1419
1:
1.871610422598624523542699503461382045071048039284837663773306199421122806781866843405275925277860248
comment: $x^3-x^2+10x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1419.1
-1420
1:
1.699317595059945129808518400127259945930264016900115578801120529817400151472170144917543445440831897
comment: $x^3-x^2-5x+17=0$; $S_3$; $h_K=1$; LMFDB 3.1.1420.1
-1423
1:
1.270345624876289572150805436793779961567990521091537223123217862957703702088577108744877875587020687
comment: $x^3-x^2+6x-7=0$; $S_3$; $h_K=2$; LMFDB 3.1.1423.1
1425
1:
1.382113375216715977161048444162284891291201049206482054002556058066086516700511096023334810069643284
comment: $x^3-x^2-8x-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.1425.1; $\zeta_K(-1)=-29/3$
-1427
1:
1.542243614571285172225514867504676731575788764832144501478611523794222471588455956992592666388355430
comment: $x^3-x^2+3x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1427.1
-1431
1:
1.251664460027743866381643007400318259566860232820677788365669966627891208949456425177330253950672269
comment: $x^3+3x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1431.1
-1432
1:
2.193093360433224411030630801337417681212848062057070437813596036119372458748517875415732944858525349
comment: $x^3+10x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1432.1
1436
1:
2.072950754729632919267425055515689517229249641535377004911883380378861554898200645298479033235738161
comment: $x^3-11x-12=0$; $S_3$; $h_K=1$; LMFDB 3.3.1436.1; $\zeta_K(-1)=-44/3$
-1439
1:
2.513348327211220154103753526562395271057684208979702063378572392108840996724378027330293098872560140
comment: $x^3+11x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.1439.1
-1448
1:
2.012719997912838423241588467198125506621883871563013420289431651833088164499315477198407652550103935
comment: $x^3+5x-14=0$; $S_3$; $h_K=1$; LMFDB 3.1.1448.1
-1452
1:
1.829040874397839479056736691361895422624216501918614743484537635947434330246400314811235708434934412
comment: $x^3-x^2-7x+13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1452.1; $K=\mathbb{Q}(\sqrt[3]{44})$, a pure cubic field
-1464
1:
2.354106278230477333486426512821823999737775171550296397309920746875800805537805544211052295061628119
comment: $x^3-x^2-7x+19=0$; $S_3$; $h_K=1$; LMFDB 3.1.1464.1
-1480
1:
2.234590850105307609203015524398297724532337238303543966930859638532034775558359293983687814878903960
comment: $x^3+7x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1480.1
-1484
1:
2.013000367660469459174245901479389281575771332563891877427766230865016772701572700501303946812767755
comment: $x^3+8x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1484.1
1489
1:
1.070871014347726678767323755075298794264781069536027038548370277350545106964016652797116767791189849
comment: $x^3-x^2-10x-7=0$; $S_3$; $h_K=1$; LMFDB 3.3.1489.1; $\zeta_K(-1)=-8$
-1491
1:
1.908653026306310558499483030667001154479190962690313423669165888464809833347717973814558354275973564
comment: $x^3-x^2+6x+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.1491.1
1492
1:
1.512493966129038909204746828937892874014686899354620328470084728646669846103108177801373076832727620
comment: $x^3-x^2-9x-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.1492.1; $\zeta_K(-1)=-34/3$
1509
1:
1.836891054447072693513012420886729700066202118900573233078125743291695250152315305137844982958818187
comment: $x^3-x^2-7x+4=0$; $S_3$; $h_K=1$; LMFDB 3.3.1509.1; $\zeta_K(-1)=-14$
-1512
1:
2.212888862625559300969472390663570482082830035847307812151811133452750321437629338841959375890355615
comment: $x^3-6x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1512.1
-1515
1:
1.982452712832467789345642147235197075171521261055316530169850567238533779230677472553358336658294743
comment: $x^3-x^2+5x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1515.1
1524
1:
1.766747049271525765196540163441402470355625542324038737402746374567288567146002697377561329316201323
comment: $x^3-x^2-7x+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.1524.1; $\zeta_K(-1)=-41/3$
-1539
1:
1.842570751256976817796050190606994926849689380349969666850277149161770255590719114250651524448991222
comment: $x^3+6x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1539.1
-1547
1:
1.592173423710473604507954563443551124352101940170358362005690660042746281343685364198171057605068764
comment: $x^3-x^2-x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1547.1
1556
1:
1.587220178485239027570899999393294225717526369578569902051214863679956769638363825760374622159214301
comment: $x^3-x^2-9x+11=0$; $S_3$; $h_K=1$; LMFDB 3.3.1556.1; $\zeta_K(-1)=-38/3$
-1559
1:
2.561038264673427042980479662361177575435543878625851400448300330969506819850431816249250103337099868
comment: $x^3-x^2-2x+16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1559.1
-1563
1:
1.950955550967716535480832370947736946123481855139183881163815600269747125086024835450475005597714645
comment: $x^3-x^2+7x-6=0$; $S_3$; $h_K=5$; LMFDB 3.1.1563.1
-1567
1:
1.319600623329387876641206800819225028561968428937147251743356034708775085518571778748723007785109953
comment: $x^3-x^2-2x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1567.1
-1572
1:
2.417303897692446980545702555660731125736561450253527331107846078323147941495784801022239964251630655
comment: $x^3-x^2+x+15=0$; $S_3$; $h_K=5$; LMFDB 3.1.1572.1
1573
1:
1.561559299878739634880606592443161264257455222223431536749736836276477724982611590373732129740217965
comment: $x^3-x^2-7x+2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1573.1; $\zeta_K(-1)=-38/3$
-1579
1:
1.700383686556666336123005757971570598875592493553958622474519756040246106224309888188255991033167861
comment: $x^3+4x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1579.1
-1580
1:
1.500050335801990948374254442381730086102469266194561393363890760843685320858990947548905570080601798
comment: $x^3-x^2+5x+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1580.1
-1583
1:
1.124951265272172568830186034716556327174896506085039243787543169845282023585552881193673417361237341
comment: $x^3-x^2-4x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1583.1
-1588
1:
2.172950472683591874835699751403705341011998355779900573636067321898217296496215870438741768455809475
comment: $x^3-11x-16=0$; $S_3$; $h_K=2$; LMFDB 3.1.1588.1
1593
1:
1.290310653492532637672123365310727696633753942494445023819896813024566806073740284817644999894634433
comment: $x^3-9x-7=0$; $S_3$; $h_K=1$; LMFDB 3.3.1593.1; $\zeta_K(-1)=-32/3$
-1599
1:
1.338553682871404207684765551969422737048223078357131772258522555121555983746023916370674715321140463
comment: $x^3+3x-23=0$; $S_3$; $h_K=1$; LMFDB 3.1.1599.1
-1603
1:
1.785236988212484063542141409980907522606380198474375696365679492252820303433483155657861208148828221
comment: $x^3-5x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1603.1
-1607
1:
2.586533822432190008937616232527152348815837827452186623073496312378252689253161968983674801075044911
comment: $x^3-x^2+2x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1607.1
-1612
1:
1.664520575470475371761915853798091259708861613037561900475246273441291132961486193649725017836245155
comment: $x^3-x^2-3x-7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1612.1
-1615
1:
1.294903804636564067824374921578816937431956389604296471168425775145685439498849374328776312310637296
comment: $x^3+7x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.1615.1
-1619
1:
1.522102981543204006538733947763697813076603104469377449415384728126732925205431734442185932081090202
comment: $x^3-x^2+x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1619.1
-1620
1:
2.230081066883736783656986757021298455720733382927181140875021521448929499425052164858297103876106536
comment: $x^3-3x-8=0$; $S_3$; $h_K=3$; LMFDB 3.1.1620.1
1620
1:
1.690689681860587956522468776489376511023419252741046030411099880082665264900289483503860239711686019
comment: $x^3-12x-14=0$; $S_3$; $h_K=1$; LMFDB 3.3.1620.1; $\zeta_K(-1)=-43/3$
-1647
1:
1.256916893089689883920100579334532848814674734700685271784117798511290598986246723381225868537568713
comment: $x^3-9x-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1647.1
-1668
1:
2.418777286724001059254719389125986652315880540576823842762126833138333207419795007521623626441611918
comment: $x^3-x^2-4x+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.1668.1
-1675
1:
1.768001122209871033620071065443386467704295916609272969668204924408483447068407439802785182612003411
comment: $x^3-x^2+7x+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1675.1
-1687
1:
1.302126208840265113408472863650483648309362695156635536737211609813414549562974409169421562253667463
comment: $x^3-5x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.1687.1
-1691
1:
2.094868420581156621630026533362834838965057132586127052862597242105415227987085235863544297070506640
comment: $x^3-x^2+x-24=0$; $S_3$; $h_K=1$; LMFDB 3.1.1691.1
-1700
1:
1.943242311201429820986851222445173934059627288501850121393197660567030434940072548905111253471358443
comment: $x^3-x^2+12x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1700.1
-1704
1:
2.329585705605726897019019594929722699798469540002578211776857990972261039004355473299442107256900350
comment: $x^3-x^2+5x-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.1704.1
-1708
1:
1.694710896408797465904006010466359382372368026922223693134731940157230024770594739255239682295192542
comment: $x^3-x^2-5x+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1708.1
1708
1:
1.961236326378437653110511923982071422029751686921868721166877643830805830271569795031270537009527538
comment: $x^3-x^2-8x-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1708.1; $\zeta_K(-1)=-18$
-1720
1:
2.241458598933850350627766776883456065174959765225317404483731179603858573628045203597700153411135440
comment: $x^3-2x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1720.1
-1727
1:
2.563602997215202989884496676438455131928472339130850670327758986761387477757892424144923763028854915
comment: $x^3-x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1727.1
-1732
1:
2.169857160133824833361668801763861393776315464158561587492071374088056607415326155939303963070211423
comment: $x^3+x-8=0$; $S_3$; $h_K=2$; LMFDB 3.1.1732.1
-1736
1:
1.923678533764159761127971162377496646393726171768922234381455793860906342247253534878844504855537226
comment: $x^3+2x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1736.1
-1740
1:
1.906634026805961477121379613261183599146967311134209167719958928425038395881172268848643383416859350
comment: $x^3-x^2-5x-15=0$; $S_3$; $h_K=1$; LMFDB 3.1.1740.1
-1743
1:
1.433629598824611640134596218079736249295418318749171369910126191947543086046891256978084522025219521
comment: $x^3-x^2-8x+15=0$; $S_3$; $h_K=1$; LMFDB 3.1.1743.1
-1751
1:
1.516002072905851725668310074550879783765254732561425013874218567524591765158670432800221826018457021
comment: $x^3-x^2-4x-23=0$; $S_3$; $h_K=1$; LMFDB 3.1.1751.1
-1755
1:
1.785359344854429003874206637806984605380456374694047459164216360193386189293593989354803881319382707
comment: $x^3+3x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1755.1
-1759
1:
2.789240417714691264504789691104376666356588563261952598072468179709525786279887001681278584135578799
comment: $x^3-x^2+10x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1759.1
-1763
1:
1.540860716571536865803152580703352484658643353149746816738039204311567913716999854256263545557604088
comment: $x^3+11x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1763.1
1765
1:
1.590408673470368201751824178823054186775593501491065343825719083099905018709271634383256177413182952
comment: $x^3-x^2-11x+16=0$; $S_3$; $h_K=1$; LMFDB 3.3.1765.1; $\zeta_K(-1)=-46/3$
-1772
1:
1.469433051847778379654981267160959581963741444143233942912248096771497281333820751850007903466035769
comment: $x^3-x^2+3x+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.1772.1
1772
1:
2.130904966528389722128137045066874017516491386209317149997156904702687672688407785489166977638628626
comment: $x^3-x^2-12x+8=0$; $S_3$; $h_K=1$; LMFDB 3.3.1772.1; $\zeta_K(-1)=-62/3$
-1807
1:
1.274750350557030755245129364627143564817977126114122142570372709091799832253128674608344054999097092
comment: $x^3-x^2+8x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.1807.1
-1812
1:
2.395243453203711998983025471477076090322284533031500795016394933384827901313163208105360749198125634
comment: $x^3-x^2+8x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.1812.1
-1815
1:
1.466440704145999285978206289425359097176189092849136067734888098450247986906389606949972482608625796
comment: $x^3-x^2+4x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.1815.1
-1823
1:
1.187413828695401055682536863324526863430880559554539837356325648609394964412863106313998834908205212
comment: $x^3+5x-7=0$; $S_3$; $h_K=2$; LMFDB 3.1.1823.1
1825
1:
1.118027747948875944981936411411938807001464382753351928679846778908729098537519667044823801385505281
comment: $x^3-x^2-8x+7=0$; $S_3$; $h_K=1$; LMFDB 3.3.1825.1; $\zeta_K(-1)=-34/3$
-1836
1:
1.767988055812012374065119764807304332191334963316933974116135176848484650664849162165094672964364511
comment: $x^3-6x-10=0$; $S_3$; $h_K=3$; LMFDB 3.1.1836.1
-1836
2:
1.593263901303191985025767335575923731498801692875127818498530465309176832170453814090896689494545791
comment: $x^3+6x-6=0$; $S_3$; $h_K=3$; LMFDB 3.1.1836.2
-1843
1:
1.758712820164538534474632600672220848236615284029951392148134117230880129680421249128105199010403650
comment: $x^3-x^2+x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1843.1
-1844
1:
2.576556281151384531451966941639818884790608141093810428810488176804715916759328921127255002986643276
comment: $x^3-7x-18=0$; $S_3$; $h_K=1$; LMFDB 3.1.1844.1
1849
1:
2.450621243805724014717250983102834964264229384722000756713976220082630456052712045511827540402584123
comment: $x^3-x^2-14x-8=0$; $C_3$, conductor $43$; $h_K=1$; LMFDB 3.3.1849.1; $\zeta_K(-1)=-76/3$; the cubic subfield of $\mathbb{Q}(\zeta_{43})$; $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$ for $\chi=\chi_{43}(6,\cdot)$
-1868
1:
1.450111300768922801416215888146279913243484701297604681178912518253926068323022483498147728965965854
comment: $x^3-x^2+7x+13=0$; $S_3$; $h_K=1$; LMFDB 3.1.1868.1
-1871
1:
1.061092350508560109205974944158097339738003678581810130587890223829032047206627795729594569077995894
comment: $x^3-x^2+8x-1=0$; $S_3$; $h_K=1$; LMFDB 3.1.1871.1
-1879
1:
2.769205649011616839706908825144450444063523498523845329390105369738628517744036798271243344893406669
comment: $x^3-x^2-2x-16=0$; $S_3$; $h_K=4$; LMFDB 3.1.1879.1
-1892
1:
1.968955649684434981715400655062378157997769628737904392341913231498677458706832555956300536123371347
comment: $x^3-x^2+x-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.1892.1
-1895
1:
1.137400580426353598637127734030711361049208466111495984136354922095473773345413937288879674093694856
comment: $x^3-7x-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.1895.1
1901
1:
1.670277200436994440655721468925249116496411123025274965478609959005972379949347682567591915871533004
comment: $x^3-x^2-9x-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.1901.1; $\zeta_K(-1)=-18$
-1915
1:
1.828440051166595042424757892473587195123117791175954730396525593334346993843284990932930233995180850
comment: $x^3-x^2-6x+20=0$; $S_3$; $h_K=1$; LMFDB 3.1.1915.1
-1927
1:
1.271707274935572749571376716401272980636768514187316730051128268459381811325871250800265722594805710
comment: $x^3-x^2+2x-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.1927.1
1929
1:
1.391962254102123766716794298431128806393531552638434562179923140557489841542011339031260169546734943
comment: $x^3-x^2-10x+13=0$; $S_3$; $h_K=1$; LMFDB 3.3.1929.1; $\zeta_K(-1)=-46/3$
-1931
1:
2.074187436905350115639778623204039218614074864297168895751994025310288505309869201610031268534736239
comment: $x^3-4x-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.1931.1
-1932
1:
1.871304844403489814120161678846958443155435967381640452297582525576478936522782666643706893318033640
comment: $x^3-x^2+7x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.1932.1
1937
1:
1.263056644183851274694561221849017955064591716422150089218056100262857313060959074316228630902519761
comment: $x^3-x^2-8x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.1937.1; $\zeta_K(-1)=-14$
1940
1:
1.680170675403724562866591657652258520062506394398453167185473269672195269681006850655582286417668130
comment: $x^3-8x-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.1940.1; $\zeta_K(-1)=-56/3$
1944
1:
2.093734539881762991285671008282031753986962957291554748110921348258507190368736471066698575251628656
comment: $x^3-9x-6=0$; $S_3$; $h_K=1$; LMFDB 3.3.1944.1; $\zeta_K(-1)=-70/3$
-1951
1:
2.768690724878558706222990666631565985381598812327550615942010432040856622010115604311529739617859558
comment: $x^3-x^2-6x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.1951.1
-1955
1:
1.620759007892931411657606850215040507134436235338118881926418192059997532071549124358727713100134649
comment: $x^3-x^2-5x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.1955.1
1957
1:
1.539873600709200171558449491811829652373336425226026980902128830105627829962000043450710993083780624
comment: $x^3-x^2-9x+10=0$; $S_3$; $h_K=2$; LMFDB 3.3.1957.1; $\zeta_K(-1)=-52/3$
-1959
1:
1.502417588729634378566889229625701782314768937665779212799381992863841082521972822429839633723882423
comment: $x^3-x^2+8x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.1959.1
-1960
1:
2.267041559910671264135207225089835981439909101378758128555784610937947766782877104800868849276709098
comment: $x^3-x^2+5x+15=0$; $S_3$; $h_K=3$; LMFDB 3.1.1960.1
-1963
1:
1.745514784481940981011866403979302337717459089924883111723013382152985109945473768815858405553452208
comment: $x^3-x^2+5x+6=0$; $S_3$; $h_K=4$; LMFDB 3.1.1963.1
-1967
1:
1.602707778148054032878072260016783744814414694628147673272362121193398971642343989998106836181967247
comment: $x^3-x^2+2x+25=0$; $S_3$; $h_K=1$; LMFDB 3.1.1967.1
-1971
1:
1.871856217078370050449514895319555424474497262721946959860599072836569373741761533364782660280622055
comment: $x^3-9x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.1971.1
-1972
1:
2.171205005588234829083975122770428504207284066090199121435331820387840128180646680958606292110225943
comment: $x^3+10x-12=0$; $S_3$; $h_K=5$; LMFDB 3.1.1972.1
-1988
1:
1.983319035507501449673266561312453792596165501191757273854441097444977616471681872036308486929048185
comment: $x^3-x^2+9x-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.1988.1
-1999
1:
2.794198852694068160243115797869053135855500502379949135879101071215723101028893619892992720958345939
comment: $x^3-x^2+10x-16=0$; $S_3$; $h_K=5$; LMFDB 3.1.1999.1
-2003
1:
1.563798925440425780610238515944547492940733718684185097577879780458245709897041744533003724960286789
comment: $x^3-x^2-3x+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2003.1
2021
1:
1.693049861402172645118343920252818764441012469240985705149638212498270398502233748654970299712012638
comment: $x^3-8x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.2021.1; $\zeta_K(-1)=-20$
-2023
1:
1.312702095357893816873781495159514440321470258069942685518366963848915344236088418335605624473969584
comment: $x^3-x^2+6x+5=0$; $S_3$; $h_K=1$; LMFDB 3.1.2023.1
2024
1:
2.083454046457609491163701612352906458316850612156924518990040668431638975841985458060176663253437423
comment: $x^3-x^2-10x-6=0$; $S_3$; $h_K=1$; LMFDB 3.3.2024.1; $\zeta_K(-1)=-74/3$
-2028
1:
1.823551527161939455707110090388465478066360608921734399275220061587281939588670623189783852339552682
comment: $x^3-26=0$; $S_3$; $h_K=3$; LMFDB 3.1.2028.1; $K=\mathbb{Q}(\sqrt[3]{26})$, a pure cubic field
-2036
1:
2.072192190088198940104814643639351268677567983754053461293907419721151764403794526988191241265192477
comment: $x^3-x^2+13x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.2036.1
-2039
1:
1.065368624879056638737662084032821057791854803601185960899792596734856086992799386478097794668497380
comment: $x^3-x^2+4x+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.2039.1
-2047
1:
1.245297182695743739519230380473608217916743543964326750160685192638173403743177266220854991182396535
comment: $x^3+7x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.2047.1
-2051
1:
1.531581523272677221406536228411846814575266025604055439562929722685407591032406724597041814210585081
comment: $x^3-x^2-7x+14=0$; $S_3$; $h_K=2$; LMFDB 3.1.2051.1
-2052
1:
2.184050194461930784622934809198682058646162363397532323739142814462367609367859284925896308571188592
comment: $x^3+9x-14=0$; $S_3$; $h_K=1$; LMFDB 3.1.2052.1
2057
1:
1.264079425168194742958867713055341810747496042733780729996100876690799536312052487384210301639743651
comment: $x^3-11x-11=0$; $S_3$; $h_K=1$; LMFDB 3.3.2057.1; $\zeta_K(-1)=-46/3$
-2063
1:
1.557598137343365787679776148907895082757255933866291311110561716983219441181099376133757557860485298
comment: $x^3-x^2-2x+27=0$; $S_3$; $h_K=1$; LMFDB 3.1.2063.1
-2068
1:
2.178966586992550066828050314541946690417177061182988514180107385883778729018940646669146286190841784
comment: $x^3-x^2-8x-10=0$; $S_3$; $h_K=4$; LMFDB 3.1.2068.1
-2071
1:
2.768802261298152144508891338053522379328660497305424449055729695576088046652584912262660563019652635
comment: $x^3+7x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.2071.1
-2075
1:
1.639341801563834101433940280956748112732643786068956814576124654035367116643785103511447422984873983
comment: $x^3-x^2-3x-8=0$; $S_3$; $h_K=3$; LMFDB 3.1.2075.3
-2075
2:
1.532305655170113356327468372291169341092570817453354474618825052627348277396513378526842057188884286
comment: $x^3-x^2+7x-8=0$; $S_3$; $h_K=3$; LMFDB 3.1.2075.2
-2075
3:
2.140857399143361476284515552467682322690309031667854244214060960853105072710794974283545382578535141
comment: $x^3-10x-15=0$; $S_3$; $h_K=3$; LMFDB 3.1.2075.1
2089
1:
2.470291112044367656668451144957966295064588350059942876859305817013159445902374115906166396217049950
comment: $x^3-13x-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.2089.1; $\zeta_K(-1)=-92/3$
-2091
1:
1.867177113049106322384538668224161283872555465932364507639659390063598520505441171224260675478069998
comment: $x^3-x^2-x-26=0$; $S_3$; $h_K=1$; LMFDB 3.1.2091.1
-2092
1:
1.736160804298241046217212640871736467976689585466122207061726382589055838971452654471094951843455322
comment: $x^3-x^2+11x-15=0$; $S_3$; $h_K=2$; LMFDB 3.1.2092.1
2101
1:
1.490791530718905756669660340265966021933266605069256061288679865312555020573337984908140163772680794
comment: $x^3-x^2-11x-8=0$; $S_3$; $h_K=1$; LMFDB 3.3.2101.1; $\zeta_K(-1)=-56/3$
-2104
1:
2.133180131861292311368394606314054785125312042622326510271109893808681756636302958934135630706345322
comment: $x^3-x^2+13x-1=0$; $S_3$; $h_K=5$; LMFDB 3.1.2104.1
-2116
1:
2.131454911535215075713635278584341963296678981565909806695047362811796397463610750662250294068321596
comment: $x^3-x^2+8x-6=0$; $S_3$; $h_K=2$; LMFDB 3.1.2116.1
-2132
1:
1.965110850387144027148714957432345802272757180470315799602127619126057905806893831771917878695330395
comment: $x^3-x^2-3x+19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2132.1
-2148
1:
2.401944979118778303873768347672268686083211029776090562223801930580809976527171229466814682903921003
comment: $x^3-x^2-7x-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.2148.1
-2155
1:
1.805027892263589868062556689334715058664017807350162183612229884228819052512127362770920933009095233
comment: $x^3-2x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2155.1
-2159
1:
1.127829406994738054889350533582341189467184551243149053850565936705891241453189347273907105828869627
comment: $x^3-x^2-4x+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2159.1
-2167
1:
1.273617028568515811992925451886805766742438039693786036002712487739910698634233245113328800878154905
comment: $x^3-x^2-12x+23=0$; $S_3$; $h_K=1$; LMFDB 3.1.2167.1
-2168
1:
1.927331509648318415766448286569572020352596683808131607496554795270011481505807585160123701304246231
comment: $x^3-x^2-3x-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.2168.1
2177
1:
1.287213248296908822594374123473314923939012100811597226999804634035024698331703060999156824025352767
comment: $x^3-x^2-8x+5=0$; $S_3$; $h_K=1$; LMFDB 3.3.2177.1; $\zeta_K(-1)=-17$
-2183
1:
1.551656928955782197409005104684960246426527071136240867588520392315201366961643381762527160398559433
comment: $x^3-x-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2183.1
-2184
1:
2.389673395874042052844785766131337997604468812393237909892998383038278126839138668554772986624983854
comment: $x^3-x^2+13x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2184.1
-2188
1:
1.679860516372295609294970331133271617015945095296090924258621809854426558421789235320284972240236072
comment: $x^3-x^2+3x+17=0$; $S_3$; $h_K=3$; LMFDB 3.1.2188.1
-2188
2:
1.656411218298748279732212249517484765496594526938087953738384781455711265705973579685492189774067123
comment: $x^3-x^2+7x-19=0$; $S_3$; $h_K=3$; LMFDB 3.1.2188.3
-2188
3:
1.668778631037669065550312603794577285867891634858681892522014888831240570633664554914817659026255655
comment: $x^3-8x-20=0$; $S_3$; $h_K=3$; LMFDB 3.1.2188.2
-2191
1:
1.260480961699262839781769933065540624576784437058777484954161025399851879258864224960579149443078299
comment: $x^3+x-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2191.1
-2199
1:
1.349301164494995687249614757316063979229488150324301131408462274541138225083439803913308430210917219
comment: $x^3+3x-27=0$; $S_3$; $h_K=1$; LMFDB 3.1.2199.1
-2200
1:
2.211742496817881643542324073799716650254737437341490792052292341575589938443602573357904820505833779
comment: $x^3-5x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2200.1
-2207
1:
1.116340034153518752394259238780550506120700184571788939037351698518055361430500655420799612592212026
comment: $x^3-x^2-6x+13=0$; $S_3$; $h_K=1$; LMFDB 3.1.2207.1
2213
1:
1.723827828992831926932882727588712470618906267591034324055000121926877517369375195262015397802865981
comment: $x^3-x^2-13x-12=0$; $S_3$; $h_K=1$; LMFDB 3.3.2213.1; $\zeta_K(-1)=-70/3$
-2219
1:
2.127187316468188340893421286368732717718270545627786487863487770305187621630665531765078251741028815
comment: $x^3+2x-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2219.1
-2220
1:
1.912737057789379104391862970041330608560913557338424825837784848075884220102347797944531289089895847
comment: $x^3-x^2-11x+21=0$; $S_3$; $h_K=1$; LMFDB 3.1.2220.1
-2227
1:
1.768446392866906438409103523956092236236468173438250602506976261746028670588705377411787303780749400
comment: $x^3-x^2+3x+8=0$; $S_3$; $h_K=1$; LMFDB 3.1.2227.1
-2228
1:
1.954602570179126949427452648125738859930552361313663364532613635260644732654706497618798850449599746
comment: $x^3+5x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.2228.1
2228
1:
1.633315153584946786401031699140898516474770682130398288016683380617626184668468400020562985376267864
comment: $x^3-x^2-13x+9=0$; $S_3$; $h_K=1$; LMFDB 3.3.2228.1; $\zeta_K(-1)=-67/3$
2233
1:
1.141912275870647922310607423863964294975929944745869261173520330961969821577938097220910901777885272
comment: $x^3-x^2-8x+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.2233.1; $\zeta_K(-1)=-47/3$
-2235
1:
2.012481285040432160085295741880652892408878918224453060180833489541217161004105202477731892870233875
comment: $x^3-x^2-5x+12=0$; $S_3$; $h_K=1$; LMFDB 3.1.2235.1
2241
1:
1.329131262386684958636562927258052608495546818904598484713865732881815220653312009152923810560274805
comment: $x^3-9x-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.2241.1; $\zeta_K(-1)=-55/3$
-2243
1:
1.553519625984336539335757736926319976968982332720882628615009612025367131571403247157450644339353588
comment: $x^3-x^2+7x+4=0$; $S_3$; $h_K=2$; LMFDB 3.1.2243.1
-2260
1:
2.248960605410127116448322002891288225747249491445861882141240139539707959651045982700232138213460052
comment: $x^3-x^2+4x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2260.1
-2264
1:
2.072211381722673734862806479121649600589066112792547734622376063759169133709105679342965205191364433
comment: $x^3-x^2-2x+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2264.1
-2283
1:
1.952618074164834944139693845942906166338450924846031995506287963129985012217691847720476483837006693
comment: $x^3-x^2-x+28=0$; $S_3$; $h_K=1$; LMFDB 3.1.2283.1
-2284
1:
1.781747052120877516077151851569248233860877865934211787062660179158724399424841924333897703996230420
comment: $x^3-x^2+11x+9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2284.1
-2291
1:
2.106805506453574482554634869872943758435834680006310575727097745727430170907031463088789620298879926
comment: $x^3+8x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.2291.1
2292
1:
1.822387178249196254518150281857183311499390221395294183528263441725889871032141565188641342806359066
comment: $x^3-x^2-13x+1=0$; $S_3$; $h_K=1$; LMFDB 3.3.2292.1; $\zeta_K(-1)=-26$
2296
1:
1.910838553988181006220525703600664599853913043995514730493743905056751277482350165360213808907476813
comment: $x^3-x^2-14x-14=0$; $S_3$; $h_K=1$; LMFDB 3.3.2296.1; $\zeta_K(-1)=-82/3$
2300
1:
2.138277380044354449318443947907577753685016774686922101015793293487362314742068854511436789046861860
comment: $x^3-x^2-8x+2=0$; $S_3$; $h_K=1$; LMFDB 3.3.2300.1; $\zeta_K(-1)=-92/3$
-2303
1:
1.581161636881398567730635949986394995848021208562531719918655620948285180094821404295891937583199590
comment: $x^3-x^2-2x-27=0$; $S_3$; $h_K=3$; LMFDB 3.1.2303.1
-2315
1:
1.593548578334775237605158594631228529103332036964590501404377569997303785894545849665416469112569627
comment: $x^3-x^2+5x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2315.1
-2316
1:
1.944001855752288636184520600452111132368922181330618430260635563133092055327758325046132076240285993
comment: $x^3-x^2+x+9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2316.1
-2319
1:
1.522031086197245534083861704825075341515561390113002263392495677457527785127875071183962375523924771
comment: $x^3-x^2-12x-15=0$; $S_3$; $h_K=2$; LMFDB 3.1.2319.1
-2327
1:
1.166511584233038224315835735875823936850685125968098409056260562720861677126732514588272150842916350
comment: $x^3-x^2+8x-7=0$; $S_3$; $h_K=2$; LMFDB 3.1.2327.1
-2344
1:
2.193961644484530980573174026759405809748915265361001805011361920653255160033472933466271034803225045
comment: $x^3+7x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.2344.1
-2348
1:
2.034519309400583896923195337319403612281606819298517458459791098898751205514894734923414894326764772
comment: $x^3-x^2+3x+27=0$; $S_3$; $h_K=1$; LMFDB 3.1.2348.1
2349
1:
1.666384291519981168041267201629424402638284026540836993942453135391660210049596802971114327428749838
comment: $x^3-12x-13=0$; $S_3$; $h_K=1$; LMFDB 3.3.2349.1; $\zeta_K(-1)=-74/3$
-2351
1:
2.492211896085725417280619530857226916238336341505893581165264756950227227799257382570165544391122713
comment: $x^3-x^2+6x+16=0$; $S_3$; $h_K=1$; LMFDB 3.1.2351.1
-2355
1:
1.997097290388735882244698980527868332342320808256660103952012993406715927062615854014275213693652098
comment: $x^3+12x-23=0$; $S_3$; $h_K=1$; LMFDB 3.1.2355.1
-2372
1:
1.943558321674382780918142998761290272159145376126885344382542562571448569732237712009716608461265989
comment: $x^3-x^2+8x+2=0$; $S_3$; $h_K=1$; LMFDB 3.1.2372.1
-2376
1:
2.186328516983763213205056791037138386170289291212330028424381786641579118368335313324634832590987999
comment: $x^3-9x-14=0$; $S_3$; $h_K=1$; LMFDB 3.1.2376.1
-2380
1:
1.758050033021532727148402231946765881994880130897380659582128043257092194493208698036437562416537519
comment: $x^3-x^2-x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2380.1
-2387
1:
1.603586965424399630933861192409733300188984056976511708637231918131657455029598109759708180154001455
comment: $x^3-x^2+6x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2387.1
-2388
1:
2.434883342881192788977948918683434795760065678343160459498583112828059171063490448201003429479727940
comment: $x^3-x^2+13x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.2388.1
-2403
1:
1.756367809588594987755360129032203881079820862597399810966198656808788549716837798390575354920205738
comment: $x^3-6x-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2403.1
-2408
1:
1.993403913040469129954508761493601950555911342685981720262299922403635968158755820234639905027078260
comment: $x^3-x^2+2x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2408.1
-2420
1:
1.999994791600307974453493567692457277379399144669446719331275593785850457599995365924545986285100976
comment: $x^3-x^2+4x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2420.1
-2423
1:
1.580164517875039273815499147891680843481838417126324576425525324009128174974637454796919897359181936
comment: $x^3-x^2+2x-29=0$; $S_3$; $h_K=1$; LMFDB 3.1.2423.1
-2424
1:
2.364103232006292172774926303536920765986048399562429206563786395714663423857209458559762440530617629
comment: $x^3-x^2+6x+6=0$; $S_3$; $h_K=1$; LMFDB 3.1.2424.1
2429
1:
1.713233994541968417081749283980935401504103198197441564632517570581337162329327235713931127555031747
comment: $x^3-x^2-14x-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.2429.1; $\zeta_K(-1)=-80/3$
-2440
1:
2.278608079868428831882649393692821969069498398101723853520829200144339982031311553225913151964577697
comment: $x^3+13x-6=0$; $S_3$; $h_K=1$; LMFDB 3.1.2440.1
-2443
1:
1.797054723168090699480553155132785514891572969595070112100565949573389264814653330910144435050986054
comment: $x^3+4x-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2443.1
-2444
1:
1.586521962147272518437258237830160720675770472787534202030033942077252573777721244772830064240252938
comment: $x^3-4x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2444.1
-2468
1:
1.960182528013365983362717070900299516459931344505993924434564710847360057336817294090723891358932976
comment: $x^3-x^2-7x+23=0$; $S_3$; $h_K=1$; LMFDB 3.1.2468.1
-2472
1:
2.433329576415723665414776225350562071134837352532693749522115061368991805613396902896524657006473469
comment: $x^3-x^2-8x+24=0$; $S_3$; $h_K=1$; LMFDB 3.1.2472.1
-2476
1:
1.664460991442270225921163608331079385965114223671972978287083279098026310122566289523380064859862354
comment: $x^3-x^2-9x-19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2476.1
-2479
1:
1.214560023867360349309547415709397699603179011870074701538079613041325728907314131937435812054103409
comment: $x^3-11x-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.2479.1
-2484
1:
2.304355568424319197233617451254539351345153581403992985045888958529664759493872000234380709136817934
comment: $x^3-6x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2484.1
-2488
1:
2.168839984719814453836047871208588517675152120375011904735408051202208590646841471685805756233866348
comment: $x^3-x^2+6x-10=0$; $S_3$; $h_K=4$; LMFDB 3.1.2488.1
-2491
1:
1.869007148210548562582815200140586380943553978219460638153368222723242693450170072536192932693488231
comment: $x^3-x^2-2x+20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2491.1
-2503
1:
1.291882591988280801243151700232885006416803547700333673673718108569091993336966365409046321128385581
comment: $x^3-x^2+2x+9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2503.1
-2504
1:
2.065164327279847049657068456372320388717082935197750261325430232047635962868350927703327363259192244
comment: $x^3-x^2+x+19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2504.1
2505
1:
1.451826508661682443956910988440719396178868142312654669776713612324437542593266200050128726358679584
comment: $x^3-x^2-10x-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.2505.1; $\zeta_K(-1)=-71/3$
-2508
1:
1.855126381036593243152943848475545582209741651014711061621452154775654585074138063599797105043003307
comment: $x^3-x^2-5x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2508.1
-2515
1:
1.826350966351503718010268085926826935516674070527990808498625997892325557073629130174964802897104591
comment: $x^3-8x-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.2515.1
-2516
1:
2.585999963868563517518497588622999948354109638415529293411778510184161704186796574733686430013037617
comment: $x^3-7x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.2516.1
-2540
1:
1.492149350068127357076268891110375968177520852171470046855468896542459965870485721966468273580810123
comment: $x^3-x^2-x-19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2540.1
-2548
1:
2.203722714988100790841459351782885516686626621560929365129722607873856883898484529088347924318425810
comment: $x^3-x^2+12x+8=0$; $S_3$; $h_K=3$; LMFDB 3.1.2548.1
-2555
1:
1.656939934241639194079799453980750668716893258156651218896785936131706688248342859894052916275377886
comment: $x^3-x^2+14x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.2555.1
2557
1:
1.546558951720887384116787290342902302145996099032696035022684911343810223803439382675443501523947331
comment: $x^3-x^2-9x-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.2557.1; $\zeta_K(-1)=-26$
-2563
1:
1.780220020098721956589021009424195318274324203486407770698469220389085331600649678266024658092674092
comment: $x^3-x^2+x-10=0$; $S_3$; $h_K=2$; LMFDB 3.1.2563.1
-2575
1:
2.859079945162386192532122726049822452593678189434376096713409468826412205934313256398460863683035965
comment: $x^3-5x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2575.1
-2579
1:
1.658385622148998696443356463056566852534169400899978958082031593473909768093800929456402572082024079
comment: $x^3-x^2-7x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2579.1
2589
1:
1.868276391310830233542358846031154200595537011399177256527996431820094817180053146357067046505737148
comment: $x^3-x^2-14x+12=0$; $S_3$; $h_K=1$; LMFDB 3.3.2589.1; $\zeta_K(-1)=-32$
-2591
1:
1.536909894533820288719238315133546933602914572240941415996802493352188690926653284782000155366460454
comment: $x^3-x^2-4x+31=0$; $S_3$; $h_K=1$; LMFDB 3.1.2591.1
-2595
1:
1.991727176107144308870162070605183137678881302180551805113114622511451365678605591575168992774190786
comment: $x^3-x^2-10x-20=0$; $S_3$; $h_K=5$; LMFDB 3.1.2595.1
2597
1:
1.743422126238132034821680658626953439250127643987481914105285362278038414617894290068166739560435013
comment: $x^3-x^2-9x+8=0$; $S_3$; $h_K=3$; LMFDB 3.3.2597.1; $\zeta_K(-1)=-30$
-2599
1:
1.228148549227840459055703556454030148473364249615186327871775987425925908479270957181432021864550586
comment: $x^3-x^2-4x-9=0$; $S_3$; $h_K=1$; LMFDB 3.1.2599.1
-2604
1:
1.828657572287106217013193604920303851340127791525773808777810154835002826388501981681073579486447635
comment: $x^3-x^2+9x-3=0$; $S_3$; $h_K=1$; LMFDB 3.1.2604.1
-2619
1:
1.690532702169152576779713975309167360662984953389814530235533572390596173081919617710472683237299223
comment: $x^3+6x-29=0$; $S_3$; $h_K=2$; LMFDB 3.1.2619.1
-2627
1:
1.574870677563784280391956487302277978129089494481699778494665597758078181427780568742221894213938545
comment: $x^3-x^2+9x-2=0$; $S_3$; $h_K=1$; LMFDB 3.1.2627.1
-2631
1:
3.053988416158989745894625262199983402993154559434949304789327344011447330021182471050060704604765431
comment: $x^3-x^2+14x-8=0$; $S_3$; $h_K=1$; LMFDB 3.1.2631.1
-2635
1:
1.793467043540162518671381516405824134373838925829901573642985217728364314766249644105212364021571929
comment: $x^3-x^2+9x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.2635.1
-2636
1:
1.578330710087839541111475714372222912528200205974130311989148481901080097234343062278679351595858119
comment: $x^3-4x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2636.1
2636
1:
2.083735279158575404579911250084267808739041218249323670313497283775875237772040585060823284618260841
comment: $x^3-14x-4=0$; $S_3$; $h_K=1$; LMFDB 3.3.2636.1; $\zeta_K(-1)=-110/3$
-2644
1:
2.200159544043797201858777356300117915373386457053684555918230766353889568730666647397452886295207479
comment: $x^3-x^2+5x-21=0$; $S_3$; $h_K=1$; LMFDB 3.1.2644.1
-2647
1:
1.289818421893944784697534227497266470022620816009947378886563494166095379928635632806809796708765569
comment: $x^3-x^2+8x+3=0$; $S_3$; $h_K=1$; LMFDB 3.1.2647.1
-2660
1:
2.066104553502108085530706356089816909402491237164151253580040753110859225949326968502304164703077936
comment: $x^3-x^2+10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2660.1
-2668
1:
1.679038485641621402878497625539537238418010360275467842280081698198154362328171272280143496378273172
comment: $x^3-2x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2668.1
2673
1:
1.261474404395502821401899938359385574681197721258631447902846603084580661723123184003480155686360486
comment: $x^3-9x-3=0$; $S_3$; $h_K=1$; LMFDB 3.3.2673.1; $\zeta_K(-1)=-68/3$
-2676
1:
2.365266292744710321322296982651468672831473444713739920040067784345986570499430065293297630651638076
comment: $x^3-x^2-11x-21=0$; $S_3$; $h_K=1$; LMFDB 3.1.2676.1
2677
1:
1.554800593428373845854868101872779658428207244949993893246017408983060694486285071625485061663831496
comment: $x^3-10x-7=0$; $S_3$; $h_K=1$; LMFDB 3.3.2677.1; $\zeta_K(-1)=-28$
-2680
1:
2.244231494560680796038618936545867819268377473715311763953268689955383368578303816413986688033230957
comment: $x^3-x^2+20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2680.1
-2687
1:
1.553262305733875676927001622947823621668912451563525464634419055087757186786326710840515176489039453
comment: $x^3+5x-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2687.1
-2692
1:
2.198251189857412628733790603802794550920963555902809565819700845627041467750803288929653861286239704
comment: $x^3-2x-20=0$; $S_3$; $h_K=5$; LMFDB 3.1.2692.1
-2695
1:
1.331092860033404931106747200173361030537524884323180016459343185768616656873563029770555380312950642
comment: $x^3+7x-7=0$; $S_3$; $h_K=3$; LMFDB 3.1.2695.1
-2696
1:
2.107248602407929707007231543399910969349376591069533091059977570719843039051913262906408525474018606
comment: $x^3-x-10=0$; $S_3$; $h_K=4$; LMFDB 3.1.2696.1
-2699
1:
1.687212287518181694838550039933947924588831733682281355596220797230593436052929687639888186053716971
comment: $x^3-x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2699.1
-2700
1:
1.709575801700967632463182006284355195203956464876012661382860484148237588182341314831727848059914004
comment: $x^3-20=0$; $S_3$; $h_K=3$; LMFDB 3.1.2700.1; $K=\mathbb{Q}(\sqrt[3]{20})$, a pure cubic field
2700
1:
2.156275902728905725671221160924890904124657694859934136417868203328015793083847117590083504431143335
comment: $x^3-15x-20=0$; $S_3$; $h_K=1$; LMFDB 3.3.2700.1; $\zeta_K(-1)=-118/3$
-2708
1:
1.926060716985699479448274026232370997355537959185881235457756689295785448068939779761002072104477045
comment: $x^3+2x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2708.1
2708
1:
1.655527391420328574671474481756012332126646434204902075200128603666372030065221659698771299402454811
comment: $x^3-x^2-11x-7=0$; $S_3$; $h_K=1$; LMFDB 3.3.2708.1; $\zeta_K(-1)=-91/3$
2713
1:
1.542098815249086645856579566977346131814634822251244183268088270012286278250133357153947399410303840
comment: $x^3-13x-15=0$; $S_3$; $h_K=1$; LMFDB 3.3.2713.1; $\zeta_K(-1)=-85/3$
-2723
1:
1.585909710843936180282768097067129787714391421130408374391598258474337478591804066393853855363456299
comment: $x^3+8x-5=0$; $S_3$; $h_K=1$; LMFDB 3.1.2723.1
-2727
1:
2.872399806408806193755428339165614950412349749084682138741606823556152330296003321044409802864776372
comment: $x^3+3x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2727.1
-2728
1:
2.184600755137248823267146734041355744385379997940517097320035078788734477183346666968445132007698185
comment: $x^3+10x-16=0$; $S_3$; $h_K=1$; LMFDB 3.1.2728.1
-2732
1:
1.466984157765644959004271791545493476037103400538485344006398056743208901896198607289653041020600166
comment: $x^3+2x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2732.1
-2740
1:
2.248680248109847387980658598065811511221967218000656513094603524429749837491378231590198386777642212
comment: $x^3-x^2-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2740.1
-2747
1:
2.141809776138402019089895564988856774393770283099423056675101945126470042345680167899174680317112593
comment: $x^3-x^2+x+30=0$; $S_3$; $h_K=1$; LMFDB 3.1.2747.1
-2759
1:
1.061803864998274243207506844351201432508889149766412204708625033360544803138050654982130875423713112
comment: $x^3-x^2+4x-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2759.1
-2764
1:
1.766843743566429284303942805633011976967521491683216604445045323996473321916390933635890899280346104
comment: $x^3+4x-20=0$; $S_3$; $h_K=2$; LMFDB 3.1.2764.1
-2767
1:
1.287415089256557573606561668150802189189972963071007181759256064430051866287498528889463067277515500
comment: $x^3-5x-11=0$; $S_3$; $h_K=2$; LMFDB 3.1.2767.1
2777
1:
1.261353002267712390345529823417762811629396464213324400661637110947670423894329646641539525175789122
comment: $x^3-x^2-14x+23=0$; $S_3$; $h_K=2$; LMFDB 3.3.2777.1; $\zeta_K(-1)=-24$
-2787
1:
1.961662188840638297667958932188137655287681852010526184035154612014512720954653309357122349265715448
comment: $x^3-6x-31=0$; $S_3$; $h_K=2$; LMFDB 3.1.2787.1
-2791
1:
1.206632552751889830269516976484145516305044909200247017920133882046057408918604770257737510794990312
comment: $x^3-x^2-2x+11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2791.1
-2795
1:
1.631937015510531833252334047712080772392391999563987916678466580104654533660145997498412397873786650
comment: $x^3-x^2+10x-20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2795.1
-2796
1:
1.767013798983032968602324557310820303597113097154669319676396660093535562685176134425767806742379471
comment: $x^3-x^2+5x-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2796.1
-2803
1:
1.743008379412602685997458725232832477843876553842331818734043315633818347977570839658703793412165672
comment: $x^3-x^2+7x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2803.1
2804
1:
1.743903014027505097449553497224409751521287752100925885373387358849314967156122325835065093436441294
comment: $x^3-x^2-9x-1=0$; $S_3$; $h_K=1$; LMFDB 3.3.2804.1; $\zeta_K(-1)=-101/3$
-2808
1:
2.198721691989449860638624020797470165973438045967874303579844530517665646959003539138940457216865790
comment: $x^3+3x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2808.1
2808
1:
2.136456223334183034259796157312243881123861772642316428314393181057119749346739067370947681222104875
comment: $x^3-9x-2=0$; $S_3$; $h_K=1$; LMFDB 3.3.2808.1; $\zeta_K(-1)=-124/3$
-2819
1:
2.085341278234652605054276962802357302496491747280529057074710050880158690826959836852198857614952976
comment: $x^3-x^2+5x-32=0$; $S_3$; $h_K=5$; LMFDB 3.1.2819.1
-2820
1:
2.483083041029268438658398589615628706174700502027928550867419187265840177216129240372035745710560543
comment: $x^3-x^2+9x+15=0$; $S_3$; $h_K=1$; LMFDB 3.1.2820.1
-2824
1:
2.189084279377103737135931375261578253155203689239683389679318458398890330639856788702474561938348197
comment: $x^3-x^2-6x+14=0$; $S_3$; $h_K=2$; LMFDB 3.1.2824.1
-2835
1:
1.835178839321981616459767224669287596079578624159915817770992695788453992064972745973369951584970458
comment: $x^3-12x-19=0$; $S_3$; $h_K=3$; LMFDB 3.1.2835.1
2836
1:
1.459846119968348023147754050262302742338999865635568399418714850365967551945371651348515966028001929
comment: $x^3-x^2-9x+7=0$; $S_3$; $h_K=1$; LMFDB 3.3.2836.1; $\zeta_K(-1)=-86/3$
-2843
1:
1.557081468663550528064100900216413120003067786318475728722575225853846271579078124806658035571755222
comment: $x^3-x^2+x+10=0$; $S_3$; $h_K=2$; LMFDB 3.1.2843.1
-2852
1:
1.925084931449446132197559392001903950948495655952252518717234094552069503218904354325533110935845082
comment: $x^3+14x-4=0$; $S_3$; $h_K=1$; LMFDB 3.1.2852.1
-2855
1:
1.127330476130991282996051349230241449530049086834138054374884680551701636851603749690050253872663052
comment: $x^3-x^2-10x-13=0$; $S_3$; $h_K=1$; LMFDB 3.1.2855.1
-2856
1:
2.387988137589348448392863241491721330981607776625068609292339743214621764520299556428504534895533505
comment: $x^3-x^2+9x-21=0$; $S_3$; $h_K=7$; LMFDB 3.1.2856.1
2857
1:
1.091229164401684004453383625956307135127460657439991404367368979422238414179032819390439370210203394
comment: $x^3-x^2-10x+11=0$; $S_3$; $h_K=1$; LMFDB 3.3.2857.1; $\zeta_K(-1)=-65/3$
-2859
1:
1.867599730120829024681666313491900286836423448712792112489883090423303219503141701343648100537904968
comment: $x^3-x^2+9x-6=0$; $S_3$; $h_K=2$; LMFDB 3.1.2859.1
-2860
1:
1.745130413113319384939746964214923362837140078438030511499780617319979699538885261684864830440482071
comment: $x^3-x^2-x+21=0$; $S_3$; $h_K=1$; LMFDB 3.1.2860.1
-2867
1:
1.584909044214826236788354683777941139858910719007061543399389549042228824599685242259920095722181937
comment: $x^3-x^2+2x+20=0$; $S_3$; $h_K=1$; LMFDB 3.1.2867.1
-2872
1:
2.206496593690782196432856168546531565257278411525236425563277909959170023307056003870851841678518777
comment: $x^3+13x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2872.1
-2879
1:
1.057467939762666601836518593281129196576987565071444744282138948770004877023284228182623537910499817
comment: $x^3-x^2+6x+7=0$; $S_3$; $h_K=1$; LMFDB 3.1.2879.1
-2888
1:
1.952810636127353718447539511474445852484786675999897692266238264090391616829015214525762393454638671
comment: $x^3-x^2+13x+7=0$; $S_3$; $h_K=3$; LMFDB 3.1.2888.1
-2891
1:
2.114407340704040572921137805035694533585150569416310600728711479240836397137724628728780106174442828
comment: $x^3-x^2-9x+36=0$; $S_3$; $h_K=3$; LMFDB 3.1.2891.2
-2891
2:
1.686005554633282881464199225876442209275702634730575496665170881793026685971992924907368491797842475
comment: $x^3-x^2-2x-20=0$; $S_3$; $h_K=3$; LMFDB 3.1.2891.3
-2891
3:
1.504083529109306638749339139962466638580160396428681831939518173616565049252001067900339968575280108
comment: $x^3-x^2+5x+8=0$; $S_3$; $h_K=3$; LMFDB 3.1.2891.1
-2892
1:
1.846857041919935417214503774429992383979515015444111947470532577975744675877147173189662239473553922
comment: $x^3-x^2-13x-17=0$; $S_3$; $h_K=1$; LMFDB 3.1.2892.1
-2895
1:
1.452468501089696379422744371814480083834631891659852564797588253041619845719273030227875801183211390
comment: $x^3+3x-31=0$; $S_3$; $h_K=1$; LMFDB 3.1.2895.1
-2911
1:
1.204338666036352332253881566404429927558504872179120481434361379610585593200703970799197893645097149
comment: $x^3-x^2+8x-9=0$; $S_3$; $h_K=2$; LMFDB 3.1.2911.1
-2915
1:
1.603836274435492676741914464412477474299049163779331330458096426527093292882523304285771430056228439
comment: $x^3-x^2-x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2915.1
2917
1:
1.562192533608420796493687202582771162860536218788928488919748695353242485310998951531785700307708740
comment: $x^3-x^2-13x+20=0$; $S_3$; $h_K=1$; LMFDB 3.3.2917.1; $\zeta_K(-1)=-32$
-2920
1:
2.287032045372371735877676892428418132549350907941957076479363606382004756746625589127507163133842960
comment: $x^3-x^2-6x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2920.1
2920
1:
1.982227614136146445636959245739448590397808155704431465120790333167861692313702710455239496163644641
comment: $x^3-x^2-15x-5=0$; $S_3$; $h_K=1$; LMFDB 3.3.2920.1; $\zeta_K(-1)=-122/3$
-2923
1:
1.761809080862359160266901257760653878140589592084270962531855675352201284290401611270118394657031450
comment: $x^3-x^2+14x-12=0$; $S_3$; $h_K=1$; LMFDB 3.1.2923.1
2941
1:
1.639553540810584593896143437799090698101150999398211746777912919166587265571340539752627902129722926
comment: $x^3-x^2-14x+4=0$; $S_3$; $h_K=1$; LMFDB 3.3.2941.1; $\zeta_K(-1)=-34$
-2951
1:
1.219071646473441162647672025873250083816520208478290987174853285572513899926645789565446223369332531
comment: $x^3-x^2+6x-11=0$; $S_3$; $h_K=1$; LMFDB 3.1.2951.1
-2955
1:
2.017235618996839694991631538581848246916275337619471293792931086116448633960126261738853864536004285
comment: $x^3-x^2-5x-30=0$; $S_3$; $h_K=1$; LMFDB 3.1.2955.1
-2956
1:
1.785732809474365003842130623485043557735249808363931057861027474775522585947853865316903460154625253
comment: $x^3+4x-10=0$; $S_3$; $h_K=1$; LMFDB 3.1.2956.1
-2964
1:
2.336931204250109404752524946797864457889414399627200045035081811197654812782971846383127444319739182
comment: $x^3-x^2+5x+19=0$; $S_3$; $h_K=1$; LMFDB 3.1.2964.1
2981
1:
1.701174091462098640332364019222953728152730791759307163602913656769944728685474489447499825620116280
comment: $x^3-x^2-11x+14=0$; $S_3$; $h_K=1$; LMFDB 3.3.2981.1; $\zeta_K(-1)=-36$
-2991
1:
3.091236908724401656245533919368293691190766279739701069821091893616985230218027556750883172791258029
comment: $x^3-x^2-6x+24=0$; $S_3$; $h_K=1$; LMFDB 3.1.2991.1
2993
1:
1.236901124833998941342242368968772975502034122457920165066220323960878451042563813339262007734016014
comment: $x^3-x^2-12x+17=0$; $S_3$; $h_K=1$; LMFDB 3.3.2993.1; $\zeta_K(-1)=-79/3$
Definition
Let $K$ be a cubic field [11] of discriminant $D$ and $\zeta_K(s)=\sum_{\mathfrak{a}}N(\mathfrak{a})^{-s}$ its Dedekind zeta function [10], summed over the nonzero ideals of $\mathcal{O}_K$. Listed is $\zeta_K(2)$.
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)
$\zeta_K(s)=\zeta(s)\,L(s,\rho)$ and so $\zeta_K(2)=\zeta(2)L(2,\rho)$ 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 $1\oplus\rho$. Here $\zeta(2)=\pi^2/6$ is in the table of values of the Riemann zeta function.
(2)
For $D<0$, $L(2,\rho)=\frac12\sum_{C}\varepsilon(C)\,Z_{Q_C}(2)$, where $C$ runs over the $h(D)$ classes of primitive positive definite binary quadratic forms of discriminant $D$, $Q_C$ is a form in the class, $Z_Q(s)=\sum_{(m,n)\neq(0,0)}Q(m,n)^{-s}$ is the Epstein zeta function of $Q$, and $\varepsilon(C)=1$ if the primes represented by $Q_C$ split completely in $K$ and $\varepsilon(C)=-\frac12$ if they stay prime. This is Hecke's description of $L(s,\rho)$ as the $L$-series of a modular form of weight one [2]: $\rho$ is induced from a cubic character $\psi$ of the ring class group of the order of discriminant $D$ in $\mathbb{Q}(\sqrt{D})$, $L(s,\rho)=\sum_C\psi(C)\zeta(s,C)$ with $\zeta(s,C)=\frac12 Z_{Q_C}(s)$, and $\psi(C)+\psi(C^{-1})=2\varepsilon(C)$. Each $Z_Q(2)$ is given by the Chowla-Selberg expansion [1] $Z_Q(2)=\frac{4}{|D|}\Bigl(2\zeta(4)y^2+\frac{\pi\zeta(3)}{y} +8\pi^2\sqrt{y}\sum_{n\geq1}n^{3/2}\sigma_{-3}(n)K_{3/2}(2\pi ny)\cos\frac{\pi nb}{a}\Bigr)$ for $Q=am^2+bmn+cn^2$ and $y=\sqrt{|D|}/(2a)$, where $K_{3/2}(z)=\sqrt{\pi/(2z)}\,e^{-z}(1+1/z)$.
(3)
$\zeta_K(2)=-\frac{8\pi^6}{D^{3/2}}\,\zeta_K(-1)$ for $D>0$ and $\zeta_K(2)=\frac{16\pi^5}{|D|^{3/2}}\,\zeta_K'(-1)$ for $D<0$, from $\Lambda_K(s)=|D|^{s/2}\Gamma_{\mathbb{R}}(s)^{r_1}\Gamma_{\mathbb{C}}(s)^{r_2}\zeta_K(s)=\Lambda_K(1-s)$ with $\Gamma_{\mathbb{R}}(s)=\pi^{-s/2}\Gamma(s/2)$, $\Gamma_{\mathbb{C}}(s)=2(2\pi)^{-s}\Gamma(s)$ and signature $(r_1,r_2)=(3,0)$ for $D>0$, $(1,1)$ for $D<0$. For $D>0$ the value $\zeta_K(-1)$ is rational and is held in the table of values of Dedekind zeta functions of totally real cubic fields at negative odd integers; for $D<0$ it is $0$.
(4)
$\zeta_K(2)=\zeta(2)L(2,\chi)L(2,\bar\chi)=\zeta(2)|L(2,\chi)|^2$ for a cyclic cubic field, where $\chi$ is either cubic Dirichlet character of conductor $\sqrt{D}$. For $D=49$ and $\chi=\chi_7(2,\cdot)$ in Conrey's notation, $L(2,\chi)=0.7992\ldots-0.1018\ldots i$ and $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2=1.0677653128\ldots$.
(5)
$\mathrm{Vol}(\text{Weeks manifold})=\frac{3\cdot 23^{3/2}}{4\pi^4}\zeta_K(2) =0.9427073627769277\ldots$ for the field $K$ of discriminant $-23$ [7].
Comments
(6)
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 and the table of residues of Dedekind zeta functions of cubic fields, which hold 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 $D$ here carries a single field, with $k=1$. The LMFDB's own index for fields sharing a discriminant is not this order, and the label in each entry's comment was read from that field's LMFDB page.
(7)
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. For a totally real field it also gives the rational number $\zeta_K(-1)$ from which the value follows by the functional equation (3); those rationals, with $\zeta_K(-3)$ and $\zeta_K(-5)$, are held in the table of values of Dedekind zeta functions of totally real cubic fields at negative odd integers.
(8)
The sign of $D$ is the signature: $D<0$ for a complex cubic field, with one real and one pair of complex embeddings, and $D>0$ for a totally real one. For $D>0$ the value is the rational multiple $-8\zeta_K(-1)/D^{3/2}$ of $\pi^6$, by the functional equation (3) and the Siegel-Klingen theorem, so that $\zeta_K(2)=8\pi^6/(21\cdot 7^3)$ for $D=49$. For $D<0$ the function $\zeta_K$ vanishes at $s=-1$, and the functional equation gives $\zeta_K(2)$ as a multiple of the derivative $\zeta_K'(-1)$ instead. By Zagier's theorem [5], $|D|^{1/2}\zeta_K(2)/\pi^4$ is then a rational linear combination of values of the Bloch-Wigner dilogarithm at elements of $K$, with no closed form known for the coefficients in general.
(9)
For $D<0$ the value is a hyperbolic volume. By Borel's formula [6], the volume of the quotient of hyperbolic 3-space by the group of units of norm one of a maximal order in a quaternion algebra over $K$, ramified at the real place of $K$ and at a finite set $S$ of primes, is $|D|^{3/2}\zeta_K(2)\prod_{\mathfrak{p}\in S}(N\mathfrak{p}-1)/(16\pi^4)$. The Weeks manifold [12], the closed hyperbolic 3-manifold of least volume, arises this way from the field of discriminant $-23$ with $S$ the prime of norm $5$ [7], and its volume $0.9427073627\ldots$ (OEIS A126774 [17]) is $3\cdot 23^{3/2}\zeta_K(2)/(4\pi^4)$, formula (5). Volumes of hyperbolic knot complements are held in the table of hyperbolic volumes of prime knots.
(10)
$D$ is a perfect square exactly for the cyclic cubic fields, those with Galois group $C_3$, all of which are totally real; the seven here have conductors $7$, $9$, $13$, $19$, $31$, $37$ and $43$. 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 $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$, formula (4); the comment on each of the seven names such a $\chi$ by its Conrey label, and $L(2,\chi)$ 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 $\zeta_K(2)=\zeta(2)L(2,\rho)$ with $\rho$ the two-dimensional representation of $S_3$, formula (1).
(11)
For a complex cubic field, $L(2,\rho)$ is a combination of Epstein zeta functions of the positive definite binary quadratic forms of discriminant $D$, formula (2), because the primes represented by the forms of one class all decompose in $K$ in the same way. 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 $D=-108$.
(12)
Every value exceeds $1$, since $\zeta_K(2)$ is an Euler product of factors greater than $1$, and the values decrease towards $1$ as the field has fewer small prime ideals. The largest here is $\zeta_K(2)=1.3529\ldots$ for $D=-2700$, where $2$, $3$ and $5$ all ramify, and the smallest is $1.0246\ldots$ for $D=-2707$; the first entry, $D=-23$, has $\zeta_K(2)=1.1100010060\ldots$.
(13)
For a quadratic field of discriminant $D$ the analogous value is $\zeta_K(2)=\zeta(2)L(2,\chi_D)$, a single Dirichlet $L$-value, held in the table of Dirichlet $L$-values for $|D|\leq 30$; for a cubic field the corresponding $L$-function has degree two and only splits into Dirichlet $L$-functions when the field is cyclic.
Programs
(P1)
PARI/GP
default(realprecision, 60);
lfun(lfuncreate(x^3 - x^2 + 1), 2)   \\ D = -23: 1.11000100601128264785301716539776257399811264047693467393859
-8*Pi^6*lfun(lfuncreate(x^3 - x^2 - 2*x + 1), -1)/49^(3/2)   \\ D = 49, from zeta_K(-1) = -1/21
(P2)
Sage
K.<a> = NumberField(x^3 - x^2 + 1)      # D = -23
K.zeta_function(prec=200)(2)            # 1.1100010060112826478530171653977625739981126404769346739386
References
[1]
S. Chowla and A. Selberg, "On Epstein's zeta-function", Journal fur die reine und angewandte Mathematik 227 (1967), 86-110.
[2]
J.-P. Serre, "Modular forms of weight one and Galois representations", in Algebraic Number Fields (Durham, 1975), Academic Press, London, 1977, 193-268.
[3]
J. Sturm, "On the congruence of modular forms", in Number Theory (New York, 1984-1985), Lecture Notes in Mathematics 1240, Springer, 1987, 275-280. (doi)
[4]
D. Zagier, "Elliptic modular forms and their applications", in The 1-2-3 of Modular Forms, Universitext, Springer, 2008, 1-103. (doi)
[5]
D. Zagier, "Hyperbolic manifolds and special values of Dedekind zeta-functions", Inventiones Mathematicae 83 (1986), 285-301. (doi)
[6]
A. Borel, "Commensurability classes and volumes of hyperbolic 3-manifolds", Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (4) 8 (1981), 1-33.
[7]
T. Chinburg, E. Friedman, K. N. Jones and A. W. Reid, "The arithmetic hyperbolic 3-manifold of smallest volume", Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (4) 30 (2001), 1-40.
[8]
Stephane R. Louboutin, "Numerical Evaluation at Negative Integers of the Dedekind Zeta Functions of Totally Real Cubic Number Fields", in Algorithmic Number Theory, ANTS-VI, Lecture Notes in Computer Science 3076, Springer, 2004, 318-326. (doi)
[9]
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 cubic fields —   the same 515 fields under the same $D$ and $k$, at the pole $s=1$
Regulators of cubic fields —   the same 515 fields under the same $D$ and $k$; its entry comments carry the fundamental units
Values of Dedekind zeta functions of totally real cubic fields at negative odd integers —   the exact $\zeta_K(-1)$ from which the values for $D>0$ follow by the functional equation
Values of Dirichlet $L$-functions at positive integers —   $\zeta_K(2)=\zeta(2)|L(2,\chi)|^2$ for the seven cyclic fields, $\chi$ a cubic character of conductor $\sqrt{D}$
Values of the Riemann zeta function at rational numbers —   the factor $\zeta(2)$ of $\zeta_K(2)=\zeta(2)L(2,\rho)$
Hyperbolic volumes of the prime knots with at most ten crossings —   hyperbolic volumes; for $D<0$ the value here is the volume of an arithmetic hyperbolic 3-manifold up to a rational and a power of $\pi$, by Borel's formula
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 at 461 bits, by one of two routes.

more

For $D<0$ it is $\zeta(2)L(2,\rho)$ with $L(2,\rho)$ the combination of Epstein zeta functions of formula (2); the identity behind that formula is made a finite check on each field by Sturm's theorem [3], since $L(s,\rho)$ is the $L$-series of a modular form of weight one, level $|D|$ and character $(D/\cdot)$ [2], the theta series $\sum q^{Q(m,n)}$ of each form of discriminant $D$ is a modular form of the same weight, level and character [4], and two such forms agree once their Fourier coefficients agree up to $|D|\prod_{p\mid D}(1+1/p)/12$. The generator computes that many coefficients and five more on both sides in exact arithmetic, from the representation numbers of the forms and from the Dirichlet coefficients of $\zeta_K(s)/\zeta(s)$ (PARI's dirzetak and Moebius inversion), and refuses the field if any differ; each $\varepsilon(C)$ is read off the decomposition in $K$ of two primes represented by $Q_C$, which must agree. Each $Z_Q(2)$ is the Chowla-Selberg expansion with $\pi$, $\zeta(3)$, the exponentials and cosines arb's, the Bessel sum cut where an explicit bound on its tail falls below $2^{-481}$ and that bound added to the radius; the expansion was checked to 137 digits against $4\zeta(2)G$ for $m^2+n^2$, $G$ Catalan's constant, and against $6\zeta(2)L(2,\chi_{-3})$ for $m^2+mn+n^2$, both from the Hurwitz zeta function in balls, and to six digits against a brute-force sum for two forms of discriminant $-23$ and $-56$. For $D>0$ the value is $-8\pi^6\zeta_K(-1)/D^{3/2}$ with $\zeta_K(-1)=-S/63$ exact, $S$ a positive integer from Siegel's formula [8] as the table of $\zeta_K(1-2m)$ computes it, and the rational compared with PARI's lfun at $s=-1$ recognised with denominator at most $10^{20}$. Every value of either kind is compared with PARI's lfun at $s=2$ at 110 digits, which uses the Dirichlet coefficients and the functional equation and shares no code with either route, and the generator refuses a value unless the two agree to 100 digits; all 515 do. The seven cyclic values are also compared with $\zeta(2)|L(2,\chi)|^2$ from the Hurwitz zeta function in balls. Each value is written to 100 significant digits, fewer than any ball supports (the worst, $D=-2991$ with $h(D)=48$, supports 136). The class number in each comment is PARI's bnfinit certified by bnfcertify. The enumeration rests on Hunter's theorem [9]: 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 [15] and A006832 [16] up to 3000 counted with multiplicity. Outside the generator, when this was written, the 96 rationals $\zeta_K(-1)$ were compared with the values stored in the table of $\zeta_K(1-2m)$; the four cyclic values of conductor at most $29$ with the $L(2,\chi)$ stored in the table of Dirichlet $L$-values; the value for $D=-23$ with the 52 digits of the Weeks volume in OEIS A126774 [17] through formula (5); and every value for $D<0$ with $16\pi^5\zeta_K'(-1)/|D|^{3/2}$ from PARI's derivative. The controls that must fail failed.



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