Residues of Dedekind zeta functions of quartic fields
edit · history · discussion · files · long url · special values L-function number theory
Numbers
$D$
$k$ 
$\kappa_K$
117
1:
0.3306306632822315867653207624292721828186045380730952281466610078714076489621729078121537336658331119
comment: $a^4 - a^3 - a^2 + a + 1=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.117.1
125
1:
0.3398372782405235354642787811589774853289772333273851484293797087888077271122332374782398773924541171
comment: $a^4 - a^3 + a^2 - a + 1=0$; signature $(0,2)$; 4T1; $h_K=1$; $w_K=10$; LMFDB 4.0.125.1
144
1:
0.3610514848760710247860130464279257266372955120064121660311702529855916408460590754896515863198678622
comment: $a^4 - a^2 + 1=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=12$; LMFDB 4.0.144.1
189
1:
0.4128232929851136832112468161938883419709688364667079731324305409013381367050987758346243828097040343
comment: $a^4 - a^3 + 2a + 1=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.189.1
225
1:
0.4221662530190670841593604158500245214684290211370094872606543895414785183244629556295971287081353372
comment: $a^4 - a^3 + 2a^2 + a + 1=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=6$; LMFDB 4.0.225.1
229
1:
0.4400768328324430737939890215268425343992565394856879934433227078766814772009083334751075126651288717
comment: $a^4 - a + 1=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.229.1
256
1:
0.5436755395907497900786176545098056792260570594331333587411988941391569933958430858256573015485641786
comment: $a^4 + 1=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=8$; LMFDB 4.0.256.1
257
1:
0.5444034309352053728926317442534040812579257011162058832245538153615043626335976202318818225548938178
comment: $a^4 + a^2 - a + 1=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.257.1
272
1:
0.4385659743484056858967140972502710671400913993792316853674444337026566192543369141736729192394833209
comment: $a^4 + a^2 - 2a + 1=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.272.1
-275
1:
0.2797607782990112146851284470896004322175362862536486875657925453548789953012285188613449884678028622
comment: $a^4 - a^3 + 2a - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.275.1
-283
1:
0.2825123282124448090397547543642282463752494452183388957323700050535515997960171282480634058034011194
comment: $a^4 - a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.283.1
320
1:
0.5855348052441591363516074143551017644847431029630881431390729796880726070610869894811519752917630251
comment: $a^4 - 2a^3 + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.320.1
-331
1:
0.2985270819557502040006698417772635812502826438036997124665556284972682956774624990677953648851496246
comment: $a^4 - a^3 + a^2 + a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.331.1
333
1:
0.5267101206437442773519790380242876117594417041075143589610674114426262521117344139701763336587088583
comment: $a^4 - a^3 - 2a^2 + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.333.1
392
1:
0.6310631165088978264148991266534670663199325901551745593805960743483539048052208300345271928897521623
comment: $a^4 - a^3 + a + 1=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.392.1
400
1:
0.4749370346464504696792804678312775866519826487791356731682361882341633331150208250832967697966522543
comment: $a^4 + 3a^2 + 1=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=4$; LMFDB 4.0.400.1
-400
1:
0.3208810857572240681600261160917460335721408850381862895185885679984212142869326553953959332467424088
comment: $a^4 - a^2 - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.400.1
432
1:
0.5264159764695239866729988491693335148820236390206959769709296823141933587891962323573723882888890400
comment: $a^4 - 3a^2 + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.432.1
441
1:
0.4909107506300430893133562486165777619681817364114638011676886848861594051433146117846926971595244852
comment: $a^4 - a^3 - a^2 - 2a + 4=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=6$; LMFDB 4.0.441.1
-448
1:
0.3312203248739979010835798889203807286342244713779530420624343820415482298041564424523079786547579622
comment: $a^4 - 2a^3 + a^2 - 2a + 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.448.1
-475
1:
0.3326498208895226646181031901173491683600096615749757639999966352675238871779697764592489901609821696
comment: $a^4 - 2a^3 + 2a^2 - a - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.475.1
-491
1:
0.3592984265979495598137345025840434428933060361290457196569880163643569407455085302541547249784689518
comment: $a^4 - a^3 - a^2 + 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.491.1
-507
1:
0.3624226244392896913941073669513791527523025872922731762886067191395512026476115080676342441643903499
comment: $a^4 - a^3 - a^2 - a + 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.507.1
512
1:
0.6667305541609389003408742153160033627987350546374188639757451788202788175394600950603028485215985617
comment: $a^4 - 2a^2 + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.512.1
513
1:
0.5708310378727093889486016982175945791011477310391425341153975205910413580561119043414206339874735564
comment: $a^4 - a^3 - 3a^2 + 2a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.513.1
549
1:
0.5937513009211044975215853307926733118731906326950267060195143607438075417237146367424815242638411014
comment: $a^4 - 2a^3 - 2a^2 + 3a + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.549.1
-563
1:
0.3729865115027340078277940497553827296391366948514852538047441441950479685702136102358468202785666224
comment: $a^4 - a^3 + a^2 - a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.563.1
576
1:
0.6284831581971562659451690988905418286174887244703223375819458814709814669653738690913329245454766700
comment: $a^4 - 2a^2 + 4=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=6$; LMFDB 4.0.576.1
576
2:
0.4832671463028887022921045817864939370898284972738963188810656836792506607963049651783620458209459365
comment: $a^4 + 2a^2 + 4=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=6$; LMFDB 4.0.576.2
592
1:
0.7446046535088097843933825396288773457605923222440093445675014759013590744619036777919058553971873592
comment: $a^4 + 2a^2 - 2a + 1=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.592.1
605
1:
0.6156857091798114321267473200122573142067796120218240364742373059206940077150047518936337028424545643
comment: $a^4 - a^3 + a^2 + a + 1=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.605.1
-643
1:
0.3569012987336687252593300419430212343842498161177473937618750982151961979610035509997742586854198809
comment: $a^4 - a^3 - 2a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.643.1
656
1:
0.9348839723915062592788009638074144238892925377841319068480165489378158763558888768824820600105398746
comment: $a^4 - 2a^3 - a^2 + 2a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.656.1
657
1:
0.5220110888857211220062985520325031683920224977989253045628990875996842909519110082567977053596559733
comment: $a^4 - a^3 + 5a^2 - 2a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.657.1
-688
1:
0.4784862756320594519714058779828526084416820263191594096442292391438607656638115627396719582876973944
comment: $a^4 - 2a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.688.1
697
1:
0.7725299773828884114755620016957466129892334363148645253145865787761952917269959170223109709914163131
comment: $a^4 - a^3 + 2a^2 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.697.1
725
1:
0.2451383019785525446304509608442345605397221715582444100284954899462595858084816672034000453901613432
comment: $a^4 - a^3 - 3a^2 + a + 1=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.725.1
-731
1:
0.4028887548260633735841498852417982515778120332397022078719806391618104677327939617883148876533921597
comment: $a^4 - a^3 + 2a^2 - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.731.1
-751
1:
0.4897077661531544181727998682098411796107182862179172563198093625319146628562274327071676147639671805
comment: $a^4 - 2a^3 + a^2 - a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.751.1
761
1:
0.7088908329916068993446501073177813293186616809200752053076332066179007838647742115197607295657822574
comment: $a^4 - a^3 + a^2 + 2a + 1=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.761.1
-775
1:
0.3917701636115281668214519560250289218006769494889822842543938666829637510086079747130941797685235703
comment: $a^4 - a^3 - 3a - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.775.1
784
1:
0.9759133155238927800387947685365623039654921646655200603825550273698540212025003875897935273094823169
comment: $a^4 - 3a^2 + 4=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=4$; LMFDB 4.0.784.1
788
1:
0.9803130675981021140270655466787702300006183242235927086495909061522309014464983572789663834434704646
comment: $a^4 - a^3 + 2a^2 - 2a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.788.1
832
1:
0.7317658363025647742111062738354575880467501144424237977598377251042899904333357651598919952799628665
comment: $a^4 - 2a^3 - 2a + 5=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.832.1
837
1:
0.5501138242175825521956837435977733390045253655821388366235845979941939468012519937107282463034659986
comment: $a^4 - a^3 - 3a^2 - a + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.837.1
-848
1:
0.4285080377501465071688296853687319722366427459732699303895312894129568396883893200782166665540649807
comment: $a^4 - a^2 - 2a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.848.1
873
1:
0.5406926984449757990989559405475177397175038968534373649489003810746846184485573227404540052148691333
comment: $a^4 - a^3 - 4a^2 + a + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.873.1
892
1:
0.8543974333337728144225414893075815444490589687478868252904315684255618001604149286417793031387909213
comment: $a^4 - a^3 - a^2 + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.892.1
-976
1:
0.3984985762209827706335893984007534110745959014096934153190457660134719006002752368644861378144511914
comment: $a^4 - 2a^3 + 3a^2 - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.976.1
981
1:
0.4521269498476929522358122168852280081825530940265301420489459978612880133528148358142607388346173881
comment: $a^4 - a^3 - 4a^2 + 4a + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.981.1
985
1:
0.8450558498554488452481458284080998567222277705870184706685847084000432360898293356938323378782753572
comment: $a^4 - a^3 + 2a^2 - 3a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.985.1
1008
1:
0.7037703446161787499893733731230852160430245027707181326115537974955812051236465791975680912593125445
comment: $a^4 - 5a^2 + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1008.1
1008
2:
0.5007206633999741567253419827811259516669660485557536426223873535144038969989668231244959712525901593
comment: $a^4 + 5a^2 + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1008.2
1016
1:
0.7891312894319112222943007472451387943864509614146588633633781596525966875705751537120799605270670525
comment: $a^4 - a^3 + a^2 - 2a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1016.1
-1024
1:
0.5290607097021002682693870500754027604603919178080847533286218955115374727175012585476087436586769362
comment: $a^4 - 2a^2 - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1024.1
1025
1:
0.5933816268876432390311726039615183106947501734060229660459589424276557151704512402373147907549693447
comment: $a^4 - a^3 + 3a^2 - 2a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1025.1
1040
1:
0.5668738787306201488095695835652427131984338788507286330539486033549184490869374300880278633008987393
comment: $a^4 - 3a^2 - 2a + 5=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.1040.1
1040
2:
1.061557287337235255118642926375993716553879810842242865139856816150885934311199154010535932734175503
comment: $a^4 + a^2 - 4a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.1040.2
1076
1:
1.069344125057608703869993053595758035609164578593449132988169371123570683560548428831946638265990047
comment: $a^4 - a^3 + 3a^2 - 3a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1076.1
1088
1:
0.7061302159290180056149419764303050809656524847258339921520317551250473799690007671424964484595397820
comment: $a^4 - 2a^3 + a^2 - 2a + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1088.1
1088
2:
1.054885494492864748305313807466892491284298384727827397104333599670442391794419520486384981222205487
comment: $a^4 - 2a^3 + 5a^2 - 4a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1088.2
1089
1:
0.7632829978339534537681626760986610742984492449106869256671264698285049092644827425148665282840927514
comment: $a^4 - a^3 - 2a^2 - 3a + 9=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=6$; LMFDB 4.0.1089.1
-1099
1:
0.3837816845481843823976326926779157759239335075833457364373263672572524231864630817045003463660021003
comment: $a^4 - a^3 + a^2 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1099.1
-1107
1:
0.4864835125896290141672500995077244781991690155019069547393604050389092918040091528965680101079731393
comment: $a^4 - a^3 - 2a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1107.1
1125
1:
0.2779772841855011885280732234004675600151106320830300871735978075795556065774717841826321834946399550
comment: $a^4 - a^3 - 4a^2 + 4a + 1=0$; signature $(4,0)$; 4T1; $h_K=1$; $w_K=2$; LMFDB 4.4.1125.1
1129
1:
0.7455057384843362939926323801916301530331308327994437857672077158470807466382226295740084289515661672
comment: $a^4 - a^3 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1129.1
-1156
1:
0.5673813053588955366005768100050747799373853401975310061279883781815269522773707920271571859324928780
comment: $a^4 - a^3 - 2a^2 - a + 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1156.1
1161
1:
0.6722785167399832186699845824925891543894821738480149619551553921680931115204337437504907895705903266
comment: $a^4 - a^3 + 6a^2 - a + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1161.1
1168
1:
0.5458779922725114776396031855350749540608353298309961265407809245976381518949588541908846087045057204
comment: $a^4 - a^2 - 4a + 5=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.1168.1
-1192
1:
0.5710669330095359959250568695844597140187760896440862055415440206175935672995386288685488755836051589
comment: $a^4 - a^3 + 2a^2 + a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1192.1
1197
1:
0.4410693749465024120474485356237438055480651179886208327816884165665039095277029830274356104289412056
comment: $a^4 - 2a^3 - 4a^2 + 5a + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1197.1
1197
2:
0.6802940411854472226130986575012058111187541710477112356110947072959238950876861036355285998520823205
comment: $a^4 - a^3 - 5a^2 + 3a + 9=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1197.2
1225
1:
0.5427851824530862510620348203786029561736944557475836264779842151247580949885952286666248797676025764
comment: $a^4 - a^3 + 5a^2 + 2a + 4=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=2$; LMFDB 4.0.1225.1
1229
1:
0.6993536029832081360799405194122869006914726953483263136811619018418264173828168730128403213917730253
comment: $a^4 - a^3 + 3a^2 - a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1229.1
-1255
1:
0.5612870849859130912808838484681391223775764344522034255827231390095554163923616021479294832173298246
comment: $a^4 - a^2 - 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1255.1
1257
1:
0.8567387780883364433510449207031366330804220215867689455103308680658504702069994593794290924033721861
comment: $a^4 - a^2 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1257.1
1264
1:
0.6413062791170611376299592549454612507661538794642288406142971222016274673819094544550463896286598068
comment: $a^4 + 3a^2 - 2a + 1=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1264.1
1280
1:
0.8106819978690658731577750541246819159159568142562943904785677729857569108016582430954951539018145472
comment: $a^4 - 4a^2 + 5=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.1280.1
-1323
1:
0.4669064815818523948909232544827874338319880118679397114062018572559407144100563260837722241648394987
comment: $a^4 - a^3 - 3a^2 - a + 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1323.1
-1328
1:
0.4713508461169588171758002159995543726406130853441533484264485371370614929260202872109231248033155321
comment: $a^4 - 3a^2 - 2a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1328.1
-1371
1:
0.4577491647105078208244624562510038680401278434094462334632080619621615884932511747903859042789296753
comment: $a^4 + 2a^2 - a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1371.1
1372
1:
0.7919138907978916562595985851605509038334887912662673390283377854589950359226547858101278627420910910
comment: $a^4 - a^3 + 3a^2 - 4a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1372.1
-1375
1:
0.4509333352971301377173466220411333019004977684870828891059369059936922346842871836850011733102123695
comment: $a^4 - a^3 + a^2 + 4a - 4=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1375.1
1384
1:
0.9632027018122984342594807113317313296337397237303350882902169200296406795410934823177540294959109700
comment: $a^4 - a^3 - a^2 + 2a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1384.1
1396
1:
1.251136293026240936560636414909277199991105393713412726900054563386111546833328594554696067266020489
comment: $a^4 - a^3 + a^2 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1396.1
-1399
1:
0.5732103492032840104394023090761105739868704979101215064552084817547450129536437212777210460019527599
comment: $a^4 - a^3 + a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1399.1
1413
1:
0.6813655600342395591878215816862521593363575558568329134029587553011712444953392454965725171569701913
comment: $a^4 - a^3 + 7a^2 - 3a + 9=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1413.1
1421
1:
1.166449017954220288177947515073610878681906027632874878292590827308211911374331748433962761241129020
comment: $a^4 - 2a^3 + 2a^2 - a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1421.1
-1423
1:
0.5655447552637838560607280153987467817725903980701014755867357593710076502552540806046942937516130917
comment: $a^4 - a^3 + a^2 - 2a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1423.1
1424
1:
0.6301602733130273381239328852083448441388220793144757524223087011171477365680115617384560016405619235
comment: $a^4 - 2a^3 - a^2 + 2a + 5=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.1424.1
-1424
1:
0.4906053660210073462707240079896246441875649024395304407320706186652239187471119469359716461363623385
comment: $a^4 + a^2 - 2a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1424.1
1436
1:
0.8313071122904704102315512748374261165469804809318915852428714781445801828625302868382579103864003228
comment: $a^4 - a^3 + 3a^2 + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1436.1
-1456
1:
0.5797902767381371814126544205585871069558112642094677897241375962960596151215900440059205826533815746
comment: $a^4 - 2a^2 - 2a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1456.1
-1472
1:
0.6407626094875965467632794435070410377801260856501171455961244185980628883882634319403391986029607275
comment: $a^4 - 2a^3 + 2a^2 - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1472.1
-1472
2:
0.4125335127281041965053714615989104837275536750887509895453062103806661584602716361576746826892844166
comment: $a^4 - 2a^3 + 3a^2 - 2a - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1472.2
-1475
1:
0.4040195459676666161127908551329926420071650049298228317159353530447235086601004901527573047696061012
comment: $a^4 - a^3 - a^2 + 5a - 5=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1475.1
1489
1:
0.9033259595693893275279528957311719398263128063255223432379972119215955770151214989131749626756808391
comment: $a^4 - a^3 + 4a^2 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1489.1
1492
1:
1.267498875948254352676991121253276995451659392981648630028663226088748377081711261393235869184778672
comment: $a^4 - a^3 + 2a^2 + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1492.1
1509
1:
0.5848142107179715905402034945951384821182321080955769754089031294059645262516562750428343572125760145
comment: $a^4 - a^3 + 2a^2 + 2a + 1=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1509.1
1521
1:
0.8062796791518998741444231692443858503949175474196287913929838431325250083113780266190227073298452558
comment: $a^4 - a^3 + 4a^2 + 3a + 9=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=6$; LMFDB 4.0.1521.1
1525
1:
0.4864756486457058714902744018883698124886460057398088051362946603939024663069913742788903700571768736
comment: $a^4 - 2a^3 + 6a^2 - 5a + 5=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1525.1
1552
1:
0.5591381857922999976642062086103620379076247087569291728126811697699457014671362783431826190662110377
comment: $a^4 - 2a^3 - 3a^2 + 4a + 5=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.1552.1
1556
1:
1.155318025254391411027111019670657095162523942627225774537813745906435129916660456977449975477392938
comment: $a^4 - a^3 - a^2 + a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1556.1
1568
1:
1.124976922364270046905622586754401362679225619285884259799594648898628266061382513711368026432870102
comment: $a^4 - a^2 + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1568.1
-1588
1:
0.6097430324525601935271796241634191644412131714380531175713688354178692620513816710712257656999143165
comment: $a^4 - a^3 - 3a^2 + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1588.1
1593
1:
1.030578592487409887523502926409019820944883961607393528538455649002156121545220237826839933475009535
comment: $a^4 - 2a^3 + 3a^2 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1593.1
1600
1:
0.3085011819666975833514942271742615552280279451950904605055543204938587317481610629744474320297283324
comment: $a^4 - 6a^2 + 4=0$; signature $(4,0)$; 4T2; $h_K=1$; $w_K=2$; LMFDB 4.4.1600.1
1600
2:
0.4749370346464504696792804678312775866519826487791356731682361882341633331150208250832967697966522543
comment: $a^4 + 6a^2 + 4=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=2$; LMFDB 4.0.1600.2
-1600
1:
0.4442648282395273649898449825881093836587338583493311304894740064284911211122874583581871563139619477
comment: $a^4 - 2a^2 - 4=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1600.1
1616
1:
0.7748187326587059219605001137630223513808661208377203830035574044334566130390823633774577390254779471
comment: $a^4 - 2a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1616.1
1629
1:
0.4200246545512023684320121970520626859607125577912155201517936747128830761505227726754522171564642587
comment: $a^4 - 2a^3 + 8a^2 - 7a + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1629.1
1728
1:
0.6304928340901963624751279730204084352187096168633769597858280434027383626127792751543711818869389523
comment: $a^4 - 6a^2 + 12=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1728.1
-1728
1:
0.6620218663486695849880139640366737336492112046356371834495510478053894374739811755390076638531917471
comment: $a^4 - 2a^3 - 2a + 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1728.1
-1732
1:
0.6194687822674451560253837203041804891064642093743825776469554959326590587129219436965360870927148687
comment: $a^4 - a^3 + 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1732.1
1737
1:
0.8213959109802040138558655912920702144454822331363879134285942116473298842497834998937386363347282098
comment: $a^4 - a^3 - 5a^2 + 6a + 12=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1737.1
1765
1:
0.6793041446446022072499694019199429923289665019636315880630936164896953104784419256329217704711625717
comment: $a^4 - a^3 - a^2 - a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1765.1
-1775
1:
0.4508950836781060056338329394336005197518988638228600182707982792727542080996611112957448313522142086
comment: $a^4 - 2a^3 + 3a^2 - 2a - 4=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1775.1
-1791
1:
0.5995538287497156730995423721897990714314829886817171139608349815621162701596518042650670009167284902
comment: $a^4 - a^3 - a^2 - 2a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1791.1
-1792
1:
0.5904563457338265495088519914865309488819446791885211692976383618248142193801760272632706716655131388
comment: $a^4 - 2a^2 - 4a - 2=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1792.1
1805
1:
0.5570306363028655497220583869536594023780754710238627300734380058550732473137995775709608332801495505
comment: $a^4 - a^3 + 3a^2 + a + 1=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1805.1
1808
1:
1.221139920768355713672318010822771803549915171064503590546634696099834949251005434393836719818896923
comment: $a^4 - 3a^2 - 4a + 8=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.1808.1
1809
1:
0.7141275070783740690479902765513142152608903392501648182678234156761482693040479739287742170048867869
comment: $a^4 - a^3 - 6a^2 + 5a + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1809.1
1813
1:
1.223808590343541133433296702959834791840358696814069618491568212587441515766267006269897344215559089
comment: $a^4 - 2a^3 + a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.1813.1
-1823
1:
0.6716115029631660516035571087917662993993190082528388880013615867115254670405919982931556707389339306
comment: $a^4 - a^3 + 3a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1823.1
1825
1:
0.9789476490967832573889396289233395683936475989538224791244446675403432362450113434505111140114328043
comment: $a^4 + a^2 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1825.1
1856
1:
0.9047880301805580944627345295632527950499076295155685493312269689105257272239342877846354974924711819
comment: $a^4 - 2a^3 - 4a + 10=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.1856.1
-1856
1:
0.5137992264242493949184532493410257016376689809733363201837430858648399186616864373060038560078344817
comment: $a^4 - 2a^3 + a^2 - 2a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1856.1
1872
1:
0.7832667660320448746238723792496331779434133976880817254162039080955227473854388117505072000201917630
comment: $a^4 + 7a^2 + 13=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=6$; LMFDB 4.0.1872.1
-1879
1:
0.4809297373743522579405213402265867217771495850064716004319990397318616355548169959632409388373302727
comment: $a^4 - a^3 - 2a^2 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1879.1
-1927
1:
0.5941375302542093561942590988790617965056159303199104691759528395413029645531616868233530613674367471
comment: $a^4 - 2a^3 + a^2 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1927.1
1929
1:
0.9403688022634642152502612353332085503207954629139443390029176770308734109092065981693143611323721204
comment: $a^4 - a^3 + 4a^2 - 3a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1929.1
-1931
1:
0.3977382734069840511005988485963769232812544745783607460054871136599785762397453695979052123984473464
comment: $a^4 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1931.1
1936
1:
0.6714073948993214766280657854002613986677219664613233423075859313587009642116488942205288863934262345
comment: $a^4 - 5a^2 + 9=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=4$; LMFDB 4.0.1936.1
1937
1:
0.7421406618085765999929139669504273707754916583154424102715698932019989141323581176537418571018509146
comment: $a^4 + a^2 - 3a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1937.1
1940
1:
1.198494218688833942497613295989363453805446351046724930165376322060097394235645677400392352963257275
comment: $a^4 - a^3 + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.1940.1
1953
1:
0.8532213548559902273689784288673812409239851787416979479332630552896925266053419699483749586409399247
comment: $a^4 - 2a^3 - 5a^2 + 6a + 12=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1953.1
1953
2:
0.5619669317289421032823291466884865142118495417018175079533678846655148706046635577346146960551524524
comment: $a^4 - a^3 + 8a^2 - 5a + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.1953.2
1957
1:
0.3469168296992059461040681659218526461500611145909220107018903081801111589323825496860861821113050415
comment: $a^4 - 4a^2 - a + 1=0$; signature $(4,0)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.4.1957.1
-1963
1:
0.4194444004997805714818076658189940916036232887402272357391934502395067549506923401663424617895184559
comment: $a^4 - a^3 + 2a^2 - 2a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1963.1
-1968
1:
0.6796182154256576272411605831181352787271767230029336003185891778961363837646525551849103210629133723
comment: $a^4 - 4a^2 - 2a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1968.1
-1975
1:
0.5022847260528011138661763656796456516903841789405369352728684225832262114088079232827940645144338618
comment: $a^4 - 2a^3 + a^2 - 5=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1975.1
-1984
1:
0.8466295429738546341611942316702643271253797418928668148090672034348280202409069733127121736245316674
comment: $a^4 - 2a^3 + a^2 - 2=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.1984.1
-1984
2:
0.6116474891346381635929174525700722210161925219839977450241866225698023495089052492789713877461126264
comment: $a^4 - 2a^3 + 2a^2 + 2a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.1984.2
2000
1:
0.3314408296378723937565407032671375822997942489939573390878018007031059710030215590562710802841941131
comment: $a^4 - 5a^2 + 5=0$; signature $(4,0)$; 4T1; $h_K=1$; $w_K=2$; LMFDB 4.4.2000.1
-2000
1:
0.4372704541973989320287256855005449212870851339293315555688042226284231729783118974850120850945485474
comment: $a^4 - 5=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.2000.1
2021
1:
1.291934820089837481968937899998287709779488381106947743805757038151377312932095363740537991258446661
comment: $a^4 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2021.1
2048
1:
0.4316524518620982852925556769648775367052207319265027843631039999737027577943990952408006667463813308
comment: $a^4 - 4a^2 + 2=0$; signature $(4,0)$; 4T1; $h_K=1$; $w_K=2$; LMFDB 4.4.2048.1
2048
2:
1.067963570726169372953513017420678297853146695260420961182107787702562751434979921142989668674225672
comment: $a^4 + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2048.2
2048
3:
0.7688733216197489348537293762242968285579995725191607536925910526511329207699370459610419303222972199
comment: $a^4 + 4a^2 + 2=0$; signature $(0,2)$; 4T1; $h_K=1$; $w_K=2$; LMFDB 4.0.2048.3
-2048
1:
0.5992342018380771873863681439134654149423896793824932527927183321603741563613069509421621318445078877
comment: $a^4 - 2=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.2048.1
-2051
1:
0.4836433383042218006911777623386259838659947568005998245566114001022854765721664290728025029783353875
comment: $a^4 - a^3 - a^2 + 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2051.1
2057
1:
0.8201395127643569475111574841516933725050642040785705347611662872473621527873982378327213199294639724
comment: $a^4 - a^3 + 3a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2057.1
2061
1:
0.4106927697232053662183851806096547401071288220784189490410525397646851766907077597727049234101303508
comment: $a^4 - a^3 + 8a^2 - 2a + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2061.1
-2068
1:
0.6390455929364820281003537388778433190758391242766117247489364851702279712462102188381919620354934216
comment: $a^4 - a^3 - 2a^2 + 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2068.1
2089
1:
0.7417844555981307557054859026531263679675440070382060631767679091642758257986242555212761640079454821
comment: $a^4 - a^3 + a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2089.1
-2092
1:
0.8557608673454278315964620564421739761251425676834725225304481693555046768393958222625553112801916436
comment: $a^4 - a^3 + a^2 - 3a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2092.1
-2096
1:
0.6927495406723522662388327282521946574052117185051217085164403159518709136827855115174234238429887277
comment: $a^4 - 2a^2 - 2a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2096.1
2112
1:
1.355013510637382504481434262205066971378092443521838759084826586110256758166922003788510189488460888
comment: $a^4 - 2a^3 + a^2 + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2112.1
2112
2:
0.6091942950723098007565131530337720925283061913453650772725384955053377793796366086685942266535155326
comment: $a^4 - 2a^3 + 5a^2 - 2a + 1=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2112.2
-2116
1:
0.6604920432536353325232185020036027033065629708803599590973293094065442562105264913914125683301153287
comment: $a^4 - a^3 + a^2 - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2116.1
2133
1:
0.5502383800044942385564666804061956197125189055620968371078635228976526067920776176275285470547551411
comment: $a^4 - 2a^3 - 6a^2 + 7a + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2133.1
-2151
1:
0.6172205221381799739226685849561071853463606215878270539162615832374260173340789115664382479639067724
comment: $a^4 - a^2 - 3a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2151.1
2156
1:
1.699805212493777902278914309310202604721836017578279408805917913839740855577276442227472302634883889
comment: $a^4 - a^3 - 2a^2 + 2a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2156.1
2156
2:
0.8378667842214915361405519086103078319880775050634449520357342245829495558991609561880382562527015630
comment: $a^4 - a^3 + a^2 + 4a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2156.2
2169
1:
0.5854122398240133582930714056413739677163543738237402985637410661858806663033329421456729649018185949
comment: $a^4 - a^3 - 7a^2 + 4a + 16=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2169.1
-2183
1:
0.6006329338608710584991126620306373859195944830267207804665129143530552849893870476654222075838755073
comment: $a^4 - 2a^3 + 3a^2 + a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2183.1
-2191
1:
0.6244054142819879305208308476768614141425935653582126055009570578803096070638558482732740155412232597
comment: $a^4 - a^3 + 3a^2 - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2191.1
2192
1:
1.260895805151268707284407734888833038677219046213510386877331818077333122489221044047490799799668936
comment: $a^4 - 2a^3 + 7a^2 - 6a + 10=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.2192.1
2197
1:
1.006297866535440685943023975212885133169635299011159899319983912412416025607121336994154954265329661
comment: $a^4 - a^3 + 2a^2 + 4a + 3=0$; signature $(0,2)$; 4T1; $h_K=1$; $w_K=2$; LMFDB 4.0.2197.1
2213
1:
0.6999078994378355120777347946016229662529365474023706074463875391022693944300360562380156494497866447
comment: $a^4 - 2a^2 - a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2213.1
-2219
1:
0.4011731196749161475862944310459545775387533771377204969469611736640622870404604983995117665480281493
comment: $a^4 - a^3 + 3a^2 - a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2219.1
2225
1:
0.3501405184910249037733249790068184950664454362747294994925635194224467579045376106445923843768359182
comment: $a^4 - a^3 - 5a^2 + 2a + 4=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.2225.1
-2243
1:
0.5156002541437694719137504682524180381299401798578903169532167641536521018786960931201146496535192609
comment: $a^4 - a^3 - a^2 - 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2243.1
2256
1:
0.9672478219883921338453515699710786438051908039707861385718901348508645698130097534393969030443786197
comment: $a^4 + 2a^2 - 2a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2256.1
2272
1:
1.383845389498243544706698553321328046379453616292155266572245008322205655701208020463123767553813005
comment: $a^4 + a^2 - 2a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2272.1
-2284
1:
0.8714088159899971687708010752140246632945114924648117142710834784728909395298470535299526233750609392
comment: $a^4 - 2a^3 + 2a^2 + 2a - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2284.1
2292
1:
1.374048358169358789823136323470262325573273616865467785311470366866864426848900530918859355784212883
comment: $a^4 - a^3 + 2a^2 - 4a + 4=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2292.1
2296
1:
1.063946499842716103125798151571123359692048150641694514874337184446455073802094320284370581052454317
comment: $a^4 - a^3 - 2a^2 + a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2296.1
2304
1:
0.4434830966983950781534472826487999682597352598324981606558393778055590315695243616596122080819555386
comment: $a^4 - 4a^2 + 1=0$; signature $(4,0)$; 4T2; $h_K=1$; $w_K=2$; LMFDB 4.4.2304.1
2304
2:
0.9427247372957343989177536483358127429262330867054835063729188222064722004480608036369993868182150049
comment: $a^4 + 9=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=4$; LMFDB 4.0.2304.2
2304
3:
1.083154454628213074358039139283777179911886536019236498093510758956774922538177226468954758959603586
comment: $a^4 + 4a^2 + 1=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=2$; LMFDB 4.0.2304.3
2312
1:
1.719848753484101682835991663841199290832864282016714352166004706526273358429348744896928031202145082
comment: $a^4 - a^3 - 2a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2312.1
-2312
1:
0.6459663359224619807892769814513869140520379406220857589247166542801803759334230664413953271831570803
comment: $a^4 - 3a^2 - 2=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.2312.1
-2319
1:
0.7036999143924657036336808510902644653982899978775635073533945285671314415804528750085276764418673479
comment: $a^4 - a^3 - 2a^2 + 3a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2319.1
2320
1:
1.220741449992957422439603990389082183721443448025155923717947683653656769401022302125872113786357726
comment: $a^4 - 2a^3 - 3a^2 + 4a + 8=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.2320.1
2320
2:
0.5165591392218778617408370886729175919101633874985610334742047445480946892875768150783607066745786601
comment: $a^4 + a^2 - 6a + 9=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.2320.2
-2327
1:
0.7019097497883122270536041929940596624847568364132257308132714729060627968731851995800869334553294242
comment: $a^4 - a^2 - a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2327.1
2349
1:
0.7505864506301075704108615493835284358882054973970946350389251655578675016453344515310407310454089054
comment: $a^4 - a^3 + 3a^2 - 3a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2349.1
2368
1:
0.8283626422819486857857433407351777738362303921381325438960166780354467290797189937293035917703471797
comment: $a^4 - 2a^3 - 4a^2 + 4a + 10=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.2368.1
-2375
1:
0.4945398597003748066270998970172260697689111853340166490377766301773928840866655410718412350136951952
comment: $a^4 - a^3 + a^2 - 6a - 4=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.2375.1
-2412
1:
0.8823515888807440932861736939386330074267641946204231286663328228505550109271943753705371508353314978
comment: $a^4 - a^3 - a^2 + a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2412.1
2429
1:
0.7594121616153645517322583559815687131394104514107810333807503993327790291140522150805046479064655740
comment: $a^4 - a^3 - 2a^2 + 2a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2429.1
-2443
1:
0.5647999709419497883604178928125831284641646339063233539892947233624875982649482045982045818849776141
comment: $a^4 - 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2443.1
2448
1:
1.289416163178332379743412326115696057348369431387471884147871448395801137369532593773945294923341939
comment: $a^4 - a^2 - 6a + 10=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=4$; LMFDB 4.0.2448.1
2457
1:
0.7134554070868307243322586732025793150943312802807124867329097221544554724859763592421471389636348435
comment: $a^4 - a^3 - 6a^2 - a + 19=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=6$; LMFDB 4.0.2457.1
2457
2:
0.7629542314900771351417762368548702725356738522645828898748978037237763461275805544297417165056210226
comment: $a^4 - a^3 + 9a^2 - 4a + 16=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=6$; LMFDB 4.0.2457.2
-2475
1:
0.4221699969294579001740896778919765385692150781601922085609545054356279520532056710660373705575560710
comment: $a^4 - a^3 - a^2 - 5a - 5=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.2475.1
-2480
1:
0.7342839108190658641663222585673165567293957005921356045063712359730073739035822171865496709940302801
comment: $a^4 - 2a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2480.1
-2488
1:
0.6576659831367486594826944765808284011089497458255790569755380865924244431393388955454753341609726165
comment: $a^4 - a^3 + a^2 + 2a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2488.1
2493
1:
0.3546849102087693232926362229775532882143612417490880139024601583650990052697025712881834904986486542
comment: $a^4 - a^3 - 7a^2 + a + 19=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2493.1
2525
1:
0.3329185680697531131812809407389401632003462508357529080881933141040025960547835831526522103431547573
comment: $a^4 - 2a^3 - 4a^2 + 5a + 5=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.2525.1
2560
1:
0.8994490888689188720091072110603931680003267701982709405712479984402714934320013891695931018326068282
comment: $a^4 - 6a^2 + 10=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.2560.1
2560
2:
0.7680254402266977268775015398737634056300007196722041660649548456743408968057303808083656594117966923
comment: $a^4 - 2a^2 + 10=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.2560.2
-2563
1:
0.3789488055833347840236080697877263921540959695830605477864273606012375284364619921035356760209883738
comment: $a^4 - 2a^3 + 4a^2 - a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2563.1
2597
1:
1.324175183608122310681661964258662998695907981318643686248371758579877769354388812715852830853001230
comment: $a^4 - 2a^3 + 4a^2 - 3a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2597.1
2597
2:
0.5188444716651760222394538724547816906408707945878655049482107025001065135693304758476526817508909347
comment: $a^4 + 4a^2 - a + 1=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2597.2
2601
1:
0.5404963183128174235258569934071229219609225124873420684781613872492998954898545747539340033040470884
comment: $a^4 - a^3 + 5a^2 + 4a + 16=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=6$; LMFDB 4.0.2601.1
-2608
1:
0.6587745022913361004239164266784531762490890500354141976718121780368646344985404543862596325715870780
comment: $a^4 - 2a^2 - 2a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2608.1
-2619
1:
0.5868518053678225417477195228122666284860931272414488069106823551612223621233036087052494067275628384
comment: $a^4 - a^3 - 3a^2 + 3a + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2619.1
2624
1:
0.3413890041227742320344151716515622294440300445014896872341783913058567449717888315604071735181093094
comment: $a^4 - 2a^3 - 3a^2 + 2a + 1=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.2624.1
2624
2:
0.7799813723974255939772963521819052157056677864180802954282792665632031505298054813121975609860954591
comment: $a^4 - 2a^3 + 3a^2 - 2a + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2624.2
2673
1:
1.111092559069779993994112888557475265703480486323639005379095931404258944268962091101276449229169568
comment: $a^4 - a^3 + a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2673.1
2677
1:
0.5502573206036813315582593762377704408728406985852967325161097527196046364647018812079683455471946866
comment: $a^4 - a^3 - 2a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2677.1
-2687
1:
0.6161935400818256673877332202074200643514705385405220220662277712543867480628130455444698074178123260
comment: $a^4 - 3a^2 - 3a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2687.1
-2696
1:
0.7728936778441718770589292800483716607592675451056447250892570833915413795302512885823942174047218892
comment: $a^4 - a^3 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2696.1
2704
1:
0.4535323195229436792062380326999670408471411204235411951585534117620453171751501399732002728730379564
comment: $a^4 + 7a^2 + 9=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=4$; LMFDB 4.0.2704.1
-2704
1:
0.6174793121455012865191127585878596548237878612065315481906990603877610613630482649064422436148159857
comment: $a^4 - 3a^2 - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.2704.1
2709
1:
0.7450335882388074346933809491863714411553724721254623861451265005639295391168072684883240261292659098
comment: $a^4 - 2a^3 + 10a^2 - 9a + 21=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2709.1
2709
2:
0.3730375116984297666630227766685722587580038810918596610348398915199115975208264953112679494284522100
comment: $a^4 - a^3 - 7a^2 + 7a + 19=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2709.2
2725
1:
0.3639257404874871427495918287264340746456747820411645570664554749954598142476677672874988411556229300
comment: $a^4 - a^3 + 5a^2 - 3a + 9=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2725.1
2736
1:
0.8200503345350437735241069814152956975885087403342941053380599177563283280048867886427363378137396273
comment: $a^4 - 8a^2 + 19=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2736.1
2736
2:
0.4973561443892437043885071223298229022012102316898975728735926152802536625908652656300595528446049906
comment: $a^4 + 8a^2 + 19=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2736.2
-2736
1:
0.6427272236106038043333388938888362030126332377026452249407857086309911519430095171892135784400527072
comment: $a^4 - 2a^3 + 2a^2 + 2a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2736.1
2744
1:
1.797251239361216898949634279615480576655342312299373117125595003818050160141482853322123682392588802
comment: $a^4 - a^3 + 3a^2 + 3a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2744.1
-2763
1:
0.4349810668954071143966819565130308495671546799229697961529031739304051923146155567610842605509176015
comment: $a^4 - 4a^2 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2763.1
-2764
1:
0.9123880433261949714676288967854908641487058406783903386700766654211371980316113343127749382239073859
comment: $a^4 - a^3 - 3a^2 + a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2764.1
-2767
1:
0.6222302866291611253685638067947757693956338465560378390532769228742333497119964357737888201444683432
comment: $a^4 - a^3 - 3a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2767.1
2777
1:
0.4613179609946126366689236551005327066419846499978715292612269403946727512569540776843862442271374573
comment: $a^4 - a^3 - 4a^2 + a + 2=0$; signature $(4,0)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.4.2777.1
2781
1:
0.5994112487878022414692240375910407154736293667130801408562647434735027921524816223140910844131075702
comment: $a^4 - a^3 - 6a^2 + 8a + 19=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2781.1
-2787
1:
0.6685562407772554441427646992014711706096998684441496143506507470927923912253157478741680952357834913
comment: $a^4 - a^3 - a^2 - 5a - 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2787.1
-2816
1:
0.7517481368814022061919288514316278886848361074533966494193396548803518825550219760396657270721368860
comment: $a^4 - 2a^2 - 4a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2816.1
2817
1:
0.9231898037724512822047488585651964496318788976346319092062051506978041626766260264604999095683560101
comment: $a^4 - a^3 - 8a^2 + 3a + 21=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.2817.1
-2824
1:
0.6929102654134098698636474276553376273527828189626090523544476172675882183636718835484488529275098194
comment: $a^4 - a^3 - a^2 - 2a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2824.1
2836
1:
1.484753639620038446280464249278746565110502181834630605445805126281058874248173216828251744610817221
comment: $a^4 - a^3 + 4a^2 - 4a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2836.1
-2843
1:
0.4800455705709540011166858475537376603460129287983396693056192600761946110449467306816405572965500387
comment: $a^4 - a^3 + 2a^2 + 2a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2843.1
-2859
1:
0.5047044774313957402521589373396058401525722250343655648642881619623617023856361844606373281970330049
comment: $a^4 - a^3 - a^2 + 3a - 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2859.1
2873
1:
0.8799819567174001986502382569259779577659173719781958612196652878446486868844836451670520362109399937
comment: $a^4 - a^3 + a^2 - 2a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.2873.1
2880
1:
0.9022269042541737634447221508560126467435291212655822066271641000814382396360527772030034081818429642
comment: $a^4 - 2a^3 - 4a^2 + 2a + 13=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=4$; LMFDB 4.0.2880.1
2889
1:
0.9786580118988063682170660884682081984745443351307281749974454360223250834586366788394649425015871017
comment: $a^4 - a^3 + 3a^2 + 2a + 1=0$; signature $(0,2)$; 4T5; $h_K=2$; $w_K=2$; LMFDB 4.0.2889.1
-2911
1:
0.6497945123557532563614582244896445456488452504867836209880304040925972088333765430122011774567786943
comment: $a^4 + a^2 - a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2911.1
2917
1:
1.544658685846654716304004701076623062927404709573974402921802444454911059045521725993295213392952296
comment: $a^4 + 4a^2 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2917.1
2920
1:
1.104863850669231032718181611743256194624496202320076505399197600071640161904553197485266253173863165
comment: $a^4 - a^2 - 2a + 4=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2920.1
2925
1:
0.7222890803313561407275104889901509167474205630403367758060451517029053129489239818939969240179109447
comment: $a^4 - a^3 - 8a^2 + 6a + 21=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=6$; LMFDB 4.0.2925.1
-2943
1:
0.7387865695077064434647285122594540732804263155544989986362744667990449543947817950672030960452327384
comment: $a^4 - a^3 - a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.2943.1
2960
1:
1.394332918695378681546883214217381373129073816410227682378105411994083081797257544530751988442885228
comment: $a^4 - 2a^3 - 5a^2 + 6a + 10=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.2960.1
2960
2:
0.4940802597734571375932683523824124068346792525216436724988929385034540225347615829898451280007526948
comment: $a^4 - 5a^2 - 4a + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.2960.2
2981
1:
1.376143289660931703023827718843050516009951334220840501239486112161357303445677940227842823436306622
comment: $a^4 - 2a^3 + 4a^2 - a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.2981.1
-3008
1:
0.9218959775914438449122298914390848288918820586282094616824807542487497332558188997332326457478467331
comment: $a^4 - 2a^3 + 3a^2 + 4a - 4=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3008.1
3024
1:
1.205069719861760188962491986676316082687029786864082999071103459008086308663786063674275442623685815
comment: $a^4 - 2a^3 + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3024.1
3024
2:
0.6794927959988797538357985414039422187824637676756962638034254389853783231945758351210516776311428558
comment: $a^4 - 9a^2 + 21=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=6$; LMFDB 4.0.3024.2
3025
1:
0.6908175049402915922607715895727673987665202164060155246083435465224193936218484728484316651587669154
comment: $a^4 + 3a^2 + 16=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=2$; LMFDB 4.0.3025.1
3028
1:
1.213159942099203179937164694870743315264771699369261605513550845878008269430939624358331808614877730
comment: $a^4 - a^3 + 2a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3028.1
3033
1:
0.6547025070596145221699260979172400993327656042223133045353070420363888928713436153605829533986618386
comment: $a^4 - 2a^3 - 7a^2 + 8a + 19=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.3033.1
-3052
1:
0.9287887581979349483245140602398499108924548807026602305554297889366770715926100457447539385058524794
comment: $a^4 - a^3 + a^2 - a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3052.1
3072
1:
0.9093551326494919026099642903368006829436747867688252832331205979252951326180006860946825132410526864
comment: $a^4 - 2a^2 + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.3072.1
3072
2:
1.337525691446768530388076268389206854652695991777605914622538508164897507290306298802969359422634498
comment: $a^4 + 2a^2 + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.3072.2
3088
1:
0.5844100571493769564594691503906878283967119687003287710170389183285301438251627365742533848473611924
comment: $a^4 - 3a^2 - 6a + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.3088.1
-3119
1:
0.6513025170468173944871177731322927000197394999868740136246975744914583132204684811464888980365284416
comment: $a^4 - a^3 - 2a^2 - 3a - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3119.1
3136
1:
1.021556732889003422292674194284792796156726448491781572865884852172290842812330019797661110538503423
comment: $a^4 - 2a^3 + 2a^2 + 2=0$; signature $(0,2)$; 4T4; $h_K=1$; $w_K=2$; LMFDB 4.0.3136.1
3136
2:
1.198481717771726746288698495242114529721566733792221425095110416714349035573002673875513089074121590
comment: $a^4 - 2a^3 + 9a^2 - 8a + 2=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=2$; LMFDB 4.0.3136.2
3136
3:
1.242686947635999520179697496022412981088130421561447677122740329460930270619069910458645260682432408
comment: $a^4 + 6a^2 + 16=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=2$; LMFDB 4.0.3136.3
3141
1:
0.7220957315796807986216482591400083518490553210488894195901158351261119630658721505694665849853643600
comment: $a^4 - a^3 + 10a^2 - 6a + 21=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.3141.1
-3163
1:
0.5856316545964832056165255375793714491694462906651283873131011557815574400225425189748701093142165140
comment: $a^4 - a^3 - 2a^2 - 2a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3163.1
3173
1:
1.335510309292054767212878133470853812844149892514774604447499308834173631221982499890272919411819741
comment: $a^4 - 2a^3 - a + 4=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3173.1
-3175
1:
0.6826406972543631631396623988119259228867855397192343867367764191854684721524011700936705369862857496
comment: $a^4 - a^2 - 3a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3175.1
-3188
1:
0.7952614632504608827781928575590406110275689518853693494820405596154120537151833921811373102736766780
comment: $a^4 - a^3 + a^2 - 4a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3188.1
-3216
1:
0.5709256220159247109297089830980414229100487732401337560456207768458948228278086491885651785215153851
comment: $a^4 - 2a^3 - a^2 + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3216.1
3221
1:
1.390812434408030514773812007400724986981365376988665347901329235604881588824186358159538889633309377
comment: $a^4 + 2a^2 - 3a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3221.1
-3223
1:
0.6234929009309722281400262845617343960923998220533972382855894181588839915071696257081068578265824862
comment: $a^4 - a^3 - a^2 + 4a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3223.1
3229
1:
0.5263444972391555035798848932927450540452778746887567424819642122498791348397852577574178649263278883
comment: $a^4 - a^3 + 2a^2 - 4a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3229.1
3249
1:
0.6591759930573395700417623248791419151460189614389662336374739836850350072208553234076130477809364789
comment: $a^4 - a^3 - 4a^2 - 5a + 25=0$; signature $(0,2)$; 4T2; $h_K=1$; $w_K=6$; LMFDB 4.0.3249.1
3261
1:
0.9340827553582951491725219268217531909766805627800260458567643904634235165083305892402208528125885478
comment: $a^4 - a^3 + 2a^2 - 2a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3261.1
-3267
1:
0.5850736322473824652764635698830065884196296184864754582898255184614558301436904513054965785998170257
comment: $a^4 - a^3 + 3a^2 + a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3267.1
-3271
1:
0.6490558169953552751948953419582352079650946984845142855221880164612671086692917676991169954293076199
comment: $a^4 + 3a^2 - a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3271.1
-3275
1:
0.3628675173295218648143029352459048424210595709782660878138608457883722042635944251506003150619285792
comment: $a^4 - a^3 + 2a^2 + 6a - 9=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3275.1
-3284
1:
0.8006738268322170404921339274433480362736107668993201937251813934317206211700020056158671587401162868
comment: $a^4 - a^3 - a^2 - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3284.1
-3303
1:
0.6278562998192163477833816669926663165450558136232780509371062773273370955113855623290513527721118778
comment: $a^4 - a^2 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3303.1
3305
1:
0.9577289844837416679928557063545374844659639131006400501867250753647484804477430184311927863572034673
comment: $a^4 - a^3 + 2a^2 + a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3305.1
-3312
1:
0.9348920739884561241182711716871656189677314837480279631227804721860280719879123649027272144287397685
comment: $a^4 - 2a^3 - a^2 + 2a - 2=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3312.1
-3312
2:
0.6345834874065520133390839697790242748875854306621923337432357803125314498518041716143579949189008355
comment: $a^4 + a^2 - 6a + 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3312.2
3316
1:
1.515420445455337084179910027594702776764663294012555482747591754872626972456587398752680567441613240
comment: $a^4 + 2a^2 - 2a + 4=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3316.1
3328
1:
0.8527348216170888989363633389245043881697443574896813148788191325646643671333343020508607322039256302
comment: $a^4 - 4a^2 + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.3328.1
3357
1:
0.7851535240527654715372171963727850342604540482842978673064013817684996266593093816331367805122518792
comment: $a^4 - 2a^3 - 8a^2 + 9a + 21=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.3357.1
3368
1:
1.859761923257258501936079620899326780589039717200158185221399361381159658924439204815997592653319223
comment: $a^4 - a^3 + a^2 - a + 4=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3368.1
-3376
1:
0.4758070957067919082952692792648881764294953514239820287018713731140020638879165158018475011048201332
comment: $a^4 - 2a^3 + a^2 - 4a + 5=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3376.1
3392
1:
0.8255289965390685228172386494529517448962018826011917635076307195590556128714189459366560024165847213
comment: $a^4 - 2a^3 - 6a + 17=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.3392.1
-3407
1:
0.5964629034386813712257047209468948699082256135425079877360881625133311751015401922629776298395122508
comment: $a^4 - a^3 - 2a^2 + a - 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3407.1
-3411
1:
0.3917307237152984788107282696738536974898161805642695673350352628166201638640523285567722320410884546
comment: $a^4 - a^3 - 4a^2 - 2a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3411.1
-3424
1:
0.9755846338224269936650697488716860337748520867825749448870019816265776492273392520508163631331796072
comment: $a^4 - 3a^2 - 2a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3424.1
3429
1:
0.5510148173896494661527084640906486273543095963127282967040111747341382242987361304785069604977765145
comment: $a^4 - a^3 - 9a^2 + 5a + 25=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.3429.1
-3431
1:
0.6187855129880304364828919919472978343139393114343839111180623817642209669868982732191338322182098537
comment: $a^4 - a^3 + a^2 + 2a - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3431.1
-3436
1:
0.9761913943477220948205451754920566783821998876082440826812311061914155810689207639574151182546908993
comment: $a^4 - a^3 - 2a^2 + 2a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3436.1
-3475
1:
0.4280686569497823711634441506930243125435488123317968798226256124083254770609724192367128618758510325
comment: $a^4 - a^3 - 2a^2 + 8a - 11=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3475.1
-3504
1:
0.7812580667995080342361204790533046834777129549617520892868050274407304752626691942236887618741216737
comment: $a^4 - 2a^3 + 4a^2 - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3504.1
3528
1:
1.860211474175828682291216696159079227167246698989818204970152957421601158487709601252765799391659751
comment: $a^4 - a^3 + 5a^2 - 5a + 4=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=2$; LMFDB 4.0.3528.1
-3544
1:
0.7159337968665534477848572157479803039600989823149803776271688965911636533273188337421400611378195486
comment: $a^4 + a^2 - 4a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3544.1
-3559
1:
0.6675765439344430202975059372604396348528262969835174433299325523110274287995842214504577937392416268
comment: $a^4 - 2a^3 + 3a^2 - a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3559.1
-3571
1:
0.6167123083649316067020746219996323700807100662646968748609923663078311269494059349806698933508258484
comment: $a^4 - a^3 - 5a^2 + 5a + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3571.1
3573
1:
0.7270998322359930964232658717927931961831008715915542406544196776390038036195546415350781534377542614
comment: $a^4 - a^3 - 8a^2 + 27=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.3573.1
3600
1:
0.3487130032814851245616964942042521481995678732568169688726595924992077571073077248317596706558279460
comment: $a^4 - 2a^3 - 7a^2 + 8a + 1=0$; signature $(4,0)$; 4T2; $h_K=1$; $w_K=2$; LMFDB 4.4.3600.1
3600
2:
1.357687171769503364524662543176742624405049885226694748849862518503428527000447614276108493954006860
comment: $a^4 - 7a^2 + 16=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=4$; LMFDB 4.0.3600.2
3600
3:
0.9051247811796689096831083621178284162700332568177964992332416790022856846669650761840723293026712401
comment: $a^4 - 5a^2 + 25=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=6$; LMFDB 4.0.3600.3
3600
4:
1.733047127405140918972862622854043487859018457630778396949617214330839876061083562350327614335365738
comment: $a^4 + a^2 + 4=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=2$; LMFDB 4.0.3600.4
-3600
1:
0.4944326896429975009738507241768845058103632394565629556590007564922393682401475792631098426911180488
comment: $a^4 - 3a^2 - 9=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3600.1
3624
1:
1.118560289965446645183983212261821220690753607906792225253124470244977854057595530940215578611675058
comment: $a^4 - a^3 + 2a^2 - 3a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3624.1
3625
1:
0.6310619830804288649414035420951401986586775722866668958215288278040077149776246405599478176358617582
comment: $a^4 - a^3 + 6a^2 - a + 11=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=2$; LMFDB 4.0.3625.1
-3632
1:
0.6289048576356957066034735837422174774234140183396164436770559250011609932131282751716166425300940908
comment: $a^4 - 2a^3 - 2a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3632.1
3636
1:
1.280862737465221808956466343795243574063066220958006905933081199720142600100872403843204332669207410
comment: $a^4 - a^3 - a^2 + a + 4=0$; signature $(0,2)$; 4T5; $h_K=2$; $w_K=2$; LMFDB 4.0.3636.1
3648
1:
1.468010005229925817026780422098032949060465635859038759664283235471594042669938041934355345706754404
comment: $a^4 - 2a^3 - a^2 + 6=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.3648.1
3648
2:
0.9915013983489359120431268635152013754249335598553302169022253072232713003826929100034107113164571885
comment: $a^4 - 2a^3 - a^2 + 2a + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.3648.2
3681
1:
0.6034461532216369376308258079593130441649008791422307920446547932323557909111944236290758968153923935
comment: $a^4 - 2a^3 + 11a^2 - 10a + 28=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.3681.1
3700
1:
1.491103797679460322053765419887301756440319001324428738721729407510003309609598083706738848861668477
comment: $a^4 - a^3 + 5a^2 - 3a + 4=0$; signature $(0,2)$; 4T5; $h_K=2$; $w_K=2$; LMFDB 4.0.3700.1
-3723
1:
0.4791485214517649271094049620736684558785048572825077852658633390889785526808840370427533160327517324
comment: $a^4 - a^3 + a^2 + 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3723.1
3725
1:
0.3112668632152237436117435118478907944608885496138221236025158806621933674908864480302057199577251923
comment: $a^4 - 2a^3 + 8a^2 - 7a + 11=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.3725.1
3728
1:
0.5613925435895552552046677891471939500166664080826485572070967657881059889230413196903992725859183338
comment: $a^4 - 2a^3 - 5a^2 + 6a + 13=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.3728.1
3732
1:
1.499564154576811944507789211715673097319933906364981867129793495796941205739385325785027628982837880
comment: $a^4 - a^3 + 4a^2 + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3732.1
-3747
1:
0.5437397748365971578130914280781812559242103777075891286500160806408476418769671638139573539983807825
comment: $a^4 - a^3 + a^2 - 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3747.1
-3751
1:
0.6706186622340089287089893144470011063898974715094190377632117628422255876278365528896661570790093710
comment: $a^4 - a^3 - 2a^2 - 3a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3751.1
3753
1:
0.8306991095114438193126151428776368857031167696084053479501430508902295870498950678644909418977419291
comment: $a^4 - a^3 - 9a^2 + 2a + 28=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.3753.1
3753
2:
1.179467581537378802568049903772326487959508646602666993046923047833047759566954489635326801812234855
comment: $a^4 - a^3 + 3a^2 + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3753.2
3757
1:
1.349160362222101764163874614633121530096406953423535609717541354111464550909672021172560353791622016
comment: $a^4 - 2a^3 + 6a^2 - 5a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.3757.1
3760
1:
0.6973322152933621049756248476571398067205144653543907097640059600269409311658462165782448200458086694
comment: $a^4 - 2a^3 - a^2 + 5=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3760.1
3773
1:
1.374715628398143174574407406040871208267410660917698168678697894964665111799149043871868777725202363
comment: $a^4 - 2a^3 - 2a^2 + 3a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.3773.1
-3775
1:
0.4781839745797733913696830050232562404754726647541725555231684669586644937366183968023956823027159832
comment: $a^4 - a^3 + 7a - 11=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3775.1
-3776
1:
0.5777043945306931241881679356199992085228648700093551476120554113398514861854008162351007523613107994
comment: $a^4 - 2a^3 - 3a^2 + 2a + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3776.1
-3776
2:
0.8003598448094864291674270953986550303761899170115946620588512838812032845559968703802781559037133655
comment: $a^4 - 2a^3 - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3776.2
3789
1:
0.3186505888413465534473198428141326207987052011949234814779095329048537454100984131285555593657435966
comment: $a^4 - a^3 + 11a^2 - 5a + 25=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.3789.1
-3816
1:
0.7280958190056292684858423615534435442357009142835696372123182475178583342855285134397116517219190888
comment: $a^4 - a^3 - a^2 - 2a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3816.1
3856
1:
0.4426512080675347387377775944745124942116890217874225279203081484349046979501440784552506541834102754
comment: $a^4 - 2a^3 + 9a^2 - 8a + 17=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.3856.1
-3875
1:
0.3972003048095338687622400393152313214894657192849917592930922011084075022691157678030818994092553291
comment: $a^4 - 2a^3 + 4a^2 - 3a - 9=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3875.1
3877
1:
0.6996568206481956236487147899638249866544315639382385050769822045642651311356028076615097167272059127
comment: $a^4 + 2a^2 - a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3877.1
-3887
1:
0.4843099074639794528656226238183542695292460277418443078801306337611035103211135676329042531802046772
comment: $a^4 - a^3 + 5a - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.3887.1
-3888
1:
0.8909906993831431858264560747741946443109193098743655066954062640293158939119667605458293430260515587
comment: $a^4 - 2a^3 - 6a + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3888.1
3889
1:
1.008539310334281996207487271026895583210478849733325263751269649127637351441086114763852988639975238
comment: $a^4 - 2a^3 + a^2 - a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3889.1
-3891
1:
0.5210694081926979142509633609890061616920451207732795981519175168553353660218833169851313586480066634
comment: $a^4 - a^3 - 4a^2 + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3891.1
3897
1:
0.9605139558865972709186689509544456855767367561731752272564167759723261632030846747060969814823790640
comment: $a^4 - a^3 - 8a^2 + 9a + 27=0$; signature $(0,2)$; 4T3; $h_K=3$; $w_K=6$; LMFDB 4.0.3897.1
-3899
1:
0.5446731940326654696899860123252668207668196775340881615348533217658955015306281939963361722075560245
comment: $a^4 - 2a^3 + 2a^2 + a - 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3899.1
3904
1:
0.6922577883683745891098083053492159922630295559852498721724617508499325180329823384608863721137025770
comment: $a^4 - 2a^3 - 4a^2 + 18=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.3904.1
-3919
1:
0.6739795986547943631188441730163391829660355721348815073657499780718689377385131351932715646195853792
comment: $a^4 + a^2 - 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3919.1
-3951
1:
0.6367022257291367367583602498877458080295229095194406752180524519872202748739176798858059283475628653
comment: $a^4 - a^3 + 2a^2 + a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3951.1
-3967
1:
0.4907513689777483127534965790737469345134417667523801973436722284360497937351449433283491450838945260
comment: $a^4 - a^3 - 2a^2 + 5a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3967.1
3973
1:
0.5047422659177181080166140027067358663373717878624709629371068210980970021754264350844262769623633131
comment: $a^4 - a^3 + 3a^2 - 5a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3973.1
3981
1:
0.4043339106498824364390901346054048395201653836719023366950323180208213355371640757624898049897778607
comment: $a^4 - a^3 - 4a^2 + 2a + 1=0$; signature $(4,0)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.4.3981.1
-3984
1:
0.5718085906677024358363412400132454706831846200643282019599517420714449637976552539289097906886004498
comment: $a^4 - 2a^3 + 2a^2 + 6a - 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.3984.1
3988
1:
1.535082437509455946213072852826094251221465878546612057436089599535828371991975936832800299919667916
comment: $a^4 - 2a + 4=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.3988.1
3993
1:
0.8671583389543703796698688458480156376688339730686795392724055899781701340358588774486925713945080695
comment: $a^4 - a^3 - a^2 + 2a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.3993.1
4001
1:
1.254659718483648177667764456710963149087222873126781665484714483518341956916497583496400395264670654
comment: $a^4 - a^3 + 3a^2 - 4a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4001.1
-4027
1:
0.5886226332392908483669764965277334885145999920178147909921527638458658701857141091817591056406399850
comment: $a^4 - a^3 + 2a - 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4027.1
-4027
2:
1.040717669421385195907141631264456806666342978729205895545430660928831113289709811374650860278938470
comment: $a^4 - 2a^2 - a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4027.2
4032
1:
0.4595203338856224646739819548228840458329155407298265048996822073138954887908300718576141586113316732
comment: $a^4 - 10a^2 + 28=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4032.1
4032
2:
0.8892404472637153681059226407083891602464057655435909337982683115776615716960641285291580853189586829
comment: $a^4 + 10a^2 + 28=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4032.2
-4032
1:
0.9763521788745977533466280232900016215805589639534512548847550127134773273851033559912886280009755222
comment: $a^4 - 2a^3 - a^2 - 4a - 2=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4032.1
-4063
1:
0.6348034371249767622149905080484528101836187324441887438484439592300621737293193123187879191874998981
comment: $a^4 - a^3 - 3a^2 - 2a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4063.1
4077
1:
0.5419184096394162776750758092956563937297872368363462077644317467851553374887426885245437888869399512
comment: $a^4 - 2a^3 + 12a^2 - 11a + 31=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4077.1
-4103
1:
0.7640911352167991593087667226344165839975448729308710859643866024084988320498329678336793023851040601
comment: $a^4 - a^3 - 2a^2 + 5a - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4103.1
-4107
1:
0.7137440097417355593868013944817811410963212534104919292400464875912813760764635183452835966572814080
comment: $a^4 + 5a^2 - 3=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4107.1
-4108
1:
0.9744306450910181956374475175402724599889603308736593234184196260830383148199804051234427744876043992
comment: $a^4 - a^3 - 2a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4108.1
4112
1:
1.372736395026588437021005654420815637929058975008424241392983736463204304350347946356290827875529109
comment: $a^4 + a^2 - 8a + 16=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.4112.1
4113
1:
0.6843897595079080266308824371626822155151335527060605505564700501226969001810981746680384323447569198
comment: $a^4 - a^3 + 11a^2 - 8a + 28=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4113.1
-4152
1:
0.8339146737591420589701633138020968240791287479507094288808179928580915260092849327489080071104079955
comment: $a^4 - a^3 + a^2 - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4152.1
-4192
1:
0.9802262912052321447993059927956687011114487277506262006561746152760474951788303960885641927900331051
comment: $a^4 + a^2 - 2a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4192.1
-4204
1:
1.010688631137876244938541572923473192463581345765690115043746863162563112909076170190473110427606588
comment: $a^4 - 2a - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4204.1
4205
1:
0.3484299120160830224080817314798272218315973207806364185419189817279020594866096147508428470823429892
comment: $a^4 - a^3 - 5a^2 - a + 1=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.4205.1
4212
1:
1.779535535938307773523443293809992785001883686187000542030562110952498840356039224211356397081789434
comment: $a^4 - a^3 + 3a^2 + a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4212.1
4221
1:
0.7033335926474614712588727664149551639871015022260379036730762579650289545529472611084414348970459106
comment: $a^4 - 2a^3 - 8a^2 + 9a + 27=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4221.1
4221
2:
0.4195442978859501731742999181449544866543908132182602773888250881530939903976145343800972743388694998
comment: $a^4 - a^3 - 10a^2 + 4a + 31=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4221.2
4225
1:
0.9553493348910211501650079145010601688582235600195044781452613226797889243230662853351128345945029206
comment: $a^4 - a^3 - 3a + 4=0$; signature $(0,2)$; 4T4; $h_K=2$; $w_K=2$; LMFDB 4.0.4225.1
4225
2:
0.3929326368169119249781027502489952729544364941650103896136042442430213989979546725973545845168683865
comment: $a^4 - 9a^2 + 4=0$; signature $(4,0)$; 4T2; $h_K=1$; $w_K=2$; LMFDB 4.4.4225.2
4232
1:
1.300832595321692376269181535843686197039078362573027779665309955970149334001234701287429735253797940
comment: $a^4 - a^3 + 4a^2 + a + 1=0$; signature $(0,2)$; 4T3; $h_K=3$; $w_K=2$; LMFDB 4.0.4232.1
4240
1:
1.306380279002928297972227033690801670601587605840978523005733046362728987981040152765200008200324026
comment: $a^4 - 5a^2 - 6a + 18=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.4240.1
4240
2:
0.6701066895396601132109231175523795925388278932686247597442548281449167041261412335995004807335859582
comment: $a^4 - a^2 - 8a + 17=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.4240.2
4257
1:
0.9150725175003948302116129764786228765791846151107415281280798634946850402839706939506966032827562146
comment: $a^4 - a^3 + 5a^2 - 2a + 1=0$; signature $(0,2)$; 4T5; $h_K=2$; $w_K=2$; LMFDB 4.0.4257.1
-4275
1:
0.3519751798968383208747640656490607406258066738905421178268902308142877034289729582326939396672533376
comment: $a^4 - 2a^3 + a - 11=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4275.1
4281
1:
0.9624090791892074431843597354595283396661904241784338618003706563167749581500566169684247008129174334
comment: $a^4 - a^3 - a^2 + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4281.1
-4287
1:
0.7709443236347495459576081769759880270940159444280717274194606228260173732572118023512055262606924468
comment: $a^4 - a^3 + 2a^2 - a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4287.1
4312
1:
1.924015877268594458254730418483285998428674583572669648973397736883429129310464291900369405094194399
comment: $a^4 - a^3 - 3a^2 - a + 8=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.4312.1
4312
2:
0.9054637954761407324222619422559755306863825419405836057500214590353600004394700745525660599655241129
comment: $a^4 - a^3 + 2a^2 - 7a + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.4312.2
-4319
1:
0.7818476373773346492778606168574366770480346316425967526728718205946946121101294444855702286152341070
comment: $a^4 - a^3 - 4a^2 - a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4319.1
4329
1:
0.6128779883267946481163691639471800084617047317883366354456605862125154419228113077546938510259997629
comment: $a^4 - a^3 - 10a^2 + 7a + 31=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=6$; LMFDB 4.0.4329.1
4329
2:
0.6032927834486552202514490439736109689551901757106743295373018452476173915967168999449696721994577680
comment: $a^4 - a^3 + 11a^2 - 2a + 28=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=6$; LMFDB 4.0.4329.2
4344
1:
1.169232295197857937319761438080197137541969063910561601342979082988056555224187469545936481146484879
comment: $a^4 - a^3 + 4a^2 - 3a + 5=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4344.1
4345
1:
1.084252241061947954770189361006274079867411818307142260323706609534089086750602719373573603479420488
comment: $a^4 - a^3 + a^2 - 2a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4345.1
4352
1:
0.8330330145530126867968500692586536767795904583930293432542997544941519671042131798082947419671779998
comment: $a^4 - 8a^2 + 17=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=4$; LMFDB 4.0.4352.1
4352
2:
0.5071022941838702209667782551955032166508426910434971745791686955798654623407024294465330070052381777
comment: $a^4 - 6a^2 - 4a + 2=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.4352.2
4352
3:
1.162769867765241475543500441329956536505672219508401076639994357545051047620552789789378573595399233
comment: $a^4 - 2a^2 - 4a + 6=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=2$; LMFDB 4.0.4352.3
4360
1:
1.125542094393740209225741836420895088415541034331161620477868338676482419412340727701979418665839028
comment: $a^4 - a^3 + a^2 + 2a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4360.1
-4384
1:
1.017921965178940839138754698321122017871625326186631188105272260149335134517174767578487871189140680
comment: $a^4 - 2a^3 + 3a^2 - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4384.1
4400
1:
0.3968029057391835275519233514720113274073406451591636350847578123245620455909455246486545361500586213
comment: $a^4 - 7a^2 + 11=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.4400.1
4400
2:
0.5727956156241087504355952826982492465335060152629233718656263005742938647648385855948736338402995368
comment: $a^4 + 7a^2 + 11=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=2$; LMFDB 4.0.4400.2
-4400
1:
0.4265477713614140910692460513000308007736471862613086385803964308870415135828807278555319350769914451
comment: $a^4 - a^2 - 11=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4400.1
4401
1:
0.7750615724564086716616106381853301932582387438149541269912850371038336303542880200740606914500887094
comment: $a^4 - 2a^3 - 9a^2 + 10a + 28=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4401.1
-4423
1:
0.7307761466425224397044363843543341008529647874549770301600123902116626901053449339961005252530792148
comment: $a^4 - a^3 - 3a^2 + 4a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4423.1
-4432
1:
0.6653827370332626665397214440882991855209600233050551670249470016201422794409236444449030884846562462
comment: $a^4 - 2a^3 - a^2 - 4a + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4432.1
4464
1:
0.8579969359834019789311466733579538976821162437947374433228725423785851924228457341760665773700359072
comment: $a^4 - 11a^2 + 31=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4464.1
4464
2:
0.4972714952622811553731069060213667140623170477161298178062367027693151247939195986473001677850123205
comment: $a^4 + 11a^2 + 31=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4464.2
-4475
1:
0.4438802982964714197053142018584880854577365153144015457797490979230835608473152780686968197471060537
comment: $a^4 - 2a^3 + 2a^2 - a - 11=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4475.1
4477
1:
0.4950146626542755869683809997733143408630926332750374359787106062070687982935898293845130487264508756
comment: $a^4 - a^3 - 4a + 5=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.4477.1
4481
1:
0.6321157794353880384280244558627801520281312177344495882208253055460562778461395177499285596538073320
comment: $a^4 - a^3 - 2a^2 + a + 5=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4481.1
-4491
1:
0.6310345741116074696329638870357396024692414970281201713426528763030360448369732449331444331641545308
comment: $a^4 - 2a^2 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4491.1
-4492
1:
0.9899211692961469692252177290697644652863626612850922929660613947423647007414089433478633323568142103
comment: $a^4 - a^3 - a^2 + a - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4492.1
4493
1:
0.6866507387137623579872592827797741422462896766457975769877641871707326867235203112975335440998850275
comment: $a^4 - a^3 + 4a^2 - 4a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4493.1
4496
1:
0.3967691507536630770780239049084463027579790150605382409517672304046631817245891851050277545883769481
comment: $a^4 - 2a^3 - a^2 + 2a + 17=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.4496.1
-4503
1:
0.7732843181653433955409188045191096880638250231496910180960571815669825643756418537171915616289267796
comment: $a^4 - 2a^3 + a^2 - 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4503.1
4508
1:
1.921446021369750589454781693608738658903037229552139390174295894887498427087664403260445780775930278
comment: $a^4 - a^3 - 6a + 8=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.4508.1
4508
2:
1.981680264041474892909506192679469528272308481690039864510698852134332517770549745735081279296157777
comment: $a^4 - a^3 + 6a^2 - 2a + 4=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.4508.2
4525
1:
0.3633417635546818562267086418376046322232990786669762119981831680243687620322651427673053272900302401
comment: $a^4 - a^3 - 7a^2 + 3a + 9=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.4525.1
-4544
1:
0.4556384466449823853817326381111933535364632400841007190505465260443865088689132255472906414278134297
comment: $a^4 - 2a^3 + a^2 - 6a - 1=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4544.1
-4564
1:
0.7567348099076937449565874019005017184260006681533380258246228879145220963378507290060651145572509772
comment: $a^4 - a^3 - 5a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4564.1
-4568
1:
0.8438101547657401591882847460584637823908921034475021757223367126759005846244107537801686366217829817
comment: $a^4 - a^3 + 2a^2 - 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4568.1
-4595
1:
0.5208848269866668850467430021920700886069805394728999584962462449968432684597506175614244889837003102
comment: $a^4 - 2a^3 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4595.1
4596
1:
1.607171510308599664017375064756372432456249648501528828600964340393540246417468964511375572170223640
comment: $a^4 - a^3 + a^2 + 3a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4596.1
4608
1:
0.8473607184935922448654537463996696269379685986980850596649373514081834583785198153909668766850660700
comment: $a^4 - 6a^2 + 18=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=4$; LMFDB 4.0.4608.1
-4608
1:
0.9156057619314705506863693687466074579648398276632406093903341096848892692914983014681230247253999775
comment: $a^4 - 2a^2 - 2=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4608.1
-4608
2:
0.6225007896448082080062303338641821339829257093661417442418717551758475503968060777505711416280740096
comment: $a^4 + 2a^2 - 2=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4608.2
-4615
1:
0.6696101580217945118709646593195427700722015064354954793540204973552625309602146372617158925841826144
comment: $a^4 - a^3 + a^2 - 4a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4615.1
4624
1:
1.216116716203839202933178235166026574412075653096519654075863121310924764852172793196351507434105949
comment: $a^4 + 9a^2 + 16=0$; signature $(0,2)$; 4T2; $h_K=2$; $w_K=4$; LMFDB 4.0.4624.1
-4648
1:
0.7092155859157675935152228063722026076601108267033657175326852847029264372424699253045875671863657432
comment: $a^4 + a^2 - 6a - 4=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4648.1
4649
1:
1.222297581353883475696538443262434906738922369191132726427063993708812438647852380344793440386026394
comment: $a^4 + 3a^2 - 3a + 2=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4649.1
-4652
1:
0.9870472491429249281555772265322922318883828414316463834354063987575560664891602351215524326673841930
comment: $a^4 - a^3 - 3a^2 + 5a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4652.1
-4663
1:
0.6265378422311593350925079131445522034360153328563472638288563518142702408147167140677480865938985547
comment: $a^4 - a^3 + 2a^2 - 5a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4663.1
-4671
1:
0.8211394207544451183523062212327395232142984368817417612211026058513178508746001524546120971578979838
comment: $a^4 - 2a^3 + 3a^2 + a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4671.1
4672
1:
1.219225288781253160928898929004755474084649254283879320040948164269260174099228852710363445158509463
comment: $a^4 - 2a^3 + 3a^2 + 4a + 2=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.4672.1
4672
2:
0.5090592708494132496240188977430477427826186726803696701365495348287660062648996714744437206215033240
comment: $a^4 - 2a^3 + 5a^2 - 2a + 7=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.4672.2
-4675
1:
0.4461966622938490101931273501839075355305274914217718286133424242520492355540617341058528396872892912
comment: $a^4 - 2a^3 - 3a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4675.1
4684
1:
1.167101794831886912592840125357818448235372276531498856089365522131096893546357151224512712968420096
comment: $a^4 - a^3 - 2a^2 - a + 5=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4684.1
-4703
1:
0.6333760489831795473835134032047609818226597286972318258902602028855568008166513004162359881711717223
comment: $a^4 - 3a^2 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4703.1
4725
1:
0.5820150007227292478303061032891084458170498035803837366858855673277145394354154937122869407558687315
comment: $a^4 - a^3 + 12a^2 - 4a + 31=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=6$; LMFDB 4.0.4725.1
4729
1:
1.044275349617821794575834175453660949565270943699300669266351608812855964923334365967008399109851821
comment: $a^4 + 3a^2 - a + 4=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4729.1
-4744
1:
0.7128729099203267508752572946035706941908904966390748379232511004007702236038153114651312098920959572
comment: $a^4 - 3a^2 - 4a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4744.1
-4748
1:
0.9911418967206875485601198502815184918861642973325329965189897767574199085790930186636988228329943489
comment: $a^4 - a^3 - 3a^2 - a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4748.1
4749
1:
0.5553609279976557674617177665361583763928091973694358719939407206684101998195880698404356671350387281
comment: $a^4 - a^3 - a^2 + 3a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4749.1
4752
1:
0.4300109381673870969308128791565952694345424134997946215187853611064537152775308432712504894665788379
comment: $a^4 - 2a^3 - 3a^2 + 4a + 1=0$; signature $(4,0)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.4.4752.1
4752
2:
1.508423907997212796198993816789788763433428294163656477198879161831585778724043469348274679474351474
comment: $a^4 + 3a^2 - 6a + 6=0$; signature $(0,2)$; 4T3; $h_K=2$; $w_K=2$; LMFDB 4.0.4752.2
-4752
1:
0.6804841977247684767158824199810921523643067093143166357774818842419044213501094012706623283222554721
comment: $a^4 - 3a^2 - 2a + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4752.1
4761
1:
0.9203826552473944457489538849188578103030149914357998811857223840512872488417958613441667969506399002
comment: $a^4 - a^3 - 5a^2 - 6a + 36=0$; signature $(0,2)$; 4T2; $h_K=3$; $w_K=6$; LMFDB 4.0.4761.1
-4775
1:
0.4959742193821442537105581426732367961502144681486940382095493461594186555568000809971303571306193501
comment: $a^4 - a^3 + 2a^2 - 9a - 9=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4775.1
-4780
1:
1.032374322324133096009884465883878581133394780179675734470868431514253897244464405330173736785950978
comment: $a^4 - a^3 - 3a^2 - 3a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4780.1
-4799
1:
0.6440734856949453135535975650855027947169384182061200353321128499215599554432856537295129008264734861
comment: $a^4 - a^3 - 4a^2 + 5a + 3=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4799.1
4805
1:
1.540779012117060286596921090705574600977559572576714149934579886711895116727404830430685979631920349
comment: $a^4 - 2a^3 + 2a^2 - a + 8=0$; signature $(0,2)$; 4T3; $h_K=3$; $w_K=2$; LMFDB 4.0.4805.1
4825
1:
0.8929072652857918872594207012745480621354563296197639997434119593507810614726973817040978987830748782
comment: $a^4 - a^3 + 2a^2 - 3a + 5=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4825.1
-4832
1:
1.162701819713509319800860920191786757197275383658773681111033784659915316376966396481856322415388003
comment: $a^4 - a^2 - 4a - 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4832.1
4857
1:
1.447915143883379980818640789342385952363151627264808304618574243243757403353974353969203340753530590
comment: $a^4 - a^3 + 5a^2 - 2a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4857.1
-4864
1:
0.6785776050151464759741165951393510518507883631868455852854823538862995991287671811560555152744162928
comment: $a^4 - 4a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4864.1
4869
1:
0.3000203972439990948309938668104491941753054523217140929334580703649547846601409851615719458233688033
comment: $a^4 - 2a^3 - 10a^2 + 11a + 31=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4869.1
4880
1:
0.6328109317544576489661685013552452308861193964547094608540937504465211481182364139430378444436804377
comment: $a^4 - 2a^3 - 7a^2 + 8a + 17=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.4880.1
4880
2:
1.500147362018928483599818810552710008887104993510039151774006020032042209476576113829546712740464294
comment: $a^4 - 3a^2 - 8a + 20=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=4$; LMFDB 4.0.4880.2
4892
1:
1.318396432426602164060577620556117965298830355585536007762102593811596794556749154681764328082339957
comment: $a^4 - a^3 - a + 3=0$; signature $(0,2)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.0.4892.1
4901
1:
0.6737506995842861394711315810088305122002986090253318880264939687100094326669055640063857954610536751
comment: $a^4 - 2a^3 + 6a^2 - 5a + 3=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.0.4901.1
-4907
1:
0.4790932659757039909164028634774170261985309308133736813771885512758938655564696738818232537831686634
comment: $a^4 - a^3 - 2a^2 - 4a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4907.1
4913
1:
0.3951320475534474519181666267861194003880049225163225922739074444575234762548627817867234552182588407
comment: $a^4 - a^3 - 6a^2 + a + 1=0$; signature $(4,0)$; 4T1; $h_K=1$; $w_K=2$; LMFDB 4.4.4913.1
-4944
1:
0.5815705936256013423330108857013115023585217776454371378401820053513918898768798847691064726160629619
comment: $a^4 - a^2 - 4a - 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4944.1
-4975
1:
0.5728813404446651571863933706349391372211109115827187948006134995527026950257369285607316957069936856
comment: $a^4 - a^3 - 2a^2 - 7a - 11=0$; signature $(2,1)$; 4T3; $h_K=1$; $w_K=2$; LMFDB 4.2.4975.1
4977
1:
0.9555339899910433126152348866877397016142431924755260195581090885174134718112613704816881765673301188
comment: $a^4 - a^3 - 11a^2 + 6a + 36=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4977.1
4977
2:
0.6556909593018139644517556588739887658809163158022219266172063925736464880865994810759423005656247885
comment: $a^4 - a^3 - 10a^2 + a + 37=0$; signature $(0,2)$; 4T3; $h_K=1$; $w_K=6$; LMFDB 4.0.4977.2
-4979
1:
0.5041431476345104116654098913319699602602932654187251377333246068089743298218651926375973698009297419
comment: $a^4 - a^3 - a^2 - 3a + 1=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4979.1
-4999
1:
0.6736860425573657677641664106396645127480255708198622105011416487477821814131717449181444501833428088
comment: $a^4 - 2a^3 - a^2 - a + 2=0$; signature $(2,1)$; 4T5; $h_K=1$; $w_K=2$; LMFDB 4.2.4999.1
Definition
Let $K$ be a quartic field [2] of discriminant $D$ and $\zeta_K(s)=\sum_{\mathfrak{a}}N(\mathfrak{a})^{-s}$ its Dedekind zeta function [1], summed over the nonzero ideals of $\mathcal{O}_K$. Listed is $\kappa_K=\lim_{s\to 1}(s-1)\zeta_K(s)$, the residue of $\zeta_K$ at its pole $s=1$.
Parameters
$D$
—   discriminant of $K$ ($D$ the discriminant of a quartic field)
$k$
—   index of $K$ among the quartic fields of discriminant $D$ ($k\geq 1$)
Formulas
(1)
$\kappa_K=\frac{2^{r_1}(2\pi)^{r_2}h_KR_K}{w_K\sqrt{|D|}}$, where $(r_1,r_2)$ is the signature, $h_K$ is the class number, $R_K$ is the regulator and $w_K$ is the number of roots of unity in $K$ [3] [4].
Comments
(2)
The fields of discriminant $D$ are numbered $k=1,2,\ldots$ by reducing their defining polynomials with PARI's polredabs and sorting the reduced polynomials lexicographically by the coefficient vector $(a_3,a_2,a_1,a_0)$ of $x^4+a_3x^3+a_2x^2+a_1x+a_0$. This is the same $D,k$ convention used for the table of residues of Dedekind zeta functions of cubic fields. For the entries in this table, $k$ agrees with the last component of the LMFDB label.
(3)
The sign of $D$ does not determine the signature of a quartic field. A negative discriminant means signature $(2,1)$, while a positive discriminant can mean either signature $(4,0)$ or $(0,2)$. The signature is therefore stated in each entry comment.
(4)
The comment on each entry gives the reduced defining polynomial $f$, so that $K=\mathbb{Q}(a)$ with $f(a)=0$; the signature; the Galois group of the Galois closure as a 4T label, where 4T1 is $C_4$, 4T2 is $V_4$, 4T3 is $D_4$, 4T4 is $A_4$ and 4T5 is $S_4$; the class number $h_K$; the number $w_K$ of roots of unity in $K$; and the LMFDB label.
(5)
Among these 456 fields, $w_K=2$ for 338 fields, $w_K=4$ for 44 fields, $w_K=6$ for 71 fields, and the three remaining fields are the cyclotomic fields $\mathbb{Q}(\zeta_8)$ at $D=256$, $\mathbb{Q}(\zeta_5)$ at $D=125$ and $\mathbb{Q}(\zeta_{12})$ at $D=144$, with $w_K=8$, $10$ and $12$, respectively. $w_K$ is a factor in the class number formula (1).
(6)
The residue is that of $\zeta_K$ itself. The completed Dedekind zeta function has a different residue at $s=1$.
Programs
(P1)
PARI/GP
default(realprecision, 110);
f = x^4 - x^3 + x^2 - x + 1;       \\ D = 125
K = bnfinit(f, 1); bnfcertify(K);
\\ class number formula
2^K.r1 * (2*Pi)^K.r2 * K.no * K.reg / (K.tu[1] * sqrt(abs(K.disc)))
\\ residue from PARI L-function machinery
polcoef(lfunrootres(lfuncreate(f))[1][1][2], -1)
Links
Similar tables
Residues of Dedekind zeta functions of quadratic fields —   the same residue for degree two, where $\kappa_K=L(1,\chi_D)$ is a single Dirichlet $L$-value
Residues of Dedekind zeta functions of cubic fields —   the same residue for degree three, with the same $D,k$ convention for non-isomorphic fields sharing a discriminant
Values of Dirichlet $L$-functions at positive integers —   for abelian quartic fields, the quotient $\zeta_K(s)/\zeta(s)$ factors into Dirichlet $L$-functions
Data properties
Entries are of type: real number
Table is complete: no (it holds every quartic field with $|D|\leq 5000$: 20 totally real, 180 of signature $(2,1)$ and 256 totally complex)
How they were obtained:

Each value is a real ball from the class number formula (1) at 525 bits, using numberdb.bits(100, losing=192).

more

The fields are enumerated by PARI's nflist("C4", [1, 5000]), nflist("V4", [1, 5000]), nflist("D4", [1, 5000]), nflist("A4", [1, 5000]) and nflist("S4", [1, 5000]), then sorted by $|D|$, positive $D$ before negative $D$ at the same absolute value, and then by $k$; the generator refuses to run unless it finds 456 fields with signature counts 20 of $(4,0)$, 180 of $(2,1)$ and 256 of $(0,2)$. The class number, roots of unity and fundamental units are PARI's, from bnfinit(f, 1), and bnfcertify is required to return 1 for every field. The fundamental units are taken exactly as polynomials in $a$; PARI's floating regulator is not used for the stored value. The roots of the reduced polynomial are isolated as complex balls, the units are evaluated at those roots by Horner's rule, and the regulator is the determinant of the logarithmic embedding matrix, with weight 1 on real embeddings and weight 2 on complex embeddings. The value is then formed with arb's $\pi$ and square root. The dry run checked that every row carries 100 digits, and compared all 456 residues with PARI's lfunrootres(lfuncreate(f)), a computation from the Dedekind zeta function rather than from bnfinit; there were no disagreements at the 100 digits stored here.