NumberDB$^\beta$ Advanced search Tags Tables Help Login
Zeros of the Dedekind zeta functions of cubic fields
edit · history · discussion · files · short url · zero L-function number theory
Numbers
$D$
$k$
$n$ 
$t_n$
-23
1
1:
5.11568332881511759855335642038
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-23
1
2:
7.15926229054170384129282782025
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-23
1
3:
8.88139657368917747496582449161
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-23
1
4:
10.2820274008521320537161800380
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-23
1
5:
11.4300363530481331189620599022
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-23
1
6:
12.9344096677184118357911814571
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-23
1
7:
14.1347251417346937904572519836
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1. Also the first Riemann zeta zero.
-23
1
8:
14.6624809545746591259804853628
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-23
1
9:
16.4982325133624013415753166534
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-23
1
10:
17.1012633035818315519487234446
comment: $a^3-a^2+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.23.1.
-31
1
1:
4.16621475268391289462455833400
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-31
1
2:
6.92572000323394459470037275402
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-31
1
3:
8.19816519868579761862437968182
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-31
1
4:
9.56826251139133716070629294145
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-31
1
5:
10.6396543841218861214415560419
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-31
1
6:
12.3188881392175172712523199379
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-31
1
7:
13.4764381420797387764467519852
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-31
1
8:
14.1347251417346937904572519836
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1. Also the first Riemann zeta zero.
-31
1
9:
15.3695501682702614557343535078
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-31
1
10:
16.1872992044860377748055637342
comment: $a^3+a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.31.1.
-44
1
1:
4.04199480857272067821281564908
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
-44
1
2:
5.79558660706818170317355578628
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
-44
1
3:
7.24907980722071614777800764527
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
-44
1
4:
8.81133696068555360396619471060
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
-44
1
5:
10.5571568107817743927169482003
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
-44
1
6:
11.7030880303261415592286595684
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
-44
1
7:
12.2248556361922555672026661318
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
-44
1
8:
13.9985159314585654821153664306
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
-44
1
9:
14.1347251417346937904572519836
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1. Also the first Riemann zeta zero.
-44
1
10:
15.2731906281385718677303786526
comment: $a^3-a^2+a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.44.1.
49
1
1:
4.35640162473628422727957479052
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,2,1)$.
49
1
2:
6.20123004275588129466099054629
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,4,1)$.
49
1
3:
7.92743089809203774838798659747
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,4,2)$.
49
1
4:
8.78555471449907536558015746318
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,2,2)$.
49
1
5:
10.7361199874933931158742415350
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,2,3)$.
49
1
6:
11.0104448620724904223936274109
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,4,3)$.
49
1
7:
12.5325478226862740080723048004
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,2,4)$.
49
1
8:
13.8298678998613675706123680948
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,4,4)$.
49
1
9:
14.1347251417346937904572519836
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also the first Riemann zeta zero.
49
1
10:
15.9374482046879595568895739989
comment: $a^3-a^2-2a+1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.49.1. Also Dirichlet $L$-function row $(7,2,5)$.
-59
1
1:
3.43180500410537741355091128030
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-59
1
2:
5.64723355410045232763599810849
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-59
1
3:
6.74805173897083286463010363905
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-59
1
4:
7.98875146988432074682400608909
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-59
1
5:
10.0068413808669359751813789876
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-59
1
6:
11.0991516556473106832852057631
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-59
1
7:
11.9697864819217872426029945010
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-59
1
8:
12.6666594262765883035083861068
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-59
1
9:
14.1347251417346937904572519836
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1. Also the first Riemann zeta zero.
-59
1
10:
14.6342077392872255962996104738
comment: $a^3+2a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.59.1.
-76
1
1:
3.27623368738075539180170835921
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
2:
4.83345700374897654801370031599
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
3:
6.75966056696874593751657456611
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
4:
7.71021732429554568325384670285
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
5:
9.20001160549634519820911967848
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
6:
10.3736301733033595817998038829
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
7:
11.5236549472489280126861156437
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
8:
12.8038309419503697159446827205
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
9:
13.3597491635213031679464190124
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1.
-76
1
10:
14.1347251417346937904572519836
comment: $a^3-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.76.1. Also the first Riemann zeta zero.
81
1
1:
3.44409315514894385547842266783
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,7,1)$.
81
1
2:
5.31957512328119563183789417848
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,4,1)$.
81
1
3:
7.53243305229040689175343096160
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,7,2)$.
81
1
4:
7.83467143898723227716911760380
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,4,2)$.
81
1
5:
9.62077285324898946095116559053
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,4,3)$.
81
1
6:
10.0165504225653356054500551868
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,7,3)$.
81
1
7:
11.5836490823449833912540673143
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,7,4)$.
81
1
8:
12.6018133930145292037928350512
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,4,4)$.
81
1
9:
13.7919495090786679090840173238
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also Dirichlet $L$-function row $(9,7,5)$.
81
1
10:
14.1347251417346937904572519836
comment: $a^3-3a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.81.1. Also the first Riemann zeta zero.
-83
1
1:
2.91606813106134337451054950253
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
2:
5.25394517311578314477026475826
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
3:
6.37890239293184761621864982629
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
4:
7.30510568839843872365517009292
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
5:
9.12164732789875808832984710751
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
6:
10.7655501024998389194578617095
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
7:
11.0144660462901178155154452949
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
8:
12.4399090886020222424083716401
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
9:
13.0958961308625314646454574320
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1.
-83
1
10:
14.1347251417346937904572519836
comment: $a^3-a^2+a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.83.1. Also the first Riemann zeta zero.
-87
1
1:
2.68368590772453422884570720998
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
2:
4.60444267458741594170483479006
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
3:
6.89861709118401082750268414601
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
4:
7.93997982908517054307383451315
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
5:
9.00485870621599583588540728973
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
6:
9.80523198552379903395122224850
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
7:
10.6571648784666296938077494135
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
8:
12.6699776878520391382831240899
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
9:
13.3216286251074918435443227037
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1.
-87
1
10:
14.1347251417346937904572519836
comment: $a^3-a^2+2a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.87.1. Also the first Riemann zeta zero.
-104
1
1:
3.31991104814500528755495843356
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
2:
4.62506222520716784109149308317
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
3:
6.08438169252065874846073663176
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
4:
6.80322656561684872784900392938
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
5:
8.37484590158824610994063609007
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
6:
10.2845562603978833145393739131
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
7:
11.3342776373652742369250167892
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
8:
11.8797001942413505676132597498
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
9:
12.9114862993119210016927933869
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-104
1
10:
13.8174163992651118089381580425
comment: $a^3-a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.104.1.
-107
1
1:
2.61608028997495214067096557530
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
2:
4.91802014171830707927308424854
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
3:
6.07457868538096646079651191674
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
4:
7.08658080864405272708817928649
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
5:
8.37372444597854522348080697503
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
6:
10.3180553532511425159897534615
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
7:
10.7186768503161740145979495597
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
8:
12.0450463843005123831141240306
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
9:
12.4171412676736742042789749463
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-107
1
10:
14.0401133799508104282963592242
comment: $a^3-a^2+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.107.1.
-108
1
1:
2.82161410923512167788607608967
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
2:
4.54012115448883134462155601253
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
3:
6.14349374284521055741894837740
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
4:
7.20655230074699554971488628053
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
5:
8.64538226151008669060911154299
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
6:
9.76436329077079209303658135031
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
7:
10.6633741771792486113756723532
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
8:
12.1139339152027562291113616274
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
9:
12.8114791015126280000356117197
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-108
1
10:
13.9283627107495041063349739228
comment: $a^3-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.108.1.
-116
1
1:
3.11568281765995191104117732931
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
2:
4.78764434142051405584396595400
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
3:
5.56304821134120925869298444888
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
4:
7.05540575330027098655761742099
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
5:
7.92765030972844696810060804427
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
6:
10.0458105286278241152059053350
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
7:
11.1670011854711225000664033158
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
8:
11.8409394345589871155866724597
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
9:
12.4973815540611687557226972521
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-116
1
10:
13.7425410651869158564279753655
comment: $a^3-a^2-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.116.1.
-135
1
1:
2.04028622872293924908533618653
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
2:
4.40323847289512931191199822637
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
3:
5.91615283308312356244034077336
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
4:
7.19935214621441948680617539145
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
5:
8.54830844078122838413455984162
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
6:
9.25356617798387847527541670059
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
7:
10.2558420672176129008938743283
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
8:
10.9865268251572600386453776539
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
9:
12.5944916393826430514216897310
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-135
1
10:
13.5157954558894152961197329826
comment: $a^3+3a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.135.1.
-139
1
1:
2.66179846285285138206480629918
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
2:
4.11573798899198049206922353487
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
3:
5.86677026918997662476998228562
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
4:
7.35631300481673533663894301533
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
5:
7.57866083817513426866234166095
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
6:
9.48634328207225108171108460256
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
7:
10.4412841288435418112798523686
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
8:
11.4087056203312827070567082359
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
9:
12.5342529157492353887071824376
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-139
1
10:
12.9648815259172565011972730587
comment: $a^3-a^2+a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.139.1.
-140
1
1:
2.27790387327828597147359808295
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
2:
4.87037486212895093408596806754
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
3:
5.48530009143023484215244134133
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
4:
6.75170062241563553981571022546
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
5:
8.10224519059734892696175582751
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
6:
9.43685697661549615433270461316
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
7:
10.6037372289822052017227315766
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
8:
11.2164447954725975897665577191
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
9:
12.3472340847898561662585839818
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
-140
1
10:
13.3306595696559752352154597166
comment: $a^3+2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.140.1.
148
1
1:
3.02402457845854349928081788748
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
2:
4.87864320119026148049100252598
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
3:
5.95486053183384985612905470167
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
4:
6.90848927933297428906833247723
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
5:
8.33078166480158471639098271155
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
6:
9.68847801375007334704989928251
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
7:
10.6008220063735483907258878678
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
8:
11.4891799862590870517287366906
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
9:
12.5882202039618661809953996669
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
148
1
10:
13.2060401279404980055744421014
comment: $a^3-a^2-3a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.148.1.
-152
1
1:
2.81196093969486835641282132237
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
2:
4.44276652764072509073740472545
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
3:
5.63050345906219303013958354741
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
4:
6.46055524279898288954266410418
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
5:
7.50781507085966449620544772843
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
6:
9.42087425267305730764695590980
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
7:
10.5609652201555853897977733983
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
8:
11.4814938104995866001223060200
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
9:
12.2922397496184178050230044421
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
-152
1
10:
13.0398444898364319641337611517
comment: $a^3-a^2-2a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.152.1.
169
1
1:
2.27313120101337092309675281123
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
2:
4.93859080845797714546122535766
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
3:
5.99433348263937573006936411548
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
4:
6.72931431168193311808562367957
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
5:
8.53434388229500193005541581861
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
6:
9.41417590921434401761017724708
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
7:
10.4577203249968513470332103487
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
8:
10.5067304850587946646257491285
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
9:
12.3257791686484817550992480946
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
169
1
10:
13.5107310282236992280186293871
comment: $a^3-a^2-4a-1=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.169.1.
-172
1
1:
2.35670911882733759644017786160
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
2:
4.19809950446455928248174479522
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
3:
5.34140749834004115624777493653
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
4:
6.86965809762068103157240752340
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
5:
7.70960526269496431025401906497
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
6:
9.00860936938666331437587547967
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
7:
10.1063213544182712877605435520
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
8:
10.8365130347789002846060302619
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
9:
12.2078041477399431081302812348
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-172
1
10:
12.8994367799962877981891467872
comment: $a^3-a^2-a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.172.1.
-175
1
1:
1.81080441085222069438971480503
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
2:
4.20961109287914824166132706629
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
3:
5.32772362441185835516557683036
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
4:
7.21219424452815957631789646245
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
5:
7.92837131535862270975552877516
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
6:
8.84686412004040775244386586334
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
7:
10.0650349989415666961447594020
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
8:
10.5854368898872801597585578215
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
9:
11.7733147476762638121980745850
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-175
1
10:
13.0367079545611763890086677207
comment: $a^3-a^2+2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.175.1.
-199
1
1:
1.67161341998937103645071112925
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
2:
4.29247503558023135235147326245
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
3:
4.88681230623114224256968764865
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
4:
7.18387079154334138510864033589
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
5:
7.90541660264201801355233356379
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
6:
8.42571972708023916626061670116
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
7:
9.77926445104291396362291433340
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
8:
10.6517714435262275585893404438
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
9:
11.5807540332586238553908784362
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-199
1
10:
12.3740074603353100455636141316
comment: $a^3-a^2+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.199.1.
-200
1
1:
2.52234865889530633241732947678
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
2:
4.28007171288186451228709174476
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
3:
5.32800143650698036361882960749
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
4:
6.18472913252883355576995074341
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
5:
7.21128182081198107883185711576
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
6:
8.56238816798914659850081622607
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
7:
10.3485689214126456117420985553
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
8:
10.9425959516058828657506837239
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
9:
11.7904745316646832661327299301
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-200
1
10:
12.7145352123240832149088728800
comment: $a^3-a^2+2a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.200.1.
-204
1
1:
2.51256673938332341097950717807
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
2:
3.79943974802985091918625662732
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
3:
4.97602311316391520571027185228
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
4:
6.82424899172616989471966838318
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
5:
7.96520298491030989847142670306
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
6:
8.28493695296874602117977978764
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
7:
9.80522212135004220977252318641
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
8:
10.4763145852070600938075997600
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
9:
11.9771606259802337928684456620
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-204
1
10:
12.5529323502092980298802890903
comment: $a^3-a^2+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.204.1.
-211
1
1:
2.29906709754737556376540443181
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
2:
3.83733924492078633030089718140
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
3:
5.18037386937466737132796711185
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
4:
6.77516729846439138358216471580
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
5:
7.46386740565527729315092106349
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
6:
8.32493261679440743297775605021
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
7:
10.0103816335674742323417109198
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
8:
10.6407865743842104618527615070
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
9:
11.7410421905341398775246101831
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-211
1
10:
12.3981478795818006598036011503
comment: $a^3-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.211.1.
-212
1
1:
2.46540880625352001412354028566
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
2:
4.26287604595125770225335555293
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
3:
5.19875632721977887819430442161
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
4:
6.25028881503830103293354510395
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
5:
7.04796772458452462662713597640
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
6:
8.48148302499790620706432521973
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
7:
10.1444523810590730364192661132
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
8:
10.9162755379984152487377736947
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
9:
11.8290166565810911672464869172
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-212
1
10:
12.4175094804517159096993494719
comment: $a^3-a^2+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.212.1.
-216
1
1:
2.79656583583197594606532856647
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
2:
3.85183234514156199639611073758
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
3:
5.07819128334573110974618909847
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
4:
6.34543035073293253125567470780
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
5:
7.34271926859890419731453562697
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
6:
8.30481637294354541132796471427
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
7:
9.92674613850641886947185069303
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
8:
10.8395222492821691047393348975
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
9:
11.8375298604226618491787041748
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
-216
1
10:
12.6198275684702752425853064560
comment: $a^3+3a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.216.1.
229
1
1:
2.61412345021266374323049581032
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
2:
4.29461456252264842722559810495
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
3:
5.62818761405109488655235373710
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
4:
6.58184225753184649419289005406
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
5:
7.58120427715052602250319401476
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
6:
8.52830552639359443799634371179
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
7:
10.2849148746005337961817404181
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
8:
11.0183212818328067961984208055
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
9:
11.5697526287642119471875640783
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
229
1
10:
12.3538718797180677925156155246
comment: $a^3-4a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.229.1.
-231
1
1:
1.84481602371897264273698743490
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
2:
3.86731545897061647676023954686
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
3:
4.71646995003231050683413418513
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
4:
7.05736954382049469435335613157
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
5:
7.78841790295682962863972826426
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
6:
8.51157033945657643953930410541
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
7:
9.25066291171760803152444868974
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
8:
10.2754374562384926368808001059
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
9:
11.3262614112868434229831348756
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-231
1
10:
12.2903444240707849206221849739
comment: $a^3-a^2+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.231.1.
-239
1
1:
2.12721823689176445206298456852
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
2:
3.60015862115289006588450814931
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
3:
4.57630416073136307777408201020
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
4:
7.27397792517399702010481856985
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
5:
7.69989522885676126640744837562
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
6:
8.54408164031426142416167263493
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
7:
9.14074928567424975622358920722
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
8:
10.0914373174536741990408120999
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
9:
11.0221661987581407175263761508
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-239
1
10:
12.6960815562719741858769689278
comment: $a^3-a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.239.1.
-243
1
1:
2.29360994373471085779290231288
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
2:
3.52875960380466377559775254870
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
3:
5.24416125057537026440986145054
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
4:
6.53938700992242303793050246921
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
5:
7.09247574894837359739474398716
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
6:
8.38778109528429702347360373741
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
7:
9.64467519845347444356024523110
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
8:
10.4387197197420871281835230612
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
9:
11.3703820070734425899255077119
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-243
1
10:
12.4669259480099940214465008663
comment: $a^3-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.243.1.
-244
1
1:
2.64366530371542938651687617004
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
2:
3.90413047644985056499535338872
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
3:
4.83876716620938424638612762836
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
4:
6.24928589640252769920597090656
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
5:
7.29655597379814193998474844706
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
6:
7.96995079183456663099087670659
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
7:
9.83150950414055123454825279619
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
8:
10.4548137718526175518901457607
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
9:
11.7701040714038376762077867101
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-244
1
10:
12.4085973683304785801659736299
comment: $a^3+a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.244.1.
-247
1
1:
1.59630075394240554173323349874
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
2:
3.79502311546946690740792804603
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
3:
5.00345205951757721128287907475
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
4:
6.61284406410786800968740889148
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
5:
7.55107587542621149939651423165
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
6:
8.58921361838117016386151387558
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
7:
9.34430734066085401263054297848
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
8:
10.3116100267539018368495048664
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
9:
10.9903383684007666896670078891
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-247
1
10:
12.2425780002474131930317433423
comment: $a^3+a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.247.1.
-255
1
1:
1.96057783206281800387009766832
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
2:
3.37311076360451534786315748985
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
3:
5.05925143337423837129356963346
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
4:
6.54803926281377576894262344659
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
5:
7.66768634965538087787340071306
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
6:
8.56897895046098167229236021961
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
7:
9.44235420618898174441081668256
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
8:
10.0202828585452717263593847445
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
9:
10.6463348998738870852584814891
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
-255
1
10:
12.6713521447495000333943874927
comment: $a^3-a^2-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.255.1.
257
1
1:
2.12932354919355521620135817903
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
2:
4.18839078433142820100221583836
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
3:
5.23478399656574050703032954397
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
4:
6.98909788376183450414678561717
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
5:
7.65206658766707379534710631295
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
6:
8.70243948040811137162035904023
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
7:
9.67281065570776986040954346074
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
8:
10.3180419160390443167581195436
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
9:
11.1787265208650435222282600838
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
257
1
10:
12.6358890509713679154055834187
comment: $a^3-a^2-4a+3=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.257.1.
-268
1
1:
2.02874026216062638503337033778
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
2:
3.82790707357604936833697742214
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
3:
4.86532088144640856003843099768
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
4:
6.31427581930325241144707466325
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
5:
7.17947020257479563698721153454
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
6:
8.34244635302332094746528991669
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
7:
9.32532706270343237687914043186
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
8:
10.3465420987478955053673344798
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
9:
11.1012447348122333663070016017
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-268
1
10:
12.3170276809601353067728001268
comment: $a^3-a^2-3a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.268.1.
-283
1
1:
2.19353375194441133963656582608
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
2:
3.43060415019741538455880658587
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
3:
5.03445355437501277594497173273
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
4:
6.31517765466829869223196098999
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
5:
7.15341918498181596628730190063
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
6:
7.93359343011215227188072282285
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
7:
9.55723750264926372914662087815
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
8:
10.1864841115568513881073394882
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
9:
11.0057049640832808986656269339
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-283
1
10:
12.3551038863908954878713103135
comment: $a^3+4a-1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.283.1.
-300
1
1:
2.30049063152907025395205531779
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
2:
3.44829529350115176093652141218
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
3:
4.65000897702590843147352066318
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
4:
6.25493360265909365346641648673
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
5:
7.22578870015588797157442167915
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
6:
8.17937512577190429443232696111
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
7:
9.29915620670035335434399926125
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
8:
9.81350576198425935960291111844
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
9:
10.8603608406180250230025553870
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-300
1
10:
12.2863571168233397645689636008
comment: $a^3-a^2-3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.300.1.
-307
1
1:
2.13864213402446312922541719952
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
2:
3.39375598982755004590744603711
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
3:
4.89058710548187596266159920229
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
4:
6.37465575081243385422938631770
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
5:
6.88410057798017071551524171991
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
6:
7.96360081657297265905950471898
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
7:
9.20934152864858792596296866197
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
8:
10.4156489719741934850017284315
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
9:
10.6838309539343447847299875107
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
-307
1
10:
12.0346979595033302712305957157
comment: $a^3-a^2+3a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.307.1.
316
1
1:
2.86162610975482018702131280921
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
2:
4.06629248339900530540113998165
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
3:
5.12954852379900098502058150254
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
4:
6.13961979138246811966597449126
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
5:
6.98809059187119979132569733501
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
6:
7.94182236103330433857854981186
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
7:
9.58188613129500362691601287656
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
8:
10.6948408812086627710468904846
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
9:
11.4097102473422887537849157384
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
316
1
10:
12.2730110962591126877864076211
comment: $a^3-a^2-4a+2=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.316.1.
321
1
1:
2.21077375692220258595305893826
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
2:
3.87318368215724466771416154789
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
3:
4.72291988983711031214487129474
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
4:
6.90100096077676159017189895535
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
5:
7.62796703441699356041453387211
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
6:
8.44694917975999930865292698474
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
7:
9.05672803896752390491640139487
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
8:
10.0393303947239617868707995436
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
9:
10.8413535219769782597632191259
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
321
1
10:
12.0401301263983944924403336534
comment: $a^3-a^2-4a+1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.321.1.
-324
1
1:
2.39124768407718997212617200088
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
2:
3.78882632007711462473940508430
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
3:
4.62590085768480636130122278343
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
4:
5.80122382318090507880480519818
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
5:
7.10118567986892139403294393430
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
6:
7.65216242953380728411403903154
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
7:
8.95494835611667412424804196320
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
8:
10.3103899358330277827336753843
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
9:
11.2260047590667597403177084926
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-324
1
10:
11.9208787125231297871946634108
comment: $a^3-3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.324.1.
-327
1
1:
1.70458306709519005726191879779
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
2:
3.48379135769085281071487237739
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
3:
4.42386325006468296262737482580
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
4:
6.50100474412380231900694567502
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
5:
7.14944691097300723106608156832
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
6:
8.46781209254480956365660828032
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
7:
9.04522434607477702231973759595
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
8:
9.62419368840389818738811584985
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
9:
10.4594518938765647209281280155
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-327
1
10:
11.7465074592772795013179581631
comment: $a^3-a^2-2a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.327.1.
-331
1
1:
1.98816870243366142600134302603
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
2:
3.57222521465823825976349946309
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
3:
4.60474706744117454383959704076
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
4:
6.20835629064935385794746843377
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
5:
7.10385284471483772626094148120
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
6:
7.79180940520932362394377395805
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
7:
8.90370617279283809537252170861
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
8:
10.2326608305518357620770802360
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
9:
10.9523744507246157052550884414
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-331
1
10:
11.7429282631479664365611127546
comment: $a^3-a^2+3a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.331.1.
-335
1
1:
1.24591638146976772616451176893
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
2:
3.41048732021627541617240222471
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
3:
5.19777585755608035074475928680
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
4:
6.01435481405194261329005114367
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
5:
6.85219842918784888139611750280
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
6:
8.24737424727990522264062474770
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
7:
9.28026399111323789117397188597
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
8:
9.77826024934081473659949259718
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
9:
10.7808861917962872030873451949
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-335
1
10:
11.3662535695428894788672732274
comment: $a^3-a^2+4a+1=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.335.1.
-339
1
1:
2.32985564369202968082399358560
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
2:
3.31108153418469351970225645516
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
3:
4.40991140314605310944429351929
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
4:
6.27919265229280506614154187535
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
5:
7.18751877613422571011121937212
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
6:
7.82162195075273451261470273369
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
7:
8.90716529312534136372367424604
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
8:
9.95190424274532141795042776150
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
9:
10.7378888614248661584332808587
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-339
1
10:
12.0451127492016314246179279960
comment: $a^3-a^2-a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.339.1.
-351
1
1:
1.31924089132326928898750164297
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
2:
3.68766173148466057722643549840
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
3:
4.41407558466250751498047916509
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
4:
6.19075407689203210695833474270
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
5:
7.22765273448491413273119793205
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
6:
8.16080291508277929160967245191
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
7:
8.93128718573633331837521029436
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
8:
9.58894503159109232997109647930
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
9:
10.8333837756204809707099461048
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-351
1
10:
11.4812008066141109053237369549
comment: $a^3+3a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.351.1.
-356
1
1:
2.00491779343604680931144269321
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
2:
4.01600802562592568972815723771
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
3:
4.72657548264463000766072728667
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
4:
5.57538027644770783049218703171
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
5:
6.72180728980827205506652916631
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
6:
7.81465077644172741318499151707
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
7:
8.48687541921660082146309017101
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
8:
10.5963060499800549957073001339
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
9:
11.1264183266609451122592334493
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
-356
1
10:
11.6766438740917625496106940500
comment: $a^3-a^2+a+7=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.356.1.
361
1
1:
1.57320808455217667944576519897
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
2:
4.40883445095759858523275964107
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
3:
4.63964563054553419922383721660
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
4:
6.29765489642468131575353719258
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
5:
7.49842260072313263559066025052
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
6:
8.18725054245401540198736533412
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
7:
8.97228608572294362591041132673
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
8:
10.1079614225298784208081944883
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
9:
11.3963253997640762501825295617
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
361
1
10:
11.4284329592837884376629839569
comment: $a^3-a^2-6a+7=0$; signature $(3,0)$; $C_3$; LMFDB 3.3.361.1.
-364
1
1:
1.76685581583524361199482323079
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
2:
3.81041668195070498360709632463
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
3:
4.41864713322176715250290835219
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
4:
5.82288963829734491658136278500
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
5:
7.12286858985095966367257588050
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
6:
7.93107548210392855239601823458
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
7:
8.64120251968729889820019204395
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
8:
9.89864760948756897814977015549
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
9:
11.0064159423052932617240774245
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-364
1
10:
11.4311581450262044800925520987
comment: $a^3+4a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.364.1.
-367
1
1:
1.37776227295614018180364030008
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
2:
3.45291986552255359285564103291
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
3:
4.55525407748349280924341827182
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
4:
6.19682774701305466624047539161
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
5:
6.96383690131722633454844107017
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
6:
8.22473687991725001625816978279
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
7:
8.81099609097268261684773532177
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
8:
9.94908459648026866168730654176
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
9:
10.2734306743241940057433692234
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-367
1
10:
11.3658246039519019750631759214
comment: $a^3-a^2+2a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.367.1.
-379
1
1:
1.90918342061892224165157621959
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
2:
3.48856746661486630986966402745
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
3:
4.47506796126829197395448055073
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
4:
6.00883495697779846838720376658
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
5:
7.01951438656325219814784676613
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
6:
7.67472080841817778853372927975
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
7:
8.62160958067206583025698043983
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
8:
10.0670280495980058461832520444
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
9:
10.6667415331911311070405599369
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
-379
1
10:
11.7081703458212189974621674234
comment: $a^3-a^2+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.379.1.
404
1
1:
2.28061396667902247177056820111
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
2:
4.00797943539768757247816516953
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
3:
4.54907361248421222583303584690
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
4:
6.11595176953717388982939728730
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
5:
7.26069024979208488514251630157
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
6:
7.81979573546568839762904294221
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
7:
8.97883690383221907455192834883
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
8:
9.93061698998567093287021047124
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
9:
10.8602033145413645179088625966
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
404
1
10:
11.7044884007950159929510552610
comment: $a^3-a^2-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.404.1.
-411
1
1:
2.16992743686203330013514209476
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
2:
3.34740423745780496534310739550
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
3:
4.11736566165569695423514503991
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
4:
6.01138996447162082756729418329
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
5:
7.00777087059962764495445353100
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
6:
7.70311784044715877802272763779
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
7:
8.56467090148828284056332716551
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
8:
9.67010187021142921537704779500
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
9:
10.5016525268135344901880822176
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-411
1
10:
11.4752547743301405581958580615
comment: $a^3-a^2+5a-2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.411.1.
-419
1
1:
1.90636981143443413693574787897
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
2:
2.96690904317689952081919897614
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
3:
5.13931080788457656047815404867
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
4:
5.95478165408733270508357939745
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
5:
6.36200565347368957082151242285
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
6:
7.28626691335368020701840276873
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
7:
9.02031221178142877783334115522
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
8:
10.0049483135729536639321317948
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
9:
10.3226072017897759067780093406
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-419
1
10:
11.3474428353733986647069848442
comment: $a^3-4a-5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.419.1.
-424
1
1:
2.18386919022154575558269287065
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
2:
3.68239261456309960937432573235
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
3:
4.41897488914849459520649603902
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
4:
5.48248747210365868695409231186
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
5:
6.78401466836540070500700965855
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
6:
7.50981489916335138690189342187
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
7:
8.34126264138619854961570146040
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
8:
9.90302086423718561916513917021
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
9:
10.7526321672611086375014208734
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-424
1
10:
11.5291189316051595507306150831
comment: $a^3-a^2+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.424.1.
-431
1
1:
2.43640383495768316417551145494
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
2:
3.78100560632556561844658094162
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
3:
4.59226487775997134985474751543
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
4:
5.57180858180196859619400189807
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
5:
6.20916850479740724792735263692
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
6:
7.32972147543743980134110036886
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
7:
8.07006399524536226015854400601
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
8:
10.3082916008838368303288929720
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
9:
11.0881477560903024174583985218
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-431
1
10:
11.4801347966508560733045247010
comment: $a^3-a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.431.1.
-436
1
1:
2.16296168900708112569294746226
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
2:
3.68057413523653462292942556358
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
3:
4.37770965986890783561180613972
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
4:
5.48145339770867735231537268450
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
5:
6.69387601254251957186027721940
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
6:
7.57938104572438814393603121238
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
7:
8.23172119343008359789940822533
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
8:
9.87712015872797204914550994996
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
9:
10.6917748908776124437357082480
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-436
1
10:
11.4847180295461766438043733993
comment: $a^3+a-4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.436.1.
-439
1
1:
1.56772093530706485978459515838
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
2:
2.87253281375891967462898987716
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
3:
4.86821437601776639546880056479
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
4:
5.67777756447323515866922714090
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
5:
6.93100875928359441996626678638
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
6:
7.63046914757755305323007828898
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
7:
9.13439747514882426253831527459
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
8:
9.76037121274030112945414986606
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
9:
9.90039669731862279867049609731
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-439
1
10:
10.7564989988499466259527999646
comment: $a^3-a^2-2a+5=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.439.1.
-440
1
1:
2.01548309327795849820138984267
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
2:
3.48796811994734313649172580572
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
3:
4.75471478260800469118493250092
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
4:
5.79859937462210122165599987861
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
5:
6.39079666766011395590792057464
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
6:
6.95124049271711626634931610216
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
7:
8.80851833896340159585559980128
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
8:
9.76906105506183762831627371868
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
9:
10.8023750182004534671606437302
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-440
1
10:
11.3076024230471840142067563450
comment: $a^3+2a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.440.1.
-451
1
1:
1.76694312476975336426016927711
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
2:
3.65354143676851465264230542808
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
3:
3.98335527433132136864128829189
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
4:
6.11355330844334228922065455073
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
5:
6.58587089774569595518377860507
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
6:
7.49189505269682984662397502083
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
7:
8.55155036242521701608968861698
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
8:
9.50729558127535192608848475638
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
9:
10.7568144067286276167339450540
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-451
1
10:
11.1437413709091127860966317877
comment: $a^3-a^2-5a+8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.451.1.
-459
1
1:
1.79702150776337982522379731182
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
2:
3.41157695909105169896883884901
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
3:
4.24865570184163956386732220654
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
4:
5.82697172062101309379474254207
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
5:
6.79390026751677811688372881790
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
6:
7.49856472666885404695352060235
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
7:
8.41422797960928901485523035263
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
8:
9.57848416085940085595690886776
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
9:
10.4698933007098609018198711485
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-459
1
10:
11.6767529047156323863611527963
comment: $a^3+3a-8=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.459.1.
-460
1
1:
1.82200002893505883255485960428
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
2:
3.21883300237861404558040464480
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
3:
4.55017852846092790303261104613
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
4:
5.72725475530356482188295812426
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
5:
6.66842863668025255627901110123
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
6:
7.34330618192148745303902546924
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
7:
8.97763485630069189988277376876
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
8:
9.40568188316289246578626675223
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
9:
10.3364656937270660661493232516
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
-460
1
10:
11.0225148530042700714772983206
comment: $a^3-a^2+5a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.460.1.
469
1
1:
2.05522764342246330875348570214
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
2:
3.68879746967997201464882862955
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
3:
4.98763182305534164209458279799
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
4:
5.77528556257392074036381616204
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
5:
6.99235063954078263177928551580
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
6:
7.63352773865929053851136346435
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
7:
8.50478973624387631596321841360
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
8:
10.0652938487329331377972529915
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
9:
10.8962622317362445414557110829
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
469
1
10:
11.6219205716160778722297577285
comment: $a^3-a^2-5a+4=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.469.1.
-472
1
1:
2.23050369734682394136455039807
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
2:
3.34847841920329681632604645067
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
3:
4.56684429375797396990716617328
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
4:
5.37912258917513824504005023745
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
5:
6.79519899146886347540741399333
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
6:
7.05508314377897558225914319674
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
7:
8.39455136989444672060048757842
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
8:
9.86052331520331836191521346486
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
9:
10.2963610303595140412917939922
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
-472
1
10:
11.3601753486123889066790772489
comment: $a^3-5a-6=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.472.1.
473
1
1:
1.72932086755047817484755787914
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
2:
3.66400718688856107280534564033
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
3:
4.58001840266581720344318257076
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
4:
6.21005025338995458136830663764
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
5:
7.00783209010461813205697960840
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
6:
7.92639713158504878323053618110
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
7:
9.09780256568972026402875160322
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
8:
9.47285324236017014683255808002
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
9:
10.3418363809945325006382854107
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
473
1
10:
11.0944062446994817228375653492
comment: $a^3-5a-1=0$; signature $(3,0)$; $S_3$; LMFDB 3.3.473.1.
-484
1
1:
2.09604669325984533985926300925
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
2:
3.59720247011790610155379616688
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
3:
4.38281363741132909415336323245
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
4:
5.28186120021799323635101609764
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
5:
6.74716231773000271791466035534
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
6:
7.28104027718829923008484759776
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
7:
8.19682121224604499014507933554
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
8:
9.59467112444028289237653582800
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
9:
10.5709849510363191381185206504
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-484
1
10:
11.4132265602972541966939963449
comment: $a^3-a^2+4a+2=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.484.1.
-491
1
1:
1.92036522329330815859370260683
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
2:
2.74249757025241159840970541830
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
3:
5.17360040554119708044884192408
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
4:
5.47935357244975221352095499572
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
5:
6.50262867980031934457943890626
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
6:
7.06100023983042368995561435827
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
7:
8.59157187320879835334393088696
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
8:
9.76053661883291168192623852656
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
9:
10.4442843953080805413093660370
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-491
1
10:
10.9407098089027964071522429829
comment: $a^3-a^2+a+4=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.491.1.
-492
1
1:
2.02801636180030848086438209036
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
2:
3.13770560201041288647957260912
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
3:
4.32213907090050053185117077265
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
4:
5.43257367319878110263601497318
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
5:
6.86253902516413034695689356499
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
6:
7.59253721723630781551931536503
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
7:
8.59777009156647389149287840086
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
8:
9.19772204261989167719925953948
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
9:
10.2965743447582790635995002407
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-492
1
10:
10.9334004213455914406642699808
comment: $a^3-a^2+3a+3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.492.1.
-499
1
1:
1.76568685843861490871355706508
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
2:
3.31315006940497582968755753083
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
3:
4.25959176211958315045966231237
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
4:
5.61696744390009473137330269776
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
5:
6.84279814362372404731576631667
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
6:
7.42066914498759717108774737561
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
7:
8.20324976637655510241107437870
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
8:
9.48543940994359627794188787855
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
9:
10.4494645459891568120123281392
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
-499
1
10:
11.2023420430323094836738988154
comment: $a^3+4a-3=0$; signature $(1,1)$; $S_3$; LMFDB 3.1.499.1.
Definition
Let $K$ be a cubic field [2] of discriminant $D$, with Dedekind zeta function $\zeta_K(s)$ [1]. Listed are the positive ordinates $t_n$ of critical-line zeros $\zeta_K(1/2+\mathrm{i}t_n)=0$, ordered increasingly from $n=1$ for each field.
Parameters
$D$
—   discriminant of $K$ ($D$ the discriminant of a cubic field)
$k$
—   index of $K$ among the cubic fields of discriminant $D$ ($k\geq1$)
$n$
—   index of the positive zero ($n\geq1$)
Formulas
(1)
The completed Dedekind zeta function is $\Lambda_K(s)=|D|^{s/2}\pi^{-r_1s/2}(2\pi)^{-r_2s} \Gamma(s/2)^{r_1}\Gamma(s)^{r_2}\zeta_K(s)$, where $(r_1,r_2)$ is the signature of $K$, with $r_1$ real places and $r_2$ pairs of complex places; it satisfies $\Lambda_K(s)=\Lambda_K(1-s)$.
Comments
(2)
Non-isomorphic cubic fields can share a discriminant. 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 coefficient vector $(a_2,a_1,a_0)$, where the polynomial is written $x^3+a_2x^2+a_1x+a_0$. No two cubic fields with $|D|\leq500$ share a discriminant, so $k=1$ throughout this table. This is the same $D,k$ convention used for the table of residues of Dedekind zeta functions of cubic fields.
(3)
Each entry comment gives a reduced defining equation $f(a)=0$, so that $K=\mathbb Q(a)$; the signature; the Galois group of the Galois closure as $C_3$ or $S_3$; and the LMFDB number-field label. The final component of the LMFDB label is the LMFDB index for that discriminant, not the $k$ used here.
(4)
The Dirichlet coefficients of $\zeta_K(s)$ are real, so non-real zeros occur in conjugate pairs. Only the positive ordinates $t_n>0$ are listed.
(5)
The trivial real zeros are not entries. For a cubic field with signature $(r_1,r_2)$, $\zeta_K(s)$ has trivial zeros at the negative even integers, and it also has trivial zeros at the negative odd integers when $r_2=1$. The table records the critical-line zeros returned by PARI's lfunzeros; it does not assert that these are all nontrivial zeros, and a missed zero would shift the index of every later zero in that field.
(6)
For every cubic field, $\zeta_K(s)=\zeta(s)L(s,\rho)$, where $\rho$ is the two-dimensional Artin representation associated to the Galois closure. Thus every zero of the Riemann zeta function is also a zero of $\zeta_K(s)$. When the Galois closure is $C_3$, the quotient $\zeta_K(s)/\zeta(s)$ factors as $L(s,\chi)L(s,\bar\chi)$ for the primitive cubic Dirichlet characters of conductor $\sqrt D$. The cyclic fields in this table have $D=49$, $81$, $169$ and $361$; the entry comments for $D=49$ and $D=81$ identify the corresponding rows of the Dirichlet zero table. The conductor-$13$ and conductor-$19$ character rows are not in that table.
Programs
(P1)
PARI/GP
default(realprecision, 80);
f = x^3 - x^2 + 1;       \\ D = -23
lfunzeros(lfuncreate(bnfinit(f, 1)), 60, 16)[1]
Links
Similar tables
Zeros of the Riemann zeta function —   stores zero ordinates for the degree-one factor $\zeta(s)$
Zeros of Dirichlet $L$-functions —   stores zero ordinates for Dirichlet $L$-functions, including the factors of the cyclic cubic rows
Zeros of the $L$-functions of level one cusp forms —   uses the same agreement-checked PARI lfunzeros convention for another family of $L$-functions
Residues of Dedekind zeta functions of cubic fields —   stores the residue at $s=1$ for cubic fields with the same $D,k$ convention
Values of Dedekind zeta functions of cubic fields at $2$ —   stores another value of $\zeta_K(s)$ for cubic fields with the same $D,k$ convention
Values of Dedekind zeta functions of totally real cubic fields at negative odd integers —   stores exact real-axis values for the totally real cubic fields under the same $D,k$ convention
Data properties
Entries are of type: real number
How well the digits are known: heuristic (agreement-checked)
Table is complete: no (it holds the first ten positive zero ordinates for every cubic field with $|D|\leq500$, the 58 complex and 12 totally real fields in that range)
How they were obtained:

The generator enumerates the fields with PARI's nflist("C3", [1, 500]) and nflist("S3", [1, 500]) [4], reduces their defining polynomials with polredabs, sorts them by increasing $|D|$ and then by $k$, and refuses to run unless it finds 70 fields, 58 with negative discriminant and 12 with positive discriminant.

more

This agrees with the same enumeration at $|D|\leq3000$ used by the cubic Dedekind residue and value tables. For each field it forms lfuncreate(bnfinit(f, 1)) and uses PARI/GP's lfunzeros [3] at 80 and 120 decimal working digits, with search height 60 and zero mesh 16. Each value is stored to 30 significant digits, and the two computations agree to at least that many. PARI's zero search is not a certified enclosure method, so the table does not claim proven zeros. Before the draft was filled, a dry run measured the chosen range: every field with $|D|\leq500$ had at least ten positive ordinates below height 60, and the largest tenth ordinate was $17.1012633035818315519487234446\ldots$ for $D=-23$.



API Python package Skill for AI Privacy Legal notice Source
Data licensed CC BY-SA 4.0. No tracking, no analytics, essential cookies only.