data:
- - A10: 0
    A2: 0
    A3: 0
    A4: 0
    A5: 0
    A6: 0
    A7: 1
    A8: 0
    A9: 2
    Lhash: '891218539083697681959762647949'
    a10:
    - 0.0
    - 0
    a2:
    - 0.0
    - 0
    a3:
    - 0.0
    - 0
    a4:
    - 0.0
    - 0
    a5:
    - 0.0
    - 0
    a6:
    - 0.0
    - 0
    a7:
    - 0.3779644730092272
    - 0
    a8:
    - 0.0
    - 0
    a9:
    - 0.6666666666666666
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 89.57942739416335
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - 1
    - - 7
      - - 1
        - -1
    bad_primes:
    - 2
    - 7
    central_character: '1404928.1'
    coefficient_field: 1.1.1.1
    conductor: 1404928
    conductor_radical: 14
    degree: 4
    euler_factors:
    - - 1
    - - 1
      - 0
      - -2
      - 0
      - 9
    - - 1
      - 0
      - -8
      - 0
      - 25
    - - 1
      - -1
    - - 1
      - -2
      - 14
      - -22
      - 121
    - - 1
      - 0
      - -4
      - 0
      - 169
    - - 1
      - 0
      - -22
      - 0
      - 289
    - - 1
      - 0
      - 14
      - 0
      - 361
    - - 1
      - 10
      - 70
      - 230
      - 529
    - - 1
      - -2
      - 10
      - -58
      - 841
    - - 1
      - 0
      - -46
      - 0
      - 961
    - - 1
      - -14
      - 122
      - -518
      - 1369
    - - 1
      - 0
      - -46
      - 0
      - 1681
    - - 1
      - 10
      - 110
      - 430
      - 1849
    - - 1
      - 0
      - -82
      - 0
      - 2209
    - - 1
      - 12
      - 126
      - 636
      - 2809
    - - 1
      - 0
      - -10
      - 0
      - 3481
    - - 1
      - 0
      - -48
      - 0
      - 3721
    - - 1
      - 8
      - 6
      - 536
      - 4489
    - - 1
      - -8
      - 142
      - -568
      - 5041
    - - 1
      - 0
      - -26
      - 0
      - 5329
    - - 1
      - 4
      - 158
      - 316
      - 6241
    - - 1
      - 0
      - -34
      - 0
      - 6889
    - - 1
      - 0
      - 38
      - 0
      - 7921
    - - 1
      - 0
      - -6
      - 0
      - 9409
    - - 1
      - 0
      - 72
      - 0
      - 10201
    - - 1
      - 0
      - 82
      - 0
      - 10609
    - - 1
      - -8
      - 166
      - -856
      - 11449
    - - 1
      - -26
      - 386
      - -2834
      - 11881
    - - 1
      - -20
      - 310
      - -2260
      - 12769
    gamma_factors:
    - []
    - - 0
      - 0
    id: 9557118
    index: 6
    label: 4-112e3-1.1-c1e2-0-6
    leading_term: '2.41885553395'
    load_key: Costa
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    - 1
    order_of_vanishing: 0
    origin: EllipticCurve/2.0.7.1/28672.6/j
    plot_delta:
      __RealLiteral__: 0
      data: '0.046875'
      prec: 27
    plot_values:
    - 2.418855533950767
    - 2.4083884158339273
    - 2.3768789424408117
    - 2.324017758879722
    - 2.2493386438008702
    - 2.152290337770059
    - 2.0323326648110402
    - 1.8890525517473438
    - 1.7222943718444748
    - 1.532297946507292
    - 1.319836577001947
    - 1.0863467041609622
    - 0.8340402739423107
    - 0.5659906925616379
    - 0.28618345960723646
    - -0.00047676140451494815
    - -0.2882096833263863
    - -0.5704588470380813
    - -0.8400499756587259
    - -1.0894083811963164
    - -1.3108322710696925
    - -1.4968151542589354
    - -1.6404067157651927
    - -1.7355977188449936
    - -1.7777109494116492
    - -1.7637772049047917
    - -1.692873131701416
    - -1.5663966055638936
    - -1.3882555763639797
    - -1.1649480591819197
    - -0.9055143737443032
    - -0.6213478434791638
    - -0.32585688215526515
    - -0.03397951293540545
    - 0.2384394557936771
    - 0.47538859515588255
    - 0.6615175574672167
    - 0.7830133508302521
    - 0.8284784172765561
    - 0.7897580154086374
    - 0.6626614282582587
    - 0.4475218561313807
    - 0.14954392070740785
    - -0.22110430661094152
    - -0.6494859994328678
    - -1.1163929070792407
    - -1.5991430661876147
    - -2.0726565913196464
    - -2.510766530316103
    - -2.8877018048029264
    - -3.179661565971651
    - -3.3663864202088787
    - -3.432623351179485
    - -3.369378985478551
    - -3.1748609646167907
    - -2.8550199804037004
    - -2.423625339436182
    - -1.9018339830506208
    - -1.317245334205041
    - -0.7024702414007254
    - -0.09327924096501686
    - 0.47356936505672537
    - 0.9626903855556636
    - 1.3424669412849992
    - 1.5873117641256647
    - 1.6796244980897475
    - 1.6112859128293202
    - 1.3845540395427676
    - 1.012263594556117
    - 0.517276751755692
    - -0.06881257551671673
    - -0.7076610842422378
    - -1.3567283354344337
    - -1.97223087350755
    - -2.5122890703511285
    - -2.9400308189174935
    - -3.2264071024544974
    - -3.3524850136158086
    - -3.3110144646138804
    - -3.1071143778354293
    - -2.757989597642147
    - -2.2916665234342104
    - -1.744817601977911
    - -1.1598254982439666
    - -0.5813097960217823
    - -0.052395540006948876
    - 0.38896217787821835
    - 0.7132745149747127
    - 0.9021325130186816
    - 0.9498823862264419
    - 0.8641802759967142
    - 0.6653381810959637
    - 0.38447957422487955
    - 0.06063374295590802
    - -0.26299797334794783
    - -0.5432832909367407
    - -0.7415248433042811
    - -0.8275394533293544
    - -0.7830483845172428
    - -0.604023948953704
    - -0.3017220864300207
    - 0.09775497302946648
    - 0.5553865870736352
    - 1.0225288072711585
    - 1.4453144480439144
    - 1.7697758293555235
    - 1.9472196716359578
    - 1.9393375904943038
    - 1.7225385697162208
    - 1.291043887911465
    - 0.6583873895900025
    - -0.1428931790536326
    - -1.0634172497395338
    - -2.0408355994424343
    - -3.005101490947725
    - -3.884670246292785
    - -4.61304740563557
    - -5.135048771060206
    - -5.412141563619257
    - -5.4263068068152505
    - -5.181994355988096
    - -4.7059226075404315
    - -4.044687997404785
    - -3.260373862654337
    - -2.4245608460436205
    - -1.6113187438573326
    - -0.8898822283027134
    - -0.3177649710720017
    - 0.06495992835476913
    - 0.2395907317715167
    - 0.21049231119192288
    - 0.004338555450038607
    - -0.3330553258334082
    - -0.7420046960895037
    - -1.155788300378333
    - -1.5083142994317122
    - -1.7417827363441651
    - -1.8134885896462942
    - -1.700985732488619
    - -1.4049980997784381
    - -0.9497043582468627
    - -0.38031154670941175
    - 0.24185987397610242
    - 0.8462669264162208
    - 1.3612588276990354
    - 1.7225037864057682
    - 1.8807575733335475
    - 1.8080559486391696
    - 1.5015737931576367
    - 0.9846474957616566
    - 0.30477687479008037
    - -0.4712269931774415
    - -1.2644416801670118
    - -1.99258547904839
    - -2.579323603301359
    - -2.9630415481483534
    - -3.1040373005919064
    - -2.989249445937985
    - -2.6339140520487194
    - -2.079899348434226
    - -1.3908627263853435
    - -0.6447624093836226
    - 0.07541134666745901
    - 0.6915858117616498
    - 1.1400308382989779
    - 1.3790945583531784
    - 1.3942702800892524
    - 1.1999265552447083
    - 0.837434467840348
    - 0.36987116246691826
    - -0.126088139671899
    - -0.570110718249542
    - -0.8887485794115172
    - -1.0252490242724412
    - -0.9473646352571153
    - -0.6521212278076977
    - -0.16686829805870287
    - 0.4536020575735266
    - 1.1335814478295687
    - 1.7858544631575584
    - 2.322839072133719
    - 2.6680556715814054
    - 2.766446843172926
    - 2.5921839727714504
    - 2.1528907630200447
    - 1.489653766708566
    - 0.6727227717516261
    - -0.2066380767610635
    - -1.0471765775437554
    - -1.7501887459396728
    - -2.23197222202921
    - -2.4345826708586733
    - -2.3334695148901012
    - -1.9409493992476907
    - -1.3050031920947096
    - -0.5034882577547173
    - 0.36553678444875665
    - 1.1961534815978425
    - 1.887998990989229
    - 2.3589988888970277
    - 2.55572893091459
    - 2.460013854793549
    - 2.0908604913883395
    - 1.5014416446009242
    - 0.7715145812381071
    - -0.0037167490854182407
    - -0.7267899954477384
    - -1.3114201470143954
    - -1.694326574657371
    - -1.8437982058790907
    - -1.7637794234718673
    - -1.4928715294331083
    - -1.0983512125477777
    - -0.6660112427148341
    - -0.2872306903214312
    - -0.04509557281532291
    - -0.0015538713853016695
    - -0.18747329781137329
    - -0.5970868393805404
    - -1.187709047817447
    - -1.8848665570728274
    - -2.5922121055482115
    - -3.2048923367533724
    - -3.624517474242121
    - -3.7736141306466986
    - -3.6074745997966255
    - -3.1216485332346644
    - -2.35391419018407
    - -1.3803364879381608
    - -0.30586030669237735
    - 0.7493202608099058
    - 1.665748408185558
    - 2.340809704410343
    - 2.702666969792113
    - 2.7200150971795276
    - 2.4062209321111623
    - 1.8172056653923803
    - 1.0433248924813867
    - 0.1963748826343411
    - -0.6064259029850362
    - -1.2591718659003404
    - -1.6822878055292996
    - -1.8336260022299713
    - -1.713999439228852
    - -1.3663175800190772
    - -0.8684344809284937
    - -0.3207571430827832
    - 0.16954552833858688
    - 0.5053669900289796
    - 0.614978229603483
    - 0.46349669609165367
    - 0.05873296721845097
    - -0.5495235699457559
    - -1.2767283171289074
    - -2.0162675442749656
    - -2.6557121457529838
    - -3.0941752309263193
    positive_zeros:
    - '0.70304746349131344247647173726084'
    - '1.55249081098435501810838380655526'
    - '1.98868925761822168438950328796183'
    - '2.81990333719384775133769833012215'
    - '3.27601579230360099330992906538779'
    - '3.98942824240376064026147735468295'
    - '4.36796661297590203351328709610053'
    - '4.72369091466956213083366103735421'
    - '5.19533750864123085075422006196375'
    - '5.98993005102216984812083460162318'
    - '6.14134670929552779051308300303325'
    - '6.63816887714249518144690975132983'
    - '7.05010148801106154077244098450959'
    - '7.58859647739024456683706443913371'
    - '7.956664309442800493331047630211743'
    prelabel: 4-112e3-1.1-c1e2-0
    primitive: true
    rational: true
    root_analytic_conductor: 3.076465650952455
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    spectral_label: c1e2-0
    st_group: SU(2)
    symmetry_type: symplectic
    trace_hash: 1819765679052322637
    z1:
      __RealLiteral__: 0
      data: '0.70304746349131344247647173726084'
      prec: 113
    z2:
      __RealLiteral__: 0
      data: '1.55249081098435501810838380655526'
      prec: 113
    z3:
      __RealLiteral__: 0
      data: '1.98868925761822168438950328796183'
      prec: 113
- - algebraic: true
    analytic_conductor: 89.57942739416335
    bad_primes:
    - 2
    - 7
    central_character: '1.1'
    conductor: 1404928
    conductor_radical: 14
    degree: 4
    dirichlet_coefficients:
    - 1
    - 0
    - 0
    - 0
    - 0
    - 0
    - 1
    - 0
    - 2
    - 0
    - 2
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -10
    - 0
    - 8
    - 0
    - 0
    - 0
    - 2
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 14
    - 0
    - 0
    - 0
    - 0
    - 0
    - -10
    - 0
    - 0
    - 0
    - 0
    - 0
    - 1
    - 0
    - 0
    - 0
    - -12
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 2
    - 0
    - 0
    - 0
    - -8
    - 0
    - 0
    - 0
    - 8
    - 0
    - 0
    - 0
    - 0
    - 0
    - 2
    - 0
    - -4
    - 0
    - -5
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 4
    - 0
    euler11:
    - 1
    - -2
    - 14
    - -22
    - 121
    euler13:
    - 1
    - 0
    - -4
    - 0
    - 169
    euler17:
    - 1
    - 0
    - -22
    - 0
    - 289
    euler19:
    - 1
    - 0
    - 14
    - 0
    - 361
    euler2:
    - 1
    - 0
    - 0
    - 0
    - 0
    euler23:
    - 1
    - 10
    - 70
    - 230
    - 529
    euler29:
    - 1
    - -2
    - 10
    - -58
    - 841
    euler3:
    - 1
    - 0
    - -2
    - 0
    - 9
    euler31:
    - 1
    - 0
    - -46
    - 0
    - 961
    euler37:
    - 1
    - -14
    - 122
    - -518
    - 1369
    euler41:
    - 1
    - 0
    - -46
    - 0
    - 1681
    euler43:
    - 1
    - 10
    - 110
    - 430
    - 1849
    euler47:
    - 1
    - 0
    - -82
    - 0
    - 2209
    euler5:
    - 1
    - 0
    - -8
    - 0
    - 25
    euler53:
    - 1
    - 12
    - 126
    - 636
    - 2809
    euler59:
    - 1
    - 0
    - -10
    - 0
    - 3481
    euler61:
    - 1
    - 0
    - -48
    - 0
    - 3721
    euler67:
    - 1
    - 8
    - 6
    - 536
    - 4489
    euler7:
    - 1
    - -1
    - 0
    - 0
    - 0
    euler71:
    - 1
    - -8
    - 142
    - -568
    - 5041
    euler73:
    - 1
    - 0
    - -26
    - 0
    - 5329
    euler79:
    - 1
    - 4
    - 158
    - 316
    - 6241
    euler83:
    - 1
    - 0
    - -34
    - 0
    - 6889
    euler89:
    - 1
    - 0
    - 38
    - 0
    - 7921
    euler97:
    - 1
    - 0
    - -6
    - 0
    - 9409
    euler_factors:
    - - 1
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 0
      - -2
      - 0
      - 9
    - - 1
      - 0
      - -8
      - 0
      - 25
    - - 1
      - -1
      - 0
      - 0
      - 0
    - - 1
      - -2
      - 14
      - -22
      - 121
    - - 1
      - 0
      - -4
      - 0
      - 169
    - - 1
      - 0
      - -22
      - 0
      - 289
    - - 1
      - 0
      - 14
      - 0
      - 361
    - - 1
      - 10
      - 70
      - 230
      - 529
    - - 1
      - -2
      - 10
      - -58
      - 841
    - - 1
      - 0
      - -46
      - 0
      - 961
    - - 1
      - -14
      - 122
      - -518
      - 1369
    - - 1
      - 0
      - -46
      - 0
      - 1681
    - - 1
      - 10
      - 110
      - 430
      - 1849
    - - 1
      - 0
      - -82
      - 0
      - 2209
    - - 1
      - 12
      - 126
      - 636
      - 2809
    - - 1
      - 0
      - -10
      - 0
      - 3481
    - - 1
      - 0
      - -48
      - 0
      - 3721
    - - 1
      - 8
      - 6
      - 536
      - 4489
    - - 1
      - -8
      - 142
      - -568
      - 5041
    - - 1
      - 0
      - -26
      - 0
      - 5329
    - - 1
      - 4
      - 158
      - 316
      - 6241
    - - 1
      - 0
      - -34
      - 0
      - 6889
    - - 1
      - 0
      - 38
      - 0
      - 7921
    - - 1
      - 0
      - -6
      - 0
      - 9409
    id: 9557118
    index: 6
    instance_types:
    - ECNF
    - BMF
    - ECNF
    - BMF
    instance_urls:
    - EllipticCurve/2.0.7.1/28672.6/j
    - ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/j
    - EllipticCurve/2.0.7.1/28672.8/j
    - ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/j
    is_instance_Artin: false
    is_instance_BMF: true
    is_instance_CMF: false
    is_instance_DIR: false
    is_instance_ECNF: true
    is_instance_ECQ: false
    is_instance_G2Q: false
    is_instance_HMF: false
    is_instance_MaassGL3: false
    is_instance_MaassGL4: false
    is_instance_MaassGSp4: false
    is_instance_NF: false
    label: 4-112e3-1.1-c1e2-0-6
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    - 1
    order_of_vanishing: 0
    prelabel: 4-112e3-1.1-c1e2-0
    primitive: true
    rational: true
    root_analytic_conductor: 3.076465650952455
    root_angle: 0.0
    self_dual: true
    spectral_label: c1e2-0
    trace_hash: 1819765679052322637
    z1:
      __RealLiteral__: 0
      data: '0.70304746349131344247647173726084'
      prec: 113
- - Lhash: '891218539083697681959762647949'
    Lhash_array:
    - '891218539083697681959762647949'
    id: 9620867
    label: 4-112e3-1.1-c1e2-0-6
    type: BMF
    url: ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/j
  - Lhash: '891218539083697681959762647949'
    Lhash_array:
    - '891218539083697681959762647949'
    id: 9620656
    label: 4-112e3-1.1-c1e2-0-6
    type: ECNF
    url: EllipticCurve/2.0.7.1/28672.8/j
  - Lhash: '891218539083697681959762647949'
    Lhash_array:
    - '891218539083697681959762647949'
    id: 9620283
    label: 4-112e3-1.1-c1e2-0-6
    type: BMF
    url: ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/j
  - Lhash: '891218539083697681959762647949'
    Lhash_array:
    - '891218539083697681959762647949'
    id: 9620111
    label: 4-112e3-1.1-c1e2-0-6
    type: ECNF
    url: EllipticCurve/2.0.7.1/28672.6/j
label_cols:
- label
- label
- label
labels:
- 4-112e3-1.1-c1e2-0-6
- 4-112e3-1.1-c1e2-0-6
- 4-112e3-1.1-c1e2-0-6
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T05:23:21.727562'