data:
- - Lhash: '898707222939069973610267968361'
    a10: -1
    a2: -1
    a3: -1
    a4: 1
    a5: 1
    a6: 1
    a7: 0
    a8: -1
    a9: 1
    accuracy: 100
    algebraic: true
    analytic_conductor: 39.90923093023596
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - 1
        - 1
    - - 3
      - - 1
        - 1
    - - 7
      - - 1
    - - 17
      - - 1
        - -1
    bad_primes:
    - 2
    - 3
    - 7
    - 17
    central_character: '4998.1'
    coefficient_field: 1.1.1.1
    conductor: 4998
    conductor_radical: 714
    degree: 2
    euler_factors:
    - - 1
      - 1
    - - 1
      - 1
    - - 1
      - -1
      - 5
    - - 1
    - - 1
      - 2
      - 11
    - - 1
      - -1
      - 13
    - - 1
      - -1
    - - 1
      - -4
      - 19
    - - 1
      - -8
      - 23
    - - 1
      - -3
      - 29
    - - 1
      - 3
      - 31
    - - 1
      - -4
      - 37
    - - 1
      - -1
      - 41
    - - 1
      - 4
      - 43
    - - 1
      - 9
      - 47
    - - 1
      - 0
      - 53
    - - 1
      - -11
      - 59
    - - 1
      - 0
      - 61
    - - 1
      - 12
      - 67
    - - 1
      - -4
      - 71
    - - 1
      - -6
      - 73
    - - 1
      - 0
      - 79
    - - 1
      - -9
      - 83
    - - 1
      - 6
      - 89
    - - 1
      - -8
      - 97
    - - 1
      - -14
      - 101
    - - 1
      - -14
      - 103
    - - 1
      - 12
      - 107
    - - 1
      - 16
      - 109
    - - 1
      - -15
      - 113
    euler_factors_factorization:
    - - - - 1
          - 1
        - 1
    - - - - 1
          - 1
        - 1
    - - - - 1
          - -1
          - 5
        - 1
    - - 1
    - - - - 1
          - 2
          - 11
        - 1
    - - - - 1
          - -1
          - 13
        - 1
    - - - - 1
          - -1
        - 1
    - - - - 1
          - -4
          - 19
        - 1
    - - - - 1
          - -8
          - 23
        - 1
    - - - - 1
          - -3
          - 29
        - 1
    - - - - 1
          - 3
          - 31
        - 1
    - - - - 1
          - -4
          - 37
        - 1
    - - - - 1
          - -1
          - 41
        - 1
    - - - - 1
          - 4
          - 43
        - 1
    - - - - 1
          - 9
          - 47
        - 1
    - - - - 1
          - 0
          - 53
        - 1
    - - - - 1
          - -11
          - 59
        - 1
    - - - - 1
          - 0
          - 61
        - 1
    - - - - 1
          - 12
          - 67
        - 1
    - - - - 1
          - -4
          - 71
        - 1
    - - - - 1
          - -6
          - 73
        - 1
    - - - - 1
          - 0
          - 79
        - 1
    - - - - 1
          - -9
          - 83
        - 1
    - - - - 1
          - 6
          - 89
        - 1
    - - - - 1
          - -8
          - 97
        - 1
    - - - - 1
          - -14
          - 101
        - 1
    - - - - 1
          - -14
          - 103
        - 1
    - - - - 1
          - 12
          - 107
        - 1
    - - - - 1
          - 16
          - 109
        - 1
    - - - - 1
          - -15
          - 113
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 20179290
    index: 16
    label: 2-4998-1.1-c1-0-16
    leading_term: '1.197458600406230306835069236770000000000000000000000000000000000000000000000000000000000000'
    load_key: CMFs-workshop
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/4998/2/a/e
    plot_delta:
      __RealLiteral__: 0
      data: '0.05078125'
      prec: 34
    plot_values:
    - 1.1974586004062302
    - 1.190949601372332
    - 1.171413177807422
    - 1.1388274275289516
    - 1.0931766167483639
    - 1.0344806808573435
    - 0.9628333952708417
    - 0.8784464654277339
    - 0.7816964610524594
    - 0.6731714276665091
    - 0.5537141124273223
    - 0.4244589920816287
    - 0.28686063757420455
    - 0.14271135036695828
    - -0.005853569691773195
    - -0.156364132497166
    - -0.306038314906964
    - -0.45181940316463154
    - -0.590427913685309
    - -0.7184275332947805
    - -0.832304058184362
    - -0.9285558422825253
    - -1.003793797538458
    - -1.0548485317421485
    - -1.078881778270785
    - -1.0734988833728631
    - -1.0368587886818248
    - -0.9677776985678229
    - -0.8658224722100697
    - -0.7313897459405518
    - -0.5657668870313279
    - -0.3711711168129878
    - -0.15076352568857498
    - 0.09136476290330452
    - 0.3502363419835923
    - 0.6200624296060442
    - 0.894349245148425
    - 1.1660351270850378
    - 1.4276565615012322
    - 1.671540150191031
    - 1.8900164091882665
    - 2.075650194932909
    - 2.2214815501342255
    - 2.321269889650429
    - 2.3697337522678725
    - 2.3627778682318628
    - 2.2976990711673135
    - 2.173362646489171
    - 1.9903410780757633
    - 1.7510078424864584
    - 1.459579905730163
    - 1.1221038896857416
    - 0.7463824690879426
    - 0.34183939796728263
    - -0.08067640346949916
    - -0.5091451058634195
    - -0.9306837502801373
    - -1.3319005217305946
    - -1.699286384038015
    - -2.0196330299365006
    - -2.2804644634803757
    - -2.470468253469605
    - -2.579911650205574
    - -2.6010274052674673
    - -2.5283543217781848
    - -2.35901831929045
    - -2.0929411308204995
    - -1.7329656451199884
    - -1.2848893270372639
    - -0.7574000313402635
    - -0.16191178667117523
    - 0.48769833821386166
    - 1.1754474863477824
    - 1.883689879673662
    - 2.5936332241693876
    - 3.2859132790591183
    - 3.9412083431499103
    - 4.540873099287058
    - 5.067569629182659
    - 5.505872566639788
    - 5.8428253720218795
    - 6.06842562786803
    - 6.1760190829345865
    - 6.162584880324986
    - 6.028897927112801
    - 5.779558592754653
    - 5.422884721278338
    - 4.970666136348986
    - 4.437787212206274
    - 3.8417284623602663
    - 3.201963237335423
    - 2.53927029772133
    - 1.8749870237576236
    - 1.2302311413880251
    - 0.6251209198099481
    - 0.07802469738591188
    - -0.3951297629736458
    - -0.7814572343362446
    - -1.0716023628171794
    - -1.2600905471918142
    - -1.3455256880961373
    - -1.3306241639239342
    - -1.2220810567878109
    - -1.0302716839118042
    - -0.7687985901360417
    - -0.4539010138491831
    - -0.10375013874373334
    - 0.26234111211078615
    - 0.624760666860786
    - 0.9644562482329193
    - 1.2637732126973156
    - 1.5072340490655745
    - 1.682224206287129
    - 1.7795524749473517
    - 1.7938592354415552
    - 1.723852317590238
    - 1.5723577318008575
    - 1.346180811398581
    - 1.0557819835091409
    - 0.7147800652060055
    - 0.3393042530641298
    - -0.05277656518009409
    - -0.4427122752302699
    - -0.811778121469814
    - -1.1421867903318264
    - -1.4179623792348959
    - -1.6257337245967982
    - -1.7554077255795075
    - -1.800688439643519
    - -1.759414640806228
    - -1.633696927386472
    - -1.4298449668354654
    - -1.158085629195404
    - -0.8320831003588018
    - -0.468282071630738
    - -0.0851042655863629
    - 0.29796359944930273
    - 0.6613462086806261
    - 0.9863722171379974
    - 1.256233135479272
    - 1.4568595247435763
    - 1.5776688302081197
    - 1.6121449170715698
    - 1.5582172573522337
    - 1.4184174030695391
    - 1.1998014081149582
    - 0.9136386914327126
    - 0.5748798728219564
    - 0.20142773937547717
    - -0.1867538993854762
    - -0.568649712562251
    - -0.9232700623869876
    - -1.2307409191180323
    - -1.4733498949761679
    - -1.636493192789029
    - -1.7094725774668398
    - -1.6860985597961713
    - -1.5650655138226512
    - -1.3500759739502322
    - -1.0497043006101208
    - -0.6770035989136421
    - -0.2488735019710772
    - 0.21478054992201318
    - 0.6920543091846818
    - 1.1601662633135172
    - 1.5966351114841009
    - 1.9804507612148212
    - 2.293175957488069
    - 2.5199186051903464
    - 2.6501211186219997
    - 2.6781224456380732
    - 2.6034603104214957
    - 2.4308950862093903
    - 2.170151812818742
    - 1.8353923942225163
    - 1.4444450888074951
    - 1.0178321863608606
    - 0.5776484537151273
    - 0.1463518296650505
    - -0.25446659256136644
    - -0.6052644134911942
    - -0.8896147641161084
    - -1.0950971621879724
    - -1.2139608555206762
    - -1.2435216384898362
    - -1.1862680609461278
    - -1.04966947480966
    - -0.8456955525481578
    - -0.5900737761184774
    - -0.3013269463142195
    - 0.0003539308730803652
    - 0.29433578129516
    - 0.5607964997886121
    - 0.7819304094225049
    - 0.9430336918489294
    - 1.033403703911364
    - 1.0469964999149473
    - 0.9828007735738927
    - 0.8449030511502814
    - 0.642237361186982
    - 0.3880317034705293
    - 0.098982302259236
    - -0.20579628002759123
    - -0.5059826386500956
    - -0.7813482152008767
    - -1.013065176636141
    - -1.184940686326909
    - -1.2844989707397019
    - -1.3038406931098618
    - -1.2402217649684284
    - -1.0963101782744138
    - -0.8800987950179919
    - -0.604473157247662
    - -0.2864550125489534
    - 0.05383693928492426
    - 0.3944488918830341
    - 0.7130008416070575
    - 0.9881560601668021
    - 1.2010588151861132
    - 1.3366478513242677
    - 1.384758763483864
    - 1.3409395954445698
    - 1.2069202213700678
    - 0.9906964265414258
    - 0.7062129295325568
    - 0.372654497957061
    - 0.013379286347059356
    - -0.345447993473901
    - -0.6764449805369728
    - -0.9527284473463503
    - -1.1496541247439178
    - -1.246470405215191
    - -1.2277791629745582
    - -1.0847060922669638
    - -0.8156984940852757
    - -0.4268895315996787
    - 0.06800654783242155
    - 0.6482753407994758
    - 1.2872368903448717
    - 1.9536825085517697
    - 2.613635830565613
    - 3.232337746078986
    - 3.7763381662913456
    - 4.215567765149008
    - 4.525260674844074
    - 4.687604948727741
    - 4.693011269014725
    - 4.540911215957443
    - 4.240023307315177
    - 3.808056432309873
    - 3.270854391921842
    - 2.6610199536521115
    - 2.016089982007712
    - 1.3763627094564195
    - 0.7825021389479206
    - 0.2730612954577246
    - -0.11792563843343526
    positive_zeros:
    - '0.70895499341637640511884680221266'
    - '1.65708709121297235432877512151086'
    - '2.73259154448507135582049623379166'
    - '3.56770037768586370273861245152220'
    - '4.83203717801140074861183066243262'
    - '5.39731027238560092165564516971691'
    - '6.13773336107594627222344609905255'
    - '6.86665791470700250919779761509192'
    - '7.54204361900201852382451429420908'
    - '8.203372130862587077556745649130990'
    prelabel: 2-4998-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 6.317375319722262
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1-0
    trace_hash: 1063040887944734994
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.70895499341637640511884680221'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '1.65708709121297235432877512151'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.73259154448507135582049623379'
      prec: 103
- - algebraic: true
    analytic_conductor: 39.90923093023596
    bad_primes:
    - 2
    - 3
    - 7
    - 17
    central_character: '1.1'
    conductor: 4998
    conductor_radical: 714
    degree: 2
    dirichlet_coefficients:
    - 1
    - -1
    - -1
    - 1
    - 1
    - 1
    - 0
    - -1
    - 1
    - -1
    - -2
    - -1
    - 1
    - 0
    - -1
    - 1
    - 1
    - -1
    - 4
    - 1
    - 0
    - 2
    - 8
    - 1
    - -4
    - -1
    - -1
    - 0
    - 3
    - 1
    - -3
    - -1
    - 2
    - -1
    - 0
    - 1
    - 4
    - -4
    - -1
    - -1
    - 1
    - 0
    - -4
    - -2
    - 1
    - -8
    - -9
    - -1
    - 0
    - 4
    - -1
    - 1
    - 0
    - 1
    - -2
    - 0
    - -4
    - -3
    - 11
    - -1
    - 0
    - 3
    - 0
    - 1
    - 1
    - -2
    - -12
    - 1
    - -8
    - 0
    - 4
    - -1
    - 6
    - -4
    - 4
    - 4
    - 0
    - 1
    - 0
    - 1
    - 1
    - -1
    - 9
    - 0
    - 1
    - 4
    - -3
    - 2
    - -6
    - -1
    - 0
    - 8
    - 3
    - 9
    - 4
    - 1
    - 8
    - 0
    - -2
    - -4
    euler11:
    - 1
    - 2
    - 11
    euler13:
    - 1
    - -1
    - 13
    euler17:
    - 1
    - -1
    - 0
    euler19:
    - 1
    - -4
    - 19
    euler2:
    - 1
    - 1
    - 0
    euler23:
    - 1
    - -8
    - 23
    euler29:
    - 1
    - -3
    - 29
    euler3:
    - 1
    - 1
    - 0
    euler31:
    - 1
    - 3
    - 31
    euler37:
    - 1
    - -4
    - 37
    euler41:
    - 1
    - -1
    - 41
    euler43:
    - 1
    - 4
    - 43
    euler47:
    - 1
    - 9
    - 47
    euler5:
    - 1
    - -1
    - 5
    euler53:
    - 1
    - 0
    - 53
    euler59:
    - 1
    - -11
    - 59
    euler61:
    - 1
    - 0
    - 61
    euler67:
    - 1
    - 12
    - 67
    euler7:
    - 1
    - 0
    - 0
    euler71:
    - 1
    - -4
    - 71
    euler73:
    - 1
    - -6
    - 73
    euler79:
    - 1
    - 0
    - 79
    euler83:
    - 1
    - -9
    - 83
    euler89:
    - 1
    - 6
    - 89
    euler97:
    - 1
    - -8
    - 97
    euler_factors:
    - - 1
      - 1
      - 0
    - - 1
      - 1
      - 0
    - - 1
      - -1
      - 5
    - - 1
      - 0
      - 0
    - - 1
      - 2
      - 11
    - - 1
      - -1
      - 13
    - - 1
      - -1
      - 0
    - - 1
      - -4
      - 19
    - - 1
      - -8
      - 23
    - - 1
      - -3
      - 29
    - - 1
      - 3
      - 31
    - - 1
      - -4
      - 37
    - - 1
      - -1
      - 41
    - - 1
      - 4
      - 43
    - - 1
      - 9
      - 47
    - - 1
      - 0
      - 53
    - - 1
      - -11
      - 59
    - - 1
      - 0
      - 61
    - - 1
      - 12
      - 67
    - - 1
      - -4
      - 71
    - - 1
      - -6
      - 73
    - - 1
      - 0
      - 79
    - - 1
      - -9
      - 83
    - - 1
      - 6
      - 89
    - - 1
      - -8
      - 97
    id: 20179290
    index: 16
    instance_types:
    - ECQ
    - CMF
    - CMF
    instance_urls:
    - EllipticCurve/Q/4998/e
    - ModularForm/GL2/Q/holomorphic/4998/2/a/e/1/1
    - ModularForm/GL2/Q/holomorphic/4998/2/a/e
    is_instance_Artin: false
    is_instance_BMF: false
    is_instance_CMF: true
    is_instance_DIR: false
    is_instance_ECNF: false
    is_instance_ECQ: true
    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: 2-4998-1.1-c1-0-16
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    order_of_vanishing: 0
    prelabel: 2-4998-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 6.317375319722262
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    trace_hash: 1063040887944734994
    z1:
      __RealLiteral__: 0
      data: '0.70895499341637640511884680221'
      prec: 103
- - Lhash: '898707222939069973610267968361'
    Lhash_array:
    - '898707222939069973610267968361'
    id: 20220340
    label: 2-4998-1.1-c1-0-16
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/4998/2/a/e
  - Lhash: '898707222939069973610267968361'
    Lhash_array:
    - '898707222939069973610267968361'
    id: 24568438
    label: 2-4998-1.1-c1-0-16
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/4998/2/a/e/1/1
  - Lhash: '1063040887944734994'
    Lhash_array:
    - '1063040887944734994'
    id: 34679
    label: 2-4998-1.1-c1-0-16
    type: ECQ
    url: EllipticCurve/Q/4998/e
label_cols:
- label
- label
- label
labels:
- 2-4998-1.1-c1-0-16
- 2-4998-1.1-c1-0-16
- 2-4998-1.1-c1-0-16
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T09:05:09.051802'