data:
- - Lhash: '1248439490164389121567699415356'
    a10: 0
    a2: 0
    a3: 1
    a4: 0
    a5: -1
    a6: 0
    a7: 4
    a8: 0
    a9: 1
    accuracy: 100
    algebraic: true
    analytic_conductor: 49.826650861278985
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - 1
    - - 3
      - - 1
        - -1
    - - 5
      - - 1
        - 1
    - - 13
      - - 1
        - 1
    bad_primes:
    - 2
    - 3
    - 5
    - 13
    central_character: '6240.1'
    coefficient_field: 1.1.1.1
    conductor: 6240
    conductor_radical: 390
    degree: 2
    euler_factors:
    - - 1
    - - 1
      - -1
    - - 1
      - 1
    - - 1
      - -4
      - 7
    - - 1
      - -4
      - 11
    - - 1
      - 1
    - - 1
      - -2
      - 17
    - - 1
      - 4
      - 19
    - - 1
      - 0
      - 23
    - - 1
      - -6
      - 29
    - - 1
      - 0
      - 31
    - - 1
      - -10
      - 37
    - - 1
      - -2
      - 41
    - - 1
      - 4
      - 43
    - - 1
      - -4
      - 47
    - - 1
      - 6
      - 53
    - - 1
      - 4
      - 59
    - - 1
      - 2
      - 61
    - - 1
      - 4
      - 67
    - - 1
      - 8
      - 71
    - - 1
      - 2
      - 73
    - - 1
      - -16
      - 79
    - - 1
      - -4
      - 83
    - - 1
      - -10
      - 89
    - - 1
      - 2
      - 97
    - - 1
      - 10
      - 101
    - - 1
      - -8
      - 103
    - - 1
      - -4
      - 107
    - - 1
      - -10
      - 109
    - - 1
      - 14
      - 113
    euler_factors_factorization:
    - - 1
    - - - - 1
          - -1
        - 1
    - - - - 1
          - 1
        - 1
    - - - - 1
          - -4
          - 7
        - 1
    - - - - 1
          - -4
          - 11
        - 1
    - - - - 1
          - 1
        - 1
    - - - - 1
          - -2
          - 17
        - 1
    - - - - 1
          - 4
          - 19
        - 1
    - - - - 1
          - 0
          - 23
        - 1
    - - - - 1
          - -6
          - 29
        - 1
    - - - - 1
          - 0
          - 31
        - 1
    - - - - 1
          - -10
          - 37
        - 1
    - - - - 1
          - -2
          - 41
        - 1
    - - - - 1
          - 4
          - 43
        - 1
    - - - - 1
          - -4
          - 47
        - 1
    - - - - 1
          - 6
          - 53
        - 1
    - - - - 1
          - 4
          - 59
        - 1
    - - - - 1
          - 2
          - 61
        - 1
    - - - - 1
          - 4
          - 67
        - 1
    - - - - 1
          - 8
          - 71
        - 1
    - - - - 1
          - 2
          - 73
        - 1
    - - - - 1
          - -16
          - 79
        - 1
    - - - - 1
          - -4
          - 83
        - 1
    - - - - 1
          - -10
          - 89
        - 1
    - - - - 1
          - 2
          - 97
        - 1
    - - - - 1
          - 10
          - 101
        - 1
    - - - - 1
          - -8
          - 103
        - 1
    - - - - 1
          - -4
          - 107
        - 1
    - - - - 1
          - -10
          - 109
        - 1
    - - - - 1
          - 14
          - 113
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 21503979
    index: 47
    label: 2-6240-1.1-c1-0-47
    leading_term: '3.20765590856183847496359510870000000000000000000000000000000000000000000000000000000000000'
    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/6240/2/a/x
    plot_delta:
      __RealLiteral__: 0
      data: '0.046875'
      prec: 27
    plot_values:
    - 3.2076559085618386
    - 3.19978808585748
    - 3.176140548279754
    - 3.1365874429748284
    - 3.0809397929742457
    - 3.0089752775520577
    - 2.9204772868653155
    - 2.8152809037759217
    - 2.6933231558218225
    - 2.5546947604004537
    - 2.3996906340418436
    - 2.22885661626275
    - 2.043030129438579
    - 1.8433728209459377
    - 1.6313935828700392
    - 1.408960697882239
    - 1.1783022067103848
    - 0.9419939294032333
    - 0.7029349004343403
    - 0.4643102998542166
    - 0.229542282544052
    - 0.0022294271875172556
    - -0.213924154262453
    - -0.41518868970407874
    - -0.5978959376291217
    - -0.7585317378073704
    - -0.8938316958050451
    - -1.0008775412152688
    - -1.0771915106020167
    - -1.1208259731446342
    - -1.1304454499659586
    - -1.1053981861474003
    - -1.0457745248395698
    - -0.9524495109021486
    - -0.8271074198481412
    - -0.6722462663423028
    - -0.4911607917914215
    - -0.28790295604768945
    - -0.06721955395724843
    - 0.1655327698312933
    - 0.4044941410840396
    - 0.6434280297340724
    - 0.8758653809094324
    - 1.0952632154824242
    - 1.2951739685395098
    - 1.469421262687498
    - 1.61227733819861
    - 1.7186370064581094
    - 1.7841827774933676
    - 1.8055357537772534
    - 1.7803869941542163
    - 1.707604341887266
    - 1.5873101821596607
    - 1.420926243494946
    - 1.2111823746689727
    - 0.9620871974111767
    - 0.6788596327119496
    - 0.3678214959461797
    - 0.03625261886211405
    - -0.3077887543162111
    - -0.6556762765257353
    - -0.9984512814319215
    - -1.3270777044342363
    - -1.6327088518357282
    - -1.9069579704408233
    - -2.142164043880853
    - -2.3316439807527494
    - -2.4699223879371894
    - -2.5529304560643715
    - -2.5781661287573705
    - -2.5448086777899195
    - -2.453782045970942
    - -2.307762820167788
    - -2.111130418920303
    - -1.8698589726358232
    - -1.5913523802208216
    - -1.2842260774665508
    - -0.9580410773338153
    - -0.622997765154323
    - -0.2895986769464591
    - 0.031709016759921126
    - 0.3308994238879309
    - 0.5987295460574786
    - 0.8270835318391354
    - 1.0092865960310247
    - 1.1403762066193743
    - 1.2173191981280485
    - 1.2391649942081915
    - 1.207127078570491
    - 1.124587188370853
    - 0.9970193473178863
    - 0.8318337210531282
    - 0.6381432658805125
    - 0.42645914516543004
    - 0.20832379129543677
    - -0.0041068210437390585
    - -0.19851776554518188
    - -0.3629107697555386
    - -0.48608358991095735
    - -0.5580951187302988
    - -0.5706980609721766
    - -0.5177215782389941
    - -0.3953875738927441
    - -0.2025462406875625
    - 0.059180920592541895
    - 0.38535925941714416
    - 0.7688053582185141
    - 1.1997587541154913
    - 1.6661579916292182
    - 2.1540138425205546
    - 2.647868504129954
    - 3.1313258597634492
    - 3.5876346142859235
    - 4.000303453584339
    - 4.353725447616983
    - 4.633787828114559
    - 4.828443098075549
    - 4.928218210765809
    - 4.92664029300788
    - 4.820560043782493
    - 4.610357437835841
    - 4.300018590639057
    - 3.897077446837331
    - 3.4124211609609834
    - 2.859963445310956
    - 2.256195548849985
    - 1.6196296791428841
    - 0.9701543659161916
    - 0.32832528070297046
    - -0.2853818152322265
    - -0.851327180240478
    - -1.3514424369315663
    - -1.7699155320425828
    - -2.0937971282011416
    - -2.313502889126492
    - -2.4231898934211937
    - -2.420990184048349
    - -2.3090900534718135
    - -2.093649860112345
    - -1.7845657196068145
    - -1.395081041231265
    - -0.9412623015118021
    - -0.44135938036172556
    - 0.0849240393676903
    - 0.6172203335281288
    - 1.135315416127357
    - 1.619959589104414
    - 2.0536373754327393
    - 2.42126331157868
    - 2.710773512463717
    - 2.913587037914345
    - 3.0249165242247953
    - 3.0439139789458594
    - 2.9736448017031583
    - 2.820890679372845
    - 2.5957896743500832
    - 2.3113292321714063
    - 1.9827146355879932
    - 1.6266413025367086
    - 1.2605039771334778
    - 0.9015790576318659
    - 0.5662178675194445
    - 0.2690885021718968
    - 0.022501949434858358
    - -0.16414545389141874
    - -0.2847863668402414
    - -0.33693327273520474
    - -0.3217530795687589
    - -0.2439611047554732
    - -0.11153871504216921
    - 0.06471252392865799
    - 0.27175923902985316
    - 0.4950390264775725
    - 0.7192435068019087
    - 0.9291431665483004
    - 1.1104129226445827
    - 1.2504167452842876
    - 1.3389111159914606
    - 1.3686305491641388
    - 1.3357237383756648
    - 1.240015878088156
    - 1.0850810454682496
    - 0.8781178204265759
    - 0.629631133276436
    - 0.3529331811882472
    - 0.06348565662286333
    - -0.2218859959740007
    - -0.4858684785437564
    - -0.7115835339090364
    - -0.8835113995624309
    - -0.9883673802342563
    - -1.0158854696421447
    - -0.9594666806067521
    - -0.8166556934129965
    - -0.5894173536714828
    - -0.28419408633602566
    - 0.08826400464590954
    - 0.5132932274494023
    - 0.9729200163462048
    - 1.4466487448169028
    - 1.9123982139705193
    - 2.3475430745539043
    - 2.730010163144671
    - 3.0393758599926968
    - 3.257909357256866
    - 3.3715082818761175
    - 3.3704774275296576
    - 3.2501082540162347
    - 3.0110260122361767
    - 2.659282426639769
    - 2.206184286772086
    - 1.6678614568913572
    - 1.064591047908823
    - 0.41990713127755264
    - -0.24046325129664825
    - -0.8897875253084964
    - -1.5015811048720482
    - -2.050865338177787
    - -2.5153670049525796
    - -2.876598486878029
    - -3.120762886168877
    - -3.2394364736226886
    - -3.229991537941086
    - -3.095735473367606
    - -2.84575615473473
    - -2.49447859217321
    - -2.060952764497134
    - -1.567906620749832
    - -1.0406107622818093
    - -0.5056115906626997
    - 0.010602846201489597
    - 0.48293589294521727
    - 0.8889451437415683
    - 1.2099690238332608
    - 1.4320574966825086
    - 1.5466570227762853
    - 1.55101238309577
    - 1.4482626056334287
    - 1.2472242487152354
    - 0.961871864996176
    - 0.6105417160936513
    - 0.21489985425052022
    - -0.20127129104958583
    - -0.6134034162328135
    - -0.9975186102114575
    - -1.3315769037441803
    - -1.5967214563369407
    - -1.7783525704231542
    - -1.8669703497416048
    - -1.8587378211630203
    - -1.7557311092287167
    - -1.5658600224985117
    - -1.3024602916195125
    - -0.9835767277794152
    - -0.6309737613670151
    - -0.2689252200936285
    - 0.07715205609983469
    positive_zeros:
    - '0.984845106324738466880579966173504'
    - '1.79498846103263043627803431516228'
    - '2.72375019871826155599027472739818'
    - '3.74525084652099810536751838018037'
    - '4.45218887336048482543536231559136'
    - '4.86537586972911831466331528478649'
    - '6.02471247122261666088290129308899'
    - '6.69564413999269920082396332545684'
    - '7.64553671108818050366414602345273'
    - '7.952648306847599084347337375452697'
    prelabel: 2-6240-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 7.058799534005693
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1-0
    trace_hash: 386388929047362836
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.984845106324738466880579966174'
      prec: 107
    z2:
      __RealLiteral__: 0
      data: '1.79498846103263043627803431516'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.72375019871826155599027472740'
      prec: 103
- - algebraic: true
    analytic_conductor: 49.826650861278985
    bad_primes:
    - 2
    - 3
    - 5
    - 13
    central_character: '1.1'
    conductor: 6240
    conductor_radical: 390
    degree: 2
    dirichlet_coefficients:
    - 1
    - 0
    - 1
    - 0
    - -1
    - 0
    - 4
    - 0
    - 1
    - 0
    - 4
    - 0
    - -1
    - 0
    - -1
    - 0
    - 2
    - 0
    - -4
    - 0
    - 4
    - 0
    - 0
    - 0
    - 1
    - 0
    - 1
    - 0
    - 6
    - 0
    - 0
    - 0
    - 4
    - 0
    - -4
    - 0
    - 10
    - 0
    - -1
    - 0
    - 2
    - 0
    - -4
    - 0
    - -1
    - 0
    - 4
    - 0
    - 9
    - 0
    - 2
    - 0
    - -6
    - 0
    - -4
    - 0
    - -4
    - 0
    - -4
    - 0
    - -2
    - 0
    - 4
    - 0
    - 1
    - 0
    - -4
    - 0
    - 0
    - 0
    - -8
    - 0
    - -2
    - 0
    - 1
    - 0
    - 16
    - 0
    - 16
    - 0
    - 1
    - 0
    - 4
    - 0
    - -2
    - 0
    - 6
    - 0
    - 10
    - 0
    - -4
    - 0
    - 0
    - 0
    - 4
    - 0
    - -2
    - 0
    - 4
    - 0
    euler11:
    - 1
    - -4
    - 11
    euler13:
    - 1
    - 1
    - 0
    euler17:
    - 1
    - -2
    - 17
    euler19:
    - 1
    - 4
    - 19
    euler2:
    - 1
    - 0
    - 0
    euler23:
    - 1
    - 0
    - 23
    euler29:
    - 1
    - -6
    - 29
    euler3:
    - 1
    - -1
    - 0
    euler31:
    - 1
    - 0
    - 31
    euler37:
    - 1
    - -10
    - 37
    euler41:
    - 1
    - -2
    - 41
    euler43:
    - 1
    - 4
    - 43
    euler47:
    - 1
    - -4
    - 47
    euler5:
    - 1
    - 1
    - 0
    euler53:
    - 1
    - 6
    - 53
    euler59:
    - 1
    - 4
    - 59
    euler61:
    - 1
    - 2
    - 61
    euler67:
    - 1
    - 4
    - 67
    euler7:
    - 1
    - -4
    - 7
    euler71:
    - 1
    - 8
    - 71
    euler73:
    - 1
    - 2
    - 73
    euler79:
    - 1
    - -16
    - 79
    euler83:
    - 1
    - -4
    - 83
    euler89:
    - 1
    - -10
    - 89
    euler97:
    - 1
    - 2
    - 97
    euler_factors:
    - - 1
      - 0
      - 0
    - - 1
      - -1
      - 0
    - - 1
      - 1
      - 0
    - - 1
      - -4
      - 7
    - - 1
      - -4
      - 11
    - - 1
      - 1
      - 0
    - - 1
      - -2
      - 17
    - - 1
      - 4
      - 19
    - - 1
      - 0
      - 23
    - - 1
      - -6
      - 29
    - - 1
      - 0
      - 31
    - - 1
      - -10
      - 37
    - - 1
      - -2
      - 41
    - - 1
      - 4
      - 43
    - - 1
      - -4
      - 47
    - - 1
      - 6
      - 53
    - - 1
      - 4
      - 59
    - - 1
      - 2
      - 61
    - - 1
      - 4
      - 67
    - - 1
      - 8
      - 71
    - - 1
      - 2
      - 73
    - - 1
      - -16
      - 79
    - - 1
      - -4
      - 83
    - - 1
      - -10
      - 89
    - - 1
      - 2
      - 97
    id: 21503979
    index: 47
    instance_types:
    - ECQ
    - CMF
    - CMF
    instance_urls:
    - EllipticCurve/Q/6240/x
    - ModularForm/GL2/Q/holomorphic/6240/2/a/x/1/1
    - ModularForm/GL2/Q/holomorphic/6240/2/a/x
    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: 2-6240-1.1-c1-0-47
    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: 2-6240-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 7.058799534005693
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    trace_hash: 386388929047362836
    z1:
      __RealLiteral__: 0
      data: '0.984845106324738466880579966174'
      prec: 107
- - Lhash: '1248439490164389121567699415356'
    Lhash_array:
    - '1248439490164389121567699415356'
    id: 21572031
    label: 2-6240-1.1-c1-0-47
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/6240/2/a/x
  - Lhash: '1248439490164389121567699415356'
    Lhash_array:
    - '1248439490164389121567699415356'
    id: 24574099
    label: 2-6240-1.1-c1-0-47
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/6240/2/a/x/1/1
  - Lhash: '386388929047362836'
    Lhash_array:
    - '386388929047362836'
    id: 27005
    label: 2-6240-1.1-c1-0-47
    type: ECQ
    url: EllipticCurve/Q/6240/x
label_cols:
- label
- label
- label
labels:
- 2-6240-1.1-c1-0-47
- 2-6240-1.1-c1-0-47
- 2-6240-1.1-c1-0-47
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T08:32:06.638142'