data:
- - Lhash: '1884084642089719692655527814285'
    a10:
    - -0.766044443118978
    - -1.3268278963378768
    a2:
    - 0.766044443118978
    - 0.6427876096865394
    a3:
    - -2.4126177261252173
    - 2.0244266441634378
    a4:
    - 0.17364817766693036
    - 0.984807753012208
    a5:
    - -1.4396926207859084
    - -0.5240052604587699
    a6:
    - -3.1494487660561257
    - -1.4104536630172788e-60
    a7:
    - 4.534238148034289
    - 1.6503277209587917
    a8:
    - -0.5
    - 0.8660254037844386
    a9:
    - 1.2014765218139845
    - -6.813911954861171
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.5908929749574752
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - -0.766044443118978
          - -0.6427876096865394
    - - 37
      - - - 1.0
          - 0
        - - -5.840378677317959
          - 1.699993207495172
    bad_primes:
    - 2
    - 37
    central_character: '74.71'
    coefficient_field: CDF
    conductor: 74
    conductor_radical: 74
    conjugate: '5339908103140470782695552631175'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -0.766044443118978
        - -0.6427876096865394
    - - - 1.0
        - 0
      - - 2.4126177261252173
        - -2.0244266441634378
      - - 0.520944533000791
        - -2.9544232590366244
    - - - 1.0
        - 0
      - - 1.4396926207859084
        - 0.5240052604587699
      - - 3.83022221559489
        - 3.2139380484326967
    - - - 1.0
        - 0
      - - -4.534238148034289
        - -1.6503277209587917
      - - 5.362311101832846
        - 4.499513267805775
    - - - 1.0
        - 0
      - - -0.5468960388810087
        - 0.9472517258000711
      - - -5.5
        - -9.526279441628825
    - - - 1.0
        - 0
      - - -0.3072841275991151
        - -1.74269488630995
      - - -12.216004070216808
        - 4.446261863233693
    - - - 1.0
        - 0
      - - -0.5115415207640848
        - 2.901096126688949
      - - -15.974774553360442
        - -5.814342436536369
    - - - 1.0
        - 0
      - - 0.6321670324612221
        - -0.530451123780647
      - - 3.2993153756716764
        - -18.711347307231954
    - - - 1.0
        - 0
      - - -0.12162042190907141
        - -0.2106527499844747
      - - -11.5
        - 19.91858428704209
    - - - 1.0
        - 0
      - - -2.7858655873392957
        - 4.825260740329371
      - - -14.5
        - -25.11473670974872
    - - - 1.0
        - 0
      - - 5.734947563027243
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - -5.840378677317959
        - 1.699993207495172
    - - - 1.0
        - 0
      - - -0.5056526198297558
        - -2.86769850988256
      - - -38.527397452222246
        - 14.022825876352417
    - - - 1.0
        - 0
      - - -4.379870002099799
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - 1.1324923516167404
        - 1.961534292183352
      - - -23.5
        - 40.703193977868615
    - - - 1.0
        - 0
      - - 5.778591627363951
        - -2.1032353483403727
      - - 40.60035548530583
        - -34.067743313386586
    - - - 1.0
        - 0
      - - 8.293008631177923
        - -3.0184082942614663
      - - 45.196622144019706
        - -37.92446897150582
    - - - 1.0
        - 0
      - - 2.0407549239521545
        - 11.573696298505176
      - - -57.32124986794041
        - 20.863228742865793
    - - - 1.0
        - 0
      - - 8.442198164541685
        - 3.0727088436699406
      - - 51.32497768897153
        - 43.066769848998135
    - - - 1.0
        - 0
      - - 0.9335350308931991
        - -0.783328900113554
      - - 12.329020614352055
        - -69.92135046386677
    - - - 1.0
        - 0
      - - -8.794176173599453
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - 2.0237890532467526
        - 0.7365989758155964
      - - 60.51751100639927
        - 50.780221165236604
    - - - 1.0
        - 0
      - - -0.8845277117176211
        - 5.016405930412199
      - - -77.9944875252304
        - -28.387671896030504
    - - - 1.0
        - 0
      - - 8.434860555671364
        - -3.070038172450456
      - - 68.17795543758905
        - -57.208097262102
    - - - 1.0
        - 0
      - - 2.179537078601259
        - 3.7750689571176226
      - - -48.5
        - 84.00446416709055
    - - - 1.0
        - 0
      - - -2.1944440225642112
        - -3.8008885414470375
      - - -50.5
        - 87.4685657822283
    - - - 1.0
        - 0
      - - 6.322622936464027
        - -10.951104163056025
      - - -51.5
        - -89.20061658979718
    - - - 1.0
        - 0
      - - -3.2749467619377497
        - -18.573146031193446
      - - -100.5471104240922
        - 36.596155335846554
    - - - 1.0
        - 0
      - - 6.445743238647986
        - 5.408620774212972
      - - 18.927651365695407
        - 107.34404507833068
    - - - 1.0
        - 0
      - - 4.890895799531977
        - 4.10394886151379
      - - 19.62224407636313
        - 111.28327609037952
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9593011
    index: 0
    label: 2-74-37.34-c1-0-0
    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/74/2/f/b/71/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 0.8546582017809369
    - 0.8015156748443291
    - 0.7580728759232105
    - 0.7202915996369069
    - 0.6838777266291204
    - 0.6445215512716075
    - 0.5980716995496141
    - 0.5406468219098846
    - 0.46871244945984436
    - 0.3791521276346
    - 0.26935240171739055
    - 0.13730982141788434
    - -0.018240920371922036
    - -0.1976847001665666
    - -0.4003803914225059
    - -0.624525318615862
    - -0.8670445389360285
    - -1.12352044244792
    - -1.388178008769679
    - -1.6539399242657047
    - -1.9125634924383226
    - -2.154867743426235
    - -2.371054325793649
    - -2.551119711801618
    - -2.6853491607171307
    - -2.7648750975035115
    - -2.7822745504443818
    - -2.7321726522389684
    - -2.611812646301288
    - -2.421548112169865
    - -2.1652109896123473
    - -1.8503101283113665
    - -1.4880200580365623
    - -1.0929287718523613
    - -0.6825265447801664
    - -0.27643480634045847
    - 0.10460592662024229
    - 0.43994826028609313
    - 0.7103874624672256
    - 0.8995651500081397
    - 0.995327304688035
    - 0.9909259742102348
    - 0.8859509321009483
    - 0.6868837625656232
    - 0.4071832332694319
    - 0.0668375492242475
    - -0.30864467851104294
    - -0.689789020196786
    - -1.045190969270692
    - -1.3439187718195298
    - -1.558123080515036
    - -1.6656552455912415
    - -1.6524711199335829
    - -1.514589451524809
    - -1.2593863275996957
    - -0.9060412320088949
    - -0.4850056567964324
    - -0.03643927545292643
    - 0.3923533708034093
    - 0.7503577377125078
    - 0.9869341651263066
    - 1.0562484229410485
    - 0.9216809133800671
    - 0.5598136128108818
    - -0.03640475758698632
    - -0.8556743979791332
    - -1.8678204287059774
    - -3.024894020688758
    - -4.26392176901873
    - -5.511169619942884
    - -6.687630493331963
    - -7.715303528773017
    - -8.523723887369762
    - -9.05613965408956
    - -9.274727314932097
    - -9.164294963053303
    - -8.734041820771395
    - -8.017115887210407
    - -7.067923830920013
    - -5.957378243498353
    - -4.76649278694237
    - -3.578929948036499
    - -2.473244908083093
    - -1.5156328043743048
    - -0.7539630150313253
    - -0.21377003463037533
    - 0.10332643218067032
    - 0.2185612824320277
    - 0.17241217170744605
    - 0.018827533744266312
    - -0.1820438602709394
    - -0.37175806161953473
    - -0.5011472148732098
    - -0.5365994997907461
    - -0.46422286631777815
    - -0.2913117824554372
    - -0.044866892508084094
    - 0.2327031920274607
    - 0.4901876623677338
    - 0.675643982192113
    - 0.7448533973625541
    - 0.6689783647476008
    - 0.4402907940376411
    - 0.07505002202688069
    - -0.3870413903390981
    - -0.8869268842185606
    - -1.35345975838084
    - -1.7129994964676403
    - -1.9001152820484568
    - -1.8679362977489868
    - -1.5966439543387594
    - -1.0987661382523326
    - -0.4202983110483056
    - 0.36279772213019895
    - 1.152543424966454
    - 1.840529523720478
    - 2.321763245791912
    - 2.508998443833854
    - 2.345594491658538
    - 1.8150406785820943
    - 0.9456433687280174
    - -0.19053232026959008
    - -1.4846180374712818
    - -2.8031279035568417
    - -4.003941275611712
    - -4.954049751771478
    - -5.546698151906553
    - -5.715536568210178
    - -5.443730705296794
    - -4.766618728901523
    - -3.767374910135029
    - -2.5661251248061685
    - -1.3039156191620107
    - -0.12372071118084702
    - 0.8488371831818984
    - 1.5222757876355928
    - 1.851076518974855
    - 1.8407582997807639
    - 1.5453947800942591
    - 1.057896765904988
    - 0.4944916850239363
    - -0.024249696613851637
    - -0.3929122428901795
    - -0.5382006238108638
    - -0.4306538261267064
    - -0.08918035624169734
    - 0.42240190947801665
    - 1.006363586308613
    - 1.5479083688662378
    - 1.9351816516192621
    - 2.0791797034038413
    - 1.9302342053964447
    - 1.488231011475819
    - 0.8046893049847832
    - -0.02386696566953157
    - -0.8703757430604832
    - -1.5973378935665152
    - -2.0793450486349077
    - -2.224331926353181
    - -1.9899641847016492
    - -1.3922937612884414
    - -0.5050381921655657
    - 0.5506246139492281
    - 1.6242617939064652
    - 2.5595265384276322
    - 3.2188447867009264
    - 3.5053584313807855
    - 3.378430203994282
    - 2.860052163709045
    - 2.0310139152928746
    - 1.0174249991888293
    - -0.030151384463464978
    - -0.9614033187260015
    - -1.6505769729137065
    - -2.016201551301651
    - -2.0328460117725125
    - -1.7329328642486435
    - -1.198415804873153
    - -0.5439611022696292
    - 0.10517780543554758
    - 0.6364283905867769
    - 0.9699377663761994
    - 1.0716224621495356
    - 0.9568033416758635
    - 0.6838167719864986
    - 0.3389569726419888
    - 0.01584064971082669
    - -0.20654882600154975
    - -0.2825279355122917
    - -0.21103611828831734
    - -0.036946730660924854
    - 0.15833074926246613
    - 0.2754619156051652
    - 0.22152967901005646
    - -0.06475431950761375
    - -0.5923021582971878
    - -1.3061254392017758
    - -2.0882378054581436
    - -2.771906076414485
    - -3.1675761714772213
    - -3.0963816885765283
    - -2.4253823815928275
    - -1.0979517530164926
    - 0.8467704316407633
    - 3.269759828603429
    - 5.945116065364292
    - 8.588919007745119
    - 10.899680835658215
    - 12.603836222134989
    - 13.498535828947034
    - 13.48422239102538
    - 12.581079206494058
    - 10.92618646430954
    - 8.751615394222451
    - 6.347110183346882
    - 4.01380897724745
    - 2.0170980607279247
    - 0.5468490457282488
    - -0.3080904319024794
    - -0.5669486229859254
    - -0.34487343352919453
    - 0.17560290622267047
    - 0.78363409853739
    - 1.2819565645517645
    - 1.5235540912806285
    - 1.436259773681769
    - 1.0310205794255547
    - 0.3929152088129837
    - -0.34249275392306827
    - -1.0219776505607396
    - -1.5094314860466875
    - -1.715177588549762
    - -1.6137504527303546
    - -1.246694733705049
    - -0.7102607075902075
    - -0.1311878870263543
    - 0.36364229794593056
    - 0.67660342454699
    - 0.7609665235904908
    - 0.6297865644655557
    - 0.34997205707212636
    - 0.022911795792890585
    - -0.2438012872009302
    - -0.36682987957159974
    - -0.3123361421483146
    - -0.1096180471449419
    - 0.15074164100470783
    - 0.3346043836501165
    - 0.29456771182230584
    - -0.09358531093389633
    - -0.8964380002548851
    - -2.098625519260606
    - -3.5949183152926216
    - -5.201608672245239
    - -6.685949501491973
    - -7.808338220973409
    - -8.36888728160935
    positive_zeros:
    - '1.48628071627190231624132091260631'
    - '4.46444877350296453794281036011989'
    - '5.64784939369976856170397718390785'
    - '7.13520937655010068884152449767758'
    - '7.993548946050369024663024827558192'
    - '10.69899250411732209496152492088750'
    - '11.13741165173208978953527849237464'
    - '12.02058390032188298817114344031833'
    - '12.89679581963278608390371199165615'
    - '14.06822256024370564219458015108233'
    prelabel: 2-74-37.34-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.7686956321961738
    root_angle: -0.5556225631331172
    root_number: -0.1738554862035071 - 0.9847711764247277*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.277811281567'
      prec: 50
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.48628071627190231624132091261'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '4.46444877350296453794281036012'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '5.64784939369976856170397718391'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.5908929749574752
    bad_primes:
    - 2
    - 37
    central_character: '37.34'
    conductor: 74
    conductor_radical: 74
    degree: 2
    id: 9593011
    index: 0
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/74/2/f/b/71/1
    is_instance_Artin: false
    is_instance_BMF: false
    is_instance_CMF: true
    is_instance_DIR: false
    is_instance_ECNF: false
    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: 2-74-37.34-c1-0-0
    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: 2-74-37.34-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.7686956321961738
    root_angle: -0.2778112815665586
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '1.48628071627190231624132091261'
      prec: 103
- - Lhash: '1884084642089719692655527814285'
    Lhash_array:
    - '1884084642089719692655527814285'
    id: 9959035
    label: 2-74-37.34-c1-0-0
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/74/2/f/b/71/1
label_cols:
- label
- label
- label
labels:
- 2-74-37.34-c1-0-0
- 2-74-37.34-c1-0-0
- 2-74-37.34-c1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T17:10:32.584648'