data:
- - Lhash: '2940882410556429695424905824864'
    a10:
    - 0.9396926207859084
    - 1.6275953626987474
    a2:
    - -0.9396926207859084
    - 0.3420201433256687
    a3:
    - 1.7232798302233832
    - 0.6272225635126262
    a4:
    - 0.766044443118978
    - -0.6427876096865394
    a5:
    - -0.32635182233306964
    - -1.8508331567966467
    a6:
    - -1.833876091079788
    - -2.804978665060675e-63
    a7:
    - 0.5984888042569352
    - 3.3941986748270985
    a8:
    - -0.5
    - 0.8660254037844386
    a9:
    - 0.2781518997184476
    - 0.23339715646500916
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.5908929749574752
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0.9396926207859084
          - -0.3420201433256687
    - - 37
      - - - 1.0
          - 0
        - - 2.563680537885292
          - -5.516116577780801
    bad_primes:
    - 2
    - 37
    central_character: '74.7'
    coefficient_field: CDF
    conductor: 74
    conductor_radical: 74
    conjugate: '3219913097137029656501749817575'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0.9396926207859084
        - -0.3420201433256687
    - - - 1.0
        - 0
      - - -1.7232798302233832
        - -0.6272225635126262
      - - 2.298133329356934
        - 1.928362829059618
    - - - 1.0
        - 0
      - - 0.32635182233306964
        - 1.8508331567966467
      - - -4.698463103929542
        - 1.7101007166283437
    - - - 1.0
        - 0
      - - -0.5984888042569352
        - -3.3941986748270985
      - - -6.5778483455013586
        - 2.3941410032796813
    - - - 1.0
        - 0
      - - -1.4048305889404245
        - 2.4332379560717237
      - - -5.5
        - -9.526279441628825
    - - - 1.0
        - 0
      - - 2.6587675754599327
        - -2.2309708919545406
      - - 2.2574263096700946
        - -12.802500789158705
    - - - 1.0
        - 0
      - - 2.374173432644299
        - 1.9921680516827283
      - - 2.952019020337816
        - 16.741731801207536
    - - - 1.0
        - 0
      - - 6.997477163163846
        - 2.546873402349146
      - - 14.554844419260583
        - 12.212964584044247
    - - - 1.0
        - 0
      - - -0.3217686344803183
        - -0.5573196232019703
      - - -11.5
        - 19.91858428704209
    - - - 1.0
        - 0
      - - 1.0844936844019368
        - -1.8783981618717218
      - - -14.5
        - -25.11473670974872
    - - - 1.0
        - 0
      - - -9.907163023239015
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - 2.563680537885292
        - -5.516116577780801
    - - - 1.0
        - 0
      - - 8.13802952121466
        - -6.828617569761039
      - - 7.119575284344144
        - -40.37711787350053
    - - - 1.0
        - 0
      - - -8.304650664725493
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - -3.9282137852612053
        - -6.803865859064866
      - - -23.5
        - 40.703193977868615
    - - - 1.0
        - 0
      - - -0.8393937742837498
        - 4.760438651595721
      - - -49.803708901653145
        - -18.127067596260442
    - - - 1.0
        - 0
      - - -0.0961039064107862
        - 0.5450323372217336
      - - -55.44186462636859
        - -20.179188456214455
    - - - 1.0
        - 0
      - - -5.371021974733378
        - 4.506822558043844
      - - 10.592538837682751
        - -60.07327293374469
    - - - 1.0
        - 0
      - - -0.03664346607961341
        - -0.20781542298508976
      - - -62.95940559265586
        - 22.915349602819806
    - - - 1.0
        - 0
      - - 4.751966949779045
        - 1.72957452393633
      - - 54.38915546144744
        - 45.63792028774429
    - - - 1.0
        - 0
      - - -10.22970029880995
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - 0.33077501569058076
        - 1.8759183328697533
      - - -74.23571704208676
        - 27.01959132272783
    - - - 1.0
        - 0
      - - -5.216503104838659
        - -4.377165831305255
      - - 14.412798746355218
        - 81.73904350001327
    - - - 1.0
        - 0
      - - 1.6822570008021132
        - -9.540553544573639
      - - -83.63264324994584
        - -30.439792755984517
    - - - 1.0
        - 0
      - - 8.52990053168934
        - 14.774221104394718
      - - -48.5
        - 84.00446416709055
    - - - 1.0
        - 0
      - - 5.9891059555342085
        - 10.373435806898598
      - - -50.5
        - 87.4685657822283
    - - - 1.0
        - 0
      - - 6.472327754613696
        - -11.21040051422911
      - - -51.5
        - -89.20061658979718
    - - - 1.0
        - 0
      - - -11.970556255837552
        - 10.044489339260172
      - - 18.580355010361547
        - -105.37442957230627
    - - - 1.0
        - 0
      - - 1.4566288215348737
        - -0.5301695334129503
      - - 83.49884429996861
        - -70.06384945583278
    - - - 1.0
        - 0
      - - -4.806291402161776
        - 1.7493470075964557
      - - 86.56302207244451
        - -72.63499989457894
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9593025
    index: 0
    label: 2-74-37.7-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/7/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 0.8866179530343891
    - 0.8824736855391156
    - 0.8892046472034342
    - 0.9049554543918471
    - 0.9271739214040833
    - 0.952819383123198
    - 0.9785383951670534
    - 1.0007908203746168
    - 1.0159388974625294
    - 1.0203235116958698
    - 1.0103499684417305
    - 0.9825981414473131
    - 0.9339640348608319
    - 0.8618333465003685
    - 0.764282592945825
    - 0.6402993065898214
    - 0.49000936518310817
    - 0.31489650856211227
    - 0.11799657697369348
    - -0.09595284951694338
    - -0.3204276627363073
    - -0.5471172646040873
    - -0.766027653113248
    - -0.9657023338946903
    - -1.1335705843055077
    - -1.2564255492114702
    - -1.3210259708537504
    - -1.3148053950692575
    - -1.2266619843762412
    - -1.0477913154313052
    - -0.7725146074341904
    - -0.3990466896610836
    - 0.06985731778868708
    - 0.6264391964473381
    - 1.2577182389501838
    - 1.9455665880294732
    - 2.6671169576996423
    - 3.395521495967407
    - 4.101057116021628
    - 4.752545873977931
    - 5.319030639139381
    - 5.771618560711718
    - 6.085380169242368
    - 6.2411729795819735
    - 6.227247707149037
    - 6.0404948393034195
    - 5.687200865749278
    - 5.183207640000743
    - 4.5534047127102335
    - 3.830531431464787
    - 3.0533202854917803
    - 2.2640713864216124
    - 1.505805196782206
    - 0.8191911624730039
    - 0.23948819870045077
    - -0.20624609361691118
    - -0.5014211083114017
    - -0.6414218295818275
    - -0.6341770079629121
    - -0.49967444985361786
    - -0.26839949846624506
    - 0.021227896963731226
    - 0.3262408645305802
    - 0.6030682415312744
    - 0.8116876862984419
    - 0.9195981983432523
    - 0.9052100947858852
    - 0.7602800057423299
    - 0.49108917659959767
    - 0.11817172031535661
    - -0.32546263342391313
    - -0.7975114766897615
    - -1.2507112660175757
    - -1.6379182680778073
    - -1.9174299014730365
    - -2.05797517144775
    - -2.042799366047813
    - -1.8723290137644653
    - -1.5650269714824747
    - -1.156225625572642
    - -0.694942571020443
    - -0.2389158073872179
    - 0.15168147505674523
    - 0.42120019252128255
    - 0.525378122976006
    - 0.43729308997033556
    - 0.15164479624047572
    - -0.3132502050534642
    - -0.9161348062212099
    - -1.596248866720233
    - -2.2792912980481113
    - -2.8853490209735875
    - -3.3379598479643637
    - -3.573284552238223
    - -3.5482852341132824
    - -3.2468607282365882
    - -2.6830779663985185
    - -1.9009466466205842
    - -0.9705824153742361
    - 0.01895368257154601
    - 0.9694183434431363
    - 1.7846629477735756
    - 2.3820856661875465
    - 2.70282822587786
    - 2.71937507936155
    - 2.4394807436896353
    - 1.9057745286399628
    - 1.1909239018522448
    - 0.3888137839743037
    - -0.3972555760143978
    - -1.0679101133565907
    - -1.540872931544706
    - -1.7622044692735328
    - -1.7140375047966738
    - -1.417642086955634
    - -0.9312437172381355
    - -0.3427128609261813
    - 0.2420462198267178
    - 0.7135528494043692
    - 0.9741482550037497
    - 0.952226530499191
    - 0.6132753433636391
    - -0.033921507978210204
    - -0.9369434156831169
    - -2.005483201229467
    - -3.1225594123464706
    - -4.159762459501913
    - -4.9944844522674865
    - -5.526736333717691
    - -5.6931471105679625
    - -5.476082915076623
    - -4.906480565727634
    - -4.05987464963191
    - -3.0460844022417772
    - -1.9939716033679706
    - -1.0334388390197764
    - -0.2772873582835251
    - 0.19438310498561806
    - 0.3448951876120361
    - 0.18520976477844295
    - -0.22901093033957223
    - -0.8070425715979278
    - -1.4379417905510459
    - -2.008263993295986
    - -2.419852902853604
    - -2.604866763538885
    - -2.53563267126403
    - -2.2277476299373875
    - -1.7359468532228717
    - -1.1434610003337486
    - -0.546686506770834
    - -0.03780886773978954
    - 0.3115984713196559
    - 0.4631047961688865
    - 0.4178193379465598
    - 0.21543428269043538
    - -0.07402207418607364
    - -0.3643460319402098
    - -0.5707481497744199
    - -0.6276838606389943
    - -0.5035798258803997
    - -0.20954938911813326
    - 0.19982850993253234
    - 0.6342209971755547
    - 0.9827634137514307
    - 1.134382710230749
    - 0.9997498983414791
    - 0.5309008464363864
    - -0.2652339151100043
    - -1.322260758768252
    - -2.52013520470929
    - -3.7009930764796586
    - -4.692830069549911
    - -5.337344664760526
    - -5.5173233885103095
    - -5.178784471256121
    - -4.3437710736470985
    - -3.111116614423095
    - -1.6444716558767924
    - -0.14905823349670455
    - 1.1593738514444534
    - 2.0884361993224454
    - 2.5002185963980645
    - 2.3343105566981674
    - 1.6186407579202855
    - 0.4660357321144352
    - -0.9431906976157953
    - -2.389890586011284
    - -3.651261328046695
    - -4.5366370157630795
    - -4.917803462869494
    - -4.748651696828432
    - -4.070822221979617
    - -3.0044478429601913
    - -1.7257396324761733
    - -0.43549991317923775
    - 0.6757448462305413
    - 1.459724172345857
    - 1.833826855659816
    - 1.7918680242796767
    - 1.40054675473173
    - 0.7826170571548872
    - 0.0902907181344716
    - -0.5257930295068413
    - -0.9459125158175997
    - -1.1032121406376911
    - -0.9940688579185896
    - -0.6750422048931843
    - -0.24729021112259011
    - 0.1681227200322625
    - 0.45874108289757426
    - 0.5469803786897217
    - 0.40850900279994357
    - 0.07873781673124804
    - -0.3541275108476816
    - -0.7681905218508871
    - -1.0352362332179037
    - -1.0506394135263544
    - -0.7593950214770385
    - -0.17250618352860045
    - 0.6301582560486452
    - 1.5116814269225471
    - 2.3026770616823797
    - 2.8339705962550705
    - 2.9708772748519023
    - 2.6420326421546445
    - 1.8566480207427378
    - 0.7062849233321525
    - -0.6496618677421532
    - -2.012237577985037
    - -3.17952186661417
    - -3.984273707740147
    - -4.324997443016332
    - -4.184030560168862
    - -3.6288507619214085
    - -2.7962474801924686
    - -1.8625906224929478
    - -1.006398311427983
    - -0.3711093343319746
    - -0.03601230473079379
    - -0.0016245227348716026
    - -0.19276665156395545
    - -0.47876926459672353
    - -0.7064801213602735
    - -0.738835310416312
    - -0.4903675303833183
    - 0.04850578140312233
    - 0.8042943203312429
    - 1.6325879394003784
    - 2.347548954509174
    - 2.762806082020342
    - 2.7350559793684015
    - 2.2007424802008315
    - 1.197331168696017
    - -0.13625640446653964
    - -1.5811437894310056
    - -2.8783022001555514
    positive_zeros:
    - '2.31994716054009641416243844544723'
    - '3.98282362841921112276334608741564'
    - '6.81210004841551863407061843341275'
    - '7.61627413552245467125509416649073'
    - '8.659827450074097166176740484543460'
    - '10.19770910535915263496537469185150'
    - '10.79591377197980021092610537142206'
    - '12.37259948542458278860797179980844'
    - '13.56049440175055657754565301190986'
    - '14.57163821606939409590157019002268'
    prelabel: 2-74-37.7-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.7686956321961738
    root_angle: -0.12091203101785276
    root_number: 0.9287179093221553 - 0.3707870614035568*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.0604560155089'
      prec: 54
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '2.31994716054009641416243844545'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '3.98282362841921112276334608742'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '6.81210004841551863407061843341'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.5908929749574752
    bad_primes:
    - 2
    - 37
    central_character: '37.7'
    conductor: 74
    conductor_radical: 74
    degree: 2
    id: 9593025
    index: 0
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/74/2/f/b/7/2
    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: 2-74-37.7-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: 2-74-37.7-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.7686956321961738
    root_angle: -0.06045601550892638
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '2.31994716054009641416243844545'
      prec: 103
- - Lhash: '2940882410556429695424905824864'
    Lhash_array:
    - '2940882410556429695424905824864'
    id: 9959052
    label: 2-74-37.7-c1-0-0
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/74/2/f/b/7/2
label_cols:
- label
- label
- label
labels:
- 2-74-37.7-c1-0-0
- 2-74-37.7-c1-0-0
- 2-74-37.7-c1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T05:43:35.591859'