data:
- - Lhash: '1879552204824026032767267500916'
    a10:
    - 0.0
    - 0.0
    a2:
    - -1.0
    - 0.0
    a3:
    - -1.0
    - 0.0
    a4:
    - 1.0
    - 0.0
    a5:
    - 0.0
    - 0.0
    a6:
    - 1.0
    - 0.0
    a7:
    - 2.3722813232690143
    - 0.0
    a8:
    - -1.0
    - 0.0
    a9:
    - 1.0
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 37.1304369398954
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 1.0
          - 0
    - - 3
      - - - 1.0
          - 0
        - - 1.0
          - 0
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 31
      - - - 1.0
          - 0
        - - 1.0
          - 0
    bad_primes:
    - 2
    - 3
    - 5
    - 31
    central_character: '4650.1'
    coefficient_field: CDF
    conductor: 4650
    conductor_radical: 930
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -2.3722813232690143
        - 0
      - - 7.0
        - 0
    - - - 1.0
        - 0
      - - -6.372281323269014
        - 0
      - - 11.0
        - 0
    - - - 1.0
        - 0
      - - -2.0
        - 0
      - - 13.0
        - 0
    - - - 1.0
        - 0
      - - 6.744562646538029
        - 0
      - - 17.0
        - 0
    - - - 1.0
        - 0
      - - 6.372281323269014
        - 0
      - - 19.0
        - 0
    - - - 1.0
        - 0
      - - -2.3722813232690143
        - 0
      - - 23.0
        - 0
    - - - 1.0
        - 0
      - - -2.7445626465380286
        - 0
      - - 29.0
        - 0
    - - - 1.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 10.744562646538029
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - 10.744562646538029
        - 0
      - - 41.0
        - 0
    - - - 1.0
        - 0
      - - 6.372281323269014
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - 4.744562646538029
        - 0
      - - 47.0
        - 0
    - - - 1.0
        - 0
      - - -4.372281323269014
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - 8.744562646538029
        - 0
      - - 59.0
        - 0
    - - - 1.0
        - 0
      - - 11.489125293076057
        - 0
      - - 61.0
        - 0
    - - - 1.0
        - 0
      - - -0.7445626465380286
        - 0
      - - 67.0
        - 0
    - - - 1.0
        - 0
      - - 2.3722813232690143
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - 9.116843969807043
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - 10.372281323269014
        - 0
      - - 79.0
        - 0
    - - - 1.0
        - 0
      - - -12.0
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - -4.372281323269014
        - 0
      - - 89.0
        - 0
    - - - 1.0
        - 0
      - - 2.0
        - 0
      - - 97.0
        - 0
    - - - 1.0
        - 0
      - - 9.116843969807043
        - 0
      - - 101.0
        - 0
    - - - 1.0
        - 0
      - - -8.0
        - 0
      - - 103.0
        - 0
    - - - 1.0
        - 0
      - - 6.372281323269014
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 6.744562646538029
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - -8.372281323269014
        - 0
      - - 113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 20036822
    index: 76
    label: 2-4650-1.1-c1-0-76
    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: 1
    origin: ModularForm/GL2/Q/holomorphic/4650/2/a/by/1/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.05078125'
      prec: 34
    plot_values:
    - -3.8650758952340685e-61
    - 0.13886547664370755
    - 0.27685991952291117
    - 0.4130753769143281
    - 0.5465334092927302
    - 0.6761579407247902
    - 0.8007570951158017
    - 0.9190159075590989
    - 1.0295010477301765
    - 1.1306779384221792
    - 1.2209399593559949
    - 1.2986488314035682
    - 1.362184792806413
    - 1.4100048023344496
    - 1.4407067197663765
    - 1.4530972036256509
    - 1.4462609140269767
    - 1.4196285042080699
    - 1.373040823353255
    - 1.3068067366887568
    - 1.2217520016987615
    - 1.1192567292491749
    - 1.0012791137209975
    - 0.8703633445151313
    - 0.7296299181238324
    - 0.5827469581481637
    - 0.4338816194538674
    - 0.2876311974671608
    - 0.14893417567120118
    - 0.0229621108042525
    - -0.08500604074063828
    - -0.16972483069100822
    - -0.2261354215090065
    - -0.24952716217450552
    - -0.23570329309968088
    - -0.1811459019868843
    - -0.08317483436804181
    - 0.05990501310701911
    - 0.24867369822859994
    - 0.4824891431874825
    - 0.7594082781191752
    - 1.0761412621899087
    - 1.428042930629151
    - 1.809144716507486
    - 2.2122292069142904
    - 2.628948237456662
    - 3.0499840379437804
    - 3.4652514548530435
    - 3.8641377388369587
    - 4.235774850112481
    - 4.569337757396103
    - 4.854360845927485
    - 5.081063366290575
    - 5.240673905543005
    - 5.325743198661047
    - 5.330434267824376
    - 5.250778916819515
    - 5.084890043737052
    - 4.833120079840259
    - 4.498157113872752
    - 4.085051901182644
    - 3.60117095155101
    - 3.0560731879803535
    - 2.4613102049602067
    - 1.8301528489971883
    - 1.1772496048568155
    - 0.5182249974987255
    - -0.13077119389990324
    - -0.753550774725302
    - -1.3343949053097772
    - -1.8585661460482252
    - -2.3128071213916632
    - -2.6858077549346184
    - -2.9686232935481565
    - -3.155026289349628
    - -3.241777345908843
    - -3.2288017336437447
    - -3.119261884879191
    - -2.9195192098861713
    - -2.6389825237685987
    - -2.2898445096384306
    - -1.8867119164473047
    - -1.4461394366116564
    - -0.9860812578816659
    - -0.5252779634449557
    - -0.08259959790258772
    - 0.32363182803723556
    - 0.6763154862741786
    - 0.9602149149096366
    - 1.1625459026157023
    - 1.2734850516048886
    - 1.2865773271899694
    - 1.1990241976048368
    - 1.011838132853271
    - 0.7298541283538291
    - 0.3615943730632964
    - -0.08101201409092464
    - -0.5830463321109967
    - -1.127141085940096
    - -1.6941251512806426
    - -2.2637494569312757
    - -2.815465380851268
    - -3.329225163649628
    - -3.786271965119832
    - -4.169886841214974
    - -4.466060961628027
    - -4.664063823685254
    - -4.756881986375914
    - -4.741507826969559
    - -4.619063830883704
    - -4.3947547293054905
    - -4.077647120136191
    - -3.68028373428264
    - -3.218146908968216
    - -2.7089927646027765
    - -2.172083723562418
    - -1.627352055087518
    - -1.0945308180162647
    - -0.5922906941683213
    - -0.13742161795659621
    - 0.2559032544240946
    - 0.5767468156159334
    - 0.8178808822958283
    - 0.9760893082696741
    - 1.05228546508406
    - 1.05143662216304
    - 0.9822966922356858
    - 0.8569578615192631
    - 0.6902403683434472
    - 0.49894770154120344
    - 0.30102135714602934
    - 0.11463465868458143
    - -0.04273128447220339
    - -0.15518485214398975
    - -0.2092503788004631
    - -0.19458251434881246
    - -0.10453201153428467
    - 0.06346681307471895
    - 0.3077083809893207
    - 0.6222398118293482
    - 0.9970981184490318
    - 1.4187516174276351
    - 1.8707261858495612
    - 2.3343874203443162
    - 2.7898414552061674
    - 3.216910622449622
    - 3.596135660654806
    - 3.9097540761850316
    - 4.142604689590199
    - 4.282911394983023
    - 4.322904622300883
    - 4.25924669266907
    - 4.093236844531724
    - 3.830782724742752
    - 3.482137040416201
    - 3.0614102504150202
    - 2.5858820069501536
    - 2.075144908292801
    - 1.5501234004076812
    - 1.032017845189302
    - 0.5412284319630966
    - 0.09631544759582414
    - -0.28694871655381604
    - -0.5963845549885872
    - -0.8240230969183866
    - -0.9665013003986787
    - -1.025211744281163
    - -1.0061960967890744
    - -0.9197855543068633
    - -0.7800052169815851
    - -0.6037724491036357
    - -0.4099309331917619
    - -0.21817170023444882
    - -0.04789933774631931
    - 0.0828945907175511
    - 0.1586884077653281
    - 0.1673579360707863
    - 0.1009216620222182
    - -0.0439403612564524
    - -0.26562569205890196
    - -0.5576246128394445
    - -0.9088138319686212
    - -1.3040158289437773
    - -1.7247957678938999
    - -2.150454108417546
    - -2.559161387027845
    - -2.929172828506974
    - -3.2400550290327055
    - -3.4738553045252325
    - -3.6161465828512274
    - -3.656886879611668
    - -3.5910421523405636
    - -3.418934181987444
    - -3.1462903989587256
    - -2.7839894149145237
    - -2.3475134930350863
    - -1.856136284264944
    - -1.3318898717368974
    - -0.7983685564964601
    - -0.27943705757401127
    - 0.20208277100834465
    - 0.6256704333452927
    - 0.9742365174831095
    - 1.2350563848654164
    - 1.4004513591389833
    - 1.4681752850878451
    - 1.4414814047172158
    - 1.328863345411734
    - 1.143483538097764
    - 0.9023214206271378
    - 0.6250911762484469
    - 0.3329934257220602
    - 0.04737629173086616
    - -0.21161215586801532
    - -0.4262963765239991
    - -0.5825904760258063
    - -0.6708881022436525
    - -0.6866662706010145
    - -0.6307611768700191
    - -0.5092939005279066
    - -0.33324552905716137
    - -0.1177033474035334
    - 0.11917901890990414
    - 0.35744557980755104
    - 0.5767485487318605
    - 0.7578168665493918
    - 0.8838882279070568
    - 0.9420101258599451
    - 0.9241213352965634
    - 0.8278368813179852
    - 0.6568763105881092
    - 0.42109609283043664
    - 0.13611103017609277
    - -0.17748477267490012
    - -0.4952610801449269
    - -0.7903983304945639
    - -1.0353564364913632
    - -1.2036673012309151
    - -1.2717417703362484
    - -1.2205772322526047
    - -1.0372545205938706
    - -0.7161222113471023
    - -0.2595824555680041
    - 0.32158566272387035
    - 1.008402792397077
    - 1.7743739868065476
    - 2.5866584299241904
    - 3.407670836591825
    - 4.197033109985837
    - 4.913770986019073
    - 5.518632302838648
    - 5.976392467404435
    - 6.2580095125820785
    - 6.342496244630489
    - 6.218390268802549
    - 5.884723539619435
    - 5.351420420682181
    positive_zeros:
    - '1.48270525370762976810609932868486'
    - '1.85955530219704585871673093710944'
    - '3.39198590475853754033954296876088'
    - '4.32630470800383424636289952300778'
    - '4.86624348356107088704035931926541'
    - '6.05975329508170626646811782589633'
    - '6.68804144562419707163809570057475'
    - '6.94043384359763290796180965101896'
    - '8.187739174110367421553311030345200'
    prelabel: 2-4650-1.1-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.093474947835217
    root_angle: 1.0
    root_number: '-1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.48270525370762976810609932868'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '1.85955530219704585871673093711'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.39198590475853754033954296876'
      prec: 103
- - algebraic: true
    analytic_conductor: 37.1304369398954
    bad_primes:
    - 2
    - 3
    - 5
    - 31
    central_character: '1.1'
    conductor: 4650
    conductor_radical: 930
    degree: 2
    id: 20036822
    index: 76
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/4650/2/a/by/1/2
    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: 2-4650-1.1-c1-0-76
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    order_of_vanishing: 1
    prelabel: 2-4650-1.1-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.093474947835217
    root_angle: 0.5
    self_dual: true
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '1.48270525370762976810609932868'
      prec: 103
- - Lhash: '1879552204824026032767267500916'
    Lhash_array:
    - '1879552204824026032767267500916'
    id: 20434047
    label: 2-4650-1.1-c1-0-76
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/4650/2/a/by/1/2
label_cols:
- label
- label
- label
labels:
- 2-4650-1.1-c1-0-76
- 2-4650-1.1-c1-0-76
- 2-4650-1.1-c1-0-76
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T10:30:53.148195'