data:
- - Lhash: '1719086495584536713702763679448'
    a10:
    - 0.0
    - 0.0
    a2:
    - -0.7330518718298263
    - 0.6801727377709194
    a3:
    - 1.9555728057861408
    - -0.2947551744109042
    a4:
    - 0.07473009358642425
    - -0.9972037971811801
    a5:
    - 0.0
    - 0.0
    a6:
    - -1.2330518718298262
    - 1.546198141555358
    a7:
    - 0.6234898018587335
    - 0.7818314824680298
    a8:
    - 0.6234898018587335
    - 0.7818314824680298
    a9:
    - 2.7818115801021355
    - -0.8580752324745262
    accuracy: 100
    algebraic: true
    analytic_conductor: 1.6628846220931641
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0.7330518718298263
          - -0.6801727377709194
    - - 7
      - - - 1.0
          - 0
        - - -0.6234898018587335
          - -0.7818314824680298
    - - 17
      - - - 1.0
          - 0
        - - -0.8262387743159949
          - 0.5633200580636221
    bad_primes:
    - 2
    - 7
    - 17
    central_character: '3332.1971'
    coefficient_field: CDF
    conductor: 3332
    conductor_radical: 238
    conjugate: '1954370889001834133254355881034'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0.7330518718298263
        - -0.6801727377709194
    - - - 1.0
        - 0
      - - -1.9555728057861408
        - 0.2947551744109042
      - - 0.9555728057861407
        - -0.2947551744109042
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.7330518718298263
        - 0.6801727377709194
    - - - 1.0
        - 0
      - - -0.6234898018587335
        - -0.7818314824680298
    - - - 1.0
        - 0
      - - 1.400968867902419
        - 0.43214166466688053
      - - 0.8262387743159949
        - 0.5633200580636221
    - - - 1.0
        - 0
      - - -0.32623877431599485
        - -1.4293454618480608
      - - -0.9009688679024191
        - 0.4338837391175581
    - - - 1.0
        - 0
      - - -0.8262387743159949
        - 0.5633200580636221
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0.3677108474634313
        - 0.2507010108732849
      - - 0.36534102436639504
        - 0.9308737486442042
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.6234898018587335
        - -0.7818314824680298
    - - - 1.0
        - 0
      - - 0.6234898018587335
        - -1.0799160148203788
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.9888308262251285
        - -0.14904226617617444
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.2225209339563144
        - -0.9749279121818236
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.2225209339563144
        - 0.9749279121818236
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.07473009358642425
        - 0.9972037971811801
    - - - 1.0
        - 0
      - - -0.05460393788372161
        - 0.7286389135284623
      - - -0.9888308262251285
        - -0.14904226617617444
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.7330518718298263
        - -0.6801727377709194
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.9888308262251285
        - -0.14904226617617444
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0.6583217782434021
        - -0.3170310594102608
      - - 0.6234898018587335
        - -0.7818314824680298
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.07473009358642425
        - -0.9972037971811801
    - - - 1.0
        - 0
      - - 0.9555728057861407
        - 1.655100649952743
      - - -0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.9009688679024191
        - 0.4338837391175581
    - - - 1.0
        - 0
      - - 1.8897996941275477
        - -0.5829260052937326
      - - 0.8262387743159949
        - -0.5633200580636221
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - -0.4400711179528193
        - 0.0663300485369759
      - - 0.9555728057861407
        - -0.2947551744109042
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.7330518718298263
        - 0.6801727377709194
    - - - 1.0
        - 0
      - - -0.14282009041008062
        - 0.04405416353761935
      - - 0.8262387743159949
        - -0.5633200580636221
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.8262387743159949
        - -0.5633200580636221
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.9009688679024191
        - 0.4338837391175581
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 19535488
    index: 1
    label: 2-3332-3332.1971-c0-0-1
    leading_term: '1.8589682947134335760914587602301'
    load_key: CMFs-workshop
    motivic_weight: 0
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 0
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/3332/1/cc/b/1971/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.05078125'
      prec: 34
    plot_values:
    - 1.8589682947134336
    - 1.8477525073730174
    - 1.8480214036350513
    - 1.8580076957011402
    - 1.8752578391627484
    - 1.8968704579844242
    - 1.9197331161378706
    - 1.940723525724846
    - 1.9568614196162488
    - 1.965413035787615
    - 1.9639581681617018
    - 1.9504314109532723
    - 1.9231474105421773
    - 1.8808169749873846
    - 1.8225580770046719
    - 1.7479036145150115
    - 1.6568063167529088
    - 1.5496402835248433
    - 1.4271981678455476
    - 1.2906828275880415
    - 1.1416922845935211
    - 0.9821969751618501
    - 0.8145085114184644
    - 0.6412394705551245
    - 0.4652540687711174
    - 0.28960994395806766
    - 0.11749165303809093
    - -0.04786312558828956
    - -0.2032433187547269
    - -0.34554839490833067
    - -0.4718744709236497
    - -0.5796002770008608
    - -0.6664704531296554
    - -0.7306735070196173
    - -0.7709117008608881
    - -0.7864601615492657
    - -0.7772126326475652
    - -0.7437115102325058
    - -0.6871601296468106
    - -0.6094156933182674
    - -0.5129617447688617
    - -0.40085969039758235
    - -0.2766795343923313
    - -0.1444107053051167
    - -0.008354594099984906
    - 0.12699883138777088
    - 0.2571072482009899
    - 0.3775212771400272
    - 0.4840345073902597
    - 0.5728334108278527
    - 0.6406419595416195
    - 0.6848555680015445
    - 0.7036589676280127
    - 0.6961228014637021
    - 0.6622741094484045
    - 0.6031364628300107
    - 0.5207362943705975
    - 0.4180729461066092
    - 0.2990510972246183
    - 0.16837551182135815
    - 0.03140942305942192
    - -0.10600069714089835
    - -0.23772979452047802
    - -0.35760273437306883
    - -0.45963977890321367
    - -0.5383110400804496
    - -0.5887909922953989
    - -0.6072034785456011
    - -0.5908473031327205
    - -0.5383925091639515
    - -0.4500378162080659
    - -0.3276204555897732
    - -0.17467078751091691
    - 0.0035943999094677857
    - 0.20034415524536947
    - 0.4072732909182312
    - 0.6148096935391941
    - 0.8123862023682398
    - 0.9887716331548059
    - 1.1324529393780767
    - 1.2320580402065642
    - 1.2768066066876176
    - 1.2569741854181793
    - 1.1643535471131798
    - 0.9926961610075562
    - 0.7381162858400139
    - 0.3994403874567525
    - -0.02151452602394037
    - -0.519748509612928
    - -1.0869848817640322
    - -1.7116848610657467
    - -2.3791771290495816
    - -3.07190501390981
    - -3.769789870520435
    - -4.450704926803536
    - -5.091049529228131
    - -5.66640951516241
    - -6.152285535317128
    - -6.524867711621249
    - -6.761832201427715
    - -6.843133188829881
    - -6.751762656382083
    - -6.4744500953782325
    - -6.002275146006158
    - -5.331168038294967
    - -4.4622756084037025
    - -3.402174528346991
    - -2.1629181053941133
    - -0.7619084358299579
    - 0.7784083427163229
    - 2.4310196741331076
    - 4.16498668175146
    - 5.9462301198029275
    - 7.738439736500591
    - 9.50407943015915
    - 11.205456273311448
    - 12.805818243792135
    - 14.27044350081058
    - 15.567683398671655
    - 16.669922210739614
    - 17.554418755431634
    - 18.20399872992896
    - 18.60757146252868
    - 18.760450831115918
    - 18.664467051207584
    - 18.327863655782547
    - 17.76498197874183
    - 16.995743498410945
    - 16.04494816986637
    - 14.941414050429382
    - 13.71698979346591
    - 12.40547667424123
    - 11.041500484124501
    - 9.659375707088815
    - 8.292004760844435
    - 6.969853701016758
    - 5.720042682618971
    - 4.565584756457325
    - 3.524800429669916
    - 2.610928086536138
    - 1.8319421522724666
    - 1.1905821376906314
    - 0.6845868051294476
    - 0.30711903801184753
    - 0.04735896529921842
    - -0.10876414682928498
    - -0.177736445215144
    - -0.17755982547099255
    - -0.1268297442754962
    - -0.0438326400267117
    - 0.05429640425179629
    - 0.1523184997014066
    - 0.23750614529406616
    - 0.30010323729564453
    - 0.33361215415553497
    - 0.33489879740668027
    - 0.304115499329656
    - 0.24445070956833775
    - 0.1617229038124296
    - 0.06384379426116167
    - -0.03981772064620722
    - -0.1391346760820143
    - -0.22394513823554085
    - -0.28475929733562083
    - -0.31341175346102057
    - -0.3036233935845708
    - -0.2514423304979198
    - -0.15554006761510997
    - -0.017347030923967128
    - 0.15897953828783323
    - 0.3667530693547219
    - 0.5971090737442101
    - 0.8394904035831797
    - 1.0822386901119452
    - 1.313258165703778
    - 1.520713754086277
    - 1.693723064310418
    - 1.8230018972565396
    - 1.9014251037755512
    - 1.9244690335486154
    - 1.890508175922611
    - 1.800946599308009
    - 1.6601740284295905
    - 1.4753463666983313
    - 1.2560006309143579
    - 1.0135240514584225
    - 0.7605059450396243
    - 0.5100083697631719
    - 0.274797073115003
    - 0.06657748701818755
    - -0.10471872757279026
    - -0.2315529352000188
    - -0.30926533978034887
    - -0.3363949061485516
    - -0.3148097795893573
    - -0.2496350424842846
    - -0.1489761526189432
    - -0.02344834437766298
    - 0.11446602565510991
    - 0.2511994169726042
    - 0.37297831759756966
    - 0.4667506086840109
    - 0.5211074431167271
    - 0.5271444180038342
    - 0.47920835557675623
    - 0.37548066999325797
    - 0.21835592417324287
    - 0.014584433733635552
    - -0.2248398419699188
    - -0.48505100091215325
    - -0.7479327287865916
    - -0.992965295392819
    - -1.1982599202536404
    - -1.3417303469492927
    - -1.4023418052805576
    - -1.3613709045601647
    - -1.2036068603126657
    - -0.918425098561075
    - -0.5006687909147302
    - 0.048717880761072814
    - 0.7223492937526098
    - 1.5063808675088273
    - 2.3808279305769573
    - 3.3202165695544474
    - 4.294543880949331
    - 5.270507567428041
    - 6.212949030430781
    - 7.086440936718104
    - 7.856940481143967
    - 8.493423865994593
    - 8.969416292341272
    - 9.264335194702516
    - 9.364572473679194
    - 9.264253759374398
    - 8.965628691174567
    - 8.479065025811943
    - 7.822640103511221
    - 7.02134469967181
    - 6.105935385465612
    - 5.111491029295119
    - 4.0757458699071485
    - 3.03728468753974
    - 2.0336941867548703
    - 1.09976821738
    - 0.26586260866696504
    - -0.4435118138698749
    - -1.010781704412434
    - -1.426029516541996
    - -1.6872982500167564
    - -1.8004659036444104
    - -1.778696817355794
    - -1.6415008522126258
    - -1.4134536217119742
    - -1.1226504519896292
    - -0.7989822529685943
    - -0.47233207801198746
    - -0.17079615679104312
    positive_zeros:
    - '1.35612012906003454602534806277873'
    - '2.23748452126035914842930989058018'
    - '3.05841681744816473345643522185573'
    - '3.70606342822045487934250674999741'
    - '4.41558787284496910939108645033472'
    - '5.51001513911989508036411613555306'
    - '7.32497587525810460632487716127816'
    - '7.58955916229801554869883680724607'
    - '8.105517268152289020637854959101652'
    - '8.536747489391904120441557406183306'
    prelabel: 2-3332-3332.1971-c0-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.2895288372476066
    root_angle: -0.20408163265306123
    root_number: 0.80141362186795665978698328953346 - 0.59811053049121596205926635490525*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.10204081632653061'
      prec: 67
    spectral_label: c0-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.35612012906003454602534806278'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.23748452126035914842930989058'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.05841681744816473345643522186'
      prec: 103
- - algebraic: true
    analytic_conductor: 1.6628846220931641
    bad_primes:
    - 2
    - 7
    - 17
    central_character: '3332.1971'
    conductor: 3332
    conductor_radical: 238
    degree: 2
    id: 19535488
    index: 1
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/3332/1/cc/b/1971/1
    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: 2-3332-3332.1971-c0-0-1
    motivic_weight: 0
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 0
    order_of_vanishing: 0
    prelabel: 2-3332-3332.1971-c0-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.2895288372476066
    root_angle: -0.10204081632653061
    self_dual: false
    spectral_label: c0-0
    z1:
      __RealLiteral__: 0
      data: '1.35612012906003454602534806278'
      prec: 103
- - Lhash: '1719086495584536713702763679448'
    Lhash_array:
    - '1719086495584536713702763679448'
    id: 19901958
    label: 2-3332-3332.1971-c0-0-1
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/3332/1/cc/b/1971/1
label_cols:
- label
- label
- label
labels:
- 2-3332-3332.1971-c0-0-1
- 2-3332-3332.1971-c0-0-1
- 2-3332-3332.1971-c0-0-1
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-01T01:44:22.302939'