data:
- - Lhash: '592083357689682644469393507557'
    a10:
    - 0
    - 0
    a2:
    - 0
    - 0
    a3:
    - 0
    - 0
    a4:
    - 0
    - 0
    a5:
    - 0.3472963553338607
    - -0.6015349327217412
    a6:
    - 0
    - 0
    a7:
    - 0.3054072893322786
    - 0
    a8:
    - 0
    - 0
    a9:
    - 0
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 10.923534996511162
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 19
      - - - 1.0
          - 0
        - - -3.064177772475912
          - -3.1001313808715523
    bad_primes:
    - 2
    - 3
    - 19
    central_character: '1368.505'
    coefficient_field: CDF
    conductor: 1368
    conductor_radical: 114
    conjugate: '1807213874962817602440880814390'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -0.3472963553338607
        - 0.6015349327217412
      - - -2.5
        - -4.330127018922194
    - - - 1.0
        - 0
      - - -0.3054072893322786
        - 0
      - - 7.0
        - 0
    - - - 1.0
        - 0
      - - 4.822948255619545
        - 0
      - - 11.0
        - 0
    - - - 1.0
        - 0
      - - 0.5
        - 0.8660254037844386
      - - -6.5
        - 11.258330249197702
    - - - 1.0
        - 0
      - - 3.7587704831436337
        - -6.5103814507949895
      - - -8.5
        - -14.722431864335457
    - - - 1.0
        - 0
      - - -3.064177772475912
        - -3.1001313808715523
    - - - 1.0
        - 0
      - - -0.3472963553338607
        - -0.6015349327217412
      - - -11.5
        - 19.91858428704209
    - - - 1.0
        - 0
      - - -5.0641777724759125
        - -8.771413200489262
      - - -14.5
        - 25.11473670974872
    - - - 1.0
        - 0
      - - 1.8229482556195458
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - -6.517540966287267
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - -2.694592710667721
        - 4.667171480581237
      - - -20.5
        - -35.50704155516198
    - - - 1.0
        - 0
      - - 1.8472963553338606
        - -3.199611144075057
      - - -21.5
        - -37.239092362730865
    - - - 1.0
        - 0
      - - 3.0
        - 5.196152422706632
      - - -23.5
        - 40.703193977868615
    - - - 1.0
        - 0
      - - -2.7168814171420514
        - -4.705776652629766
      - - -26.5
        - 45.89934640057525
    - - - 1.0
        - 0
      - - 2.0418890660015823
        - -3.5366556057341008
      - - -29.5
        - -51.09549882328188
    - - - 1.0
        - 0
      - - 0.1945927106677214
        - 0.3370444616590437
      - - -30.5
        - 52.827549630850754
    - - - 1.0
        - 0
      - - -3.9114741278097727
        - -6.774871921857687
      - - -33.5
        - 58.023702053557386
    - - - 1.0
        - 0
      - - -5.453363193811355
        - 9.44550212380735
      - - -35.5
        - -61.48780366869514
    - - - 1.0
        - 0
      - - -2.194592710667721
        - 3.8011460767967984
      - - -36.5
        - -63.21985447626402
    - - - 1.0
        - 0
      - - 7.2168814171420514
        - -12.500005286689714
      - - -39.5
        - -68.41600689897065
    - - - 1.0
        - 0
      - - 0.7391701236163815
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 0.4114741278097728
        - 0.7126940953666164
      - - -44.5
        - 77.07626093681505
    - - - 1.0
        - 0
      - - 5.453363193811355
        - -9.44550212380735
      - - -48.5
        - -84.00446416709055
    - - - 1.0
        - 0
      - - -4.758770483143634
        - -8.242432258363866
      - - -50.5
        - 87.4685657822283
    - - - 1.0
        - 0
      - - 2.305407289332279
        - 0
      - - 103.0
        - 0
    - - - 1.0
        - 0
      - - 9.517540966287267
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 6.758770483143634
        - -11.706533873501622
      - - -54.5
        - -94.39676901250381
    - - - 1.0
        - 0
      - - -21.079659345523194
        - 0
      - - 113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23189381
    index: 3
    label: 2-1368-19.11-c1-0-3
    leading_term: '1.143204636295487046387206959407546680241710935615040211'
    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/1368/2/s/j/505/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 1.143204636295487
    - 1.027896033053584
    - 0.9052328677675436
    - 0.7748601447161317
    - 0.6363668105574404
    - 0.48935537843911103
    - 0.33351251416468874
    - 0.16867666718137328
    - -0.005100541324898023
    - -0.187501692099173
    - -0.377901462617605
    - -0.5753361540294119
    - -0.7784854692187732
    - -0.9856668221505042
    - -1.1948422391514235
    - -1.403637765957907
    - -1.6093751747246554
    - -1.8091156363739105
    - -1.9997148615158375
    - -2.1778890055561053
    - -2.340290378561783
    - -2.483591703828744
    - -2.6045773423126017
    - -2.7002395583201557
    - -2.7678775625882457
    - -2.8051967507953077
    - -2.8104052776990534
    - -2.7823048881263035
    - -2.72037278355435
    - -2.624831252904354
    - -2.4967018519479702
    - -2.3378410879455127
    - -2.1509548617131005
    - -1.9395893410034861
    - -1.7080964849581557
    - -1.4615731024789376
    - -1.2057730954306924
    - -0.9469933930444077
    - -0.6919350039757359
    - -0.44754156959946545
    - -0.2208187644738798
    - -0.018638822288543938
    - 0.15246466951827975
    - 0.2865058045189273
    - 0.37825270503884045
    - 0.4234242326489029
    - 0.4188698906026357
    - 0.3627257675029494
    - 0.2545396527330074
    - 0.09535900870971235
    - -0.1122236847404868
    - -0.3640726008574908
    - -0.6545602925964794
    - -0.9766709543124779
    - -1.3221549605282712
    - -1.6817325657070519
    - -2.0453427318998205
    - -2.4024311451228475
    - -2.742269661629323
    - -3.0542977698035085
    - -3.3284752397701936
    - -3.555634034853495
    - -3.7278168435358965
    - -3.838589313886332
    - -3.8833132771654197
    - -3.859368959484256
    - -3.7663154069591416
    - -3.605980076903565
    - -3.3824707395049964
    - -3.102105433410813
    - -2.77325914575545
    - -2.4061290440665952
    - -2.0124233592767946
    - -1.6049822780073602
    - -1.1973423124655147
    - -0.8032584389433584
    - -0.43620069530439876
    - -0.10884377748115383
    - 0.1674306361867759
    - 0.38299866562820695
    - 0.5304063225573952
    - 0.6047103442590963
    - 0.6037312556550734
    - 0.5282050084829014
    - 0.38182312898823756
    - 0.1711554947523899
    - -0.0945454917202817
    - -0.40365563826572654
    - -0.7425959071537906
    - -1.096341999510452
    - -1.44900850240288
    - -1.7844855895506433
    - -2.087103117535291
    - -2.3422947727681107
    - -2.5372338464540585
    - -2.6614123485869614
    - -2.7071365706685344
    - -2.6699148678575244
    - -2.5487172935471367
    - -2.3460916628843913
    - -2.068126469863537
    - -1.7242576074410885
    - -1.3269227705116453
    - -0.8910744538503186
    - -0.43356926781821403
    - 0.027542444936275473
    - 0.4737973166748608
    - 0.8871363792344427
    - 1.2507227790677244
    - 1.5497221394972434
    - 1.7720084409629342
    - 1.9087605813395099
    - 1.9549188101218806
    - 1.9094758789217356
    - 1.7755848081250245
    - 1.5604733491815812
    - 1.2751641694511993
    - 0.9340090941132094
    - 0.5540549642945245
    - 0.1542673545109068
    - -0.24535391430532066
    - -0.6247272466973607
    - -0.9646650023989178
    - -1.2478253158912205
    - -1.4595926620220596
    - -1.588842004580828
    - -1.6285458769248484
    - -1.576190442463862
    - -1.43397520530298
    - -1.2087812158117377
    - -0.9119038761931921
    - -0.5585582571959126
    - -0.16717660012790567
    - 0.24147121035732283
    - 0.6452935548879905
    - 1.0219806621094167
    - 1.3501413810450023
    - 1.6104155403661147
    - 1.7865040822739666
    - 1.8660619622861012
    - 1.8414045710969515
    - 1.70998694936194
    - 1.474625964977983
    - 1.1434483991045499
    - 0.7295619175194785
    - 0.2504604750095249
    - -0.27280995365917565
    - -0.8166860812809881
    - -1.3562716327069677
    - -1.866611311852388
    - -2.3239882855484697
    - -2.707176330549688
    - -2.9985787318851425
    - -3.1851906846262983
    - -3.2593301849565406
    - -3.21909384542387
    - -3.068508189005305
    - -2.817363057163294
    - -2.4807309673846234
    - -2.0781936467136948
    - -1.6328135821240963
    - -1.1699033140625263
    - -0.7156574738637893
    - -0.29572146909061264
    - 0.06622433696350251
    - 0.34978550561318034
    - 0.5390039035303891
    - 0.6232702882007563
    - 0.5979440795406926
    - 0.4646409846308167
    - 0.23116741768480967
    - -0.08889946892677304
    - -0.47696696549032724
    - -0.910478341013615
    - -1.364204041311683
    - -1.811700946269281
    - -2.2268570420701113
    - -2.585432429582367
    - -2.8665062484641077
    - -3.0537430456966717
    - -3.1364012465327185
    - -3.110020274013249
    - -2.9767407948070717
    - -2.7452335690741996
    - -2.430235266935466
    - -2.0517130576236475
    - -1.6337023863217175
    - -1.2028827504144126
    - -0.7869731931591872
    - -0.4130415501164427
    - -0.10582836498053942
    - 0.11381270054502259
    - 0.2302613898389211
    - 0.23417896047572215
    - 0.12318917755473632
    - -0.09785534719753398
    - -0.41704452728523755
    - -0.8160165734722616
    - -1.2709681843299656
    - -1.7540138375437828
    - -2.2348164561841326
    - -2.682393692354752
    - -3.0669916240873203
    - -3.361911688331289
    - -3.5451776773368695
    - -3.6009376861645963
    - -3.5205106532291013
    - -3.303007792819061
    - -2.955484598536888
    - -2.4926076960196846
    - -1.9358509025753872
    - -1.3122645398807091
    - -0.6528894579981621
    - 0.009089416044048677
    - 0.6403374535425418
    - 1.2093891834270964
    - 1.6885649780755845
    - 2.055663706749284
    - 2.295322150396323
    - 2.399951807086461
    - 2.370189587823525
    - 2.2148292470678954
    - 1.9502333294454521
    - 1.599258857006096
    - 1.189761769524443
    - 0.7527731690589591
    - 0.32046281901597146
    - -0.07597945029923045
    - -0.40840688872625025
    - -0.6535879994710274
    - -0.7947631458080979
    - -0.8227802793850927
    - -0.7367309718014728
    - -0.5440400044363444
    - -0.25999739123880544
    - 0.09324143107959587
    - 0.488125842565326
    - 0.8935572253193855
    - 1.2769933167689176
    - 1.606671298389799
    - 1.8538015444587967
    - 1.994584115789463
    - 2.011910192354043
    - 1.8966301727924626
    - 1.6482979582039188
    - 1.2753352326988987
    - 0.7945981321563046
    - 0.2303690035168551
    - -0.387164714788951
    - -1.0238468099029876
    - -1.643776644908474
    - -2.2116731750108856
    - -2.6952189186502
    - -3.0672236198028116
    - -3.307457779795518
    - -3.4040271243732447
    - -3.3541891248238382
    positive_zeros:
    - '0.46707141351337917191615402969328'
    - '2.40821147042629645041435822304704'
    - '2.89965496176559572892509945095271'
    - '4.53342190598774434080154771439609'
    - '5.01941661437313986176489374019346'
    - '6.14881390644942302402376883029322'
    - '6.99511085983117686360823090768862'
    - '7.75846745321920192609229206640817'
    - '8.524598924143990088850319151014194'
    - '9.597740319249801648853037428735969'
    prelabel: 2-1368-19.11-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.305077154396121
    root_angle: -0.48256341915612855
    root_number: 0.0547512426960612125779543337808964031437010446933099891 - 0.9985000257502435356269998002287647820247817129963582550*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.24128170957806427'
      prec: 67
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.46707141351337917191615402969'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.40821147042629645041435822305'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.89965496176559572892509945095'
      prec: 103
- - algebraic: true
    analytic_conductor: 10.923534996511162
    bad_primes:
    - 2
    - 3
    - 19
    central_character: '19.11'
    conductor: 1368
    conductor_radical: 114
    degree: 2
    id: 23189381
    index: 3
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1368/2/s/j/505/2
    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: 2-1368-19.11-c1-0-3
    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: 2-1368-19.11-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.305077154396121
    root_angle: -0.24128170957806427
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '0.46707141351337917191615402969'
      prec: 103
- - Lhash: '592083357689682644469393507557'
    Lhash_array:
    - '592083357689682644469393507557'
    id: 23559891
    label: 2-1368-19.11-c1-0-3
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1368/2/s/j/505/2
label_cols:
- label
- label
- label
labels:
- 2-1368-19.11-c1-0-3
- 2-1368-19.11-c1-0-3
- 2-1368-19.11-c1-0-3
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T16:24:09.762202'