data:
- - Lhash: '1329962191838253196138789879044'
    a10:
    - 0
    - 0
    a2:
    - 0
    - 0
    a3:
    - 3.1462643699419726
    - 0
    a4:
    - 0
    - 0
    a5:
    - 0
    - 0
    a6:
    - 0
    - 0
    a7:
    - 0
    - 0
    a8:
    - 0
    - 0
    a9:
    - 6.898979485566356
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 25.552128646809734
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 2
    - 5
    central_character: '3200.449'
    coefficient_field: CDF
    conductor: 3200
    conductor_radical: 10
    conjugate: '1720700827126552140744340313049'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -3.1462643699419726
        - 0
      - - 3.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -7.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -6.610365985079727
      - - -11.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 13.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 7.898979485566356
      - - -17.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -2.510589879550408
      - - -19.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -23.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -29.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - -12.797958971132712
        - 0
      - - 41.0
        - 0
    - - - 1.0
        - 0
      - - -8.48528137423857
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -47.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -14.142135623730951
      - - -59.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -61.0
        - 0
    - - - 1.0
        - 0
      - - 7.881714965862856
        - 0
      - - 67.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -13.696938456699069
      - - -73.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 79.0
        - 0
    - - - 1.0
        - 0
      - - 14.1742437057468
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 13.898979485566356
        - 0
      - - 89.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 10.0
      - - -97.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -101.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -103.0
        - 0
    - - - 1.0
        - 0
      - - -4.703342513905033
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -109.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0.7979589711327124
      - - -113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23355713
    index: 47
    label: 2-3200-40.29-c1-0-47
    leading_term: '3.872015880537152373124431335179564814168975855112822761'
    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/3200/2/f/s/449/8
    plot_delta:
      __RealLiteral__: 0
      data: '0.05078125'
      prec: 34
    plot_values:
    - 3.8720158805371523
    - 3.8089176476782916
    - 3.734255777302439
    - 3.6477589943076896
    - 3.5489904752435186
    - 3.4373968216864554
    - 3.312366247647647
    - 3.1732926670358377
    - 3.019642275987798
    - 2.8510193833634765
    - 2.667228581113525
    - 2.468330786396128
    - 2.2546911594881593
    - 2.0270173546459564
    - 1.7863869660106935
    - 1.534263378009624
    - 1.272499524469725
    - 1.0033293161336383
    - 0.7293467286764922
    - 0.45347276787916935
    - 0.1789107571157434
    - -0.09090936796726867
    - -0.35239681920113125
    - -0.6018745661762711
    - -0.8356613210296335
    - -1.0501591512497848
    - -1.2419447155462298
    - -1.4078618830027314
    - -1.5451132967947274
    - -1.6513482929099432
    - -1.7247444931486344
    - -1.764080370590374
    - -1.7687961433960888
    - -1.7390404958001404
    - -1.6757008573880652
    - -1.580415294262956
    - -1.4555644762699147
    - -1.3042426774550973
    - -1.1302073332662916
    - -0.9378073050677574
    - -0.731890674439457
    - -0.5176935875285258
    - -0.30071237188405003
    - -0.08656183115408976
    - 0.11917673818779316
    - 0.31111369480362605
    - 0.48421077760963116
    - 0.6339374650683077
    - 0.7564188106733437
    - 0.848569540518496
    - 0.908209315783646
    - 0.9341543620962466
    - 0.9262811522946343
    - 0.8855584959331971
    - 0.8140452278602035
    - 0.7148516822453569
    - 0.592064263430434
    - 0.45063365017776347
    - 0.2962284585408467
    - 0.135057498820273
    - -0.02633495188351713
    - -0.18129522642442575
    - -0.3233009665835832
    - -0.44620879495671967
    - -0.5445006033448304
    - -0.6135196497783069
    - -0.6496874943348021
    - -0.6506929567818623
    - -0.6156447620576634
    - -0.545180356570202
    - -0.4415245207559882
    - -0.3084928498878045
    - -0.15143689135579197
    - 0.022870334403047227
    - 0.20640759906684047
    - 0.39013448891088104
    - 0.5642709387399096
    - 0.7186198782279157
    - 0.8429235877045543
    - 0.927242590744287
    - 0.9623444567301206
    - 0.9400888219784262
    - 0.8537943265720913
    - 0.6985730555619847
    - 0.47161850088245716
    - 0.17243403846466626
    - -0.19700956278106604
    - -0.6321970453023201
    - -1.1260789216375968
    - -1.669173129714821
    - -2.249758923955183
    - -2.854160442337412
    - -3.4671139159457516
    - -4.072209070572296
    - -4.652392045750712
    - -5.190514260850697
    - -5.669909220318224
    - -6.074977389022596
    - -6.391758085191936
    - -6.60846691176251
    - -6.715977629851259
    - -6.708228593186808
    - -6.58253589989863
    - -6.339798234498113
    - -5.984581890950171
    - -5.525078578039482
    - -4.972933172200214
    - -4.342943437178257
    - -3.6526386916915934
    - -2.921749280523184
    - -2.1715832912104114
    - -1.424331060970927
    - -0.7023214517487575
    - -0.02725647037866545
    - 0.580547561092315
    - 1.102883524870887
    - 1.5243135357345172
    - 1.8327390264430827
    - 2.019857285899127
    - 2.0814847311594753
    - 2.0177319908223303
    - 1.833021414377624
    - 1.535943691888554
    - 1.1389566329180045
    - 0.6579355541664473
    - 0.1115908928064381
    - -0.47922567092724633
    - -1.0923003876557735
    - -1.7048917905406995
    - -2.2945873621781776
    - -2.840148239892174
    - -3.322307692921666
    - -3.72449057490394
    - -4.033423856054904
    - -4.239612578648926
    - -4.337661001624085
    - -4.326425092933816
    - -4.208989629754285
    - -3.9924706759364286
    - -3.6876517958170107
    - -3.3084696941348968
    - -2.871371706914499
    - -2.394573390161637
    - -1.8972490785948422
    - -1.3986914803216284
    - -0.917477961095451
    - -0.4706810500571132
    - -0.07315884185866794
    - 0.2630425669203124
    - 0.5291475500789927
    - 0.7199496881472786
    - 0.8339375868129685
    - 0.8732427707823897
    - 0.8434131545884574
    - 0.7530240283040943
    - 0.6131464505979898
    - 0.4367000180130508
    - 0.23772281568211193
    - 0.030595641590346705
    - -0.1707399059286267
    - -0.3535293361721544
    - -0.5068804859958843
    - -0.622330799737171
    - -0.6942766871736972
    - -0.7202418548232208
    - -0.700969672606827
    - -0.6403337032695874
    - -0.5450700400538712
    - -0.424344589082848
    - -0.2891774064871063
    - -0.1517541806841137
    - -0.024661500856255777
    - 0.07991270012957127
    - 0.15096948615428532
    - 0.17943562721468098
    - 0.15880424743812876
    - 0.08564127542290392
    - -0.04007400424769439
    - -0.21479770861749284
    - -0.4314730777272783
    - -0.6797880727012124
    - -0.9466305800420232
    - -1.2167219092860246
    - -1.473398962027708
    - -1.6995064446492596
    - -1.8783533125624527
    - -1.994682706514462
    - -2.0356023005370676
    - -1.9914224276416885
    - -1.8563526422352403
    - -1.6290134264998162
    - -1.3127283111604025
    - -0.9155723773982842
    - -0.45016542915008734
    - 0.06678853536386657
    - 0.6152002489745839
    - 1.1725039034416027
    - 1.7147349010421362
    - 2.2177254563214075
    - 2.6583588783337255
    - 3.0158182650960903
    - 3.2727634998965436
    - 3.4163720492795524
    - 3.4391841420985685
    - 3.3397012903365857
    - 3.122698446624574
    - 2.7992238639930465
    - 2.3862762690141177
    - 1.9061655053352802
    - 1.3855795008564367
    - 0.854396377193478
    - 0.34429488839921546
    - -0.11277165696738889
    - -0.48616396755009367
    - -0.7481285910916361
    - -0.875272539107919
    - -0.8498632433740252
    - -0.6608834737934453
    - -0.3047817936617453
    - 0.21412657000770371
    - 0.8836365883830564
    - 1.684017364444987
    - 2.588752795029233
    - 3.565629085602439
    - 4.578120899437953
    - 5.58701176672068
    - 6.552171308763762
    - 7.4344025986709825
    - 8.197268140561428
    - 8.808802836075866
    - 9.24302700094792
    - 9.481181818737038
    - 9.512623142145658
    - 9.335326608408693
    - 8.955976755167915
    - 8.38963417986075
    - 7.65899664751025
    - 6.793291244002393
    - 5.826854040534136
    - 4.797470211318316
    - 3.7445602083546157
    - 2.7073057213436447
    - 1.7228122578307665
    - 0.82440306185402
    - 0.04013183071102931
    - -0.6084103413589793
    - -1.1069345265558082
    - -1.4489001848300005
    - -1.6355497964869952
    - -1.6755362469275894
    - -1.5841696111487629
    - -1.382330752662645
    - -1.0951171987369683
    - -0.7503010490646751
    - -0.3766883948184424
    - -0.0024743049757592283
    - 0.3463133936190509
    positive_zeros:
    - '1.04915517856324537507270032163906'
    - '2.20462981083968075415354924776492'
    - '3.03850540824081876243881689516615'
    - '3.70056966729130069987874686345276'
    - '4.34128428266210633565032872472470'
    - '5.74043306232134414332336472566894'
    - '6.35748788928443585368827483395198'
    - '7.47509736126888225559663828782530'
    - '8.030979918585618768487476142104915'
    - '8.694456966113265450858356815616583'
    prelabel: 2-3200-40.29-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.054911339164094
    root_angle: -0.14758361765043326
    root_number: 0.89442719099991587856366946749251049417624734384461028971 - 0.44721359549995793928183473374625524708812367192230514485*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.07379180882521663'
      prec: 67
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.04915517856324537507270032164'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.20462981083968075415354924776'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.03850540824081876243881689517'
      prec: 103
- - algebraic: true
    analytic_conductor: 25.552128646809734
    bad_primes:
    - 2
    - 5
    central_character: '40.29'
    conductor: 3200
    conductor_radical: 10
    degree: 2
    id: 23355713
    index: 47
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/3200/2/f/s/449/8
    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: 2-3200-40.29-c1-0-47
    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: 2-3200-40.29-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.054911339164094
    root_angle: -0.07379180882521663
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '1.04915517856324537507270032164'
      prec: 103
- - Lhash: '1329962191838253196138789879044'
    Lhash_array:
    - '1329962191838253196138789879044'
    id: 23724132
    label: 2-3200-40.29-c1-0-47
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/3200/2/f/s/449/8
label_cols:
- label
- label
- label
labels:
- 2-3200-40.29-c1-0-47
- 2-3200-40.29-c1-0-47
- 2-3200-40.29-c1-0-47
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-24T01:12:46.661057'