data:
- - Lhash: '4736787083600932785073107969536'
    a10:
    - -5.411474127809773
    - 1.780565171543984e-60
    a2:
    - 0.9396926207859084
    - -1.6275953626987474
    a3:
    - -1.7057370639048863
    - -0.3007674663608706
    a4:
    - -0.766044443118978
    - -1.3268278963378768
    a5:
    - -1.4396926207859084
    - -2.493620766483186
    a6:
    - -2.092396265452048
    - 2.493620766483186
    a7:
    - 0.32635182233306964
    - -0.565257937423568
    a8:
    - 0.8793852415718167
    - 0.0
    a9:
    - 2.8190778623577253
    - 1.0260604299770062
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.7905189800106762
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 1.7057370639048863
          - 0.3007674663608706
    - - 11
      - - - 1.0
          - 0
        - - -0.5
          - 0.8660254037844386
    bad_primes:
    - 3
    - 11
    central_character: '99.34'
    coefficient_field: CDF
    conductor: 99
    conductor_radical: 33
    conjugate: '1815981478195618079524847314444'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -0.9396926207859084
        - 1.6275953626987474
      - - -1.0
        - -1.7320508075688772
    - - - 1.0
        - 0
      - - 1.7057370639048863
        - 0.3007674663608706
    - - - 1.0
        - 0
      - - 1.4396926207859084
        - 2.493620766483186
      - - -2.5
        - 4.330127018922194
    - - - 1.0
        - 0
      - - -0.32635182233306964
        - 0.565257937423568
      - - -3.5
        - -6.06217782649107
    - - - 1.0
        - 0
      - - -0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - -3.379385241571817
        - -5.853266936750811
      - - -6.5
        - 11.258330249197702
    - - - 1.0
        - 0
      - - -0.18479253090409536
        - 0
      - - 17.0
        - 0
    - - - 1.0
        - 0
      - - 5.226681596905678
        - 0
      - - 19.0
        - 0
    - - - 1.0
        - 0
      - - -1.5923962654520476
        - -2.7581112375458834
      - - -11.5
        - 19.91858428704209
    - - - 1.0
        - 0
      - - -2.011144353237165
        - 3.483404201162019
      - - -14.5
        - -25.11473670974872
    - - - 1.0
        - 0
      - - 0.5530334192387472
        - 0.9578819804050495
      - - -15.5
        - 26.846787517317598
    - - - 1.0
        - 0
      - - -0.10606683847749424
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - -2.80793350912056
        - -4.863483502071977
      - - -20.5
        - 35.50704155516198
    - - - 1.0
        - 0
      - - 1.9298924410222824
        - -3.342671760993716
      - - -21.5
        - -37.239092362730865
    - - - 1.0
        - 0
      - - 6.0038703932618205
        - -10.399008563188008
      - - -23.5
        - -40.703193977868615
    - - - 1.0
        - 0
      - - 10.071918558999553
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - 5.2771887963561435
        - 9.14035911642209
      - - -29.5
        - 51.09549882328188
    - - - 1.0
        - 0
      - - -3.6736481776669305
        - 6.362945292851941
      - - -30.5
        - -52.827549630850754
    - - - 1.0
        - 0
      - - -5.9042001678344285
        - -10.226374668745922
      - - -33.5
        - 58.023702053557386
    - - - 1.0
        - 0
      - - 2.475651900285685
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - -10.461103980334997
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - -0.733955556881022
        - 1.2712483150154392
      - - -39.5
        - -68.41600689897065
    - - - 1.0
        - 0
      - - -0.520944533000791
        - 0.9023023990826118
      - - -41.5
        - -71.88010851410841
    - - - 1.0
        - 0
      - - 3.019600359527252
        - 0
      - - 89.0
        - 0
    - - - 1.0
        - 0
      - - -2.869585061808191
        - 4.970267123692463
      - - -48.5
        - -84.00446416709055
    - - - 1.0
        - 0
      - - -2.209607457166707
        - 3.827152380595808
      - - -50.5
        - -87.4685657822283
    - - - 1.0
        - 0
      - - 5.219407636930333
        - 9.04027921257635
      - - -51.5
        - 89.20061658979718
    - - - 1.0
        - 0
      - - 8.313148075855919
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 15.98814042699639
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - -2.5320888862379562
        - -4.385706600244631
      - - -56.5
        - 97.86087062764156
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9598193
    index: 8
    label: 2-99-9.7-c1-0-8
    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/99/2/e/d/34/3
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 1.0371355019845947
    - 1.127034307192341
    - 1.2363103471302668
    - 1.3673811801126947
    - 1.521455468874041
    - 1.6985767865904915
    - 1.8976995758066908
    - 2.1167417205079437
    - 2.352596090868999
    - 2.6011126329420664
    - 2.8570759251022
    - 3.1142049886395946
    - 3.3651985619831226
    - 3.6018437304930213
    - 3.815200157442987
    - 3.9958663832656436
    - 4.134328558322294
    - 4.221385384389018
    - 4.248635975532392
    - 4.209010033651754
    - 4.097312583360169
    - 3.910749095228384
    - 3.6493918209352363
    - 3.3165452885626694
    - 2.9189688551301005
    - 2.466917574867221
    - 1.9739698142866215
    - 1.4566211554033683
    - 0.9336389590460193
    - 0.42518989777208616
    - -0.04822721891105607
    - -0.46699034813660517
    - -0.8136323396635009
    - -1.0740993787285158
    - -1.2388896396082416
    - -1.3039679844904803
    - -1.2713572165573261
    - -1.1493208150304395
    - -0.9520764600855368
    - -0.6990132510246724
    - -0.41342652691417114
    - -0.12082975201197887
    - 0.1530507755381315
    - 0.3844500979540066
    - 0.5537254278461827
    - 0.6473007895336303
    - 0.6591893812690156
    - 0.5919045404164337
    - 0.4566085145035145
    - 0.27240692413501516
    - 0.06477252024181683
    - -0.136831079191851
    - -0.3019642719672244
    - -0.4026184687954803
    - -0.4166991461501864
    - -0.33122450368373163
    - -0.14486817857392703
    - 0.13049781522430526
    - 0.4695353395223321
    - 0.8346163476375045
    - 1.1784741046755245
    - 1.448203265915544
    - 1.5903213722309706
    - 1.5564566827808535
    - 1.3091116725832506
    - 0.8268848899705445
    - 0.10852942792436963
    - -0.8247084844444862
    - -1.9288921575310969
    - -3.139562902730873
    - -4.376256519076889
    - -5.549085943612527
    - -6.56685106145108
    - -7.345917508986135
    - -7.818954807639892
    - -7.942564858948364
    - -7.70288046367641
    - -7.118374173596698
    - -6.239381120997429
    - -5.144182585252864
    - -3.9318849918924985
    - -2.7127180698645263
    - -1.5967182713478882
    - -0.6820132839713333
    - -0.04404238703728273
    - 0.2729891127080869
    - 0.2613217882486945
    - -0.049232095486630274
    - -0.5945396330323315
    - -1.2835411904270655
    - -2.0090287678003698
    - -2.660594316500645
    - -3.138209385238862
    - -3.3647556548737416
    - -3.295895647754888
    - -2.925956711609256
    - -2.2889728928242468
    - -1.4546348516967318
    - -0.5195621936817855
    - 0.40505237079274176
    - 1.2078605670590008
    - 1.791949410070341
    - 2.087643965150305
    - 2.0617576607978774
    - 1.7219764806856834
    - 1.1157138022809556
    - 0.32353728792526276
    - -0.5519583299678592
    - -1.4002910647344178
    - -2.1182419083683226
    - -2.623835476246576
    - -2.867112702056013
    - -2.836108006895408
    - -2.557145191608007
    - -2.0894198376343436
    - -1.5147141052698558
    - -0.9238561170634358
    - -0.4020661396834682
    - -0.015533411569464767
    - 0.1986026479636299
    - 0.23722010254804846
    - 0.13029455834595097
    - -0.06577455684133181
    - -0.2794824361165969
    - -0.43825568226124845
    - -0.48276549462857393
    - -0.3789611322189332
    - -0.12559107601420813
    - 0.24429599844444624
    - 0.6683596880142726
    - 1.0658257468793515
    - 1.3524479194508652
    - 1.4570003504412006
    - 1.3363161683099856
    - 0.9859888313080187
    - 0.44447643328793623
    - -0.21058547934932523
    - -0.8737135392560405
    - -1.4290005282514633
    - -1.7708767466607853
    - -1.8246603184170944
    - -1.563140707611609
    - -1.0158902752281542
    - -0.26906839612835304
    - 0.5449794728635732
    - 1.2672626618361502
    - 1.7380715151964052
    - 1.8252214008092502
    - 1.4498651164753742
    - 0.6052317602711057
    - -0.6354254960866506
    - -2.123764138910576
    - -3.6541785229315114
    - -4.99232717072015
    - -5.910232336197627
    - -6.222496608475699
    - -5.817727437551269
    - -4.679798025574961
    - -2.895051552896967
    - -0.6437565297496537
    - 1.823310947803035
    - 4.219780854728819
    - 6.264724541523176
    - 7.72330788690329
    - 8.440517116247841
    - 8.362492140361022
    - 7.542037593539885
    - 6.127530963436224
    - 4.337250906600802
    - 2.4236105766076683
    - 0.6334573723447019
    - -0.8288149237375497
    - -1.8292138205134756
    - -2.3187387756050133
    - -2.3326877679484994
    - -1.9755590270188133
    - -1.3950249422873837
    - -0.750355951593868
    - -0.18151856531342175
    - 0.21519175818714853
    - 0.4006158979219252
    - 0.39324985849157845
    - 0.2574564822821265
    - 0.082514381798254
    - -0.04253323646116111
    - -0.05250580070112989
    - 0.07708359365955128
    - 0.3236940142642919
    - 0.6232564950018431
    - 0.8861875059352607
    - 1.0202118999247156
    - 0.9546994053396632
    - 0.6607780572524936
    - 0.1623173315757395
    - -0.4651794548984044
    - -1.1080687176313029
    - -1.6379245682759205
    - -1.9398884653632014
    - -1.939788232500326
    - -1.6237911603732724
    - -1.0457339580865743
    - -0.3197926492784845
    - 0.4006911229786289
    - 0.9542933838515809
    - 1.2061738306487662
    - 1.078888467027563
    - 0.5723887341105891
    - -0.23172481488746283
    - -1.1834203839590087
    - -2.092915897478868
    - -2.7693448660148356
    - -3.061494696586482
    - -2.8918845517338543
    - -2.2764944474829827
    - -1.3252218020827589
    - -0.22209933438914795
    - 0.8113506465007763
    - 1.5624536900796129
    - 1.8738361469527385
    - 1.6799854212149505
    - 1.0256240548465383
    - 0.06117958291607811
    - -0.9846336350347872
    - -1.8501920018605065
    - -2.29533664423394
    - -2.153527986064314
    - -1.3706428193958566
    - -0.021745074996321924
    - 1.6984335380152904
    - 3.5101170132541246
    - 5.101676650490636
    - 6.190760864484225
    - 6.580810597231901
    - 6.2011233328219335
    - 5.121887259858219
    - 3.540757510739042
    - 1.7435113357572058
    - 0.046822193539824294
    - -1.2649646400011405
    - -1.9958454611239298
    - -2.0752564607854556
    - -1.568589283672456
    - -0.6591613543649907
    - 0.39418662057021236
    - 1.314474071217093
    - 1.8664004146133095
    - 1.9056691142352493
    - 1.4073441819495671
    - 0.4675210911218508
    - -0.7214307659268677
    - -1.9159485521602337
    - -2.8761706060339747
    - -3.4181647988029997
    - -3.4518971240436556
    - -2.9968600212096943
    - -2.172580443566444
    - -1.1670661098644568
    positive_zeros:
    - '3.73666614660862836087454104850461'
    - '5.17843851421376892230602417199201'
    - '6.28886996829218224912112058239602'
    - '7.07013772828168894407102789620661'
    - '8.266052948927218701638265756798612'
    - '10.51179848334022285439567020509997'
    - '10.86059941714504891459072775708511'
    - '12.31907917792042465022701315280192'
    - '13.29674243050505664512120908318743'
    - '14.75648955819797762141413907904026'
    prelabel: 2-99-9.7-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.8891113428647034
    root_angle: 0.6666666666666667
    root_number: -0.5000000000000002 + 0.8660254037844385*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.333333333333'
      prec: 47
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '3.73666614660862836087454104850'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '5.17843851421376892230602417199'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '6.28886996829218224912112058240'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.7905189800106762
    bad_primes:
    - 3
    - 11
    central_character: '9.7'
    conductor: 99
    conductor_radical: 33
    degree: 2
    id: 9598193
    index: 8
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/99/2/e/d/34/3
    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: 2-99-9.7-c1-0-8
    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: 2-99-9.7-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.8891113428647034
    root_angle: 0.33333333333333337
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '3.73666614660862836087454104850'
      prec: 103
- - Lhash: '4736787083600932785073107969536'
    Lhash_array:
    - '4736787083600932785073107969536'
    id: 9964218
    label: 2-99-9.7-c1-0-8
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/99/2/e/d/34/3
label_cols:
- label
- label
- label
labels:
- 2-99-9.7-c1-0-8
- 2-99-9.7-c1-0-8
- 2-99-9.7-c1-0-8
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-17T14:17:12.364242'