data:
- - Lhash: '1091764933321042439259531322861'
    a10:
    - 0.0
    - 0.0
    a2:
    - 0.0
    - 0.0
    a3:
    - -0.7653668647301796
    - 0.0
    a4:
    - 0.0
    - 0.0
    a5:
    - 2.9301512653149673
    - 0.0
    a6:
    - 0.0
    - 0.0
    a7:
    - -1.4142135623730951
    - 0.0
    a8:
    - 0.0
    - 0.0
    a9:
    - -2.414213562373095
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 32.70672466791646
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 2
    central_character: '4096.1'
    coefficient_field: CDF
    conductor: 4096
    conductor_radical: 2
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0.7653668647301796
        - 0
      - - 3.0
        - 0
    - - - 1.0
        - 0
      - - -2.9301512653149673
        - 0
      - - 5.0
        - 0
    - - - 1.0
        - 0
      - - 1.4142135623730951
        - 0
      - - 7.0
        - 0
    - - - 1.0
        - 0
      - - -4.460884994775326
        - 0
      - - 11.0
        - 0
    - - - 1.0
        - 0
      - - -0.7653668647301796
        - 0
      - - 13.0
        - 0
    - - - 1.0
        - 0
      - - 2.8284271247461903
        - 0
      - - 17.0
        - 0
    - - - 1.0
        - 0
      - - -4.0125434656073615
        - 0
      - - 19.0
        - 0
    - - - 1.0
        - 0
      - - -8.242640687119286
        - 0
      - - 23.0
        - 0
    - - - 1.0
        - 0
      - - 3.3784927944829324
        - 0
      - - 29.0
        - 0
    - - - 1.0
        - 0
      - - 4.0
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - 0.7653668647301796
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - -0.24264068711928516
        - 0
      - - 41.0
        - 0
    - - - 1.0
        - 0
      - - -5.094935665899755
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - -0.3431457505076198
        - 0
      - - 47.0
        - 0
    - - - 1.0
        - 0
      - - 1.2137083938981446
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - -4.909226523943292
        - 0
      - - 59.0
        - 0
    - - - 1.0
        - 0
      - - 1.8477590650225735
        - 0
      - - 61.0
        - 0
    - - - 1.0
        - 0
      - - 5.9916187242356855
        - 0
      - - 67.0
        - 0
    - - - 1.0
        - 0
      - - -8.242640687119286
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - -9.899494936611665
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - -6.0
        - 0
      - - 79.0
        - 0
    - - - 1.0
        - 0
      - - -4.909226523943292
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 12.242640687119286
        - 0
      - - 89.0
        - 0
    - - - 1.0
        - 0
      - - -18.48528137423857
        - 0
      - - 97.0
        - 0
    - - - 1.0
        - 0
      - - -3.5642019364393964
        - 0
      - - 101.0
        - 0
    - - - 1.0
        - 0
      - - -13.414213562373096
        - 0
      - - 103.0
        - 0
    - - - 1.0
        - 0
      - - 4.460884994775326
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - -14.91338871378634
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - -6.343145750507619
        - 0
      - - 113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 20062875
    index: 39
    label: 2-2e12-1.1-c1-0-39
    leading_term: '2.05997568437270077711625967081'
    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/4096/2/a/f/1/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.05078125'
      prec: 34
    plot_values:
    - 2.059975684372701
    - 2.0528394964862224
    - 2.0313781978333547
    - 1.99544098679686
    - 1.9448006923332237
    - 1.8791882838713083
    - 1.7983379050796997
    - 1.7020395660992367
    - 1.5901963110969823
    - 1.46288260533457
    - 1.3204008141689068
    - 1.1633329165160227
    - 0.992584948448247
    - 0.8094220606836414
    - 0.6154924645183736
    - 0.41283891795063593
    - 0.2038967638923374
    - -0.008522119653115917
    - -0.22125975299849635
    - -0.4308568171658776
    - -0.6336113281935135
    - -0.8256504284220312
    - -1.0030141077187724
    - -1.1617492665566016
    - -1.2980121319133484
    - -1.4081766481879847
    - -1.488946103115264
    - -1.5374649288461466
    - -1.551427357427375
    - -1.5291794241495982
    - -1.4698107169274044
    - -1.3732322785294222
    - -1.2402371920668929
    - -1.0725406264340125
    - -0.8727964913060554
    - -0.6445883504365597
    - -0.39239286221894315
    - -0.12151474768395262
    - 0.16200688686502968
    - 0.45152014262164974
    - 0.7399081527505142
    - 1.0197604789929033
    - 1.283564455098188
    - 1.5239119309379165
    - 1.733716031375769
    - 1.9064318215438207
    - 2.036274200208209
    - 2.1184259578373092
    - 2.1492287641398398
    - 2.1263499140009445
    - 2.0489179768119548
    - 1.9176210700022298
    - 1.7347623119503406
    - 1.5042680914712585
    - 1.2316460997607162
    - 0.9238915749683106
    - 0.5893418687407638
    - 0.237481208556362
    - -0.12130065770919354
    - -0.47599045091211173
    - -0.8152667838126344
    - -1.1278402537960592
    - -1.4028080942711318
    - -1.6300122100011547
    - -1.800388697823419
    - -1.9062966188516675
    - -1.9418138779365457
    - -1.9029886034514671
    - -1.7880354120559263
    - -1.5974673784107405
    - -1.3341563803594092
    - -1.0033167093147481
    - -0.6124093596503736
    - -0.17096716008063864
    - 0.30965620904201474
    - 0.8166073599635681
    - 1.3359157257007577
    - 1.8529260673759291
    - 2.3527672395088373
    - 2.820841593082532
    - 3.2433180104700794
    - 3.6076107740944154
    - 3.9028263325090036
    - 4.120160580535356
    - 4.2532305249851685
    - 4.298326146912482
    - 4.254570848797663
    - 4.123982015358313
    - 3.911426817508097
    - 3.624472323811796
    - 3.273133105945309
    - 2.8695236725543425
    - 2.4274270691069426
    - 1.961794667512613
    - 1.4881953714942655
    - 1.022235027904979
    - 0.5789686265670948
    - 0.1723287850305272
    - -0.1854060237802419
    - -0.48408106950482016
    - -0.7160523652564287
    - -0.8764735916609334
    - -0.9634692492668163
    - -0.978184839502989
    - -0.9247099097845408
    - -0.8098751738712245
    - -0.6429304102911375
    - -0.43511521121380553
    - -0.1991396589079565
    - 0.05140358937508232
    - 0.3026707433252072
    - 0.5412142098798686
    - 0.7546167623832273
    - 0.9320833559335134
    - 1.0649625727501795
    - 1.147172170718256
    - 1.175506942965735
    - 1.1498119488360454
    - 1.0730099626552059
    - 0.9509784714941657
    - 0.7922784603166638
    - 0.6077442457519715
    - 0.40995043434739686
    - 0.2125783610727028
    - 0.029709795384601206
    - -0.12492000017539803
    - -0.23867485265075986
    - -0.30073953796993236
    - -0.3027748755551362
    - -0.23947206519215988
    - -0.10897600871370426
    - 0.08684733785446211
    - 0.3423178648990168
    - 0.6480329791422076
    - 0.9911460324943085
    - 1.3558245961933264
    - 1.7238728030091266
    - 2.075493585241491
    - 2.390159131000358
    - 2.6475516585977
    - 2.8285320127592772
    - 2.916090893216298
    - 2.896236928905815
    - 2.758777406213897
    - 2.497951239810817
    - 2.1128796243567036
    - 1.607807503670863
    - 0.9921182214049015
    - 0.2801140684795623
    - -0.5094335564297326
    - -1.3539495274364604
    - -2.2279103527287996
    - -3.1038541972399156
    - -3.9535019524331507
    - -4.748939359227195
    - -5.463806094179153
    - -6.074436181796907
    - -6.560895241708947
    - -6.90786393132237
    - -7.105323379292974
    - -7.149007165319504
    - -7.040595105257618
    - -6.787636256111483
    - -6.403201584907414
    - -5.905280010860827
    - -5.315944365171063
    - -4.660325555917118
    - -3.965443255148914
    - -3.258949192612757
    - -2.5678442004035724
    - -1.917232189579326
    - -1.3291730873549672
    - -0.8216924180978101
    - -0.4079978358274788
    - -0.09594283552368696
    - 0.1122344401483726
    - 0.2198833205146114
    - 0.23562453923894947
    - 0.1727618901236081
    - 0.04845191086567734
    - -0.11732511183009187
    - -0.3029386535444431
    - -0.48636368536946767
    - -0.6464514212001528
    - -0.7641464953566814
    - -0.8235842824822996
    - -0.8130079766758569
    - -0.725454301587308
    - -0.559168880449222
    - -0.3177267399929481
    - -0.00984940267067454
    - 0.3510733138226268
    - 0.7477322278442909
    - 1.1598785840896901
    - 1.56548152036044
    - 1.9419994890947971
    - 2.2676947771889258
    - 2.522916992707712
    - 2.6912822203229503
    - 2.760679511611403
    - 2.7240452629318934
    - 2.5798584088108796
    - 2.332324583660929
    - 1.991234666768179
    - 1.5715014811711647
    - 1.0923968423218025
    - 0.5765285995311588
    - 0.04861276996174352
    - -0.46589158668063424
    - -0.9422082338133818
    - -1.3576492250143979
    - -1.692918804076692
    - -1.933239213262817
    - -2.0692310157137066
    - -2.0974937075314455
    - -2.0208489126643605
    - -1.848227421342822
    - -1.5942016930121394
    - -1.2781860389132362
    - -0.923346333442261
    - -0.5552786163230878
    - -0.20053028059218897
    - 0.11495219828685967
    - 0.3673595199506165
    - 0.536449962420482
    - 0.6067889795687564
    - 0.5687229906019889
    - 0.4190268689963115
    - 0.16118292967123188
    - -0.1947297300665796
    - -0.6325340568094636
    - -1.1308176786844508
    - -1.664113220167582
    - -2.204330791022732
    - -2.722361377370344
    - -3.189758690599888
    - -3.5804011936249607
    - -3.8720359566941798
    - -4.047611791037741
    - -4.096320511948817
    - -4.014281595682903
    - -3.8048260070238054
    - -3.4783584139397243
    - -3.0518020032288184
    - -2.5476551800282397
    - -1.9927130591088715
    - -1.4165273842543737
    - -0.8496950433607027
    - -0.3220766153563463
    - 0.1389483712622684
    - 0.5100839753990026
    - 0.7734803189887771
    - 0.9177718527860669
    - 0.938726288439172
    - 0.8394623186395935
    - 0.6302203409327928
    - 0.32769777220925234
    positive_zeros:
    - '0.861250673588195133176180452832657'
    - '1.90088098073121330925499240519118'
    - '2.92815817530618094709578774488506'
    - '3.72550579344052382439544066774254'
    - '4.94928562724744873809332586146023'
    - '5.52484016574616715552493761348472'
    - '6.30583384465341812978344227872346'
    - '6.63179091674743259614464418007150'
    - '7.53414710337617039749418878705435'
    - '8.856313051979487730953540238595799'
    prelabel: 2-2e12-1.1-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.718979337951525
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.861250673588195133176180452833'
      prec: 107
    z2:
      __RealLiteral__: 0
      data: '1.90088098073121330925499240519'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.92815817530618094709578774489'
      prec: 103
- - algebraic: true
    analytic_conductor: 32.70672466791646
    bad_primes:
    - 2
    central_character: '1.1'
    conductor: 4096
    conductor_radical: 2
    degree: 2
    id: 20062875
    index: 39
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/4096/2/a/f/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: 2-2e12-1.1-c1-0-39
    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: 2-2e12-1.1-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.718979337951525
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '0.861250673588195133176180452833'
      prec: 107
- - Lhash: '1091764933321042439259531322861'
    Lhash_array:
    - '1091764933321042439259531322861'
    id: 20462044
    label: 2-2e12-1.1-c1-0-39
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/4096/2/a/f/1/2
label_cols:
- label
- label
- label
labels:
- 2-2e12-1.1-c1-0-39
- 2-2e12-1.1-c1-0-39
- 2-2e12-1.1-c1-0-39
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-12T19:18:28.297576'