data:
- - Lhash: '2062397894333316370074834340367'
    a10:
    - 0.0
    - 0.0
    a2:
    - 0.0
    - 0.0
    a3:
    - 11.524174696260024
    - 0.0
    a4:
    - 0.0
    - 0.0
    a5:
    - 0.0
    - 0.0
    a6:
    - 0.0
    - 0.0
    a7:
    - -27.04834939252005
    - 0.0
    a8:
    - 0.0
    - 0.0
    a9:
    - -110.1933975700802
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 64.15352792519226
    analytic_normalization:
      __RealLiteral__: 0
      data: '2.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 2
    - 5
    central_character: '400.1'
    coefficient_field: CDF
    conductor: 400
    conductor_radical: 10
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -11.524174696260024
        - 0
      - - 243.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 27.04834939252005
        - 0
      - - 16807.0
        - 0
    - - - 1.0
        - 0
      - - 226.0076686214605
        - 0
      - - 161051.0
        - 0
    - - - 1.0
        - 0
      - - -511.2570842055212
        - 0
      - - 371293.0
        - 0
    - - - 1.0
        - 0
      - - -387.38679514016036
        - 0
      - - 1419857.0
        - 0
    - - - 1.0
        - 0
      - - -1335.9263070793413
        - 0
      - - 2476099.0
        - 0
    - - - 1.0
        - 0
      - - 545.3691202334824
        - 0
      - - 6436343.0
        - 0
    - - - 1.0
        - 0
      - - 4637.577855046484
        - 0
      - - 20511149.0
        - 0
    - - - 1.0
        - 0
      - - 2991.5578424760483
        - 0
      - - 28629151.0
        - 0
    - - - 1.0
        - 0
      - - 1263.7005529898515
        - 0
      - - 69343957.0
        - 0
    - - - 1.0
        - 0
      - - 17197.627515699383
        - 0
      - - 115856201.0
        - 0
    - - - 1.0
        - 0
      - - -16592.011973175784
        - 0
      - - 147008443.0
        - 0
    - - - 1.0
        - 0
      - - 13036.0
        - 0
      - - 229345007.0
        - 0
    - - - 1.0
        - 0
      - - 28994.702890653607
        - 0
      - - 418195493.0
        - 0
    - - - 1.0
        - 0
      - - -34429.94332635583
        - 0
      - - 714924299.0
        - 0
    - - - 1.0
        - 0
      - - 24149.06368663544
        - 0
      - - 844596301.0
        - 0
    - - - 1.0
        - 0
      - - 29389.69157310801
        - 0
      - - 1350125107.0
        - 0
    - - - 1.0
        - 0
      - - 9064.316095513448
        - 0
      - - 1804229351.0
        - 0
    - - - 1.0
        - 0
      - - 55528.740578130724
        - 0
      - - 2073071593.0
        - 0
    - - - 1.0
        - 0
      - - -101587.0229199482
        - 0
      - - 3077056399.0
        - 0
    - - - 1.0
        - 0
      - - 73240.35500833475
        - 0
      - - 3939040643.0
        - 0
    - - - 1.0
        - 0
      - - 42498.45367401036
        - 0
      - - 5584059449.0
        - 0
    - - - 1.0
        - 0
      - - -10565.86384578809
        - 0
      - - 8587340257.0
        - 0
    - - - 1.0
        - 0
      - - -46486.01311260379
        - 0
      - - 10510100501.0
        - 0
    - - - 1.0
        - 0
      - - 119525.97662336243
        - 0
      - - 11592740743.0
        - 0
    - - - 1.0
        - 0
      - - -22922.362306183022
        - 0
      - - 14025517307.0
        - 0
    - - - 1.0
        - 0
      - - -210121.088772415
        - 0
      - - 15386239549.0
        - 0
    - - - 1.0
        - 0
      - - 203886.4688394209
        - 0
      - - 18424351793.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 19670753
    index: 37
    label: 2-20e2-1.1-c5-0-37
    load_key: CMFs-workshop
    motivic_weight: 5
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 5
    order_of_vanishing: 1
    origin: ModularForm/GL2/Q/holomorphic/400/6/a/r/1/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 0.0
    - 0.28745196687364444
    - 0.5712056433774702
    - 0.8476066986643013
    - 1.1130884520255913
    - 1.3642150176245744
    - 1.5977236106618373
    - 1.8105656997887902
    - 1.999946662532874
    - 2.1633635684877635
    - 2.298640680950009
    - 2.4039622336942212
    - 2.4779020079951795
    - 2.5194492082561064
    - 2.528030115144717
    - 2.5035249853761323
    - 2.446279669482518
    - 2.3571114351246334
    - 2.2373085154855836
    - 2.0886229514265846
    - 1.9132563633236526
    - 1.7138383742876897
    - 1.4933975106914215
    - 1.2553245278857998
    - 1.003328247366498
    - 0.7413841444953359
    - 0.4736760906079587
    - 0.20453182675186216
    - -0.06164707537304098
    - -0.3204598307459343
    - -0.5675845272598473
    - -0.7988584058428161
    - -1.0103589083210678
    - -1.1984839357079695
    - -1.3600296537879308
    - -1.4922641076186125
    - -1.5929948667527218
    - -1.6606289229094615
    - -1.6942231051315713
    - -1.6935233669032128
    - -1.6589914370034295
    - -1.5918175115817763
    - -1.4939178983207186
    - -1.3679168024515644
    - -1.217111765214306
    - -1.0454226230058852
    - -0.8573242433815391
    - -0.6577637042820109
    - -0.4520630060725489
    - -0.24580883176753518
    - -0.04473128780696583
    - 0.1454260461082991
    - 0.31904206677034697
    - 0.47075708840001707
    - 0.595611507271318
    - 0.6891807328846972
    - 0.7477028187051531
    - 0.7681952042896211
    - 0.7485570550382453
    - 0.687653860500067
    - 0.5853812292410018
    - 0.4427051969792402
    - 0.2616768411904276
    - 0.0454195626826952
    - -0.20191195746949947
    - -0.47520140211360584
    - -0.7684685737544207
    - -1.074993974278557
    - -1.3874681124876016
    - -1.6981626470821813
    - -1.9991197132929048
    - -2.2823550834521322
    - -2.540070200037801
    - -2.764867617680298
    - -2.949964020057111
    - -3.0893947576066654
    - -3.178203798224825
    - -3.2126131070326425
    - -3.190165779551546
    - -3.109837746443485
    - -2.9721135428422265
    - -2.7790224806785497
    - -2.534132561683877
    - -2.242500599426726
    - -1.910578252721529
    - -1.5460749769911126
    - -1.1577802373955595
    - -0.7553486572577561
    - -0.34905305492673927
    - 0.050488491665503114
    - 0.43260436366059274
    - 0.7868718411875608
    - 1.103421543806446
    - 1.3732347381425556
    - 1.5884242385534448
    - 1.7424897755949564
    - 1.8305391549299648
    - 1.8494672758073458
    - 1.7980861128964527
    - 1.6772000673686647
    - 1.4896226317995707
    - 1.2401320482165117
    - 0.9353655201830148
    - 0.5836535114443745
    - 0.19479766270283383
    - -0.2202021821176576
    - -0.6494644967447881
    - -1.0805771210169175
    - -1.5009723821576975
    - -1.898314699569106
    - -2.260888301917148
    - -2.577972297777828
    - -2.840190377748982
    - -3.039822902659429
    - -3.1710700502257576
    - -3.2302560363182704
    - -3.2159661659752756
    - -3.1291105568647892
    - -2.972910752764988
    - -2.7528080324379034
    - -2.4762949346602237
    - -2.1526742695141
    - -1.792752570521002
    - -1.408477461314056
    - -1.0125306657879491
    - -0.6178902893600916
    - -0.2373774580378451
    - 0.11679664848721821
    - 0.4334669469741071
    - 0.7029175720002905
    - 0.9172365775012239
    - 1.070608248685335
    - 1.159531042902696
    - 1.182951677237381
    - 1.142308812458258
    - 1.0414830496403584
    - 0.8866534426974462
    - 0.6860643097977696
    - 0.4497096633336107
    - 0.18894593259308165
    - -0.08395331160859772
    - -0.35628433490245204
    - -0.615423603749374
    - -0.8493418629271865
    - -1.047101634632886
    - -1.1993180168620095
    - -1.2985636337100488
    - -1.339700357739068
    - -1.320122938735507
    - -1.2399028563233512
    - -1.101824458318927
    - -0.9113096180825266
    - -0.6762315859532576
    - -0.4066232491393594
    - -0.11428946818942712
    - 0.1876626593510497
    - 0.48535802715202064
    - 0.7647315492827388
    - 1.0121269580399126
    - 1.2148918862393594
    - 1.3619442754075761
    - 1.4442857042186696
    - 1.455438819987705
    - 1.3917886449182713
    - 1.252811039516806
    - 1.0411759178825966
    - 0.7627177652255033
    - 0.42627141617059294
    - 0.043376696901638374
    - -0.3721388183802226
    - -0.8046842768052433
    - -1.237517649135668
    - -1.6534216410342828
    - -2.0354162622610916
    - -2.367478649206675
    - -2.6352396842724013
    - -2.8266271852482823
    - -2.932426975541622
    - -2.9467359621119034
    - -2.86728535569286
    - -2.6956172259136744
    - -2.4371035004922095
    - -2.100803057514611
    - -1.6991594532771375
    - -1.2475487820895121
    - -0.7636938745052922
    - -0.26696720442706534
    - 0.2223897931011268
    - 0.6840990503538569
    - 1.0986949634447116
    - 1.448353913210184
    - 1.717667972949323
    - 1.894328277572751
    - 1.9696868093909905
    - 1.9391700959812792
    - 1.8025243373018103
    - 1.563878541684756
    - 1.2316200592100326
    - 0.8180851203753334
    - 0.33907525481332507
    - -0.1867815953308919
    - -0.7387992085423373
    - -1.2950982019711672
    - -1.8335310174626522
    - -2.332626402187528
    - -2.7725115359150294
    - -3.1357703690800802
    - -3.408199053943457
    - -3.579423506208835
    - -3.6433499698248437
    - -3.598426734415647
    - -3.4477035608025663
    - -3.198684533225439
    - -2.8629795610415285
    - -2.4557691565875106
    - -1.9951059735364673
    - -1.5010844719942806
    - -0.99491659082614
    - -0.49795611964848757
    - -0.030717312726271807
    - 0.3880659960357361
    - 0.7422960049593996
    - 1.0192401684799781
    - 1.210098605453699
    - 1.3103817398954107
    - 1.3200791523824489
    - 1.243610593653839
    - 1.0895606574421166
    - 0.8702092190491192
    - 0.6008798982738325
    - 0.2991379911431652
    - -0.01612293635102035
    - -0.3256606961348048
    - -0.6108815379583123
    - -0.8548044505993088
    - -1.0429436911365055
    - -1.1640641682169106
    - -1.2107702837254204
    - -1.1798968918659407
    - -1.0726807919752201
    - -0.8947021643761371
    - -0.6555970482995107
    - -0.36855376244998767
    - -0.0496174801715974
    - 0.28316259622232764
    - 0.610700408266813
    - 0.9139049938393673
    - 1.17472360650942
    - 1.3771410649234967
    - 1.5080819098066722
    - 1.5581662711144184
    - 1.522277308935794
    - 1.3999073737834837
    - 1.1952611924258563
    - 0.9171068749381278
    - 0.5783787271071653
    - 0.19554906032859198
    positive_zeros:
    - '1.62694506984968860545250238412937'
    - '2.94310999864192487169989714009943'
    - '3.70270476818462225555822481114226'
    - '5.20732936628718263341057791394702'
    - '6.12161321556378951404977117394629'
    - '7.42147561562159808907983681689457'
    - '8.185213220029995711251466559034958'
    - '9.045691449675921951607111563743709'
    - '9.850050317417212823167231161775972'
    prelabel: 2-20e2-1.1-c5-0
    primitive: true
    rational: false
    root_analytic_conductor: 8.009589747620803
    root_angle: 1.0
    root_number: '-1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    spectral_label: c5-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.62694506984968860545250238413'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.94310999864192487169989714010'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.70270476818462225555822481114'
      prec: 103
- - algebraic: true
    analytic_conductor: 64.15352792519226
    bad_primes:
    - 2
    - 5
    central_character: '1.1'
    conductor: 400
    conductor_radical: 10
    degree: 2
    id: 19670753
    index: 37
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/400/6/a/r/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: 2-20e2-1.1-c5-0-37
    motivic_weight: 5
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 5
    order_of_vanishing: 1
    prelabel: 2-20e2-1.1-c5-0
    primitive: true
    rational: false
    root_analytic_conductor: 8.009589747620803
    root_angle: 0.5
    self_dual: true
    spectral_label: c5-0
    z1:
      __RealLiteral__: 0
      data: '1.62694506984968860545250238413'
      prec: 103
- - Lhash: '2062397894333316370074834340367'
    Lhash_array:
    - '2062397894333316370074834340367'
    id: 20041834
    label: 2-20e2-1.1-c5-0-37
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/400/6/a/r/1/2
label_cols:
- label
- label
- label
labels:
- 2-20e2-1.1-c5-0-37
- 2-20e2-1.1-c5-0-37
- 2-20e2-1.1-c5-0-37
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T18:39:56.241542'