data:
- - Lhash: '696935800900175563375925032482'
    a10:
    - 0.0
    - 0.0
    a2:
    - 0.0
    - 0.0
    a3:
    - -2.124885419764574
    - 0.0
    a4:
    - 0.0
    - 0.0
    a5:
    - -1.4848619528719296
    - 0.0
    a6:
    - 0.0
    - 0.0
    a7:
    - 0.0
    - 0.0
    a8:
    - 0.0
    - 0.0
    a9:
    - 1.5151380471280704
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 14.820234615149646
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 29
      - - - 1.0
          - 0
        - - 1.0
          - 0
    bad_primes:
    - 2
    - 29
    central_character: '1856.1'
    coefficient_field: CDF
    conductor: 1856
    conductor_radical: 58
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 2.124885419764574
        - 0
      - - 3.0
        - 0
    - - - 1.0
        - 0
      - - 1.4848619528719296
        - 0
      - - 5.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 7.0
        - 0
    - - - 1.0
        - 0
      - - -3.155161514020715
        - 0
      - - 11.0
        - 0
    - - - 1.0
        - 0
      - - 6.764908886657219
        - 0
      - - 13.0
        - 0
    - - - 1.0
        - 0
      - - -2.0
        - 0
      - - 17.0
        - 0
    - - - 1.0
        - 0
      - - 1.030276094256141
        - 0
      - - 19.0
        - 0
    - - - 1.0
        - 0
      - - 4.249770839529148
        - 0
      - - 23.0
        - 0
    - - - 1.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - -1.8751145802354259
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - -0.9697239057438589
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - 7.529817773314438
        - 0
      - - 41.0
        - 0
    - - - 1.0
        - 0
      - - -1.094609325508433
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - -9.344380165037581
        - 0
      - - 47.0
        - 0
    - - - 1.0
        - 0
      - - 5.734632792401078
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - -8.249770839529148
        - 0
      - - 59.0
        - 0
    - - - 1.0
        - 0
      - - -10.499541679058296
        - 0
      - - 61.0
        - 0
    - - - 1.0
        - 0
      - - 4.4995416790582965
        - 0
      - - 67.0
        - 0
    - - - 1.0
        - 0
      - - 10.189218651016866
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - -11.529817773314438
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - -13.094609325508433
        - 0
      - - 79.0
        - 0
    - - - 1.0
        - 0
      - - -16.24977083952915
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - -13.59036996182672
        - 0
      - - 89.0
        - 0
    - - - 1.0
        - 0
      - - 4.969723905743859
        - 0
      - - 97.0
        - 0
    - - - 1.0
        - 0
      - - -9.469265584802155
        - 0
      - - 101.0
        - 0
    - - - 1.0
        - 0
      - - 4.249770839529148
        - 0
      - - 103.0
        - 0
    - - - 1.0
        - 0
      - - 6.560093867570579
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - -12.954127537674085
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - 0.060552188512282085
        - 0
      - - 113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 20224493
    index: 5
    label: 2-1856-1.1-c1-0-5
    leading_term: '0.62198943504592709504603827072906'
    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/1856/2/a/y/1/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 0.6219894350459271
    - 0.6152815538171023
    - 0.5950847756610009
    - 0.5611891552725454
    - 0.5132755860060628
    - 0.4509595737932007
    - 0.37384801846274107
    - 0.2816052335639581
    - 0.1740241921420135
    - 0.05109908016532269
    - -0.08690444254780134
    - -0.23938444985474966
    - -0.4053461635853401
    - -0.5833559164484559
    - -0.7715076678701134
    - -0.9674037890694978
    - -1.168151570345754
    - -1.3703766351679219
    - -1.5702541449611225
    - -1.7635583248647286
    - -1.945730422058548
    - -2.1119647210377868
    - -2.257311689033648
    - -2.3767967212286982
    - -2.465552317033193
    - -2.518960867802912
    - -2.5328045990217007
    - -2.5034186147607524
    - -2.4278424692199945
    - -2.303965269650424
    - -2.130659026216016
    - -1.9078948342965563
    - -1.636836526578531
    - -1.3199066842196783
    - -0.9608203602942378
    - -0.5645825490758458
    - -0.13744632753631608
    - 0.31317031233542597
    - 0.7788096527303271
    - 1.2501407592798057
    - 1.717165091670059
    - 2.169457425770641
    - 2.59643672910584
    - 2.9876601279978625
    - 3.3331317313273123
    - 3.6236168986454764
    - 3.8509516234059165
    - 4.008336104501623
    - 4.09060135229558
    - 4.094437859214997
    - 4.018575986389478
    - 3.863908787344084
    - 3.6335495000409557
    - 3.3328178629902796
    - 2.9691517033499855
    - 2.551942839085214
    - 2.0922991493304774
    - 1.6027375970115407
    - 1.096815922509322
    - 0.5887135446545848
    - 0.09277477930838719
    - -0.3769703090980773
    - -0.8072903900061897
    - -1.1862245258426045
    - -1.5035224072989606
    - -1.7510348660358181
    - -1.9230374482055435
    - -2.0164716979150987
    - -2.031091417521784
    - -1.9695044740757026
    - -1.8371046055497162
    - -1.64189201086685
    - -1.3941861191272316
    - -1.1062386373310154
    - -0.7917595674654555
    - -0.4653731504510185
    - -0.14202442520289296
    - 0.1636399131591395
    - 0.4378905882025831
    - 0.6685079559065215
    - 0.8453206978053452
    - 0.9606656859507415
    - 1.0097462820656933
    - 0.990870064753977
    - 0.9055517562727189
    - 0.7584727721012094
    - 0.5572951185159508
    - 0.31233404788394964
    - 0.03610064736178229
    - -0.25726793731985387
    - -0.5526669823897261
    - -0.8347426351949219
    - -1.088637694959299
    - -1.3007296075841528
    - -1.4593246864353968
    - -1.5552734291828647
    - -1.5824744254569116
    - -1.538238692277941
    - -1.4234921954679305
    - -1.2428015900098208
    - -1.0042165347638268
    - -0.7189309324695841
    - -0.4007746868841113
    - -0.06555659389845735
    - 0.2697126801588541
    - 0.5876813920200901
    - 0.8715595288903715
    - 1.1060181865544048
    - 1.2780385978311393
    - 1.3776647958701542
    - 1.398617240021638
    - 1.3387304438333079
    - 1.2001855264975756
    - 0.9895183375845222
    - 0.7173949435972832
    - 0.3981582818435079
    - 0.04916207911118249
    - -0.3100799456108293
    - -0.6588906779433097
    - -0.9765238436073039
    - -1.2433006966169562
    - -1.441729639389083
    - -1.557547954722874
    - -1.5806267605428552
    - -1.505685485900219
    - -1.3327704601559178
    - -1.0674632787464324
    - -0.7207979640127604
    - -0.30888093723733107
    - 0.14777630003276218
    - 0.6251859494742763
    - 1.097033239659457
    - 1.5359919597445428
    - 1.9151409648375424
    - 2.2094087003647536
    - 2.3969688172119703
    - 2.4605100691091333
    - 2.388308038696595
    - 2.1750347359495046
    - 1.8222544221198806
    - 1.338569576555077
    - 0.7393989806689806
    - 0.04638951232032461
    - -0.713516627387796
    - -1.5093180122332268
    - -2.3074343802299437
    - -3.0733572794390316
    - -3.7733856599570963
    - -4.376354303973171
    - -4.8552611840013356
    - -5.188703279978313
    - -5.3620390194432614
    - -5.368208979283074
    - -5.208164158196577
    - -4.89087208806315
    - -4.432894173191599
    - -3.8575516435933066
    - -3.1937210091742436
    - -2.4743215249019737
    - -1.7345756152302543
    - -1.0101373063016252
    - -0.3351925516971892
    - 0.2593617228869393
    - 0.747556286375384
    - 1.1097117950737116
    - 1.3334454016121366
    - 1.4142626457839713
    - 1.3556992621186812
    - 1.1690037396044413
    - 0.8723785602354777
    - 0.4898243960507188
    - 0.04965554047302412
    - -0.41722501838876414
    - -0.8791875068794293
    - -1.3057620832473604
    - -1.6694362012523154
    - -1.9472535079186537
    - -2.1221170416757182
    - -2.183717558724274
    - -2.129031011724043
    - -1.9623561407218082
    - -1.6948921514374753
    - -1.343885725849081
    - -0.9314042590196357
    - -0.4828164382871857
    - -0.025080458527302608
    - 0.4150470197148413
    - 0.8127625428860056
    - 1.14681178395834
    - 1.400823295764326
    - 1.5642908396778037
    - 1.6331383381061277
    - 1.6098294975568765
    - 1.5030150357238947
    - 1.3267421885579498
    - 1.0992816403831633
    - 0.8416541226964434
    - 0.5759607601793933
    - 0.3236362175321893
    - 0.10375066211698196
    - -0.06851512959340281
    - -0.18310758660662493
    - -0.23595570467862143
    - -0.2293741972826327
    - -0.1719757301763264
    - -0.07808798136016548
    - 0.033293207227872025
    - 0.13994917051735636
    - 0.2181864810529815
    - 0.24476760823884658
    - 0.19888756812446778
    - 0.06405268727970612
    - -0.17027969672185392
    - -0.5074290342540205
    - -0.9426931370083595
    - -1.4630995163043405
    - -2.0477459665744067
    - -2.6687295212169744
    - -3.292621427789935
    - -3.8824060497855513
    - -4.399766426681701
    - -4.80757119391683
    - -5.072398831882667
    - -5.166927338641332
    - -5.072021249199351
    - -4.778363504673855
    - -4.28750623843913
    - -3.6122505375967946
    - -2.776308403037383
    - -1.8132476580372088
    - -0.7647692567337793
    - 0.3215870280201734
    - 1.3951714808687212
    - 2.4052181774833383
    - 3.3039121024974523
    - 4.049329050118612
    - 4.608052123751371
    - 4.9572865979840195
    - 5.086325417081084
    - 4.997258813123492
    - 4.704870780212516
    - 4.235719167028182
    - 3.626451277592632
    - 2.9214592810048843
    - 2.1700257273093415
    - 1.4231457361359248
    - 0.7302362834199552
    - 0.13595260704324755
    - -0.32267378865519225
    - -0.6185815410630814
    - -0.7363504536048685
    - -0.6730829884243816
    - -0.43843609332937267
    - -0.05380187507446844
    - 0.44930520387121275
    - 1.0315414478777911
    - 1.6485464091193487
    positive_zeros:
    - '0.54978540677904334919663387981335'
    - '2.12752472267340193791689713496008'
    - '3.52689088308962823922966992056638'
    - '4.47976621685674879321493778804997'
    - '5.16358704870627051564025232692594'
    - '6.04651957334448189316370596550183'
    - '6.80491798489944905710564185999393'
    - '7.54007372699774709849394215875581'
    - '8.324018514517283215030725231429921'
    - '9.465468168476728427348750021679977'
    prelabel: 2-1856-1.1-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.849705782933242
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.54978540677904334919663387981'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.12752472267340193791689713496'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.52689088308962823922966992057'
      prec: 103
- - algebraic: true
    analytic_conductor: 14.820234615149646
    bad_primes:
    - 2
    - 29
    central_character: '1.1'
    conductor: 1856
    conductor_radical: 58
    degree: 2
    id: 20224493
    index: 5
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1856/2/a/y/1/1
    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: 2-1856-1.1-c1-0-5
    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: 2-1856-1.1-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.849705782933242
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '0.54978540677904334919663387981'
      prec: 103
- - Lhash: '696935800900175563375925032482'
    Lhash_array:
    - '696935800900175563375925032482'
    id: 20691555
    label: 2-1856-1.1-c1-0-5
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1856/2/a/y/1/1
label_cols:
- label
- label
- label
labels:
- 2-1856-1.1-c1-0-5
- 2-1856-1.1-c1-0-5
- 2-1856-1.1-c1-0-5
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T12:46:16.349411'