data:
- - Lhash: '1204786518141272972508174326849'
    a10: 0
    a2: 0
    a3: 0
    a4: 0
    a5: 1
    a6: 0
    a7: 4
    a8: 0
    a9: 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 66.11613287362019
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - 1
    - - 3
      - - 1
    - - 5
      - - 1
        - -1
    - - 23
      - - 1
        - 1
    bad_primes:
    - 2
    - 3
    - 5
    - 23
    central_character: '8280.1'
    coefficient_field: 1.1.1.1
    conductor: 8280
    conductor_radical: 690
    degree: 2
    euler_factors:
    - - 1
    - - 1
    - - 1
      - -1
    - - 1
      - -4
      - 7
    - - 1
      - 4
      - 11
    - - 1
      - -6
      - 13
    - - 1
      - -2
      - 17
    - - 1
      - -4
      - 19
    - - 1
      - 1
    - - 1
      - -2
      - 29
    - - 1
      - 0
      - 31
    - - 1
      - -2
      - 37
    - - 1
      - 2
      - 41
    - - 1
      - 0
      - 43
    - - 1
      - 0
      - 47
    - - 1
      - -6
      - 53
    - - 1
      - -8
      - 59
    - - 1
      - 2
      - 61
    - - 1
      - 16
      - 67
    - - 1
      - -4
      - 71
    - - 1
      - -10
      - 73
    - - 1
      - 0
      - 79
    - - 1
      - 4
      - 83
    - - 1
      - 6
      - 89
    - - 1
      - 2
      - 97
    - - 1
      - -10
      - 101
    - - 1
      - -4
      - 103
    - - 1
      - 4
      - 107
    - - 1
      - -14
      - 109
    - - 1
      - 14
      - 113
    euler_factors_factorization:
    - - 1
    - - 1
    - - - - 1
          - -1
        - 1
    - - - - 1
          - -4
          - 7
        - 1
    - - - - 1
          - 4
          - 11
        - 1
    - - - - 1
          - -6
          - 13
        - 1
    - - - - 1
          - -2
          - 17
        - 1
    - - - - 1
          - -4
          - 19
        - 1
    - - - - 1
          - 1
        - 1
    - - - - 1
          - -2
          - 29
        - 1
    - - - - 1
          - 0
          - 31
        - 1
    - - - - 1
          - -2
          - 37
        - 1
    - - - - 1
          - 2
          - 41
        - 1
    - - - - 1
          - 0
          - 43
        - 1
    - - - - 1
          - 0
          - 47
        - 1
    - - - - 1
          - -6
          - 53
        - 1
    - - - - 1
          - -8
          - 59
        - 1
    - - - - 1
          - 2
          - 61
        - 1
    - - - - 1
          - 16
          - 67
        - 1
    - - - - 1
          - -4
          - 71
        - 1
    - - - - 1
          - -10
          - 73
        - 1
    - - - - 1
          - 0
          - 79
        - 1
    - - - - 1
          - 4
          - 83
        - 1
    - - - - 1
          - 6
          - 89
        - 1
    - - - - 1
          - 2
          - 97
        - 1
    - - - - 1
          - -10
          - 101
        - 1
    - - - - 1
          - -4
          - 103
        - 1
    - - - - 1
          - 4
          - 107
        - 1
    - - - - 1
          - -14
          - 109
        - 1
    - - - - 1
          - 14
          - 113
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 22272778
    index: 51
    label: 2-8280-1.1-c1-0-51
    leading_term: '3.13225593280161177439912185386000000000000000000000000000000000000000000000000000000000000'
    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/8280/2/a/v
    plot_delta:
      __RealLiteral__: 0
      data: '0.046875'
      prec: 27
    plot_values:
    - 3.1322559328016117
    - 3.123402437413323
    - 3.0968177166632156
    - 3.0524359925605276
    - 2.9901702395811793
    - 2.9099444523930336
    - 2.8117357004323025
    - 2.6956231900080403
    - 2.5618411852145595
    - 2.410832496156224
    - 2.243299303153009
    - 2.060248308956433
    - 1.8630275519513153
    - 1.653352628902195
    - 1.4333205312224246
    - 1.205409769535822
    - 0.9724659328656181
    - 0.7376722942407934
    - 0.5045055318647516
    - 0.2766770843925892
    - 0.058061100361007194
    - -0.1473896261757422
    - -0.3357379232981092
    - -0.5031645035782543
    - -0.6460756442464076
    - -0.7612133812084452
    - -0.8457650400464131
    - -0.8974687219211777
    - -0.9147112381457784
    - -0.8966149564712047
    - -0.8431100953927887
    - -0.7549891880908663
    - -0.6339407398338479
    - -0.48255952293834303
    - -0.30433148868419424
    - -0.10359191845569062
    - 0.11454382523108973
    - 0.34427676986208355
    - 0.5792469730255246
    - 0.8126803699935828
    - 1.0375569542241565
    - 1.246796529223056
    - 1.433457441822859
    - 1.590942970307302
    - 1.7132094285032369
    - 1.7949695897015285
    - 1.8318847596452863
    - 1.8207387590119735
    - 1.7595872303502476
    - 1.64787607310509
    - 1.4865234362903204
    - 1.2779605562676342
    - 1.026127802846063
    - 0.7364235674208547
    - 0.41560506023039756
    - 0.07164163988480785
    - -0.2864770703620605
    - -0.6489743721055254
    - -1.005555462849552
    - -1.3457051446409558
    - -1.6590058644623566
    - -1.9354665359234167
    - -2.165851719293815
    - -2.342000184900729
    - -2.4571216927453454
    - -2.506061017187809
    - -2.485518845127107
    - -2.394220180350403
    - -2.2330222814361838
    - -2.0049559158381673
    - -1.7151957830798088
    - -1.370958285147722
    - -0.9813273287038878
    - -0.5570114469633496
    - -0.11003813579978279
    - 0.3466061897093059
    - 0.7993798958113119
    - 1.2346207424668445
    - 1.6389970251967414
    - 1.9999596941244118
    - 2.306179263122864
    - 2.5479512723111877
    - 2.717554632190628
    - 2.80954836410941
    - 2.820994041726795
    - 2.7515935889375425
    - 2.6037349339612237
    - 2.382441266521495
    - 2.0952231841553943
    - 1.7518367165231876
    - 1.363953942280291
    - 0.9447565132853347
    - 0.5084657256142141
    - 0.06982568045442519
    - -0.35644157434656154
    - -0.7561883573965266
    - -1.1163796519320943
    - -1.425595850924611
    - -1.6744792143561655
    - -1.8561049797101048
    - -1.9662605789660719
    - -2.0036196913717674
    - -1.969801793023826
    - -1.869312311657548
    - -1.709363290226836
    - -1.4995794164502012
    - -1.2515991837373248
    - -0.9785856018663932
    - -0.6946650662290375
    - -0.41431652701834143
    - -0.15173579991279634
    - 0.07979841748140655
    - 0.26852962201059777
    - 0.40477298595146866
    - 0.4813842347898253
    - 0.49412572794684045
    - 0.441911411204361
    - 0.3269170866033961
    - 0.154547957439739
    - -0.06673856601465769
    - -0.3257505197343783
    - -0.60900892658349
    - -0.901308644724725
    - -1.186370495692487
    - -1.4475580162907715
    - -1.6686286044499035
    - -1.8344865021708756
    - -1.931904122046844
    - -1.9501787625724702
    - -1.8816937921727765
    - -1.7223568656362154
    - -1.471892554613695
    - -1.1339727463174356
    - -0.7161750529330001
    - -0.22976699014189836
    - 0.31067849996042246
    - 0.8878228390364847
    - 1.4822362149161366
    - 2.073179297199396
    - 2.6394594554666044
    - 3.160324530176572
    - 3.6163546690095174
    - 3.990311967460794
    - 4.267908724994029
    - 4.438458045377742
    - 4.495375183004934
    - 4.436504291286145
    - 4.264252809785243
    - 3.985524308490252
    - 3.6114498085159368
    - 3.156926996535868
    - 2.6399859023248813
    - 2.081008071848571
    - 1.5018336206659317
    - 0.9247964148697503
    - 0.3717316825084795
    - -0.1369976299012168
    - -0.5834096174165568
    - -0.9527035597969534
    - -1.2339122804284632
    - -1.4203741061489144
    - -1.510000074559479
    - -1.505321637731263
    - -1.4133146108343022
    - -1.2450060123365858
    - -1.0148812084100167
    - -0.7401188712632338
    - -0.4396901731276858
    - -0.13336589546577365
    - 0.15931966050419888
    - 0.4200962239683403
    - 0.6329245217829168
    - 0.7848529275183116
    - 0.8667189157765134
    - 0.8736576605375932
    - 0.8053893695996454
    - 0.6662678090591962
    - 0.4650844209139895
    - 0.2146348845841546
    - -0.06893270795532982
    - -0.366957338381578
    - -0.6592513021466054
    - -0.9251840377051241
    - -1.144808512195059
    - -1.2999720035053632
    - -1.375352947914256
    - -1.3593683755113357
    - -1.244902243419963
    - -1.029813455281322
    - -0.7171931344942075
    - -0.31535327946969977
    - 0.1624573516436127
    - 0.6986000989402051
    - 1.2718320681385127
    - 1.8582937802322395
    - 2.4326507925483747
    - 2.969332428845874
    - 3.443804747871156
    - 3.8338120851321134
    - 4.120522128216596
    - 4.289513560189341
    - 4.3315526732821885
    - 4.2431156818779785
    - 4.026626250283854
    - 3.6903923559916576
    - 3.2482422820427543
    - 2.7188754500869745
    - 2.1249591174801314
    - 1.4920158330227709
    - 0.8471582051061519
    - 0.21773631746203181
    - -0.3700314898295817
    - -0.8923721184131235
    - -1.3291453869079715
    - -1.6648418641309788
    - -1.889336479084557
    - -1.9983562463224451
    - -1.993635595855695
    - -1.8827495819036646
    - -1.6786327646226726
    - -1.3988088577051867
    - -1.0643723528622333
    - -0.6987773596093779
    - -0.3265000265567204
    - 0.028351522147063032
    - 0.34340226722817396
    - 0.5992736772351172
    - 0.780673740050243
    - 0.8772511331362322
    - 0.8841637942718896
    - 0.802327885274329
    - 0.638330984814014
    - 0.40401232330277903
    - 0.11573192321554697
    - -0.2066314490556843
    - -0.5408976200282015
    - -0.863948731806665
    - -1.1531612216493894
    - -1.3878230634293216
    - -1.550453113204762
    - -1.627944020691996
    - -1.612459376282783
    - -1.5020290983855522
    - -1.3008038222474252
    - -1.018948314340536
    - -0.6721746316800565
    - -0.28093669871357746
    - 0.13067202262570443
    - 0.5362582142706722
    - 0.9086314912185732
    - 1.2213854591088
    - 1.450466374155402
    - 1.575638092697358
    - 1.5817566461383605
    - 1.459777529298613
    - 1.207433153885262
    - 0.829536124542642
    positive_zeros:
    - '0.950408983298995558454951528613965'
    - '1.66327876536016891391595409133314'
    - '2.58761177646133317525090584817301'
    - '3.48008440775626251414324873887943'
    - '4.36691986594063349208128250707877'
    - '5.18608418173652300323324898320961'
    - '5.56490917809100656125096643835336'
    - '6.30167121334597291857036751592817'
    - '7.29936423092044665287347241009717'
    - '7.895908578706044276541732863707281'
    prelabel: 2-8280-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 8.131182747523278
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1-0
    trace_hash: 1151070497758668937
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.950408983298995558454951528614'
      prec: 107
    z2:
      __RealLiteral__: 0
      data: '1.66327876536016891391595409133'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.58761177646133317525090584817'
      prec: 103
- - algebraic: true
    analytic_conductor: 66.11613287362019
    bad_primes:
    - 2
    - 3
    - 5
    - 23
    central_character: '1.1'
    conductor: 8280
    conductor_radical: 690
    degree: 2
    dirichlet_coefficients:
    - 1
    - 0
    - 0
    - 0
    - 1
    - 0
    - 4
    - 0
    - 0
    - 0
    - -4
    - 0
    - 6
    - 0
    - 0
    - 0
    - 2
    - 0
    - 4
    - 0
    - 0
    - 0
    - -1
    - 0
    - 1
    - 0
    - 0
    - 0
    - 2
    - 0
    - 0
    - 0
    - 0
    - 0
    - 4
    - 0
    - 2
    - 0
    - 0
    - 0
    - -2
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 9
    - 0
    - 0
    - 0
    - 6
    - 0
    - -4
    - 0
    - 0
    - 0
    - 8
    - 0
    - -2
    - 0
    - 0
    - 0
    - 6
    - 0
    - -16
    - 0
    - 0
    - 0
    - 4
    - 0
    - 10
    - 0
    - 0
    - 0
    - -16
    - 0
    - 0
    - 0
    - 0
    - 0
    - -4
    - 0
    - 2
    - 0
    - 0
    - 0
    - -6
    - 0
    - 24
    - 0
    - 0
    - 0
    - 4
    - 0
    - -2
    - 0
    - 0
    - 0
    euler11:
    - 1
    - 4
    - 11
    euler13:
    - 1
    - -6
    - 13
    euler17:
    - 1
    - -2
    - 17
    euler19:
    - 1
    - -4
    - 19
    euler2:
    - 1
    - 0
    - 0
    euler23:
    - 1
    - 1
    - 0
    euler29:
    - 1
    - -2
    - 29
    euler3:
    - 1
    - 0
    - 0
    euler31:
    - 1
    - 0
    - 31
    euler37:
    - 1
    - -2
    - 37
    euler41:
    - 1
    - 2
    - 41
    euler43:
    - 1
    - 0
    - 43
    euler47:
    - 1
    - 0
    - 47
    euler5:
    - 1
    - -1
    - 0
    euler53:
    - 1
    - -6
    - 53
    euler59:
    - 1
    - -8
    - 59
    euler61:
    - 1
    - 2
    - 61
    euler67:
    - 1
    - 16
    - 67
    euler7:
    - 1
    - -4
    - 7
    euler71:
    - 1
    - -4
    - 71
    euler73:
    - 1
    - -10
    - 73
    euler79:
    - 1
    - 0
    - 79
    euler83:
    - 1
    - 4
    - 83
    euler89:
    - 1
    - 6
    - 89
    euler97:
    - 1
    - 2
    - 97
    euler_factors:
    - - 1
      - 0
      - 0
    - - 1
      - 0
      - 0
    - - 1
      - -1
      - 0
    - - 1
      - -4
      - 7
    - - 1
      - 4
      - 11
    - - 1
      - -6
      - 13
    - - 1
      - -2
      - 17
    - - 1
      - -4
      - 19
    - - 1
      - 1
      - 0
    - - 1
      - -2
      - 29
    - - 1
      - 0
      - 31
    - - 1
      - -2
      - 37
    - - 1
      - 2
      - 41
    - - 1
      - 0
      - 43
    - - 1
      - 0
      - 47
    - - 1
      - -6
      - 53
    - - 1
      - -8
      - 59
    - - 1
      - 2
      - 61
    - - 1
      - 16
      - 67
    - - 1
      - -4
      - 71
    - - 1
      - -10
      - 73
    - - 1
      - 0
      - 79
    - - 1
      - 4
      - 83
    - - 1
      - 6
      - 89
    - - 1
      - 2
      - 97
    id: 22272778
    index: 51
    instance_types:
    - ECQ
    - CMF
    - CMF
    instance_urls:
    - EllipticCurve/Q/8280/v
    - ModularForm/GL2/Q/holomorphic/8280/2/a/v/1/1
    - ModularForm/GL2/Q/holomorphic/8280/2/a/v
    is_instance_Artin: false
    is_instance_BMF: false
    is_instance_CMF: true
    is_instance_DIR: false
    is_instance_ECNF: false
    is_instance_ECQ: true
    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: 2-8280-1.1-c1-0-51
    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: 2-8280-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 8.131182747523278
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    trace_hash: 1151070497758668937
    z1:
      __RealLiteral__: 0
      data: '0.950408983298995558454951528614'
      prec: 107
- - Lhash: '1204786518141272972508174326849'
    Lhash_array:
    - '1204786518141272972508174326849'
    id: 22309144
    label: 2-8280-1.1-c1-0-51
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/8280/2/a/v
  - Lhash: '1204786518141272972508174326849'
    Lhash_array:
    - '1204786518141272972508174326849'
    id: 24583381
    label: 2-8280-1.1-c1-0-51
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/8280/2/a/v/1/1
  - Lhash: '1151070497758668937'
    Lhash_array:
    - '1151070497758668937'
    id: 26661
    label: 2-8280-1.1-c1-0-51
    type: ECQ
    url: EllipticCurve/Q/8280/v
label_cols:
- label
- label
- label
labels:
- 2-8280-1.1-c1-0-51
- 2-8280-1.1-c1-0-51
- 2-8280-1.1-c1-0-51
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T22:35:17.657784'