data:
- - Lhash: '921615586971141650660016940344'
    a10: 0
    a2: -1
    a3: 0
    a4: 1
    a5: 0
    a6: 0
    a7: -2
    a8: -1
    a9: 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 68.27209372819476
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - 1
        - 1
    - - 3
      - - 1
    - - 5
      - - 1
    - - 19
      - - 1
        - 1
    bad_primes:
    - 2
    - 3
    - 5
    - 19
    central_character: '8550.1'
    coefficient_field: 1.1.1.1
    conductor: 8550
    conductor_radical: 570
    degree: 2
    euler_factors:
    - - 1
      - 1
    - - 1
    - - 1
    - - 1
      - 2
      - 7
    - - 1
      - -6
      - 11
    - - 1
      - 0
      - 13
    - - 1
      - -2
      - 17
    - - 1
      - 1
    - - 1
      - -4
      - 23
    - - 1
      - -8
      - 29
    - - 1
      - 8
      - 31
    - - 1
      - -4
      - 37
    - - 1
      - -4
      - 41
    - - 1
      - -6
      - 43
    - - 1
      - 12
      - 47
    - - 1
      - -6
      - 53
    - - 1
      - -4
      - 59
    - - 1
      - -2
      - 61
    - - 1
      - -8
      - 67
    - - 1
      - 0
      - 71
    - - 1
      - 6
      - 73
    - - 1
      - -8
      - 79
    - - 1
      - -4
      - 83
    - - 1
      - -4
      - 89
    - - 1
      - 12
      - 97
    - - 1
      - -10
      - 101
    - - 1
      - 0
      - 103
    - - 1
      - 12
      - 107
    - - 1
      - 14
      - 109
    - - 1
      - -14
      - 113
    euler_factors_factorization:
    - - - - 1
          - 1
        - 1
    - - 1
    - - 1
    - - - - 1
          - 2
          - 7
        - 1
    - - - - 1
          - -6
          - 11
        - 1
    - - - - 1
          - 0
          - 13
        - 1
    - - - - 1
          - -2
          - 17
        - 1
    - - - - 1
          - 1
        - 1
    - - - - 1
          - -4
          - 23
        - 1
    - - - - 1
          - -8
          - 29
        - 1
    - - - - 1
          - 8
          - 31
        - 1
    - - - - 1
          - -4
          - 37
        - 1
    - - - - 1
          - -4
          - 41
        - 1
    - - - - 1
          - -6
          - 43
        - 1
    - - - - 1
          - 12
          - 47
        - 1
    - - - - 1
          - -6
          - 53
        - 1
    - - - - 1
          - -4
          - 59
        - 1
    - - - - 1
          - -2
          - 61
        - 1
    - - - - 1
          - -8
          - 67
        - 1
    - - - - 1
          - 0
          - 71
        - 1
    - - - - 1
          - 6
          - 73
        - 1
    - - - - 1
          - -8
          - 79
        - 1
    - - - - 1
          - -4
          - 83
        - 1
    - - - - 1
          - -4
          - 89
        - 1
    - - - - 1
          - 12
          - 97
        - 1
    - - - - 1
          - -10
          - 101
        - 1
    - - - - 1
          - 0
          - 103
        - 1
    - - - - 1
          - 12
          - 107
        - 1
    - - - - 1
          - 14
          - 109
        - 1
    - - - - 1
          - -14
          - 113
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 22273645
    index: 34
    label: 2-8550-1.1-c1-0-34
    leading_term: '1.554764610055068509496257297710000000000000000000000000000000000000000000000000000000000000'
    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/8550/2/a/g
    plot_delta:
      __RealLiteral__: 0
      data: '0.046875'
      prec: 27
    plot_values:
    - 1.5547646100550685
    - 1.5474108256075698
    - 1.5253632438177047
    - 1.4886684300820898
    - 1.4374210994977856
    - 1.3717884254697639
    - 1.292041496707618
    - 1.1985916208196523
    - 1.0920288573264814
    - 0.9731600331077493
    - 0.843043532655747
    - 0.7030183347061614
    - 0.5547250513316805
    - 0.4001170822532145
    - 0.2414603983813987
    - 0.08132089424763775
    - -0.07746131409030574
    - -0.23181082846090934
    - -0.37846888794255407
    - -0.5140575739134982
    - -0.6351551760047585
    - -0.7383811746076379
    - -0.8204888936112427
    - -0.8784635014893932
    - -0.9096227005280547
    - -0.9117171551889683
    - -0.8830274845026517
    - -0.8224544932511603
    - -0.7295992551516303
    - -0.6048296994555227
    - -0.4493304993126951
    - -0.2651333220079675
    - -0.05512488036513738
    - 0.17696928015594487
    - 0.4266267186167237
    - 0.6885965144688422
    - 0.9569941261147252
    - 1.2254218001759818
    - 1.4871127417474737
    - 1.735096343825614
    - 1.9623808781013237
    - 2.1621492019910065
    - 2.327962271848278
    - 2.453964603408128
    - 2.5350853199952033
    - 2.5672281065580616
    - 2.5474432688534545
    - 2.4740752024759245
    - 2.346878919764649
    - 2.1670998701902353
    - 1.9375121194454585
    - 1.66241101289076
    - 1.3475577196224484
    - 1.0000745042834716
    - 0.6282911659229429
    - 0.24154476966175306
    - -0.15006347644462661
    - -0.5359486397116582
    - -0.9053525920194935
    - -1.247675988266118
    - -1.5528217662230461
    - -1.8115392452660886
    - -2.0157572328205213
    - -2.1588942507618674
    - -2.2361341045873013
    - -2.2446555580715906
    - -2.1838058527522906
    - -2.05520921630772
    - -1.8628033112444937
    - -1.6127987428921347
    - -1.3135592146727684
    - -0.9754026149199093
    - -0.6103261557970403
    - -0.23166156300630517
    - 0.1463308707006594
    - 0.5089179142643477
    - 0.8413848972006797
    - 1.1295472959710802
    - 1.3602651381593553
    - 1.5219420338658287
    - 1.6049903541540538
    - 1.6022444623646133
    - 1.5093049858791228
    - 1.3247988875392858
    - 1.0505425240472803
    - 0.6915979023296327
    - 0.25621587638855037
    - -0.24433604565819775
    - -0.79605942547317
    - -1.3826179900275566
    - -1.9858276904009067
    - -2.586229286296457
    - -3.1637253771666116
    - -3.698260707106549
    - -4.170522170351287
    - -4.5626333616299295
    - -4.858817847682438
    - -5.046005647064643
    - -5.11435872212625
    - -5.057693597092529
    - -4.873782465730867
    - -4.564518246600714
    - -4.135933850205455
    - -3.5980712725769535
    - -2.964701826820312
    - -2.252904648683451
    - -1.482516331247545
    - -0.6754699198218899
    - 0.14495370104255695
    - 0.9549349873988843
    - 1.7309554153350968
    - 2.4506357058164476
    - 3.093540006997479
    - 3.6419141299389057
    - 4.081327945778344
    - 4.4011953469547676
    - 4.595149649802621
    - 4.661257814387355
    - 4.602063174385088
    - 4.424453257804773
    - 4.139356458699076
    - 3.7612784898470357
    - 3.3076963973284013
    - 2.798334145505891
    - 2.2543490994395916
    - 1.6974628875153661
    - 1.14907291091296
    - 0.6293820246270058
    - 0.1565835572345299
    - -0.2538631563475627
    - -0.589835130026856
    - -0.8429994018650677
    - -1.009097754112553
    - -1.088049498301748
    - -1.0838673354755366
    - -1.0043896363072893
    - -0.8608407922988408
    - -0.6672391866378717
    - -0.439679450865451
    - -0.19552166808093616
    - 0.047475243685237
    - 0.2720358220063409
    - 0.46222479321825705
    - 0.6042378424333058
    - 0.6870887464628997
    - 0.7031597387298264
    - 0.6485881461045022
    - 0.5234698712314313
    - 0.33186885435108804
    - 0.08163084347258845
    - -0.21599080015380953
    - -0.546880382882015
    - -0.8947509098162839
    - -1.241948188830387
    - -1.570329481237424
    - -1.8621741274613255
    - -2.101081562240856
    - -2.272812284199966
    - -2.3660296870629836
    - -2.3729051141240944
    - -2.2895548768299023
    - -2.116285995791844
    - -1.8576367039412343
    - -1.5222078519615534
    - -1.1222917809550357
    - -0.6733154561659833
    - -0.19312416829044932
    - 0.2988595880721367
    - 0.7825607969653364
    - 1.2382142659958326
    - 1.647316381990336
    - 1.9935181122071226
    - 2.2634136446234248
    - 2.447183997314256
    - 2.5390620217500355
    - 2.537594142285466
    - 2.4456844773963122
    - 2.2704181602065288
    - 2.022672144541569
    - 1.7165329502764748
    - 1.3685510754100507
    - 0.9968706260267335
    - 0.6202795999682759
    - 0.25723081083580057
    - -0.0751146215469962
    - -0.3617701026430637
    - -0.590685171452987
    - -0.7533445081045371
    - -0.8451714394659481
    - -0.8657134025054763
    - -0.8185985379299128
    - -0.7112650348306814
    - -0.5544773628541221
    - -0.3616554279414386
    - -0.1480533080985312
    - 0.07016703813274977
    - 0.27691535868604755
    - 0.4571507070140901
    - 0.5978012494543856
    - 0.6885730689818879
    - 0.7226003666871361
    - 0.6968978366760846
    - 0.6125867060216581
    - 0.4748784302039476
    - 0.2928136463926964
    - 0.07876796614117576
    - -0.15225024617720173
    - -0.38347258715602545
    - -0.5973658354306921
    - -0.7766937759567338
    - -0.9055848484799984
    - -0.9705433492006166
    - -0.9613439596871433
    - -0.8717549156877684
    - -0.7000439174033222
    - -0.44923248830545354
    - -0.1270783077015009
    - 0.25421967087579156
    - 0.678582592262683
    - 1.1268532040319716
    - 1.577796676486988
    - 2.0092475012801025
    - 2.399339606628304
    - 2.727750614478508
    - 2.9768887993107547
    - 3.132953012721509
    - 3.1868016063479176
    - 3.1345759774356643
    - 2.978037309511726
    - 2.7245907135166787
    - 2.3869884497810094
    - 1.9827222594765708
    - 1.5331330134220054
    - 1.0622828394602533
    - 0.5956496063771144
    - 0.15871521780788767
    - -0.2244731398006038
    - -0.532686380713782
    - -0.748760561280154
    - -0.8606327812942497
    - -0.8621018069306585
    - -0.7532639015503328
    - -0.5405921790868253
    - -0.23664786057362572
    - 0.140567001668556
    - 0.568584676294397
    - 1.0217243603833364
    - 1.4725545659295212
    - 1.8934839298775796
    - 2.258389868754963
    - 2.544190371084968
    - 2.732265544317129
    - 2.8096423524015743
    - 2.7698680184731654
    - 2.613514234989874
    - 2.3482747465582587
    - 1.988641933784332
    positive_zeros:
    - '0.72702650620384893619493677336403'
    - '1.51151407902078207431966553419602'
    - '2.60702654530372970473798787781748'
    - '3.45047751789024331205747911919811'
    - '4.05592693224714429133111330347410'
    - '5.05421353474036241439585476427118'
    - '6.01697868283080134194078234387278'
    - '6.55316173473956503983251578216978'
    - '6.99790758745763956176962111980634'
    - '7.79967888136435362574213149503146'
    prelabel: 2-8550-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 8.262692885990303
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1-0
    trace_hash: 588878038566434585
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.72702650620384893619493677336'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '1.51151407902078207431966553420'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.60702654530372970473798787782'
      prec: 103
- - algebraic: true
    analytic_conductor: 68.27209372819476
    bad_primes:
    - 2
    - 3
    - 5
    - 19
    central_character: '1.1'
    conductor: 8550
    conductor_radical: 570
    degree: 2
    dirichlet_coefficients:
    - 1
    - -1
    - 0
    - 1
    - 0
    - 0
    - -2
    - -1
    - 0
    - 0
    - 6
    - 0
    - 0
    - 2
    - 0
    - 1
    - 2
    - 0
    - -1
    - 0
    - 0
    - -6
    - 4
    - 0
    - 0
    - 0
    - 0
    - -2
    - 8
    - 0
    - -8
    - -1
    - 0
    - -2
    - 0
    - 0
    - 4
    - 1
    - 0
    - 0
    - 4
    - 0
    - 6
    - 6
    - 0
    - -4
    - -12
    - 0
    - -3
    - 0
    - 0
    - 0
    - 6
    - 0
    - 0
    - 2
    - 0
    - -8
    - 4
    - 0
    - 2
    - 8
    - 0
    - 1
    - 0
    - 0
    - 8
    - 2
    - 0
    - 0
    - 0
    - 0
    - -6
    - -4
    - 0
    - -1
    - -12
    - 0
    - 8
    - 0
    - 0
    - -4
    - 4
    - 0
    - 0
    - -6
    - 0
    - -6
    - 4
    - 0
    - 0
    - 4
    - 0
    - 12
    - 0
    - 0
    - -12
    - 3
    - 0
    - 0
    euler11:
    - 1
    - -6
    - 11
    euler13:
    - 1
    - 0
    - 13
    euler17:
    - 1
    - -2
    - 17
    euler19:
    - 1
    - 1
    - 0
    euler2:
    - 1
    - 1
    - 0
    euler23:
    - 1
    - -4
    - 23
    euler29:
    - 1
    - -8
    - 29
    euler3:
    - 1
    - 0
    - 0
    euler31:
    - 1
    - 8
    - 31
    euler37:
    - 1
    - -4
    - 37
    euler41:
    - 1
    - -4
    - 41
    euler43:
    - 1
    - -6
    - 43
    euler47:
    - 1
    - 12
    - 47
    euler5:
    - 1
    - 0
    - 0
    euler53:
    - 1
    - -6
    - 53
    euler59:
    - 1
    - -4
    - 59
    euler61:
    - 1
    - -2
    - 61
    euler67:
    - 1
    - -8
    - 67
    euler7:
    - 1
    - 2
    - 7
    euler71:
    - 1
    - 0
    - 71
    euler73:
    - 1
    - 6
    - 73
    euler79:
    - 1
    - -8
    - 79
    euler83:
    - 1
    - -4
    - 83
    euler89:
    - 1
    - -4
    - 89
    euler97:
    - 1
    - 12
    - 97
    euler_factors:
    - - 1
      - 1
      - 0
    - - 1
      - 0
      - 0
    - - 1
      - 0
      - 0
    - - 1
      - 2
      - 7
    - - 1
      - -6
      - 11
    - - 1
      - 0
      - 13
    - - 1
      - -2
      - 17
    - - 1
      - 1
      - 0
    - - 1
      - -4
      - 23
    - - 1
      - -8
      - 29
    - - 1
      - 8
      - 31
    - - 1
      - -4
      - 37
    - - 1
      - -4
      - 41
    - - 1
      - -6
      - 43
    - - 1
      - 12
      - 47
    - - 1
      - -6
      - 53
    - - 1
      - -4
      - 59
    - - 1
      - -2
      - 61
    - - 1
      - -8
      - 67
    - - 1
      - 0
      - 71
    - - 1
      - 6
      - 73
    - - 1
      - -8
      - 79
    - - 1
      - -4
      - 83
    - - 1
      - -4
      - 89
    - - 1
      - 12
      - 97
    id: 22273645
    index: 34
    instance_types:
    - ECQ
    - CMF
    - CMF
    instance_urls:
    - EllipticCurve/Q/8550/g
    - ModularForm/GL2/Q/holomorphic/8550/2/a/g/1/1
    - ModularForm/GL2/Q/holomorphic/8550/2/a/g
    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: 2-8550-1.1-c1-0-34
    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: 2-8550-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 8.262692885990303
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    trace_hash: 588878038566434585
    z1:
      __RealLiteral__: 0
      data: '0.72702650620384893619493677336'
      prec: 103
- - Lhash: '921615586971141650660016940344'
    Lhash_array:
    - '921615586971141650660016940344'
    id: 22607104
    label: 2-8550-1.1-c1-0-34
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/8550/2/a/g
  - Lhash: '921615586971141650660016940344'
    Lhash_array:
    - '921615586971141650660016940344'
    id: 24584520
    label: 2-8550-1.1-c1-0-34
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/8550/2/a/g/1/1
  - Lhash: '588878038566434585'
    Lhash_array:
    - '588878038566434585'
    id: 35666
    label: 2-8550-1.1-c1-0-34
    type: ECQ
    url: EllipticCurve/Q/8550/g
label_cols:
- label
- label
- label
labels:
- 2-8550-1.1-c1-0-34
- 2-8550-1.1-c1-0-34
- 2-8550-1.1-c1-0-34
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-20T02:50:29.953722'