data:
- - Lhash: '1650963551963899547889216180100'
    a10:
    - 0
    - 0
    a2:
    - 0
    - 0
    a3:
    - 0.805830250144402
    - 0.805830250144402
    a4:
    - 0
    - 0
    a5:
    - 0
    - -0.2513322496523631
    a6:
    - 0
    - 0
    a7:
    - 0.7071067811865476
    - 0.7071067811865476
    a8:
    - 0
    - 0
    a9:
    - 0
    - -1.701275215904421
    accuracy: 100
    algebraic: true
    analytic_conductor: 9.166826152042992
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 7
      - - - 1.0
          - 0
        - - -0.7071067811865476
          - -0.7071067811865476
    - - 41
      - - - 1.0
          - 0
        - - 6.165286805461699
          - -1.7289414699173224
    bad_primes:
    - 2
    - 7
    - 41
    central_character: '1148.337'
    coefficient_field: CDF
    conductor: 1148
    conductor_radical: 574
    conjugate: '1242944481651174921544366531770'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -0.805830250144402
        - -0.805830250144402
      - - 0
        - 3.0
    - - - 1.0
        - 0
      - - 0
        - 0.2513322496523631
      - - -5.0
        - 0
    - - - 1.0
        - 0
      - - -0.7071067811865476
        - -0.7071067811865476
    - - - 1.0
        - 0
      - - 2.939361829451804
        - 2.939361829451804
      - - 0
        - 11.0
    - - - 1.0
        - 0
      - - -1.8928308766636857
        - -1.8928308766636857
      - - 0
        - 13.0
    - - - 1.0
        - 0
      - - -2.3356220653343254
        - 2.3356220653343254
      - - 0
        - -17.0
    - - - 1.0
        - 0
      - - -1.3391732264759928
        - 1.3391732264759928
      - - 0
        - -19.0
    - - - 1.0
        - 0
      - - -6.672794838182372
        - 0
      - - 23.0
        - 0
    - - - 1.0
        - 0
      - - 0.015514399490592612
        - 0.015514399490592612
      - - 0
        - 29.0
    - - - 1.0
        - 0
      - - 3.6161392081827497
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - -9.221956870084206
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - 6.165286805461699
        - -1.7289414699173224
    - - - 1.0
        - 0
      - - 0
        - 1.9731838759439455
      - - -43.0
        - 0
    - - - 1.0
        - 0
      - - 2.410643541046108
        - -2.410643541046108
      - - 0
        - -47.0
    - - - 1.0
        - 0
      - - -3.1627245523658516
        - -3.1627245523658516
      - - 0
        - 53.0
    - - - 1.0
        - 0
      - - 4.9100511812668985
        - 0
      - - 59.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -9.530724407324879
      - - -61.0
        - 0
    - - - 1.0
        - 0
      - - -8.59321137153204
        - 8.59321137153204
      - - 0
        - -67.0
    - - - 1.0
        - 0
      - - 9.309979927353359
        - 9.309979927353359
      - - 0
        - 71.0
    - - - 1.0
        - 0
      - - 0
        - -5.527106853250111
      - - -73.0
        - 0
    - - - 1.0
        - 0
      - - -4.222697192070265
        - -4.222697192070265
      - - 0
        - 79.0
    - - - 1.0
        - 0
      - - -6.7823055010348146
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 1.7266239266230214
        - 1.7266239266230214
      - - 0
        - 89.0
    - - - 1.0
        - 0
      - - 2.760741780343525
        - -2.760741780343525
      - - 0
        - -97.0
    - - - 1.0
        - 0
      - - -11.986956400210996
        - 11.986956400210996
      - - 0
        - -101.0
    - - - 1.0
        - 0
      - - 0
        - 2.768910072330372
      - - -103.0
        - 0
    - - - 1.0
        - 0
      - - 3.2513710070270143
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 3.328058955692947
        - -3.328058955692947
      - - 0
        - -109.0
    - - - 1.0
        - 0
      - - 6.478978114293148
        - 0
      - - 113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23223158
    index: 14
    label: 2-1148-41.9-c1-0-14
    leading_term: '1.9880143590128178422614482969324225380758733842608187438'
    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/1148/2/k/b/337/12
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 1.9880143590128179
    - 2.011895523848233
    - 2.0287882712558396
    - 2.038474188086909
    - 2.0404903217857564
    - 2.0341599088622493
    - 2.0186356184202117
    - 1.9929523494400316
    - 1.9560864190946334
    - 1.9070181135290158
    - 1.8447949260251366
    - 1.7685932539586386
    - 1.677776761709161
    - 1.5719499766077716
    - 1.4510059432528646
    - 1.3151669227135188
    - 1.1650172103532674
    - 1.0015271899876474
    - 0.826067773515775
    - 0.6404144202233751
    - 0.44674000845320555
    - 0.2475959574624466
    - 0.0458811761664488
    - -0.1552013499491948
    - -0.3522002345519154
    - -0.5414831943243232
    - -0.719315572706543
    - -0.8819486744539498
    - -1.0257162875930195
    - -1.1471373566401273
    - -1.2430223763167123
    - -1.3105807157154992
    - -1.347525776513047
    - -1.3521746526757235
    - -1.3235388095563
    - -1.2614022521368846
    - -1.1663837179805392
    - -1.0399796197877547
    - -0.8845847812753171
    - -0.7034884601515105
    - -0.5008437302892508
    - -0.2816089937527748
    - -0.051461198776464954
    - 0.18331876652955645
    - 0.4159870768561739
    - 0.6395019468327621
    - 0.8467091633829242
    - 1.0305437893048148
    - 1.1842427599162249
    - 1.3015623099193143
    - 1.3769935307745065
    - 1.4059689060537521
    - 1.3850524359610077
    - 1.3121059695905637
    - 1.1864246347424698
    - 1.0088348020711144
    - 0.7817488452687281
    - 0.5091720536144738
    - 0.1966583981600346
    - -0.14878658264042133
    - -0.5188557696995998
    - -0.9041414462735092
    - -1.2943834684671092
    - -1.6787588862980953
    - -2.0462054281271533
    - -2.385769565663964
    - -2.686968412099172
    - -2.940153545148784
    - -3.1368640562698267
    - -3.2701557635003824
    - -3.3348936318363784
    - -3.3279950495931323
    - -3.24861272154773
    - -3.0982475497200936
    - -2.8807839494415077
    - -2.602442539769923
    - -2.271647980755807
    - -1.8988128140563705
    - -1.496041390068034
    - -1.07676121324319
    - -0.6552921779600143
    - -0.24636706674705278
    - 0.13538079108107695
    - 0.475944773841672
    - 0.7624677891761257
    - 0.9837405998914265
    - 1.1306556440323918
    - 1.1965972031537533
    - 1.1777504553857652
    - 1.073314424867541
    - 0.8856070446594645
    - 0.6200543896601423
    - 0.28506047992287603
    - -0.10824125532272064
    - -0.5463489087973492
    - -1.0138546586341382
    - -1.4939936260809048
    - -1.9692595659688759
    - -2.42206445649099
    - -2.8354164152147256
    - -3.1935887142433708
    - -3.482752116078349
    - -3.691543376573776
    - -3.8115445867743825
    - -3.8376510228291925
    - -3.7683092596222516
    - -3.6056123429048665
    - -3.355244620359018
    - -3.026275174245712
    - -2.6308054119533026
    - -2.183482966144398
    - -1.7009003314061264
    - -1.200902318882312
    - -0.7018311595775552
    - -0.22174167613754675
    - 0.2223788392486266
    - 0.6153507120746083
    - 0.9444675344421442
    - 1.2000555305379823
    - 1.3758989239772443
    - 1.4695091562910165
    - 1.4822225899337933
    - 1.4191190524282746
    - 1.2887619027800812
    - 1.1027688464192487
    - 0.8752310840911975
    - 0.6220061398393412
    - 0.3599164733092813
    - 0.10589137567634185
    - -0.12390663628441574
    - -0.3149279184496425
    - -0.4550115602802072
    - -0.5350506902575591
    - -0.5495114023387224
    - -0.49677590265598165
    - -0.3792885678596998
    - -0.20349301522305063
    - 0.020441423116304827
    - 0.27909474770055936
    - 0.5564532480128139
    - 0.8347189023412982
    - 1.0952331196349114
    - 1.3194697856611666
    - 1.4900477543001733
    - 1.5917105370238551
    - 1.6122211931350097
    - 1.5431233831835762
    - 1.3803251517010569
    - 1.1244700453293204
    - 0.7810703053250807
    - 0.36038863360733686
    - -0.12293214894872037
    - -0.6504789980587788
    - -1.2008925784295843
    - -1.7508677217784154
    - -2.276282542308349
    - -2.7534002251297034
    - -3.160082130504957
    - -3.47694860015706
    - -3.688424927732814
    - -3.7836144073877898
    - -3.7569480644884226
    - -3.6085712825599945
    - -3.344440583792893
    - -2.976118661505744
    - -2.5202716485638943
    - -1.997888701718975
    - -1.4332594165784036
    - -0.852758499336586
    - -0.28349870497450447
    - 0.24807839305124135
    - 0.7175992635108158
    - 1.1040673514024717
    - 1.3910116265942403
    - 1.5674094432150312
    - 1.628329327980012
    - 1.5752534972214822
    - 1.4160566388108478
    - 1.1646359186263289
    - 0.8402062950630096
    - 0.4662939961038009
    - 0.06947836984900467
    - -0.3220527490972581
    - -0.6800574078587032
    - -0.9778193399839268
    - -1.1916659402985326
    - -1.3023390297714892
    - -1.2961397738119185
    - -1.165780442973475
    - -0.9108910671021182
    - -0.5381476412070456
    - -0.06100939603732873
    - 0.5009254030080069
    - 1.1229138605613846
    - 1.7763613957001156
    - 2.430343784415072
    - 3.05327478234624
    - 3.614626326784937
    - 4.08660406788429
    - 4.445682311336946
    - 4.6739093939095016
    - 4.759906753554568
    - 4.6995018710118
    - 4.495955932635203
    - 4.159770334676914
    - 3.708080678729306
    - 3.1636712555505984
    - 2.553665721535296
    - 1.9079693503305366
    - 1.2575536592342196
    - 0.6326843681230742
    - 0.06119785021180483
    - -0.43307086902596914
    - -0.8316138854264165
    - -1.122249518569663
    - -1.2997336112279188
    - -1.3659451721789244
    - -1.3296343785859208
    - -1.2057478554178143
    - -1.014372429587874
    - -0.7793625720072981
    - -0.526736959789781
    - -0.28294469178121134
    - -0.07311064937342053
    - 0.08062834462440806
    - 0.16058979200415166
    - 0.1547191428776288
    - 0.05739361430950768
    - -0.13019790512476967
    - -0.40012616307893206
    - -0.7382424518688651
    - -1.1251183198119181
    - -1.5373456990918488
    - -1.9491148784796304
    - -2.3339685869537052
    - -2.666617640184168
    - -2.9246980747908746
    - -3.0903519387402425
    - -3.151523907418371
    - -3.102883135158713
    - -2.946303229977021
    - -2.6908615261865387
    - -2.352350153645675
    - -1.95232375770796
    - -1.5167399971668556
    - -1.0742770545522808
    - -0.6544354171260194
    - -0.2855475080792275
    - 0.0071728434971186465
    - 0.20340931828145947
    - 0.28922762041037925
    - 0.2581601383156927
    - 0.11180999789379815
    - -0.14007569051122581
    - -0.48007909309652613
    - -0.8841109078161312
    - -1.3228795474603656
    positive_zeros:
    - '1.30238060208913875996547950407628'
    - '2.47382259211329319473806232143488'
    - '3.43238921356898905469411423634468'
    - '4.78328580911136979733208265941045'
    - '5.43382710540975224447037260329156'
    - '6.70821890630327131882037513302043'
    - '7.52600546990487815835925784149956'
    - '8.022400131201230762780804265591220'
    - '8.833340259532516159329212931578942'
    - '9.932897400526939743683294831251134'
    prelabel: 2-1148-41.9-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.0276766921259926
    root_angle: 0.05558288317194563
    root_number: 0.98479284129807887568439270458540908711978502839352782460 + 0.17373272497735374338944579702983362981350266662001817486*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.027791441585972815'
      prec: 67
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.30238060208913875996547950408'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.47382259211329319473806232143'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.43238921356898905469411423634'
      prec: 103
- - algebraic: true
    analytic_conductor: 9.166826152042992
    bad_primes:
    - 2
    - 7
    - 41
    central_character: '41.9'
    conductor: 1148
    conductor_radical: 574
    degree: 2
    id: 23223158
    index: 14
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1148/2/k/b/337/12
    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: 2-1148-41.9-c1-0-14
    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: 2-1148-41.9-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.0276766921259926
    root_angle: 0.027791441585972815
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '1.30238060208913875996547950408'
      prec: 103
- - Lhash: '1650963551963899547889216180100'
    Lhash_array:
    - '1650963551963899547889216180100'
    id: 23595966
    label: 2-1148-41.9-c1-0-14
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1148/2/k/b/337/12
label_cols:
- label
- label
- label
labels:
- 2-1148-41.9-c1-0-14
- 2-1148-41.9-c1-0-14
- 2-1148-41.9-c1-0-14
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-11T22:14:37.712047'