data:
- - Lhash: '1036222599614020709955625654916'
    a10:
    - -1.0511023019022032
    - -0.6068541969490723
    a2:
    - -0.3587194676071504
    - 0.20710678118654752
    a3:
    - 0.0
    - 0.0
    a4:
    - -0.914213562373095
    - 1.5834643389987395
    a5:
    - 1.4650756326574836
    - 2.5375854326938785
    a6:
    - 0.0
    - 0.0
    a7:
    - 0.0
    - 0.0
    a8:
    - 0.0
    - -1.5857864376269049
    a9:
    - 0.0
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 3.5214027291384666
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 7
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 3
    - 7
    central_character: '441.80'
    coefficient_field: CDF
    conductor: 441
    conductor_radical: 21
    conjugate: '2643518300587997005216192648840'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0.3587194676071504
        - -0.20710678118654752
      - - 1.0
        - -1.7320508075688772
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -1.4650756326574836
        - -2.5375854326938785
      - - -2.5
        - 4.330127018922194
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -4.1815405503520555
        - -2.414213562373095
      - - 5.5
        - 9.526279441628825
    - - - 1.0
        - 0
      - - 0
        - 2.9301512653149673
      - - -13.0
        - 0
    - - - 1.0
        - 0
      - - 3.5370054622640397
        - -6.12627316728996
      - - -8.5
        - -14.722431864335457
    - - - 1.0
        - 0
      - - 5.075170865387757
        - -2.9301512653149673
      - - 9.5
        - -16.454482671904334
    - - - 1.0
        - 0
      - - -1.7320508075688772
        - 1.0
      - - 11.5
        - -19.91858428704209
    - - - 1.0
        - 0
      - - 0
        - -0.8284271247461901
      - - -29.0
        - 0
    - - - 1.0
        - 0
      - - 5.075170865387757
        - 2.9301512653149673
      - - 15.5
        - 26.846787517317598
    - - - 1.0
        - 0
      - - -2.7071067811865475
        - -4.688846486529344
      - - -18.5
        - 32.04293994002423
    - - - 1.0
        - 0
      - - -1.2137083938981446
        - 0
      - - 41.0
        - 0
    - - - 1.0
        - 0
      - - -4.48528137423857
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - -2.9301512653149673
        - -5.075170865387757
      - - -23.5
        - 40.703193977868615
    - - - 1.0
        - 0
      - - 6.123724356957945
        - 3.5355339059327378
      - - 26.5
        - 45.89934640057525
    - - - 1.0
        - 0
      - - -2.9301512653149673
        - 5.075170865387757
      - - -29.5
        - -51.09549882328188
    - - - 1.0
        - 0
      - - 1.0511023019022032
        - -0.6068541969490723
      - - 30.5
        - -52.827549630850754
    - - - 1.0
        - 0
      - - -4.242640687119285
        - 7.3484692283495345
      - - -33.5
        - -58.023702053557386
    - - - 1.0
        - 0
      - - 0
        - 0.8284271247461901
      - - -71.0
        - 0
    - - - 1.0
        - 0
      - - -6.12627316728996
        - -3.5370054622640397
      - - 36.5
        - 63.21985447626402
    - - - 1.0
        - 0
      - - 0.8284271247461901
        - 1.4348778704286016
      - - -39.5
        - 68.41600689897065
    - - - 1.0
        - 0
      - - -11.72060506125987
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 5.608935291870596
        - 9.714960901886043
      - - -44.5
        - 77.07626093681505
    - - - 1.0
        - 0
      - - 0
        - -7.074010924528079
      - - -97.0
        - 0
    - - - 1.0
        - 0
      - - 2.678784026555628
        - -4.639790036498285
      - - -50.5
        - -87.4685657822283
    - - - 1.0
        - 0
      - - -12.25254633457992
        - 7.074010924528079
      - - 51.5
        - -89.20061658979718
    - - - 1.0
        - 0
      - - -11.53000977870159
        - 6.656854249492381
      - - 53.5
        - -92.66471820493493
    - - - 1.0
        - 0
      - - -2.7071067811865475
        - 4.688846486529344
      - - -54.5
        - -94.39676901250381
    - - - 1.0
        - 0
      - - 0
        - -13.899494936611665
      - - -113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 10420949
    index: 3
    label: 2-21e2-21.17-c1-0-3
    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/441/2/p/c/80/4
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 1.136990430171729
    - 0.9828521352937833
    - 0.8275935717789668
    - 0.6660956367349706
    - 0.49395268868292974
    - 0.3087161286743532
    - 0.11081379582059334
    - -0.09588912407441935
    - -0.3038690382328805
    - -0.502046023424432
    - -0.6762128935854228
    - -0.809806779967162
    - -0.8850309742994937
    - -0.8843080718883974
    - -0.7920049297046083
    - -0.5963222604505684
    - -0.2911940136487407
    - 0.12199842337572377
    - 0.6331171803701954
    - 1.222586914368287
    - 1.8615401168934471
    - 2.512931742947613
    - 3.133680950026383
    - 3.6777872846596313
    - 4.100242362027303
    - 4.3614295777696555
    - 4.431590518953062
    - 4.294855815536652
    - 3.95230759349346
    - 3.4235741812443994
    - 2.7465625424950915
    - 1.9751084706350657
    - 1.1745569302406362
    - 0.4155525446926494
    - -0.2334085990381301
    - -0.7138777101211891
    - -0.9848509920585453
    - -1.028659487160444
    - -0.854421923375826
    - -0.4983503656250688
    - -0.020547223918773318
    - 0.5016222191461608
    - 0.9830077878139012
    - 1.3419620729235828
    - 1.512026284150898
    - 1.4523968810624965
    - 1.155566554408248
    - 0.650786065317757
    - 0.002478360312938968
    - -0.6965949315367235
    - -1.3368457153482667
    - -1.806722578292433
    - -2.0089696686332608
    - -1.8759443852384288
    - -1.3816077844226096
    - -0.5481264802254932
    - 0.5542925543623572
    - 1.814750440419003
    - 3.095495222241524
    - 4.250474096795211
    - 5.145947039993847
    - 5.6800096705766245
    - 5.797864228174794
    - 5.500200929011322
    - 4.843058870693476
    - 3.9288872921070745
    - 2.890012157980384
    - 1.8670759714902583
    - 0.9860078978348225
    - 0.3374922334307604
    - -0.03737810777055623
    - -0.15254453370404314
    - -0.07232403265012732
    - 0.10272515177104127
    - 0.25698403173337875
    - 0.28413218272761254
    - 0.11004469455472617
    - -0.29033251133564597
    - -0.8857130173522645
    - -1.592656734328867
    - -2.290868114580469
    - -2.8470100626791948
    - -3.142580087607901
    - -3.1003295180089627
    - -2.7036989638477533
    - -2.004862117700988
    - -1.1190576227245679
    - -0.2055769887423131
    - 0.5614518218104668
    - 1.0270596934330511
    - 1.0874906875504584
    - 0.7136236220520744
    - -0.03950596158536445
    - -1.039744436442945
    - -2.1007734945311816
    - -3.0169839019438727
    - -3.603593662682908
    - -3.733928952645738
    - -3.3660268046692083
    - -2.5526419024250733
    - -1.4320193943958495
    - -0.2007908031530503
    - 0.9257719490249451
    - 1.7580013774850347
    - 2.1711817768721957
    - 2.1313584697382995
    - 1.7016591348363381
    - 1.0272928644952648
    - 0.3020768763233682
    - -0.27643301571607826
    - -0.5533378555993507
    - -0.4537802145365201
    - -0.0024864908283444786
    - 0.6795762487094464
    - 1.4013811362836388
    - 1.9455373113452659
    - 2.1199310440885077
    - 1.805552197753634
    - 0.9892067462999281
    - -0.22707214561701897
    - -1.6429618716935666
    - -3.000143485247799
    - -4.037403056791106
    - -4.548257634137433
    - -4.427853999205978
    - -3.6980170017543026
    - -2.5041492719534855
    - -1.0841426806128973
    - 0.28394128633204946
    - 1.3435118281637115
    - 1.9160756722590813
    - 1.9394862596859868
    - 1.478670551270929
    - 0.7062113789117088
    - -0.14255398003830608
    - -0.8289925866393972
    - -1.1705925308840495
    - -1.0856303767548399
    - -0.6119447033130617
    - 0.10491382087054534
    - 0.851179726952888
    - 1.401976816235376
    - 1.5813835076169396
    - 1.3099023823015197
    - 0.6268710819856848
    - -0.31826645094142925
    - -1.3038333164445775
    - -2.093250526388621
    - -2.4968626116462955
    - -2.4218840405028677
    - -1.8970087925424064
    - -1.0647926447100797
    - -0.1434650480728054
    - 0.6318939317432638
    - 1.0731066410564394
    - 1.0902423169797295
    - 0.7162695864264913
    - 0.09777018108553516
    - -0.5463307772327523
    - -0.9871605245854819
    - -1.0524222107787422
    - -0.6784478303211998
    - 0.06729430591816271
    - 1.0004814279863528
    - 1.8681526185026929
    - 2.418378305161747
    - 2.472450962602616
    - 1.979301490947261
    - 1.0361260027917611
    - -0.13187151675679026
    - -1.228493326959591
    - -1.9657360575139178
    - -2.1438415931027683
    - -1.7099144762824838
    - -0.7780389114267688
    - 0.3959903816472231
    - 1.4797761222793286
    - 2.152456505848924
    - 2.1921777805541804
    - 1.5387606881447262
    - 0.31372461376039357
    - -1.2087068984921625
    - -2.67248209601517
    - -3.733543863032884
    - -4.150964408650445
    - -3.8501664514059075
    - -2.9405560715055774
    - -1.682569719781898
    - -0.41341018053132
    - 0.5474546304359668
    - 0.9860702648230257
    - 0.8499170255307595
    - 0.25596821637762185
    - -0.5512320664220559
    - -1.2789282147237693
    - -1.6792642902636423
    - -1.6281790400132765
    - -1.1660734571861806
    - -0.4874049358347773
    - 0.1184554992636686
    - 0.3580182416522534
    - 0.02913689097030134
    - -0.9078464203984082
    - -2.3055953648596144
    - -3.860743017799648
    - -5.192738275304608
    - -5.948517281836718
    - -5.902792779098452
    - -5.024484515580576
    - -3.4893522049782093
    - -1.6345098094271748
    - 0.13241280322295038
    - 1.4432600018990152
    - 2.0665953110013477
    - 1.9641335661378463
    - 1.2905549609895275
    - 0.33791129907801676
    - -0.5575655108841536
    - -1.1173431349063234
    - -1.2000719367758879
    - -0.8350163364095203
    - -0.20050518818591126
    - 0.444114379256914
    - 0.8499208789367871
    - 0.8629886479182837
    - 0.47439531344584357
    - -0.18046916045939582
    - -0.8725804535461326
    - -1.3625264588538994
    - -1.4878052870323921
    - -1.2239004530462978
    - -0.697194355050445
    - -0.14366746444004927
    - 0.17431429955194747
    - 0.06602333113674928
    - -0.5081147682671929
    - -1.404130190786572
    - -2.323405371738257
    - -2.897245805601646
    - -2.8027273383833666
    - -1.873833818233292
    - -0.171567696622672
    - 2.011835657893868
    - 4.219527311817957
    - 5.950176371813675
    - 6.79680572731829
    - 6.562569447174225
    - 5.317800674704833
    - 3.3801614167854215
    - 1.2232852991681769
    - -0.6585003076674798
    - -1.8880778119712411
    - -2.304052613014783
    - -1.990490605988568
    - -1.2305122976807825
    - -0.40071313040658907
    - 0.15786555695561513
    positive_zeros:
    - '0.817435497941986455493466828645608'
    - '2.09119416216593469476841220879514'
    - '4.20175228854807131295539411652007'
    - '5.00498950744690053462465164552276'
    - '6.00044826500447758174708338708580'
    - '6.94025150909168473493777404697150'
    - '8.731853538563880585840083935234789'
    - '9.055159077324915474100747359451798'
    - '9.542130590926080234903550636847136'
    - '10.90525934838017594978547447974847'
    prelabel: 2-21e2-21.17-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.8765400952653442
    root_angle: -0.6530780509683655
    root_number: -0.46258515695519037 - 0.8865748544622399*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.326539025484'
      prec: 50
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.817435497941986455493466828646'
      prec: 107
    z2:
      __RealLiteral__: 0
      data: '2.09119416216593469476841220880'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '4.20175228854807131295539411652'
      prec: 103
- - algebraic: true
    analytic_conductor: 3.5214027291384666
    bad_primes:
    - 3
    - 7
    central_character: '21.17'
    conductor: 441
    conductor_radical: 21
    degree: 2
    id: 10420949
    index: 3
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/441/2/p/c/80/4
    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: 2-21e2-21.17-c1-0-3
    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: 2-21e2-21.17-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.8765400952653442
    root_angle: -0.32653902548418273
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '0.817435497941986455493466828646'
      prec: 107
- - Lhash: '1036222599614020709955625654916'
    Lhash_array:
    - '1036222599614020709955625654916'
    id: 10787013
    label: 2-21e2-21.17-c1-0-3
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/441/2/p/c/80/4
label_cols:
- label
- label
- label
labels:
- 2-21e2-21.17-c1-0-3
- 2-21e2-21.17-c1-0-3
- 2-21e2-21.17-c1-0-3
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T20:59:39.068736'