data:
- - Lhash: '408755577797167456643501287810'
    a10:
    - 0.0
    - 0.0
    a2:
    - -0.43139055754696165
    - 0.7471903635768031
    a3:
    - -1.5395680228570532
    - 2.666610037296779
    a4:
    - 0.6278043737186432
    - 1.0873890724946491
    a5:
    - 0.0
    - 0.0
    a6:
    - -1.328310215523555
    - -2.3007007814995633
    a7:
    - 0.5665197076922784
    - 0.0
    a8:
    - -2.8088777454234726
    - 0.0
    a9:
    - -3.2405393940079517
    - -5.612778874350234
    accuracy: 100
    algebraic: true
    analytic_conductor: 3.79289409601082
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 19
      - - - 1.0
          - 0
        - - 2.368343767726595
          - 3.6593643980711454
    bad_primes:
    - 5
    - 19
    central_character: '475.201'
    coefficient_field: CDF
    conductor: 475
    conductor_radical: 95
    conjugate: '3647582925568777525320191164416'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0.43139055754696165
        - -0.7471903635768031
      - - -1.0
        - -1.7320508075688772
    - - - 1.0
        - 0
      - - 1.5395680228570532
        - -2.666610037296779
      - - -1.5
        - -2.598076211353316
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -0.5665197076922784
        - 0
      - - 7.0
        - 0
    - - - 1.0
        - 0
      - - 1.9122291784843966
        - 0
      - - 11.0
        - 0
    - - - 1.0
        - 0
      - - 0.0972656465153458
        - 0.16846904159561366
      - - -6.5
        - 11.258330249197702
    - - - 1.0
        - 0
      - - 2.647745488167145
        - -4.586029711016755
      - - -8.5
        - -14.722431864335457
    - - - 1.0
        - 0
      - - 2.368343767726595
        - 3.6593643980711454
    - - - 1.0
        - 0
      - - 1.6876987265578756
        - 2.9231799422675344
      - - -11.5
        - 19.91858428704209
    - - - 1.0
        - 0
      - - -4.368343767726595
        - -7.566193350629321
      - - -14.5
        - 25.11473670974872
    - - - 1.0
        - 0
      - - -5.65662043104711
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - -0.9555822937536617
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - 5.024964198773706
        - -8.703493298490693
      - - -20.5
        - -35.50704155516198
    - - - 1.0
        - 0
      - - -2.4662157486919587
        - 4.27161097916099
      - - -21.5
        - -37.239092362730865
    - - - 1.0
        - 0
      - - 4.419708307684861
        - 7.6551593435444385
      - - -23.5
        - 40.703193977868615
    - - - 1.0
        - 0
      - - -4.103049418064358
        - -7.106690058053383
      - - -26.5
        - 45.89934640057525
    - - - 1.0
        - 0
      - - 1.8571262728520224
        - -3.2166370606507244
      - - -29.5
        - -51.09549882328188
    - - - 1.0
        - 0
      - - -1.7556087474372863
        - -3.0408035487737366
      - - -30.5
        - 52.827549630850754
    - - - 1.0
        - 0
      - - 2.0218236375894914
        - 3.501901264248724
      - - -33.5
        - 58.023702053557386
    - - - 1.0
        - 0
      - - 2.597665666859974
        - -4.499288916078765
      - - -35.5
        - -61.48780366869514
    - - - 1.0
        - 0
      - - 4.302045178950657
        - -7.451360826399281
      - - -36.5
        - -63.21985447626402
    - - - 1.0
        - 0
      - - 3.313240862094221
        - -5.738701510860499
      - - -39.5
        - -68.41600689897065
    - - - 1.0
        - 0
      - - 4.517365804211523
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 1.6867591379057794
        - 2.9215525269838882
      - - -44.5
        - 77.07626093681505
    - - - 1.0
        - 0
      - - 7.5961099999143125
        - -13.15684845973361
      - - -48.5
        - -84.00446416709055
    - - - 1.0
        - 0
      - - 1.7706781008666208
        - 3.0669044345505565
      - - -50.5
        - 87.4685657822283
    - - - 1.0
        - 0
      - - -15.691941635972176
        - 0
      - - 103.0
        - 0
    - - - 1.0
        - 0
      - - -1.057312408124615
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - -3.372195626281357
        - 5.84081415778086
      - - -54.5
        - -94.39676901250381
    - - - 1.0
        - 0
      - - 7.900908493015856
        - 0
      - - 113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 10631767
    index: 0
    label: 2-475-19.11-c1-0-0
    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/475/2/e/g/201/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 0.4510922290181146
    - 0.26172658879546284
    - 0.09142777097091276
    - -0.06321833242566642
    - -0.202982144539395
    - -0.3258643723763249
    - -0.4274611861080645
    - -0.5016983291705821
    - -0.5418180704747896
    - -0.541531086209744
    - -0.4962604017517208
    - -0.40439788693102324
    - -0.26847274919058545
    - -0.09610742541837435
    - 0.09938060334570181
    - 0.29887460678699335
    - 0.4779776173929226
    - 0.6082397135224458
    - 0.6591156055612943
    - 0.6005924263108553
    - 0.40633317542218533
    - 0.05708457929924304
    - -0.4559880651100491
    - -1.1284380211418872
    - -1.940568163021104
    - -2.856750872818624
    - -3.8263478743347035
    - -4.786400326234649
    - -5.666069848722044
    - -6.3925893762107435
    - -6.898253537778685
    - -7.127772257664
    - -7.045161421846557
    - -6.639281592483791
    - -5.927183404132602
    - -4.9545877314547795
    - -3.7931150575562333
    - -2.5342584605981533
    - -1.2805271728664318
    - -0.13461719492472934
    - 0.8121716914336141
    - 1.490819973966454
    - 1.863269673749818
    - 1.9275609437663919
    - 1.7184597833828301
    - 1.3031747206580298
    - 0.7724420788641506
    - 0.22796862688628577
    - -0.23215139978606883
    - -0.52798946440253
    - -0.6100928309365529
    - -0.4675166865574218
    - -0.13006399361802354
    - 0.33596870045723504
    - 0.8382420793577671
    - 1.2736867012548472
    - 1.5464381122481516
    - 1.5855496115113676
    - 1.359463218469347
    - 0.8845456184501206
    - 0.2258120502176059
    - -0.5108313071147725
    - -1.194074573427267
    - -1.6882669080353243
    - -1.8767684879549027
    - -1.683668533793949
    - -1.0899596009203847
    - -0.1409718001998847
    - 1.0567907561817196
    - 2.3495019824706054
    - 3.558742269042972
    - 4.509594230448174
    - 5.0594345934729565
    - 5.122377250593522
    - 4.684858877436612
    - 3.8092616827794816
    - 2.624524579875609
    - 1.3050500641054867
    - 0.041433407999756144
    - -0.9918136021345558
    - -1.6656511826219593
    - -1.9175110178297132
    - -1.7598865642716242
    - -1.2748198289644308
    - -0.5953304355565048
    - 0.12255110972996255
    - 0.7315336891749454
    - 1.1221339915320394
    - 1.2430652040461976
    - 1.1086914795017546
    - 0.7919933598166708
    - 0.40460352695325014
    - 0.06834141968091903
    - -0.1153404768103355
    - -0.09096444022987057
    - 0.1364032286879913
    - 0.5013487841995555
    - 0.8934796701432519
    - 1.1848060212203366
    - 1.2629741761781221
    - 1.0624795596709233
    - 0.5860364672110322
    - -0.08981295506785268
    - -0.8273421364632358
    - -1.456789896869526
    - -1.8161676129065767
    - -1.7928833186950237
    - -1.3572436533894143
    - -0.5790768960591783
    - 0.3779389383768542
    - 1.284799224764473
    - 1.8937650815420903
    - 1.993649188003188
    - 1.4616989789590586
    - 0.2998961373504604
    - -1.3537675303355012
    - -3.2433722532747584
    - -5.040421116273164
    - -6.408046421086444
    - -7.0709116434108665
    - -6.875667925419855
    - -5.82821131442799
    - -4.098584506197945
    - -1.9912539286042688
    - 0.11383254640042295
    - 1.8372932326385802
    - 2.87720521227474
    - 3.0700488790879517
    - 2.422224250992303
    - 1.1051418524326713
    - -0.5849075598853171
    - -2.292882905726235
    - -3.6819729377330725
    - -4.5038811431341275
    - -4.646618540268426
    - -4.1495124332474616
    - -3.183083134361499
    - -1.9998859095393082
    - -0.8692772670749482
    - -0.012635142198747236
    - 0.4450490304707317
    - 0.49591323929161496
    - 0.2384462949974742
    - -0.16035919150876451
    - -0.5184664842454527
    - -0.6925657095540934
    - -0.6171896349442264
    - -0.31863137207414066
    - 0.09956804241526404
    - 0.4946026970049805
    - 0.7341024307241021
    - 0.7423315181697037
    - 0.5285626654888468
    - 0.18839406563941027
    - -0.12330067517984675
    - -0.24055433289719066
    - -0.04167257732237519
    - 0.505020941148148
    - 1.3198852270089312
    - 2.2234738616984075
    - 2.9799568557304768
    - 3.3620282856648442
    - 3.21984198908503
    - 2.5341346022696474
    - 1.436895543150753
    - 0.1911073331420725
    - -0.8678612598370813
    - -1.415666768408754
    - -1.2259142941582877
    - -0.2371051733113335
    - 1.4196352300132213
    - 3.441512034730616
    - 5.4203387941509815
    - 6.938376234026884
    - 7.669455009612251
    - 7.458984506140936
    - 6.36151040678165
    - 4.625518102553494
    - 2.629259799361289
    - 0.784644555424878
    - -0.5650565611051639
    - -1.226295673932103
    - -1.1937183871745978
    - -0.6366250563668577
    - 0.16130400149017737
    - 0.8906093245930558
    - 1.3067670825620836
    - 1.296642861605842
    - 0.9018817444557511
    - 0.293554164279501
    - -0.29281574610727007
    - -0.6406484457467525
    - -0.6273000502720606
    - -0.26639575800810417
    - 0.29659118637475235
    - 0.834867815059097
    - 1.1214327673954139
    - 1.0148519999940075
    - 0.5212364319476881
    - -0.18968364326300596
    - -0.8228957327906796
    - -1.0424777560625842
    - -0.5785633631942577
    - 0.675059315897513
    - 2.6037461824603056
    - 4.875741326336295
    - 7.010184948235564
    - 8.49368550422162
    - 8.914624586617563
    - 8.07779832233143
    - 6.066239801721097
    - 3.2311614509031665
    - 0.11096897427089861
    - -2.699567762857851
    - -4.6945906399819926
    - -5.577286008702284
    - -5.322526304949202
    - -4.1662543045866665
    - -2.5268551065706317
    - -0.882949730439979
    - 0.35628334898537123
    - 0.9513873215147115
    - 0.8768226199390273
    - 0.30022514971326936
    - -0.4922766691148723
    - -1.1979899398572103
    - -1.5933569983207947
    - -1.5939739173414662
    - -1.2626959321528919
    - -0.7674906213195986
    - -0.3072937557088217
    - -0.033966893114763225
    - 0.0015883615616299376
    - -0.13917289638313612
    - -0.31594748959858665
    - -0.3738953016963239
    - -0.21333221230064853
    - 0.16270002076514992
    - 0.6424952557884054
    - 1.0454952352418865
    - 1.1945563713708185
    - 0.9941731049290026
    - 0.48413128243380554
    - -0.15489488683645453
    - -0.6511306344036507
    - -0.7342024093472853
    - -0.2407528816067879
    - 0.8040787823469616
    - 2.1615996569629083
    - 3.4265142790018825
    - 4.137996810635582
    - 3.9243469718498014
    - 2.6366275867198965
    - 0.42650448109865974
    - -2.2618503857121524
    - -4.790446522842366
    - -6.492854550533448
    positive_zeros:
    - '0.32245129511521123450540693934827'
    - '1.68762232768748586571225411580292'
    - '2.64116635791619730581787046314903'
    - '4.89107335733928854722546536027040'
    - '5.93261357016730290286510435914934'
    - '6.53748252280722401333515163584175'
    - '7.53874647345897980470514627432982'
    - '8.390855671524220097383597847740151'
    - '9.754425043033534137794462705607866'
    - '10.60295444475932514819899414955718'
    prelabel: 2-475-19.11-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.9475353901818626
    root_angle: 0.5827412746231437
    root_number: -0.25702196934712657 + 0.9664055604521968*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.291370637312'
      prec: 47
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.32245129511521123450540693935'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '1.68762232768748586571225411580'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.64116635791619730581787046315'
      prec: 103
- - algebraic: true
    analytic_conductor: 3.79289409601082
    bad_primes:
    - 5
    - 19
    central_character: '19.11'
    conductor: 475
    conductor_radical: 95
    degree: 2
    id: 10631767
    index: 0
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/475/2/e/g/201/2
    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: 2-475-19.11-c1-0-0
    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: 2-475-19.11-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.9475353901818626
    root_angle: 0.29137063731157187
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '0.32245129511521123450540693935'
      prec: 103
- - Lhash: '408755577797167456643501287810'
    Lhash_array:
    - '408755577797167456643501287810'
    id: 10997828
    label: 2-475-19.11-c1-0-0
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/475/2/e/g/201/2
label_cols:
- label
- label
- label
labels:
- 2-475-19.11-c1-0-0
- 2-475-19.11-c1-0-0
- 2-475-19.11-c1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T16:16:02.999637'