data:
- - Lhash: '2298421850495695692353508658053'
    a10:
    - 0.0
    - 0.0
    a2:
    - 0.0
    - 0.0
    a3:
    - -0.9888308262251285
    - -0.14904226617617444
    a4:
    - 0.0
    - 0.0
    a5:
    - 0.0
    - 0.0
    a6:
    - 0.0
    - 0.0
    a7:
    - -0.7330518718298263
    - -0.6801727377709194
    a8:
    - 0.0
    - 0.0
    a9:
    - 0.9555728057861407
    - 0.2947551744109042
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.2934502274282054
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 3
      - - - 1.0
          - 0
        - - 0.9888308262251285
          - 0.14904226617617444
    - - 7
      - - - 1.0
          - 0
        - - 0.7330518718298263
          - 0.6801727377709194
    bad_primes:
    - 2
    - 3
    - 7
    central_character: '588.401'
    coefficient_field: CDF
    conductor: 588
    conductor_radical: 42
    conjugate: '1077993617813974955654021307368'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0.9888308262251285
        - 0.14904226617617444
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.7330518718298263
        - -0.6801727377709194
    - - - 1.0
        - 0
      - - 0.7330518718298263
        - 0.6801727377709194
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.8262387743159949
        - 0.5633200580636221
    - - - 1.0
        - 0
      - - -0.4400711179528193
        - 1.9280775458253845
      - - -0.9009688679024191
        - -0.4338837391175581
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.36534102436639504
        - -0.9308737486442042
    - - - 1.0
        - 0
      - - -0.7330518718298263
        - 1.2696830865927278
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.36534102436639504
        - 0.9308737486442042
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.6234898018587335
        - 0.7818314824680298
    - - - 1.0
        - 0
      - - 0.07473009358642425
        - 0.12943631894606392
      - - -0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - -0.12348980185873352
        - 1.6478568862524685
      - - -0.9888308262251285
        - -0.14904226617617444
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.2225209339563144
        - 0.9749279121818236
    - - - 1.0
        - 0
      - - -1.19157979868239
        - -1.4941938067078262
      - - -0.2225209339563144
        - 0.9749279121818236
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.07473009358642425
        - -0.9972037971811801
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.9888308262251285
        - -0.14904226617617444
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.7330518718298263
        - 0.6801727377709194
    - - - 1.0
        - 0
      - - 0.134658975633605
        - -1.7968991524286428
      - - -0.9888308262251285
        - -0.14904226617617444
    - - - 1.0
        - 0
      - - 0.36534102436639504
        - 0.6327892162918554
      - - -0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.6234898018587335
        - -0.7818314824680298
    - - - 1.0
        - 0
      - - 1.211351760181443
        - -1.123970178357998
      - - 0.07473009358642425
        - -0.9972037971811801
    - - - 1.0
        - 0
      - - 0.07473009358642425
        - -0.12943631894606392
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.9009688679024191
        - -0.4338837391175581
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.8262387743159949
        - -0.5633200580636221
    - - - 1.0
        - 0
      - - 0.4450418679126288
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.9555728057861407
        - -0.2947551744109042
    - - - 1.0
        - 0
      - - -0.6982198954451578
        - -1.77903527964921
      - - -0.7330518718298263
        - 0.6801727377709194
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -0.8262387743159949
        - -0.5633200580636221
    - - - 1.0
        - 0
      - - -0.6982198954451578
        - 0.21537231471315033
      - - 0.8262387743159949
        - -0.5633200580636221
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.9009688679024191
        - -0.4338837391175581
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 19440111
    index: 0
    label: 2-588-147.107-c0-0-0
    leading_term: '0.60399697680846309755774607473039'
    load_key: CMFs-workshop
    motivic_weight: 0
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 0
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/588/1/z/a/401/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.0703125'
      prec: 30
    plot_values:
    - 0.6039969768084631
    - 0.6420048593249796
    - 0.6903830730043053
    - 0.7493626249809185
    - 0.8181878165372138
    - 0.8953611178236396
    - 0.9788849032281336
    - 1.0664388251612695
    - 1.1554860730933358
    - 1.2433285954264
    - 1.327135424752058
    - 1.403962676102274
    - 1.470776874270827
    - 1.524487931927762
    - 1.5619946110773764
    - 1.580243146578866
    - 1.576298363901075
    - 1.5474257205402309
    - 1.4911820305972336
    - 1.4055120868686544
    - 1.2888479281892162
    - 1.1402071004360335
    - 0.9592859354795941
    - 0.7465436412376631
    - 0.5032728799306393
    - 0.23165253335292027
    - -0.06522146583558446
    - -0.38333100250628105
    - -0.717759571649071
    - -1.0627474889643893
    - -1.4117800979911104
    - -1.7577094666365378
    - -2.092908833997084
    - -2.4094577240971007
    - -2.699354230255405
    - -2.9547495445628775
    - -3.1681984210799734
    - -3.3329179838656855
    - -3.4430461897684657
    - -3.4938903989958723
    - -3.482155958535125
    - -3.406144522473389
    - -3.26591206677544
    - -3.063377237877779
    - -2.802371821225718
    - -2.488626724436867
    - -2.1296889150048077
    - -1.734767186079342
    - -1.3145073742316729
    - -0.8807006261949316
    - -0.44593139313785324
    - -0.02317489015696054
    - 0.37464334754399653
    - 0.7351106009150656
    - 1.0467954682405298
    - 1.2997028900575904
    - 1.4856960702066973
    - 1.5988657066394676
    - 1.6358278836980806
    - 1.5959338439660826
    - 1.4813776409507393
    - 1.2971913158239314
    - 1.051121636435647
    - 0.7533874322314973
    - 0.4163219587525754
    - 0.0539102972926188
    - -0.318762721932744
    - -0.6861334691185389
    - -1.032824266266245
    - -1.344323324482449
    - -1.6076488718784656
    - -1.8119654691613114
    - -1.9491210236707124
    - -2.0140751295129258
    - -2.005193085806843
    - -1.9243851968741175
    - -1.7770775707591033
    - -1.5720083544910775
    - -1.3208518472000985
    - -1.0376818211461836
    - -0.7382942124270262
    - -0.4394176456749682
    - -0.15784755399551142
    - 0.09045450818135396
    - 0.2912507922809218
    - 0.43285918526696354
    - 0.5068802659939932
    - 0.5087761206890161
    - 0.43826318564152716
    - 0.2994894868104501
    - 0.10097680961532729
    - -0.1446798817090107
    - -0.42135060593457363
    - -0.7101276791375857
    - -0.9902708021195501
    - -1.2402966449947583
    - -1.4391595411451517
    - -1.5674622484114433
    - -1.6086311103568682
    - -1.5499887856398953
    - -1.3836602648564276
    - -1.1072542165174808
    - -0.7242716352893074
    - -0.24420692409670017
    - 0.31767766585775387
    - 0.9409056678116263
    - 1.6006509710038535
    - 2.268877752266237
    - 2.915702951205819
    - 3.510913515696542
    - 4.025558961763102
    - 4.4335322319558985
    - 4.713049042661539
    - 4.847938271787283
    - 4.828663549222543
    - 4.653008854235038
    - 4.326378059783257
    - 3.8616791561003807
    - 3.2787872331299046
    - 2.6036048929240283
    - 1.8667631511376424
    - 1.102028570333238
    - 0.34450188492398093
    - -0.37129160055174476
    - -1.0133101363282695
    - -1.5537894501751828
    - -1.970813550596949
    - -2.2495641454786863
    - -2.3831674883702534
    - -2.373080119609017
    - -2.2289819641862625
    - -1.968175016665598
    - -1.614516579667697
    - -1.1969457886326007
    - -0.7476890038019074
    - -0.3002517505884305
    - 0.11267934437692442
    - 0.4612929690037773
    - 0.7205363675942302
    - 0.8717025875451737
    - 0.9036158745985119
    - 0.8133337050517498
    - 0.6063142613560762
    - 0.29603259191483494
    - -0.09693495128452642
    - -0.5463025337246563
    - -1.0218545152932725
    - -1.4914968981592829
    - -1.9234440760478397
    - -2.288392930145249
    - -2.561534766786094
    - -2.724264353968995
    - -2.765464055412255
    - -2.6822687392054814
    - -2.480252047714548
    - -2.17301448615107
    - -1.781195926155286
    - -1.330976589657346
    - -0.8521683958382729
    - -0.3760299086952957
    - 0.06703941837959759
    - 0.4497583065568528
    - 0.750008834673522
    - 0.952512971607112
    - 1.0500097512037694
    - 1.0438366485572175
    - 0.943860948695169
    - 0.7677542055408004
    - 0.539651913014767
    - 0.2882876618351895
    - 0.04473277222375741
    - -0.16009459526353056
    - -0.2979652634789684
    - -0.3457260041335221
    - -0.28735003636112183
    - -0.11548398412714597
    - 0.16764201968925266
    - 0.5500295612287952
    - 1.0104881413882623
    - 1.5199508883723862
    - 2.0434512118472874
    - 2.5426290034205
    - 2.978590622360078
    - 3.3149146289508646
    - 3.520577865483287
    - 3.5725758080620644
    - 3.458027669079776
    - 3.175589762946277
    - 2.7360481104172547
    - 2.162019931783736
    - 1.4867593884780075
    - 0.752130832053507
    - 0.005877753312267497
    - -0.7016274836043721
    - -1.3209237863949936
    - -1.807034163110875
    - -2.1228051508039485
    - -2.2417580251443034
    - -2.150228028809754
    - -1.848616795351864
    - -1.3516466087370855
    - -0.687578547164753
    - 0.10356556134527653
    - 0.9726610555508177
    - 1.864833003838379
    - 2.723262297732208
    - 3.493165933870159
    - 4.125654930240668
    - 4.581178885475632
    - 4.832294517442068
    - 4.865544785745272
    - 4.682301878998968
    - 4.298506433871694
    - 3.743320755972163
    - 3.056798812953537
    - 2.28675355289506
    - 1.4850663082869247
    - 0.7037283056954968
    - -0.00907331260270356
    - -0.6125151636262183
    - -1.0760609368230107
    - -1.381517193136875
    - -1.524060690780787
    - -1.5121602127806224
    - -1.366406771628425
    - -1.1173564686067716
    - -0.8025726480683613
    - -0.4631213228827347
    - -0.13982032217848875
    - 0.13043594000305556
    - 0.31795987040180507
    - 0.40287874987039346
    - 0.3768411116198119
    - 0.24367225856960376
    - 0.018920428727924633
    - -0.2716682735142298
    - -0.5946138170951412
    - -0.9118890200849511
    - -1.1845474570893118
    - -1.3764691144354106
    - -1.4578867178222175
    - -1.408371572520633
    - -1.219002330161002
    - -0.8935098445490971
    - -0.4482804368802181
    - 0.08879912639141078
    - 0.680567604213389
    - 1.2837009820262046
    - 1.85244180101055
    - 2.342617800531092
    - 2.7155898242344096
    - 2.9417690633556473
    - 3.003376290178746
    - 2.8961784739605347
    - 2.630026021829647
    - 2.228119438081465
    - 1.7250482884510174
    positive_zeros:
    - '1.81313514156178756525041020053400'
    - '3.58989539608701462091752793780383'
    - '4.58053483721138891425619758812400'
    - '5.80893858356009987357686940213396'
    - '6.35843250444775185597883629755326'
    - '7.27387488018695372656256939125661'
    - '8.611254634631003346435018234610535'
    - '9.542405071276280526906127657122652'
    - '10.10873822640107706742314434413305'
    - '11.23882470857432918760872504501586'
    prelabel: 2-588-147.107-c0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.5417104645732861
    root_angle: 0.3945578231292517
    root_number: 0.32523134988754714627901667587550 + 0.94563447962218672837451281764749*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.19727891156462585'
      prec: 64
    spectral_label: c0-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.81313514156178756525041020053'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '3.58989539608701462091752793780'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '4.58053483721138891425619758812'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.2934502274282054
    bad_primes:
    - 2
    - 3
    - 7
    central_character: '147.107'
    conductor: 588
    conductor_radical: 42
    degree: 2
    id: 19440111
    index: 0
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/588/1/z/a/401/1
    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: 2-588-147.107-c0-0-0
    motivic_weight: 0
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 0
    order_of_vanishing: 0
    prelabel: 2-588-147.107-c0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.5417104645732861
    root_angle: 0.19727891156462585
    self_dual: false
    spectral_label: c0-0
    z1:
      __RealLiteral__: 0
      data: '1.81313514156178756525041020053'
      prec: 103
- - Lhash: '2298421850495695692353508658053'
    Lhash_array:
    - '2298421850495695692353508658053'
    id: 19807188
    label: 2-588-147.107-c0-0-0
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/588/1/z/a/401/1
label_cols:
- label
- label
- label
labels:
- 2-588-147.107-c0-0-0
- 2-588-147.107-c0-0-0
- 2-588-147.107-c0-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T16:45:47.742647'