data:
- - Lhash: '10404589834488903709036215901'
    a10:
    - 4.688531711816379
    - -0.9318670183179527
    a2:
    - -1.2909581498933793
    - 0.5774314290232764
    a3:
    - -0.2225209339563144
    - 0.9749279121818236
    a4:
    - 1.3331458895522739
    - -1.490879618604358
    a5:
    - -3.295393764224954
    - -0.752152122230338
    a6:
    - -0.27568880431303916
    - -1.3870817146716508
    a7:
    - 2.539668989202787
    - -0.7416747435916189
    a8:
    - -0.8601548024419753
    - 2.694463530247906
    a9:
    - -0.9009688679024191
    - -0.4338837391175581
    accuracy: 100
    algebraic: true
    analytic_conductor: 4.6952036388512886
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 1.2909581498933793
          - -0.5774314290232764
    - - 3
      - - - 1.0
          - 0
        - - 0.2225209339563144
          - -0.9749279121818236
    - - 7
      - - - 1.0
          - 0
        - - -2.539668989202787
          - 0.7416747435916189
    bad_primes:
    - 2
    - 3
    - 7
    central_character: '588.223'
    coefficient_field: CDF
    conductor: 588
    conductor_radical: 42
    conjugate: '2372934759186871628654921042101'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 1.2909581498933793
        - -0.5774314290232764
    - - - 1.0
        - 0
      - - 0.2225209339563144
        - -0.9749279121818236
    - - - 1.0
        - 0
      - - 3.295393764224954
        - 0.752152122230338
      - - 4.504844339512096
        - 2.1694186955877908
    - - - 1.0
        - 0
      - - -2.539668989202787
        - 0.7416747435916189
    - - - 1.0
        - 0
      - - -0.23888510580770805
        - -0.4960500335321523
      - - -6.858387820446069
        - 8.600146307148329
    - - - 1.0
        - 0
      - - -1.8939268959402344
        - -3.9327797229637262
      - - -8.105367424163536
        - 10.163809272084388
    - - - 1.0
        - 0
      - - 0.9128961788462281
        - -0.7280104094422987
      - - 3.782855877257345
        - -16.573774507091002
    - - - 1.0
        - 0
      - - 5.824281371051619
        - 0
      - - 19.0
        - 0
    - - - 1.0
        - 0
      - - 3.598772628491597
        - 2.8699254038604303
      - - 5.1179814809952315
        - 22.42334198018194
    - - - 1.0
        - 0
      - - 2.9772040159534066
        - 3.7332957531356916
      - - -6.453107084733118
        - 28.272909453272884
    - - - 1.0
        - 0
      - - 10.017400290136864
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - 3.962779049179886
        - 4.9691677545922985
      - - -8.233274556383632
        - 36.072332750727476
    - - - 1.0
        - 0
      - - -5.886033292625521
        - -1.343448689084943
      - - 36.93972358399918
        - 17.789233303819884
    - - - 1.0
        - 0
      - - 4.654483840589951
        - -1.0623555632690593
      - - 38.741661319804024
        - -18.657000782055
    - - - 1.0
        - 0
      - - -3.916632982293658
        - 1.8861510354570623
      - - 29.304020687360477
        - -36.7460796759974
    - - - 1.0
        - 0
      - - 2.028424186710987
        - -2.5435634780913046
      - - -11.793609499684663
        - -51.67117934563665
    - - - 1.0
        - 0
      - - 1.1003757734779502
        - 4.821061265466953
      - - -53.15716320624273
        - 25.59914060793593
    - - - 1.0
        - 0
      - - 11.496667441617742
        - -9.168286345520897
      - - 13.573776971335178
        - -59.47060264309124
    - - - 1.0
        - 0
      - - 0
        - 6.978898347612638
      - - -67.0
        - 0
    - - - 1.0
        - 0
      - - 4.405995003699744
        - 3.513663766999375
      - - 15.798986310898323
        - 69.21988176490947
    - - - 1.0
        - 0
      - - 4.053561895487983
        - -8.417308008311114
      - - -45.51475553568755
        - -57.07369822016618
    - - - 1.0
        - 0
      - - 0
        - 4.403848808134891
      - - -79.0
        - 0
    - - - 1.0
        - 0
      - - 12.318891916583707
        - 5.932465678859945
      - - 51.749653554274886
        - 64.89201304484648
    - - - 1.0
        - 0
      - - 7.1346399730998815
        - -14.815232560982185
      - - -55.49059236542728
        - -69.58300193965465
    - - - 1.0
        - 0
      - - 0
        - 2.327505841690826
      - - -97.0
        - 0
    - - - 1.0
        - 0
      - - -5.342746390602389
        - -1.2194469989765222
      - - 90.99785565814433
        - 43.82225765087337
    - - - 1.0
        - 0
      - - -4.071729957902373
        - 17.839414549667808
      - - -92.79979339394917
        - -44.690025129108484
    - - - 1.0
        - 0
      - - 6.487141900932209
        - -13.470688959886674
      - - -66.71340879888449
        - -83.6559686240792
    - - - 1.0
        - 0
      - - 9.360089470245057
        - -4.507581518637626
      - - 67.96038840260195
        - -85.21963158901525
    - - - 1.0
        - 0
      - - -0.7518295473095219
        - -0.36206202765381984
      - - 70.45434761003689
        - 88.34695751888736
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 11573892
    index: 0
    label: 2-588-196.27-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/588/2/x/a/223/4
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 0.010816819578834574
    - -0.1508472511219908
    - -0.3068702992355308
    - -0.4572992768808955
    - -0.5996429836135209
    - -0.7285369254636572
    - -0.8359488774130756
    - -0.9118330868430213
    - -0.9451347883287495
    - -0.9250621012896103
    - -0.84254483679732
    - -0.691780575787559
    - -0.4717351298226848
    - -0.1874296861304324
    - 0.14917742796719757
    - 0.5189105545841831
    - 0.8958710777967445
    - 1.2488249470649257
    - 1.5435164493894447
    - 1.7458295468303648
    - 1.8255898855190524
    - 1.760670619322056
    - 1.5409519081911764
    - 1.171607606043026
    - 0.6751726221284021
    - 0.09189599125099898
    - -0.5219843486383351
    - -1.0982012039257751
    - -1.5625382698050936
    - -1.8426118111338279
    - -1.876632954190068
    - -1.622175806602509
    - -1.0638171464595512
    - -0.21848868743667973
    - 0.862480206784972
    - 2.0953464893961304
    - 3.3702266234776235
    - 4.561362411150895
    - 5.540487971796522
    - 6.19186101578585
    - 6.427116238655439
    - 6.1979150429064145
    - 5.504461795277542
    - 4.398353400151519
    - 2.978901177705905
    - 1.3829386916766826
    - -0.230909482346438
    - -1.7016194037279768
    - -2.886247267704849
    - -3.678574502540443
    - -4.023082138021879
    - -3.9219668493939506
    - -3.4338731975425163
    - -2.6642661031450636
    - -1.748715904340528
    - -0.8315913627581977
    - -0.04353099131356601
    - 0.5185904209343706
    - 0.8057660205551702
    - 0.8225044547667357
    - 0.6229030934967525
    - 0.29771754973822395
    - -0.045329570715550126
    - -0.30441640174887064
    - -0.4053473045287949
    - -0.31786976878975326
    - -0.06319582856865247
    - 0.2890716320220554
    - 0.6343803962943144
    - 0.8547199402647154
    - 0.8441040182783421
    - 0.5329725814873353
    - -0.0935958748983097
    - -0.9879607396614799
    - -2.0444709525229317
    - -3.116204358905412
    - -4.041055152479984
    - -4.6722325092943695
    - -4.907063140346849
    - -4.708052498768635
    - -4.111514108623988
    - -3.221508015876719
    - -2.189872693521251
    - -1.1861602011044357
    - -0.36362539296329316
    - 0.1714811116067087
    - 0.38052543917322906
    - 0.2982201364339503
    - 0.021863884202734305
    - -0.31381264213159715
    - -0.570692238369584
    - -0.6423996155925311
    - -0.4821007800204587
    - -0.11590462631930887
    - 0.36210612149504967
    - 0.8129588157758012
    - 1.089301903512252
    - 1.0770621048058904
    - 0.7321276160508848
    - 0.10241376517138974
    - -0.6714917268080104
    - -1.3792155534027115
    - -1.7835812991218343
    - -1.6751158144939853
    - -0.9260455331371977
    - 0.4690926727495249
    - 2.376937645583232
    - 4.538739541013954
    - 6.613020136682477
    - 8.239890978519904
    - 9.113964608493234
    - 9.05002692475778
    - 8.026416780626066
    - 6.1953933755157555
    - 3.85682118521234
    - 1.3997281541888775
    - -0.776202384407428
    - -2.342176621369451
    - -3.106693566208024
    - -3.051713938851901
    - -2.3302265714168766
    - -1.2257051200972422
    - -0.08286869478702594
    - 0.7740171888982079
    - 1.1160446987754615
    - 0.8601186175346147
    - 0.08321589828026711
    - -1.0024732930630278
    - -2.106860972202421
    - -2.9371111266193095
    - -3.2716856649149584
    - -3.0147989266822552
    - -2.2179284757291557
    - -1.0635583599006606
    - 0.1839355666842772
    - 1.2469379224150527
    - 1.904581218815501
    - 2.0458053432344996
    - 1.6920062010254229
    - 0.984131915364246
    - 0.13873515170242817
    - -0.6141766391349102
    - -1.0939195828531132
    - -1.2151439198262024
    - -1.0047172366839645
    - -0.5856050661000365
    - -0.1334041228035107
    - 0.1809640670337544
    - 0.2449926740177694
    - 0.03857417174739584
    - -0.36193164791679727
    - -0.8105988406976674
    - -1.141336637366386
    - -1.2242410727808095
    - -1.0109030276366933
    - -0.5537361291746976
    - 0.007823073034577726
    - 0.491100576355243
    - 0.731098866299554
    - 0.6395658014728697
    - 0.24278211292084123
    - -0.31575939564196454
    - -0.8113491428771661
    - -1.004302161608427
    - -0.717890072001929
    - 0.09562629876646694
    - 1.322546121320343
    - 2.7018542332655886
    - 3.885680984746415
    - 4.531805028269436
    - 4.40324116813303
    - 3.446081199723393
    - 1.8212308865911953
    - -0.12235081757066325
    - -1.928999425724773
    - -3.1523240184900967
    - -3.4748299797184767
    - -2.7976660848507118
    - -1.2740722310734585
    - 0.7248495182592306
    - 2.7045176749673376
    - 4.1765250810646615
    - 4.7879951446870335
    - 4.4143941692625726
    - 3.189361337400455
    - 1.462798518828743
    - -0.30100239144038127
    - -1.6560164726886117
    - -2.2996772697997825
    - -2.1544281294657703
    - -1.3822204537601546
    - -0.328322665601094
    - 0.5882426305126416
    - 1.0044615033443132
    - 0.7241801891068083
    - -0.22322763303824902
    - -1.5937364062560389
    - -3.005251768187021
    - -4.056046995230187
    - -4.448497718472011
    - -4.0801032538602895
    - -3.0740401991883175
    - -1.7402995086591708
    - -0.47996992132468397
    - 0.33725932200199704
    - 0.4842646295872403
    - -0.057858788243119935
    - -1.0992206787731817
    - -2.3045642401512816
    - -3.2995550253356445
    - -3.7856699506960716
    - -3.627411815468354
    - -2.8852161859381447
    - -1.785489629495157
    - -0.6397607585700906
    - 0.2588103007408828
    - 0.7266497352344443
    - 0.7388507704852576
    - 0.42123477626851363
    - -0.009689501231794665
    - -0.336070463080799
    - -0.4247006836459007
    - -0.2785223236796208
    - -0.034956208495291574
    - 0.08858387140633611
    - -0.11745127759899103
    - -0.7653735460139005
    - -1.8125051292972716
    - -3.0576741242944014
    - -4.195757349168103
    - -4.913381587613357
    - -4.9936122497090025
    - -4.393126588129366
    - -3.2638214969588164
    - -1.9094232533560034
    - -0.6901693168983574
    - 0.09281369445177384
    - 0.293881800203613
    - -0.03373947147211754
    - -0.6633618804214753
    - -1.2807984827040344
    - -1.600844404643736
    - -1.472525197377852
    - -0.9342930694559313
    - -0.19741360580439415
    - 0.43858949675994796
    - 0.7092353732794665
    - 0.5020391085301231
    - -0.07826326238873131
    - -0.7253748767271413
    - -1.0293423718588608
    - -0.627982482338379
    - 0.6386845203915477
    - 2.6268257298931297
    - 4.881852269579087
    - 6.738455632833737
    - 7.504219908062612
    positive_zeros:
    - '0.008207774155288253976257076659554'
    - '1.69658298827286277436172284727724'
    - '3.14379233730032804587238266133938'
    - '4.15231041304453540172701624230382'
    - '5.73171220215289271493050520049221'
    - '7.00799991647347868657660944179195'
    - '7.73241189771093820700103171105003'
    - '8.274105042525984579364357078869410'
    - '8.984535464225847611800656871258633'
    - '10.57597881776789706813284173810859'
    prelabel: 2-588-196.27-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.166841858293145
    root_angle: 0.7860477783429026
    root_number: -0.7824842822651545 + 0.6226703365409227*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.393023889171'
      prec: 47
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.008207774155288253976257076660'
      prec: 107
    z2:
      __RealLiteral__: 0
      data: '1.69658298827286277436172284728'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.14379233730032804587238266134'
      prec: 103
- - algebraic: true
    analytic_conductor: 4.6952036388512886
    bad_primes:
    - 2
    - 3
    - 7
    central_character: '196.27'
    conductor: 588
    conductor_radical: 42
    degree: 2
    id: 11573892
    index: 0
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/588/2/x/a/223/4
    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: 2-588-196.27-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: 2-588-196.27-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.166841858293145
    root_angle: 0.3930238891714513
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '0.008207774155288253976257076660'
      prec: 107
- - Lhash: '10404589834488903709036215901'
    Lhash_array:
    - '10404589834488903709036215901'
    id: 11939947
    label: 2-588-196.27-c1-0-0
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/588/2/x/a/223/4
label_cols:
- label
- label
- label
labels:
- 2-588-196.27-c1-0-0
- 2-588-196.27-c1-0-0
- 2-588-196.27-c1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T11:33:32.717534'