data:
- - Lhash: '263319734715451709599824581248'
    a10:
    - 0
    - 0
    a2:
    - 0
    - 0
    a3:
    - 0
    - 0
    a4:
    - 0
    - 0
    a5:
    - -3.398979485566356
    - -1.9624017209617515
    a6:
    - 0
    - 0
    a7:
    - -6.398979485566356
    - -11.083357585591886
    a8:
    - 0
    - 0
    a9:
    - 0
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 47.084589681459306
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.0'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 2
    - 3
    central_character: '1728.449'
    coefficient_field: CDF
    conductor: 1728
    conductor_radical: 6
    conjugate: '792244200491509730800614257654'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 3.398979485566356
        - 1.9624017209617515
      - - 12.5
        - 21.650635094610966
    - - - 1.0
        - 0
      - - 6.398979485566356
        - 11.083357585591886
      - - -24.5
        - 42.4352447854375
    - - - 1.0
        - 0
      - - 14.297958971132712
        - -8.254930460845696
      - - 60.5
        - -104.78907385791707
    - - - 1.0
        - 0
      - - 1.3989794855663562
        - -2.4231035477474996
      - - -84.5
        - -146.35829323957014
    - - - 1.0
        - 0
      - - 0
        - -2.542697961566258
      - - -289.0
        - 0
    - - - 1.0
        - 0
      - - 21.595917942265423
        - 0
      - - 361.0
        - 0
    - - - 1.0
        - 0
      - - 2.601020514433644
        - 1.5016998941760031
      - - 264.5
        - 458.12743860196804
    - - - 1.0
        - 0
      - - 13.196938456699069
        - -7.619255970454132
      - - 420.5
        - -728.3273645827129
    - - - 1.0
        - 0
      - - -13.601020514433644
        - 23.55765856578566
      - - -480.5
        - -832.2504130368455
    - - - 1.0
        - 0
      - - -10.404082057734575
        - 0
      - - 1369.0
        - 0
    - - - 1.0
        - 0
      - - -34.5
        - -19.91858428704209
      - - 840.5
        - 1455.7887037616413
    - - - 1.0
        - 0
      - - -17.095917942265423
        - -29.610998478032087
      - - -924.5
        - 1601.280971597427
    - - - 1.0
        - 0
      - - 58.196938456699066
        - -33.600018083987294
      - - 1104.5
        - -1913.050116959825
    - - - 1.0
        - 0
      - - 0
        - 100.68045983814312
      - - -2809.0
        - 0
    - - - 1.0
        - 0
      - - -5.297958971132712
        - -3.058778038139064
      - - 1740.5
        - 3014.634430573631
    - - - 1.0
        - 0
      - - -20.398979485566358
        - -35.33206889155617
      - - -1860.5
        - 3222.4805274818964
    - - - 1.0
        - 0
      - - -54.48979485566356
        - 94.37909318401452
      - - -2244.5
        - -3887.5880375883453
    - - - 1.0
        - 0
      - - 0
        - 52.882927880637816
      - - -5041.0
        - 0
    - - - 1.0
        - 0
      - - -68.78775382679628
        - 0
      - - 5329.0
        - 0
    - - - 1.0
        - 0
      - - -12.792856398964494
        - -22.15787725693913
      - - -3120.5
        - 5404.864545018681
    - - - 1.0
        - 0
      - - -52.085712797928984
        - 30.071700304817835
      - - 3444.5
        - -5966.049006670998
    - - - 1.0
        - 0
      - - 0
        - -7.628093884698774
      - - -7921.0
        - 0
    - - - 1.0
        - 0
      - - -50.702041028867285
        - -87.81851110943994
      - - -4704.5
        - 8148.433024207783
    - - - 1.0
        - 0
      - - 1.1969384566990686
        - -0.6910527401786225
      - - 5100.5
        - -8834.325144005059
    - - - 1.0
        - 0
      - - -0.7928563989644933
        - 1.3732675661126028
      - - -5304.5
        - -9187.66350874911
    - - - 1.0
        - 0
      - - 0
        - 103.22315779970937
      - - -11449.0
        - 0
    - - - 1.0
        - 0
      - - 14.404082057734575
        - 0
      - - 11881.0
        - 0
    - - - 1.0
        - 0
      - - -92.07550765359255
        - -53.15981912957311
      - - 6384.5
        - 11058.278380923497
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23637080
    index: 6
    label: 2-12e3-9.5-c2-0-6
    leading_term: '0.481706374450616389397877453734783248555316820320337106'
    load_key: CMFs-workshop
    motivic_weight: 2
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 2
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/1728/3/q/e/449/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.05078125'
      prec: 34
    plot_values:
    - 0.48170637445061637
    - 0.39139229531974734
    - 0.2828192658030697
    - 0.15666911604518086
    - 0.013738467302769088
    - -0.1450528097902228
    - -0.3186516800357998
    - -0.5058613724530174
    - -0.7053310249424941
    - -0.9155464515598118
    - -1.1348229378256278
    - -1.3613009337587645
    - -1.5929454469746462
    - -1.8275498428572492
    - -2.0627446394950493
    - -2.296011745871777
    - -2.5247044367167093
    - -2.7460731902375524
    - -2.9572973392577264
    - -3.155522305475325
    - -3.337902004002081
    - -3.5016458244121647
    - -3.644069418744856
    - -3.7626483599654064
    - -3.8550735802148015
    - -3.9193073608917492
    - -3.953638530470582
    - -3.9567354352731647
    - -3.9276951874032777
    - -3.8660876667021857
    - -3.7719927634693886
    - -3.6460293988001746
    - -3.489374951941658
    - -3.3037738603425657
    - -3.0915343382553053
    - -2.8555123827993665
    - -2.599082499938474
    - -2.3260948830855988
    - -2.0408191088288143
    - -1.747874770958314
    - -1.4521498476226993
    - -1.158707977882901
    - -0.8726862029480512
    - -0.5991850929256349
    - -0.3431535203974256
    - -0.10927064569787659
    - 0.098172066317079
    - 0.2753857832223115
    - 0.41919305619626873
    - 0.5271272005862649
    - 0.597519162514232
    - 0.6295688618153622
    - 0.6233982303860031
    - 0.580083489225364
    - 0.5016646244586382
    - 0.39113052673172355
    - 0.2523788407456079
    - 0.09015022043334803
    - -0.09006261449779507
    - -0.28212989080886725
    - -0.47942198479264697
    - -0.6749661978964603
    - -0.8616197772767612
    - -1.0322551990004905
    - -1.1799531553717386
    - -1.298198212914504
    - -1.3810717550966443
    - -1.4234366126798468
    - -1.4211077301061386
    - -1.3710033300600948
    - -1.2712713270916016
    - -1.1213862065497902
    - -0.9222122230464428
    - -0.6760295733505922
    - -0.3865211461976734
    - -0.05871852436388902
    - 0.30109291455298426
    - 0.6855087148461467
    - 1.086177525560854
    - 1.4940071396799346
    - 1.8993995716810643
    - 2.2925092397744646
    - 2.6635173371835332
    - 3.0029146679838843
    - 3.301784622999588
    - 3.552077610776349
    - 3.7468681620307365
    - 3.880586109924305
    - 3.9492137211065876
    - 3.9504414123654388
    - 3.883775723654051
    - 3.7505945088803028
    - 3.5541458198877445
    - 3.299488655911047
    - 2.9933755813933134
    - 2.6440791231849334
    - 2.2611657820268514
    - 1.8552233674302923
    - 1.437549122674476
    - 1.0198076815505508
    - 0.613669227826951
    - 0.23043925502689325
    - -0.11930800113022627
    - -0.4260801012436698
    - -0.6817886887267189
    - -0.8800318650769404
    - -1.0163259868618157
    - -1.0882776203067877
    - -1.095688169846004
    - -1.0405858064942701
    - -0.9271816977607132
    - -0.7617501078866122
    - -0.5524346099996053
    - -0.30898533730906286
    - -0.042434801263895
    - 0.23527777777555584
    - 0.5117215430673601
    - 0.7744146223903166
    - 1.0112751193030192
    - 1.2110664865075151
    - 1.3638210446903618
    - 1.461225753332675
    - 1.4969552829763002
    - 1.466938967205692
    - 1.3695502901608
    - 1.2057101323151056
    - 0.9788979730580321
    - 0.6950685340389325
    - 0.3624748272943395
    - -0.00859787990698587
    - -0.406179189935248
    - -0.8170305169455684
    - -1.227117631261452
    - -1.6221221098125769
    - -1.987973088266739
    - -2.3113794681853985
    - -2.580342225937551
    - -2.7846267423495994
    - -2.9161761367985486
    - -2.96944842918766
    - -2.941662918901219
    - -2.83294438156268
    - -2.6463574336903375
    - -2.387827568323488
    - -2.0659497667825035
    - -1.6916900731423659
    - -1.2779899001863702
    - -0.8392869382724533
    - -0.3909701870301829
    - 0.05121033749631887
    - 0.4717563921423154
    - 0.8560325605628406
    - 1.1908508903521822
    - 1.46500498136036
    - 1.669730946895219
    - 1.799075190678226
    - 1.8501523528877608
    - 1.823280960532452
    - 1.7219891169669845
    - 1.5528877982194647
    - 1.3254147818204358
    - 1.0514576932402553
    - 0.7448698854949015
    - 0.4208976416736189
    - 0.09554129369115255
    - -0.21512390837176498
    - -0.49563912373449975
    - -0.7318363180747849
    - -0.9114667475328576
    - -1.0247559342782009
    - -1.0648601406038332
    - -1.028203083355735
    - -0.9146763643580178
    - -0.7276926446023395
    - -0.47408673895055886
    - -0.1638663004959234
    - 0.1901796757447141
    - 0.5729999570504177
    - 0.9679073702308774
    - 1.3572868045679876
    - 1.7233553721512411
    - 2.0489423307271304
    - 2.318254896276118
    - 2.5175960604283634
    - 2.6360020156560786
    - 2.665769746773614
    - 2.602849671826007
    - 2.4470837461517934
    - 2.2022759591220553
    - 1.876089382770336
    - 1.479771565350386
    - 1.027717765125922
    - 0.5368889436175682
    - 0.02610824076829123
    - -0.48473448503334243
    - -0.9755358379011047
    - -1.4268524070177973
    - -1.8207557272712458
    - -2.141629994617053
    - -2.376875842762244
    - -2.517487191548768
    - -2.5584734585580704
    - -2.4991060712482973
    - -2.3429759465306064
    - -2.0978570806159182
    - -1.7753802345860632
    - -1.3905295055166893
    - -0.960982927318812
    - -0.5063257504274283
    - -0.04717133732676574
    - 0.3957706362732937
    - 0.8026360189051327
    - 1.1553143971547264
    - 1.438281058997646
    - 1.63931314462929
    - 1.7500554069841499
    - 1.7664077039364339
    - 1.6887144693972178
    - 1.5217455968167013
    - 1.2744679933637533
    - 0.9596170646179044
    - 0.593087088765227
    - 0.19316836220143374
    - -0.22033330017108013
    - -0.6270530412054606
    - -1.0070535991875234
    - -1.3417943189886188
    - -1.6150350821166488
    - -1.8136303625022154
    - -1.928173512158805
    - -1.9534583099777871
    - -1.8887334596490917
    - -1.7377356997868276
    - -1.508498018431486
    - -1.2129406217207526
    - -0.8662632431028968
    - -0.4861675462511283
    - -0.09194725133194388
    - 0.29650926508789127
    - 0.6597541676136055
    - 0.9798008773718908
    - 1.2410780712861837
    - 1.4312674151111702
    - 1.5419807103610792
    - 1.5692396905420445
    - 1.5137312389058724
    - 1.3808218680396158
    - 1.1803273647196306
    - 0.9260459648871447
    - 0.6350756554476967
    - 0.3269475742227508
    - 0.022617401521516332
    - -0.25663542531786493
    - -0.49034532920807483
    - -0.6599769307392276
    - -0.7499621631148848
    - -0.7486033670399074
    positive_zeros:
    - '0.20772264429018792308871420731857'
    - '2.31103504013228149963099954614298'
    - '2.92046249838482300599648958405199'
    - '3.81717122987854392817187423574558'
    - '5.16171857271938035107179669192297'
    - '5.79689869101160703263901050923023'
    - '6.54965055892769027593061059423215'
    - '7.56042990914203305332323579852162'
    - '8.343371887337811970464914160458304'
    - '8.910880372004163638036437171633423'
    prelabel: 2-12e3-9.5-c2-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.861821163616792
    root_angle: -0.22222222222222227
    root_number: 0.76604444311897803520239265055541667393583245708039524585 - 0.6427876096865393263226434099072634329075598842056817904*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.1111111111111111'
      prec: 64
    spectral_label: c2-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.20772264429018792308871420732'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.31103504013228149963099954614'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.92046249838482300599648958405'
      prec: 103
- - algebraic: true
    analytic_conductor: 47.084589681459306
    bad_primes:
    - 2
    - 3
    central_character: '9.5'
    conductor: 1728
    conductor_radical: 6
    degree: 2
    id: 23637080
    index: 6
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1728/3/q/e/449/1
    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: 2-12e3-9.5-c2-0-6
    motivic_weight: 2
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 2
    order_of_vanishing: 0
    prelabel: 2-12e3-9.5-c2-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.861821163616792
    root_angle: -0.11111111111111113
    self_dual: false
    spectral_label: c2-0
    z1:
      __RealLiteral__: 0
      data: '0.20772264429018792308871420732'
      prec: 103
- - Lhash: '263319734715451709599824581248'
    Lhash_array:
    - '263319734715451709599824581248'
    id: 24004145
    label: 2-12e3-9.5-c2-0-6
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1728/3/q/e/449/1
label_cols:
- label
- label
- label
labels:
- 2-12e3-9.5-c2-0-6
- 2-12e3-9.5-c2-0-6
- 2-12e3-9.5-c2-0-6
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T08:39:46.827407'