data:
- - Lhash: '2292288602868283761697624691883'
    a10:
    - 1.3246817089013687
    - 2.2944160236743363
    a2:
    - 1.2091277786054495
    - 1.0145786730740365
    a3:
    - 0.0
    - 0.0
    a4:
    - 0.08532374580481544
    - 0.48389500836453264
    a5:
    - 1.5772811732064957
    - 0.5740833981156388
    a6:
    - 0.0
    - 0.0
    a7:
    - 0.48261723577308857
    - -2.737058355074071
    a8:
    - 1.1906219716593345
    - -2.062217747521799
    a9:
    - 0.0
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 5.821094307351343
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 3
    central_character: '729.406'
    coefficient_field: CDF
    conductor: 729
    conductor_radical: 3
    conjugate: '1575293837946723688019366560896'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -1.2091277786054495
        - -1.0145786730740365
      - - 0.3472963553338607
        - 1.969615506024416
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -1.5772811732064957
        - -0.5740833981156388
      - - 3.83022221559489
        - 3.2139380484326967
    - - - 1.0
        - 0
      - - -0.48261723577308857
        - 2.737058355074071
      - - -6.5778483455013586
        - -2.3941410032796813
    - - - 1.0
        - 0
      - - 3.9008727929839875
        - -1.4198015843050371
      - - 8.426488874308758
        - -7.070663706551932
    - - - 1.0
        - 0
      - - -5.267356074153333
        - 4.419836539101468
      - - 2.2574263096700946
        - -12.802500789158705
    - - - 1.0
        - 0
      - - -0.48827562245501116
        - -0.8457181861893983
      - - -8.5
        - 14.722431864335457
    - - - 1.0
        - 0
      - - 1.342644497436104
        - -2.3255284860621135
      - - -9.5
        - -16.454482671904334
    - - - 1.0
        - 0
      - - 0.2801239863789319
        - 1.5886620711896753
      - - -21.612930278075893
        - 7.866463296490381
    - - - 1.0
        - 0
      - - -6.302919235431563
        - -5.288777205790808
      - - 5.03579715234098
        - 28.559424837354033
    - - - 1.0
        - 0
      - - -0.1813007216219864
        - -1.028207486418343
      - - -29.13047124436316
        - 10.602624443095731
    - - - 1.0
        - 0
      - - -0.6541723177697278
        - -1.1330596912822615
      - - -18.5
        - 32.04293994002423
    - - - 1.0
        - 0
      - - -3.7139136846800787
        - 3.116343603039307
      - - 7.119575284344144
        - -40.37711787350053
    - - - 1.0
        - 0
      - - 9.246790125132254
        - -3.365556368054793
      - - 32.93991105411605
        - -27.639867216521193
    - - - 1.0
        - 0
      - - 2.1702029228280884
        - -12.307832381116153
      - - -44.16555317693769
        - -16.07494673630643
    - - - 1.0
        - 0
      - - 7.3427960798548115
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - -8.505981023173947
        - -3.095923905668493
      - - 45.196622144019706
        - 37.92446897150582
    - - - 1.0
        - 0
      - - 0.2232667283216312
        - -1.2662085372559932
      - - -57.32124986794041
        - -20.863228742865793
    - - - 1.0
        - 0
      - - 3.5592718302284934
        - -2.9865836800044114
      - - 11.634427903684333
        - -65.98211945181794
    - - - 1.0
        - 0
      - - -2.811867242232503
        - -4.8702969276852786
      - - -35.5
        - 61.48780366869514
    - - - 1.0
        - 0
      - - -2.2807215449285905
        - 3.950325593733303
      - - -36.5
        - -63.21985447626402
    - - - 1.0
        - 0
      - - -3.5673165590112017
        - -2.993334008958903
      - - 13.718206035687498
        - 77.79981248796443
    - - - 1.0
        - 0
      - - 4.415780355323144
        - 3.705279667511529
      - - 14.412798746355218
        - 81.73904350001327
    - - - 1.0
        - 0
      - - -2.272209372379202
        - 3.9355820783949684
      - - -44.5
        - -77.07626093681505
    - - - 1.0
        - 0
      - - 8.058278783385045
        - -2.9329736165710227
      - - 74.30631098254086
        - -62.35039813959431
    - - - 1.0
        - 0
      - - -1.3554461120920092
        - 7.687116892978919
      - - -94.90895469937675
        - -34.544034475892545
    - - - 1.0
        - 0
      - - -2.0355125545338457
        - -0.7408659813254799
      - - 78.90257764125474
        - 66.20712379771355
    - - - 1.0
        - 0
      - - 12.584949885350023
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 12.213999771064275
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - -0.4236444814857131
        - -0.15419398117193883
      - - 86.56302207244451
        - 72.63499989457894
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 13392398
    index: 25
    label: 2-3e6-27.16-c1-0-25
    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/729/2/e/l/406/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 2.701102597284484
    - 2.7518417898058436
    - 2.79219802834955
    - 2.816469678338713
    - 2.8148944320360574
    - 2.775705832429954
    - 2.6873420802009473
    - 2.5404962054025737
    - 2.3298511543308855
    - 2.055419695699751
    - 1.72341687734455
    - 1.3465762497964349
    - 0.9438161527884031
    - 0.5391864493578613
    - 0.16008242475958465
    - -0.1652042322869152
    - -0.41042811623281455
    - -0.5545561827598449
    - -0.5848010381440736
    - -0.4991119585758119
    - -0.3077092894448023
    - -0.033302880311979075
    - 0.2902456288865317
    - 0.6208787085418576
    - 0.9127577842899088
    - 1.121739596870433
    - 1.2112959847917577
    - 1.1580943936776071
    - 0.956384795053499
    - 0.6203887033598278
    - 0.18407135979259578
    - -0.30200759377114833
    - -0.7766560688608504
    - -1.1762542655943786
    - -1.4441932778809041
    - -1.5401991852730175
    - -1.4480281653661777
    - -1.1800814962968074
    - -0.7778071490364806
    - -0.30731123518902154
    - 0.14966281461471967
    - 0.5084189185807179
    - 0.6959336168151486
    - 0.6651414622475842
    - 0.40636784474254584
    - -0.04642332045874028
    - -0.6162825253030785
    - -1.1915416493808353
    - -1.6411516151143541
    - -1.8352311281130904
    - -1.667824068272717
    - -1.0781249610836254
    - -0.06628418336369103
    - 1.2995544862127837
    - 2.88712090484465
    - 4.51519539732978
    - 5.978512370003895
    - 7.0789072588263116
    - 7.657776960885863
    - 7.624250741798562
    - 6.973772864906402
    - 5.793115953486457
    - 4.2500180765570095
    - 2.568326918734132
    - 0.9922679071498496
    - -0.25429528812082186
    - -1.0064461549189767
    - -1.1874763246379618
    - -0.8230246285099115
    - -0.03687770334686722
    - 0.9714258457192416
    - 1.963530254755177
    - 2.7071035598801414
    - 3.020150645600221
    - 2.806170390344143
    - 2.0730686257367195
    - 0.931783046610544
    - -0.42543412238526057
    - -1.7629864656702336
    - -2.8486373472772164
    - -3.4994698226474776
    - -3.6176156361690883
    - -3.208281145670172
    - -2.3762697396337975
    - -1.3017790566930536
    - -0.2007529703629175
    - 0.7215137850903648
    - 1.3132864163442
    - 1.5063335861704905
    - 1.3263408066006768
    - 0.8816998991314245
    - 0.3335923897462622
    - -0.14533004797743404
    - -0.4136648153690581
    - -0.39504675574352466
    - -0.09485481878658704
    - 0.40410343564707235
    - 0.9656232664738562
    - 1.4375477589237884
    - 1.6928471187627052
    - 1.66352371684776
    - 1.3582893014973492
    - 0.859131167257059
    - 0.2974584051624295
    - -0.18392375609147854
    - -0.47270311475084303
    - -0.5210905636745659
    - -0.3619989611986347
    - -0.10193354481308094
    - 0.10856280092798269
    - 0.11968542206915472
    - -0.16959523915551714
    - -0.7738891008373439
    - -1.6057861387578682
    - -2.488575443999112
    - -3.1960707297612054
    - -3.5106547131109442
    - -3.284895127871128
    - -2.489955529084256
    - -1.2363579908524078
    - 0.2408822814154567
    - 1.6316263024316064
    - 2.623924198047657
    - 2.983493717867397
    - 2.6186975709956335
    - 1.6128551492180458
    - 0.21327658062874244
    - -1.2227286877840398
    - -2.313183924259281
    - -2.7474888125552157
    - -2.3686417039639394
    - -1.2195617306702449
    - 0.46009725595936957
    - 2.2877589859138747
    - 3.8301598312604463
    - 4.711211704379087
    - 4.707810750319305
    - 3.808268620306187
    - 2.2172698473386365
    - 0.3050803849164025
    - -1.4864659954297201
    - -2.756900535873256
    - -3.2492161222374243
    - -2.9138926857953273
    - -1.917596817134276
    - -0.5941444861617726
    - 0.6489902264958537
    - 1.4431300852752305
    - 1.559048772644106
    - 0.9682781050854333
    - -0.15157681022640757
    - -1.468574140684896
    - -2.590379984201215
    - -3.173862362627972
    - -3.0195971665761268
    - -2.1251123976443687
    - -0.6826899414283617
    - 0.9765099026368754
    - 2.4749763462338747
    - 3.4908751663950492
    - 3.8403549793666882
    - 3.517442944035154
    - 2.6819331942569025
    - 1.601327602946211
    - 0.5663490049088602
    - -0.193254976491129
    - -0.5670850662106828
    - -0.5801895664249652
    - -0.3644617370182087
    - -0.09736834933025101
    - 0.06969318726111784
    - 0.06833217388339828
    - -0.06410166082106944
    - -0.2033985519836518
    - -0.191802988979887
    - 0.09362970229701677
    - 0.6826929145782966
    - 1.4858327054799696
    - 2.3114924155361414
    - 2.9233153297516066
    - 3.1191334314590633
    - 2.804947766621619
    - 2.037289119098904
    - 1.0167776729936269
    - 0.031587043860017
    - -0.6332514665328113
    - -0.792007130009991
    - -0.42746396022651045
    - 0.29212369871817057
    - 1.057565246372771
    - 1.5138485553848635
    - 1.3772843073786096
    - 0.5370401604636361
    - -0.8936087923668297
    - -2.5963157131579337
    - -4.1348843162645155
    - -5.086007721010805
    - -5.173274052902597
    - -4.361096603655357
    - -2.8762363419496113
    - -1.14671678570361
    - 0.3256058642815153
    - 1.1202786557292124
    - 1.03216270660931
    - 0.13993002760543335
    - -1.2153073814949589
    - -2.5373464098831384
    - -3.336242985310977
    - -3.2930532016928793
    - -2.374577660848729
    - -0.8592053722401574
    - 0.7375120750071061
    - 1.8169471252628842
    - 1.8844010892988434
    - 0.7106213686217117
    - -1.5836844442334783
    - -4.548311440521571
    - -7.52415538740966
    - -9.827529114538324
    - -10.94167739290002
    - -10.656904236564868
    - -9.117389909431592
    - -6.762713741933656
    - -4.18549127716243
    - -1.952446974184861
    - -0.44628089467806764
    - 0.2232007311616141
    - 0.21473377294665968
    - -0.134301122774173
    - -0.44767639601545367
    - -0.44943107080891137
    - -0.05455521173149391
    - 0.6173345727618272
    - 1.3055074621800509
    - 1.7215431272717403
    - 1.6685514078387165
    - 1.1215774829022553
    - 0.24024994104231132
    - -0.6894390671333563
    - -1.3609251685583235
    - -1.5598405959834192
    - -1.241230763782662
    - -0.5426588394738889
    - 0.27083547300434446
    - 0.9081333844300198
    - 1.1606086740368236
    - 0.9762938959652417
    - 0.4715778560272477
    - -0.12331317705719237
    - -0.5629545645732242
    - -0.6899719706075349
    - -0.5012573373344433
    - -0.1497373695151234
    - 0.12036550839461062
    - 0.08002812346928095
    - -0.3788489081889578
    - -1.1824641621954057
    positive_zeros:
    - '1.80829686228648276669424081988719'
    - '2.63851372297280956250664876446229'
    - '3.79803093107750623640888962078766'
    - '4.95717705187961298713356025618237'
    - '5.61388287960138199912892839789857'
    - '6.50681592971676960649775989423195'
    - '8.095519029831740829739320770717515'
    - '8.629906550504637773620123745772465'
    - '9.586663975902543337051108741323408'
    - '10.64951790727712446526183225067711'
    prelabel: 2-3e6-27.16-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.4126944081982997
    root_angle: -0.03703703703703704
    root_number: 0.993238357741943 - 0.11609291412523025*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.0185185185185'
      prec: 54
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.80829686228648276669424081989'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.63851372297280956250664876446'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.79803093107750623640888962079'
      prec: 103
- - algebraic: true
    analytic_conductor: 5.821094307351343
    bad_primes:
    - 3
    central_character: '27.16'
    conductor: 729
    conductor_radical: 3
    degree: 2
    id: 13392398
    index: 25
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/729/2/e/l/406/2
    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: 2-3e6-27.16-c1-0-25
    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: 2-3e6-27.16-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.4126944081982997
    root_angle: -0.01851851851851852
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '1.80829686228648276669424081989'
      prec: 103
- - Lhash: '2292288602868283761697624691883'
    Lhash_array:
    - '2292288602868283761697624691883'
    id: 13758452
    label: 2-3e6-27.16-c1-0-25
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/729/2/e/l/406/2
label_cols:
- label
- label
- label
labels:
- 2-3e6-27.16-c1-0-25
- 2-3e6-27.16-c1-0-25
- 2-3e6-27.16-c1-0-25
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-24T06:34:26.595817'