data:
- - Lhash: '1890902847341349922940523876174'
    a10:
    - 0
    - 0
    a2:
    - 0
    - 0
    a3:
    - -3.0
    - 0
    a4:
    - 8.0
    - 0
    a5:
    - 0
    - -5.196152422706632
    a6:
    - 0
    - 0
    a7:
    - 0
    - 10.392304845413264
    a8:
    - 0
    - 0
    a9:
    - 9.0
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 29.913968372910507
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 3.0
          - 0
    - - 13
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 3
    - 13
    central_character: '507.337'
    coefficient_field: CDF
    conductor: 507
    conductor_radical: 39
    conjugate: '576493055633070696032812534412'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -8.0
        - 0
    - - - 1.0
        - 0
      - - 3.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 5.196152422706632
      - - -125.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -10.392304845413264
      - - -343.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 51.96152422706632
      - - -1331.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 117.0
        - 0
      - - 4913.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 24.24871130596428
      - - -6859.0
        - 0
    - - - 1.0
        - 0
      - - -18.0
        - 0
      - - 12167.0
        - 0
    - - - 1.0
        - 0
      - - 99.0
        - 0
      - - 24389.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 193.98969044771425
      - - -29791.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 112.58330249197702
      - - -50653.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -36.373066958946424
      - - -68921.0
        - 0
    - - - 1.0
        - 0
      - - 82.0
        - 0
      - - 79507.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -72.74613391789285
      - - -103823.0
        - 0
    - - - 1.0
        - 0
      - - 261.0
        - 0
      - - 148877.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 789.8151682514081
      - - -205379.0
        - 0
    - - - 1.0
        - 0
      - - 719.0
        - 0
      - - 226981.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -703.2126278729642
      - - -300763.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 467.6537180435969
      - - -357911.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 684.1600689897066
      - - -389017.0
        - 0
    - - - 1.0
        - 0
      - - 440.0
        - 0
      - - 493039.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 1195.1150572225254
      - - -571787.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 1517.2765074303366
      - - -704969.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 1157.00993945601
      - - -912673.0
        - 0
    - - - 1.0
        - 0
      - - -1575.0
        - 0
      - - 1030301.0
        - 0
    - - - 1.0
        - 0
      - - -794.0
        - 0
      - - 1092727.0
        - 0
    - - - 1.0
        - 0
      - - -450.0
        - 0
      - - 1225043.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 595.8254778036938
      - - -1295029.0
        - 0
    - - - 1.0
        - 0
      - - 1701.0
        - 0
      - - 1442897.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23838138
    index: 56
    label: 2-507-13.12-c3-0-56
    leading_term: '1.450193101552394887766224807950544502996837588878133550'
    load_key: CMFs-workshop
    motivic_weight: 3
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 3
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/507/4/b/a/337/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.0625'
      prec: 20
    plot_values:
    - 1.4501931015523948
    - 1.6120906201747798
    - 1.7592959784275728
    - 1.8902411978847842
    - 2.003469448483784
    - 2.097643842812316
    - 2.17155920474564
    - 2.224156930532436
    - 2.254542865892226
    - 2.262007926025302
    - 2.2460509936498845
    - 2.206403449811117
    - 2.1430545291606964
    - 2.056276550870302
    - 1.946648962759898
    - 1.8150800533226448
    - 1.6628251371782483
    - 1.4915000065409865
    - 1.3030884664208535
    - 1.0999428357760093
    - 0.8847764013672529
    - 0.660646955595072
    - 0.4309307332859264
    - 0.19928628346945806
    - -0.030391932164692756
    - -0.2540301362000744
    - -0.46744163827138147
    - -0.6664023236647408
    - -0.8467341661732172
    - -1.004395360044515
    - -1.135575330322171
    - -1.2367925644210431
    - -1.3049929220540402
    - -1.3376458376284412
    - -1.3328356408978024
    - -1.2893450994604903
    - -1.2067282411828717
    - -1.0853695549339626
    - -0.9265268014022069
    - -0.732354897122968
    - -0.5059086662885239
    - -0.2511226853861535
    - 0.027233029308825752
    - 0.3236221300670316
    - 0.6318357949103837
    - 0.9451105424391096
    - 1.2562684293130089
    - 1.5578772547195623
    - 1.8424276036377591
    - 2.102522803592401
    - 2.3310771764103038
    - 2.521517366131851
    - 2.6679810449467354
    - 2.7655069673170414
    - 2.8102101819501852
    - 2.799436241598419
    - 2.7318884862914707
    - 2.6077229249462643
    - 2.4286059047657704
    - 2.197730631221852
    - 1.9197896694217382
    - 1.6009017977507642
    - 1.2484929662317603
    - 0.8711325967800451
    - 0.4783280053775158
    - 0.08028127638154706
    - -0.31238557823671154
    - -0.6889299443655977
    - -1.0388039508601727
    - -1.3519763533987876
    - -1.6192507312986906
    - -1.8325693430720702
    - -1.985291911441389
    - -2.0724389129278515
    - -2.090889644430257
    - -2.039526428753121
    - -1.9193177870068139
    - -1.733335216737772
    - -1.4867003235793945
    - -1.1864613994012687
    - -0.8414010462839223
    - -0.461779026793213
    - -0.059017082031782145
    - 0.35466510045932825
    - 0.7666513685618661
    - 1.1643547402189003
    - 1.5356524117353656
    - 1.8693143747735983
    - 2.1554094542657904
    - 2.385672767654528
    - 2.5538194309994053
    - 2.6557908009623445
    - 2.689921618761042
    - 2.657019061338095
    - 2.5603478284267482
    - 2.405518899466649
    - 2.2002833571985048
    - 1.9542365531703196
    - 1.6784417294017804
    - 1.3849858481938957
    - 1.0864836562481286
    - 0.7955487641695245
    - 0.524252616096692
    - 0.28359353536247484
    - 0.08299846668088184
    - -0.07012046779727185
    - -0.17073394584395057
    - -0.2164697124333959
    - -0.20777818824873748
    - -0.14797855024129106
    - -0.04317913877033295
    - 0.09792876234898541
    - 0.2643992723390419
    - 0.4434723969042009
    - 0.6211113756212068
    - 0.7826167855590588
    - 0.9132931422276833
    - 0.9991404867489176
    - 1.0275412801600654
    - 0.9879119870093939
    - 0.8722891169597211
    - 0.6758212452349659
    - 0.397141630215028
    - 0.03860040657830701
    - -0.39365918935921895
    - -0.8897897115307184
    - -1.4364956068646908
    - -2.0174512005955116
    - -2.6138677734826485
    - -3.205189779246043
    - -3.7698937332130016
    - -4.286357756437719
    - -4.733765478466774
    - -5.0930052342751395
    - -5.347524423254792
    - -5.484099644199551
    - -5.493485812173239
    - -5.370911846551703
    - -5.116396552290587
    - -4.734865771976551
    - -4.236060460813265
    - -3.6342346612788106
    - -2.9476520095885848
    - -2.197898941563679
    - -1.4090417196292868
    - -0.606662325712402
    - 0.18318525858269766
    - 0.9350521919874207
    - 1.6251565581721363
    - 2.2323807135953255
    - 2.7391571716385004
    - 3.132200378842122
    - 3.4030483012965003
    - 3.5483862180693984
    - 3.570135146354436
    - 3.475298442397849
    - 3.275571806177666
    - 2.9867335941625206
    - 2.627843423913502
    - 2.2202869600029307
    - 1.7867129687143724
    - 1.349914757248864
    - 0.931711608151542
    - 0.5518865386017088
    - 0.22723455177236987
    - -0.029229454095776927
    - -0.2088616015637186
    - -0.3077472152971669
    - -0.3268065078531976
    - -0.271641068657148
    - -0.1521281126279764
    - 0.018217012700701963
    - 0.2230768628042475
    - 0.4443221202887532
    - 0.6631026801872352
    - 0.8609800158077725
    - 1.021038115336313
    - 1.1289105194480693
    - 1.1736646669607946
    - 1.148491749787934
    - 1.051160284884482
    - 0.8842041495060318
    - 0.6548302633830125
    - 0.37454668081436326
    - 0.05852773609667882
    - -0.275251814133235
    - -0.6070678614059339
    - -0.9166258613400532
    - -1.1843016307714487
    - -1.3923730082381587
    - -1.5261702275218494
    - -1.575075809161867
    - -1.5333117567330399
    - -1.4004625613682788
    - -1.1816964565367594
    - -0.8876638140458528
    - -0.5340696565838826
    - -0.14093598853761607
    - 0.26841204271215724
    - 0.6685853119703989
    - 1.033530021745608
    - 1.3380109992870182
    - 1.559095976157713
    - 1.6775555883989874
    - 1.6790964412069695
    - 1.555352023331078
    - 1.3045682281385764
    - 0.9319361636773307
    - 0.4495439905092744
    - -0.12405931358263791
    - -0.7646732758883629
    - -1.4435916004586302
    - -2.1290273109722717
    - -2.787743170448444
    - -3.3867997704046076
    - -3.8953250481613035
    - -4.28620575262218
    - -4.537603849205223
    - -4.634209017158849
    - -4.5681518935083885
    - -4.339520878808408
    - -3.95644716971975
    - -3.4347470095004535
    - -2.797135562146665
    - -2.0720518355935096
    - -1.2921572115893938
    - -0.4925899729156618
    - 0.29092649112906266
    - 1.0240143690803187
    - 1.6755000409880356
    - 2.2190926757754945
    - 2.634784356310632
    - 2.909888777872705
    - 3.0396562418564206
    - 3.0274273483506926
    - 2.884315043041255
    - 2.628432876063335
    - 2.283714775360587
    - 1.8783966330040138
    - 1.4432509790406807
    - 1.0096816241446913
    - 0.607794349657372
    - 0.26456185235388247
    - 0.002195981907846361
    - -0.1631719355101589
    - -0.22242054349276222
    - -0.1739194977822372
    - -0.023531784877389158
    - 0.21586297193935106
    - 0.5252941715999994
    - 0.8810160918831274
    - 1.2561299227869167
    - 1.622407826768273
    - 1.9522012281466063
    - 2.2203093295409344
    - 2.4056855906554615
    - 2.4928695779176997
    positive_zeros:
    - '1.49165933183868599628163184016342'
    - '2.61907955212781802327804428359646'
    - '4.07515370850593451866546208597382'
    - '5.13397355008655610771556281911324'
    - '6.53130323875136454742302039663733'
    - '6.89568623477962945494789150529025'
    - '7.69352686227346422618522077820121'
    - '9.110307475348683644266951629778609'
    - '10.30434883002948537473483227863177'
    - '10.68146975157105867078297431533990'
    prelabel: 2-507-13.12-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.469366359361064
    root_angle: 0.5894561875110335
    root_number: -0.2773500981126145610091708667284996881731766595265574010 + 0.9607689228305228008995220186061222247804553812294855859*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.29472809375551673'
      prec: 64
    spectral_label: c3-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.49165933183868599628163184016'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.61907955212781802327804428360'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '4.07515370850593451866546208597'
      prec: 103
- - algebraic: true
    analytic_conductor: 29.913968372910507
    bad_primes:
    - 3
    - 13
    central_character: '13.12'
    conductor: 507
    conductor_radical: 39
    degree: 2
    id: 23838138
    index: 56
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/507/4/b/a/337/1
    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: 2-507-13.12-c3-0-56
    motivic_weight: 3
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 3
    order_of_vanishing: 0
    prelabel: 2-507-13.12-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.469366359361064
    root_angle: 0.29472809375551673
    self_dual: false
    spectral_label: c3-0
    z1:
      __RealLiteral__: 0
      data: '1.49165933183868599628163184016'
      prec: 103
- - Lhash: '1890902847341349922940523876174'
    Lhash_array:
    - '1890902847341349922940523876174'
    id: 24209156
    label: 2-507-13.12-c3-0-56
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/507/4/b/a/337/1
label_cols:
- label
- label
- label
labels:
- 2-507-13.12-c3-0-56
- 2-507-13.12-c3-0-56
- 2-507-13.12-c3-0-56
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-20T02:35:24.064861'