data:
- - Lhash: '518802074501762485590458220395'
    a10:
    - 0
    - 0
    a2:
    - 0
    - -5.0
    a3:
    - 0
    - -3.0
    a4:
    - -17.0
    - 0
    a5:
    - 0
    - 0
    a6:
    - -15.0
    - 0
    a7:
    - 0
    - -7.0
    a8:
    - 0
    - 45.0
    a9:
    - -9.0
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 30.976002753013837
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 3.0
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 7
      - - - 1.0
          - 0
        - - 0
          - 7.0
    bad_primes:
    - 3
    - 5
    - 7
    central_character: '525.274'
    coefficient_field: CDF
    conductor: 525
    conductor_radical: 105
    conjugate: '1501920463879001840616501717510'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 5.0
      - - -8.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 3.0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 7.0
    - - - 1.0
        - 0
      - - -12.0
        - 0
      - - 1331.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -30.0
      - - -2197.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -134.0
      - - -4913.0
        - 0
    - - - 1.0
        - 0
      - - -92.0
        - 0
      - - 6859.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -112.0
      - - -12167.0
        - 0
    - - - 1.0
        - 0
      - - -58.0
        - 0
      - - 24389.0
        - 0
    - - - 1.0
        - 0
      - - 224.0
        - 0
      - - 29791.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -146.0
      - - -50653.0
        - 0
    - - - 1.0
        - 0
      - - -18.0
        - 0
      - - 68921.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -340.0
      - - -79507.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 208.0
      - - -103823.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 754.0
      - - -148877.0
        - 0
    - - - 1.0
        - 0
      - - 380.0
        - 0
      - - 205379.0
        - 0
    - - - 1.0
        - 0
      - - -718.0
        - 0
      - - 226981.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 412.0
      - - -300763.0
        - 0
    - - - 1.0
        - 0
      - - 960.0
        - 0
      - - 357911.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -1066.0
      - - -389017.0
        - 0
    - - - 1.0
        - 0
      - - 896.0
        - 0
      - - 493039.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -436.0
      - - -571787.0
        - 0
    - - - 1.0
        - 0
      - - -1038.0
        - 0
      - - 704969.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -702.0
      - - -912673.0
        - 0
    - - - 1.0
        - 0
      - - -46.0
        - 0
      - - 1030301.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -1880.0
      - - -1092727.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 732.0
      - - -1225043.0
        - 0
    - - - 1.0
        - 0
      - - -378.0
        - 0
      - - 1295029.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -1458.0
      - - -1442897.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23698465
    index: 13
    label: 2-525-5.4-c3-0-13
    leading_term: '1.166728381427593245510346962580607624334090557809012401'
    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/525/4/d/a/274/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.0625'
      prec: 20
    plot_values:
    - 1.1667283814275933
    - 1.0646011749386783
    - 0.9358455697527007
    - 0.7797665416994857
    - 0.5958579064514499
    - 0.38382278134109815
    - 0.14359693552883224
    - -0.12462545923631252
    - -0.42036436133004457
    - -0.7428255390169008
    - -1.0908724174979372
    - -1.4629992421517544
    - -1.8573068033946607
    - -2.271482029655699
    - -2.7027827781093325
    - -3.148029136269392
    - -3.6036024901952715
    - -4.065453516364063
    - -4.529120114290929
    - -4.989756116459614
    - -5.442171392526537
    - -5.8808837084195345
    - -6.300182411189955
    - -6.6942036917266226
    - -7.057016835335905
    - -7.382720511622708
    - -7.665547788218768
    - -7.8999781870411665
    - -8.080854747342688
    - -8.203503728132803
    - -8.263854285518208
    - -8.25855521034294
    - -8.185085620320478
    - -8.04185638024885
    - -7.82829898451203
    - -7.544938687065318
    - -7.193448812704759
    - -6.776683434446116
    - -6.298685957261012
    - -5.7646716069936765
    - -5.180982380255058
    - -4.555013657992402
    - -3.895112409995119
    - -3.210447703804226
    - -2.5108550597646326
    - -1.8066570414989005
    - -1.1084633123642715
    - -0.42695419587822836
    - 0.2273474772357401
    - 0.8443108001005195
    - 1.4144315316080585
    - 1.9290607976497873
    - 2.380621187450926
    - 2.7628036599691668
    - 3.070738861352029
    - 3.3011368563804018
    - 3.452389896808807
    - 3.524633682157739
    - 3.519763600465113
    - 3.4414036462801496
    - 3.2948270713139047
    - 3.0868292926481495
    - 2.8255551205142138
    - 2.520283923035507
    - 2.1811778654484875
    - 1.8189997901757298
    - 1.4448085852037198
    - 1.0696409666121995
    - 0.7041894257534115
    - 0.3584866175350906
    - 0.04160665686052631
    - -0.2386063808192247
    - -0.47577300594192395
    - -0.6651670831451725
    - -0.8038512831680412
    - -0.8907533013534433
    - -0.9266788381688422
    - -0.914259483316147
    - -0.8578359548983746
    - -0.7632795381204885
    - -0.6377569554579567
    - -0.48944618853575855
    - -0.32721286613660056
    - -0.160258640256803
    - 0.0022455931534158804
    - 0.15152778586680138
    - 0.27956982219957593
    - 0.37943535494077035
    - 0.4455568043073846
    - 0.4739691627554974
    - 0.46248003237253466
    - 0.4107676098385016
    - 0.32040105396981494
    - 0.19478072779654457
    - 0.03899908670841565
    - -0.14037364336379723
    - -0.33557152901410425
    - -0.5379721335515711
    - -0.7384794687691046
    - -0.9279349824148696
    - -1.0975391492836892
    - -1.239265214397756
    - -1.3462463945327043
    - -1.4131184247688457
    - -1.436300750356813
    - -1.4142018842799962
    - -1.3473374127065336
    - -1.2383527321278254
    - -1.0919467069928936
    - -0.9146968786867063
    - -0.7147914455244649
    - -0.50167776256021
    - -0.2856413655411592
    - -0.0773332936596789
    - 0.11273342834148606
    - 0.2746950633308138
    - 0.399831885588483
    - 0.48102194065152576
    - 0.5131304816921824
    - 0.49331394564680825
    - 0.42122066916857276
    - 0.2990748854451786
    - 0.1316357238493202
    - -0.07397125787719641
    - -0.3085462989815142
    - -0.5612214411473807
    - -0.8199642854064723
    - -1.0721579452104366
    - -1.3052309358112753
    - -1.5073071295015987
    - -1.66784362079247
    - -1.7782235621317228
    - -1.8322718602104335
    - -1.8266641012429745
    - -1.7612031561500465
    - -1.6389434760184711
    - -1.4661499167365037
    - -1.2520857472659583
    - -1.0086329527354867
    - -0.7497566458979589
    - -0.4908339207835748
    - -0.24787538074856139
    - -0.036674419287633916
    - 0.1280752723884912
    - 0.23364989638889921
    - 0.2701078278822615
    - 0.23099908228740224
    - 0.1139300944164534
    - -0.07905276440445294
    - -0.34129008733105887
    - -0.6615666481443078
    - -1.0244081118563142
    - -1.410614718224032
    - -1.7980172811385269
    - -2.162428873675416
    - -2.478754374538138
    - -2.722210242615528
    - -2.8695990256234998
    - -2.900577685730233
    - -2.7988562265725414
    - -2.5532635917834425
    - -2.1586214881575176
    - -1.616373620937143
    - -0.9349276046775036
    - -0.12967916083369058
    - 0.7772973853002697
    - 1.7578924858046525
    - 2.7789223335952604
    - 3.8033747849730544
    - 4.791892272089147
    - 5.70443018937265
    - 6.502018247941366
    - 7.148544513797548
    - 7.612477793513483
    - 7.868444046318344
    - 7.898576727579769
    - 7.693569336638051
    - 7.253370666019359
    - 6.587478833829041
    - 5.714808440208862
    - 4.6631252742482
    - 3.468063939525029
    - 2.171764519298952
    - 0.8211838988619948
    - -0.5338454310657766
    - -1.842722293816669
    - -3.05625273649676
    - -4.12879290819597
    - -5.020256627182067
    - -5.697890260175901
    - -6.137727459791109
    - -6.32565084087669
    - -6.258006160269414
    - -5.941736110178601
    - -5.3940243736902955
    - -4.641464923631133
    - -3.7187954086565433
    - -2.667255599162785
    - -1.532651066660671
    - -0.3632174866739439
    - 0.7926086720446862
    - 1.8884023900598907
    - 2.881835446284236
    - 3.73653169178077
    - 4.423601191013762
    - 4.922779166631944
    - 5.223116657936701
    - 5.323193638470783
    - 5.230850743701737
    - 4.962461343639563
    - 4.541790042198559
    - 3.998505437115001
    - 3.3664329089058933
    - 2.6816463100982744
    - 1.98050495107772
    - 1.2977437960221048
    - 0.6647202050774246
    - 0.10791015351751622
    - -0.35226876778335103
    - -0.7022501981482088
    - -0.9356933915468304
    - -1.0534296674516086
    - -1.0629965895706395
    - -0.9777994713471788
    - -0.8159611212416624
    - -0.5989381594298909
    - -0.3499947220149591
    - -0.09263117955629144
    - 0.15093375905174763
    - 0.3611345274445035
    - 0.522201804980798
    - 0.6230113564096845
    - 0.6575927744492057
    - 0.6252750331446388
    - 0.530469730134221
    - 0.38211655267654643
    - 0.19283731909628302
    - -0.022136487949846215
    - -0.24618367297459517
    - -0.4625730104007584
    - -0.6557121219018959
    - -0.8122783560454276
    - -0.9221537248424976
    - -0.9791004818003483
    - -0.9811327620526338
    - -0.9305615735792719
    - -0.8337138413045626
    - -0.7003495577369586
    - -0.5428227692895238
    - -0.3750506100845259
    - -0.21136857209180163
    - -0.06535865525576602
    - 0.051260672461531924
    - 0.12959788310458978
    - 0.1643306273542502
    - 0.15416807413115466
    - 0.10199490087832834
    positive_zeros:
    - '0.40926267412199916161492296752747'
    - '2.97792479975793590736842334954795'
    - '4.38375148537717703945141083608875'
    - '5.24910831615715771093284791000705'
    - '5.88921960399178111643206010911501'
    - '7.08702854628003906995801771605549'
    - '7.66615696543583308656028630781845'
    - '8.887350438553412334698872153534567'
    - '9.227145245004230714359924725356746'
    - '10.25933895455305968310546091819010'
    prelabel: 2-525-5.4-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.56560892922004
    root_angle: 0.35241638234956674
    root_number: 0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.17620819117478337'
      prec: 64
    spectral_label: c3-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.40926267412199916161492296753'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.97792479975793590736842334955'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '4.38375148537717703945141083609'
      prec: 103
- - algebraic: true
    analytic_conductor: 30.976002753013837
    bad_primes:
    - 3
    - 5
    - 7
    central_character: '5.4'
    conductor: 525
    conductor_radical: 105
    degree: 2
    id: 23698465
    index: 13
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/525/4/d/a/274/1
    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: 2-525-5.4-c3-0-13
    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: 2-525-5.4-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.56560892922004
    root_angle: 0.17620819117478337
    self_dual: false
    spectral_label: c3-0
    z1:
      __RealLiteral__: 0
      data: '0.40926267412199916161492296753'
      prec: 103
- - Lhash: '518802074501762485590458220395'
    Lhash_array:
    - '518802074501762485590458220395'
    id: 24066677
    label: 2-525-5.4-c3-0-13
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/525/4/d/a/274/1
label_cols:
- label
- label
- label
labels:
- 2-525-5.4-c3-0-13
- 2-525-5.4-c3-0-13
- 2-525-5.4-c3-0-13
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-11T16:34:25.672110'