data:
- - Lhash: '2092724193141833052346144426951'
    a10: 0
    a2: 0
    a3: 0
    a4: 0
    a5: 5
    a6: 0
    a7: -2
    a8: 0
    a9: 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 42.481375204133265
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - 1
    - - 3
      - - 1
    - - 5
      - - 1
        - -5
    bad_primes:
    - 2
    - 3
    - 5
    central_character: '720.1'
    coefficient_field: 1.1.1.1
    conductor: 720
    conductor_radical: 30
    degree: 2
    euler_factors:
    - - 1
    - - 1
    - - 1
      - -5
    - - 1
      - 2
      - 343
    - - 1
      - -34
      - 1331
    - - 1
      - 68
      - 2197
    - - 1
      - 38
      - 4913
    - - 1
      - 4
      - 6859
    - - 1
      - 152
      - 12167
    - - 1
      - 46
      - 24389
    - - 1
      - -260
      - 29791
    - - 1
      - 312
      - 50653
    - - 1
      - -48
      - 68921
    - - 1
      - -200
      - 79507
    - - 1
      - 104
      - 103823
    - - 1
      - 414
      - 148877
    - - 1
      - -2
      - 205379
    - - 1
      - 38
      - 226981
    - - 1
      - -244
      - 300763
    - - 1
      - 708
      - 357911
    - - 1
      - 378
      - 389017
    - - 1
      - -852
      - 493039
    - - 1
      - 844
      - 571787
    - - 1
      - 1380
      - 704969
    - - 1
      - -514
      - 912673
    - - 1
      - 702
      - 1030301
    - - 1
      - 898
      - 1092727
    - - 1
      - 876
      - 1225043
    - - 1
      - -602
      - 1295029
    - - 1
      - -1350
      - 1442897
    euler_factors_factorization:
    - - 1
    - - 1
    - - - - 1
          - -5
        - 1
    - - - - 1
          - 2
          - 343
        - 1
    - - - - 1
          - -34
          - 1331
        - 1
    - - - - 1
          - 68
          - 2197
        - 1
    - - - - 1
          - 38
          - 4913
        - 1
    - - - - 1
          - 4
          - 6859
        - 1
    - - - - 1
          - 152
          - 12167
        - 1
    - - - - 1
          - 46
          - 24389
        - 1
    - - - - 1
          - -260
          - 29791
        - 1
    - - - - 1
          - 312
          - 50653
        - 1
    - - - - 1
          - -48
          - 68921
        - 1
    - - - - 1
          - -200
          - 79507
        - 1
    - - - - 1
          - 104
          - 103823
        - 1
    - - - - 1
          - 414
          - 148877
        - 1
    - - - - 1
          - -2
          - 205379
        - 1
    - - - - 1
          - 38
          - 226981
        - 1
    - - - - 1
          - -244
          - 300763
        - 1
    - - - - 1
          - 708
          - 357911
        - 1
    - - - - 1
          - 378
          - 389017
        - 1
    - - - - 1
          - -852
          - 493039
        - 1
    - - - - 1
          - 844
          - 571787
        - 1
    - - - - 1
          - 1380
          - 704969
        - 1
    - - - - 1
          - -514
          - 912673
        - 1
    - - - - 1
          - 702
          - 1030301
        - 1
    - - - - 1
          - 898
          - 1092727
        - 1
    - - - - 1
          - 876
          - 1225043
        - 1
    - - - - 1
          - -602
          - 1295029
        - 1
    - - - - 1
          - -1350
          - 1442897
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 20193398
    index: 27
    label: 2-720-1.1-c3-0-27
    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: 1
    origin: ModularForm/GL2/Q/holomorphic/720/4/a/x
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - -1.6450881208173936e-60
    - 0.23045364832802875
    - 0.4584477026451161
    - 0.681533735238517
    - 0.8972863161603329
    - 1.1033161401832972
    - 1.2972850112623708
    - 1.47692314745856
    - 1.6400491433171662
    - 1.7845927786182214
    - 1.9086206977248168
    - 2.0103648083873638
    - 2.08825306897493
    - 2.1409421548651695
    - 2.1673513241440614
    - 2.1666966455798087
    - 2.138524613410574
    - 2.082744058766043
    - 1.999655180999088
    - 1.8899744677931152
    - 1.7548542540272085
    - 1.595895688794453
    - 1.415153939745653
    - 1.2151345653413816
    - 0.9987801290087254
    - 0.769446313972173
    - 0.5308670218992586
    - 0.28710819949678507
    - 0.04251043055504731
    - -0.1983793489151325
    - -0.430886314776908
    - -0.6502953486790655
    - -0.8519463582712559
    - -1.0313355741115644
    - -1.1842207467211725
    - -1.3067278711625028
    - -1.395456813194141
    - -1.4475830122273186
    - -1.4609523031487948
    - -1.4341658417616772
    - -1.366652145867733
    - -1.2587233827309874
    - -1.111613248380536
    - -0.9274940968029385
    - -0.7094713863992941
    - -0.4615540127270009
    - -0.18859968266331373
    - 0.10376485562650058
    - 0.40924819494005654
    - 0.721021973620568
    - 1.0318698353148408
    - 1.3343548035520112
    - 1.6210014869730487
    - 1.884488843088032
    - 2.1178486231751315
    - 2.314664124627923
    - 2.4692635144384303
    - 2.5769017807672445
    - 2.6339253373559948
    - 2.6379134620396303
    - 2.587791104596495
    - 2.48390815327646
    - 2.328080999480619
    - 2.1235931750055874
    - 1.8751529374833025
    - 1.588806921400455
    - 1.2718103217760368
    - 0.9324554964154375
    - 0.579862316583244
    - 0.22373501682434477
    - -0.12590835820655213
    - -0.4590265903236029
    - -0.7658576426400012
    - -1.0372235459592252
    - -1.2648280755932342
    - -1.4415372263779354
    - -1.5616325735348109
    - -1.6210280352281097
    - -1.6174413348874344
    - -1.5505125906317132
    - -1.4218639151910786
    - -1.2350956589167772
    - -0.9957169241058471
    - -0.711010162145587
    - -0.3898319664475425
    - -0.04235451566034197
    - 0.3202455811259229
    - 0.6861421202443423
    - 1.0432469580672292
    - 1.3796179811115625
    - 1.6838736296652175
    - 1.9455994040444595
    - 2.1557314774608263
    - 2.306902775633569
    - 2.3937376792547838
    - 2.4130828588754545
    - 2.3641636384280367
    - 2.248657656840595
    - 2.070680388727153
    - 1.8366802064602952
    - 1.5552440107832584
    - 1.2368179047885919
    - 0.8933508055289503
    - 0.5378721421275312
    - 0.1840177421566423
    - -0.15447947225559952
    - -0.464315391086252
    - -0.7331373297362562
    - -0.9500428836834869
    - -1.1060347848839345
    - -1.194412566492457
    - -1.2110837018177716
    - -1.1547795146517472
    - -1.0271644858693172
    - -0.8328314975672088
    - -0.5791799234836569
    - -0.2761781303070572
    - 0.06398328344337673
    - 0.42733651078303336
    - 0.7986644363840923
    - 1.1620921269108524
    - 1.501719392077746
    - 1.8022694951941758
    - 2.049727655684086
    - 2.2319426135119427
    - 2.3391652728971373
    - 2.364500320107611
    - 2.304249678592657
    - 2.1581306360463075
    - 1.9293563164289045
    - 1.6245716961613752
    - 1.2536443608102101
    - 0.82931542038396
    - 0.36672218206799007
    - -0.11718995539776933
    - -0.6043436420742595
    - -1.0762665694465487
    - -1.5148587609600257
    - -1.9031574878337285
    - -2.226066409636446
    - -2.4710162802868796
    - -2.6285267849406884
    - -2.692642728936073
    - -2.6612227663717074
    - -2.536064948222965
    - -2.3228603449526024
    - -2.0309735637862993
    - -1.6730568061189741
    - -1.2645118423579176
    - -0.8228215586658112
    - -0.366779200388468
    - 0.0843512256301321
    - 0.5117060066765393
    - 0.8976845760332065
    - 1.2267640187994067
    - 1.4862264818957904
    - 1.6667639923039752
    - 1.7629302015651303
    - 1.7734151598673258
    - 1.7011271093074296
    - 1.5530741314707794
    - 1.3400478905962967
    - 1.076121241978892
    - 0.7779806681346536
    - 0.46412290719340205
    - 0.15395231839828702
    - -0.1331788952016159
    - -0.37894183303299545
    - -0.566966137052167
    - -0.6836928326962288
    - -0.7191013658266282
    - -0.6672727323271258
    - -0.5267579071088649
    - -0.3007297864978555
    - 0.003092843053226693
    - 0.3727496881446474
    - 0.7925606793446687
    - 1.2438429550848304
    - 1.705790771351437
    - 2.1564771743822484
    - 2.573929317324813
    - 2.9372246249132163
    - 3.2275529071187923
    - 3.429190164014655
    - 3.53033324401852
    - 3.5237506083772216
    - 3.4072129676737375
    - 3.1836781108486982
    - 2.8612163474396874
    - 2.4526760398673755
    - 1.9751020599424962
    - 1.4489329750103577
    - 0.8970146695448404
    - 0.34347829152296677
    - -0.18746169257625517
    - -0.6727284107172797
    - -1.0915594901870715
    - -1.4265781897755911
    - -1.6647014781482876
    - -1.7978353674116945
    - -1.8233181724835932
    - -1.7440850088331714
    - -1.568541138504264
    - -1.3101469984818863
    - -0.9867331007962061
    - -0.619577658950899
    - -0.23229296713637657
    - 0.1504225036839172
    - 0.5041012620943459
    - 0.8058234737977554
    - 1.035462418049192
    - 1.1767907873787922
    - 1.2183864426526632
    - 1.1542862398294274
    - 0.9843495253581481
    - 0.7143081991200363
    - 0.355497069785925
    - -0.07572432151769509
    - -0.558830110254679
    - -1.0702226112692823
    - -1.5845051234915533
    - -2.0758645800763063
    - -2.519488561826558
    - -2.892938265462252
    - -3.1774004310432473
    - -3.3587469849592795
    - -3.428341001830692
    - -3.3835410493276785
    - -3.2278723586114904
    - -2.970851684272223
    - -2.6274721717649387
    - -2.2173739486393966
    - -1.7637443908363113
    - -1.2920080239346416
    - -0.8283788449511909
    - -0.3983567005424489
    - -0.025253652946469758
    - 0.27116432214105574
    - 0.4758404833375114
    - 0.5793257181283458
    - 0.5783570003902744
    - 0.476078569649995
    - 0.28188878252136496
    - 0.01091718724197811
    - -0.3168419572624026
    - -0.6776930224653789
    - -1.045634459532378
    - -1.393907067323859
    - -1.6966056866623402
    - -1.930259931314541
    - -2.075290057115038
    - -2.117250114304347
    - -2.0477818611023504
    - -1.8652189564443593
    - -1.5748008235937418
    - -1.1884781664493147
    - -0.7243161266506557
    positive_zeros:
    - '1.65086830137977796718777133938782'
    - '2.73347584249626969031515742757047'
    - '4.08023009761609070257363231588768'
    - '4.98740401536024880923986762491940'
    - '6.12512338147538544757501891690938'
    - '6.84481843013476577981970739626897'
    - '7.83749257028573088129008820398180'
    - '8.836536231239757968855699558389465'
    - '9.698554711068980100534474093858851'
    prelabel: 2-720-1.1-c3-0
    primitive: true
    rational: true
    root_analytic_conductor: 6.517773792034613
    root_angle: 1.0
    root_number: '-1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    spectral_label: c3-0
    trace_hash: 563363331408429583
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.65086830137977796718777133939'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.73347584249626969031515742757'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '4.08023009761609070257363231589'
      prec: 103
- - algebraic: true
    analytic_conductor: 42.481375204133265
    bad_primes:
    - 2
    - 3
    - 5
    central_character: '1.1'
    conductor: 720
    conductor_radical: 30
    degree: 2
    dirichlet_coefficients:
    - 1
    - 0
    - 0
    - 0
    - 5
    - 0
    - -2
    - 0
    - 0
    - 0
    - 34
    - 0
    - -68
    - 0
    - 0
    - 0
    - -38
    - 0
    - -4
    - 0
    - 0
    - 0
    - -152
    - 0
    - 25
    - 0
    - 0
    - 0
    - -46
    - 0
    - 260
    - 0
    - 0
    - 0
    - -10
    - 0
    - -312
    - 0
    - 0
    - 0
    - 48
    - 0
    - 200
    - 0
    - 0
    - 0
    - -104
    - 0
    - -339
    - 0
    - 0
    - 0
    - -414
    - 0
    - 170
    - 0
    - 0
    - 0
    - 2
    - 0
    - -38
    - 0
    - 0
    - 0
    - -340
    - 0
    - 244
    - 0
    - 0
    - 0
    - -708
    - 0
    - -378
    - 0
    - 0
    - 0
    - -68
    - 0
    - 852
    - 0
    - 0
    - 0
    - -844
    - 0
    - -190
    - 0
    - 0
    - 0
    - -1380
    - 0
    - 136
    - 0
    - 0
    - 0
    - -20
    - 0
    - 514
    - 0
    - 0
    - 0
    euler11:
    - 1
    - -34
    - 1331
    euler13:
    - 1
    - 68
    - 2197
    euler17:
    - 1
    - 38
    - 4913
    euler19:
    - 1
    - 4
    - 6859
    euler2:
    - 1
    - 0
    - 0
    euler23:
    - 1
    - 152
    - 12167
    euler29:
    - 1
    - 46
    - 24389
    euler3:
    - 1
    - 0
    - 0
    euler31:
    - 1
    - -260
    - 29791
    euler37:
    - 1
    - 312
    - 50653
    euler41:
    - 1
    - -48
    - 68921
    euler43:
    - 1
    - -200
    - 79507
    euler47:
    - 1
    - 104
    - 103823
    euler5:
    - 1
    - -5
    - 0
    euler53:
    - 1
    - 414
    - 148877
    euler59:
    - 1
    - -2
    - 205379
    euler61:
    - 1
    - 38
    - 226981
    euler67:
    - 1
    - -244
    - 300763
    euler7:
    - 1
    - 2
    - 343
    euler71:
    - 1
    - 708
    - 357911
    euler73:
    - 1
    - 378
    - 389017
    euler79:
    - 1
    - -852
    - 493039
    euler83:
    - 1
    - 844
    - 571787
    euler89:
    - 1
    - 1380
    - 704969
    euler97:
    - 1
    - -514
    - 912673
    euler_factors:
    - - 1
      - 0
      - 0
    - - 1
      - 0
      - 0
    - - 1
      - -5
      - 0
    - - 1
      - 2
      - 343
    - - 1
      - -34
      - 1331
    - - 1
      - 68
      - 2197
    - - 1
      - 38
      - 4913
    - - 1
      - 4
      - 6859
    - - 1
      - 152
      - 12167
    - - 1
      - 46
      - 24389
    - - 1
      - -260
      - 29791
    - - 1
      - 312
      - 50653
    - - 1
      - -48
      - 68921
    - - 1
      - -200
      - 79507
    - - 1
      - 104
      - 103823
    - - 1
      - 414
      - 148877
    - - 1
      - -2
      - 205379
    - - 1
      - 38
      - 226981
    - - 1
      - -244
      - 300763
    - - 1
      - 708
      - 357911
    - - 1
      - 378
      - 389017
    - - 1
      - -852
      - 493039
    - - 1
      - 844
      - 571787
    - - 1
      - 1380
      - 704969
    - - 1
      - -514
      - 912673
    id: 20193398
    index: 27
    instance_types:
    - CMF
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/720/4/a/x/1/1
    - ModularForm/GL2/Q/holomorphic/720/4/a/x
    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: 2-720-1.1-c3-0-27
    motivic_weight: 3
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 3
    order_of_vanishing: 1
    prelabel: 2-720-1.1-c3-0
    primitive: true
    rational: true
    root_analytic_conductor: 6.517773792034613
    root_angle: 0.5
    self_dual: true
    spectral_label: c3-0
    trace_hash: 563363331408429583
    z1:
      __RealLiteral__: 0
      data: '1.65086830137977796718777133939'
      prec: 103
- - Lhash: '2092724193141833052346144426951'
    Lhash_array:
    - '2092724193141833052346144426951'
    id: 20418439
    label: 2-720-1.1-c3-0-27
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/720/4/a/x
  - Lhash: '2092724193141833052346144426951'
    Lhash_array:
    - '2092724193141833052346144426951'
    id: 24569831
    label: 2-720-1.1-c3-0-27
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/720/4/a/x/1/1
label_cols:
- label
- label
- label
labels:
- 2-720-1.1-c3-0-27
- 2-720-1.1-c3-0-27
- 2-720-1.1-c3-0-27
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-23T10:38:24.894581'