data:
- - Lhash: '1653944136607495829114383744799'
    a10: -2
    a2: -1
    a3: 0
    a4: 1
    a5: 2
    a6: 0
    a7: 0
    a8: -1
    a9: 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 77.47086004104627
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - 1
        - 1
    - - 3
      - - 1
    - - 7
      - - 1
    - - 11
      - - 1
        - 1
    bad_primes:
    - 2
    - 3
    - 7
    - 11
    central_character: '9702.1'
    coefficient_field: 1.1.1.1
    conductor: 9702
    conductor_radical: 462
    degree: 2
    euler_factors:
    - - 1
      - 1
    - - 1
    - - 1
      - -2
      - 5
    - - 1
    - - 1
      - 1
    - - 1
      - -2
      - 13
    - - 1
      - 2
      - 17
    - - 1
      - 0
      - 19
    - - 1
      - 0
      - 23
    - - 1
      - -2
      - 29
    - - 1
      - 4
      - 31
    - - 1
      - 2
      - 37
    - - 1
      - 10
      - 41
    - - 1
      - -4
      - 43
    - - 1
      - -4
      - 47
    - - 1
      - -2
      - 53
    - - 1
      - 12
      - 59
    - - 1
      - -2
      - 61
    - - 1
      - -12
      - 67
    - - 1
      - 8
      - 71
    - - 1
      - 6
      - 73
    - - 1
      - 8
      - 79
    - - 1
      - 8
      - 83
    - - 1
      - 14
      - 89
    - - 1
      - -14
      - 97
    - - 1
      - 10
      - 101
    - - 1
      - 4
      - 103
    - - 1
      - -12
      - 107
    - - 1
      - -14
      - 109
    - - 1
      - 18
      - 113
    euler_factors_factorization:
    - - - - 1
          - 1
        - 1
    - - 1
    - - - - 1
          - -2
          - 5
        - 1
    - - 1
    - - - - 1
          - 1
        - 1
    - - - - 1
          - -2
          - 13
        - 1
    - - - - 1
          - 2
          - 17
        - 1
    - - - - 1
          - 0
          - 19
        - 1
    - - - - 1
          - 0
          - 23
        - 1
    - - - - 1
          - -2
          - 29
        - 1
    - - - - 1
          - 4
          - 31
        - 1
    - - - - 1
          - 2
          - 37
        - 1
    - - - - 1
          - 10
          - 41
        - 1
    - - - - 1
          - -4
          - 43
        - 1
    - - - - 1
          - -4
          - 47
        - 1
    - - - - 1
          - -2
          - 53
        - 1
    - - - - 1
          - 12
          - 59
        - 1
    - - - - 1
          - -2
          - 61
        - 1
    - - - - 1
          - -12
          - 67
        - 1
    - - - - 1
          - 8
          - 71
        - 1
    - - - - 1
          - 6
          - 73
        - 1
    - - - - 1
          - 8
          - 79
        - 1
    - - - - 1
          - 8
          - 83
        - 1
    - - - - 1
          - 14
          - 89
        - 1
    - - - - 1
          - -14
          - 97
        - 1
    - - - - 1
          - 10
          - 101
        - 1
    - - - - 1
          - 4
          - 103
        - 1
    - - - - 1
          - -12
          - 107
        - 1
    - - - - 1
          - -14
          - 109
        - 1
    - - - - 1
          - 18
          - 113
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 22729562
    index: 133
    label: 2-9702-1.1-c1-0-133
    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: 1
    origin: ModularForm/GL2/Q/holomorphic/9702/2/a/r
    plot_delta:
      __RealLiteral__: 0
      data: '0.046875'
      prec: 27
    plot_values:
    - -8.289250819338474e-61
    - 0.17681795443291343
    - 0.35222468774184756
    - 0.5247785989887337
    - 0.692980560979911
    - 0.8552529907171343
    - 1.0099276509902009
    - 1.1552440630884255
    - 1.2893596788301627
    - 1.410372199222743
    - 1.5163536960747583
    - 1.605395535072007
    - 1.6756625399606273
    - 1.7254543877646302
    - 1.7532718832776133
    - 1.7578855198366967
    - 1.7384035828967082
    - 1.6943369843833205
    - 1.6256580230001476
    - 1.5328503453803868
    - 1.4169475345282454
    - 1.2795579762648568
    - 1.1228739526208606
    - 0.9496632837397075
    - 0.7632422854782073
    - 0.5674293244896611
    - 0.36647882894503975
    - 0.16499624050465525
    - -0.03216494252620562
    - -0.22002219733644754
    - -0.39359656827182526
    - -0.5480556443980364
    - -0.6788631406913196
    - -0.7819307668300964
    - -0.8537676343252049
    - -0.8916221445100713
    - -0.8936111390067016
    - -0.85883109966791
    - -0.7874463712725354
    - -0.6807497566559708
    - -0.541191403504258
    - -0.3723726608190026
    - -0.17900251976705261
    - 0.03318465066936429
    - 0.25755013463657894
    - 0.48670940138805907
    - 0.7127254872853024
    - 0.9273331786701499
    - 1.1221885856948883
    - 1.2891374265395987
    - 1.4204942144733765
    - 1.5093236093465736
    - 1.5497145094666445
    - 1.5370370630806678
    - 1.4681727069380635
    - 1.341707619113609
    - 1.1580806195304272
    - 0.9196775666863015
    - 0.6308656712928762
    - 0.2979628507202829
    - -0.07086075842459577
    - -0.46574978332427414
    - -0.8753973505394667
    - -1.2873413453038312
    - -1.6883164784695097
    - -2.064653050113274
    - -2.4027110924887727
    - -2.6893366527045375
    - -2.9123254278284882
    - -3.060877873942553
    - -3.126029345286479
    - -3.1010388331452607
    - -2.981720500293055
    - -2.766703457387982
    - -2.4576070906656184
    - -2.059121688712186
    - -1.578987068229288
    - -1.027865278834219
    - -0.4191071674914847
    - 0.2315835222616341
    - 0.906580893739531
    - 1.586851011484637
    - 2.2525343193622667
    - 2.883578106724951
    - 3.4603981309648675
    - 3.9645465517035205
    - 4.379362171470372
    - 4.690578693175264
    - 4.88686734777471
    - 4.960291832876134
    - 4.906656013526658
    - 4.725728210261749
    - 4.421330038621507
    - 4.001282534778564
    - 3.4772075375550076
    - 2.864187805172242
    - 2.1802949130309517
    - 1.4459993824050514
    - 0.683482502177514
    - -0.08412629350810093
    - -0.833559043182603
    - -1.5422358302090184
    - -2.1890768105727494
    - -2.7552679765940207
    - -3.2249500037508514
    - -3.5858018817790827
    - -3.829494616339592
    - -3.9519949930695635
    - -3.9537050588449927
    - -3.839429385545182
    - -3.618169089770598
    - -3.302748707816568
    - -2.9092890697175693
    - -2.456545973845303
    - -1.9651404357375535
    - -1.4567112933736657
    - -0.9530247514539884
    - -0.4750778406556451
    - -0.042233611965965596
    - 0.3285748965700148
    - 0.6235373001390002
    - 0.8325244786974261
    - 0.9494879380551827
    - 0.9726813349261634
    - 0.9046931698932046
    - 0.7522878755845998
    - 0.526061027159751
    - 0.23992279866620136
    - -0.08956830328004357
    - -0.44399235062024456
    - -0.8039406297059122
    - -1.1499347394081607
    - -1.4633502796092244
    - -1.727302539704701
    - -1.927452842175565
    - -2.0526973878934043
    - -2.095705477369093
    - -2.053280645636371
    - -1.9265262652187791
    - -1.720806187701395
    - -1.445500599718441
    - -1.1135670157884618
    - -0.740925753455857
    - -0.3456978758614866
    - 0.05266898886064734
    - 0.4343457154893853
    - 0.7800924851277269
    - 1.0722083928699992
    - 1.2954134112750382
    - 1.4376190231744421
    - 1.4905487830804198
    - 1.4501769902152681
    - 1.316962249558531
    - 1.0958625622454135
    - 0.796129253355024
    - 0.4308879940765816
    - 0.016525862309252615
    - -0.4280867307611231
    - -0.8825018523184854
    - -1.325683403857063
    - -1.737031172876688
    - -2.0973884919698684
    - -2.3899827444837487
    - -2.601250874493218
    - -2.7215074589704336
    - -2.7454205421300735
    - -2.672269955745864
    - -2.5059737901931682
    - -2.2548804922246637
    - -1.9313361448563808
    - -1.5510482052381964
    - -1.1322777187439146
    - -0.6949012131117194
    - -0.2593905988141872
    - 0.15423594499167342
    - 0.5274372172791069
    - 0.8440924815085395
    - 1.0913151651660655
    - 1.2600933245252004
    - 1.345722401043294
    - 1.348006715963985
    - 1.2712184525764856
    - 1.123815913563234
    - 0.9179359153861998
    - 0.6686875803576865
    - 0.3932858224964805
    - 0.11007187125352946
    - -0.16252528772178315
    - -0.407029049069679
    - -0.6078989191933851
    - -0.7524026045750855
    - -0.8313270763007164
    - -0.8394879181533419
    - -0.7760073379293638
    - -0.6443440904933664
    - -0.4520725274052654
    - -0.2104222783659128
    - 0.06639612122318703
    - 0.36204180723020174
    - 0.6590219924392781
    - 0.9397419406429666
    - 1.1875655010512525
    - 1.3878239074765544
    - 1.5287128513820964
    - 1.602023662022757
    - 1.6036634937825471
    - 1.5339312609414262
    - 1.3975300342279018
    - 1.2033119458492778
    - 0.9637674698586314
    - 0.6942863361406556
    - 0.41223138843960405
    - 0.13587855834865847
    - -0.11671494318218777
    - -0.32884670275391376
    - -0.48624043191583066
    - -0.5779861022695764
    - -0.5972890336873228
    - -0.5419783783463427
    - -0.4147389199925622
    - -0.22304603434447354
    - 0.021198858525012174
    - 0.3023169800463781
    - 0.6017521153901425
    - 0.8991729010387698
    - 1.1737151889393203
    - 1.4052921931657616
    - 1.5758942111873053
    - 1.670798341952516
    - 1.679611990384569
    - 1.5970819687619429
    - 1.4236133169656697
    - 1.1654579383050718
    - 0.8345519242941045
    - 0.44800097050515775
    - 0.027234385841414816
    - -0.40313137517600467
    - -0.816660208875438
    - -1.1866199824344306
    - -1.4875759763773242
    - -1.6969612964539673
    - -1.7965302068339994
    - -1.7736047055813655
    - -1.6220344766370647
    - -1.3428051626894522
    - -0.9442489539760242
    - -0.4418337513718814
    - 0.14246860654244617
    - 0.7812097556610045
    - 1.4428386384749785
    - 2.093350941444674
    - 2.6981253928475426
    - 3.2238450626994157
    - 3.640394399936167
    - 3.922621613772592
    - 4.051861365428068
    - 4.0171244101997186
    positive_zeros:
    - '1.30473186878917396922066338558525'
    - '2.00850567963734584766683280983450'
    - '2.80378494620370130161308447702827'
    - '3.68670878539381830801305511268750'
    - '4.63545890380665990141670986612751'
    - '5.53618566531056577967176687481944'
    - '5.98771079406763610733343708056025'
    - '6.74373972124873346554358089110488'
    - '7.31428750094090372811842113001399'
    prelabel: 2-9702-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 8.801753236773129
    root_angle: 1.0
    root_number: '-1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    spectral_label: c1-0
    trace_hash: 1743366973646870504
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.30473186878917396922066338559'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.00850567963734584766683280983'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.80378494620370130161308447703'
      prec: 103
- - algebraic: true
    analytic_conductor: 77.47086004104627
    bad_primes:
    - 2
    - 3
    - 7
    - 11
    central_character: '1.1'
    conductor: 9702
    conductor_radical: 462
    degree: 2
    dirichlet_coefficients:
    - 1
    - -1
    - 0
    - 1
    - 2
    - 0
    - 0
    - -1
    - 0
    - -2
    - -1
    - 0
    - 2
    - 0
    - 0
    - 1
    - -2
    - 0
    - 0
    - 2
    - 0
    - 1
    - 0
    - 0
    - -1
    - -2
    - 0
    - 0
    - 2
    - 0
    - -4
    - -1
    - 0
    - 2
    - 0
    - 0
    - -2
    - 0
    - 0
    - -2
    - -10
    - 0
    - 4
    - -1
    - 0
    - 0
    - 4
    - 0
    - 0
    - 1
    - 0
    - 2
    - 2
    - 0
    - -2
    - 0
    - 0
    - -2
    - -12
    - 0
    - 2
    - 4
    - 0
    - 1
    - 4
    - 0
    - 12
    - -2
    - 0
    - 0
    - -8
    - 0
    - -6
    - 2
    - 0
    - 0
    - 0
    - 0
    - -8
    - 2
    - 0
    - 10
    - -8
    - 0
    - -4
    - -4
    - 0
    - 1
    - -14
    - 0
    - 0
    - 0
    - 0
    - -4
    - 0
    - 0
    - 14
    - 0
    - 0
    - -1
    euler11:
    - 1
    - 1
    - 0
    euler13:
    - 1
    - -2
    - 13
    euler17:
    - 1
    - 2
    - 17
    euler19:
    - 1
    - 0
    - 19
    euler2:
    - 1
    - 1
    - 0
    euler23:
    - 1
    - 0
    - 23
    euler29:
    - 1
    - -2
    - 29
    euler3:
    - 1
    - 0
    - 0
    euler31:
    - 1
    - 4
    - 31
    euler37:
    - 1
    - 2
    - 37
    euler41:
    - 1
    - 10
    - 41
    euler43:
    - 1
    - -4
    - 43
    euler47:
    - 1
    - -4
    - 47
    euler5:
    - 1
    - -2
    - 5
    euler53:
    - 1
    - -2
    - 53
    euler59:
    - 1
    - 12
    - 59
    euler61:
    - 1
    - -2
    - 61
    euler67:
    - 1
    - -12
    - 67
    euler7:
    - 1
    - 0
    - 0
    euler71:
    - 1
    - 8
    - 71
    euler73:
    - 1
    - 6
    - 73
    euler79:
    - 1
    - 8
    - 79
    euler83:
    - 1
    - 8
    - 83
    euler89:
    - 1
    - 14
    - 89
    euler97:
    - 1
    - -14
    - 97
    euler_factors:
    - - 1
      - 1
      - 0
    - - 1
      - 0
      - 0
    - - 1
      - -2
      - 5
    - - 1
      - 0
      - 0
    - - 1
      - 1
      - 0
    - - 1
      - -2
      - 13
    - - 1
      - 2
      - 17
    - - 1
      - 0
      - 19
    - - 1
      - 0
      - 23
    - - 1
      - -2
      - 29
    - - 1
      - 4
      - 31
    - - 1
      - 2
      - 37
    - - 1
      - 10
      - 41
    - - 1
      - -4
      - 43
    - - 1
      - -4
      - 47
    - - 1
      - -2
      - 53
    - - 1
      - 12
      - 59
    - - 1
      - -2
      - 61
    - - 1
      - -12
      - 67
    - - 1
      - 8
      - 71
    - - 1
      - 6
      - 73
    - - 1
      - 8
      - 79
    - - 1
      - 8
      - 83
    - - 1
      - 14
      - 89
    - - 1
      - -14
      - 97
    id: 22729562
    index: 133
    instance_types:
    - ECQ
    - CMF
    - CMF
    instance_urls:
    - EllipticCurve/Q/9702/r
    - ModularForm/GL2/Q/holomorphic/9702/2/a/r/1/1
    - ModularForm/GL2/Q/holomorphic/9702/2/a/r
    is_instance_Artin: false
    is_instance_BMF: false
    is_instance_CMF: true
    is_instance_DIR: false
    is_instance_ECNF: false
    is_instance_ECQ: true
    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: 2-9702-1.1-c1-0-133
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    order_of_vanishing: 1
    prelabel: 2-9702-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 8.801753236773129
    root_angle: 0.5
    self_dual: true
    spectral_label: c1-0
    trace_hash: 1743366973646870504
    z1:
      __RealLiteral__: 0
      data: '1.30473186878917396922066338559'
      prec: 103
- - Lhash: '1653944136607495829114383744799'
    Lhash_array:
    - '1653944136607495829114383744799'
    id: 22691723
    label: 2-9702-1.1-c1-0-133
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/9702/2/a/r
  - Lhash: '1653944136607495829114383744799'
    Lhash_array:
    - '1653944136607495829114383744799'
    id: 24589772
    label: 2-9702-1.1-c1-0-133
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/9702/2/a/r/1/1
  - Lhash: '1743366973646870504'
    Lhash_array:
    - '1743366973646870504'
    id: 99664
    label: 2-9702-1.1-c1-0-133
    type: ECQ
    url: EllipticCurve/Q/9702/r
label_cols:
- label
- label
- label
labels:
- 2-9702-1.1-c1-0-133
- 2-9702-1.1-c1-0-133
- 2-9702-1.1-c1-0-133
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-16T11:13:07.450795'