data:
- - Lhash: '1090424961078908481949437335412'
    a10:
    - -3.79128784747792
    - 0.0
    a2:
    - 0.0
    - 1.0
    a3:
    - -2.79128784747792
    - 0.0
    a4:
    - -1.0
    - 0.0
    a5:
    - 0.0
    - 3.79128784747792
    a6:
    - 0.0
    - -2.79128784747792
    a7:
    - -2.0
    - 0.0
    a8:
    - 0.0
    - -1.0
    a9:
    - 4.79128784747792
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.5908929749574752
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - -1.0
    - - 37
      - - - 1.0
          - 0
        - - -4.0
          - 4.58257569495584
    bad_primes:
    - 2
    - 37
    central_character: '74.73'
    coefficient_field: CDF
    conductor: 74
    conductor_radical: 74
    conjugate: '4884587312533140388355016419594'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - -1.0
    - - - 1.0
        - 0
      - - 2.79128784747792
        - 0
      - - 3.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -3.79128784747792
      - - -5.0
        - 0
    - - - 1.0
        - 0
      - - 2.0
        - 0
      - - 7.0
        - 0
    - - - 1.0
        - 0
      - - -3.79128784747792
        - 0
      - - 11.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0.79128784747792
      - - -13.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -1.58257569495584
      - - -17.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -7.58257569495584
      - - -19.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0.79128784747792
      - - -23.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -0.79128784747792
      - - -29.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 5.37386354243376
      - - -31.0
        - 0
    - - - 1.0
        - 0
      - - -4.0
        - 4.58257569495584
    - - - 1.0
        - 0
      - - -5.20871215252208
        - 0
      - - 41.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -6.0
      - - -43.0
        - 0
    - - - 1.0
        - 0
      - - -1.58257569495584
        - 0
      - - 47.0
        - 0
    - - - 1.0
        - 0
      - - -7.58257569495584
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -7.58257569495584
      - - -59.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 8.20871215252208
      - - -61.0
        - 0
    - - - 1.0
        - 0
      - - 7.37386354243376
        - 0
      - - 67.0
        - 0
    - - - 1.0
        - 0
      - - -9.16515138991168
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - -9.37386354243376
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 12.79128784747792
      - - -79.0
        - 0
    - - - 1.0
        - 0
      - - 3.16515138991168
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 6.0
      - - -89.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -4.41742430504416
      - - -97.0
        - 0
    - - - 1.0
        - 0
      - - 1.58257569495584
        - 0
      - - 101.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 2.20871215252208
      - - -103.0
        - 0
    - - - 1.0
        - 0
      - - -8.37386354243376
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 6.0
      - - -109.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -19.58257569495584
      - - -113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9593033
    index: 0
    label: 2-74-37.36-c1-0-0
    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/74/2/b/a/73/3
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 0.497557581489229
    - 0.4322219952053279
    - 0.37080991274266845
    - 0.30931241273302507
    - 0.24376587846390296
    - 0.1704455830195038
    - 0.08599685982613212
    - -0.012480140620150936
    - -0.12736478265860923
    - -0.260447065429724
    - -0.41284436117604645
    - -0.5849028303727711
    - -0.7760896454692641
    - -0.9848863796850564
    - -1.2086962129606715
    - -1.4437786725368333
    - -1.6852257940824522
    - -1.9269929273287802
    - -2.1619958467270814
    - -2.382283253234592
    - -2.5792900862494235
    - -2.744172294334402
    - -2.868217928694157
    - -2.943322830917189
    - -2.9625121184371315
    - -2.9204815828900856
    - -2.8141265721998683
    - -2.64302057205439
    - -2.4098022214435497
    - -2.120428560646535
    - -1.784254509728972
    - -1.4139043516842675
    - -1.0249105638259586
    - -0.6351086306109784
    - -0.26379306404343195
    - 0.06934103702805607
    - 0.3454261070012536
    - 0.5477548433301169
    - 0.6631341240615135
    - 0.6831621969166363
    - 0.6053225060122654
    - 0.43378631259210965
    - 0.17982391031635037
    - -0.13825850370893128
    - -0.49571236074873254
    - -0.8624911022290813
    - -1.2049233621015853
    - -1.48784630424283
    - -1.6770833816633255
    - -1.742107415713711
    - -1.6586947387907265
    - -1.4113535821082341
    - -0.9953037305075894
    - -0.41779748228254715
    - 0.30139455276608573
    - 1.130455822647273
    - 2.0270064887793575
    - 2.9405647707734754
    - 3.8158653055319025
    - 4.596824335322211
    - 5.230863362415212
    - 5.67324386521826
    - 5.891033681584844
    - 5.866326819802757
    - 5.598376145039738
    - 5.104372601602408
    - 4.418711557249515
    - 3.5907188378942254
    - 2.680954939902589
    - 1.7563619988219477
    - 0.8846491640856516
    - 0.12841297793590076
    - -0.4604531341966112
    - -0.8455019372195789
    - -1.0091236848845702
    - -0.9541923972293925
    - -0.7037344838489342
    - -0.29858336060531265
    - 0.20680347047374684
    - 0.7499817217914626
    - 1.2670521928666998
    - 1.69940319384692
    - 1.9999258242192746
    - 2.137992500372457
    - 2.1026013502232774
    - 1.9032778914322244
    - 1.5685733380118214
    - 1.1422799047870273
    - 0.6777654735945754
    - 0.23107823326357377
    - -0.14634673813426785
    - -0.4144597476006328
    - -0.5499526490917144
    - -0.5494440153761951
    - -0.4299841987347087
    - -0.22669792290788904
    - 0.01224725899472798
    - 0.23278931373268014
    - 0.38336109739076973
    - 0.423422824849293
    - 0.3309502999880899
    - 0.10775619934299518
    - -0.2182574081006212
    - -0.5944587123428237
    - -0.9485442441447995
    - -1.1968808534951931
    - -1.2552377297675366
    - -1.0506237053139678
    - -0.5327022689957024
    - 0.3167944381195217
    - 1.4780706534563612
    - 2.8917441624233304
    - 4.462316215705185
    - 6.0665170875468215
    - 7.565748514623578
    - 8.821248666149744
    - 9.710162356837948
    - 10.140479559923188
    - 10.062852461427786
    - 9.477623792125819
    - 8.435966905442266
    - 7.034784320345073
    - 5.4058402404418695
    - 3.700400810936072
    - 2.071308850631346
    - 0.6548277915085965
    - -0.44531661606058714
    - -1.1695154011764526
    - -1.5078610311372715
    - -1.4989377503259522
    - -1.221972312642961
    - -0.783458126726586
    - -0.3001859209358243
    - 0.11883122583194067
    - 0.3888534950156079
    - 0.4618476130254631
    - 0.3329581909304042
    - 0.04000494217504851
    - -0.3439421529381473
    - -0.7237762939531669
    - -0.999292375790488
    - -1.0831591121873834
    - -0.9170162784656755
    - -0.4830298127288441
    - 0.1910871769729033
    - 1.034564895850917
    - 1.9433555311534148
    - 2.7957788636121155
    - 3.4716137529903808
    - 3.871582736646624
    - 3.9340290787512724
    - 3.645961460353847
    - 3.0464956858068426
    - 2.2219286468812873
    - 1.2930474176549935
    - 0.3965819910275121
    - -0.33626736863927187
    - -0.8007389287481197
    - -0.9353797315422014
    - -0.7320045990822587
    - -0.23697564647156102
    - 0.4565333158356768
    - 1.2240987456336792
    - 1.930890974214424
    - 2.4543064908531185
    - 2.7045314607244326
    - 2.639477779421411
    - 2.2714603768795354
    - 1.664393908693148
    - 0.9219416771175937
    - 0.168661728288164
    - -0.4725247644038037
    - -0.9025083548195422
    - -1.0637798173438093
    - -0.9505403795448283
    - -0.6091980908827984
    - -0.1290585540395237
    - 0.37516027350401093
    - 0.7857950187867587
    - 1.0054824832684182
    - 0.9767332975406162
    - 0.6939682048154885
    - 0.20548743992829283
    - -0.39529545363405594
    - -0.9879712952754448
    - -1.4493579876752642
    - -1.6792712036152133
    - -1.6227984863566165
    - -1.2844943768813957
    - -0.7312774060235373
    - -0.08285222708160073
    - 0.5091585917821829
    - 0.8899449891289679
    - 0.9329807344290535
    - 0.5683182600328632
    - -0.19791839621159818
    - -1.2770954665738916
    - -2.5066991597960473
    - -3.6733251802965055
    - -4.546611022265837
    - -4.9185072877750144
    - -4.641050891578008
    - -3.6557896870145643
    - -2.009260470851606
    - 0.14875130157029937
    - 2.5844421974058593
    - 5.013851293968144
    - 7.1458046198610425
    - 8.726671198152232
    - 9.57923295291768
    - 9.628949817444573
    - 8.91312362834009
    - 7.571528930149523
    - 5.8204175677462064
    - 3.914788404803406
    - 2.1058758274838443
    - 0.6015554644683574
    - -0.46335013482315734
    - -1.041918100548429
    - -1.1731297305357475
    - -0.9643263437741519
    - -0.5623802390614356
    - -0.11990732352270214
    - 0.23640423829224594
    - 0.4289829203118243
    - 0.439719859749832
    - 0.3059895050145461
    - 0.10400315848195693
    - -0.07610920944406634
    - -0.15734463952734953
    - -0.0984734074618704
    - 0.0931697971529281
    - 0.3619052328641985
    - 0.6170601675603384
    - 0.756472873792993
    - 0.6946865944806866
    - 0.38908109729878604
    - -0.14259063669669794
    - -0.8180691370451563
    - -1.501779123699368
    - -2.0298210136830988
    - -2.243992105833913
    - -2.02774728673922
    - -1.3361724142298328
    - -0.21293450030740357
    - 1.2103358477970063
    - 2.733167485750598
    - 4.120841365990931
    - 5.147933253315682
    - 5.6420746485840505
    - 5.518789897475662
    - 4.799815307269361
    - 3.6105453042133933
    - 2.156536251419404
    - 0.6834358124905046
    - -0.5716619384795603
    - -1.4274190984238824
    positive_zeros:
    - '0.860193621872294310796872716452911'
    - '4.34737798094927207572296928874737'
    - '5.32315482422903812575679653539712'
    - '6.70025664105353145292165270197554'
    - '8.899194145903140863029741060291120'
    - '9.700846868135914281300537808868306'
    - '11.19778113783628699812117761310847'
    - '11.99360225742833307502145749866160'
    - '12.66999285057884744547093174535970'
    - '13.58372145412640746794111169644029'
    prelabel: 2-74-37.36-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.7686956321961738
    root_angle: -0.7715734282458674
    root_number: -0.7533708035008841 - 0.657595949221429*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.385786714123'
      prec: 50
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.860193621872294310796872716453'
      prec: 107
    z2:
      __RealLiteral__: 0
      data: '4.34737798094927207572296928875'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '5.32315482422903812575679653540'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.5908929749574752
    bad_primes:
    - 2
    - 37
    central_character: '37.36'
    conductor: 74
    conductor_radical: 74
    degree: 2
    id: 9593033
    index: 0
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/74/2/b/a/73/3
    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: 2-74-37.36-c1-0-0
    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: 2-74-37.36-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.7686956321961738
    root_angle: -0.3857867141229337
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '0.860193621872294310796872716453'
      prec: 107
- - Lhash: '1090424961078908481949437335412'
    Lhash_array:
    - '1090424961078908481949437335412'
    id: 9959062
    label: 2-74-37.36-c1-0-0
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/74/2/b/a/73/3
label_cols:
- label
- label
- label
labels:
- 2-74-37.36-c1-0-0
- 2-74-37.36-c1-0-0
- 2-74-37.36-c1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-20T04:25:29.151006'