data:
- - Lhash: '840447942743256939779438506475'
    a10: 0
    a2: 1
    a3: 0
    a4: -1
    a5: 0
    a6: 0
    a7: -4
    a8: -3
    a9: 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 19.762974500266903
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - 1
    - - 5
      - - 1
    - - 11
      - - 1
        - 1
    bad_primes:
    - 3
    - 5
    - 11
    central_character: '2475.1'
    coefficient_field: 1.1.1.1
    conductor: 2475
    conductor_radical: 165
    degree: 2
    euler_factors:
    - - 1
      - -1
      - 2
    - - 1
    - - 1
    - - 1
      - 4
      - 7
    - - 1
      - 1
    - - 1
      - -2
      - 13
    - - 1
      - 2
      - 17
    - - 1
      - 0
      - 19
    - - 1
      - -8
      - 23
    - - 1
      - -6
      - 29
    - - 1
      - 8
      - 31
    - - 1
      - 6
      - 37
    - - 1
      - -2
      - 41
    - - 1
      - 0
      - 43
    - - 1
      - -8
      - 47
    - - 1
      - -6
      - 53
    - - 1
      - -4
      - 59
    - - 1
      - -6
      - 61
    - - 1
      - -4
      - 67
    - - 1
      - 0
      - 71
    - - 1
      - -14
      - 73
    - - 1
      - 4
      - 79
    - - 1
      - -12
      - 83
    - - 1
      - -6
      - 89
    - - 1
      - 2
      - 97
    - - 1
      - 2
      - 101
    - - 1
      - 8
      - 103
    - - 1
      - 12
      - 107
    - - 1
      - 2
      - 109
    - - 1
      - 6
      - 113
    euler_factors_factorization:
    - - - - 1
          - -1
          - 2
        - 1
    - - 1
    - - 1
    - - - - 1
          - 4
          - 7
        - 1
    - - - - 1
          - 1
        - 1
    - - - - 1
          - -2
          - 13
        - 1
    - - - - 1
          - 2
          - 17
        - 1
    - - - - 1
          - 0
          - 19
        - 1
    - - - - 1
          - -8
          - 23
        - 1
    - - - - 1
          - -6
          - 29
        - 1
    - - - - 1
          - 8
          - 31
        - 1
    - - - - 1
          - 6
          - 37
        - 1
    - - - - 1
          - -2
          - 41
        - 1
    - - - - 1
          - 0
          - 43
        - 1
    - - - - 1
          - -8
          - 47
        - 1
    - - - - 1
          - -6
          - 53
        - 1
    - - - - 1
          - -4
          - 59
        - 1
    - - - - 1
          - -6
          - 61
        - 1
    - - - - 1
          - -4
          - 67
        - 1
    - - - - 1
          - 0
          - 71
        - 1
    - - - - 1
          - -14
          - 73
        - 1
    - - - - 1
          - 4
          - 79
        - 1
    - - - - 1
          - -12
          - 83
        - 1
    - - - - 1
          - -6
          - 89
        - 1
    - - - - 1
          - 2
          - 97
        - 1
    - - - - 1
          - 2
          - 101
        - 1
    - - - - 1
          - 8
          - 103
        - 1
    - - - - 1
          - 12
          - 107
        - 1
    - - - - 1
          - 2
          - 109
        - 1
    - - - - 1
          - 6
          - 113
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 20375116
    index: 10
    label: 2-2475-1.1-c1-0-10
    leading_term: '1.417322571321434123683904092086300000000000000000000000000000000000000000000000000000000000'
    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/2475/2/a/g
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 1.4173225713214341
    - 1.4071979445421392
    - 1.3766824930962573
    - 1.3253662473630903
    - 1.2526138994922569
    - 1.1576328462753018
    - 1.03956120240178
    - 0.8975697543958862
    - 0.7309714848037671
    - 0.53933251480889
    - 0.32257890153353136
    - 0.08109448775422996
    - -0.1841942176363012
    - -0.4717494417996974
    - -0.7793725412142515
    - -1.1041755795658361
    - -1.4425758208906458
    - -1.790314412322351
    - -2.142500040416495
    - -2.4936777910973658
    - -2.8379228102936263
    - -3.1689576487400934
    - -3.4802913912139446
    - -3.765377839177188
    - -4.017789166312022
    - -4.231400634862853
    - -4.4005811872380365
    - -4.520384054212339
    - -4.5867309905303975
    - -4.596583400897048
    - -4.5480934902870915
    - -4.440728692116808
    - -4.275363017940787
    - -4.054329645017765
    - -3.7814300140816215
    - -3.4618959372771148
    - -3.1023026906559674
    - -2.710432748743001
    - -2.2950916594331594
    - -1.865879492966227
    - -1.432923255883937
    - -1.006577558825725
    - -0.5971025800171867
    - -0.21432988720103288
    - 0.13267211511926605
    - 0.4359205369682372
    - 0.6888152293394482
    - 0.8863981295184118
    - 1.0255626840017382
    - 1.1052025821484333
    - 1.1262908546535009
    - 1.0918827195170804
    - 1.0070383290754863
    - 0.8786646939613113
    - 0.715279419234313
    - 0.5267023500955602
    - 0.32368464011384307
    - 0.11748796506262264
    - -0.08057055075329989
    - -0.2595898072029928
    - -0.40955305474270387
    - -0.5217726584947843
    - -0.5892908919552113
    - -0.6072172960929426
    - -0.5729850352326081
    - -0.4865114996831909
    - -0.3502520708704937
    - -0.1691403555100258
    - 0.04958685493597127
    - 0.29667633935502363
    - 0.5612479341902751
    - 0.8312724869457396
    - 1.0941191329073767
    - 1.3371485449837557
    - 1.5483255172810106
    - 1.7168220883880745
    - 1.8335815635151154
    - 1.8918143730928672
    - 1.8873987612211691
    - 1.819162809945541
    - 1.6890291780055446
    - 1.5020099925573798
    - 1.266046334544777
    - 0.9916943942710449
    - 0.6916682832318999
    - 0.38025727569441475
    - 0.07264250633691317
    - -0.21585553984178496
    - -0.47056242420441785
    - -0.6782283902007155
    - -0.8277591868459758
    - -0.9108587238122146
    - -0.9225460694764369
    - -0.8615143035968063
    - -0.730305712454786
    - -0.5352864934474291
    - -0.28641413768332474
    - 0.0031984904614449114
    - 0.31790720451699284
    - 0.6403226413405415
    - 0.9522224974915099
    - 1.2355453751292331
    - 1.4734153070539582
    - 1.651142067420802
    - 1.7571412399815964
    - 1.7837199123590417
    - 1.7276788370058522
    - 1.5906898214565681
    - 1.3794176846157757
    - 1.105368880240526
    - 0.7844632347933453
    - 0.4363404459391342
    - 0.08342822706123293
    - -0.25018659322292003
    - -0.5400299505309166
    - -0.7625910442115275
    - -0.8966799644046796
    - -0.9247175280466092
    - -0.8338830478588759
    - -0.61705061469808
    - -0.27345345293103135
    - 0.1909713217312182
    - 0.7635892186879057
    - 1.4254394004974027
    - 2.1519635296050748
    - 2.914065403312315
    - 3.6794547560949478
    - 4.414210925510412
    - 5.084487401105595
    - 5.658267573616733
    - 6.107076050077476
    - 6.407549227533335
    - 6.542773662654246
    - 6.503311059225843
    - 6.287844017969523
    - 5.903396336708089
    - 5.36510461255145
    - 4.695542944819532
    - 3.9236282605057333
    - 3.0831586834848155
    - 2.2110599394617116
    - 1.345433611878133
    - 0.5235148962682485
    - -0.22034464341488724
    - -0.856552590520927
    - -1.361898425545632
    - -1.7208249363869006
    - -1.9262684034535393
    - -1.9800116352135173
    - -1.8925218590451396
    - -1.6822757794507637
    - -1.374605014281182
    - -1.0001247313946753
    - -0.5928347774791617
    - -0.18800420140372848
    - 0.1800346380311656
    - 0.4800483381879151
    - 0.6858873136050305
    - 0.7781680396884036
    - 0.7455440092947421
    - 0.5854804102757859
    - 0.3044770305828029
    - -0.08228250266499475
    - -0.5518413687492474
    - -1.074890763787624
    - -1.6176192152607212
    - -2.1438789616341034
    - -2.617536270191222
    - -3.004858526940087
    - -3.2767860196430063
    - -3.4109410628416073
    - -3.393241384215952
    - -3.2190077848045004
    - -2.893486690641652
    - -2.431744499295217
    - -1.8579303479043705
    - -1.2039445708375207
    - -0.5075890408475036
    - 0.18968978022581154
    - 0.8453262655597306
    - 1.4182713180743984
    - 1.8715707724488615
    - 2.174720402041618
    - 2.305643795245563
    - 2.2521619985842847
    - 2.0128553839226706
    - 1.5972567231344608
    - 1.0253574811080184
    - 0.3264540567933696
    - -0.46259585985880614
    - -1.2995974238381443
    - -2.1395815589362894
    - -2.9375418268836277
    - -3.651168111701868
    - -4.243399508040833
    - -4.684630286275022
    - -4.954425593426479
    - -5.042636184990152
    - -4.949841814418476
    - -4.6870982181000045
    - -4.275009827257221
    - -3.7421961488095112
    - -3.123260978803265
    - -2.4564073258066235
    - -1.7808647081138897
    - -1.134307607066327
    - -0.5504433819234811
    - -0.05693484361867581
    - 0.3262021838855099
    - 0.5876208880324539
    - 0.7250221169507707
    - 0.7448736785740016
    - 0.6615024186349295
    - 0.4956369120753828
    - 0.27251853541990984
    - 0.019729867845057154
    - -0.2350905645037051
    - -0.46647078970291017
    - -0.6530946246700509
    - -0.7794059609783989
    - -0.8367068374760642
    - -0.8236678080803895
    - -0.7462152731831829
    - -0.6168095024667387
    - -0.4531752847035833
    - -0.2765907646743781
    - -0.10987564220618377
    - 0.024755340004475976
    - 0.10779585627720271
    - 0.12433279809456475
    - 0.06555296064903311
    - -0.07025877474405251
    - -0.27732029479184345
    - -0.5425950203465967
    - -0.8466676631313823
    - -1.1651921635831026
    - -1.4708031487614244
    - -1.7353423187893633
    - -1.9322224915372752
    - -2.0387371111746724
    - -2.0381233172725914
    - -1.9212024579314062
    - -1.6874522661611133
    - -1.345407677695577
    - -0.9123392885588975
    - -0.41321576181930497
    - 0.12098538583179953
    - 0.6554999022956703
    - 1.1543671051861828
    - 1.5831898214349716
    - 1.9118467447996172
    - 2.1169383590858666
    - 2.183763505892999
    - 2.107656316298658
    - 1.8945603587693758
    - 1.56077504733766
    - 1.131874200532507
    positive_zeros:
    - '0.66299652490358276934219865410970'
    - '2.55490898649220854449117581352943'
    - '3.37409785551698507568515532804691'
    - '3.97182275742999473711448669059943'
    - '5.05334108529123054060716186456578'
    - '5.68297890149735059120081895573775'
    - '6.57667809882336453792833363635474'
    - '7.06746602683221101194508851953892'
    - '8.360742840269281397590237858671264'
    - '9.052312079360069985753137252747289'
    prelabel: 2-2475-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 4.445556714323517
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1-0
    trace_hash: 2156057543737001656
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.66299652490358276934219865411'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.55490898649220854449117581353'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.37409785551698507568515532805'
      prec: 103
- - algebraic: true
    analytic_conductor: 19.762974500266903
    bad_primes:
    - 3
    - 5
    - 11
    central_character: '1.1'
    conductor: 2475
    conductor_radical: 165
    degree: 2
    dirichlet_coefficients:
    - 1
    - 1
    - 0
    - -1
    - 0
    - 0
    - -4
    - -3
    - 0
    - 0
    - -1
    - 0
    - 2
    - -4
    - 0
    - -1
    - -2
    - 0
    - 0
    - 0
    - 0
    - -1
    - 8
    - 0
    - 0
    - 2
    - 0
    - 4
    - 6
    - 0
    - -8
    - 5
    - 0
    - -2
    - 0
    - 0
    - -6
    - 0
    - 0
    - 0
    - 2
    - 0
    - 0
    - 1
    - 0
    - 8
    - 8
    - 0
    - 9
    - 0
    - 0
    - -2
    - 6
    - 0
    - 0
    - 12
    - 0
    - 6
    - 4
    - 0
    - 6
    - -8
    - 0
    - 7
    - 0
    - 0
    - 4
    - 2
    - 0
    - 0
    - 0
    - 0
    - 14
    - -6
    - 0
    - 0
    - 4
    - 0
    - -4
    - 0
    - 0
    - 2
    - 12
    - 0
    - 0
    - 0
    - 0
    - 3
    - 6
    - 0
    - -8
    - -8
    - 0
    - 8
    - 0
    - 0
    - -2
    - 9
    - 0
    - 0
    euler11:
    - 1
    - 1
    - 0
    euler13:
    - 1
    - -2
    - 13
    euler17:
    - 1
    - 2
    - 17
    euler19:
    - 1
    - 0
    - 19
    euler2:
    - 1
    - -1
    - 2
    euler23:
    - 1
    - -8
    - 23
    euler29:
    - 1
    - -6
    - 29
    euler3:
    - 1
    - 0
    - 0
    euler31:
    - 1
    - 8
    - 31
    euler37:
    - 1
    - 6
    - 37
    euler41:
    - 1
    - -2
    - 41
    euler43:
    - 1
    - 0
    - 43
    euler47:
    - 1
    - -8
    - 47
    euler5:
    - 1
    - 0
    - 0
    euler53:
    - 1
    - -6
    - 53
    euler59:
    - 1
    - -4
    - 59
    euler61:
    - 1
    - -6
    - 61
    euler67:
    - 1
    - -4
    - 67
    euler7:
    - 1
    - 4
    - 7
    euler71:
    - 1
    - 0
    - 71
    euler73:
    - 1
    - -14
    - 73
    euler79:
    - 1
    - 4
    - 79
    euler83:
    - 1
    - -12
    - 83
    euler89:
    - 1
    - -6
    - 89
    euler97:
    - 1
    - 2
    - 97
    euler_factors:
    - - 1
      - -1
      - 2
    - - 1
      - 0
      - 0
    - - 1
      - 0
      - 0
    - - 1
      - 4
      - 7
    - - 1
      - 1
      - 0
    - - 1
      - -2
      - 13
    - - 1
      - 2
      - 17
    - - 1
      - 0
      - 19
    - - 1
      - -8
      - 23
    - - 1
      - -6
      - 29
    - - 1
      - 8
      - 31
    - - 1
      - 6
      - 37
    - - 1
      - -2
      - 41
    - - 1
      - 0
      - 43
    - - 1
      - -8
      - 47
    - - 1
      - -6
      - 53
    - - 1
      - -4
      - 59
    - - 1
      - -6
      - 61
    - - 1
      - -4
      - 67
    - - 1
      - 0
      - 71
    - - 1
      - -14
      - 73
    - - 1
      - 4
      - 79
    - - 1
      - -12
      - 83
    - - 1
      - -6
      - 89
    - - 1
      - 2
      - 97
    id: 20375116
    index: 10
    instance_types:
    - ECQ
    - CMF
    - CMF
    instance_urls:
    - EllipticCurve/Q/2475/g
    - ModularForm/GL2/Q/holomorphic/2475/2/a/g/1/1
    - ModularForm/GL2/Q/holomorphic/2475/2/a/g
    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: 2-2475-1.1-c1-0-10
    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: 2-2475-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 4.445556714323517
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    trace_hash: 2156057543737001656
    z1:
      __RealLiteral__: 0
      data: '0.66299652490358276934219865411'
      prec: 103
- - Lhash: '840447942743256939779438506475'
    Lhash_array:
    - '840447942743256939779438506475'
    id: 20667337
    label: 2-2475-1.1-c1-0-10
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/2475/2/a/g
  - Lhash: '840447942743256939779438506475'
    Lhash_array:
    - '840447942743256939779438506475'
    id: 24557386
    label: 2-2475-1.1-c1-0-10
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/2475/2/a/g/1/1
  - Lhash: '2156057543737001656'
    Lhash_array:
    - '2156057543737001656'
    id: 36967
    label: 2-2475-1.1-c1-0-10
    type: ECQ
    url: EllipticCurve/Q/2475/g
label_cols:
- label
- label
- label
labels:
- 2-2475-1.1-c1-0-10
- 2-2475-1.1-c1-0-10
- 2-2475-1.1-c1-0-10
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T16:36:50.379805'