data:
- - Lhash: '2282175801263388020087686324566'
    a10:
    - 0.0
    - 0.0
    a2:
    - 0.5
    - -0.8660254037844386
    a3:
    - 0.0
    - 0.0
    a4:
    - -0.5
    - -0.8660254037844386
    a5:
    - 0.0
    - 0.0
    a6:
    - 0.0
    - 0.0
    a7:
    - 0.0
    - 0.0
    a8:
    - -1.0
    - 3.9689140359382235e-80
    a9:
    - 0.0
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.6827209372819473
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - -0.5
          - 0.8660254037844386
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 19
      - - - 1.0
          - 0
        - - 0.5
          - 0.8660254037844386
    bad_primes:
    - 2
    - 3
    - 19
    central_character: '1368.163'
    coefficient_field: CDF
    conductor: 1368
    conductor_radical: 114
    conjugate: '1338821290854864655340449902504'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - -1.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - -1.0
        - 1.7320508075688772
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - 0.5
        - -0.8660254037844386
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 1.0
        - -1.7320508075688772
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0.5
        - -0.8660254037844386
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - -0.5
        - -0.8660254037844386
      - - -0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - -0.5
        - 0.8660254037844386
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - -1.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - -1.0
        - -1.7320508075688772
      - - -0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - -0.5
        - 0.8660254037844386
      - - -0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - 2.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - -1.0
        - 0
      - - 1.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 19447340
    index: 0
    label: 2-1368-152.11-c0-0-0
    leading_term: '1.3233596428529643534872604903788'
    load_key: CMFs-workshop
    motivic_weight: 0
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 0
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/1368/1/bz/a/163/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 1.3233596428529644
    - 1.3865009424403163
    - 1.4655955448413998
    - 1.5609692076870914
    - 1.6718732140519288
    - 1.796665005655881
    - 1.9330257761902436
    - 2.0781561729697025
    - 2.2289238054452176
    - 2.3819622061046193
    - 2.5337336001620274
    - 2.6805704107454416
    - 2.8187080429853566
    - 2.944317771674468
    - 3.053545180867811
    - 3.1425570411861288
    - 3.207597708850693
    - 3.24505489192824
    - 3.2515337660516814
    - 3.223937797929266
    - 3.1595541645249527
    - 3.0561412906587555
    - 2.9120157446156827
    - 2.7261355222753534
    - 2.498176616368505
    - 2.2285997145427343
    - 1.9187039056934814
    - 1.570664406176945
    - 1.1875515523496925
    - 0.7733286472141444
    - 0.33282669739977966
    - -0.12830537093364286
    - -0.6036757798665839
    - -1.0862502803937037
    - -1.568477073750016
    - -2.042434652349538
    - -2.500000068036555
    - -2.9330342699280743
    - -3.333580325573618
    - -3.6940695802794346
    - -4.007530153699238
    - -4.267791653040304
    - -4.469679629363042
    - -4.60919314496687
    - -4.6836588784455255
    - -4.6918554861699775
    - -4.634102473796685
    - -4.512308609490699
    - -4.329975923178816
    - -4.092156564778682
    - -3.805361210501123
    - -3.4774192718137327
    - -3.117292829292225
    - -2.7348479282998515
    - -2.3405885738323864
    - -1.9453603822060985
    - -1.5600323197862505
    - -1.1951662164890595
    - -0.8606847205934868
    - -0.5655490040585969
    - -0.3174577858748218
    - -0.12257907877135392
    - 0.014674539929694074
    - 0.09181738470729026
    - 0.1084005841025091
    - 0.06605409834263355
    - -0.03154329387260844
    - -0.17876763621863886
    - -0.3682259303382028
    - -0.5910008021942736
    - -0.8369569123589643
    - -1.095099625299739
    - -1.3539739980367935
    - -1.6020900531875715
    - -1.8283586732252675
    - -2.022521386245874
    - -2.1755568847332767
    - -2.280047380793152
    - -2.3304888802684642
    - -2.323531150423556
    - -2.2581355263013116
    - -2.135641682240318
    - -1.959737989234623
    - -1.7363339592192846
    - -1.4733373929107771
    - -1.1803430284218608
    - -0.8682435510190395
    - -0.5487775828945435
    - -0.23403254215235406
    - 0.06407712874996278
    - 0.3343340630734579
    - 0.5667212243851741
    - 0.7528812833012217
    - 0.8865102802142301
    - 0.9636659822798513
    - 0.9829745797455403
    - 0.9457234902612468
    - 0.8558328970757557
    - 0.7197040422717845
    - 0.5459479981362546
    - 0.34500439081806755
    - 0.12866507784088344
    - -0.09047719059744455
    - -0.299630831989849
    - -0.4864306585044244
    - -0.6395566620498464
    - -0.7493160557394961
    - -0.8081590308547744
    - -0.8111009291289308
    - -0.7560272044595687
    - -0.6438625358414242
    - -0.47859156268581043
    - -0.2671256875536203
    - -0.019017916686387356
    - 0.253964570087888
    - 0.5383928937916241
    - 0.8198298113003788
    - 1.0835537263125572
    - 1.3153184956014021
    - 1.5021110556132624
    - 1.6328676302501057
    - 1.699109990475941
    - 1.6954659683668314
    - 1.6200431274517324
    - 1.4746309974859713
    - 1.2647153330145304
    - 0.9992970959638664
    - 0.6905188589434
    - 0.3531115841688819
    - 0.0036847228433296445
    - -0.34010823850683525
    - -0.6604888063272744
    - -0.9405110566421291
    - -1.1650078891438733
    - -1.3214747463785472
    - -1.4008409259069086
    - -1.3980826783389924
    - -1.3126389721892517
    - -1.1485998700040343
    - -0.9146485123929622
    - -0.6237502360486208
    - -0.29259574463333626
    - 0.05918118015037479
    - 0.4099779231979696
    - 0.7373439960180243
    - 1.0191937068563655
    - 1.2350483549534672
    - 1.3672416645270289
    - 1.4020215086014218
    - 1.3304839178405337
    - 1.14928191213429
    - 0.8610616218666333
    - 0.47459107569521114
    - 0.004562335706527067
    - -0.528935383493104
    - -1.101256231510475
    - -1.6843189047591025
    - -2.2479590602004307
    - -2.7614491329193895
    - -3.1951102792992203
    - -3.521933398506928
    - -3.719122662125782
    - -3.7694760549835014
    - -3.6625232070648157
    - -3.395351126669378
    - -2.973062919382043
    - -2.4088325408527234
    - -1.723539210704053
    - -0.9449872602127851
    - -0.10673972403392142
    - 0.7533843193970139
    - 1.5950790326057491
    - 2.377501707681289
    - 3.0613050782975018
    - 3.6106467546209413
    - 3.9950689436481976
    - 4.191145909348978
    - 4.183806671028461
    - 3.96725583009024
    - 3.545435435512038
    - 2.931994444316536
    - 2.1497583686789383
    - 1.2297187201111988
    - 0.20958836428742278
    - -0.8680066206112759
    - -1.9576069635960693
    - -3.0131641749026077
    - -3.9903299906560865
    - -4.848668707127413
    - -5.553672548750934
    - -6.07846973426211
    - -6.405130797556916
    - -6.525500181359109
    - -6.441506008301219
    - -6.164929819885375
    - -5.716648330092979
    - -5.125389127501049
    - -4.426070028599808
    - -3.6578157815571943
    - -2.8617645860175194
    - -2.0787892603967584
    - -1.3472630471058096
    - -0.7009976112413849
    - -0.16747082330969112
    - 0.2335550597130023
    - 0.49094723800543505
    - 0.6025984276616737
    - 0.5752861861084628
    - 0.4240086641773098
    - 0.17084135531761274
    - -0.15661180063691085
    - -0.5270752241369885
    - -0.9076502422122495
    - -1.2659278891311
    - -1.5720350304987214
    - -1.8004875650598187
    - -1.93173702786887
    - -1.9533166253072516
    - -1.8605183704666557
    - -1.656562961904539
    - -1.3522564733520466
    - -0.965160736086927
    - -0.5183353952699223
    - -0.03873699445923225
    - 0.44461769962670433
    - 0.9026020226324403
    - 1.3079143456877944
    - 1.6368700951786563
    - 1.8709332541916837
    - 1.9978874359223755
    - 2.012570958666754
    - 1.917129749000887
    - 1.7207744170206474
    - 1.4390613220012882
    - 1.0927496321183319
    - 0.7063150983113895
    - 0.30622454508693947
    - -0.08090868435966964
    - -0.43016005474335683
    - -0.7199924256085617
    - -0.933699953180662
    - -1.0604971307493425
    - -1.0961775912778393
    - -1.043297457144496
    - -0.910871484969103
    - -0.7136047072969254
    - -0.470715311908342
    - -0.20443378994745548
    - 0.06171317182249889
    - 0.30470969286604654
    - 0.503817103318737
    - 0.6421704813002199
    - 0.7080875660974866
    - 0.6959923722743327
    - 0.6068831394414399
    - 0.44830691358744845
    - 0.23383878313731538
    positive_zeros:
    - '1.80031926845812421099671004846548'
    - '3.62509479241877635208500933009886'
    - '3.85134957783059151022850704897856'
    - '5.20185141778349170490553110825190'
    - '5.95224180534742166519737696206469'
    - '6.62532180372079981880622406667131'
    - '7.55921138106756165977651633891519'
    - '8.310543646827297557422856591370167'
    - '8.965372255574945273045409780896195'
    - '9.909641356401712306348470799423325'
    prelabel: 2-1368-152.11-c0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.82626928859903
    root_angle: 0.5989133786043899
    root_number: -0.30576855776155245201166452061865 + 0.95210587073309245599954997573793*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.29945668930219493'
      prec: 64
    spectral_label: c0-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.80031926845812421099671004847'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '3.62509479241877635208500933010'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.85134957783059151022850704898'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.6827209372819473
    bad_primes:
    - 2
    - 3
    - 19
    central_character: '152.11'
    conductor: 1368
    conductor_radical: 114
    degree: 2
    id: 19447340
    index: 0
    instance_types:
    - CMF
    - Artin
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1368/1/bz/a/163/1
    - ArtinRepresentation/2.1368.12t18.b.b
    is_instance_Artin: true
    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: 2-1368-152.11-c0-0-0
    motivic_weight: 0
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 0
    order_of_vanishing: 0
    prelabel: 2-1368-152.11-c0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.82626928859903
    root_angle: 0.29945668930219493
    self_dual: false
    spectral_label: c0-0
    z1:
      __RealLiteral__: 0
      data: '1.80031926845812421099671004847'
      prec: 103
- - Lhash: '2282175801263388020087686324566'
    Lhash_array:
    - '2282175801263388020087686324566'
    id: 24604567
    label: 2-1368-152.11-c0-0-0
    type: Artin
    url: ArtinRepresentation/2.1368.12t18.b.b
  - Lhash: '2282175801263388020087686324566'
    Lhash_array:
    - '2282175801263388020087686324566'
    id: 19813494
    label: 2-1368-152.11-c0-0-0
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1368/1/bz/a/163/1
label_cols:
- label
- label
- label
labels:
- 2-1368-152.11-c0-0-0
- 2-1368-152.11-c0-0-0
- 2-1368-152.11-c0-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-20T04:25:08.045277'