data:
- - Lhash: '2163866576673420416677444499077'
    a10:
    - 0
    - 0
    a2:
    - 0
    - 0
    a3:
    - 1.5
    - -0.8660254037844386
    a4:
    - 0
    - 0
    a5:
    - 0
    - 0
    a6:
    - 0
    - 0
    a7:
    - 0
    - 0
    a8:
    - 0
    - 0
    a9:
    - 1.5
    - -2.598076211353316
    accuracy: 100
    algebraic: true
    analytic_conductor: 9.58204824255365
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 3
      - - - 1.0
          - 0
        - - -1.5
          - 0.8660254037844386
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 2
    - 3
    - 5
    central_character: '1200.1151'
    coefficient_field: CDF
    conductor: 1200
    conductor_radical: 30
    conjugate: '936519242405329771635258668442'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -1.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -7.0
        - 0
    - - - 1.0
        - 0
      - - 3.0
        - 0
      - - 11.0
        - 0
    - - - 1.0
        - 0
      - - 2.0
        - 0
      - - 13.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 5.196152422706632
      - - -17.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 5.196152422706632
      - - -19.0
        - 0
    - - - 1.0
        - 0
      - - -6.0
        - 0
      - - 23.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 10.392304845413264
      - - -29.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -3.4641016151377544
      - - -31.0
        - 0
    - - - 1.0
        - 0
      - - -8.0
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 5.196152422706632
      - - -41.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -3.4641016151377544
      - - -43.0
        - 0
    - - - 1.0
        - 0
      - - 6.0
        - 0
      - - 47.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -10.392304845413264
      - - -53.0
        - 0
    - - - 1.0
        - 0
      - - 12.0
        - 0
      - - 59.0
        - 0
    - - - 1.0
        - 0
      - - -8.0
        - 0
      - - 61.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -12.12435565298214
      - - -67.0
        - 0
    - - - 1.0
        - 0
      - - -6.0
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - -1.0
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 6.928203230275509
      - - -79.0
        - 0
    - - - 1.0
        - 0
      - - 9.0
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 5.196152422706632
      - - -89.0
        - 0
    - - - 1.0
        - 0
      - - -10.0
        - 0
      - - 97.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -101.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -17.320508075688775
      - - -103.0
        - 0
    - - - 1.0
        - 0
      - - -3.0
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 8.0
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -5.196152422706632
      - - -113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23142339
    index: 31
    label: 2-1200-12.11-c1-0-31
    leading_term: '1.9211452752196666901639490553569277784630733049432714746'
    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/1200/2/h/h/1151/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 1.9211452752196667
    - 2.033293050252732
    - 2.141468382826073
    - 2.2455517739118136
    - 2.3451360312291314
    - 2.4395168393306252
    - 2.527699684285048
    - 2.6084218865216564
    - 2.6801877632368623
    - 2.7413145718271026
    - 2.7899868260743106
    - 2.824316727698699
    - 2.842408707986678
    - 2.8424263360833444
    - 2.822660062191137
    - 2.7815943976766078
    - 2.717973188178485
    - 2.6308616253201054
    - 2.5197035911813783
    - 2.3843728632462815
    - 2.2252166505447617
    - 2.043089905037631
    - 1.8393788725074316
    - 1.6160124264588345
    - 1.3754598747416884
    - 1.1207141458293546
    - 0.8552595503249674
    - 0.5830236703226779
    - 0.3083133484654972
    - 0.03573522056673188
    - -0.2298982517736928
    - -0.48367575399310564
    - -0.7207050559269615
    - -0.9362393376213679
    - -1.1258088243380464
    - -1.2853542020582331
    - -1.4113579109948036
    - -1.5009691377255063
    - -1.5521181663290946
    - -1.5636157227016352
    - -1.5352330681011193
    - -1.467758877773144
    - -1.363029383111432
    - -1.2239288603787175
    - -1.054358308505703
    - -0.8591710592807867
    - -0.6440750850441743
    - -0.41550288497711985
    - -0.18045100829504568
    - 0.053707527210672665
    - 0.27943348248417044
    - 0.4892487567922779
    - 0.6759743041461905
    - 0.8329712093096611
    - 0.954376889426569
    - 1.0353279965860371
    - 1.0721614867166294
    - 1.0625855177608245
    - 1.0058123619455417
    - 0.9026463685280496
    - 0.755521187422719
    - 0.5684819399521098
    - 0.347109766262021
    - 0.09838814190068289
    - -0.16948752169245077
    - -0.4473532680183268
    - -0.7253670356711934
    - -0.9933380684078038
    - -1.2410852485173822
    - -1.4588126000681934
    - -1.63748884845195
    - -1.7692169875175079
    - -1.8475793620676195
    - -1.8679438726869582
    - -1.8277175840641071
    - -1.7265352778729497
    - -1.5663723239758902
    - -1.3515736114983048
    - -1.0887931215332514
    - -0.7868419491464653
    - -0.4564460852223087
    - -0.10991892091298602
    - 0.23924290323297231
    - 0.5768281667211267
    - 0.88842890564222
    - 1.159989302184914
    - 1.3783653449570124
    - 1.531873529997946
    - 1.6108062467743889
    - 1.6078917630466678
    - 1.5186779256330718
    - 1.341820830797036
    - 1.0792627475299734
    - 0.7362874172845023
    - 0.32144538236591097
    - -0.15365294732208562
    - -0.6746733848941554
    - -1.2250145956662144
    - -1.7863712459224692
    - -2.3393846081078107
    - -2.8643571096404754
    - -3.3420036817169327
    - -3.7542101514799593
    - -4.084767488916067
    - -4.320050586727779
    - -4.44961148191607
    - -4.466659527657532
    - -4.3684049366884565
    - -4.15624722331998
    - -3.835796190377045
    - -3.4167200046141546
    - -2.9124222975374807
    - -2.3395578002879454
    - -1.7174034310750597
    - -1.0671086539909045
    - -0.4108549801442434
    - 0.22904062728613314
    - 0.8310402247470294
    - 1.3752772073367474
    - 1.8443864282975528
    - 2.2242339124074526
    - 2.504511633221829
    - 2.679168225956999
    - 2.746653436248672
    - 2.7099622795075247
    - 2.576473954124287
    - 2.357590105317181
    - 2.0681866268733695
    - 1.7259023490086254
    - 1.3502962299451962
    - 0.9619116121661709
    - 0.5812913379305855
    - 0.22799073094804476
    - -0.08036357866952715
    - -0.3289223961391252
    - -0.5063274244043791
    - -0.6052525818442044
    - -0.6227442886127579
    - -0.5603414625624121
    - -0.4239667967698063
    - -0.22359240282381712
    - 0.02730547751809059
    - 0.3124768638915576
    - 0.6137776630412702
    - 0.912154258717206
    - 1.1886825205297389
    - 1.4256069259512696
    - 1.6073245116048889
    - 1.7212603026502538
    - 1.7585856891303255
    - 1.7147387466902801
    - 1.5897154059094423
    - 1.3881121906921847
    - 1.1189143848199399
    - 0.7950372698453935
    - 0.43264177378682045
    - 0.05025872740218623
    - -0.33223278521001093
    - -0.6947184370357532
    - -1.0179922212299326
    - -1.2848667138351721
    - -1.4811866169006531
    - -1.5966861488688047
    - -1.6256382654785593
    - -1.5672542234235178
    - -1.425805138578064
    - -1.2104522764786894
    - -0.9347890504359283
    - -0.6161142080550508
    - -0.2744715334685796
    - 0.06849433764692948
    - 0.39080455683039683
    - 0.6714650635248156
    - 0.8917629616512879
    - 1.0364645452514123
    - 1.0948428224586593
    - 1.0614702009112538
    - 0.9367237244710996
    - 0.7269653309106264
    - 0.44437726304035663
    - 0.10645206921304654
    - -0.2648434922909751
    - -0.6441920075825527
    - -1.0042801478014622
    - -1.3173134445602737
    - -1.5566087646331404
    - -1.698175411096353
    - -1.7221940022279918
    - -1.6143057048495801
    - -1.3666329684584408
    - -0.9784662610211597
    - -0.45656879699172503
    - 0.18492803716948314
    - 0.9250430394212457
    - 1.7368581725429488
    - 2.588783912070802
    - 3.4461135111123777
    - 4.272784729977568
    - 5.0332539029593395
    - 5.694378770447156
    - 6.227203909977647
    - 6.608546140783562
    - 6.822286880838241
    - 6.860293668269486
    - 6.72291313916835
    - 6.419001592252967
    - 5.96548552878116
    - 5.386471719751854
    - 4.711952820449588
    - 3.976178730951589
    - 3.2157843011358977
    - 2.467779308592268
    - 1.7675158873972814
    - 1.1467510940394399
    - 0.6319178005398649
    - 0.24270576317055523
    - -0.00896289091410806
    - -0.11950241148245812
    - -0.09374192440562974
    - 0.05549155307937207
    - 0.3082609469999922
    - 0.6388245165338559
    - 1.017279838464903
    - 1.411446382800535
    - 1.7888716230681725
    - 2.118837574263414
    - 2.3742441922174025
    - 2.5332533198686504
    - 2.580591462657161
    - 2.508430780013494
    - 2.316794029471405
    - 2.0134591779817224
    - 1.6133711295178126
    - 1.137599497146585
    - 0.6119105469045375
    - 0.06504645365278622
    - -0.47317582710165645
    - -0.9738217592964309
    - -1.4107241930385366
    - -1.7621721625711368
    - -2.012292118218926
    - -2.1520301672005653
    - -2.179670069791756
    - -2.100852446310555
    - -1.9280939099042465
    - -1.6798384646934341
    - -1.3791052564120487
    - -1.0518244831675867
    - -0.7249750545759065
    - -0.42465188528723075
    - -0.1741964607886987
    - 0.007478983520149625
    - 0.10725557328850194
    - 0.11876258156472069
    - 0.042852714592046426
    - -0.11243965957630035
    - -0.3324592557376941
    positive_zeros:
    - '1.70698974645208637812633518352001'
    - '2.85753585158968917578674971709915'
    - '3.71331411593505908329064024068389'
    - '4.76447631261619758628405568918695'
    - '5.54815261604095958672505092947438'
    - '6.77560219337028756121239169547986'
    - '7.77666664841938190662447383816039'
    - '8.255774497202089660090663603470469'
    - '9.148258902572960841846009259247392'
    - '9.949071215160877709405285288688915'
    prelabel: 2-1200-12.11-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.095488368990207
    root_angle: 0.5
    root_number: 0.e-56 + 1.00000000000000000000000000000000000000000000000000000000*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.25'
      prec: 14
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.70698974645208637812633518352'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.85753585158968917578674971710'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.71331411593505908329064024068'
      prec: 103
- - algebraic: true
    analytic_conductor: 9.58204824255365
    bad_primes:
    - 2
    - 3
    - 5
    central_character: '12.11'
    conductor: 1200
    conductor_radical: 30
    degree: 2
    id: 23142339
    index: 31
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1200/2/h/h/1151/1
    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: 2-1200-12.11-c1-0-31
    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: 2-1200-12.11-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.095488368990207
    root_angle: 0.25
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '1.70698974645208637812633518352'
      prec: 103
- - Lhash: '2163866576673420416677444499077'
    Lhash_array:
    - '2163866576673420416677444499077'
    id: 23509690
    label: 2-1200-12.11-c1-0-31
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1200/2/h/h/1151/1
label_cols:
- label
- label
- label
labels:
- 2-1200-12.11-c1-0-31
- 2-1200-12.11-c1-0-31
- 2-1200-12.11-c1-0-31
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T14:58:13.032492'