data:
- - Lhash: '3359047523966920042580757190649'
    a10:
    - -3.0791966589786424
    - 0.7201027255432156
    a2:
    - 1.39193335542393
    - -0.25004306440747254
    a3:
    - 1.0185566515121856
    - 1.4009076870587456
    a4:
    - 1.8749569318834411
    - -0.6960865632823502
    a5:
    - -2.2330466148626473
    - 0.11620161724550729
    a6:
    - 1.7680502286528723
    - 1.6952871110701355
    a7:
    - -2.2904106208671786
    - -2.2904106208671786
    a8:
    - 2.43576347609589
    - -1.4377260825752818
    a9:
    - -0.925084695320568
    - 2.853807685616473
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.9582048242553651
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - -1.39193335542393
          - 0.25004306440747254
    - - 3
      - - - 1.0
          - 0
        - - -1.0185566515121856
          - -1.4009076870587456
    - - 5
      - - - 1.0
          - 0
        - - 2.2330466148626473
          - -0.11620161724550729
    bad_primes:
    - 2
    - 3
    - 5
    central_character: '120.77'
    coefficient_field: CDF
    conductor: 120
    conductor_radical: 30
    conjugate: '3926080098094705500581674992883'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -1.39193335542393
        - 0.25004306440747254
    - - - 1.0
        - 0
      - - -1.0185566515121856
        - -1.4009076870587456
    - - - 1.0
        - 0
      - - 2.2330466148626473
        - -0.11620161724550729
    - - - 1.0
        - 0
      - - 2.2904106208671786
        - 2.2904106208671786
      - - 0
        - 7.0
    - - - 1.0
        - 0
      - - 2.283780582032915
        - 0
      - - 11.0
        - 0
    - - - 1.0
        - 0
      - - -1.0563452319544744
        - -1.0563452319544744
      - - 0
        - 13.0
    - - - 1.0
        - 0
      - - -3.043908506684475
        - 3.043908506684475
      - - 0
        - -17.0
    - - - 1.0
        - 0
      - - 3.368313232840088
        - 0
      - - 19.0
        - 0
    - - - 1.0
        - 0
      - - -3.6878475329952694
        - -3.6878475329952694
      - - 0
        - 23.0
    - - - 1.0
        - 0
      - - 0
        - -2.714611484294485
      - - -29.0
        - 0
    - - - 1.0
        - 0
      - - 6.4919616243623475
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - -2.3119680008856136
        - 2.3119680008856136
      - - 0
        - -37.0
    - - - 1.0
        - 0
      - - 0
        - -10.805553302053424
      - - -41.0
        - 0
    - - - 1.0
        - 0
      - - 1.1638415696397917
        - 1.1638415696397917
      - - 0
        - 43.0
    - - - 1.0
        - 0
      - - 1.837678142354133
        - -1.837678142354133
      - - 0
        - -47.0
    - - - 1.0
        - 0
      - - -5.82856178749576
        - 5.82856178749576
      - - 0
        - -53.0
    - - - 1.0
        - 0
      - - 0
        - 7.4131079485107945
      - - -59.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -8.970443171835539
      - - -61.0
        - 0
    - - - 1.0
        - 0
      - - -8.663669297173556
        - 8.663669297173556
      - - 0
        - -67.0
    - - - 1.0
        - 0
      - - 0
        - 7.375695065990539
      - - -71.0
        - 0
    - - - 1.0
        - 0
      - - -1.8344095007315364
        - 1.8344095007315364
      - - 0
        - -73.0
    - - - 1.0
        - 0
      - - 0
        - -8.288436612967303
      - - -79.0
        - 0
    - - - 1.0
        - 0
      - - 5.279275167533425
        - -5.279275167533425
      - - 0
        - -83.0
    - - - 1.0
        - 0
      - - -11.531140016655465
        - 0
      - - 89.0
        - 0
    - - - 1.0
        - 0
      - - 2.796474988604956
        - 2.796474988604956
      - - 0
        - 97.0
    - - - 1.0
        - 0
      - - 8.942512090697035
        - 0
      - - 101.0
        - 0
    - - - 1.0
        - 0
      - - 2.543998879864358
        - -2.543998879864358
      - - 0
        - -103.0
    - - - 1.0
        - 0
      - - 5.148339867382945
        - 5.148339867382945
      - - 0
        - 107.0
    - - - 1.0
        - 0
      - - 1.4052762814607627
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - 13.287170470718351
        - 13.287170470718351
      - - 0
        - 113.0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9605434
    index: 13
    label: 2-120-120.77-c1-0-13
    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/120/2/w/c/77/15
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 1.7417058863572257
    - 1.7395008494067257
    - 1.7586828661636422
    - 1.7959105442840744
    - 1.8464922124700949
    - 1.904816968977603
    - 1.9647355736661942
    - 2.019851377052166
    - 2.063740048471348
    - 2.0901402447158235
    - 2.0931534810391454
    - 2.067476133989115
    - 2.0086701385020698
    - 1.913465482062788
    - 1.7800775053235471
    - 1.6085147156839996
    - 1.4008478138992795
    - 1.1614077925457251
    - 0.8968804596883249
    - 0.6162668919497719
    - 0.3306844477297671
    - 0.052991263809652016
    - -0.2027714238654223
    - -0.4221105996126168
    - -0.5909616214832284
    - -0.6966751242111074
    - -0.7290517076183359
    - -0.6813506398744149
    - -0.5511878945539018
    - -0.3412336382193382
    - -0.05962139751153068
    - 0.2800082524666014
    - 0.6588869711543308
    - 1.053949951544156
    - 1.4391122778325258
    - 1.7869420721244398
    - 2.070638750954377
    - 2.26618322267546
    - 2.3544918208403383
    - 2.3233818340842043
    - 2.1691479281603274
    - 1.8975589078425361
    - 1.5241150245586415
    - 1.07345736468724
    - 0.577890467072418
    - 0.07506255661095917
    - -0.39506225524095945
    - -0.7937174794628808
    - -1.0870349901224605
    - -1.2495801622727625
    - -1.2673450103450274
    - -1.139836974179165
    - -0.8809561455053102
    - -0.5184492440761573
    - -0.09185904307968068
    - 0.35095709509278217
    - 0.7585009469033713
    - 1.0811035111060943
    - 1.2766650411276534
    - 1.316053303665034
    - 1.1875235607766428
    - 0.8995695568643682
    - 0.48173391097921064
    - -0.016906994055105106
    - -0.5316289332200542
    - -0.9880922099009034
    - -1.3100255386557866
    - -1.4278275968883456
    - -1.2871774386652315
    - -0.8566617850676099
    - -0.13345516469765292
    - 0.8537645887756381
    - 2.0452246149896625
    - 3.3539996124835922
    - 4.673295606301036
    - 5.886468664300562
    - 6.878800865296191
    - 7.549776404762575
    - 7.824456319167316
    - 7.662570025747752
    - 7.064135779411581
    - 6.070778190122886
    - 4.76239461670099
    - 3.2493793418606822
    - 1.661176758952306
    - 0.13242843918909616
    - -1.2116660076421568
    - -2.268993760384292
    - -2.971465495948463
    - -3.291827762626384
    - -3.2454348354033926
    - -2.886707715859032
    - -2.300713046758132
    - -1.590964944294851
    - -0.8650914831731563
    - -0.22033184503103154
    - 0.26911617346046735
    - 0.5611147440421009
    - 0.6496902812736339
    - 0.5636491190696972
    - 0.3599414012238215
    - 0.11280719259171688
    - -0.09960054921585357
    - -0.2090049458601836
    - -0.16899704703140728
    - 0.03672970896457193
    - 0.3912929939888736
    - 0.8472615454989543
    - 1.3346672087155034
    - 1.7731283923520076
    - 2.0860949980481895
    - 2.2148016060742917
    - 2.129483185438093
    - 1.83578968862168
    - 1.3750878888502407
    - 0.8183509297829629
    - 0.25444811579439097
    - -0.22532681395613924
    - -0.5438934108129466
    - -0.653250216002158
    - -0.54478572597092
    - -0.2529065090551912
    - 0.1490773039149435
    - 0.5605499284585531
    - 0.8710593311695823
    - 0.9808961401279828
    - 0.8212877851583473
    - 0.37055400493609325
    - -0.3369536152572305
    - -1.2112378255056806
    - -2.116971067233337
    - -2.8926377432038697
    - -3.37578508698246
    - -3.4304283788550567
    - -2.9720405815286592
    - -1.9857050382481487
    - -0.533939113626343
    - 1.2477148713986232
    - 3.167232699614472
    - 5.002602449186786
    - 6.53428485166681
    - 7.578466534360543
    - 8.015596417903879
    - 7.809307602859523
    - 7.012318372456352
    - 5.758045912533783
    - 4.239097687364398
    - 2.676103576079029
    - 1.2820999453219826
    - 0.22854243295704513
    - -0.38117573266775356
    - -0.5260825163839719
    - -0.26736324365062875
    - 0.2664161685130181
    - 0.9058570425544153
    - 1.4741370014137773
    - 1.8210805859175492
    - 1.8515399406405808
    - 1.5427718233871173
    - 0.9475512264817062
    - 0.18246047908522262
    - -0.5963687235098969
    - -1.2253479602320212
    - -1.5670937751423424
    - -1.539038743841754
    - -1.131307342706686
    - -0.4102349531500509
    - 0.4932884968291191
    - 1.4084680116529933
    - 2.1574591714973774
    - 2.5899611285541577
    - 2.612671478714949
    - 2.2076982787814634
    - 1.4361978011367256
    - 0.4264594551227427
    - -0.6511990297688901
    - -1.6176734525225447
    - -2.319721670535306
    - -2.6589836502542075
    - -2.609487823596151
    - -2.2201424878318976
    - -1.6018448025702412
    - -0.9020721120155477
    - -0.2724662567372624
    - 0.16359129929983535
    - 0.33642244016950756
    - 0.24304276932888347
    - -0.05504511064095101
    - -0.44864484429696194
    - -0.8083789461847979
    - -1.0166178951142868
    - -0.9964661020971846
    - -0.7310334736992401
    - -0.2683604658357537
    - 0.28938997999613647
    - 0.8102152709940472
    - 1.1645474664049413
    - 1.2579823954689522
    - 1.0565568928430549
    - 0.5981278085534008
    - -0.013567828286272166
    - -0.6316345344127181
    - -1.1009688325190843
    - -1.2977349923246646
    - -1.1641458367695157
    - -0.7298743341856732
    - -0.11400819034121211
    - 0.49440217104978934
    - 0.8743278426403014
    - 0.8219572023980452
    - 0.20074315915952515
    - -1.0189304698971011
    - -2.74009386868322
    - -4.745337240063236
    - -6.729217456616195
    - -8.351680815422933
    - -9.302427106848011
    - -9.36328832600971
    - -8.455530363622087
    - -6.661646851495393
    - -4.216218829638464
    - -1.4667452713105271
    - 1.188333782137603
    - 3.372274209412408
    - 4.798748432276971
    - 5.322719829663357
    - 4.963175341134551
    - 3.8932914235752456
    - 2.4004571371702297
    - 0.8249120478551075
    - -0.5098181455833591
    - -1.3599680992529843
    - -1.6050297764827808
    - -1.2631955243246715
    - -0.47657953037569994
    - 0.5292447397902718
    - 1.5013016223210103
    - 2.2176289992543268
    - 2.5347662372637596
    - 2.414038877545538
    - 1.921686242864075
    - 1.2042196462535169
    - 0.4462371715286192
    - -0.17813476369330736
    - -0.5478759415879644
    - -0.6214079700136362
    - -0.4407101814980957
    - -0.1131415636708523
    - 0.22334861976466253
    - 0.4417285261563054
    - 0.4626198162622945
    - 0.2761940995185748
    - -0.0567617779312682
    - -0.4249214944330747
    - -0.7021343378925601
    - -0.788864869708997
    - -0.6476173324055312
    positive_zeros:
    - '2.64982127043694289258862022966167'
    - '3.77338372295083905536486703812499'
    - '5.64412936629592742128139491279653'
    - '6.77583212803665820241976890696577'
    - '7.87092181815821649738201924798845'
    - '8.768900006681544833093619218258602'
    - '10.63643924654515772583486820642149'
    - '11.92567997588791401248898200788074'
    - '12.68611457031687562516319739613734'
    - '13.10833475658546002814765516393539'
    prelabel: 2-120-120.77-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.9788793716568784
    root_angle: -0.0625975754934426
    root_number: 0.9807254308568771 - 0.1953909651713528*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.0312987877467'
      prec: 54
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '2.64982127043694289258862022966'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '3.77338372295083905536486703812'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '5.64412936629592742128139491280'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.9582048242553651
    bad_primes:
    - 2
    - 3
    - 5
    central_character: '120.77'
    conductor: 120
    conductor_radical: 30
    degree: 2
    id: 9605434
    index: 13
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/120/2/w/c/77/15
    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: 2-120-120.77-c1-0-13
    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: 2-120-120.77-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.9788793716568784
    root_angle: -0.0312987877467213
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '2.64982127043694289258862022966'
      prec: 103
- - Lhash: '3359047523966920042580757190649'
    Lhash_array:
    - '3359047523966920042580757190649'
    id: 9971464
    label: 2-120-120.77-c1-0-13
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/120/2/w/c/77/15
label_cols:
- label
- label
- label
labels:
- 2-120-120.77-c1-0-13
- 2-120-120.77-c1-0-13
- 2-120-120.77-c1-0-13
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T08:49:03.265022'