data:
- - Lhash: '2778436081761717437723660083013'
    a10:
    - -0.17364817766693036
    - -0.3007674663608706
    a2:
    - 0.17364817766693036
    - -0.984807753012208
    a3:
    - 0.5049223020338081
    - 2.863556671843858
    a4:
    - -0.9396926207859084
    - -0.3420201433256687
    a5:
    - 0.266044443118978
    - -0.22323779409789932
    a6:
    - 2.9077316492332286
    - -6.952070529321909e-61
    a7:
    - 0.7735858473596819
    - -0.6491155992034727
    a8:
    - -0.5
    - 0.8660254037844386
    a9:
    - -5.125932419412627
    - 1.8656868235263353
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.5908929749574752
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - -0.17364817766693036
          - 0.984807753012208
    - - 37
      - - - 1.0
          - 0
        - - 5.88520553336152
          - 1.537646197956781
    bad_primes:
    - 2
    - 37
    central_character: '74.33'
    coefficient_field: CDF
    conductor: 74
    conductor_radical: 74
    conjugate: '3998668500975439478341855517579'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -0.17364817766693036
        - 0.984807753012208
    - - - 1.0
        - 0
      - - -0.5049223020338081
        - -2.863556671843858
      - - -2.8190778623577253
        - 1.0260604299770062
    - - - 1.0
        - 0
      - - -0.266044443118978
        - 0.22323779409789932
      - - 0.8682408883346517
        - -4.924038765061041
    - - - 1.0
        - 0
      - - -0.7735858473596819
        - 0.6491155992034727
      - - 1.2155372436685123
        - -6.893654271085456
    - - - 1.0
        - 0
      - - -2.7323739740101045
        - 4.732610548264384
      - - -5.5
        - -9.526279441628825
    - - - 1.0
        - 0
      - - 5.978921151850915
        - 2.17614933229833
      - - 9.958577760546714
        - 8.35623892592501
    - - - 1.0
        - 0
      - - 0.4907490982031021
        - -0.1786180642389106
      - - 13.022755533022627
        - -10.927389364671168
    - - - 1.0
        - 0
      - - -0.8699503858908457
        - -4.933733807472164
      - - -17.854159794932258
        - 6.498382723187706
    - - - 1.0
        - 0
      - - 0.72149185060651
        - 1.2496605424973692
      - - -11.5
        - 19.91858428704209
    - - - 1.0
        - 0
      - - -3.1671442927622047
        - 5.485654829965937
      - - -14.5
        - -25.11473670974872
    - - - 1.0
        - 0
      - - -3.3077669362468067
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - 5.88520553336152
        - 1.537646197956781
    - - - 1.0
        - 0
      - - -1.0341222751471253
        - -0.37638972674519733
      - - 31.4078221678781
        - 26.354291997148113
    - - - 1.0
        - 0
      - - 6.2703666424190505
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - -5.719098759935294
        - -9.90576962571209
      - - -23.5
        - 40.703193977868615
    - - - 1.0
        - 0
      - - -0.07068165738063778
        - -0.059308952639092034
      - - 9.203353416347309
        - 52.194810909647025
    - - - 1.0
        - 0
      - - -2.2905919251162303
        - -1.9220348395426845
      - - 10.24524248234889
        - 58.10365742772028
    - - - 1.0
        - 0
      - - 3.585708426663249
        - 1.3050911360629187
      - - 46.728711030257664
        - 39.2100441908789
    - - - 1.0
        - 0
      - - 0.8922507072599822
        - -0.7486872393795183
      - - 11.634427903684333
        - -65.98211945181794
    - - - 1.0
        - 0
      - - -0.05433316840829592
        - -0.30813871019619593
      - - -66.71817607579949
        - 24.28343017612248
    - - - 1.0
        - 0
      - - -13.232543538458168
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - -7.129393064287803
        - 5.982271090761754
      - - 13.718206035687498
        - -77.79981248796443
    - - - 1.0
        - 0
      - - 8.893953804353158
        - -3.237134449723201
      - - 63.581688778875176
        - -53.35137160398276
    - - - 1.0
        - 0
      - - 12.078844432107656
        - 10.135353908029277
      - - 15.4546878123568
        - 87.64789001808651
    - - - 1.0
        - 0
      - - -0.46456399413613575
        - -0.804648441210917
      - - -48.5
        - 84.00446416709055
    - - - 1.0
        - 0
      - - 4.280931274932687
        - 7.414790471894024
      - - -50.5
        - 87.4685657822283
    - - - 1.0
        - 0
      - - 2.479563312236257
        - -4.294729637376969
      - - -51.5
        - -89.20061658979718
    - - - 1.0
        - 0
      - - -3.3530666004989658
        - -1.2204164360937875
      - - 81.96675541373065
        - 68.77827423645971
    - - - 1.0
        - 0
      - - 0.1699473488531736
        - -0.963819309843232
      - - -102.42649566566402
        - -37.28019562249789
    - - - 1.0
        - 0
      - - -1.6039920168386452
        - 9.096690763908951
      - - -106.18526614880764
        - -38.64827619580057
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9593010
    index: 1
    label: 2-74-37.33-c1-0-1
    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/f/b/33/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 1.0203075691059114
    - 1.012280105963773
    - 1.0171898694487334
    - 1.0326927607480731
    - 1.055681931423394
    - 1.0825026306533776
    - 1.1091271741280944
    - 1.1312720393091722
    - 1.144472199454953
    - 1.1441405981559347
    - 1.1256384074910952
    - 1.0843735020070027
    - 1.0159360899853076
    - 0.9162735863351539
    - 0.7819015615579407
    - 0.6101434005963011
    - 0.3993876889263915
    - 0.1493490956541246
    - -0.13868434590880066
    - -0.4616369842142707
    - -0.814485266533731
    - -1.1901727891749716
    - -1.5796210634584174
    - -1.9718537550614688
    - -2.354247719113461
    - -2.7129178627593906
    - -3.0332348263750766
    - -3.3004649642511525
    - -3.50051159242072
    - -3.620725607188198
    - -3.6507431792132885
    - -3.5832992355780795
    - -3.4149588609272215
    - -3.1467055678533016
    - -2.784326485570565
    - -2.338540560681183
    - -1.8248272037370428
    - -1.262929389264615
    - -0.676026481769203
    - -0.08959695226305742
    - 0.4699819095947667
    - 0.9770232295732807
    - 1.4082100846935823
    - 1.744247030255282
    - 1.9713530716058711
    - 2.0824629427864516
    - 2.0780122592183448
    - 1.96620294655908
    - 1.7626781114884047
    - 1.489578829841568
    - 1.1740065700873201
    - 0.8459703727027744
    - 0.5359527389137102
    - 0.2722770955077815
    - 0.078497180580245
    - -0.028950398702523517
    - -0.04258902135844385
    - 0.03497788594251005
    - 0.19084061422504428
    - 0.40255244976473
    - 0.6399089466933037
    - 0.8676533530084011
    - 1.0489236553559962
    - 1.1491637488202737
    - 1.1401465498017231
    - 1.0037103366790237
    - 0.734799291989148
    - 0.3434302680049772
    - -0.14471852144744404
    - -0.6892880719995064
    - -1.2378349481931126
    - -1.7299259538283447
    - -2.1024459919894416
    - -2.2956805248448804
    - -2.2596129036129415
    - -1.959804491477014
    - -1.3822146481226358
    - -0.5363753538425895
    - 0.5435384577544636
    - 1.8000146948116038
    - 3.1559254445369787
    - 4.520447663274117
    - 5.796715119328241
    - 6.890514163928656
    - 7.719176837660164
    - 8.219749036906181
    - 8.355534158475214
    - 8.120238616763928
    - 7.539167795678911
    - 6.667220189814547
    - 5.583773772777417
    - 4.384914087050354
    - 3.173776316548592
    - 2.050022772038287
    - 1.0996180449120523
    - 0.3860728487787922
    - -0.05580456072493322
    - -0.22287521445730846
    - -0.14295199360795022
    - 0.12956691091717773
    - 0.521226782923713
    - 0.9493118334331544
    - 1.3327008906625333
    - 1.6024092159581471
    - 1.7104468873735394
    - 1.6358088024871122
    - 1.3867601518486345
    - 0.9990552694395003
    - 0.5302689237020407
    - 0.05095679004881029
    - -0.3661779680696866
    - -0.6576197235516692
    - -0.7792650024681974
    - -0.7140266778152924
    - -0.47562762115915186
    - -0.10789648159295855
    - 0.3204990980072554
    - 0.7252876797582589
    - 1.0186018283629545
    - 1.1221082384853884
    - 0.9793760330564045
    - 0.565630630059218
    - -0.10665428593172654
    - -0.9873273630989428
    - -1.9935745177981832
    - -3.0198677725550103
    - -3.9515869907624124
    - -4.680459075635697
    - -5.119617632585438
    - -5.216060558117436
    - -4.958591640352034
    - -4.379942880350413
    - -3.5526066909528797
    - -2.5788430701211005
    - -1.576226206099145
    - -0.6608167057788414
    - 0.06953016563231389
    - 0.5491619448086579
    - 0.7537252386694692
    - 0.7028653256829095
    - 0.45600658460729815
    - 0.10178090078076862
    - -0.25729274112409967
    - -0.5224612458070015
    - -0.61585779435595
    - -0.494227779841041
    - -0.15687235876103373
    - 0.35369194279641164
    - 0.9586891133678974
    - 1.5567146482513672
    - 2.0419345854206394
    - 2.3238834669569384
    - 2.3454926242774996
    - 2.0961312783407786
    - 1.6171444364627787
    - 0.9985307448554537
    - 0.3668461300514515
    - -0.13408502384306728
    - -0.36677035888863546
    - -0.22420718657964187
    - 0.3494384866612484
    - 1.3452818827787645
    - 2.6859319480985357
    - 4.232596304290006
    - 5.802451027143117
    - 7.193922684753733
    - 8.216130319209153
    - 8.717909439954273
    - 8.611749240026109
    - 7.888659237961882
    - 6.621352186052063
    - 4.954975527217703
    - 3.0866446108979044
    - 1.2368884268751488
    - -0.38250789792495216
    - -1.599136017365331
    - -2.3041567723642316
    - -2.4661831275180113
    - -2.1326997936257874
    - -1.418961095040471
    - -0.4864236461190924
    - 0.48546582983901704
    - 1.32920928151787
    - 1.915772668662568
    - 2.17320929649282
    - 2.094399429376209
    - 1.7329220061267743
    - 1.1882469476090098
    - 0.5833737641782193
    - 0.03938245230782812
    - -0.3481477013887634
    - -0.5263527101984661
    - -0.4927533627489884
    - -0.2921344099396499
    - -0.0035624936614775606
    - 0.27953802671646794
    - 0.47192216573232415
    - 0.5168040401344673
    - 0.39945891740400047
    - 0.15109522235545908
    - -0.15802898950770683
    - -0.43498349521487734
    - -0.5866910399650022
    - -0.5438072038476413
    - -0.28067312810746486
    - 0.17333666811824006
    - 0.7341352436785177
    - 1.275646111537454
    - 1.653064949263067
    - 1.732459382922583
    - 1.4209201654022576
    - 0.6910036382313528
    - -0.4060061877727113
    - -1.7415384397132527
    - -3.126633416765477
    - -4.341987976474058
    - -5.176083836581045
    - -5.464458508316325
    - -5.122597075682402
    - -4.165807734207822
    - -2.7116785408046185
    - -0.9639049794934241
    - 0.8201715160886234
    - 2.3727577651232044
    - 3.4617472149254427
    - 3.9312392977386383
    - 3.728755658396556
    - 2.91387204884411
    - 1.6464718961117641
    - 0.15673003753247064
    - -1.2975161568348486
    - -2.477871334105298
    - -3.207929022344196
    - -3.403117787449642
    - -3.0822245928699052
    - -2.358633262007877
    - -1.4133823741580043
    - -0.45579268944142065
    - 0.3201126238432666
    - 0.7743900254518973
    - 0.8472383013368326
    - 0.5671543795993038
    - 0.03981605340126501
    - -0.579565416783863
    - -1.1241526384446954
    - -1.455190259768176
    - -1.494683746532185
    - -1.243760573745824
    - -0.782565321465046
    - -0.25161222244648296
    - 0.18135375999309694
    - 0.3616550795512232
    - 0.18610280573257026
    - -0.369224669141472
    - -1.2383949668180452
    - -2.2750724597432734
    - -3.2804519450265364
    positive_zeros:
    - '2.19179960255726958692821388548297'
    - '4.89447097243458177858122036152773'
    - '6.82882691075811576949023221097923'
    - '7.08390411798279786996538289575883'
    - '8.464910518162430431752206534219860'
    - '9.690104649648977455411997334394262'
    - '11.97861067913557097953870966237390'
    - '12.32421374721966689575954077474684'
    - '13.63895973436123503488484599952195'
    - '14.40724414514435799414318761009960'
    prelabel: 2-74-37.33-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.7686956321961738
    root_angle: -0.07395209959647453
    root_number: 0.9731331697840911 - 0.23024298874442903*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.0369760497982'
      prec: 54
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '2.19179960255726958692821388548'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '4.89447097243458177858122036153'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '6.82882691075811576949023221098'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.5908929749574752
    bad_primes:
    - 2
    - 37
    central_character: '37.33'
    conductor: 74
    conductor_radical: 74
    degree: 2
    id: 9593010
    index: 1
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/74/2/f/b/33/2
    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: 2-74-37.33-c1-0-1
    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: 2-74-37.33-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.7686956321961738
    root_angle: -0.036976049798237265
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '2.19179960255726958692821388548'
      prec: 103
- - Lhash: '2778436081761717437723660083013'
    Lhash_array:
    - '2778436081761717437723660083013'
    id: 9959034
    label: 2-74-37.33-c1-0-1
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/74/2/f/b/33/2
label_cols:
- label
- label
- label
labels:
- 2-74-37.33-c1-0-1
- 2-74-37.33-c1-0-1
- 2-74-37.33-c1-0-1
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-23T15:56:07.797374'