data:
- - Lhash: '1050752982767697281499742560203'
    a10:
    - 1.6496778812305681
    - 5.0360580398369015
    a2:
    - 0
    - -0.47399002261589657
    a3:
    - 0
    - 0
    a4:
    - 7.775333458460582
    - 0
    a5:
    - -10.624818666104984
    - 3.4804063429989203
    a6:
    - 0
    - 0
    a7:
    - 0
    - -8.20657084539417
    a8:
    - 0
    - -7.477350662749041
    a9:
    - 0
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 23.89577355232496
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 5
      - - - 1.0
          - 0
        - - 10.624818666104984
          - -3.4804063429989203
    bad_primes:
    - 3
    - 5
    central_character: '405.244'
    coefficient_field: CDF
    conductor: 405
    conductor_radical: 15
    conjugate: '1420066007754663348577614444797'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0.47399002261589657
      - - -8.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 10.624818666104984
        - -3.4804063429989203
    - - - 1.0
        - 0
      - - 0
        - 8.20657084539417
      - - -343.0
        - 0
    - - - 1.0
        - 0
      - - 5.26582882949711
        - 0
      - - 1331.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -77.03424327234838
      - - -2197.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 88.9396515450851
      - - -4913.0
        - 0
    - - - 1.0
        - 0
      - - -91.73576714287941
        - 0
      - - 6859.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -154.44075092555
      - - -12167.0
        - 0
    - - - 1.0
        - 0
      - - -168.3033686521316
        - 0
      - - 24389.0
        - 0
    - - - 1.0
        - 0
      - - -72.78850773836572
        - 0
      - - 29791.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -154.83637714124305
      - - -50653.0
        - 0
    - - - 1.0
        - 0
      - - 7.951574164075759
        - 0
      - - 68921.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 23.20140201587203
      - - -79507.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -301.3980514944436
      - - -103823.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -344.54183649984844
      - - -148877.0
        - 0
    - - - 1.0
        - 0
      - - -251.5575509418938
        - 0
      - - 205379.0
        - 0
    - - - 1.0
        - 0
      - - -272.9017796264445
        - 0
      - - 226981.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 835.4674063230921
      - - -300763.0
        - 0
    - - - 1.0
        - 0
      - - 351.15198289905123
        - 0
      - - 357911.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -522.7492164417944
      - - -389017.0
        - 0
    - - - 1.0
        - 0
      - - -700.1068346332382
        - 0
      - - 493039.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 241.3026570767701
      - - -571787.0
        - 0
    - - - 1.0
        - 0
      - - -1021.3895044027918
        - 0
      - - 704969.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -389.2843894246734
      - - -912673.0
        - 0
    - - - 1.0
        - 0
      - - -864.5191699099821
        - 0
      - - 1030301.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -1228.2061093961977
      - - -1092727.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 1860.3420457073548
      - - -1225043.0
        - 0
    - - - 1.0
        - 0
      - - 1037.3079963300133
        - 0
      - - 1295029.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -1407.7347508543387
      - - -1442897.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 24061529
    index: 22
    label: 2-405-5.4-c3-0-22
    leading_term: '2.0539863540972584101831933175045179654470673584676728420'
    load_key: CMFs-workshop
    motivic_weight: 3
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 3
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/405/4/b/f/244/8
    plot_delta:
      __RealLiteral__: 0
      data: '0.0625'
      prec: 20
    plot_values:
    - 2.0539863540972583
    - 1.9985985929064571
    - 1.9239652480063474
    - 1.830549214144919
    - 1.7189308680311253
    - 1.589815095674131
    - 1.4440399997347146
    - 1.2825866995077104
    - 1.106589544346179
    - 0.9173459927119131
    - 0.7163253654553506
    - 0.5051756643991475
    - 0.2857276560784225
    - 0.059995455209982035
    - -0.16982709773044627
    - -0.4013748867702455
    - -0.6321253144501614
    - -0.8594178288283242
    - -1.080479427408063
    - -1.2924562201891394
    - -1.4924509584530223
    - -1.6775662493861485
    - -1.844952982609691
    - -1.9918632970058303
    - -2.115707219315672
    - -2.214111914752941
    - -2.284982309719883
    - -2.3265616834032814
    - -2.3374906846101497
    - -2.3168631188232287
    - -2.2642767741828185
    - -2.1798775197027913
    - -2.0643949197401734
    - -1.9191676700133338
    - -1.7461572757253387
    - -1.547948563742025
    - -1.3277358489409712
    - -1.0892938587266978
    - -0.8369328563724809
    - -0.5754377883940607
    - -0.30999170664309134
    - -0.046084173259831517
    - 0.21059416486742524
    - 0.45426915862059924
    - 0.6792107416428596
    - 0.8798679036466647
    - 1.051008015851792
    - 1.1878571045869883
    - 1.2862373720124265
    - 1.3426980522356615
    - 1.3546355811150903
    - 1.3203990610844762
    - 1.23937712808336
    - 1.1120625826304518
    - 0.9400915339879763
    - 0.7262543238155826
    - 0.4744761377706131
    - 0.18976596952602617
    - -0.12186654377627647
    - -0.4535259626233758
    - -0.7975761237684772
    - -1.1458130047206716
    - -1.4896619155902184
    - -1.8203945927513443
    - -2.1293608767741152
    - -2.408228875563077
    - -2.64922687703564
    - -2.8453798160072084
    - -2.9907328455145312
    - -3.0805545368262592
    - -3.111512451760151
    - -3.0818143051064073
    - -2.991308665026505
    - -2.8415401172682437
    - -2.6357550274488464
    - -2.378855447497699
    - -2.0773002913406837
    - -1.7389546061644552
    - -1.3728895366736786
    - -0.989137362052306
    - -0.5984077158833128
    - -0.21177271277689882
    - 0.15966986338712727
    - 0.5051449686829825
    - 0.8145490817704529
    - 1.078787605712028
    - 1.2900889975710101
    - 1.4422840178696028
    - 1.5310392095912917
    - 1.5540348658931245
    - 1.5110793081537834
    - 1.4041532355257251
    - 1.2373801711982797
    - 1.0169215508443503
    - 0.7507976929732224
    - 0.4486386653212768
    - 0.12137181359926635
    - -0.2191446584844336
    - -0.5605302843211928
    - -0.8903192892298494
    - -1.196410487906859
    - -1.4675136306848502
    - -1.6935752216093065
    - -1.8661669900159485
    - -1.9788210227671317
    - -2.027297055789686
    - -2.00976955306032
    - -1.9269249131392292
    - -1.7819623553683002
    - -1.5804956426617651
    - -1.3303566664047122
    - -1.0413059048016275
    - -0.7246587102672286
    - -0.392840119101893
    - -0.05888424320490792
    - 0.26410285804971356
    - 0.5634957597498341
    - 0.8276952645103655
    - 1.046644071436307
    - 1.2122900368213547
    - 1.3189759589370615
    - 1.3637371825206908
    - 1.346491568059881
    - 1.270110404961692
    - 1.1403635256195586
    - 0.9657370241400092
    - 0.7571273954434616
    - 0.527421363132161
    - 0.2909759215674956
    - 0.0630179407671713
    - -0.14101315754664087
    - -0.30615285830143957
    - -0.4186001192392834
    - -0.46637698115898396
    - -0.4399294098458613
    - -0.3326411366250773
    - -0.14123515302646925
    - 0.13395836596414687
    - 0.48888372408432246
    - 0.9158008547293334
    - 1.4034890963873152
    - 1.9376095860684588
    - 2.5012150580771526
    - 3.075388891580293
    - 3.639988895733706
    - 4.174465868165059
    - 4.658722694210533
    - 5.073976909075798
    - 5.403588404349897
    - 5.633814437127955
    - 5.754456331113713
    - 5.759366199996598
    - 5.6467875473192315
    - 5.4195104976141515
    - 5.084830411647209
    - 4.654307392792109
    - 4.143333312325269
    - 3.5705220480098783
    - 2.956947209955701
    - 2.3252592961784244
    - 1.6987205828681553
    - 1.1002007663659896
    - 0.5511791591490143
    - 0.07079990936947596
    - -0.324974831467432
    - -0.624072614063346
    - -0.8188439187002292
    - -0.9063932352485309
    - -0.8886895388344435
    - -0.7724480351828107
    - -0.5687860198140959
    - -0.2926667782965174
    - 0.037843897425156474
    - 0.4024743318402747
    - 0.7797543012995669
    - 1.1480844118887834
    - 1.486814909283752
    - 1.7772799321903636
    - 2.0037345414351257
    - 2.1541458777116835
    - 2.220796386132054
    - 2.2006659230671275
    - 2.0955703323214365
    - 1.912046236240925
    - 1.6609847393875619
    - 1.3570298364309452
    - 1.0177698747146866
    - 0.6627617774137421
    - 0.3124372616374799
    - -0.013052557707401838
    - -0.29499343805779604
    - -0.5172031695103593
    - -0.6670056462974671
    - -0.7360290977400925
    - -0.7207819788912317
    - -0.6229709330392731
    - -0.4495382938666447
    - -0.21241114940624833
    - 0.0720306994914386
    - 0.3837452894552108
    - 0.7000405608417752
    - 0.9967582149255718
    - 1.2495692953148214
    - 1.435314091423499
    - 1.5333151008549244
    - 1.5265916921011211
    - 1.402908872083044
    - 1.1556000693147812
    - 0.7841147696695351
    - 0.2942556691408334
    - -0.3019139541470151
    - -0.9864945272571354
    - -1.7364901323182127
    - -2.524830762859895
    - -3.321627653501447
    - -4.095598961592214
    - -4.815592774034775
    - -5.4521279248567955
    - -5.978870874868132
    - -6.373969131247772
    - -6.621168333801369
    - -6.71065091819864
    - -6.639548658049691
    - -6.41209864584855
    - -6.039431478783318
    - -5.539000521257018
    - -4.933681001637876
    - -4.250586236690706
    - -3.519664388937292
    - -2.772151893753758
    - -2.038968264346273
    - -1.3491408389599546
    - -0.7283468830349261
    - -0.19765429159095677
    - 0.2274687627361266
    - 0.5378199586392093
    - 0.730767873077116
    - 0.8101798272109983
    - 0.7859782907130437
    - 0.6733533495341096
    - 0.4916790700060305
    - 0.2631992785832994
    - 0.011562234144986569
    - -0.23970698517095074
    - -0.4687034491399029
    - -0.6565172108006843
    - -0.7884015156534507
    - -0.8546620835766167
    - -0.8512118922032983
    - -0.7797562049553269
    - -0.6475952988990276
    - -0.4670561025316189
    - -0.2545873088586289
    - -0.029574040373058743
    - 0.18705354757646503
    - 0.374329415231575
    - 0.5127816285739955
    positive_zeros:
    - '0.828897949149803896013174363248159'
    - '2.57355310935018226107201399723638'
    - '3.60111187189801712071253013087575'
    - '5.09770090519289561175703810635022'
    - '6.02243979005083481064955965391512'
    - '7.13616647195230287108638288182321'
    - '8.080834861520871573899606550287140'
    - '8.534391717658377293923877711077051'
    - '10.19770912385192263577053901491027'
    - '10.74322645379831194242323795429966'
    prelabel: 2-405-5.4-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.8883303440259604
    root_angle: -0.10076339743086177
    root_number: 0.9503126714407753548142500573551913555198640724187528816 - 0.3112970068906814100926469407956912176298493693246510726*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.05038169871543089'
      prec: 67
    spectral_label: c3-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.828897949149803896013174363248'
      prec: 107
    z2:
      __RealLiteral__: 0
      data: '2.57355310935018226107201399724'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.60111187189801712071253013088'
      prec: 103
- - algebraic: true
    analytic_conductor: 23.89577355232496
    bad_primes:
    - 3
    - 5
    central_character: '5.4'
    conductor: 405
    conductor_radical: 15
    degree: 2
    id: 24061529
    index: 22
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/405/4/b/f/244/8
    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: 2-405-5.4-c3-0-22
    motivic_weight: 3
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 3
    order_of_vanishing: 0
    prelabel: 2-405-5.4-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.8883303440259604
    root_angle: -0.050381698715430884
    self_dual: false
    spectral_label: c3-0
    z1:
      __RealLiteral__: 0
      data: '0.828897949149803896013174363248'
      prec: 107
- - Lhash: '1050752982767697281499742560203'
    Lhash_array:
    - '1050752982767697281499742560203'
    id: 24436898
    label: 2-405-5.4-c3-0-22
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/405/4/b/f/244/8
label_cols:
- label
- label
- label
labels:
- 2-405-5.4-c3-0-22
- 2-405-5.4-c3-0-22
- 2-405-5.4-c3-0-22
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-16T09:04:42.014376'