data:
- - Lhash: 334010275599263873523527205339,1917804669470357407689259755791,2309687313557868015840846439902,2537790157681856355655495002355
    a10: 0
    a2: 0
    a3: 2
    a4: 1
    a5: 0
    a6: 0
    a7: 0
    a8: 0
    a9: 1
    accuracy: 100
    algebraic: true
    analytic_conductor: 268.6211879468495
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - 1
        - -2
        - 3
        - -2
        - 1
    - - 13
      - - 1
    bad_primes:
    - 3
    - 13
    central_character: '507.1'
    coefficient_field: 1.1.1.1
    conductor: 66074188401
    conductor_radical: 39
    degree: 8
    euler_factors:
    - - 1
      - 0
      - -1
      - 0
      - -3
      - 0
      - -4
      - 0
      - 16
    - - 1
      - -2
      - 3
      - -2
      - 1
    - - 1
      - 0
      - 20
      - 0
      - 150
      - 0
      - 500
      - 0
      - 625
    - - 1
      - 0
      - -2
      - 0
      - -45
      - 0
      - -98
      - 0
      - 2401
    - - 1
      - 0
      - -10
      - 0
      - -21
      - 0
      - -1210
      - 0
      - 14641
    - - 1
    - - 1
      - 12
      - 74
      - 432
      - 2163
      - 7344
      - 21386
      - 58956
      - 83521
    - - 1
      - 0
      - -26
      - 0
      - 315
      - 0
      - -9386
      - 0
      - 130321
    - - 1
      - 0
      - -46
      - 0
      - 1587
      - 0
      - -24334
      - 0
      - 279841
    - - 1
      - 12
      - 50
      - 432
      - 3819
      - 12528
      - 42050
      - 292668
      - 707281
    - - 1
      - 0
      - 100
      - 0
      - 4422
      - 0
      - 96100
      - 0
      - 923521
    - - 1
      - 0
      - -26
      - 0
      - -693
      - 0
      - -35594
      - 0
      - 1874161
    - - 1
      - 0
      - -34
      - 0
      - -525
      - 0
      - -57154
      - 0
      - 2825761
    - - 1
      - 8
      - -38
      - 128
      - 5803
      - 5504
      - -70262
      - 636056
      - 3418801
    - - 1
      - 0
      - 164
      - 0
      - 11142
      - 0
      - 362276
      - 0
      - 4879681
    - - 1
      - -24
      - 428
      - -4680
      - 41046
      - -248040
      - 1202252
      - -3573048
      - 7890481
    - - 1
      - 0
      - -10
      - 0
      - -3381
      - 0
      - -34810
      - 0
      - 12117361
    - - 1
      - -4
      - -110
      - -16
      - 11179
      - -976
      - -409310
      - -907924
      - 13845841
    - - 1
      - 0
      - -26
      - 0
      - -3813
      - 0
      - -116714
      - 0
      - 20151121
    - - 1
      - 0
      - -130
      - 0
      - 11859
      - 0
      - -655330
      - 0
      - 25411681
    - - 1
      - 0
      - 292
      - 0
      - 31974
      - 0
      - 1556068
      - 0
      - 28398241
    - - 1
      - 32
      - 700
      - 9632
      - 102214
      - 760928
      - 4368700
      - 15777248
      - 38950081
    - - 1
      - 0
      - 308
      - 0
      - 37494
      - 0
      - 2121812
      - 0
      - 47458321
    - - 1
      - 0
      - -130
      - 0
      - 8979
      - 0
      - -1029730
      - 0
      - 62742241
    - - 1
      - 0
      - -2
      - 0
      - -9405
      - 0
      - -18818
      - 0
      - 88529281
    - - 1
      - -12
      - -94
      - -432
      - 31899
      - -43632
      - -958894
      - -12363612
      - 104060401
    - - 1
      - 32
      - 796
      - 11936
      - 146854
      - 1229408
      - 8444764
      - 34967264
      - 112550881
    - - 1
      - 24
      - 218
      - 3456
      - 55083
      - 369792
      - 2495882
      - 29401032
      - 131079601
    - - 1
      - 0
      - 340
      - 0
      - 52662
      - 0
      - 4039540
      - 0
      - 141158161
    - - 1
      - -12
      - -118
      - -432
      - 39603
      - -48816
      - -1506742
      - -17314764
      - 163047361
    euler_factors_factorization:
    - - - - 1
          - 0
          - -1
          - 0
          - -3
          - 0
          - -4
          - 0
          - 16
        - 1
    - - - - 1
          - -1
          - 1
        - 2
    - - - - 1
          - 0
          - 5
        - 4
    - - - - 1
          - 0
          - -13
          - 0
          - 49
        - 1
      - - - 1
          - 0
          - 11
          - 0
          - 49
        - 1
    - - - - 1
          - 0
          - -10
          - 0
          - -21
          - 0
          - -1210
          - 0
          - 14641
        - 1
    - - 1
    - - - - 1
          - 6
          - 19
          - 102
          - 289
        - 2
    - - - - 1
          - 0
          - -37
          - 0
          - 361
        - 1
      - - - 1
          - 0
          - 11
          - 0
          - 361
        - 1
    - - - - 1
          - 0
          - -23
          - 0
          - 529
        - 2
    - - - - 1
          - 6
          - 7
          - 174
          - 841
        - 2
    - - - - 1
          - 0
          - 50
          - 0
          - 961
        - 2
    - - - - 1
          - 0
          - -73
          - 0
          - 1369
        - 1
      - - - 1
          - 0
          - 47
          - 0
          - 1369
        - 1
    - - - - 1
          - 0
          - -34
          - 0
          - -525
          - 0
          - -57154
          - 0
          - 2825761
        - 1
    - - - - 1
          - 4
          - -27
          - 172
          - 1849
        - 2
    - - - - 1
          - 0
          - 82
          - 0
          - 2209
        - 2
    - - - - 1
          - -6
          - 53
        - 4
    - - - - 1
          - 0
          - -10
          - 0
          - -3381
          - 0
          - -34810
          - 0
          - 12117361
        - 1
    - - - - 1
          - -2
          - -57
          - -122
          - 3721
        - 2
    - - - - 1
          - 0
          - -26
          - 0
          - -3813
          - 0
          - -116714
          - 0
          - 20151121
        - 1
    - - - - 1
          - 0
          - -130
          - 0
          - 11859
          - 0
          - -655330
          - 0
          - 25411681
        - 1
    - - - - 1
          - 0
          - 73
        - 4
    - - - - 1
          - 8
          - 79
        - 4
    - - - - 1
          - 0
          - 154
          - 0
          - 6889
        - 2
    - - - - 1
          - 0
          - -130
          - 0
          - 8979
          - 0
          - -1029730
          - 0
          - 62742241
        - 1
    - - - - 1
          - 0
          - -169
          - 0
          - 9409
        - 1
      - - - 1
          - 0
          - 167
          - 0
          - 9409
        - 1
    - - - - 1
          - -6
          - -65
          - -606
          - 10201
        - 2
    - - - - 1
          - 8
          - 103
        - 4
    - - - - 1
          - 12
          - 37
          - 1284
          - 11449
        - 2
    - - - - 1
          - 0
          - 170
          - 0
          - 11881
        - 2
    - - - - 1
          - -6
          - -77
          - -678
          - 12769
        - 2
    gamma_factors:
    - []
    - - 0
      - 0
      - 0
      - 0
    group: GL2
    id: 10859156
    index: 4
    label: 8-507e4-1.1-c1e4-0-4
    load_key: CMFs-workshop
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    - 1
    - 1
    - 1
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/507/2/e/e
    plot_delta:
      __RealLiteral__: 0
      data: '0.03125'
      prec: 24
    plot_values:
    - 0.9838901723828212
    - 0.9682608449655005
    - 0.9280526610035251
    - 0.8619380505924805
    - 0.7684564424533832
    - 0.6462125631982415
    - 0.4945312450286243
    - 0.31292034493380144
    - 0.10090543799318386
    - -0.14197865360327433
    - -0.41624531864629816
    - -0.7222196735825812
    - -1.0599346933894196
    - -1.4290055584982637
    - -1.8283163813794978
    - -2.256101054275146
    - -2.709948204496492
    - -3.186679892458971
    - -3.682073087586264
    - -4.191006793919249
    - -4.707525848922591
    - -5.224786804250488
    - -5.734888802742487
    - -6.22918520555719
    - -6.698480273122315
    - -7.133145712491338
    - -7.523237516505719
    - -7.858898367837761
    - -8.130661061925608
    - -8.329747059267717
    - -8.448481931927692
    - -8.480618362017513
    - -8.421604236628475
    - -8.268921459392088
    - -8.022605184466096
    - -7.685206923502998
    - -7.261783706372434
    - -6.760013045907227
    - -6.1904668111513566
    - -5.566007278607955
    - -4.901327957668541
    - -4.212653756481802
    - -3.517526654737949
    - -2.8337565243219847
    - -2.1786520303745944
    - -1.5684365616059102
    - -1.0177025348086326
    - -0.538473127837635
    - -0.13962814917816652
    - 0.17347213382530371
    - 0.39929908085284166
    - 0.5402931207496441
    - 0.6026970683756963
    - 0.596234813260018
    - 0.5336838499735889
    - 0.4300195906597111
    - 0.3014925069791534
    - 0.16469333917739423
    - 0.03557535660647972
    - -0.07168607158466231
    - -0.1456045722928928
    - -0.17810694747361583
    - -0.1651029648356581
    - -0.10676200739739104
    - -0.00743998909490197
    - 0.12467912339555699
    - 0.2782524106008777
    - 0.4397553560697379
    - 0.5946107572249498
    - 0.7284637358408143
    - 0.828645258938281
    - 0.8853057038153163
    - 0.8923568969552216
    - 0.8482744270990514
    - 0.7567233433790788
    - 0.6262125266175815
    - 0.46948105085045755
    - 0.30264254032841276
    - 0.14396589882752658
    - 0.011945406868637348
    - -0.07650847476658713
    - -0.10781271717870922
    - -0.0734484669108433
    - 0.02865147861864682
    - 0.19330981328214283
    - 0.40783933523902166
    - 0.6524487444926179
    - 0.9014497358203009
    - 1.124979778893431
    - 1.2912916542931108
    - 1.36985414744211
    - 1.3340096537462813
    - 1.1634790787798555
    - 0.8468773786077757
    - 0.38426735414545227
    - -0.21252415472741937
    - -0.9201431369876856
    - -1.7044588517232986
    - -2.5222000166519236
    - -3.3245039055739083
    - -4.060434326531383
    - -4.6808138389795015
    - -5.142914306922679
    - -5.413845400513757
    - -5.473051253780165
    - -5.314573268469713
    - -4.949350485629847
    - -4.403104858721678
    - -3.713795444707669
    - -2.9291192846610694
    - -2.1038524973903674
    - -1.2933052849860007
    - -0.548292347549491
    - 0.08859549476023558
    - 0.5859472415837842
    - 0.9270270303455482
    - 1.1105484133629229
    - 1.1496207555592752
    - 1.0695018409797472
    - 0.9042320415159719
    - 0.6920325843610629
    - 0.4704240585962026
    - 0.2716430119048539
    - 0.11865057740165894
    - 0.022524897114671524
    - -0.018434027138226547
    - -0.01776075604616269
    - 0.001901180496863794
    - 0.013109910904023603
    - -0.010962998280796376
    - -0.09089234477970529
    - -0.2357238116238504
    - -0.4386155925729752
    - -0.6743216160665562
    - -0.9001765542640389
    - -1.0586031048153317
    - -1.0816822246313507
    - -0.8985851708243124
    - -0.44685709422824993
    - 0.3193896529020052
    - 1.4216589695431183
    - 2.8494552197770897
    - 4.55386516010929
    - 6.448830060628901
    - 8.414926488419177
    - 10.306391739100324
    - 11.963539680880348
    - 13.226609721095343
    - 13.949953377616914
    - 14.017881051988239
    - 13.362910823690065
    - 11.971516012658153
    - 9.887482638975452
    - 7.213501813442279
    - 4.10911357293478
    - 0.7731829159823455
    - -2.5728898281869093
    - -5.702708640756196
    - -8.405927118272523
    - -10.509082395167907
    - -11.889950081253334
    - -12.48866228854158
    - -12.316736637518758
    - -11.450709606231186
    - -10.021336097581756
    - -8.200700855325179
    - -6.186452345043532
    - -4.17600036745045
    - -2.346122069267269
    - -0.837026816967617
    - 0.26055815393220544
    - 0.9129586322821471
    - 1.1419381100973212
    - 1.0171895844472927
    - 0.6443245714604029
    - 0.1466416249571718
    - -0.3536684743949605
    - -0.7527154774653549
    - -0.9794086162704213
    - -1.0048144122417806
    - -0.8444779220122427
    - -0.5543939063687999
    - -0.2209040273036713
    - 0.054700484472288896
    - 0.17338740864417193
    - 0.055656180522530636
    - -0.34330808033911
    - -1.024387046046985
    - -1.9410929824355965
    - -3.0027649823504445
    - -4.086607338102309
    - -5.053326726137302
    - -5.7645249886359995
    - -6.102478423908344
    - -5.99240928429159
    - -5.410987027961098
    - -4.389626825664775
    - -3.014191060448068
    - -1.419963092641611
    - 0.23050006290889863
    - 1.7689420934268874
    - 3.041341305828618
    - 3.926713074818918
    - 4.356311887457328
    - 4.322322378540474
    - 3.8776032357540453
    - 3.1275293694781046
    - 2.2158458788657387
    - 1.3042378903730425
    - 0.5488538061041621
    - 0.07740732985684758
    - -0.02725250948011615
    - 0.26121996373961703
    - 0.9084112768828496
    - 1.8264815207142853
    - 2.8878564605655246
    - 3.9420135089069417
    - 4.837311811198546
    - 5.448790916045227
    - 5.691634422534413
    - 5.529842259924989
    - 4.982152571309478
    - 4.123235553090233
    - 3.065066332651985
    - 1.9385222702033131
    - 0.8756801122406327
    - -0.008741629597705877
    - -0.6359432598540833
    - -0.9720363211916616
    - -1.029722254921075
    - -0.863456019968152
    - -0.5568855499882798
    - -0.20640472356477158
    - 0.09691472819084553
    - 0.2851614682843649
    - 0.3244564426610709
    - 0.22017072423422981
    - 0.016367168926213708
    - -0.2126878558542791
    - -0.3786004940106507
    - -0.39474348463075837
    - -0.1926259840945375
    - 0.2605404729587522
    - 0.9555000354477188
    - 1.8417996520493163
    - 2.832874475626438
    - 3.815453914923184
    - 4.670638469020008
    - 5.292742779925218
    - 5.604740653613938
    - 5.57077673128981
    - 5.202138503311546
    - 4.553980748657601
    - 3.7159073691575637
    - 2.798233891704961
    - 1.9118244298350087
    - 1.1499244060938474
    - 0.5743457846152661
    - 0.20723420168806236
    - 0.029048955829582012
    - -0.014838395039131395
    - -0.001195745249932337
    - -0.012242275052394693
    - -0.11849067815423386
    - -0.3637002973210063
    - -0.7548472972347706
    - -1.2608729905802087
    - -1.8179243000178127
    - -2.339995755181382
    - -2.735154727937621
    - -2.927243081247465
    - -2.8690925398208846
    - -2.5512545334146193
    - -2.0065251482442577
    - -1.308342831562591
    - -0.5551780845308941
    - 0.14693373864653136
    - 0.7024686930613407
    - 1.044647872325502
    - 1.148035823183294
    - 1.0325957808799022
    - 0.7603114692752352
    - 0.4243316744953346
    - 0.12929405924131335
    - -0.029171465320434957
    - 0.016609450196591182
    - 0.29175554868975095
    - 0.7726652942208673
    - 1.3898650142572548
    - 2.0396547472541435
    - 2.6053218869221832
    - 2.978503747181211
    - 3.0788083181257524
    - 2.871057553529983
    - 2.37731227696436
    - 1.6699957471475197
    - 0.8587451481292291
    - 0.07238624927721357
    - -0.5650252355026946
    - -0.9604497987988498
    - -1.0688737472424887
    - -0.9021836388789951
    - -0.5297234927543407
    - -0.06354778617388125
    - 0.36422938847129677
    - 0.6271792708936236
    - 0.6299866486725177
    - 0.33025788976206993
    - -0.2505199529081401
    - -1.0287049517248028
    - -1.87519117040559
    - -2.6380806538225356
    - -3.170204312806241
    - -3.359655523135666
    - -3.1590097941870465
    - -2.5914836041868408
    - -1.7478202314828353
    - -0.7739807030484378
    - 0.1542953053809223
    - 0.8696065517781016
    - 1.2439851805696336
    - 1.2137425011991898
    - 0.7974179413797615
    - 0.0914724497297658
    - -0.749458753851835
    - -1.5419870065727892
    - -2.1109892275842137
    - -2.3300958603710016
    - -2.151193265319938
    - -1.620045164607995
    - -0.8749213857815236
    - -0.12385845731178537
    - 0.3919202311656824
    - 0.4436679734757134
    - -0.1363302342735138
    - -1.4178097709035227
    - -3.3502251409544255
    - -5.759433125524876
    - -8.37313898256125
    - -10.861110531645737
    - -12.881878645381295
    - -14.138770635617147
    - -14.446357254533343
    - -13.749801361921932
    - -12.127590414453095
    - -9.784927294302022
    - -7.034642124098873
    - -4.227075975888427
    - -1.6907788412642242
    - 0.31321736777036446
    - 1.6261632562172612
    - 2.2186534820770145
    - 2.1843051874057164
    - 1.7106479128947338
    - 1.036063826409893
    - 0.401648865640105
    - 0.003851773330856609
    - -0.042049821279240195
    - 0.2821046008128098
    - 0.903163178005122
    - 1.6773386706447777
    - 2.4257353623334805
    - 2.9832695826384494
    - 3.231646430642721
    - 3.1204886308113626
    - 2.6783189393242504
    - 2.0091501264259923
    - 1.2576231023024644
    - 0.5732544512878649
    - 0.07773537712800727
    - -0.16360171770666096
    - -0.15835933575384784
    - 0.018366301455465237
    - 0.24511640618430766
    - 0.38586148542630927
    - 0.3283050924127015
    - 0.017017259754276606
    - -0.5273233307705595
    - -1.2107311861618262
    - -1.8839817405746873
    - -2.376060953863264
    - -2.541397608725631
    - -2.313787262325299
    - -1.7301405315258833
    - -0.9401647311092863
    - -0.19870192695388483
    - 0.17151291324685553
    - -0.15327484216100132
    - -1.4348070895759981
    - -3.812702585477671
    - -7.249714971631951
    - -11.519237433501262
    - -16.22503399304742
    - -20.84768050457225
    - -24.822735277801623
    - -27.629729915741887
    - -28.871812948812956
    - -28.34489548143029
    - -26.0917448003256
    - -22.382839389031943
    - -17.671868442110902
    - -12.532715990133429
    - -7.575798947871858
    - -3.3433197986991345
    - -0.2340022741097437
    - 1.5465576665121155
    - 2.008178792472157
    - 1.350981831172746
    - -0.08551610534496408
    - -1.8890104840882393
    - -3.654809637637322
    - -5.053220709807004
    - -5.870375816374274
    - -6.02956044058312
    - -5.594133912838829
    - -4.722749131163536
    - -3.6200840710405737
    - -2.4926997795945054
    - -1.5113206925183067
    - -0.7761750340181566
    - -0.31152099579475356
    - -0.07948005396762028
    - -0.004643428517041127
    - -0.0033370802681651443
    - -0.011223386363339536
    - -0.000404347419500558
    - 0.01746557698413715
    - 0.0013895064620202758
    - -0.09889955698099956
    - -0.31911082644385136
    - -0.662322162212733
    - -1.0902369790816362
    - -1.5255327983042786
    - -1.867996454382278
    - -2.0260349469767793
    - -1.940821992896162
    - -1.6048654666987032
    - -1.0733887743817339
    - -0.462542658971127
    - 0.07828609411533173
    - 0.4000134977172214
    - 0.38934235860126215
    - 0.0024224139427835734
    - -0.7170686471819613
    - -1.6389547030027838
    - -2.566512887692063
    - -3.276686641609278
    - -3.566066310907285
    - -3.2940237644956984
    - -2.4188919089726397
    - -1.0176610924034688
    - 0.7302158479002846
    - 2.5728852771479285
    - 4.230197712868026
    - 5.454984232282216
    - 6.078808625857848
    - 6.037717129863237
    - 5.384515509591445
    - 4.285694695115699
    - 2.9706423834691043
    - 1.6795544064220596
    - 0.6178834870294848
    - -0.08186413127499124
    - -0.39009183997228764
    - -0.37762777940069986
    - -0.1900364474825859
    - -0.007325502766843444
    - 0.0021235953191726885
    - -0.27502901714295497
    - -0.867570722035781
    - -1.7147513677249182
    - -2.6810807843659994
    - -3.585550788492727
    - -4.2443160757821765
    - -4.5228932435234155
    - -4.360085783445645
    - -3.777699388069774
    - -2.8781569709637504
    - -1.8253903123035602
    - -0.7987573200763006
    - 0.045333000388057945
    - 0.6029026037342518
    - 0.8428117653948574
    - 0.8057279754912461
    - 0.5847904746222092
    - 0.29730831376809075
    - 0.05306302506519262
    - -0.07521382588329
    - -0.06682346024596214
    - 0.04735325521609553
    - 0.20019293748734598
    - 0.31356929465321676
    - 0.32467953229995156
    - 0.2074808848829187
    - -0.017274821727513375
    - -0.28997861299250155
    - -0.5308074623124842
    - -0.6651987643326114
    - -0.6519711196629185
    - -0.4984473338072677
    - -0.259896980833082
    - -0.02488349711421617
    - 0.11281558310488403
    - 0.09221558950870103
    - -0.08447162344324993
    - -0.3361423989873569
    - -0.5087154240770033
    - -0.4042588024856024
    - 0.17180527090488928
    - 1.3541909842590605
    - 3.1661463256368596
    - 5.491455449912486
    - 8.071648185541925
    - 10.537685684715347
    - 12.488622504934954
    - 13.565854385741204
    - 13.524478233339487
    - 12.301976534778758
    - 10.07097338804125
    - 7.196635211509983
    - 4.1710403945067664
    - 1.5311882177671947
    - -0.24349564882110536
    - -0.8432506078824311
    - -0.19085431764677446
    - 1.5408974046102795
    - 3.961721661384409
    - 6.546268992534471
    - 8.740853646559808
    - 10.079322723533656
    - 10.295214429450798
    - 9.363598607454366
    - 7.496297052165543
    - 5.097147670907744
    - 2.675929433436556
    - 0.7210428089129426
    - -0.404649033860024
    - -0.5380215005759946
    - 0.25285815889400204
    - 1.69797767500312
    - 3.3940126127415913
    - 4.899866786483302
    - 5.85250330754202
    - 6.0423203946441735
    - 5.446176747063152
    - 4.225680887821962
    - 2.6872540412146755
    - 1.1815857512423567
    - 0.011395950027711746
    - -0.6406601064251914
    - -0.7574619294500137
    - -0.4862802467784155
    - -0.09074812379026928
    - 0.12465262419181951
    - -0.097265755700897
    - -0.8903433665845527
    - -2.2236008297818333
    - -3.901845352815716
    - -5.615316875615481
    - -7.01547514966893
    - -7.797714070210665
    - -7.7818308707482675
    - -6.975201104838844
    - -5.55565830668429
    - -3.823987819106223
    - -2.137154666073824
    - -0.8239967677532117
    - -0.08889778178104556
    - 0.03404999843351752
    - -0.31763189295867755
    - -0.8736729233012026
    - -1.3073824840606012
    - -1.3295024619999563
    - -0.7714188410735633
    - 0.364761964520568
    - 1.899156843902383
    - 3.51243692562609
    - 4.827364873331587
    - 5.524633432002351
    - 5.419355232548042
    - 4.511355235676454
    - 3.004643093695153
    - 1.282814133262591
    - -0.20199884658504547
    - -1.0395254740260262
    - -0.9578332311170275
    - 0.10929487787556463
    - 1.98885191727597
    - 4.301296918382278
    - 6.546649125827079
    - 8.234264883012814
    - 8.990350558003271
    - 8.643674562208986
    - 7.27460644689529
    - 5.20751012168643
    - 2.926177689301644
    - 0.9653779884076661
    - -0.21049874275835856
    - -0.32133335353616893
    - 0.6729500253972284
    - 2.563777911238111
    - 4.935650767270617
    - 7.275835370991727
    - 9.087499716295916
    - 9.982210361575353
    - 9.760675949425854
    - 8.477628453417434
    - 6.38891268721853
    - 3.875868634990241
    - 1.3655887348983566
    - -0.7525107203934888
    - -2.217046334589856
    - -2.931140669988989
    - -2.9582989636535846
    - -2.4870294452182247
    - -1.7630157930426464
    - -1.0227294042187203
    - -0.44119769250998375
    - -0.1011781994092534
    - 0.008121622229914178
    - -0.035286004125940434
    - -0.12575660697188656
    - -0.1722233719609426
    - -0.12815469227133627
    - -0.0014863259168450026
    - 0.15459595708126483
    - 0.2676580626504964
    - 0.2778142951570405
    - 0.16234756459271207
    - -0.052260436194863945
    - -0.295410608423878
    - -0.4764101417890326
    - -0.5146389304112561
    - -0.368091060593002
    - -0.05228220379448687
    - 0.3608784427779204
    - 0.7607295016783873
    - 1.028094905618028
    - 1.0732036833301493
    - 0.8616444504360579
    - 0.42519358816788455
    - -0.14354314982635172
    - -0.7154015659700875
    - -1.1627294895673035
    - -1.3925337002939158
    - -1.3707138520485227
    - -1.1323722399313616
    - -0.7644608450197872
    - -0.37653276391534435
    - -0.06783916534115428
    - 0.10287007799003563
    - 0.13297607115723714
    - 0.07000164532253632
    - -0.010974710967152088
    - -0.040683552776491765
    - 0.011548074159637866
    - 0.11987467866062967
    - 0.20500868054379132
    - 0.16195330510427558
    - -0.09540902750510868
    - -0.5864953669009498
    - -1.225575293340129
    - -1.8109030954989958
    - -2.0505412517653863
    - -1.6165747220263
    - -0.2231454447999212
    - 2.282555403755272
    - 5.86068864247203
    - 10.25121329869856
    - 14.990631789551928
    - 19.496923909260445
    - 23.16665158440574
    - 25.475208085740924
    - 26.08482090636983
    - 24.952292295559314
    - 22.29706448508302
    - 18.542075883227074
    - 14.241047228465293
    - 9.986287263367375
    - 6.26839216516005
    - 3.3987836911238416
    - 1.4824852780832811
    - 0.43338136006899053
    - 0.03301275230867802
    - 0.009994110512172201
    - 0.1169963906456148
    - 0.19100262714205207
    - 0.17306412024697088
    - 0.08979037115797592
    - 0.01257299755869786
    - 0.005690746406018262
    - 0.08116009670509605
    - 0.18373375346926982
    - 0.2059971202975775
    - 0.02729140450303985
    - -0.43284744002167996
    - -1.168642572944291
    - -2.068640050964769
    - -2.9410786124952377
    - -3.5604917283714284
    - -3.7307500092484167
    - -3.357205289737793
    - -2.509524063882289
    - -1.4005593722794327
    - -0.331281489118857
    - 0.3892640722982258
    - 0.546403554145862
    - 0.12466067884916214
    - -0.6488009496557325
    - -1.3240923567205205
    - -1.319445148420444
    - -0.06334496779628465
    - 2.84825966120754
    - 7.510496595320453
    - 13.619568447166332
    - 20.496052851918982
    - 27.18713149139195
    - 32.63993394802589
    - 35.940665690024005
    - 36.50395132485369
    - 34.19344448568069
    - 29.371110241769934
    - 22.852458438495233
    - 15.699505521687602
    - 8.99849551329965
    - 3.6479686034159275
    - 0.175724666669341
    - -1.3439320388971454
    - -1.2539274967170335
    - -0.1938888626822007
    - 1.0810801788279536
    - 1.9092948205319
    - 1.8795258722782269
    - 0.9116957075089381
    - -0.7627713932471959
    - -2.6997426641041327
    - -4.383121203701873
    - -5.382575947942256
    - -5.498729614956356
    - -4.787130169459845
    - -3.516307740613368
    - -2.079586162766488
    - -0.8688425775221228
    - -0.13069586129205693
    - 0.10761987799030141
    - 0.04136507945637808
    - 0.022130109934765548
    - 0.4335753733805599
    - 1.5515033099693252
    - 3.4287808945168288
    - 5.848008057702774
    - 8.351417901752091
    - 10.336755823715839
    - 11.211437626439967
    - 10.584119685223598
    - 8.364251702514101
    - 4.80288359427092
    - 0.4704012910792659
    - -3.8567904113151132
    - -7.389322388657734
    - -9.491719232403213
    - -9.819345994698216
    - -8.412098031132562
    - -5.654749955781162
    - -2.171259064012315
    - 1.3179327900933884
    - 4.165756407976383
    - 5.936335060318244
    - 6.469219499274421
    - 5.883566215574619
    - 4.525581095326102
    - 2.837358237071514
    - 1.2371436937845974
    - 0.028353499370727443
    - -0.6534947275068955
    - -0.8400039486789513
    - -0.680989967921782
    - -0.37367944421974814
    - -0.08858310959241172
    - 0.07715716063155234
    - 0.10995540297855538
    - 0.06079302017348214
    - 0.004406841884357811
    - -0.011022172965743824
    - 0.0077225341289646286
    - -0.0022962891358007612
    - -0.1350478326630848
    - -0.47117868563812637
    - -1.0320764312385213
    - -1.7514588917894847
    - -2.482450595330018
    - -3.0320503916404093
    - -3.216232632068631
    - -2.9269595552742507
    - -2.192781692368149
    - -1.1820503710784531
    - -0.1735596919587441
    - 0.5028461214303412
    - 0.5563320282516171
    - -0.17716112422882535
    - -1.6828331864810624
    - -3.7545339353033853
    - -6.033549551334031
    - -8.093128067764535
    - -9.533697554366002
    - -10.076671184600533
    - -9.643041274733134
    - -8.350744495795189
    - -6.4736216656150125
    - -4.3745955312954745
    - -2.4173933893492663
    - -0.8751527782478234
    - 0.11607722073577473
    - 0.5664122619170411
    - 0.6067073042671693
    - 0.4229691318734188
    - 0.1918139625360975
    - 0.03252359666138234
    - -0.016392737797768727
    - 0.011445916478737614
    - 0.04590036778953368
    - 0.02440903069657905
    - -0.07149559339173649
    - -0.20219135947237113
    - -0.28272437320751004
    - -0.21745371776428382
    - 0.05444122394211017
    - 0.5248528255396712
    - 1.1038758643352442
    - 1.6358745091810836
    - 1.9500592887049473
    - 1.9129689357552369
    - 1.473936371685491
    - 0.6956466630696735
    - -0.24753169308733738
    - -1.1237798943387143
    - -1.7059154181678347
    - -1.8357016436169353
    - -1.4842529078607969
    - -0.7582199728760372
    - 0.1335696326076362
    - 0.9363562712151025
    - 1.4208416837564857
    - 1.4599541973423622
    - 1.0644989175378643
    - 0.37616058916735745
    - -0.381259178568507
    - -0.975300556488001
    - -1.2381863188736852
    - -1.1220271281445622
    - -0.7192961352822502
    - -0.2223178254001721
    - 0.14492317697013732
    - 0.20426566490056186
    - -0.10950449798064991
    - -0.7189159494287622
    - -1.424319758592357
    - -1.967028078778763
    - -2.1262215534794433
    - -1.7994479935808771
    - -1.047383216067507
    - -0.09402380560931765
    - 0.7288371914400056
    - 1.0896848122890215
    - 0.7633643016417171
    - -0.2868837377041123
    - -1.8762888749769295
    - -3.6431955401030764
    - -5.144288638017049
    - -5.981478006574368
    - -5.938852731975666
    - -5.044013773300986
    - -3.5611919099767286
    - -1.924176485956999
    - -0.6115491967302578
    - 0.019259869085187533
    - -0.1521614157989144
    - -0.961026753458584
    - -1.9968233702007392
    - -2.7261193217622073
    - -2.6563901102352507
    - -1.5026548415367043
    - 0.6830275738347716
    - 3.5059186576058647
    - 6.316438604851807
    - 8.369986046235082
    - 9.033189465303256
    - 7.975562987556574
    - 5.279270275020339
    - 1.4420594713221357
    - -2.757666147630466
    - -6.449594951842313
    - -8.876393712940567
    - -9.593930762348542
    - -8.621268355558422
    - -6.3720715376067405
    - -3.5186463332795035
    - -0.8152377348202744
    - 1.1145207198228135
    - 1.9643266931664063
    - 1.801960490677486
    - 1.022792977937034
    - 0.2163721556449363
    - -0.03927487925791761
    - 0.6346728995433933
    - 2.2958638380934664
    - 4.664133304439998
    - 7.205253370702716
    - 9.280655528186234
    - 10.338222167386407
    - 10.106694849446841
    - 8.641975545214875
    - 6.295973463559378
    - 3.62634866604033
    - 1.2430894683778897
    - -0.38969497717002904
    - -1.0632251878061183
    - -0.8544422352120438
    - -0.08278964552627191
    - 0.8201128693489461
    - 1.4624499324701659
    - 1.6152763647037929
    - 1.279069077897418
    - 0.6697443461486636
    - 0.12882109915216983
    - -0.00752274958852559
    - 0.4673131747480283
    - 1.5553395580009646
    - 3.039433181865211
    - 4.543788676862334
    - 5.677109421430908
    - 6.144507588666867
    - 5.8246221802754965
    - 4.813274414325257
    - 3.4122716348568356
    - 1.9936908523332222
    - 0.8744626465862465
    - 0.22332702302395813
    - 0.00869895349499346
    - 0.009444902503576642
    - -0.09699096831000828
    - -0.6124256392164955
    - -1.7033107560390042
    - -3.3292090555488643
    - -5.23453987336938
    - -7.0152584704643965
    - -8.26244059106261
    - -8.674826303876507
    - -8.140333045222732
    - -6.782328135974538
    - -4.947630552835693
    - -3.063319162104776
    - -1.504739025229817
    - -0.49588672289653307
    - -0.051636730049491465
    - 0.015267304749822278
    - 0.0013333515693279697
    - 0.18142764995839347
    - 0.6825550444610616
    - 1.4057983309995754
    - 2.024366594086041
    - 2.065657107239436
    - 1.0659933389275924
    - -1.2731467790989146
    - -4.957873214862298
    - -9.63901096114853
    - -14.668828472562579
    - -19.238826612601912
    - -22.545676534122506
    - -23.982355160559777
    - -23.336930633468988
    - -20.795423780827736
    - -16.87079686516323
    - -12.289881910022343
    - -7.838140641480224
    - -4.14656919767242
    - -1.573058659332649
    - -0.1680706956156556
    - 0.2862210316490288
    - 0.16486841229271018
    - -0.13203736534484659
    - -0.2951674598409968
    - -0.17802205355885914
    - 0.19724680391324745
    - 0.6864443049762773
    - 1.1002299441344414
    - 1.2925429713309253
    - 1.2090994937152237
    - 0.8947219865667677
    - 0.46932756243760304
    - 0.07939909195302536
    - -0.16439355350378015
    - -0.22179564827616602
    - -0.12692807051621763
    - 0.03632671457020615
    - 0.17596309436853982
    - 0.23067513966983114
    - 0.1919741957097168
    - 0.10144996508098636
    - 0.0205408461872109
    - -0.006236204888946675
    - 0.020370602761287045
    - 0.048234293055824475
    - -0.0036152756248178913
    - -0.20319476543518353
    - -0.5590884736998285
    - -0.9924625485436541
    - -1.3447655997641514
    - -1.4162405748932902
    - -1.0343227508820871
    - -0.1481614299078951
    - 1.1331920945930893
    - 2.5497547450776974
    - 3.7420796080543752
    - 4.343550234414322
    - 4.089442522643599
    - 2.899950215928201
    - 0.924941185316558
    - -1.4412760669315943
    - -3.6304932023619996
    - -5.074157833582758
    - -5.441124377462149
    - -4.85782961022795
    - -3.665081878678966
    positive_zeros:
    - '0.26348764836235493063783754691676'
    - '1.51288112759546948772989045945555'
    - '1.82202202495074669595275408454291'
    - '2.00196344104988349130777804530601'
    - '2.47213258723872095346986646650701'
    - '2.58674421072034485304408973566352'
    - '2.95834841522328463941104787985057'
    - '3.52649651814239581667528243385178'
    - '3.88752404187981442698898770881202'
    - '3.96586037906396517021802940316955'
    - '4.02311220813120766645505299471106'
    - '4.33232017353456202698221065040381'
    - '4.85090603086031049925575186468713'
    - '5.30381557664612946007544395455754'
    - '5.47761857973137237889707746894347'
    - '5.71132870315572181055302443724118'
    - '5.78741246628291012785137877972124'
    - '6.21434428146745364696109689730980'
    - '6.57274609028942619329965000869576'
    - '6.60014161382903242036073866969580'
    - '7.06214387103409971680685012791600'
    - '7.27017958399500349143551862433962'
    - '7.40846100464523643984076280573005'
    - '7.54680014348575957132171804626274'
    - '8.105864610898901813475340139241319'
    - '8.159046673784514648429178492490852'
    - '8.175185999031981602091841397726137'
    - '8.618032925928548847544400093121940'
    - '8.865447672719745198249203519295349'
    - '8.902722682514192041147811383761777'
    - '9.284378420836485645111047704114177'
    - '9.473024598556610034544765491971128'
    - '9.613084657114825132540688034066101'
    - '9.931929061707536169344873352416197'
    - '10.09730016357816042317696211800123'
    - '10.34970142411798494226516679032207'
    - '10.43263562530561293191616817986263'
    - '10.90062390626560329053170751235470'
    - '11.12552305658876342010011729395198'
    - '11.16326265903685375828083795416667'
    prelabel: 8-507e4-1.1-c1e4-0
    primitive: false
    rational: true
    root_analytic_conductor: 2.0120674398436345
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    spectral_label: c1e4-0
    trace_hash: 1914720887379295860
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.26348764836235493063783754692'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '1.51288112759546948772989045946'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '1.82202202495074669595275408454'
      prec: 103
- - algebraic: true
    analytic_conductor: 268.6211879468495
    bad_primes:
    - 3
    - 13
    central_character: '1.1'
    conductor: 66074188401
    conductor_radical: 39
    degree: 8
    dirichlet_coefficients:
    - 1
    - 0
    - 2
    - 1
    - 0
    - 0
    - 0
    - 0
    - 1
    - 0
    - 0
    - 2
    - 0
    - 0
    - 0
    - 4
    - -12
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -20
    - 0
    - -2
    - 0
    - -12
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 1
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -8
    - 0
    - 0
    - 0
    - 0
    - 8
    - 2
    - 0
    - -24
    - 0
    - 24
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 4
    - 0
    - 0
    - 11
    - 0
    - 0
    - 0
    - -12
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -40
    - 0
    - 0
    - 0
    - -32
    - 0
    - -4
    - 0
    - 0
    - 0
    - 0
    - 0
    - -24
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -20
    euler11:
    - 1
    - 0
    - -10
    - 0
    - -21
    - 0
    - -1210
    - 0
    - 14641
    euler13:
    - 1
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    euler17:
    - 1
    - 12
    - 74
    - 432
    - 2163
    - 7344
    - 21386
    - 58956
    - 83521
    euler19:
    - 1
    - 0
    - -26
    - 0
    - 315
    - 0
    - -9386
    - 0
    - 130321
    euler2:
    - 1
    - 0
    - -1
    - 0
    - -3
    - 0
    - -4
    - 0
    - 16
    euler23:
    - 1
    - 0
    - -46
    - 0
    - 1587
    - 0
    - -24334
    - 0
    - 279841
    euler29:
    - 1
    - 12
    - 50
    - 432
    - 3819
    - 12528
    - 42050
    - 292668
    - 707281
    euler3:
    - 1
    - -2
    - 3
    - -2
    - 1
    - 0
    - 0
    - 0
    - 0
    euler31:
    - 1
    - 0
    - 100
    - 0
    - 4422
    - 0
    - 96100
    - 0
    - 923521
    euler37:
    - 1
    - 0
    - -26
    - 0
    - -693
    - 0
    - -35594
    - 0
    - 1874161
    euler41:
    - 1
    - 0
    - -34
    - 0
    - -525
    - 0
    - -57154
    - 0
    - 2825761
    euler43:
    - 1
    - 8
    - -38
    - 128
    - 5803
    - 5504
    - -70262
    - 636056
    - 3418801
    euler47:
    - 1
    - 0
    - 164
    - 0
    - 11142
    - 0
    - 362276
    - 0
    - 4879681
    euler5:
    - 1
    - 0
    - 20
    - 0
    - 150
    - 0
    - 500
    - 0
    - 625
    euler53:
    - 1
    - -24
    - 428
    - -4680
    - 41046
    - -248040
    - 1202252
    - -3573048
    - 7890481
    euler59:
    - 1
    - 0
    - -10
    - 0
    - -3381
    - 0
    - -34810
    - 0
    - 12117361
    euler61:
    - 1
    - -4
    - -110
    - -16
    - 11179
    - -976
    - -409310
    - -907924
    - 13845841
    euler67:
    - 1
    - 0
    - -26
    - 0
    - -3813
    - 0
    - -116714
    - 0
    - 20151121
    euler7:
    - 1
    - 0
    - -2
    - 0
    - -45
    - 0
    - -98
    - 0
    - 2401
    euler71:
    - 1
    - 0
    - -130
    - 0
    - 11859
    - 0
    - -655330
    - 0
    - 25411681
    euler73:
    - 1
    - 0
    - 292
    - 0
    - 31974
    - 0
    - 1556068
    - 0
    - 28398241
    euler79:
    - 1
    - 32
    - 700
    - 9632
    - 102214
    - 760928
    - 4368700
    - 15777248
    - 38950081
    euler83:
    - 1
    - 0
    - 308
    - 0
    - 37494
    - 0
    - 2121812
    - 0
    - 47458321
    euler89:
    - 1
    - 0
    - -130
    - 0
    - 8979
    - 0
    - -1029730
    - 0
    - 62742241
    euler97:
    - 1
    - 0
    - -2
    - 0
    - -9405
    - 0
    - -18818
    - 0
    - 88529281
    euler_factors:
    - - 1
      - 0
      - -1
      - 0
      - -3
      - 0
      - -4
      - 0
      - 16
    - - 1
      - -2
      - 3
      - -2
      - 1
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 0
      - 20
      - 0
      - 150
      - 0
      - 500
      - 0
      - 625
    - - 1
      - 0
      - -2
      - 0
      - -45
      - 0
      - -98
      - 0
      - 2401
    - - 1
      - 0
      - -10
      - 0
      - -21
      - 0
      - -1210
      - 0
      - 14641
    - - 1
      - 0
      - 0
      - 0
      - 0
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 12
      - 74
      - 432
      - 2163
      - 7344
      - 21386
      - 58956
      - 83521
    - - 1
      - 0
      - -26
      - 0
      - 315
      - 0
      - -9386
      - 0
      - 130321
    - - 1
      - 0
      - -46
      - 0
      - 1587
      - 0
      - -24334
      - 0
      - 279841
    - - 1
      - 12
      - 50
      - 432
      - 3819
      - 12528
      - 42050
      - 292668
      - 707281
    - - 1
      - 0
      - 100
      - 0
      - 4422
      - 0
      - 96100
      - 0
      - 923521
    - - 1
      - 0
      - -26
      - 0
      - -693
      - 0
      - -35594
      - 0
      - 1874161
    - - 1
      - 0
      - -34
      - 0
      - -525
      - 0
      - -57154
      - 0
      - 2825761
    - - 1
      - 8
      - -38
      - 128
      - 5803
      - 5504
      - -70262
      - 636056
      - 3418801
    - - 1
      - 0
      - 164
      - 0
      - 11142
      - 0
      - 362276
      - 0
      - 4879681
    - - 1
      - -24
      - 428
      - -4680
      - 41046
      - -248040
      - 1202252
      - -3573048
      - 7890481
    - - 1
      - 0
      - -10
      - 0
      - -3381
      - 0
      - -34810
      - 0
      - 12117361
    - - 1
      - -4
      - -110
      - -16
      - 11179
      - -976
      - -409310
      - -907924
      - 13845841
    - - 1
      - 0
      - -26
      - 0
      - -3813
      - 0
      - -116714
      - 0
      - 20151121
    - - 1
      - 0
      - -130
      - 0
      - 11859
      - 0
      - -655330
      - 0
      - 25411681
    - - 1
      - 0
      - 292
      - 0
      - 31974
      - 0
      - 1556068
      - 0
      - 28398241
    - - 1
      - 32
      - 700
      - 9632
      - 102214
      - 760928
      - 4368700
      - 15777248
      - 38950081
    - - 1
      - 0
      - 308
      - 0
      - 37494
      - 0
      - 2121812
      - 0
      - 47458321
    - - 1
      - 0
      - -130
      - 0
      - 8979
      - 0
      - -1029730
      - 0
      - 62742241
    - - 1
      - 0
      - -2
      - 0
      - -9405
      - 0
      - -18818
      - 0
      - 88529281
    id: 10859156
    index: 4
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/507/2/e/e
    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: 8-507e4-1.1-c1e4-0-4
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    - 1
    - 1
    - 1
    order_of_vanishing: 0
    prelabel: 8-507e4-1.1-c1e4-0
    primitive: false
    rational: true
    root_analytic_conductor: 2.0120674398436345
    root_angle: 0.0
    self_dual: true
    spectral_label: c1e4-0
    trace_hash: 1914720887379295860
    z1:
      __RealLiteral__: 0
      data: '0.26348764836235493063783754692'
      prec: 103
- - Lhash: 334010275599263873523527205339,1917804669470357407689259755791,2309687313557868015840846439902,2537790157681856355655495002355
    Lhash_array:
    - '334010275599263873523527205339'
    - '1917804669470357407689259755791'
    - '2309687313557868015840846439902'
    - '2537790157681856355655495002355'
    id: 11219767
    label: 8-507e4-1.1-c1e4-0-4
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/507/2/e/e
label_cols:
- label
- label
- label
labels:
- 8-507e4-1.1-c1e4-0-4
- 8-507e4-1.1-c1e4-0-4
- 8-507e4-1.1-c1e4-0-4
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-23T15:43:38.168790'