data:
- - Lhash: 467528266875375026240171307392,864852411495932843851915673276,1814998438003680282125427589367,2127492421537721406090785811052
    a10: 0
    a2: 0
    a3: 0
    a4: -8
    a5: 0
    a6: 0
    a7: 0
    a8: 0
    a9: 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 476.1369573827687
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - 1
    - - 5
      - - 1
        - 0
        - 10
        - 0
        - 25
    - - 13
      - - 1
        - 0
        - -26
        - 0
        - 169
    bad_primes:
    - 3
    - 5
    - 13
    central_character: '585.1'
    coefficient_field: 1.1.1.1
    conductor: 117117950625
    conductor_radical: 195
    degree: 8
    euler_factors:
    - - 1
      - 0
      - 8
      - 0
      - 24
      - 0
      - 32
      - 0
      - 16
    - - 1
    - - 1
      - 0
      - 10
      - 0
      - 25
    - - 1
      - 0
      - 2
      - 0
      - 99
      - 0
      - 98
      - 0
      - 2401
    - - 1
      - 0
      - -34
      - 0
      - 531
      - 0
      - -4114
      - 0
      - 14641
    - - 1
      - 0
      - -26
      - 0
      - 169
    - - 1
      - 0
      - 62
      - 0
      - 1539
      - 0
      - 17918
      - 0
      - 83521
    - - 1
      - 0
      - -76
      - 0
      - 2166
      - 0
      - -27436
      - 0
      - 130321
    - - 1
      - 0
      - 38
      - 0
      - 1419
      - 0
      - 20102
      - 0
      - 279841
    - - 1
      - 0
      - 116
      - 0
      - 5046
      - 0
      - 97556
      - 0
      - 707281
    - - 1
      - 0
      - -124
      - 0
      - 5766
      - 0
      - -119164
      - 0
      - 923521
    - - 1
      - 0
      - 122
      - 0
      - 6459
      - 0
      - 167018
      - 0
      - 1874161
    - - 1
      - 0
      - 86
      - 0
      - 5211
      - 0
      - 144566
      - 0
      - 2825761
    - - 1
      - 0
      - -172
      - 0
      - 11094
      - 0
      - -318028
      - 0
      - 3418801
    - - 1
      - 0
      - 188
      - 0
      - 13254
      - 0
      - 415292
      - 0
      - 4879681
    - - 1
      - 0
      - -82
      - 0
      - 7299
      - 0
      - -230338
      - 0
      - 7890481
    - - 1
      - 0
      - -76
      - 0
      - 8406
      - 0
      - -264556
      - 0
      - 12117361
    - - 1
      - 28
      - 538
      - 6496
      - 60595
      - 396256
      - 2001898
      - 6355468
      - 13845841
    - - 1
      - 0
      - -148
      - 0
      - 14454
      - 0
      - -664372
      - 0
      - 20151121
    - - 1
      - 0
      - 206
      - 0
      - 20691
      - 0
      - 1038446
      - 0
      - 25411681
    - - 1
      - 0
      - 188
      - 0
      - 19494
      - 0
      - 1001852
      - 0
      - 28398241
    - - 1
      - -44
      - 1042
      - -15752
      - 166795
      - -1244408
      - 6503122
      - -21693716
      - 38950081
    - - 1
      - 0
      - 332
      - 0
      - 41334
      - 0
      - 2287148
      - 0
      - 47458321
    - - 1
      - 0
      - -346
      - 0
      - 45771
      - 0
      - -2740666
      - 0
      - 62742241
    - - 1
      - 0
      - 362
      - 0
      - 51579
      - 0
      - 3406058
      - 0
      - 88529281
    - - 1
      - 0
      - 404
      - 0
      - 61206
      - 0
      - 4121204
      - 0
      - 104060401
    - - 1
      - 0
      - -412
      - 0
      - 63654
      - 0
      - -4370908
      - 0
      - 112550881
    - - 1
      - 0
      - -298
      - 0
      - 45099
      - 0
      - -3411802
      - 0
      - 131079601
    - - 1
      - 0
      - -436
      - 0
      - 71286
      - 0
      - -5180116
      - 0
      - 141158161
    - - 1
      - 0
      - 68
      - 0
      - 26694
      - 0
      - 868292
      - 0
      - 163047361
    euler_factors_factorization:
    - - - - 1
          - 0
          - 2
        - 4
    - - 1
    - - - - 1
          - 0
          - 5
        - 2
    - - - - 1
          - 0
          - 1
          - 0
          - 49
        - 2
    - - - - 1
          - 0
          - -17
          - 0
          - 121
        - 2
    - - - - 1
          - 0
          - -13
        - 2
    - - - - 1
          - 0
          - 31
          - 0
          - 289
        - 2
    - - - - 1
          - 0
          - -19
        - 4
    - - - - 1
          - 0
          - 19
          - 0
          - 529
        - 2
    - - - - 1
          - 0
          - 29
        - 4
    - - - - 1
          - 0
          - -31
        - 4
    - - - - 1
          - 0
          - 61
          - 0
          - 1369
        - 2
    - - - - 1
          - 0
          - 43
          - 0
          - 1681
        - 2
    - - - - 1
          - 0
          - -43
        - 4
    - - - - 1
          - 0
          - 47
        - 4
    - - - - 1
          - 0
          - -41
          - 0
          - 2809
        - 2
    - - - - 1
          - 0
          - -38
          - 0
          - 3481
        - 2
    - - - - 1
          - 7
          - 61
        - 4
    - - - - 1
          - 0
          - -74
          - 0
          - 4489
        - 2
    - - - - 1
          - 0
          - 103
          - 0
          - 5041
        - 2
    - - - - 1
          - 0
          - 94
          - 0
          - 5329
        - 2
    - - - - 1
          - -11
          - 79
        - 4
    - - - - 1
          - 0
          - 83
        - 4
    - - - - 1
          - 0
          - -173
          - 0
          - 7921
        - 2
    - - - - 1
          - 0
          - 181
          - 0
          - 9409
        - 2
    - - - - 1
          - 0
          - 101
        - 4
    - - - - 1
          - 0
          - -103
        - 4
    - - - - 1
          - 0
          - -149
          - 0
          - 11449
        - 2
    - - - - 1
          - 0
          - -109
        - 4
    - - - - 1
          - 0
          - 34
          - 0
          - 12769
        - 2
    gamma_factors:
    - []
    - - 0
      - 0
      - 0
      - 0
    group: GL2
    id: 11547544
    index: 1
    label: 8-585e4-1.1-c1e4-0-1
    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/585/2/h/e
    plot_delta:
      __RealLiteral__: 0
      data: '0.03125'
      prec: 24
    plot_values:
    - 0.4409726671216687
    - 0.43559835517896767
    - 0.42418750183153886
    - 0.40612766856189875
    - 0.3809357517575198
    - 0.3484380245597738
    - 0.3091685273966406
    - 0.26396071380727854
    - 0.21381726095139558
    - 0.1598828835882213
    - 0.10338883996734693
    - 0.04580181263109845
    - -0.011127625637193538
    - -0.0653482442089244
    - -0.11448866534678805
    - -0.1559186257584875
    - -0.18679513294256814
    - -0.20410818785586288
    - -0.20475441728521848
    - -0.18565442836462337
    - -0.14386764824668444
    - -0.07673160554138993
    - 0.01792264930585188
    - 0.14159965730476853
    - 0.2949805495300796
    - 0.4777279378178693
    - 0.6882036256011775
    - 0.9233809635542167
    - 1.1787770121957188
    - 1.4483671410214345
    - 1.7244736895619324
    - 1.9979615334679315
    - 2.2584619539126165
    - 2.4946337906369402
    - 2.6945235194929817
    - 2.8461400632158993
    - 2.938049771102384
    - 2.960061529790854
    - 2.9041036120975288
    - 2.764915921721424
    - 2.5407243534020507
    - 2.233990200423206
    - 1.852275428177537
    - 1.408356016925076
    - 0.9202795813180142
    - 0.4113910146949471
    - -0.0898073652662835
    - -0.5508283467766091
    - -0.9363821515434476
    - -1.2097006798850254
    - -1.3343141858627214
    - -1.2763603801057173
    - -1.0067074276472696
    - -0.5031561920779183
    - 0.24698998486085494
    - 1.2450323548084867
    - 2.479440209220297
    - 3.924664585553245
    - 5.540253481581483
    - 7.271511744731476
    - 9.05071999167775
    - 10.7990369916329
    - 12.429626852435206
    - 13.85136278046412
    - 14.972838171787945
    - 15.707242285023753
    - 15.97884366715019
    - 15.726856591320203
    - 14.909219433385225
    - 13.506986495525018
    - 11.529628586987569
    - 9.014256378772059
    - 6.024835805761635
    - 2.65163921624833
    - -0.9897124017397949
    - -4.765648885663996
    - -8.531104501179376
    - -12.135697875742133
    - -15.431003798195391
    - -18.280018903919107
    - -20.564462205140234
    - -22.191296898036928
    - -23.09966299964648
    - -23.264035546550314
    - -22.69516496504395
    - -21.440009349726395
    - -19.580851363581072
    - -17.22845822763056
    - -14.514853105735217
    - -11.585823360951046
    - -8.592403948661442
    - -5.680515507196625
    - -2.982527771015823
    - -0.6097342751121123
    - 1.3551135579733051
    - 2.860670622648023
    - 3.8877154353391736
    - 4.4488987311195
    - 4.587646961188463
    - 4.37031905464338
    - 3.8788295664893124
    - 3.2039219514354222
    - 2.438443316379257
    - 1.667680954415049
    - 0.9629873355158369
    - 0.37765340775478495
    - -0.055838465568855
    - -0.32703320543309883
    - -0.4456761468254127
    - -0.43821541967190236
    - -0.34327145922095764
    - -0.20561388292347899
    - -0.07008351201460088
    - 0.023846864049701502
    - 0.04652406378453713
    - -0.018620039282861316
    - -0.1737114420824842
    - -0.40691089705665273
    - -0.6948584872186049
    - -1.00610438468881
    - -1.3052652943901422
    - -1.5577848625708555
    - -1.7352503265266155
    - -1.818295666917867
    - -1.798456655683745
    - -1.679257519355027
    - -1.476412898559111
    - -1.214354975384288
    - -0.9225386617346962
    - -0.631812187801407
    - -0.37077993139463244
    - -0.161311553177968
    - -0.01588924203647968
    - 0.06346823349829242
    - 0.0849069308655163
    - 0.06524947717453755
    - 0.027015511238156646
    - -0.0053893362994850355
    - -0.009743571017194143
    - 0.030417091294668373
    - 0.12300106554024823
    - 0.26579756279053063
    - 0.44680369031531014
    - 0.6459310054435943
    - 0.8377489106047546
    - 0.9953948180646071
    - 1.095771209357434
    - 1.1228745035831624
    - 1.0702948891174298
    - 0.9430561510321823
    - 0.7584192894886455
    - 0.5427536472268284
    - 0.3277604011188325
    - 0.14628832025383345
    - 0.027581690377466602
    - -0.007914602531848731
    - 0.04809390371914227
    - 0.19014554874346482
    - 0.399337011572503
    - 0.645845133508451
    - 0.8931340138142332
    - 1.103485686723359
    - 1.244673925566279
    - 1.294717176886939
    - 1.245247548160651
    - 1.1035355581723838
    - 0.892632075309968
    - 0.6462612681410936
    - 0.4027998091183304
    - 0.19874317634416724
    - 0.06160532805542531
    - 0.002622419182112219
    - 0.0129122344132716
    - 0.0627511952517115
    - 0.10402864780782368
    - 0.07664408196111537
    - -0.08215004330669644
    - -0.4269692754128896
    - -0.9934515617362348
    - -1.788932448308799
    - -2.7864570356169525
    - -3.9236267398722178
    - -5.108451989972111
    - -6.228166140105498
    - -7.161771538531077
    - -7.7968460903374845
    - -8.050654240080005
    - -7.8805401831151825
    - -7.291186928631718
    - -6.3390017877565255
    - -5.131518723118795
    - -3.80866093410893
    - -2.522508865592187
    - -1.4160953490728898
    - -0.6007110076801107
    - -0.13214440631023971
    - 0.0026551194659023437
    - -0.11091206228847612
    - -0.32235354230988505
    - -0.4353107956498094
    - -0.23671945413597578
    - 0.4672592051004358
    - 1.81259390924837
    - 3.8439246896390706
    - 6.488794031739871
    - 9.54482408442945
    - 12.690586061493239
    - 15.508570604239768
    - 17.520462909317274
    - 18.24069027950495
    - 17.255748480662074
    - 14.271849512512
    - 9.156926048880441
    - 1.9816342231595199
    - -6.9450600499770205
    - -17.10870876787578
    - -27.831265977917422
    - -38.32259908437345
    - -47.75163033278401
    - -55.33981563630027
    - -60.43850568208551
    - -62.597384153629
    - -61.627039127879975
    - -57.609762742929064
    - -50.887015040750704
    - -42.02959553752018
    - -31.78495851650813
    - -20.984335956037505
    - -10.459702771158229
    - -0.9652229614236983
    - 6.9031301162660315
    - 12.753383582004217
    - 16.41434372964014
    - 17.93629442418932
    - 17.577609541991876
    - 15.739409720229823
    - 12.901478391751494
    - 9.564029053215204
    - 6.19298612860984
    - 3.1626874807008765
    - 0.7273534320538448
    - -0.9871890233082122
    - -1.976723752895991
    - -2.3344165447284966
    - -2.216420055718787
    - -1.8054378275460825
    - -1.2762499591920407
    - -0.7681962565355327
    - -0.3704700309379657
    - -0.11872161077670759
    - -0.0019440356274998882
    - 0.020621414582260984
    - 0.00015840050029971767
    - -0.019932378566773417
    - -0.018433040080712716
    - -0.00303472081187818
    - -0.008431355985853059
    - -0.08746061983156632
    - -0.29665030963979655
    - -0.6800223349094303
    - -1.2551467007902348
    - -2.003863388374753
    - -2.8706974601395507
    - -3.768834295636061
    - -4.5918397149142365
    - -5.2306978595437155
    - -5.595625632990368
    - -5.629453879401192
    - -5.316651105848024
    - -4.688043207562859
    - -3.819154936496944
    - -2.814386415443459
    - -1.7903125885724107
    - -0.8585304046682978
    - -0.10785822736133747
    - 0.4081326758436137
    - 0.6756124697940937
    - 0.7192056479481453
    - 0.5952368684706786
    - 0.3764044398326818
    - 0.13675189786083566
    - -0.06146903084038543
    - -0.17815174783525803
    - -0.20031639087883105
    - -0.1403578106286041
    - -0.029550790319723092
    - 0.09213758372577366
    - 0.1874399068413441
    - 0.23086390020778005
    - 0.21445716078018787
    - 0.14939791624532717
    - 0.06133322457942959
    - -0.017381406782659117
    - -0.056726298829886564
    - -0.03773799477635121
    - 0.04166681164436285
    - 0.16547382707242628
    - 0.3029404047085742
    - 0.41670478584993914
    - 0.47262721034357197
    - 0.448973028859498
    - 0.34366512410685207
    - 0.17782122309749626
    - -0.008570461805874247
    - -0.16505401253486704
    - -0.241926561159311
    - -0.20315841406742574
    - -0.03710022839709397
    - 0.23820325342019755
    - 0.5757730540411742
    - 0.908057830077006
    - 1.1606671787390725
    - 1.2678843800943909
    - 1.188423964758943
    - 0.9192184498659193
    - 0.496925286925849
    - -0.007841441552586892
    - -0.5025688395998151
    - -0.8915024013033384
    - -1.0983623506846578
    - -1.0835869564292708
    - -0.8548206916885736
    - -0.4683607976084633
    - -0.016652981794690103
    - 0.3924304650978806
    - 0.6611379084747744
    - 0.7291481408161592
    - 0.5922985229785732
    - 0.3087894010607899
    - -0.007914715736922167
    - -0.21138971471214593
    - -0.15864923044497498
    - 0.25123401653066824
    - 1.0420663764206441
    - 2.1372512644022716
    - 3.3580030680871733
    - 4.442912188174356
    - 5.089850792420113
    - 5.021680625575436
    - 4.047296966006851
    - 2.1153411720370103
    - -0.6447014272146763
    - -3.908251691688662
    - -7.194651130577077
    - -9.929648961904178
    - -11.531162697631542
    - -11.520955294295005
    - -9.621137461632475
    - -5.822276897582705
    - -0.4198267068049872
    - 5.997748427834865
    - 12.624433304713099
    - 18.54203765450521
    - 22.85581266100063
    - 24.862795734219503
    - 24.155276498492825
    - 20.687254721101876
    - 14.808448678829135
    - 7.248820110371302
    - -1.019529344926622
    - -8.928521262317549
    - -15.467389732180543
    - -19.85037204398852
    - -21.645498902045652
    - -20.8307422663267
    - -17.796471069463113
    - -13.293846845903632
    - -8.287653395447308
    - -3.7935156753666512
    - -0.7170431607191107
    - 0.2949886246416243
    - -1.0414547030351442
    - -4.612535239459009
    - -9.933284105857314
    - -16.24358622351054
    - -22.64229760610663
    - -28.227222655037316
    - -32.23775659770518
    - -34.19609589228716
    - -33.941217028826756
    - -31.618397647607907
    - -27.641249633328307
    - -22.624791760852556
    - -17.241385893717684
    - -12.107382229542193
    - -7.7015047474732805
    - -4.311312190312666
    - -2.011275709695263
    - -0.6907497695642232
    - -0.11035633370152552
    - 0.026982185507672576
    - 0.003324005889996041
    - 0.030573614651885624
    - 0.219110693232015
    - 0.5750039887922771
    - 1.0230366737300625
    - 1.444064085342592
    - 1.7186958583726493
    - 1.7703052057223965
    - 1.5848343326512204
    - 1.2123594085477105
    - 0.7536774679704623
    - 0.33333207644800567
    - 0.06185897742805306
    - 0.005803050290446748
    - 0.16952870005711582
    - 0.49310120477308145
    - 0.8671431738164249
    - 1.159132637528814
    - 1.246467056596332
    - 1.0510285337326024
    - 0.5570785985669966
    - -0.18392614461473783
    - -1.0614590275607996
    - -1.9296246364472642
    - -2.640943695674306
    - -3.075988537287756
    - -3.167826189410392
    - -2.918593250697318
    - -2.3927212806987423
    - -1.699532025086985
    - -0.9696692075744319
    - -0.326697676653182
    - 0.13919191135803002
    - 0.38516376334671737
    - 0.41912256277367654
    - 0.292920933136498
    - 0.08261032981881451
    - -0.13267895277230518
    - -0.28944388248539954
    - -0.3536102752570426
    - -0.3239283227843404
    - -0.22611946515174822
    - -0.10136073104346842
    - 0.008552374776754478
    - 0.0750069335720057
    - 0.08947613607066411
    - 0.06371342750760747
    - 0.02363769963330967
    - -0.0024136219232577284
    - 0.004843902293864845
    - 0.047749623349189335
    - 0.10942162582512814
    - 0.15886977164181215
    - 0.16171239877738094
    - 0.0929806993772146
    - -0.05233451454437447
    - -0.25431226174696153
    - -0.4705475801121929
    - -0.6467311673231818
    - -0.7346928776198618
    - -0.7069737177327963
    - -0.5668261191108147
    - -0.35126761039172305
    - -0.12314413444907994
    - 0.05077437141154528
    - 0.1240134046844951
    - 0.09329842160734314
    - 0.01455058319072981
    - 0.0017552594834905275
    - 0.20926085172585623
    - 0.7995622108402147
    - 1.899700102061071
    - 3.5593826555473123
    - 5.719704630343217
    - 8.201228372601696
    - 10.727431005876344
    - 12.962641939620946
    - 14.562534111543355
    - 15.241515055674398
    - 14.858269489300193
    - 13.429616340185524
    - 11.124602415361988
    - 8.246706445782616
    - 5.197816388095961
    - 2.3782306159255606
    - 0.11134284147149001
    - -1.4067739119606837
    - -2.1356543745236602
    - -2.1851659736094677
    - -1.7715985567094024
    - -1.1553180995966363
    - -0.5728813898977014
    - -0.1760903078762351
    - -0.0065107082093877194
    - -0.005796828381729419
    - -0.05898927601684946
    - -0.061377019855805924
    - 0.013536862474755459
    - 0.06640240841584069
    - -0.13636436252600975
    - -0.9185727115682507
    - -2.604260619171194
    - -5.396034447633953
    - -9.251808486668251
    - -13.792600834776026
    - -18.26377196937648
    - -21.57772482362057
    - -22.47712803189591
    - -19.7281643679031
    - -12.345300950546271
    - 0.1668581577075826
    - 17.604625639193348
    - 39.020948905059285
    - 62.76600609579885
    - 86.64809104148883
    - 108.28617328833212
    - 125.41267768184177
    - 136.15781567897992
    - 139.35646101129632
    - 134.87293625259335
    - 123.47587597898605
    - 106.66570886244163
    - 86.48660153197683
    - 65.28860577762765
    - 45.26019079447777
    - 28.126271761366247
    - 14.972657458786966
    - 6.169190739790913
    - 1.4078588670871874
    - -0.13340007765271616
    - 0.4345308072052382
    - 1.9694791059341503
    - 3.517568008464746
    - 4.4437926713383105
    - 4.488089784350542
    - 3.7487976856429066
    - 2.5529332101572093
    - 1.3112477498091777
    - 0.38924813958588755
    - 0.00537322093988651
    - 0.17552812367485895
    - 0.7327645432481087
    - 1.394776709007471
    - 1.8561061049414054
    - 1.882920194884358
    - 1.3817909683020957
    - 0.42626181967122456
    - -0.768190072756605
    - -1.9043584684820953
    - -2.681094538932334
    - -2.8745731991554786
    - -2.4032781866893456
    - -1.3409799392939803
    - 0.10247029698952621
    - 1.629936705963377
    - 2.9361964306345607
    - 3.7777877367432326
    - 4.019944297133224
    - 3.662331246974523
    - 2.8386123146260807
    - 1.764505218383801
    - 0.6802971346609229
    - -0.2033283428407644
    - -0.7509975899773732
    - -0.9249382390869437
    - -0.7787814086167477
    - -0.4315708707533824
    - -0.02694717243824852
    - 0.3088223407792261
    - 0.4949734507796135
    - 0.5100203528516963
    - 0.3894976896581037
    - 0.20168418016037198
    - 0.020619681656217338
    - -0.09723907033663577
    - -0.12939198296998594
    - -0.08966469893454695
    - -0.01702433222045479
    - 0.04189816507220441
    - 0.051552520019418485
    - 0.0013301826372575166
    - -0.09195980559979038
    - -0.19202889336297002
    - -0.2578607736344762
    - -0.26072466226967506
    - -0.19667154496124556
    - -0.08962120055770108
    - 0.018239727552372288
    - 0.08290600666710755
    - 0.07714112819880638
    - 0.0068101721714456985
    - -0.08252869042486402
    - -0.11581573970142298
    - -0.008236607438272751
    - 0.3087174191496253
    - 0.8591112097320426
    - 1.6066142667907897
    - 2.453622536658562
    - 3.2573519999515304
    - 3.8658603302297463
    - 4.151710918223143
    - 4.041504423847163
    - 3.53932766968672
    - 2.7370979818268864
    - 1.7826002311494316
    - 0.8435265182533392
    - 0.07140330486839044
    - -0.4336280098038246
    - -0.6467469096385272
    - -0.6148275069041885
    - -0.43489654376058295
    - -0.2205622149917359
    - -0.0619066542820623
    - 0.002585655050009886
    - -0.004332074254481961
    - -0.009902769615110437
    - 0.07849485483535878
    - 0.3348816136020346
    - 0.780050533147186
    - 1.3645750256636493
    - 1.975037028032552
    - 2.460715633936122
    - 2.6781532300839195
    - 2.5472934724441005
    - 2.0776673662689094
    - 1.371479851772812
    - 0.6038708031423058
    - -0.023915210599482192
    - -0.35743297430843174
    - -0.3453603141353791
    - -0.07014151630863505
    - 0.25731987933361056
    - 0.3490112882626109
    - -0.07884575136280725
    - -1.213491811748989
    - -3.0652884983893993
    - -5.436270602499981
    - -7.940357862194463
    - -10.079870329915273
    - -11.383099315614084
    - -11.527000002487926
    - -10.42823381868711
    - -8.294485990470749
    - -5.611917369558429
    - -2.993431879331071
    - -1.0010223848179387
    - 0.029116607751046224
    - 0.1365254408080529
    - -0.18941265590554482
    - -0.07002952975461
    - 1.5877047671564952
    - 5.835516984740534
    - 13.389040958868456
    - 24.360306957532288
    - 38.09771845237358
    - 53.25167265544755
    - 67.92932628199857
    - 79.9614065591891
    - 87.31772881179644
    - 88.68054202116605
    - 83.63031436170728
    - 72.72412395108043
    - 57.49599845446977
    - 40.316766191693965
    - 23.833381979601114
    - 10.477397129618948
    - 2.0579084031682164
    - -0.5543335368739705
    - 2.4240839649954533
    - 9.777184448273763
    - 19.565735308192625
    - 29.586097506074935
    - 37.79135449010896
    - 42.630133520515976
    - 43.31799727407213
    - 40.01213175190667
    - 33.584302300876274
    - 25.345131318562583
    - 16.76969238459994
    - 9.213335559544818
    - 3.595432080741126
    - 0.29082056137952267
    - -0.8418778654851392
    - -0.3451070212243878
    - 1.034170222780457
    - 2.5576319724350065
    - 3.6632615890735734
    - 4.059713762307901
    - 3.7365713579237045
    - 2.8996266988396417
    - 1.8620773516683053
    - 0.9238086054698952
    - 0.2843792588318012
    - 0.0040294621712857566
    - 0.011940208335185
    - 0.1598134282864283
    - 0.294648833234218
    - 0.31715575974458465
    - 0.21579577811723702
    - 0.06799025404701549
    - 0.00037726034203323195
    - 0.13437999496172998
    - 0.5351000230875451
    - 1.1801531069326627
    - 1.958314526084065
    - 2.6961304382516125
    - 3.2089508959579645
    - 3.3682028652895237
    - 3.1315842099824107
    - 2.5524088534050184
    - 1.7707075814908497
    - 0.9801852852767298
    - 0.35955834494611205
    - 0.025624643758065457
    - 0.008345768482145738
    - 0.24643376888902743
    - 0.6114956864330546
    - 0.9536574246811611
    - 1.1486319090193127
    - 1.1328578717521127
    - 0.919172506098163
    - 0.5871329387372418
    - 0.25170813865487834
    - 0.02014958944182085
    - -0.041348370064409196
    - 0.07242390252173982
    - 0.3044457820895902
    - 0.5599097551339605
    - 0.7416990551415001
    - 0.7811122603798121
    - 0.6611677338856387
    - 0.4271458256496306
    - 0.1655681395590036
    - -0.026897850438018813
    - -0.0752406164250068
    - 0.04834223935263862
    - 0.31441391521863266
    - 0.6454807166056742
    - 0.9411446501439197
    - 1.1151565627453657
    - 1.120355153446816
    - 0.9596960003269575
    - 0.684980594081679
    - 0.3812956060589387
    - 0.12971617284979764
    - -0.01975388866775555
    - -0.06108203108109403
    - -0.030635798657660487
    - 0.009698750166826758
    - 0.0019515151144965251
    - -0.08010350022534075
    - -0.2160052976176494
    - -0.34194682337344645
    - -0.3718246518083772
    - -0.2312796754318953
    - 0.10672523696860647
    - 0.6041440159933489
    - 1.1588672452386835
    - 1.6282140273333072
    - 1.878236404804583
    - 1.8278084393667755
    - 1.4772875774160135
    - 0.9187876462642104
    - 0.3197747568680855
    - -0.13609982768896903
    - -0.31014272753159
    - -0.1581252361934536
    - 0.24382856465552505
    - 0.7135793613441138
    - 1.0151306690328958
    - 0.9345775421297514
    - 0.361145646096407
    - -0.6672714728384599
    - -1.959437943795552
    - -3.212162773484651
    - -4.1041739279839895
    - -4.398074304892776
    - -4.014504690544755
    - -3.070492203503663
    - -1.8655407918877163
    - -0.7715986514842411
    - -0.1045628470451404
    - -0.011071099031919121
    - -0.39441344325840233
    - -0.918971041498139
    - -1.120581125049634
    - -0.5909946752258406
    - 0.8334354435272798
    - 2.904277165568452
    - 4.867847894799896
    - 5.522404680078414
    - 3.532599646980805
    - -2.2865309558165223
    - -12.670658152007956
    - -27.581598281894383
    - -45.910893104637786
    - -65.65073471580293
    - -84.19810004497035
    - -98.76697304261755
    - -106.94029055027767
    - -107.18728510450946
    - -99.1794229566918
    - -83.92189684674986
    - -63.65850584059837
    - -41.34341012999698
    - -20.08078203902202
    - -2.5715528235717464
    - 9.413300671147956
    - 15.30208604275756
    - 15.683206050996029
    - 12.069506966802061
    - 6.4990008603209475
    - 0.9652714125804913
    - -3.0181941127893475
    - -4.6820927179384295
    - -4.084978158722967
    - -1.9556053959867674
    - 0.624660909473068
    - 2.5840476756829056
    - 3.178354519831582
    - 2.193381881543457
    - -0.027640577818322208
    - -2.721910062931515
    - -4.984185752678471
    - -6.035278389618906
    - -5.439263641369852
    - -3.233528665967242
    - 0.08515951878475257
    - 3.7376893097116364
    - 6.873578468352853
    - 8.793016470755248
    - 9.157219696926377
    - 8.03005038558468
    - 5.815989546901007
    - 3.1341346387987548
    - 0.6456579421974156
    - -1.1377394614635203
    - -1.9637510229717208
    - -1.869610612978648
    - -1.1312211427927434
    - -0.136402115028041
    - 0.7412436712455919
    - 1.2462721985053684
    - 1.306806570956239
    - 1.0167147756798809
    - 0.5670787317246764
    - 0.16221356482622065
    - -0.05958084948848026
    - -0.0803144193613346
    - 0.0007132536475770061
    - 0.014166496461210007
    - -0.20870313847650726
    - -0.7673815263543607
    - -1.6458814127891925
    - -2.706363856002834
    - -3.735909335198051
    - -4.507527402644504
    - -4.841921170982315
    - -4.662057660356079
    - -4.026157582973649
    - -3.093155631045648
    - -2.070789964484669
    - -1.1585164770804217
    - -0.49397036982397124
    - -0.12277378441975763
    - -0.0021849904070998924
    - -0.02926978357692756
    - -0.08753883721732396
    - -0.09145434999741917
    - -0.008913159194406464
    - 0.1364062944012058
    - 0.28126576679892157
    - 0.3595872891572115
    - 0.3338683563916737
    - 0.21129607251242588
    - 0.04007453675946283
    - -0.11051032929487507
    - -0.17903380952391074
    - -0.13889138829979014
    - -0.012582682098031718
    - 0.13869858735469814
    - 0.23976853559878625
    - 0.23257780287215213
    - 0.10386700121075015
    - -0.10434558049132958
    - -0.3057659457006266
    - -0.39854067104571256
    - -0.3056247883130643
    - -0.005541768064383009
    - 0.45425762113608403
    - 0.9663320433739903
    - 1.3987705378301616
    - 1.6366699955126265
    - 1.6168626577689884
    - 1.351136333702398
    - 0.9287796384325183
    - 0.47607997061234797
    - 0.11297937009956209
    - -0.08409415037071014
    - -0.10748048773030616
    - -0.017195582953142052
    - 0.08926274316969031
    - 0.1191877563684448
    - 0.024065843368194006
    - -0.17826132946245882
    - -0.4104641708335787
    - -0.5698858680964263
    - -0.5805652761053798
    - -0.43124697520297944
    - -0.1881913036522252
    - 0.024575494213491724
    - 0.08115113492515262
    - -0.06928079059313427
    - -0.3432394840916131
    - -0.5012463645734189
    - -0.1880415424083992
    - 0.970449251332442
    - 3.2399487608225654
    - 6.651278622158039
    - 10.92275344086787
    - 15.470632744483723
    - 19.498460397276478
    - 22.174865173520715
    - 22.901233862854742
    - 21.45062091339537
    - 18.03492997313818
    - 13.303694312977651
    - 8.237958639319345
    - 3.8326757275418752
    - 0.8315439822189994
    - -0.46118301627916136
    - -0.27048610845708126
    - 0.7133920301492475
    - 1.5534078351402913
    - 1.3618259932770607
    - -0.3931348147181642
    - -3.700975927157213
    - -7.9797216721361535
    - -12.213732709299014
    - -15.269800069835727
    - -16.249367372008347
    - -14.767140307077769
    - -11.121700475695441
    - -6.302279107889921
    - -1.6796878124312928
    - 1.3841180536417284
    - 1.9235532425745339
    - -0.3212134332693978
    - -4.77176099492852
    - -10.138873591519125
    - -14.762745736751098
    - -17.115215739843332
    - -16.233139685019605
    - -12.011277557768564
    - -5.29333516854869
    - 2.3173794297408294
    - 8.909227018048412
    - 12.759744538632985
    - 12.814277112629723
    - 9.044293693974662
    - 2.4171359595755715
    - -5.359954986128297
    - -12.266125331155509
    - -16.535550157634194
    - -17.144705526926085
    - -14.060152228610027
    - -8.254328961623527
    - -1.4548656466706342
    - 4.350800039872046
    - 7.420034258750539
    - 6.6963715618039545
    - 2.105912944883849
    - -5.493914237793828
    - -14.557308415293935
    - -23.229808838845187
    - -29.84333988905546
    - -33.28009262955488
    - -33.146009734780066
    - -29.79875131778272
    - -24.22897482123759
    - -17.69098713906533
    - -11.381210663104355
    - -6.199747650650891
    - -2.6044564859297727
    - -0.6024524574644553
    - 0.13263319822778147
    - 0.09274291313286409
    - -0.2397408699064724
    - -0.5236622549606199
    - -0.6031276350147413
    - -0.4857568193581479
    - -0.27664146478036944
    - -0.09217165642300722
    - -0.000866210473865879
    - -0.0028612831543655317
    - -0.04613752176935404
    - -0.06645147795414946
    - -0.02628573606964116
    - 0.06473667830668205
    - 0.15785506803741545
    - 0.1963673017283469
    - 0.15190546508031558
    - 0.05091083849000205
    - -0.02276073585617992
    - 0.042989768506467824
    - 0.3434232975148951
    - 0.9109199751129077
    - 1.6885247548390048
    - 2.5350064998265016
    - 3.2575369483767567
    - 3.6688044148135717
    - 3.6607406871524053
    - 3.2321184551224453
    - 2.4869064485262316
    - 1.6085423079151613
    - 0.8089994021403724
    - 0.2531245567179654
    - 0.011889282935774173
    - 0.048211840579450896
    - 0.2375842421742701
    - 0.41848110408054623
    - 0.4509900920021756
    - 0.2653609580625878
    - -0.11625335469788499
    - -0.5975724385303768
    - -1.0448770129630238
    - -1.331829118970783
    - -1.3850388333460348
    - -1.2114545417965095
    - -0.8892694063344447
    - -0.533167518629776
    - -0.24422296101118457
    - -0.06917054501711611
    positive_zeros:
    - '0.36881477182371913175736337205529'
    - '0.68224825621525657989964919454926'
    - '1.43178131077830570229078081032522'
    - '1.67829559750508934113047189298463'
    - '2.30417404089142620941606930762335'
    - '2.91522951295656554951821953701831'
    - '3.30771624253727757590719213019064'
    - '3.52111941443955530834076750880820'
    - '3.58807539949549318511065618997098'
    - '4.12964500371094541039026739454367'
    - '4.27441167677038615005817656130804'
    - '4.32471463026495286290800673738819'
    - '4.82696543800890614048691086723681'
    - '4.85373335881621089496087951449554'
    - '5.34921946222101366361750820004337'
    - '5.35786814989100892331454260842256'
    - '5.48767134600582876150675813109118'
    - '6.11926811965491154687413270639888'
    - '6.12852378394196762989542180482031'
    - '6.26370395043105482593932232570417'
    - '6.66370143666822466027739805186989'
    - '7.15971788054442718420816909103011'
    - '7.51166875015286550108672545056244'
    - '7.81341848863773237605860557535442'
    - '7.87519005697604201429292484777185'
    - '7.981797626051396352199631059162215'
    - '7.982407112202709319686642544950111'
    - '8.567924488198617211728970963846055'
    - '8.770328079607653569085796537422675'
    - '8.913686922027174635693349457405128'
    - '9.117041957776312102367674665629155'
    - '9.205035657676327071547999323178097'
    - '9.467286210922240625733817239538894'
    - '9.598693601273356216215560229930802'
    - '9.874525492569226838286547095566852'
    - '10.09491540690317150538558088762014'
    - '10.28039557025511575792994619932578'
    - '10.35953442359925804597739457524052'
    - '10.64959093880742045827143833002068'
    - '10.90840719798179187576143132498586'
    prelabel: 8-585e4-1.1-c1e4-0
    primitive: false
    rational: true
    root_analytic_conductor: 2.161307131863703
    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: 2220796141455389495
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.36881477182371913175736337206'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '0.68224825621525657989964919455'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '1.43178131077830570229078081033'
      prec: 103
- - algebraic: true
    analytic_conductor: 476.1369573827687
    bad_primes:
    - 3
    - 5
    - 13
    central_character: '1.1'
    conductor: 117117950625
    conductor_radical: 195
    degree: 8
    dirichlet_coefficients:
    - 1
    - 0
    - 0
    - -8
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 40
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -10
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -2
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -28
    - 0
    - 0
    - -160
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 44
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 80
    euler11:
    - 1
    - 0
    - -34
    - 0
    - 531
    - 0
    - -4114
    - 0
    - 14641
    euler13:
    - 1
    - 0
    - -26
    - 0
    - 169
    - 0
    - 0
    - 0
    - 0
    euler17:
    - 1
    - 0
    - 62
    - 0
    - 1539
    - 0
    - 17918
    - 0
    - 83521
    euler19:
    - 1
    - 0
    - -76
    - 0
    - 2166
    - 0
    - -27436
    - 0
    - 130321
    euler2:
    - 1
    - 0
    - 8
    - 0
    - 24
    - 0
    - 32
    - 0
    - 16
    euler23:
    - 1
    - 0
    - 38
    - 0
    - 1419
    - 0
    - 20102
    - 0
    - 279841
    euler29:
    - 1
    - 0
    - 116
    - 0
    - 5046
    - 0
    - 97556
    - 0
    - 707281
    euler3:
    - 1
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    euler31:
    - 1
    - 0
    - -124
    - 0
    - 5766
    - 0
    - -119164
    - 0
    - 923521
    euler37:
    - 1
    - 0
    - 122
    - 0
    - 6459
    - 0
    - 167018
    - 0
    - 1874161
    euler41:
    - 1
    - 0
    - 86
    - 0
    - 5211
    - 0
    - 144566
    - 0
    - 2825761
    euler43:
    - 1
    - 0
    - -172
    - 0
    - 11094
    - 0
    - -318028
    - 0
    - 3418801
    euler47:
    - 1
    - 0
    - 188
    - 0
    - 13254
    - 0
    - 415292
    - 0
    - 4879681
    euler5:
    - 1
    - 0
    - 10
    - 0
    - 25
    - 0
    - 0
    - 0
    - 0
    euler53:
    - 1
    - 0
    - -82
    - 0
    - 7299
    - 0
    - -230338
    - 0
    - 7890481
    euler59:
    - 1
    - 0
    - -76
    - 0
    - 8406
    - 0
    - -264556
    - 0
    - 12117361
    euler61:
    - 1
    - 28
    - 538
    - 6496
    - 60595
    - 396256
    - 2001898
    - 6355468
    - 13845841
    euler67:
    - 1
    - 0
    - -148
    - 0
    - 14454
    - 0
    - -664372
    - 0
    - 20151121
    euler7:
    - 1
    - 0
    - 2
    - 0
    - 99
    - 0
    - 98
    - 0
    - 2401
    euler71:
    - 1
    - 0
    - 206
    - 0
    - 20691
    - 0
    - 1038446
    - 0
    - 25411681
    euler73:
    - 1
    - 0
    - 188
    - 0
    - 19494
    - 0
    - 1001852
    - 0
    - 28398241
    euler79:
    - 1
    - -44
    - 1042
    - -15752
    - 166795
    - -1244408
    - 6503122
    - -21693716
    - 38950081
    euler83:
    - 1
    - 0
    - 332
    - 0
    - 41334
    - 0
    - 2287148
    - 0
    - 47458321
    euler89:
    - 1
    - 0
    - -346
    - 0
    - 45771
    - 0
    - -2740666
    - 0
    - 62742241
    euler97:
    - 1
    - 0
    - 362
    - 0
    - 51579
    - 0
    - 3406058
    - 0
    - 88529281
    euler_factors:
    - - 1
      - 0
      - 8
      - 0
      - 24
      - 0
      - 32
      - 0
      - 16
    - - 1
      - 0
      - 0
      - 0
      - 0
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 0
      - 10
      - 0
      - 25
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 0
      - 2
      - 0
      - 99
      - 0
      - 98
      - 0
      - 2401
    - - 1
      - 0
      - -34
      - 0
      - 531
      - 0
      - -4114
      - 0
      - 14641
    - - 1
      - 0
      - -26
      - 0
      - 169
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 0
      - 62
      - 0
      - 1539
      - 0
      - 17918
      - 0
      - 83521
    - - 1
      - 0
      - -76
      - 0
      - 2166
      - 0
      - -27436
      - 0
      - 130321
    - - 1
      - 0
      - 38
      - 0
      - 1419
      - 0
      - 20102
      - 0
      - 279841
    - - 1
      - 0
      - 116
      - 0
      - 5046
      - 0
      - 97556
      - 0
      - 707281
    - - 1
      - 0
      - -124
      - 0
      - 5766
      - 0
      - -119164
      - 0
      - 923521
    - - 1
      - 0
      - 122
      - 0
      - 6459
      - 0
      - 167018
      - 0
      - 1874161
    - - 1
      - 0
      - 86
      - 0
      - 5211
      - 0
      - 144566
      - 0
      - 2825761
    - - 1
      - 0
      - -172
      - 0
      - 11094
      - 0
      - -318028
      - 0
      - 3418801
    - - 1
      - 0
      - 188
      - 0
      - 13254
      - 0
      - 415292
      - 0
      - 4879681
    - - 1
      - 0
      - -82
      - 0
      - 7299
      - 0
      - -230338
      - 0
      - 7890481
    - - 1
      - 0
      - -76
      - 0
      - 8406
      - 0
      - -264556
      - 0
      - 12117361
    - - 1
      - 28
      - 538
      - 6496
      - 60595
      - 396256
      - 2001898
      - 6355468
      - 13845841
    - - 1
      - 0
      - -148
      - 0
      - 14454
      - 0
      - -664372
      - 0
      - 20151121
    - - 1
      - 0
      - 206
      - 0
      - 20691
      - 0
      - 1038446
      - 0
      - 25411681
    - - 1
      - 0
      - 188
      - 0
      - 19494
      - 0
      - 1001852
      - 0
      - 28398241
    - - 1
      - -44
      - 1042
      - -15752
      - 166795
      - -1244408
      - 6503122
      - -21693716
      - 38950081
    - - 1
      - 0
      - 332
      - 0
      - 41334
      - 0
      - 2287148
      - 0
      - 47458321
    - - 1
      - 0
      - -346
      - 0
      - 45771
      - 0
      - -2740666
      - 0
      - 62742241
    - - 1
      - 0
      - 362
      - 0
      - 51579
      - 0
      - 3406058
      - 0
      - 88529281
    id: 11547544
    index: 1
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/585/2/h/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: 8-585e4-1.1-c1e4-0-1
    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: 8-585e4-1.1-c1e4-0
    primitive: false
    rational: true
    root_analytic_conductor: 2.161307131863703
    root_angle: 0.0
    self_dual: true
    spectral_label: c1e4-0
    trace_hash: 2220796141455389495
    z1:
      __RealLiteral__: 0
      data: '0.36881477182371913175736337206'
      prec: 103
- - Lhash: 467528266875375026240171307392,864852411495932843851915673276,1814998438003680282125427589367,2127492421537721406090785811052
    Lhash_array:
    - '467528266875375026240171307392'
    - '864852411495932843851915673276'
    - '1814998438003680282125427589367'
    - '2127492421537721406090785811052'
    id: 11910717
    label: 8-585e4-1.1-c1e4-0-1
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/585/2/h/e
label_cols:
- label
- label
- label
labels:
- 8-585e4-1.1-c1e4-0-1
- 8-585e4-1.1-c1e4-0-1
- 8-585e4-1.1-c1e4-0-1
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T21:18:28.069042'