data:
- - Lhash: 1450747004685524927921228507502,1727479170722166120835648667822,1731756680369770539688745589275,2620109864203985957120094537489
    a10: 0
    a2: 0
    a3: 2
    a4: 1
    a5: 0
    a6: 0
    a7: 0
    a8: 0
    a9: 1
    accuracy: 100
    algebraic: true
    analytic_conductor: 0.36738962761016053
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    bad_lfactors:
    - - 2
      - - 1
        - 0
        - -1
        - 0
        - 1
    - - 3
      - - 1
        - -2
        - 3
        - -2
        - 1
    - - 5
      - - 1
        - 0
        - 2
        - 0
        - 1
    - - 13
      - - 1
        - -4
        - 6
        - -4
        - 1
    bad_primes:
    - 2
    - 3
    - 5
    - 13
    central_character: '1560.1'
    coefficient_field: 1.1.1.1
    conductor: 5922408960000
    conductor_radical: 390
    degree: 8
    euler_factors:
    - - 1
      - 0
      - -1
      - 0
      - 1
    - - 1
      - -2
      - 3
      - -2
      - 1
    - - 1
      - 0
      - 2
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    - - 1
      - -4
      - 6
      - -4
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    - - 1
      - 0
      - 2
      - 0
      - 3
      - 0
      - 2
      - 0
      - 1
    - - 1
      - -6
      - 17
      - -30
      - 36
      - -30
      - 17
      - -6
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 2
      - 1
      - 2
      - 4
      - 2
      - 1
      - 2
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - -4
      - 0
      - 6
      - 0
      - -4
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    - - 1
      - 0
      - 2
      - 0
      - 3
      - 0
      - 2
      - 0
      - 1
    - - 1
      - 0
      - 2
      - 0
      - 3
      - 0
      - 2
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - 4
      - 0
      - 6
      - 0
      - 4
      - 0
      - 1
    - - 1
      - 4
      - 10
      - 16
      - 19
      - 16
      - 10
      - 4
      - 1
    - - 1
      - 0
      - 4
      - 0
      - 6
      - 0
      - 4
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - -4
      - 0
      - 6
      - 0
      - -4
      - 0
      - 1
    - - 1
      - 0
      - 2
      - 0
      - 3
      - 0
      - 2
      - 0
      - 1
    - - 1
      - 0
      - 4
      - 0
      - 6
      - 0
      - 4
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    euler_factors_factorization:
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 1
    - - - - 1
          - -1
          - 1
        - 2
    - - - - 1
          - 0
          - 1
        - 2
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - 0
          - 1
        - 2
      - - - 1
          - 0
          - -1
          - 0
          - 1
        - 1
    - - - - 1
          - -1
        - 4
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - 0
          - 1
        - 2
      - - - 1
          - 0
          - -1
          - 0
          - 1
        - 1
    - - - - 1
          - 0
          - 1
        - 2
      - - - 1
          - 0
          - -1
          - 0
          - 1
        - 1
    - - - - 1
          - -1
          - 1
        - 2
      - - - 1
          - 1
          - 1
        - 2
    - - - - 1
          - -1
        - 4
      - - - 1
          - -1
          - 1
        - 2
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - 1
        - 4
      - - - 1
          - -1
          - 1
        - 2
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - -1
        - 4
      - - - 1
          - 1
        - 4
    - - - - 1
          - 0
          - 1
        - 2
      - - - 1
          - 0
          - -1
          - 0
          - 1
        - 1
    - - - - 1
          - -1
          - 1
        - 2
      - - - 1
          - 1
          - 1
        - 2
    - - - - 1
          - -1
          - 1
        - 2
      - - - 1
          - 1
          - 1
        - 2
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - 0
          - 1
        - 4
    - - - - 1
          - 1
          - 1
        - 4
    - - - - 1
          - 0
          - 1
        - 4
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - 0
          - -1
          - 0
          - 1
        - 2
    - - - - 1
          - -1
        - 4
      - - - 1
          - 1
        - 4
    - - - - 1
          - -1
          - 1
        - 2
      - - - 1
          - 1
          - 1
        - 2
    - - - - 1
          - 0
          - 1
        - 4
    - - - - 1
          - 0
          - 1
        - 2
      - - - 1
          - 0
          - -1
          - 0
          - 1
        - 1
    gamma_factors:
    - []
    - - 0
      - 0
      - 0
      - 0
    group: GL2
    id: 19477357
    index: 2
    label: 8-1560e4-1.1-c0e4-0-2
    leading_term: '3.7377346697611952354400510948969753678494607224207912954392235434561774367301914958260029'
    load_key: CMFs-workshop
    motivic_weight: 0
    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:
    - 0
    - 0
    - 0
    - 0
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/1560/1/dk/b
    plot_delta:
      __RealLiteral__: 0
      data: '0.0146484375'
      prec: 40
    plot_values:
    - 3.737734669761195
    - 3.748326303118904
    - 3.7617307313089827
    - 3.7809185010585016
    - 3.8088890882759014
    - 3.847631759562963
    - 3.8967444630469843
    - 3.955357081247443
    - 4.022665024493572
    - 4.098169219185365
    - 4.181827111345735
    - 4.273709992662208
    - 4.37383893945383
    - 4.482139684739032
    - 4.598324569559698
    - 4.722032735165572
    - 4.852881032575772
    - 4.990448966734476
    - 5.134275252898927
    - 5.283843354752
    - 5.438575362992417
    - 5.597824021169726
    - 5.760854569635746
    - 5.926860575674968
    - 6.094960316910673
    - 6.2641980924833796
    - 6.433562023966653
    - 6.601972120806701
    - 6.768273982501035
    - 6.931253745205153
    - 7.089666858194718
    - 7.242217068035436
    - 7.387557814192686
    - 7.524321603096235
    - 7.651149898072282
    - 7.766672219243607
    - 7.869517527595516
    - 7.958343063961963
    - 8.031868855288636
    - 8.088861541271491
    - 8.128151831294469
    - 8.14865192470076
    - 8.14940334421417
    - 8.129564676396173
    - 8.088416568919882
    - 8.025376834753034
    - 7.9400588591957275
    - 7.832254408913308
    - 7.701917699178011
    - 7.549185452304021
    - 7.374441024475729
    - 7.178272594631625
    - 6.961448554783811
    - 6.72493880575705
    - 6.469970952671551
    - 6.1979616265870385
    - 5.910490612663163
    - 5.609319174997503
    - 5.296419147018766
    - 4.973895248019439
    - 4.643956684642104
    - 4.308921680131716
    - 3.971222245827454
    - 3.6333280522305205
    - 3.297715484855237
    - 2.9668504134488254
    - 2.64318533273188
    - 2.3290890023484727
    - 2.0268100757836827
    - 1.7384518432401093
    - 1.4659685652726482
    - 1.211106313264856
    - 0.9753663080310875
    - 0.7599890303895483
    - 0.5659527399319781
    - 0.3939304708185565
    - 0.24426985350509073
    - 0.11699244339970165
    - 0.011799205076191827
    - -0.07194650310078804
    - -0.13521370963374693
    - -0.17928763285791724
    - -0.20575072143413492
    - -0.2164676156553598
    - -0.21355663413095444
    - -0.19935654330070587
    - -0.1763889886007492
    - -0.1473183840276951
    - -0.1149068586998027
    - -0.08196635343730782
    - -0.05130829630543257
    - -0.025691906110159837
    - -0.007772444635072795
    - -4.924335034211727e-05
    - -0.004816003796613176
    - -0.02411277454997032
    - -0.059681474453372
    - -0.11292682002770267
    - -0.18488142155877932
    - -0.2761764351318365
    - -0.3870211074840731
    - -0.5171898414650968
    - -0.6660150987596583
    - -0.8323894780928475
    - -1.0147779474681609
    - -1.2112379322851445
    - -1.419449528068191
    - -1.6367504893349523
    - -1.860178616707423
    - -2.0865243265918294
    - -2.3123975966015347
    - -2.534282221458373
    - -2.7485978008608694
    - -2.951774229674515
    - -3.1403386671143734
    - -3.310968997901446
    - -3.4605584195919517
    - -3.5862870889179512
    - -3.68570674835262
    - -3.756772819513493
    - -3.797886776062824
    - -3.8079390912075546
    - -3.7863706240449355
    - -3.7331666785572986
    - -3.648851131572102
    - -3.5344906622792744
    - -3.3917165823840367
    - -3.2226676299565935
    - -3.029934797234253
    - -2.8165268893876862
    - -2.5858456823017564
    - -2.3415827870919785
    - -2.087637868680938
    - -1.8280555423185307
    - -1.5669572543898027
    - -1.3084294475439815
    - -1.0564408662902431
    - -0.8147703616789138
    - -0.5869227697908699
    - -0.3760495417423658
    - -0.18489089602699235
    - -0.015720672830369868
    - 0.12971373015774518
    - 0.25021389417563966
    - 0.34514265001421507
    - 0.4144341374815571
    - 0.458606639864392
    - 0.4787217100973296
    - 0.47634109644955225
    - 0.45348478327907726
    - 0.41259456659793886
    - 0.35644239659405713
    - 0.2880447010199213
    - 0.21058724252856936
    - 0.12735545731278744
    - 0.04162383370651274
    - -0.043435926011980125
    - -0.1248321273265511
    - -0.19982569829705965
    - -0.26601400301061495
    - -0.32139068320259556
    - -0.36439233969733364
    - -0.39393700342446775
    - -0.4094463721378404
    - -0.4108494869411152
    - -0.3985753777193578
    - -0.373533930554775
    - -0.33707038664352956
    - -0.2909107445234828
    - -0.2370985315522497
    - -0.1779257098508235
    - -0.11584139050315846
    - -0.05336131930317988
    - 0.007021835578184153
    - 0.0629257291053583
    - 0.11217321114926324
    - 0.15287534980053344
    - 0.18350288730508107
    - 0.2029489297294906
    - 0.21058035230353192
    - 0.20626947302027343
    - 0.19041023156035347
    - 0.16391976498727892
    - 0.1282170544453113
    - 0.08518462331203262
    - 0.037115174069465524
    - -0.013358006116022518
    - -0.06334657152788829
    - -0.10980165251063927
    - -0.14961805786567983
    - -0.1797447403549707
    - -0.19729413876210297
    - -0.19965087394763859
    - -0.18457554078923372
    - -0.15030032189590461
    - -0.09560866281952456
    - -0.01990172821499441
    - 0.07675481888532201
    - 0.19360506621990234
    - 0.3291972792897832
    - 0.48139952117997703
    - 0.6474373930642072
    - 0.8239728362950525
    - 1.0071823080325362
    - 1.1928419230152159
    - 1.376443767767636
    - 1.553375128908983
    - 1.7190265673105323
    - 1.8688993472347633
    - 1.998761366011896
    - 2.1048665174240813
    - 2.1840045314728425
    - 2.233577649765175
    - 2.251735616686946
    - 2.237526540065229
    - 2.190843570991388
    - 2.112423756801443
    - 2.0038885758835034
    - 1.8677652505980253
    - 1.7073307903336328
    - 1.5265167917133586
    - 1.329818436266218
    - 1.1222151679189019
    - 0.9089499867301386
    - 0.6953602253640244
    - 0.4867228673832222
    - 0.28813436949293214
    - 0.10429873836257342
    - -0.06063374121346048
    - -0.20318007799043303
    - -0.32061506061129824
    - -0.4110887440481294
    - -0.4736759850444245
    - -0.5083869447652917
    - -0.5161661829794804
    - -0.4988500240357236
    - -0.4590781155753196
    - -0.40019261325387234
    - -0.3261196970674289
    - -0.2411958796466356
    - -0.1499957321925336
    - -0.0571665957229717
    - 0.03275945065301098
    - 0.1155555305375206
    - 0.18745859427965264
    - 0.24531319913169522
    - 0.2867108822864197
    - 0.3100803008760167
    - 0.31473726113985223
    - 0.3009103113148847
    - 0.26973749575508116
    - 0.22319682646562475
    - 0.16400496485566488
    - 0.0954902513782433
    - 0.021440009359563084
    - -0.05409728499753588
    - -0.12701804712757098
    - -0.1933742457017988
    - -0.24958942188068822
    - -0.29266601877833165
    - -0.32036861068241645
    - -0.33138473512604166
    - -0.3254607294928665
    - -0.30347161505997466
    - -0.2674491716142133
    - -0.22056848279690905
    - -0.16708352854049005
    - -0.11218267234124812
    - -0.061807198392429256
    - -0.022429209977189356
    - -0.0007856326615434074
    - -0.0035702871687508645
    - -0.03711612314255532
    - -0.10706964952461089
    - -0.21806645520453424
    - -0.3734280204064826
    - -0.5748931321853096
    - -0.8223902264772461
    - -1.1138822262649979
    - -1.445274927869837
    - -1.8103862143985783
    - -2.201001023781961
    - -2.607086026058229
    - -3.0170116867130936
    - -3.4178173287080145
    - -3.7956087195244446
    - -4.136178321993935
    - -4.4254121530929
    - -4.649739999953143
    - -4.796741386360208
    - -4.85593108206674
    - -4.819066338275389
    - -4.6805190775241465
    - -4.437771560235224
    - -4.091955819177691
    - -3.647777991441501
    - -3.1135052702719035
    - -2.500982287491003
    - -1.8256348419137018
    - -1.105842313958344
    - -0.3623635359704704
    - 0.38223322577579955
    - 1.104150849589827
    - 1.7794463026416618
    - 2.385011956777649
    - 2.8994738193889615
    - 3.3041116379211646
    - 3.5839763058051073
    - 3.728777733768644
    - 3.733648535405624
    - 3.599878826145625
    - 3.3354546205505393
    - 2.95532938330933
    - 2.481539661401145
    - 1.943172929574476
    - 1.3759269456813186
    - 0.8214610807865363
    - 0.326564792651949
    - -0.057874983301339764
    - -0.2782343250609458
    - -0.27963182766815925
    - -0.007502777253330352
    - 0.5906968824143186
    - 1.56370041749852
    - 2.9547391800924196
    - 4.799883596673631
    - 7.126419844071076
    - 9.9514836982924
    - 13.281037007504935
    - 17.108789210320765
    - 21.415684232887937
    - 26.169891053059725
    - 31.32669197696095
    - 36.82863560409634
    - 42.60714926487851
    - 48.583832227028054
    - 54.67095350577954
    - 60.77327007756041
    - 66.79215763177085
    - 72.62651983038111
    - 78.17390669963018
    - 83.33397313065468
    - 88.01338340143107
    - 92.12528898719151
    - 95.59077688171631
    - 98.34302414174024
    - 100.330228060103
    - 101.51402177870308
    - 101.87078305980715
    - 101.39367747387945
    - 100.09356364083365
    - 97.99648513428438
    - 95.14389284942709
    - 91.59114491523152
    - 87.40763575446233
    - 82.67374064536459
    - 77.47839842024945
    - 71.91633046153575
    - 66.08777812859653
    - 60.09507717693607
    - 54.03867350236862
    - 48.01515057877807
    - 42.1170271288495
    - 36.429168733709375
    - 31.026127023486467
    - 25.971483991848405
    - 21.317935289958236
    - 17.10515824871468
    - 13.35942104720265
    - 10.094270596256878
    - 7.311186037835264
    - 4.999808321319597
    - 3.139180465160583
    - 1.6993330018950783
    - 0.6428017339485713
    - -0.07374297579536147
    - -0.497635779273925
    - -0.6783810987847244
    - -0.6659178887928391
    - -0.5089705912084387
    - -0.2535534725643255
    - 0.0583144374257368
    - 0.3896466023155933
    - 0.7092476055205227
    - 0.9921930196189903
    - 1.2200330781259712
    - 1.3807721741595285
    - 1.46851601058197
    - 1.4828964710765167
    - 1.428367676154422
    - 1.3133950406926023
    - 1.1494229381810825
    - 0.9498575410866907
    - 0.7290941324880527
    - 0.5015549699103432
    - 0.2807891346211073
    - 0.0787506133584128
    - -0.09479156375335876
    - -0.23271343806459188
    - -0.33074064523857344
    - -0.3874915339346054
    - -0.404379831050827
    - -0.38535570301314165
    - -0.3364508905249222
    - -0.2652704695236899
    - -0.18041704718169818
    - -0.09086197473214516
    - -0.005314087704093607
    - 0.068343698301032
    - 0.1235548115826282
    - 0.15552671691638337
    - 0.16149227153794946
    - 0.14082946150037357
    - 0.09506718011487376
    - 0.027778392324830828
    - -0.055747160101197304
    - -0.14891406403804916
    - -0.24429481495844005
    - -0.3341821140495661
    - -0.41120830835908345
    - -0.4689187360261257
    - -0.5023141579025199
    - -0.5083466885280117
    - -0.4862717113530199
    - -0.43786939213456005
    - -0.36754608642995906
    - -0.28227614629023395
    - -0.1913287352643502
    - -0.1058668070118767
    - -0.03841308312490672
    - -0.0021884199378229283
    - -0.01033328604519644
    - -0.07510179538573047
    - -0.207043523527677
    - -0.4141850088525404
    - -0.7013085244126721
    - -1.0693559678030757
    - -1.5149619576739901
    - -2.0301448822394024
    - -2.602275927736893
    - -3.21422313936624
    - -3.8447105025742334
    - -4.468935907985317
    - -5.059377930913289
    - -5.586744569443528
    - -6.02113184620743
    - -6.333248640269514
    - -6.495615242309521
    - -6.4838587270114285
    - -6.278016455323131
    - -5.863389745937405
    - -5.231495633902013
    - -4.380946830062832
    - -3.317875777692455
    - -2.055641920718581
    - -0.6150184899753943
    - 0.9759978126312265
    - 2.683069649947159
    - 4.467154575730315
    - 6.285156199642531
    - 8.091076749494647
    - 9.837680674815786
    - 11.479103120617214
    - 12.971761696571425
    - 14.275365804807716
    - 15.354575335501778
    - 16.1817310842023
    - 16.73674636643722
    - 17.007122232816634
    - 16.98889835537027
    - 16.688357245791032
    - 16.120149400638006
    - 15.30627013519991
    - 14.276004800578711
    - 13.06574249654097
    - 11.716167508089386
    - 10.2706548155883
    - 8.774305193336698
    - 7.272549648751289
    - 5.8086884519135396
    - 4.422510314391862
    - 3.1491216577987697
    - 2.0178516206621815
    - 1.0510447466617487
    - 0.26357738758936206
    - -0.3374025101527407
    - -0.7524762061261958
    - -0.9896319896812746
    - -1.063552644466317
    - -0.9946980528840192
    - -0.8082865204384351
    - -0.5329286756524757
    - -0.1991809076375108
    - 0.16185844209348071
    - 0.5198952517355481
    - 0.8468329161321821
    - 1.117953985088647
    - 1.3128967970128185
    - 1.4164185008144339
    - 1.4188781215237531
    - 1.3164588670588149
    - 1.1111411997265739
    - 0.8103536027918175
    - 0.4263936641930253
    - -0.024309136911845712
    - -0.5221403395755798
    - -1.0454410717968654
    - -1.5715634712723192
    - -2.077972265501602
    - -2.5433513072209
    - -2.9487176259374572
    - -3.278149121665587
    - -3.51941337142622
    - -3.664442614554035
    - -3.7097529901197572
    - -3.6563309244611326
    - -3.5093340358402436
    - -3.2777495313323532
    - -2.973983177431556
    - -2.6129760164650166
    - -2.211344764290157
    - -1.7866038150505474
    - -1.3563216851580673
    - -0.9371805803452186
    - -0.5442688354846822
    - -0.19047680979373927
    - 0.11411235284002894
    - 0.36250045978320944
    - 0.5508652426558529
    - 0.6785792404937756
    - 0.7481446418092363
    - 0.764720320482542
    - 0.735624611321074
    - 0.6698205244621421
    - 0.5773750445274215
    - 0.46869675098153823
    - 0.3538939518553756
    - 0.2422229990423982
    - 0.14162541826750963
    - 0.058267559847392375
    - -0.0037264798537969108
    - -0.04238603212068009
    - -0.05787943035125004
    - -0.052386717564334405
    - -0.029825685706090583
    - 0.0045213585544203235
    - 0.044456486418870574
    - 0.08335941109822156
    - 0.1146934901885187
    - 0.13250063933030332
    - 0.13184982800196138
    - 0.10919643417643117
    - 0.0626559216920627
    - -0.007833719939167394
    - -0.10049198108193184
    - -0.21177638875362356
    - -0.33657874251081416
    - -0.4685463144576299
    - -0.6004928994020067
    - -0.7248169562052661
    - -0.8339942597798292
    - -0.9210518391578253
    - -0.9800391022870786
    - -1.0064001098371116
    - -0.9972812232397746
    - -0.9517126138215107
    - -0.8707233957449004
    - -0.7573134415464847
    - -0.6162708530331653
    - -0.4539154949018703
    - -0.27772323934371335
    - -0.09590325502160647
    - 0.08305582513737529
    - 0.2508749520818275
    - 0.4000859357647632
    - 0.5243767068305558
    - 0.6188879567232044
    - 0.6805449918398215
    - 0.7083617237231604
    - 0.7033039786605281
    - 0.6681698002479823
    - 0.6074800766064348
    - 0.5272273428626841
    - 0.43433306993768245
    - 0.3362073125176787
    - 0.24029292606663238
    - 0.15358559380648806
    - 0.0821092388421808
    - 0.030534849265610488
    - 0.0018739210345380239
    - -0.0027224238974388284
    - 0.01595525926184124
    - 0.055242568141947404
    - 0.11079487700638134
    - 0.17690228446021122
    - 0.2469204352442272
    - 0.3137646008643797
    - 0.3704495222776224
    - 0.4106876139270713
    - 0.4294107361926761
    - 0.4232170665939696
    - 0.39076550454049197
    - 0.3330854664630757
    - 0.25362978677491244
    - 0.15821380364342538
    - 0.05482706067403542
    - -0.04673200267252041
    - -0.13539143237506596
    - -0.19943267507205995
    - -0.2272229822603269
    - -0.20794710786058354
    - -0.13233196703173677
    - 0.006580071605688544
    - 0.2128524946676377
    - 0.487258926191302
    - 0.8269193869200901
    - 1.2251207539692097
    - 1.671549847413134
    - 2.1527023416964726
    - 2.652184259643562
    - 3.1514980341656185
    - 3.6309912544552585
    - 4.070892817954431
    - 4.452146428972755
    - 4.75748230856044
    - 4.972391616205893
    - 5.08613527233705
    - 5.092282127821732
    - 4.9890829262305765
    - 4.779693074597177
    - 4.472442795562416
    - 4.080274672768486
    - 3.6200636656884004
    - 3.111889933412
    - 2.5782416908740804
    - 2.0426365794799017
    - 1.528378111289749
    - 1.0574083533851846
    - 0.6491008306428127
    - 0.3191450013137572
    - 0.07873157798282579
    - -0.06606692992457765
    - -0.11474472900824083
    - -0.07230645277880009
    - 0.05105991063976737
    - 0.2405396419923372
    - 0.4775317259484612
    - 0.7408560545605016
    - 1.0080343502079037
    - 1.2566608545061941
    - 1.4659053003777085
    - 1.617867262749976
    - 1.6987488649765912
    - 1.699876425340582
    - 1.6185464111705978
    - 1.4583076665651813
    - 1.2289418204991749
    - 0.9461400566838483
    - 0.6307953079675245
    - 0.30784686948142764
    - 0.004927733223621173
    - -0.24921571452105373
    - -0.42654806942919316
    - -0.5014544860044093
    - -0.45240200255478874
    - -0.26351858798718497
    - 0.07404294204571472
    - 0.5612879210762662
    - 1.1908275840204574
    - 1.9467448281468798
    - 2.805194003540307
    - 3.7352332809089006
    - 4.6999278687952
    - 5.658050488044658
    - 6.566801541540501
    - 7.3835028469148245
    - 8.067438726469813
    - 8.582306005090935
    - 8.899525280296675
    - 8.998926390861932
    - 8.869638038662533
    - 8.511482000657638
    - 7.936687411118461
    - 7.168248556393467
    - 6.238754175463883
    - 5.189604963638958
    - 4.0701584156566595
    - 2.9341716508927695
    - 1.837068760960004
    - 0.8336327302716975
    - -0.024327967775232818
    - -0.6914351949946523
    - -1.131116802617713
    - -1.317372195015298
    - -1.2363511868578465
    - -0.8874705781388255
    - -0.2835104339410411
    - 0.5498638914001492
    - 1.5749416973457606
    - 2.7438784460127974
    - 4.001089133061537
    - 5.2859052429987505
    - 6.535540708488538
    - 7.688403632440064
    - 8.687210451278563
    - 9.481959677615064
    - 10.03283363249359
    - 10.31217874462914
    - 10.305935431270628
    - 10.014614852597251
    - 9.453839979635731
    - 8.653322732093415
    - 7.655377094919666
    - 6.513063195416481
    - 5.287945327405119
    - 4.046678137988479
    - 2.857610110178562
    - 1.7875801083677032
    - 0.898641589583465
    - 0.2447183395876018
    - -0.13107337867261046
    - -0.19853577036909956
    - 0.05801437435917569
    - 0.638940930194216
    - 1.5292076326269992
    - 2.6989545617928203
    - 4.105293928975649
    - 5.694290822026542
    - 7.403117843689257
    - 9.163050304954112
    - 10.903908599969762
    - 12.556439432602224
    - 14.054824348433158
    - 15.340152828158349
    - 16.364516239656798
    - 17.09132687230904
    - 17.496160065894347
    - 17.568317907510526
    - 17.31224293774884
    - 16.745050473073153
    - 15.895033995647756
    - 14.800400604221256
    - 13.508334598368386
    - 12.070984469067932
    - 10.54263016630852
    - 8.977358149563008
    - 7.427531751789995
    - 5.940538448724174
    - 4.556718843330456
    - 3.308298389447908
    - 2.2189596536735334
    - 1.302932597304371
    - 0.5651252394487015
    - 0.001963791208483305
    - -0.3974729691852485
    - -0.6502181013350281
    - -0.7777631709795373
    - -0.804310212176281
    - -0.755086852456947
    - -0.6547165969944787
    - -0.5258118219075344
    - -0.38786601551935374
    - -0.25645713153825606
    - -0.14281032896133844
    - -0.0537364186107314
    - 0.00811000089062355
    - 0.043697150495374586
    - 0.05681897052531254
    - 0.05317706986606972
    - 0.03941514587661569
    - 0.022169886640475273
    - 0.007220582772050679
    - -0.0011705429911825311
    - -0.0006992685359909794
    - 0.008802334168173467
    - 0.025459556248499066
    - 0.04567617740840689
    - 0.064672105641202
    - 0.07724769745283937
    - 0.07854348423164628
    - 0.06478990065502083
    - 0.03404373549733621
    - -0.013146937042205776
    - -0.073513778019433
    - -0.14104613754684886
    - -0.20719339435206072
    - -0.2613722441673205
    - -0.2919418441536428
    - -0.2873074949419139
    - -0.23716814503058606
    - -0.13393261296954267
    - 0.02588850019987656
    - 0.24050709624828154
    - 0.501884391033812
    - 0.7949716478125006
    - 1.097597931487706
    - 1.3808473585456582
    - 1.6098260554866934
    - 1.74495849079105
    - 1.7440224456688072
    - 1.5644292810461924
    - 1.165725928879656
    - 0.5124473306617402
    - -0.4229910648145803
    - -1.6577194902379808
    - -3.196158246654255
    - -5.028273384473256
    - -7.128337442458344
    - -9.454464011766012
    - -11.94923888223727
    - -14.541766288029313
    - -17.149377833234517
    - -19.680396341013672
    - -22.03840297780256
    - -24.128009910513242
    - -25.85818666969453
    - -27.14646924424649
    - -27.924320592224376
    - -28.143653446301947
    - -27.77812271693965
    - -26.824865513682067
    - -25.307297579917197
    - -23.278190637229407
    - -20.81555746283045
    - -18.01969257438528
    - -15.011352119803497
    - -11.928961874131533
    - -8.919754936899553
    - -6.133889148860769
    - -3.718886699607662
    - -1.8130316484848001
    - -0.537328541271833
    - 0.00988133286203759
    - -0.2421375739359532
    - -1.3321855276816919
    - -3.2644634375331174
    - -6.007506242708069
    - -9.495116335762644
    - -13.627979388120664
    - -18.276999234304007
    - -23.28870545388863
    - -28.492884430163098
    - -33.70755058554427
    - -38.74635086134369
    - -43.42845711943891
    - -47.5857320452621
    - -51.067970220269586
    - -53.7499247147967
    - -55.53820504874928
    - -56.37221748823567
    - -56.226905747163535
    - -55.11476478713345
    - -53.08324230570514
    - -50.21079046854363
    - -46.60519146897298
    - -42.39808695867674
    - -37.73669972497213
    - -32.7777408739632
    - -27.682520945178442
    - -22.608451782013724
    - -17.702173030915404
    - -13.094640671199665
    - -8.89697976997741
    - -5.1962187729859926
    - -2.0531683218514174
    - 0.4982658061162714
    - 2.450626774311839
    - 3.82128022804772
    - 4.649577633703618
    - 4.993159127705669
    - 4.923966751839482
    - 4.523407854367034
    - 3.8769809296091413
    - 3.0700850884916124
    - 2.1841766479882416
    - 1.2927872406850862
    - 0.4585310188490079
    - -0.2687018383108567
    - -0.8536047455919838
    - -1.2776342097274807
    - -1.5359299770403123
    - -1.6349533896263546
    - -1.5886618306798292
    - -1.4182525167000355
    - -1.1534765998279166
    - -0.8317472231728535
    - -0.4946077170205097
    - -0.17229882221070947
    positive_zeros:
    - '1.14443759536289464974120539365966'
    - '1.36274078236633075997521077275318'
    - '1.36611514249903159304354701171019'
    - '2.06690223925445867820585087037888'
    - '2.27762895805750125527464955582679'
    - '2.53243022209966109439006292742605'
    - '2.72075417532501447626349524381086'
    - '2.87438392119721906576580221640774'
    - '3.33423933166108371963427203566127'
    - '3.53948554509852849544682552848102'
    - '3.72485575481078228146443938005410'
    - '3.95628963074027665640315371396132'
    - '3.96570368644413284660659492057301'
    - '4.40163434110818350839373503106511'
    - '4.65560123037762148718833491251948'
    - '4.70240415410724919191751222982141'
    - '5.49130417752778000527620131424966'
    - '5.57842945439289366493766661320378'
    - '5.80709278743815082680386530165845'
    - '5.96288141344355515965707928038895'
    - '6.06959555173148651715270340916000'
    - '6.30147937369691704182802415681410'
    - '6.30630499702309665938167186922576'
    - '6.67085040090931358860414144843641'
    - '7.09571907216870890942660305613975'
    - '7.21516919212762012480718421770459'
    - '7.38206524854918235867297610833627'
    - '7.69928082763020614707185682120954'
    - '7.909092766835187813818465545863772'
    - '7.981649550827213231055438448840047'
    - '8.099167677494231285040073208021805'
    - '8.372034355589957277742947362708313'
    - '8.629740357635297811490702453535529'
    - '8.646420308462960873973441205217676'
    - '8.870082181200963869882888897449286'
    - '8.964281422071023221027159244050116'
    - '9.381746402308461814223184871267446'
    - '9.428519944071580907051698187475836'
    - '9.668223901845045325762117862640676'
    - '9.753141025373196879606336122098110'
    prelabel: 8-1560e4-1.1-c0e4-0
    primitive: false
    rational: true
    root_analytic_conductor: 0.8823499417507115
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    spectral_label: c0e4-0
    trace_hash: 1921184322872617398
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.14443759536289464974120539366'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '1.36274078236633075997521077275'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '1.36611514249903159304354701171'
      prec: 103
- - algebraic: true
    analytic_conductor: 0.36738962761016053
    bad_primes:
    - 2
    - 3
    - 5
    - 13
    central_character: '1.1'
    conductor: 5922408960000
    conductor_radical: 390
    degree: 8
    dirichlet_coefficients:
    - 1
    - 0
    - 2
    - 1
    - 0
    - 0
    - 0
    - 0
    - 1
    - 0
    - 0
    - 2
    - 4
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -2
    - 0
    - -2
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 1
    - 6
    - 0
    - 8
    - 0
    - 0
    - 0
    - -2
    - 0
    - 0
    - 0
    - 0
    - 0
    - 2
    - 0
    - 0
    - 4
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -1
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -4
    - 0
    - 0
    - 0
    - -4
    - 0
    - -4
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -2
    euler11:
    - 1
    - 0
    - 1
    - 0
    - 0
    - 0
    - 1
    - 0
    - 1
    euler13:
    - 1
    - -4
    - 6
    - -4
    - 1
    - 0
    - 0
    - 0
    - 0
    euler17:
    - 1
    - 0
    - -2
    - 0
    - 3
    - 0
    - -2
    - 0
    - 1
    euler19:
    - 1
    - 0
    - -2
    - 0
    - 3
    - 0
    - -2
    - 0
    - 1
    euler2:
    - 1
    - 0
    - -1
    - 0
    - 1
    - 0
    - 0
    - 0
    - 0
    euler23:
    - 1
    - 0
    - 1
    - 0
    - 0
    - 0
    - 1
    - 0
    - 1
    euler29:
    - 1
    - 0
    - 1
    - 0
    - 0
    - 0
    - 1
    - 0
    - 1
    euler3:
    - 1
    - -2
    - 3
    - -2
    - 1
    - 0
    - 0
    - 0
    - 0
    euler31:
    - 1
    - 0
    - 2
    - 0
    - 3
    - 0
    - 2
    - 0
    - 1
    euler37:
    - 1
    - -6
    - 17
    - -30
    - 36
    - -30
    - 17
    - -6
    - 1
    euler41:
    - 1
    - 0
    - -2
    - 0
    - 3
    - 0
    - -2
    - 0
    - 1
    euler43:
    - 1
    - 2
    - 1
    - 2
    - 4
    - 2
    - 1
    - 2
    - 1
    euler47:
    - 1
    - 0
    - -2
    - 0
    - 3
    - 0
    - -2
    - 0
    - 1
    euler5:
    - 1
    - 0
    - 2
    - 0
    - 1
    - 0
    - 0
    - 0
    - 0
    euler53:
    - 1
    - 0
    - -4
    - 0
    - 6
    - 0
    - -4
    - 0
    - 1
    euler59:
    - 1
    - 0
    - 1
    - 0
    - 0
    - 0
    - 1
    - 0
    - 1
    euler61:
    - 1
    - 0
    - 2
    - 0
    - 3
    - 0
    - 2
    - 0
    - 1
    euler67:
    - 1
    - 0
    - 2
    - 0
    - 3
    - 0
    - 2
    - 0
    - 1
    euler7:
    - 1
    - 0
    - -2
    - 0
    - 3
    - 0
    - -2
    - 0
    - 1
    euler71:
    - 1
    - 0
    - -2
    - 0
    - 3
    - 0
    - -2
    - 0
    - 1
    euler73:
    - 1
    - 0
    - 4
    - 0
    - 6
    - 0
    - 4
    - 0
    - 1
    euler79:
    - 1
    - 4
    - 10
    - 16
    - 19
    - 16
    - 10
    - 4
    - 1
    euler83:
    - 1
    - 0
    - 4
    - 0
    - 6
    - 0
    - 4
    - 0
    - 1
    euler89:
    - 1
    - 0
    - -2
    - 0
    - 3
    - 0
    - -2
    - 0
    - 1
    euler97:
    - 1
    - 0
    - -2
    - 0
    - 3
    - 0
    - -2
    - 0
    - 1
    euler_factors:
    - - 1
      - 0
      - -1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 0
    - - 1
      - -2
      - 3
      - -2
      - 1
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 0
      - 2
      - 0
      - 1
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    - - 1
      - -4
      - 6
      - -4
      - 1
      - 0
      - 0
      - 0
      - 0
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    - - 1
      - 0
      - 2
      - 0
      - 3
      - 0
      - 2
      - 0
      - 1
    - - 1
      - -6
      - 17
      - -30
      - 36
      - -30
      - 17
      - -6
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 2
      - 1
      - 2
      - 4
      - 2
      - 1
      - 2
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - -4
      - 0
      - 6
      - 0
      - -4
      - 0
      - 1
    - - 1
      - 0
      - 1
      - 0
      - 0
      - 0
      - 1
      - 0
      - 1
    - - 1
      - 0
      - 2
      - 0
      - 3
      - 0
      - 2
      - 0
      - 1
    - - 1
      - 0
      - 2
      - 0
      - 3
      - 0
      - 2
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - 4
      - 0
      - 6
      - 0
      - 4
      - 0
      - 1
    - - 1
      - 4
      - 10
      - 16
      - 19
      - 16
      - 10
      - 4
      - 1
    - - 1
      - 0
      - 4
      - 0
      - 6
      - 0
      - 4
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    - - 1
      - 0
      - -2
      - 0
      - 3
      - 0
      - -2
      - 0
      - 1
    id: 19477357
    index: 2
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1560/1/dk/b
    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: 8-1560e4-1.1-c0e4-0-2
    motivic_weight: 0
    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:
    - 0
    - 0
    - 0
    - 0
    order_of_vanishing: 0
    prelabel: 8-1560e4-1.1-c0e4-0
    primitive: false
    rational: true
    root_analytic_conductor: 0.8823499417507115
    root_angle: 0.0
    self_dual: true
    spectral_label: c0e4-0
    trace_hash: 1921184322872617398
    z1:
      __RealLiteral__: 0
      data: '1.14443759536289464974120539366'
      prec: 103
- - Lhash: 1450747004685524927921228507502,1727479170722166120835648667822,1731756680369770539688745589275,2620109864203985957120094537489
    Lhash_array:
    - '1450747004685524927921228507502'
    - '1727479170722166120835648667822'
    - '1731756680369770539688745589275'
    - '2620109864203985957120094537489'
    id: 19827882
    label: 8-1560e4-1.1-c0e4-0-2
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1560/1/dk/b
label_cols:
- label
- label
- label
labels:
- 8-1560e4-1.1-c0e4-0-2
- 8-1560e4-1.1-c0e4-0-2
- 8-1560e4-1.1-c0e4-0-2
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-23T07:01:40.159103'