data:
- - Lhash: '1458571112262815521945838820077'
    a10:
    - 0.7192235935955849
    - -1.2457318061098228
    a2:
    - 2.218369809027932
    - 1.2807764064044151
    a3:
    - -0.5
    - 0.8660254037844386
    a4:
    - 2.280776406404415
    - 3.950420616596809
    a5:
    - 0.0
    - -0.5615528128088303
    a6:
    - -2.218369809027932
    - 1.2807764064044151
    a7:
    - -3.0843952128123706
    - 1.7807764064044151
    a8:
    - 0.0
    - 6.56155281280883
    a9:
    - -0.5
    - -0.8660254037844386
    accuracy: 100
    algebraic: true
    analytic_conductor: 4.048415382478917
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 0.5
          - -0.8660254037844386
    - - 13
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 3
    - 13
    central_character: '507.316'
    coefficient_field: CDF
    conductor: 507
    conductor_radical: 39
    conjugate: '3530212272609772084523560932684'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -2.218369809027932
        - -1.2807764064044151
      - - 1.0
        - 1.7320508075688772
    - - - 1.0
        - 0
      - - 0.5
        - -0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0.5615528128088303
      - - -5.0
        - 0
    - - - 1.0
        - 0
      - - 3.0843952128123706
        - -1.7807764064044151
      - - 3.5
        - -6.06217782649107
    - - - 1.0
        - 0
      - - -1.7320508075688772
        - -1.0
      - - 5.5
        - 9.526279441628825
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -1.2807764064044151
        - -2.218369809027932
      - - -8.5
        - 14.722431864335457
    - - - 1.0
        - 0
      - - -0.9726380029181091
        - 0.5615528128088303
      - - 9.5
        - -16.454482671904334
    - - - 1.0
        - 0
      - - -1.0
        - 1.7320508075688772
      - - -11.5
        - -19.91858428704209
    - - - 1.0
        - 0
      - - -2.842329219213245
        - 4.923058619514918
      - - -14.5
        - -25.11473670974872
    - - - 1.0
        - 0
      - - 0
        - -1.5615528128088303
      - - -31.0
        - 0
    - - - 1.0
        - 0
      - - 2.9777826136787002
        - 1.7192235935955849
      - - 18.5
        - 32.04293994002423
    - - - 1.0
        - 0
      - - -2.218369809027932
        - -1.2807764064044151
      - - 20.5
        - 35.50704155516198
    - - - 1.0
        - 0
      - - -0.21922359359558485
        - -0.3797064023253841
      - - -21.5
        - 37.239092362730865
    - - - 1.0
        - 0
      - - 0
        - 8.246211251235321
      - - -47.0
        - 0
    - - - 1.0
        - 0
      - - -11.68465843842649
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - 9.632892040762496
        - -5.56155281280883
      - - 29.5
        - -51.09549882328188
    - - - 1.0
        - 0
      - - 6.06155281280883
        - 10.498917444546935
      - - -30.5
        - 52.827549630850754
    - - - 1.0
        - 0
      - - -0.3797064023253841
        - -0.21922359359558485
      - - 33.5
        - 58.023702053557386
    - - - 1.0
        - 0
      - - 12.12435565298214
        - -7.0
      - - 35.5
        - -61.48780366869514
    - - - 1.0
        - 0
      - - 0
        - 1.8768943743823394
      - - -73.0
        - 0
    - - - 1.0
        - 0
      - - -9.56155281280883
        - 0
      - - 79.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -9.12310562561766
      - - -83.0
        - 0
    - - - 1.0
        - 0
      - - 11.364942848331372
        - 6.56155281280883
      - - 44.5
        - 77.07626093681505
    - - - 1.0
        - 0
      - - -3.8438080174631386
        - 2.219223593595585
      - - 48.5
        - -84.00446416709055
    - - - 1.0
        - 0
      - - 1.7192235935955849
        - -2.9777826136787002
      - - -50.5
        - -87.4685657822283
    - - - 1.0
        - 0
      - - -7.56155281280883
        - 0
      - - 103.0
        - 0
    - - - 1.0
        - 0
      - - 4.123105625617661
        - -7.14142842854285
      - - -53.5
        - -92.66471820493493
    - - - 1.0
        - 0
      - - 0
        - 17.80776406404415
      - - -109.0
        - 0
    - - - 1.0
        - 0
      - - -7.403882032022076
        - -12.823899852708536
      - - -56.5
        - 97.86087062764156
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 10854467
    index: 10
    label: 2-507-13.4-c1-0-10
    load_key: CMFs-workshop
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/507/2/j/g/316/4
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 2.786929950194232
    - 2.5105063522410185
    - 2.249160446201173
    - 1.9907065445752377
    - 1.723457557816624
    - 1.438140244358619
    - 1.1292525316222959
    - 0.7958355479985945
    - 0.4417394350715505
    - 0.0754652368676849
    - -0.29037222217719755
    - -0.6399444946540734
    - -0.9554584636900911
    - -1.2187154578040258
    - -1.412900235338993
    - -1.5244711441391796
    - -1.5449777907484834
    - -1.4726003869248891
    - -1.3131937924125934
    - -1.080635517939338
    - -0.7963241871680939
    - -0.4877530050828645
    - -0.1861869222788229
    - 0.07640714838651794
    - 0.2709045576269692
    - 0.3746608032366046
    - 0.37478756776956257
    - 0.2705876542584401
    - 0.07470989118191447
    - -0.187304655182545
    - -0.4792374254416874
    - -0.7580926205480587
    - -0.9793541102147574
    - -1.1030254433867972
    - -1.0996826921575131
    - -0.9556597936851401
    - -0.6764942315814124
    - -0.2879053319044262
    - 0.16614287632086505
    - 0.628350643240679
    - 1.0355616717417653
    - 1.3279503941852446
    - 1.4586673116031006
    - 1.4024516952982005
    - 1.161689574457065
    - 0.7686092936890255
    - 0.2827675384955093
    - -0.21635564915712133
    - -0.6410461393054407
    - -0.9099274329452467
    - -0.9633448126755955
    - -0.7770819427860953
    - -0.37188356302453063
    - 0.18336772822096303
    - 0.7761855888530154
    - 1.2629712163380626
    - 1.4884071882504961
    - 1.3094169737179815
    - 0.6203125540058012
    - -0.6248382217119612
    - -2.396579474028332
    - -4.584441360656192
    - -7.003281578552264
    - -9.411779855429419
    - -11.541289439009864
    - -13.131385774490438
    - -13.967041774735968
    - -13.91168837030867
    - -12.93066977152023
    - -11.100807267327975
    - -8.603806491426159
    - -5.703784920790099
    - -2.711845087233545
    - 0.05708972759903055
    - 2.3284584035746576
    - 3.906146862440266
    - 4.69819546637127
    - 4.72582948417947
    - 4.114324041723038
    - 3.0673710770632816
    - 1.8295416397888844
    - 0.643574401511703
    - -0.28985904888953773
    - -0.8427686617786265
    - -0.9755662161887443
    - -0.7355117761982208
    - -0.23887097740279203
    - 0.3590646905109723
    - 0.8996172326513725
    - 1.2545488717218323
    - 1.3511607062586768
    - 1.1837540066692207
    - 0.8095846093288719
    - 0.33086476362805156
    - -0.13257358067945138
    - -0.4733289626881381
    - -0.6220705990041023
    - -0.5627904019417104
    - -0.3342336412721312
    - -0.017443587668397244
    - 0.28723836035178235
    - 0.487749954544037
    - 0.5253073831331468
    - 0.39025081046871596
    - 0.12441784022674955
    - -0.19084658221639436
    - -0.4581607807198704
    - -0.5929995521102869
    - -0.5502201044298037
    - -0.34066358599930147
    - -0.03252210122364712
    - 0.2640413870469844
    - 0.42607702132098635
    - 0.35389948950620326
    - 0.004618980270626941
    - -0.5863890421525906
    - -1.303251652757242
    - -1.9693155931953374
    - -2.3859523791768384
    - -2.3822650813436073
    - -1.8638343173416865
    - -0.8477028834782209
    - 0.5269271380492097
    - 2.0176335558536156
    - 3.325693235642367
    - 4.1621184231847
    - 4.318344728400401
    - 3.724646153697348
    - 2.4809010285091513
    - 0.8498094743346521
    - -0.7890018243962347
    - -2.0162179178481834
    - -2.4655497551780514
    - -1.911269144423534
    - -0.32981289071740183
    - 2.080399054519216
    - 4.927813747571883
    - 7.7010699847549695
    - 9.872016896494014
    - 11.006141816249148
    - 10.855649357852096
    - 9.413775158146745
    - 6.917451731206058
    - 3.7972428691318285
    - 0.5857326763058226
    - -2.1946902646163404
    - -4.138903595400829
    - -5.036605967354648
    - -4.90326702135319
    - -3.958793111588577
    - -2.5609288432772566
    - -1.11121675966283
    - 0.04247622610206816
    - 0.682825839020086
    - 0.7613416234163819
    - 0.3906422436488983
    - -0.20454474970759992
    - -0.7623165268819911
    - -1.062884952831936
    - -0.9903726143198697
    - -0.5609198940373159
    - 0.08915926458852166
    - 0.7500391445521222
    - 1.2050630648762342
    - 1.29739382004931
    - 0.9771631098666406
    - 0.3158060020562449
    - -0.515845732787573
    - -1.2984300675338611
    - -1.8282064811300525
    - -1.9751833578058668
    - -1.7180678619822862
    - -1.146146644514356
    - -0.42836056657791993
    - 0.24019935074974602
    - 0.6974082582257968
    - 0.8604180296877108
    - 0.7450314239064415
    - 0.45271534277209263
    - 0.13024216196897126
    - -0.08421467311446612
    - -0.11028414474852141
    - 0.046856714562388574
    - 0.2999137431692469
    - 0.5133709555302312
    - 0.5566359448093506
    - 0.3581118161984986
    - -0.05934558504408307
    - -0.5757666629914625
    - -1.0078815567228436
    - -1.1706362719936614
    - -0.9472621960365516
    - -0.34403408642154926
    - 0.4912291958665203
    - 1.2976926123867762
    - 1.773164704697329
    - 1.6702441201804934
    - 0.8882461313275026
    - -0.46954753108889397
    - -2.095954180886687
    - -3.544196192073416
    - -4.3440402026774025
    - -4.140131119921836
    - -2.813235215906484
    - -0.5465758571075678
    - 2.1875962869132275
    - 4.724705189188617
    - 6.3674106021574985
    - 6.568068814325025
    - 5.0849800119978745
    - 2.067791045189024
    - -1.9550986139559856
    - -6.188300188865032
    - -9.754229695468348
    - -11.903961593485542
    - -12.198971291380289
    - -10.61566161701048
    - -7.545144740724292
    - -3.689126176092185
    - 0.11913359159109628
    - 3.119949084458108
    - 4.803652285324018
    - 5.01308484347271
    - 3.9488769493433074
    - 2.082117025013572
    - 0.004508430534609116
    - -1.7381473366165714
    - -2.781594769101686
    - -3.0126307162603743
    - -2.5591927133132093
    - -1.7123331244609923
    - -0.8109166612713653
    - -0.12857567543327578
    - 0.20183092549005638
    - 0.20621468397822362
    - 0.030296389827386652
    - -0.13671724556588905
    - -0.14505381988912588
    - 0.056827729807652314
    - 0.4075556331348716
    - 0.765021623341632
    - 0.9706739811926131
    - 0.9196797360235771
    - 0.6091545148040075
    - 0.14543289980766602
    - -0.2928707742769933
    - -0.5223104833457197
    - -0.42698857078614755
    - -0.007913982074829575
    - 0.6105027992655389
    - 1.2209016499013767
    - 1.6067558526665153
    - 1.622772423376201
    - 1.251709839962042
    - 0.6151466305642126
    - -0.06779876979628517
    - -0.5603969664719132
    positive_zeros:
    - '1.15060972794886268533283965689223'
    - '2.83574566805473002639543772657163'
    - '3.53828062474881842608722733893221'
    - '4.70539492821493616775028867546372'
    - '5.81982599204644179174743940536697'
    - '6.58598803678703886616545672541884'
    - '7.31916912698959727757925500845743'
    - '9.122219005705239874338202507098420'
    - '10.20601414122346704873503368120560'
    - '10.80055076306839713733597194109830'
    prelabel: 2-507-13.4-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.0120674398436345
    root_angle: -0.7479590486074333
    root_number: -0.7025584230735236 - 0.7116260690618661*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.373979524304'
      prec: 50
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.15060972794886268533283965689'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.83574566805473002639543772657'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.53828062474881842608722733893'
      prec: 103
- - algebraic: true
    analytic_conductor: 4.048415382478917
    bad_primes:
    - 3
    - 13
    central_character: '13.4'
    conductor: 507
    conductor_radical: 39
    degree: 2
    id: 10854467
    index: 10
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/507/2/j/g/316/4
    is_instance_Artin: false
    is_instance_BMF: false
    is_instance_CMF: true
    is_instance_DIR: false
    is_instance_ECNF: false
    is_instance_ECQ: false
    is_instance_G2Q: false
    is_instance_HMF: false
    is_instance_MaassGL3: false
    is_instance_MaassGL4: false
    is_instance_MaassGSp4: false
    is_instance_NF: false
    label: 2-507-13.4-c1-0-10
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    order_of_vanishing: 0
    prelabel: 2-507-13.4-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.0120674398436345
    root_angle: -0.37397952430371667
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '1.15060972794886268533283965689'
      prec: 103
- - Lhash: '1458571112262815521945838820077'
    Lhash_array:
    - '1458571112262815521945838820077'
    id: 11220510
    label: 2-507-13.4-c1-0-10
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/507/2/j/g/316/4
label_cols:
- label
- label
- label
labels:
- 2-507-13.4-c1-0-10
- 2-507-13.4-c1-0-10
- 2-507-13.4-c1-0-10
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T02:32:41.183483'