data:
- - Lhash: '2537790157681856355655495002355'
    a10:
    - 0.0
    - 0.0
    a2:
    - -0.8660254037844386
    - 1.5
    a3:
    - 0.5
    - -0.8660254037844386
    a4:
    - -0.5
    - -0.8660254037844386
    a5:
    - 0.0
    - 0.0
    a6:
    - 0.8660254037844386
    - 1.5
    a7:
    - -1.7320508075688772
    - -3.0
    a8:
    - -1.7320508075688772
    - 0.0
    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: '507.22'
    coefficient_field: CDF
    conductor: 507
    conductor_radical: 39
    conjugate: '334010275599263873523527205339'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0.8660254037844386
        - -1.5
      - - -1.0
        - -1.7320508075688772
    - - - 1.0
        - 0
      - - -0.5
        - 0.8660254037844386
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 5.0
        - 0
    - - - 1.0
        - 0
      - - 1.7320508075688772
        - 3.0
      - - -3.5
        - 6.06217782649107
    - - - 1.0
        - 0
      - - 1.7320508075688772
        - -3.0
      - - -5.5
        - -9.526279441628825
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 3.0
        - 5.196152422706632
      - - -8.5
        - 14.722431864335457
    - - - 1.0
        - 0
      - - 1.7320508075688772
        - 3.0
      - - -9.5
        - 16.454482671904334
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -11.5
        - -19.91858428704209
    - - - 1.0
        - 0
      - - 3.0
        - -5.196152422706632
      - - -14.5
        - -25.11473670974872
    - - - 1.0
        - 0
      - - 3.4641016151377544
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - -3.4641016151377544
        - 6.0
      - - -18.5
        - -32.04293994002423
    - - - 1.0
        - 0
      - - -3.4641016151377544
        - 6.0
      - - -20.5
        - -35.50704155516198
    - - - 1.0
        - 0
      - - 2.0
        - 3.4641016151377544
      - - -21.5
        - 37.239092362730865
    - - - 1.0
        - 0
      - - 3.4641016151377544
        - 0
      - - 47.0
        - 0
    - - - 1.0
        - 0
      - - -6.0
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - -5.196152422706632
        - -9.0
      - - -29.5
        - 51.09549882328188
    - - - 1.0
        - 0
      - - -1.0
        - -1.7320508075688772
      - - -30.5
        - 52.827549630850754
    - - - 1.0
        - 0
      - - -5.196152422706632
        - 9.0
      - - -33.5
        - -58.023702053557386
    - - - 1.0
        - 0
      - - 1.7320508075688772
        - 3.0
      - - -35.5
        - 61.48780366869514
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - 8.0
        - 0
      - - 79.0
        - 0
    - - - 1.0
        - 0
      - - 3.4641016151377544
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - 3.4641016151377544
        - -6.0
      - - -44.5
        - -77.07626093681505
    - - - 1.0
        - 0
      - - -6.928203230275509
        - -12.0
      - - -48.5
        - 84.00446416709055
    - - - 1.0
        - 0
      - - -3.0
        - 5.196152422706632
      - - -50.5
        - -87.4685657822283
    - - - 1.0
        - 0
      - - 8.0
        - 0
      - - 103.0
        - 0
    - - - 1.0
        - 0
      - - 6.0
        - -10.392304845413264
      - - -53.5
        - -92.66471820493493
    - - - 1.0
        - 0
      - - -6.928203230275509
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - -3.0
        - -5.196152422706632
      - - -56.5
        - 97.86087062764156
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 10854111
    index: 19
    label: 2-507-13.9-c1-0-19
    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/e/e/22/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 0.4088779630224224
    - 0.5804235289119324
    - 0.7432095131133681
    - 0.8983515149355824
    - 1.0439263612901706
    - 1.1751010340550292
    - 1.2847126939842506
    - 1.3641507096404513
    - 1.404424392688633
    - 1.3973369375484865
    - 1.3366980889220361
    - 1.2194958970587377
    - 1.0469244215195375
    - 0.8251427183144662
    - 0.5656308558763155
    - 0.285017559184006
    - 0.0042849030989999815
    - -0.2526911043851105
    - -0.4612316980485908
    - -0.5984582397117374
    - -0.6461941430927788
    - -0.5938677800599544
    - -0.44105407668597646
    - -0.19926351052025562
    - 0.10739441634898123
    - 0.44297256503234816
    - 0.7620415158515534
    - 1.013627852406021
    - 1.14650990479764
    - 1.1154208596807105
    - 0.887504937662938
    - 0.4482222929832142
    - -0.1941653345163873
    - -1.0063479660265608
    - -1.9306061738443823
    - -2.8886867506528797
    - -3.7888726144516287
    - -4.535753028225466
    - -5.041749693124289
    - -5.239072169013928
    - -5.0905306144762
    - -4.597582966402995
    - -3.8041740294218016
    - -2.795341467998316
    - -1.690187850421377
    - -0.6295810118479997
    - 0.24025223098926385
    - 0.7863508461543465
    - 0.9074535808740005
    - 0.5496196107699155
    - -0.2834231130125637
    - -1.5271039622122586
    - -3.0610084402061384
    - -4.721905492735563
    - -6.323437941688034
    - -7.680000829359298
    - -8.631524920006092
    - -9.06553635025043
    - -8.933074433967816
    - -8.255827582017973
    - -7.123105201207872
    - -5.678823676401318
    - -4.1003020687579825
    - -2.572063431626071
    - -1.2587637445626534
    - -0.2816315511834604
    - 0.29768671047391126
    - 0.4831712581502475
    - 0.33937289651585073
    - -0.023784624633786094
    - -0.4735492727241293
    - -0.8800652728628033
    - -1.1404811336979823
    - -1.1969112503622648
    - -1.0448690036280937
    - -0.730629013335528
    - -0.33816995920202697
    - 0.03153029759947501
    - 0.28446392342571863
    - 0.35569394124359144
    - 0.2247599340974163
    - -0.07909531924555986
    - -0.4832222016609304
    - -0.8882141294824266
    - -1.1913833238600406
    - -1.3118575277792803
    - -1.2115033737230745
    - -0.9065719564373484
    - -0.46684928019745064
    - -0.001823027975098613
    - 0.36362106530901384
    - 0.5188534776231412
    - 0.39579878689995895
    - -0.010963850596291527
    - -0.6376883671705663
    - -1.361118089142185
    - -2.0232756076291185
    - -2.466711867685987
    - -2.572721946381804
    - -2.293754676638908
    - -1.6719132879223595
    - -0.8380536753944133
    - 0.009927848980584056
    - 0.6463064487189449
    - 0.8666283255110095
    - 0.5362334413979614
    - -0.3729006253629712
    - -1.7662148414922123
    - -3.4366107494396987
    - -5.099983507945848
    - -6.449926134990089
    - -7.220552770997675
    - -7.243915022975853
    - -6.488979115166866
    - -5.072647700170146
    - -3.2391967907063415
    - -1.311508707536512
    - 0.37596339023999065
    - 1.548020074741594
    - 2.047475394397803
    - 1.868255593014185
    - 1.1547520182772566
    - 0.16693724555753622
    - -0.7812901465173062
    - -1.396625879831974
    - -1.4765024047025674
    - -0.9582784272738838
    - 0.06446252525211454
    - 1.3628367305445928
    - 2.626321839244339
    - 3.536745744046333
    - 3.8451158675144157
    - 3.4328765920069504
    - 2.3427240596025416
    - 0.7713317082188327
    - -0.9744720433339615
    - -2.5476269355481556
    - -3.640014854316186
    - -4.051764795359238
    - -3.7340439806821935
    - -2.795325311506839
    - -1.4702610767315474
    - -0.059619532495267885
    - 1.1431351832064494
    - 1.9199573457108314
    - 2.1741225795976424
    - 1.9431394743450041
    - 1.3767550768705814
    - 0.6873770980316672
    - 0.08736908011881589
    - -0.26921256027449714
    - -0.3246057044482299
    - -0.12530012468667556
    - 0.20107199483479013
    - 0.49205180647648167
    - 0.6054553678959493
    - 0.46649530708818626
    - 0.09271303282688369
    - -0.4107489266287902
    - -0.8840256932032634
    - -1.1634603856900738
    - -1.1348461605520144
    - -0.7722919010157437
    - -0.1501531137185789
    - 0.576447390891634
    - 1.217294850452553
    - 1.6053523112219992
    - 1.6495558583703667
    - 1.3650467039977485
    - 0.8701103524774029
    - 0.34911578812865657
    - -0.008481861350887077
    - -0.07478418080682213
    - 0.1655525697094284
    - 0.5977931625515718
    - 1.0016503640996735
    - 1.11387709185005
    - 0.7126956218523942
    - -0.3003267150347277
    - -1.8466734551481385
    - -3.66489294031029
    - -5.358901691770246
    - -6.491639401703815
    - -6.701043050975231
    - -5.806992220828822
    - -3.8781454296154494
    - -1.2368725904422375
    - 1.603396079536487
    - 4.055436601349723
    - 5.601211893972208
    - 5.923149100534233
    - 4.987955743296776
    - 3.0589809190041253
    - 0.6320063773160639
    - -1.6897966638647872
    - -3.3490542327442308
    - -3.974678499664867
    - -3.4719628426490523
    - -2.0383172691965084
    - -0.10121608592099693
    - 1.8035248002348627
    - 3.1786289295353938
    - 3.6963591812167707
    - 3.2778068781792946
    - 2.100033825525686
    - 0.5316657432842306
    - -0.9819840583857945
    - -2.049262411116939
    - -2.4396568310031737
    - -2.138132179345471
    - -1.3328970698185896
    - -0.3435693318301609
    - 0.4856063981877107
    - 0.8932068032900794
    - 0.7756704367646344
    - 0.2082817056439127
    - -0.5917176458949172
    - -1.3452303927089815
    - -1.8067265468773017
    - -1.8432264923333406
    - -1.4716339587258565
    - -0.8438374334760339
    - -0.18675705070448517
    - 0.28052810396590394
    - 0.4232332569794802
    - 0.23444865082226193
    - -0.168691222296412
    - -0.5939587432648634
    - -0.8498593956256548
    - -0.8205296994385856
    - -0.5121070151966151
    - -0.05296954834112059
    - 0.3533248678516457
    - 0.5063712896118343
    - 0.29057065343822325
    - -0.2701323883051957
    - -1.0062065388750745
    - -1.6503917614852657
    - -1.9255247830893814
    - -1.6433416419379188
    - -0.7797587692224094
    - 0.5014803970028364
    - 1.8883384237736178
    - 3.0133203597879477
    - 3.5707037062919285
    - 3.4193262756644303
    - 2.635131446848362
    - 1.4932004950935596
    - 0.3822250652093445
    - -0.32237175588079303
    - -0.3851690212227473
    - 0.20588440693811458
    - 1.2296760595561997
    - 2.3020060434977223
    - 3.0047512004756287
    - 3.0322252759327646
    - 2.3051644135378804
    positive_zeros:
    - '2.00196344104988349130777804530601'
    - '2.95834841522328463941104787985057'
    - '3.96586037906396517021802940316955'
    - '5.71132870315572181055302443724118'
    - '6.21434428146745364696109689730980'
    - '8.175185999031981602091841397726137'
    - '8.618032925928548847544400093121940'
    - '9.613084657114825132540688034066101'
    - '10.09730016357816042317696211800123'
    - '11.12552305658876342010011729395198'
    prelabel: 2-507-13.9-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.0120674398436345
    root_angle: 0.4959180972148666
    root_number: 0.012823324336887883 + 0.9999177777962301*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.247959048607'
      prec: 47
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '2.00196344104988349130777804531'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.95834841522328463941104787985'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.96586037906396517021802940317'
      prec: 103
- - algebraic: true
    analytic_conductor: 4.048415382478917
    bad_primes:
    - 3
    - 13
    central_character: '13.9'
    conductor: 507
    conductor_radical: 39
    degree: 2
    id: 10854111
    index: 19
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/507/2/e/e/22/1
    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: 2-507-13.9-c1-0-19
    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: 2-507-13.9-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.0120674398436345
    root_angle: 0.2479590486074333
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '2.00196344104988349130777804531'
      prec: 103
- - Lhash: '2537790157681856355655495002355'
    Lhash_array:
    - '2537790157681856355655495002355'
    id: 11220153
    label: 2-507-13.9-c1-0-19
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/507/2/e/e/22/1
label_cols:
- label
- label
- label
labels:
- 2-507-13.9-c1-0-19
- 2-507-13.9-c1-0-19
- 2-507-13.9-c1-0-19
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-13T12:07:46.446982'