data:
- - Lhash: '2999214261022966042145842143706'
    a10:
    - -0.4396926207859084
    - -0.7615699589143088
    a2:
    - 0.17364817766693036
    - -0.984807753012208
    a3:
    - 0.0
    - 0.0
    a4:
    - -0.9396926207859084
    - -0.3420201433256687
    a5:
    - 0.6736481776669303
    - -0.565257937423568
    a6:
    - 0.0
    - 0.0
    a7:
    - 3.3190778623577253
    - -1.2080455471101075
    a8:
    - -0.5
    - 0.8660254037844386
    a9:
    - 0.0
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 1.293576512744743
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - -0.17364817766693036
          - 0.984807753012208
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 2
    - 3
    central_character: '162.73'
    coefficient_field: CDF
    conductor: 162
    conductor_radical: 6
    conjugate: '1937899824306887549487696691021'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -0.17364817766693036
        - 0.984807753012208
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -0.6736481776669303
        - 0.565257937423568
      - - 0.8682408883346517
        - -4.924038765061041
    - - - 1.0
        - 0
      - - -3.3190778623577253
        - 1.2080455471101075
      - - 5.362311101832846
        - -4.499513267805775
    - - - 1.0
        - 0
      - - 2.7378259501428426
        - 2.297308744992445
      - - 1.9101299543362338
        - 10.832885283134289
    - - - 1.0
        - 0
      - - 0.6415592914289743
        - 3.6384635456879617
      - - -12.216004070216808
        - 4.446261863233693
    - - - 1.0
        - 0
      - - -3.1244851516900036
        - -5.411767030221637
      - - -8.5
        - 14.722431864335457
    - - - 1.0
        - 0
      - - 2.085122305476703
        - -3.611537773080803
      - - -9.5
        - -16.454482671904334
    - - - 1.0
        - 0
      - - -1.9396926207859084
        - -0.7059903775918711
      - - 17.619022191736494
        - 14.784115022790404
    - - - 1.0
        - 0
      - - 0.028218492976135545
        - -0.16003502619256754
      - - -27.251086002791343
        - -9.918584156444393
    - - - 1.0
        - 0
      - - 1.5393628462133007
        - 0.560282255756943
      - - 23.747377736688318
        - 19.92641590028272
    - - - 1.0
        - 0
      - - -3.8584407085710257
        - -6.683015345237076
      - - -18.5
        - 32.04293994002423
    - - - 1.0
        - 0
      - - -1.3374961755702346
        - -7.585317744319688
      - - -38.527397452222246
        - 14.022825876352417
    - - - 1.0
        - 0
      - - 8.29085936938159
        - 6.956857038990788
      - - 7.466871639678005
        - 42.34673337952495
    - - - 1.0
        - 0
      - - 6.024814926262612
        - -2.1928533001223154
      - - 36.00408882659197
        - -30.211017655267348
    - - - 1.0
        - 0
      - - 0.7168814171420514
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - -5.3511667485956815
        - 4.490162045114761
      - - 10.24524248234889
        - -58.10365742772028
    - - - 1.0
        - 0
      - - -1.1920664908794398
        - 0.4338767199462795
      - - 46.728711030257664
        - -39.2100441908789
    - - - 1.0
        - 0
      - - -0.6244851516900037
        - -3.541631287400726
      - - -62.95940559265586
        - 22.915349602819806
    - - - 1.0
        - 0
      - - 6.769914836380798
        - 11.725836459525885
      - - -35.5
        - 61.48780366869514
    - - - 1.0
        - 0
      - - -1.1638479979033043
        - 2.015843864655839
      - - -36.5
        - -63.21985447626402
    - - - 1.0
        - 0
      - - 1.1493000779526152
        - -6.518004637377883
      - - -74.23571704208676
        - -27.01959132272783
    - - - 1.0
        - 0
      - - -0.7733184030943225
        - 4.385706600244631
      - - -77.9944875252304
        - -28.387671896030504
    - - - 1.0
        - 0
      - - -4.624485151690004
        - 8.009843241574954
      - - -44.5
        - -77.07626093681505
    - - - 1.0
        - 0
      - - 8.649300077952615
        - 7.257624505351659
      - - 16.843873233692243
        - 95.52635204218419
    - - - 1.0
        - 0
      - - -8.809277682594098
        - 3.2063148618498025
      - - 77.37048875501678
        - -64.92154857834048
    - - - 1.0
        - 0
      - - 2.4717815070238642
        - -2.074070950894546
      - - 17.885762299693827
        - -101.43519856025743
    - - - 1.0
        - 0
      - - -2.2831185828579486
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - -10.419214914333415
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - 8.528685319524433
        - -7.156416706040034
      - - 19.62224407636313
        - -111.28327609037952
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9629233
    index: 2
    label: 2-162-27.25-c1-0-2
    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/162/2/e/a/73/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 1.268012335659721
    - 1.337369516938389
    - 1.4201458785542833
    - 1.515872730028362
    - 1.6220838571445404
    - 1.7345314128965044
    - 1.847462537032564
    - 1.9538931040835237
    - 2.0458687369504966
    - 2.1147368739862653
    - 2.1514624048815225
    - 2.1470121875732957
    - 2.0928198792150066
    - 1.981327201355086
    - 1.8065831209686765
    - 1.5648691864828363
    - 1.2553078582098947
    - 0.8804017327288259
    - 0.44644593227936835
    - -0.036245406010631566
    - -0.5533537087078889
    - -1.0868569322856145
    - -1.6156461274791103
    - -2.1164646933863738
    - -2.565150216964409
    - -2.9381281926548253
    - -3.214075304702289
    - -3.375640338214661
    - -3.4110865784781756
    - -3.315704283562308
    - -3.0928387249790985
    - -2.754390940913878
    - -2.3206761626895243
    - -1.819568767033505
    - -1.2849206825704695
    - -0.754308621975679
    - -0.2662386646764478
    - 0.14299259238969508
    - 0.44252098000353685
    - 0.6099211776419915
    - 0.6336809863579804
    - 0.5148447063722699
    - 0.26757839406521583
    - -0.08150493578994786
    - -0.4953080405262238
    - -0.9294143502159792
    - -1.3362289330279102
    - -1.6697379321894792
    - -1.8904229447159102
    - -1.9698023314132296
    - -1.894061407002882
    - -1.666285842086943
    - -1.3069286578357244
    - -0.8523142990980175
    - -0.3511987325839196
    - 0.1403596453504959
    - 0.5653346487584425
    - 0.8725968064676122
    - 1.0235055022834851
    - 0.9973890118283624
    - 0.7951387980363356
    - 0.44031666028426
    - -0.022559678835067452
    - -0.5325506343095732
    - -1.0192785305221312
    - -1.4116375710369706
    - -1.6472165649721175
    - -1.68124043561844
    - -1.493800869089154
    - -1.0942746844445848
    - -0.5221186802957637
    - 0.1563430895351199
    - 0.8550062513586887
    - 1.4782705643670044
    - 1.9333502126736295
    - 2.1430661171737495
    - 2.057390997527946
    - 1.6620619181346503
    - 0.9828618029650946
    - 0.08467990209150396
    - -0.9348639999789983
    - -1.9566905410937403
    - -2.8551521697603874
    - -3.5146687933950145
    - -3.8458610804243225
    - -3.7988674632472303
    - -3.371798685332832
    - -2.61287041311288
    - -1.6155939379077646
    - -0.5073876944521696
    - 0.5670413638501803
    - 1.465357588511377
    - 2.067552884505552
    - 2.2932854984001825
    - 2.1139538443248505
    - 1.5575430384093056
    - 0.705301700628752
    - -0.31948129241833007
    - -1.369107755460751
    - -2.292977166572105
    - -2.95975708370661
    - -3.276808254062998
    - -3.2037978618804144
    - -2.7582826352343943
    - -2.012280052835667
    - -1.0802822380260795
    - -0.1005722545857529
    - 0.7871602131895543
    - 1.4642393786674113
    - 1.8517286877214914
    - 1.9222960180028088
    - 1.7031780665652454
    - 1.2697091499200301
    - 0.7305163939736278
    - 0.2069665010546926
    - -0.18948983217204562
    - -0.3779952361945736
    - -0.3231951606830729
    - -0.04157794494144705
    - 0.4020285288794442
    - 0.9072734468025578
    - 1.3581271143070262
    - 1.6460887415254437
    - 1.6923662212731765
    - 1.464718804509088
    - 0.9855607860885557
    - 0.32951341419049307
    - -0.3894161269946951
    - -1.038824481028614
    - -1.493198775070831
    - -1.6586572868424596
    - -1.4922448795971492
    - -1.0117907443801184
    - -0.29406703786187227
    - 0.5387657267885803
    - 1.3421017567261337
    - 1.9769286589324997
    - 2.3374816684506703
    - 2.372900029355857
    - 2.0982667844317886
    - 1.592386245241301
    - 0.9822502504264811
    - 0.4168668747424676
    - 0.035425635568431466
    - -0.06383731175158355
    - 0.15244100526610996
    - 0.6413838911494338
    - 1.2880724667048284
    - 1.9252605253030557
    - 2.3653652015863913
    - 2.4388079851646105
    - 2.031182731136945
    - 1.1115943948217009
    - -0.2540606490084316
    - -1.9083366381025595
    - -3.6258715184087897
    - -5.151556595066389
    - -6.246296052005941
    - -6.731609288261312
    - -6.5242411013765915
    - -5.653651864477418
    - -4.2584753156814
    - -2.562144626983245
    - -0.8320785872789761
    - 0.6697748424679264
    - 1.7353486849335307
    - 2.248187760725326
    - 2.2029082260515414
    - 1.7024409833863163
    - 0.9336383900659285
    - 0.12629176398303663
    - -0.4959251426797774
    - -0.7623568045512176
    - -0.5903125657566836
    - -0.0007793673983652281
    - 0.8882863687952421
    - 1.8894699859827202
    - 2.7881125741554453
    - 3.3899475886085515
    - 3.5637140529365805
    - 3.2694254213034877
    - 2.566162539237648
    - 1.5978222166911764
    - 0.560181300077585
    - -0.3431753160626447
    - -0.9460189346908547
    - -1.1554693943369352
    - -0.9706761847507618
    - -0.48005188009924127
    - 0.16210479616908333
    - 0.773959499871323
    - 1.1903259481811115
    - 1.3021695915988643
    - 1.0820233899870886
    - 0.5892583309050596
    - -0.046022408383969954
    - -0.6565295042970996
    - -1.0805664830143358
    - -1.2035048286083663
    - -0.9876279721416586
    - -0.4827607003428413
    - 0.18524302749364888
    - 0.8456143782028258
    - 1.3258977179965252
    - 1.496606989492743
    - 1.3060147782620288
    - 0.7959747140366964
    - 0.09421159760842508
    - -0.6156776875639222
    - -1.1395977376818407
    - -1.3226756158735589
    - -1.090829162287908
    - -0.47330589003644014
    - 0.4002653269281733
    - 1.3285633655020521
    - 2.086761665013405
    - 2.482800096967341
    - 2.407833112767651
    - 1.867848863240981
    - 0.9876587977924633
    - -0.014965090238446142
    - -0.8798345825620808
    - -1.3680093911266267
    - -1.3232659492927294
    - -0.7159747503017703
    - 0.3422632264787734
    - 1.6180914412775675
    - 2.806622404103469
    - 3.601360284320228
    - 3.7675478142501753
    - 3.2012825031477266
    - 1.9596654807845058
    - 0.25386647375245425
    - -1.5942253034537461
    - -3.2222582326508062
    - -4.308373067304582
    - -4.643776438612184
    - -4.179606589127289
    - -3.036787831028111
    - -1.4764401422162936
    - 0.16203338156956035
    - 1.5401828832785405
    - 2.397858253925758
    - 2.6099818199231715
    - 2.2092386450452928
    - 1.3697218687815735
    - 0.3563452835440219
    - -0.5466327560865779
    - -1.109512715867481
    - -1.2146305805458713
    - -0.8829879275066189
    - -0.26373245810898355
    - 0.41011677258614015
    - 0.8875495534005551
    - 0.9693701568308318
    - 0.5633887986136906
    - -0.2895106073395694
    positive_zeros:
    - '2.36596287690234497643672623156607'
    - '4.57784777941659498859603044667474'
    - '5.34826355233230935211879246032080'
    - '6.83818532377423263228962317260458'
    - '7.74432069757878621046640440759631'
    - '8.847120417109826465186501354746830'
    - '9.885773102355795428751047799644194'
    - '11.18250721533402859762324020255969'
    - '12.08720653479349764700901999887947'
    - '13.26322270181277319969556239631291'
    prelabel: 2-162-27.25-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.1373550513119213
    root_angle: 0.4074074074074074
    root_number: 0.2868032327110903 + 0.9579895123154889*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.203703703704'
      prec: 47
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '2.36596287690234497643672623157'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '4.57784777941659498859603044667'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '5.34826355233230935211879246032'
      prec: 103
- - algebraic: true
    analytic_conductor: 1.293576512744743
    bad_primes:
    - 2
    - 3
    central_character: '27.25'
    conductor: 162
    conductor_radical: 6
    degree: 2
    id: 9629233
    index: 2
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/162/2/e/a/73/1
    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: 2-162-27.25-c1-0-2
    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: 2-162-27.25-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.1373550513119213
    root_angle: 0.2037037037037037
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '2.36596287690234497643672623157'
      prec: 103
- - Lhash: '2999214261022966042145842143706'
    Lhash_array:
    - '2999214261022966042145842143706'
    id: 9995260
    label: 2-162-27.25-c1-0-2
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/162/2/e/a/73/1
label_cols:
- label
- label
- label
labels:
- 2-162-27.25-c1-0-2
- 2-162-27.25-c1-0-2
- 2-162-27.25-c1-0-2
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-16T18:07:53.908796'