data:
- - Lhash: '1467823673117774127401618430787'
    a10:
    - -1.0
    - 1.0
    a2:
    - 0.0
    - -1.0
    a3:
    - 0.0
    - 0.0
    a4:
    - -1.0
    - 0.0
    a5:
    - -1.0
    - -1.0
    a6:
    - 0.0
    - 0.0
    a7:
    - 0.0
    - 0.0
    a8:
    - 0.0
    - 1.0
    a9:
    - 0.0
    - 1.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 1.6628846220931641
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 1.0
    - - 7
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 17
      - - - 1.0
          - 0
        - - 0
          - 1.0
    bad_primes:
    - 2
    - 7
    - 17
    central_character: '3332.3039'
    coefficient_field: CDF
    conductor: 3332
    conductor_radical: 238
    conjugate: '908348404993769536115596493314'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0
        - -1.0
    - - - 1.0
        - 0
      - - 1.0
        - 1.0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - -2.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - 1.0
        - 1.0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0
        - -1.0
    - - - 1.0
        - 0
      - - -1.0
        - -1.0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - -1.0
        - 1.0
      - - 0
        - -1.0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - -1.0
        - 1.0
      - - 0
        - -1.0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0
        - -1.0
    - - - 1.0
        - 0
      - - 1.0
        - 1.0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 2.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 1.0
        - 1.0
      - - 0
        - 1.0
    - - - 1.0
        - 0
      - - -2.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 0
        - -1.0
    - - - 1.0
        - 0
      - - -1.0
        - 1.0
      - - 0
        - -1.0
    - - - 1.0
        - 0
      - - 1.0
        - -1.0
      - - 0
        - -1.0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 19542179
    index: 2
    label: 2-3332-68.47-c0-0-2
    leading_term: '0.94107124471331076257887770798633'
    load_key: CMFs-workshop
    motivic_weight: 0
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 0
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/3332/1/m/a/3039/1
    plot_delta:
      __RealLiteral__: 0
      data: '0.05078125'
      prec: 34
    plot_values:
    - 0.9410712447133107
    - 0.9935676143842199
    - 1.0514382633186825
    - 1.1146940329911643
    - 1.1826415890543818
    - 1.2539306455201868
    - 1.3266419721729306
    - 1.3983911046682984
    - 1.4664298577988881
    - 1.5277369922057336
    - 1.579096619892201
    - 1.6171669514520954
    - 1.6385433619144376
    - 1.6398195503137964
    - 1.617649668006596
    - 1.5688132175725724
    - 1.4902835237329506
    - 1.3792997327210497
    - 1.233441613528012
    - 1.050705893495652
    - 0.8295824385187238
    - 0.5691282663828727
    - 0.26903714892690594
    - -0.0702975911022705
    - -0.4477295513326834
    - -0.8613174391732019
    - -1.3082973335889485
    - -1.7850711936937633
    - -2.2872135246137324
    - -2.8094977644416894
    - -3.3459435305562337
    - -3.889885365365136
    - -4.434063059622311
    - -4.970733017634357
    - -5.491799477445697
    - -5.988963727573857
    - -6.453888789428382
    - -6.878376382392264
    - -7.254552379161554
    - -7.575056415442554
    - -7.833230863493743
    - -8.023304035334125
    - -8.140562268989012
    - -8.181505487505534
    - -8.143980919710119
    - -8.027289943525208
    - -7.832263461776501
    - -7.561301845803954
    - -7.2183762767286686
    - -6.808989264442897
    - -6.3400932103852785
    - -5.819967075813517
    - -5.2580524906739425
    - -4.6647519522660446
    - -4.051193076509824
    - -3.428964133534569
    - -2.8098272776703657
    - -2.2054169237922965
    - -1.6269315829650768
    - -1.0848281093928256
    - -0.5885276917770108
    - -0.14614301604736707
    - 0.23576418792402135
    - 0.5523865369093699
    - 0.8008274975062143
    - 0.9802043404027458
    - 1.0916923337940319
    - 1.138506665347497
    - 1.1258204892768564
    - 1.0606195518367358
    - 0.9514959898060648
    - 0.8083860502457892
    - 0.6422585693016206
    - 0.4647629943622849
    - 0.28784745963081104
    - 0.12335885617737524
    - -0.0173620931436525
    - -0.12387709289306387
    - -0.18702401959446985
    - -0.19925460698804262
    - -0.15492333511384654
    - -0.050516090869076415
    - 0.11519105734081862
    - 0.34105042855117174
    - 0.6235435395187161
    - 0.9568662153922906
    - 1.333097038805704
    - 1.7424450801136588
    - 2.1735697979461968
    - 2.6139631072446914
    - 3.0503810002949683
    - 3.469309888021504
    - 3.8574511062937704
    - 4.202205892174921
    - 4.492142645171037
    - 4.717428492470835
    - 4.870208092440104
    - 4.9449142265235695
    - 4.938497006357761
    - 4.850561391676561
    - 4.683406079658637
    - 4.441960567505262
    - 4.13362116665469
    - 3.7679908032406146
    - 3.3565314099683654
    - 2.9121414316324934
    - 2.4486742665817176
    - 1.98041619775447
    - 1.5215443963656023
    - 1.0855868010759773
    - 0.6849060086535396
    - 0.33022871746215066
    - 0.03024074015102473
    - -0.20873481529344376
    - -0.3829618279868085
    - -0.4914074698075617
    - -0.5357445670281806
    - -0.5202388877654902
    - -0.45152522290459374
    - -0.3382810692769456
    - -0.19081138624542748
    - -0.02056206361301183
    - 0.16041679162156788
    - 0.3400340461339133
    - 0.5067219251487385
    - 0.6499758438603943
    - 0.76084464255794
    - 0.8323480555534946
    - 0.859801230906267
    - 0.8410301107504509
    - 0.7764663222047624
    - 0.6691157129024214
    - 0.5244005527743232
    - 0.34988144766208484
    - 0.15487088837456497
    - -0.05004419346432959
    - -0.2535487469854409
    - -0.44418889217172214
    - -0.6109756381058771
    - -0.7439731800749735
    - -0.8348420419714432
    - -0.8773089069294949
    - -0.8675379824321823
    - -0.8043830713029407
    - -0.6895049937943828
    - -0.5273453928595312
    - -0.32495496617662445
    - -0.09168147557871471
    - 0.16126986752296446
    - 0.4213842170962892
    - 0.6754676370578294
    - 0.9103299636266179
    - 1.113486022651989
    - 1.273839302156301
    - 1.3823120078949753
    - 1.4323870885536942
    - 1.420531283862948
    - 1.3464734077275504
    - 1.2133187239608005
    - 1.0274881162273375
    - 0.798479437114577
    - 0.5384575292438685
    - 0.26168849305593306
    - -0.016157634227228948
    - -0.278803982933382
    - -0.5102256655277255
    - -0.6955277038801052
    - -0.821796983283969
    - -0.8788828942942
    - -0.8600633971936503
    - -0.7625576193922228
    - -0.5878526289509188
    - -0.34182045708526015
    - -0.03461140128076095
    - 0.3196793310276552
    - 0.7035630114460147
    - 1.0969066578051065
    - 1.4778491323519436
    - 1.8238433499981614
    - 2.1127759621110944
    - 2.3241101969095457
    - 2.4399944519291057
    - 2.4462789949638064
    - 2.3333858459479693
    - 2.0969825423589272
    - 1.7384188411808914
    - 1.2648961397598535
    - 0.689352029483344
    - 0.030056338947927894
    - -0.6900704016685284
    - -1.4443906697401596
    - -2.203696807649316
    - -2.937519968932187
    - -3.615540316742866
    - -4.209030694802233
    - -4.692262326322064
    - -5.043800998413633
    - -5.247625768402297
    - -5.294009405429323
    - -5.180110286171883
    - -4.910238845590553
    - -4.495777326519665
    - -3.9547487235665706
    - -3.31104862458546
    - -2.5933712060490914
    - -1.833877014374225
    - -1.066664478005157
    - -0.32611854416778924
    - 0.35478225105255634
    - 0.946115091818769
    - 1.4225338414545545
    - 1.7645817959805663
    - 1.9597255145431538
    - 2.0030520270309182
    - 1.8975880198486583
    - 1.6542183975581506
    - 1.2912019731563162
    - 0.8333029108896169
    - 0.3105768394503958
    - -0.2431308164353854
    - -0.7919007928682867
    - -1.2995843780187313
    - -1.731682332913838
    - -2.0571612056702855
    - -2.250111751890097
    - -2.2911610950547847
    - -2.168561972839461
    - -1.8788983730515791
    - -1.4273662815139696
    - -0.8276101572454592
    - -0.10111897974560509
    - 0.7237909511437969
    - 1.6133570971585445
    - 2.5300464597001144
    - 3.4344405188407148
    - 4.287231851450363
    - 5.051228109150913
    - 5.693257744638385
    - 6.185876266123931
    - 6.508781701543969
    - 6.649862888088286
    - 6.605823405730665
    - 6.3823464372666185
    - 5.993790360270609
    - 5.462430128240241
    - 4.817284093113263
    - 4.092588494800018
    - 3.3260011292871576
    - 2.5566306102540213
    - 1.822997300106032
    - 1.161035831569871
    - 0.6022469196635482
    - 0.17209796543409767
    - -0.1112417942448057
    - -0.2377643858881089
    - -0.20603956942376284
    - -0.023164657604585144
    positive_zeros:
    - '1.15790871148051782974946018627553'
    - '3.11611928451943545657526856908906'
    - '3.85246361645720185831238690569512'
    - '4.13088693244731173451210324300846'
    - '5.69325487277978777709354685503053'
    - '6.15038956349376653971524218848829'
    - '6.84314331405163844154461594750155'
    - '7.48358014587181380502623646717053'
    - '8.274342717562745769936631149974686'
    - '8.790390094214946818624091041977628'
    prelabel: 2-3332-68.47-c0-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.2895288372476066
    root_angle: 0.7110104348113153
    root_number: -0.61541220940263568453061943924181 + 0.78820543801610915221774562678970*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.35550521740565766'
      prec: 64
    spectral_label: c0-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.15790871148051782974946018628'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '3.11611928451943545657526856909'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.85246361645720185831238690570'
      prec: 103
- - algebraic: true
    analytic_conductor: 1.6628846220931641
    bad_primes:
    - 2
    - 7
    - 17
    central_character: '68.47'
    conductor: 3332
    conductor_radical: 238
    degree: 2
    id: 19542179
    index: 2
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/3332/1/m/a/3039/1
    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: 2-3332-68.47-c0-0-2
    motivic_weight: 0
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 0
    order_of_vanishing: 0
    prelabel: 2-3332-68.47-c0-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.2895288372476066
    root_angle: 0.35550521740565766
    self_dual: false
    spectral_label: c0-0
    z1:
      __RealLiteral__: 0
      data: '1.15790871148051782974946018628'
      prec: 103
- - Lhash: '1467823673117774127401618430787'
    Lhash_array:
    - '1467823673117774127401618430787'
    id: 19909395
    label: 2-3332-68.47-c0-0-2
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/3332/1/m/a/3039/1
label_cols:
- label
- label
- label
labels:
- 2-3332-68.47-c0-0-2
- 2-3332-68.47-c0-0-2
- 2-3332-68.47-c0-0-2
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T20:29:44.617818'