data:
- - Lhash: '4009622288132470315513539300235'
    a10:
    - -34.6320112359526
    - 0.0
    a2:
    - 2.0
    - 0.0
    a3:
    - 8.772001872658766
    - 0.0
    a4:
    - 4.0
    - 0.0
    a5:
    - -17.3160056179763
    - 0.0
    a6:
    - 17.544003745317532
    - 0.0
    a7:
    - -26.08800749063506
    - 0.0
    a8:
    - 8.0
    - 0.0
    a9:
    - 49.94801685392889
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 2.2420725802181445
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - -2.0
          - 0
    - - 19
      - - - 1.0
          - 0
        - - -19.0
          - 0
    bad_primes:
    - 2
    - 19
    central_character: '38.1'
    coefficient_field: CDF
    conductor: 38
    conductor_radical: 38
    conjugate: '4009622288132470315513539300235'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -2.0
        - 0
    - - - 1.0
        - 0
      - - -8.772001872658766
        - 0
      - - 27.0
        - 0
    - - - 1.0
        - 0
      - - 17.3160056179763
        - 0
      - - 125.0
        - 0
    - - - 1.0
        - 0
      - - 26.08800749063506
        - 0
      - - 343.0
        - 0
    - - - 1.0
        - 0
      - - 4.227998127341235
        - 0
      - - 1331.0
        - 0
    - - - 1.0
        - 0
      - - -64.03602434456396
        - 0
      - - 2197.0
        - 0
    - - - 1.0
        - 0
      - - 48.54400374531753
        - 0
      - - 4913.0
        - 0
    - - - 1.0
        - 0
      - - -19.0
        - 0
    - - - 1.0
        - 0
      - - -92.03602434456396
        - 0
      - - 12167.0
        - 0
    - - - 1.0
        - 0
      - - 88.21203932583408
        - 0
      - - 24389.0
        - 0
    - - - 1.0
        - 0
      - - 81.96808239698568
        - 0
      - - 29791.0
        - 0
    - - - 1.0
        - 0
      - - 23.616052434445436
        - 0
      - - 50653.0
        - 0
    - - - 1.0
        - 0
      - - -17.720018726587657
        - 0
      - - 68921.0
        - 0
    - - - 1.0
        - 0
      - - -368.40401310861137
        - 0
      - - 79507.0
        - 0
    - - - 1.0
        - 0
      - - 497.81213295877234
        - 0
      - - 103823.0
        - 0
    - - - 1.0
        - 0
      - - 536.875968164801
        - 0
      - - 148877.0
        - 0
    - - - 1.0
        - 0
      - - 36.69995318353086
        - 0
      - - 205379.0
        - 0
    - - - 1.0
        - 0
      - - -630.692207865123
        - 0
      - - 226981.0
        - 0
    - - - 1.0
        - 0
      - - -282.55585580527503
        - 0
      - - 300763.0
        - 0
    - - - 1.0
        - 0
      - - -595.5522172284168
        - 0
      - - 357911.0
        - 0
    - - - 1.0
        - 0
      - - 597.0483445692129
        - 0
      - - 389017.0
        - 0
    - - - 1.0
        - 0
      - - -427.2238913857916
        - 0
      - - 493039.0
        - 0
    - - - 1.0
        - 0
      - - -493.7683632958005
        - 0
      - - 571787.0
        - 0
    - - - 1.0
        - 0
      - - 921.1363520598479
        - 0
      - - 704969.0
        - 0
    - - - 1.0
        - 0
      - - -1082.744191011194
        - 0
      - - 912673.0
        - 0
    - - - 1.0
        - 0
      - - 712.4477827715832
        - 0
      - - 1030301.0
        - 0
    - - - 1.0
        - 0
      - - 26.479700374597506
        - 0
      - - 1092727.0
        - 0
    - - - 1.0
        - 0
      - - 740.9963614231417
        - 0
      - - 1225043.0
        - 0
    - - - 1.0
        - 0
      - - 1983.076623595369
        - 0
      - - 1295029.0
        - 0
    - - - 1.0
        - 0
      - - 718.720486891279
        - 0
      - - 1442897.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9622197
    index: 3
    label: 2-38-1.1-c3-0-3
    load_key: CMFs-workshop
    motivic_weight: 3
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 3
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/38/4/a/c/1/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 2.226196849892092
    - 2.2264381696775306
    - 2.2269794819217306
    - 2.2272796561274886
    - 2.2264592109104115
    - 2.223332951646834
    - 2.2164539957907277
    - 2.204168027124479
    - 2.1846767841744925
    - 2.1561100340470882
    - 2.1166054691905556
    - 2.0643959754234644
    - 1.997903490211129
    - 1.9158381899633063
    - 1.8173010470100803
    - 1.701886942494254
    - 1.5697845880066865
    - 1.421868580836899
    - 1.25977808219626
    - 1.0859759518734446
    - 0.9037817821045204
    - 0.7173722295850583
    - 0.5317424214334041
    - 0.35262306970341234
    - 0.18634931198882446
    - 0.03967921925692961
    - -0.0804376398063965
    - -0.16713827081482632
    - -0.21396436566348256
    - -0.21521034146091433
    - -0.16628763874274488
    - -0.0640882488366782
    - 0.09267246726871732
    - 0.30315577627986695
    - 0.564165641365786
    - 0.8700039753132845
    - 1.2124365339634444
    - 1.5807875757498173
    - 1.9621763440457067
    - 2.3419016695202535
    - 2.703972721034406
    - 3.0317744803239584
    - 3.3088463469115212
    - 3.5197419987916385
    - 3.650928956192392
    - 3.691678009884257
    - 3.6348865977867932
    - 3.4777771256928824
    - 3.2224118096398993
    - 2.8759703756083423
    - 2.4507461514353723
    - 1.9638296878182036
    - 1.436466663360526
    - 0.8930977039251827
    - 0.3601107518884138
    - -0.1356397036000574
    - -0.5684696012522352
    - -0.9155618648240292
    - -1.1586110756589176
    - -1.285296571268089
    - -1.2904641628996536
    - -1.1769056685361823
    - -0.9556439830232938
    - -0.6456591193628329
    - -0.27302641351665624
    - 0.1305200675972093
    - 0.5295406496669681
    - 0.8872561634495195
    - 1.168181903671611
    - 1.3408502246577838
    - 1.3804196830145403
    - 1.2709600496919395
    - 1.0072104279581136
    - 0.5956331408107505
    - 0.054628569842044936
    - -0.5861662425899253
    - -1.2875032101464625
    - -2.0030051781302722
    - -2.682359960873458
    - -3.275011814474892
    - -3.7340783029063718
    - -4.020182294588057
    - -4.104874907019433
    - -3.97333892561683
    - -3.6261046085659436
    - -3.0795792968954814
    - -2.365284614932915
    - -1.5278034550420279
    - -0.6215544503487895
    - 0.2933761337844423
    - 1.1560171422663748
    - 1.9095085832384575
    - 2.5058697711841105
    - 2.9100981378570823
    - 3.103199513194201
    - 3.0838340005950156
    - 2.868380396770444
    - 2.4893668025012112
    - 1.9923726394925139
    - 1.431662461876195
    - 0.8649486236418683
    - 0.34778274192340153
    - -0.07186779870241518
    - -0.3583010163325252
    - -0.49151946716064493
    - -0.4690410623289547
    - -0.30585552301139857
    - -0.0324927162102287
    - 0.3086258408850315
    - 0.6681851850797135
    - 0.9957934452448018
    - 1.2459729381839715
    - 1.3836371915770673
    - 1.3883969520558466
    - 1.2571472485542161
    - 1.0045658049383717
    - 0.6613838451652237
    - 0.270549699228837
    - -0.11833522408292854
    - -0.4557002487654612
    - -0.6990327636875202
    - -0.8193880017144037
    - -0.8065342573806142
    - -0.6720038513758355
    - -0.4495329255599
    - -0.19266153708177533
    - 0.03040079274125224
    - 0.144197696866018
    - 0.07498270875214502
    - -0.2397784136344367
    - -0.8424765950417774
    - -1.7481163088241656
    - -2.9397410836833693
    - -4.367245041967151
    - -5.949922325796301
    - -7.5826776650763215
    - -9.145378972498516
    - -10.514430548428802
    - -11.575335081687676
    - -12.234837301673178
    - -12.431230372743753
    - -12.141567298944718
    - -11.384841715803478
    - -10.22065246462089
    - -8.743393368898918
    - -7.072550514988311
    - -5.340176250957422
    - -3.6769781441361986
    - -2.198660824414542
    - -0.9941573468060145
    - -0.11717771143321681
    - 0.41789428033473386
    - 0.6352628532025232
    - 0.5922614922804872
    - 0.3699047760610146
    - 0.06070807124705826
    - -0.24459864927832123
    - -0.4696786179938403
    - -0.5628135407391385
    - -0.5033556351309332
    - -0.30352569191176504
    - -0.005317395543881254
    - 0.327045649005527
    - 0.6180172631057473
    - 0.7934218128019181
    - 0.7930736805514803
    - 0.5814436095244465
    - 0.1547431854797125
    - -0.45670830672740537
    - -1.191299767497047
    - -1.9638362064703518
    - -2.6771150461475117
    - -3.235745357857452
    - -3.560206648939602
    - -3.599052513786605
    - -3.3373822122976744
    - -2.8002072666078894
    - -2.050064168675341
    - -1.1790667313804508
    - -0.29642965918669223
    - 0.48679784361235395
    - 1.0735841404876738
    - 1.3950030258328023
    - 1.4204138772958559
    - 1.1621283844000079
    - 0.6737553478865654
    - 0.0423573626357008
    - -0.6244999011027978
    - -1.2149195805129422
    - -1.6296452071596563
    - -1.7972367763789576
    - -1.6850815316387158
    - -1.3044708355344705
    - -0.7088679613317727
    - 0.014454800552129233
    - 0.7581796073737024
    - 1.4119941278625507
    - 1.8802489108710652
    - 2.0973862501819207
    - 2.038604156292932
    - 1.723935092286352
    - 1.2149499586655446
    - 0.6044861275968414
    - 0.0009558609906753204
    - -0.490271608114927
    - -0.7853651831046994
    - -0.837284130840579
    - -0.6451095148915517
    - -0.2556770833887781
    - 0.24304034201612543
    - 0.7359923023520405
    - 1.1004678393796694
    - 1.2278099382083423
    - 1.0438621754007358
    - 0.5246500544939895
    - -0.2955509536667589
    - -1.3254634939062984
    - -2.4276061131218327
    - -3.437312288016272
    - -4.187242138691538
    - -4.533656740446528
    - -4.380300418827675
    - -3.695977453709689
    - -2.5227971710459847
    - -0.9734685237298567
    - 0.7822650035397802
    - 2.54022035127951
    - 4.090087246503685
    - 5.2451693919477185
    - 5.8689680781259375
    - 5.894464651683777
    - 5.333081546405306
    - 4.271929770982328
    - 2.859820263966145
    - 1.2843187153033655
    - -0.256443624449146
    - -1.5826703589869735
    - -2.557913144380222
    - -3.1063025261911967
    - -3.2194557156601946
    - -2.9522947712568564
    - -2.4088963232490905
    - -1.7211669216440104
    - -1.0243037221554194
    - -0.4334540246080831
    - -0.02565029563768214
    - 0.1699676815753816
    - 0.17223046631905373
    - 0.03874264917363049
    - -0.15042034110320626
    - -0.3126365562301278
    - -0.382149203565737
    - -0.324980390326135
    - -0.14628429323753395
    - 0.11139511038642565
    - 0.37865049100584797
    - 0.576398920038366
    positive_zeros:
    - '3.16303426781052515390090952769568'
    - '3.93149329831377357804181671820072'
    - '6.83945744702810489928646858931639'
    - '8.084959882271028323143027320107485'
    - '9.261357644577212813933289374129952'
    - '11.08453363412813674368454222799189'
    - '12.72576187683773906907546760817579'
    - '13.38775329037008038079963478557052'
    - '14.71090850537627076555606662756194'
    - '15.72995924244702178401287918599219'
    prelabel: 2-38-1.1-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.4973551950750177
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    spectral_label: c3-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '3.16303426781052515390090952770'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '3.93149329831377357804181671820'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '6.83945744702810489928646858932'
      prec: 103
- - algebraic: true
    analytic_conductor: 2.2420725802181445
    bad_primes:
    - 2
    - 19
    central_character: '1.1'
    conductor: 38
    conductor_radical: 38
    degree: 2
    id: 9622197
    index: 3
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/38/4/a/c/1/2
    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: 2-38-1.1-c3-0-3
    motivic_weight: 3
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 3
    order_of_vanishing: 0
    prelabel: 2-38-1.1-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.4973551950750177
    root_angle: 0.0
    self_dual: true
    spectral_label: c3-0
    z1:
      __RealLiteral__: 0
      data: '3.16303426781052515390090952770'
      prec: 103
- - Lhash: '4009622288132470315513539300235'
    Lhash_array:
    - '4009622288132470315513539300235'
    id: 9988223
    label: 2-38-1.1-c3-0-3
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/38/4/a/c/1/2
label_cols:
- label
- label
- label
labels:
- 2-38-1.1-c3-0-3
- 2-38-1.1-c3-0-3
- 2-38-1.1-c3-0-3
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T17:54:19.797528'