data:
- - Lhash: '1185066606646595147193267472117'
    a10:
    - 6.0
    - 0.0
    a2:
    - 1.7320508075688772
    - 0.0
    a3:
    - 0.0
    - 0.0
    a4:
    - 1.0
    - 0.0
    a5:
    - 3.4641016151377544
    - 0.0
    a6:
    - 0.0
    - 0.0
    a7:
    - -1.0
    - 0.0
    a8:
    - -1.7320508075688772
    - 0.0
    a9:
    - 0.0
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 60.86996146082207
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 7
      - - - 1.0
          - 0
        - - 1.0
          - 0
    - - 11
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 3
    - 7
    - 11
    central_character: '7623.1'
    coefficient_field: CDF
    conductor: 7623
    conductor_radical: 231
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -1.7320508075688772
        - 0
      - - 2.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -3.4641016151377544
        - 0
      - - 5.0
        - 0
    - - - 1.0
        - 0
      - - 1.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 2.0
        - 0
      - - 13.0
        - 0
    - - - 1.0
        - 0
      - - -3.4641016151377544
        - 0
      - - 17.0
        - 0
    - - - 1.0
        - 0
      - - -4.0
        - 0
      - - 19.0
        - 0
    - - - 1.0
        - 0
      - - -3.4641016151377544
        - 0
      - - 23.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 29.0
        - 0
    - - - 1.0
        - 0
      - - 4.0
        - 0
      - - 31.0
        - 0
    - - - 1.0
        - 0
      - - -2.0
        - 0
      - - 37.0
        - 0
    - - - 1.0
        - 0
      - - -10.392304845413264
        - 0
      - - 41.0
        - 0
    - - - 1.0
        - 0
      - - -4.0
        - 0
      - - 43.0
        - 0
    - - - 1.0
        - 0
      - - 6.928203230275509
        - 0
      - - 47.0
        - 0
    - - - 1.0
        - 0
      - - -6.928203230275509
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - -6.928203230275509
        - 0
      - - 59.0
        - 0
    - - - 1.0
        - 0
      - - -10.0
        - 0
      - - 61.0
        - 0
    - - - 1.0
        - 0
      - - 4.0
        - 0
      - - 67.0
        - 0
    - - - 1.0
        - 0
      - - -10.392304845413264
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - 14.0
        - 0
      - - 73.0
        - 0
    - - - 1.0
        - 0
      - - 8.0
        - 0
      - - 79.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 83.0
        - 0
    - - - 1.0
        - 0
      - - -3.4641016151377544
        - 0
      - - 89.0
        - 0
    - - - 1.0
        - 0
      - - -14.0
        - 0
      - - 97.0
        - 0
    - - - 1.0
        - 0
      - - -3.4641016151377544
        - 0
      - - 101.0
        - 0
    - - - 1.0
        - 0
      - - 4.0
        - 0
      - - 103.0
        - 0
    - - - 1.0
        - 0
      - - -17.320508075688775
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 2.0
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 113.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 21613393
    index: 137
    label: 2-7623-1.1-c1-0-137
    leading_term: '4.89778687668015362967931730684'
    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/7623/2/a/bi/1/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.046875'
      prec: 27
    plot_values:
    - 4.897786876680153
    - 4.8853955336384915
    - 4.848137553756291
    - 4.785770672831015
    - 4.697922474765378
    - 4.584135377720838
    - 4.443925716482303
    - 4.2768534586387394
    - 4.08259864301066
    - 3.861040463187853
    - 3.612335002759944
    - 3.336987907031145
    - 3.03591868713382
    - 2.7105138395490584
    - 2.362666482046894
    - 1.9948007256227338
    - 1.6098795047330852
    - 1.2113950696068354
    - 0.8033418063310769
    - 0.39017149785559085
    - -0.02326842257996757
    - -0.4318126412341142
    - -0.8300703446027634
    - -1.2125303788712944
    - -1.5736769502077812
    - -1.9081132461386363
    - -2.21069001182748
    - -2.476635817362674
    - -2.7016855170606164
    - -2.8822032430514266
    - -3.01529620578663
    - -3.098915604602907
    - -3.131941090658952
    - -3.114245477950404
    - -3.0467367676563684
    - -2.931375034779449
    - -2.771162317686383
    - -2.570104340170596
    - -2.3331436671625427
    - -2.066064730216078
    - -1.7753720346594775
    - -1.4681437508641741
    - -1.1518637689795035
    - -0.8342361295567301
    - -0.5229865008814846
    - -0.22565602705444357
    - 0.050606610087450724
    - 0.2992487135521712
    - 0.5145063010281559
    - 0.6915796896587797
    - 0.8267858205101692
    - 0.9176816615221027
    - 0.9631536961199191
    - 0.9634693769327779
    - 0.9202874817240762
    - 0.8366255253383301
    - 0.7167837234364791
    - 0.566226430617253
    - 0.39142344123356976
    - 0.1996549956462591
    - -0.0012142749162469646
    - -0.2029859587634346
    - -0.39739541999344086
    - -0.576387806424284
    - -0.7323933923200607
    - -0.8585928144096819
    - -0.9491627600307112
    - -0.9994930075468621
    - -1.006366405436537
    - -0.9680943986490098
    - -0.8846020466631481
    - -0.7574580916351173
    - -0.589847478997144
    - -0.38648574741291647
    - -0.15347682100946328
    - 0.10188212222851771
    - 0.3713429473879861
    - 0.6459883211389997
    - 0.9165435038486417
    - 1.1737073208160647
    - 1.408490397924411
    - 1.612548110187553
    - 1.7784955210480302
    - 1.9001919118288755
    - 1.972983321688151
    - 1.9938928260221778
    - 1.9617500423120768
    - 1.8772535136235906
    - 1.742962109215553
    - 1.5632143100966025
    - 1.3439771121669752
    - 1.0926291678950315
    - 0.8176855805258424
    - 0.5284743427008125
    - 0.23477665811779366
    - -0.05355480640405121
    - -0.32698441316210286
    - -0.5766727917393372
    - -0.7948308077264779
    - -0.9750329108106774
    - -1.1124758531652057
    - -1.204170756300616
    - -1.249059074573019
    - -1.2480460660156643
    - -1.203948820322132
    - -1.121359572518532
    - -1.0064287956914617
    - -0.8665762534750715
    - -0.7101416358938539
    - -0.5459894376493764
    - -0.38308521456600547
    - -0.23006213904843847
    - -0.09479776210836655
    - 0.01597899747436539
    - 0.09703141571810762
    - 0.14489156726759556
    - 0.15805503907743348
    - 0.13708218555629428
    - 0.0845983797413985
    - 0.005190238350089933
    - -0.09480036737125463
    - -0.20757777019064078
    - -0.32427788394462465
    - -0.4354214984058502
    - -0.5314156204491496
    - -0.6030799035577001
    - -0.6421730832865405
    - -0.6418933142642997
    - -0.5973264795101945
    - -0.5058179581014548
    - -0.36724597901144124
    - -0.1841784854552651
    - 0.03809974396643833
    - 0.29169730692558027
    - 0.5663650362074923
    - 0.8498782038282527
    - 1.1285401091873228
    - 1.387788700787718
    - 1.6128820760819769
    - 1.7896337835815033
    - 1.9051650871133823
    - 1.9486389728063795
    - 1.9119398582553335
    - 1.7902638073521093
    - 1.5825865963019332
    - 1.2919811702327402
    - 0.9257617492563788
    - 0.4954388839684863
    - 0.016477848100071822
    - -0.4921384458318146
    - -1.008531697345387
    - -1.5087162887642545
    - -1.967525310225254
    - -2.3596390919530004
    - -2.6606745472531315
    - -2.8482890582767304
    - -2.903250024190139
    - -2.8104207370458525
    - -2.559615059065201
    - -2.1462774477885747
    - -1.5719511070641399
    - -0.8445052204118576
    - 0.021897962818422136
    - 1.007104369410992
    - 2.08553404323176
    - 3.2269961107651857
    - 4.397725372011221
    - 5.561602272500472
    - 6.681508583425236
    - 7.72076359123323
    - 8.644580387655575
    - 9.421479271158308
    - 10.024595520892166
    - 10.432821955221415
    - 10.631732673336089
    - 10.614242997326372
    - 10.38097154858183
    - 9.940283151995551
    - 9.308005308596035
    - 8.506825679214243
    - 7.565392697454745
    - 6.5171553817858445
    - 5.398990963203577
    - 4.249679456651547
    - 3.1082922342170787
    - 2.012566571182853
    - 0.9973397337889337
    - 0.09311431612904437
    - -0.6751787653927744
    - -1.2891617579663814
    - -1.737689616802255
    - -2.017195017335406
    - -2.1316818352969475
    - -2.0923667146408667
    - -1.9169851962427507
    - -1.6287951432329737
    - -1.255325062439463
    - -0.8269276309383835
    - -0.37520863109784747
    - 0.06859195533410888
    - 0.475187117236168
    - 0.818719759028973
    - 1.0780559322796175
    - 1.237829581844451
    - 1.2891860762665983
    - 1.2301865957400795
    - 1.0658523031242246
    - 0.8078452959118106
    - 0.473801726756041
    - 0.0863502547456335
    - -0.3281347651432968
    - -0.7409820795843024
    - -1.1228002947439875
    - -1.4451015183459575
    - -1.6818878660653949
    - -1.8111181697310095
    - -1.815977857983302
    - -1.6858846407624217
    - -1.4171758559105234
    - -1.0134394760020644
    - -0.48546901280314914
    - 0.14915803740825426
    - 0.8668589967060519
    - 1.6391441400933755
    - 2.433979391451898
    - 3.217344709999153
    - 3.954908714055418
    - 4.613733610262623
    - 5.16392249412521
    - 5.580123699386637
    - 5.842813991670486
    - 5.939293676339383
    - 5.864341546313294
    - 5.620495260431573
    - 5.2179422876705255
    - 4.674026939969119
    - 4.012399156844724
    - 3.2618495150848337
    - 2.454891398949954
    - 1.6261644848690122
    - 0.8107429460412343
    - 0.042436556449144264
    - -0.6478270966898907
    - -1.2334558057815268
    - -1.6934070758992656
    - -2.0131025491894565
    - -2.1849979573505127
    - -2.208782884291254
    - -2.0912047833746414
    - -1.845532054267812
    - -1.490690411731957
    - -1.0501241919349662
    - -0.5504486726151496
    - -0.019970131059759266
    - 0.5128433580735919
    - 1.0208558125408165
    - 1.4796405535652328
    positive_zeros:
    - '0.934852716066425773251603952265846'
    - '2.14733469973242328850796662665893'
    - '2.81221919345149224655959512511752'
    - '3.49731789265229192892405087545440'
    - '4.44427879050057226096831479175317'
    - '5.28931211461111501227249077657873'
    - '5.58078473018795340354153216957024'
    - '6.17996084228759277528875838950773'
    - '6.93905191034998487611484152843769'
    - '7.59264416772538769030529440663638'
    prelabel: 2-7623-1.1-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 7.80192037006416
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.934852716066425773251603952266'
      prec: 107
    z2:
      __RealLiteral__: 0
      data: '2.14733469973242328850796662666'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '2.81221919345149224655959512512'
      prec: 103
- - algebraic: true
    analytic_conductor: 60.86996146082207
    bad_primes:
    - 3
    - 7
    - 11
    central_character: '1.1'
    conductor: 7623
    conductor_radical: 231
    degree: 2
    id: 21613393
    index: 137
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/7623/2/a/bi/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: 2-7623-1.1-c1-0-137
    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: 2-7623-1.1-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 7.80192037006416
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '0.934852716066425773251603952266'
      prec: 107
- - Lhash: '1185066606646595147193267472117'
    Lhash_array:
    - '1185066606646595147193267472117'
    id: 21983583
    label: 2-7623-1.1-c1-0-137
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/7623/2/a/bi/1/2
label_cols:
- label
- label
- label
labels:
- 2-7623-1.1-c1-0-137
- 2-7623-1.1-c1-0-137
- 2-7623-1.1-c1-0-137
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-23T23:22:30.384821'