data:
- - Lhash: '263642693486164250456277616060'
    a10:
    - 0
    - 0
    a2:
    - 1.224744871391589
    - 0.7071067811865476
    a3:
    - -0.8660254037844386
    - -1.5
    a4:
    - 1.0
    - 1.7320508075688772
    a5:
    - 0
    - 0
    a6:
    - 0
    - -2.449489742783178
    a7:
    - -4.0103705131194305
    - -5.73732763118006
    a8:
    - 0
    - 2.8284271247461903
    a9:
    - -1.5
    - 2.598076211353316
    accuracy: 100
    algebraic: true
    analytic_conductor: 28.61042775783118
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.0'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - -1.224744871391589
          - -0.7071067811865476
    - - 3
      - - - 1.0
          - 0
        - - 0.8660254037844386
          - 1.5
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 7
      - - - 1.0
          - 0
        - - 4.0103705131194305
          - 5.73732763118006
    bad_primes:
    - 2
    - 3
    - 5
    - 7
    central_character: '1050.649'
    coefficient_field: CDF
    conductor: 1050
    conductor_radical: 210
    conjugate: '1968423848801101490004204953220'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -1.224744871391589
        - -0.7071067811865476
    - - - 1.0
        - 0
      - - 0.8660254037844386
        - 1.5
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 4.0103705131194305
        - 5.73732763118006
    - - - 1.0
        - 0
      - - -8.692592189606207
        - -15.056011321874347
      - - -60.5
        - 104.78907385791707
    - - - 1.0
        - 0
      - - 7.22559103962552
        - 0
      - - 169.0
        - 0
    - - - 1.0
        - 0
      - - -1.3259972366836108
        - -2.2966945846319478
      - - -144.5
        - 250.28134169370276
    - - - 1.0
        - 0
      - - 2.2012811325234614
        - 1.2709102544244646
      - - 180.5
        - 312.63517076618234
    - - - 1.0
        - 0
      - - 34.728878177429166
        - 20.050727164392452
      - - 264.5
        - 458.12743860196804
    - - - 1.0
        - 0
      - - 47.00798333340114
        - 0
      - - 841.0
        - 0
    - - - 1.0
        - 0
      - - -34.902502637269
        - 20.150969293018882
      - - 480.5
        - -832.2504130368455
    - - - 1.0
        - 0
      - - -28.148201963023237
        - -16.25137198055542
      - - 684.5
        - 1185.5887777808964
    - - - 1.0
        - 0
      - - 0
        - -70.66793358750787
      - - -1681.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -37.37320655919866
      - - -1849.0
        - 0
    - - - 1.0
        - 0
      - - 16.724228046315247
        - -28.96721269358639
      - - -1104.5
        - -1913.050116959825
    - - - 1.0
        - 0
      - - 61.39114139615825
        - -35.444192010930344
      - - 1404.5
        - -2432.6653592304883
    - - - 1.0
        - 0
      - - 87.08633689892675
        - -50.2793200513338
      - - 1740.5
        - -3014.634430573631
    - - - 1.0
        - 0
      - - 11.16213486237802
        - 6.444461567524856
      - - 1860.5
        - 3222.4805274818964
    - - - 1.0
        - 0
      - - 81.46890668634748
        - -47.03609520594722
      - - 2244.5
        - -3887.5880375883453
    - - - 1.0
        - 0
      - - 11.579253196576497
        - 0
      - - 5041.0
        - 0
    - - - 1.0
        - 0
      - - 11.334523216049936
        - 19.63197008976748
      - - -2664.5
        - 4615.049376767273
    - - - 1.0
        - 0
      - - 12.05419763178598
        - -20.878482742729755
      - - -3120.5
        - -5404.864545018681
    - - - 1.0
        - 0
      - - -111.66429257896881
        - 0
      - - 6889.0
        - 0
    - - - 1.0
        - 0
      - - -110.77043899580437
        - -63.953342772480674
      - - 3960.5
        - 6859.787223376538
    - - - 1.0
        - 0
      - - -7.482556572393294
        - 0
      - - 9409.0
        - 0
    - - - 1.0
        - 0
      - - 81.92280294545479
        - -47.298152333326996
      - - 5100.5
        - -8834.325144005059
    - - - 1.0
        - 0
      - - -29.91087343536272
        - 51.80715248881048
      - - -5304.5
        - -9187.66350874911
    - - - 1.0
        - 0
      - - -5.59592081775474
        - -3.23080639049453
      - - 5724.5
        - 9915.124847928038
    - - - 1.0
        - 0
      - - 81.92007180508483
        - 141.8897265260976
      - - -5940.5
        - 10289.247822362915
    - - - 1.0
        - 0
      - - 0
        - 105.43352238505531
      - - -12769.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 24016957
    index: 8
    label: 2-1050-35.19-c2-0-8
    leading_term: '0.847673879353904077021144936204961001119438441175437293'
    load_key: CMFs-workshop
    motivic_weight: 2
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 2
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/1050/3/q/e/649/15
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 0.847673879353904
    - 0.6158283898446056
    - 0.3776987422726542
    - 0.1348572605907001
    - -0.1110699512809003
    - -0.3583802124162437
    - -0.6052740877073625
    - -0.8498394828844245
    - -1.0900414687260402
    - -1.3237190393730214
    - -1.548589717084498
    - -1.7622625985524905
    - -1.9622601100117172
    - -2.1460484111635445
    - -2.31107606984223
    - -2.454820326342938
    - -2.5748399825192063
    - -2.66883368921427
    - -2.734702169096442
    - -2.7706127036025707
    - -2.7750640361990775
    - -2.746949704088046
    - -2.685617712074355
    - -2.590924411295099
    - -2.4632804477176844
    - -2.303686706214096
    - -2.1137583002685227
    - -1.895734848330854
    - -1.6524755371101951
    - -1.3874377992093083
    - -1.1046388244973213
    - -0.8085995759105764
    - -0.5042714825858469
    - -0.19694652519973252
    - 0.10784800373853674
    - 0.4044682044219353
    - 0.6872833102231644
    - 0.9508134953948673
    - 1.1898722913227613
    - 1.399709733986331
    - 1.5761520388242576
    - 1.715733384618718
    - 1.815815302794807
    - 1.8746892271215019
    - 1.891657971742576
    - 1.8670922786216135
    - 1.8024591093589264
    - 1.700319045545784
    - 1.5642909947418024
    - 1.3989833578015187
    - 1.2098918733766908
    - 1.0032654868223256
    - 0.7859427580141509
    - 0.5651624859650948
    - 0.3483533446421185
    - 0.14290834928160337
    - -0.044049139150106144
    - -0.20590045526030784
    - -0.3367598115972378
    - -0.43168748323436906
    - -0.48687990354682004
    - -0.49982892863332373
    - -0.4694431853690187
    - -0.39612538158662336
    - -0.2818007110288563
    - -0.1298930025073631
    - 0.054752998350394315
    - 0.2660029176223255
    - 0.49661529912677554
    - 0.738471044601056
    - 0.9828433774722583
    - 1.22070007823025
    - 1.4430280667708688
    - 1.6411690236418341
    - 1.8071537221096297
    - 1.9340221508321056
    - 2.016116393953988
    - 2.04933363663567
    - 2.0313275954312293
    - 1.9616481296219093
    - 1.8418107443977632
    - 1.6752900998017033
    - 1.4674344186166666
    - 1.2253007493169623
    - 0.9574142762270375
    - 0.6734581530562235
    - 0.383903532864939
    - 0.09959243724308228
    - -0.16871128909806732
    - -0.41078558713996166
    - -0.6174095169490771
    - -0.7807987060674185
    - -0.8949973240668989
    - -0.9562078514185771
    - -0.9630416150431447
    - -0.9166755889596473
    - -0.8209042433857071
    - -0.6820791694102593
    - -0.508933673958821
    - -0.31229436513956665
    - -0.10468673961850034
    - 0.10015326860619371
    - 0.2878451349069912
    - 0.4439861441890927
    - 0.5548060001558259
    - 0.6078266858970699
    - 0.5924990566508515
    - 0.5007872610741715
    - 0.32767295826106263
    - 0.071553450159673
    - -0.265488747556567
    - -0.6775628076151692
    - -1.1550052965468807
    - -1.684580617106924
    - -2.2498451574411815
    - -2.8316668717396136
    - -3.408884805062667
    - -3.95908622400238
    - -4.459472852601391
    - -4.887782551562747
    - -5.223228899194795
    - -5.447418769833895
    - -5.545207335540897
    - -5.505451045110073
    - -5.321622087443549
    - -4.992252566794897
    - -4.521182962738037
    - -3.9175971930004376
    - -3.1958354419880344
    - -2.374985496725092
    - -1.4782632297099134
    - -0.5322026370746346
    - 0.43431497968597516
    - 1.3911549601133457
    - 2.3081019501586955
    - 3.1560620219420685
    - 3.9082422463725788
    - 4.541255301334892
    - 5.03609870220146
    - 5.378962650962301
    - 5.561827184144685
    - 5.582818011901321
    - 5.446300827971819
    - 5.162705485679607
    - 4.748083756601833
    - 4.223416841999372
    - 3.6137007932830523
    - 2.9468489213597135
    - 2.2524595741538582
    - 1.5605048387276808
    - 0.9000003715923148
    - 0.29771838463577005
    - -0.22299534586559117
    - -0.6432437384553434
    - -0.9493902469547455
    - -1.1336201953337284
    - -1.1942232754446458
    - -1.1355822421017965
    - -0.9678671757108828
    - -0.7064492807293572
    - -0.3710623099473812
    - 0.015247382513357603
    - 0.42733014004992304
    - 0.839241119960356
    - 1.2255811685655251
    - 1.5628022053659336
    - 1.8304101845505678
    - 2.0120035228795126
    - 2.0960930140107688
    - 2.0766603177755094
    - 1.9534255805778358
    - 1.7318099315480704
    - 1.4225947228114388
    - 1.0412955887895363
    - 0.6072848143306502
    - 0.1427092755239387
    - -0.32873742616854773
    - -0.7831217354981316
    - -1.1975842184578527
    - -1.5515885305100785
    - -1.8280360572840928
    - -2.0141840772163895
    - -2.102315910214803
    - -2.0901251335575792
    - -1.9807918443224728
    - -1.7827462622573709
    - -1.5091327368260452
    - -1.177004441654951
    - -0.8062947156298444
    - -0.4186242190554273
    - -0.0360130167627493
    - 0.3204272474582931
    - 0.6317441707846398
    - 0.8822642130705959
    - 1.0605140325866282
    - 1.1598875889961124
    - 1.1790176532506287
    - 1.1218275910227709
    - 0.9972581770133659
    - 0.8186836576231512
    - 0.6030501594149055
    - 0.3697867027668253
    - 0.13955346649630465
    - -0.06709735238856904
    - -0.23106643840092272
    - -0.3359749257889684
    - -0.3692751291013157
    - -0.32313341885585684
    - -0.19502719163212265
    - 0.0119853794072061
    - 0.2893445727934052
    - 0.6234178562618912
    - 0.9962570316401003
    - 1.3866419715311167
    - 1.7713506306326707
    - 2.126579909937039
    - 2.429431244939083
    - 2.6593692293681226
    - 2.799561621145413
    - 2.838014816983371
    - 2.768430083738066
    - 2.5907219103260513
    - 2.3111598888895872
    - 1.9421183753603994
    - 1.5014424444157821
    - 1.0114628495896112
    - 0.49771530525429547
    - -0.012561030672762836
    - -0.4920557701669934
    - -0.9150502637542726
    - -1.259007663274333
    - -1.505989174891469
    - -1.6438047902072086
    - -1.6668219569636453
    - -1.5763759634979095
    - -1.3807500741840995
    - -1.0947202000088383
    - -0.7386864619711456
    - -0.3374406590636716
    - 0.08135733787718262
    - 0.4889014728135674
    - 0.8570526974547197
    - 1.1601289313116676
    - 1.3765569192130882
    - 1.490278185663422
    - 1.4918154434656183
    - 1.3789262843853014
    - 1.1567965590077525
    - 0.8377549798661938
    - 0.4405213302238836
    - -0.0109687472457866
    - -0.48909107590784906
    - -0.9643169061653647
    - -1.4071396873294555
    - -1.7900196270083595
    - -2.089217843044115
    - -2.2863971386295705
    positive_zeros:
    - '0.20797741383840128326457395459250'
    - '1.97133107291605266200817252132386'
    - '3.26679017086830233870534521336974'
    - '3.85075539841766744408911353287045'
    - '5.11888136874078448644255394939669'
    - '5.88896568464266844069876540677489'
    - '6.40038948990989310839326763847962'
    - '7.70808276139174256296713498786419'
    - '8.879872576038904653158671721983582'
    - '9.431376893894583348365192693646385'
    prelabel: 2-1050-35.19-c2-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.348871634076778
    root_angle: -0.8014232912305301
    root_number: -0.8116371218442962338225356832995580178848172030558225086 - 0.5841619488158288364238471463964233662460007824456832689*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.40071164561526507'
      prec: 67
    spectral_label: c2-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '0.20797741383840128326457395459'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '1.97133107291605266200817252132'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.26679017086830233870534521337'
      prec: 103
- - algebraic: true
    analytic_conductor: 28.61042775783118
    bad_primes:
    - 2
    - 3
    - 5
    - 7
    central_character: '35.19'
    conductor: 1050
    conductor_radical: 210
    degree: 2
    id: 24016957
    index: 8
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1050/3/q/e/649/15
    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: 2-1050-35.19-c2-0-8
    motivic_weight: 2
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 2
    order_of_vanishing: 0
    prelabel: 2-1050-35.19-c2-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.348871634076778
    root_angle: -0.40071164561526507
    self_dual: false
    spectral_label: c2-0
    z1:
      __RealLiteral__: 0
      data: '0.20797741383840128326457395459'
      prec: 103
- - Lhash: '263642693486164250456277616060'
    Lhash_array:
    - '263642693486164250456277616060'
    id: 24391475
    label: 2-1050-35.19-c2-0-8
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1050/3/q/e/649/15
label_cols:
- label
- label
- label
labels:
- 2-1050-35.19-c2-0-8
- 2-1050-35.19-c2-0-8
- 2-1050-35.19-c2-0-8
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T19:52:28.561904'