data:
- - Lhash: '1413040434206505831339074688434'
    a10:
    - 0
    - 0
    a2:
    - 0
    - 0
    a3:
    - 0
    - 0
    a4:
    - 0
    - 0
    a5:
    - 0
    - 6.631030293135233
    a6:
    - 0
    - 0
    a7:
    - 0
    - -13.48528137423857
    a8:
    - 0
    - 0
    a9:
    - 0
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 47.084589681459306
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.0'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 2
    - 3
    central_character: '1728.1567'
    coefficient_field: CDF
    conductor: 1728
    conductor_radical: 6
    conjugate: '806330298156462962867580184403'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -6.631030293135233
      - - -25.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 13.48528137423857
      - - -49.0
        - 0
    - - - 1.0
        - 0
      - - -18.4582130089771
        - 0
      - - 121.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -169.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 289.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 361.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -529.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -29.393876913398138
      - - -841.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 61.42640687119285
      - - -961.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -1369.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 1681.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 1849.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -2209.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 105.90128538356902
      - - -2809.0
        - 0
    - - - 1.0
        - 0
      - - 117.57550765359255
        - 0
      - - 3481.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -3721.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 4489.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -5041.0
        - 0
    - - - 1.0
        - 0
      - - -143.79393923933998
        - 0
      - - 5329.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 58.0
      - - -6241.0
        - 0
    - - - 1.0
        - 0
      - - -165.03719896277835
        - 0
      - - 6889.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 7921.0
        - 0
    - - - 1.0
        - 0
      - - -128.94112549695427
        - 0
      - - 9409.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 130.25197032007884
      - - -10201.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 10.0
      - - -10609.0
        - 0
    - - - 1.0
        - 0
      - - 23.5014049858654
        - 0
      - - 11449.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - -11881.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
      - - 12769.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23685714
    index: 45
    label: 2-12e3-8.3-c2-0-45
    leading_term: '2.088188643519154398082809322055597819414532901084332597'
    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/1728/3/b/h/1567/7
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - 2.0881886435191546
    - 2.1759645211469167
    - 2.2403521172380483
    - 2.280634727226073
    - 2.296263770218599
    - 2.28687362263869
    - 2.2523039905853715
    - 2.1926287030170957
    - 2.1081893021159233
    - 1.9996313905502854
    - 1.8679413843572472
    - 1.7144811235934887
    - 1.5410177128604292
    - 1.3497459973298982
    - 1.1433012206775908
    - 0.9247596512114596
    - 0.6976252924789241
    - 0.4658012054606691
    - 0.23354445155598963
    - 0.005404208813776534
    - -0.2138567929188569
    - -0.419356741850931
    - -0.6062036902531449
    - -0.7696168897687213
    - -0.9050577854749129
    - -1.0083673303805194
    - -1.0759057335956623
    - -1.1046902906446867
    - -1.0925265878088026
    - -1.038128147561592
    - -0.9412195106094654
    - -0.8026178500092024
    - -0.6242884980685421
    - -0.409370245388641
    - -0.1621669449870844
    - 0.11189718302021405
    - 0.406360113242357
    - 0.7138428204556275
    - 1.0262073941153766
    - 1.3347501327539972
    - 1.6304258573870007
    - 1.9040982661944683
    - 2.146809807046777
    - 2.3500633287101627
    - 2.506106744868391
    - 2.6082111642921495
    - 2.6509324576105344
    - 2.630346090727281
    - 2.5442452914226155
    - 2.39229325103422
    - 2.1761211046765623
    - 1.8993648723712888
    - 1.5676363535591762
    - 1.1884251048803158
    - 0.7709310346207966
    - 0.3258297394030297
    - -0.1350246021101615
    - -0.598951280604888
    - -1.052839988615658
    - -1.4835802357148828
    - -1.8785088587244583
    - -2.225859702569913
    - -2.5151985591327293
    - -2.737826090945403
    - -2.887131791687549
    - -2.9588830783693583
    - -2.951435373931715
    - -2.8658514954231764
    - -2.705921751107264
    - -2.478079776837318
    - -2.1912131845671468
    - -1.8563724038593372
    - -1.4863854987304146
    - -1.0953910496051826
    - -0.6983052080148568
    - -0.3102425649224027
    - 0.05408666328524016
    - 0.3809786006699955
    - 0.6583112480574104
    - 0.8760680353897528
    - 1.0267849997627552
    - 1.1058995098632174
    - 1.1119818729172672
    - 1.0468355832396712
    - 0.9154572524762423
    - 0.7258532020987628
    - 0.4887160575912973
    - 0.21697118650071034
    - -0.07479082772734513
    - -0.37097359352643866
    - -0.6556989873946805
    - -0.9135645956980979
    - -1.1304004167302566
    - -1.2939893990366018
    - -1.3947166927047887
    - -1.426114473992167
    - -1.3852728550616342
    - -1.273092611953633
    - -1.094362075269441
    - -0.8576482717437501
    - -0.5750009543719246
    - -0.26147713127317224
    - 0.06549732357896575
    - 0.38690386436614865
    - 0.6830125134235907
    - 0.9343290467524448
    - 1.1225643591457142
    - 1.2315795590765704
    - 1.2482598596648726
    - 1.1632721648894058
    - 0.9716654032304946
    - 0.6732790188589202
    - 0.2729333596658788
    - -0.2196143436395206
    - -0.7899535769336941
    - -1.4195370973941366
    - -2.086411952044117
    - -2.766135133992621
    - -3.4328338555671016
    - -4.0603619340032875
    - -4.623497516934148
    - -5.09912372853811
    - -5.467333076740762
    - -5.712398767617427
    - -5.823561408212299
    - -5.795587763607581
    - -5.629068928637779
    - -5.330437991655488
    - -4.91170139246997
    - -4.389892995586384
    - -3.786274636393872
    - -3.1253207521901354
    - -2.4335369024314017
    - -1.7381717982908798
    - -1.0658892920969627
    - -0.44147015880939233
    - 0.11338685318592685
    - 0.58109940471962
    - 0.9490139673375418
    - 1.2099500797776594
    - 1.362444378921296
    - 1.4106785278194751
    - 1.3640926300600806
    - 1.2367034945033808
    - 1.0461641938972028
    - 0.8126167499428426
    - 0.5574025469135243
    - 0.30170441902596895
    - 0.06519963987287766
    - -0.13519615197391047
    - -0.28641789785554667
    - -0.3801051313040955
    - -0.41316582744119945
    - -0.3880109907220845
    - -0.3124397195449799
    - -0.19917499057262456
    - -0.06507140783132956
    - 0.06996357238027295
    - 0.1842751275934618
    - 0.25591826204707097
    - 0.2641806176430426
    - 0.1910786153457377
    - 0.02273383439285751
    - -0.24945867587281204
    - -0.627948210174513
    - -1.1084951679608848
    - -1.6800301352196205
    - -2.324926070965575
    - -3.0196799300514403
    - -3.7359751764489553
    - -4.442072840230406
    - -5.104457526206071
    - -5.689647456694171
    - -6.166065386853306
    - -6.505860949687966
    - -6.686575207343582
    - -6.692545057110469
    - -6.515958408877098
    - -6.157490056826391
    - -5.626471879826989
    - -4.940578070818955
    - -4.125034920636285
    - -3.2113935212366482
    - -2.235930818031667
    - -1.2377680091197474
    - -0.2568138169324445
    - 0.6683476181400166
    - 1.5024994473591922
    - 2.215643285936499
    - 2.7845469867226478
    - 3.1938945776526872
    - 3.436967526502701
    - 3.5158148926306465
    - 3.4409013968938402
    - 3.23025503421744
    - 2.9081675013383874
    - 2.5035293660926623
    - 2.0479056669612516
    - 1.5734748840892405
    - 1.1109637384982771
    - 0.6877113082484947
    - 0.3259882931496212
    - 0.04168127421221397
    - -0.1565715829785689
    - -0.26773631612727883
    - -0.29820690336266387
    - -0.2611089091801948
    - -0.17513014495512103
    - -0.06295788492020979
    - 0.050570317807278636
    - 0.14047453106925414
    - 0.18365910867081164
    - 0.16081524946649475
    - 0.058063365788837105
    - -0.1317846209879813
    - -0.4084382573824141
    - -0.763880376644859
    - -1.182684788376048
    - -1.6428878312568516
    - -2.1173628830232314
    - -2.575610840601593
    - -2.9858488589784926
    - -3.3172564932239608
    - -3.542224570589604
    - -3.638448767275345
    - -3.5907174157116346
    - -3.392261215547236
    - -3.045560216494982
    - -2.562538950881578
    - -1.9641216064294174
    - -1.2791629032726715
    - -0.5428138827500144
    - 0.20557790661901373
    - 0.9249001977824595
    - 1.574880631086303
    - 2.1186901492205896
    - 2.5253679825951334
    - 2.771900194894032
    - 2.8448047516682182
    - 2.7411076584486063
    - 2.4686348656575503
    - 2.0455906905268595
    - 1.4994423302803905
    - 0.8651782516532369
    - 0.1830524369395567
    - -0.5040365328486338
    - -1.15335549642236
    - -1.72514467781395
    - -2.1852305897450086
    - -2.5072625772883774
    - -2.674416349103156
    - -2.6804438522564418
    - -2.5299938114247267
    - -2.2381780853636752
    - -1.8294121340745846
    - -1.3356095588986254
    - -0.7938571430767496
    positive_zeros:
    - '1.11469235604203576448167252777032'
    - '2.02746237702728661581668228539563'
    - '3.26419613613599966692003804426546'
    - '4.44408650306505733183794867772029'
    - '5.14143946869875417138192830151928'
    - '5.96485746409565333334229958747415'
    - '6.59621032407331689077448657660705'
    - '7.956051519634870508045340585752107'
    - '8.689624402717965065512928371048407'
    - '9.168346418221849069679151955685864'
    prelabel: 2-12e3-8.3-c2-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.861821163616792
    root_angle: 0.25
    root_number: 0.7071067811865475244008443621048490392848359376884740366 + 0.7071067811865475244008443621048490392848359376884740366*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    spectral_label: c2-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.11469235604203576448167252777'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.02746237702728661581668228540'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.26419613613599966692003804427'
      prec: 103
- - algebraic: true
    analytic_conductor: 47.084589681459306
    bad_primes:
    - 2
    - 3
    central_character: '8.3'
    conductor: 1728
    conductor_radical: 6
    degree: 2
    id: 23685714
    index: 45
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/1728/3/b/h/1567/7
    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: 2-12e3-8.3-c2-0-45
    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: 2-12e3-8.3-c2-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.861821163616792
    root_angle: 0.125
    self_dual: false
    spectral_label: c2-0
    z1:
      __RealLiteral__: 0
      data: '1.11469235604203576448167252777'
      prec: 103
- - Lhash: '1413040434206505831339074688434'
    Lhash_array:
    - '1413040434206505831339074688434'
    id: 24053683
    label: 2-12e3-8.3-c2-0-45
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/1728/3/b/h/1567/7
label_cols:
- label
- label
- label
labels:
- 2-12e3-8.3-c2-0-45
- 2-12e3-8.3-c2-0-45
- 2-12e3-8.3-c2-0-45
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T16:06:55.152245'