data:
- - Lhash: '1479665466105009675008327710640'
    a10: 0
    a2: -11
    a3: 0
    a4: 89
    a5: 0
    a6: 0
    a7: 0
    a8: -627
    a9: 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 70.72926453752447
    analytic_normalization:
      __RealLiteral__: 0
      data: '2.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - 1
    - - 7
      - - 1
    bad_primes:
    - 3
    - 7
    central_character: '441.1'
    coefficient_field: 1.1.1.1
    conductor: 441
    conductor_radical: 21
    degree: 2
    euler_factors:
    - - 1
      - 11
      - 32
    - - 1
    - - 1
      - 0
      - 3125
    - - 1
    - - 1
      - -76
      - 161051
    - - 1
      - 0
      - 371293
    - - 1
      - 0
      - 1419857
    - - 1
      - 0
      - 2476099
    - - 1
      - -4952
      - 6436343
    - - 1
      - 7282
      - 20511149
    - - 1
      - 0
      - 28629151
    - - 1
      - 8886
      - 69343957
    - - 1
      - 0
      - 115856201
    - - 1
      - -11748
      - 147008443
    - - 1
      - 0
      - 229345007
    - - 1
      - 24550
      - 418195493
    - - 1
      - 0
      - 714924299
    - - 1
      - 0
      - 844596301
    - - 1
      - -69364
      - 1350125107
    - - 1
      - -2224
      - 1804229351
    - - 1
      - 0
      - 2073071593
    - - 1
      - -80168
      - 3077056399
    - - 1
      - 0
      - 3939040643
    - - 1
      - 0
      - 5584059449
    - - 1
      - 0
      - 8587340257
    - - 1
      - 0
      - 10510100501
    - - 1
      - 0
      - 11592740743
    - - 1
      - -64900
      - 14025517307
    - - 1
      - 219582
      - 15386239549
    - - 1
      - 123202
      - 18424351793
    euler_factors_factorization:
    - - - - 1
          - 11
          - 32
        - 1
    - - 1
    - - - - 1
          - 0
          - 3125
        - 1
    - - 1
    - - - - 1
          - -76
          - 161051
        - 1
    - - - - 1
          - 0
          - 371293
        - 1
    - - - - 1
          - 0
          - 1419857
        - 1
    - - - - 1
          - 0
          - 2476099
        - 1
    - - - - 1
          - -4952
          - 6436343
        - 1
    - - - - 1
          - 7282
          - 20511149
        - 1
    - - - - 1
          - 0
          - 28629151
        - 1
    - - - - 1
          - 8886
          - 69343957
        - 1
    - - - - 1
          - 0
          - 115856201
        - 1
    - - - - 1
          - -11748
          - 147008443
        - 1
    - - - - 1
          - 0
          - 229345007
        - 1
    - - - - 1
          - 24550
          - 418195493
        - 1
    - - - - 1
          - 0
          - 714924299
        - 1
    - - - - 1
          - 0
          - 844596301
        - 1
    - - - - 1
          - -69364
          - 1350125107
        - 1
    - - - - 1
          - -2224
          - 1804229351
        - 1
    - - - - 1
          - 0
          - 2073071593
        - 1
    - - - - 1
          - -80168
          - 3077056399
        - 1
    - - - - 1
          - 0
          - 3939040643
        - 1
    - - - - 1
          - 0
          - 5584059449
        - 1
    - - - - 1
          - 0
          - 8587340257
        - 1
    - - - - 1
          - 0
          - 10510100501
        - 1
    - - - - 1
          - 0
          - 11592740743
        - 1
    - - - - 1
          - -64900
          - 14025517307
        - 1
    - - - - 1
          - 219582
          - 15386239549
        - 1
    - - - - 1
          - 123202
          - 18424351793
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 20176271
    index: 48
    label: 2-21e2-1.1-c5-0-48
    load_key: CMFs-workshop
    motivic_weight: 5
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 5
    order_of_vanishing: 1
    origin: ModularForm/GL2/Q/holomorphic/441/6/a/a
    plot_delta:
      __RealLiteral__: 0
      data: '0.05859375'
      prec: 34
    plot_values:
    - -1.0124554153238928e-60
    - 0.11110120146653497
    - 0.219743197201329
    - 0.3235105929657566
    - 0.42007516832934294
    - 0.5072383351489206
    - 0.5829722270551309
    - 0.6454589401763916
    - 0.6931274279219608
    - 0.7246875341285663
    - 0.739160631245236
    - 0.735906315723262
    - 0.7146446037861944
    - 0.6754730697428164
    - 0.6188783784163293
    - 0.5457416854190182
    - 0.45733741601153843
    - 0.35532498694704817
    - 0.24173310740852097
    - 0.1189363858125421
    - -0.010375920776774135
    - -0.14323904888140238
    - -0.27645964967425646
    - -0.40667021257403163
    - -0.5303905375657736
    - -0.6440956140413164
    - -0.7442890684768619
    - -0.8275811451947991
    - -0.8907699888660603
    - -0.9309248098698636
    - -0.9454693400965508
    - -0.932263833461688
    - -0.889683738592186
    - -0.8166930770604068
    - -0.7129105051182077
    - -0.5786660255823411
    - -0.41504635412541946
    - -0.22392703462191613
    - -0.007989544182491527
    - 0.2292781684046736
    - 0.48359900686057034
    - 0.7499428943964305
    - 1.0225823954110507
    - 1.2951679882304832
    - 1.5608227290943941
    - 1.8122555595421892
    - 2.0418919996534504
    - 2.2420204500733494
    - 2.4049518095602833
    - 2.523189616153217
    - 2.5896074539368743
    - 2.5976299491174992
    - 2.541413323988404
    - 2.416021200125945
    - 2.2175911565766824
    - 1.9434874671427624
    - 1.5924354734220767
    - 1.1646332048236248
    - 0.6618361382621575
    - 0.08741140025263469
    - -0.5536417493212412
    - -1.2547076552328433
    - -2.007607962039852
    - -2.8026941363329594
    - -3.6289787413590595
    - -4.474304386294089
    - -5.325548235766962
    - -6.168858922115479
    - -6.9899216826324375
    - -7.7742465774202705
    - -8.507473761585086
    - -9.175689019083691
    - -9.765742143864998
    - -10.265560303834032
    - -10.664448267953405
    - -10.953367335379166
    - -11.125184991459639
    - -11.174887736135672
    - -11.099750186434065
    - -10.89945443978629
    - -10.576154784803338
    - -10.134484139374022
    - -9.581500053744257
    - -8.926569703018174
    - -8.181194967705947
    - -7.358780415900108
    - -6.474348705957765
    - -5.5442095713959505
    - -4.5855900765011635
    - -3.6162351893066984
    - -2.653988858263684
    - -1.7163666548667438
    - -0.8201316177821498
    - 0.019114826250227455
    - 0.78731510476355
    - 1.472299626263025
    - 2.0640823584214636
    - 2.5550986229258936
    - 2.940377396797675
    - 3.217642223961964
    - 3.3873368953552006
    - 3.452574291999822
    - 3.4190091356800507
    - 3.294637781891533
    - 3.089530541022223
    - 2.8155042458872135
    - 2.485744817421873
    - 2.1143913400502696
    - 1.7160945752610959
    - 1.3055638570383221
    - 0.8971168788817546
    - 0.5042469663850987
    - 0.13922201498087347
    - -0.187271639854127
    - -0.46642854422909374
    - -0.6915565977023241
    - -0.8582348561961314
    - -0.9643913872553949
    - -1.0102986731377444
    - -0.9984869694071423
    - -0.9335789729368141
    - -0.8220520250351594
    - -0.6719367637680511
    - -0.4924635390823479
    - -0.29366991751738003
    - -0.08598414454566924
    - 0.12019956794413997
    - 0.3149376546443105
    - 0.48912965077946113
    - 0.6348712695336725
    - 0.7457543355172508
    - 0.8171018209166174
    - 0.8461287412864034
    - 0.8320225847830247
    - 0.7759401632871743
    - 0.6809211624005271
    - 0.5517220951910968
    - 0.39457769184495567
    - 0.21689984431296686
    - 0.026926937922274855
    - -0.1666613810863254
    - -0.3551473364839231
    - -0.5301784515804031
    - -0.6841534810643194
    - -0.8105736157885399
    - -0.9043430549257102
    - -0.9620050812945283
    - -0.9819024631170503
    - -0.9642542372967764
    - -0.9111445769928647
    - -0.8264233592020906
    - -0.7155220594139815
    - -0.5851925339199539
    - -0.4431799278398859
    - -0.2978441961057741
    - -0.15774738705851216
    - -0.031225776924304685
    - 0.0740329504754524
    - 0.1513870853354489
    - 0.195593184885146
    - 0.2030953078167057
    - 0.1722357870793875
    - 0.10337550022040547
    - -0.0010843776164926118
    - -0.13678263005964691
    - -0.2975789330977449
    - -0.4758292247783921
    - -0.6627445043350796
    - -0.8488176615663547
    - -1.0242991384455964
    - -1.179699220557932
    - -1.30629271695019
    - -1.396600845170132
    - -1.444825378693811
    - -1.4472115689806002
    - -1.4023190001761
    - -1.3111832897367617
    - -1.1773562758502554
    - -1.006817843712089
    - -0.8077586039364905
    - -0.5902389785193843
    - -0.36573657948188676
    - -0.146599777943106
    - 0.05456924505710275
    - 0.22557418492418554
    - 0.3552959234358956
    - 0.43434238174351497
    - 0.4556433867362355
    - 0.4149581751912202
    - 0.31126593029966315
    - 0.14701406734510292
    - -0.07179528133107435
    - -0.33569320155791327
    - -0.6320111250996742
    - -0.9453234941637938
    - -1.2580536752311717
    - -1.5512224026234172
    - -1.8053102097299316
    - -2.0011984911758156
    - -2.12114839906335
    - -2.1497730270923014
    - -2.0749565267354435
    - -1.888674096556241
    - -1.5876692627715208
    - -1.1739494993647352
    - -0.6550678893694867
    - -0.044166974309649
    - 0.6402291487338553
    - 1.3746774502822308
    - 2.1315247194556948
    - 2.8798422208968244
    - 3.5865548778349092
    - 4.2177234539159745
    - 4.739929579706573
    - 5.1217068211405365
    - 5.334956696757719
    - 5.356286900650572
    - 5.1682101461595265
    - 4.760146052536471
    - 4.129175261263526
    - 3.2805042659641885
    - 2.227610919045991
    - 0.9920537749503164
    - -0.39705721521684256
    - -1.903916260350208
    - -3.487176403430085
    - -5.101362274425033
    - -6.6984874760607696
    - -8.2298128593435
    - -9.64767428801033
    - -10.907303890865752
    - -11.968567542114412
    - -12.797543524903487
    - -13.367872993498572
    - -13.661821762028087
    - -13.671004761203148
    - -13.396738722317277
    - -12.850004649214098
    - -12.05101870584623
    - -11.028427497428764
    - -9.818160547480153
    - -8.46198827318882
    - -7.005847190163793
    - -5.498004775513255
    - -3.9871438481974577
    - -2.520450101117994
    - -1.1417863258952325
    - 0.10996712040748273
    - 1.20233378674411
    - 2.1103638400157156
    - 2.817411319878065
    - 3.3155354556831043
    - 3.605513221900709
    - 3.6964685515379183
    - 3.60514156657117
    - 3.3548379394164733
    - 2.9741132428112986
    positive_zeros:
    - '1.16725023901586829333008032762600'
    - '2.22861911413953242114506158430143'
    - '3.46538043135167707891574985562819'
    - '5.44783047269685256139659023579570'
    - '6.58655060304073121121350194866881'
    - '7.34843659534065527948588249252156'
    - '8.152686373300926948644608764286686'
    - '9.156662431591949536526275608151537'
    - '9.550255366381160969867957058372859'
    prelabel: 2-21e2-1.1-c5-0
    primitive: true
    rational: true
    root_analytic_conductor: 8.410069235001842
    root_angle: 1.0
    root_number: '-1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    spectral_label: c5-0
    trace_hash: 2197034075981573504
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.16725023901586829333008032763'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.22861911413953242114506158430'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.46538043135167707891574985563'
      prec: 103
- - algebraic: true
    analytic_conductor: 70.72926453752447
    bad_primes:
    - 3
    - 7
    central_character: '1.1'
    conductor: 441
    conductor_radical: 21
    degree: 2
    dirichlet_coefficients:
    - 1
    - -11
    - 0
    - 89
    - 0
    - 0
    - 0
    - -627
    - 0
    - 0
    - 76
    - 0
    - 0
    - 0
    - 0
    - 4049
    - 0
    - 0
    - 0
    - 0
    - 0
    - -836
    - 4952
    - 0
    - -3125
    - 0
    - 0
    - 0
    - -7282
    - 0
    - 0
    - -24475
    - 0
    - 0
    - 0
    - 0
    - -8886
    - 0
    - 0
    - 0
    - 0
    - 0
    - 11748
    - 6764
    - 0
    - -54472
    - 0
    - 0
    - 0
    - 34375
    - 0
    - 0
    - -24550
    - 0
    - 0
    - 0
    - 0
    - 80102
    - 0
    - 0
    - 0
    - 0
    - 0
    - 139657
    - 0
    - 0
    - 69364
    - 0
    - 0
    - 0
    - 2224
    - 0
    - 0
    - 97746
    - 0
    - 0
    - 0
    - 0
    - 80168
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -129228
    - 0
    - -47652
    - 0
    - 0
    - 0
    - 440728
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - 0
    - -278125
    euler11:
    - 1
    - -76
    - 161051
    euler13:
    - 1
    - 0
    - 371293
    euler17:
    - 1
    - 0
    - 1419857
    euler19:
    - 1
    - 0
    - 2476099
    euler2:
    - 1
    - 11
    - 32
    euler23:
    - 1
    - -4952
    - 6436343
    euler29:
    - 1
    - 7282
    - 20511149
    euler3:
    - 1
    - 0
    - 0
    euler31:
    - 1
    - 0
    - 28629151
    euler37:
    - 1
    - 8886
    - 69343957
    euler41:
    - 1
    - 0
    - 115856201
    euler43:
    - 1
    - -11748
    - 147008443
    euler47:
    - 1
    - 0
    - 229345007
    euler5:
    - 1
    - 0
    - 3125
    euler53:
    - 1
    - 24550
    - 418195493
    euler59:
    - 1
    - 0
    - 714924299
    euler61:
    - 1
    - 0
    - 844596301
    euler67:
    - 1
    - -69364
    - 1350125107
    euler7:
    - 1
    - 0
    - 0
    euler71:
    - 1
    - -2224
    - 1804229351
    euler73:
    - 1
    - 0
    - 2073071593
    euler79:
    - 1
    - -80168
    - 3077056399
    euler83:
    - 1
    - 0
    - 3939040643
    euler89:
    - 1
    - 0
    - 5584059449
    euler97:
    - 1
    - 0
    - 8587340257
    euler_factors:
    - - 1
      - 11
      - 32
    - - 1
      - 0
      - 0
    - - 1
      - 0
      - 3125
    - - 1
      - 0
      - 0
    - - 1
      - -76
      - 161051
    - - 1
      - 0
      - 371293
    - - 1
      - 0
      - 1419857
    - - 1
      - 0
      - 2476099
    - - 1
      - -4952
      - 6436343
    - - 1
      - 7282
      - 20511149
    - - 1
      - 0
      - 28629151
    - - 1
      - 8886
      - 69343957
    - - 1
      - 0
      - 115856201
    - - 1
      - -11748
      - 147008443
    - - 1
      - 0
      - 229345007
    - - 1
      - 24550
      - 418195493
    - - 1
      - 0
      - 714924299
    - - 1
      - 0
      - 844596301
    - - 1
      - -69364
      - 1350125107
    - - 1
      - -2224
      - 1804229351
    - - 1
      - 0
      - 2073071593
    - - 1
      - -80168
      - 3077056399
    - - 1
      - 0
      - 3939040643
    - - 1
      - 0
      - 5584059449
    - - 1
      - 0
      - 8587340257
    id: 20176271
    index: 48
    instance_types:
    - CMF
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/441/6/a/a/1/1
    - ModularForm/GL2/Q/holomorphic/441/6/a/a
    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: 2-21e2-1.1-c5-0-48
    motivic_weight: 5
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 5
    order_of_vanishing: 1
    prelabel: 2-21e2-1.1-c5-0
    primitive: true
    rational: true
    root_analytic_conductor: 8.410069235001842
    root_angle: 0.5
    self_dual: true
    spectral_label: c5-0
    trace_hash: 2197034075981573504
    z1:
      __RealLiteral__: 0
      data: '1.16725023901586829333008032763'
      prec: 103
- - Lhash: '1479665466105009675008327710640'
    Lhash_array:
    - '1479665466105009675008327710640'
    id: 20131953
    label: 2-21e2-1.1-c5-0-48
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/441/6/a/a
  - Lhash: '1479665466105009675008327710640'
    Lhash_array:
    - '1479665466105009675008327710640'
    id: 24585920
    label: 2-21e2-1.1-c5-0-48
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/441/6/a/a/1/1
label_cols:
- label
- label
- label
labels:
- 2-21e2-1.1-c5-0-48
- 2-21e2-1.1-c5-0-48
- 2-21e2-1.1-c5-0-48
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T08:17:45.910061'