data:
- - Lhash: '1762179109841826530406027904061'
    a10:
    - -17.872874638453347
    - 0
    a2:
    - 1.7872874638453347
    - 3.0956726951110425
    a3:
    - 0
    - 0
    a4:
    - -2.388792956837377
    - 4.137510770005025
    a5:
    - -2.5
    - 4.330127018922194
    a6:
    - 0
    - 0
    a7:
    - -7.079870597486294
    - -12.262695585859285
    a8:
    - 11.518760599615462
    - 0
    a9:
    - 0
    - 0
    accuracy: 100
    algebraic: true
    analytic_conductor: 23.89577355232496
    analytic_normalization:
      __RealLiteral__: 0
      data: '1.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 5
      - - - 1.0
          - 0
        - - 2.5
          - -4.330127018922194
    bad_primes:
    - 3
    - 5
    central_character: '405.271'
    coefficient_field: CDF
    conductor: 405
    conductor_radical: 15
    conjugate: '914092402475900993305923559828'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -1.7872874638453347
        - -3.0956726951110425
      - - -4.0
        - 6.928203230275509
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 2.5
        - -4.330127018922194
    - - - 1.0
        - 0
      - - 7.079870597486294
        - 12.262695585859285
      - - -171.5
        - 297.04671349806245
    - - - 1.0
        - 0
      - - 31.831902067766457
        - 55.13447168292831
      - - -665.5
        - 1152.6798124370878
    - - - 1.0
        - 0
      - - -5.19795338570351
        - 9.003119359413144
      - - -1098.5
        - -1902.6578121144116
    - - - 1.0
        - 0
      - - -108.60513271456755
        - 0
      - - 4913.0
        - 0
    - - - 1.0
        - 0
      - - -18.614538856902772
        - 0
      - - 6859.0
        - 0
    - - - 1.0
        - 0
      - - -64.41195735717638
        - 111.56478275758944
      - - -6083.5
        - -10536.931087845265
    - - - 1.0
        - 0
      - - 41.82478130906608
        - 72.4426462427596
      - - -12194.5
        - 21121.493572898675
    - - - 1.0
        - 0
      - - -5.236375768255649
        - 9.069668878141297
      - - -14895.5
        - -25799.76280414221
    - - - 1.0
        - 0
      - - 81.88854456630324
        - 0
      - - 50653.0
        - 0
    - - - 1.0
        - 0
      - - -153.72636121901976
        - 266.26186809402816
      - - -34460.5
        - -59687.336854227295
    - - - 1.0
        - 0
      - - -111.21968397872507
        - -192.6381434529061
      - - -39753.5
        - 68855.08177868936
    - - - 1.0
        - 0
      - - 180.96531380356953
        - 313.4411179154279
      - - -51911.5
        - 89913.35549711177
    - - - 1.0
        - 0
      - - -562.2147804506022
        - 0
      - - 148877.0
        - 0
    - - - 1.0
        - 0
      - - 231.15491777974574
        - -400.37206201392604
      - - -102689.5
        - -177863.43140384424
    - - - 1.0
        - 0
      - - -324.5334580844275
        - -562.108438158253
      - - -113490.5
        - 196571.31217639567
    - - - 1.0
        - 0
      - - 127.08996640823187
        - -220.1262789512795
      - - -150381.5
        - -260468.39851841913
    - - - 1.0
        - 0
      - - 1092.9257600699164
        - 0
      - - 357911.0
        - 0
    - - - 1.0
        - 0
      - - -1034.5186006394254
        - 0
      - - 389017.0
        - 0
    - - - 1.0
        - 0
      - - 575.9265473309816
        - 997.5340414049818
      - - -246519.5
        - 426984.29905647587
    - - - 1.0
        - 0
      - - 262.1601231254412
        - 454.07465297177674
      - - -285893.5
        - 495182.06755369285
    - - - 1.0
        - 0
      - - -656.4848291905853
        - 0
      - - 704969.0
        - 0
    - - - 1.0
        - 0
      - - 562.7553606323124
        - 974.7208768469116
      - - -456336.5
        - 790398.003348155
    - - - 1.0
        - 0
      - - -190.16222054005974
        - -329.37062765550144
      - - -515150.5
        - 892266.8395445109
    - - - 1.0
        - 0
      - - 382.1387185896008
        - -661.8836761364539
      - - -546363.5
        - -946329.3414011582
    - - - 1.0
        - 0
      - - 816.0831196009872
        - 0
      - - 1225043.0
        - 0
    - - - 1.0
        - 0
      - - -606.7754557616707
        - 0
      - - 1295029.0
        - 0
    - - - 1.0
        - 0
      - - -13.661302429251567
        - 23.662069905027842
      - - -721448.5
        - -1249585.457044355
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 23936345
    index: 33
    label: 2-405-9.4-c3-0-33
    leading_term: '2.447976288550129216475749824168734173243117094317742970'
    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/405/4/e/w/271/5
    plot_delta:
      __RealLiteral__: 0
      data: '0.0625'
      prec: 20
    plot_values:
    - 2.4479762885501293
    - 2.5218815952102087
    - 2.5728670872177712
    - 2.601169875067635
    - 2.6071276626458424
    - 2.591181497350544
    - 2.5538811671190724
    - 2.495892767123131
    - 2.418007844232101
    - 2.321153434347098
    - 2.2064022389346287
    - 2.074982144160946
    - 1.9282842697009537
    - 1.7678687445735883
    - 1.5954674436354868
    - 1.4129829795726587
    - 1.222483329937822
    - 1.0261915852854984
    - 0.8264704308170895
    - 0.6258011179844275
    - 0.4267568417621838
    - 0.2319706110135397
    - 0.04409788038482775
    - -0.13422560111496906
    - -0.3004300813214505
    - -0.4520614068882312
    - -0.5868329293785133
    - -0.7026785444382198
    - -0.7978055475303794
    - -0.8707458689533791
    - -0.9204041606444721
    - -0.946101153183752
    - -0.947610688632035
    - -0.9251888678634889
    - -0.8795938334892047
    - -0.8120948437655671
    - -0.7244694801253795
    - -0.6189880706715898
    - -0.49838470190273904
    - -0.3658145269986792
    - -0.22479745514917243
    - -0.07914871467375134
    - 0.06710278681107493
    - 0.20980694079238119
    - 0.34479395185190603
    - 0.46798266261515487
    - 0.5754930755810146
    - 0.6637601162228395
    - 0.7296454037620227
    - 0.7705435965634916
    - 0.7844797719631568
    - 0.7701942974521292
    - 0.7272117610169783
    - 0.6558907595606317
    - 0.5574516986558512
    - 0.43398023337469505
    - 0.2884045732193455
    - 0.124445574321355
    - -0.053460665484709805
    - -0.24026712747540577
    - -0.4304456120567863
    - -0.6181394632456126
    - -0.7973359125889015
    - -0.9620537877439579
    - -1.1065415158583292
    - -1.225479645878135
    - -1.3141815503960887
    - -1.368785577754695
    - -1.3864317363302856
    - -1.365416027750222
    - -1.3053158205138373
    - -1.2070801790017986
    - -1.0730798357482667
    - -0.9071125086523525
    - -0.7143605015803232
    - -0.5012989590350485
    - -0.27555473639209516
    - -0.04571755107585943
    - 0.1788931562426852
    - 0.3885004572828742
    - 0.5731743750438768
    - 0.7231600619415843
    - 0.8292198792364328
    - 0.8829784263026854
    - 0.8772587741279759
    - 0.8063977337137862
    - 0.6665279775755946
    - 0.45581525947028473
    - 0.17463985729796072
    - -0.1742873059270042
    - -0.58588164814101
    - -1.0527206542249605
    - -1.5651614857698048
    - -2.111540864538733
    - -2.6784546876442885
    - -3.2511118219573305
    - -3.813753545001162
    - -4.350127264157558
    - -4.844000571627117
    - -5.27969949254205
    - -5.64265306361231
    - -5.919925233062184
    - -6.100714575907004
    - -6.17680252737802
    - -6.142931782562668
    - -5.9970981958489835
    - -5.740741914223033
    - -5.378826538736408
    - -4.919798744068832
    - -4.375424884972224
    - -3.7605055437689106
    - -3.0924735678068
    - -2.3908857375115424
    - -1.676822613178618
    - -0.9722151487641784
    - -0.299120156079898
    - 0.3210305113619776
    - 0.8681802526110968
    - 1.3243697249089572
    - 1.6744028794223393
    - 1.9064305233889054
    - 2.01242717365843
    - 1.9885402801675733
    - 1.8352951646015494
    - 1.557644103845678
    - 1.164853714157485
    - 0.670230950125762
    - 0.0906943851505471
    - -0.5537962680397501
    - -1.2409334707735247
    - -1.9468536965925238
    - -2.646998932125605
    - -3.3170154756158134
    - -3.933655398077005
    - -4.475645132067607
    - -4.924486205804896
    - -5.26515516850926
    - -5.486673215688706
    - -5.582520815577879
    - -5.55087859313303
    - -5.39468262191104
    - -5.1214898338414665
    - -4.743157170789189
    - -4.275346032483087
    - -3.7368711739626383
    - -3.1489201273212135
    - -2.5341751423393704
    - -1.915874269367095
    - -1.316851306500235
    - -0.7585957256620698
    - -0.26037327589220965
    - 0.16155428528721572
    - 0.49457589819615794
    - 0.7302155507549037
    - 0.8644325151493143
    - 0.8977238532881875
    - 0.8350244554190915
    - 0.6854091019252165
    - 0.4616101799146432
    - 0.17937330997915954
    - -0.14331917499967756
    - -0.48712059218758125
    - -0.8322470914831963
    - -1.1594158314526213
    - -1.450749592182025
    - -1.6906046878058745
    - -1.8662825757256902
    - -1.9685910702179965
    - -1.9922283149979005
    - -1.9359713199780602
    - -1.8026605117689891
    - -1.5989819161978749
    - -1.3350587784009433
    - -1.0238741142589793
    - -0.6805543730639251
    - -0.3215516132255782
    - 0.036233045591828134
    - 0.37633873711977606
    - 0.6836001490991609
    - 0.9449236555111512
    - 1.1499431568453278
    - 1.291520765410811
    - 1.3660656663306259
    - 1.3736542051272027
    - 1.3179450025564907
    - 1.2058941130523815
    - 1.0472863235736645
    - 0.8541090274555952
    - 0.6398041224615851
    - 0.4184405521715622
    - 0.2038550030148588
    - 0.008810569036876511
    - -0.15577727761884477
    - -0.28150135116288205
    - -0.36296995025214596
    - -0.3981288476719089
    - -0.3883766698231586
    - -0.33846404290439586
    - -0.25617946165277183
    - -0.15183751535852866
    - -0.037597159570174205
    - 0.07335155881499539
    - 0.16768518333590557
    - 0.2328756095566297
    - 0.2580933842183074
    - 0.23502902569683667
    - 0.1585792068462456
    - 0.027351230628942062
    - -0.15605123898160864
    - -0.38498622196569005
    - -0.6489864200329548
    - -0.9342233955304806
    - -1.224203957649735
    - -1.500665208973338
    - -1.7446216357481668
    - -1.9375068743857902
    - -2.06234506138661
    - -2.1048825277486665
    - -2.054610394946452
    - -1.9056125125680987
    - -1.6571810585074087
    - -1.3141536753273904
    - -0.8869406894225482
    - -0.3912280001112741
    - 0.15264028302312688
    - 0.7205764671376296
    - 1.2859199453577397
    - 1.820806215586813
    - 2.2976628734176487
    - 2.6907512034349472
    - 2.9776663851339302
    - 3.1407085901474003
    - 3.168041583860556
    - 3.054564774059635
    - 2.802438594338897
    - 2.4212210103939724
    - 1.927593879824563
    - 1.3446807597453494
    - 0.7009812718947174
    - 0.028969953846725773
    - -0.6365717027816727
    - -1.2604038733352703
    - -1.8087585110507582
    - -2.251244093177439
    - -2.5626163998615223
    - -2.724311191686966
    - -2.7256452585101094
    - -2.564608617870525
    - -2.248191859549194
    - -1.792217667039638
    - -1.2206730453673205
    - -0.5645672142949097
    - 0.13963214363141543
    - 0.851906192444304
    - 1.5308361947702191
    - 2.135882787709887
    - 2.6296673618278694
    positive_zeros:
    - '1.39011420775138007015408401250121'
    - '2.59624352281687024516706137479048'
    - '3.60662631633878096178404450612252'
    - '4.82501899586508614595735365555657'
    - '5.53274729425361471433551915671894'
    - '7.21685397383618803838142423812436'
    - '7.946638926353170770169610450061844'
    - '9.412072514706420877565612488110902'
    - '9.972966852575052982611652923374668'
    - '10.99357559421015316651257952120721'
    prelabel: 2-405-9.4-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.8883303440259604
    root_angle: -0.055555555555555566
    root_number: 0.9848077530122080593667430245895230136706432517198424188 - 0.173648177666930348851716626769314796000375677184069388*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.027777777777777776'
      prec: 70
    spectral_label: c3-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.39011420775138007015408401250'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.59624352281687024516706137479'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.60662631633878096178404450612'
      prec: 103
- - algebraic: true
    analytic_conductor: 23.89577355232496
    bad_primes:
    - 3
    - 5
    central_character: '9.4'
    conductor: 405
    conductor_radical: 15
    degree: 2
    id: 23936345
    index: 33
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/405/4/e/w/271/5
    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: 2-405-9.4-c3-0-33
    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: 2-405-9.4-c3-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.8883303440259604
    root_angle: -0.027777777777777783
    self_dual: false
    spectral_label: c3-0
    z1:
      __RealLiteral__: 0
      data: '1.39011420775138007015408401250'
      prec: 103
- - Lhash: '1762179109841826530406027904061'
    Lhash_array:
    - '1762179109841826530406027904061'
    id: 24309263
    label: 2-405-9.4-c3-0-33
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/405/4/e/w/271/5
label_cols:
- label
- label
- label
labels:
- 2-405-9.4-c3-0-33
- 2-405-9.4-c3-0-33
- 2-405-9.4-c3-0-33
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-23T06:19:42.011723'