data:
- - Lhash: '1312430046139412043625110163236'
    a10:
    - 0.0
    - 0.0
    a2:
    - 0.0
    - 0.0
    a3:
    - 19.524174696260022
    - 0.0
    a4:
    - 0.0
    - 0.0
    a5:
    - 0.0
    - 0.0
    a6:
    - 0.0
    - 0.0
    a7:
    - -35.048349392520045
    - 0.0
    a8:
    - 0.0
    - 0.0
    a9:
    - 138.19339757008018
    - 0.0
    accuracy: 100
    algebraic: true
    analytic_conductor: 64.15352792519226
    analytic_normalization:
      __RealLiteral__: 0
      data: '2.5'
      prec: 10
    bad_lfactors:
    - - 2
      - - - 1.0
          - 0
        - - 0
          - 0
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 2
    - 5
    central_character: '400.1'
    coefficient_field: CDF
    conductor: 400
    conductor_radical: 10
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - -19.524174696260022
        - 0
      - - 243.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 35.048349392520045
        - 0
      - - 16807.0
        - 0
    - - - 1.0
        - 0
      - - -426.0076686214605
        - 0
      - - 161051.0
        - 0
    - - - 1.0
        - 0
      - - -1103.2570842055213
        - 0
      - - 371293.0
        - 0
    - - - 1.0
        - 0
      - - -109.38679514016037
        - 0
      - - 1419857.0
        - 0
    - - - 1.0
        - 0
      - - 495.9263070793414
        - 0
      - - 2476099.0
        - 0
    - - - 1.0
        - 0
      - - 2497.369120233482
        - 0
      - - 6436343.0
        - 0
    - - - 1.0
        - 0
      - - 42.42214495351649
        - 0
      - - 20511149.0
        - 0
    - - - 1.0
        - 0
      - - -7999.557842476049
        - 0
      - - 28629151.0
        - 0
    - - - 1.0
        - 0
      - - 13763.70055298985
        - 0
      - - 69343957.0
        - 0
    - - - 1.0
        - 0
      - - -11863.627515699382
        - 0
      - - 115856201.0
        - 0
    - - - 1.0
        - 0
      - - -16816.011973175784
        - 0
      - - 147008443.0
        - 0
    - - - 1.0
        - 0
      - - -13036.0
        - 0
      - - 229345007.0
        - 0
    - - - 1.0
        - 0
      - - -17817.297109346393
        - 0
      - - 418195493.0
        - 0
    - - - 1.0
        - 0
      - - -47346.05667364417
        - 0
      - - 714924299.0
        - 0
    - - - 1.0
        - 0
      - - 22782.93631336456
        - 0
      - - 844596301.0
        - 0
    - - - 1.0
        - 0
      - - -39418.308426891985
        - 0
      - - 1350125107.0
        - 0
    - - - 1.0
        - 0
      - - -1616.316095513448
        - 0
      - - 1804229351.0
        - 0
    - - - 1.0
        - 0
      - - -53293.259421869276
        - 0
      - - 2073071593.0
        - 0
    - - - 1.0
        - 0
      - - -6516.977080051807
        - 0
      - - 3077056399.0
        - 0
    - - - 1.0
        - 0
      - - 46016.35500833475
        - 0
      - - 3939040643.0
        - 0
    - - - 1.0
        - 0
      - - -113488.45367401036
        - 0
      - - 5584059449.0
        - 0
    - - - 1.0
        - 0
      - - -107417.86384578809
        - 0
      - - 8587340257.0
        - 0
    - - - 1.0
        - 0
      - - 197554.01311260377
        - 0
      - - 10510100501.0
        - 0
    - - - 1.0
        - 0
      - - -81026.02337663757
        - 0
      - - 11592740743.0
        - 0
    - - - 1.0
        - 0
      - - -137442.36230618303
        - 0
      - - 14025517307.0
        - 0
    - - - 1.0
        - 0
      - - 68693.08877241501
        - 0
      - - 15386239549.0
        - 0
    - - - 1.0
        - 0
      - - 139632.4688394209
        - 0
      - - 18424351793.0
        - 0
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 20146631
    index: 20
    label: 2-20e2-1.1-c5-0-20
    leading_term: '3.80261502095185065125613345299'
    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: 0
    origin: ModularForm/GL2/Q/holomorphic/400/6/a/u/1/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.0625'
      prec: 20
    plot_values:
    - 3.8026150209518508
    - 3.7832288204061877
    - 3.7253398900986605
    - 3.629754259288964
    - 3.49780535291259
    - 3.3313390296193237
    - 3.1326925897971125
    - 2.904667724846134
    - 2.650497393541081
    - 2.373806641640455
    - 2.0785674290327694
    - 1.7690475959223726
    - 1.4497541862490733
    - 1.125371452171892
    - 0.8006939865354644
    - 0.4805555683280264
    - 0.1697544558572716
    - -0.12702398052486039
    - -0.4052862348381928
    - -0.6608100435351417
    - -0.8897228109958888
    - -1.0885775975220982
    - -1.2544250768242797
    - -1.3848797911914605
    - -1.4781789893096624
    - -1.5332323298606363
    - -1.5496607786300107
    - -1.5278231219365217
    - -1.468828667592071
    - -1.3745349077144693
    - -1.247529175320486
    - -1.0910936367334871
    - -0.9091533205702765
    - -0.7062072856013927
    - -0.4872434663307797
    - -0.2576381970419342
    - -0.023041890866500242
    - 0.21074717286578135
    - 0.4379185364550966
    - 0.6527918757117878
    - 0.8499626947018718
    - 1.0244478325442192
    - 1.171826957728526
    - 1.2883760620992042
    - 1.371188906634694
    - 1.4182824252105306
    - 1.428682268721209
    - 1.4024849750668718
    - 1.3408936817024337
    - 1.246224853737012
    - 1.1218841746483392
    - 0.9723105267331587
    - 0.8028878581481832
    - 0.6198256721681684
    - 0.43000985744923925
    - 0.24082657747725608
    - 0.05996292200190948
    - -0.10481103990348717
    - -0.24587331050237046
    - -0.355987883907634
    - -0.42854271187806675
    - -0.45778047833898367
    - -0.43901473919872386
    - -0.3688240036743798
    - -0.24521659469601884
    - -0.06775963701675926
    - 0.16233371766297092
    - 0.4421637177157157
    - 0.7671537553418439
    - 1.131112670953056
    - 1.5263502809687273
    - 1.9438450941647871
    - 2.3734614185867673
    - 2.804211289308772
    - 3.224554928037098
    - 3.6227318419886863
    - 3.9871132449276847
    - 4.306565298720847
    - 4.57081178554258
    - 4.770784278029851
    - 4.898947716871678
    - 4.949589560511176
    - 4.919061354376674
    - 4.805962676978997
    - 4.611258941086565
    - 4.338326427513419
    - 3.9929201582411076
    - 3.5830627108169844
    - 3.118854759660213
    - 2.612210912894082
    - 2.0765271975838475
    - 1.5262892281884868
    - 0.9766325671596536
    - 0.44286894962802115
    - -0.06000620095287273
    - -0.5178082788802068
    - -0.9176426424838363
    - -1.248350944688909
    - -1.500907769289803
    - -1.6687519315342416
    - -1.7480386809848616
    - -1.737801522235507
    - -1.6400153749429947
    - -1.4595562342528914
    - -1.2040562494838052
    - -0.88365707790642
    - -0.5106683428012079
    - -0.09914187349553674
    - 0.3356240297471856
    - 0.7776329365807112
    - 1.210771320237516
    - 1.6194005373683404
    - 1.9889369866348905
    - 2.306397544517277
    - 2.560888169284938
    - 2.744015285882793
    - 2.8502021792059065
    - 2.8768960550617186
    - 2.8246555632202677
    - 2.6971132666270266
    - 2.5008126063589957
    - 2.244924150868917
    - 1.940851112253852
    - 1.6017390364818707
    - 1.241909006121763
    - 0.8762374231555464
    - 0.519508278419809
    - 0.18576560748647453
    - -0.11230553504522266
    - -0.36394184803765983
    - -0.5607824106759047
    - -0.6972443195393009
    - -0.770774650539029
    - -0.781965180543469
    - -0.7345221863901193
    - -0.6350900435333183
    - -0.4929339986742452
    - -0.31949409442055343
    - -0.1278284743714735
    - 0.06803010614523412
    - 0.25377607632257443
    - 0.4155591865584631
    - 0.5407049251035924
    - 0.6183925905486688
    - 0.6402574411326658
    - 0.6008860012978875
    - 0.4981778091603015
    - 0.3335524892496711
    - 0.11198781479110008
    - -0.15811789953332933
    - -0.46525749572132097
    - -0.7952907590924054
    - -1.1320660787460641
    - -1.4581621681772843
    - -1.7557174335611168
    - -2.0073093309126806
    - -2.1968424590039644
    - -2.3104024224409443
    - -2.3370328150437447
    - -2.2693950701508783
    - -2.1042753542384953
    - -1.8429089944811794
    - -1.4911008829543604
    - -1.0591295542503047
    - -0.5614327776820398
    - -0.01608307018655413
    - 0.5559279851120371
    - 1.131567856432991
    - 1.6867660977891918
    - 2.1974976008634073
    - 2.64089616992326
    - 2.996345634709233
    - 3.246495343461717
    - 3.378149117583315
    - 3.38298156670514
    - 3.258042893046704
    - 3.0060226649231816
    - 2.6352541028350105
    - 2.1594526903764533
    - 1.5971958124196675
    - 0.9711630019657993
    - 0.30716859408455355
    - -0.36697049507928836
    - -1.022680111388095
    - -1.6319289318454133
    - -2.1685210102254184
    - -2.609317750838185
    - -2.9353286323025922
    - -3.1326154956577907
    - -3.192963615672442
    - -3.1142837236464675
    - -2.900722135051679
    - -2.5624705274980966
    - -2.115281995928472
    - -1.5797150111657692
    - -0.9801410394198659
    - -0.34356408598679805
    - 0.3016893832736959
    - 0.9273443959864701
    - 1.506545600720407
    - 2.015149519580526
    - 2.4328742244670902
    - 2.7442466619582766
    - 2.9392980486230615
    - 3.0139707329005843
    - 2.9702150172603177
    - 2.8157708716614382
    - 2.563646373553063
    - 2.231321164743672
    - 1.8397183117849127
    - 1.4120008414877145
    - 0.9722591500879244
    - 0.5441618566592663
    - 0.1496450787378508
    - -0.19228664497202935
    - -0.46658043918667713
    - -0.6629185760452694
    - -0.7762208557695122
    - -0.8068371620146995
    - -0.7604190689831047
    - -0.6474778168093083
    - -0.48265420663505004
    - -0.28374294370258907
    - -0.07052867424185735
    - 0.13649747050626387
    - 0.31746431734776076
    - 0.4544102723758819
    - 0.5324576661062389
    - 0.540799381887784
    - 0.4734357277806594
    - 0.3296137645677794
    - 0.11393863310959888
    - -0.1638541387563691
    - -0.4894559429480595
    - -0.844842387705103
    - -1.2093821653654175
    - -1.561132854008743
    - -1.8782463982977462
    - -2.140398831305134
    - -2.3301556344988037
    - -2.434186284320149
    - -2.444248984987011
    - -2.3578790028804946
    - -2.178730755764785
    - -1.9165439521030492
    - -1.5867264768917473
    - -1.209570072506635
    - -0.8091377697381469
    - -0.41188308357471176
    - -0.045078877723942194
    - 0.26485263979571466
    - 0.4940090255364733
    - 0.6225736307177399
    - 0.6361801174628277
    - 0.5269868559011357
    - 0.2943880502019391
    - -0.054691293257211906
    positive_zeros:
    - '1.03532475423679087487587356142637'
    - '2.25612514199185473571426732836097'
    - '3.52189963238889718297822664587637'
    - '4.08242977034811974254808353409185'
    - '5.86727311680305987173083706129845'
    - '6.70196640617827131516589353407886'
    - '7.975404600083867171843554572149005'
    - '8.665656914040454513598236539186064'
    - '9.277151883823512591451170063467020'
    - '10.31428617868854528135934790250169'
    prelabel: 2-20e2-1.1-c5-0
    primitive: true
    rational: false
    root_analytic_conductor: 8.009589747620803
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c5-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.03532475423679087487587356143'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.25612514199185473571426732836'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.52189963238889718297822664588'
      prec: 103
- - algebraic: true
    analytic_conductor: 64.15352792519226
    bad_primes:
    - 2
    - 5
    central_character: '1.1'
    conductor: 400
    conductor_radical: 10
    degree: 2
    id: 20146631
    index: 20
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/400/6/a/u/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: 2-20e2-1.1-c5-0-20
    motivic_weight: 5
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 5
    order_of_vanishing: 0
    prelabel: 2-20e2-1.1-c5-0
    primitive: true
    rational: false
    root_analytic_conductor: 8.009589747620803
    root_angle: 0.0
    self_dual: true
    spectral_label: c5-0
    z1:
      __RealLiteral__: 0
      data: '1.03532475423679087487587356143'
      prec: 103
- - Lhash: '1312430046139412043625110163236'
    Lhash_array:
    - '1312430046139412043625110163236'
    id: 20551780
    label: 2-20e2-1.1-c5-0-20
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/400/6/a/u/1/2
label_cols:
- label
- label
- label
labels:
- 2-20e2-1.1-c5-0-20
- 2-20e2-1.1-c5-0-20
- 2-20e2-1.1-c5-0-20
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T12:26:30.755250'