data:
- - Lhash: '1599988830517897128367818516663'
    a10:
    - 1.2689993013165934
    - 6.5761031196582784e-62
    a2:
    - -1.0989856323248732
    - 0.6344996506582967
    a3:
    - 1.583922787246021
    - 0.700848488649862
    a4:
    - -0.1948203866289989
    - 0.33743880799163845
    a5:
    - -0.8660254037844386
    - -0.5
    a6:
    - -2.1853965071080768
    - 0.2347760357145156
    a7:
    - 4.162284709943296
    - -2.4030961977296252
    a8:
    - 0.0
    - -3.0324524716620433
    a9:
    - 2.0176227919144085
    - 2.2201797831589016
    accuracy: 100
    algebraic: true
    analytic_conductor: 4.671248518244905
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - -1.583922787246021
          - -0.700848488649862
    - - 5
      - - - 1.0
          - 0
        - - 0.8660254037844386
          - 0.5
    - - 13
      - - - 1.0
          - 0
        - - -3.093931961509988
          - -1.851373818964435
    bad_primes:
    - 3
    - 5
    - 13
    central_character: '585.571'
    coefficient_field: CDF
    conductor: 585
    conductor_radical: 195
    conjugate: '1654473714078107092313259306361'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - 1.0989856323248732
        - -0.6344996506582967
      - - 1.0
        - -1.7320508075688772
    - - - 1.0
        - 0
      - - -1.583922787246021
        - -0.700848488649862
    - - - 1.0
        - 0
      - - 0.8660254037844386
        - 0.5
    - - - 1.0
        - 0
      - - -4.162284709943296
        - 2.4030961977296252
      - - 3.5
        - -6.06217782649107
    - - - 1.0
        - 0
      - - 3.257049435126678
        - -1.8804583681343061
      - - 5.5
        - -9.526279441628825
    - - - 1.0
        - 0
      - - -3.093931961509988
        - -1.851373818964435
    - - - 1.0
        - 0
      - - -2.3613482860956987
        - 0
      - - 17.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 4.609515219467015
      - - -19.0
        - 0
    - - - 1.0
        - 0
      - - -4.077453382677168
        - 7.0623564242904395
      - - -11.5
        - -19.91858428704209
    - - - 1.0
        - 0
      - - -2.7264373258193935
        - -4.722327971971411
      - - -14.5
        - 25.11473670974872
    - - - 1.0
        - 0
      - - 1.3106621014625404
        - 0.7567111170960383
      - - 15.5
        - 26.846787517317598
    - - - 1.0
        - 0
      - - 0
        - -9.704260875835827
      - - -37.0
        - 0
    - - - 1.0
        - 0
      - - -3.95888616549659
        - -2.2856639933405414
      - - 20.5
        - 35.50704155516198
    - - - 1.0
        - 0
      - - 0.9812449746097216
        - 1.6995661506956707
      - - -21.5
        - 37.239092362730865
    - - - 1.0
        - 0
      - - 8.483585566026012
        - -4.898000410238342
      - - 23.5
        - -40.703193977868615
    - - - 1.0
        - 0
      - - 8.051655897144732
        - 0
      - - 53.0
        - 0
    - - - 1.0
        - 0
      - - 0.8391554229213003
        - 0.484486609315547
      - - 29.5
        - 51.09549882328188
    - - - 1.0
        - 0
      - - -4.761344198539517
        - -8.246890064193758
      - - -30.5
        - 52.827549630850754
    - - - 1.0
        - 0
      - - 1.7679883939152714
        - 1.020748575151116
      - - 33.5
        - 58.023702053557386
    - - - 1.0
        - 0
      - - 0
        - -7.789514493445372
      - - -71.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - -1.999764717351854
      - - -73.0
        - 0
    - - - 1.0
        - 0
      - - 3.6191706747353285
        - 6.268587489904924
      - - -39.5
        - 68.41600689897065
    - - - 1.0
        - 0
      - - 3.04623193806431
        - -1.7587428294554646
      - - 41.5
        - -71.88010851410841
    - - - 1.0
        - 0
      - - 0
        - 17.250979660015652
      - - -89.0
        - 0
    - - - 1.0
        - 0
      - - 2.999762025822508
        - -1.7319134131134422
      - - 48.5
        - -84.00446416709055
    - - - 1.0
        - 0
      - - 5.8487840089654775
        - 10.13039106602459
      - - -50.5
        - 87.4685657822283
    - - - 1.0
        - 0
      - - -8.045899396651539
        - 13.935906547588239
      - - -51.5
        - -89.20061658979718
    - - - 1.0
        - 0
      - - -8.396299322403976
        - 0
      - - 107.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 10.40831076684344
      - - -109.0
        - 0
    - - - 1.0
        - 0
      - - -2.732961768595094
        - 4.73362863835
      - - -56.5
        - -97.86087062764156
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 11541022
    index: 28
    label: 2-585-117.103-c1-0-28
    load_key: CMFs-workshop
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    order_of_vanishing: 0
    origin: ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/17
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 1.4045786801474855
    - 1.356875080824046
    - 1.2972966630291405
    - 1.2220689423704003
    - 1.126162012486019
    - 1.0048132317062421
    - 0.8549441225142774
    - 0.6763080028459446
    - 0.4722958813482474
    - 0.25036223157403764
    - 0.022030741690109615
    - -0.19756547978311625
    - -0.39064455610154875
    - -0.5382399240081048
    - -0.6221169163200574
    - -0.6270231436728778
    - -0.5430812502600751
    - -0.3680661696854061
    - -0.10926108167084865
    - 0.2154310936924268
    - 0.5774204454471789
    - 0.9386362779046845
    - 1.254117389698471
    - 1.4759366373151939
    - 1.5582217680677006
    - 1.4628398361015131
    - 1.1651385032105157
    - 0.6590140216260967
    - -0.03946882353999629
    - -0.890622768548218
    - -1.8323987499003938
    - -2.7846317607660924
    - -3.656176957807964
    - -4.354427105514781
    - -4.796293537803808
    - -4.919391375779813
    - -4.691958480224097
    - -4.120009454844073
    - -3.2504137391857166
    - -2.1689943068625155
    - -0.9933402310489287
    - 0.13925296825437442
    - 1.0875516287744866
    - 1.7240318708776021
    - 1.9521120998919939
    - 1.7205067631798043
    - 1.0324297791061217
    - -0.05206141116031201
    - -1.4214063480825507
    - -2.925295597184679
    - -4.3934160218961065
    - -5.657742599439288
    - -6.575220399338837
    - -7.0474265620041905
    - -7.034088929319259
    - -6.558161709076157
    - -5.701420657957218
    - -4.591055438317488
    - -3.379258154311986
    - -2.2190656214172897
    - -1.240465468676424
    - -0.5308532411079783
    - -0.12327219616056115
    - 0.005444377844371741
    - -0.07372949529426565
    - -0.25912852370495926
    - -0.4409879406060554
    - -0.5251367547848934
    - -0.4530896151266902
    - -0.21442437549841326
    - 0.15122608745554794
    - 0.563190658005321
    - 0.9181377947351598
    - 1.1141316187307448
    - 1.0753223756694135
    - 0.7718669546659219
    - 0.2304522070938286
    - -0.46738850579227326
    - -1.1994441597096441
    - -1.827019241654947
    - -2.2243270045940644
    - -2.3068157899583754
    - -2.0520186343267084
    - -1.5077922661619276
    - -0.7853175919095677
    - -0.03749281943393808
    - 0.5733179235530786
    - 0.9115590327796174
    - 0.9008213398437784
    - 0.5446605033885206
    - -0.06956340034285947
    - -0.7857776641487982
    - -1.4109895331661853
    - -1.7576010001264877
    - -1.6872755968187823
    - -1.1464699272729888
    - -0.1850341141899399
    - 1.0473702634815645
    - 2.3275315958127023
    - 3.4029744857133037
    - 4.0452392291435615
    - 4.10058421464172
    - 3.5265389841175803
    - 2.4054145794186166
    - 0.9307576106290938
    - -0.6312132947886145
    - -1.997290490752179
    - -2.9279097100809106
    - -3.278968806844175
    - -3.032662541628921
    - -2.2997083844535005
    - -1.2918782027513491
    - -0.27079638013691915
    - 0.5151679410192108
    - 0.8908751702585936
    - 0.7965561061235332
    - 0.3013725900683953
    - -0.4156079187401264
    - -1.1130559114866625
    - -1.5523967554736724
    - -1.564216893047617
    - -1.0991585639979273
    - -0.2496889219189382
    - 0.7640413425541269
    - 1.6422437646235313
    - 2.076823289087313
    - 1.8291195978624928
    - 0.7949469108592063
    - -0.9596928602724598
    - -3.202113341298089
    - -5.576141777096725
    - -7.675709226732895
    - -9.131847854259538
    - -9.692525503717059
    - -9.276256189238632
    - -7.98673238426225
    - -6.085289354271646
    - -3.9284178415185576
    - -1.886116047553624
    - -0.2613856028010804
    - 0.7695559386662082
    - 1.1825574225747395
    - 1.091815135989229
    - 0.7029633043076269
    - 0.24732625959347201
    - -0.08384601907450306
    - -0.18713089570900288
    - -0.0644343036132535
    - 0.19288870964331195
    - 0.4466052450357004
    - 0.5664846968172202
    - 0.47976778373545176
    - 0.1995050958647497
    - -0.17719511232517443
    - -0.5004511636002997
    - -0.6184433367567685
    - -0.4313783153346128
    - 0.06925154639480222
    - 0.7897615944552753
    - 1.5567109073357344
    - 2.1670864846641718
    - 2.451366189810787
    - 2.3295938914463012
    - 1.8416586320562764
    - 1.1400701386102943
    - 0.44477797960234605
    - -0.028285547415340166
    - -0.1439803004619203
    - 0.09426492197208748
    - 0.5260015469076873
    - 0.8643768481816266
    - 0.7711816288236313
    - -0.04232845167041371
    - -1.7168867080352792
    - -4.178612917604137
    - -7.126892759801187
    - -10.084989215320741
    - -12.504011056132706
    - -13.894922704294826
    - -13.953800533649172
    - -12.645619750634298
    - -10.221909072651675
    - -7.165131973738516
    - -4.072840909516077
    - -1.5117428219071036
    - 0.1192352360714662
    - 0.6797899144201337
    - 0.3085182875263469
    - -0.6320841247123365
    - -1.6693451935676331
    - -2.359717539058441
    - -2.4135307302599602
    - -1.7697907185285342
    - -0.600713341410146
    - 0.7533280504722916
    - 1.8971343653526627
    - 2.5069209976409237
    - 2.4308257265064106
    - 1.7335258926160944
    - 0.6724033304968771
    - -0.3860378481345944
    - -1.0824415478452105
    - -1.176735945732212
    - -0.6211369042260565
    - 0.4282098455772147
    - 1.663545175857269
    - 2.724129803472891
    - 3.309141081956494
    - 3.268761285874448
    - 2.644980670053054
    - 1.6503222789938115
    - 0.5929996996020078
    - -0.2256975193280648
    - -0.607381341563565
    - -0.51434571475233
    - -0.07090957190515701
    - 0.49060581108131873
    - 0.9193807349948017
    - 1.0392374135153892
    - 0.8125399069072847
    - 0.35227489262877565
    - -0.12209086108556169
    - -0.3695157011319856
    - -0.22288607024628818
    - 0.33940935187592575
    - 1.172674733601757
    - 2.0054046708228523
    - 2.5275014364860335
    - 2.4979726447844617
    - 1.83492242797614
    - 0.6554529602089021
    - -0.7506527170239876
    - -2.0072022881709626
    - -2.7706151392958813
    - -2.842304457724935
    - -2.236083763674306
    - -1.1765635653359512
    - -0.02747882903706486
    - 0.8271785797768749
    - 1.1097158975138561
    - 0.740094570352249
    - -0.1394357091643122
    - -1.215416242787115
    - -2.1128560125253264
    - -2.5257315502133073
    - -2.322689752542153
    - -1.5903681355683215
    - -0.5982343510644618
    - 0.303447069542805
    - 0.8166263375327716
    - 0.8114180527016787
    - 0.3816406847839298
    - -0.18298637282972247
    - -0.5015058073238066
    - -0.24849940161811637
    - 0.7087725962347894
    - 2.233874061492995
    positive_zeros:
    - '1.26216863718585636745249912273304'
    - '2.29448567333412523826339275852652'
    - '3.49367042222112343199042105407295'
    - '5.10880872553820193501982016699766'
    - '5.86976541189051419831518895843960'
    - '7.85199107264057582607264494583054'
    - '7.910677176840745021631588250397804'
    - '8.701931342310324421609310202046226'
    - '9.543458625721087010876420658865222'
    - '10.63168036169244347623604601715771'
    prelabel: 2-585-117.103-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.161307131863703
    root_angle: -0.28537586266991055
    root_number: 0.6243206826579153 - 0.7811681542443693*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.142687931335'
      prec: 50
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '1.26216863718585636745249912273'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '2.29448567333412523826339275853'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '3.49367042222112343199042105407'
      prec: 103
- - algebraic: true
    analytic_conductor: 4.671248518244905
    bad_primes:
    - 3
    - 5
    - 13
    central_character: '117.103'
    conductor: 585
    conductor_radical: 195
    degree: 2
    id: 11541022
    index: 28
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/17
    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: 2-585-117.103-c1-0-28
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    order_of_vanishing: 0
    prelabel: 2-585-117.103-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.161307131863703
    root_angle: -0.14268793133495528
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '1.26216863718585636745249912273'
      prec: 103
- - Lhash: '1599988830517897128367818516663'
    Lhash_array:
    - '1599988830517897128367818516663'
    id: 11907067
    label: 2-585-117.103-c1-0-28
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/17
label_cols:
- label
- label
- label
labels:
- 2-585-117.103-c1-0-28
- 2-585-117.103-c1-0-28
- 2-585-117.103-c1-0-28
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-24T15:36:10.528595'