data:
- - Lhash: '3907421520300782863670736257718'
    a10:
    - 0.0
    - 0.0
    a2:
    - 1.806641746768046
    - -1.043065098825747
    a3:
    - 1.3827563775342475
    - -1.043065098825747
    a4:
    - 1.1759696007767309
    - -2.036839096701787
    a5:
    - 0.0
    - 0.0
    a6:
    - 1.4101605968747633
    - -3.326749869720024
    a7:
    - -3.538692554336923
    - 2.043065098825747
    a8:
    - 0.0
    - -0.7341909960980323
    a9:
    - 0.8240303992232691
    - -2.8846098351693836
    accuracy: 100
    algebraic: true
    analytic_conductor: 1.7966340454788094
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 3
      - - - 1.0
          - 0
        - - -1.3827563775342475
          - 1.043065098825747
    - - 5
      - - - 1.0
          - 0
        - - 0
          - 0
    bad_primes:
    - 3
    - 5
    central_character: '225.49'
    coefficient_field: CDF
    conductor: 225
    conductor_radical: 15
    conjugate: '2777851492691286098418776032847'
    degree: 2
    euler_factors:
    - - - 1.0
        - 0
      - - -1.806641746768046
        - 1.043065098825747
      - - 1.0
        - -1.7320508075688772
    - - - 1.0
        - 0
      - - -1.3827563775342475
        - 1.043065098825747
    - - - 1.0
        - 0
      - - 0
        - 0
    - - - 1.0
        - 0
      - - 3.538692554336923
        - -2.043065098825747
      - - 3.5
        - -6.06217782649107
    - - - 1.0
        - 0
      - - -0.6759696007767309
        - -1.1708136929173483
      - - -5.5
        - 9.526279441628825
    - - - 1.0
        - 0
      - - 0.5612371146515289
        - 0.3240303992232691
      - - 6.5
        - 11.258330249197702
    - - - 1.0
        - 0
      - - 0
        - -1.3519392015534617
      - - -17.0
        - 0
    - - - 1.0
        - 0
      - - 0.6480607984465382
        - 0
      - - 19.0
        - 0
    - - - 1.0
        - 0
      - - 4.148269132602743
        - 2.3950043003792088
      - - 11.5
        - 19.91858428704209
    - - - 1.0
        - 0
      - - -1.9380693992049558
        - -3.3568346680174725
      - - -14.5
        - 25.11473670974872
    - - - 1.0
        - 0
      - - -3.848229996079719
        - 6.665329872420655
      - - -15.5
        - -26.846787517317598
    - - - 1.0
        - 0
      - - 0
        - 7.52419959685645
      - - -37.0
        - 0
    - - - 1.0
        - 0
      - - -0.0898394031252368
        - 0.15560641073457235
      - - -20.5
        - -35.50704155516198
    - - - 1.0
        - 0
      - - 0.7104189930498663
        - -0.4101605968747632
      - - 21.5
        - -37.239092362730865
    - - - 1.0
        - 0
      - - 9.445263970093421
        - -5.45322569570051
      - - 23.5
        - -40.703193977868615
    - - - 1.0
        - 0
      - - 0
        - -4.172260395302988
      - - -53.0
        - 0
    - - - 1.0
        - 0
      - - -2.086130197651494
        - 3.613283493536092
      - - -29.5
        - -51.09549882328188
    - - - 1.0
        - 0
      - - -1.9101605968747633
        - -3.308495204403182
      - - -30.5
        - 52.827549630850754
    - - - 1.0
        - 0
      - - -7.051133633088968
        - -4.07097390115594
      - - 33.5
        - 58.023702053557386
    - - - 1.0
        - 0
      - - 6.116442790642603
        - 0
      - - 71.0
        - 0
    - - - 1.0
        - 0
      - - 0
        - 12.344520790605976
      - - -73.0
        - 0
    - - - 1.0
        - 0
      - - -5.172260395302988
        - -8.95861779464106
      - - -39.5
        - 68.41600689897065
    - - - 1.0
        - 0
      - - 10.61607766301077
        - -6.129195296477241
      - - 41.5
        - -71.88010851410841
    - - - 1.0
        - 0
      - - -3.0
        - 0
      - - 89.0
        - 0
    - - - 1.0
        - 0
      - - -11.76063988034324
        - 6.7900086007584175
      - - 48.5
        - -84.00446416709055
    - - - 1.0
        - 0
      - - -0.7341909960980323
        - -1.2716561077013953
      - - -50.5
        - 87.4685657822283
    - - - 1.0
        - 0
      - - 6.516147994022318
        - 3.762099798428225
      - - 51.5
        - 89.20061658979718
    - - - 1.0
        - 0
      - - 0
        - 1.2099913992415823
      - - -107.0
        - 0
    - - - 1.0
        - 0
      - - 14.104216798373285
        - 0
      - - 109.0
        - 0
    - - - 1.0
        - 0
      - - -10.326952829571038
        - -5.962268996061406
      - - 56.5
        - 97.86087062764156
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9697505
    index: 14
    label: 2-15e2-45.4-c1-0-14
    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/225/2/k/b/49/5
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 2.54316322847727
    - 2.6516900861876476
    - 2.7911478528252847
    - 2.9602565304722095
    - 3.154560430590431
    - 3.366908670361593
    - 3.588020559303118
    - 3.807021755435193
    - 4.011934457314817
    - 4.190161340870814
    - 4.329013407235181
    - 4.416315061781389
    - 4.4410932214531185
    - 4.394330673107938
    - 4.269741068891531
    - 4.064505129211441
    - 3.7798955632783544
    - 3.4217127782598524
    - 3.000455634954845
    - 2.5311621978101253
    - 2.032875042104623
    - 1.5277138874366254
    - 1.039573809563693
    - 0.5925076304660297
    - 0.2088928109119188
    - -0.09247811750712112
    - -0.29821379122339786
    - -0.4018593579670215
    - -0.4049630286496531
    - -0.31750631236619475
    - -0.15757285130658388
    - 0.04980577436894813
    - 0.2746082789139354
    - 0.4844758275694192
    - 0.647855571731664
    - 0.7373502551286949
    - 0.7329271747315484
    - 0.6246107043724792
    - 0.41429454907929647
    - 0.11636776298812578
    - -0.2430479496679596
    - -0.6283093055590955
    - -0.9978008282944517
    - -1.3085338569052298
    - -1.5213408561070432
    - -1.606081623246261
    - -1.5462075990871111
    - -1.3420362800425147
    - -1.0121793462185908
    - -0.5927448257734095
    - -0.1341828244703194
    - 0.3040583609109629
    - 0.6605880740165316
    - 0.8800801318937147
    - 0.9212568276146843
    - 0.7637722817193551
    - 0.4129502792406923
    - -0.0984863096426542
    - -0.7122343172854089
    - -1.349882066940865
    - -1.9216412097594413
    - -2.337449474351206
    - -2.519132379996221
    - -2.412032033557222
    - -1.9944305643143683
    - -1.2832479064411348
    - -0.3348809352790304
    - 0.7593591097510283
    - 1.8830279266973284
    - 2.90859714687465
    - 3.714120340395173
    - 4.200345399453273
    - 4.3058575315970185
    - 4.01792915274321
    - 3.377198763732435
    - 2.4750639163248658
    - 1.4436645838699806
    - 0.4394200882126903
    - -0.37789394016288264
    - -0.8677450743207356
    - -0.929906600932985
    - -0.5208007193663463
    - 0.33753925602792584
    - 1.5575868496541976
    - 2.995937090340624
    - 4.471413795024765
    - 5.789323616924855
    - 6.7684667606892885
    - 7.266951705806246
    - 7.20289699394159
    - 6.566762027741677
    - 5.423253905025122
    - 3.902336275369471
    - 2.1805749811833883
    - 0.4556155807916046
    - -1.0822666331616024
    - -2.277080416858906
    - -3.028241214195992
    - -3.3025752447128927
    - -3.1353846351905283
    - -2.620592885615844
    - -1.891847520706348
    - -1.0980032988186124
    - -0.3773613138156471
    - 0.16478725920937162
    - 0.47141532643867445
    - 0.5392846137681836
    - 0.4140585089951521
    - 0.17629893946530906
    - -0.0786214153218752
    - -0.2625082887840361
    - -0.31372060488458553
    - -0.2099833512318573
    - 0.02793605787792235
    - 0.3423462464309596
    - 0.6531243479157932
    - 0.8773469009002292
    - 0.9496613615186434
    - 0.8387576234267342
    - 0.5560597775763207
    - 0.15439775537891848
    - -0.2833820856050608
    - -0.6636035051481067
    - -0.9045706772406422
    - -0.9577571899839099
    - -0.8221799108025395
    - -0.5479947379001764
    - -0.22756366521035407
    - 0.024989658085573657
    - 0.1019720854525439
    - -0.06781712930366138
    - -0.493999221804085
    - -1.1108667150522566
    - -1.7794007858154728
    - -2.30640815988218
    - -2.478496624431922
    - -2.1051628125361206
    - -1.062768504077238
    - 0.6697587411188656
    - 2.991731816890348
    - 5.683505960396174
    - 8.432668869024067
    - 10.880335951205533
    - 12.679959170064196
    - 13.558042968652332
    - 13.365145327427477
    - 12.106848169884488
    - 9.947857252683232
    - 7.187419296810068
    - 4.209848217463629
    - 1.4189924390330366
    - -0.8311171874440684
    - -2.2961887498296196
    - -2.8805796173135874
    - -2.6476890301860703
    - -1.8000067010950838
    - -0.6331168440001913
    - 0.5267577832561372
    - 1.3887755326633904
    - 1.753553276577123
    - 1.54804250172657
    - 0.832581911727315
    - -0.22046544073623917
    - -1.3709739494426088
    - -2.3678571608533123
    - -3.005545715404726
    - -3.167663819032402
    - -2.848604467168684
    - -2.148938205540355
    - -1.246671830763638
    - -0.3518938172952857
    - 0.34397794832624046
    - 0.7121439008249798
    - 0.7132851157185787
    - 0.4014127415167229
    - -0.09549742601818059
    - -0.6125835549927167
    - -0.9930991575396585
    - -1.1297250608786797
    - -0.9916740537921536
    - -0.6308086410744552
    - -0.16544044559904725
    - 0.25373442638121835
    - 0.4864576661667885
    - 0.4430643729813614
    - 0.11118398557022761
    - -0.4383400216250915
    - -1.0682114906398748
    - -1.610016311636049
    - -1.9089977210159335
    - -1.8664367882227662
    - -1.468185535460393
    - -0.7913391503948108
    - 0.013306545441168785
    - 0.7589313862996804
    - 1.2709029503829634
    - 1.432827950997096
    - 1.21797043518837
    - 0.6971577981209143
    - 0.020405524629567358
    - -0.6234407608614397
    - -1.0585962275556697
    - -1.1717769224832444
    - -0.9453515747523853
    - -0.46430902027483395
    - 0.10602480666314544
    - 0.5665956575546054
    - 0.7436014107184878
    - 0.5437845769793263
    - -0.00993652002919382
    - -0.7739952903435099
    - -1.514471703612217
    - -1.9664087999641486
    - -1.9080299152546984
    - -1.2306498604104634
    - 0.015169781901798443
    - 1.6117281487194168
    - 3.2099511452342697
    - 4.403107659970814
    - 4.822482423345908
    - 4.232281830610826
    - 2.5998093362534864
    - 0.12178866308491783
    - -2.802329660072589
    - -5.646502974320514
    - -7.867718317808053
    - -9.024295615608487
    - -8.875106200616393
    - -7.43579629680033
    - -4.977979548218316
    - -1.9708988246779526
    - 1.0210874559901761
    - 3.461148051174359
    - 4.953898979553096
    - 5.324073954624057
    - 4.642297488819115
    - 3.1934855058823852
    - 1.3974953469486906
    - -0.29693006974901165
    - -1.5180150815631501
    - -2.0507986895663946
    - -1.8728223182149133
    - -1.1395496740587945
    - -0.12658192193214202
    - 0.8534817579491416
    - 1.5360826415050943
    - 1.7690925801674886
    - 1.5409554465922717
    - 0.9678430469426045
    - 0.24671578809116862
    - -0.40971304281851834
    - -0.8360031969768829
    - -0.9567809175665793
    - -0.7981884988149912
    - -0.4669497803346393
    - -0.10595460175347104
    - 0.15790731678381353
    positive_zeros:
    - '3.08241207758453772675010584640120'
    - '3.84658638109977286883962175325895'
    - '4.91730462906252309738136138182823'
    - '6.28687550158791771099418701197707'
    - '7.10320351464674741927789138792882'
    - '8.289469020947547280395295816625262'
    - '9.687181291793119590077432791550131'
    - '10.20757573526463969247941445780121'
    - '11.78489078013547450417519388939189'
    - '12.95624176630262810650774633253363'
    prelabel: 2-15e2-45.4-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.3403857823323886
    root_angle: 0.38543168495805213
    root_number: 0.3522058902204472 + 0.935922545349786*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.192715842479'
      prec: 47
    spectral_label: c1-0
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '3.08241207758453772675010584640'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '3.84658638109977286883962175326'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '4.91730462906252309738136138183'
      prec: 103
- - algebraic: true
    analytic_conductor: 1.7966340454788094
    bad_primes:
    - 3
    - 5
    central_character: '45.4'
    conductor: 225
    conductor_radical: 15
    degree: 2
    id: 9697505
    index: 14
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/225/2/k/b/49/5
    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: 2-15e2-45.4-c1-0-14
    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: 2-15e2-45.4-c1-0
    primitive: true
    rational: false
    root_analytic_conductor: 1.3403857823323886
    root_angle: 0.19271584247902607
    self_dual: false
    spectral_label: c1-0
    z1:
      __RealLiteral__: 0
      data: '3.08241207758453772675010584640'
      prec: 103
- - Lhash: '3907421520300782863670736257718'
    Lhash_array:
    - '3907421520300782863670736257718'
    id: 10063533
    label: 2-15e2-45.4-c1-0-14
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/225/2/k/b/49/5
label_cols:
- label
- label
- label
labels:
- 2-15e2-45.4-c1-0-14
- 2-15e2-45.4-c1-0-14
- 2-15e2-45.4-c1-0-14
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T19:44:43.975709'