data:
- - Lhash: '3267273504816153220826459279697'
    a10: 6
    a2: 2
    a3: 0
    a4: 2
    a5: 3
    a6: 0
    a7: -4
    a8: 0
    a9: -3
    accuracy: 100
    algebraic: true
    analytic_conductor: 1.4293221961809195
    analytic_normalization:
      __RealLiteral__: 0
      data: '0.5'
      prec: 10
    bad_lfactors:
    - - 179
      - - 1
        - -1
    bad_primes:
    - 179
    central_character: '179.1'
    coefficient_field: 1.1.1.1
    conductor: 179
    conductor_radical: 179
    degree: 2
    euler_factors:
    - - 1
      - -2
      - 2
    - - 1
      - 0
      - 3
    - - 1
      - -3
      - 5
    - - 1
      - 4
      - 7
    - - 1
      - -4
      - 11
    - - 1
      - 1
      - 13
    - - 1
      - -1
      - 17
    - - 1
      - 3
      - 19
    - - 1
      - -6
      - 23
    - - 1
      - -3
      - 29
    - - 1
      - 8
      - 31
    - - 1
      - -2
      - 37
    - - 1
      - -12
      - 41
    - - 1
      - 11
      - 43
    - - 1
      - -1
      - 47
    - - 1
      - 0
      - 53
    - - 1
      - 5
      - 59
    - - 1
      - -14
      - 61
    - - 1
      - 9
      - 67
    - - 1
      - 0
      - 71
    - - 1
      - -10
      - 73
    - - 1
      - -10
      - 79
    - - 1
      - -17
      - 83
    - - 1
      - 1
      - 89
    - - 1
      - 14
      - 97
    - - 1
      - -9
      - 101
    - - 1
      - 6
      - 103
    - - 1
      - 4
      - 107
    - - 1
      - 14
      - 109
    - - 1
      - 4
      - 113
    euler_factors_factorization:
    - - - - 1
          - -2
          - 2
        - 1
    - - - - 1
          - 0
          - 3
        - 1
    - - - - 1
          - -3
          - 5
        - 1
    - - - - 1
          - 4
          - 7
        - 1
    - - - - 1
          - -4
          - 11
        - 1
    - - - - 1
          - 1
          - 13
        - 1
    - - - - 1
          - -1
          - 17
        - 1
    - - - - 1
          - 3
          - 19
        - 1
    - - - - 1
          - -6
          - 23
        - 1
    - - - - 1
          - -3
          - 29
        - 1
    - - - - 1
          - 8
          - 31
        - 1
    - - - - 1
          - -2
          - 37
        - 1
    - - - - 1
          - -12
          - 41
        - 1
    - - - - 1
          - 11
          - 43
        - 1
    - - - - 1
          - -1
          - 47
        - 1
    - - - - 1
          - 0
          - 53
        - 1
    - - - - 1
          - 5
          - 59
        - 1
    - - - - 1
          - -14
          - 61
        - 1
    - - - - 1
          - 9
          - 67
        - 1
    - - - - 1
          - 0
          - 71
        - 1
    - - - - 1
          - -10
          - 73
        - 1
    - - - - 1
          - -10
          - 79
        - 1
    - - - - 1
          - -17
          - 83
        - 1
    - - - - 1
          - 1
          - 89
        - 1
    - - - - 1
          - 14
          - 97
        - 1
    - - - - 1
          - -9
          - 101
        - 1
    - - - - 1
          - 6
          - 103
        - 1
    - - - - 1
          - 4
          - 107
        - 1
    - - - - 1
          - 14
          - 109
        - 1
    - - - - 1
          - 4
          - 113
        - 1
    gamma_factors:
    - []
    - - 0
    group: GL2
    id: 9644009
    index: 10
    label: 2-179-1.1-c1-0-10
    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/179/2/a/a
    plot_delta:
      __RealLiteral__: 0
      data: '0.125'
      prec: 17
    plot_values:
    - 2.2601982546813812
    - 2.2728908998047435
    - 2.3095453017265988
    - 2.3660900960060918
    - 2.436320947773513
    - 2.512546515901295
    - 2.58620304362687
    - 2.6483682899982965
    - 2.6901878797989087
    - 2.703262076710462
    - 2.680036870206323
    - 2.6142215722975655
    - 2.5012310563982254
    - 2.338630829062733
    - 2.126548803764911
    - 1.8680087619987797
    - 1.5691367463901953
    - 1.2391930260183153
    - 0.8903889807350037
    - 0.5374603796971531
    - 0.19698588552174462
    - -0.11353848457884744
    - -0.3768330520133443
    - -0.577113939995503
    - -0.701430580013143
    - -0.7409522568007803
    - -0.6920805571174946
    - -0.5572605376970415
    - -0.34537185644935
    - -0.07160348366525253
    - 0.24324791392506112
    - 0.5740666810046003
    - 0.8932461168261177
    - 1.1729446008205817
    - 1.387597441553216
    - 1.5164597066146452
    - 1.545919717282126
    - 1.4713109795249018
    - 1.2979674085621058
    - 1.0413155460030186
    - 0.7258774334760495
    - 0.3831643430715286
    - 0.048566087613350496
    - -0.24252908672914156
    - -0.45902792387307617
    - -0.5783870640796444
    - -0.5903227961179432
    - -0.49946796067422455
    - -0.32652896569623363
    - -0.10761954693750249
    - 0.10837197828294991
    - 0.26430346570292257
    - 0.3008681568873274
    - 0.16370047318587638
    - -0.1892462625834607
    - -0.7809181489339826
    - -1.6098720624367293
    - -2.6472960325914907
    - -3.8369603787588393
    - -5.098425305204615
    - -6.3334592534048175
    - -7.435215397330126
    - -8.299320685857351
    - -8.835706239173046
    - -8.979800240007787
    - -8.701654986555658
    - -8.0117116261513
    - -6.962220043958041
    - -5.643803210014358
    - -4.177236403839541
    - -2.7011334469235506
    - -1.3568132478243566
    - -0.27207736510739683
    - 0.4541106525835263
    - 0.7640429928888047
    - 0.6490418701887783
    - 0.1513660288531654
    - -0.6402568494514301
    - -1.6011453506535689
    - -2.586063780791271
    - -3.4476211905136114
    - -4.055290991309612
    - -4.312490617360545
    - -4.169336861826386
    - -3.6292207359653763
    - -2.748166703645515
    - -1.6269474350661808
    - -0.39697444648808783
    - 0.7980801053002277
    - 1.8223029235842183
    - 2.566278339396965
    - 2.961769184129326
    - 2.9901415041700736
    - 2.683272507514824
    - 2.1168405518682003
    - 1.3970975823567888
    - 0.6432735263502282
    - -0.03151918708122503
    - -0.5377548110647036
    - -0.8224714173183337
    - -0.8756406907035937
    - -0.7289414896747483
    - -0.44726636592069574
    - -0.11457443284667262
    - 0.18327466581236543
    - 0.37550392899173257
    - 0.4200225335263178
    - 0.31104846372684286
    - 0.07924591535270471
    - -0.21571443697728343
    - -0.4987898283244273
    - -0.6967528258490515
    - -0.7554963830178233
    - -0.6538668090898665
    - -0.4109806891365801
    - -0.08515650848808194
    - 0.2358014838881019
    - 0.45148301374423067
    - 0.46988113512678165
    - 0.22846242312225237
    - -0.28905405252900124
    - -1.043989690084166
    - -1.9444851258282603
    - -2.858236614595792
    - -3.634493083398583
    - -4.131637875105665
    - -4.245296075844841
    - -3.9314359828675336
    - -3.2195266444491204
    - -2.2124260801171918
    - -1.072054933366305
    - 0.007362750752446298
    - 0.8341529903376543
    - 1.2559302262189422
    - 1.1912395215724056
    - 0.6496693975322188
    - -0.26415807662751006
    - -1.36446689258233
    - -2.414471974059055
    - -3.1679589689077194
    - -3.4150089140976334
    - -3.0234076941577244
    - -1.967695021082119
    - -0.33980300574380273
    - 1.6615079772312114
    - 3.761272396139949
    - 5.6539884157395495
    - 7.056279889507161
    - 7.7569187724251565
    - 7.654816498270175
    - 6.777666507603935
    - 5.277470302848113
    - 3.40354235172087
    - 1.4579176627809851
    - -0.25848359186318054
    - -1.4987507689876836
    - -2.1119190341749072
    - -2.0660853359691007
    - -1.4485745760460622
    - -0.4435904094658628
    - 0.7077475603969208
    - 1.756627663489243
    - 2.494961794745004
    - 2.793299727309881
    - 2.6209368340586865
    - 2.044798252481823
    - 1.2082354516789378
    - 0.29510560868711927
    - -0.5124966832329111
    - -1.0733699507834038
    - -1.3147128209905599
    - -1.2423973207308088
    - -0.932487876175233
    - -0.5068494530191947
    - -0.09932203376846896
    - 0.17899800272303848
    - 0.26681475609524713
    - 0.1655088142606626
    - -0.06508492140280012
    - -0.3266089593073637
    - -0.5124670234158284
    - -0.5404454671260781
    - -0.3789846352751704
    - -0.05992292192993027
    - 0.32610238733498986
    - 0.6509990499993257
    - 0.7823234475542082
    - 0.6199055305175187
    - 0.12649587739549617
    - -0.6559430772103397
    - -1.609368444392044
    - -2.5625260484477597
    - -3.3288219486354187
    - -3.7503767215385047
    - -3.737403143444323
    - -3.2926656059227737
    - -2.5140283505228638
    - -1.5732904746819756
    - -0.675428108069436
    - -0.007563693085376088
    - 0.3098878292454636
    - 0.25728313039484885
    - -0.07458277399769468
    - -0.503221432429612
    - -0.7986958149316463
    - -0.7438482402442378
    - -0.19637012568629078
    - 0.8628158490855958
    - 2.308022696493334
    - 3.8815329483344363
    - 5.240126989074686
    - 6.026713233329014
    - 5.951800340659031
    - 4.866309005218943
    - 2.8082392534890857
    - 0.010930892626544389
    - -3.130997732702589
    - -6.132347430155774
    - -8.510375750048434
    - -9.880332028624498
    - -10.032568743209353
    - -8.97406317881668
    - -6.924987014367871
    - -4.271039094146931
    - -1.4822550516519495
    - 0.9834434626672427
    - 2.77040612299581
    - 3.6893277282264565
    - 3.741843911746386
    - 3.1017306155312165
    - 2.059040978630396
    - 0.9420469143942842
    - 0.036605585660631455
    - -0.4775721808212702
    - -0.5592014612225323
    - -0.3001004805130691
    - 0.11418729260089303
    - 0.46576616868969073
    - 0.5705199683031914
    - 0.33119395707940663
    - -0.23629051015803992
    - -1.0094117357299113
    - -1.7956069131373962
    - -2.387867587162265
    - -2.623509860455022
    - -2.4297473762132107
    - -1.843666216769446
    - -1.0015137166865424
    - -0.10082235987544862
    - 0.6535954118994732
    - 1.1044042311512752
    - 1.1819005238468745
    - 0.9185684521957524
    - 0.43448485358333705
    - -0.10157110390369137
    - -0.5234812506493776
    - -0.7162851138891635
    positive_zeros:
    - '2.57742433461389850447314956434326'
    - '3.65455224933898053965548391575567'
    - '5.26927125289354544444142895539671'
    - '6.18510863780788689281989494770010'
    - '6.69315229163834238910355551442606'
    - '9.039531184742746287388806553535529'
    - '9.527249149175652297561485725769351'
    - '10.91540134714576928534303180515763'
    - '12.11851077920995702575878930035937'
    - '12.91966077992607962496402669629966'
    prelabel: 2-179-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 1.1955426367055755
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    spectral_label: c1-0
    trace_hash: 1179237647618595272
    types:
    - CMF
    z1:
      __RealLiteral__: 0
      data: '2.57742433461389850447314956434'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '3.65455224933898053965548391576'
      prec: 103
    z3:
      __RealLiteral__: 0
      data: '5.26927125289354544444142895540'
      prec: 103
- - algebraic: true
    analytic_conductor: 1.4293221961809195
    bad_primes:
    - 179
    central_character: '1.1'
    conductor: 179
    conductor_radical: 179
    degree: 2
    dirichlet_coefficients:
    - 1
    - 2
    - 0
    - 2
    - 3
    - 0
    - -4
    - 0
    - -3
    - 6
    - 4
    - 0
    - -1
    - -8
    - 0
    - -4
    - 1
    - -6
    - -3
    - 6
    - 0
    - 8
    - 6
    - 0
    - 4
    - -2
    - 0
    - -8
    - 3
    - 0
    - -8
    - -8
    - 0
    - 2
    - -12
    - -6
    - 2
    - -6
    - 0
    - 0
    - 12
    - 0
    - -11
    - 8
    - -9
    - 12
    - 1
    - 0
    - 9
    - 8
    - 0
    - -2
    - 0
    - 0
    - 12
    - 0
    - 0
    - 6
    - -5
    - 0
    - 14
    - -16
    - 12
    - -8
    - -3
    - 0
    - -9
    - 2
    - 0
    - -24
    - 0
    - 0
    - 10
    - 4
    - 0
    - -6
    - -16
    - 0
    - 10
    - -12
    - 9
    - 24
    - 17
    - 0
    - 3
    - -22
    - 0
    - 0
    - -1
    - -18
    - 4
    - 12
    - 0
    - 2
    - -9
    - 0
    - -14
    - 18
    - -12
    - 8
    euler11:
    - 1
    - -4
    - 11
    euler13:
    - 1
    - 1
    - 13
    euler17:
    - 1
    - -1
    - 17
    euler19:
    - 1
    - 3
    - 19
    euler2:
    - 1
    - -2
    - 2
    euler23:
    - 1
    - -6
    - 23
    euler29:
    - 1
    - -3
    - 29
    euler3:
    - 1
    - 0
    - 3
    euler31:
    - 1
    - 8
    - 31
    euler37:
    - 1
    - -2
    - 37
    euler41:
    - 1
    - -12
    - 41
    euler43:
    - 1
    - 11
    - 43
    euler47:
    - 1
    - -1
    - 47
    euler5:
    - 1
    - -3
    - 5
    euler53:
    - 1
    - 0
    - 53
    euler59:
    - 1
    - 5
    - 59
    euler61:
    - 1
    - -14
    - 61
    euler67:
    - 1
    - 9
    - 67
    euler7:
    - 1
    - 4
    - 7
    euler71:
    - 1
    - 0
    - 71
    euler73:
    - 1
    - -10
    - 73
    euler79:
    - 1
    - -10
    - 79
    euler83:
    - 1
    - -17
    - 83
    euler89:
    - 1
    - 1
    - 89
    euler97:
    - 1
    - 14
    - 97
    euler_factors:
    - - 1
      - -2
      - 2
    - - 1
      - 0
      - 3
    - - 1
      - -3
      - 5
    - - 1
      - 4
      - 7
    - - 1
      - -4
      - 11
    - - 1
      - 1
      - 13
    - - 1
      - -1
      - 17
    - - 1
      - 3
      - 19
    - - 1
      - -6
      - 23
    - - 1
      - -3
      - 29
    - - 1
      - 8
      - 31
    - - 1
      - -2
      - 37
    - - 1
      - -12
      - 41
    - - 1
      - 11
      - 43
    - - 1
      - -1
      - 47
    - - 1
      - 0
      - 53
    - - 1
      - 5
      - 59
    - - 1
      - -14
      - 61
    - - 1
      - 9
      - 67
    - - 1
      - 0
      - 71
    - - 1
      - -10
      - 73
    - - 1
      - -10
      - 79
    - - 1
      - -17
      - 83
    - - 1
      - 1
      - 89
    - - 1
      - 14
      - 97
    id: 9644009
    index: 10
    instance_types:
    - ECQ
    - CMF
    - CMF
    instance_urls:
    - EllipticCurve/Q/179/a
    - ModularForm/GL2/Q/holomorphic/179/2/a/a/1/1
    - ModularForm/GL2/Q/holomorphic/179/2/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: true
    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: 2-179-1.1-c1-0-10
    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: 2-179-1.1-c1-0
    primitive: true
    rational: true
    root_analytic_conductor: 1.1955426367055755
    root_angle: 0.0
    self_dual: true
    spectral_label: c1-0
    trace_hash: 1179237647618595272
    z1:
      __RealLiteral__: 0
      data: '2.57742433461389850447314956434'
      prec: 103
- - Lhash: '3267273504816153220826459279697'
    Lhash_array:
    - '3267273504816153220826459279697'
    id: 10008878
    label: 2-179-1.1-c1-0-10
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/179/2/a/a
  - Lhash: '3267273504816153220826459279697'
    Lhash_array:
    - '3267273504816153220826459279697'
    id: 24547762
    label: 2-179-1.1-c1-0-10
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/179/2/a/a/1/1
  - Lhash: '1179237647618595272'
    Lhash_array:
    - '1179237647618595272'
    id: 21943
    label: 2-179-1.1-c1-0-10
    type: ECQ
    url: EllipticCurve/Q/179/a
label_cols:
- label
- label
- label
labels:
- 2-179-1.1-c1-0-10
- 2-179-1.1-c1-0-10
- 2-179-1.1-c1-0-10
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-17T21:11:51.767336'