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    positive_zeros:
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    - '0.792612472193496644052679307863572'
    - '1.59124711584340676922929112786814'
    - '2.04964569977334677336367017866309'
    - '2.86142006283351617578994245020201'
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    - '8.452700606269748405984881845755071'
    - '8.544881459057269762140229875293417'
    prelabel: 4-4368e2-1.1-c1e2-0
    primitive: false
    rational: true
    root_analytic_conductor: 5.905815405419923
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg: 0
    spectral_label: c1e2-0
    trace_hash: 1994076201534892678
    types:
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    z1:
      __RealLiteral__: 0
      data: '0.70228106745844854077682498338'
      prec: 103
    z2:
      __RealLiteral__: 0
      data: '0.792612472193496644052679307864'
      prec: 107
    z3:
      __RealLiteral__: 0
      data: '1.59124711584340676922929112787'
      prec: 103
- - algebraic: true
    analytic_conductor: 1216.520616665379
    bad_primes:
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    - 3
    - 7
    - 13
    central_character: '1.1'
    conductor: 19079424
    conductor_radical: 546
    degree: 4
    dirichlet_coefficients:
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    euler11:
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    euler13:
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    euler17:
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    euler19:
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    euler2:
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    euler23:
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    euler29:
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    euler3:
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    euler31:
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    euler37:
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    euler41:
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    euler43:
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    euler47:
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    euler5:
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    euler53:
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    euler59:
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    euler61:
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    euler67:
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    euler73:
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    euler79:
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    euler83:
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    euler89:
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    euler97:
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    euler_factors:
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    - - 1
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    - - 1
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      - -1464
      - 3721
    - - 1
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    - - 1
      - 0
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      - 0
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    - - 1
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      - 50
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    - - 1
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      - 0
      - 6241
    - - 1
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      - 6889
    - - 1
      - 0
      - -162
      - 0
      - 7921
    - - 1
      - 0
      - -190
      - 0
      - 9409
    id: 23583030
    index: 13
    instance_types:
    - CMF
    instance_urls:
    - ModularForm/GL2/Q/holomorphic/4368/2/h/f
    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: 4-4368e2-1.1-c1e2-0-13
    motivic_weight: 1
    mu_imag: []
    mu_real: []
    nu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    nu_real_doubled:
    - 1
    - 1
    order_of_vanishing: 0
    prelabel: 4-4368e2-1.1-c1e2-0
    primitive: false
    rational: true
    root_analytic_conductor: 5.905815405419923
    root_angle: 0.0
    self_dual: true
    spectral_label: c1e2-0
    trace_hash: 1994076201534892678
    z1:
      __RealLiteral__: 0
      data: '0.70228106745844854077682498338'
      prec: 103
- - Lhash: 890247016692623955493374216413,1004755676124466807078909406948
    Lhash_array:
    - '890247016692623955493374216413'
    - '1004755676124466807078909406948'
    id: 23877952
    label: 4-4368e2-1.1-c1e2-0-13
    type: CMF
    url: ModularForm/GL2/Q/holomorphic/4368/2/h/f
label_cols:
- label
- label
- label
labels:
- 4-4368e2-1.1-c1e2-0-13
- 4-4368e2-1.1-c1e2-0-13
- 4-4368e2-1.1-c1e2-0-13
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-19T22:51:12.139243'