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    prelabel: 1-52-52.51-r1-0
    primitive: true
    rational: true
    root_analytic_conductor: 5.588176089320501
    root_angle: 0.0
    root_number: '1'
    self_dual: true
    sign_arg:
      __RealLiteral__: 0
      data: '0.0'
      prec: 10
    spectral_label: r1-0
    st_group: mu(2)
    symmetry_type: orthogonal
    types:
    - DIR
    values:
    - - 1
      - '0.871321030702998284041002278863'
    z1:
      __RealLiteral__: 0
      data: '1.09268043848'
      prec: 44
    z2:
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      data: '3.94068315499'
      prec: 44
    z3:
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      data: '5.23953945516'
      prec: 44
- - algebraic: true
    analytic_conductor: 5.588176089320501
    bad_primes:
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    - 13
    central_character: '52.51'
    conductor: 52
    conductor_radical: 26
    degree: 1
    dirichlet_coefficients:
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    euler11:
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    euler2:
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    euler23:
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    euler29:
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    euler31:
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    euler61:
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    euler67:
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    euler71:
    - 1
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    euler73:
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    euler79:
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    euler83:
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    euler89:
    - 1
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    euler97:
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    euler_factors:
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      - -1
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    id: 495
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/52/51
    is_instance_Artin: false
    is_instance_BMF: false
    is_instance_CMF: false
    is_instance_DIR: true
    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: 1-52-52.51-r1-0-0
    motivic_weight: 0
    mu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    mu_real:
    - 1
    nu_imag: []
    nu_real_doubled: []
    order_of_vanishing: 0
    prelabel: 1-52-52.51-r1-0
    primitive: true
    rational: true
    root_analytic_conductor: 5.588176089320501
    root_angle: 0.0
    self_dual: true
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '1.09268043848'
      prec: 44
- - Lhash: dirichlet_L_52.51
    Lhash_array:
    - dirichlet_L_52.51
    id: 1781911
    label: 1-52-52.51-r1-0-0
    type: DIR
    url: Character/Dirichlet/52/51
label_cols:
- label
- label
- label
labels:
- 1-52-52.51-r1-0-0
- 1-52-52.51-r1-0-0
- 1-52-52.51-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T03:58:27.199289'