data:
- - Lhash: dirichlet_L_43.19
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    algebraic: true
    analytic_conductor: 4.620991766168876
    analytic_normalization: 0
    bad_lfactors:
    - - 43
      - - 1
    bad_primes:
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    central_character: '43.19'
    coeff_info:
    - x^42 - 1
    - 0.988830826225129 + 0.149042266176174*I
    - \\zeta_{42}
    conductor: 43
    conductor_radical: 43
    conjugate: dirichlet_L_43.34
    degree: 1
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    euler_factors:
    - - 1
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    - - 1
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    - - 1
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    - - 1
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    - - 1
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    - - 0
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    - - 1
      - a^11
    - - 1
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    - - 1
      - a^14
    - - 1
      - a^40
    - - 1
      - a^19
    - - 1
      - a^24
    - - 1
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    gamma_factors:
    - - 1
    - []
    id: 333
    index: 0
    label: 1-43-43.19-r1-0-0
    leading_term: -0.125037550182888563650964319839+0.180553023983371747470827294133*I
    load_key: dirichlet
    motivic_weight: 0
    mu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    mu_real:
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    nu_imag: []
    nu_real_doubled: []
    order_of_vanishing: 0
    origin: Character/Dirichlet/43/19
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-43-43.19-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.620991766168876
    root_angle: -0.6144046239060322
    root_number: -0.351724544687294996486203138310-0.936103543773078035163890591708*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.307202311953'
      prec: 50
    spectral_label: r1-0
    st_group: mu(42)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.427511556448818009546145846833+0.374808131312487732819483311161*I
    z1:
      __RealLiteral__: 0
      data: '3.83838507623'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '5.25453097317'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '6.76247294655'
      prec: 44
- - algebraic: true
    analytic_conductor: 4.620991766168876
    bad_primes:
    - 43
    central_character: '43.19'
    conductor: 43
    conductor_radical: 43
    degree: 1
    id: 333
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/43/19
    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: 1-43-43.19-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: 1-43-43.19-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.620991766168876
    root_angle: -0.3072023119530161
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '3.83838507623'
      prec: 44
- - Lhash: dirichlet_L_43.19
    Lhash_array:
    - dirichlet_L_43.19
    id: 1781756
    label: 1-43-43.19-r1-0-0
    type: DIR
    url: Character/Dirichlet/43/19
label_cols:
- label
- label
- label
labels:
- 1-43-43.19-r1-0-0
- 1-43-43.19-r1-0-0
- 1-43-43.19-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T20:27:17.362711'