data:
- - Lhash: dirichlet_L_43.27
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    a9:
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    algebraic: true
    analytic_conductor: 4.620991766168876
    analytic_normalization: 0
    bad_lfactors:
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      - - 1
    bad_primes:
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    central_character: '43.27'
    coeff_info:
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    - 0.900968867902419 + 0.433883739117558*I
    - \\zeta_{14}
    conductor: 43
    conductor_radical: 43
    conjugate: dirichlet_L_43.8
    degree: 1
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    euler_factors:
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    - - 1
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    - - 0
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      - a^12
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    - - 1
      - a^0
    - - 1
      - a^8
    - - 1
      - a^1
    - - 1
      - a^2
    - - 1
      - a^12
    gamma_factors:
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    - []
    id: 342
    index: 0
    label: 1-43-43.27-r1-0-0
    leading_term: 2.85453050095121074205274180318-1.04256637202497504099907800884*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/43/27
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-43-43.27-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.620991766168876
    root_angle: -0.22293133130969298
    root_number: 0.764610584982664555190418694408-0.644492554908485738198715866925*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.111465665655'
      prec: 50
    spectral_label: r1-0
    st_group: mu(14)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 2.08523825469539091410514726367-0.535916261447461773266056970786*I
    z1:
      __RealLiteral__: 0
      data: '1.93292510242'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '3.70143206259'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '4.91655164305'
      prec: 44
- - algebraic: true
    analytic_conductor: 4.620991766168876
    bad_primes:
    - 43
    central_character: '43.27'
    conductor: 43
    conductor_radical: 43
    degree: 1
    id: 342
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/43/27
    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: 1-43-43.27-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: 1-43-43.27-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.620991766168876
    root_angle: -0.11146566565484649
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '1.93292510242'
      prec: 44
- - Lhash: dirichlet_L_43.27
    Lhash_array:
    - dirichlet_L_43.27
    id: 1781764
    label: 1-43-43.27-r1-0-0
    type: DIR
    url: Character/Dirichlet/43/27
label_cols:
- label
- label
- label
labels:
- 1-43-43.27-r1-0-0
- 1-43-43.27-r1-0-0
- 1-43-43.27-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-20T03:54:47.944184'