data:
- - Lhash: dirichlet_L_57.35
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    a9:
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    algebraic: true
    analytic_conductor: 6.1255007132936266
    analytic_normalization: 0
    bad_lfactors:
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    central_character: '57.35'
    coeff_info:
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    - \\zeta_{18}
    conductor: 57
    conductor_radical: 57
    conjugate: dirichlet_L_57.44
    degree: 1
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    euler_factors:
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      - a^15
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      - a^11
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      - a^4
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    gamma_factors:
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    - []
    id: 593
    index: 0
    label: 1-57-57.35-r1-0-0
    leading_term: 1.43832872643025399875698910097+0.0108976491705432250545386007742*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/57/35
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-57-57.35-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.1255007132936266
    root_angle: 0.004823324501136236
    root_number: 0.999885196692032377071131996891+0.0151523409457326279126372653097*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.00241166225057'
      prec: 54
    spectral_label: r1-0
    st_group: mu(18)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 1.05633203241689919127743361071-0.169798383327829645034791195315*I
    z1:
      __RealLiteral__: 0
      data: '1.73108246791'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '3.08517801606'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '5.01415196699'
      prec: 44
- - algebraic: true
    analytic_conductor: 6.1255007132936266
    bad_primes:
    - 3
    - 19
    central_character: '57.35'
    conductor: 57
    conductor_radical: 57
    degree: 1
    id: 593
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/57/35
    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: 1-57-57.35-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: 1-57-57.35-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.1255007132936266
    root_angle: 0.002411662250568118
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '1.73108246791'
      prec: 44
- - Lhash: dirichlet_L_57.35
    Lhash_array:
    - dirichlet_L_57.35
    id: 1782010
    label: 1-57-57.35-r1-0-0
    type: DIR
    url: Character/Dirichlet/57/35
label_cols:
- label
- label
- label
labels:
- 1-57-57.35-r1-0-0
- 1-57-57.35-r1-0-0
- 1-57-57.35-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T03:42:14.576032'