data:
- - Lhash: dirichlet_L_57.5
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    a2:
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    a3:
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    a8:
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    a9:
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    algebraic: true
    analytic_conductor: 6.1255007132936266
    analytic_normalization: 0
    bad_lfactors:
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      - - 1
    - - 19
      - - 1
    bad_primes:
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    central_character: '57.5'
    coeff_info:
    - x^18 - 1
    - 0.939692620785908 + 0.342020143325669*I
    - \\zeta_{18}
    conductor: 57
    conductor_radical: 57
    conjugate: dirichlet_L_57.23
    degree: 1
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    euler_factors:
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    - - 0
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      - a^13
    - - 1
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    - - 0
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    - - 1
      - a^1
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      - a^4
    - - 1
      - a^11
    - - 1
      - a^5
    - - 1
      - a^7
    - - 1
      - a^14
    - - 1
      - a^2
    - - 1
      - a^13
    - - 1
      - a^10
    - - 1
      - a^10
    - - 1
      - a^15
    - - 1
      - a^17
    - - 1
      - a^16
    - - 1
      - a^17
    gamma_factors:
    - - 1
    - []
    id: 597
    index: 0
    label: 1-57-57.5-r1-0-0
    leading_term: 0.109504461184498488802514037390+0.443033895773943984496313970010*I
    load_key: dirichlet
    motivic_weight: 0
    mu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    mu_real:
    - 1
    nu_imag: []
    nu_real_doubled: []
    order_of_vanishing: 0
    origin: Character/Dirichlet/57/5
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-57-57.5-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.1255007132936266
    root_angle: 0.8457388277580616
    root_number: -0.884849358430303511453962230446+0.465877250877825396425660631731*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.422869413879'
      prec: 47
    spectral_label: r1-0
    st_group: mu(18)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.526953482570403358605041897039+0.215399746762814158779958184867*I
    z1:
      __RealLiteral__: 0
      data: '1.85928442958'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '4.65494985913'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '6.05295160871'
      prec: 44
- - algebraic: true
    analytic_conductor: 6.1255007132936266
    bad_primes:
    - 3
    - 19
    central_character: '57.5'
    conductor: 57
    conductor_radical: 57
    degree: 1
    id: 597
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/57/5
    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: 1-57-57.5-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: 1-57-57.5-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 6.1255007132936266
    root_angle: 0.4228694138790308
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '1.85928442958'
      prec: 44
- - Lhash: dirichlet_L_57.5
    Lhash_array:
    - dirichlet_L_57.5
    id: 1782001
    label: 1-57-57.5-r1-0-0
    type: DIR
    url: Character/Dirichlet/57/5
label_cols:
- label
- label
- label
labels:
- 1-57-57.5-r1-0-0
- 1-57-57.5-r1-0-0
- 1-57-57.5-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-16T21:59:18.316041'