data:
- - Lhash: dirichlet_L_69.2
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    a8:
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    a9:
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    algebraic: true
    analytic_conductor: 7.415079810829127
    analytic_normalization: 0
    bad_lfactors:
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      - - 1
    - - 23
      - - 1
    bad_primes:
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    central_character: '69.2'
    coeff_info:
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    - 0.959492973614497 + 0.281732556841430*I
    - \\zeta_{22}
    conductor: 69
    conductor_radical: 69
    conjugate: dirichlet_L_69.35
    degree: 1
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    euler_factors:
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    - - 0
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      - a^13
    - - 1
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      - a^10
    - - 1
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      - a^5
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    - - 1
      - a^12
    - - 1
      - a^4
    - - 1
      - a^15
    - - 1
      - a^8
    - - 1
      - a^6
    - - 1
      - a^9
    - - 1
      - a^21
    - - 1
      - a^2
    - - 1
      - a^9
    gamma_factors:
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    - []
    id: 873
    index: 0
    label: 1-69-69.2-r1-0-0
    leading_term: 0.304517217690840598210182687748+0.204527266432591236467811980562*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/69/2
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-69-69.2-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 7.415079810829127
    root_angle: 0.3765228911482685
    root_number: 0.378258949294250814005877835767+0.925699825688008537834359561624*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.188261445574'
      prec: 47
    spectral_label: r1-0
    st_group: mu(22)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.546492849959045707274308234439-0.173864089069625766102195820041*I
    z1:
      __RealLiteral__: 0
      data: '1.56636609866'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '3.67657999812'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '4.6254202035'
      prec: 40
- - algebraic: true
    analytic_conductor: 7.415079810829127
    bad_primes:
    - 3
    - 23
    central_character: '69.2'
    conductor: 69
    conductor_radical: 69
    degree: 1
    id: 873
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/69/2
    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: 1-69-69.2-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: 1-69-69.2-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 7.415079810829127
    root_angle: 0.18826144557413424
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '1.56636609866'
      prec: 44
- - Lhash: dirichlet_L_69.2
    Lhash_array:
    - dirichlet_L_69.2
    id: 1782285
    label: 1-69-69.2-r1-0-0
    type: DIR
    url: Character/Dirichlet/69/2
label_cols:
- label
- label
- label
labels:
- 1-69-69.2-r1-0-0
- 1-69-69.2-r1-0-0
- 1-69-69.2-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T22:53:27.315528'