data:
- - Lhash: dirichlet_L_23.12
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    algebraic: true
    analytic_conductor: 0.10681155095483924
    analytic_normalization: 0
    bad_lfactors:
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      - - 1
    bad_primes:
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    central_character: '23.12'
    coeff_info:
    - x^11 - 1
    - 0.841253532831181 + 0.540640817455598*I
    - \\zeta_{11}
    conductor: 23
    conductor_radical: 23
    conjugate: dirichlet_L_23.2
    degree: 1
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    euler_factors:
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      - a^1
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    - - 1
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    gamma_factors:
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    - []
    id: 87
    index: 0
    label: 1-23-23.12-r0-0-0
    leading_term: 0.498433456503090591958510715786-0.449877653406267566590145754166*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/23/12
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-23-23.12-r0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.10681155095483924
    root_angle: -0.4674319820573594
    root_number: 0.102137025295887673968089863113-0.994770339356631200419579148800*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.233715991029'
      prec: 50
    spectral_label: r0-0
    st_group: mu(11)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.765628629796300101380720315052-0.471976532774942477113278313331*I
    z1:
      __RealLiteral__: 0
      data: '1.96977154105'
      prec: 44
    z2:
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      data: '4.88022173549'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '6.09438811947'
      prec: 44
- - algebraic: true
    analytic_conductor: 0.10681155095483924
    bad_primes:
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    central_character: '23.12'
    conductor: 23
    conductor_radical: 23
    degree: 1
    id: 87
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/23/12
    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: 1-23-23.12-r0-0-0
    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
    prelabel: 1-23-23.12-r0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.10681155095483924
    root_angle: -0.2337159910286797
    self_dual: false
    spectral_label: r0-0
    z1:
      __RealLiteral__: 0
      data: '1.96977154105'
      prec: 44
- - Lhash: dirichlet_L_23.12
    Lhash_array:
    - dirichlet_L_23.12
    id: 1781510
    label: 1-23-23.12-r0-0-0
    type: DIR
    url: Character/Dirichlet/23/12
label_cols:
- label
- label
- label
labels:
- 1-23-23.12-r0-0-0
- 1-23-23.12-r0-0-0
- 1-23-23.12-r0-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T12:03:57.062542'