data:
- - Lhash: dirichlet_L_23.15
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    a9:
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    algebraic: true
    analytic_conductor: 2.4716932702763756
    analytic_normalization: 0
    bad_lfactors:
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      - - 1
    bad_primes:
    - 23
    central_character: '23.15'
    coeff_info:
    - x^22 - 1
    - 0.959492973614497 + 0.281732556841430*I
    - \\zeta_{22}
    conductor: 23
    conductor_radical: 23
    conjugate: dirichlet_L_23.20
    degree: 1
    dirichlet_coefficients:
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    euler_factors:
    - - 1
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    - - 1
      - a^8
    - - 1
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    - - 1
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    - - 1
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    - - 0
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      - a^19
    - - 1
      - a^0
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    - - 1
      - a^3
    - - 1
      - a^1
    - - 1
      - a^12
    - - 1
      - a^2
    - - 1
      - a^7
    - - 1
      - a^5
    - - 1
      - a^19
    - - 1
      - a^17
    - - 1
      - a^16
    gamma_factors:
    - - 1
    - []
    id: 90
    index: 0
    label: 1-23-23.15-r1-0-0
    leading_term: 0.409090220635924711932539081410-0.414735829019441764970961119709*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/23/15
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-23-23.15-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.4716932702763756
    root_angle: -0.49563736827156174
    root_number: 0.0137051827067220266461431800331-0.999906079572964376474736542022*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.252181315864'
      prec: 50
    spectral_label: r1-0
    st_group: mu(22)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.544121945967641946035049624686-0.179460633784732664362312693987*I
    z1:
      __RealLiteral__: 0
      data: '0.689271678051'
      prec: 47
    z2:
      __RealLiteral__: 0
      data: '4.01800461035'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '6.35513516932'
      prec: 44
- - algebraic: true
    analytic_conductor: 2.4716932702763756
    bad_primes:
    - 23
    central_character: '23.15'
    conductor: 23
    conductor_radical: 23
    degree: 1
    id: 90
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/23/15
    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: 1-23-23.15-r1-0-0
    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: 1-23-23.15-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 2.4716932702763756
    root_angle: -0.24781868413578087
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '0.689271678051'
      prec: 47
- - Lhash: dirichlet_L_23.15
    Lhash_array:
    - dirichlet_L_23.15
    id: 1781513
    label: 1-23-23.15-r1-0-0
    type: DIR
    url: Character/Dirichlet/23/15
label_cols:
- label
- label
- label
labels:
- 1-23-23.15-r1-0-0
- 1-23-23.15-r1-0-0
- 1-23-23.15-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T10:26:27.738627'