data:
- - Lhash: dirichlet_L_29.8
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    a9:
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    algebraic: true
    analytic_conductor: 3.116482819044126
    analytic_normalization: 0
    bad_lfactors:
    - - 29
      - - 1
    bad_primes:
    - 29
    central_character: '29.8'
    coeff_info:
    - x^28 - 1
    - 0.974927912181824 + 0.222520933956314*I
    - \\zeta_{28}
    conductor: 29
    conductor_radical: 29
    conjugate: dirichlet_L_29.11
    degree: 1
    dirichlet_coefficients:
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    euler_factors:
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    - - 1
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    - - 1
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    - - 1
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    - - 1
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    - - 1
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    - - 1
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    - - 0
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      - a^3
    - - 1
      - a^9
    - - 1
      - a^21
    - - 1
      - a^11
    - - 1
      - a^5
    - - 1
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    - - 1
      - a^0
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      - a^15
    - - 1
      - a^2
    - - 1
      - a^26
    - - 1
      - a^25
    - - 1
      - a^23
    - - 1
      - a^20
    - - 1
      - a^3
    - - 1
      - a^13
    - - 1
      - a^11
    gamma_factors:
    - - 1
    - []
    id: 166
    index: 0
    label: 1-29-29.8-r1-0-0
    leading_term: 0.526649435010190872399078460462+1.13919872914296743502539911550*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/29/8
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-29-29.8-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.116482819044126
    root_angle: 0.7243220873271536
    root_number: -0.647827120739686914880886418057+0.761787386108569739367629997180*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.362161043664'
      prec: 47
    spectral_label: r1-0
    st_group: mu(28)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.855897730770074483228686022507+0.658980095122537512842157508381*I
    z1:
      __RealLiteral__: 0
      data: '3.31077422201'
      prec: 44
    z2:
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      data: '5.43731734385'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '6.53395156253'
      prec: 44
- - algebraic: true
    analytic_conductor: 3.116482819044126
    bad_primes:
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    central_character: '29.8'
    conductor: 29
    conductor_radical: 29
    degree: 1
    id: 166
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/29/8
    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: 1-29-29.8-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: 1-29-29.8-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.116482819044126
    root_angle: 0.3621610436635768
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '3.31077422201'
      prec: 44
- - Lhash: dirichlet_L_29.8
    Lhash_array:
    - dirichlet_L_29.8
    id: 1781562
    label: 1-29-29.8-r1-0-0
    type: DIR
    url: Character/Dirichlet/29/8
label_cols:
- label
- label
- label
labels:
- 1-29-29.8-r1-0-0
- 1-29-29.8-r1-0-0
- 1-29-29.8-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-18T16:54:52.292456'