data:
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    - \\zeta_{30}
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    conjugate: dirichlet_L_1287.1219
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    - []
    id: 305844
    index: 0
    label: 1-1287-1287.511-r0-0-0
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    load_key: dirichlet
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      data: '0.0'
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    origin: Character/Dirichlet/1287/511
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    - '197.4214633697770662669175781539'
    - '198.121264009746454511304111212707'
    - '198.76272377651863936762575222382'
    - '199.235700525638684897020821526330'
    - '199.53802785911254012603470862914'
    prelabel: 1-1287-1287.511-r0-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.9768028729947
    root_angle: 0.8339606073687915
    root_number: -0.867009041327832866240456276716+0.498292406379820523306774454567*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.416980303684'
      prec: 47
    spectral_label: r0-0
    st_group: mu(30)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.669600095286657912070964497929+0.605455289671636864661185817654*I
    z1:
      __RealLiteral__: 0
      data: '1.00775789456'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '2.92658581216'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '3.37743850655'
      prec: 44
- - algebraic: true
    analytic_conductor: 5.9768028729947
    bad_primes:
    - 3
    - 11
    - 13
    central_character: '1287.511'
    conductor: 1287
    conductor_radical: 429
    degree: 1
    id: 305844
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/1287/511
    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: 1-1287-1287.511-r0-0-0
    motivic_weight: 0
    mu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    mu_real:
    - 0
    nu_imag: []
    nu_real_doubled: []
    order_of_vanishing: 0
    prelabel: 1-1287-1287.511-r0-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.9768028729947
    root_angle: 0.41698030368439576
    self_dual: false
    spectral_label: r0-0
    z1:
      __RealLiteral__: 0
      data: '1.00775789456'
      prec: 44
- - Lhash: dirichlet_L_1287.511
    Lhash_array:
    - dirichlet_L_1287.511
    id: 2026641
    label: 1-1287-1287.511-r0-0-0
    type: DIR
    url: Character/Dirichlet/1287/511
label_cols:
- label
- label
- label
labels:
- 1-1287-1287.511-r0-0-0
- 1-1287-1287.511-r0-0-0
- 1-1287-1287.511-r0-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T15:42:14.904050'