data:
- - Lhash: dirichlet_L_55.3
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    analytic_normalization: 0
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    central_character: '55.3'
    coeff_info:
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    - \\zeta_{20}
    conductor: 55
    conductor_radical: 55
    conjugate: dirichlet_L_55.37
    degree: 1
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      - a^10
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      - a^11
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    gamma_factors:
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    - []
    id: 558
    index: 0
    label: 1-55-55.3-r1-0-0
    leading_term: 0.748461625303207513330601337603+0.0190787689275366504255334168807*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/55/3
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-55-55.3-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.910570863704376
    root_angle: 0.016224334620873183
    root_number: 0.998701297986191754128251232807+0.0509481834876948498084842050941*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.00811216731044'
      prec: 54
    spectral_label: r1-0
    st_group: mu(20)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.616382733105427614656789817644-0.0890514384640482648893972059921*I
    z1:
      __RealLiteral__: 0
      data: '1.19781457554'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '2.93722983948'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '5.77085977827'
      prec: 44
- - algebraic: true
    analytic_conductor: 5.910570863704376
    bad_primes:
    - 5
    - 11
    central_character: '55.3'
    conductor: 55
    conductor_radical: 55
    degree: 1
    id: 558
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/55/3
    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: 1-55-55.3-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: 1-55-55.3-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 5.910570863704376
    root_angle: 0.008112167310436591
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '1.19781457554'
      prec: 44
- - Lhash: dirichlet_L_55.3
    Lhash_array:
    - dirichlet_L_55.3
    id: 1781964
    label: 1-55-55.3-r1-0-0
    type: DIR
    url: Character/Dirichlet/55/3
label_cols:
- label
- label
- label
labels:
- 1-55-55.3-r1-0-0
- 1-55-55.3-r1-0-0
- 1-55-55.3-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-21T08:04:24.073833'