data:
- - Lhash: dirichlet_L_41.7
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    a9:
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    algebraic: true
    analytic_conductor: 4.406061916579626
    analytic_normalization: 0
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    bad_primes:
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    central_character: '41.7'
    coeff_info:
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    - \\zeta_{40}
    conductor: 41
    conductor_radical: 41
    conjugate: dirichlet_L_41.6
    degree: 1
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    euler_factors:
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      - a^1
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    gamma_factors:
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    - []
    id: 321
    index: 0
    label: 1-41-41.7-r1-0-0
    leading_term: 0.708271391157945722069475900638+0.368316600972914507732650080673*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/41/7
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-41-41.7-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.406061916579626
    root_angle: 0.30528241313780774
    root_number: 0.574279141273299967652557464676+0.818659555553101192535222546790*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.152641206569'
      prec: 47
    spectral_label: r1-0
    st_group: mu(40)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.649260490932499006252731143485+0.180036933200298001252504976839*I
    z1:
      __RealLiteral__: 0
      data: '1.24944840552'
      prec: 44
    z2:
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      data: '4.66650029732'
      prec: 44
    z3:
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      data: '6.35801007816'
      prec: 44
- - algebraic: true
    analytic_conductor: 4.406061916579626
    bad_primes:
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    central_character: '41.7'
    conductor: 41
    conductor_radical: 41
    degree: 1
    id: 321
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/41/7
    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: 1-41-41.7-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: 1-41-41.7-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 4.406061916579626
    root_angle: 0.15264120656890387
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '1.24944840552'
      prec: 44
- - Lhash: dirichlet_L_41.7
    Lhash_array:
    - dirichlet_L_41.7
    id: 1781705
    label: 1-41-41.7-r1-0-0
    type: DIR
    url: Character/Dirichlet/41/7
label_cols:
- label
- label
- label
labels:
- 1-41-41.7-r1-0-0
- 1-41-41.7-r1-0-0
- 1-41-41.7-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-22T14:50:30.568041'