data:
- - Lhash: dirichlet_L_29.14
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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: '29.14'
    coeff_info:
    - x^28 - 1
    - 0.974927912181824 + 0.222520933956314*I
    - \\zeta_{28}
    conductor: 29
    conductor_radical: 29
    conjugate: dirichlet_L_29.27
    degree: 1
    dirichlet_coefficients:
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    euler_factors:
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    - - 1
      - a^9
    - - 1
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    - - 1
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    - - 1
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    - - 0
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      - a^13
    - - 1
      - a^11
    - - 1
      - a^7
    - - 1
      - a^1
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      - a^3
    - - 1
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      - a^0
    - - 1
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    - - 1
      - a^18
    - - 1
      - a^10
    - - 1
      - a^15
    - - 1
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    - - 1
      - a^12
    - - 1
      - a^13
    - - 1
      - a^19
    - - 1
      - a^1
    gamma_factors:
    - - 1
    - []
    id: 145
    index: 0
    label: 1-29-29.14-r1-0-0
    leading_term: -0.0389302290779572012440857398327+0.294536156176745767418887451716*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/29/14
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-29-29.14-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.116482819044126
    root_angle: -0.9163399061636572
    root_number: -0.965659627113145848185261695496-0.259810478163795610756722720389*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.458169953082'
      prec: 50
    spectral_label: r1-0
    st_group: mu(28)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.374725061631104012637608749045+0.251130908703851519224015733975*I
    z1:
      __RealLiteral__: 0
      data: '3.11052327319'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '5.81118686132'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '7.23613516405'
      prec: 44
- - algebraic: true
    analytic_conductor: 3.116482819044126
    bad_primes:
    - 29
    central_character: '29.14'
    conductor: 29
    conductor_radical: 29
    degree: 1
    id: 145
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/29/14
    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: 1-29-29.14-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: 1-29-29.14-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.116482819044126
    root_angle: -0.4581699530818286
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '3.11052327319'
      prec: 44
- - Lhash: dirichlet_L_29.14
    Lhash_array:
    - dirichlet_L_29.14
    id: 1781568
    label: 1-29-29.14-r1-0-0
    type: DIR
    url: Character/Dirichlet/29/14
label_cols:
- label
- label
- label
labels:
- 1-29-29.14-r1-0-0
- 1-29-29.14-r1-0-0
- 1-29-29.14-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T07:46:45.589458'