data:
- - Lhash: dirichlet_L_29.10
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    a2:
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    a8:
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    a9:
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    - 0.9749279121818236
    algebraic: true
    analytic_conductor: 3.116482819044126
    analytic_normalization: 0
    bad_lfactors:
    - - 29
      - - 1
    bad_primes:
    - 29
    central_character: '29.10'
    coeff_info:
    - x^28 - 1
    - 0.974927912181824 + 0.222520933956314*I
    - \\zeta_{28}
    conductor: 29
    conductor_radical: 29
    conjugate: dirichlet_L_29.3
    degree: 1
    dirichlet_coefficients:
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    euler_factors:
    - - 1
      - a^23
    - - 1
      - a^3
    - - 1
      - a^2
    - - 1
      - a^24
    - - 1
      - a^15
    - - 1
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    - - 1
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    - - 1
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    - - 1
      - a^12
    - - 0
    - - 1
      - a^23
    - - 1
      - a^13
    - - 1
      - a^21
    - - 1
      - a^19
    - - 1
      - a^1
    - - 1
      - a^16
    - - 1
      - a^0
    - - 1
      - a^3
    - - 1
      - a^6
    - - 1
      - a^22
    - - 1
      - a^5
    - - 1
      - a^27
    - - 1
      - a^4
    - - 1
      - a^23
    - - 1
      - a^25
    - - 1
      - a^19
    gamma_factors:
    - - 1
    - []
    id: 141
    index: 0
    label: 1-29-29.10-r1-0-0
    leading_term: 2.01952654170705272062095207747-0.821982719239893555334933002588*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/29/10
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
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    prelabel: 1-29-29.10-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.116482819044126
    root_angle: -0.24607983512881315
    root_number: 0.715761354017874579398809876971-0.698344960670941490895969728303*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.123039917564'
      prec: 50
    spectral_label: r1-0
    st_group: mu(28)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 1.60777525031608803320412930048-0.505159415068798323150041752860*I
    z1:
      __RealLiteral__: 0
      data: '2.10538499408'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '3.75069900662'
      prec: 44
    z3:
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      data: '5.49032656138'
      prec: 44
- - algebraic: true
    analytic_conductor: 3.116482819044126
    bad_primes:
    - 29
    central_character: '29.10'
    conductor: 29
    conductor_radical: 29
    degree: 1
    id: 141
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/29/10
    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: 1-29-29.10-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: 1-29-29.10-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 3.116482819044126
    root_angle: -0.12303991756440658
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '2.10538499408'
      prec: 44
- - Lhash: dirichlet_L_29.10
    Lhash_array:
    - dirichlet_L_29.10
    id: 1781564
    label: 1-29-29.10-r1-0-0
    type: DIR
    url: Character/Dirichlet/29/10
label_cols:
- label
- label
- label
labels:
- 1-29-29.10-r1-0-0
- 1-29-29.10-r1-0-0
- 1-29-29.10-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-16T15:40:53.114553'