data:
- - class_group: []
    class_number: 1
    cm: false
    coeffs:
    - -9
    - 36
    - -12
    - 15
    - -14
    - 0
    - 2
    - -3
    - 1
    conductor: 0
    degree: 8
    dirichlet_group: []
    disc_abs: 4709390625
    disc_rad: 915
    disc_sign: 1
    frobs:
    - - 2
      - - - 4
          - 2
    - - 3
      - - 0
    - - 5
      - - 0
    - - 7
      - - - 4
          - 2
    - - 11
      - - - 4
          - 2
    - - 13
      - - - 4
          - 2
    - - 17
      - - - 4
          - 2
    - - 19
      - - - 2
          - 4
    - - 23
      - - - 4
          - 2
    - - 29
      - - - 2
          - 2
        - - 1
          - 4
    - - 31
      - - - 2
          - 2
        - - 1
          - 4
    - - 37
      - - - 4
          - 2
    - - 41
      - - - 2
          - 4
    - - 43
      - - - 4
          - 2
    - - 47
      - - - 4
          - 2
    - - 53
      - - - 4
          - 2
    - - 59
      - - - 2
          - 2
        - - 1
          - 4
    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: true
    galois_disc_exponents:
    - 16
    - 24
    - 16
    galois_label: 8T20
    galt: 20
    grd: 45.23275582376457
    id: 12723920
    index: 1
    inessentialp: []
    is_galois: false
    is_minimal_sibling: false
    iso_number: 2
    label: 8.4.4709390625.2
    local_algs:
    - 3.4.2.2
    - 3.4.2.2
    - 5.4.3.1
    - 5.4.3.1
    - 61.1.0.1
    - 61.1.0.1
    - 61.2.1.1
    - 61.2.1.2
    - 61.2.0.1
    minimal_sibling:
    - 5
    - 10
    - 50
    - 10
    - -1
    - 4
    - -5
    - -1
    - 1
    monogenic: 0
    num_ram: 3
    r2: 2
    ramps:
    - 3
    - 5
    - 61
    rd: 16.185293879
    regulator:
      __RealLiteral__: 0
      data: '84.8366562454'
      prec: 44
    res: {}
    subfield_mults:
    - 1
    - 1
    subfields:
    - -1.-1.1
    - 1.4.-4.-1.1
    torsion_gen: \( -1 \)
    torsion_order: 2
    units:
    - \( \frac{61}{1416} a^{7} - \frac{49}{354} a^{6} + \frac{49}{708} a^{5} + \frac{65}{708}
      a^{4} - \frac{233}{354} a^{3} + \frac{1427}{1416} a^{2} - \frac{81}{472} a +
      \frac{285}{472} \)
    - \( \frac{25}{472} a^{7} - \frac{19}{177} a^{6} - \frac{7}{236} a^{5} - \frac{11}{708}
      a^{4} - \frac{51}{118} a^{3} + \frac{265}{1416} a^{2} - \frac{235}{472} a +
      \frac{451}{472} \)
    - \( \frac{89}{1416} a^{7} - \frac{113}{708} a^{6} + \frac{43}{354} a^{5} - \frac{7}{177}
      a^{4} - \frac{677}{708} a^{3} + \frac{401}{1416} a^{2} - \frac{389}{472} a +
      \frac{263}{472} \)
    - \( \frac{29}{354} a^{7} - \frac{79}{708} a^{6} - \frac{49}{708} a^{5} - \frac{65}{708}
      a^{4} - \frac{773}{708} a^{3} - \frac{625}{708} a^{2} - \frac{130}{59} a + \frac{123}{236}
      \)
    - \( \frac{55}{1416} a^{7} - \frac{10}{177} a^{6} + \frac{79}{708} a^{5} - \frac{71}{708}
      a^{4} - \frac{65}{354} a^{3} + \frac{37}{1416} a^{2} - \frac{15}{472} a + \frac{79}{472}
      \)
    used_grh: false
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - a^4
    - 1/2*a^5 - 1/2*a^3 - 1/2*a - 1/2
    - 1/12*a^6 - 1/4*a^5 - 1/12*a^4 - 1/4*a^3 + 1/12*a^2 - 1/4
    - 1/1416*a^7 + 5/354*a^6 - 5/708*a^5 - 115/708*a^4 - 73/177*a^3 - 673/1416*a^2
      - 129/472*a - 123/472
label_cols:
- label
labels:
- 8.4.4709390625.2
tables:
- nf_fields
timestamp: '2024-05-22T01:34:07.566723'