data:
- - class_group: []
    class_number: 1
    cm: false
    coeffs:
    - -96360
    - -74536
    - 0
    - 6776
    - 0
    - -154
    - 0
    - 1
    conductor: 0
    degree: 7
    dirichlet_group: []
    disc_abs: 32027016613996096
    disc_rad: 154
    disc_sign: 1
    frobs:
    - - 2
      - - 0
    - - 3
      - - - 3
          - 2
        - - 1
          - 1
    - - 5
      - - - 3
          - 2
        - - 1
          - 1
    - - 7
      - - 0
    - - 11
      - - 0
    - - 13
      - - - 7
          - 1
    - - 17
      - - - 3
          - 2
        - - 1
          - 1
    - - 19
      - - - 3
          - 2
        - - 1
          - 1
    - - 23
      - - - 3
          - 2
        - - 1
          - 1
    - - 29
      - - - 7
          - 1
    - - 31
      - - - 3
          - 2
        - - 1
          - 1
    - - 37
      - - - 3
          - 2
        - - 1
          - 1
    - - 41
      - - - 7
          - 1
    - - 43
      - - - 7
          - 1
    - - 47
      - - - 3
          - 2
        - - 1
          - 1
    - - 53
      - - - 3
          - 2
        - - 1
          - 1
    - - 59
      - - - 3
          - 2
        - - 1
          - 1
    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: true
    galois_disc_exponents:
    - 18
    - 32
    - 18
    galois_label: 7T3
    galt: 3
    grd: 274.42043856096353
    id: 12306597
    index: 1
    inessentialp: []
    is_galois: false
    is_minimal_sibling: true
    iso_number: 4
    label: 7.7.32027016613996096.4
    local_algs:
    - 2.7.6.1
    - 7.7.10.3
    - 11.7.6.1
    monogenic: 0
    num_ram: 3
    r2: 0
    ramps:
    - 2
    - 7
    - 11
    rd: 227.997941756
    regulator:
      __RealLiteral__: 0
      data: '2396810.65353'
      prec: 44
    res:
      gal:
      - 805565125,-121575388550,-359725843575,-104842778481,339974339453,184714810784,-113898240232,-81302376703,15925250054,16279999729,-737532649,-1718052693,-31781988,100699536,4224345,-3286052,-136780,56987,1638,-441,-7,1
    subfield_mults: []
    subfields: []
    torsion_gen: \( -1 \)
    torsion_order: 2
    units:
    - \( \frac{1}{452} a^{6} - \frac{11}{452} a^{5} - \frac{37}{226} a^{4} + \frac{253}{113}
      a^{3} + \frac{115}{113} a^{2} - \frac{3201}{113} a - \frac{4463}{113} \)
    - \( \frac{1}{226} a^{6} + \frac{11}{452} a^{5} - \frac{1}{2} a^{4} - \frac{627}{226}
      a^{3} + \frac{1153}{113} a^{2} + \frac{6512}{113} a + \frac{6751}{113} \)
    - \( \frac{12}{113} a^{6} - \frac{41}{226} a^{5} - \frac{3619}{226} a^{4} + \frac{3093}{113}
      a^{3} + \frac{75600}{113} a^{2} - \frac{129842}{113} a - \frac{661823}{113}
      \)
    - \( \frac{1}{226} a^{6} - \frac{13}{226} a^{5} - \frac{145}{226} a^{4} + \frac{1451}{226}
      a^{3} + \frac{3546}{113} a^{2} - \frac{17744}{113} a - \frac{51851}{113} \)
    - \( \frac{139}{226} a^{6} - \frac{2393}{452} a^{5} - \frac{11119}{226} a^{4}
      + \frac{47869}{113} a^{3} + \frac{59302}{113} a^{2} - \frac{511740}{113} a -
      \frac{777851}{113} \)
    - \( \frac{53}{452} a^{6} + \frac{122}{113} a^{5} - \frac{907}{113} a^{4} - \frac{16009}{226}
      a^{3} + \frac{14776}{113} a^{2} + \frac{112821}{113} a + \frac{119287}{113}
      \)
    used_grh: false
    zk:
    - '1'
    - a
    - a^2
    - 1/2*a^3
    - 1/226*a^4 - 19/226*a^3 - 44/113*a^2 - 51/113*a + 32/113
    - 1/452*a^5 - 55/226*a^3 - 48/113*a^2 + 40/113*a - 35/113
    - 1/452*a^6 - 11/226*a^3 - 7/113*a^2 - 15/113*a - 48/113
label_cols:
- label
labels:
- 7.7.32027016613996096.4
tables:
- nf_fields
timestamp: '2024-05-17T19:24:34.975384'