data:
- - class_group: []
    class_number: 1
    cm: false
    coeffs:
    - 1
    - -3
    - 2
    - 2
    - -1
    - -2
    - -1
    - 2
    - 2
    - 0
    - 1
    - -2
    - -1
    - 1
    conductor: 0
    degree: 13
    dirichlet_group: []
    disc_abs: 4082190012125
    disc_rad: 163287600485
    disc_sign: 1
    frobs:
    - - 2
      - - - 7
          - 1
        - - 6
          - 1
    - - 3
      - - - 10
          - 1
        - - 3
          - 1
    - - 5
      - - 0
    - - 7
      - - - 13
          - 1
    - - 11
      - - - 8
          - 1
        - - 3
          - 1
        - - 2
          - 1
    - - 13
      - - - 7
          - 1
        - - 4
          - 1
        - - 2
          - 1
    - - 17
      - - - 11
          - 1
        - - 2
          - 1
    - - 19
      - - - 7
          - 1
        - - 4
          - 1
        - - 2
          - 1
    - - 23
      - - - 11
          - 1
        - - 2
          - 1
    - - 29
      - - - 7
          - 1
        - - 2
          - 3
    - - 31
      - - - 7
          - 1
        - - 2
          - 2
        - - 1
          - 2
    - - 37
      - - - 12
          - 1
        - - 1
          - 1
    - - 41
      - - - 12
          - 1
        - - 1
          - 1
    - - 43
      - - - 7
          - 1
        - - 6
          - 1
    - - 47
      - - - 5
          - 1
        - - 4
          - 1
        - - 2
          - 2
    - - 53
      - - - 9
          - 1
        - - 4
          - 1
    - - 59
      - - - 8
          - 1
        - - 3
          - 1
        - - 2
          - 1
    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: false
    galois_disc_exponents:
    - 4670265600
    - 3113510400
    - 3113510400
    galois_label: 13T9
    galt: 9
    grd: 604253.4026112618
    id: 18579493
    index: 1
    inessentialp: []
    is_galois: false
    is_minimal_sibling: true
    iso_number: 1
    label: 13.1.4082190012125.1
    local_algs:
    - 5.3.0.1
    - 5.4.3.1
    - 5.6.0.1
    - 73.1.0.1
    - 73.2.1.2
    - 73.10.0.1
    - m447363289.1.1.0
    - m447363289.1.1.0
    - m447363289.1.2.0
    - m447363289.2.1.1
    - m447363289.1.3.0
    - m447363289.1.4.0
    monogenic: 0
    num_ram: 3
    r2: 6
    ramps:
    - 5
    - 73
    - 447363289
    rd: 9.33401960871
    regulator:
      __RealLiteral__: 0
      data: '6.75913142567'
      prec: 44
    res: {}
    subfield_mults: []
    subfields: []
    torsion_gen: \( -1 \)
    torsion_order: 2
    units:
    - \( a \)
    - \( \frac{250}{143} a^{12} - \frac{152}{143} a^{11} - \frac{547}{143} a^{10}
      + \frac{31}{143} a^{9} + \frac{3}{143} a^{8} + \frac{36}{11} a^{7} + \frac{656}{143}
      a^{6} - \frac{2}{143} a^{5} - \frac{431}{143} a^{4} - \frac{324}{143} a^{3}
      + \frac{381}{143} a^{2} + \frac{66}{13} a - \frac{486}{143} \)
    - \( \frac{259}{143} a^{12} + \frac{29}{143} a^{11} - \frac{589}{143} a^{10} -
      \frac{370}{143} a^{9} - \frac{248}{143} a^{8} + \frac{27}{11} a^{7} + \frac{1064}{143}
      a^{6} + \frac{785}{143} a^{5} + \frac{70}{143} a^{4} - \frac{529}{143} a^{3}
      - \frac{179}{143} a^{2} + \frac{43}{13} a - \frac{150}{143} \)
    - \( \frac{72}{143} a^{12} - \frac{125}{143} a^{11} - \frac{193}{143} a^{10} +
      \frac{224}{143} a^{9} + \frac{137}{143} a^{8} + \frac{16}{11} a^{7} + \frac{118}{143}
      a^{6} - \frac{425}{143} a^{5} - \frac{425}{143} a^{4} - \frac{67}{143} a^{3}
      + \frac{382}{143} a^{2} + \frac{24}{13} a - \frac{315}{143} \)
    - \( \frac{265}{143} a^{12} - \frac{184}{143} a^{11} - \frac{617}{143} a^{10}
      + \frac{30}{143} a^{9} + \frac{109}{143} a^{8} + \frac{54}{11} a^{7} + \frac{764}{143}
      a^{6} - \frac{25}{143} a^{5} - \frac{740}{143} a^{4} - \frac{761}{143} a^{3}
      + \frac{258}{143} a^{2} + \frac{58}{13} a - \frac{498}{143} \)
    - \( \frac{34}{11} a^{12} - \frac{8}{11} a^{11} - \frac{78}{11} a^{10} - \frac{25}{11}
      a^{9} - \frac{12}{11} a^{8} + \frac{64}{11} a^{7} + \frac{126}{11} a^{6} + \frac{52}{11}
      a^{5} - \frac{47}{11} a^{4} - \frac{79}{11} a^{3} + \frac{5}{11} a^{2} + 7 a
      - \frac{36}{11} \)
    used_grh: false
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - a^4
    - a^5
    - a^6
    - a^7
    - a^8
    - a^9
    - a^10
    - a^11
    - 1/143*a^12 + 36/143*a^11 + 43/143*a^10 + 19/143*a^9 - 12/143*a^8 - 1/11*a^7
      - 50/143*a^6 + 8/143*a^5 + 8/143*a^4 + 9/143*a^3 + 49/143*a^2 - 4/13*a - 58/143
label_cols:
- label
labels:
- 13.1.4082190012125.1
tables:
- nf_fields
timestamp: '2024-05-20T00:47:20.725668'