data:
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    gal_is_solvable: true
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    grd: 30.645530678223075
    id: 19811856
    inessentialp:
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    is_galois: true
    is_minimal_sibling: true
    iso_number: 1
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    - 7.8.4.1
    monogenic: -1
    num_ram: 4
    r2: 16
    ramps:
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    rd: 30.6455306782
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    torsion_gen: \( \frac{1}{48950} a^{31} - \frac{7193}{48950} a \)
    torsion_order: 60
    used_grh: true
    zk:
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    - a^4
    - a^5
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    - 1/4*a^18 + 1/4*a^16 - 1/4*a^12 - 1/4*a^10 - 1/4*a^8 + 1/4*a^4 + 1/4*a^2
    - 1/8*a^19 + 1/8*a^17 - 1/8*a^13 - 1/8*a^11 - 1/8*a^9 + 1/8*a^5 + 1/8*a^3
    - 1/176*a^20 - 1/16*a^18 + 1/4*a^16 + 5/16*a^14 - 7/16*a^12 + 43/176*a^10 - 1/4*a^8
      - 5/16*a^6 + 7/16*a^4 + 1/4*a^2 - 2/11
    - 1/352*a^21 - 1/32*a^19 + 1/8*a^17 - 11/32*a^15 + 9/32*a^13 - 133/352*a^11 -
      1/8*a^9 + 11/32*a^7 - 9/32*a^5 + 1/8*a^3 + 9/22*a
    - 1/704*a^22 + 1/704*a^20 - 1/8*a^18 + 5/64*a^16 + 5/64*a^14 + 351/704*a^12 -
      29/88*a^10 + 27/64*a^8 + 27/64*a^6 - 1/8*a^4 + 5/11*a^2 + 5/11
    - 1/1408*a^23 + 1/1408*a^21 - 1/16*a^19 + 5/128*a^17 - 59/128*a^15 + 351/1408*a^13
      - 29/176*a^11 + 27/128*a^9 - 37/128*a^7 + 7/16*a^5 - 3/11*a^3 + 5/22*a
    - 1/14080*a^24 + 1/2816*a^22 - 1/704*a^20 - 27/1280*a^18 - 123/256*a^16 - 1153/2816*a^14
      - 59/3520*a^12 + 565/2816*a^10 + 27/256*a^8 - 7/320*a^6 - 31/88*a^4 - 3/22*a^2
      - 14/55
    - 1/28160*a^25 + 1/5632*a^23 - 1/1408*a^21 - 27/2560*a^19 - 123/512*a^17 - 1153/5632*a^15
      - 59/7040*a^13 + 565/5632*a^11 + 27/512*a^9 - 7/640*a^7 + 57/176*a^5 - 3/44*a^3
      - 7/55*a
    - 1/25062400*a^26 + 193/25062400*a^24 - 237/626560*a^22 + 27463/25062400*a^20
      + 48389/2278400*a^18 + 1266179/5012480*a^16 + 767593/3132800*a^14 - 1794663/25062400*a^12
      - 1911467/5012480*a^10 + 141669/284800*a^8 + 411321/1566400*a^6 - 20597/78320*a^4
      - 8869/97900*a^2 + 11667/24475
    - 1/50124800*a^27 + 193/50124800*a^25 - 237/1253120*a^23 + 27463/50124800*a^21
      + 48389/4556800*a^19 + 1266179/10024960*a^17 + 767593/6265600*a^15 - 1794663/50124800*a^13
      - 1911467/10024960*a^11 + 141669/569600*a^9 + 411321/3132800*a^7 - 20597/156640*a^5
      - 8869/195800*a^3 + 11667/48950*a
    - 1/100249600*a^28 + 1/100249600*a^26 + 413/12531200*a^24 - 39177/100249600*a^22
      + 100983/100249600*a^20 - 10419553/100249600*a^18 - 13933/140800*a^16 + 5837289/100249600*a^14
      + 12111721/100249600*a^12 + 2466949/12531200*a^10 - 628117/1566400*a^8 + 741977/1566400*a^6
      - 143039/391600*a^4 + 19079/97900*a^2 - 651/24475
    - 1/200499200*a^29 + 1/200499200*a^27 + 413/25062400*a^25 - 39177/200499200*a^23
      + 100983/200499200*a^21 - 10419553/200499200*a^19 - 13933/281600*a^17 - 94412311/200499200*a^15
      - 88137879/200499200*a^13 + 2466949/25062400*a^11 - 628117/3132800*a^9 - 824423/3132800*a^7
      + 248561/783200*a^5 - 78821/195800*a^3 - 651/48950*a
    - 1/400998400*a^30 + 1/400998400*a^28 - 1/50124800*a^26 + 5127/400998400*a^24
      + 170743/400998400*a^22 + 581391/400998400*a^20 + 3644777/50124800*a^18 - 128966951/400998400*a^16
      - 162762007/400998400*a^14 + 9092791/50124800*a^12 + 9525477/25062400*a^10 -
      1900949/6265600*a^8 + 655029/1566400*a^6 + 55237/195800*a^4 - 6217/24475*a^2
      + 11961/24475
    - 1/801996800*a^31 + 1/801996800*a^29 - 1/100249600*a^27 + 5127/801996800*a^25
      + 170743/801996800*a^23 + 581391/801996800*a^21 + 3644777/100249600*a^19 - 128966951/801996800*a^17
      - 162762007/801996800*a^15 - 41032009/100249600*a^13 + 9525477/50124800*a^11
      - 1900949/12531200*a^9 - 911371/3132800*a^7 - 140563/391600*a^5 + 9129/24475*a^3
      + 11961/48950*a
label_cols:
- label
labels:
- 32.0.366225584701948244050176000000000000000000000000.1
tables:
- nf_fields
timestamp: '2024-05-17T08:24:02.843505'