data:
- - class_group: []
    class_number: 1
    cm: false
    coeffs:
    - -1
    - 1
    - 1
    - 4
    - 3
    - -22
    - -31
    - -69
    - -42
    - 72
    - 160
    - 277
    - 152
    - 27
    - 37
    - -18
    - -35
    - 3
    - -13
    - 1
    - 2
    - -1
    - 1
    conductor: 0
    degree: 22
    dirichlet_group: []
    disc_abs: 1734677982017693835986328125
    disc_rad: 29801931595
    disc_sign: 1
    frobs:
    - - 2
      - - - 22
          - 1
    - - 3
      - - - 6
          - 1
        - - 4
          - 4
    - - 5
      - - 0
    - - 7
      - - - 22
          - 1
    - - 11
      - - - 5
          - 2
        - - 4
          - 2
        - - 2
          - 2
    - - 13
      - - - 10
          - 1
        - - 4
          - 2
        - - 2
          - 2
    - - 17
      - - - 22
          - 1
    - - 19
      - - - 6
          - 2
        - - 3
          - 2
        - - 2
          - 2
    - - 23
      - - - 18
          - 1
        - - 2
          - 2
    - - 29
      - - - 8
          - 2
        - - 3
          - 2
    - - 31
      - - - 5
          - 2
        - - 2
          - 4
        - - 1
          - 4
    - - 37
      - - - 10
          - 2
        - - 2
          - 1
    - - 41
      - - - 7
          - 2
        - - 2
          - 2
        - - 1
          - 4
    - - 43
      - - - 10
          - 1
        - - 4
          - 2
        - - 2
          - 2
    - - 47
      - - - 8
          - 2
        - - 6
          - 1
    - - 53
      - - - 6
          - 1
        - - 4
          - 2
        - - 2
          - 4
    - - 59
      - - - 11
          - 2
    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: false
    galois_disc_exponents:
    - 39916800
    - 39916800
    - 39916800
    galois_label: 22T47
    galt: 47
    grd: 172632.35964036407
    id: 18685211
    index: 1
    inessentialp: []
    is_galois: false
    is_minimal_sibling: true
    iso_number: 1
    label: 22.2.1734677982017693835986328125.1
    local_algs:
    - 5.6.3.1
    - 5.6.3.1
    - 5.10.5.1
    - m64661.1.1.0
    - m64661.1.1.0
    - m64661.2.1.1
    - m64661.2.1.1
    - m64661.1.3.0
    - m64661.1.3.0
    - m64661.1.5.0
    - m64661.1.5.0
    - m92179.1.2.0
    - m92179.1.2.0
    - m92179.2.1.1
    - m92179.2.1.1
    - m92179.1.3.0
    - m92179.1.3.0
    - m92179.1.4.0
    - m92179.1.4.0
    monogenic: 0
    num_ram: 3
    r2: 10
    ramps:
    - 5
    - 64661
    - 92179
    rd: 17.3039922569
    regulator:
      __RealLiteral__: 0
      data: '38336.3977164'
      prec: 44
    res: {}
    subfield_mults:
    - 1
    - 1
    subfields:
    - -1.-1.1
    - 1.1.0.1.0.-2.1.-2.0.1.-1.1
    torsion_gen: \( -1 \)
    torsion_order: 2
    units:
    - \( \frac{1319022478040683642982}{2124470127291230454011} a^{21} - \frac{1325922995996056467671}{2124470127291230454011}
      a^{20} + \frac{2652047385221629833259}{2124470127291230454011} a^{19} + \frac{1292058929397354233009}{2124470127291230454011}
      a^{18} - \frac{17130376483276901687603}{2124470127291230454011} a^{17} + \frac{4037675940370171213396}{2124470127291230454011}
      a^{16} - \frac{46280504820437703927299}{2124470127291230454011} a^{15} - \frac{23384161891799832446334}{2124470127291230454011}
      a^{14} + \frac{48581578073897362896363}{2124470127291230454011} a^{13} + \frac{35508488314265843606893}{2124470127291230454011}
      a^{12} + \frac{200540345839019747265131}{2124470127291230454011} a^{11} + \frac{364155555594847000728253}{2124470127291230454011}
      a^{10} + \frac{210465914935697729300935}{2124470127291230454011} a^{9} + \frac{94500173833171103190729}{2124470127291230454011}
      a^{8} - \frac{55404230787474271197172}{2124470127291230454011} a^{7} - \frac{90668614382664561663278}{2124470127291230454011}
      a^{6} - \frac{40810153084951647132822}{2124470127291230454011} a^{5} - \frac{28880338799121752524606}{2124470127291230454011}
      a^{4} + \frac{3955041368111844547441}{2124470127291230454011} a^{3} + \frac{5252693900872203007746}{2124470127291230454011}
      a^{2} + \frac{1320303940024606374495}{2124470127291230454011} a + \frac{1308452621036902141662}{2124470127291230454011}
      \)
    - \( \frac{1404952042808792592373}{2124470127291230454011} a^{21} - \frac{1539295187955586333537}{2124470127291230454011}
      a^{20} + \frac{3072852595373433791970}{2124470127291230454011} a^{19} + \frac{835470967692813115529}{2124470127291230454011}
      a^{18} - \frac{17682621936592516362068}{2124470127291230454011} a^{17} + \frac{5306443693460489731229}{2124470127291230454011}
      a^{16} - \frac{50657216370791427890539}{2124470127291230454011} a^{15} - \frac{18059436655949234291290}{2124470127291230454011}
      a^{14} + \frac{45676774574990619291064}{2124470127291230454011} a^{13} + \frac{39369536258390928649747}{2124470127291230454011}
      a^{12} + \frac{206939790469948962811942}{2124470127291230454011} a^{11} + \frac{366632681089743028175489}{2124470127291230454011}
      a^{10} + \frac{213634709553345051600595}{2124470127291230454011} a^{9} + \frac{92766896350353321854776}{2124470127291230454011}
      a^{8} - \frac{56532086841871221755661}{2124470127291230454011} a^{7} - \frac{53290608118191739398702}{2124470127291230454011}
      a^{6} - \frac{41450817576264262630545}{2124470127291230454011} a^{5} - \frac{28688088852517903535097}{2124470127291230454011}
      a^{4} - \frac{5040722386987313273835}{2124470127291230454011} a^{3} - \frac{240457511266378059401}{2124470127291230454011}
      a^{2} + \frac{1329859253909041738976}{2124470127291230454011} a - \frac{837093004323914861225}{2124470127291230454011}
      \)
    - \( \frac{184913429824504562502}{2124470127291230454011} a^{21} - \frac{504159685245124369910}{2124470127291230454011}
      a^{20} + \frac{1227835046108119220456}{2124470127291230454011} a^{19} - \frac{1049156368720175146708}{2124470127291230454011}
      a^{18} - \frac{1526847084615964895407}{2124470127291230454011} a^{17} + \frac{4988582964596681897237}{2124470127291230454011}
      a^{16} - \frac{14167578829242720491238}{2124470127291230454011} a^{15} + \frac{9908608447225932201480}{2124470127291230454011}
      a^{14} - \frac{6965919056004613308025}{2124470127291230454011} a^{13} - \frac{13395850769565948482753}{2124470127291230454011}
      a^{12} + \frac{36522981874058386669574}{2124470127291230454011} a^{11} + \frac{18129665589716112613192}{2124470127291230454011}
      a^{10} + \frac{20306709049340673383416}{2124470127291230454011} a^{9} + \frac{102330823965360791108813}{2124470127291230454011}
      a^{8} + \frac{50969443453239099493861}{2124470127291230454011} a^{7} + \frac{35912793546780108841488}{2124470127291230454011}
      a^{6} - \frac{5261848427816264772312}{2124470127291230454011} a^{5} - \frac{14574923145610764920017}{2124470127291230454011}
      a^{4} - \frac{8258159033992066783509}{2124470127291230454011} a^{3} - \frac{5596583620383925242932}{2124470127291230454011}
      a^{2} + \frac{410941856820802354531}{2124470127291230454011} a - \frac{218381158855023932264}{2124470127291230454011}
      \)
    - \( \frac{92420234753459114644}{2124470127291230454011} a^{21} - \frac{270875320539631000928}{2124470127291230454011}
      a^{20} + \frac{751438284908825192293}{2124470127291230454011} a^{19} - \frac{514419015973535734642}{2124470127291230454011}
      a^{18} - \frac{982350794127351898733}{2124470127291230454011} a^{17} + \frac{3606072319763246225917}{2124470127291230454011}
      a^{16} - \frac{9244096806646187606645}{2124470127291230454011} a^{15} + \frac{3866342681579134731604}{2124470127291230454011}
      a^{14} - \frac{3253793476482322421781}{2124470127291230454011} a^{13} - \frac{18006080625744830950755}{2124470127291230454011}
      a^{12} + \frac{29468449932001750556877}{2124470127291230454011} a^{11} + \frac{15328431442988074648934}{2124470127291230454011}
      a^{10} + \frac{16715498911673103671559}{2124470127291230454011} a^{9} + \frac{104396894975923125135191}{2124470127291230454011}
      a^{8} + \frac{52151104764508405223623}{2124470127291230454011} a^{7} - \frac{1340165496445641870588}{2124470127291230454011}
      a^{6} - \frac{4562118128219108086231}{2124470127291230454011} a^{5} - \frac{29363840758604190622945}{2124470127291230454011}
      a^{4} - \frac{8252291806531606901792}{2124470127291230454011} a^{3} - \frac{5680472615733522377461}{2124470127291230454011}
      a^{2} - \frac{3032491896163087753607}{2124470127291230454011} a + \frac{1928428800502009210731}{2124470127291230454011}
      \)
    - \( \frac{706246718126120449183}{2124470127291230454011} a^{21} + \frac{334522676793522858908}{2124470127291230454011}
      a^{20} - \frac{90633524298945381919}{2124470127291230454011} a^{19} + \frac{3180149374393455527845}{2124470127291230454011}
      a^{18} - \frac{8848483730119676924934}{2124470127291230454011} a^{17} - \frac{12098670670230874164594}{2124470127291230454011}
      a^{16} - \frac{15527342760285338628040}{2124470127291230454011} a^{15} - \frac{49192159896971707513582}{2124470127291230454011}
      a^{14} + \frac{21253371078586571348700}{2124470127291230454011} a^{13} + \frac{68016583604381853911654}{2124470127291230454011}
      a^{12} + \frac{115996090290882775427739}{2124470127291230454011} a^{11} + \frac{333039310430438395633710}{2124470127291230454011}
      a^{10} + \frac{337311988223237864418845}{2124470127291230454011} a^{9} + \frac{84792899126468029094434}{2124470127291230454011}
      a^{8} - \frac{28239941412869448878360}{2124470127291230454011} a^{7} - \frac{88539595600115574283395}{2124470127291230454011}
      a^{6} - \frac{53054140096566616368435}{2124470127291230454011} a^{5} - \frac{13744687577084257704878}{2124470127291230454011}
      a^{4} - \frac{7095870589367816938611}{2124470127291230454011} a^{3} + \frac{5753393069836283564213}{2124470127291230454011}
      a^{2} + \frac{3677699992869250915542}{2124470127291230454011} a - \frac{311082050067289069203}{2124470127291230454011}
      \)
    - \( \frac{6900517955372824689}{2124470127291230454011} a^{21} - \frac{14002429140262547295}{2124470127291230454011}
      a^{20} + \frac{26963548643329409973}{2124470127291230454011} a^{19} - \frac{16915731251985671163}{2124470127291230454011}
      a^{18} - \frac{80608506248120284450}{2124470127291230454011} a^{17} + \frac{114718089013776422929}{2124470127291230454011}
      a^{16} - \frac{358242712932473127342}{2124470127291230454011} a^{15} + \frac{222253613607931893971}{2124470127291230454011}
      a^{14} + \frac{105118592832614753621}{2124470127291230454011} a^{13} - \frac{48929176835833531867}{2124470127291230454011}
      a^{12} + \frac{1213670822422368377761}{2124470127291230454011} a^{11} + \frac{577681550811653576185}{2124470127291230454011}
      a^{10} + \frac{469444585758119103975}{2124470127291230454011} a^{9} + \frac{5286709765558191928}{2124470127291230454011}
      a^{8} - \frac{343936602142609702480}{2124470127291230454011} a^{7} - \frac{79543734309545799620}{2124470127291230454011}
      a^{6} - \frac{138155717773287620998}{2124470127291230454011} a^{5} + \frac{2026066010206381505}{2124470127291230454011}
      a^{4} + \frac{23396011290531564182}{2124470127291230454011} a^{3} - \frac{1281461983922731513}{2124470127291230454011}
      a^{2} + \frac{10569857003781501320}{2124470127291230454011} a - \frac{1319022478040683642982}{2124470127291230454011}
      \)
    - \( \frac{395820342383853045720}{2124470127291230454011} a^{21} - \frac{1076870803743560856133}{2124470127291230454011}
      a^{20} + \frac{1870267739245172447643}{2124470127291230454011} a^{19} - \frac{1247920169286856257985}{2124470127291230454011}
      a^{18} - \frac{5352944113336288915606}{2124470127291230454011} a^{17} + \frac{10943332764678446475350}{2124470127291230454011}
      a^{16} - \frac{21372105569965409220001}{2124470127291230454011} a^{15} + \frac{16183203419628512089437}{2124470127291230454011}
      a^{14} + \frac{16303334045089284928498}{2124470127291230454011} a^{13} - \frac{27341733941709337117296}{2124470127291230454011}
      a^{12} + \frac{60974520269366246883083}{2124470127291230454011} a^{11} + \frac{23928113286369485894007}{2124470127291230454011}
      a^{10} - \frac{73252974286546000315984}{2124470127291230454011} a^{9} + \frac{46128594535819930888224}{2124470127291230454011}
      a^{8} + \frac{3737497779247321151384}{2124470127291230454011} a^{7} - \frac{1600597903122996739025}{2124470127291230454011}
      a^{6} + \frac{20683042573640090461274}{2124470127291230454011} a^{5} - \frac{20605067031402103334853}{2124470127291230454011}
      a^{4} - \frac{1912974068653417886267}{2124470127291230454011} a^{3} - \frac{365995653934900456871}{2124470127291230454011}
      a^{2} - \frac{4755433058131368010742}{2124470127291230454011} a + \frac{1749035951948365159383}{2124470127291230454011}
      \)
    - \( \frac{545469740815559925419}{2124470127291230454011} a^{21} + \frac{795216122280172161262}{2124470127291230454011}
      a^{20} - \frac{1355893649380497947144}{2124470127291230454011} a^{19} + \frac{4050157594989936180715}{2124470127291230454011}
      a^{18} - \frac{7139886091949053381297}{2124470127291230454011} a^{17} - \frac{18117050064912096662547}{2124470127291230454011}
      a^{16} + \frac{73529795907396547368}{2124470127291230454011} a^{15} - \frac{55844284287882650635369}{2124470127291230454011}
      a^{14} + \frac{26467672614716502330660}{2124470127291230454011} a^{13} + \frac{97110014288056001475869}{2124470127291230454011}
      a^{12} + \frac{66233320404517596532844}{2124470127291230454011} a^{11} + \frac{307223941542630130075826}{2124470127291230454011}
      a^{10} + \frac{309447985619848024585712}{2124470127291230454011} a^{9} - \frac{84086252610589164368518}{2124470127291230454011}
      a^{8} - \frac{112050920473597640441367}{2124470127291230454011} a^{7} - \frac{86220438894968206222569}{2124470127291230454011}
      a^{6} - \frac{45440468566555592928964}{2124470127291230454011} a^{5} + \frac{24759683949850683947982}{2124470127291230454011}
      a^{4} + \frac{657358887835232170842}{2124470127291230454011} a^{3} + \frac{14944559723859008845594}{2124470127291230454011}
      a^{2} + \frac{5130312713082751548244}{2124470127291230454011} a - \frac{5545834329484503918247}{2124470127291230454011}
      \)
    - \( \frac{652179574499410298723}{2124470127291230454011} a^{21} - \frac{1737885361887583083688}{2124470127291230454011}
      a^{20} + \frac{1985646150495296835531}{2124470127291230454011} a^{19} - \frac{1186603222329343784037}{2124470127291230454011}
      a^{18} - \frac{10190832939287741416047}{2124470127291230454011} a^{17} + \frac{15205317984967579048506}{2124470127291230454011}
      a^{16} - \frac{20437120015554789382866}{2124470127291230454011} a^{15} + \frac{25680933845735028187009}{2124470127291230454011}
      a^{14} + \frac{55997796871938697464640}{2124470127291230454011} a^{13} - \frac{9679412688678969555236}{2124470127291230454011}
      a^{12} + \frac{51345618524785743586879}{2124470127291230454011} a^{11} + \frac{6805306138059341134191}{2124470127291230454011}
      a^{10} - \frac{253004509447257323762905}{2124470127291230454011} a^{9} - \frac{255694837207383972701208}{2124470127291230454011}
      a^{8} - \frac{178894245985196845520087}{2124470127291230454011} a^{7} - \frac{37140124003259012510352}{2124470127291230454011}
      a^{6} + \frac{32602573411966643473039}{2124470127291230454011} a^{5} + \frac{37609694626748900603612}{2124470127291230454011}
      a^{4} + \frac{39457526899481714902281}{2124470127291230454011} a^{3} + \frac{13985678024666897961667}{2124470127291230454011}
      a^{2} + \frac{666608658769490566095}{2124470127291230454011} a - \frac{274385090730102945487}{2124470127291230454011}
      \)
    - \( \frac{426281000176029419845}{2124470127291230454011} a^{21} - \frac{1164490203872957583560}{2124470127291230454011}
      a^{20} + \frac{1554083480001998761425}{2124470127291230454011} a^{19} - \frac{939555612041671654327}{2124470127291230454011}
      a^{18} - \frac{6589270340125514669626}{2124470127291230454011} a^{17} + \frac{11110850161236751943846}{2124470127291230454011}
      a^{16} - \frac{16790688979054980514273}{2124470127291230454011} a^{15} + \frac{16758859944302066618284}{2124470127291230454011}
      a^{14} + \frac{32772289175244439207150}{2124470127291230454011} a^{13} - \frac{17629782586287093315845}{2124470127291230454011}
      a^{12} + \frac{46607127329191951003287}{2124470127291230454011} a^{11} + \frac{12295858165312166351088}{2124470127291230454011}
      a^{10} - \frac{147440797795763057274197}{2124470127291230454011} a^{9} - \frac{93231598435395352653846}{2124470127291230454011}
      a^{8} - \frac{77501498170843787305242}{2124470127291230454011} a^{7} - \frac{38088758878765361964749}{2124470127291230454011}
      a^{6} + \frac{17698570371128988483627}{2124470127291230454011} a^{5} + \frac{14058846605426285947548}{2124470127291230454011}
      a^{4} + \frac{19242623605215402589831}{2124470127291230454011} a^{3} + \frac{5124716513747940930297}{2124470127291230454011}
      a^{2} - \frac{4921645317469414501509}{2124470127291230454011} a - \frac{275898821462360272929}{2124470127291230454011}
      \)
    - \( \frac{898909193641201610290}{2124470127291230454011} a^{21} - \frac{1072972537729809697223}{2124470127291230454011}
      a^{20} + \frac{2355947265120398603795}{2124470127291230454011} a^{19} + \frac{307202265004522494869}{2124470127291230454011}
      a^{18} - \frac{11468683649844348966726}{2124470127291230454011} a^{17} + \frac{5960635300427688190618}{2124470127291230454011}
      a^{16} - \frac{37388474405361997541324}{2124470127291230454011} a^{15} - \frac{10867284698557021172340}{2124470127291230454011}
      a^{14} + \frac{26648722625829019743338}{2124470127291230454011} a^{13} + \frac{3935603826370229702172}{2124470127291230454011}
      a^{12} + \frac{151848734252962730848489}{2124470127291230454011} a^{11} + \frac{239640984188352372096713}{2124470127291230454011}
      a^{10} + \frac{146199132168298423235974}{2124470127291230454011} a^{9} + \frac{162814373420891754944327}{2124470127291230454011}
      a^{8} + \frac{18345269734053939163865}{2124470127291230454011} a^{7} - \frac{57269428450016078602307}{2124470127291230454011}
      a^{6} - \frac{29610828861680852745196}{2124470127291230454011} a^{5} - \frac{47216961417063176314245}{2124470127291230454011}
      a^{4} - \frac{5837116242752313623986}{2124470127291230454011} a^{3} + \frac{3128805992904415407293}{2124470127291230454011}
      a^{2} + \frac{1208064985250560700296}{2124470127291230454011} a + \frac{4869117827277084875008}{2124470127291230454011}
      \)
    used_grh: true
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - a^4
    - a^5
    - a^6
    - a^7
    - a^8
    - a^9
    - a^10
    - a^11
    - a^12
    - a^13
    - a^14
    - a^15
    - a^16
    - a^17
    - a^18
    - a^19
    - a^20
    - 1/2124470127291230454011*a^21 + 432162695892207561224/2124470127291230454011*a^20
      - 653641761206245262533/2124470127291230454011*a^19 + 167982702717637181560/2124470127291230454011*a^18
      + 532665987662589956145/2124470127291230454011*a^17 + 625983005593256221797/2124470127291230454011*a^16
      - 463273244278987969270/2124470127291230454011*a^15 - 518926591257159751500/2124470127291230454011*a^14
      + 508818139788462937089/2124470127291230454011*a^13 + 749396289026961292787/2124470127291230454011*a^12
      + 856956959840666211577/2124470127291230454011*a^11 + 556372178049218564352/2124470127291230454011*a^10
      + 828731590687777909608/2124470127291230454011*a^9 - 463905878846124332921/2124470127291230454011*a^8
      + 215007940286959093640/2124470127291230454011*a^7 - 674937675082602811008/2124470127291230454011*a^6
      - 243201499321128170322/2124470127291230454011*a^5 - 616326127851568785886/2124470127291230454011*a^4
      - 832659424940701796791/2124470127291230454011*a^3 - 819262980435466447033/2124470127291230454011*a^2
      + 1046535151217522863157/2124470127291230454011*a + 930991225635280714244/2124470127291230454011
label_cols:
- label
labels:
- 22.2.1734677982017693835986328125.1
tables:
- nf_fields
timestamp: '2024-05-22T10:03:40.588428'