Artin representation data - 64.719933110879108418401109238696387231342540582121195715032894095538766618866388147719113668556936783743869239242501068711297990225608268349414970292861315663373870401392179803417315921071821539489149438180762038692473066953268319471624946168749004061160936150343397003083499136451090805856265187637809930229624276721783527970358462420784953037168924893582056336022049452938550575104.168.a

Formats: - HTML - YAML - JSON - 2024-04-25T13:55:11.782887

• artin_reps •

  Column	Type
  BadPrimes	jsonb
  Baselabel	text
  CharacterField	smallint
  Conductor	numeric
  Container	text
  Dets	text[]
  Dim	smallint
  GalConjSigns	jsonb
  Galn	smallint
  GaloisConjugates	jsonb
  GaloisConjugatesSigns	integer[]
  GaloisLabel	text
  Galt	integer
  HardPrimes	jsonb
  Hide	smallint
  Indicator	smallint
  Is_Even	boolean
  NFGal	jsonb
  NumBadPrimes	smallint
  Proj_GAP	integer[]
  Proj_Polynomial	numeric[]
  Proj_nTj	integer[]

  
  {'BadPrimes': [2, 823547], 'Baselabel': '64.719933110879108418401109238696387231342540582121195715032894095538766618866388147719113668556936783743869239242501068711297990225608268349414970292861315663373870401392179803417315921071821539489149438180762038692473066953268319471624946168749004061160936150343397003083499136451090805856265187637809930229624276721783527970358462420784953037168924893582056336022049452938550575104.168.a', 'CharacterField': 1, 'Conductor': 719933110879108418401109238696387231342540582121195715032894095538766618866388147719113668556936783743869239242501068711297990225608268349414970292861315663373870401392179803417315921071821539489149438180762038692473066953268319471624946168749004061160936150343397003083499136451090805856265187637809930229624276721783527970358462420784953037168924893582056336022049452938550575104, 'Container': '168', 'Dets': ['1.1.1t1.a.a'], 'Dim': 64, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [15, 16], 'LocalFactors': [[[1], [-64], [2016], [-41664], [635376], [-7624512], [74974368], [-621216192], [4426165368], [-27540584512], [151473214816], [-743595781824], [3284214703056], [-13136858812224], [47855699958816], [-159518999862720], [488526937079580], [-1379370175283520], [3601688791018080], [-8719878125622720], [19619725782651120], [-41107996877935680], [80347448443237920], [-146721427591999680], [250649105469666120], [-401038568751465792], [601557853127198688], [-846636978475316672], [1118770292985239888], [-1388818294740297792], [1620288010530347424], [-1777090076065542336], [1832624140942590534], [-1777090076065542336], [1620288010530347424], [-1388818294740297792], [1118770292985239888], [-846636978475316672], [601557853127198688], [-401038568751465792], [250649105469666120], [-146721427591999680], [80347448443237920], [-41107996877935680], [19619725782651120], [-8719878125622720], [3601688791018080], [-1379370175283520], [488526937079580], [-159518999862720], [47855699958816], [-13136858812224], [3284214703056], [-743595781824], [151473214816], [-27540584512], [4426165368], [-621216192], [74974368], [-7624512], [635376], [-41664], [2016], [-64], [1]], [[1], [0], [-32], [0], [496], [0], [-4960], [0], [35960], [0], [-201376], [0], [906192], [0], [-3365856], [0], [10518300], [0], [-28048800], [0], [64512240], [0], [-129024480], [0], [225792840], [0], [-347373600], [0], [471435600], [0], [-565722720], [0], [601080390], [0], [-565722720], [0], [471435600], [0], [-347373600], [0], [225792840], [0], [-129024480], [0], [64512240], [0], [-28048800], [0], [10518300], [0], [-3365856], [0], [906192], [0], [-201376], [0], [35960], [0], [-4960], [0], [496], [0], [-32], [0], [1]], [[1], [0], [-32], [0], [496], [0], [-4960], [0], [35960], [0], [-201376], [0], [906192], [0], [-3365856], [0], [10518300], [0], [-28048800], [0], [64512240], [0], [-129024480], [0], [225792840], [0], [-347373600], [0], [471435600], [0], [-565722720], [0], [601080390], [0], [-565722720], [0], [471435600], [0], [-347373600], [0], [225792840], [0], [-129024480], [0], [64512240], [0], [-28048800], [0], [10518300], [0], [-3365856], [0], [906192], [0], [-201376], [0], [35960], [0], [-4960], [0], [496], [0], [-32], [0], [1]], [[1], [-4], [6], [-24], [81], [-120], [270], [-780], [1140], [-1900], [4750], [-6840], [9405], [-20520], [29070], [-34884], [66861], [-93024], [100776], [-170544], [232560], [-232560], [348840], [-465120], [436050], [-581400], [755820], [-671840], [797810], [-1007760], [856596], [-906984], [1108536], [-906984], [856596], [-1007760], [797810], [-671840], [755820], [-581400], [436050], [-465120], [348840], [-232560], [232560], [-170544], [100776], [-93024], [66861], [-34884], [29070], [-20520], [9405], [-6840], [4750], [-1900], [1140], [-780], [270], [-120], [81], [-24], [6], [-4], [1]], [[1], [2], [3], [-18], [-39], [-60], [150], [360], [570], [-760], [-2090], [-3420], [2565], [8550], [14535], [-5814], [-26163], [-46512], [7752], [62016], [116280], [0], [-116280], [-232560], [-29070], [174420], [377910], [83980], [-209950], [-503880], [-151164], [201552], [554268], [201552], [-151164], [-503880], [-209950], [83980], [377910], [174420], [-29070], [-232560], [-116280], [0], [116280], [62016], [7752], [-46512], [-26163], [-5814], [14535], [8550], [2565], [-3420], [-2090], [-760], [570], [360], [150], [-60], [-39], [-18], [3], [2], [1]], [[1], [0], [0], [0], [-16], [0], [0], [0], [120], [0], [0], [0], [-560], [0], [0], [0], [1820], [0], [0], [0], [-4368], [0], [0], [0], [8008], [0], [0], [0], [-11440], [0], [0], [0], [12870], [0], [0], [0], [-11440], [0], [0], [0], [8008], [0], [0], [0], [-4368], [0], [0], [0], [1820], [0], [0], [0], [-560], [0], [0], [0], [120], [0], [0], [0], [-16], [0], [0], [0], [1]], [[1], [0], [0], [0], [-16], [0], [0], [0], [120], [0], [0], [0], [-560], [0], [0], [0], [1820], [0], [0], [0], [-4368], [0], 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[-90], [0], [45], [0], [-10], [0], [20], [0], [-10], [0], [1], [0], [-2], [0], [1]], [[1], [0], [1], [0], [1], [0], [-10], [0], [-10], [0], [-10], [0], [45], [0], [45], [0], [45], [0], [-120], [0], [-120], [0], [-120], [0], [210], [0], [210], [0], [210], [0], [-252], [0], [-252], [0], [-252], [0], [210], [0], [210], [0], [210], [0], [-120], [0], [-120], [0], [-120], [0], [45], [0], [45], [0], [45], [0], [-10], [0], [-10], [0], [-10], [0], [1], [0], [1], [0], [1]], [[1], [-1], [0], [0], [0], [0], [0], [-9], [9], [0], [0], [0], [0], [0], [36], [-36], [0], [0], [0], [0], [0], [-84], [84], [0], [0], [0], [0], [0], [126], [-126], [0], [0], [0], [0], [0], [-126], [126], [0], [0], [0], [0], [0], [84], [-84], [0], [0], [0], [0], [0], [-36], [36], [0], [0], [0], [0], [0], [9], [-9], [0], [0], [0], [0], [0], [-1], [1]], [[1], [-1], [0], [0], [0], [0], [0], [-9], [9], [0], [0], [0], [0], [0], [36], [-36], [0], [0], [0], [0], [0], [-84], [84], [0], [0], [0], [0], [0], [126], [-126], [0], [0], [0], [0], [0], [-126], [126], [0], [0], [0], [0], [0], [84], [-84], [0], [0], [0], [0], [0], [-36], [36], [0], [0], [0], [0], [0], [9], [-9], [0], [0], [0], [0], [0], [-1], [1]], [[1], [1], [1], [1], [1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-4], [-4], [-4], [-4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [6], [6], [6], [6], [6], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-4], [-4], [-4], [-4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1], [1], [1], [1], [1]], [[1], [1], [1], [1], [1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-4], [-4], [-4], [-4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [6], [6], [6], [6], [6], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-4], [-4], [-4], [-4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1], [1], [1], [1], [1]], [[1], [0], [-1]], [[1], [2], [3], [0], [-3], [-6], [-3], [0], [3], [2], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T49', 'Galt': 49, 'HardPrimes': [2, 823547], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [823540, -48, -140, -224, -210, -112, -28, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [823540, -48, -140, -224, -210, -112, -28, 0, 1], 'Proj_nTj': [8, 49]}
• artin_field_data •

  Column	Type
  ArtinReps	jsonb
  ComplexConjugation	smallint
  ConjClasses	jsonb
  FrobResolvents	jsonb
  Frobs	jsonb
  G-Gens	jsonb
  G-Name	text
  Polynomial	jsonb
  QpRts	jsonb
  QpRts-minpoly	jsonb
  QpRts-p	integer
  QpRts-prec	integer
  Size	numeric
  TransitiveDegree	smallint

  
  {'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '7.81784359890073480322911752930604437733376.8t49.a', 'Character': [[7], [-1], [3], [4], [1], [-1], [1], [2], [0], [-1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.6688681522629059894447701828132486277117719106262300617903325598556888716464357376.15t72.a', 'Character': [[14], [6], [2], [-1], [2], [2], [0], [-1], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.547029536836779699858012917683136285591492999321384203197524227912514679443684375958596873750716116462505497785041866981376.28t433.a', 'Character': [[20], [4], [4], [5], [-1], [0], [0], [0], [1], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.8962531931533798602473683643320504903131021300881558785188236950118640508005324815705651179531732852121690075710125948622864384.56.a', 'Character': [[21], [-3], [1], [6], [0], [1], [-1], [1], [-2], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.8962531931533798602473683643320504903131021300881558785188236950118640508005324815705651179531732852121690075710125948622864384.336.a', 'Character': [[21, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 1, -1, 2, -1, 0, 1], [1, -2, -1, 1, -2, 1, 0, -1]], 'CharacterField': 15}, {'GalConj': 2, 'Baselabel': '21.8962531931533798602473683643320504903131021300881558785188236950118640508005324815705651179531732852121690075710125948622864384.336.a', 'Character': [[21, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -1, 1, -2, 1, 0, -1], [-2, 2, 1, -1, 2, -1, 0, 1]], 'CharacterField': 15}, {'GalConj': 1, 'Baselabel': '28.732994937014835594343922787568735276640655956500143039287970614417420015751966366350311187573216748758414775961149950250196844190367140597713160077101731096913598480384.56.a', 'Character': [[28], [-4], [4], [1], [1], [0], [0], [-2], [1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.982180195965715369519840621577574947340427253463945807461917116116307941007505951619024865791798575843397295583205761015471240810405538451405051249544597052686825221299394435186197104534584839043728391505451155456.70.a', 'Character': [[35], [3], [-5], [5], [2], [-1], [-1], [0], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '45.735100197979878227945901802391917273917968494699525772714711118762853892343418475008322534337855711304665563455763934786941230638992245426752766265958008439832151939349913292451103350499757573283846346142471583105329304800833798085566412438785393935444358211786620283327086592.336.a', 'Character': [[45, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0], [-1, -1, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '45.735100197979878227945901802391917273917968494699525772714711118762853892343418475008322534337855711304665563455763934786941230638992245426752766265958008439832151939349913292451103350499757573283846346142471583105329304800833798085566412438785393935444358211786620283327086592.336.a', 'Character': [[45, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, -1, -1, 0, -1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]], 'CharacterField': 7}, {'GalConj': 1, 'Baselabel': '56.537281577689382800083182574873156428347509260071480498614785259921984295370042412566511831425773401323395997529028309169930235053955419387035882914938729036066801704424236832032316443590777778687479733449935869933202696580670578705796332776333904300985550215887248234236795192289927842593232587759691023810716825397459825087954032787456.105.a', 'Character': [[56], [8], [0], [-4], [-1], [0], [0], [1], [0], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '64.719933110879108418401109238696387231342540582121195715032894095538766618866388147719113668556936783743869239242501068711297990225608268349414970292861315663373870401392179803417315921071821539489149438180762038692473066953268319471624946168749004061160936150343397003083499136451090805856265187637809930229624276721783527970358462420784953037168924893582056336022049452938550575104.168.a', 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '70.58879268636917178090307276066089468716922590271927335486481393258509749086006556798236164886876607276454294068421370378957351495043184350437504833457630248835678819848349153736947272343994232458824954713017237586527676061948221453109682283010450884780360606151615748164639052275184686204234481227618237501859260491003650959528740177942990889245205594736002637772447185808683448784666546995563854691984615346946603015471104.120.a', 'Character': [[70], [-2], [2], [-5], [1], [-2], [0], [0], [-1], [1], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '105', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 8, 7]}, {'Size': '210', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6, 7, 8]}, {'Size': '112', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6, 7, 8]}, {'Size': '1120', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4, 7, 8]}, {'Size': '1260', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 7, 8, 5]}, {'Size': '2520', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5, 7, 8]}, {'Size': '1344', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6, 7, 8]}, {'Size': '1680', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 7, 6, 8]}, {'Size': '3360', 'Order': 6, 'Representative': [2, 3, 4, 5, 6, 1, 8, 7]}, {'Size': '2880', 'Order': 7, 'Representative': [2, 3, 4, 5, 6, 7, 1, 8]}, {'Size': '2880', 'Order': 7, 'Representative': [3, 1, 4, 5, 6, 7, 2, 8]}, {'Size': '1344', 'Order': 15, 'Representative': [2, 3, 4, 5, 1, 7, 8, 6]}, {'Size': '1344', 'Order': 15, 'Representative': [3, 1, 4, 5, 2, 7, 8, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 5]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 3]}, {'Data': [1, 3, 4, 5, 6, 7, 8, 2], 'Classes': [{'RootOf': ['-4575674390935046742016', '1'], 'ConjugacyClass': 12}, {'RootOf': ['4575674390935046742016', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'ALT', 'CycleType': [1, 7]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': [2, 3, 1, 5, 6, 7, 8, 4], 'Classes': [{'RootOf': ['-4575674390935046742016', '1'], 'ConjugacyClass': 14}, {'RootOf': ['4575674390935046742016', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'ALT', 'CycleType': [3, 5]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [6, 14, 11, 6, 6, 14, 6, 10, 8, 11, 12, 12, 13, 10, 14, 11, 10, 12, 9, 5, 12, 12, 12, 9, 9, 11, 11, 10, 14, 11, 13, 11, 12, 14, 11, 7, 10, 12, 10, 11, 9, 7, 9, 10, 10, 12, 11, 5, 12, 10, 9, 9, 10, 5, 12, 10, 11, 11, 11, 9, 11, 7, 11, 6, 8, 7, 10, 12, 11, 10, 13, 12, 7, 8, 6, 10, 14, 12, 10, 5, 11, 14, 11, 13, 12, 5, 14, 7, 5, 8, 10, 10, 14, 10, 12, 10, 12, 14, 6, 5, 9, 11, 10, 10, 12, 14, 12, 10, 11, 11, 11, 8, 6, 12, 7, 8, 9, 9, 10, 5, 9, 7, 12, 10, 9, 14, 11, 6, 7, 10, 13, 12, 8, 11, 11, 13, 14, 10, 8, 14, 7, 8, 5, 5, 12, 9, 9, 12, 12, 13, 12, 7, 8, 5, 12, 8, 5, 12, 11, 3, 8, 10, 8, 11, 11, 12, 8, 7], 'G-Gens': [[2, 1, 4, 5, 6, 7, 8, 3], [2, 3, 1, 4, 5, 6, 7, 8]], 'G-Name': 'A8', 'Polynomial': [823540, -48, -140, -224, -210, -112, -28, 0, 1], 'QpRts': [['-62697344210110665314415257', '0'], ['-88997229716187132867079802', '-138254496225245421288593816'], ['-86012431957470549916993035', '-98232338489557057488803681'], ['270197928455179520897251406', '98232338489557057488803681'], ['285260218060418255894677574', '138254496225245421288593816'], ['-47618058926115576670497103', '0'], ['13707925013212123996372769', '0'], ['-283841006718925976019316552', '0']], 'QpRts-minpoly': [2, 940, 1], 'QpRts-p': 941, 'QpRts-prec': 9, 'Size': 20160, 'TransitiveDegree': 8}