Artin representation data - 28.2797131779857379480059363657929504149714304101342158003114628839814991388825363251170912630328984178136968590919305331876086608201815805686600653681590649084706816.56.a

Formats: - HTML - YAML - JSON - 2024-04-19T04:33:24.099215

• 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, 11, 74869], 'Baselabel': '28.2797131779857379480059363657929504149714304101342158003114628839814991388825363251170912630328984178136968590919305331876086608201815805686600653681590649084706816.56.a', 'CharacterField': 1, 'Conductor': 2797131779857379480059363657929504149714304101342158003114628839814991388825363251170912630328984178136968590919305331876086608201815805686600653681590649084706816, 'Container': '56', 'Dets': ['1.1.1t1.a.a'], 'Dim': 28, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[28], [-4], [4], [1], [1], [0], [0], [-2], [1], [-1], [0], [0], [1], [1]], 'GalOrbIndex': 1, 'HardFactors': [15, 16, 16], 'LocalFactors': [[[1], [-28], [378], [-3276], [20475], [-98280], [376740], [-1184040], [3108105], [-6906900], [13123110], [-21474180], [30421755], [-37442160], [40116600], [-37442160], [30421755], [-21474180], [13123110], [-6906900], [3108105], [-1184040], [376740], [-98280], [20475], [-3276], [378], [-28], [1]], [[1], [4], [-6], [-44], [-5], [216], [164], [-616], [-759], [1100], [1958], [-1188], [-3333], [528], [3960], [528], [-3333], [-1188], [1958], [1100], [-759], [-616], [164], [216], [-5], [-44], [-6], [4], [1]], [[1], [-4], [-6], [44], [-5], [-216], [164], [616], [-759], [-1100], [1958], [1188], [-3333], [-528], [3960], [-528], [-3333], [1188], [1958], [-1100], [-759], [616], [164], [-216], [-5], [44], [-6], [-4], [1]], [[1], [-1], [0], [-9], [9], [0], [36], [-36], [0], [-84], [84], [0], [126], [-126], [0], [-126], [126], [0], [84], [-84], [0], [-36], [36], [0], [9], [-9], [0], [-1], [1]], [[1], [-1], [0], [-9], [9], [0], [36], [-36], [0], [-84], [84], [0], [126], [-126], [0], [-126], [126], [0], [84], [-84], [0], [-36], [36], [0], [9], [-9], [0], [-1], [1]], [[1], [0], [2], [0], [-5], [0], [-12], [0], [9], [0], [30], [0], [-5], [0], [-40], [0], [-5], [0], [30], [0], [9], [0], [-12], [0], [-5], [0], [2], [0], [1]], [[1], [0], [-2], [0], [-5], [0], [12], [0], [9], [0], [-30], [0], [-5], [0], [40], [0], [-5], [0], [-30], [0], [9], [0], [12], [0], [-5], [0], [-2], [0], [1]], [[1], [2], [3], [4], [5], [0], [-5], [-10], [-15], [-20], [-10], [0], [10], [20], [30], [20], [10], [0], [-10], [-20], [-15], [-10], [-5], [0], [5], [4], [3], [2], [1]], [[1], [-1], [0], [-1], [1], [0], [-4], [4], [0], [4], [-4], [0], [6], [-6], [0], [-6], [6], [0], [-4], [4], [0], [4], [-4], [0], [1], [-1], [0], [-1], [1]], [[1], [1], [0], [1], [1], [0], [-4], [-4], [0], [-4], [-4], [0], [6], [6], [0], [6], [6], [0], [-4], [-4], [0], [-4], [-4], [0], [1], [1], [0], [1], [1]], [[1], [0], [0], [0], [0], [0], [0], [-4], [0], [0], [0], [0], [0], [0], [6], [0], [0], [0], [0], [0], [0], [-4], [0], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [-4], [0], [0], [0], [0], [0], [0], [6], [0], [0], [0], [0], [0], [0], [-4], [0], [0], [0], [0], [0], [0], [1]], [[1], [-1], [0], [1], [-1], [0], [1], [-1], [0], [1], [-1], [0], [1], [-1], [0], [-1], [1], [0], [-1], [1], [0], [-1], [1], [0], [-1], [1], [0], [-1], [1]], [[1], [-1], [0], [1], [-1], [0], [1], [-1], [0], [1], [-1], [0], [1], [-1], [0], [-1], [1], [0], [-1], [1], [0], [-1], [1], [0], [-1], [1], [0], [-1], [1]], [[1], [-6], [15], [-20], [15], [-6], [1]], [[1], [-1], [0], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T49', 'Galt': 49, 'HardPrimes': [2, 11, 74869], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [823552, -48, -140, -224, -210, -112, -28, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [823552, -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': '7.1277992348243533546275162547509832257536.8t49.a', 'Character': [[7], [-1], [3], [4], [1], [-1], [1], [2], [0], [-1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.1672462788781077628212461429257073559252773822150610226815652187349252330282287104.15t72.a', 'Character': [[14], [6], [2], [-1], [2], [2], [0], [-1], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.2137394646784258250014618598911933531686243896834922265701066990390630213741642889168063160349795867751421018385619615744.28t433.a', 'Character': [[20], [4], [4], [5], [-1], [0], [0], [0], [1], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.2188692118307080448014969445285819936446713750358960400077892598160005338871442318508096676198190968577455122826874486521856.56.a', 'Character': [[21], [-3], [1], [6], [0], [1], [-1], [1], [-2], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.2188692118307080448014969445285819936446713750358960400077892598160005338871442318508096676198190968577455122826874486521856.336.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': '21.2188692118307080448014969445285819936446713750358960400077892598160005338871442318508096676198190968577455122826874486521856.336.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': '28.2797131779857379480059363657929504149714304101342158003114628839814991388825363251170912630328984178136968590919305331876086608201815805686600653681590649084706816.56.a', 'Character': [[28], [-4], [4], [1], [1], [0], [0], [-2], [1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.959579717361211553842988919500953290370421261604192110406623265050542260103928921736204883731234098510866945404596251193562702179552188009594799959659316095943665675681799623649991602247171072647957825460371456.70.a', 'Character': [[35], [3], [-5], [5], [2], [-1], [-1], [0], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '45.701444675132121311322522785958619229928302656314859493237899917946578054337176920938179313497323930731269413598158363802620167769300597237218644842130489613229545950816134619243385664406107158248412168562754634493076975950096487004585617335963293034102645383475480231936.336.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': '45.701444675132121311322522785958619229928302656314859493237899917946578054337176920938179313497323930731269413598158363802620167769300597237218644842130489613229545950816134619243385664406107158248412168562754634493076975950096487004585617335963293034102645383475480231936.336.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': '56.2051000551050605133144571343287475912597313651587397447779573624869222656668031469202591145350275750820727455935558084836740787026061504366712118854007859073795201147998595675935088927353307830189606695095306663631071514908230679262290869382316888678013210602388251572450987323872744527121210442167688367608795366008468762225803264.105.a', 'Character': [[56], [8], [0], [-4], [-1], [0], [0], [1], [0], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '64.2684070922737606818342860579382404347792906608764151548994564307699678783767196198612375484270782111345292738942168642864474588832944034075481540456505614397445191368779086876526207691957822802939204355807969510087976380967301854941615533369501114568136647002152540476989476393968700866358217541711924057549946861235872449297219630782167942457176663637268773146744215044096.168.a', 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '70.3430222101401622035943139069703920045747713309353484167383770939513661686160342143786561972937146121931470430529230778402264393155210144481892268775888508467758379747155091899951141525507186293702588936664431342589398559548121215018176032881684361207672048729218326171982077646781903603823238959806664769598328543061930292636211072279249814192841697842887639982875558769741048791671847852066830436791717468307456.120.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': ['-9151748823830788161536', '1'], 'ConjugacyClass': 12}, {'RootOf': ['9151748823830788161536', '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': ['-9151748823830788161536', '1'], 'ConjugacyClass': 14}, {'RootOf': ['9151748823830788161536', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'ALT', 'CycleType': [3, 5]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [1, 13, 10, 12, 5, 13, 9, 12, 10, 11, 10, 7, 10, 7, 6, 7, 10, 13, 10, 12, 6, 9, 12, 12, 12, 9, 10, 10, 7, 8, 5, 12, 9, 10, 6, 12, 7, 12, 10, 7, 8, 11, 9, 14, 9, 5, 14, 10, 13, 9, 13, 5, 10, 9, 11, 14, 7, 11, 12, 14, 5, 10, 9, 7, 6, 8, 5, 6, 11, 11, 9, 13, 8, 10, 10, 7, 12, 8, 14, 13, 7, 6, 10, 12, 12, 13, 12, 12, 10, 11, 11, 13, 14, 9, 12, 6, 8, 11, 5, 10, 10, 14, 6, 11, 11, 12, 9, 10, 10, 13, 12, 12, 7, 8, 10, 8, 11, 11, 14, 10, 7, 6, 12, 5, 12, 10, 9, 7, 5, 12, 8, 7, 7, 12, 7, 14, 8, 2, 14, 6, 10, 11, 5, 9, 9, 11, 8, 13, 8, 10, 8, 11, 5, 5, 10, 7, 12, 7, 14, 12, 6, 12, 12, 7, 13, 12, 8, 6], 'G-Gens': [[2, 1, 4, 5, 6, 7, 8, 3], [2, 3, 1, 4, 5, 6, 7, 8]], 'G-Name': 'A8', 'Polynomial': [823552, -48, -140, -224, -210, -112, -28, 0, 1], 'QpRts': [['-34170332820151138783670534259', '13001561407443543237157738789'], ['-13995554616116644887224328131', '28891340038016891947949562235'], ['-22479907404194546526493964462', '19143523933504593926993317856'], ['-44817369606438627461042743325', '-13001561407443543237157738789'], ['12472860123546443483758839861', '17671360638155567244583337053'], ['-22714861479414237984201290749', '-17671360638155567244583337053'], ['-29863488231522455328771004193', '-19143523933504593926993317856'], ['-26727421491857676364651590440', '-28891340038016891947949562235']], 'QpRts-minpoly': [2, 786, 1], 'QpRts-p': 787, 'QpRts-prec': 10, 'Size': 20160, 'TransitiveDegree': 8}