Artin representation data - 28.1369985957978855766074925414349594593210745375538155355104217370436278546968386509855743320535848477488724883102859030862521820760312231108266782737157166060278348730556077616406238068736.56.a

Formats: - HTML - YAML - JSON - 2024-04-23T09:22:33.569602

• 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, 7, 268913], 'Baselabel': '28.1369985957978855766074925414349594593210745375538155355104217370436278546968386509855743320535848477488724883102859030862521820760312231108266782737157166060278348730556077616406238068736.56.a', 'CharacterField': 1, 'Conductor': 1369985957978855766074925414349594593210745375538155355104217370436278546968386509855743320535848477488724883102859030862521820760312231108266782737157166060278348730556077616406238068736, '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, 17], '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], [0], [-1]], [[1], [-2], [1]], [[1], [-4], [6], [-4], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T49', 'Galt': 49, 'HardPrimes': [2, 7, 268913], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [210826000, -6144, -8960, -7168, -3360, -896, -112, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [210826000, -6144, -8960, -7168, -3360, -896, -112, 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': '7.36574214064047828349270556528863627894423814144.8t49.a', 'Character': [[7], [-1], [3], [4], [1], [-1], [1], [2], [0], [-1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.5102818048106361254368211643330139880729076301788352402570820255594874476369628463366144.15t72.a', 'Character': [[14], [6], [2], [-1], [2], [2], [0], [-1], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.9144946421445109520341125456392578140698020985398958145890669708398077282803927182780688615160606806828002819242114237012594390219096064.28t433.a', 'Character': [[20], [4], [4], [5], [-1], [0], [0], [0], [1], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.37457700542239168595317249869384000064299093956194132565568183125598524550364885740669700567697845480767499547615699914803586622337417478144.56.a', 'Character': [[21], [-3], [1], [6], [0], [1], [-1], [1], [-2], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.37457700542239168595317249869384000064299093956194132565568183125598524550364885740669700567697845480767499547615699914803586622337417478144.336.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': '21.37457700542239168595317249869384000064299093956194132565568183125598524550364885740669700567697845480767499547615699914803586622337417478144.336.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': '28.1369985957978855766074925414349594593210745375538155355104217370436278546968386509855743320535848477488724883102859030862521820760312231108266782737157166060278348730556077616406238068736.56.a', 'Character': [[28], [-4], [4], [1], [1], [0], [0], [-2], [1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.12232949143520093686791748501181429462484074117179301908541981017186582277498592696184347525706988386463816935467983090213261749633159367748618949200036197247218074467384046094673969243736851598558695931644093608244108658531631104.70.a', 'Character': [[35], [3], [-5], [5], [2], [-1], [-1], [0], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '45.4192661050291637623239631601694682235959359481663684470474651324147594816235269810292554242741497319796140754607495200348488208136220988391679784984163259670232085805479377831137436224577608720224937997736521814420551051158558357369498820289842785457311836940287262452085381471011498264879893355429888.336.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': '45.4192661050291637623239631601694682235959359481663684470474651324147594816235269810292554242741497319796140754607495200348488208136220988391679784984163259670232085805479377831137436224577608720224937997736521814420551051158558357369498820289842785457311836940287262452085381471011498264879893355429888.336.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': '56.5481613560193950813183784784156126526216754399126570326999832834481791386536915457400003866824365765669188310355616018604503005365211483847443094565395915347166972486465182092732326315270417250822940594235269591991419683160245271691262348186913096242758685803922027702832071996954719004527438303135022167781001559847462235924823739936123899437505790892840764932358144.105.a', 'Character': [[56], [8], [0], [-4], [-1], [0], [0], [1], [0], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '64.40238283491652088887019503069214971180548809738820121789676822584281848850056526530987479149954416332584167567678930574125006183395539853739856149638784557633120590018236836773318273787252756155066566574560208514090744143384888907466657382880267305335892371719628175337291741534950171069763729826654667977574466400856333680293184143349201375230862711256338379332521889908299763326977595902015712423339969389931102470144.168.a', 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '70.30034359061092354829459045330595362550080149795604015519759181112368035229983606866571254021805226426622187393067378404533511857696412274387981500961918938924705853876854876908069702908227533875805125422000363808732399688682237640770021620722720503058006111815101167456040532482530879573043842961255619206250292030266518273696619401336465466132264626608741591540275943460478313248162769975386999254800335276497460496627929735333638322475286568967357408348905406464.120.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': ['-1074735416090068574854178668544', '1'], 'ConjugacyClass': 12}, {'RootOf': ['1074735416090068574854178668544', '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': ['-1074735416090068574854178668544', '1'], 'ConjugacyClass': 14}, {'RootOf': ['1074735416090068574854178668544', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'ALT', 'CycleType': [3, 5]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [3, 13, 12, 1, 7, 6, 11, 9, 10, 12, 11, 12, 12, 11, 10, 12, 14, 10, 13, 10, 8, 14, 5, 10, 10, 10, 12, 6, 7, 9, 14, 11, 10, 11, 11, 12, 8, 11, 8, 11, 12, 11, 7, 14, 12, 7, 6, 10, 8, 13, 12, 11, 8, 12, 12, 12, 7, 10, 14, 14, 12, 7, 11, 14, 9, 10, 5, 6, 13, 12, 13, 14, 11, 9, 9, 12, 13, 11, 11, 9, 14, 8, 4, 12, 5, 10, 12, 10, 10, 9, 10, 6, 13, 12, 11, 11, 14, 13, 14, 10, 10, 9, 9, 11, 9, 7, 12, 12, 5, 11, 10, 11, 11, 10, 8, 11, 14, 12, 8, 11, 8, 7, 5, 9, 13, 13, 11, 7, 12, 12, 9, 10, 11, 12, 8, 11, 12, 9, 13, 7, 14, 12, 10, 10, 11, 7, 5, 7, 11, 6, 10, 13, 11, 11, 13, 11, 12, 10, 6, 12, 6, 11, 10, 14, 8, 10, 7, 11], 'G-Gens': [[2, 1, 4, 5, 6, 7, 8, 3], [2, 3, 1, 4, 5, 6, 7, 8]], 'G-Name': 'A8', 'Polynomial': [210826000, -6144, -8960, -7168, -3360, -896, -112, 0, 1], 'QpRts': [['-3242578697343419177562047561157808', '-8065828945083396628075209043755607', '-12287827370430764574056896743382927'], ['4315428257460637744347525868144242', '-5610724464739401986851829991490030', '10749014621715894322305755462675441'], ['-6264117729940303273105034347210304', '613869168627564580697159881996378', '5459241628015423813579475354998168'], ['-14652454445940619781211049455151449', '4996855296111837406154670109493652', '-16208256249731318135885230817673609'], ['16397496051829582929465816825170910', '0', '0'], ['2981171739765490809492871496102274', '3510537961238174586743467138241621', '-9175952151876309580529437214752886'], ['6097737815022707250494297807027281', '0', '0'], ['-5632682990854076501922380632925146', '4555290983845222041331741905513986', '-13482879517186093236237063279266596']], 'QpRts-minpoly': [81, 3, 0, 1], 'QpRts-p': 83, 'QpRts-prec': 18, 'Size': 20160, 'TransitiveDegree': 8}