Artin representation data - 28.63847776567570238235447619563167307119419147963794860651919965150253064122368864375441507521485960861958340731631668647922434733280685843724292995768995238123176240662285272535256949160256671101561111549313024.56.a

Formats: - HTML - YAML - JSON - 2024-04-24T01:03:36.847939

• 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, 29, 37, 49121], 'Baselabel': '28.63847776567570238235447619563167307119419147963794860651919965150253064122368864375441507521485960861958340731631668647922434733280685843724292995768995238123176240662285272535256949160256671101561111549313024.56.a', 'CharacterField': 1, 'Conductor': 63847776567570238235447619563167307119419147963794860651919965150253064122368864375441507521485960861958340731631668647922434733280685843724292995768995238123176240662285272535256949160256671101561111549313024, '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, 10, 16, 17, 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], [-3], [3], [-1]], [[1], [-4], [6], [-4], [1]], [[1], [-1], [0], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T49', 'Galt': 49, 'HardPrimes': [2, 3, 29, 37, 49121], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [210825540, -6144, -8960, -7168, -3360, -896, -112, 0, 1], 'NumBadPrimes': 4, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [210825540, -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': '7.5620066455663197695561554590870531303687507769819136.8t49.a', 'Character': [[7], [-1], [3], [4], [1], [-1], [1], [2], [0], [-1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.123379480336213661207646179183607816022041065648493536747069045712844181484795703149961320661742780416.15t72.a', 'Character': [[14], [6], [2], [-1], [2], [2], [0], [-1], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.693400878754711506104386119881156659648640182014757452993542831057608605467401906909994470547407799340325815713062202475380467426278461025238386082840576.28t433.a', 'Character': [[20], [4], [4], [5], [-1], [0], [0], [0], [1], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.11360679997517193316014262188132870711683320742129786109846205744047859391977912842813349405448729384391898164642811125356633578312146305437505717581259997184.56.a', 'Character': [[21], [-3], [1], [6], [0], [1], [-1], [1], [-2], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.11360679997517193316014262188132870711683320742129786109846205744047859391977912842813349405448729384391898164642811125356633578312146305437505717581259997184.336.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': '21.11360679997517193316014262188132870711683320742129786109846205744047859391977912842813349405448729384391898164642811125356633578312146305437505717581259997184.336.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': '28.63847776567570238235447619563167307119419147963794860651919965150253064122368864375441507521485960861958340731631668647922434733280685843724292995768995238123176240662285272535256949160256671101561111549313024.56.a', 'Character': [[28], [-4], [4], [1], [1], [0], [0], [-2], [1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.1435314989424320940198956657653212261933937754072946629454534616715994460538759625973326224680309034898375743287636318813709860279512345172717635320985009110969491196995127742432287895337815184974165986834810769676201513508550333875476145181867861131766116909056.70.a', 'Character': [[35], [3], [-5], [5], [2], [-1], [-1], [0], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '45.19351265663208806397223533917997873048894810679867874510331535054651248189068766465669145043128501096903607178566261510844704704176106283832449948027226916236142692582278425533702167787021442904542330530442998369844012880791922297372394938432816025542858841391108704558668966730739556851638283722757521056306193580823422872006302831768240128.336.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': '45.19351265663208806397223533917997873048894810679867874510331535054651248189068766465669145043128501096903607178566261510844704704176106283832449948027226916236142692582278425533702167787021442904542330530442998369844012880791922297372394938432816025542858841391108704558668966730739556851638283722757521056306193580823422872006302831768240128.336.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': '56.995248674956633591890372333458841589454098790953141026811991847354246276243250196948820412816193214146453280487212806378831494744385519742991140016648733682557905043505216852673706285416155775586620652463313873975879942283699137458951131132843575295466485284083633590406176766789903760289817549699808103324651174033854492228590345313861985700352530187068017934278618148460710055393758453937135131399245645538656256.105.a', 'Character': [[56], [8], [0], [-4], [-1], [0], [0], [1], [0], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '64.91641670748848482832403196711945603240247718111273033244589178562712452372568054853495805267834328481580386515777517380942993629003169127244600785859214182603634034597536619998685360883426251038869742819115533880506609428884855573755881411446556815069418421014037949117475102106370659846354282996796928548392095158824994261231634684500171550501405225850346102377743167791739485384057130734154900626854500288026058857501770814530644432993058036873304718121461267084345344.168.a', 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '70.515032279716534633102079631518330199783418041514749767510985855869341934761392210495237217330955785246179923266129287533183612995632780458627572856510443047134047818251730643809097369404567433725336703991055588343559968131942505027958961921166781166866931564372307126496377543256137691901011658304407993998315326936170603506781758080021346693412756396337287262843898068900680029281949265589057636602511343997921012622601820956634919199639399925438562008265433303784885955726356758628022564672406163550515930753379843702784.120.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': ['-690896816542740301062515195904', '1'], 'ConjugacyClass': 12}, {'RootOf': ['690896816542740301062515195904', '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': ['-690896816542740301062515195904', '1'], 'ConjugacyClass': 14}, {'RootOf': ['690896816542740301062515195904', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'ALT', 'CycleType': [3, 5]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [1, 10, 12, 6, 13, 9, 9, 5, 10, 1, 8, 5, 10, 14, 9, 14, 11, 7, 13, 5, 9, 10, 14, 8, 6, 14, 10, 7, 10, 5, 12, 8, 7, 12, 9, 11, 8, 11, 12, 10, 12, 7, 7, 6, 5, 12, 11, 9, 13, 5, 9, 12, 14, 12, 11, 5, 10, 11, 7, 12, 10, 10, 12, 9, 10, 9, 13, 7, 8, 11, 10, 10, 11, 13, 11, 8, 11, 13, 13, 7, 6, 14, 11, 10, 11, 9, 7, 9, 11, 10, 8, 10, 7, 9, 12, 6, 10, 11, 9, 9, 14, 8, 10, 5, 11, 6, 5, 8, 9, 7, 6, 11, 7, 12, 7, 11, 13, 6, 7, 13, 4, 13, 10, 12, 6, 11, 9, 11, 5, 11, 11, 14, 14, 11, 9, 14, 9, 7, 7, 7, 12, 14, 2, 11, 9, 14, 8, 9, 12, 7, 7, 6, 11, 11, 9, 6, 10, 6, 12, 13, 14, 6, 14, 10, 11, 12, 13, 13], 'G-Gens': [[2, 1, 4, 5, 6, 7, 8, 3], [2, 3, 1, 4, 5, 6, 7, 8]], 'G-Name': 'A8', 'Polynomial': [210825540, -6144, -8960, -7168, -3360, -896, -112, 0, 1], 'QpRts': [['-11752656516576906345546909658468857', '-29912033311436157750737355209724111'], ['-45488324886921829453681184269414167', '41556125096702180977987873371133125'], ['19233218067362742715134175886040642', '-41556125096702180977987873371133125'], ['12007088243313125026769765562777946', '-19062529941516721470559329680466165'], ['10376455256247783253555148647546355', '-39594013465814687323304283820732674'], ['19743463850246207590041245617227940', '29912033311436157750737355209724111'], ['19596599408830788159111573189817009', '19062529941516721470559329680466165'], ['-23715843422501910945383814975526868', '39594013465814687323304283820732674']], 'QpRts-minpoly': [3, 821, 1], 'QpRts-p': 823, 'QpRts-prec': 12, 'Size': 20160, 'TransitiveDegree': 8}