Artin representation data - 6.7802490888622528.42t82.a

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• 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, 23], 'Baselabel': '6.7802490888622528.42t82.a', 'CharacterField': 1, 'Conductor': 7802490888622528, 'Container': '42t82', 'Dets': ['1.7.2t1.a.a'], 'Dim': 6, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[6], [-2], [0], [0], [2], [0], [-1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [10, 3, 10, 10, 6, 3, 2], 'LocalFactors': [[[1], [-6], [15], [-20], [15], [-6], [1]], [[1], [2], [-1], [-4], [-1], [2], [1]], [[1], [0], [-3], [0], [3], [0], [-1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [-2], [3], [-4], [3], [-2], [1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [1], [1], [1], [1], [1], [1]], [[1], [0], [-1], [0], [1], [0], [-1]], [[1], [0], [-1], [0], [1], [0], [-1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T43', 'Galt': 43, 'HardPrimes': [2, 3, 7, 23, 173, 1279, 6869], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-17946, 22167, -9779, 2765, -819, 91, -21, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [336, 208], 'Proj_Polynomial': [-17946, 22167, -9779, 2765, -819, 91, -21, -1, 1], 'Proj_nTj': [8, 43]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.7.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.7802490888622528.42t82.a', 'Character': [[6], [-2], [0], [0], [2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.7802490888622528.14t16.a', 'Character': [[6, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, -1, 0, 1], [0, 1, 0, -1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '6.7802490888622528.14t16.a', 'Character': [[6, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 1, 0, -1], [0, -1, 0, 1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '7.7802490888622528.8t43.a', 'Character': [[7], [-1], [1], [1], [-1], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '7.54617436220357696.16t713.a', 'Character': [[7], [-1], [-1], [1], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.382322053542503872.42t81.b', 'Character': [[8], [0], [-2], [-1], [0], [1], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.382322053542503872.21t20.b', 'Character': [[8], [0], [2], [-1], [0], [-1], [1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '21', 'Order': 2, 'Representative': [2, 1, 5, 7, 3, 8, 4, 6]}, {'Size': '28', 'Order': 2, 'Representative': [8, 7, 3, 4, 6, 5, 2, 1]}, {'Size': '56', 'Order': 3, 'Representative': [2, 5, 3, 4, 1, 8, 6, 7]}, {'Size': '42', 'Order': 4, 'Representative': [3, 1, 4, 2, 7, 8, 6, 5]}, {'Size': '56', 'Order': 6, 'Representative': [6, 8, 3, 4, 7, 2, 1, 5]}, {'Size': '48', 'Order': 7, 'Representative': [2, 3, 8, 1, 7, 6, 4, 5]}, {'Size': '42', 'Order': 8, 'Representative': [8, 6, 5, 7, 4, 1, 2, 3]}, {'Size': '42', 'Order': 8, 'Representative': [5, 8, 7, 6, 2, 3, 1, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 6]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 7]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [4, 4]}, {'Data': {'Powers': [1, 7], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['45472930259215653652260411089852565223276407448', '290654633225154778338095993365091201091338360', '-274541692143507557130141794377529941015900960', '15661270154394702325144170100338234713823656', '-468926112703198743816041511204114714947416', '9225912465978285557582821884920472433072', '-131349263941581812014615886820749927720', '1431068391728202707619234778143044940', '-12379315618432687790242939502388392', '87213950660814348601861319160220', '-509378448240914529070726718688', '2497435167443661178788931576', '-10367715695833125107228912', '36614910002870826551176', '-110044931342024519290', '280512585428059530', '-603301977729794', '1080184144704', '-1573929728', '1873032', '-1512', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-278820008210327710491412762040866507291767870552', '963915222008487607420785446587002429527020872', '44623053283531830051072751004453484450423456', '-522933672995153120137755903867781780421112', '2369094059024240824699977120064327327904', '6290953247310489290803373908722438696', '-170427852758162404845793829674202088', '1222142129220372608674821889960220', '-12489131489954295270523918520808', '207909693601417004830539895716', '-2935754680654565844006483208', '30373209054217655829445116', '-241437595956126627099728', '1525930685820039855440', '-7870225638744863130', '33362435105419714', '-116538334947510', '330853817952', '-746937128', '1277976', '-1512', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [4, 3, 9, 1, 4, 6, 9, 8, 4, 7, 3, 4, 9, 5, 3, 7, 9, 6, 7, 2, 8, 5, 3, 6, 9, 6, 6, 4, 2, 2, 7, 8, 5, 8, 4, 5, 9, 1, 6, 6, 4, 8, 7, 4, 5, 6, 4, 6, 8, 6, 7, 5, 8, 3, 6, 4, 3, 6, 2, 4, 3, 8, 6, 6, 6, 5, 4, 5, 5, 6, 9, 5, 9, 4, 4, 9, 2, 3, 4, 8, 8, 2, 4, 6, 6, 7, 2, 4, 8, 7, 8, 8, 5, 5, 5, 6, 9, 6, 6, 7, 4, 4, 3, 2, 2, 9, 3, 6, 4, 6, 9, 4, 5, 3, 7, 2, 8, 9, 2, 7, 6, 7, 8, 4, 9, 2, 2, 6, 9, 8, 7, 5, 7, 4, 8, 9, 9, 6, 9, 4, 9, 5, 7, 4, 9, 8, 8, 3, 8, 7, 4, 8, 4, 9, 7, 4, 4, 9, 6, 8, 7, 5, 7, 9, 5, 8, 2, 6], 'G-Gens': [[2, 1, 5, 7, 3, 8, 4, 6], [6, 8, 3, 4, 7, 2, 1, 5]], 'G-Name': 'PSL(2,7).C2', 'Polynomial': [-17946, 22167, -9779, 2765, -819, 91, -21, -1, 1], 'QpRts': [['6626942815643764838158524495942561729488892815146785343442491370668894495092054', '0', '0'], ['-5653713089615936342130234983457881130829496742453947814529288038820241640451622', '-1324833630715326229280525870898590573764029199262563204380867185091251432073769', '925182674815185418611610064402057226216867306325302847658541916619837144559004'], ['-4732599649388918674312520610198170264149295341896186053810961740493380385211656', '-6240846435440223601844156365483739493675396480652265100237908999869969977383427', '5879733206618732480001461810845632176814192084900943519580118019025803036997708'], ['6513399790684868712512010405501281576029484422487146438201812863926263113589239', '-1795074098083446833014385323381697015999219407917274336075369897433285952434713', '-442619478968495836466534168928164822378224047746896331413059839301482408162171'], ['6460141501513943718273954770106978134082258808045132858425249879903766675943023', '3119907728798773062294911194280287589763248607179837540456237082524537384508482', '-482563195846689582145075895473892403838643258578406516245482077318354736396833'], ['-4957132803269930931215270130567887816701365579710470972380206398648080728644414', '2865327746232704300880216283454454982454584799542089506899899652843688372264625', '-1284091201464883410048819179464718706759412078645116748426767096577687632744741'], ['-4211737414276381773363721014248151685704690878674170902106715266045190989218415', '0', '0'], ['-45301151291409547922742933078730542215787502944288897242382670492030541098208', '3375518689207519300963940082029284511220811681110175593338009347026281605118802', '-4595642005153849069952642631380913470054780006255826771153350922448115404252967']], 'QpRts-minpoly': [9, 2, 0, 1], 'QpRts-p': 11, 'QpRts-prec': 76, 'Size': 336, 'TransitiveDegree': 8}