Artin representation data - 12.19871009045337088.18t315.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, 23, 37], 'Baselabel': '12.19871009045337088.18t315.a', 'CharacterField': 1, 'Conductor': 19871009045337088, 'Container': '18t315', 'Dets': ['1.37.2t1.a.a'], 'Dim': 12, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[12], [4], [2], [0], [0], [2], [0], [3], [-3], [0], [0], [0], [2], [-1], [-2], [1], [0], [-1], [-1], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [23, 24, 25], 'LocalFactors': [[[1], [-12], [66], [-220], [495], [-792], [924], [-792], [495], [-220], [66], [-12], [1]], [[1], [-4], [2], [12], [-17], [-8], [28], [-8], [-17], [12], [2], [-4], [1]], [[1], [-2], [-4], [10], [5], [-20], [0], [20], [-5], [-10], [4], [2], [-1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [-2], [-4], [10], [5], [-20], [0], [20], [-5], [-10], [4], [2], [-1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [-3], [3], [-4], [9], [-9], [6], [-9], [9], [-4], [3], [-3], [1]], [[1], [3], [6], [5], [0], [-9], [-12], [-9], [0], [5], [6], [3], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [0], [0], [0], [-3], [0], [0], [0], [3], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-3], [0], [0], [0], [3], [0], [0], [0], [-1]], [[1], [-2], [2], [-2], [2], [-2], [0], [2], [-2], [2], [-2], [2], [-1]], [[1], [1], [2], [1], [2], [1], [0], [-1], [-2], [-1], [-2], [-1], [-1]], [[1], [2], [2], [0], [-2], [-2], [-2], [-2], [-2], [0], [2], [2], [1]], [[1], [-1], [2], [-3], [4], [-5], [4], [-5], [4], [-3], [2], [-1], [1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [1], [-1], [-2], [-1], [1], [0], [-1], [1], [2], [1], [-1], [-1]], [[1], [1], [2], [1], [2], [1], [0], [-1], [-2], [-1], [-2], [-1], [-1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-1]], [[1], [1], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [0], [1], [-1], [1], [-1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T31', 'Galt': 31, 'HardPrimes': [2, 23, 37], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, -3, -6, 2, -2, 6, -2, 2, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [1296, 3490], 'Proj_Polynomial': [1, -3, -6, 2, -2, 6, -2, 2, -3, 1], 'Proj_nTj': [9, 31]}
• 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], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.37.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [1], [1], [-1], [-1], [1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.851.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [-1], [1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.23.2t1.a', 'Character': [[1], [-1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [-1], [1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.78292.6t3.a', 'Character': [[2], [-2], [0], [-2], [2], [0], [2], [2], [2], [-1], [0], [0], [0], [0], [-2], [-2], [2], [0], [0], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.148.3t2.a', 'Character': [[2], [2], [0], [2], [2], [0], [2], [2], [2], [-1], [0], [0], [0], [0], [2], [2], [2], [0], [0], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.78292.4t5.a', 'Character': [[3], [-1], [1], [3], [-1], [1], [3], [3], [3], [0], [-1], [-1], [1], [1], [-1], [-1], [-1], [1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.3404.6t11.b', 'Character': [[3], [1], [-1], [-3], [-1], [1], [3], [3], [3], [0], [-1], [1], [-1], [-1], [1], [1], [-1], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.2896804.6t8.a', 'Character': [[3], [-1], [-1], [3], [-1], [-1], [3], [3], [3], [0], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.125948.6t11.b', 'Character': [[3], [1], [1], [-3], [-1], [-1], [3], [3], [3], [0], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.74561216.9t31.a', 'Character': [[6], [4], [2], [0], [2], [0], [3], [-3], [0], [0], [2], [0], [-1], [2], [1], [-2], [-1], [-1], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.20865285246656.18t300.a', 'Character': [[6], [-4], [-2], [0], [2], [0], [3], [-3], [0], [0], [2], [0], [1], [-2], [-1], [2], [-1], [1], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.74561216.18t319.a', 'Character': [[6], [4], [-2], [0], [2], [0], [3], [-3], [0], [0], [-2], [0], [1], [-2], [1], [-2], [-1], [1], [0], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.20865285246656.18t311.a', 'Character': [[6], [-4], [2], [0], [2], [0], [3], [-3], [0], [0], [-2], [0], [-1], [2], [-1], [2], [-1], [-1], [0], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.134263574630656.24t2893.a', 'Character': [[8], [0], [-4], [0], [0], [0], [-4], [-1], [2], [2], [0], [0], [2], [2], [0], [0], [0], [-1], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.134263574630656.12t213.a', 'Character': [[8], [0], [4], [0], [0], [0], [-4], [-1], [2], [2], [0], [0], [-2], [-2], [0], [0], [0], [1], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.5560723042256176043008.36t2217.a', 'Character': [[12], [-4], [-2], [0], [0], [2], [0], [3], [-3], [0], [0], [0], [-2], [1], [2], [-1], [0], [1], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.7612629844848705002877952.36t2214.a', 'Character': [[12], [-4], [2], [0], [0], [-2], [0], [3], [-3], [0], [0], [0], [2], [-1], [2], [-1], [0], [-1], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.1555741040177531293696.36t2210.a', 'Character': [[12], [0], [0], [0], [-4], [0], [6], [-6], [0], [0], [0], [0], [0], [0], [0], [0], [2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.27203411383066473472.36t2216.a', 'Character': [[12], [4], [-2], [0], [0], [-2], [0], [3], [-3], [0], [0], [0], [-2], [1], [-2], [1], [0], [1], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.19871009045337088.18t315.a', 'Character': [[12], [4], [2], [0], [0], [2], [0], [3], [-3], [0], [0], [0], [2], [-1], [-2], [1], [0], [-1], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.4506676868150433361703747584.24t2912.a', 'Character': [[16], [0], [0], [0], [0], [0], [-8], [-2], [4], [-2], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [5, 2, 3, 4, 1, 6, 7, 8, 9]}, {'Size': '18', 'Order': 2, 'Representative': [7, 2, 3, 4, 8, 9, 1, 5, 6]}, {'Size': '27', 'Order': 2, 'Representative': [5, 3, 2, 4, 1, 6, 8, 7, 9]}, {'Size': '27', 'Order': 2, 'Representative': [5, 3, 2, 4, 1, 6, 7, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [2, 1, 5, 6, 3, 4, 8, 7, 9]}, {'Size': '6', 'Order': 3, 'Representative': [1, 3, 4, 2, 5, 6, 7, 8, 9]}, {'Size': '8', 'Order': 3, 'Representative': [6, 4, 2, 3, 1, 5, 9, 7, 8]}, {'Size': '12', 'Order': 3, 'Representative': [6, 4, 2, 3, 1, 5, 7, 8, 9]}, {'Size': '72', 'Order': 3, 'Representative': [7, 1, 5, 6, 8, 9, 2, 3, 4]}, {'Size': '54', 'Order': 4, 'Representative': [2, 5, 1, 6, 3, 4, 7, 8, 9]}, {'Size': '162', 'Order': 4, 'Representative': [2, 5, 1, 6, 3, 4, 8, 7, 9]}, {'Size': '36', 'Order': 6, 'Representative': [7, 3, 4, 2, 8, 9, 1, 5, 6]}, {'Size': '36', 'Order': 6, 'Representative': [2, 6, 1, 5, 3, 4, 7, 8, 9]}, {'Size': '36', 'Order': 6, 'Representative': [5, 3, 4, 2, 1, 6, 7, 8, 9]}, {'Size': '36', 'Order': 6, 'Representative': [5, 3, 4, 2, 1, 6, 8, 9, 7]}, {'Size': '54', 'Order': 6, 'Representative': [5, 4, 2, 3, 1, 6, 8, 7, 9]}, {'Size': '72', 'Order': 6, 'Representative': [7, 3, 4, 2, 8, 9, 6, 1, 5]}, {'Size': '108', 'Order': 6, 'Representative': [2, 6, 1, 5, 3, 4, 8, 7, 9]}, {'Size': '216', 'Order': 6, 'Representative': [7, 5, 1, 6, 8, 9, 2, 3, 4]}, {'Size': '144', 'Order': 9, 'Representative': [7, 6, 1, 5, 8, 9, 2, 3, 4]}, {'Size': '108', 'Order': 12, 'Representative': [7, 3, 4, 2, 8, 9, 5, 1, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 15, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-9603518851', '-295135534510', '-1173219698547', '4075734824620', '-5155091331960', '3730035962500', '-1750939294904', '553737094204', '-114148693270', '12036967912', '868285770', '-616519356', '129398432', '-16814692', '1491936', '-91180', '3697', '-90', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-2946221921498601535225', '6473060924813940763231', '-5605623500456698424795', '2138995144467010713869', '-132245956229463572318', '23990356635052817010', '-342162949261416371410', '373783265903610356510', '-227365570118371363059', '97580356875555497173', '-32417705702177470641', '8755246821351379719', '-1980607619274947604', '382676600394176460', '-63967911008946412', '9326583105992372', '-1191221726378191', '133410881088153', '-13071985297421', '1114370642891', '-81890818990', '5116527010', '-266478370', '11245134', '-368677', '8787', '-135', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 4]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 6]}, {'Data': 0, 'Classes': 17, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 3]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 4]}, {'Data': 0, 'Classes': 16, 'Algorithm': 'CYC', 'CycleType': [1, 2, 3, 3]}, {'Data': 0, 'Classes': 19, 'Algorithm': 'CYC', 'CycleType': [1, 2, 6]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 3]}, {'Data': 0, 'Classes': 22, 'Algorithm': 'CYC', 'CycleType': [2, 3, 4]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['0', '0', '0', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['137646934344877268220772352', '1864528450961104509910122496', '1647905697499644761609338880', '2590338641903371184062332928', '1704446897030701128699871232', '452799886824457139547799552', '-787701793542871700438253568', '179884205189513238215131136', '-856664608084037556764672', '-10617021833024816410525696', '4883154861412810795778048', '-788474864247310335475712', '-185171092089819555823616', '88313725748260739547136', '-7335739854213087002624', '-1957121432819972079616', '460988621459363561472', '-13738089440439500800', '-6503917128316485632', '1060191489413312512', '-55788728278151168', '-10050347289430016', '2925391955414016', '-167727804556800', '-35857568040192', '5549331645440', '109291437696', '-67357577344', '2242188352', '459109408', '-31909664', '-1730048', '202816', '3240', '-656', '0', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['709320901005401882525433856', '29303314979400472714991894528', '286134268816225233577774678016', '-333760567298828716663765991424', '245470220577691853190024134656', '-89107717926874970628470865920', '13255201212596452074088038400', '3584147791731538517808906240', '-1942065445918520138412326912', '76955260420337129575940096', '68519329045346516388806656', '-839822989494395022868480', '-1453825221835346770395136', '-365294787529626677280768', '35381714618986717577216', '18771200110928539451392', '-565597849495673061376', '-464718724450109210624', '-14522835977601257472', '7212414185213648896', '1054476687805923328', '-78857152985309184', '-28072422331776000', '668312921244672', '450200026509824', '-4729031623680', '-4827772639232', '27713835136', '35644581184', '-120392704', '-179756272', '324352', '592720', '-392', '-1152', '0', '1'], 'ConjugacyClass': 18}, {'RootOf': ['243308562631826808593253185318382600689768010462093912619654524917985613644189021503488', '-1502039465269073846675976993184346737940643183101214626561442279278669888096254350589952', '4303810193848156881427051123426915222587400696468869081469033762569651291051229622304768', '-7532878365550111090937221623402754168418601389738961400579035293969534203553126346129408', '8865200087034522589699634008074816753953509152396459232279062937154742528749312166330368', '-7181359753930520114876835012141616522540831500775887208325785830114739013475202211250176', '3781980316148989358884173547758424457554295420988934947070644025533969675990928730357760', '-877773632884687376517266401633446885969830109508528519760799487105457589427604312555520', '-444258565825621791511820198942731941400002593362653657679872056052416488938130154455040', '545839768758864470468969821321758649541077158816242934747204086334596434763476740603904', '-249319905280303383737109897478906491536771910268250343768803911435483809678577018863616', '35895940236798352811067174346741427429499499684533537654949944865561773790060037013504', '25322037689833608384638576095359422904052479164337889915313464625275805255612005089280', '-18115141046655521552169643979610145961193340481379493457604495428280459746376601829376', '4498017015502718582034696808562106103846854796358374216571145343188329441034590224384', '521556760460868457969175750722003994335468127316553541388982687192815236777179611136', 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