Artin representation data - 64.721445260473156418793768088129412079379893809486403681275927482148552081802223356386357154964875347572775714778963241367202153708093250233189608021684192795967042951023489910358569369510211600245886005204248239495803783922909435131315168886175355499073444071046324359434284952020516195727565536253553630606833962148208975720077332008665047606903798541028889290913259521711376695296.168.a

Formats: - HTML - YAML - JSON - 2024-04-23T05:30:49.425185

• 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, 43, 107, 179], 'Baselabel': '64.721445260473156418793768088129412079379893809486403681275927482148552081802223356386357154964875347572775714778963241367202153708093250233189608021684192795967042951023489910358569369510211600245886005204248239495803783922909435131315168886175355499073444071046324359434284952020516195727565536253553630606833962148208975720077332008665047606903798541028889290913259521711376695296.168.a', 'CharacterField': 1, 'Conductor': 721445260473156418793768088129412079379893809486403681275927482148552081802223356386357154964875347572775714778963241367202153708093250233189608021684192795967042951023489910358569369510211600245886005204248239495803783922909435131315168886175355499073444071046324359434284952020516195727565536253553630606833962148208975720077332008665047606903798541028889290913259521711376695296, 'Container': '168', 'Dets': ['1.1.1t1.a.a'], 'Dim': 64, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [15, 10, 16, 17, 17], 'LocalFactors': [[[1], [-64], [2016], [-41664], [635376], [-7624512], [74974368], [-621216192], [4426165368], [-27540584512], [151473214816], [-743595781824], [3284214703056], [-13136858812224], [47855699958816], [-159518999862720], [488526937079580], [-1379370175283520], [3601688791018080], [-8719878125622720], [19619725782651120], [-41107996877935680], [80347448443237920], [-146721427591999680], [250649105469666120], [-401038568751465792], [601557853127198688], [-846636978475316672], [1118770292985239888], [-1388818294740297792], [1620288010530347424], [-1777090076065542336], [1832624140942590534], [-1777090076065542336], [1620288010530347424], [-1388818294740297792], [1118770292985239888], [-846636978475316672], [601557853127198688], [-401038568751465792], [250649105469666120], [-146721427591999680], [80347448443237920], [-41107996877935680], [19619725782651120], [-8719878125622720], [3601688791018080], [-1379370175283520], [488526937079580], [-159518999862720], [47855699958816], [-13136858812224], [3284214703056], [-743595781824], [151473214816], [-27540584512], [4426165368], [-621216192], [74974368], [-7624512], [635376], [-41664], [2016], [-64], [1]], [[1], [0], [-32], [0], [496], [0], [-4960], [0], [35960], [0], [-201376], [0], [906192], [0], [-3365856], [0], [10518300], [0], [-28048800], [0], [64512240], [0], [-129024480], [0], [225792840], [0], [-347373600], [0], [471435600], [0], [-565722720], [0], [601080390], [0], [-565722720], [0], [471435600], [0], [-347373600], [0], [225792840], [0], [-129024480], [0], [64512240], [0], [-28048800], [0], [10518300], [0], [-3365856], [0], [906192], [0], [-201376], [0], [35960], [0], [-4960], [0], [496], [0], [-32], [0], [1]], [[1], [0], [-32], [0], [496], [0], [-4960], [0], [35960], [0], [-201376], [0], [906192], [0], [-3365856], [0], [10518300], [0], [-28048800], [0], [64512240], 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[-120], [0], [45], [0], [-90], [0], [45], [0], [-10], [0], [20], [0], [-10], [0], [1], [0], [-2], [0], [1]], [[1], [0], [1], [0], [1], [0], [-10], [0], [-10], [0], [-10], [0], [45], [0], [45], [0], [45], [0], [-120], [0], [-120], [0], [-120], [0], [210], [0], [210], [0], [210], [0], [-252], [0], [-252], [0], [-252], [0], [210], [0], [210], [0], [210], [0], [-120], [0], [-120], [0], [-120], [0], [45], [0], [45], [0], [45], [0], [-10], [0], [-10], [0], [-10], [0], [1], [0], [1], [0], [1]], [[1], [-1], [0], [0], [0], [0], [0], [-9], [9], [0], [0], [0], [0], [0], [36], [-36], [0], [0], [0], [0], [0], [-84], [84], [0], [0], [0], [0], [0], [126], [-126], [0], [0], [0], [0], [0], [-126], [126], [0], [0], [0], [0], [0], [84], [-84], [0], [0], [0], [0], [0], [-36], [36], [0], [0], [0], [0], [0], [9], [-9], [0], [0], [0], [0], [0], [-1], [1]], [[1], [-1], [0], [0], [0], [0], [0], [-9], [9], [0], [0], [0], [0], [0], [36], [-36], [0], [0], [0], [0], [0], [-84], [84], [0], [0], [0], [0], [0], [126], [-126], [0], [0], [0], [0], [0], [-126], [126], [0], [0], [0], [0], [0], [84], [-84], [0], [0], [0], [0], [0], [-36], [36], [0], [0], [0], [0], [0], [9], [-9], [0], [0], [0], [0], [0], [-1], [1]], [[1], [1], [1], [1], [1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-4], [-4], [-4], [-4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [6], [6], [6], [6], [6], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-4], [-4], [-4], [-4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1], [1], [1], [1], [1]], [[1], [1], [1], [1], [1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-4], [-4], [-4], [-4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [6], [6], [6], [6], [6], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-4], [-4], [-4], [-4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1], [1], [1], [1], [1]], [[1], [0], [-1]], [[1], [-10], [45], [-120], [210], [-252], [210], [-120], [45], [-10], [1]], [[1], [2], [3], [0], [-3], [-6], [-3], [0], [3], [2], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T49', 'Galt': 49, 'HardPrimes': [2, 3, 43, 107, 179], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [823572, -48, -140, -224, -210, -112, -28, 0, 1], 'NumBadPrimes': 4, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [823572, -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': '7.81803428774472904272307991671908472193024.8t49.a', 'Character': [[7], [-1], [3], [4], [1], [-1], [1], [2], [0], [-1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.6691800959260261524989557833098666914517263464001265492376454314331705835914264576.15t72.a', 'Character': [[14], [6], [2], [-1], [2], [2], [0], [-1], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.547412263143796260651164809894166661274444549795150539175566846599677122422153050393355170500734625865226237535402877517824.28t433.a', 'Character': [[20], [4], [4], [5], [-1], [0], [0], [0], [1], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.8968802519347957934508684245306026578320499503843746433852487214689109973764555577644731113484036110175866675780040745252028416.56.a', 'Character': [[21], [-3], [1], [6], [0], [1], [-1], [1], [-2], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.8968802519347957934508684245306026578320499503843746433852487214689109973764555577644731113484036110175866675780040745252028416.336.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': '21.8968802519347957934508684245306026578320499503843746433852487214689109973764555577644731113484036110175866675780040745252028416.336.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': '28.733678798083793818846815636790003837121534483383039940204043295757973822380008242845044637712290728843841211596848422914144058391616775997435785101670508706667884969984.56.a', 'Character': [[28], [-4], [4], [1], [1], [0], [0], [-2], [1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.983325758298333432739472346831683783169622592307299367168097164471684040029546894302854739614807015997808894697736296766395145328333406700978570876843002102554323628771691186864824483122404006192367745338435436544.70.a', 'Character': [[35], [3], [-5], [5], [2], [-1], [-1], [0], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '45.736214988834978586824887078598173735275964917576818599485961174434340917836333119386105088018830740312720246096531719787116632898806474746056411901316029275157243411745889882971880737948397841553939846010489069307152807525320767876076842238534161528215633189725005713722310656.336.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': '45.736214988834978586824887078598173735275964917576818599485961174434340917836333119386105088018830740312720246096531719787116632898806474746056411901316029275157243411745889882971880737948397841553939846010489069307152807525320767876076842238534161528215633189725005713722310656.336.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': '56.538284578757680300589744289132322142683998493574226142765564994366343221986364558883559728599936751140369714421690446513768293869991191354539408359254142399337930987866903143880965182991872182987829542930464965100423944595192085932805372471483858045893714873563660627810139245008445987992462882337262524015158627175711694538528580960256.105.a', 'Character': [[56], [8], [0], [-4], [-1], [0], [0], [1], [0], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '64.721445260473156418793768088129412079379893809486403681275927482148552081802223356386357154964875347572775714778963241367202153708093250233189608021684192795967042951023489910358569369510211600245886005204248239495803783922909435131315168886175355499073444071046324359434284952020516195727565536253553630606833962148208975720077332008665047606903798541028889290913259521711376695296.168.a', 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '70.59016695979796903189671030336103880599899536546706113510462398485376470448700933031830794227899628932208516683788334840174015716296149275377437708869762337735502451514804547629053801764946043923320308820115603135729471109879488607470957425543316278921060343998528431568953907942937110754123402384112093599769621745776180854427079692241715708815385536672320002657161858536581947903538610248914145586055856607561722944815104.120.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': ['-13728623379508433854464', '1'], 'ConjugacyClass': 12}, {'RootOf': ['13728623379508433854464', '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': ['-13728623379508433854464', '1'], 'ConjugacyClass': 14}, {'RootOf': ['13728623379508433854464', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'ALT', 'CycleType': [3, 5]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [6, 10, 10, 5, 8, 9, 11, 5, 12, 11, 12, 6, 10, 1, 9, 10, 5, 10, 9, 14, 9, 7, 14, 7, 6, 12, 12, 5, 10, 5, 11, 12, 9, 13, 8, 5, 7, 5, 11, 12, 5, 10, 10, 12, 10, 12, 8, 10, 14, 6, 10, 9, 11, 12, 7, 7, 12, 12, 6, 5, 10, 12, 3, 11, 11, 6, 11, 12, 7, 8, 9, 13, 6, 7, 11, 6, 6, 7, 6, 11, 7, 14, 11, 10, 9, 8, 10, 7, 14, 12, 9, 11, 8, 11, 10, 6, 12, 6, 12, 14, 14, 9, 10, 10, 11, 9, 12, 7, 12, 11, 12, 7, 5, 6, 11, 10, 12, 7, 7, 10, 11, 5, 12, 14, 11, 8, 12, 7, 8, 10, 8, 7, 9, 12, 11, 14, 12, 12, 6, 12, 9, 11, 11, 13, 9, 2, 12, 7, 7, 14, 10, 13, 13, 7, 12, 12, 13, 11, 6, 12, 11, 12, 12, 7, 11, 5, 11, 9], 'G-Gens': [[2, 1, 4, 5, 6, 7, 8, 3], [2, 3, 1, 4, 5, 6, 7, 8]], 'G-Name': 'A8', 'Polynomial': [823572, -48, -140, -224, -210, -112, -28, 0, 1], 'QpRts': [['-956750977732820120175032683', '-297357969501543116893601543'], ['-586384788787750393938202822', '-101336861341843648138076413'], ['602621688307392848841629617', '0'], ['994462534450373223010400198', '297357969501543116893601543'], ['600342938742116141555980882', '0'], ['68388259091319492554362662', '0'], ['742586396720072460894299797', '101336861341843648138076413'], ['817819209601321999211860792', '0']], 'QpRts-minpoly': [5, 306, 1], 'QpRts-p': 307, 'QpRts-prec': 11, 'Size': 20160, 'TransitiveDegree': 8}