-
artin_reps • Show schema
Hide schema
{'BadPrimes': [2, 11, 299471], 'Baselabel': '64.222782940600756385339091727279237526407392092855181675863732794294136438488707022116623676959110654898198705916683193436931318538237048069715568972966574362920667188382068848292204257944747801973055768638886694462264709775626557550848455283088658044237764903357173983532203985013961077608039995256096613560536889413501430034033745991126713635159774837808561810866203012718294368424701749227367395334067060736.168.a', 'CharacterField': 1, 'Conductor': 222782940600756385339091727279237526407392092855181675863732794294136438488707022116623676959110654898198705916683193436931318538237048069715568972966574362920667188382068848292204257944747801973055768638886694462264709775626557550848455283088658044237764903357173983532203985013961077608039995256096613560536889413501430034033745991126713635159774837808561810866203012718294368424701749227367395334067060736, '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, 16], '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], [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], [-4], [6], [-24], [81], [-120], [270], [-780], [1140], [-1900], [4750], [-6840], [9405], [-20520], [29070], [-34884], [66861], [-93024], [100776], [-170544], [232560], [-232560], [348840], [-465120], [436050], [-581400], [755820], [-671840], [797810], [-1007760], [856596], [-906984], [1108536], [-906984], [856596], [-1007760], [797810], [-671840], [755820], [-581400], [436050], [-465120], [348840], [-232560], [232560], [-170544], [100776], [-93024], [66861], [-34884], [29070], [-20520], [9405], [-6840], [4750], [-1900], [1140], [-780], [270], [-120], [81], [-24], [6], [-4], [1]], [[1], [2], [3], [-18], [-39], [-60], [150], [360], [570], [-760], [-2090], [-3420], [2565], [8550], [14535], [-5814], [-26163], [-46512], [7752], [62016], [116280], [0], [-116280], [-232560], [-29070], [174420], [377910], [83980], [-209950], [-503880], [-151164], [201552], [554268], [201552], [-151164], [-503880], [-209950], [83980], [377910], [174420], [-29070], [-232560], [-116280], [0], [116280], [62016], [7752], [-46512], [-26163], [-5814], [14535], [8550], [2565], [-3420], [-2090], [-760], [570], [360], [150], [-60], [-39], [-18], [3], [2], [1]], [[1], [0], [0], [0], [-16], [0], [0], [0], [120], [0], [0], [0], [-560], [0], [0], [0], [1820], [0], [0], [0], [-4368], [0], [0], [0], [8008], [0], [0], [0], [-11440], [0], [0], [0], [12870], [0], [0], [0], [-11440], [0], [0], [0], [8008], [0], [0], [0], [-4368], [0], [0], [0], [1820], [0], [0], [0], [-560], [0], [0], [0], [120], [0], [0], [0], [-16], [0], [0], [0], [1]], [[1], [0], [0], [0], [-16], [0], [0], [0], [120], [0], [0], [0], [-560], [0], [0], [0], [1820], [0], [0], [0], [-4368], [0], [0], [0], [8008], [0], [0], [0], [-11440], [0], [0], [0], [12870], [0], [0], [0], [-11440], [0], [0], [0], [8008], [0], [0], [0], [-4368], [0], [0], [0], [1820], [0], [0], [0], [-560], [0], [0], [0], [120], [0], [0], [0], [-16], [0], [0], [0], [1]], [[1], [1], [1], [1], [1], [-12], [-12], [-12], [-12], [-12], [66], [66], [66], [66], [66], [-220], [-220], [-220], [-220], [-220], [495], [495], [495], [495], [495], [-792], [-792], [-792], [-792], [-792], [924], [924], [924], [924], [924], [-792], [-792], [-792], [-792], [-792], [495], [495], [495], [495], [495], [-220], [-220], [-220], [-220], [-220], [66], [66], [66], [66], [66], [-12], [-12], [-12], [-12], [-12], [1], [1], [1], [1], [1]], [[1], [0], [-2], [0], [1], [0], [-10], [0], [20], [0], [-10], [0], [45], [0], [-90], [0], [45], [0], [-120], [0], [240], [0], [-120], [0], [210], [0], [-420], [0], [210], [0], [-252], [0], [504], [0], [-252], [0], [210], [0], [-420], [0], [210], [0], [-120], [0], [240], [0], [-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], [-2], [0], [1]], [[1], [2], [3], [0], [-3], [-6], [-3], [0], [3], [2], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T49', 'Galt': 49, 'HardPrimes': [2, 3, 11, 299471], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [210825792, -6144, -8960, -7168, -3360, -896, -112, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [210825792, -6144, -8960, -7168, -3360, -896, -112, 0, 1], 'Proj_nTj': [8, 49]}
-
artin_field_data • Show schema
Hide schema
{'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': '7.1339937868468943908837290142533567581866950656.8t49.a', 'Character': [[7], [-1], [3], [4], [1], [-1], [1], [2], [0], [-1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.438338254725853717543446829737130375000396931678017648045960239296340672482463308578816.15t72.a', 'Character': [[14], [6], [2], [-1], [2], [2], [0], [-1], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.587346026705757409329097953127806904090246605498616150767261977216511544966369656947223250595617079578935403719680114832430958903296.28t433.a', 'Character': [[20], [4], [4], [5], [-1], [0], [0], [0], [1], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.38492309206188517577791763456183953266458401537957308056683280938861300610916001837693222951034360927285110618172956005658195322686406656.56.a', 'Character': [[21], [-3], [1], [6], [0], [1], [-1], [1], [-2], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.38492309206188517577791763456183953266458401537957308056683280938861300610916001837693222951034360927285110618172956005658195322686406656.336.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': '21.38492309206188517577791763456183953266458401537957308056683280938861300610916001837693222951034360927285110618172956005658195322686406656.336.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': '28.51577302750187748588590471952791540826124128220997782700503019645669848909511515305373354480806526235835053354867991580825992502595090562913390893953764220187797719803331068701966336.56.a', 'Character': [[28], [-4], [4], [1], [1], [0], [0], [-2], [1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.4319398819278998150154580240099628827633543521348918785108266724309694580512138186010755734135578909623671844864396633508138331608324264565536848061113872060837182026221944448738049339470776931792566724807172552456499967819776.70.a', 'Character': [[35], [3], [-5], [5], [2], [-1], [-1], [0], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '45.13559081488031440338690741620556694597258118450913697862626112088885164315842073373145304923857022281205723656485753675489228137170683659141154518652553737628933896487685615396915258072549735965214348326100559241049324419521718273662165111913146981263516393938827478785990194729083722227416825856.336.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': '45.13559081488031440338690741620556694597258118450913697862626112088885164315842073373145304923857022281205723656485753675489228137170683659141154518652553737628933896487685615396915258072549735965214348326100559241049324419521718273662165111913146981263516393938827478785990194729083722227416825856.336.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': '56.2536981734261059469308154282456916553450687052433371413837018169845053242516074376537429932819331354881291480049003300937240010207478469767552305760730457122238084674127654451615317955777147919481819653905863090024056156185388897041732455219269621243680177925961942123949810546997760188530347493398746849200676680165894353753292175349982617395901957140381696.105.a', 'Character': [[56], [8], [0], [-4], [-1], [0], [0], [1], [0], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '64.222782940600756385339091727279237526407392092855181675863732794294136438488707022116623676959110654898198705916683193436931318538237048069715568972966574362920667188382068848292204257944747801973055768638886694462264709775626557550848455283088658044237764903357173983532203985013961077608039995256096613560536889413501430034033745991126713635159774837808561810866203012718294368424701749227367395334067060736.168.a', 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '70.298515298559820853146233553293501185646239431513941697786107861212612015335439044482418409802042655473725360710184592210062785864175414127761635729685882647604942402453254279368411873356190395086615057118546071120575571101323478875596763342603808612092989805280636460128151607849287824483698133709585623836766828635522191819110721701718454776812411717039031467214142968137432207804925435102074975207894646681184099457660251232850569538568377069067042816.120.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': ['-921199058685091995364167254016', '1'], 'ConjugacyClass': 12}, {'RootOf': ['921199058685091995364167254016', '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': ['-921199058685091995364167254016', '1'], 'ConjugacyClass': 14}, {'RootOf': ['921199058685091995364167254016', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'ALT', 'CycleType': [3, 5]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [7, 10, 10, 6, 5, 6, 10, 13, 10, 5, 9, 14, 7, 11, 13, 13, 8, 14, 6, 8, 7, 7, 12, 7, 12, 12, 10, 10, 7, 9, 6, 12, 12, 14, 8, 12, 9, 11, 9, 10, 9, 6, 11, 10, 6, 11, 11, 14, 7, 7, 11, 7, 12, 6, 11, 9, 8, 12, 12, 11, 6, 9, 6, 6, 5, 7, 12, 9, 7, 7, 10, 7, 4, 12, 10, 5, 9, 7, 6, 10, 5, 6, 10, 11, 9, 7, 7, 8, 8, 13, 12, 6, 5, 14, 7, 11, 10, 12, 12, 5, 12, 7, 13, 13, 5, 10, 11, 8, 13, 14, 9, 9, 13, 5, 10, 6, 9, 14, 13, 10, 10, 10, 11, 7, 9, 12, 7, 6, 11, 7, 12, 14, 4, 12, 9, 7, 12, 11, 7, 11, 10, 11, 9, 6, 7, 7, 7, 5, 10, 3, 11, 11, 9, 11, 10, 12, 9, 11, 10, 13, 12, 7, 9, 12, 12, 13, 8, 12], 'G-Gens': [[2, 1, 4, 5, 6, 7, 8, 3], [2, 3, 1, 4, 5, 6, 7, 8]], 'G-Name': 'A8', 'Polynomial': [210825792, -6144, -8960, -7168, -3360, -896, -112, 0, 1], 'QpRts': [['-71402288426963660147051744089306822', '0'], ['50538919355550880218485251486032422', '-55970917994284244212529755169135901'], ['56589502422196881627389568290972296', '0'], ['934075947670166610943596703667761', '55970917994284244212529755169135901'], ['83572598151168843303126485155513975', '0'], ['-6361411719565977174188569119170824', '0'], ['7240202604302299770671952316244072', '-47366405341386104069087470272119924'], ['49547540020696746797012825371162001', '47366405341386104069087470272119924']], 'QpRts-minpoly': [5, 862, 1], 'QpRts-p': 863, 'QpRts-prec': 12, 'Size': 20160, 'TransitiveDegree': 8}