# Degree-13 polynomials (x^13 - a, Gaussian periods, Hilbert class polynomials of class
# number 13, random ones) labeled nTk by Magma, used as an oracle.  Per line: nTk magma c0,...,c13
13T6 magma -2,0,0,0,0,0,0,0,0,0,0,0,0,1
13T6 magma -3,0,0,0,0,0,0,0,0,0,0,0,0,1
13T6 magma -5,0,0,0,0,0,0,0,0,0,0,0,0,1
13T6 magma -6,0,0,0,0,0,0,0,0,0,0,0,0,1
13T6 magma -7,0,0,0,0,0,0,0,0,0,0,0,0,1
13T6 magma -10,0,0,0,0,0,0,0,0,0,0,0,0,1
13T6 magma -12,0,0,0,0,0,0,0,0,0,0,0,0,1
13T6 magma 2,0,0,0,0,0,0,0,0,0,0,0,0,1
13T6 magma -17,0,0,0,0,0,0,0,0,0,0,0,0,1
13T1 magma 1,10,-68,-291,215,738,-246,-601,116,190,-19,-24,1,1
13T1 magma -293,-2196,-411,6321,4575,-4414,-5541,-617,1193,365,-77,-36,1,1
13T1 magma -15667,21271,34869,-47723,-20328,33548,3352,-9610,33,1199,-27,-60,1,1
13T1 magma -61399,217458,-127412,-196272,121902,81708,-32367,-16810,3386,1672,-129,-72,1,1
13T2 magma 58256749348304523248144969888837463340160093969294532742146556156000521034802783,42312753036411362230230450305478672870803475782951657706005442304434341869586,14061234326903814621176226216076159779271092623995827091347309743554898127,-49375911707911743432917242207615322174325427611237741682026488846612521,15253788701960481284921391493158919700255797559466559311296323232498,-832818220571586800392164744000358270319532131590078379471735694,541808230910284083390456000848314355028531599104942728173485,-14768638405830894134972427622171024141266129942650181658,199518440359885837424153227327826660336955370546108,-103386239396269087020741974285554789917453508,51536266750679803854633551771840260203,-14412129900790076822258611,7178874489555770070,1
13T2 magma 1288185729855109347493715381276499192204085431957219681118500147931626997888088226318359375,-4487212542386417035130564561724254020346483123482676773093024865374900400638580322265625,6162774782812542130030147316585405729653544328652457605331892962567508220672607421875,596774975718198603949702355142508889167524972921148663966583088040351867675781250,-217712350218237684687170899414325350050388748483588898629844188690185546875000,-43719503450979282495514171655395663354927991909842598140180110931396484375,11458136561160708300394038317028343694717312841071722625732421875000000,47530953928226416306068505409986490840011703185605743408203125000,98905316949525970240143951409615108996096316126037597656250,-4165394082070752123229551692087292204450178222656250,179032706285420766577202734457392432796875000,-311327635162565982167010546875,13380310119466658931625,1
13T2 magma 11519115710035287018473328141372652675649454583445370429622647612498386837821723369639585143886506557464599609375,-240317539442818520192751624074828010843673086411608002114819900818459951248055733247572788968682289123535156250,3988155071408114411295694889185759142996963782684927697658472199444165403979948357002460397779941558837890625,-4429449678268013018785245114671821292953516362622360972243325589668153294096397651018574833869934082031250,1704340529572448674192692228160868488122266882887702724956808289231009774690171325810253620147705078125,-163642832135862249153138962106022832188503123403654369826332502212063598588051693201065063476562500,5915301798521730108735134375157669341029171112059898291380405539294412955982899665832519531250,-69536993690712286041436506010668186541710390043917915136697707476086986544780731201171875,1088351782637490009232842780816302492370128023211204145250884545339565275482177734375,-6074990022333135084946369465252933458014385229104768369917482488719970703125,16954698414786914379537235213798470561807328035373783977334318359375,-1475374716862965778854158583513018002437500,4117608336739534302646656269382375,1
13T2 magma 48668589815855299748298210055677743227589101961574298931238399166511537678757736985039474811935347964330195688146418398703,-8747283983298973190411177410444584687836684413149849228580766662875033130995135867781755965859319526383720025602954395,6928961385498166519131105761029786976217585199393407897035551469593030115468126529463991715691132231759560836798238,-3081518568422945717403648927396784808822914789541391437282531069081214767069886740352572144751151330038926076483,1073173317913830975249376747249638573248556873857427975668178237400735599165115979933650245274479573558693936,-47109323964213368819670732466702772686747049706706425930669021271651021185165695316900501049017196670304,2455708815800362817222425653652743568558698587684365028534038214066201807700468235358644582234402386,220921400799324121840679222218904131567539279547037061246015932269490391459277926807620242449,48894505097388402303173659269471487163308279207527189114612985707570355269467418136527,185277539710930684981422449666478372462633721142022915745801138989080597002695,351144512579171597020888800421786044118591035090198841055403706275042,9887320409826741068444662011134426717509587,18738850353721585617385401522188589,1
13T9 magma -1,-1,5,5,-3,5,-2,5,-3,-2,5,-3,-3,1
13T9 magma -4,3,-2,-1,-5,1,-3,5,4,-5,-1,-3,-4,1
13T9 magma -1,2,1,-3,-1,0,-2,2,3,4,1,5,0,1
13T9 magma 1,5,0,5,-4,0,4,5,-1,2,3,4,-3,1
13T9 magma 2,5,2,3,-3,-1,-2,-3,3,0,-1,0,2,1
13T9 magma -1,4,-1,1,-3,4,2,3,-2,4,-2,-2,0,1
13T9 magma -3,-4,1,5,5,2,1,-5,1,-5,-2,-3,2,1
13T9 magma 2,5,-1,-3,1,-1,0,-2,5,0,3,5,-3,1
13T9 magma 4,-2,2,-2,4,-5,4,4,-5,0,4,4,0,1
13T9 magma -3,-1,-2,-3,5,3,-4,-2,-3,-4,1,5,4,1
13T9 magma 3,3,-5,2,0,5,-4,3,-5,-3,-1,-4,1,1
13T9 magma -1,-1,4,4,-4,2,3,0,-5,-5,0,0,-3,1
13T9 magma 2,3,3,3,2,-2,5,-2,-1,-5,1,3,-3,1
13T9 magma -3,-1,1,5,-2,-1,1,4,-2,0,-2,4,-1,1
13T9 magma 1,-2,5,0,1,-5,0,1,2,-4,-4,-5,4,1
13T9 magma -5,5,-1,-2,2,2,3,1,0,-5,-1,3,1,1
13T9 magma -3,-3,-5,-4,0,-3,-2,-1,-1,4,1,-1,-5,1
13T9 magma -3,-5,0,-3,3,-3,-5,-2,5,-3,-4,2,0,1
13T9 magma -4,0,-1,-2,-5,-2,5,-2,3,2,-2,4,1,1
13T9 magma 4,-5,3,-5,-4,4,-3,3,0,3,1,-1,-3,1
13T9 magma 3,-1,-1,-4,0,-5,-5,-3,-5,-4,3,-1,-4,1
13T9 magma 2,1,-1,-3,-3,2,-1,-5,3,-5,3,-1,-1,1
13T9 magma 2,-2,1,2,-2,-5,4,-5,2,3,-3,-3,-4,1
13T9 magma -5,4,-3,-1,-4,2,4,3,-5,-2,5,1,-5,1
13T9 magma 3,-5,5,-3,-1,4,-3,5,-5,3,1,-1,-2,1
13T9 magma 2,-5,4,-4,-2,0,3,3,-5,4,2,0,5,1
13T9 magma -2,4,-5,3,1,-2,3,-5,-4,0,-3,2,0,1
13T9 magma -3,5,0,-2,5,-1,4,-4,-1,-3,-3,-3,4,1
13T9 magma -4,-5,3,5,-3,4,3,-5,2,0,1,4,4,1
13T9 magma 2,4,3,1,-4,2,3,-1,0,1,5,-4,-2,1
13T9 magma 5,0,1,4,-4,2,1,-1,-5,2,1,1,2,1
13T9 magma 4,-5,-4,-1,-2,-5,-3,3,0,-1,3,-2,1,1
13T9 magma -2,0,-3,-5,-3,-3,-5,-5,-2,1,4,-3,5,1
13T9 magma 1,-4,2,3,-3,-4,-5,0,4,-5,3,3,-3,1
13T9 magma -4,1,-1,1,-1,-2,-1,-1,4,3,1,-1,-1,1
13T9 magma -2,-4,5,-4,-3,-5,-4,-1,-3,-2,4,-1,-4,1
13T9 magma -4,2,2,4,-4,-5,4,3,1,-3,2,-2,2,1
13T9 magma 5,3,-3,-2,0,-3,1,1,-5,0,0,0,0,1
13T9 magma -2,-4,-3,-3,4,-3,5,1,-5,4,1,-4,2,1
13T9 magma 1,3,-2,-3,4,1,-5,1,1,0,1,1,-1,1
13T9 magma -4,3,-2,1,-3,4,3,-5,2,2,-4,3,3,1
13T9 magma 2,-3,3,-5,3,-2,-5,-2,1,-5,2,-1,1,1
13T9 magma -5,0,-2,2,1,4,-3,2,-2,1,4,1,-5,1
