QuadFieldClassGroup.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Welcome to Nemo version 0.16.4-dev\n",
      "\n",
      "Nemo comes with absolutely no warranty whatsoever\n",
      "\n",
      "\n",
      "Welcome to \n"
     ]
    },
    {
     "data": {
      "text/html": [
       "$\\require{action}$"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\u001b[31m    _    _           _\u001b[39m\n",
      "\u001b[31m   | |  | |         | |\u001b[39m\n",
      "\u001b[31m   | |__| | ___  ___| | _____\u001b[39m\n",
      "\u001b[31m   |  __  |/ _ \\/ __| |/ / _ \\\u001b[39m\n",
      "\u001b[31m   | |  | |  __/ (__|   <  __/\u001b[39m\n",
      "\u001b[31m   |_|  |_|\\___|\\___|_|\\_\\___|\u001b[39m\n",
      "\u001b[31m    \u001b[39m\n",
      "Version\u001b[32m 0.7.3-dev \u001b[39m... \n",
      " ... which comes with absolutely no warranty whatsoever\n",
      "(c) 2015-2019 by Claus Fieker, Tommy Hofmann and Carlo Sircana\n",
      "\n"
     ]
    }
   ],
   "source": [
    "using Revise, Hecke, Profile\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 50.594719 seconds (287.40 M allocations: 14.746 GiB, 15.01% gc time)\n",
      "MSet{fmpz}(Dict{fmpz,Int64}(5 => 6,56 => 3,16 => 36,224 => 1,20 => 1,72 => 3,60 => 3,12 => 21,24 => 15,8 => 86,17 => 1,28 => 3,1 => 62,160 => 1,32 => 19,30 => 1,6 => 22,136 => 1,3954 => 1,36 => 3,11 => 1,344 => 1,9 => 3,14 => 2,3 => 14,80 => 3,96 => 2,64 => 2,112 => 1,7 => 3,900 => 1,108 => 1,128 => 1,3328 => 1,48 => 4,40 => 5,4 => 142,15 => 1,2 => 114,10 => 5,304 => 1,1134 => 1,88 => 3,27 => 1,26 => 2,120 => 1,124 => 1,240 => 1,132 => 1))\n",
      "MSet{fmpq}(Dict{fmpq,Int64}(-1 => 74,1 => 534))\n"
     ]
    }
   ],
   "source": [
    "Zx, x = FlintZZ[\"x\"]\n",
    "C = MSet{fmpz}()\n",
    "U = MSet{fmpq}()\n",
    "@time for i=2:1000\n",
    "    I = i+10^10\n",
    "    if all(isone, values(factor(I).fac))\n",
    "        k,a = number_field(x^2-I)\n",
    "        zk = maximal_order(k)\n",
    "        c, mc = class_group(zk)\n",
    "        u, mu = unit_group_fac_elem(zk)\n",
    "        push!(C, order(c))\n",
    "        push!(U, norm(mu(u[2])))\n",
    "    end\n",
    "end\n",
    "println(C)\n",
    "println(U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2: [23.718998110600402149589646668302651977 +/- 7.58e-37]\n",
      "3: [53775.001969344941401102778200736400756 +/- 8.42e-34]\n",
      "5: [22.802707378876247084366744456546828406 +/- 1.44e-37]\n",
      "6: [75248.22606100858884630479844446704000 +/- 3.32e-33]\n",
      "7: [9486.9983170275303577725747702959752784 +/- 9.65e-35]\n",
      "9: [69106.46846518896695163432716826048701 +/- 5.55e-33]\n",
      "10: [22.109560198566301774808887335179797671 +/- 3.03e-37]\n",
      "11: [2800.4515845029548153697301494493287761 +/- 5.64e-35]\n",
      "13: [12078.868703592633003473809623861486566 +/- 3.71e-34]\n",
      "14: [44202.383142452250516599441679436338984 +/- 3.57e-34]\n",
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      "19: [147160.386105856838352646420259947692178 +/- 8.63e-34]\n",
      "21: [8782.6285978398194089913132599361831592 +/- 8.55e-35]\n",
      "22: [13658.477726421415706835993944357348203 +/- 1.80e-34]\n",
      "23: [8560.920355678123795849181933073264683 +/- 4.35e-34]\n",
      "27: [56294.344774768991793561643159415881399 +/- 5.54e-34]\n",
      "29: [3143.5946972349255021641796165182150518 +/- 3.53e-35]\n",
      "30: [471.5003126241200547585821321609935933 +/- 4.85e-35]\n",
      "31: [1620.6027026859799307968327271837731503 +/- 3.10e-35]\n",
      "33: [192603.79019329515081298829768729647213 +/- 4.41e-33]\n",
      "34: [15897.556194521651241274213743689879116 +/- 5.23e-34]\n",
      "37: [4642.3701374097095239703946112854282632 +/- 6.00e-35]\n",
      "38: [4840.6467268016116357467898140048206109 +/- 8.63e-35]\n",
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      "46: [35748.487432147548278706609767681135521 +/- 8.48e-34]\n",
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      "59: [41614.614590365407772970858870058569381 +/- 4.69e-34]\n",
      "61: [12470.95068274418530539913078477358774 +/- 3.33e-33]\n",
      "63: [39617.68542497601123124649404665518634 +/- 4.36e-33]\n",
      "65: [30111.144027217700442485663841933190080 +/- 2.44e-34]\n",
      "67: [15820.998718330351412514187949151352666 +/- 4.51e-34]\n",
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      "73: [29056.724685115761109608568816907787764 +/- 4.92e-34]\n",
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      "77: [18126.609495958827732725268986548535387 +/- 5.52e-34]\n",
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      "81: [56314.79686451575660916809440771448467 +/- 4.43e-33]\n",
      "82: [16101.347756694134836335317145773173733 +/- 3.16e-34]\n",
      "83: [5395.2385277946101398119916769586573907 +/- 4.21e-35]\n",
      "85: [15558.253745480385924496029447157002534 +/- 4.93e-34]\n",
      "86: [5150.583856729530627328904396596352879 +/- 4.59e-34]\n",
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      "97: [56147.621681131523270728757539226061840 +/- 4.88e-34]\n",
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      "101: [1138.6784089036069862581619796854494529 +/- 6.03e-35]\n",
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      "139: [11151.404681639110331572144991769729172 +/- 3.17e-34]\n",
      "141: [49255.651283477749578091484502786471338 +/- 7.56e-34]\n",
      "142: [12036.0081146376739855678447873950863817 +/- 9.71e-35]\n",
      "145: [10116.5574745154977989917786711536864160 +/- 9.79e-35]\n",
      "146: [8389.803817233284693983657694968588831 +/- 3.11e-34]\n",
      "147: [183795.89585285874101224154808611779515 +/- 5.90e-33]\n",
      "149: [358.24606490800611148219276742632361560 +/- 6.57e-36]\n",
      "151: [53698.561018855711401929758688085370812 +/- 5.95e-34]\n",
      "153: [55573.79203512932702379110325152226561 +/- 8.96e-33]\n",
      "154: [17261.42847516946261442182192380914887 +/- 1.19e-33]\n",
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      "171: [39856.023942949207159997241031568070941 +/- 5.55e-34]\n",
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      "181: [6960.1188858528288060719368955633433653 +/- 9.07e-35]\n",
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      "193: [9107.928965315934019134004461080818208 +/- 2.05e-34]\n",
      "194: [582.7353230242807011686940792011687488 +/- 5.05e-35]\n",
      "195: [34023.08892937722943875373588390551185 +/- 4.43e-33]\n",
      "198: [119819.809704300627724879555565747623065 +/- 4.99e-34]\n",
      "199: [18992.736316167443258082151055790579003 +/- 4.93e-34]\n",
      "201: [167291.83704598109563783671762849941874 +/- 1.71e-33]\n",
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      "203: [8157.9586094384751937888108836449438249 +/- 4.26e-35]\n",
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    {
     "name": "stdout",
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     "text": [
      "286: [12450.71853443725214544745813586892820 +/- 2.18e-33]\n",
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      "478: [25033.558037894900962841204315323403450 +/- 3.97e-34]\n",
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      "482: [98.28598308316246460577461247715786388 +/- 4.85e-36]\n",
      "483: [48680.339348813119696942263407969466456 +/- 6.86e-34]\n",
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      "531: [35141.045064386676606527137927425314564 +/- 6.87e-34]\n",
      "533: [5762.9435502776745589699393134170662097 +/- 8.01e-35]\n",
      "534: [87947.393574923251534967011391492991765 +/- 6.75e-34]\n",
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      "537: [104180.282714721385919765960955713206283 +/- 7.67e-34]\n",
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      "555: [18326.500141891383239716798330586065200 +/- 2.08e-34]\n",
      "558: [72497.79940996950781542139264082913084 +/- 2.53e-33]\n",
      "559: [19615.299386488516153549050109430305891 +/- 5.05e-34]\n",
      "561: [96185.432827417041421117931119942808816 +/- 4.46e-34]\n",
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      "563: [19738.506120905026261523744842078087381 +/- 1.27e-34]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "715: [36707.548928549250881754911470063801584 +/- 2.95e-34]\n",
      "717: [42716.770658070343699828542856922453092 +/- 3.10e-34]\n",
      "718: [44510.619481240683077982887259571654324 +/- 3.20e-34]\n",
      "721: [25168.887964387526948441189019993230910 +/- 6.30e-34]\n",
      "722: [747.4047579018504411413193457559403961 +/- 3.17e-35]\n",
      "723: [34634.624969545878978645010723835297664 +/- 4.42e-34]\n",
      "726: [60447.033824843149149722957741503711839 +/- 4.92e-34]\n",
      "727: [2604.3019508758025443331419753845238216 +/- 5.70e-35]\n",
      "729: [37567.245964995880828695386292360219825 +/- 8.63e-34]\n",
      "730: [7795.6824897931564098362578569160388935 +/- 6.24e-35]\n",
      "731: [7099.9934250484576410688933200116198290 +/- 5.06e-35]\n",
      "733: [28757.187698330659302634186071387052700 +/- 1.37e-34]\n",
      "734: [13647.358588704798593277284730831029995 +/- 4.19e-34]\n",
      "735: [36349.695458656062405195461298603154842 +/- 5.93e-34]\n",
      "739: [16604.180377841944727757128355120864179 +/- 6.04e-34]\n",
      "741: [61043.229059357372534212079396991644105 +/- 9.60e-34]\n",
      "742: [15068.0183529512967097851934868852766838 +/- 6.92e-35]\n",
      "743: [827.02390447636081779341828717507240607 +/- 7.81e-36]\n",
      "745: [33856.778541977642870915403494133275402 +/- 6.65e-34]\n",
      "747: [14254.272923374581982837466342695890308 +/- 2.93e-34]\n",
      "749: [43867.335565989673410470658661241122029 +/- 3.58e-34]\n",
      "751: [691.32661378409609019368597141670502034 +/- 6.06e-36]\n",
      "753: [35925.464110858367369224027666371697108 +/- 6.44e-34]\n",
      "754: [49214.102881344434580943532910671780852 +/- 5.39e-34]\n",
      "757: [4152.237194174770235122150821654132938 +/- 3.31e-34]\n",
      "758: [8348.6862363676849305429077544635206842 +/- 9.51e-35]\n",
      "759: [46464.856969094881108041267664672244122 +/- 4.52e-34]\n",
      "761: [177897.60867565578882546254607577613298 +/- 2.81e-33]\n",
      "762: [13341.000164743544391209342296356033361 +/- 3.46e-34]\n",
      "763: [18978.207489511835326177313328141185804 +/- 4.04e-34]\n",
      "765: [19183.047095639227085028461506473197072 +/- 2.46e-34]\n",
      "766: [3870.1374573383579301912726962320616706 +/- 2.85e-35]\n",
      "767: [37313.183055543495055588905287715444035 +/- 7.25e-34]\n",
      "769: [16674.628545254780042127272841331456994 +/- 3.48e-34]\n",
      "770: [4136.2119524295568431877962741589240674 +/- 3.05e-35]\n",
      "771: [39966.489245022437133240924632439275788 +/- 4.27e-34]\n",
      "774: [24989.831364405732387778788003551960045 +/- 3.27e-34]\n",
      "777: [30558.004098060144435849552286195697976 +/- 4.60e-34]\n",
      "778: [18688.362751845612582953641270464714548 +/- 2.58e-34]\n",
      "779: [28124.528387765762924609058010090745133 +/- 5.34e-34]\n",
      "781: [21154.464556786075158266770319532938484 +/- 4.95e-34]\n",
      "783: [48226.870845677692589150534086830557809 +/- 7.78e-34]\n",
      "785: [2389.9159230305311342960261108708696247 +/- 6.36e-35]\n",
      "786: [41225.491908136927481545779842046595941 +/- 6.37e-34]\n",
      "787: [14812.739638290405706774978263489859747 +/- 5.46e-34]\n",
      "789: [18992.183557406431176985066866364452333 +/- 3.31e-34]\n",
      "790: [2734.7015759521094048369664708415899417 +/- 5.55e-35]\n",
      "793: [60608.55648126436221708925731846924856 +/- 1.86e-33]\n",
      "794: [8985.934780046555690861472440428701841 +/- 4.61e-34]\n",
      "795: [3367.5894056902112498678187695194237900 +/- 6.22e-35]\n",
      "797: [9772.6664162400335551689407608352710632 +/- 8.20e-35]\n",
      "798: [18838.142637862596701948837832427499242 +/- 5.55e-34]\n",
      "799: [81873.740957985500167067944669632380158 +/- 8.31e-34]\n",
      "802: [16994.070871163453605823021933005878864 +/- 1.72e-34]\n",
      "803: [3670.9348372851856427813428532641496626 +/- 1.41e-35]\n",
      "805: [5165.880880534663116752576522584757368 +/- 4.81e-34]\n",
      "806: [3460.2106165159114367346096667221900967 +/- 4.10e-35]\n",
      "807: [22382.919739655222907882523986676370077 +/- 4.96e-34]\n",
      "810: [9843.547523451317228996192550527245837 +/- 2.12e-34]\n",
      "811: [17717.481095464581562330269019650638412 +/- 4.30e-34]\n",
      "813: [10613.426824035865932013313166115427128 +/- 5.07e-34]\n",
      "814: [23999.591514416703273734711832414861646 +/- 2.74e-34]\n",
      "815: [4439.8225696240484729516153032691429662 +/- 9.09e-35]\n",
      "817: [15735.680055318564975843057076799710129 +/- 5.70e-34]\n",
      "819: [16471.793659842469583766233375778607253 +/- 3.03e-34]\n",
      "821: [14309.312646846721691823195588505052575 +/- 4.25e-34]\n",
      "822: [2101.6135118678603010262876742641286738 +/- 6.54e-35]\n",
      "823: [28220.883787791097177528894908397688052 +/- 2.71e-34]\n",
      "826: [17308.275313859540587634762773478255086 +/- 6.38e-34]\n",
      "829: [1429.8004482353932213329151647592351782 +/- 8.48e-36]\n",
      "830: [16206.140181685104135202288597081879052 +/- 4.59e-34]\n",
      "833: [13964.5336451416701053006239757964719290 +/- 5.38e-35]\n",
      "834: [9559.510785234902063312608613773102395 +/- 1.13e-34]\n",
      "837: [44485.064699601746993941427683864678062 +/- 3.85e-34]\n",
      "838: [78455.640816854812955365589879451653887 +/- 4.73e-34]\n",
      "839: [37506.569755131211694338710796790886165 +/- 4.98e-34]\n",
      "841: [21073.718353872248536518844156670045202 +/- 3.69e-34]\n",
      "842: [17641.431354880573089456107776688315966 +/- 1.45e-34]\n",
      "843: [15981.0195800456494523938186156292841290 +/- 9.43e-35]\n",
      "846: [46494.014591877357290378360421182386512 +/- 7.38e-34]\n",
      "847: [39969.506720824749968688954089630245266 +/- 7.83e-34]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "849: [40846.659064696828185747473686888665684 +/- 5.36e-34]\n",
      "851: [33984.156837170346998491993527748691172 +/- 5.81e-34]\n",
      "853: [14572.638439561088108709343481161496259 +/- 1.81e-34]\n",
      "855: [31818.890940945193984383226318818626399 +/- 7.58e-34]\n",
      "857: [24187.155763104113761563374936628610448 +/- 4.37e-34]\n",
      "858: [43386.266688158384242512134512020442028 +/- 2.43e-34]\n",
      "859: [2669.7043277448183441263418511496344270 +/- 2.96e-35]\n",
      "861: [19439.202974029489196172016916085659285 +/- 2.59e-34]\n",
      "862: [16338.5744099434195411359614285770398872 +/- 5.69e-35]\n",
      "865: [8024.2471678260361102820526743831646848 +/- 8.27e-35]\n",
      "866: [34061.52882365954149312351787492060274 +/- 3.53e-33]\n",
      "867: [8356.8581681324312525604947240211548251 +/- 6.83e-35]\n",
      "869: [48358.527911125088628854117420795945884 +/- 6.48e-34]\n",
      "870: [61698.459737901018498808770714608714777 +/- 3.13e-34]\n",
      "871: [31369.222421828010258965102028171326927 +/- 4.18e-34]\n",
      "873: [154034.31632224062777741818139916851322 +/- 2.00e-33]\n",
      "874: [8342.873860770691293314169867757687124 +/- 4.61e-34]\n",
      "877: [2024.1272850151194707501213641782095809 +/- 2.84e-35]\n",
      "878: [4681.753253868070903351312485291222208 +/- 3.81e-34]\n",
      "879: [11397.3450702305416714695462566586373802 +/- 8.33e-35]\n",
      "882: [22186.073685249980222967175632196340177 +/- 4.24e-34]\n",
      "883: [53518.374681795435301460141189431655653 +/- 7.62e-34]\n",
      "885: [26464.975282136354378231639297875044613 +/- 4.40e-34]\n",
      "886: [22376.394342065953333071356702469851109 +/- 5.98e-34]\n",
      "887: [19468.784957136538049394308502508530370 +/- 3.19e-34]\n",
      "889: [34927.888299876704791418926086026445695 +/- 7.07e-34]\n",
      "891: [22793.378778172855694987443201161392042 +/- 3.20e-34]\n",
      "893: [5244.1508726087962486187883354617134026 +/- 5.10e-35]\n",
      "894: [53666.596940122100659745206001874145577 +/- 4.13e-34]\n",
      "895: [738.804919126162731498041096436244799 +/- 3.54e-34]\n",
      "897: [44528.761004563798609009413760296718936 +/- 8.92e-34]\n",
      "898: [13389.1984400176166600012319028154286515 +/- 8.07e-35]\n",
      "901: [2140.7968348401216597148633569572382583 +/- 5.34e-35]\n",
      "902: [30693.43376573957876709136054490050505 +/- 6.37e-34]\n",
      "903: [77430.002819664568376198923067689256992 +/- 7.90e-34]\n",
      "905: [45298.270609468085327041823887435443255 +/- 5.78e-34]\n",
      "906: [105629.127286034206199105734766249623301 +/- 7.91e-34]\n",
      "909: [15297.654041148285220472230764450573774 +/- 3.66e-34]\n",
      "910: [13154.734132180598813610216869365562389 +/- 2.54e-34]\n",
      "911: [11507.609925501957929056087482348735158 +/- 3.58e-34]\n",
      "913: [62094.118940649751041270622598438976343 +/- 6.59e-34]\n",
      "914: [15800.1213229673241062792210591189045089 +/- 5.13e-35]\n",
      "915: [10412.641519410111018067049204396850867 +/- 4.22e-34]\n",
      "918: [22715.687945318296789266019571710656295 +/- 6.62e-34]\n",
      "919: [10859.005379750131387379332632332476234 +/- 2.96e-34]\n",
      "921: [118522.27911456665438274908620890646391 +/- 3.10e-33]\n",
      "922: [4322.2206267475796044257127141541803967 +/- 8.31e-35]\n",
      "923: [4628.591899997904836804951668837026254 +/- 2.71e-34]\n",
      "927: [16698.818265316005649942782530547993613 +/- 5.16e-34]\n",
      "929: [23582.839577794079434991983678970241030 +/- 4.86e-34]\n",
      "930: [27840.305941852646722933593679711905221 +/- 4.74e-34]\n",
      "931: [20257.789982193792784873995936976470196 +/- 2.62e-34]\n",
      "933: [1654.42540700242429673974197672655200968 +/- 7.43e-36]\n",
      "934: [363.33170192075992868421295637500516987 +/- 3.06e-36]\n",
      "937: [7436.4395332155188613053388201233604976 +/- 4.86e-35]\n",
      "938: [47375.131675077650641174190784466970292 +/- 2.42e-34]\n",
      "939: [20154.97904829699460126129454642406537 +/- 2.51e-33]\n",
      "941: [8885.567973183586413640623627195371514 +/- 4.58e-34]\n",
      "942: [36114.200475199678409429563730806331676 +/- 5.77e-34]\n",
      "943: [45338.728469816658155692442629635700065 +/- 6.17e-34]\n",
      "945: [50711.147914569863921457148795250334641 +/- 8.70e-34]\n",
      "946: [27912.170167264334507308304469636909238 +/- 6.53e-34]\n",
      "947: [19914.925606351945909875751410044149268 +/- 8.33e-34]\n",
      "949: [12544.4475354361647146041761384355128461 +/- 7.06e-35]\n",
      "951: [1101.5873482366868699571383515680602136 +/- 4.33e-35]\n",
      "954: [79989.39273042410075827168936308293004 +/- 4.15e-33]\n",
      "955: [7994.7833894556061908185979270717102844 +/- 4.00e-35]\n",
      "957: [10885.938585280868961303769547051864227 +/- 7.77e-34]\n",
      "958: [60376.639179067075910717603900020064196 +/- 4.44e-34]\n",
      "959: [37727.619904652795453877538820612366467 +/- 4.13e-34]\n",
      "961: [7956.8911597277137590411712225229475671 +/- 5.04e-35]\n",
      "963: [149943.14191311218515124610005741855935 +/- 5.35e-33]\n",
      "965: [1306.2113907009726102182026008778815020 +/- 3.47e-35]\n",
      "966: [6182.3786829200805258339513498262240761 +/- 8.32e-35]\n",
      "967: [1647.4352931677931562733215466483086676 +/- 4.59e-35]\n",
      "969: [14145.568743953715526958113367774531086 +/- 6.43e-34]\n",
      "970: [18566.241393058258815284466452847482630 +/- 8.73e-34]\n",
      "973: [10669.4478678907259843709843127263932839 +/- 8.71e-35]\n",
      "974: [12075.621693727854270053502327250354412 +/- 2.32e-34]\n",
      "977: [21332.315238223533277593563849561447154 +/- 3.43e-34]\n",
      "979: [23192.256470475079484133484120520711414 +/- 5.46e-34]\n",
      "981: [34931.956128890321931796429418826113407 +/- 5.88e-34]\n",
      "982: [19153.706777722813583471738136385363656 +/- 2.49e-34]\n",
      "983: [6173.3095597932495354110367393604458879 +/- 8.56e-35]\n",
      "985: [11536.609915847405422943538167029880429 +/- 6.75e-34]\n",
      "986: [32979.938835775485697089827427883959983 +/- 5.80e-34]\n",
      "987: [11846.647174775295597737138152508379681 +/- 3.88e-34]\n",
      "990: [35044.391204865176087497131528650917212 +/- 7.59e-34]\n",
      "991: [93207.967146500732552327463600159329134 +/- 8.25e-34]\n",
      "993: [17467.768590595585158976532225137547739 +/- 4.18e-34]\n",
      "994: [3391.0242124729165971935323253998869190 +/- 1.61e-35]\n",
      "995: [495.07711505248270697255498874244493182 +/- 2.91e-36]\n",
      "999: [237483.53652137323177272466255941514715 +/- 3.63e-33]\n"
     ]
    }
   ],
   "source": [
    "for i=2:1000\n",
    "    I = i+10^10\n",
    "    if all(isone, values(factor(I).fac))\n",
    "        k,a = number_field(x^2-I)\n",
    "        zk = maximal_order(k)\n",
    "        c, mc = class_group(zk)\n",
    "        u, mu = unit_group_fac_elem(zk)\n",
    "        println(\"$i: $(regulator(zk))\")\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Factored element with data\n",
       "Dict{nf_elem,fmpz}(17 => 109586,-681*_a+97625433 => -77098,103 => 40222,3 => 34,37 => 40222,-3085*_a+298709996 => 52380,3*_a-5536245 => -16278,23 => 63146,157 => 77098,-293*_a-27814463 => 77098,-17248*_a+1341738629 => -12628,19 => -87004,-19*_a+11151746 => 57274,-376*_a-30244189 => -88864,9618*_a-1037264025 => 40222,21*_a+117264 => -45508,2 => -13415,11 => 32418,-76*_a-375877 => 29730,_a-56831 => -20362,693*_a+36997884 => 25718,-17*_a-1313930 => -77098,31 => -52380,2183*_a+256277096 => -40222,-3*_a+521043 => 63470,391*_a-31303358 => -19860,41 => 77098,43 => -77098,7 => -30112)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k,a = number_field(x^2-10^10-147)\n",
    "u, mu = unit_group_fac_elem(maximal_order(k))\n",
    "mu(u[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Factored element with data\n",
       "Dict{nf_elem,fmpz}(79//1580619049*_a-15881273//3161238098 => -16,14//1179387*_a-2798435//2358774 => -4,1//496710369*_a+94903//496710369 => -2,2 => 1,-1//7203*_a-98891//7203 => -8192,-65//926045761*_a-9006619//1852091522 => -512,-41//294849*_a-4099985//294849 => -8,-71//4219680978*_a-1307923//4219680978 => -4096,-43//1286545743*_a+2925823//1286545743 => -256,1 => -491518,-5//266389362*_a+219871//266389362 => -2048,27//1146098*_a+2706451//1146098 => -1024,-59//1459404338*_a-6041643//1459404338 => -128,-205//2686562*_a+20501087//2686562 => -64,-71//550257138*_a-5341669//550257138 => -32,_a+100000 => -16384)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hecke.compact_presentation(mu(u[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.ValueIterator for a Dict{nf_elem,fmpz} with 16 entries. Values:\n",
       "  -16\n",
       "  -4\n",
       "  -2\n",
       "  1\n",
       "  -8192\n",
       "  -512\n",
       "  -8\n",
       "  -4096\n",
       "  -256\n",
       "  -491518\n",
       "  -2048\n",
       "  -1024\n",
       "  -128\n",
       "  -64\n",
       "  -32\n",
       "  -16384"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values(ans.fac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[183795.89585285874101224154808611779515 +/- 5.90e-33]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regulator(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.ValueIterator for a Dict{nf_elem,fmpz} with 7 entries. Values:\n",
       "  -16\n",
       "  -8\n",
       "  -2\n",
       "  1\n",
       "  -32\n",
       "  -958\n",
       "  -4"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k, a = number_field(x^2-10^10-257)\n",
    "u, mu = unit_group_fac_elem(maximal_order(k))\n",
    "values(Hecke.compact_presentation(mu(u[2])).fac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[350.93152166376055570946479504643163602 +/- 2.86e-36]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regulator(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Factored element with data\n",
       "Dict{nf_elem,fmpz}(5//2*_a-914415//2 => 3,3 => 20,245//2*_a+24581625//2 => -4,109 => -3,15//2*_a-15997125//2 => 3,1290330*_a-141887136240 => -3,733//2*_a-64522345//2 => -1,-1947//2*_a-193556445//2 => 1,85//2*_a-9762725//2 => 1,-87//2*_a+8633553//2 => 4,2 => 3,-105//2*_a-8664075//2 => -4,151 => -1,31 => -4,5 => 5,-75*_a-19267620 => 1,61 => 3,7 => 4)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k,a = number_field(x^2-10^10-5)\n",
    "u, mu = unit_group_fac_elem(maximal_order(k))\n",
    "mu(u[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.ValueIterator for a Dict{nf_elem,fmpz} with 18 entries. Values:\n",
       "  3\n",
       "  20\n",
       "  -4\n",
       "  -3\n",
       "  3\n",
       "  -3\n",
       "  -1\n",
       "  1\n",
       "  1\n",
       "  4\n",
       "  3\n",
       "  -4\n",
       "  -1\n",
       "  -4\n",
       "  5\n",
       "  1\n",
       "  3\n",
       "  4"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values(ans.fac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "$-40000\\alpha+4000000001$"
      ],
      "text/plain": [
       "-40000*_a+4000000001"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate(mu(u[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "($\\text{Abelian Group with Invariants: }Z/1134$, $\\text{Map from }\\text{Abelian Group with Invariants: }Z/1134\\to \\text{Set of ideals of }\\mathcal O_k$)"
      ],
      "text/plain": [
       "(GrpAb: Z/1134, ClassGroup map of \n",
       "Set of ideals of O_k\n",
       ")"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class_group(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "3: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "5: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "6: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "7: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "9: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(499//2*_a-277950503//2 => 5921,3 => 54711,-63//2*_a-3199869//2 => -5417,137 => -1238,157 => 5417,23 => -19353,109 => 18115,53 => 12442,73 => -19353,20603//2*_a+1350785693//2 => -12442,_a+52021 => -5665,1556*_a+20151658 => -18115,9//2*_a+720675//2 => 17151,210*_a-20047206 => 22990,2 => -58630,-51//2*_a-2063937//2 => -14440,-17//2*_a-8983331//2 => 5545,2117//2*_a-145864293//2 => 19353,5 => 10880,2989//2*_a+108275887//2 => -6221,-8083089//2*_a-15987517827//2 => -5673,-_a+7748153 => 1780,1523//2*_a-201620611//2 => 1238))\n",
      "10: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "11: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "13: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 1417,722*_a-76825058 => -2040,23 => -1983,2*_a+185518 => 1194,1 => -8,-296*_a+82379688 => -909,-1//2*_a-99629//2 => 0,46*_a-4508690 => -2040,-52*_a-5180960 => 987,15*_a+496267 => 4237,10612*_a-187139924 => -61,1250*_a+141319088 => -2225,132*_a-122088764 => 1068,-136*_a+12872264 => -2404,4*_a+106460 => 987,2 => 4438,11 => 61,97 => 2223,31 => -4238,149 => -987,16*_a+1554528 => -1877,8048*_a+328605440 => 2021,-166013//7346*_a+12800653945//7346 => 0,13 => -2902,61 => -2021,47 => -1068,_a+127248 => 1,-92*_a+5221368 => 2021,67 => 2040,43 => 2404))\n",
      "14: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "15: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "18: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "19: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "21: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "22: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "23: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "27: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "29: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "30: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "31: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "33: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -937,23//2*_a-5601625//2 => 20643,3 => -42682,3713//2*_a-142636433//2 => 16335,-5//2*_a+383389//2 => -2157,1//243174426*_a+327691//243174426 => -1,137 => 14894,-23//3348*_a-5601625//3348 => 1,1 => -14,19 => 2156,-122*_a+28475105 => -3667,-1//2*_a+103519//2 => 1,-429*_a+42375190 => 20378,-34*_a+2811137 => -2362,3247//2*_a+408782629//2 => 3291,103519//2*_a-10358091697//2 => 0,2 => -2812,11 => 9408,7//2*_a+434411//2 => -2157,193//2*_a+14319553//2 => -19155,151 => 3667,31 => -2,103//2*_a-10340557//2 => 22194,-3//2*_a-1217741//2 => -14894,26*_a-1481168 => -2192,1945//2*_a+437228229//2 => -20002,13 => -3293,61 => 5823,715//2*_a+73041111//2 => -14894,-11//2623713768*_a-804259//2623713768 => -1,1//2*_a-103519//2 => 0,7 => -19630,_a+448493 => -2623))\n",
      "34: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "37: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "38: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "39: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "41: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "42: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(127 => -33764,3 => 26153,-13*_a-1271590 => -13574,37*_a+3698665 => 18650,23 => 31094,53 => 60247,382*_a+26404631 => -10068,73 => 27068,71 => -88150,-1046*_a+37489510 => -17000,205*_a+25650502 => -96015,751*_a-89730247 => -27068,-6*_a-1542153 => -27068,173 => -88150,64*_a+1027441 => 33764,2 => 62993,3*_a+545588 => 55406,_a+1821442 => -27068,97 => 27068,-128*_a-8464535 => 88268,-413*_a+114040652 => 13574,151 => 99923,31 => 40609,-2*_a+159579 => 115218,-8*_a+538438 => -33764,41*_a+11608672 => 88150,33*_a+4500270 => -50179,79 => 27068,-65*_a+1548531 => -49744,61 => -55406,41 => 96015,5*_a-472048 => -11634,_a-35243 => -113497,7 => 52243,-15039*_a-54718054 => 16882))\n",
      "43: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "45: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "46: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "47: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "49: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 933,-79//2*_a+10597171//2 => 825,55//2*_a-5832679//2 => 1075,19 => -5632,73 => 826,-19//2*_a-2178293//2 => -150,-136*_a+37435462 => 448,1//2*_a+39559//2 => -2742,1547//2*_a-7425379//2 => 1503,139 => -1075,7//2*_a+187901//2 => -1651,2 => 3945,-5//2*_a+610997//2 => 1075,221*_a+111450963 => -2050,97 => -1273,59 => 2050,83 => 1225,5 => 1673,79 => 150,13 => -150,12*_a+1582256 => 1234,-228*_a+12023960 => 1273,73//2*_a-4268657//2 => -1225,41 => -1075,-5*_a-39525 => -826,1//2*_a-158457//2 => 1651,7 => 4545,45190*_a-2919116330 => -697))\n",
      "51: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "54: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "55: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "57: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "58: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -95,-24*_a+53488430 => 8374,-75*_a-12819517 => -8721,338*_a-98801456 => -2637,-6789*_a-133045180 => -8374,-2101*_a-160796196 => -6622,3888*_a-172861523 => -232,8091*_a+562106942 => 232,2 => 22535,11 => 3496,179 => -8374,-64*_a+10275951 => 8374,31 => 8142,5332513570928604010496*_a+447467040823719091188262912 => -3037,-387*_a+649471871 => 5979,10068*_a-170309014 => 12211,13 => 2332,-5423*_a-146049244 => -2621,-215*_a+12204862 => 5870,29 => -1432,41 => -8374,43 => -3128))\n",
      "59: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "61: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(961//2*_a+80062429//2 => -1807,127 => 1328,-321//2*_a+34445365//2 => 1086,37 => 1328,23 => -1972,-1631//2*_a-158149607//2 => -1328,131 => 978,99//2*_a-15670085//2 => -978,-47//2*_a+46505941//2 => 1547,-47//2*_a-4216471//2 => -1068,833//2*_a-167180993//2 => 982,-12035//2*_a-420789333//2 => 757,253//2*_a+108022743//2 => 495,185//2*_a+23104391//2 => -1328,31 => 1807,-20199//2*_a+2428599329//2 => 1547,-3069//2*_a+222163471//2 => 479,49//2*_a+47381971//2 => 1721,-2*_a-297807 => 479,83 => -1236,5 => -2443,79 => -1547,13 => 2026,61 => 1807,29 => -1843,41 => -479,1741*_a+88599428 => -2026,7 => -4078,19//2*_a+6936567//2 => -978))\n",
      "63: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "65: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "67: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "69: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(103 => 4278,137 => 10653,23 => 12107,101 => 28648,_a+13 => -10653,73 => 10653,67//2*_a+10716851//2 => 3775,_a-13 => -10653,1562027//2*_a-6642334591//2 => -2944,2 => 21306,11 => -9799,-77*_a-4286174 => -12785,7//2*_a+1138161//2 => 5333,-11//2*_a-27626993//2 => -4278,757//2*_a-71806613//2 => -12107,-86*_a-10178143 => 7381,5 => 11114,13//2*_a+648263//2 => -4278,5*_a-363256 => 13619,-11//2*_a-1067957//2 => 12902,61 => 2944,201//2*_a-99626387//2 => -13717,3107//2*_a-48654319//2 => 7550,67 => 22727,43 => -7381))\n",
      "70: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "73: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "74: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "77: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "78: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "79: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "81: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(3 => 39683,7//2*_a-5003663//2 => -12216,-89//2*_a-21715199//2 => 2125,1123*_a-234581582 => -12478,109 => -12478,53 => -2370,15*_a+1230905 => 7247,1271//2*_a+113558561//2 => 262,-11//2*_a-1101881//2 => 4975,191//2*_a-48374849//2 => -12478,89 => -2125,3//2*_a-650297//2 => 12478,-7523*_a+825947173 => -5785,2 => -67156,11 => -862,97 => -12216,6393//2*_a+406717663//2 => 12478,5 => -1462,179//2*_a+328677689//2 => 12216,-1//2*_a+275359//2 => -5141,79 => 10282,3//2*_a+755943//2 => 2370,29 => -8155,41 => -5507,39//2*_a-15053601//2 => 12216,21//2*_a+54262311//2 => -10282,7 => 10091,-19//2*_a-2854059//2 => 4491))\n",
      "82: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "83: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "85: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "86: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "87: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "90: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(776*_a-7598588 => 10,3 => -105,37 => 23,1 => 0,10*_a+351620 => 28,22*_a+1278200 => -23,53 => 63,19 => 57,2*_a-7900120 => -57,126*_a+29081984 => -91,318*_a-2772204 => 54,2 => -22,11 => 43,26*_a-788680 => -34,-1880*_a+208437950 => -23,170*_a-1530840 => -34,31 => -3,163 => 23,230*_a+22978730 => 88,-16*_a+427760 => 28,5 => -20,79 => -28,-68*_a+5961500 => 28,47 => 47,29 => 58,41 => -28,58*_a-9464020 => 3))\n",
      "91: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "93: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "94: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "95: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "97: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(135*_a+15613379 => 11226,127 => 1432,-407//2*_a-20828521//2 => 2713,3405//2*_a+98054317//2 => 105,37 => -11264,-21//2*_a+3306461//2 => -6740,137 => -758,-1559//2*_a+341664313//2 => 379,101 => 1432,53 => 379,13//2*_a-110419959//2 => -1432,19 => 888,-83//2*_a+11192053//2 => -379,76*_a+192778 => 758,1//2*_a-42895//2 => -5498,37//2*_a+1731045//2 => 8551,2 => -21777,5//2*_a-467703//2 => -1537,547//2*_a-88029861//2 => -1432,31 => 379,107 => -105,-1234*_a+24472178 => 465,113 => -2818,47 => -8551,13 => 2909,29 => 3031,41 => -465,7221//2*_a-805127435//2 => -3031,533//2*_a-69396899//2 => -5733,10*_a+1021978 => 6172,343//2*_a-249524013//2 => 105))\n",
      "99: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "101: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "102: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "103: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "105: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "106: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "110: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "111: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "113: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "114: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "117: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 964,3 => 1398,37 => 4374,23 => 477,-27//2*_a+2659757//2 => 2390,-509//2*_a+43052521//2 => 121,67//2*_a+4591543//2 => -3383,71 => 2433,44*_a-6539149 => 3203,789//2*_a+45209369//2 => 1113,1642*_a-185814743 => -1956,-599//2*_a+110488933//2 => 28,1001//2*_a+1404859937//2 => -2433,2 => 1398,253//2*_a+23201319//2 => 1956,-835//2*_a-104059591//2 => -28,-217//2*_a+13542389//2 => 56,-1619//2*_a+162065863//2 => 742,247//2*_a+15001935//2 => -4374,83 => 1984,13 => 8205,-26679039582*_a-705888811623216 => -1398,29 => -1113,67 => -56,43 => -1113,7 => -354,103//2*_a-91359155//2 => 3339))\n",
      "118: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "119: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "121: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -4634,1//2*_a-10997//2 => 1939,14*_a+4386054 => -207,-611//2*_a+12904039//2 => 569,108*_a+13515097 => -6626,3//2*_a-454591//2 => 7788,-4029//2*_a-405416969//2 => 4634,-727//2*_a-49199437//2 => 7788,19 => 7551,201//2*_a+1955011//2 => -6626,139 => 6626,42137*_a-5108781770 => -6128,-307//2*_a+221739583//2 => -5559,80*_a+10885515 => 15783,2 => -1009,11 => 12185,931//2*_a+111179431//2 => -569,4963//2*_a+163785393//2 => -5352,593//2*_a+70658983//2 => 207,97 => 6128,7505//2*_a+643869435//2 => -3491,1508*_a-228829037 => -4576,5 => 6506,79 => 4576,61 => -7788,47 => -7788,41 => 6128,67 => 5559,5//2*_a+5101245//2 => -6086,913//2*_a+114201043//2 => 6086))\n",
      "122: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "123: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "126: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "127: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "129: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "130: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "131: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "133: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "135: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "137: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "139: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "141: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-19*_a-7822984 => -8345,3 => -3734,-411*_a+27738004 => -12729,1//2*_a-1239421//2 => 16567,1 => -9,-9 => 1,531441 => 0,19 => 7751,-379//518558613950*_a+37776659//518558613950 => -1,71 => -4385,869//2*_a+246047475//2 => 6364,1//2*_a-7385//2 => -6583,-447//2*_a-45454197//2 => 3782,-4479*_a+588353916 => 7917,-18*_a+1833963 => -7917,89//2*_a+21556277//2 => 297,-4*_a+847357 => -13564,5 => -26331,79 => -6364,113 => 8345,47 => -4384,13 => -6364,-5//2*_a+497885//2 => -3838,31//2*_a+345379//2 => 4952,-8*_a-4741655 => 4384,-23//2*_a+41057437//2 => 7874,43 => -4952))\n",
      "142: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "145: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "146: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "147: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "149: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "151: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "153: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "154: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-8467*_a+1111758696 => -960918,127 => 3573,1070*_a-253729264 => -772,-5904*_a-49605298 => 323259,-244*_a+26624068 => -318642,37 => 3573,103 => 2571180,23 => 322057,1 => 114336,391*_a-73914502 => -318482,-14*_a+731288 => 1281382,53 => 1604488,101 => 324037,13*_a+4353960 => -961815,19 => 341691,73 => 324037,-339*_a+37398386 => -324037,-266*_a+10638518 => -642673,-26*_a-1460693 => 319278,-1651*_a-26323232 => 637948,-124//7414930762057*_a-12695469//7414930762057 => 3573,-508*_a+60824828 => 1604277,-6*_a+247813 => 1648,5300*_a+539958428 => 318482,581*_a-58232776 => 772,131 => 2889822,-1 => -3573,2 => 12451,11 => 6106816,19*_a+4899264 => 318847,_a+459980 => 318609,142*_a+101734632 => -324037,-6691*_a-427274168 => 319414,675//59257*_a-242970493//59257 => -3573,31 => -318847,5573//55525948177700*_a-140476503//27762974088850 => 3573,_a+23 => -2571180,5 => 9960689,-968*_a+130590636 => -318482,13 => 36746,47 => -1281382,144*_a+22376212 => -1604488,41 => 324037,_a-23 => -2890594,7 => 4826958))\n",
      "155: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "157: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "158: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "159: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "162: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "163: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "165: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(103 => 902,77//2*_a-17997035//2 => -1426,3 => 10413,1109//2*_a-103257277//2 => -569,71//2*_a-2602123//2 => -1626,-121//2*_a+57355877//2 => -1426,10909*_a+73992922 => 1426,-1811//2*_a-441034249//2 => -902,-46*_a+7460275 => 613,-1107*_a+135829392 => -737,11 => -1426,399*_a-65504124 => -333,-4159//2*_a-418231507//2 => 1899,-262*_a+7051769 => 1899,1015//2*_a-78643705//2 => -1559,151 => 1426,-_a-710260 => 1331,5 => 1300,13 => -806,61 => 333,41 => 737,67 => 333,43 => -1899,7 => 2705))\n",
      "166: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "167: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "169: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(155*_a-5150526 => -852,93//2*_a-2048015//2 => -1318,23 => 1451,1//2*_a+52257//2 => -11411,19 => -773,71 => 3452,-305//2*_a+44934297//2 => -5868,-57//2*_a-5133059//2 => -5095,1163//2*_a-32559869//2 => 5868,-67//2*_a-359855423//2 => -1318,11//2*_a+3232097//2 => 8092,367//2*_a+61404755//2 => 5868,3333//2*_a-188051281//2 => -3452,537//2*_a-43094653//2 => -4480,2 => 21254,11 => 21794,-63//2*_a-1001681//2 => -3452,631//2*_a-59062031//2 => -4480,-76*_a+5147982 => 1388,31 => 28604,-92*_a-6996071 => -2839,59 => 4480,5 => 9713,1023//2*_a+102547907//2 => -15023,79 => 1318,13 => 12046,61 => 1726,47 => 15023,-9//2*_a+595553//2 => -3612,13//2*_a-1407035//2 => 15638,149*_a+26250622 => 4480))\n",
      "171: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "173: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "174: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "177: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "178: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "181: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "182: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "183: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "185: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "186: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "187: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "189: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 21,103 => -257898,-222*_a+998799 => -429953,3 => -258067,137 => 86059,1 => 0,157 => -257898,70*_a-6659695 => 343798,-55//2*_a+5221029//2 => 257898,109 => -257806,101 => 86059,55//2*_a-119933//2 => 171899,73 => 86059,71 => 343948,476*_a+54830629 => 515872,1633//2*_a+524889439//2 => 85831,-92*_a-8574491 => 257898,2 => 172118,11 => -515989,_a-17 => -86059,97 => -257898,1079//2*_a-35208563//2 => -171920,-67911//2*_a-2606686713//2 => 343713,151 => -171899,31 => 85598,3465//2*_a+688743825//2 => -429629,284*_a-32721415 => -429779,217//2*_a+40000261//2 => -429311,737*_a+40859522 => 171899,33//2*_a+2299209//2 => -85831,5 => 257949,-77*_a-214676 => 257898,-137*_a-14611066 => -257880,13 => 171920,67//2*_a+2055411//2 => 257898,_a+17 => -86059,7 => -258628,-291//2*_a+19021687//2 => -250))\n",
      "190: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "191: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "193: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "194: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "195: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "198: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "199: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "201: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "202: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "203: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "205: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(23*_a+4344561 => 85,37 => -337,19 => -94,-28*_a-2811055 => -906,-3//2*_a+280033//2 => -600,-396*_a+43060810 => 822,23//2*_a-1847315//2 => 600,-49//2*_a-27803035//2 => -126,2 => -454,13*_a-113737 => 337,151 => -468,59 => -85,5 => 323,113 => 164,61 => 600,13 => -213,-15//2*_a+1319149//2 => 468,-1567*_a+17468700 => -164,-20770*_a+3613878690 => -354,-63375*_a-7025564065 => -82))\n",
      "207: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "209: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "210: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -1192,3 => 5632,-5620*_a+246083210 => 58,-1165*_a-909845950 => 1216,73 => -1192,71 => -6215,-1005*_a-170534890 => 1216,15*_a-9270000 => -3643,167 => -1216,2421855*_a+210374871900 => -1240,-885*_a+228377325 => -1240,-305*_a-28212500 => -4894,65*_a+10311025 => -1400,2 => 1759,6199*_a-549509330 => -1216,-35*_a-999425 => 6215,97 => 1240,179 => 1240,1256*_a-101528365 => -5,65*_a+39903350 => -58,-235*_a+31734730 => 3643,-60*_a+5908335 => 1192,5 => 841,-5*_a+436645 => -1240,79 => 58,113 => 1211,61 => 4889,-3305*_a+362690375 => 1192,-985*_a-68412025 => 5,61*_a-82750370 => 1342,7 => -8899))\n",
      "211: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "214: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "217: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "218: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "219: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "221: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "222: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "223: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "226: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "227: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "229: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "234: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "235: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "237: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "238: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "239: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "241: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "243: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "245: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "246: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "247: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "249: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 25553,-10097//2*_a+768611029//2 => 15690,-185//2*_a-44759455//2 => 510,2*_a+2083706 => 23970,3 => 8250,37 => 7410,21*_a+2332245 => 15938,17//2*_a+19980851//2 => 7571,23 => 13095,1 => 0,-417//2*_a-14199339//2 => 626,53 => 15446,19 => -6042,191//2*_a+16386893//2 => 12979,-561//2*_a+578547213//2 => 626,1//2*_a-61457//2 => -1841,131 => -23460,2 => -70383,-375//2*_a-48628185//2 => 1777,45*_a+1193805 => -7571,_a+75073 => -510,904*_a-84364958 => -9412,-887//2*_a+102076459//2 => -15446,319*_a+39151087 => -13095,-7//2*_a+59723//2 => 510,381//2*_a+328532655//2 => -13605,17//2*_a-1320781//2 => -8168,-3*_a+626433 => -510,5 => 14931,-269//2*_a+22714897//2 => 13605,79 => -1136,61 => -626,37//2*_a-7325519//2 => -1529,491//2*_a-46558987//2 => -12979,67 => -15938,17//2*_a+1422611//2 => -5220,7 => -4782,43 => 1841))\n",
      "254: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "255: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "257: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "258: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(74*_a-5077843 => -561,3 => 6284,37 => 561,7*_a+936930 => 561,692*_a+10738146 => 1098,1 => 0,157 => -630,1161*_a+465308406 => 102,19 => -1167,71 => -52,_a-91446 => -807,5528414489*_a+525990914323706 => 622,5*_a-141947 => -391,7*_a+683531 => -254,6340*_a+1198337461 => 52,131 => 952,-27314*_a+5282539456 => -630,2 => 533,15*_a-5408466 => -1060,97 => 254,-13*_a-12329746 => 1260,83 => 177,113 => -622,13 => -1882,-250*_a-20234009 => 630,-9*_a+1073700 => -2050))\n",
      "259: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "261: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "263: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "265: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(73 => 734,99705//2*_a+8883065225//2 => 1133,2 => 2648,127 => 75,1075*_a-173562975 => 394,-2297//2*_a+308448181//2 => 45,37 => -664,19//2*_a-109707//2 => 559,-481//2*_a+46852915//2 => -469,1 => 0,-425//2*_a+49835275//2 => -75,-165//2*_a+15433295//2 => -636,5 => 817,41 => -439,-173375//2*_a+18440506275//2 => -1142))\n",
      "266: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "267: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "270: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "271: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "273: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "274: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "277: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(24649 => 0,127 => 212,103 => -278,37 => -14,157 => -382,1 => -8,-3722*_a-355101448 => 289,-4086*_a-289814126 => 111,-1391*_a+71312145 => 34,145*_a-213897143 => 191,113//47631471118*_a-45099853//47631471118 => -1,73 => 324,-503*_a+16431115 => 250,19 => -3,-2998*_a+220289158 => 324,-53*_a+10116459 => -46,2334*_a+295553870 => -324,139 => -289,-233//24496399154*_a-32370647//24496399154 => -1,-16*_a-812380 => -223,-360*_a-43368772 => -212,-2146*_a-737440710 => 226,2 => -1194,11 => -77,2*_a+208308 => -171,97 => -226,3501*_a+214980977 => -79,16//16131127243*_a-165569//16131127243 => -1,440*_a-51396688 => 554,-17*_a-35490003 => -212,59 => -1,83 => -112,29 => -56,-46*_a+9211534 => 289,2446*_a+637935122 => -358,-1400*_a+215771682 => -390,41 => -1,7 => -380))\n",
      "279: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "281: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "282: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-11568*_a-333919680 => -4230,3 => 6424,37 => 1774,157 => -2235,1918*_a+84270832 => 4817,101 => -4817,19 => -2233,-35*_a-3609092 => -5229,-358*_a-856129972 => 7462,2 => 13201,466*_a-72951980 => -5227,220*_a+38436142 => 2235,-18230*_a-1592957321 => 4357,31 => -460,-124*_a+61352906 => 460,37*_a-4976426 => -6591,-138*_a-11201826 => -413,83 => -7462,13 => 12405,43*_a+182578 => 2235,-8*_a+1288325 => -7352,65*_a-5031624 => -4467,576*_a-117377091 => 5227,67 => 2234,43 => -2235,329*_a+33818545 => 2233))\n",
      "283: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "285: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "286: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "289: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -18084,11//2*_a+997573//2 => -12875,103 => -317,37 => 4876,33//2*_a+3072161//2 => 9201,-81//2*_a+4153127//2 => 3923,157 => 3674,73 => -150,3*_a-4855724 => 2571,21//2*_a+568643//2 => -2421,89 => 5026,1//2*_a-57143//2 => -4876,7//2*_a-511827//2 => 317,13//2*_a-2127781//2 => 317,2 => 25555,11 => -10487,-5//2*_a+518475//2 => 319,61//2*_a+3470627//2 => 2571,-661//2*_a+58772133//2 => -5026,5 => -30792,113 => -2571,47 => -9201,1//2*_a+121153//2 => -14977,29 => -14410,-1//2*_a+278817//2 => 150,1//2*_a-308947//2 => -7597,-17//2*_a-773211//2 => 15513,43 => 14977,15//2*_a-1674335//2 => 14260))\n",
      "290: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "291: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "293: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "294: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "295: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "297: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "298: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(37 => -509,-354*_a-40702330 => 241,101 => 1432,_a+94366 => 19,117214*_a-6785105006 => 185,-111*_a-48806848 => 509,-2536*_a+252952432 => -865,2 => 3865,-382*_a-37536251 => 324,892*_a+95950844 => 356,179 => -290,149 => 1413,_a-364624 => -1413,12*_a-1072250 => -1413,59 => -20,10949*_a-1062148143 => 290,-766*_a-154882885 => 105,47 => 865,2323*_a-180791010 => -19,-41699*_a-4594903656 => -221,7 => 1836))\n",
      "299: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "301: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(147//2*_a+12998447//2 => 2661,103 => 2152,625//2*_a+39791105//2 => 652,_a-26 => -2152,12*_a-606118 => -369,23 => -2661,1533//2*_a-165543925//2 => 377,73 => -377,_a+26 => -989,4828*_a+310617422 => 2540,-2083//2*_a-383328533//2 => 369,-50379658*_a-21590384050858 => -1,131 => 2152,_a-419099 => 369,4*_a+870866 => 1880,2 => -446,11 => 9527,3*_a+298771 => -275,271*_a+32929039 => -1156,107 => -369,1069*_a-5043706 => -1888,2479*_a-207750317 => -2172,79 => -377,113 => 1,17//2*_a-3127933//2 => 780,-119//2*_a-23101669//2 => -1163,67 => 2172,-327*_a-208140602 => -1887,7 => 2725,-188*_a-877938 => -369))\n",
      "302: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "303: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "306: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "307: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "309: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(103 => 2626,3 => -1438,1287//2*_a+1120103595//2 => 4335,451324315//2*_a+7510886251765//2 => -1999,23 => -4916,52*_a+8989825 => 5641,53 => -5744,-102*_a+16211091 => 2675,61//2*_a-14933477//2 => 1320,-1//2*_a+340223//2 => 5641,15//2*_a+1067391//2 => 1320,1//2*_a+360997//2 => -6067,-133//2*_a+14302483//2 => -5641,5//2*_a+542789//2 => 4916,-1431//2*_a-27935505//2 => 1409,-15*_a+1468688 => -2626,-_a+71422 => -2569,-4*_a-1549171 => -2626,83 => -4335,5 => 5817,79 => -5641,13 => -3686,13//2*_a-2309567//2 => -3167,29 => 1758,41 => 4321,67 => -1320,43 => 1999))\n",
      "310: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "313: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "315: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "317: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "318: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "319: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "322: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -2322,-2059*_a+285208040 => -3571,103 => 1646,23 => -6115,157 => 1456,-7861*_a+835163251 => -2513,-746*_a+26499122 => -5468,73 => -2314,-289*_a+352143610 => 623,5*_a+541762 => 2314,-149*_a-29889234 => 3133,10*_a+1381213 => -5217,4*_a+59172 => -1,204*_a-1948642 => -1456,89 => -4649,1189*_a+666134872 => -4557,2 => -5240,11 => -4428,-10906*_a+238251234 => 4649,145*_a+1124337 => 1270,107 => 1270,-391*_a-80248840 => -1645,-155*_a-5974274 => 3571,-275*_a-17634188 => -1456,227*_a-5274970 => -1270,318*_a-34760882 => 4649,_a-112788 => -1270,13 => 1080,-4816*_a-66631682 => -1646,79 => 5217,29 => 15728,41 => 4557,-578*_a+249546009 => -3043,17*_a+911574 => 7070,43 => 1646,7 => -5522,-581*_a-58837610 => 6086))\n",
      "326: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "327: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "329: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "330: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 7628,10*_a+31360 => 1060,3 => 5097,37 => -1,-32*_a+2102260 => -8497,137 => -375,23 => 4603,2*_a+19000 => -3026,1 => -14,-8*_a+909004 => 3377,19 => -2784,73 => 4603,10*_a+1558720 => -318,-274*_a+21785740 => 375,3087625*_a-198504728750 => -4603,83//11735537938850*_a-6106576//5867768969425 => -1,-246*_a-15978320 => -129,36*_a-2360036 => -3118,2 => -1254,11 => -15107,-186*_a+19822870 => -92,1022528529 => 0,-4*_a+184740 => -4603,31977 => 1,149 => 318,12*_a-6220400 => 259,-4*_a+2157580 => 3231,59 => 3118,-12*_a-1189220 => 11729,5 => 11523,79 => -3232,38*_a+520100 => -259,61 => 129,-179*_a-28719980 => 129,43 => 8496,355*_a-55443330 => 4285))\n",
      "331: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "333: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "334: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "335: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "337: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "338: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "339: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "342: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "343: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "345: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "346: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "347: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "349: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "353: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "354: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "355: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "357: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "358: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "361: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(88*_a-20149622 => 3405,127 => 239,-41//2*_a-1300221//2 => 2818,37 => -2818,8*_a+614398 => -4331,155*_a+14228380 => -1035,23 => -598,1 => 0,109 => -9735,49*_a-2164981 => -9776,19 => 7433,73 => 9776,-47//2*_a+2234493//2 => -6594,131 => -7372,-4303//2*_a-826459443//2 => -7433,-479//2*_a+481701//2 => -4888,355//2*_a+37204255//2 => 9735,203//2*_a+38552243//2 => -433,-173//2*_a-5460213//2 => -216,-239//2*_a+60765191//2 => -239,2 => -2912,23*_a+6164713 => 4929,77//2*_a-4935063//2 => -239,10343//2*_a-471038917//2 => -41,-35//2*_a-6831335//2 => 7611,1//2*_a+4900981//2 => -1957,-367//2*_a+25550473//2 => -3147,-6*_a-761111 => 6594,31 => 10770,1//2*_a+21581//2 => 1468,857*_a-82386833 => 9329,5 => -21199,79 => 1251,13 => 6623,61 => -2972,-9*_a-5838554 => 4888,248*_a-14036087 => -9735,5*_a+274405 => 4888,67 => 3147,43 => 216,7 => -12251))\n",
      "362: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "363: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "365: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "366: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "367: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "369: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-2561//2*_a+317548627//2 => -68702,43//2*_a-5800841//2 => -87594,103 => 68702,3 => -308942,7//2*_a+4239151//2 => 51420,1//2*_a-115343//2 => -126028,99*_a+24129549 => 21879,5*_a-7700825 => -46096,53 => 126028,19 => 46096,-51//2*_a+3952929//2 => -68702,13//2*_a-785901//2 => 24944,131 => -24944,31//2*_a-2849117//2 => 188457,1//2*_a-78887//2 => -39012,2 => -333575,79//2*_a-10728313//2 => 34571,4781//2*_a+746374997//2 => -68702,157//2*_a-21377739//2 => 68702,151 => 68702,31 => -188457,5 => 309528,17*_a+1256876 => 24944,3*_a+173469 => 103414,47 => -68702,7 => -57550))\n",
      "370: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "371: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "373: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "374: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "378: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(103 => -329,3 => 69,_a+3469 => 379,-667*_a+2029681 => -378,23 => 377,-6*_a-800175 => -155,9*_a+1963470 => 67,1 => -16,109 => -1200,19 => 658,_a-148265 => 1200,51017467//378*_a+2539994999510//189 => 0,-1813*_a-107992668 => 329,-1621*_a-79799021 => -600,51*_a+1264764 => 329,-41*_a+1299244 => -2909,2 => -215,11 => -1200,17*_a-1692865 => 1,-1312*_a+338967705 => 174,-1843*_a-151995824 => -684,59 => 155,-4161*_a+83244358 => -329,_a+154576 => -378,169 => -1,113 => 378,13 => 155,11*_a-508101 => 1200,29 => 378,41 => -553,-367*_a+73157519 => 600,-3*_a+299958 => 4005,_a-100000 => 0,7 => -1336,43 => -1))\n",
      "379: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "381: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "382: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "383: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "385: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "387: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "389: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "390: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "391: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "393: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "394: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(37 => -1210,296*_a-104708927 => 1472,53 => 4239,-1259*_a-164650798 => 1472,_a+106613 => -805,1775564999264686704187472*_a+113252616660351406966771943336 => -2639,167 => 805,131 => -1472,14*_a-420988 => 739,2 => 7429,111*_a+5627293 => 7525,-27*_a+2575276 => 5578,7*_a+2503274 => -5242,-814*_a-54298092 => -1122,31*_a-3372972 => 2125,-2389*_a+215280618 => 1122,_a+490863 => 532,5 => -4456,61 => 5278,6845*_a-195931280 => -2930,67 => -1472))\n",
      "397: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(10*_a-2049689 => 66,57*_a-2245135 => 1044,37 => -115,1//2*_a+771487//2 => 612,1 => 0,1//2*_a-107377//2 => -429,19 => -1044,-4*_a-300662 => 871,71 => -494,71//2*_a+3518973//2 => -66,27//2*_a+2829131//2 => 472,139 => 66,131 => -472,-9//2*_a+854293//2 => -1555,2 => -190,-23*_a+2125999 => -2167,2104*_a-313515578 => 530,625*_a+40549151 => -560,-165*_a-86067217 => 472,1//2*_a+134569//2 => -612,-5*_a+248788 => -66,13 => 68,113 => 2167,61 => -442,47 => -101,-6*_a+448087 => 560,7 => 1091))\n",
      "398: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "399: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "402: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "403: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "405: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 5,-89//2*_a-7511245//2 => -848,3 => -1925,1 => 0,31//2*_a-3818549//2 => -498,101 => -242,53 => -65,-13922591//2*_a+270502534145//2 => -228,73 => 848,71 => -518,-3//2*_a-376341//2 => -327,10*_a+1484225 => 518,-19//2*_a-1960975//2 => -848,89 => 249,-2*_a+6298135 => 65,-5//2*_a+2380099//2 => -249,-40*_a-10299355 => -3,-22*_a+743135 => 766,-_a+508330 => 782,2*_a+412445 => 518,31 => -6,151 => 848,107 => 249,-297//2*_a+33973805//2 => -249,59 => 749,145//2*_a-59851745//2 => 252,83 => 498,5 => -1286,4*_a-1598375 => 34,113 => -518,55//2*_a-939401//2 => 484,29 => -1035,3//2*_a+218445//2 => 528,-4*_a+405383 => -521,43 => 249,-43*_a-1310124 => -249))\n",
      "406: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "407: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "410: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "411: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "414: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "415: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "417: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "418: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "419: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "421: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "423: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "426: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-10*_a+1171910 => -922,3 => -2175,-200*_a-80897570 => 121,1 => -8,13*_a+1300338 => 1740,48*_a-1890877 => -466,157 => -441,101 => 466,53 => 551,19 => -121,5*_a+1122455 => 1043,167 => -121,35*_a-4357600 => 97,1185*_a-116513670 => 1292,-6*_a+439894 => -1043,2 => 748,11 => 1296,4279*_a+599619504 => -648,-3*_a+276549 => 1,-7150*_a-324682930 => -905,4*_a+869804 => 441,31 => -28,151 => 466,22*_a+250822 => -183,-8*_a+183742 => 148,14//13949746875*_a+8049647//27899493750 => -1,-2*_a+153658 => 85,83 => 648,5 => 196,23*_a-199552 => 121,13 => -600,61 => 1223,47 => 1042,64*_a+19194279 => -851,-186*_a+400015289 => -121,-88*_a-8101093 => 439,67 => -121,13*_a+10738 => -466))\n",
      "427: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "429: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "430: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "433: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(2878*_a-130071639 => 4561,-1629*_a+115779851 => -1841,23 => 10516,77*_a+12437865 => -131,-6193//2*_a-613610173//2 => -9912,71 => 131,-29*_a-1139463 => 6533,2887//2*_a-126975279//2 => -4692,761*_a+85900073 => 10239,205//2*_a+12238111//2 => -10516,2 => -329,11 => 17154,-702999//2*_a-75114202207//2 => -7111,-797//2*_a+48421243//2 => 6316,7//2*_a-790641//2 => -5369,395*_a-50759229 => 8280,31 => 2236,59 => 1841,29 => -2911))\n",
      "434: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "435: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "437: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "438: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "439: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "441: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -3954,1224*_a-75314046 => 4629,3 => 8932,37 => 6003,3//2*_a+23559//2 => -6004,1 => -16,101 => 4629,19//2*_a+1898235//2 => 11290,71 => -1,17//2*_a+1912007//2 => -680,1//2*_a-159189//2 => 10537,37//2*_a-780473//2 => -2107,20*_a+992270 => -1974,13*_a+1418773 => 8983,951//46118*_a+275835029//46118 => 1,2 => -16554,1//2*_a-473621//2 => 1427,-845//2*_a-102095375//2 => -1974,13//2*_a+200349//2 => -3349,25//2*_a+697451//2 => -1554,-395//2*_a+39690295//2 => -8983,-6022441//2*_a+869588372489//2 => -4629,59 => -2,-574 => 1,5 => 28038,113 => 1974,329476 => 0,41 => -1280,-251//61787512860*_a-26475311//61787512860 => -1,67 => 3349,7 => -3660,7//2*_a-721283//2 => -4629))\n",
      "442: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 8,127 => -2018,-22*_a-2531045 => 752,157 => 10,1 => -8,-3730//11279*_a+437211194//11279 => 1,109 => -109,56793*_a-17203504868 => 504,-2*_a+263053 => -2008,82*_a+5576205 => 1555,2699*_a-42373428 => 293,167 => -504,-1036*_a-61148581 => -797,-2407*_a+713618138 => 504,-6*_a+509702 => -797,226*_a+14166444 => 10,89 => 2230,336*_a-21255314 => -10,-205*_a-63151152 => 2018,94*_a+41303996 => -1555,-1 => 1,575*_a-308506938 => 2018,2 => 3193,11 => 97,3//87829189514*_a+23296//43914594757 => -1,3139*_a-527128314 => 1706,179 => 797,_a+99576 => -3937,-86*_a-46270322 => -874,113 => -2018,13 => -754,493*_a+15501892 => -10,29 => 303,41 => -3856,409*_a-37620802 => 109,43 => 1961,-5959*_a-979172066 => -1597))\n",
      "443: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "445: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(163//2*_a-19060525//2 => 1956,37 => -2890,26*_a+3601435 => -3245,1 => 0,-449//2*_a+16837253//2 => 1424,53 => -2488,71 => 3245,-53//2*_a+1021331//2 => -240,3//2*_a-327485//2 => -2117,139 => 240,131 => -532,-357//2*_a+11440855//2 => -3245,-1305//2*_a-274935341//2 => -1424,-7//2*_a-1830255//2 => 1706,-899//2*_a-203754725//2 => 532,97 => 3245,-236*_a+32841965 => 3912,31 => 240,107 => 3245,129//2*_a+13932215//2 => -2473,-4*_a-406529 => 548,59 => -934,5 => 1873,1//2*_a+28981//2 => -120,11//2*_a-3352009//2 => 934,29 => 3781,-377//2*_a-5921655//2 => -772,365*_a-30909138 => -240,43 => 1377,7 => -1467))\n",
      "446: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "447: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "451: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "453: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 2325,5*_a-673126 => 1412,3 => -8206,53 => -3301,-4*_a-401623 => -3880,-11*_a+1487992 => 1412,10123//2*_a+195521399//2 => 1889,10171//2*_a+980228137//2 => -703,1//2*_a+81021//2 => 490,-43//2*_a-4458679//2 => -4487,11 => -1412,-9//2*_a-2563791//2 => 1622,149 => -2803,-3461//2*_a+245610895//2 => -1622,-23*_a+2246084 => 1565,13 => 5190,29 => -1412,-_a+40826 => 5606,-5//2*_a-230381//2 => -1730,7 => 703))\n",
      "454: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "455: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "457: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -183,-21*_a+2100113 => 1,23 => -421,1 => -16,-575//2*_a+50704903//2 => 450,-277//2*_a+28428063//2 => 404,101 => -380,73 => -380,-73//2*_a-15677261//2 => 380,495//2*_a-81560113//2 => -458,1//2*_a+20573//2 => 201,131 => -16,-23//2*_a+2516315//2 => 394,-4335//2*_a-433524329//2 => -714,720*_a-71028052 => 146,2 => -2660,2927//2*_a+14278735//2 => 309,46*_a-1344120 => -130,-11//2*_a+521781//2 => 16,-962*_a-35712835 => -54,113 => 54,47 => -1,6046//33713*_a-154176870//33713 => 0,29 => -451,-2323//2*_a-94792039//2 => -293,3919*_a-391900008 => 0))\n",
      "459: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "461: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "462: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "463: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "465: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "466: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "469: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(127 => 644,-93//2*_a+7488391//2 => 426,4*_a+143983 => -2730,31//2*_a-2073807//2 => 4918,23*_a-1986146 => -5266,71 => 5266,2 => -19737,41*_a+10554633 => 15450,20*_a+848069 => 4172,97 => 9888,-81//2*_a-5678771//2 => -4622,31 => -4700,31//2*_a+1357397//2 => -4726,-19//2*_a-1168023//2 => -9888,59 => 2730,2*_a+199324 => 9333,5 => 23076,13 => 13750,61 => -4172,-1284275917852603*_a+13478876149333115261 => -4210,-18*_a+3299384 => -4918,-83*_a+9525216 => -644,62*_a+75651656 => 4082))\n",
      "470: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "471: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "473: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "474: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "477: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(127 => -575,3 => -1609,2*_a+565055 => 1239,1 => 0,53 => 66,-164077//2*_a+6738015269//2 => -413,19 => 4138,71 => 1369,4629//2*_a+552222861//2 => 1239,1//2*_a-413495//2 => -1305,-19//2*_a-7161613//2 => -830,139 => 1305,63//2*_a+4545773//2 => -1305,2*_a+6083795 => 1147,3//2*_a+295813//2 => 281,1//2*_a+37195//2 => -1369,11 => -992,-147//2*_a-864825//2 => -575,-31//2*_a+2960933//2 => 1251,263*_a-30401750 => -1132,-19//2*_a+1665269//2 => 413,83 => -1147,113 => -1239,61 => -413,47 => -162,13 => -1535,-111//2*_a+7479237//2 => 1497,-1475//2*_a-278660837//2 => 575,323//2*_a-32116783//2 => -1939,737//2*_a+432331867//2 => 575))\n",
      "478: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "479: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "481: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(127 => 1926,103 => -14446,37 => -8086,-65//2*_a+24033745//2 => -23745,1//2*_a-130491//2 => -1926,73 => -4153,-18*_a+412015 => -1926,-299//2*_a+22407291//2 => 15509,53//2*_a+102099443//2 => -9299,-3393//2*_a+292237147//2 => 23282,7//2*_a+441385//2 => 4153,1//2*_a+52847//2 => 8549,-349//2*_a-32561267//2 => -1429,-15//2*_a-256147//2 => 14446,-275//2*_a+29797867//2 => 11252,7//2*_a+1730783//2 => 7099,2 => -22362,11 => -23309,6*_a+194296 => 1429,-31//2*_a-105927071//2 => -9689,-43*_a-30081768 => -7099,1//2*_a+1014951//2 => -9299,149 => 9299,5 => 20498,-51//2*_a-5794601//2 => -8836,13 => -11252,47 => -8549,29 => -23282,67 => 9299,43 => 7099,7 => 15512))\n",
      "482: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "483: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "486: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "489: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "490: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "491: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "493: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "495: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "497: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "498: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(3 => 1496,37 => 742,-2718*_a+130000770 => 4782,23 => 3239,-8*_a+748789 => 1359,26*_a-2586721 => -1708,2*_a-762890 => -1773,173 => 252,_a-677774 => -1091,-9*_a+1941750 => -252,801*_a+286285446 => 626,2 => -692,11 => -349,6*_a-594357 => -4172,-9*_a+470268 => 349,59 => 252,-115*_a+6296066 => -733,83 => -626,762*_a+68328024 => -1663,-11*_a-1135262 => 1456,47 => 3546,-20*_a-1056029 => -1359))\n",
      "499: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "501: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-287//2*_a+39302231//2 => -4534,9//2*_a+1073811//2 => 8091,103 => 2474,3 => 30997,37 => -20472,-229*_a+14835630 => -30338,1//2*_a-1753103//2 => -15854,51//2*_a-3122523//2 => -31708,157 => 31708,-13//2*_a+1601867//2 => -5036,7//2*_a+1744457//2 => 1688,19 => -3748,9//2*_a+746303//2 => 2060,6626392*_a+779956549642 => -5573,89 => 31708,2 => 5573,97 => -1897,-107//2*_a-20068547//2 => 33437,379//2*_a+160417129//2 => -6053,-85//2*_a-1412211//2 => 15854,-587//2*_a+58213273//2 => 20472,-23//2*_a+864937//2 => 1897,5 => -19477,79 => 19018,13 => -11885,29//2*_a-137665//2 => -12965,3//2*_a-252307//2 => 209,41 => 4534,67 => -2060,161//2*_a-33760801//2 => 11386,7 => 13379))\n",
      "502: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "505: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "506: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "509: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "510: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "511: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "513: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "514: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "515: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "517: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "518: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "519: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "522: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "523: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "526: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "527: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "529: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 987,61//2*_a+4022415//2 => -126,37 => 1301,19//2*_a-3256885//2 => -342,-69//2*_a+3529741//2 => -14,23 => 14,1 => 0,-19//2*_a+321993//2 => -905,1//2*_a+100591//2 => 1835,-51*_a+2950673 => -987,19 => -1160,-15//2*_a-519193//2 => 342,1//2*_a+63123//2 => 252,-7*_a-693478 => 1337,-64*_a-2692981 => 14,-4*_a+559758 => -1301,-2*_a-369788 => -1975,1//2*_a+23257//2 => 1835,139 => 126,-19//2*_a-1845527//2 => 2407,2 => 945,-8*_a-125221 => -140,31 => -230,-29//2*_a+7380101//2 => -314,-15//2*_a-2368577//2 => -432,5 => 1266,-15//2*_a+2376553//2 => 454,113 => -1835,13 => 1575,29 => 14,43 => 140,7 => 628,11//2*_a+2965043//2 => -670))\n",
      "531: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "533: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "534: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "535: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "537: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(3 => -63258,75//2*_a+9518469//2 => 16303,-69*_a+13733898 => -15121,23 => 6940,31//2*_a+1351051//2 => 115,12*_a-763754 => -115,-11//2*_a-1307469//2 => 7940,-1771//2*_a+141734313//2 => -14790,17//2*_a+481315//2 => -13681,277//2*_a-25640537//2 => -27429,2 => 17893,41//2*_a+44661341//2 => 8181,297//2*_a-20412663//2 => 14922,2*_a+300056 => 8181,97 => -115,-2*_a+128568 => 8181,79 => 115,-13*_a-3790988 => -8181,-27//2*_a-2221321//2 => 12476,41 => -8181,-6443//2*_a-439709909//2 => 13838,7 => -25392))\n",
      "538: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "541: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "543: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "545: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "546: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "547: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "549: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "551: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "553: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "554: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "555: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "558: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "559: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "561: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "562: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-474*_a+35407793 => -18,470*_a-133229088 => -883,-38*_a+3438506 => -1182,-451*_a+27811692 => -849,101 => 851,53 => -857,19 => 2049,-217*_a-143836962 => -11,-1681*_a-168099925 => 1182,1060*_a-63321114 => 857,-26*_a-2567354 => 518,2 => 5279,29248*_a+2738636272 => -851,-30*_a-4050412 => 658,31 => 2610,83 => 1182,113 => 867,67*_a-32463979 => -534,34162*_a+107838832 => -867,67 => 542,-3986*_a-10927067 => 883))\n",
      "563: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "565: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "567: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "570: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "571: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "573: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-4*_a+351461 => 227,1//2*_a+112351//2 => -366,111//2*_a-11191127//2 => 241,83 => 183,3 => 219,37 => 199,136*_a+4024669 => -354,-35687630781829//2*_a+3369942495227056793//2 => -56,25//2*_a-254159//2 => 846,37//2*_a-2630515//2 => -73,29 => -115,41 => -276,89 => -29,31 => -101,83//2*_a+7353551//2 => -183,259//2*_a+145166281//2 => -126))\n",
      "574: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "577: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "578: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "579: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "581: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "582: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "583: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "585: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-3//2*_a+840165//2 => 15272,127 => -16561,3 => 17496,23 => 8590,63//2*_a-6065955//2 => 16662,101 => 8884,-1261//2*_a-121610665//2 => 14488,19 => -15097,3//2*_a-1743375//2 => -22448,2 => -74481,11 => 21338,-511//2*_a-170552095//2 => -15097,8685//2*_a-405770031//2 => -15097,-23//2*_a-2755055//2 => 54379,6049//2*_a-705940955//2 => -23372,3357//2*_a-186867495//2 => 15097,121//2*_a-4983935//2 => 16561,31 => -15272,149 => 15097,-23//2*_a+89815//2 => -16225,1//2*_a+787375//2 => -19059,5 => 3527,3//2*_a-675945//2 => 1249,-439*_a-304027855 => 15097,13 => 15097,47 => -31934,53//2*_a-7042465//2 => 16561,3//2*_a-347505//2 => -22445,1//2*_a-690605//2 => -8884,-25*_a-2071780 => -22445,43 => 22445,7 => -1565))\n",
      "586: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "587: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "589: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 10282,37 => 4865,-559*_a+111409108 => 4322,109 => 3850,19 => 552,73 => -4322,-189//2*_a-17242997//2 => 6522,281//2*_a-8638699//2 => -3180,7*_a-644159 => -3850,89 => 5000,2 => 5000,431//2*_a-154603647//2 => -3850,-4625//2*_a+300054275//2 => -5417,19//2*_a-958873//2 => -552,-17//2*_a+6419999//2 => 552,-3*_a-58451192 => 910,-37//2*_a-12340351//2 => 5000,5 => 10834,-11*_a-20115913 => -1150,1//2*_a-114117//2 => 2860,43 => 3850,-2189//2*_a+239174273//2 => -4448,1158*_a+763971839 => -1820))\n",
      "590: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "591: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "594: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "595: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "597: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 9468,3 => 26548,-325//2*_a-20814949//2 => 7407,-445//2*_a+241247759//2 => 6755,1//2*_a+62647//2 => 18798,-11//2*_a+688019//2 => -7678,667//2*_a-120080387//2 => -7407,53 => 20572,19 => 4989,229*_a+11693898 => -11744,2033//2*_a+2753119//2 => -6755,-907//2*_a+110889635//2 => 3839,-53//2*_a+9344483//2 => -4989,47//2*_a+51456747//2 => 18798,139 => 7678,131 => -18798,11 => 7589,-47//2*_a+2084561//2 => -3831,279//2*_a-106822121//2 => -5297,248*_a-6683225 => 4188,151 => 4989,-19//2*_a+24726125//2 => 1766,-_a+7016 => -11866,113 => 4989,1//2*_a-61355//2 => -19756,29 => 7407,-583//2*_a+155657821//2 => 65))\n",
      "598: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "599: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "601: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -12553,103 => -7326,-5537//2*_a-617308717//2 => 9252,21*_a-701695 => -4583,101 => 12081,44*_a+3468936 => 4117,1035*_a-7919255 => -6803,139 => 4583,131 => -4117,63//2*_a-25051837//2 => 12553,-155//2*_a-14626055//2 => 6803,-59//2*_a-2260059//2 => 7498,2 => -28669,2029//2*_a-157803839//2 => 19691,9*_a-597541 => 13247,-1741*_a+49851209 => 7326,149 => -19691,-5799//2*_a-117040499//2 => -12081,59 => 31255,-26717//2*_a+393224143//2 => -21582,-610*_a+3458700 => 10920,5 => -34728,-59//2*_a-6381263//2 => -31255,113 => -9252,61 => -23473))\n",
      "603: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "606: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "607: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "609: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "610: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "613: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "614: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "615: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "617: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "618: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "619: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "621: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-22*_a+427445 => 367,3 => 770,-17//2*_a+1517587//2 => -83,-6*_a+610109 => -83,137 => -367,1 => 0,23 => 111,-18975//2*_a+1807271115//2 => -111,101 => 83,53 => -94,71 => -269,-16*_a+485213 => 367,94*_a-10039055 => -305,139 => 83,55//2*_a-32316245//2 => 170,977//2*_a-84678253//2 => -83,-29//2*_a-4805069//2 => -96,5 => 437,-22153//2*_a+2247355767//2 => -68,1//2*_a+117449//2 => -330,13 => 123,3//2*_a+437173//2 => 269))\n",
      "622: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "623: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "626: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "627: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "630: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "631: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "633: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "634: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-214292*_a-8028375251 => -66237,4//99756377818825*_a+2231//301834728650 => 0,-600//10568829567023*_a-16160713//812986889771 => 59,-52*_a-6421831 => -66172,109 => -66167,13*_a+1673776 => -132414,73 => 66248,26*_a+24172577 => -66181,-1 => 0,-73 => -1,221*_a+14863888 => 132394,31 => 61,3429//21578989918058*_a-171434272//10789494959029 => 59,39*_a+11215438 => 132414,83 => 66247,-3589//63482*_a-8111988//31741 => 0,767*_a-80798224 => -66247,41 => 67,67 => 1,-19269//354462954163176950*_a+2169831043//354462954163176950 => 1,13*_a+374504 => 54,137 => 6,1 => 186,23 => 77,53 => 132409,13*_a+2784444 => 66246,19 => 1,15145*_a+2463004310 => 66181,-715*_a+136375980 => -9,173 => 66172,179 => 1,-22607*_a-2229039696 => 56,5 => -66138,79 => 7,127 => 5,5*_a+950742 => -132429,-13868880799*_a+1367367763693924 => -59,2 => -100757,26*_a+12771603 => -66172,5629*_a-501778238 => -20,-3726190*_a+392623760880 => 34569,13 => 132434,829//883882357330*_a+16312721//441941178665 => 1,103 => 21,12233*_a-267548801 => -6,35828*_a-3785703766 => 2,-169*_a+4168723 => -6,10609 => 59,-9685*_a+305404970 => 66167,64562043452642 => 59,-2231//4566335064846018100*_a-4//150917364325 => 0,-1863095*_a+196311880440 => -34587,7 => 66317))\n",
      "635: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "637: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "639: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "641: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "642: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 473,127 => 43,6624*_a+94597308 => -618,3 => -1531,9*_a+898395 => 886,975*_a-45986406 => 816,282*_a+51783960 => 618,5726*_a+585744584 => 43,1 => 0,-5232*_a-355147788 => -43,19 => -575,-15*_a-1703082 => 575,-1674*_a+308464128 => -618,-11*_a-1995213 => 413,-1886*_a+29953684 => -675,89 => -618,173 => 618,-4658*_a-94069160 => -886,2 => 867,11 => -83,-3634*_a-14625922 => -86,4*_a+274510 => 1914,97 => 675,1400*_a+674670338 => 86,67*_a+17355412 => -43,61 => -859,788*_a+77588054 => 144,67 => -1871,-6*_a+559667 => -675,7 => -1154))\n",
      "643: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "645: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "646: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "649: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(103 => -13095,37 => 3217,-10*_a-1336400 => -18961,-623//2*_a+24145821//2 => 3092,_a+32 => 10003,167//2*_a+10207481//2 => -3469,53 => 3469,1 => -2,1//2*_a-245081//2 => -3469,5//2*_a-11185//2 => -10060,2711//2*_a-613868347//2 => 15765,1925 => 1,1//2*_a+101027//2 => -21600,131 => -10003,3//2*_a-14779721//2 => -10897,176*_a-10252022 => 10897,2 => 36539,11 => -36570,-205//2*_a-122549335//2 => 9669,_a-32 => 10003,-16*_a-3551939 => -4477,-41*_a-550085 => 6843,67//2*_a-3156519//2 => 3092,83 => 3469,637//2*_a-109646663//2 => -3469,79 => 3469,456533 => 0,15625 => 0,139*_a+12947183 => 1272,7 => -12692))\n",
      "651: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "653: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "655: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "657: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 3456,3 => 1266,37 => 1924,27*_a-1331139 => 304,137 => -837,1 => 0,23 => -168,-1073//2*_a-25916465//2 => 417,7559//2*_a-417392497//2 => -533,-_a+23163 => -86,-863//2*_a+124481665//2 => 931,-4942*_a-2439829522 => 86,-6647//2*_a+56572617//2 => -365,-179//2*_a-49019419//2 => 837,-12*_a+1176168 => -2050,-187//2*_a-10168227//2 => -1769,139 => 540,1//2*_a+19609//2 => -278,3131//2*_a+316573531//2 => 1801,1617//2*_a+228373409//2 => 279,-71//2*_a-142796471//2 => 540,2 => 7585,11 => -279,12005//2*_a-198558667//2 => -540,151 => -540,-1739//2*_a+248708413//2 => -540,-1190*_a+47367406 => -957,113 => 739,-65*_a-3712589 => 2341,777*_a-42463235 => -1801,-52*_a+10357684 => -739,1432*_a-278295748 => 533))\n",
      "658: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "659: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "661: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "662: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "663: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "666: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-473*_a-31903463 => 185039,3 => -185743,37 => 2028,_a-278621 => -740839,138*_a+19993074 => 740719,1 => -720,26*_a+56242306 => 370315,-56*_a+5717227 => 716,73 => -368608,71 => -72,_a+793306 => -94,73*_a-1176278 => -716,5*_a+393440 => 184304,139 => 94,3*_a-379986 => -94,-756*_a-46505901 => 368608,_a-2994865 => -47,2 => -1075,6640*_a-55477765 => -554651,-187*_a+2152092 => -370332,23*_a+2167133 => 554651,107 => -370387,-925*_a+66256085 => -1312,5 => 2779035,3171*_a-248862984 => -740839,79 => 94,113 => 740839,61 => 740767,11*_a+441178 => -554651,4700925956*_a-167173567542124 => -184392,-1231//1006334924163750*_a+63560888//503167462081875 => -72,67 => 740695,43 => -184970,-2*_a+199933 => 742290))\n",
      "667: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "669: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "670: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "671: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "673: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "677: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "678: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "679: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "681: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "682: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "685: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-100*_a+19983125 => 3082,157 => -1679,135//2*_a+2278225//2 => -1681,101 => 4993,53 => -3082,73 => 3789,2950*_a-370176100 => 513,4585//2*_a+486060725//2 => -2847,-25//2*_a+5336105//2 => 1204,-25//2*_a-1461675//2 => -2611,-440*_a+72378845 => -1162,2 => 429,11 => 2324,15//2*_a+1133525//2 => -513,-707//2*_a-114635//2 => -4993,-390*_a+312193115 => 1166,5 => -68,-5*_a+592500 => 2324,113 => 1681,47 => 2611,13 => -2845,29 => 1679,-2*_a+392025 => 3314,-8092750*_a+156995391750 => -471,705//2*_a+75208135//2 => 1679))\n",
      "686: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "687: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "689: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "690: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(43*_a-5441444 => -3230,3 => -4563,37 => -69,53 => -1813,2*_a+839393 => 5918,-65*_a+10938655 => -5782,-174*_a+4476599 => 1813,71 => 1813,64*_a+12962159 => -4105,-2355194855937500*_a+1825227470538954062500 => -739,-3*_a+305428 => -138,173 => 739,2 => 1975,11 => 542,21*_a-19419897 => 4904,229*_a+24696292 => -2669,167*_a+6397980 => 5043,34*_a+3651593 => 69,162*_a+24810150 => 1813,-14*_a+493495 => 2292,34*_a-379387 => -1511,59 => 5782,5 => 8126,_a+595060 => -1813,13 => 5782,47 => -1813,29 => 4910,83*_a-4276012 => -1813,7 => -5784,427*_a-38353805 => -1677))\n",
      "691: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "693: (true, Factored element with data\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dict{nf_elem,fmpz}(17 => -703,103 => 586,3 => 14709,37 => 3926,-15//2*_a+707019//2 => -233,-211//2*_a-15907595//2 => 1414,2183//2*_a-217472791//2 => -2103,-37//2*_a+1177821//2 => 799,139 => -1598,-238*_a-19559503 => 140,11 => 1838,3//2*_a+242091//2 => -586,177//2*_a+61834455//2 => 1838,31 => 4,5217//2*_a+190481365//2 => -919,-423//2*_a+40583043//2 => -5828,7//2*_a+388241//2 => 1598,61 => 2,47 => 5142,-18736245810285245283602015807801//2*_a-2698615613521276033810159740550897931//2 => -2,-17273055227689//2*_a-1658884806949416455//2 => 563,7 => -2724))\n",
      "694: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "695: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "698: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "699: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "702: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "705: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(3 => 12286,37 => -3023,315*_a+120305892 => -6850,-60*_a-4151635 => 6352,23 => 6850,-703//2*_a+549191333//2 => 6861,1//2*_a+11324449//2 => -6352,-1237//2*_a-147617569//2 => 3284,19 => -7370,73 => 6850,71 => 6117,39//2*_a-73920177//2 => -2938,5535*_a-306007764 => 6048,-6744*_a+552854559 => -3284,-1381//2*_a+105111329//2 => 2764,2 => 54902,-55//2*_a+1648937//2 => -6225,97 => 6225,-287//2*_a+3402385//2 => -2484,31 => 5597,-279//2*_a+17345275//2 => -5597,-869//2*_a-26250479//2 => 6225,-963//2*_a+631981443//2 => -6225,1467//2*_a+497636571//2 => 3284,-123//2*_a-11277747//2 => 3838,5 => -3898,-648*_a+3553125 => -498,113 => -6048,61 => -6048,47 => 2377,43//2*_a-13182355//2 => -2377,41 => -7402,193//2*_a-10752737//2 => -3838,10*_a+4616782 => -5166,43 => -2764,7 => 9334,3263//2*_a+32408645//2 => 6048))\n",
      "706: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(13*_a+1306427 => -921,23 => 608,1095*_a+125863972 => 154,109 => -431,-565*_a+39441939 => 4,24*_a+2474734 => 431,73 => -360,44*_a+21150899 => 154,-114*_a-19621021 => 154,127*_a+24099232 => -4,23*_a+728272 => -154,-29*_a+3548701 => 246,2 => 496,11 => -308,13*_a-575992 => 448,-7*_a-1480048 => 427,151 => -167,5 => 494,113 => -423,61 => -448,-10827*_a-421308422 => -154,29 => -246,_a-224229 => 167,142*_a+20697022 => 206,3151*_a+292201016 => -808,2748752*_a+13601591072 => -281,7*_a+825196 => 354,10*_a+1576371 => 423))\n",
      "707: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "709: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "711: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "715: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "717: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "718: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "721: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "722: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "723: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "726: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "727: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "729: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -1659,-4639//2*_a+765098923//2 => -4982,3 => -27656,17//2*_a-897685//2 => 3415,26*_a+4139330 => 6056,23 => 19030,-19//2*_a-132753//2 => 4892,397//2*_a-16430049//2 => 1549,101 => -6758,-237//2*_a+77165329//2 => -4892,19 => -8307,71 => -5209,-22*_a+1199154 => -7585,17//2*_a+954091//2 => 11643,2 => -14303,11 => 9961,-13*_a+1109301 => -8084,47//2*_a-17494955//2 => 5209,-15//2*_a-918805//2 => -19030,151 => 13066,5//2*_a-352529//2 => -13066,107 => 4892,8*_a+2181916 => 5274,23//2*_a+482749//2 => 11643,53//2*_a-11998345//2 => 5209,-89//2*_a+14922301//2 => 4892,5 => 22620,-17*_a+2575857 => -16852,13 => -6056,-27//2*_a+696983//2 => 9964,-243//2*_a-6656729//2 => -4892,41 => -5209,43 => -11643,-2087//2*_a-107462525//2 => 8084,261//2*_a+46548023//2 => -1549))\n",
      "730: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "731: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "733: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "734: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "735: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "739: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "741: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(_a+29 => -6765,3 => -1,11//2*_a-1167241//2 => -222,7//2*_a-111893//2 => 222,137 => 6765,101 => -11306,19 => -17036,73 => 6765,-357//2*_a-17536803//2 => 12223,38*_a-3969309 => 8866,139 => -5848,211//2*_a-40078739//2 => 25,2*_a+300821 => 5848,-61//2*_a+6427083//2 => -22514,-19//2*_a+3420893//2 => -12223,2 => -1,11 => -25251,5//2*_a-3085855//2 => 9638,75*_a-6406100 => 414,118*_a-14407636 => 1308,31 => -1308,_a-29 => 5458,5 => -47750,-76*_a+1113191 => -11962,13 => -247,1//2*_a+48151//2 => 5848,206*_a+21222791 => -11668,29 => -222,41 => -2616,-83//2*_a-7119473//2 => 31941))\n",
      "742: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "743: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "745: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "747: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "749: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "751: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "753: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(291//2*_a+48287397//2 => 18052,-_a+101135 => -1440,-1789//2*_a-129840421//2 => 7827,3 => 9274,101 => -2434,-31//2*_a+3443015//2 => -5871,73 => -4024,71 => 9748,1//2*_a+20791//2 => -9748,7*_a+745087 => -3209,1//2*_a-302945//2 => -775,147*_a+22842918 => 4024,5*_a-228566 => 4024,-_a+1382926 => -14178,2 => 13235,27420257*_a-81954703448299 => -4024,31 => 5871,23//2*_a-2329241//2 => -5756,29 => 775,7 => -1630,57//2*_a-5805057//2 => 2434))\n",
      "754: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "757: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "758: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "759: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "761: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "762: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "763: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "765: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(103 => -1711,3 => 6504,-539//2*_a+77206915//2 => -716,109 => -4535,53 => 5663,-136*_a+13616375 => -2407,113//2*_a-2967025//2 => -2407,-601*_a-63913470 => 1711,1821*_a-2457183207 => -3638,2 => 3638,61//2*_a-6808655//2 => -7374,151 => 2407,-140*_a+65815045 => 1711,-829*_a+207684890 => 4619,5 => -1615,35*_a-9625040 => -1344,13 => -3819,61 => -4535,47 => -4535,-117//2*_a+194337273//2 => 4535,605//2*_a-172324835//2 => 5251,130*_a+14977495 => -716,43 => 1344))\n",
      "766: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "767: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "769: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "770: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "771: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "774: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "777: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(127 => 333,3 => -895,37 => -224,574*_a+140960911 => 697,1 => 0,-293//2*_a+9974575//2 => -333,19 => 1051,73 => 333,9827//2*_a+5738071313//2 => -333,-279*_a-13323924 => 335,895//2*_a-25994501//2 => -333,17//2*_a-2176675//2 => -147,2 => -866,115//2*_a+20029351//2 => 810,31 => -305,59 => 571,-73//2*_a+6125561//2 => -93,79 => -126,113 => 333,13 => 323,11109//2*_a+312460239//2 => 126,29 => 36,41 => -697,-2063//2*_a+121112149//2 => -422,14649//2*_a-129054783//2 => -571,2183*_a-414773515 => 224,7 => -616,-31//2*_a+59419529//2 => -30))\n",
      "778: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "779: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "781: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "783: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "785: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "786: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(3 => 12057,-9*_a+1978146 => 7112,-55*_a+5532770 => -15039,-5*_a-4977845 => 12055,157 => -12055,-35*_a-729020 => -7069,-1062*_a+33794073 => -5645,101 => 3757,-71*_a+6230437 => 5171,157*_a-2287808 => 4277,-3*_a-717357 => 3312,164*_a+95268461 => 5645,2769*_a+545400276 => -5645,2 => 4717,-2899*_a-136413394 => 12055,263*_a-75375634 => -3757,31 => -11389,-8*_a+11264407 => -7122,5 => -23993,13 => -24110,47 => 1368,29 => 5655,41 => -5645,-1569*_a-30140694 => -1368,43 => 20684))\n",
      "787: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "789: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "790: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "793: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 2608,-13*_a-1097471 => -1900,37 => -19938,157 => 5290,53 => 26584,-7*_a+26804 => -4122,-7//2*_a+665375//2 => 1984,25//2*_a-3524631//2 => 3754,5//2*_a+1481097//2 => 19938,-3//2*_a+244453//2 => -8676,2 => -14728,-31*_a+1142186 => -5290,-17//2*_a+2481643//2 => -2608,4*_a+961943 => -13292,247//2*_a-9958069//2 => -15816,-1327//2*_a-135126021//2 => 8048,_a+98948 => 8977,87//2*_a+5901583//2 => 6408,29 => 5290))\n",
      "794: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "795: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "797: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "798: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "799: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "802: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "803: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "805: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "806: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "807: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "810: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 443593,322*_a-4580534 => 524,103 => -221944,3 => 446380,_a-183133 => 650,1 => 0,637*_a-65520938 => 226,-255*_a-18488010 => -443593,-98*_a+9422542 => -1019,-13//77760913129095*_a-11//1157113398 => 0,181890*_a+11493295635 => -416,139 => -524,7*_a-1616040 => 221944,870*_a+74420989 => -581,-143*_a-14447245 => 733,8*_a-1705735 => 1248,2 => 989,189*_a-17618580 => -1426,179 => 581,31 => -222070,59 => -650,_a-59336 => -733,2567*_a+261912260 => 221944,5 => 222015,-2002*_a+193669625 => 126,47 => 416,2432*_a-162493765 => -581,29 => 1315,-4*_a+317571 => 524,41 => 0,67 => -650,43 => -108,7 => -797,-12123*_a-1265918784 => 650))\n",
      "811: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "813: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "814: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "815: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "817: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "819: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "821: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "822: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "823: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "826: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "829: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "830: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "833: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "834: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-14501392*_a+1145772259424 => -1,-2*_a+698383 => 1316,37*_a+2501404 => -103,3 => -5479,37 => -2894,-23*_a+3242881 => 1614,137 => 1,157 => -197,-13707298*_a+241861049006 => 197,109 => -1316,53 => 7991,-403*_a-22207816 => -3163,19 => 1353,13*_a+3393736 => 1316,-64*_a-16121317 => -1316,71 => 2966,348*_a+27164271 => 2894,58*_a-167591 => -1352,-11*_a+5317453 => 1084,357*_a-29114529 => -103,_a-1031858 => 1281,29*_a-1718656 => 197,2 => 2167,-62*_a-6938327 => -1,145*_a+2434753 => -7991,_a+1248520 => -4247,179 => -2894,_a+45049 => 2894,31 => -2531,163 => -1281,83 => 103,5 => 385,47 => -1614,29 => 6253,298*_a-28696883 => 4054,43 => 7991))\n",
      "837: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "838: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "839: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "841: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-15//2*_a-1754873//2 => 9255,103 => 2303,-1147*_a-88737322 => 434,37 => 5386,37//2*_a+1625003//2 => -4323,23 => 1494,-23//2*_a+18954323//2 => 5441,-989//2*_a-19556831//2 => -6935,1//2*_a-7638909//2 => -2303,71//2*_a-7595059//2 => -13812,-5//2*_a+549249//2 => 4172,-347*_a-36574463 => -434,2 => 32707,-78*_a+605137 => 6935,37//2*_a+20017//2 => -4172,31 => -5441,57//2*_a-23763583//2 => 10749,-885//2*_a-14989255//2 => -1494,5 => 17417,13 => -5224,47 => -9255,29 => -4172,-259//2*_a+585601479//2 => -2303))\n",
      "842: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "843: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "846: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "847: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "849: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -2151561,-1//2*_a+101117//2 => 6453807,103 => -4299828,3 => -23652366,-115//2*_a+13670699//2 => -8601425,1 => 0,157 => -2151561,-3133//2*_a+178646069//2 => -6449778,8*_a-1830058 => -2152837,73 => -2150532,1//2*_a-8057//2 => 2151561,11//2*_a-212707//2 => 4299828,-144*_a-18129438 => 4299828,-4*_a+368513 => -2150716,9//2*_a+973989//2 => -2150160,89 => 2150160,9//2*_a-108487413//2 => -2150160,-143//2*_a-6235967//2 => 4300039,-_a+69815 => 2151561,-423//2*_a-3633429//2 => 4301064,-3311//2*_a-214162553//2 => 6452665,3//2*_a-148251//2 => -892,2 => -25807676,11 => -15054442,-762*_a+160783158 => 4300455,-29*_a+4352827 => -4299828,1//2*_a+57085//2 => 6449433,_a+147043 => -10752704,-9//2*_a+1470105//2 => 6452665,5 => 12899555,79 => -6452665,47 => -8602128,67 => -2151561))\n",
      "851: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "853: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "855: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "857: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "858: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "859: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "861: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "862: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "865: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "866: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "867: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "869: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "870: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "871: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "873: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "874: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -6658,_a+41132 => -1640,4019*_a+423068600 => 1680,23 => 3578,137 => 1114,155*_a+4514730 => -1114,101 => -1641,1547*_a-28447154 => 1641,-53*_a-3296434 => -1023,-19*_a+6533948 => -3487,187*_a+18186549 => -1154,19 => 3487,79*_a+7891622 => 2071,167 => -1641,139 => -971,89 => 2464,4*_a+290253 => 3777,2 => 4881,-36*_a+2153758 => -670,61*_a-2800632 => -1114,-23*_a+1333793 => -2464,187*_a-18501134 => 818,97 => 2464,26*_a-3017218 => 1641,-20*_a+2832738 => 2085,5 => -4823,867*_a-3243464 => 1641,61 => 1114,_a+139362 => 1023,47 => 818,_a-354702 => -2464,67 => -2085,-15295860480*_a-2419464326228480 => -818))\n",
      "877: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(11//2*_a+1071961//2 => 607,127 => 607,103 => 724,157 => 607,-1//2*_a+77817//2 => 1372,193*_a-19495755 => 1229,-16*_a+1583154 => -753,-31//2*_a-1740183//2 => -174,1//2*_a+1935131//2 => -2737,9*_a+1637344 => 677,181//2*_a+10432433//2 => -190,139 => -1354,13//2*_a-804791//2 => -724,2 => -169,11 => -839,-_a+214772 => -607,21//2*_a+855203//2 => 1140,-3*_a+340048 => 1448,-_a+520352 => -724,17//2*_a+1613949//2 => 1354,19//2*_a+1114511//2 => 174,31 => -174,25*_a-1577904 => -1140,-41//2*_a+3165127//2 => -607,79 => 914,13 => 550,1//2*_a+26931//2 => -607,-17*_a+105901 => -307,67 => 1921))\n",
      "878: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "879: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "882: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -3998,12376*_a-1236590030 => -2242,3 => -7687,37 => 937,-5*_a+154003 => 508,23 => -1647,1 => -33,53 => -1642,19 => -825,-416*_a-39476788 => 1642,34*_a+76458520 => -2001,-68*_a+37746290 => -1231,92*_a+2511784 => 1642,-331//44895370674*_a-2960015//22447685337 => -2,116769//98*_a+5490939764//49 => 0,139 => -1,28*_a+6949432 => -937,-13079//118249416688971*_a-803743157//118249416688971 => -1,_a+100000 => 0,2 => 4741,11 => 1062,34*_a+3659794 => 3715,520*_a-51556648 => -829,-62*_a+11882796 => -1761,-8*_a+1341352 => -327,31 => 117,-34*_a-3400177 => 1,-408*_a+2408934 => 4003,-34//86687*_a-62947838//86687 => 2,59 => -2,83 => -1,13 => 1981,61 => 2001,-304*_a+73367120 => -1334,-663*_a+134968236 => -1064,-85*_a+105812726 => 1887,7 => -2235))\n",
      "883: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "885: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "886: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "887: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "889: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-91//2*_a-37418227//2 => -3371,103 => 2295,1//2*_a-139907//2 => 2990,23 => -4702,19//2*_a+1031567//2 => 13256,19 => -21291,-3//2*_a-1684927//2 => 4301,46*_a+1557008 => 8716,-133//2*_a+6781271//2 => -2448,89 => -2534,-233//2*_a-30805429//2 => -2883,41*_a-1253726 => -2295,-31*_a+649027 => 588,2 => 24765,57//2*_a-6719179//2 => -2773,-5//2*_a+206337//2 => -5345,-54468302*_a+5463535273434 => -6566,5*_a+712925 => 2534,151 => -2990,-_a+945632 => 2990,-160*_a+28094145 => -107,11*_a+893593 => -2295,5 => -1351,71//2*_a+1030667//2 => 2295,29 => 5221,23*_a-1071087 => -1241,7 => 23922))\n",
      "891: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "893: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "894: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "895: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "897: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "898: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 2144,473*_a+23467044 => -951,143*_a+3064698 => -1072,19220*_a-3402119707 => -2935,13*_a-57944 => 1260,-49961*_a-8828171205 => 892,-3511*_a+692368120 => 927,2 => 6,31 => -2306,-20*_a+2533909 => -1569,-239*_a-20072978 => 1485,83 => 1557,-1982*_a+320663446 => -367,-117*_a+9425890 => -927,13 => 1072,62*_a+6533715 => 4088,29 => -1854,1613*_a+163210383 => 12))\n",
      "901: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "902: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "903: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "905: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "906: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "909: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "910: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "911: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "913: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "914: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "915: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "918: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "919: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "921: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-1453//2*_a+44467433//2 => -12421,-27//2*_a-15471273//2 => -3439,-7*_a-831775 => 22438,103 => -2512,3 => 4414,83*_a+7809913 => 12421,-195//2*_a+115822239//2 => 5339,125 => 0,1537//2*_a+648051835//2 => 1900,1 => -1,229*_a+11513689 => 1782,41//2*_a-2982709//2 => 1121,609*_a+128349795 => 809,59211//2*_a-14338119735//2 => -8321,131 => -2512,_a+36 => 2512,203//2*_a-9076159//2 => -2045,2 => -71106,11 => -27823,_a-36 => 2512,97 => -11219,3//2*_a+1321653//2 => -5339,151 => 15994,-16*_a-2734196 => 2045,5 => 1,13 => 2982,47 => 15994,-141//2*_a-30468831//2 => -15994,29 => -664,41 => 1197,7//2*_a-133403//2 => -15994,67 => 3439,43 => 8321,1//2*_a+96379//2 => 33165,7 => -23741))\n",
      "922: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "923: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "927: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "929: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "930: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(3 => 2512,23 => 26800,-3725*_a+36107497 => 6947,1267*_a-198192095 => -6700,109 => -6947,71 => -8171,-2743*_a-284960962 => 1226,163*_a-28768358 => -13368,2 => 27906,207*_a+130198820 => -2737,1139*_a+61694605 => 8171,-1261*_a+89363495 => 27781,163 => 5474,_a+137572 => 9684,5 => -9039,79 => -6947,13 => -8907,-458*_a-43000105 => -13157,874*_a+23649244 => -13400,6688*_a+234913595 => 4720,67 => 4986,315*_a+19242228 => -10417))\n",
      "931: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "933: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "934: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "937: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "938: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "939: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "941: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "942: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "943: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "945: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "946: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -5504,7203*_a-170967238 => 4937,403*_a+40147432 => 2069,3744*_a+396872359 => -5811,13*_a+305968 => -437,37*_a+610922 => -437,137 => -4937,858*_a-26651482 => 7835,2522*_a-312424099 => -5850,13208*_a-183939600 => -3742,19 => 16628,73 => 437,172*_a+6143969 => -9274,_a-278486 => -124,-1685*_a+74605232 => -874,139 => 9274,89 => -2069,-2444*_a-47311134 => 5941,-1973*_a-794095185 => -9904,2 => -3668,11 => -6201,97 => 15754,-143*_a+55053284 => -9904,-299*_a-45365294 => 4937,-55*_a-9248525 => 8270,-13*_a-1333059 => 12163,-611*_a+101029461 => 5211,5 => -19991,83 => -4937,79 => 874,13 => -3375,61 => 4967,47 => -5211,29 => -8270,-2197*_a+177698690 => 5811,-65*_a+15237833 => -9274,43 => 9711))\n",
      "947: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "949: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -2487,597//2*_a+80424119//2 => 1663,673*_a+51279775 => 5453,-744*_a+75459788 => 1265,62*_a+5131426 => 1265,-377//2*_a-119817711//2 => -1483,3421*_a-289138803 => -3743,-56*_a+2136092 => -47,-41*_a+4118262 => -2,2 => 3508,11 => 3062,-330*_a+122107810 => -1483,_a+59193 => -1265,-1022*_a+54219354 => -2344,149 => 1483,151 => -5453,13//2*_a-1973361//2 => -2104,5 => 15258,13 => 3587,61 => 1265,248*_a-167527161 => 3790,250*_a-31902625 => -1988,9*_a+1233437 => -1265,7 => 2391))\n",
      "951: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "954: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => -12683,103 => -884,3 => -88272,6*_a-12404187 => -1132,-77*_a-181049 => 17809,5565472*_a+399382171936 => -1132,23 => 3525,157 => 1132,53 => -1132,73 => -7363,-90*_a-1889883 => 12333,-153*_a+40343856 => -6894,2 => -224,11 => -23173,-2091*_a+14411988 => 884,_a-154052 => 7267,-2024*_a+330567523 => -3525,-47*_a+4401784 => 7363,107 => 3525,-107*_a-25386671 => -4970,4*_a-2912942 => 1132,-24*_a-2405871 => -22748,5 => -22725,66*_a+3399693 => 10021,-4616*_a+415264807 => -3525,43 => 4970,2895*_a-323918160 => 884))\n",
      "955: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "957: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-5//2*_a-697691//2 => -1265,-1337//2*_a-5252737//2 => 188,3 => -2865,121//2*_a-18336131//2 => 60,19 => -790,73 => 2474,-6*_a-4054248 => -132,104*_a-42187393 => -76,21//2*_a+2114903//2 => 115,2 => 132,11 => 1216,-365//2*_a-35683349//2 => -2398,-_a+106670 => 790,97 => 1265,-2*_a+48761 => -175,19//2*_a-1610183//2 => 1265,29 => 132,-3//2*_a+743439//2 => 746,7 => -1218,-_a+98858 => 561))\n",
      "958: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "959: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "961: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(103 => 3410,-291//2*_a-1053479//2 => 777,4028*_a-229784822 => 3542,19 => -494,-3567*_a-1606740125 => -68,251//2*_a-27469109//2 => 1094,-7127*_a+690804943 => -1094,3*_a-288683 => 358,2 => -1544,11 => -532,-1135//2*_a+53700617//2 => -358,33//2*_a+1847681//2 => 532,487*_a-20991783 => -3410,-14045//2*_a-1429985813//2 => -3342,31 => -3048,5 => -5020,123*_a-607687 => 1524,47 => 1716,-17*_a-46560527 => -683,-3131*_a-69179941 => 3048,353*_a+7998951 => -1524,43 => -1524))\n",
      "963: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "965: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "966: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "967: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "969: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "970: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-185*_a-3134330 => -2724,127 => 4972,27*_a+11709620 => -6389,20350*_a-716171730 => -1760,-134*_a+1649808 => -1251,2*_a+217191 => 1417,-835*_a-101177330 => 6314,73 => -6314,71 => 7352,320*_a-45468852 => -3212,94*_a+6249120 => 4549,53*_a+2932500 => -2868,2 => 1239,11 => 4275,97 => -3656,-197*_a-11648169 => -1407,-1275*_a-124716110 => 6314,-12*_a+3502970 => -5692,163 => -6314,5 => -9258,113 => 4275,47 => -1816,_a+144292 => -1551,-270*_a+23122070 => 6314,67 => -2405,43 => -4549,7 => 1760,-47*_a+643148 => 3656))\n",
      "973: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "974: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "977: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "979: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "981: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(43 => 2490,127 => -1345,3 => -11790,137 => -8982,38*_a+4368493 => -2584,53 => -1186,10*_a+2718160 => -1,2*_a+201345 => -3676,1//2*_a-745417//2 => 1186,-137//2*_a-23896849//2 => 1345,1//2*_a+463141//2 => 1452,7//2*_a-229403//2 => 2300,5//2*_a-31626361//2 => -1345,2 => 1,-25*_a-457220 => 158,11 => -955,-_a+89710 => -2490,3//2*_a+746573//2 => -4693,31 => 2319,107 => 2490,-13*_a+34814 => -2837,59 => 2490,-1620642143//2*_a-919049707691813//2 => 1187,5 => 1030,-59//2*_a-2824891//2 => -1187,2*_a-217991 => 1471,113 => -158,13 => -3826,43//2*_a+3816121//2 => -2490,29 => -284,7//2*_a+453007//2 => 1346,1//2*_a-135549//2 => 7530,-9//2*_a-2753999//2 => 158,1//2*_a-57073//2 => 8982,1//2*_a+97211//2 => -2319))\n",
      "982: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "983: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "985: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(137 => -1246,23 => -507,-44*_a+5042703 => 2492,3//2*_a-2924479//2 => 2059,53 => 3157,1//2*_a+246873//2 => 2492,5//2*_a-3294265//2 => 1246,19 => 1159,975*_a+95455555 => -494,-_a+812890 => -2344,41*_a-364572 => 26,2 => -3250,7//2*_a-2339853//2 => -3157,97 => -2492,-23//2*_a-1452899//2 => -1246,-39//2*_a-13738205//2 => 48,-63//2*_a-3471065//2 => -3276,137//2*_a+3391635//2 => 1172,107 => 2318,1//2*_a-866219//2 => 2492,4*_a-111575 => -813,83 => -2492,5 => 2176,5//2*_a-190405//2 => -1159,13 => 2124,65//2*_a+6466395//2 => -1511,29 => -1734,41 => -26,5//2*_a+280665//2 => 1638,-26*_a+2650700 => 1421,7 => -3664))\n",
      "986: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "987: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "990: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "991: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "993: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(17 => 4162,-25//2*_a-3436177//2 => 5592,5//2*_a+103277//2 => -4162,3 => -1653,37 => -8001,-39//2*_a-3920265//2 => -2816,-31//2*_a+6436709//2 => -4335,1//2*_a+37777//2 => -1505,-_a+568613 => 8809,73 => 4335,71 => -2409,1//2*_a+2377729//2 => 2409,-39//2*_a+3960837//2 => -7704,-451//2*_a+87240251//2 => -1699,89 => -8809,471//2*_a+53334555//2 => 5254,2 => -4847,11 => 7704,13//2*_a-2362927//2 => -4335,-11//2*_a+733133//2 => 3542,-67//2*_a+4845497//2 => 4335,1//2*_a-81509//2 => 8559,113 => 4162,109//2*_a-10207379//2 => -2776,29 => -8559,41 => -1843,9*_a-1124574 => -2796,13//2*_a-5838389//2 => -1926))\n",
      "994: (true, Factored element with data\n",
      "Dict{nf_elem,fmpz}(-3407*_a-200168706 => 2330,-9108*_a-3487069861 => 694,103 => -3078,1 => 0,_a-1540250 => -1130,73 => 41,-11*_a+954008 => 1538,45*_a-268955 => -482,_a-37 => 1902,153*_a-13313564 => -2282,131 => -3032,276*_a+9935878 => 631,-1933*_a+100056451 => -1606,-763*_a-1415309 => -48,2 => -1123,11 => -8248,-79*_a-1142859 => -1693,91*_a+17034108 => 46,31 => -2260,97*_a-696579 => 1130,-130*_a+12929839 => 964,61*_a-8197452 => 482,59 => 642,5 => -6256,56*_a+3137603 => -594,13 => 6329,20*_a-177215 => -41,113*_a-12568141 => -694,_a+37 => 3032,7 => -915))\n",
      "995: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n",
      "999: (false, Factored element with data\n",
      "Dict{nf_elem,fmpz}(1 => 1))\n"
     ]
    }
   ],
   "source": [
    "for i=2:1000\n",
    "    I = i+10^10\n",
    "    if all(isone, values(factor(I).fac))\n",
    "        k,a = number_field(x^2-I)\n",
    "        zk = maximal_order(k)\n",
    "        println(\"$i: \", isnorm(k, -1))\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GrpAb: Z/14\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/2 x Z/6\n",
      "GrpAb: Z/7\n",
      "GrpAb: Z/14\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/7\n",
      "GrpAb: Z/4\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/14\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/2^2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/3\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/7^2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/7\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/7\n",
      "GrpAb: Z/7\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/7\n",
      "GrpAb: Z/3\n",
      "GrpAb: Z/2^2\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/1\n",
      "GrpAb: Z/2\n"
     ]
    }
   ],
   "source": [
    "for i=2:50\n",
    "    k,a = wildanger_field(7, i+100)\n",
    "    println(class_group(k)[1])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "$\\text{Number field over Rational field with defining polynomial }x^{7}-150x^{6}+150x^{5}-150x^{4}+150x^{3}-150x^{2}+150x-150$"
      ],
      "text/plain": [
       "Number field over Rational Field with defining polynomial x^7-150*x^6+150*x^5-150*x^4+150*x^3-150*x^2+150*x-150"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "$\\text{Maximal order of }\\text{Number field over Rational field with defining polynomial }x^{7}-150x^{6}+150x^{5}-150x^{4}+150x^{3}-150x^{2}+150x-150\\text{ with basis }[1, \\alpha, \\alpha^{2}, \\alpha^{3}, \\frac{1}{5}\\alpha^{4}, \\frac{1}{5}\\alpha^{5}, \\frac{1}{5}\\alpha^{6}]$"
      ],
      "text/plain": [
       "Maximal order of Number field over Rational Field with defining polynomial x^7-150*x^6+150*x^5-150*x^4+150*x^3-150*x^2+150*x-150 \n",
       "with basis nf_elem[1, _$, _$^2, _$^3, 1//5*_$^4, 1//5*_$^5, 1//5*_$^6]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zk = maximal_order(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ctx for class group of Maximal order of Number field over Rational Field with defining polynomial x^7-150*x^6+150*x^5-150*x^4+150*x^3-150*x^2+150*x-150 \n",
       "with basis nf_elem[1, 1//5*_$^5 - 149//5*_$^4 - 4, 1//5*_$^6 - 149//5*_$^5 + 4, 1//5*_$^6 - 30*_$^5 + 30*_$^4 - 30*_$^3 + 30*_$^2 - 30*_$ + 26, _$-21, -2//5*_$^4 + 60*_$^3 - 59*_$^2 - 89*_$ - 13, 2//5*_$^4 - 59*_$^3 - 89*_$^2 - 60*_$ + 13]\n",
       "Factorbase with 205 ideals of norm up to 1069\n",
       "Relations module: Sparse module over FlintZZ of (current) rank 205 and further 43\n",
       "current index: 2\n",
       "\n"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = Hecke._get_ClassGrpCtx_of_order(lll(zk))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "$[\\alpha+1, \\alpha-9, \\alpha+3, \\alpha+8, \\alpha-5, 7, \\alpha+2, \\alpha-1, \\alpha-2, 5, 3, \\alpha, \\frac{1}{5}\\alpha^{6} - 30\\alpha^{5} + 30\\alpha^{4} - 30\\alpha^{3} + 30\\alpha^{2} - 30\\alpha + 26, -\\frac{413}{5}\\alpha^{6} + \\frac{61721}{5}\\alpha^{5} - 5495\\alpha^{4} + 1827\\alpha^{3} - 10294\\alpha^{2} + 6489\\alpha - 10725, \\frac{86}{5}\\alpha^{6} - 2629\\alpha^{5} + 9891\\alpha^{4} - 4069\\alpha^{3} + 2431\\alpha^{2} - 2679\\alpha + 30, -\\frac{192}{5}\\alpha^{6} + 5756\\alpha^{5} - 5136\\alpha^{4} + 1571\\alpha^{3} - 3210\\alpha^{2} + 3192\\alpha - 180, -2\\alpha^{6} + \\frac{1516}{5}\\alpha^{5} - 794\\alpha^{4} + 2889\\alpha^{3} - 4213\\alpha^{2} + 1587\\alpha - 2865, \\frac{4}{5}\\alpha^{6} - 109\\alpha^{5} - 1516\\alpha^{4} - 550\\alpha^{3} - 2400\\alpha^{2} - 2061\\alpha - 330, 30\\alpha^{6} - \\frac{22318}{5}\\alpha^{5} - 941\\alpha^{4} - 1884\\alpha^{3} + 1035\\alpha^{2} - 7608\\alpha + 150, -17\\alpha^{6} + \\frac{12683}{5}\\alpha^{5} - 548\\alpha^{4} + 1737\\alpha^{3} - 1248\\alpha^{2} - 5010\\alpha + 4470, \\frac{391}{5}\\alpha^{6} - 11662\\alpha^{5} + 1549\\alpha^{4} - 4413\\alpha^{3} + 9303\\alpha^{2} - 5415\\alpha + 12240, -26\\alpha^{6} + \\frac{19403}{5}\\alpha^{5} - 979\\alpha^{4} - 640\\alpha^{3} - 2346\\alpha^{2} + 3180\\alpha - 1650, -\\frac{22}{5}\\alpha^{6} + \\frac{3144}{5}\\alpha^{5} + 4003\\alpha^{4} - 1411\\alpha^{3} - 7359\\alpha^{2} + 4215\\alpha + 780, -\\frac{308}{5}\\alpha^{6} + 9104\\alpha^{5} + 11010\\alpha^{4} + 11393\\alpha^{3} - 19022\\alpha^{2} - 20940\\alpha + 9600, -\\frac{434}{5}\\alpha^{6} + \\frac{65202}{5}\\alpha^{5} - 16005\\alpha^{4} + 5054\\alpha^{3} - 38504\\alpha^{2} + 49335\\alpha - 11160, \\frac{252}{5}\\alpha^{6} - \\frac{37044}{5}\\alpha^{5} - 14944\\alpha^{4} - 11056\\alpha^{3} - 22232\\alpha^{2} + 9615\\alpha - 33255, \\frac{354}{5}\\alpha^{6} - \\frac{55194}{5}\\alpha^{5} + 73292\\alpha^{4} - 50853\\alpha^{3} - 6678\\alpha^{2} - 13500\\alpha + 36960, -\\frac{3579}{5}\\alpha^{6} + \\frac{533723}{5}\\alpha^{5} - 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254840\\alpha^{2} + 276470\\alpha - 362310, \\frac{694}{5}\\alpha^{6} - 20428\\alpha^{5} - 36512\\alpha^{4} - 181622\\alpha^{3} + 92510\\alpha^{2} - 92340\\alpha - 38130, -\\frac{3468}{5}\\alpha^{6} + 104289\\alpha^{5} - 141594\\alpha^{4} + 171429\\alpha^{3} - 87947\\alpha^{2} + 103990\\alpha - 100440, -\\frac{2758}{5}\\alpha^{6} + 82743\\alpha^{5} - 82890\\alpha^{4} + 38039\\alpha^{3} - 16167\\alpha^{2} + 109340\\alpha - 82440, \\frac{682}{5}\\alpha^{6} - 20227\\alpha^{5} - 14472\\alpha^{4} + 12390\\alpha^{3} - 101363\\alpha^{2} + 37450\\alpha - 95010, -\\frac{2383}{5}\\alpha^{6} + 71243\\alpha^{5} - 34415\\alpha^{4} + 31036\\alpha^{3} - 82320\\alpha^{2} + 42720\\alpha - 150120, 53\\alpha^{6} - 7672\\alpha^{5} - 33730\\alpha^{4} + 30982\\alpha^{3} - 64885\\alpha^{2} - 32090\\alpha - 53640, -\\frac{2168}{5}\\alpha^{6} + 65142\\alpha^{5} - 80247\\alpha^{4} + 65895\\alpha^{3} + 7714\\alpha^{2} + 15550\\alpha - 66690, 196\\alpha^{6} - 29495\\alpha^{5} + 43101\\alpha^{4} + 38085\\alpha^{3} + 52620\\alpha^{2} + 85740\\alpha - 51720, -182\\alpha^{6} + 27505\\alpha^{5} - 58097\\alpha^{4} + 65714\\alpha^{3} - 155825\\alpha^{2} - 47570\\alpha - 115170, 733\\alpha^{6} - 109338\\alpha^{5} + 18290\\alpha^{4} - 38670\\alpha^{3} - 31980\\alpha^{2} - 95760\\alpha - 51420, 441\\alpha^{6} - 66893\\alpha^{5} + 175189\\alpha^{4} + 182115\\alpha^{3} + 105860\\alpha^{2} - 55010\\alpha + 45690, 1787\\alpha^{6} - 266481\\alpha^{5} + 33848\\alpha^{4} - 203452\\alpha^{3} - 10485\\alpha^{2} - 260970\\alpha + 95130, -782\\alpha^{6} + 117112\\alpha^{5} - 88870\\alpha^{4} + 53784\\alpha^{3} + 66380\\alpha^{2} + 142960\\alpha + 53370, -767\\alpha^{6} + 114755\\alpha^{5} - 70329\\alpha^{4} + 608\\alpha^{3} - 69140\\alpha^{2} + 113400\\alpha - 17550, 38\\alpha^{6} - 5919\\alpha^{5} + 38484\\alpha^{4} - 28440\\alpha^{3} - 3055\\alpha^{2} + 35125\\alpha + 15120, 307\\alpha^{6} - 46238\\alpha^{5} + 74088\\alpha^{4} - 50030\\alpha^{3} + 61760\\alpha^{2} - 33970\\alpha + 15750, -37\\alpha^{6} + 5723\\alpha^{5} - 31178\\alpha^{4} - 16720\\alpha^{3} + 4740\\alpha^{2} + 4680\\alpha + 54060, 159\\alpha^{6} - 24117\\alpha^{5} + 63535\\alpha^{4} - 9495\\alpha^{3} + 61005\\alpha^{2} - 76630\\alpha + 34650, 13\\alpha^{6} - 2539\\alpha^{5} + 90100\\alpha^{4} - 60530\\alpha^{3} + 94025\\alpha^{2} + 21390\\alpha - 17910, 313\\alpha^{6} - 47028\\alpha^{5} + 58499\\alpha^{4} - 35623\\alpha^{3} - 20620\\alpha^{2} + 30390\\alpha + 15840, 74\\alpha^{6} - 11124\\alpha^{5} + 14501\\alpha^{4} + 14923\\alpha^{3} + 18980\\alpha^{2} - 31805\\alpha - 3720, 122\\alpha^{6} - 17581\\alpha^{5} - 88618\\alpha^{4} - 49908\\alpha^{3} - 710\\alpha^{2} - 51420\\alpha + 110520, 244\\alpha^{6} - 36578\\alpha^{5} + 33205\\alpha^{4} - 19459\\alpha^{3} + 80375\\alpha^{2} - 76440\\alpha + 58260, -\\frac{722}{5}\\alpha^{6} + 21114\\alpha^{5} + 59863\\alpha^{4} - 3681\\alpha^{3} + 2605\\alpha^{2} - 42590\\alpha + 108390, -452\\alpha^{6} + 67796\\alpha^{5} - 66801\\alpha^{4} + 7602\\alpha^{3} - 45125\\alpha^{2} + 41825\\alpha - 10950, \\frac{496}{5}\\alpha^{6} - 14848\\alpha^{5} + 10032\\alpha^{4} - 2668\\alpha^{3} - 28955\\alpha^{2} + 33870\\alpha - 18000, -288\\alpha^{6} + 43167\\alpha^{5} - 38455\\alpha^{4} + 69173\\alpha^{3} - 94685\\alpha^{2} + 55320\\alpha - 53760, \\frac{187}{5}\\alpha^{6} - 5428\\alpha^{5} - 21461\\alpha^{4} - 12611\\alpha^{3} + 4820\\alpha^{2} + 68310\\alpha + 6930, -\\frac{636}{5}\\alpha^{6} + 18749\\alpha^{5} + 30462\\alpha^{4} - 14098\\alpha^{3} - 26077\\alpha^{2} - 26540\\alpha + 13590, -114\\alpha^{6} + 17043\\alpha^{5} - 8216\\alpha^{4} - 41293\\alpha^{3} + 2891\\alpha^{2} + 14005\\alpha + 27870, \\frac{1138}{5}\\alpha^{6} - 34413\\alpha^{5} + 75035\\alpha^{4} - 66681\\alpha^{3} + 42936\\alpha^{2} - 35340\\alpha + 2130, -\\frac{2163}{5}\\alpha^{6} + 64400\\alpha^{5} + 8244\\alpha^{4} + 46398\\alpha^{3} - 61900\\alpha^{2} - 25560\\alpha - 65370, -\\frac{2028}{5}\\alpha^{6} + 60787\\alpha^{5} - 52653\\alpha^{4} + 17709\\alpha^{3} - 72659\\alpha^{2} + 67410\\alpha - 42750, -\\frac{813}{5}\\alpha^{6} + 24006\\alpha^{5} + 32596\\alpha^{4} + 58451\\alpha^{3} + 6797\\alpha^{2} + 18990\\alpha + 13290, -\\frac{2348}{5}\\alpha^{6} + 70275\\alpha^{5} - 45655\\alpha^{4} + 40660\\alpha^{3} - 73084\\alpha^{2} + 19970\\alpha - 24370, -\\frac{263}{5}\\alpha^{6} + 7873\\alpha^{5} - 5302\\alpha^{4} - 330\\alpha^{3} - 4165\\alpha^{2} + 7800\\alpha - 2150, -\\frac{842}{5}\\alpha^{6} + 25021\\alpha^{5} + 10408\\alpha^{4} + 16716\\alpha^{3} - 17588\\alpha^{2} + 14270\\alpha - 8990]$"
      ],
      "text/plain": [
       "205-element Array{Union{FacElem{nf_elem,AnticNumberField}, nf_elem},1}:\n",
       " _$+1\n",
       " _$-9\n",
       " _$+3\n",
       " _$+8\n",
       " _$-5\n",
       " 7\n",
       " _$+2\n",
       " _$-1\n",
       " _$-2\n",
       " 5\n",
       " 3\n",
       " _$\n",
       " 1//5*_$^6 - 30*_$^5 + 30*_$^4 - 30*_$^3 + 30*_$^2 - 30*_$ + 26\n",
       " ⋮\n",
       " 496//5*_$^6 - 14848*_$^5 + 10032*_$^4 - 2668*_$^3 - 28955*_$^2 + 33870*_$ - 18000\n",
       " -288*_$^6 + 43167*_$^5 - 38455*_$^4 + 69173*_$^3 - 94685*_$^2 + 55320*_$ - 53760\n",
       " 187//5*_$^6 - 5428*_$^5 - 21461*_$^4 - 12611*_$^3 + 4820*_$^2 + 68310*_$ + 6930\n",
       " -636//5*_$^6 + 18749*_$^5 + 30462*_$^4 - 14098*_$^3 - 26077*_$^2 - 26540*_$ + 13590\n",
       " -114*_$^6 + 17043*_$^5 - 8216*_$^4 - 41293*_$^3 + 2891*_$^2 + 14005*_$ + 27870\n",
       " 1138//5*_$^6 - 34413*_$^5 + 75035*_$^4 - 66681*_$^3 + 42936*_$^2 - 35340*_$ + 2130\n",
       " -2163//5*_$^6 + 64400*_$^5 + 8244*_$^4 + 46398*_$^3 - 61900*_$^2 - 25560*_$ - 65370\n",
       " -2028//5*_$^6 + 60787*_$^5 - 52653*_$^4 + 17709*_$^3 - 72659*_$^2 + 67410*_$ - 42750\n",
       " -813//5*_$^6 + 24006*_$^5 + 32596*_$^4 + 58451*_$^3 + 6797*_$^2 + 18990*_$ + 13290\n",
       " -2348//5*_$^6 + 70275*_$^5 - 45655*_$^4 + 40660*_$^3 - 73084*_$^2 + 19970*_$ - 24370\n",
       " -263//5*_$^6 + 7873*_$^5 - 5302*_$^4 - 330*_$^3 - 4165*_$^2 + 7800*_$ - 2150\n",
       " -842//5*_$^6 + 25021*_$^5 + 10408*_$^4 + 16716*_$^3 - 17588*_$^2 + 14270*_$ - 8990"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.R_gen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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