//Standard generators of L2(43) are a and b where a has order 2, b has order 3
//and ab has order 43.
//Standard generators of the double cover 2.L2(43) = SL2(43) are preimages A and
//B where B has order 3 and AB has order 43.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a^-1,b^-1 ]]
             where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents, interchanged by _LR`AI[1][1]
_LR`G :=
MatrixGroup<21, ext<K|Polynomial(K, [11, -1, 1])> where K is RationalField() |
[[-3348812,-80196],[752293,637873
],[872892,-722052],[-1643173,
667764],[-1205977,1180623],[
-1457033,1104452],[-1567474,-101912],[
207622,344530],[-1245825,882247],
[-310934,1413181],[457113,1395440
],[52445,-687499],[-1616259,
1171688],[1513349,-1527368],[
1174972,1299447],[1672884,-378331],[
370022,1249147],[960599,306910],[
-142217,175949],[34046,655411],[
1984195,-1269620],[815119,-330753
],[-875350,2933],[617241,171756
],[-389726,-243707],[-1057196,
-258370],[-917735,-275088],[
453421,-147403],[-429745,-18589],[
-715346,-228061],[-1510830,-194277],[
-1657425,-114259],[756414,84481],
[-958324,-298995],[1377833,329499
],[-1705754,-30326],[60057,213399
],[-1475177,-106257],[-550868,
62187],[-165682,-34696],[-739317,
-72006],[987973,347625],[
-1295854,-106289],[142380,280819],[
516039,-280262],[-805508,240958],[
-756871,463084],[-837184,426033],
[-591106,-76434],[-1130,147343],
[-700928,338533],[-461183,579006
],[-155312,588406],[185552,
-283836],[-915848,450430],[
960774,-600111],[149629,564273],[
747727,-120334],[-154408,525864],[
303595,148171],[-98064,69832],[
-143888,272421],[1083834,-482999],[
-324827,-428296],[-758090,251792],[
1080769,-74834],[-1107431,-32676],
[-1738592,149334],[-1668878,99616
],[-65735,-216629],[-435116,
111780],[-1343695,69588],[
-1934834,316795],[-1811891,405955],[
928518,-166162],[-1779580,97084],
[2243165,-198899],[-1590509,469358
],[723215,108942],[-1626992,
358622],[-287461,194112],[
-254260,26828],[-874331,168650],[
1958383,-76818],[892432,151590],[
56869,-228799],[-541075,193906],[
731467,-147778],[823536,-325408],[
861312,-292001],[390995,91179],[
85645,-116080],[710674,-230161],[
672668,-432254],[452989,-455669],[
-299928,214017],[933243,-307115],
[-1052464,422746],[214692,-452604
],[-619516,55723],[416323,-406419
],[-138124,-132679],[112362,
-49912],[262697,-207200],[
-1075612,323996],[863635,-855481],[
-1925557,231202],[1850297,176217],[
-1551527,-375247],[-3067683,-231933
],[-2806948,-300484],[584065,
-404477],[-1002085,74416],[
-2226570,-260837],[-3888269,10003],[
-3985409,203932],[1910477,-29962],
[-2964355,-336688],[3977590,288162
],[-3854361,380190],[737332,
401013],[-3560105,172606],[
-1040803,263265],[-464343,-25038],[
-1837360,49906],[3167650,423960],[
1096710,-165429],[-625208,-122324
],[168203,234280],[105960,-263109
],[-344266,-370774],[-219167,
-365124],[552679,-60869],[
-275523,-77110],[-149440,-296217],[
-766414,-380881],[-995863,-333643],[
403769,179804],[-210444,-391271],
[460020,477068],[-1161781,-269059
],[-292150,190290],[-879204,
-300841],[-488100,-25595],[
-63042,-53172],[-411216,-166743],[
155184,436911],[646180,-289603],[
-748080,14701],[554220,135845],[
-370726,-199547],[-943749,-202552],[
-827063,-218563],[365072,-130325],
[-370343,-9630],[-646765,-181836
],[-1321808,-142301],[-1434862,
-72946],[659813,60490],[-865445,
-238105],[1228868,257901],[
-1463288,-1670],[84161,178660],[
-1277791,-68761],[-461501,60008],[
-147013,-26869],[-643276,-50235],[
898277,278596],[537370,-134507],[
-411973,-35797],[209027,114183],[
-68582,-141305],[-374798,-177248],
[-301546,-179860],[281775,-56103
],[-192866,-27823],[-228653,
-147174],[-617624,-163782],[
-723890,-129085],[315214,75457],[
-309379,-193822],[491861,227305],[
-785899,-88198],[-71849,111750],[
-642156,-117225],[-287544,8348],[
-61453,-24813],[-313042,-68345],[
300495,219968],[-2554530,284826],[
1257657,330315],[-153729,-546846],
[-473391,589561],[414324,871953],
[145418,848676],[-1266711,92369],
[532963,198338],[55825,686148],[
1329975,930125],[1875994,841816],
[-719791,-442586],[102333,907414
],[-570484,-1123347],[2298731,
708761],[814558,-408428],[
1650478,757490],[1045948,98894],[
89372,126185],[748084,413501],[
60581,-1006609],[-887424,1059262],[
2334755,-318962],[-2328153,-179015],[
2000560,427345],[3847142,223401],
[3538913,311981],[-637142,504220
],[1224791,-110048],[2811967,
274873],[4811638,-87299],[
4890693,-325518],[-2358847,73419],[
3741480,353062],[-4985574,-274351],[
4691002,-537793],[-998043,-474474
],[4370815,-279125],[1232600,
-340947],[580186,21545],[2264089,
-96312],[-4011706,-455494],[
-1237007,162477],[657532,148863],[
-132601,-264525],[-173881,291179],[
295314,420202],[159606,411402],[
-618431,56800],[284664,91468],[
98432,333194],[755236,439911],[
1016812,391842],[-402468,-208510],
[144305,440374],[-398652,-541007
],[1212659,323166],[361690,
-206281],[896319,352943],[528714,
38293],[57318,60534],[413494,
194099],[-73770,-490146],[
-845108,-20309],[189708,161006],[
220453,-182218],[-414832,168501],[
-304614,297949],[-367954,278719],[
-395554,-25753],[52320,86959],[
-314602,222642],[-78788,356661],[
115044,352200],[13390,-173514],[
-408154,295685],[382263,-385456],
[296230,327987],[422265,-95451],
[93099,315275],[242352,77479],[
-35929,44404],[8443,165417],[
501030,-320394],[1799323,32239],[
-425650,-337830],[-443308,387835],
[858419,-361305],[606133,-633453
],[743452,-593618],[844435,49422
],[-123304,-183095],[637830,
-474446],[117920,-754667],[
-293500,-742791],[-4350,366827],[
826548,-629977],[-759034,819348],[
-675294,-689337],[-884371,207035],[
-241721,-665041],[-525953,-160661
],[70206,-94286],[-40938,-349441
],[-1020547,683364],[-1506264,
591269],[1578175,3581],[-1093391,
-317615],[675241,445729],[
1876738,479093],[1623486,507980],[
-833791,262589],[772551,38065],[
1263930,420678],[2701594,367524],[
2974784,223966],[-1354014,-160828
],[1693973,551729],[-2446744,
-611288],[3071285,72312],[-84392,
-387438],[2647173,207607],[
999914,-107128],[294768,64578],[
1324592,138040],[-1741981,-640182],[
410504,430207],[738563,-268048],[
-1102769,93306],[1149155,15559],[
1768903,-179528],[1705644,-127875
],[105867,219167],[429651,-120568
],[1375160,-92165],[1942152,
-352890],[1799575,-441566],[
-929552,183718],[1820387,-127066],[
-2281181,237959],[1559879,-502488],[
-765827,-99214],[1616969,-390501],
[262758,-201909],[257817,-31326],
[873166,-185383],[-2008556,109316
],[1667655,201153],[-56018,
-390462],[-816575,361410],[
1181735,-295177],[1222248,-601280],[
1311207,-547119],[747486,130011],
[71140,-201612],[1089213,-433216
],[885051,-772642],[484001,
-798650],[-380140,380500],[
1427021,-577131],[-1557328,780061],[
68341,-778723],[-1048128,132568],
[453250,-713091],[-332429,-215841
],[163008,-91361],[319515,-366668
],[-1665114,614488],[-979009,
372267],[1001968,7762],[-682154,
-206574],[411748,286917],[
1173398,312387],[1011487,329951],[
-539459,164756],[489100,26983],[
786509,272966],[1701421,244018],[
1880369,153312],[-853628,-107378],[
1054574,358127],[-1530293,-398764
],[1947433,56824],[-38799,-247651
],[1672967,141731],[639009,-64926
],[184707,42252],[835815,92727],
[-1081683,-414766],[0,0],[
0,0],[0,0],[0,
0],[0,0],[0,0],[
0,0],[0,0],[0,
0],[0,0],[0,0],[
0,0],[0,0],[0,
0],[0,0],[0,0],[
0,0],[0,0],[1,
0],[0,0],[0,0],[
-65230,-439166],[-850176,210062],
[1053577,-19057],[-1018574,-88400
],[-1710997,59228],[-1618000,
13695],[59284,-217130],[-469710,
88256],[-1296807,547],[-1988122,
214549],[-1922748,308777],[
961974,-116910],[-1720229,5583],[
2211033,-82561],[-1750850,382576],[
616327,144187],[-1723245,271438],[
-377394,176999],[-253007,13585],[
-912631,122113],[1876325,23484],[
1046625,-53356],[-390100,-163941],
[-87054,224772],[336756,-226873],
[74504,-362495],[170509,-346582],
[505989,-6704],[-149789,-93065],
[161322,-278716],[-258014,-408155
],[-489022,-385663],[155815,
196317],[202511,-369284],[-82034,
467894],[-685081,-342101],[
-418229,145401],[-425749,-346121],[
-371206,-65272],[-397,-53170],[
-174305,-185244],[-290815,405442]],
[[-8458903,343022],[2978487,
1364823],[912522,-1817635],[
-2920541,1813164],[-942293,2937015],[
-1698485,2799528],[-4071327,10816
],[1115112,768595],[-1560310,
2249249],[1685776,3336437],[
3562964,3173717],[-1065615,-1607515],[
-1977099,2981109],[1102735,-3792200
],[5179356,2836900],[3497822,
-1144596],[3092131,2847184],[
2920259,562007],[-47231,431771],[
1224658,1519196],[2720804,-3267096],[
-1356748,-386612],[-395059,418363
],[1192476,-296574],[-1464080,
188479],[-1854170,507641],[
-1876670,441134],[-562370,-215389],[
-299256,205572],[-1534512,343973],
[-1729917,723884],[-1377952,793229
],[798878,-362305],[-2021398,
460750],[2378499,-661538],[
-959325,815570],[1150140,-30634],[
-1250418,706048],[68638,262736],[
-260114,79504],[-725272,354021],[
2290982,-475361],[-1425717,514747],[
1405042,23670],[-928557,-301143],
[537896,411488],[1603219,457192],
[1373554,480014],[-779989,226470
],[682626,44397],[1065760,396475
],[2353741,367062],[2617494,
240885],[-1183001,-162850],[
1430101,520456],[-2092049,-584019],[
2725039,105105],[-19980,-351168],
[2328049,221862],[905799,-83850],
[253328,62167],[1160044,141879],
[-1460260,-601001],[-1815629,
-266899],[-33668,446740],[
1002486,-394024],[-1394577,310269],[
-1515404,658598],[-1601542,594810
],[-803985,-165095],[-129306,
228427],[-1325147,469835],[
-1180527,861670],[-738376,900337],[
519050,-425593],[-1738482,626453],[
1934290,-855057],[-268548,886924],
[1205022,-127742],[-682869,803411
],[318575,253711],[-204861,100580
],[-447827,411171],[2014001,
-663735],[-45610,168243],[344903,
-67790],[-389228,-7902],[359383,
48335],[636573,2060],[595275,
18068],[-56105,81864],[186151,
-26862],[475453,18454],[762747,
-53123],[753698,-89961],[-371136,
30694],[631465,22629],[-823565,
-367],[702368,-120549],[-203102,
-63799],[674657,-78607],[166363,
-61998],[94894,-1534],[353874,
-33386],[-684085,-35949],[
-929429,331732],[908375,17162],[
-596249,-196360],[342015,267362],[
1030362,298362],[881501,312854],[
-507690,145752],[440856,29657],[
683627,258317],[1517048,240927],[
1689433,159500],[-762785,-107069],[
917495,339136],[-1344704,-381186],
[1760925,71648],[-7912,-227600],
[1502504,146797],[587023,-53164],
[162953,40616],[748235,93449],[
-935850,-391372],[-3138964,36024],
[924903,547683],[554807,-675537],
[-1289523,651687],[-701614,1097436
],[-961809,1037230],[-1492072,
-40857],[314995,302220],[-844406,
831190],[212189,1277104],[919297,
1236445],[-195018,-618113],[
-1085873,1102646],[864188,-1418239],[
1552049,1127239],[1419729,-393133
],[786540,1108081],[1001051,
244220],[-69716,162342],[263976,
586555],[1392910,-1202312],[
-438724,-690589],[-1245477,390715],[
1725304,-102353],[-1748504,-70114
],[-2780556,210979],[-2661318,
132542],[-65774,-347708],[
-709060,171866],[-2140878,89726],[
-3121075,475791],[-2942109,620445],[
1500293,-250947],[-2836234,126708
],[3588629,-282171],[-2602642,
725465],[1126360,185971],[
-2640827,547678],[-489740,305991],[
-407523,38837],[-1414895,255800],[
3115887,-91401],[3721797,-373538],
[-1750441,-499963],[125820,797194
],[783120,-849353],[-443854,
-1273814],[-61344,-1235730],[
1837015,-114205],[-731637,-296688],[
39162,-998101],[-1750014,-1372845
],[-2550303,-1253140],[957701,
654623],[10816,-1320415],[624591,
1641649],[-3181159,-1066452],[
-1242036,580704],[-2240790,-1127015],[
-1486375,-160275],[-106517,-184806
],[-1003433,-612799],[-262273,
1462003],[1348640,-48917],[
-463465,-220207],[-159160,289860],[
478648,-287743],[172494,-468739],[
291766,-446238],[647924,1114],[
-171537,-123616],[265553,-358388],
[-242625,-534410],[-542579,-509714
],[157220,257659],[337494,-475064
],[-204591,605304],[-802370,
-457012],[-565373,180489],[
-470165,-457199],[-460364,-91860],[
10832,-68973],[-183205,-243655],[
-458031,520252],[3166359,-146533],[
-1150752,-502695],[-298625,680175
],[1052346,-682910],[282799,
-1097890],[569915,-1048251],[
1527712,-12963],[-437041,-284324],[
531332,-842634],[-713152,-1241155],[
-1413737,-1176326],[438701,597440
],[670101,-1116611],[-322384,
1417318],[-2012244,-1047113],[
-1285126,434728],[-1229156,-1055527],[
-1109533,-203286],[7312,-161201],
[-496260,-564139],[-942314,1224946
],[1257648,-307361],[-949478,
-87137],[471586,267317],[-143743,
-328984],[-848493,-415443],[
-678719,-420807],[657930,-127646],[
-443331,-66501],[-513509,-344159],[
-1411790,-386490],[-1661352,-306893
],[721387,178357],[-695368,
-453323],[1114069,532877],[
-1809161,-212487],[-178073,258962],[
-1473480,-278550],[-666227,16631],
[-139573,-58244],[-717113,-161812
],[672042,513989],[-2665535,
1280579],[3255734,-99457],[
-2489781,-559391],[1723041,843060],[
4224463,828425],[3723900,903124],
[-1523581,579852],[1620732,23710
],[2917886,753351],[5841832,
550270],[6298294,245599],[
-2910506,-229193],[3901701,985587],[
-5497627,-1053487],[6384533,-63278
],[-461821,-766752],[5610838,
235113],[1981515,-281123],[
655581,108842],[2832928,185748],[
-4066376,-1158697],[1798029,-1576104],[
-3603839,388784],[3366719,369210],
[-2768121,-733745],[-5596372,
-499838],[-5099387,-621926],[
1173919,-741331],[-1864394,116738],[
-4039582,-535252],[-7166823,-66765
],[-7392671,292689],[3527428,
-13897],[-5380673,-692887],[
7259352,624667],[-7193800,624207],[
1261684,763901],[-6601450,243623],[
-1981368,468003],[-849533,-56885],
[-3397522,52689],[5734167,860075
],[-1405334,809770],[1982543,
-113234],[-1631547,-293389],[
1211922,475677],[2746357,425620],[
2452335,478554],[-830896,371896],[
1000226,-12585],[1929846,402303],
[3689687,232583],[3914838,42860],
[-1830102,-88991],[2576570,524929
],[-3569582,-539178],[3911724,
-143265],[-423056,-450873],[
3490497,47941],[1166551,-200825],[
422617,54259],[1774539,64293],[
-2709205,-625725],[-3406977,298572],[
1516660,477260],[-12444,-730257],
[-814649,767458],[239068,1169655
],[-101386,1130427],[-1672721,
83222],[622795,279673],[-161962,
912024],[1405548,1275254],[
2143143,1175047],[-781455,-609509],[
-177266,1207016],[-355552,-1508019
],[2736284,1011650],[1194828,
-516564],[1879746,1056173],[
1321385,163668],[72705,170180],[
828040,571801],[422215,-1333557],[
1753513,-1316545],[-3078771,279556],[
2760969,362585],[-2202392,-664473
],[-4607372,-505722],[-4172021,
-602588],[1099592,-614551],[
-1579477,72752],[-3298251,-513615],[
-5990492,-159365],[-6236156,143528
],[2955807,38617],[-4396387,
-667044],[5980195,635816],[
-6121791,428704],[936261,668609],[
-5565922,113058],[-1732691,370227],[
-702388,-60596],[-2853138,-3723],
[4666075,814483],[-1708504,9518],
[483475,302655],[325874,-367803],
[-724619,352368],[-420788,598158
],[-560154,564373],[-810047,
-27199],[160524,166375],[-488941,
452024],[69794,699426],[455828,
679476],[-83990,-338819],[
-629965,599761],[520666,-773150],[
803867,621781],[786202,-210484],[
388207,608814],[535728,136870],[
-43716,88595],[122623,321777],[
800515,-653294],[2448217,-203819],[
-1068651,-347800],[-16476,524876],[
609595,-549000],[-130408,-841390],
[111837,-812121],[1199800,-54527
],[-435917,-202970],[147595,
-654963],[-961405,-920970],[
-1492666,-851282],[537979,440525],[
168796,-866925],[201998,1084941],[
-1922765,-735722],[-872905,367480
],[-1308330,-765014],[-939823,
-121803],[-46110,-122539],[
-572625,-413571],[-348463,957097],[
-1963998,-248104],[43827,464908],[
988222,-425760],[-1416993,345033],
[-1482655,709055],[-1584915,644142
],[-878018,-158623],[-95914,
239527],[-1315355,509772],[
-1093080,914730],[-619475,947781],[
472298,-450766],[-1723846,679245],[
1889929,-920030],[-125906,926251],
[1249327,-152244],[-578102,846135
],[381363,258575],[-198383,107857
],[-399677,434625],[2008063,
-722448],[-633263,-393583],[
-605603,291529],[1061444,-140858],[
-1163860,38583],[-1687322,254588],[
-1650148,202092],[-218742,-205318
],[-370416,135667],[-1336015,
152446],[-1772789,428961],[
-1583956,507389],[840901,-219524],[
-1765979,206659],[2172676,-334494],[
-1311649,554671],[821135,59516],[
-1426437,449900],[-160883,205927],
[-243284,42056],[-783334,218496],
[1964343,-198393]]>;

return _LR;
