//Standard generators of L2(29) are a and b where a has order 2, b has order 3
//and ab has order 29.
//Standard generators of the double cover 2.L2(29) = SL2(29) are pre-images A
//and B where B has order 3 and AB has order 29.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a^-1,b*a*b*a*b*a*b^-1*a*b^-1*a*b*a*b^-1*a*b^-1*a^-1]]
             where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents interchanged by _LR`AI[1][1]
_LR`G :=
MatrixGroup<14, ext<K|Polynomial(K, [49, 0, 15, 0, 1])> where K is 
RationalField() |
[[1810,-7883/7,85,-673/7],[4214,
1114/7,523,288/7],[-6902,5094,-682,488],[
16230,-73928/7,1642,-7169/7],[
-8856,-100285/7,-999,-11315/7],[-1304,16628/7,
-126,1599/7],[-9834,3184,-981,307],[
9757,-63542/7,1038,-7941/7],[
-57642,141501/7,-5925,13107/7],[9497,-4520,932,
-628],[1519,-140872/7,243,-13759/7],[
-569,-19557/7,-426,-1231/7],[
29601,-157336/7,2988,-15159/7],[8988,-63570/7,428,
-5785/7],[-900,-1433/7,101,-558/7],[
-5065,-5534/7,-832,-788/7],[8764,
-12304/7,904,-1013/7],[-19549,27379/7,-2073,2571/7
],[2516,13217,1109,1786],[2928,
-8279/7,294,-726/7],[8975,-2143/7,934,-148/7],[
-7236,59028/7,-254,10175/7],[
59636,-16575/7,6820,-216/7],[-3810,30642/7,98,
6226/7],[-18582,12411,-2077,1221],[
1257,-9064/7,770,-3275/7],[-38911,
60124/7,-4136,5370/7],[-7329,8063/7,211,-1107/7],
[1970,-2984/7,467,-254/7],[-1020,
-9672/7,-242,-1678/7],[2214,11776/7,179,1360/7],
[-5727,-25547/7,-625,-2846/7],[
-14072,32661/7,-1990,6971/7],[1156,3756/7,88,
438/7],[1102,1774,122,193],[
-14230,20298/7,-2613,5703/7],[9115,90126/7,1046,
11425/7],[-7873,16367/7,-1569,4572/7],[
-14336,-2691,-1585,-323],[9527,
-9873/7,2206,-1480/7],[-11679,-50844/7,-1176,
-5876/7],[7156,-16089/7,2005,-1298/7],[
-6,4467/7,-154,288/7],[-112,
10497/7,0,1516/7],[-5735,-17527/7,-521,-1819/7],
[12479,38172/7,1228,3970/7],[
23422,-22955/7,3013,-4139/7],[-2837,-601,-257,-63
],[-3320,-3019,-321,-308],[
17959,7048/7,2820,-876/7],[-21237,-130915/7,-1921,
-14400/7],[9809,7619/7,1709,-592/7],[
26783,17051/7,2690,1994/7],[-2556,
4953/7,-1030,186/7],[26520,10649,2534,1119],[
4746,24778/7,-257,1657/7],[-86,
1203/7,-9,76/7],[-538,1046/7,-75,129/7],[
-28,-5560/7,4,-541/7],[-17,
11834/7,-12,1173/7],[3951,8342/7,511,887/7],[
-238,-2084/7,-21,-201/7],[529,
-4800/7,56,-474/7],[1386,1272,262,148],[
3109,-29430/7,386,-2928/7],[415,
5493/7,140,642/7],[3149,15696/7,297,1570/7],[
77,1721/7,-17,-22/7],[356,
24398/7,7,2404/7],[119,8696/7,12,653/7],[
-322,-70,-119,-14],[525,3209/7,
76,570/7],[-1441,864/7,-123,24/7],[
3498,-879/7,354,31/7],[4455,
-20400/7,743,-3131/7],[-437,926/7,-33,72/7],[
-1451,-1082/7,-143,-151/7],[6485,
-11273/7,1141,-2131/7],[-8578,-10482/7,-818,
-1879/7],[4409,-6962/7,775,-1530/7],[
4340,-10706/7,472,-892/7],[-2915,
-1570/7,-711,-163/7],[6696,-3581/7,639,-60/7],[
-715,-5122/7,-481,-775/7],[1277,
1346/7,160,-306/7],[-2682,6604/7,-519,815/7],[
-3908,-14823/7,-318,-1376/7],[
8051,35912/7,671,3600/7],[25082,11875/7,3673,
2460/7],[-2092,-4287/7,-184,-374/7],[
-1625,-18176/7,-114,-1796/7],[
16052,41675/7,2722,6367/7],[-6763,-107391/7,215,
-10588/7],[10051,4478,1916,660],[
19995,23381/7,1809,2549/7],[2875,-11055/7,211,
-3173/7],[17294,66828/7,1397,6530/7],[
10105,10473/7,1194,-1035/7],[78,
-220/7,-5,-24/7],[213,558/7,27,89/7],[
-590,1115/7,-56,100/7],[1348,
-1985/7,135,-179/7],[584,-910,88,-114],[
-165,633/7,-15,59/7],[-626,226/7,
-62,16/7],[1251,-3083/7,182,-472/7],[
-3773,174,-376,0],[918,-1423/7,
129,-275/7],[1222,-905,128,-86],[
-203,-792/7,-79,-57/7],[2591,-4836/7,255,-433/7
],[599,-2402/7,-1,-253/7],[325,
1898/7,-8,204/7],[405,3153/7,73,402/7],[
-2740,-656,-267,-69],[5818,
9967/7,586,1021/7],[6273,-12665/7,636,-1836/7],[
-1217,-650/7,-117,-76/7],[-1892,
-6679/7,-190,-673/7],[4706,-442/7,570,-680/7],[
-12504,-39513/7,-1295,-4233/7],[
2273,1903/7,285,-309/7],[10418,-2334/7,1055,
-185/7],[334,3120/7,-140,488/7],[
12302,2674,1227,280],[3391,8971/7,141,949/7],
[376,2446/7,33,199/7],[-431,
2785/7,-62,307/7],[-1987,-8551/7,-188,-837/7],[
4058,18940/7,389,1874/7],[8255,
2516/7,936,269/7],[-1107,-2644/7,-106,-257/7],[
-762,-1349,-71,-133],[3947,
12529/7,523,1343/7],[-5380,-8019,-452,-797],[
1585,9619/7,261,1009/7],[10400,
13791/7,1011,1387/7],[1307,411,89,15],[
8976,36920/7,854,3642/7],[3615,
14438/7,340,1222/7],[715,-2938/7,102,-509/7],[
-843,634/7,-222,109/7],[-942,
4619/7,-61,503/7],[2125,-8382/7,145,-801/7],[
5174,-599,1101,65],[-232,2382/7,
-13,261/7],[-1262,2174/7,-100,214/7],[
6448,6662/7,1161,2007/7],[-4413,
2290,20,240],[5459,6756/7,976,1611/7],[
508,-17623/7,-37,-1621/7],[855,
-13058/7,113,-2369/7],[3805,-19036/7,219,-1921/7
],[3968,-17098/7,568,-2713/7],[
-47,3229/7,27,331/7],[-864,474/7,-96,-44/7],[
336,-11105/7,27,-1067/7],[-1224,
23634/7,-125,2277/7],[4013,22151/7,295,2593/7],[
-291,-4579/7,-32,-442/7],[1573,
-8877/7,155,-855/7],[-2118,18596/7,-377,2216/7],
[8156,-53658/7,799,-4959/7],[
-2682,11206/7,-378,1420/7],[4686,34253/7,442,
3306/7],[1613,7171/7,310,689/7],[
-1375,48409/7,-132,4645/7],[544,21845/7,204,
2224/7],[74,1613/7,36,129/7],[
-752,278/7,-107,-30/7],[211,-944,22,-89],[
-714,14205/7,-85,1367/7],[3323,
15102/7,361,1942/7],[-196,-2682/7,-20,-253/7],[
940,-5420/7,97,-520/7],[-498,
14004/7,-77,1901/7],[5327,-32058/7,603,-2903/7],
[-975,8844/7,-100,1270/7],[2808,
20460/7,247,1987/7],[1225,2504/7,236,40/7],[
-871,29034/7,-111,2763/7],[848,
11632/7,225,1013/7],[-516,-2557/7,-19,-226/7],[
-39,-4042/7,-9,-493/7],[3309,
7723/7,317,779/7],[-7020,-17249/7,-691,-1737/7],
[-9731,9312/7,-1086,1311/7],[
1601,1699/7,153,173/7],[2012,10155/7,197,1013/7
],[-6390,-6850/7,-829,-326/7],[
13328,59943/7,1286,6197/7],[-3057,-7193/7,-441,
-417/7],[-13845,-3732/7,-1373,-428/7],[
-1015,-2935/7,58,-254/7],[-14882,
-32616/7,-1450,-3307/7],[-4909,-13228/7,-334,
-1167/7]],
[[2011,1040,289,113],[-571,
3670/7,-68,86/7],[-5783,-18918/7,-591,-1796/7],[
11152,41985/7,1088,3989/7],[13999,
10907/7,989,2171/7],[-3062,-779,-312,-74],[
-2584,-22059/7,-255,-2116/7],[
2037,34947/7,-401,4364/7],[-18748,-123007/7,-1908,
-11147/7],[-1610,29196/7,-570,3653/7],[
25987,24384/7,2508,2208/7],[8507,
10932/7,1294,1195/7],[25167,80413/7,2509,7585/7],
[14107,40381/7,1807,4331/7],[
4958,-2707/7,717,79/7],[3232,-5714/7,365,-1360/7
],[-9004,27765/7,-965,2859/7],[
18614,-58132/7,1850,-6073/7],[-13838,-55285/7,
-2779,-2813/7],[-2777,2022,-311,203],[
-10030,14249/7,-1003,1530/7],[
-6165,-17910/7,-2546,108/7],[-61548,115737/7,
-6511,13796/7],[-3113,4899/7,-1705,2176/7],[
9243,-127224/7,848,-13047/7],[
15312,-11418/7,2736,-127/7],[37107,-125749/7,3823,
-13140/7],[25433,-32972/7,3568,-1507/7],[
825,8720/7,-23,1776/7],[6102,143,
1158,-25],[-7341,1648/7,-854,-25/7],[
15368,-6051/7,1765,-717/7],[
-15495,-63948/7,-4031,-9439/7],[-2662,2762/7,-304,
165/7],[-6334,-566,-719,-54],[
-12785,-52013/7,-3554,-10307/7],[-50150,-2656,
-6788,-286],[-12123,-28061/7,-3084,-6347/7],[
18957,-46461/7,2202,-5049/7],[
3789,36028/7,382,8000/7],[32166,-14759/7,3789,
-1305/7],[6210,33563/7,21,7628/7],[
910,863/7,106,128/7],[517,1088/7,
65,38/7],[-2742,80,-278,9],[
5777,97/7,573,-22/7],[2185,-12703/7,54,-1097/7],
[-1082,1367/7,-110,135/7],[-2260,
-2627/7,-225,-247/7],[1681,-456/7,-34,13/7],[
-14609,-11840/7,-1502,-969/7],[
646,3516/7,-85,415/7],[7543,-15753/7,741,-1599/7
],[2583,110/7,353,166/7],[11760,
-2944/7,1180,-354/7],[5650,1044/7,627,316/7],[
1359,245,119,22],[590,4281/7,59,
466/7],[-5462,-2657/7,-532,-270/7],[
11597,7327/7,1138,740/7],[9855,
-25035/7,1034,-2635/7],[-2273,1138/7,-221,109/7],
[-4306,-8329/7,-422,-825/7],[
8290,1986/7,912,47/7],[-26827,-44774/7,-2616,
-4538/7],[4610,7349/7,522,594/7],[
17249,-3122,1698,-302],[2903,-979/7,212,-125/7
],[23922,10113/7,2341,1041/7],[
9659,4590/7,879,376/7],[2324,-6911/7,467,-849/7
],[-1094,-1106,-344,-182],[803,
20201/7,78,2183/7],[-2090,-41753/7,-312,-4338/7],
[-9381,10866/7,-838,4741/7],[869,
7662/7,75,830/7],[-1057,17158/7,-71,1786/7],[
-5038,12923/7,-941,5328/7],[-1057,
16957,428,1961],[-333,1936,-237,638],[
-13958,-51105/7,-1585,-5234/7],[
7834,-23900/7,1769,-3726/7],[-5365,-86445/7,-688,
-9200/7],[9210,-40997/7,2070,-4758/7],[
1539,-10629/7,409,-1249/7],[-1357,
-1689,-400,-243],[4858,4215,479,445],[
-10653,-62592/7,-1166,-6396/7],[
-18983,20471/7,-1710,6002/7],[2823,1424,267,152
],[1383,29382/7,173,2992/7],[
-10149,3940/7,-1416,4850/7],[15909,189842/7,2175,
20855/7],[-2091,4230/7,-373,3845/7],[
-30756,-55718/7,-3257,-5689/7],[
5518,-29811/7,1611,-4513/7],[-23470,-125884/7,
-2491,-13128/7],[2633,-59956/7,1518,-6791/7],[
133,-2398/7,40,-277/7],[-56,
-1865/7,-44,-227/7],[903,962,92,98],[
-1807,-14390/7,-195,-1433/7],[
-3756,-983/7,-294,354/7],[570,2348/7,56,241/7],
[62,6492/7,12,647/7],[-973,
-3564/7,-81,195/7],[1889,40545/7,289,4194/7],[
357,-2288/7,64,183/7],[-6228,
-14338/7,-642,-1416/7],[100,-6115/7,111,-858/7],
[-4224,-28865/7,-447,-2909/7],[
-387,-13928/7,94,-1559/7],[319,323/7,29,71/7],[
423,454/7,64,27/7],[-1183,971/7,
-122,89/7],[2564,-1693/7,262,-174/7],[
132,-8093/7,-98,-897/7],[-428,
865/7,-44,81/7],[-1080,-464/7,-110,-44/7],[
511,-3207/7,-56,-505/7],[-7134,
-1368/7,-778,-122/7],[166,-537/7,-70,-180/7],[
2893,-9123/7,297,-919/7],[773,
601/7,86,244/7],[5124,-4588/7,529,-451/7],[
1989,-212/7,181,166/7],[-205,
-978/7,-3,-75/7],[-8,-1887/7,0,-242/7],[
1440,3194/7,136,324/7],[-3126,
-7193/7,-306,-732/7],[-4473,4713/7,-530,667/7],[
689,108,65,11],[917,618,89,62
],[-3169,-415,-440,-18],[5939,
25724/7,556,2701/7],[-1662,-2934/7,-255,-148/7],
[-6027,-1145/7,-597,-151/7],[
-266,-811/7,63,-27/7],[-6523,-13640/7,-630,
-1397/7],[-2002,-4974/7,-115,-382/7],[
448,363/7,31,-155/7],[-902,
3680/7,-185,509/7],[-2108,-5536/7,-175,-531/7],[
4605,13563/7,408,1397/7],[11568,
-2213/7,1724,-50/7],[-1057,-1228/7,-92,-108/7],[
-1233,-7650/7,-103,-769/7],[8829,
1859,1488,266],[-6233,-45582/7,-256,-4751/7],[
5641,10553/7,1042,1383/7],[9571,
4847/7,892,626/7],[318,-5049/7,-128,-1332/7],[
9485,24953/7,806,2532/7],[4064,
2273/7,359,-702/7],[-58,-3841/7,26,-432/7],[
-55,-3121/7,-54,-356/7],[2007,
10807/7,202,1091/7],[-4095,-22992/7,-424,-2279/7
],[-6985,-657/7,-582,484/7],[
1199,3515/7,118,358/7],[586,11034/7,65,1094/7],
[-2382,-7906/7,-199,-101/7],[
5798,67016/7,702,6823/7],[73,-5916/7,54,-78/7],
[-11577,-19535/7,-1174,-1923/7],[
-630,-8758/7,54,-1191/7],[-9289,-45971/7,-955,
-4601/7],[-2145,-22179/7,-54,-2425/7],[
-999,-418/7,-99,-26/7],[-441,
-2203/7,-35,-222/7],[3427,-585/7,334,-60/7],[
-7431,82/7,-725,5/7],[-5066,
17534/7,-537,1679/7],[1343,-1523/7,131,-151/7],[
2961,3439/7,289,338/7],[-4952,
-177/7,-524,-93/7],[18116,16444/7,1747,1618/7],[
-3052,-4295/7,-330,-473/7],[-9725,
20232/7,-949,1976/7],[-2144,2493/7,-207,316/7],[
-14993,457,-1461,45],[-6465,
1418/7,-639,207/7],[117,-773/7,7,11/7],[
830,-1054/7,131,-144/7],[-263,
5519/7,-39,528/7],[735,-12252/7,95,-1220/7],[
-4795,-10868/7,-718,-1285/7],[107,
308,6,29],[-837,4591/7,-91,454/7],[
-1950,-11034/7,-430,-1493/7],[
-5505,28838/7,-712,2861/7],[-956,-6645/7,-287,
-926/7],[-2269,-2531,-194,-256],[
90,8,34,59],[1059,-24655/7,162,-2423/7],[
34,-6742/7,-26,-246/7]]>;

return _LR;
