//Standard generators of L2(59) are a and b where a has order 2, b has order 3
//and ab has order 59.
//Standard generators of the double cover 2.L2(59) = SL2(59) are preimages A and
//B where B has order 3 and AB has order 59.
_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 auto
_LR`G :=
/*
Original group: c9Group("l259p")
From DB /nb/reps/l2/l259/d29.l259.deg2.X2.M
Schur index: 1
Character: ( 29, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, zeta(59)_59^57 + zeta(59)_59^53 + zeta(59)_59^51 +
zeta(59)_59^49 + zeta(59)_59^48 + zeta(59)_59^46 + zeta(59)_59^45 + 
zeta(59)_59^41 + zeta(59)_59^36 + zeta(59)_59^35 + zeta(59)_59^29 + 
zeta(59)_59^28 + zeta(59)_59^27 + zeta(59)_59^26 + zeta(59)_59^25 + 
zeta(59)_59^22 + zeta(59)_59^21 + zeta(59)_59^20 + zeta(59)_59^19 + 
zeta(59)_59^17 + zeta(59)_59^16 + zeta(59)_59^15 + zeta(59)_59^12 + 
zeta(59)_59^9 + zeta(59)_59^7 + zeta(59)_59^5 + zeta(59)_59^4 + zeta(59)_59^3 + 
zeta(59)_59, -zeta(59)_59^57 - zeta(59)_59^53 - zeta(59)_59^51 - zeta(59)_59^49 
- zeta(59)_59^48 - zeta(59)_59^46 - zeta(59)_59^45 - zeta(59)_59^41 - 
zeta(59)_59^36 - zeta(59)_59^35 - zeta(59)_59^29 - zeta(59)_59^28 - 
zeta(59)_59^27 - zeta(59)_59^26 - zeta(59)_59^25 - zeta(59)_59^22 - 
zeta(59)_59^21 - zeta(59)_59^20 - zeta(59)_59^19 - zeta(59)_59^17 - 
zeta(59)_59^16 - zeta(59)_59^15 - zeta(59)_59^12 - zeta(59)_59^9 - zeta(59)_59^7
- zeta(59)_59^5 - zeta(59)_59^4 - zeta(59)_59^3 - zeta(59)_59 - 1 )
*/

MatrixGroup<29,K | [
Matrix(K,29,29,
[[208/59,-882/59],[10139/59,336/59],[-5007/59,3556/59
],[-9707/59,-4428/59],[28841/59,2517/59],[-21834/59,
6777/59],[-13303/59,-8198/59],[28679/59,2842/59],
[-19770/59,5654/59],[-19794/59,-6489/59],[26305/59,
-1670/59],[-9184/59,7061/59],[-20044/59,-8228/59],[
33412/59,1983/59],[-26191/59,2724/59],[14813/59,-7249/59
],[14906/59,8513/59],[-28204/59,-2482/59],[20516/59,
-3985/59],[11998/59,7535/59],[-31533/59,654/59],[135,
-122],[20050/59,7650/59],[-35950/59,21/59],[8339/59,
-6568/59],[8464/59,4302/59],[-14456/59,-1064/59],[
4076/59,-2055/59],[2991/59,377/59],[1120/59,175/59],
[-1375/59,672/59],[-2644/59,-981/59],[5189/59,407/59],
[-6397/59,1189/59],[-2429/59,-2262/59],[6870/59,760/59
],[-5194/59,763/59],[-2719/59,-1721/59],[6724/59,
-299/59],[-1342/59,1741/59],[-4436/59,-1910/59],[
9189/59,619/59],[-6510/59,963/59],[3356/59,-1607/59],
[2194/59,2146/59],[-7028/59,-840/59],[4534/59,-667/59],
[926/59,1498/59],[-7379/59,-303/59],[2250/59,-1931/59
],[4456/59,1714/59],[-8560/59,-423/59],[4209/59,
-1671/59],[2827/59,1170/59],[-3078/59,-374/59],[
1739/59,-416/59],[1195/59,325/59],[-47/59,142/59],
[-2031/59,9/59],[-632/59,-1618/59],[9938/59,937/59],
[-10446/59,1705/59],[1758/59,-5039/59],[21125/59,
4313/59],[-21654/59,1886/59],[4756/59,-5238/59],
[16651/59,4038/59],[-15368/59,2717/59],[-7133/59,
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[913/59,-6375/59],[12901/59,5329/59],[-23564/59,
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[-12844/59,-4153/59],[18273/59,-1391/59],[4729/59,
5387/59],[-20639/59,-1807/59],[17969/59,-3356/59],
[4224/59,6619/59],[-19434/59,-2406/59],[12180/59,
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1349/59,-370/59],[1284/59,621/59],[-6483/59,840/59],
[-2445/59,-3061/59],[13061/59,2227/59],[-21866/59,
1167/59],[3664/59,-7068/59],[20219/59,4743/59],
[-22151/59,656/59],[4106/59,-5830/59],[21157/59,
2607/59],[-13484/59,3830/59],[-5215/59,-6064/59],
[25184/59,3994/59],[-24585/59,1806/59],[13215/59,
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[-24083/59,-3562/59],[22519/59,-3460/59],[3726/59,
5505/59],[-11270/59,-2362/59],[10343/59,-554/59],[
272/59,1783/59],[-2258/59,27/59],[-2805/59,349/59],
[-5588/59,-2208/59],[14184/59,-601/59],[-6943/59,
4050/59],[-11473/59,-7016/59],[35527/59,1375/59],
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[27583/59,-1415/59],[-11764/59,7919/59],[-16591/59,
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[-12040/59,818/59],[-309/59,-2801/59],[8499/59,1894/59
],[-12079/59,622/59],[3249/59,-2824/59],[3250/59,
2488/59],[-9320/59,-2238/59],[13250/59,-404/59],[
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],[-1750/59,3285/59],[-9528/59,-1769/59],[11658/59,
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[804/59,-339/59],[-404/59,254/59],[-2523/59,-503/59
],[4353/59,-439/59],[-1867/59,1576/59],[-5471/59,
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],[-7411/59,-1193/59],[9321/59,-769/59],[-3415/59,
2787/59],[-4993/59,-2788/59],[9432/59,1754/59],[
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[-8949/59,687/59],[2643/59,-2620/59],[7300/59,2210/59],
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[6464/59,1364/59],[-6489/59,356/59],[878/59,-1548/59],
[94,11],[-3301/59,1186/59],[-2794/59,-1753/59],[
7960/59,934/59],[-7580/59,770/59],[3518/59,-1755/59],
[1449/59,2190/59],[-6933/59,-1417/59],[6634/59,-302/59
],[-1649/59,1363/59],[-4845/59,-958/59],[4481/59,
-1068/59],[2661/59,1782/59],[-7385/59,-787/59],[
6198/59,-1115/59],[823/59,1705/59],[-3727/59,-728/59],
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[682/59,-347/59],[4266/59,567/59],[-4300/59,1194/59
],[-1519/59,-2094/59],[10947/59,2129/59],[-13435/59,
1863/59],[-1333/59,-3787/59],[11109/59,2217/59],[-207,
26],[-4798/59,-3460/59],[12540/59,418/59],[-8096/59,
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],[-14231/59,-1027/59],[7590/59,-2520/59],[4308/59,
3778/59],[-15832/59,-1338/59],[7360/59,-2390/59],[
1481/59,2077/59],[-5921/59,-986/59],[3076/59,-692/59],
[1086/59,284/59],[1391/59,9/59],[292/59,1174/59],
[-7399/59,-697/59],[7739/59,-1337/59],[-1058/59,
3784/59],[-16399/59,-3298/59],[16920/59,-1560/59],
[-3458/59,4176/59],[-12912/59,-3227/59],[12428/59,
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[14593/59,-2674/59],[48/59,4993/59],[-10927/59,
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[-3160/59,-4137/59],[15892/59,1340/59],[-13544/59,
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-9719/59,1094/59],[1780/59,-2104/59],[4335/59,941/59],
[-1331/59,288/59],[-287/59,606/59],[-7215/59,-329/59],
[59,-45],[8123/59,3207/59],[-21730/59,-1511/59],
[16160/59,-5617/59],[12613/59,6700/59],[-24598/59,
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6057/59],[-27355/59,-784/59],[19351/59,-3188/59],
[-8708/59,6361/59],[-14741/59,-7003/59],[25028/59,
1853/59],[-17329/59,3397/59],[-8505/59,-6095/59],
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[11307/59,3203/59],[-14806/59,478/59],[5393/59,-3020/59
],[7983/59,2927/59],[-10829/59,998/59],[-2369/59,
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[-12292/59,-1633/59],[12517/59,-1516/59],[-500/59,
4074/59],[-11448/59,-2187/59],[8525/59,-414/59],[
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[560/59,-1/59],[397/59,440/59],[-2728/59,-146/59],
[2247/59,-580/59],[445/59,1362/59],[-6440/59,-844/59],
[4953/59,-891/59],[153/59,1486/59],[-5481/59,-873/59],
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],[4100/59,-1181/59],[1513/59,1669/59],[-4388/59,
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[-2754/59,-1732/59],[5690/59,229/59],[-2540/59,584/59],
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],[-10380/59,-936/59],[13761/59,-1860/59],[3029/59,
5527/59],[-18660/59,-2451/59],[15348/59,-1872/59],
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[-13100/59,3949/59],[-8015/59,-4230/59],[10731/59,
1107/59],[-7471/59,1106/59],[-1648/59,-1526/59],[
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],[-9990/59,-2752/59],[11851/59,-488/59],[-4164/59,
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],[14858/59,747/59],[-17124/59,3571/59],[-9553/59,
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[1861/59,2483/59],[-8678/59,-1308/59],[5067/59,-1607/59
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[-7344/59,2186/59],[-2235/59,-2641/59],[7303/59,1331/59
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4785/59],[-331,-19],[10015/59,-3806/59],[7457/59,
5297/59],[-22336/59,-1661/59],[10391/59,-3349/59],[
2292/59,2991/59],[-8203/59,-1361/59],[4234/59,-913/59],
[1350/59,399/59],[-810/59,209/59],[-2618/59,-811/59
],[5966/59,-399/59],[-2809/59,1934/59],[-5961/59,
-3072/59],[15788/59,660/59],[-8240/59,2813/59],[
-3870/59,-3315/59],[12490/59,849/59],[-3350/59,2740/59
],[-9616/59,-1945/59],[12445/59,-775/59],[-5354/59,
3688/59],[-7447/59,-3861/59],[13206/59,2163/59],[
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],[-10823/59,-1232/59],[6278/59,-2312/59],[9432/59,
2521/59],[-12356/59,776/59],[4610/59,-3465/59],
[172,58],[-12115/59,137/59],[4512/59,-1596/59],[
1856/59,1588/59],[-3677/59,-156/59],[123/59,-285/59],
[282/59,-380/59],[4899/59,476/59],[-4684/59,1606/59],
[-3182/59,-2765/59],[14643/59,2323/59],[-285,42],[
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],[-5535/59,-4049/59],[15454/59,346/59],[-9436/59,
3371/59],[-6278/59,-5240/59],[18633/59,2692/59],[
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[-14408/59,-2856/59],[14318/59,-982/59],[1060/59,4126/59
],[-17084/59,-1128/59],[9389/59,-3406/59],[6420/59,
4875/59],[-20220/59,-1736/59],[10596/59,-2880/59],[
1372/59,2803/59],[-7241/59,-1384/59],[4134/59,-700/59],
[1052/59,393/59],[2663/59,311/59],[-1868/59,1928/59],[
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[3508/59,5777/59],[-20611/59,-3521/59],[25356/59,
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22414/59,4531/59],[-27204/59,1288/59],[8515/59,-5508/59
],[11838/59,5445/59],[-24590/59,380/59],[-33/59,
-6615/59],[21511/59,3315/59],[-23938/59,2274/59],[
949/59,-7542/59],[21114/59,3347/59],[-14058/59,853/59],
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[-24181/59,-4112/59],[23791/59,-3394/59],[4187/59,
5483/59],[-10943/59,-2298/59],[10468/59,-658/59],[
953/59,1906/59],[-2353/59,132/59],[-220/59,445/59],
[-5234/59,-261/59],[3029/59,-1848/59],[4975/59,2398/59
],[-15219/59,-1469/59],[12651/59,-3490/59],[6539/59,
4582/59],[-15537/59,-1751/59],[11593/59,-2833/59],[
9642/59,3649/59],[-14349/59,684/59],[5451/59,-3730/59],
[10281/59,4514/59],[-18319/59,-1238/59],[14655/59,
-1429/59],[-8642/59,3897/59],[-7407/59,-4784/59],
[15492/59,1602/59],[-11793/59,1961/59],[-5294/59,
-4098/59],[17047/59,-67/59],[-4957/59,3833/59],
[-10271/59,-4199/59],[19716/59,256/59],[-5579/59,
3533/59],[-4296/59,-2456/59],[7859/59,732/59],[
-2658/59,1056/59],[-1485/59,-256/59],[1218/59,430/59
],[-4676/59,855/59],[-3668/59,-2439/59],[11730/59,
1276/59],[-16306/59,1844/59],[-1212/59,-6200/59],[
19950/59,3261/59],[-17986/59,1552/59],[546/59,-5221/59
],[18889/59,1670/59],[-9054/59,3722/59],[-7941/59,
-4849/59],[22676/59,2282/59],[-18770/59,2757/59],
[6830/59,-4748/59],[6072/59,5831/59],[-21371/59,
-3271/59],[17686/59,-1680/59],[-3263/59,4448/59],[
-16823/59,-2966/59],[13119/59,-3616/59],[8519/59,4884/59
],[-21526/59,-1988/59],[16510/59,-3914/59],[6609/59,
4840/59],[-194,-27],[148,-15],[963/59,1631/59],[
-2113/59,22/59],[-1355/59,-55/59],[-729/59,-927/59],
[4875/59,251/59],[-3691/59,878/59],[-297/59,-2364/59
],[11165/59,1208/59],[-6964/59,1707/59],[-1216/59,
-2373/59],[10402/59,1216/59],[-5093/59,2204/59],[
-5771/59,-1984/59],[9023/59,346/59],[-6439/59,1990/59],
[-2970/59,-2459/59],[6143/59,1489/59],[-9661/59,-560/59
],[6982/59,-1848/59],[2095/59,2302/59],[-8043/59,
-1336/59],[7905/59,-1536/59],[5630/59,2587/59],[
-9115/59,-117/59],[6034/59,-1974/59],[5674/59,2793/59],
[-8965/59,124/59],[3087/59,-1024/59],[1452/59,1252/59],
[-3525/59,-88/59],[-320/59,-345/59],[-26/59,951/59],
[-10907/59,-161/59],[4060/59,-4034/59],[12527/59,
4581/59],[-31996/59,-1924/59],[20971/59,-8267/59],
[18826/59,8978/59],[-33285/59,-2319/59],[20109/59,
-6923/59],[24025/59,6986/59],[-28203/59,2535/59],
[6607/59,-8085/59],[25676/59,8518/59],[-37733/59,
-1008/59],[26784/59,-4193/59],[-12034/59,8736/59],
[-20950/59,-9273/59],[33079/59,1966/59],[-21419/59,
5129/59],[-15605/59,-8259/59],[34384/59,-1442/59],
[-5396/59,8324/59],[-431,-134],[39753/59,-1088/59],
[-6453/59,7921/59],[-11916/59,-4716/59],[16818/59,
832/59],[-4179/59,2498/59],[-3633/59,-422/59],[317/59,
-428/59],[4907/59,374/59],[-3359/59,1601/59],[-3605/59,
-2254/59],[13479/59,1647/59],[-12492/59,2923/59],
[-4953/59,-4183/59],[13950/59,1822/59],[-11649/59,
2426/59],[-8052/59,-3596/59],[13577/59,-281/59],[
-6317/59,3178/59],[-7829/59,-4212/59],[16133/59,1409/59
],[-13437/59,1033/59],[8650/59,-3350/59],[5886/59,
4397/59],[-14043/59,-1654/59],[11608/59,-1623/59],[
3821/59,3925/59],[-15848/59,-308/59],[5697/59,-3297/59],
[8056/59,3958/59],[-18093/59,-550/59],[100,-53],[
3499/59,2278/59],[-7219/59,-809/59],[2806/59,-937/59],
[1353/59,287/59],[-1662/59,-197/59],[914/59,-1240/59],
[7009/59,1097/59],[-8328/59,808/59],[4493/59,-3522/59],
[14663/59,3838/59],[-17259/59,1000/59],[5545/59,-3778/59
],[11980/59,3723/59],[-14065/59,1724/59],[-3475/59,
-3764/59],[14198/59,1964/59],[-16046/59,1892/59],
[2350/59,-4563/59],[7665/59,3884/59],[-16115/59,
-2730/59],[18138/59,-1248/59],[-4844/59,3882/59],[
-8563/59,-3556/59],[15945/59,-442/59],[1213/59,4373/59
],[-14857/59,-1866/59],[15159/59,-1896/59],[807/59,
5154/59],[-14987/59,-2067/59],[9410/59,-768/59],[
-2358/59,2010/59],[-4592/59,-983/59],[1025/59,-369/59],
[-2306/59,-364/59],[2187/59,-1644/59],[8296/59,1724/59
],[-10816/59,552/59],[8160/59,-3976/59],[16342/59,
4954/59],[-20626/59,992/59],[6708/59,-4402/59],
[15044/59,4718/59],[-18850/59,2184/59],[-2982/59,
-4902/59],[16216/59,2932/59],[-20088/59,1596/59],
[4152/59,-4912/59],[6628/59,4170/59],[-16726/59,
-3362/59],[20898/59,-1274/59],[-5220/59,4546/59],
[-10626/59,-4378/59],[21216/59,-402/59],[-92/59,
5716/59],[-17446/59,-2678/59],[18990/59,-1786/59],
[-208/59,6074/59],[-17986/59,-2342/59],[10416/59,
-998/59],[-2306/59,2468/59],[-6248/59,-1168/59],
[1108/59,-616/59],[763/59,-67/59],[784/59,447/59],
[-2152/59,-56/59],[1771/59,-293/59],[227/59,985/59],
[-3817/59,-259/59],[1206/59,-597/59],[1119/59,645/59],
[-4017/59,-10/59],[574/59,-1094/59],[2745/59,711/59],
[-3544/59,-185/59],[2322/59,-607/59],[378/59,579/59],
[-776/59,-431/59],[2429/59,197/59],[-1001/59,594/59],
[-1525/59,-513/59],[3237/59,161/59],[-2144/59,963/59],
[-3108/59,-906/59],[3103/59,11/59],[-1848/59,670/59],
[-2433/59,-736/59],[1834/59,-344/59],[-101/59,329/59],
[-1153/59,-300/59],[1060/59,-181/59],[409/59,110/59
],[-26,7],[-5989/59,-1181/59],[8133/59,-1552/59],
[693/59,3392/59],[-268,-69],[24699/59,-2050/59],
[-2060/59,6323/59],[-16249/59,-4532/59],[22743/59,
-1301/59],[3412/59,5821/59],[-20006/59,-1544/59],
[15560/59,-3277/59],[2824/59,6710/59],[-21334/59,
-4141/59],[22161/59,426/59],[-20066/59,3233/59],[
1250/59,-6763/59],[16853/59,4324/59],[-20600/59,277/59
],[3617/59,-5569/59],[22211/59,2709/59],[-15196/59,
3533/59],[-3206/59,-6412/59],[25497/59,3440/59],[
-15852/59,3342/59],[85/59,-3547/59],[8881/59,2186/59],
[-6411/59,807/59],[-1501/59,-583/59]])
]> where w := K.1 where K := ext<K|Polynomial(K,[15,1,1])> where K
is RationalField();

return _LR;
