INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1440 Minimal number of generators: 241 Number of equivalence classes of cusps: 80 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -9/20 -8/19 -7/18 -1/3 -5/16 -3/14 -2/13 -1/7 0/1 2/9 5/17 1/3 3/8 1/2 4/7 9/13 5/7 23/32 5/6 1/1 6/5 37/29 7/5 13/9 3/2 11/7 27/17 34/21 41/25 5/3 7/4 9/5 2/1 15/7 11/5 23/10 7/3 31/13 17/7 5/2 111/43 8/3 3/1 67/21 16/5 135/41 10/3 17/5 7/2 69/19 11/3 26/7 15/4 87/23 35/9 4/1 17/4 13/3 9/2 14/3 24/5 73/15 5/1 37/7 16/3 11/2 28/5 17/3 6/1 19/3 13/2 7/1 15/2 23/3 39/5 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 -1/2 -1/1 0/1 -7/15 -3/2 1/0 -6/13 -1/1 -6/7 -11/24 -5/7 -2/3 -5/11 -3/4 -1/2 -14/31 -2/3 -3/5 -9/20 -1/2 -22/49 -2/5 -1/3 -13/29 -1/2 -1/4 -4/9 -1/1 0/1 -11/25 -3/2 1/0 -18/41 -1/1 0/1 -25/57 -3/2 1/0 -7/16 -4/3 -1/1 -10/23 -1/1 -8/9 -13/30 -1/1 -4/5 -3/7 -3/4 -1/2 -14/33 -1/1 -2/3 -11/26 -3/5 -4/7 -8/19 -1/2 -21/50 -3/7 -2/5 -13/31 -1/2 -3/8 -5/12 -1/3 0/1 -17/41 -3/2 1/0 -12/29 -1/1 0/1 -7/17 -1/2 1/0 -9/22 -1/1 0/1 -11/27 -3/2 1/0 -2/5 -1/1 -2/3 -11/28 -2/3 -3/5 -20/51 -3/5 -10/17 -9/23 -7/12 -1/2 -7/18 -1/2 -12/31 -3/7 -2/5 -17/44 -2/5 -1/3 -5/13 -1/2 -1/4 -18/47 0/1 1/5 -13/34 -1/1 0/1 -8/21 -1/1 0/1 -11/29 -1/2 1/0 -14/37 -1/1 -4/5 -3/8 -1/1 0/1 -10/27 -1/1 -4/5 -17/46 -1/1 -2/3 -7/19 -3/4 -1/2 -25/68 -1/1 0/1 -43/117 -3/4 -1/2 -18/49 -1/1 -4/5 -11/30 -1/1 -2/3 -4/11 -1/1 -2/3 -13/36 -5/7 -2/3 -9/25 -3/4 -1/2 -14/39 -2/3 -7/11 -5/14 -2/3 -3/5 -16/45 -4/7 -13/23 -11/31 -11/20 -1/2 -6/17 -1/2 -7/20 -2/5 -1/3 -1/3 -1/2 1/0 -6/19 -2/3 -3/5 -5/16 -1/2 -9/29 -1/2 -9/20 -13/42 -10/23 -3/7 -4/13 -2/5 -1/3 -11/36 -4/11 -1/3 -18/59 -1/3 -4/13 -7/23 -1/2 -1/4 -10/33 -1/3 -2/7 -13/43 -1/2 -1/4 -3/10 -1/3 0/1 -11/37 -1/2 -3/8 -19/64 -6/17 -1/3 -8/27 -1/3 0/1 -21/71 -1/2 -1/4 -13/44 -1/5 0/1 -18/61 -1/1 0/1 -5/17 -1/2 -1/4 -12/41 -1/3 0/1 -7/24 -1/5 0/1 -2/7 -1/1 0/1 -11/39 -1/2 -1/4 -9/32 -1/5 0/1 -7/25 -1/2 1/0 -12/43 -1/1 0/1 -5/18 -1/1 0/1 -13/47 -1/2 1/0 -21/76 1/0 -8/29 -1/1 0/1 -11/40 -6/5 -1/1 -14/51 -1/1 -10/11 -3/11 -3/4 -1/2 -10/37 -2/3 -3/5 -7/26 -3/5 -4/7 -4/15 -1/2 -5/19 -1/2 -5/12 -6/23 -2/5 -1/3 -7/27 -3/8 -5/14 -1/4 -1/3 0/1 -6/25 0/1 1/5 -5/21 1/2 1/0 -4/17 -1/1 0/1 -7/30 -1/1 0/1 -10/43 1/0 -3/13 -1/2 1/0 -8/35 -1/1 0/1 -5/22 -1/1 0/1 -12/53 -1/3 0/1 -7/31 1/2 1/0 -2/9 -1/1 -2/3 -7/32 -1/1 -2/3 -12/55 -2/3 -11/17 -5/23 -5/8 -1/2 -3/14 -1/2 -7/33 -1/2 -7/16 -4/19 -3/7 -2/5 -5/24 -1/3 0/1 -1/5 -1/2 -1/4 -4/21 -1/5 0/1 -7/37 -1/6 -1/8 -10/53 -1/5 0/1 -3/16 -1/9 0/1 -2/11 0/1 1/3 -7/39 1/2 1/0 -5/28 -1/1 0/1 -8/45 0/1 1/1 -11/62 0/1 1/1 -3/17 1/2 1/0 -1/6 -1/1 0/1 -4/25 -1/1 -4/5 -3/19 -3/4 -1/2 -2/13 -1/2 -5/33 -1/2 -5/12 -3/20 -2/5 -1/3 -1/7 -1/2 -1/4 -4/29 -1/3 0/1 -3/22 -1/3 0/1 -2/15 -1/3 -2/7 -1/8 -1/7 0/1 -2/17 0/1 1/9 -1/9 1/2 1/0 0/1 -1/1 0/1 1/8 -1/1 0/1 2/15 -1/1 0/1 1/7 -1/2 -1/4 1/6 0/1 1/5 2/11 2/3 1/1 1/5 1/2 1/0 6/29 0/1 1/3 5/24 4/5 1/1 4/19 1/1 2/1 3/14 1/1 2/1 2/9 1/0 5/22 -3/1 -2/1 8/35 -2/1 -5/3 3/13 -3/2 1/0 1/4 -1/1 0/1 5/19 -3/2 1/0 4/15 -1/1 -2/3 7/26 -1/2 3/11 -1/2 -1/4 5/18 -1/1 0/1 7/25 -1/2 -1/4 2/7 -1/5 0/1 5/17 0/1 8/27 0/1 1/19 3/10 0/1 1/7 4/13 0/1 1/3 5/16 0/1 1/3 6/19 0/1 1/1 1/3 1/2 1/0 7/20 1/1 2/1 6/17 1/1 2/1 5/14 0/1 1/1 14/39 1/1 2/1 9/25 3/2 1/0 13/36 1/1 2/1 4/11 2/1 3/1 3/8 1/0 8/21 -4/1 -3/1 21/55 -7/2 1/0 34/89 -4/1 -11/3 47/123 -7/2 1/0 13/34 -4/1 -3/1 31/81 -13/4 -19/6 18/47 -3/1 -14/5 5/13 -5/2 1/0 2/5 -2/1 -1/1 7/17 -1/2 -1/4 5/12 -1/1 0/1 3/7 -1/2 1/0 4/9 -1/1 0/1 9/20 -1/3 0/1 14/31 -1/5 0/1 5/11 -1/2 -1/4 1/2 0/1 1/1 6/11 1/1 2/1 11/20 2/1 7/3 5/9 5/2 1/0 4/7 1/0 11/19 -11/2 1/0 18/31 -5/1 -4/1 25/43 -9/2 -17/4 32/55 -4/1 -27/7 7/12 -4/1 -3/1 24/41 -3/1 -2/1 17/29 -5/2 1/0 10/17 -3/1 -2/1 23/39 -5/2 1/0 13/22 -3/1 -2/1 16/27 -3/1 -2/1 3/5 -3/2 1/0 11/18 -1/1 -6/7 19/31 -3/4 -1/2 8/13 -1/1 0/1 5/8 -1/1 0/1 7/11 -1/2 1/0 16/25 -1/3 0/1 9/14 0/1 1/3 2/3 -1/1 0/1 9/13 0/1 16/23 0/1 1/7 7/10 0/1 1/3 26/37 0/1 1/1 45/64 0/1 1/3 19/27 1/4 1/2 12/17 0/1 1/1 17/24 0/1 1/1 22/31 -1/1 0/1 5/7 1/2 1/0 28/39 1/1 2/1 23/32 1/0 18/25 -1/1 0/1 49/68 0/1 1/1 31/43 1/2 1/0 13/18 0/1 1/3 8/11 0/1 1/1 3/4 0/1 1/1 10/13 2/3 1/1 7/9 1/2 1/0 11/14 1/1 4/3 26/33 5/3 2/1 15/19 3/2 1/0 4/5 1/1 2/1 21/26 2/1 3/1 17/21 5/2 1/0 13/16 3/1 10/3 9/11 9/2 1/0 5/6 1/0 11/13 -11/2 1/0 17/20 -13/3 -4/1 6/7 -3/1 -2/1 13/15 -3/2 1/0 20/23 -2/1 -5/3 27/31 -3/2 1/0 7/8 -2/1 -1/1 8/9 -1/1 0/1 1/1 -1/2 1/0 8/7 0/1 1/1 15/13 1/2 1/0 7/6 1/1 2/1 6/5 1/0 17/14 -9/1 -8/1 28/23 -7/1 -20/3 11/9 -11/2 1/0 27/22 -5/1 -4/1 43/35 -9/2 1/0 16/13 -13/3 -4/1 5/4 -3/1 -2/1 24/19 -3/1 -2/1 43/34 1/0 19/15 -5/2 1/0 33/26 -3/1 -8/3 14/11 -7/3 -2/1 37/29 -2/1 60/47 -2/1 -25/13 23/18 -2/1 -9/5 9/7 -3/2 1/0 13/10 -2/1 -5/3 17/13 -3/2 1/0 4/3 -2/1 -1/1 15/11 -5/2 1/0 41/30 -3/1 -2/1 67/49 -5/2 -9/4 26/19 -11/5 -2/1 11/8 -2/1 -1/1 29/21 -3/2 1/0 18/13 -4/3 -1/1 25/18 -1/1 0/1 32/23 1/0 39/28 -3/1 -2/1 7/5 -3/2 1/0 24/17 -2/1 -1/1 41/29 -7/4 -3/2 17/12 -2/1 -1/1 44/31 -2/1 -5/3 27/19 -3/2 -5/4 37/26 -2/1 -1/1 10/7 -4/3 -1/1 13/9 -1/1 16/11 -1/1 -4/5 3/2 -1/1 0/1 17/11 -3/2 1/0 14/9 -4/3 -1/1 25/16 -1/1 -2/3 36/23 -1/1 -2/3 11/7 -1/2 1/0 19/12 -1/1 0/1 27/17 -1/2 1/0 35/22 -1/1 0/1 8/5 -1/1 0/1 21/13 -1/2 1/0 55/34 -1/1 0/1 34/21 -1/2 81/50 -2/5 -1/3 47/29 -1/2 -1/4 13/8 -1/1 0/1 44/27 -1/1 0/1 31/19 -1/2 -1/4 49/30 -1/3 -2/7 18/11 -1/7 0/1 41/25 0/1 64/39 0/1 1/25 23/14 0/1 1/9 5/3 1/2 1/0 27/16 1/1 2/1 49/29 3/2 1/0 22/13 1/1 2/1 83/49 3/2 1/0 61/36 1/1 2/1 39/23 3/2 1/0 56/33 2/1 7/3 17/10 1/1 2/1 46/27 2/1 3/1 29/17 3/2 1/0 12/7 2/1 3/1 7/4 1/0 16/9 -6/1 -5/1 57/32 -36/7 -5/1 98/55 -5/1 -64/13 41/23 -19/4 -9/2 66/37 -4/1 -3/1 25/14 -5/1 -4/1 9/5 -7/2 1/0 11/6 -3/1 -2/1 13/7 -5/2 -9/4 15/8 -2/1 -13/7 2/1 -2/1 -1/1 15/7 -1/1 28/13 -1/1 -14/15 13/6 -1/1 -6/7 11/5 -3/4 -1/2 31/14 -1/1 -4/5 20/9 -1/1 -2/3 29/13 -5/8 -1/2 9/4 -1/1 0/1 16/7 -1/1 0/1 23/10 -1/2 30/13 -1/1 0/1 7/3 -1/2 1/0 19/8 -1/1 0/1 31/13 -1/2 1/0 43/18 -1/1 0/1 12/5 -1/1 0/1 29/12 -2/1 -1/1 46/19 -8/7 -1/1 17/7 -3/4 -1/2 39/16 -1/2 22/9 -2/5 -1/3 5/2 0/1 1/1 18/7 0/1 1/1 49/19 3/4 5/6 80/31 14/15 1/1 111/43 1/1 142/55 1/1 26/25 31/12 1/1 6/5 75/29 5/4 3/2 44/17 1/1 2/1 57/22 1/1 2/1 13/5 3/2 1/0 8/3 1/0 19/7 -9/2 1/0 49/18 -21/5 -4/1 128/47 -4/1 -59/15 79/29 -23/6 -15/4 30/11 -4/1 -3/1 71/26 -10/3 -3/1 41/15 -7/2 1/0 11/4 -4/1 -3/1 47/17 -5/2 -9/4 36/13 -3/1 -2/1 97/35 -5/2 1/0 61/22 -3/1 -2/1 25/9 -5/2 1/0 64/23 -3/1 -2/1 39/14 -3/1 -2/1 14/5 -2/1 -1/1 31/11 -5/2 1/0 48/17 -3/1 -2/1 65/23 -5/2 1/0 17/6 -3/1 -2/1 3/1 -3/2 1/0 19/6 -2/1 -1/1 35/11 -3/2 -5/4 51/16 -4/3 -1/1 67/21 -3/2 -5/4 16/5 -4/3 -1/1 29/9 -3/2 1/0 13/4 -4/3 -1/1 23/7 -5/4 -7/6 79/24 -6/5 -1/1 135/41 -5/4 -7/6 56/17 -6/5 -1/1 33/10 -4/3 -1/1 10/3 -8/7 -1/1 17/5 -1/1 24/7 -1/1 -16/17 7/2 -1/1 -4/5 39/11 -3/4 -1/2 71/20 -1/1 -2/3 103/29 -3/4 -1/2 32/9 -1/1 -2/3 25/7 -3/4 -1/2 68/19 -2/3 -3/5 43/12 -1/2 18/5 -1/1 0/1 29/8 -1/1 -2/3 69/19 -3/4 -1/2 109/30 -1/1 -2/3 40/11 -1/1 -2/3 11/3 -3/4 -1/2 26/7 -1/2 15/4 -1/3 0/1 34/9 -1/9 0/1 87/23 0/1 140/37 0/1 1/31 53/14 0/1 1/11 19/5 1/2 1/0 23/6 -1/1 -2/3 27/7 -1/2 1/0 31/8 -1/1 0/1 35/9 -1/2 1/0 4/1 -1/1 0/1 17/4 0/1 1/3 13/3 1/2 1/0 9/2 1/0 23/5 -7/2 1/0 60/13 -4/1 -3/1 217/47 -7/2 1/0 157/34 -4/1 -3/1 97/21 -7/2 1/0 37/8 -10/3 -3/1 51/11 -5/2 1/0 14/3 -3/1 -2/1 33/7 -3/2 1/0 19/4 -3/1 -2/1 24/5 -2/1 -9/5 29/6 -4/3 -1/1 34/7 -2/1 -1/1 73/15 -3/2 1/0 39/8 -2/1 -1/1 5/1 -3/2 1/0 21/4 -2/1 -1/1 37/7 -3/2 1/0 53/10 -2/1 -1/1 16/3 -2/1 -1/1 11/2 -2/1 -5/3 28/5 -3/2 17/3 -3/2 -11/8 6/1 -6/5 -1/1 19/3 -1/1 32/5 -1/1 -26/27 13/2 -1/1 -10/11 7/1 -3/4 -1/2 15/2 -1/1 0/1 23/3 -1/2 1/0 31/4 -1/1 0/1 39/5 -1/2 1/0 8/1 -1/1 0/1 9/1 -1/2 1/0 10/1 1/0 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(415,194,246,115) (-1/2,-7/15) -> (5/3,27/16) Hyperbolic Matrix(249,116,-908,-423) (-7/15,-6/13) -> (-14/51,-3/11) Hyperbolic Matrix(893,410,734,337) (-6/13,-11/24) -> (17/14,28/23) Hyperbolic Matrix(647,296,-2188,-1001) (-11/24,-5/11) -> (-21/71,-13/44) Hyperbolic Matrix(1445,654,886,401) (-5/11,-14/31) -> (44/27,31/19) Hyperbolic Matrix(719,324,-1600,-721) (-14/31,-9/20) -> (-9/20,-22/49) Parabolic Matrix(4951,2222,1914,859) (-22/49,-13/29) -> (75/29,44/17) Hyperbolic Matrix(157,70,-554,-247) (-13/29,-4/9) -> (-2/7,-11/39) Hyperbolic Matrix(549,242,946,417) (-4/9,-11/25) -> (11/19,18/31) Hyperbolic Matrix(783,344,-2588,-1137) (-11/25,-18/41) -> (-10/33,-13/43) Hyperbolic Matrix(1801,790,2510,1101) (-18/41,-25/57) -> (5/7,28/39) Hyperbolic Matrix(4703,2062,1722,755) (-25/57,-7/16) -> (71/26,41/15) Hyperbolic Matrix(545,238,158,69) (-7/16,-10/23) -> (24/7,7/2) Hyperbolic Matrix(853,370,-2174,-943) (-10/23,-13/30) -> (-11/28,-20/51) Hyperbolic Matrix(79,34,230,99) (-13/30,-3/7) -> (1/3,7/20) Hyperbolic Matrix(75,32,232,99) (-3/7,-14/33) -> (6/19,1/3) Hyperbolic Matrix(1453,616,1144,485) (-14/33,-11/26) -> (33/26,14/11) Hyperbolic Matrix(607,256,-1444,-609) (-11/26,-8/19) -> (-8/19,-21/50) Parabolic Matrix(2577,1082,1822,765) (-21/50,-13/31) -> (41/29,17/12) Hyperbolic Matrix(225,94,-754,-315) (-13/31,-5/12) -> (-3/10,-11/37) Hyperbolic Matrix(829,344,976,405) (-5/12,-17/41) -> (11/13,17/20) Hyperbolic Matrix(449,186,-1726,-715) (-17/41,-12/29) -> (-6/23,-7/27) Hyperbolic Matrix(223,92,-972,-401) (-12/29,-7/17) -> (-3/13,-8/35) Hyperbolic Matrix(371,152,-1340,-549) (-7/17,-9/22) -> (-5/18,-13/47) Hyperbolic Matrix(519,212,448,183) (-9/22,-11/27) -> (15/13,7/6) Hyperbolic Matrix(521,212,-1708,-695) (-11/27,-2/5) -> (-18/59,-7/23) Hyperbolic Matrix(361,142,-1594,-627) (-2/5,-11/28) -> (-5/22,-12/53) Hyperbolic Matrix(2607,1022,-7094,-2781) (-20/51,-9/23) -> (-43/117,-18/49) Hyperbolic Matrix(215,84,796,311) (-9/23,-7/18) -> (7/26,3/11) Hyperbolic Matrix(289,112,1076,417) (-7/18,-12/31) -> (4/15,7/26) Hyperbolic Matrix(1361,526,1938,749) (-12/31,-17/44) -> (7/10,26/37) Hyperbolic Matrix(503,194,70,27) (-17/44,-5/13) -> (7/1,15/2) Hyperbolic Matrix(73,28,-644,-247) (-5/13,-18/47) -> (-2/17,-1/9) Hyperbolic Matrix(1709,654,358,137) (-18/47,-13/34) -> (19/4,24/5) Hyperbolic Matrix(283,108,-1208,-461) (-13/34,-8/21) -> (-4/17,-7/30) Hyperbolic Matrix(495,188,-1772,-673) (-8/21,-11/29) -> (-7/25,-12/43) Hyperbolic Matrix(707,268,1844,699) (-11/29,-14/37) -> (18/47,5/13) Hyperbolic Matrix(69,26,-422,-159) (-14/37,-3/8) -> (-1/6,-4/25) Hyperbolic Matrix(209,78,142,53) (-3/8,-10/27) -> (16/11,3/2) Hyperbolic Matrix(557,206,630,233) (-10/27,-17/46) -> (7/8,8/9) Hyperbolic Matrix(2095,774,766,283) (-17/46,-7/19) -> (41/15,11/4) Hyperbolic Matrix(4735,1742,2922,1075) (-7/19,-25/68) -> (81/50,47/29) Hyperbolic Matrix(10925,4016,2364,869) (-25/68,-43/117) -> (97/21,37/8) Hyperbolic Matrix(207,76,-1528,-561) (-18/49,-11/30) -> (-3/22,-2/15) Hyperbolic Matrix(137,50,-622,-227) (-11/30,-4/11) -> (-2/9,-7/32) Hyperbolic Matrix(343,124,-1928,-697) (-4/11,-13/36) -> (-5/28,-8/45) Hyperbolic Matrix(621,224,-2204,-795) (-13/36,-9/25) -> (-11/39,-9/32) Hyperbolic Matrix(345,124,-1444,-519) (-9/25,-14/39) -> (-6/25,-5/21) Hyperbolic Matrix(1717,616,616,221) (-14/39,-5/14) -> (39/14,14/5) Hyperbolic Matrix(1641,584,340,121) (-5/14,-16/45) -> (24/5,29/6) Hyperbolic Matrix(3891,1382,2182,775) (-16/45,-11/31) -> (41/23,66/37) Hyperbolic Matrix(1157,410,206,73) (-11/31,-6/17) -> (28/5,17/3) Hyperbolic Matrix(747,262,134,47) (-6/17,-7/20) -> (11/2,28/5) Hyperbolic Matrix(607,212,272,95) (-7/20,-1/3) -> (29/13,9/4) Hyperbolic Matrix(645,206,454,145) (-1/3,-6/19) -> (44/31,27/19) Hyperbolic Matrix(1093,344,448,141) (-6/19,-5/16) -> (39/16,22/9) Hyperbolic Matrix(1403,436,576,179) (-5/16,-9/29) -> (17/7,39/16) Hyperbolic Matrix(2293,710,830,257) (-9/29,-13/42) -> (11/4,47/17) Hyperbolic Matrix(317,98,1530,473) (-13/42,-4/13) -> (6/29,5/24) Hyperbolic Matrix(569,174,1586,485) (-4/13,-11/36) -> (5/14,14/39) Hyperbolic Matrix(1775,542,822,251) (-11/36,-18/59) -> (28/13,13/6) Hyperbolic Matrix(191,58,-1202,-365) (-7/23,-10/33) -> (-4/25,-3/19) Hyperbolic Matrix(503,152,-2836,-857) (-13/43,-3/10) -> (-11/62,-3/17) Hyperbolic Matrix(4633,1376,1000,297) (-11/37,-19/64) -> (37/8,51/11) Hyperbolic Matrix(2563,760,1440,427) (-19/64,-8/27) -> (16/9,57/32) Hyperbolic Matrix(311,92,-2248,-665) (-8/27,-21/71) -> (-1/7,-4/29) Hyperbolic Matrix(623,184,-3308,-977) (-13/44,-18/61) -> (-10/53,-3/16) Hyperbolic Matrix(2681,790,750,221) (-18/61,-5/17) -> (25/7,68/19) Hyperbolic Matrix(997,292,2612,765) (-5/17,-12/41) -> (8/21,21/55) Hyperbolic Matrix(1801,526,1058,309) (-12/41,-7/24) -> (17/10,46/27) Hyperbolic Matrix(433,126,622,181) (-7/24,-2/7) -> (16/23,7/10) Hyperbolic Matrix(1833,514,674,189) (-9/32,-7/25) -> (19/7,49/18) Hyperbolic Matrix(1649,460,1036,289) (-12/43,-5/18) -> (35/22,8/5) Hyperbolic Matrix(3465,958,2738,757) (-13/47,-21/76) -> (43/34,19/15) Hyperbolic Matrix(2795,772,3892,1075) (-21/76,-8/29) -> (28/39,23/32) Hyperbolic Matrix(305,84,1456,401) (-8/29,-11/40) -> (5/24,4/19) Hyperbolic Matrix(1943,534,302,83) (-11/40,-14/51) -> (32/5,13/2) Hyperbolic Matrix(59,16,424,115) (-3/11,-10/37) -> (2/15,1/7) Hyperbolic Matrix(1629,440,1144,309) (-10/37,-7/26) -> (37/26,10/7) Hyperbolic Matrix(901,242,242,65) (-7/26,-4/15) -> (26/7,15/4) Hyperbolic Matrix(659,174,178,47) (-4/15,-5/19) -> (11/3,26/7) Hyperbolic Matrix(237,62,-1250,-327) (-5/19,-6/23) -> (-4/21,-7/37) Hyperbolic Matrix(475,122,1242,319) (-7/27,-1/4) -> (13/34,31/81) Hyperbolic Matrix(815,198,638,155) (-1/4,-6/25) -> (60/47,23/18) Hyperbolic Matrix(347,82,402,95) (-5/21,-4/17) -> (6/7,13/15) Hyperbolic Matrix(2637,614,1894,441) (-7/30,-10/43) -> (32/23,39/28) Hyperbolic Matrix(517,120,56,13) (-10/43,-3/13) -> (9/1,10/1) Hyperbolic Matrix(1769,404,740,169) (-8/35,-5/22) -> (43/18,12/5) Hyperbolic Matrix(5117,1158,1878,425) (-12/53,-7/31) -> (79/29,30/11) Hyperbolic Matrix(967,218,794,179) (-7/31,-2/9) -> (28/23,11/9) Hyperbolic Matrix(1409,308,2420,529) (-7/32,-12/55) -> (32/55,7/12) Hyperbolic Matrix(3433,748,2024,441) (-12/55,-5/23) -> (39/23,56/33) Hyperbolic Matrix(167,36,-784,-169) (-5/23,-3/14) -> (-3/14,-7/33) Parabolic Matrix(1397,296,892,189) (-7/33,-4/19) -> (36/23,11/7) Hyperbolic Matrix(833,174,1058,221) (-4/19,-5/24) -> (11/14,26/33) Hyperbolic Matrix(167,34,54,11) (-5/24,-1/5) -> (3/1,19/6) Hyperbolic Matrix(763,146,162,31) (-1/5,-4/21) -> (14/3,33/7) Hyperbolic Matrix(2171,410,2494,471) (-7/37,-10/53) -> (20/23,27/31) Hyperbolic Matrix(161,30,542,101) (-3/16,-2/11) -> (8/27,3/10) Hyperbolic Matrix(1557,280,4076,733) (-2/11,-7/39) -> (21/55,34/89) Hyperbolic Matrix(1717,308,1232,221) (-7/39,-5/28) -> (39/28,7/5) Hyperbolic Matrix(7385,1312,2032,361) (-8/45,-11/62) -> (109/30,40/11) Hyperbolic Matrix(479,84,268,47) (-3/17,-1/6) -> (25/14,9/5) Hyperbolic Matrix(103,16,-676,-105) (-3/19,-2/13) -> (-2/13,-5/33) Parabolic Matrix(2693,406,1970,297) (-5/33,-3/20) -> (41/30,67/49) Hyperbolic Matrix(671,100,208,31) (-3/20,-1/7) -> (29/9,13/4) Hyperbolic Matrix(1889,260,356,49) (-4/29,-3/22) -> (53/10,16/3) Hyperbolic Matrix(303,40,356,47) (-2/15,-1/8) -> (17/20,6/7) Hyperbolic Matrix(903,110,550,67) (-1/8,-2/17) -> (64/39,23/14) Hyperbolic Matrix(147,16,248,27) (-1/9,0/1) -> (16/27,3/5) Hyperbolic Matrix(197,-24,156,-19) (0/1,1/8) -> (5/4,24/19) Hyperbolic Matrix(1207,-158,466,-61) (1/8,2/15) -> (44/17,57/22) Hyperbolic Matrix(191,-28,116,-17) (1/7,1/6) -> (23/14,5/3) Hyperbolic Matrix(187,-32,76,-13) (1/6,2/11) -> (22/9,5/2) Hyperbolic Matrix(409,-76,296,-55) (2/11,1/5) -> (29/21,18/13) Hyperbolic Matrix(1533,-316,4012,-827) (1/5,6/29) -> (34/89,47/123) Hyperbolic Matrix(217,-46,618,-131) (4/19,3/14) -> (7/20,6/17) Hyperbolic Matrix(73,-16,324,-71) (3/14,2/9) -> (2/9,5/22) Parabolic Matrix(1827,-416,1076,-245) (5/22,8/35) -> (56/33,17/10) Hyperbolic Matrix(715,-164,824,-189) (8/35,3/13) -> (13/15,20/23) Hyperbolic Matrix(107,-26,70,-17) (3/13,1/4) -> (3/2,17/11) Hyperbolic Matrix(557,-146,454,-119) (1/4,5/19) -> (11/9,27/22) Hyperbolic Matrix(1077,-286,418,-111) (5/19,4/15) -> (18/7,49/19) Hyperbolic Matrix(449,-124,344,-95) (3/11,5/18) -> (13/10,17/13) Hyperbolic Matrix(1171,-326,722,-201) (5/18,7/25) -> (47/29,13/8) Hyperbolic Matrix(585,-164,824,-231) (7/25,2/7) -> (22/31,5/7) Hyperbolic Matrix(171,-50,578,-169) (2/7,5/17) -> (5/17,8/27) Parabolic Matrix(203,-62,370,-113) (3/10,4/13) -> (6/11,11/20) Hyperbolic Matrix(873,-272,536,-167) (4/13,5/16) -> (13/8,44/27) Hyperbolic Matrix(1271,-400,1808,-569) (5/16,6/19) -> (26/37,45/64) Hyperbolic Matrix(455,-162,778,-277) (6/17,5/14) -> (7/12,24/41) Hyperbolic Matrix(2461,-884,1456,-523) (14/39,9/25) -> (49/29,22/13) Hyperbolic Matrix(2425,-874,874,-315) (9/25,13/36) -> (61/22,25/9) Hyperbolic Matrix(2651,-958,1486,-537) (13/36,4/11) -> (66/37,25/14) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(4967,-1898,1018,-389) (47/123,13/34) -> (39/8,5/1) Hyperbolic Matrix(9865,-3776,5536,-2119) (31/81,18/47) -> (98/55,41/23) Hyperbolic Matrix(127,-50,94,-37) (5/13,2/5) -> (4/3,15/11) Hyperbolic Matrix(187,-76,32,-13) (2/5,7/17) -> (17/3,6/1) Hyperbolic Matrix(343,-142,186,-77) (7/17,5/12) -> (11/6,13/7) Hyperbolic Matrix(217,-92,92,-39) (5/12,3/7) -> (7/3,19/8) Hyperbolic Matrix(245,-108,152,-67) (3/7,4/9) -> (8/5,21/13) Hyperbolic Matrix(1033,-464,728,-327) (4/9,9/20) -> (17/12,44/31) Hyperbolic Matrix(1879,-848,2608,-1177) (9/20,14/31) -> (18/25,49/68) Hyperbolic Matrix(2363,-1068,1728,-781) (14/31,5/11) -> (67/49,26/19) Hyperbolic Matrix(271,-124,212,-97) (5/11,1/2) -> (23/18,9/7) Hyperbolic Matrix(343,-186,142,-77) (1/2,6/11) -> (12/5,29/12) Hyperbolic Matrix(737,-406,1022,-563) (11/20,5/9) -> (31/43,13/18) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(3005,-1746,1086,-631) (18/31,25/43) -> (47/17,36/13) Hyperbolic Matrix(9849,-5728,3616,-2103) (25/43,32/55) -> (128/47,79/29) Hyperbolic Matrix(2663,-1560,944,-553) (24/41,17/29) -> (31/11,48/17) Hyperbolic Matrix(249,-146,278,-163) (17/29,10/17) -> (8/9,1/1) Hyperbolic Matrix(1413,-832,304,-179) (10/17,23/39) -> (51/11,14/3) Hyperbolic Matrix(3237,-1910,1910,-1127) (23/39,13/22) -> (61/36,39/23) Hyperbolic Matrix(2461,-1456,884,-523) (13/22,16/27) -> (64/23,39/14) Hyperbolic Matrix(191,-116,28,-17) (3/5,11/18) -> (13/2,7/1) Hyperbolic Matrix(709,-434,874,-535) (11/18,19/31) -> (17/21,13/16) Hyperbolic Matrix(873,-536,272,-167) (19/31,8/13) -> (16/5,29/9) Hyperbolic Matrix(245,-152,108,-67) (8/13,5/8) -> (9/4,16/7) Hyperbolic Matrix(297,-188,188,-119) (5/8,7/11) -> (11/7,19/12) Hyperbolic Matrix(1289,-824,912,-583) (7/11,16/25) -> (24/17,41/29) Hyperbolic Matrix(403,-258,214,-137) (16/25,9/14) -> (15/8,2/1) Hyperbolic Matrix(107,-70,26,-17) (9/14,2/3) -> (4/1,17/4) Hyperbolic Matrix(235,-162,338,-233) (2/3,9/13) -> (9/13,16/23) Parabolic Matrix(3617,-2544,1136,-799) (45/64,19/27) -> (35/11,51/16) Hyperbolic Matrix(1033,-728,464,-327) (19/27,12/17) -> (20/9,29/13) Hyperbolic Matrix(1289,-912,824,-583) (12/17,17/24) -> (25/16,36/23) Hyperbolic Matrix(747,-530,926,-657) (17/24,22/31) -> (4/5,21/26) Hyperbolic Matrix(1843,-1326,1458,-1049) (23/32,18/25) -> (24/19,43/34) Hyperbolic Matrix(4961,-3576,1508,-1087) (49/68,31/43) -> (23/7,79/24) Hyperbolic Matrix(409,-296,76,-55) (13/18,8/11) -> (16/3,11/2) Hyperbolic Matrix(127,-94,50,-37) (8/11,3/4) -> (5/2,18/7) Hyperbolic Matrix(449,-344,124,-95) (3/4,10/13) -> (18/5,29/8) Hyperbolic Matrix(347,-268,224,-173) (10/13,7/9) -> (17/11,14/9) Hyperbolic Matrix(271,-212,124,-97) (7/9,11/14) -> (13/6,11/5) Hyperbolic Matrix(1723,-1358,1402,-1105) (26/33,15/19) -> (43/35,16/13) Hyperbolic Matrix(197,-156,24,-19) (15/19,4/5) -> (8/1,9/1) Hyperbolic Matrix(2505,-2026,706,-571) (21/26,17/21) -> (39/11,71/20) Hyperbolic Matrix(557,-454,146,-119) (13/16,9/11) -> (19/5,23/6) Hyperbolic Matrix(121,-100,144,-119) (9/11,5/6) -> (5/6,11/13) Parabolic Matrix(5643,-4918,1222,-1065) (27/31,7/8) -> (157/34,97/21) Hyperbolic Matrix(249,-278,146,-163) (1/1,8/7) -> (46/27,29/17) Hyperbolic Matrix(941,-1084,204,-235) (8/7,15/13) -> (23/5,60/13) Hyperbolic Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(1679,-2062,434,-533) (27/22,43/35) -> (27/7,31/8) Hyperbolic Matrix(709,-874,434,-535) (16/13,5/4) -> (49/30,18/11) Hyperbolic Matrix(1047,-1328,272,-345) (19/15,33/26) -> (23/6,27/7) Hyperbolic Matrix(2147,-2738,1682,-2145) (14/11,37/29) -> (37/29,60/47) Parabolic Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(553,-724,152,-199) (17/13,4/3) -> (40/11,11/3) Hyperbolic Matrix(855,-1168,112,-153) (15/11,41/30) -> (15/2,23/3) Hyperbolic Matrix(557,-764,148,-203) (26/19,11/8) -> (15/4,34/9) Hyperbolic Matrix(481,-664,92,-127) (11/8,29/21) -> (5/1,21/4) Hyperbolic Matrix(609,-844,184,-255) (18/13,25/18) -> (33/10,10/3) Hyperbolic Matrix(203,-282,18,-25) (25/18,32/23) -> (10/1,1/0) Hyperbolic Matrix(585,-824,164,-231) (7/5,24/17) -> (32/9,25/7) Hyperbolic Matrix(1271,-1808,400,-569) (27/19,37/26) -> (19/6,35/11) Hyperbolic Matrix(235,-338,162,-233) (10/7,13/9) -> (13/9,16/11) Parabolic Matrix(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(919,-1458,578,-917) (19/12,27/17) -> (27/17,35/22) Parabolic Matrix(2017,-3262,1194,-1931) (21/13,55/34) -> (27/16,49/29) Hyperbolic Matrix(2857,-4624,1764,-2855) (55/34,34/21) -> (34/21,81/50) Parabolic Matrix(1303,-2128,368,-601) (31/19,49/30) -> (7/2,39/11) Hyperbolic Matrix(2051,-3362,1250,-2049) (18/11,41/25) -> (41/25,64/39) Parabolic Matrix(899,-1522,114,-193) (22/13,83/49) -> (39/5,8/1) Hyperbolic Matrix(2923,-4952,376,-637) (83/49,61/36) -> (31/4,39/5) Hyperbolic Matrix(455,-778,162,-277) (29/17,12/7) -> (14/5,31/11) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(6249,-11132,2420,-4311) (57/32,98/55) -> (142/55,31/12) Hyperbolic Matrix(203,-370,62,-113) (9/5,11/6) -> (13/4,23/7) Hyperbolic Matrix(523,-974,138,-257) (13/7,15/8) -> (53/14,19/5) Hyperbolic Matrix(211,-450,98,-209) (2/1,15/7) -> (15/7,28/13) Parabolic Matrix(1205,-2666,466,-1031) (11/5,31/14) -> (31/12,75/29) Hyperbolic Matrix(1081,-2396,328,-727) (31/14,20/9) -> (56/17,33/10) Hyperbolic Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(1239,-2854,346,-797) (23/10,30/13) -> (68/19,43/12) Hyperbolic Matrix(517,-1198,186,-431) (30/13,7/3) -> (25/9,64/23) Hyperbolic Matrix(807,-1922,338,-805) (19/8,31/13) -> (31/13,43/18) Parabolic Matrix(1491,-3614,578,-1401) (46/19,17/7) -> (49/19,80/31) Hyperbolic Matrix(9547,-24642,3698,-9545) (80/31,111/43) -> (111/43,142/55) Parabolic Matrix(661,-1714,86,-223) (57/22,13/5) -> (23/3,31/4) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(5011,-13644,1324,-3605) (49/18,128/47) -> (140/37,53/14) Hyperbolic Matrix(1203,-3284,248,-677) (30/11,71/26) -> (29/6,34/7) Hyperbolic Matrix(595,-1648,152,-421) (36/13,97/35) -> (35/9,4/1) Hyperbolic Matrix(1855,-5142,478,-1325) (97/35,61/22) -> (31/8,35/9) Hyperbolic Matrix(1507,-4256,472,-1333) (48/17,65/23) -> (67/21,16/5) Hyperbolic Matrix(1575,-4454,494,-1397) (65/23,17/6) -> (51/16,67/21) Hyperbolic Matrix(217,-618,46,-131) (17/6,3/1) -> (33/7,19/4) Hyperbolic Matrix(11645,-38338,2522,-8303) (79/24,135/41) -> (217/47,157/34) Hyperbolic Matrix(6149,-20252,1332,-4387) (135/41,56/17) -> (60/13,217/47) Hyperbolic Matrix(171,-578,50,-169) (10/3,17/5) -> (17/5,24/7) Parabolic Matrix(2591,-9200,532,-1889) (71/20,103/29) -> (73/15,39/8) Hyperbolic Matrix(1643,-5838,338,-1201) (103/29,32/9) -> (34/7,73/15) Hyperbolic Matrix(2623,-9522,722,-2621) (29/8,69/19) -> (69/19,109/30) Parabolic Matrix(4003,-15138,1058,-4001) (34/9,87/23) -> (87/23,140/37) Parabolic Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(519,-2738,98,-517) (21/4,37/7) -> (37/7,53/10) Parabolic Matrix(115,-722,18,-113) (6/1,19/3) -> (19/3,32/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,0,1) Matrix(415,194,246,115) -> Matrix(1,2,0,1) Matrix(249,116,-908,-423) -> Matrix(3,4,-4,-5) Matrix(893,410,734,337) -> Matrix(29,22,-4,-3) Matrix(647,296,-2188,-1001) -> Matrix(3,2,-8,-5) Matrix(1445,654,886,401) -> Matrix(3,2,-8,-5) Matrix(719,324,-1600,-721) -> Matrix(7,4,-16,-9) Matrix(4951,2222,1914,859) -> Matrix(11,4,8,3) Matrix(157,70,-554,-247) -> Matrix(1,0,0,1) Matrix(549,242,946,417) -> Matrix(1,-4,0,1) Matrix(783,344,-2588,-1137) -> Matrix(1,2,-4,-7) Matrix(1801,790,2510,1101) -> Matrix(1,2,0,1) Matrix(4703,2062,1722,755) -> Matrix(1,-2,0,1) Matrix(545,238,158,69) -> Matrix(7,8,-8,-9) Matrix(853,370,-2174,-943) -> Matrix(17,14,-28,-23) Matrix(79,34,230,99) -> Matrix(3,2,4,3) Matrix(75,32,232,99) -> Matrix(3,2,4,3) Matrix(1453,616,1144,485) -> Matrix(19,12,-8,-5) Matrix(607,256,-1444,-609) -> Matrix(11,6,-24,-13) Matrix(2577,1082,1822,765) -> Matrix(19,8,-12,-5) Matrix(225,94,-754,-315) -> Matrix(1,0,0,1) Matrix(829,344,976,405) -> Matrix(1,-4,0,1) Matrix(449,186,-1726,-715) -> Matrix(3,2,-8,-5) Matrix(223,92,-972,-401) -> Matrix(1,0,0,1) Matrix(371,152,-1340,-549) -> Matrix(1,0,0,1) Matrix(519,212,448,183) -> Matrix(1,2,0,1) Matrix(521,212,-1708,-695) -> Matrix(1,2,-4,-7) Matrix(361,142,-1594,-627) -> Matrix(3,2,-8,-5) Matrix(2607,1022,-7094,-2781) -> Matrix(3,2,-8,-5) Matrix(215,84,796,311) -> Matrix(7,4,-16,-9) Matrix(289,112,1076,417) -> Matrix(9,4,-16,-7) Matrix(1361,526,1938,749) -> Matrix(5,2,12,5) Matrix(503,194,70,27) -> Matrix(5,2,-8,-3) Matrix(73,28,-644,-247) -> Matrix(1,0,4,1) Matrix(1709,654,358,137) -> Matrix(1,-2,0,1) Matrix(283,108,-1208,-461) -> Matrix(1,0,0,1) Matrix(495,188,-1772,-673) -> Matrix(1,0,0,1) Matrix(707,268,1844,699) -> Matrix(1,-2,0,1) Matrix(69,26,-422,-159) -> Matrix(1,0,0,1) Matrix(209,78,142,53) -> Matrix(1,0,0,1) Matrix(557,206,630,233) -> Matrix(5,4,-4,-3) Matrix(2095,774,766,283) -> Matrix(13,10,-4,-3) Matrix(4735,1742,2922,1075) -> Matrix(3,2,-8,-5) Matrix(10925,4016,2364,869) -> Matrix(13,10,-4,-3) Matrix(207,76,-1528,-561) -> Matrix(3,2,-8,-5) Matrix(137,50,-622,-227) -> Matrix(1,0,0,1) Matrix(343,124,-1928,-697) -> Matrix(3,2,4,3) Matrix(621,224,-2204,-795) -> Matrix(3,2,-8,-5) Matrix(345,124,-1444,-519) -> Matrix(3,2,4,3) Matrix(1717,616,616,221) -> Matrix(19,12,-8,-5) Matrix(1641,584,340,121) -> Matrix(17,10,-12,-7) Matrix(3891,1382,2182,775) -> Matrix(71,40,-16,-9) Matrix(1157,410,206,73) -> Matrix(41,22,-28,-15) Matrix(747,262,134,47) -> Matrix(19,8,-12,-5) Matrix(607,212,272,95) -> Matrix(5,2,-8,-3) Matrix(645,206,454,145) -> Matrix(5,4,-4,-3) Matrix(1093,344,448,141) -> Matrix(7,4,-16,-9) Matrix(1403,436,576,179) -> Matrix(13,6,-24,-11) Matrix(2293,710,830,257) -> Matrix(41,18,-16,-7) Matrix(317,98,1530,473) -> Matrix(5,2,12,5) Matrix(569,174,1586,485) -> Matrix(11,4,8,3) Matrix(1775,542,822,251) -> Matrix(29,10,-32,-11) Matrix(191,58,-1202,-365) -> Matrix(5,2,-8,-3) Matrix(503,152,-2836,-857) -> Matrix(1,0,4,1) Matrix(4633,1376,1000,297) -> Matrix(21,8,-8,-3) Matrix(2563,760,1440,427) -> Matrix(23,6,-4,-1) Matrix(311,92,-2248,-665) -> Matrix(1,0,0,1) Matrix(623,184,-3308,-977) -> Matrix(1,0,-4,1) Matrix(2681,790,750,221) -> Matrix(5,2,-8,-3) Matrix(997,292,2612,765) -> Matrix(15,4,-4,-1) Matrix(1801,526,1058,309) -> Matrix(9,2,4,1) Matrix(433,126,622,181) -> Matrix(1,0,8,1) Matrix(1833,514,674,189) -> Matrix(1,-4,0,1) Matrix(1649,460,1036,289) -> Matrix(1,0,0,1) Matrix(3465,958,2738,757) -> Matrix(1,-2,0,1) Matrix(2795,772,3892,1075) -> Matrix(1,2,0,1) Matrix(305,84,1456,401) -> Matrix(1,2,0,1) Matrix(1943,534,302,83) -> Matrix(15,16,-16,-17) Matrix(59,16,424,115) -> Matrix(3,2,-8,-5) Matrix(1629,440,1144,309) -> Matrix(17,10,-12,-7) Matrix(901,242,242,65) -> Matrix(7,4,-16,-9) Matrix(659,174,178,47) -> Matrix(9,4,-16,-7) Matrix(237,62,-1250,-327) -> Matrix(5,2,-28,-11) Matrix(475,122,1242,319) -> Matrix(15,4,-4,-1) Matrix(815,198,638,155) -> Matrix(15,2,-8,-1) Matrix(347,82,402,95) -> Matrix(1,-2,0,1) Matrix(2637,614,1894,441) -> Matrix(1,-2,0,1) Matrix(517,120,56,13) -> Matrix(1,0,0,1) Matrix(1769,404,740,169) -> Matrix(1,0,0,1) Matrix(5117,1158,1878,425) -> Matrix(15,4,-4,-1) Matrix(967,218,794,179) -> Matrix(1,-6,0,1) Matrix(1409,308,2420,529) -> Matrix(13,10,-4,-3) Matrix(3433,748,2024,441) -> Matrix(13,8,8,5) Matrix(167,36,-784,-169) -> Matrix(11,6,-24,-13) Matrix(1397,296,892,189) -> Matrix(9,4,-16,-7) Matrix(833,174,1058,221) -> Matrix(11,4,8,3) Matrix(167,34,54,11) -> Matrix(7,2,-4,-1) Matrix(763,146,162,31) -> Matrix(7,2,-4,-1) Matrix(2171,410,2494,471) -> Matrix(15,2,-8,-1) Matrix(161,30,542,101) -> Matrix(1,0,16,1) Matrix(1557,280,4076,733) -> Matrix(1,-4,0,1) Matrix(1717,308,1232,221) -> Matrix(1,-2,0,1) Matrix(7385,1312,2032,361) -> Matrix(3,-2,-4,3) Matrix(479,84,268,47) -> Matrix(1,-4,0,1) Matrix(103,16,-676,-105) -> Matrix(7,4,-16,-9) Matrix(2693,406,1970,297) -> Matrix(21,8,-8,-3) Matrix(671,100,208,31) -> Matrix(7,2,-4,-1) Matrix(1889,260,356,49) -> Matrix(7,2,-4,-1) Matrix(303,40,356,47) -> Matrix(15,4,-4,-1) Matrix(903,110,550,67) -> Matrix(1,0,16,1) Matrix(147,16,248,27) -> Matrix(1,-2,0,1) Matrix(197,-24,156,-19) -> Matrix(1,-2,0,1) Matrix(1207,-158,466,-61) -> Matrix(1,2,0,1) Matrix(191,-28,116,-17) -> Matrix(1,0,4,1) Matrix(187,-32,76,-13) -> Matrix(1,0,-4,1) Matrix(409,-76,296,-55) -> Matrix(1,-2,0,1) Matrix(1533,-316,4012,-827) -> Matrix(1,-4,0,1) Matrix(217,-46,618,-131) -> Matrix(1,0,0,1) Matrix(73,-16,324,-71) -> Matrix(1,-4,0,1) Matrix(1827,-416,1076,-245) -> Matrix(1,4,0,1) Matrix(715,-164,824,-189) -> Matrix(1,0,0,1) Matrix(107,-26,70,-17) -> Matrix(1,0,0,1) Matrix(557,-146,454,-119) -> Matrix(1,-4,0,1) Matrix(1077,-286,418,-111) -> Matrix(3,2,4,3) Matrix(449,-124,344,-95) -> Matrix(7,2,-4,-1) Matrix(1171,-326,722,-201) -> Matrix(1,0,0,1) Matrix(585,-164,824,-231) -> Matrix(1,0,4,1) Matrix(171,-50,578,-169) -> Matrix(1,0,24,1) Matrix(203,-62,370,-113) -> Matrix(7,-2,4,-1) Matrix(873,-272,536,-167) -> Matrix(1,0,-4,1) Matrix(1271,-400,1808,-569) -> Matrix(1,0,0,1) Matrix(455,-162,778,-277) -> Matrix(1,-4,0,1) Matrix(2461,-884,1456,-523) -> Matrix(1,0,0,1) Matrix(2425,-874,874,-315) -> Matrix(1,-4,0,1) Matrix(2651,-958,1486,-537) -> Matrix(1,-6,0,1) Matrix(97,-36,256,-95) -> Matrix(1,-6,0,1) Matrix(4967,-1898,1018,-389) -> Matrix(1,2,0,1) Matrix(9865,-3776,5536,-2119) -> Matrix(39,122,-8,-25) Matrix(127,-50,94,-37) -> Matrix(1,0,0,1) Matrix(187,-76,32,-13) -> Matrix(5,4,-4,-3) Matrix(343,-142,186,-77) -> Matrix(1,-2,0,1) Matrix(217,-92,92,-39) -> Matrix(1,0,0,1) Matrix(245,-108,152,-67) -> Matrix(1,0,0,1) Matrix(1033,-464,728,-327) -> Matrix(7,2,-4,-1) Matrix(1879,-848,2608,-1177) -> Matrix(1,0,4,1) Matrix(2363,-1068,1728,-781) -> Matrix(1,-2,0,1) Matrix(271,-124,212,-97) -> Matrix(7,2,-4,-1) Matrix(343,-186,142,-77) -> Matrix(1,-2,0,1) Matrix(737,-406,1022,-563) -> Matrix(1,-2,0,1) Matrix(113,-64,196,-111) -> Matrix(1,-8,0,1) Matrix(3005,-1746,1086,-631) -> Matrix(1,2,0,1) Matrix(9849,-5728,3616,-2103) -> Matrix(31,128,-8,-33) Matrix(2663,-1560,944,-553) -> Matrix(1,0,0,1) Matrix(249,-146,278,-163) -> Matrix(1,2,0,1) Matrix(1413,-832,304,-179) -> Matrix(1,0,0,1) Matrix(3237,-1910,1910,-1127) -> Matrix(1,4,0,1) Matrix(2461,-1456,884,-523) -> Matrix(1,0,0,1) Matrix(191,-116,28,-17) -> Matrix(3,4,-4,-5) Matrix(709,-434,874,-535) -> Matrix(11,8,4,3) Matrix(873,-536,272,-167) -> Matrix(5,4,-4,-3) Matrix(245,-152,108,-67) -> Matrix(1,0,0,1) Matrix(297,-188,188,-119) -> Matrix(1,0,0,1) Matrix(1289,-824,912,-583) -> Matrix(7,2,-4,-1) Matrix(403,-258,214,-137) -> Matrix(7,2,-4,-1) Matrix(107,-70,26,-17) -> Matrix(1,0,0,1) Matrix(235,-162,338,-233) -> Matrix(1,0,8,1) Matrix(3617,-2544,1136,-799) -> Matrix(11,-4,-8,3) Matrix(1033,-728,464,-327) -> Matrix(3,-2,-4,3) Matrix(1289,-912,824,-583) -> Matrix(3,-2,-4,3) Matrix(747,-530,926,-657) -> Matrix(1,2,0,1) Matrix(1843,-1326,1458,-1049) -> Matrix(1,-2,0,1) Matrix(4961,-3576,1508,-1087) -> Matrix(5,-6,-4,5) Matrix(409,-296,76,-55) -> Matrix(1,-2,0,1) Matrix(127,-94,50,-37) -> Matrix(1,0,0,1) Matrix(449,-344,124,-95) -> Matrix(3,-2,-4,3) Matrix(347,-268,224,-173) -> Matrix(1,-2,0,1) Matrix(271,-212,124,-97) -> Matrix(3,-2,-4,3) Matrix(1723,-1358,1402,-1105) -> Matrix(1,-6,0,1) Matrix(197,-156,24,-19) -> Matrix(1,-2,0,1) Matrix(2505,-2026,706,-571) -> Matrix(3,-8,-4,11) Matrix(557,-454,146,-119) -> Matrix(1,-4,0,1) Matrix(121,-100,144,-119) -> Matrix(1,-10,0,1) Matrix(5643,-4918,1222,-1065) -> Matrix(1,-2,0,1) Matrix(249,-278,146,-163) -> Matrix(1,2,0,1) Matrix(941,-1084,204,-235) -> Matrix(1,-4,0,1) Matrix(121,-144,100,-119) -> Matrix(1,-10,0,1) Matrix(1679,-2062,434,-533) -> Matrix(1,4,0,1) Matrix(709,-874,434,-535) -> Matrix(1,4,-4,-15) Matrix(1047,-1328,272,-345) -> Matrix(1,2,0,1) Matrix(2147,-2738,1682,-2145) -> Matrix(31,64,-16,-33) Matrix(249,-322,58,-75) -> Matrix(1,2,0,1) Matrix(553,-724,152,-199) -> Matrix(3,4,-4,-5) Matrix(855,-1168,112,-153) -> Matrix(1,2,0,1) Matrix(557,-764,148,-203) -> Matrix(1,2,-4,-7) Matrix(481,-664,92,-127) -> Matrix(1,0,0,1) Matrix(609,-844,184,-255) -> Matrix(5,4,-4,-3) Matrix(203,-282,18,-25) -> Matrix(1,0,0,1) Matrix(585,-824,164,-231) -> Matrix(3,4,-4,-5) Matrix(1271,-1808,400,-569) -> Matrix(1,0,0,1) Matrix(235,-338,162,-233) -> Matrix(7,8,-8,-9) Matrix(997,-1556,412,-643) -> Matrix(5,4,-4,-3) Matrix(919,-1458,578,-917) -> Matrix(1,0,0,1) Matrix(2017,-3262,1194,-1931) -> Matrix(1,2,0,1) Matrix(2857,-4624,1764,-2855) -> Matrix(3,2,-8,-5) Matrix(1303,-2128,368,-601) -> Matrix(5,2,-8,-3) Matrix(2051,-3362,1250,-2049) -> Matrix(1,0,32,1) Matrix(899,-1522,114,-193) -> Matrix(1,-2,0,1) Matrix(2923,-4952,376,-637) -> Matrix(1,-2,0,1) Matrix(455,-778,162,-277) -> Matrix(1,-4,0,1) Matrix(113,-196,64,-111) -> Matrix(1,-8,0,1) Matrix(6249,-11132,2420,-4311) -> Matrix(13,66,12,61) Matrix(203,-370,62,-113) -> Matrix(5,14,-4,-11) Matrix(523,-974,138,-257) -> Matrix(1,2,4,9) Matrix(211,-450,98,-209) -> Matrix(15,16,-16,-17) Matrix(1205,-2666,466,-1031) -> Matrix(1,2,0,1) Matrix(1081,-2396,328,-727) -> Matrix(9,8,-8,-7) Matrix(481,-1102,134,-307) -> Matrix(1,0,0,1) Matrix(1239,-2854,346,-797) -> Matrix(5,2,-8,-3) Matrix(517,-1198,186,-431) -> Matrix(1,-2,0,1) Matrix(807,-1922,338,-805) -> Matrix(1,0,0,1) Matrix(1491,-3614,578,-1401) -> Matrix(7,6,8,7) Matrix(9547,-24642,3698,-9545) -> Matrix(41,-40,40,-39) Matrix(661,-1714,86,-223) -> Matrix(1,-2,0,1) Matrix(97,-256,36,-95) -> Matrix(1,-6,0,1) Matrix(5011,-13644,1324,-3605) -> Matrix(1,4,16,65) Matrix(1203,-3284,248,-677) -> Matrix(1,2,0,1) Matrix(595,-1648,152,-421) -> Matrix(1,2,0,1) Matrix(1855,-5142,478,-1325) -> Matrix(1,2,0,1) Matrix(1507,-4256,472,-1333) -> Matrix(5,14,-4,-11) Matrix(1575,-4454,494,-1397) -> Matrix(5,14,-4,-11) Matrix(217,-618,46,-131) -> Matrix(1,0,0,1) Matrix(11645,-38338,2522,-8303) -> Matrix(11,14,-4,-5) Matrix(6149,-20252,1332,-4387) -> Matrix(11,14,-4,-5) Matrix(171,-578,50,-169) -> Matrix(23,24,-24,-25) Matrix(2591,-9200,532,-1889) -> Matrix(5,4,-4,-3) Matrix(1643,-5838,338,-1201) -> Matrix(5,4,-4,-3) Matrix(2623,-9522,722,-2621) -> Matrix(1,0,0,1) Matrix(4003,-15138,1058,-4001) -> Matrix(1,0,40,1) Matrix(73,-324,16,-71) -> Matrix(1,-4,0,1) Matrix(519,-2738,98,-517) -> Matrix(1,0,0,1) Matrix(115,-722,18,-113) -> Matrix(31,32,-32,-33) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 30 Degree of the the map X: 60 Degree of the the map Y: 240 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 360 Minimal number of generators: 61 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 30 Genus: 16 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/1 6/5 7/5 13/9 27/17 7/4 2/1 15/7 23/10 7/3 31/13 13/5 8/3 3/1 17/5 7/2 69/19 11/3 87/23 4/1 13/3 9/2 5/1 37/7 17/3 6/1 19/3 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 0/1 -1/1 0/1 1/6 0/1 1/5 2/11 2/3 1/1 1/5 1/2 1/0 2/9 1/0 3/13 -3/2 1/0 1/4 -1/1 0/1 3/11 -1/2 -1/4 5/18 -1/1 0/1 2/7 -1/5 0/1 1/3 1/2 1/0 3/8 1/0 5/13 -5/2 1/0 2/5 -2/1 -1/1 7/17 -1/2 -1/4 5/12 -1/1 0/1 3/7 -1/2 1/0 4/9 -1/1 0/1 1/2 0/1 1/1 5/9 5/2 1/0 4/7 1/0 3/5 -3/2 1/0 11/18 -1/1 -6/7 8/13 -1/1 0/1 5/8 -1/1 0/1 7/11 -1/2 1/0 9/14 0/1 1/3 2/3 -1/1 0/1 5/7 1/2 1/0 13/18 0/1 1/3 8/11 0/1 1/1 3/4 0/1 1/1 10/13 2/3 1/1 7/9 1/2 1/0 11/14 1/1 4/3 4/5 1/1 2/1 9/11 9/2 1/0 5/6 1/0 1/1 -1/2 1/0 6/5 1/0 11/9 -11/2 1/0 5/4 -3/1 -2/1 9/7 -3/2 1/0 13/10 -2/1 -5/3 17/13 -3/2 1/0 4/3 -2/1 -1/1 15/11 -5/2 1/0 11/8 -2/1 -1/1 29/21 -3/2 1/0 18/13 -4/3 -1/1 25/18 -1/1 0/1 7/5 -3/2 1/0 10/7 -4/3 -1/1 13/9 -1/1 3/2 -1/1 0/1 17/11 -3/2 1/0 14/9 -4/3 -1/1 25/16 -1/1 -2/3 11/7 -1/2 1/0 19/12 -1/1 0/1 27/17 -1/2 1/0 8/5 -1/1 0/1 21/13 -1/2 1/0 34/21 -1/2 47/29 -1/2 -1/4 13/8 -1/1 0/1 5/3 1/2 1/0 7/4 1/0 9/5 -7/2 1/0 11/6 -3/1 -2/1 13/7 -5/2 -9/4 2/1 -2/1 -1/1 15/7 -1/1 13/6 -1/1 -6/7 11/5 -3/4 -1/2 9/4 -1/1 0/1 16/7 -1/1 0/1 23/10 -1/2 7/3 -1/2 1/0 19/8 -1/1 0/1 31/13 -1/2 1/0 12/5 -1/1 0/1 17/7 -3/4 -1/2 22/9 -2/5 -1/3 5/2 0/1 1/1 18/7 0/1 1/1 49/19 3/4 5/6 31/12 1/1 6/5 13/5 3/2 1/0 8/3 1/0 3/1 -3/2 1/0 10/3 -8/7 -1/1 17/5 -1/1 7/2 -1/1 -4/5 25/7 -3/4 -1/2 43/12 -1/2 18/5 -1/1 0/1 29/8 -1/1 -2/3 69/19 -3/4 -1/2 40/11 -1/1 -2/3 11/3 -3/4 -1/2 15/4 -1/3 0/1 34/9 -1/9 0/1 87/23 0/1 53/14 0/1 1/11 19/5 1/2 1/0 4/1 -1/1 0/1 17/4 0/1 1/3 13/3 1/2 1/0 9/2 1/0 5/1 -3/2 1/0 21/4 -2/1 -1/1 37/7 -3/2 1/0 16/3 -2/1 -1/1 11/2 -2/1 -5/3 17/3 -3/2 -11/8 6/1 -6/5 -1/1 19/3 -1/1 13/2 -1/1 -10/11 7/1 -3/4 -1/2 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(59,-8,96,-13) (0/1,1/6) -> (11/18,8/13) Hyperbolic Matrix(187,-32,76,-13) (1/6,2/11) -> (22/9,5/2) Hyperbolic Matrix(409,-76,296,-55) (2/11,1/5) -> (29/21,18/13) Hyperbolic Matrix(90,-19,19,-4) (1/5,2/9) -> (9/2,5/1) Hyperbolic Matrix(234,-53,53,-12) (2/9,3/13) -> (13/3,9/2) Hyperbolic Matrix(107,-26,70,-17) (3/13,1/4) -> (3/2,17/11) Hyperbolic Matrix(157,-42,86,-23) (1/4,3/11) -> (9/5,11/6) Hyperbolic Matrix(449,-124,344,-95) (3/11,5/18) -> (13/10,17/13) Hyperbolic Matrix(499,-140,360,-101) (5/18,2/7) -> (18/13,25/18) Hyperbolic Matrix(51,-16,16,-5) (2/7,1/3) -> (3/1,10/3) Hyperbolic Matrix(48,-17,17,-6) (1/3,3/8) -> (8/3,3/1) Hyperbolic Matrix(208,-79,79,-30) (3/8,5/13) -> (13/5,8/3) Hyperbolic Matrix(127,-50,94,-37) (5/13,2/5) -> (4/3,15/11) Hyperbolic Matrix(187,-76,32,-13) (2/5,7/17) -> (17/3,6/1) Hyperbolic Matrix(343,-142,186,-77) (7/17,5/12) -> (11/6,13/7) Hyperbolic Matrix(217,-92,92,-39) (5/12,3/7) -> (7/3,19/8) Hyperbolic Matrix(245,-108,152,-67) (3/7,4/9) -> (8/5,21/13) Hyperbolic Matrix(107,-48,136,-61) (4/9,1/2) -> (11/14,4/5) Hyperbolic Matrix(157,-86,42,-23) (1/2,5/9) -> (11/3,15/4) Hyperbolic Matrix(126,-71,71,-40) (5/9,4/7) -> (7/4,9/5) Hyperbolic Matrix(70,-41,41,-24) (4/7,3/5) -> (5/3,7/4) Hyperbolic Matrix(191,-116,28,-17) (3/5,11/18) -> (13/2,7/1) Hyperbolic Matrix(245,-152,108,-67) (8/13,5/8) -> (9/4,16/7) Hyperbolic Matrix(297,-188,188,-119) (5/8,7/11) -> (11/7,19/12) Hyperbolic Matrix(523,-334,202,-129) (7/11,9/14) -> (31/12,13/5) Hyperbolic Matrix(107,-70,26,-17) (9/14,2/3) -> (4/1,17/4) Hyperbolic Matrix(91,-64,64,-45) (2/3,5/7) -> (7/5,10/7) Hyperbolic Matrix(499,-360,140,-101) (5/7,13/18) -> (7/2,25/7) Hyperbolic Matrix(409,-296,76,-55) (13/18,8/11) -> (16/3,11/2) Hyperbolic Matrix(127,-94,50,-37) (8/11,3/4) -> (5/2,18/7) Hyperbolic Matrix(449,-344,124,-95) (3/4,10/13) -> (18/5,29/8) Hyperbolic Matrix(347,-268,224,-173) (10/13,7/9) -> (17/11,14/9) Hyperbolic Matrix(271,-212,124,-97) (7/9,11/14) -> (13/6,11/5) Hyperbolic Matrix(327,-266,134,-109) (4/5,9/11) -> (17/7,22/9) Hyperbolic Matrix(132,-109,109,-90) (9/11,5/6) -> (6/5,11/9) Hyperbolic Matrix(12,-11,11,-10) (5/6,1/1) -> (1/1,6/5) Parabolic Matrix(167,-206,30,-37) (11/9,5/4) -> (11/2,17/3) Hyperbolic Matrix(107,-136,48,-61) (5/4,9/7) -> (11/5,9/4) Hyperbolic Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(553,-724,152,-199) (17/13,4/3) -> (40/11,11/3) Hyperbolic Matrix(363,-496,232,-317) (15/11,11/8) -> (25/16,11/7) Hyperbolic Matrix(481,-664,92,-127) (11/8,29/21) -> (5/1,21/4) Hyperbolic Matrix(911,-1266,562,-781) (25/18,7/5) -> (47/29,13/8) Hyperbolic Matrix(118,-169,81,-116) (10/7,13/9) -> (13/9,3/2) Parabolic Matrix(679,-1060,180,-281) (14/9,25/16) -> (15/4,34/9) Hyperbolic Matrix(460,-729,289,-458) (19/12,27/17) -> (27/17,8/5) Parabolic Matrix(446,-721,193,-312) (21/13,34/21) -> (23/10,7/3) Hyperbolic Matrix(1772,-2871,495,-802) (34/21,47/29) -> (25/7,43/12) Hyperbolic Matrix(59,-96,8,-13) (13/8,5/3) -> (7/1,1/0) Hyperbolic Matrix(175,-332,68,-129) (13/7,2/1) -> (18/7,49/19) Hyperbolic Matrix(106,-225,49,-104) (2/1,15/7) -> (15/7,13/6) Parabolic Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(404,-961,169,-402) (19/8,31/13) -> (31/13,12/5) Parabolic Matrix(123,-296,32,-77) (12/5,17/7) -> (19/5,4/1) Hyperbolic Matrix(1235,-3186,326,-841) (49/19,31/12) -> (53/14,19/5) Hyperbolic Matrix(86,-289,25,-84) (10/3,17/5) -> (17/5,7/2) Parabolic Matrix(1312,-4761,361,-1310) (29/8,69/19) -> (69/19,40/11) Parabolic Matrix(2002,-7569,529,-2000) (34/9,87/23) -> (87/23,53/14) Parabolic Matrix(260,-1369,49,-258) (21/4,37/7) -> (37/7,16/3) Parabolic Matrix(58,-361,9,-56) (6/1,19/3) -> (19/3,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,1,-2,-1) Matrix(59,-8,96,-13) -> Matrix(1,1,-2,-1) Matrix(187,-32,76,-13) -> Matrix(1,0,-4,1) Matrix(409,-76,296,-55) -> Matrix(1,-2,0,1) Matrix(90,-19,19,-4) -> Matrix(1,-2,0,1) Matrix(234,-53,53,-12) -> Matrix(1,2,0,1) Matrix(107,-26,70,-17) -> Matrix(1,0,0,1) Matrix(157,-42,86,-23) -> Matrix(5,3,-2,-1) Matrix(449,-124,344,-95) -> Matrix(7,2,-4,-1) Matrix(499,-140,360,-101) -> Matrix(1,1,-2,-1) Matrix(51,-16,16,-5) -> Matrix(3,-1,-2,1) Matrix(48,-17,17,-6) -> Matrix(1,-2,0,1) Matrix(208,-79,79,-30) -> Matrix(1,4,0,1) Matrix(127,-50,94,-37) -> Matrix(1,0,0,1) Matrix(187,-76,32,-13) -> Matrix(5,4,-4,-3) Matrix(343,-142,186,-77) -> Matrix(1,-2,0,1) Matrix(217,-92,92,-39) -> Matrix(1,0,0,1) Matrix(245,-108,152,-67) -> Matrix(1,0,0,1) Matrix(107,-48,136,-61) -> Matrix(3,1,2,1) Matrix(157,-86,42,-23) -> Matrix(1,-1,-2,3) Matrix(126,-71,71,-40) -> Matrix(1,-6,0,1) Matrix(70,-41,41,-24) -> Matrix(1,2,0,1) Matrix(191,-116,28,-17) -> Matrix(3,4,-4,-5) Matrix(245,-152,108,-67) -> Matrix(1,0,0,1) Matrix(297,-188,188,-119) -> Matrix(1,0,0,1) Matrix(523,-334,202,-129) -> Matrix(3,1,2,1) Matrix(107,-70,26,-17) -> Matrix(1,0,0,1) Matrix(91,-64,64,-45) -> Matrix(3,-1,-2,1) Matrix(499,-360,140,-101) -> Matrix(1,1,-2,-1) Matrix(409,-296,76,-55) -> Matrix(1,-2,0,1) Matrix(127,-94,50,-37) -> Matrix(1,0,0,1) Matrix(449,-344,124,-95) -> Matrix(3,-2,-4,3) Matrix(347,-268,224,-173) -> Matrix(1,-2,0,1) Matrix(271,-212,124,-97) -> Matrix(3,-2,-4,3) Matrix(327,-266,134,-109) -> Matrix(1,-3,-2,7) Matrix(132,-109,109,-90) -> Matrix(1,-10,0,1) Matrix(12,-11,11,-10) -> Matrix(1,0,0,1) Matrix(167,-206,30,-37) -> Matrix(3,11,-2,-7) Matrix(107,-136,48,-61) -> Matrix(1,3,-2,-5) Matrix(249,-322,58,-75) -> Matrix(1,2,0,1) Matrix(553,-724,152,-199) -> Matrix(3,4,-4,-5) Matrix(363,-496,232,-317) -> Matrix(1,3,-2,-5) Matrix(481,-664,92,-127) -> Matrix(1,0,0,1) Matrix(911,-1266,562,-781) -> Matrix(1,1,-2,-1) Matrix(118,-169,81,-116) -> Matrix(3,4,-4,-5) Matrix(679,-1060,180,-281) -> Matrix(1,1,-6,-5) Matrix(460,-729,289,-458) -> Matrix(1,1,-2,-1) Matrix(446,-721,193,-312) -> Matrix(1,0,0,1) Matrix(1772,-2871,495,-802) -> Matrix(5,2,-8,-3) Matrix(59,-96,8,-13) -> Matrix(1,1,-2,-1) Matrix(175,-332,68,-129) -> Matrix(1,1,2,3) Matrix(106,-225,49,-104) -> Matrix(7,8,-8,-9) Matrix(481,-1102,134,-307) -> Matrix(1,0,0,1) Matrix(404,-961,169,-402) -> Matrix(1,1,-2,-1) Matrix(123,-296,32,-77) -> Matrix(1,1,-2,-1) Matrix(1235,-3186,326,-841) -> Matrix(1,-1,6,-5) Matrix(86,-289,25,-84) -> Matrix(11,12,-12,-13) Matrix(1312,-4761,361,-1310) -> Matrix(7,5,-10,-7) Matrix(2002,-7569,529,-2000) -> Matrix(1,0,20,1) Matrix(260,-1369,49,-258) -> Matrix(3,5,-2,-3) Matrix(58,-361,9,-56) -> Matrix(15,16,-16,-17) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 3 Number of equivalence classes of elliptic points of order 2: 2 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 15 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 (-1/1,0/1).(-1/2,1/0) 0 1 1/1 (-1/2,1/0) 0 11 6/5 1/0 5 2 11/9 (-6/1,-5/1).(-11/2,1/0) 0 11 5/4 (-3/1,-2/1) 0 22 9/7 (-2/1,-1/1).(-3/2,1/0) 0 11 13/10 (-2/1,-5/3) 0 22 4/3 (-2/1,-1/1) 0 22 11/8 (-2/1,-1/1) 0 22 18/13 (-4/3,-1/1) 0 22 7/5 (-2/1,-1/1).(-3/2,1/0) 0 11 13/9 -1/1 4 1 3/2 (-1/1,0/1) 0 22 14/9 (-4/3,-1/1) 0 22 11/7 (-1/2,1/0) 0 11 27/17 (-1/1,0/1).(-1/2,1/0) 0 1 8/5 (-1/1,0/1) 0 22 13/8 (-1/1,0/1) 0 22 5/3 (0/1,1/1).(1/2,1/0) 0 11 7/4 1/0 4 2 9/5 (-7/2,1/0) 0 11 2/1 (-2/1,-1/1) 0 22 15/7 -1/1 8 1 11/5 (-1/1,-2/3).(-3/4,-1/2) 0 11 9/4 (-1/1,0/1) 0 22 16/7 (-1/1,0/1) 0 22 23/10 -1/2 1 2 7/3 (-1/2,1/0) 0 11 31/13 (-1/1,0/1).(-1/2,1/0) 0 1 12/5 (-1/1,0/1) 0 22 17/7 (-1/1,-2/3).(-3/4,-1/2) 0 11 5/2 (0/1,1/1) 0 22 18/7 (0/1,1/1) 0 22 31/12 (1/1,6/5) 0 22 13/5 (3/2,1/0) 0 11 8/3 1/0 3 2 3/1 (-2/1,-1/1).(-3/2,1/0) 0 11 17/5 -1/1 12 1 7/2 (-1/1,-4/5) 0 22 25/7 (-1/1,-2/3).(-3/4,-1/2) 0 11 43/12 -1/2 1 2 18/5 (-1/1,0/1) 0 22 29/8 (-1/1,-2/3) 0 22 69/19 (-1/1,-2/3).(-3/4,-1/2) 0 1 11/3 (-3/4,-1/2) 0 11 15/4 (-1/3,0/1) 0 22 34/9 (-1/9,0/1) 0 22 87/23 0/1 20 1 19/5 (0/1,1/1).(1/2,1/0) 0 11 4/1 (-1/1,0/1) 0 22 17/4 (0/1,1/3) 0 22 13/3 (0/1,1/1).(1/2,1/0) 0 11 9/2 1/0 2 2 5/1 (-3/2,1/0) 0 11 37/7 (-2/1,-1/1).(-3/2,1/0) 0 1 16/3 (-2/1,-1/1) 0 22 11/2 (-2/1,-5/3) 0 22 17/3 (-3/2,-11/8).(-7/5,-4/3) 0 11 6/1 (-6/5,-1/1) 0 22 19/3 -1/1 16 1 7/1 (-1/1,-2/3).(-3/4,-1/2) 0 11 1/0 (-1/1,0/1) 0 22 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(11,-12,10,-11) (1/1,6/5) -> (1/1,6/5) Reflection Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(167,-206,30,-37) (11/9,5/4) -> (11/2,17/3) Hyperbolic Matrix(107,-136,48,-61) (5/4,9/7) -> (11/5,9/4) Hyperbolic Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(344,-449,95,-124) (13/10,4/3) -> (18/5,29/8) Glide Reflection Matrix(94,-127,37,-50) (4/3,11/8) -> (5/2,18/7) Glide Reflection Matrix(296,-409,55,-76) (11/8,18/13) -> (16/3,11/2) Glide Reflection Matrix(360,-499,101,-140) (18/13,7/5) -> (7/2,25/7) Glide Reflection Matrix(64,-91,45,-64) (7/5,13/9) -> (7/5,13/9) Reflection Matrix(53,-78,36,-53) (13/9,3/2) -> (13/9,3/2) Reflection Matrix(70,-107,17,-26) (3/2,14/9) -> (4/1,17/4) Glide Reflection Matrix(334,-523,129,-202) (14/9,11/7) -> (31/12,13/5) Glide Reflection Matrix(188,-297,119,-188) (11/7,27/17) -> (11/7,27/17) Reflection Matrix(271,-432,170,-271) (27/17,8/5) -> (27/17,8/5) Reflection Matrix(152,-245,67,-108) (8/5,13/8) -> (9/4,16/7) Glide Reflection Matrix(59,-96,8,-13) (13/8,5/3) -> (7/1,1/0) Hyperbolic Matrix(41,-70,24,-41) (5/3,7/4) -> (5/3,7/4) Reflection Matrix(71,-126,40,-71) (7/4,9/5) -> (7/4,9/5) Reflection Matrix(86,-157,23,-42) (9/5,2/1) -> (11/3,15/4) Glide Reflection Matrix(29,-60,14,-29) (2/1,15/7) -> (2/1,15/7) Reflection Matrix(76,-165,35,-76) (15/7,11/5) -> (15/7,11/5) Reflection Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(139,-322,60,-139) (23/10,7/3) -> (23/10,7/3) Reflection Matrix(92,-217,39,-92) (7/3,31/13) -> (7/3,31/13) Reflection Matrix(311,-744,130,-311) (31/13,12/5) -> (31/13,12/5) Reflection Matrix(123,-296,32,-77) (12/5,17/7) -> (19/5,4/1) Hyperbolic Matrix(76,-187,13,-32) (17/7,5/2) -> (17/3,6/1) Glide Reflection Matrix(418,-1077,111,-286) (18/7,31/12) -> (15/4,34/9) Glide Reflection Matrix(79,-208,30,-79) (13/5,8/3) -> (13/5,8/3) Reflection Matrix(17,-48,6,-17) (8/3,3/1) -> (8/3,3/1) Reflection Matrix(16,-51,5,-16) (3/1,17/5) -> (3/1,17/5) Reflection Matrix(69,-238,20,-69) (17/5,7/2) -> (17/5,7/2) Reflection Matrix(601,-2150,168,-601) (25/7,43/12) -> (25/7,43/12) Reflection Matrix(1103,-4002,304,-1103) (29/8,69/19) -> (29/8,69/19) Reflection Matrix(208,-759,57,-208) (69/19,11/3) -> (69/19,11/3) Reflection Matrix(1565,-5916,414,-1565) (34/9,87/23) -> (34/9,87/23) Reflection Matrix(436,-1653,115,-436) (87/23,19/5) -> (87/23,19/5) Reflection Matrix(53,-234,12,-53) (13/3,9/2) -> (13/3,9/2) Reflection Matrix(19,-90,4,-19) (9/2,5/1) -> (9/2,5/1) Reflection Matrix(36,-185,7,-36) (5/1,37/7) -> (5/1,37/7) Reflection Matrix(223,-1184,42,-223) (37/7,16/3) -> (37/7,16/3) Reflection Matrix(37,-228,6,-37) (6/1,19/3) -> (6/1,19/3) Reflection Matrix(20,-133,3,-20) (19/3,7/1) -> (19/3,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(0,1,1,0) -> Matrix(1,1,0,-1) (-1/1,1/1) -> (-1/2,1/0) Matrix(11,-12,10,-11) -> Matrix(1,1,0,-1) (1/1,6/5) -> (-1/2,1/0) Matrix(109,-132,90,-109) -> Matrix(1,11,0,-1) (6/5,11/9) -> (-11/2,1/0) Matrix(167,-206,30,-37) -> Matrix(3,11,-2,-7) Matrix(107,-136,48,-61) -> Matrix(1,3,-2,-5) Matrix(249,-322,58,-75) -> Matrix(1,2,0,1) 1/0 Matrix(344,-449,95,-124) -> Matrix(3,5,-4,-7) Matrix(94,-127,37,-50) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(296,-409,55,-76) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(360,-499,101,-140) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(64,-91,45,-64) -> Matrix(3,4,-2,-3) (7/5,13/9) -> (-2/1,-1/1) Matrix(53,-78,36,-53) -> Matrix(-1,0,2,1) (13/9,3/2) -> (-1/1,0/1) Matrix(70,-107,17,-26) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(334,-523,129,-202) -> Matrix(3,2,2,1) Matrix(188,-297,119,-188) -> Matrix(1,1,0,-1) (11/7,27/17) -> (-1/2,1/0) Matrix(271,-432,170,-271) -> Matrix(-1,0,2,1) (27/17,8/5) -> (-1/1,0/1) Matrix(152,-245,67,-108) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(59,-96,8,-13) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(41,-70,24,-41) -> Matrix(-1,1,0,1) (5/3,7/4) -> (1/2,1/0) Matrix(71,-126,40,-71) -> Matrix(1,7,0,-1) (7/4,9/5) -> (-7/2,1/0) Matrix(86,-157,23,-42) -> Matrix(1,2,-2,-5) Matrix(29,-60,14,-29) -> Matrix(3,4,-2,-3) (2/1,15/7) -> (-2/1,-1/1) Matrix(76,-165,35,-76) -> Matrix(5,4,-6,-5) (15/7,11/5) -> (-1/1,-2/3) Matrix(481,-1102,134,-307) -> Matrix(1,0,0,1) Matrix(139,-322,60,-139) -> Matrix(1,1,0,-1) (23/10,7/3) -> (-1/2,1/0) Matrix(92,-217,39,-92) -> Matrix(1,1,0,-1) (7/3,31/13) -> (-1/2,1/0) Matrix(311,-744,130,-311) -> Matrix(-1,0,2,1) (31/13,12/5) -> (-1/1,0/1) Matrix(123,-296,32,-77) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(76,-187,13,-32) -> Matrix(5,1,-4,-1) Matrix(418,-1077,111,-286) -> Matrix(1,-1,-4,3) Matrix(79,-208,30,-79) -> Matrix(-1,3,0,1) (13/5,8/3) -> (3/2,1/0) Matrix(17,-48,6,-17) -> Matrix(1,3,0,-1) (8/3,3/1) -> (-3/2,1/0) Matrix(16,-51,5,-16) -> Matrix(3,4,-2,-3) (3/1,17/5) -> (-2/1,-1/1) Matrix(69,-238,20,-69) -> Matrix(9,8,-10,-9) (17/5,7/2) -> (-1/1,-4/5) Matrix(601,-2150,168,-601) -> Matrix(5,3,-8,-5) (25/7,43/12) -> (-3/4,-1/2) Matrix(1103,-4002,304,-1103) -> Matrix(5,4,-6,-5) (29/8,69/19) -> (-1/1,-2/3) Matrix(208,-759,57,-208) -> Matrix(5,3,-8,-5) (69/19,11/3) -> (-3/4,-1/2) Matrix(1565,-5916,414,-1565) -> Matrix(-1,0,18,1) (34/9,87/23) -> (-1/9,0/1) Matrix(436,-1653,115,-436) -> Matrix(1,0,2,-1) (87/23,19/5) -> (0/1,1/1) Matrix(53,-234,12,-53) -> Matrix(-1,1,0,1) (13/3,9/2) -> (1/2,1/0) Matrix(19,-90,4,-19) -> Matrix(1,3,0,-1) (9/2,5/1) -> (-3/2,1/0) Matrix(36,-185,7,-36) -> Matrix(1,3,0,-1) (5/1,37/7) -> (-3/2,1/0) Matrix(223,-1184,42,-223) -> Matrix(3,4,-2,-3) (37/7,16/3) -> (-2/1,-1/1) Matrix(37,-228,6,-37) -> Matrix(11,12,-10,-11) (6/1,19/3) -> (-6/5,-1/1) Matrix(20,-133,3,-20) -> Matrix(5,4,-6,-5) (19/3,7/1) -> (-1/1,-2/3) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.