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 1/0 -6/13 -1/1 -1/2 -11/24 -1/1 0/1 -5/11 -1/2 1/0 -14/31 -2/1 1/0 -9/20 -1/1 -22/49 -3/4 -2/3 -13/29 -1/2 -4/9 -1/1 -1/2 -11/25 -3/4 -1/2 -18/41 -1/1 -1/2 -25/57 -1/2 -7/16 -1/1 0/1 -10/23 -1/1 -2/3 -13/30 -1/1 -1/2 -3/7 -1/2 -14/33 -2/5 -1/3 -11/26 -1/3 0/1 -8/19 0/1 -21/50 -1/1 0/1 -13/31 -1/2 1/0 -5/12 -1/2 0/1 -17/41 -1/2 -12/29 -2/3 -1/2 -7/17 -1/2 -1/4 -9/22 -1/3 0/1 -11/27 -1/4 -2/5 -1/1 0/1 -11/28 -1/2 -1/3 -20/51 -1/3 0/1 -9/23 -1/2 -1/4 -7/18 0/1 -12/31 0/1 1/3 -17/44 1/1 1/0 -5/13 1/0 -18/47 0/1 1/1 -13/34 -2/1 1/0 -8/21 -1/1 0/1 -11/29 -1/2 1/0 -14/37 -1/1 -1/2 -3/8 -1/2 0/1 -10/27 0/1 1/6 -17/46 0/1 1/3 -7/19 1/2 -25/68 0/1 1/1 -43/117 1/2 1/0 -18/49 0/1 1/1 -11/30 0/1 1/1 -4/11 1/1 1/0 -13/36 -2/1 1/0 -9/25 1/0 -14/39 -1/1 -2/3 -5/14 -1/1 0/1 -16/45 -1/1 0/1 -11/31 -1/2 -6/17 0/1 -7/20 0/1 1/1 -1/3 -1/2 1/0 -6/19 -2/1 -1/1 -5/16 -1/1 -9/29 -1/2 -13/42 -1/1 0/1 -4/13 -1/1 0/1 -11/36 -1/3 0/1 -18/59 0/1 1/3 -7/23 1/0 -10/33 1/1 1/0 -13/43 3/2 1/0 -3/10 -2/1 1/0 -11/37 -3/2 1/0 -19/64 -2/1 -1/1 -8/27 -2/1 -1/1 -21/71 -3/2 1/0 -13/44 -2/1 -1/1 -18/61 -2/1 -1/1 -5/17 -3/2 -12/41 -4/3 -1/1 -7/24 -7/6 -1/1 -2/7 -1/1 -1/2 -11/39 -1/2 -9/32 -1/2 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 0/1 -8/29 1/1 1/0 -11/40 -2/1 -1/1 -14/51 -1/1 -1/2 -3/11 1/0 -10/37 -2/1 1/0 -7/26 -4/3 -1/1 -4/15 -1/1 -5/19 -3/4 -1/2 -6/23 -2/3 -1/2 -7/27 -1/2 -1/4 -1/1 0/1 -6/25 -1/1 -6/7 -5/21 -3/4 -4/17 -1/1 -2/3 -7/30 -1/2 0/1 -10/43 -1/1 -3/13 -3/4 -1/2 -8/35 -4/7 -1/2 -5/22 -1/2 -1/3 -12/53 -1/1 0/1 -7/31 -1/2 -2/9 -1/1 -1/2 -7/32 -1/1 0/1 -12/55 -1/1 0/1 -5/23 -1/2 1/0 -3/14 -1/1 -7/33 -3/4 -1/2 -4/19 -1/1 -2/3 -5/24 -2/3 -3/5 -1/5 -1/2 -4/21 -1/2 0/1 -7/37 -1/2 -1/4 -10/53 -1/3 0/1 -3/16 -1/3 0/1 -2/11 -1/1 0/1 -7/39 -1/2 -5/28 -1/2 0/1 -8/45 -3/5 -1/2 -11/62 -1/2 -4/9 -3/17 -1/2 -1/4 -1/6 -1/2 0/1 -4/25 -1/1 -1/2 -3/19 -1/2 -2/13 0/1 -5/33 1/2 -3/20 1/1 1/0 -1/7 -1/2 1/0 -4/29 -1/1 0/1 -3/22 -1/1 0/1 -2/15 -1/1 0/1 -1/8 -1/2 0/1 -2/17 0/1 1/1 -1/9 1/0 0/1 -1/1 0/1 1/8 -1/1 0/1 2/15 -1/2 0/1 1/7 -1/2 1/6 0/1 1/0 2/11 -1/1 0/1 1/5 -1/2 1/0 6/29 -1/1 0/1 5/24 -1/1 0/1 4/19 -3/5 -1/2 3/14 -1/2 -1/3 2/9 0/1 5/22 1/2 1/1 8/35 0/1 1/1 3/13 1/0 1/4 0/1 1/0 5/19 1/0 4/15 -1/1 0/1 7/26 0/1 3/11 1/2 1/0 5/18 0/1 1/0 7/25 1/0 2/7 -1/1 0/1 5/17 0/1 8/27 0/1 1/3 3/10 0/1 1/1 4/13 0/1 1/0 5/16 4/1 1/0 6/19 -2/1 -1/1 1/3 1/0 7/20 -1/1 1/0 6/17 3/1 1/0 5/14 -3/1 -2/1 14/39 -2/1 -1/1 9/25 -3/2 1/0 13/36 -2/1 1/0 4/11 -2/1 -1/1 3/8 -1/1 8/21 -1/1 0/1 21/55 -1/2 34/89 -1/1 0/1 47/123 -1/2 1/0 13/34 -1/1 0/1 31/81 -1/2 18/47 -1/1 -1/2 5/13 -1/2 1/0 2/5 -1/1 1/0 7/17 1/0 5/12 1/1 1/0 3/7 -3/2 1/0 4/9 -2/1 -1/1 9/20 -2/1 -1/1 14/31 -2/1 -1/1 5/11 -3/2 1/2 -1/1 0/1 6/11 -2/1 1/0 11/20 -2/1 -1/1 5/9 -3/2 1/0 4/7 -1/1 11/19 -7/8 -5/6 18/31 -1/1 -5/6 25/43 -5/6 32/55 -1/1 -4/5 7/12 -1/1 -4/5 24/41 -19/25 -3/4 17/29 -3/4 -13/18 10/17 -2/3 -1/2 23/39 -3/4 -1/2 13/22 -1/1 -2/3 16/27 -1/1 -2/3 3/5 -1/2 11/18 -1/1 -2/3 19/31 -3/4 -1/2 8/13 -1/2 -1/3 5/8 -1/1 0/1 7/11 -1/2 1/0 16/25 -1/1 0/1 9/14 0/1 1/0 2/3 -1/1 1/0 9/13 -1/1 16/23 -1/1 -15/16 7/10 -1/1 -7/8 26/37 -6/7 -11/13 45/64 -36/43 -5/6 19/27 -5/6 -13/16 12/17 -1/1 -4/5 17/24 -1/1 -4/5 22/31 -1/1 -4/5 5/7 -3/4 28/39 -1/1 -3/4 23/32 -2/3 18/25 -1/1 -2/3 49/68 -1/1 -2/3 31/43 -3/4 -1/2 13/18 -1/1 -2/3 8/11 -1/1 -2/3 3/4 -2/3 -1/2 10/13 -1/2 -1/3 7/9 -1/2 11/14 0/1 1/1 26/33 -1/1 0/1 15/19 -1/2 1/0 4/5 -1/1 0/1 21/26 -1/1 0/1 17/21 -1/2 1/0 13/16 -1/1 0/1 9/11 1/0 5/6 -1/1 11/13 -3/4 17/20 -3/4 -2/3 6/7 -1/1 -2/3 13/15 -3/4 20/23 -1/1 -2/3 27/31 -3/4 -1/2 7/8 -1/1 -2/3 8/9 -2/3 -5/8 1/1 -1/2 1/0 8/7 -1/3 0/1 15/13 -1/4 7/6 -1/3 0/1 6/5 0/1 17/14 0/1 1/1 28/23 1/1 1/0 11/9 1/0 27/22 0/1 1/0 43/35 -1/2 1/0 16/13 -1/1 0/1 5/4 -1/1 0/1 24/19 -1/1 0/1 43/34 0/1 19/15 -1/2 1/0 33/26 -1/1 0/1 14/11 -2/1 -1/1 37/29 -1/1 60/47 -1/1 -10/11 23/18 -1/1 -4/5 9/7 -1/2 13/10 -2/3 -1/2 17/13 -5/8 -1/2 4/3 -1/2 -1/3 15/11 -1/2 -1/4 41/30 -1/3 -1/4 67/49 -1/2 26/19 -1/3 0/1 11/8 -1/3 0/1 29/21 -1/2 -1/4 18/13 -1/3 0/1 25/18 -1/3 0/1 32/23 -1/3 39/28 -1/4 0/1 7/5 -1/4 24/17 -1/5 0/1 41/29 -1/4 -1/6 17/12 -1/5 0/1 44/31 -1/5 0/1 27/19 -3/16 -1/6 37/26 -2/13 -1/7 10/7 -1/8 0/1 13/9 0/1 16/11 0/1 1/8 3/2 0/1 1/0 17/11 1/0 14/9 -1/1 1/0 25/16 -1/1 0/1 36/23 -1/1 0/1 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 -1/1 81/50 -1/1 -2/3 47/29 -1/2 13/8 -2/3 -1/2 44/27 -1/2 -2/5 31/19 -1/2 -1/4 49/30 -1/3 0/1 18/11 -1/3 0/1 41/25 0/1 64/39 0/1 1/3 23/14 0/1 1/0 5/3 -1/2 27/16 -1/3 0/1 49/29 -1/2 -1/4 22/13 -1/3 0/1 83/49 -1/2 -1/4 61/36 -1/3 0/1 39/23 -1/2 -1/4 56/33 -1/3 0/1 17/10 -1/2 -1/3 46/27 -1/3 -2/7 29/17 -5/18 -1/4 12/7 -1/5 0/1 7/4 0/1 16/9 0/1 1/3 57/32 0/1 1/3 98/55 1/3 1/2 41/23 1/2 66/37 0/1 1/3 25/14 0/1 1/2 9/5 1/2 1/0 11/6 1/1 1/0 13/7 1/0 15/8 0/1 1/0 2/1 -1/1 0/1 15/7 0/1 28/13 0/1 1/11 13/6 0/1 1/5 11/5 1/2 31/14 0/1 1/1 20/9 0/1 1/1 29/13 -1/2 1/0 9/4 0/1 1/1 16/7 -1/1 1/0 23/10 0/1 30/13 0/1 1/1 7/3 1/2 1/0 19/8 3/1 1/0 31/13 1/0 43/18 -7/1 1/0 12/5 -2/1 1/0 29/12 -1/1 0/1 46/19 -1/1 1/0 17/7 1/0 39/16 -1/1 22/9 -1/1 0/1 5/2 0/1 1/0 18/7 -1/1 0/1 49/19 1/0 80/31 -1/1 1/0 111/43 -1/1 142/55 -1/1 -1/2 31/12 -1/1 0/1 75/29 1/0 44/17 -1/2 0/1 57/22 -1/1 0/1 13/5 -1/2 1/0 8/3 0/1 19/7 1/2 1/0 49/18 0/1 1/0 128/47 0/1 1/1 79/29 1/0 30/11 0/1 1/1 71/26 0/1 1/1 41/15 1/0 11/4 0/1 1/1 47/17 1/0 36/13 1/1 1/0 97/35 1/0 61/22 0/1 1/0 25/9 1/2 1/0 64/23 0/1 1/1 39/14 0/1 1/1 14/5 1/1 2/1 31/11 9/2 1/0 48/17 13/1 1/0 65/23 1/0 17/6 -4/1 1/0 3/1 1/0 19/6 0/1 1/1 35/11 7/2 1/0 51/16 12/1 1/0 67/21 1/0 16/5 -5/1 1/0 29/9 -5/2 1/0 13/4 -1/1 1/0 23/7 -3/2 1/0 79/24 -2/1 -1/1 135/41 -3/2 1/0 56/17 -2/1 -1/1 33/10 -2/1 -1/1 10/3 -2/1 -1/1 17/5 -1/1 24/7 -1/1 -2/3 7/2 -1/1 0/1 39/11 -1/2 1/0 71/20 -1/1 0/1 103/29 -1/2 1/0 32/9 -1/1 0/1 25/7 1/0 68/19 -1/1 0/1 43/12 0/1 18/5 -1/1 1/0 29/8 2/1 1/0 69/19 1/0 109/30 -12/1 1/0 40/11 -5/1 1/0 11/3 -3/2 1/0 26/7 -1/1 15/4 -1/1 0/1 34/9 -1/1 0/1 87/23 0/1 140/37 0/1 1/1 53/14 0/1 1/0 19/5 1/0 23/6 -1/1 0/1 27/7 -1/2 1/0 31/8 0/1 1/0 35/9 1/0 4/1 -1/1 1/0 17/4 0/1 1/0 13/3 1/0 9/2 -1/1 23/5 -3/4 60/13 -1/1 -2/3 217/47 -3/4 -1/2 157/34 -1/1 -2/3 97/21 -3/4 -1/2 37/8 -1/1 -2/3 51/11 -3/4 -1/2 14/3 -2/3 -1/2 33/7 -1/2 19/4 -1/2 -2/5 24/5 -1/1 0/1 29/6 -1/1 0/1 34/7 -1/1 0/1 73/15 -1/2 1/0 39/8 -1/1 0/1 5/1 -1/2 1/0 21/4 -1/1 0/1 37/7 -1/2 1/0 53/10 -1/1 0/1 16/3 -1/1 0/1 11/2 -1/1 0/1 28/5 0/1 17/3 1/0 6/1 -1/1 1/0 19/3 -1/1 32/5 -1/1 -5/6 13/2 -1/1 -2/3 7/1 -1/2 15/2 -1/1 -1/2 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 -1/1 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(1,0,-2,1) Matrix(249,116,-908,-423) -> Matrix(1,0,0,1) Matrix(893,410,734,337) -> Matrix(1,0,2,1) Matrix(647,296,-2188,-1001) -> Matrix(3,2,-2,-1) Matrix(1445,654,886,401) -> Matrix(1,0,-2,1) Matrix(719,324,-1600,-721) -> Matrix(3,4,-4,-5) Matrix(4951,2222,1914,859) -> Matrix(3,2,-2,-1) Matrix(157,70,-554,-247) -> Matrix(1,0,0,1) Matrix(549,242,946,417) -> Matrix(3,4,-4,-5) Matrix(783,344,-2588,-1137) -> Matrix(1,0,2,1) Matrix(1801,790,2510,1101) -> Matrix(1,2,-2,-3) Matrix(4703,2062,1722,755) -> Matrix(1,0,2,1) Matrix(545,238,158,69) -> Matrix(1,0,0,1) Matrix(853,370,-2174,-943) -> Matrix(3,2,-8,-5) Matrix(79,34,230,99) -> Matrix(3,2,-2,-1) Matrix(75,32,232,99) -> Matrix(1,0,2,1) Matrix(1453,616,1144,485) -> Matrix(1,0,2,1) Matrix(607,256,-1444,-609) -> Matrix(1,0,2,1) Matrix(2577,1082,1822,765) -> Matrix(1,0,-4,1) Matrix(225,94,-754,-315) -> Matrix(3,2,-2,-1) Matrix(829,344,976,405) -> Matrix(1,2,-2,-3) Matrix(449,186,-1726,-715) -> Matrix(1,0,0,1) Matrix(223,92,-972,-401) -> Matrix(5,2,-8,-3) Matrix(371,152,-1340,-549) -> Matrix(1,0,2,1) Matrix(519,212,448,183) -> Matrix(1,0,0,1) Matrix(521,212,-1708,-695) -> Matrix(1,0,4,1) Matrix(361,142,-1594,-627) -> Matrix(1,0,0,1) Matrix(2607,1022,-7094,-2781) -> Matrix(1,0,4,1) Matrix(215,84,796,311) -> Matrix(1,0,4,1) Matrix(289,112,1076,417) -> Matrix(1,0,-4,1) Matrix(1361,526,1938,749) -> Matrix(7,-6,-8,7) Matrix(503,194,70,27) -> Matrix(1,0,-2,1) Matrix(73,28,-644,-247) -> Matrix(1,0,0,1) Matrix(1709,654,358,137) -> Matrix(1,0,-2,1) Matrix(283,108,-1208,-461) -> Matrix(1,2,-2,-3) Matrix(495,188,-1772,-673) -> Matrix(1,0,0,1) Matrix(707,268,1844,699) -> Matrix(1,0,0,1) Matrix(69,26,-422,-159) -> Matrix(1,0,0,1) Matrix(209,78,142,53) -> Matrix(1,0,2,1) Matrix(557,206,630,233) -> Matrix(7,-2,-10,3) Matrix(2095,774,766,283) -> Matrix(1,0,-2,1) Matrix(4735,1742,2922,1075) -> Matrix(3,-2,-4,3) Matrix(10925,4016,2364,869) -> Matrix(3,-2,-4,3) Matrix(207,76,-1528,-561) -> Matrix(1,0,-2,1) Matrix(137,50,-622,-227) -> Matrix(1,0,-2,1) Matrix(343,124,-1928,-697) -> Matrix(1,2,-2,-3) Matrix(621,224,-2204,-795) -> Matrix(1,2,-2,-3) Matrix(345,124,-1444,-519) -> Matrix(3,4,-4,-5) Matrix(1717,616,616,221) -> Matrix(1,0,2,1) Matrix(1641,584,340,121) -> Matrix(1,0,0,1) Matrix(3891,1382,2182,775) -> Matrix(1,0,4,1) Matrix(1157,410,206,73) -> Matrix(1,0,2,1) Matrix(747,262,134,47) -> Matrix(1,0,-2,1) Matrix(607,212,272,95) -> Matrix(1,0,0,1) Matrix(645,206,454,145) -> Matrix(1,2,-6,-11) Matrix(1093,344,448,141) -> Matrix(1,2,-2,-3) Matrix(1403,436,576,179) -> Matrix(3,2,-2,-1) Matrix(2293,710,830,257) -> Matrix(1,0,2,1) Matrix(317,98,1530,473) -> Matrix(1,0,0,1) Matrix(569,174,1586,485) -> Matrix(3,2,-2,-1) Matrix(1775,542,822,251) -> Matrix(1,0,8,1) Matrix(191,58,-1202,-365) -> Matrix(1,0,-2,1) Matrix(503,152,-2836,-857) -> Matrix(1,-2,-2,5) Matrix(4633,1376,1000,297) -> Matrix(3,4,-4,-5) Matrix(2563,760,1440,427) -> Matrix(1,2,2,5) Matrix(311,92,-2248,-665) -> Matrix(1,2,-2,-3) Matrix(623,184,-3308,-977) -> Matrix(1,2,-4,-7) Matrix(2681,790,750,221) -> Matrix(1,2,-2,-3) Matrix(997,292,2612,765) -> Matrix(3,4,-4,-5) Matrix(1801,526,1058,309) -> Matrix(5,6,-16,-19) Matrix(433,126,622,181) -> Matrix(13,14,-14,-15) Matrix(1833,514,674,189) -> Matrix(1,0,2,1) Matrix(1649,460,1036,289) -> Matrix(1,0,0,1) Matrix(3465,958,2738,757) -> Matrix(1,0,0,1) Matrix(2795,772,3892,1075) -> Matrix(3,-2,-4,3) Matrix(305,84,1456,401) -> Matrix(1,2,-2,-3) Matrix(1943,534,302,83) -> Matrix(3,4,-4,-5) Matrix(59,16,424,115) -> Matrix(1,2,-2,-3) Matrix(1629,440,1144,309) -> Matrix(1,2,-8,-15) Matrix(901,242,242,65) -> Matrix(3,4,-4,-5) Matrix(659,174,178,47) -> Matrix(5,4,-4,-3) Matrix(237,62,-1250,-327) -> Matrix(3,2,-8,-5) Matrix(475,122,1242,319) -> Matrix(1,0,0,1) Matrix(815,198,638,155) -> Matrix(3,4,-4,-5) Matrix(347,82,402,95) -> Matrix(1,0,0,1) Matrix(2637,614,1894,441) -> Matrix(1,0,-2,1) Matrix(517,120,56,13) -> Matrix(3,2,-2,-1) Matrix(1769,404,740,169) -> Matrix(11,6,-2,-1) Matrix(5117,1158,1878,425) -> Matrix(1,0,2,1) Matrix(967,218,794,179) -> Matrix(1,0,2,1) Matrix(1409,308,2420,529) -> Matrix(3,4,-4,-5) Matrix(3433,748,2024,441) -> Matrix(1,0,-2,1) Matrix(167,36,-784,-169) -> Matrix(1,2,-2,-3) Matrix(1397,296,892,189) -> Matrix(3,2,-2,-1) Matrix(833,174,1058,221) -> Matrix(3,2,-2,-1) Matrix(167,34,54,11) -> Matrix(3,2,-2,-1) Matrix(763,146,162,31) -> Matrix(5,2,-8,-3) Matrix(2171,410,2494,471) -> Matrix(5,2,-8,-3) Matrix(161,30,542,101) -> Matrix(1,0,4,1) Matrix(1557,280,4076,733) -> Matrix(1,0,0,1) Matrix(1717,308,1232,221) -> Matrix(1,0,-2,1) Matrix(7385,1312,2032,361) -> Matrix(15,8,-2,-1) Matrix(479,84,268,47) -> Matrix(1,0,4,1) Matrix(103,16,-676,-105) -> Matrix(1,0,4,1) Matrix(2693,406,1970,297) -> Matrix(1,0,-4,1) Matrix(671,100,208,31) -> Matrix(1,-2,0,1) Matrix(1889,260,356,49) -> Matrix(1,0,0,1) Matrix(303,40,356,47) -> Matrix(1,2,-2,-3) Matrix(903,110,550,67) -> Matrix(1,0,2,1) Matrix(147,16,248,27) -> Matrix(1,2,-2,-3) Matrix(197,-24,156,-19) -> Matrix(1,0,0,1) Matrix(1207,-158,466,-61) -> Matrix(1,0,0,1) Matrix(191,-28,116,-17) -> Matrix(1,0,0,1) Matrix(187,-32,76,-13) -> Matrix(1,0,0,1) Matrix(409,-76,296,-55) -> Matrix(1,0,-2,1) Matrix(1533,-316,4012,-827) -> Matrix(1,0,0,1) Matrix(217,-46,618,-131) -> Matrix(1,0,2,1) Matrix(73,-16,324,-71) -> Matrix(1,0,4,1) Matrix(1827,-416,1076,-245) -> Matrix(1,0,-4,1) Matrix(715,-164,824,-189) -> Matrix(3,-2,-4,3) Matrix(107,-26,70,-17) -> Matrix(1,0,0,1) Matrix(557,-146,454,-119) -> Matrix(1,0,0,1) Matrix(1077,-286,418,-111) -> Matrix(1,0,0,1) Matrix(449,-124,344,-95) -> Matrix(1,2,-2,-3) Matrix(1171,-326,722,-201) -> Matrix(1,2,-2,-3) Matrix(585,-164,824,-231) -> Matrix(3,4,-4,-5) Matrix(171,-50,578,-169) -> Matrix(1,0,4,1) Matrix(203,-62,370,-113) -> Matrix(1,-2,0,1) Matrix(873,-272,536,-167) -> Matrix(1,-2,-2,5) Matrix(1271,-400,1808,-569) -> Matrix(5,16,-6,-19) Matrix(455,-162,778,-277) -> Matrix(3,10,-4,-13) Matrix(2461,-884,1456,-523) -> Matrix(1,2,-4,-7) Matrix(2425,-874,874,-315) -> Matrix(1,2,0,1) Matrix(2651,-958,1486,-537) -> Matrix(1,2,2,5) Matrix(97,-36,256,-95) -> Matrix(1,2,-2,-3) Matrix(4967,-1898,1018,-389) -> Matrix(1,0,0,1) Matrix(9865,-3776,5536,-2119) -> Matrix(1,0,4,1) Matrix(127,-50,94,-37) -> Matrix(1,0,-2,1) Matrix(187,-76,32,-13) -> Matrix(1,0,0,1) Matrix(343,-142,186,-77) -> Matrix(1,0,0,1) Matrix(217,-92,92,-39) -> Matrix(1,2,0,1) Matrix(245,-108,152,-67) -> Matrix(1,2,-2,-3) Matrix(1033,-464,728,-327) -> Matrix(1,2,-6,-11) Matrix(1879,-848,2608,-1177) -> Matrix(3,4,-4,-5) Matrix(2363,-1068,1728,-781) -> Matrix(1,2,-4,-7) Matrix(271,-124,212,-97) -> Matrix(3,4,-4,-5) Matrix(343,-186,142,-77) -> Matrix(1,0,0,1) Matrix(737,-406,1022,-563) -> Matrix(3,4,-4,-5) Matrix(113,-64,196,-111) -> Matrix(7,8,-8,-9) Matrix(3005,-1746,1086,-631) -> Matrix(5,4,6,5) Matrix(9849,-5728,3616,-2103) -> Matrix(5,4,6,5) Matrix(2663,-1560,944,-553) -> Matrix(27,20,4,3) Matrix(249,-146,278,-163) -> Matrix(11,8,-18,-13) Matrix(1413,-832,304,-179) -> Matrix(1,0,0,1) Matrix(3237,-1910,1910,-1127) -> Matrix(3,2,-8,-5) Matrix(2461,-1456,884,-523) -> Matrix(3,2,4,3) Matrix(191,-116,28,-17) -> Matrix(1,0,0,1) Matrix(709,-434,874,-535) -> Matrix(3,2,-2,-1) Matrix(873,-536,272,-167) -> Matrix(7,4,-2,-1) Matrix(245,-152,108,-67) -> Matrix(1,0,2,1) Matrix(297,-188,188,-119) -> Matrix(1,0,0,1) Matrix(1289,-824,912,-583) -> Matrix(1,0,-4,1) Matrix(403,-258,214,-137) -> Matrix(1,0,0,1) Matrix(107,-70,26,-17) -> Matrix(1,0,0,1) Matrix(235,-162,338,-233) -> Matrix(15,16,-16,-17) Matrix(3617,-2544,1136,-799) -> Matrix(29,24,6,5) Matrix(1033,-728,464,-327) -> Matrix(5,4,6,5) Matrix(1289,-912,824,-583) -> Matrix(5,4,-4,-3) Matrix(747,-530,926,-657) -> Matrix(5,4,-4,-3) Matrix(1843,-1326,1458,-1049) -> Matrix(3,2,-2,-1) Matrix(4961,-3576,1508,-1087) -> Matrix(5,4,-4,-3) Matrix(409,-296,76,-55) -> Matrix(3,2,-2,-1) Matrix(127,-94,50,-37) -> Matrix(3,2,-2,-1) Matrix(449,-344,124,-95) -> Matrix(1,0,2,1) Matrix(347,-268,224,-173) -> Matrix(1,0,2,1) Matrix(271,-212,124,-97) -> Matrix(1,0,4,1) Matrix(1723,-1358,1402,-1105) -> Matrix(1,0,0,1) Matrix(197,-156,24,-19) -> Matrix(1,0,0,1) Matrix(2505,-2026,706,-571) -> Matrix(1,0,0,1) Matrix(557,-454,146,-119) -> Matrix(1,0,0,1) Matrix(121,-100,144,-119) -> Matrix(3,4,-4,-5) Matrix(5643,-4918,1222,-1065) -> Matrix(1,0,0,1) Matrix(249,-278,146,-163) -> Matrix(5,2,-18,-7) Matrix(941,-1084,204,-235) -> Matrix(5,2,-8,-3) Matrix(121,-144,100,-119) -> Matrix(1,0,4,1) Matrix(1679,-2062,434,-533) -> Matrix(1,0,0,1) Matrix(709,-874,434,-535) -> Matrix(1,0,-2,1) Matrix(1047,-1328,272,-345) -> Matrix(1,0,0,1) Matrix(2147,-2738,1682,-2145) -> Matrix(11,12,-12,-13) Matrix(249,-322,58,-75) -> Matrix(3,2,-2,-1) Matrix(553,-724,152,-199) -> Matrix(7,4,-2,-1) Matrix(855,-1168,112,-153) -> Matrix(1,0,2,1) Matrix(557,-764,148,-203) -> Matrix(1,0,2,1) Matrix(481,-664,92,-127) -> Matrix(1,0,2,1) Matrix(609,-844,184,-255) -> Matrix(7,2,-4,-1) Matrix(203,-282,18,-25) -> Matrix(1,0,2,1) Matrix(585,-824,164,-231) -> Matrix(1,0,4,1) Matrix(1271,-1808,400,-569) -> Matrix(13,2,6,1) Matrix(235,-338,162,-233) -> Matrix(1,0,16,1) Matrix(997,-1556,412,-643) -> Matrix(1,0,0,1) Matrix(919,-1458,578,-917) -> Matrix(1,0,0,1) Matrix(2017,-3262,1194,-1931) -> Matrix(1,0,-2,1) Matrix(2857,-4624,1764,-2855) -> Matrix(1,2,-2,-3) Matrix(1303,-2128,368,-601) -> Matrix(1,0,2,1) Matrix(2051,-3362,1250,-2049) -> Matrix(1,0,6,1) Matrix(899,-1522,114,-193) -> Matrix(1,0,2,1) Matrix(2923,-4952,376,-637) -> Matrix(1,0,2,1) Matrix(455,-778,162,-277) -> Matrix(9,2,4,1) Matrix(113,-196,64,-111) -> Matrix(1,0,8,1) Matrix(6249,-11132,2420,-4311) -> Matrix(1,0,-4,1) Matrix(203,-370,62,-113) -> Matrix(1,-2,0,1) Matrix(523,-974,138,-257) -> Matrix(1,0,0,1) Matrix(211,-450,98,-209) -> Matrix(1,0,12,1) Matrix(1205,-2666,466,-1031) -> Matrix(1,0,-2,1) Matrix(1081,-2396,328,-727) -> Matrix(1,-2,0,1) Matrix(481,-1102,134,-307) -> Matrix(1,0,0,1) Matrix(1239,-2854,346,-797) -> Matrix(1,0,-2,1) Matrix(517,-1198,186,-431) -> Matrix(1,0,0,1) Matrix(807,-1922,338,-805) -> Matrix(1,-10,0,1) Matrix(1491,-3614,578,-1401) -> Matrix(1,0,0,1) Matrix(9547,-24642,3698,-9545) -> Matrix(1,2,-2,-3) Matrix(661,-1714,86,-223) -> Matrix(1,0,0,1) Matrix(97,-256,36,-95) -> Matrix(1,0,2,1) Matrix(5011,-13644,1324,-3605) -> Matrix(1,0,0,1) Matrix(1203,-3284,248,-677) -> Matrix(1,0,-2,1) Matrix(595,-1648,152,-421) -> Matrix(1,-2,0,1) Matrix(1855,-5142,478,-1325) -> Matrix(1,0,0,1) Matrix(1507,-4256,472,-1333) -> Matrix(1,-18,0,1) Matrix(1575,-4454,494,-1397) -> Matrix(1,16,0,1) Matrix(217,-618,46,-131) -> Matrix(1,2,-2,-3) Matrix(11645,-38338,2522,-8303) -> Matrix(3,4,-4,-5) Matrix(6149,-20252,1332,-4387) -> Matrix(3,4,-4,-5) Matrix(171,-578,50,-169) -> Matrix(3,4,-4,-5) Matrix(2591,-9200,532,-1889) -> Matrix(1,0,0,1) Matrix(1643,-5838,338,-1201) -> Matrix(1,0,0,1) Matrix(2623,-9522,722,-2621) -> Matrix(1,-14,0,1) Matrix(4003,-15138,1058,-4001) -> Matrix(1,0,2,1) Matrix(73,-324,16,-71) -> Matrix(3,4,-4,-5) Matrix(519,-2738,98,-517) -> Matrix(1,0,0,1) Matrix(115,-722,18,-113) -> Matrix(5,6,-6,-7) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 40 Degree of the the map X: 40 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): 720 Minimal number of generators: 121 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: 50 Genus: 36 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 2/9 1/3 3/8 4/7 5/7 5/6 1/1 6/5 7/5 13/9 27/17 34/21 5/3 83/49 7/4 2/1 15/7 11/5 23/10 31/13 17/7 13/5 8/3 97/35 65/23 3/1 135/41 17/5 103/29 69/19 11/3 87/23 4/1 17/4 13/3 9/2 14/3 5/1 37/7 16/3 11/2 17/3 6/1 19/3 13/2 7/1 8/1 9/1 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 1/8 -1/1 0/1 1/7 -1/2 1/6 0/1 1/0 2/11 -1/1 0/1 1/5 -1/2 1/0 4/19 -3/5 -1/2 3/14 -1/2 -1/3 2/9 0/1 5/22 1/2 1/1 8/35 0/1 1/1 3/13 1/0 1/4 0/1 1/0 5/19 1/0 4/15 -1/1 0/1 3/11 1/2 1/0 5/18 0/1 1/0 7/25 1/0 2/7 -1/1 0/1 5/17 0/1 3/10 0/1 1/1 4/13 0/1 1/0 5/16 4/1 1/0 1/3 1/0 6/17 3/1 1/0 5/14 -3/1 -2/1 9/25 -3/2 1/0 13/36 -2/1 1/0 4/11 -2/1 -1/1 3/8 -1/1 8/21 -1/1 0/1 13/34 -1/1 0/1 5/13 -1/2 1/0 2/5 -1/1 1/0 7/17 1/0 5/12 1/1 1/0 3/7 -3/2 1/0 4/9 -2/1 -1/1 9/20 -2/1 -1/1 14/31 -2/1 -1/1 5/11 -3/2 1/2 -1/1 0/1 6/11 -2/1 1/0 11/20 -2/1 -1/1 5/9 -3/2 1/0 4/7 -1/1 11/19 -7/8 -5/6 7/12 -1/1 -4/5 24/41 -19/25 -3/4 17/29 -3/4 -13/18 10/17 -2/3 -1/2 23/39 -3/4 -1/2 13/22 -1/1 -2/3 3/5 -1/2 11/18 -1/1 -2/3 19/31 -3/4 -1/2 8/13 -1/2 -1/3 5/8 -1/1 0/1 7/11 -1/2 1/0 16/25 -1/1 0/1 9/14 0/1 1/0 2/3 -1/1 1/0 9/13 -1/1 7/10 -1/1 -7/8 19/27 -5/6 -13/16 12/17 -1/1 -4/5 17/24 -1/1 -4/5 22/31 -1/1 -4/5 5/7 -3/4 23/32 -2/3 18/25 -1/1 -2/3 49/68 -1/1 -2/3 31/43 -3/4 -1/2 13/18 -1/1 -2/3 8/11 -1/1 -2/3 3/4 -2/3 -1/2 10/13 -1/2 -1/3 7/9 -1/2 11/14 0/1 1/1 15/19 -1/2 1/0 4/5 -1/1 0/1 21/26 -1/1 0/1 17/21 -1/2 1/0 13/16 -1/1 0/1 9/11 1/0 5/6 -1/1 11/13 -3/4 6/7 -1/1 -2/3 7/8 -1/1 -2/3 1/1 -1/2 1/0 8/7 -1/3 0/1 7/6 -1/3 0/1 6/5 0/1 17/14 0/1 1/1 11/9 1/0 27/22 0/1 1/0 16/13 -1/1 0/1 5/4 -1/1 0/1 24/19 -1/1 0/1 19/15 -1/2 1/0 14/11 -2/1 -1/1 37/29 -1/1 23/18 -1/1 -4/5 9/7 -1/2 13/10 -2/3 -1/2 17/13 -5/8 -1/2 4/3 -1/2 -1/3 15/11 -1/2 -1/4 41/30 -1/3 -1/4 26/19 -1/3 0/1 11/8 -1/3 0/1 29/21 -1/2 -1/4 18/13 -1/3 0/1 25/18 -1/3 0/1 32/23 -1/3 7/5 -1/4 24/17 -1/5 0/1 17/12 -1/5 0/1 27/19 -3/16 -1/6 10/7 -1/8 0/1 13/9 0/1 3/2 0/1 1/0 17/11 1/0 14/9 -1/1 1/0 25/16 -1/1 0/1 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 55/34 -1/1 0/1 34/21 -1/1 47/29 -1/2 13/8 -2/3 -1/2 31/19 -1/2 -1/4 49/30 -1/3 0/1 18/11 -1/3 0/1 41/25 0/1 23/14 0/1 1/0 5/3 -1/2 22/13 -1/3 0/1 83/49 -1/2 -1/4 61/36 -1/3 0/1 39/23 -1/2 -1/4 17/10 -1/2 -1/3 29/17 -5/18 -1/4 12/7 -1/5 0/1 7/4 0/1 16/9 0/1 1/3 9/5 1/2 1/0 11/6 1/1 1/0 13/7 1/0 15/8 0/1 1/0 2/1 -1/1 0/1 15/7 0/1 13/6 0/1 1/5 11/5 1/2 31/14 0/1 1/1 20/9 0/1 1/1 9/4 0/1 1/1 16/7 -1/1 1/0 23/10 0/1 30/13 0/1 1/1 7/3 1/2 1/0 19/8 3/1 1/0 31/13 1/0 12/5 -2/1 1/0 29/12 -1/1 0/1 46/19 -1/1 1/0 17/7 1/0 22/9 -1/1 0/1 5/2 0/1 1/0 18/7 -1/1 0/1 49/19 1/0 80/31 -1/1 1/0 111/43 -1/1 31/12 -1/1 0/1 44/17 -1/2 0/1 13/5 -1/2 1/0 8/3 0/1 19/7 1/2 1/0 30/11 0/1 1/1 11/4 0/1 1/1 36/13 1/1 1/0 97/35 1/0 61/22 0/1 1/0 25/9 1/2 1/0 14/5 1/1 2/1 31/11 9/2 1/0 48/17 13/1 1/0 65/23 1/0 17/6 -4/1 1/0 3/1 1/0 16/5 -5/1 1/0 13/4 -1/1 1/0 23/7 -3/2 1/0 79/24 -2/1 -1/1 135/41 -3/2 1/0 56/17 -2/1 -1/1 33/10 -2/1 -1/1 10/3 -2/1 -1/1 17/5 -1/1 7/2 -1/1 0/1 39/11 -1/2 1/0 71/20 -1/1 0/1 103/29 -1/2 1/0 32/9 -1/1 0/1 25/7 1/0 43/12 0/1 18/5 -1/1 1/0 29/8 2/1 1/0 69/19 1/0 40/11 -5/1 1/0 11/3 -3/2 1/0 15/4 -1/1 0/1 34/9 -1/1 0/1 87/23 0/1 53/14 0/1 1/0 19/5 1/0 23/6 -1/1 0/1 4/1 -1/1 1/0 17/4 0/1 1/0 13/3 1/0 9/2 -1/1 23/5 -3/4 37/8 -1/1 -2/3 14/3 -2/3 -1/2 19/4 -1/2 -2/5 5/1 -1/2 1/0 21/4 -1/1 0/1 37/7 -1/2 1/0 16/3 -1/1 0/1 11/2 -1/1 0/1 17/3 1/0 6/1 -1/1 1/0 19/3 -1/1 13/2 -1/1 -2/3 7/1 -1/2 8/1 -1/1 0/1 9/1 -1/2 1/0 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(197,-24,156,-19) (0/1,1/8) -> (5/4,24/19) Hyperbolic Matrix(194,-27,115,-16) (1/8,1/7) -> (5/3,22/13) 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(654,-137,401,-84) (1/5,4/19) -> (13/8,31/19) Hyperbolic Matrix(146,-31,471,-100) (4/19,3/14) -> (4/13,5/16) Hyperbolic Matrix(73,-16,324,-71) (3/14,2/9) -> (2/9,5/22) Parabolic Matrix(2222,-507,859,-196) (5/22,8/35) -> (31/12,44/17) Hyperbolic Matrix(788,-181,357,-82) (8/35,3/13) -> (11/5,31/14) 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(242,-65,417,-112) (4/15,3/11) -> (11/19,7/12) 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(238,-69,69,-20) (2/7,5/17) -> (17/5,7/2) Hyperbolic Matrix(340,-101,101,-30) (5/17,3/10) -> (10/3,17/5) Hyperbolic Matrix(203,-62,370,-113) (3/10,4/13) -> (6/11,11/20) Hyperbolic Matrix(34,-11,99,-32) (5/16,1/3) -> (1/3,6/17) Parabolic Matrix(455,-162,778,-277) (6/17,5/14) -> (7/12,24/41) Hyperbolic Matrix(616,-221,485,-174) (5/14,9/25) -> (19/15,14/11) Hyperbolic Matrix(2425,-874,874,-315) (9/25,13/36) -> (61/22,25/9) Hyperbolic Matrix(872,-315,227,-82) (13/36,4/11) -> (23/6,4/1) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(1082,-413,765,-292) (8/21,13/34) -> (24/17,17/12) Hyperbolic Matrix(446,-171,699,-268) (13/34,5/13) -> (7/11,16/25) 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(212,-95,183,-82) (4/9,9/20) -> (8/7,7/6) Hyperbolic Matrix(1879,-848,2608,-1177) (9/20,14/31) -> (18/25,49/68) Hyperbolic Matrix(1120,-507,243,-110) (14/31,5/11) -> (23/5,37/8) 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(2663,-1560,944,-553) (24/41,17/29) -> (31/11,48/17) Hyperbolic Matrix(526,-309,749,-440) (17/29,10/17) -> (7/10,19/27) Hyperbolic Matrix(1854,-1093,1357,-800) (10/17,23/39) -> (15/11,41/30) Hyperbolic Matrix(3237,-1910,1910,-1127) (23/39,13/22) -> (61/36,39/23) Hyperbolic Matrix(194,-115,27,-16) (13/22,3/5) -> (7/1,8/1) 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(654,-401,137,-84) (19/31,8/13) -> (19/4,5/1) 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(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(78,-53,53,-36) (2/3,9/13) -> (13/9,3/2) Hyperbolic Matrix(260,-181,181,-126) (9/13,7/10) -> (10/7,13/9) Hyperbolic Matrix(206,-145,233,-164) (19/27,12/17) -> (7/8,1/1) Hyperbolic Matrix(774,-547,283,-200) (12/17,17/24) -> (30/11,11/4) Hyperbolic Matrix(747,-530,926,-657) (17/24,22/31) -> (4/5,21/26) Hyperbolic Matrix(1742,-1251,1075,-772) (5/7,23/32) -> (34/21,47/29) Hyperbolic Matrix(2610,-1877,1613,-1160) (23/32,18/25) -> (55/34,34/21) 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(616,-485,221,-174) (11/14,15/19) -> (25/9,14/5) 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(262,-223,47,-40) (11/13,6/7) -> (11/2,17/3) Hyperbolic Matrix(212,-183,95,-82) (6/7,7/8) -> (20/9,9/4) Hyperbolic Matrix(206,-233,145,-164) (1/1,8/7) -> (17/12,27/19) Hyperbolic Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(436,-531,179,-218) (17/14,11/9) -> (17/7,22/9) Hyperbolic Matrix(710,-873,257,-316) (27/22,16/13) -> (11/4,36/13) Hyperbolic Matrix(709,-874,434,-535) (16/13,5/4) -> (49/30,18/11) Hyperbolic Matrix(1224,-1549,757,-958) (24/19,19/15) -> (21/13,55/34) Hyperbolic Matrix(542,-691,251,-320) (14/11,37/29) -> (15/7,13/6) Hyperbolic Matrix(328,-419,155,-198) (37/29,23/18) -> (2/1,15/7) 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(1376,-1881,297,-406) (41/30,26/19) -> (37/8,14/3) 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(1104,-1535,479,-666) (25/18,32/23) -> (23/10,30/13) Hyperbolic Matrix(790,-1101,221,-308) (32/23,7/5) -> (25/7,43/12) Hyperbolic Matrix(585,-824,164,-231) (7/5,24/17) -> (32/9,25/7) Hyperbolic Matrix(526,-749,309,-440) (27/19,10/7) -> (17/10,29/17) Hyperbolic Matrix(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(514,-805,189,-296) (25/16,11/7) -> (19/7,30/11) Hyperbolic Matrix(460,-729,289,-458) (19/12,27/17) -> (27/17,8/5) Parabolic Matrix(1303,-2128,368,-601) (31/19,49/30) -> (7/2,39/11) Hyperbolic Matrix(534,-875,83,-136) (18/11,41/25) -> (19/3,13/2) Hyperbolic Matrix(416,-683,67,-110) (41/25,23/14) -> (6/1,19/3) Hyperbolic Matrix(4068,-6889,2401,-4066) (22/13,83/49) -> (83/49,61/36) Parabolic Matrix(1142,-1937,441,-748) (39/23,17/10) -> (44/17,13/5) 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(174,-311,47,-84) (16/9,9/5) -> (11/3,15/4) 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(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(120,-277,13,-30) (30/13,7/3) -> (9/1,1/0) Hyperbolic Matrix(404,-961,169,-402) (19/8,31/13) -> (31/13,12/5) Parabolic Matrix(1491,-3614,578,-1401) (46/19,17/7) -> (49/19,80/31) Hyperbolic Matrix(4976,-12843,1315,-3394) (80/31,111/43) -> (87/23,53/14) Hyperbolic Matrix(2506,-6471,663,-1712) (111/43,31/12) -> (34/9,87/23) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(3396,-9409,1225,-3394) (36/13,97/35) -> (97/35,61/22) Parabolic Matrix(1496,-4225,529,-1494) (48/17,65/23) -> (65/23,17/6) Parabolic Matrix(34,-99,11,-32) (17/6,3/1) -> (3/1,16/5) Parabolic Matrix(146,-471,31,-100) (16/5,13/4) -> (14/3,19/4) Hyperbolic Matrix(5536,-18225,1681,-5534) (79/24,135/41) -> (135/41,56/17) Parabolic Matrix(2988,-10609,841,-2986) (71/20,103/29) -> (103/29,32/9) Parabolic Matrix(1312,-4761,361,-1310) (29/8,69/19) -> (69/19,40/11) Parabolic Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(260,-1369,49,-258) (21/4,37/7) -> (37/7,16/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,1,-2,-1) Matrix(197,-24,156,-19) -> Matrix(1,0,0,1) Matrix(194,-27,115,-16) -> Matrix(1,1,-4,-3) Matrix(191,-28,116,-17) -> Matrix(1,0,0,1) Matrix(187,-32,76,-13) -> Matrix(1,0,0,1) Matrix(409,-76,296,-55) -> Matrix(1,0,-2,1) Matrix(654,-137,401,-84) -> Matrix(1,1,-4,-3) Matrix(146,-31,471,-100) -> Matrix(3,1,2,1) Matrix(73,-16,324,-71) -> Matrix(1,0,4,1) Matrix(2222,-507,859,-196) -> Matrix(1,-1,0,1) Matrix(788,-181,357,-82) -> Matrix(1,-1,2,-1) Matrix(107,-26,70,-17) -> Matrix(1,0,0,1) Matrix(557,-146,454,-119) -> Matrix(1,0,0,1) Matrix(1077,-286,418,-111) -> Matrix(1,0,0,1) Matrix(242,-65,417,-112) -> Matrix(5,1,-6,-1) Matrix(449,-124,344,-95) -> Matrix(1,2,-2,-3) Matrix(1171,-326,722,-201) -> Matrix(1,2,-2,-3) Matrix(585,-164,824,-231) -> Matrix(3,4,-4,-5) Matrix(238,-69,69,-20) -> Matrix(1,1,-2,-1) Matrix(340,-101,101,-30) -> Matrix(3,-1,-2,1) Matrix(203,-62,370,-113) -> Matrix(1,-2,0,1) Matrix(34,-11,99,-32) -> Matrix(1,-1,0,1) Matrix(455,-162,778,-277) -> Matrix(3,10,-4,-13) Matrix(616,-221,485,-174) -> Matrix(1,1,0,1) Matrix(2425,-874,874,-315) -> Matrix(1,2,0,1) Matrix(872,-315,227,-82) -> Matrix(1,1,0,1) Matrix(97,-36,256,-95) -> Matrix(1,2,-2,-3) Matrix(1082,-413,765,-292) -> Matrix(1,1,-6,-5) Matrix(446,-171,699,-268) -> Matrix(1,1,-2,-1) Matrix(127,-50,94,-37) -> Matrix(1,0,-2,1) Matrix(187,-76,32,-13) -> Matrix(1,0,0,1) Matrix(343,-142,186,-77) -> Matrix(1,0,0,1) Matrix(217,-92,92,-39) -> Matrix(1,2,0,1) Matrix(245,-108,152,-67) -> Matrix(1,2,-2,-3) Matrix(212,-95,183,-82) -> Matrix(1,1,-2,-1) Matrix(1879,-848,2608,-1177) -> Matrix(3,4,-4,-5) Matrix(1120,-507,243,-110) -> Matrix(1,3,-2,-5) Matrix(271,-124,212,-97) -> Matrix(3,4,-4,-5) Matrix(343,-186,142,-77) -> Matrix(1,0,0,1) Matrix(737,-406,1022,-563) -> Matrix(3,4,-4,-5) Matrix(113,-64,196,-111) -> Matrix(7,8,-8,-9) Matrix(2663,-1560,944,-553) -> Matrix(27,20,4,3) Matrix(526,-309,749,-440) -> Matrix(19,13,-22,-15) Matrix(1854,-1093,1357,-800) -> Matrix(1,1,-6,-5) Matrix(3237,-1910,1910,-1127) -> Matrix(3,2,-8,-5) Matrix(194,-115,27,-16) -> Matrix(1,1,-4,-3) Matrix(191,-116,28,-17) -> Matrix(1,0,0,1) Matrix(709,-434,874,-535) -> Matrix(3,2,-2,-1) Matrix(654,-401,137,-84) -> Matrix(1,1,-4,-3) Matrix(245,-152,108,-67) -> Matrix(1,0,2,1) Matrix(297,-188,188,-119) -> Matrix(1,0,0,1) Matrix(403,-258,214,-137) -> Matrix(1,0,0,1) Matrix(107,-70,26,-17) -> Matrix(1,0,0,1) Matrix(78,-53,53,-36) -> Matrix(1,1,0,1) Matrix(260,-181,181,-126) -> Matrix(1,1,-16,-15) Matrix(206,-145,233,-164) -> Matrix(11,9,-16,-13) Matrix(774,-547,283,-200) -> Matrix(1,1,-4,-3) Matrix(747,-530,926,-657) -> Matrix(5,4,-4,-3) Matrix(1742,-1251,1075,-772) -> Matrix(7,5,-10,-7) Matrix(2610,-1877,1613,-1160) -> Matrix(1,1,-4,-3) Matrix(4961,-3576,1508,-1087) -> Matrix(5,4,-4,-3) Matrix(409,-296,76,-55) -> Matrix(3,2,-2,-1) Matrix(127,-94,50,-37) -> Matrix(3,2,-2,-1) Matrix(449,-344,124,-95) -> Matrix(1,0,2,1) Matrix(347,-268,224,-173) -> Matrix(1,0,2,1) Matrix(271,-212,124,-97) -> Matrix(1,0,4,1) Matrix(616,-485,221,-174) -> Matrix(1,1,0,1) Matrix(197,-156,24,-19) -> Matrix(1,0,0,1) Matrix(2505,-2026,706,-571) -> Matrix(1,0,0,1) Matrix(557,-454,146,-119) -> Matrix(1,0,0,1) Matrix(121,-100,144,-119) -> Matrix(3,4,-4,-5) Matrix(262,-223,47,-40) -> Matrix(1,1,-4,-3) Matrix(212,-183,95,-82) -> Matrix(1,1,-2,-1) Matrix(206,-233,145,-164) -> Matrix(3,1,-16,-5) Matrix(121,-144,100,-119) -> Matrix(1,0,4,1) Matrix(436,-531,179,-218) -> Matrix(1,-1,0,1) Matrix(710,-873,257,-316) -> Matrix(1,1,0,1) Matrix(709,-874,434,-535) -> Matrix(1,0,-2,1) Matrix(1224,-1549,757,-958) -> Matrix(1,1,-2,-1) Matrix(542,-691,251,-320) -> Matrix(1,1,6,7) Matrix(328,-419,155,-198) -> Matrix(1,1,-6,-5) Matrix(249,-322,58,-75) -> Matrix(3,2,-2,-1) Matrix(553,-724,152,-199) -> Matrix(7,4,-2,-1) Matrix(1376,-1881,297,-406) -> Matrix(5,1,-6,-1) Matrix(557,-764,148,-203) -> Matrix(1,0,2,1) Matrix(481,-664,92,-127) -> Matrix(1,0,2,1) Matrix(609,-844,184,-255) -> Matrix(7,2,-4,-1) Matrix(1104,-1535,479,-666) -> Matrix(3,1,2,1) Matrix(790,-1101,221,-308) -> Matrix(3,1,-4,-1) Matrix(585,-824,164,-231) -> Matrix(1,0,4,1) Matrix(526,-749,309,-440) -> Matrix(7,1,-22,-3) Matrix(997,-1556,412,-643) -> Matrix(1,0,0,1) Matrix(514,-805,189,-296) -> Matrix(1,1,0,1) Matrix(460,-729,289,-458) -> Matrix(1,1,-2,-1) Matrix(1303,-2128,368,-601) -> Matrix(1,0,2,1) Matrix(534,-875,83,-136) -> Matrix(5,1,-6,-1) Matrix(416,-683,67,-110) -> Matrix(1,-1,0,1) Matrix(4068,-6889,2401,-4066) -> Matrix(3,1,-10,-3) Matrix(1142,-1937,441,-748) -> Matrix(3,1,-4,-1) Matrix(455,-778,162,-277) -> Matrix(9,2,4,1) Matrix(113,-196,64,-111) -> Matrix(1,0,8,1) Matrix(174,-311,47,-84) -> Matrix(3,-1,-2,1) Matrix(203,-370,62,-113) -> Matrix(1,-2,0,1) Matrix(523,-974,138,-257) -> Matrix(1,0,0,1) Matrix(1081,-2396,328,-727) -> Matrix(1,-2,0,1) Matrix(481,-1102,134,-307) -> Matrix(1,0,0,1) Matrix(120,-277,13,-30) -> Matrix(1,-1,0,1) Matrix(404,-961,169,-402) -> Matrix(1,-5,0,1) Matrix(1491,-3614,578,-1401) -> Matrix(1,0,0,1) Matrix(4976,-12843,1315,-3394) -> Matrix(1,1,0,1) Matrix(2506,-6471,663,-1712) -> Matrix(1,1,-2,-1) Matrix(97,-256,36,-95) -> Matrix(1,0,2,1) Matrix(3396,-9409,1225,-3394) -> Matrix(1,-1,0,1) Matrix(1496,-4225,529,-1494) -> Matrix(1,-17,0,1) Matrix(34,-99,11,-32) -> Matrix(1,-1,0,1) Matrix(146,-471,31,-100) -> Matrix(1,3,-2,-5) Matrix(5536,-18225,1681,-5534) -> Matrix(3,5,-2,-3) Matrix(2988,-10609,841,-2986) -> Matrix(1,1,-2,-1) Matrix(1312,-4761,361,-1310) -> Matrix(1,-7,0,1) Matrix(73,-324,16,-71) -> Matrix(3,4,-4,-5) Matrix(260,-1369,49,-258) -> Matrix(1,1,-2,-1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 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): 40 ----------------------------------------------------------------------- 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 8/7 (-1/3,0/1) 0 22 7/6 (-1/3,0/1) 0 22 6/5 0/1 2 2 17/14 (0/1,1/1) 0 22 11/9 1/0 1 11 16/13 (-1/1,0/1) 0 22 5/4 (-1/1,0/1) 0 22 19/15 (-1/2,1/0) 0 11 14/11 (-2/1,-1/1) 0 22 9/7 -1/2 1 11 13/10 (-2/3,-1/2) 0 22 4/3 (-1/2,-1/3) 0 22 11/8 (-1/3,0/1) 0 22 18/13 (-1/3,0/1) 0 22 25/18 (-1/3,0/1) 0 22 32/23 -1/3 1 2 7/5 -1/4 1 11 24/17 (-1/5,0/1) 0 22 17/12 (-1/5,0/1) 0 22 27/19 (-3/16,-1/6) 0 11 10/7 (-1/8,0/1) 0 22 13/9 0/1 8 1 3/2 (0/1,1/0) 0 22 14/9 (-1/1,1/0) 0 22 25/16 (-1/1,0/1) 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 (-2/3,-1/2) 0 22 31/19 (-1/2,-1/4) 0 11 49/30 (-1/3,0/1) 0 22 18/11 (-1/3,0/1) 0 22 5/3 -1/2 1 11 22/13 (-1/3,0/1) 0 22 83/49 (-1/2,-1/4).(-1/3,0/1) 0 1 39/23 (-1/2,-1/4) 0 11 17/10 (-1/2,-1/3) 0 22 29/17 (-5/18,-1/4) 0 11 12/7 (-1/5,0/1) 0 22 7/4 0/1 4 2 16/9 (0/1,1/3) 0 22 9/5 (1/2,1/0) 0 11 11/6 (1/1,1/0) 0 22 2/1 (-1/1,0/1) 0 22 15/7 0/1 6 1 13/6 (0/1,1/5) 0 22 11/5 1/2 1 11 31/14 (0/1,1/1) 0 22 20/9 (0/1,1/1) 0 22 9/4 (0/1,1/1) 0 22 16/7 (-1/1,1/0) 0 22 23/10 0/1 1 2 30/13 (0/1,1/1) 0 22 7/3 (1/2,1/0) 0 11 31/13 1/0 5 1 12/5 (-2/1,1/0) 0 22 29/12 (-1/1,0/1) 0 22 46/19 (-1/1,1/0) 0 22 17/7 1/0 1 11 5/2 (0/1,1/0) 0 22 18/7 (-1/1,0/1) 0 22 31/12 (-1/1,0/1) 0 22 44/17 (-1/2,0/1) 0 22 13/5 (-1/2,1/0) 0 11 8/3 0/1 1 2 19/7 (1/2,1/0) 0 11 30/11 (0/1,1/1) 0 22 11/4 (0/1,1/1) 0 22 36/13 (1/1,1/0) 0 22 97/35 1/0 1 1 25/9 (1/2,1/0) 0 11 14/5 (1/1,2/1) 0 22 31/11 (9/2,1/0) 0 11 65/23 1/0 17 1 17/6 (-4/1,1/0) 0 22 3/1 1/0 1 11 16/5 (-5/1,1/0) 0 22 13/4 (-1/1,1/0) 0 22 23/7 (-3/2,1/0) 0 11 135/41 (-2/1,-1/1).(-3/2,1/0) 0 1 56/17 (-2/1,-1/1) 0 22 33/10 (-2/1,-1/1) 0 22 10/3 (-2/1,-1/1) 0 22 17/5 -1/1 2 1 7/2 (-1/1,0/1) 0 22 39/11 (-1/2,1/0) 0 11 103/29 (-1/1,0/1).(-1/2,1/0) 0 1 32/9 (-1/1,0/1) 0 22 25/7 1/0 1 11 43/12 0/1 1 2 18/5 (-1/1,1/0) 0 22 29/8 (2/1,1/0) 0 22 69/19 1/0 7 1 11/3 (-3/2,1/0) 0 11 15/4 (-1/1,0/1) 0 22 34/9 (-1/1,0/1) 0 22 87/23 0/1 1 1 53/14 (0/1,1/0) 0 22 19/5 1/0 1 11 23/6 (-1/1,0/1) 0 22 4/1 (-1/1,1/0) 0 22 17/4 (0/1,1/0) 0 22 13/3 1/0 1 11 9/2 -1/1 2 2 23/5 -3/4 1 11 37/8 (-1/1,-2/3) 0 22 14/3 (-2/3,-1/2) 0 22 19/4 (-1/2,-2/5) 0 22 5/1 (-1/2,1/0) 0 11 37/7 (-1/1,0/1).(-1/2,1/0) 0 1 16/3 (-1/1,0/1) 0 22 11/2 (-1/1,0/1) 0 22 17/3 1/0 1 11 6/1 (-1/1,1/0) 0 22 19/3 -1/1 3 1 13/2 (-1/1,-2/3) 0 22 7/1 -1/2 1 11 8/1 (-1/1,0/1) 0 22 9/1 (-1/2,1/0) 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(206,-233,145,-164) (1/1,8/7) -> (17/12,27/19) Hyperbolic Matrix(183,-212,82,-95) (8/7,7/6) -> (20/9,9/4) Glide Reflection Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(337,-410,60,-73) (17/14,11/9) -> (11/2,17/3) Glide Reflection Matrix(454,-557,119,-146) (11/9,16/13) -> (19/5,23/6) Glide Reflection Matrix(709,-874,434,-535) (16/13,5/4) -> (49/30,18/11) Hyperbolic Matrix(156,-197,19,-24) (5/4,19/15) -> (8/1,9/1) Glide Reflection Matrix(485,-616,174,-221) (19/15,14/11) -> (25/9,14/5) Glide Reflection Matrix(212,-271,97,-124) (14/11,9/7) -> (13/6,11/5) Glide Reflection 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(609,-844,184,-255) (18/13,25/18) -> (33/10,10/3) Hyperbolic Matrix(1104,-1535,479,-666) (25/18,32/23) -> (23/10,30/13) Hyperbolic Matrix(790,-1101,221,-308) (32/23,7/5) -> (25/7,43/12) Hyperbolic Matrix(585,-824,164,-231) (7/5,24/17) -> (32/9,25/7) Hyperbolic Matrix(547,-774,200,-283) (24/17,17/12) -> (30/11,11/4) Glide Reflection Matrix(526,-749,309,-440) (27/19,10/7) -> (17/10,29/17) Hyperbolic Matrix(181,-260,126,-181) (10/7,13/9) -> (10/7,13/9) 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(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(514,-805,189,-296) (25/16,11/7) -> (19/7,30/11) Hyperbolic 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(401,-654,84,-137) (13/8,31/19) -> (19/4,5/1) Glide Reflection Matrix(1303,-2128,368,-601) (31/19,49/30) -> (7/2,39/11) Hyperbolic Matrix(116,-191,17,-28) (18/11,5/3) -> (13/2,7/1) Glide Reflection Matrix(115,-194,16,-27) (5/3,22/13) -> (7/1,8/1) Glide Reflection Matrix(2157,-3652,1274,-2157) (22/13,83/49) -> (22/13,83/49) Reflection Matrix(1910,-3237,1127,-1910) (83/49,39/23) -> (83/49,39/23) Reflection Matrix(1142,-1937,441,-748) (39/23,17/10) -> (44/17,13/5) 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(174,-311,47,-84) (16/9,9/5) -> (11/3,15/4) Hyperbolic Matrix(203,-370,62,-113) (9/5,11/6) -> (13/4,23/7) Hyperbolic Matrix(186,-343,77,-142) (11/6,2/1) -> (12/5,29/12) Glide Reflection Matrix(29,-60,14,-29) (2/1,15/7) -> (2/1,15/7) Reflection Matrix(181,-390,84,-181) (15/7,13/6) -> (15/7,13/6) Reflection Matrix(507,-1120,110,-243) (11/5,31/14) -> (23/5,37/8) Glide Reflection 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(120,-277,13,-30) (30/13,7/3) -> (9/1,1/0) Hyperbolic 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(732,-1775,193,-468) (46/19,17/7) -> (53/14,19/5) Glide Reflection 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(797,-2062,172,-445) (31/12,44/17) -> (37/8,14/3) Glide Reflection Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(315,-872,82,-227) (11/4,36/13) -> (23/6,4/1) Glide Reflection Matrix(2521,-6984,910,-2521) (36/13,97/35) -> (36/13,97/35) Reflection Matrix(874,-2425,315,-874) (97/35,25/9) -> (97/35,25/9) Reflection Matrix(714,-2015,253,-714) (31/11,65/23) -> (31/11,65/23) Reflection Matrix(781,-2210,276,-781) (65/23,17/6) -> (65/23,17/6) Reflection Matrix(34,-99,11,-32) (17/6,3/1) -> (3/1,16/5) Parabolic Matrix(146,-471,31,-100) (16/5,13/4) -> (14/3,19/4) Hyperbolic Matrix(944,-3105,287,-944) (23/7,135/41) -> (23/7,135/41) Reflection Matrix(4591,-15120,1394,-4591) (135/41,56/17) -> (135/41,56/17) Reflection Matrix(101,-340,30,-101) (10/3,17/5) -> (10/3,17/5) Reflection Matrix(69,-238,20,-69) (17/5,7/2) -> (17/5,7/2) Reflection Matrix(1132,-4017,319,-1132) (39/11,103/29) -> (39/11,103/29) Reflection Matrix(1855,-6592,522,-1855) (103/29,32/9) -> (103/29,32/9) 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(2437,-9222,644,-2437) (87/23,53/14) -> (87/23,53/14) Reflection Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic 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(77,-494,12,-77) (19/3,13/2) -> (19/3,13/2) 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(206,-233,145,-164) -> Matrix(3,1,-16,-5) -1/4 Matrix(183,-212,82,-95) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(121,-144,100,-119) -> Matrix(1,0,4,1) 0/1 Matrix(337,-410,60,-73) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(454,-557,119,-146) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(709,-874,434,-535) -> Matrix(1,0,-2,1) 0/1 Matrix(156,-197,19,-24) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(485,-616,174,-221) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(212,-271,97,-124) -> Matrix(1,1,4,3) Matrix(249,-322,58,-75) -> Matrix(3,2,-2,-1) -1/1 Matrix(344,-449,95,-124) -> Matrix(1,1,2,1) Matrix(94,-127,37,-50) -> Matrix(3,1,-2,-1) Matrix(296,-409,55,-76) -> Matrix(3,1,-2,-1) Matrix(609,-844,184,-255) -> Matrix(7,2,-4,-1) Matrix(1104,-1535,479,-666) -> Matrix(3,1,2,1) Matrix(790,-1101,221,-308) -> Matrix(3,1,-4,-1) -1/2 Matrix(585,-824,164,-231) -> Matrix(1,0,4,1) 0/1 Matrix(547,-774,200,-283) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(526,-749,309,-440) -> Matrix(7,1,-22,-3) Matrix(181,-260,126,-181) -> Matrix(-1,0,16,1) (10/7,13/9) -> (-1/8,0/1) Matrix(53,-78,36,-53) -> Matrix(1,0,0,-1) (13/9,3/2) -> (0/1,1/0) Matrix(70,-107,17,-26) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(997,-1556,412,-643) -> Matrix(1,0,0,1) Matrix(514,-805,189,-296) -> Matrix(1,1,0,1) 1/0 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(1,1,2,1) Matrix(401,-654,84,-137) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(1303,-2128,368,-601) -> Matrix(1,0,2,1) 0/1 Matrix(116,-191,17,-28) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(115,-194,16,-27) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(2157,-3652,1274,-2157) -> Matrix(-1,0,6,1) (22/13,83/49) -> (-1/3,0/1) Matrix(1910,-3237,1127,-1910) -> Matrix(3,1,-8,-3) (83/49,39/23) -> (-1/2,-1/4) Matrix(1142,-1937,441,-748) -> Matrix(3,1,-4,-1) -1/2 Matrix(455,-778,162,-277) -> Matrix(9,2,4,1) Matrix(113,-196,64,-111) -> Matrix(1,0,8,1) 0/1 Matrix(174,-311,47,-84) -> Matrix(3,-1,-2,1) Matrix(203,-370,62,-113) -> Matrix(1,-2,0,1) 1/0 Matrix(186,-343,77,-142) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(29,-60,14,-29) -> Matrix(-1,0,2,1) (2/1,15/7) -> (-1/1,0/1) Matrix(181,-390,84,-181) -> Matrix(1,0,10,-1) (15/7,13/6) -> (0/1,1/5) Matrix(507,-1120,110,-243) -> Matrix(1,-2,-2,3) Matrix(1081,-2396,328,-727) -> Matrix(1,-2,0,1) 1/0 Matrix(481,-1102,134,-307) -> Matrix(1,0,0,1) Matrix(120,-277,13,-30) -> Matrix(1,-1,0,1) 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(1,4,0,-1) (31/13,12/5) -> (-2/1,1/0) Matrix(732,-1775,193,-468) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(76,-187,13,-32) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(418,-1077,111,-286) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(797,-2062,172,-445) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(97,-256,36,-95) -> Matrix(1,0,2,1) 0/1 Matrix(315,-872,82,-227) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2521,-6984,910,-2521) -> Matrix(-1,2,0,1) (36/13,97/35) -> (1/1,1/0) Matrix(874,-2425,315,-874) -> Matrix(-1,1,0,1) (97/35,25/9) -> (1/2,1/0) Matrix(714,-2015,253,-714) -> Matrix(-1,9,0,1) (31/11,65/23) -> (9/2,1/0) Matrix(781,-2210,276,-781) -> Matrix(1,8,0,-1) (65/23,17/6) -> (-4/1,1/0) Matrix(34,-99,11,-32) -> Matrix(1,-1,0,1) 1/0 Matrix(146,-471,31,-100) -> Matrix(1,3,-2,-5) Matrix(944,-3105,287,-944) -> Matrix(1,3,0,-1) (23/7,135/41) -> (-3/2,1/0) Matrix(4591,-15120,1394,-4591) -> Matrix(3,4,-2,-3) (135/41,56/17) -> (-2/1,-1/1) Matrix(101,-340,30,-101) -> Matrix(3,4,-2,-3) (10/3,17/5) -> (-2/1,-1/1) Matrix(69,-238,20,-69) -> Matrix(-1,0,2,1) (17/5,7/2) -> (-1/1,0/1) Matrix(1132,-4017,319,-1132) -> Matrix(1,1,0,-1) (39/11,103/29) -> (-1/2,1/0) Matrix(1855,-6592,522,-1855) -> Matrix(-1,0,2,1) (103/29,32/9) -> (-1/1,0/1) Matrix(1103,-4002,304,-1103) -> Matrix(-1,4,0,1) (29/8,69/19) -> (2/1,1/0) Matrix(208,-759,57,-208) -> Matrix(1,3,0,-1) (69/19,11/3) -> (-3/2,1/0) Matrix(1565,-5916,414,-1565) -> Matrix(-1,0,2,1) (34/9,87/23) -> (-1/1,0/1) Matrix(2437,-9222,644,-2437) -> Matrix(1,0,0,-1) (87/23,53/14) -> (0/1,1/0) Matrix(73,-324,16,-71) -> Matrix(3,4,-4,-5) -1/1 Matrix(36,-185,7,-36) -> Matrix(1,1,0,-1) (5/1,37/7) -> (-1/2,1/0) Matrix(223,-1184,42,-223) -> Matrix(-1,0,2,1) (37/7,16/3) -> (-1/1,0/1) Matrix(37,-228,6,-37) -> Matrix(1,2,0,-1) (6/1,19/3) -> (-1/1,1/0) Matrix(77,-494,12,-77) -> Matrix(5,4,-6,-5) (19/3,13/2) -> (-1/1,-2/3) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.