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 0/1 -1/2 0/1 1/3 -7/15 1/4 -6/13 1/3 1/2 -11/24 0/1 1/1 -5/11 1/4 1/2 -14/31 1/2 1/1 -9/20 0/1 -22/49 1/6 1/5 -13/29 1/4 -4/9 0/1 1/4 -11/25 1/4 3/10 -18/41 1/4 1/3 -25/57 1/4 -7/16 2/7 1/3 -10/23 1/3 3/8 -13/30 0/1 1/2 -3/7 1/2 -14/33 0/1 1/0 -11/26 0/1 1/1 -8/19 0/1 -21/50 0/1 1/7 -13/31 1/6 1/4 -5/12 1/5 1/4 -17/41 1/4 -12/29 1/5 1/4 -7/17 1/4 3/10 -9/22 0/1 1/3 -11/27 3/10 -2/5 1/3 1/2 -11/28 1/2 2/3 -20/51 1/1 1/0 -9/23 1/2 1/0 -7/18 0/1 -12/31 0/1 1/4 -17/44 0/1 1/6 -5/13 1/4 -18/47 1/4 4/15 -13/34 1/4 1/3 -8/21 3/10 1/3 -11/29 1/4 1/2 -14/37 1/4 1/3 -3/8 1/4 1/3 -10/27 1/3 7/20 -17/46 1/3 4/11 -7/19 3/8 -25/68 1/3 2/5 -43/117 3/8 1/2 -18/49 1/3 3/8 -11/30 2/5 3/7 -4/11 1/3 1/2 -13/36 7/19 3/8 -9/25 3/8 -14/39 2/5 9/22 -5/14 2/5 3/7 -16/45 2/5 1/2 -11/31 1/2 -6/17 1/2 -7/20 2/3 1/1 -1/3 1/4 1/2 -6/19 3/7 1/2 -5/16 1/2 -9/29 1/2 -13/42 4/7 3/5 -4/13 1/2 2/3 -11/36 4/5 1/1 -18/59 1/1 3/2 -7/23 1/2 -10/33 1/2 1/1 -13/43 1/2 3/4 -3/10 1/1 1/0 -11/37 1/2 1/0 -19/64 0/1 1/1 -8/27 0/1 1/0 -21/71 1/4 1/2 -13/44 0/1 1/1 -18/61 1/2 2/3 -5/17 1/0 -12/41 -1/2 0/1 -7/24 -1/4 0/1 -2/7 0/1 1/4 -11/39 1/4 -9/32 3/13 1/4 -7/25 1/4 3/10 -12/43 5/16 1/3 -5/18 1/3 2/5 -13/47 1/4 1/2 -21/76 1/3 -8/29 1/3 1/2 -11/40 0/1 1/3 -14/51 1/3 3/8 -3/11 1/2 -10/37 1/4 1/3 -7/26 1/3 2/5 -4/15 1/2 -5/19 1/2 1/0 -6/23 1/3 1/2 -7/27 1/2 -1/4 0/1 1/1 -6/25 0/1 1/14 -5/21 1/8 -4/17 1/6 1/5 -7/30 1/5 1/4 -10/43 0/1 -3/13 1/6 1/4 -8/35 3/13 1/4 -5/22 1/4 2/7 -12/53 1/5 1/4 -7/31 1/4 -2/9 1/4 1/3 -7/32 0/1 1/5 -12/55 1/4 6/23 -5/23 1/4 3/10 -3/14 1/3 -7/33 3/8 1/2 -4/19 2/5 1/2 -5/24 1/3 2/5 -1/5 1/2 -4/21 1/3 1/2 -7/37 1/2 1/0 -10/53 1/2 2/3 -3/16 0/1 1/1 -2/11 0/1 1/4 -7/39 1/4 -5/28 1/5 1/4 -8/45 3/10 1/3 -11/62 1/3 3/8 -3/17 1/4 1/2 -1/6 1/4 1/3 -4/25 1/4 1/3 -3/19 1/4 -2/13 1/3 -5/33 7/20 -3/20 4/11 3/8 -1/7 3/8 1/2 -4/29 7/18 2/5 -3/22 2/5 7/17 -2/15 3/7 1/2 -1/8 3/7 1/2 -2/17 1/2 4/7 -1/9 1/2 0/1 0/1 1/2 1/8 0/1 1/1 2/15 1/4 1/3 1/7 1/2 1/6 1/2 3/5 2/11 1/2 3/5 1/5 1/2 3/4 6/29 2/3 3/4 5/24 4/5 1/1 4/19 3/4 1/1 3/14 3/4 4/5 2/9 1/1 5/22 5/4 4/3 8/35 3/2 8/5 3/13 1/0 1/4 1/1 1/0 5/19 1/0 4/15 0/1 1/0 7/26 0/1 3/11 1/2 1/0 5/18 -1/1 1/0 7/25 1/0 2/7 0/1 1/0 5/17 0/1 8/27 0/1 1/6 3/10 0/1 1/3 4/13 1/2 1/1 5/16 1/2 1/1 6/19 0/1 1/0 1/3 1/2 7/20 1/2 2/3 6/17 1/2 1/1 5/14 2/3 1/1 14/39 0/1 1/0 9/25 1/2 1/0 13/36 1/2 1/1 4/11 1/2 2/3 3/8 1/1 8/21 3/2 2/1 21/55 1/0 34/89 2/1 1/0 47/123 3/2 1/0 13/34 1/1 2/1 31/81 1/0 18/47 1/1 1/0 5/13 3/2 1/0 2/5 1/1 1/0 7/17 1/0 5/12 2/1 1/0 3/7 -1/2 1/0 4/9 -1/1 -1/2 9/20 -1/3 0/1 14/31 -2/3 -1/2 5/11 -1/4 1/2 0/1 1/3 6/11 1/2 1/1 11/20 0/1 1/3 5/9 1/4 1/2 4/7 1/2 11/19 1/2 3/4 18/31 0/1 1/2 25/43 1/2 32/55 1/2 8/15 7/12 2/3 1/1 24/41 1/2 1/1 17/29 1/2 1/0 10/17 1/1 1/0 23/39 1/2 1/0 13/22 0/1 1/3 16/27 0/1 1/2 3/5 1/2 11/18 0/1 1/1 19/31 1/2 3/4 8/13 1/2 1/1 5/8 2/3 1/1 7/11 3/2 1/0 16/25 3/1 1/0 9/14 -3/1 1/0 2/3 0/1 1/0 9/13 0/1 16/23 0/1 1/16 7/10 0/1 1/8 26/37 0/1 1/6 45/64 1/8 1/7 19/27 1/8 1/6 12/17 0/1 1/6 17/24 0/1 1/5 22/31 0/1 1/4 5/7 1/4 28/39 1/4 1/3 23/32 1/3 18/25 2/5 1/2 49/68 0/1 1/1 31/43 1/4 1/2 13/18 0/1 1/3 8/11 0/1 1/4 3/4 1/4 1/3 10/13 1/3 1/2 7/9 1/2 11/14 1/3 4/11 26/33 4/11 3/8 15/19 3/8 1/2 4/5 2/5 1/2 21/26 2/5 3/7 17/21 5/12 1/2 13/16 3/7 4/9 9/11 1/2 5/6 1/2 11/13 1/2 17/20 1/2 3/5 6/7 1/2 3/5 13/15 3/4 20/23 1/2 4/7 27/31 1/2 5/8 7/8 2/3 1/1 8/9 1/1 1/0 1/1 1/2 1/0 8/7 0/1 1/2 15/13 1/4 7/6 1/3 2/5 6/5 1/2 17/14 5/9 4/7 28/23 1/2 3/5 11/9 1/2 27/22 1/2 3/5 43/35 1/2 7/12 16/13 1/2 2/3 5/4 3/5 2/3 24/19 1/2 2/3 43/34 3/5 19/15 1/2 5/8 33/26 7/11 2/3 14/11 9/14 2/3 37/29 2/3 60/47 2/3 43/64 23/18 2/3 17/25 9/7 3/4 13/10 3/4 7/9 17/13 3/4 5/6 4/3 1/2 1/1 15/11 1/2 1/0 41/30 0/1 1/4 67/49 3/8 26/19 4/9 1/2 11/8 3/5 2/3 29/21 7/10 3/4 18/13 3/4 1/1 25/18 2/3 1/1 32/23 2/3 39/28 5/7 3/4 7/5 3/4 24/17 3/4 1/1 41/29 3/4 11/14 17/12 4/5 1/1 44/31 9/11 5/6 27/19 5/6 7/8 37/26 4/5 1/1 10/7 7/8 1/1 13/9 1/1 16/11 1/1 9/8 3/2 1/1 1/0 17/11 1/0 14/9 1/1 1/0 25/16 0/1 1/1 36/23 0/1 1/2 11/7 1/2 1/0 19/12 4/5 1/1 27/17 1/1 35/22 1/1 10/9 8/5 1/1 3/2 21/13 3/2 1/0 55/34 1/1 2/1 34/21 2/1 81/50 2/1 3/1 47/29 1/0 13/8 1/1 1/0 44/27 1/1 1/0 31/19 5/2 1/0 49/30 3/1 4/1 18/11 4/1 1/0 41/25 1/0 64/39 -10/1 1/0 23/14 -3/1 1/0 5/3 1/0 27/16 -1/1 0/1 49/29 -1/2 1/0 22/13 -1/2 0/1 83/49 0/1 61/36 0/1 1/3 39/23 1/2 1/0 56/33 -4/1 1/0 17/10 -1/2 0/1 46/27 0/1 1/0 29/17 -1/2 1/0 12/7 0/1 1/0 7/4 0/1 16/9 0/1 1/4 57/32 0/1 1/5 98/55 1/5 1/4 41/23 1/4 66/37 1/4 2/7 25/14 1/4 1/3 9/5 1/4 1/2 11/6 2/5 1/2 13/7 1/2 15/8 1/2 7/13 2/1 1/2 1/1 15/7 1/1 28/13 1/1 13/12 13/6 1/1 6/5 11/5 3/2 31/14 1/1 2/1 20/9 2/1 1/0 29/13 5/2 1/0 9/4 0/1 1/1 16/7 1/1 1/0 23/10 1/1 30/13 3/2 2/1 7/3 3/2 1/0 19/8 4/1 1/0 31/13 1/0 43/18 -6/1 1/0 12/5 -1/1 1/0 29/12 0/1 1/1 46/19 1/1 1/0 17/7 1/0 39/16 1/0 22/9 -1/1 1/0 5/2 -1/1 1/0 18/7 0/1 1/0 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 -1/2 44/17 -1/1 1/0 57/22 -1/3 0/1 13/5 -1/2 1/0 8/3 0/1 19/7 1/6 1/4 49/18 5/21 1/4 128/47 1/4 12/47 79/29 1/4 30/11 1/4 1/3 71/26 2/7 1/3 41/15 1/4 11/4 0/1 1/3 47/17 1/2 36/13 0/1 1/2 97/35 1/2 61/22 1/2 1/1 25/9 1/2 1/0 64/23 0/1 1/0 39/14 0/1 1/1 14/5 0/1 1/4 31/11 1/4 1/2 48/17 1/4 1/3 65/23 1/3 17/6 1/3 1/2 3/1 1/2 19/6 0/1 1/1 35/11 1/2 3/4 51/16 3/4 1/1 67/21 1/1 16/5 1/2 1/1 29/9 1/2 3/4 13/4 0/1 1/2 23/7 1/2 3/4 79/24 3/5 2/3 135/41 2/3 56/17 2/3 3/4 33/10 2/3 1/1 10/3 3/4 1/1 17/5 1/1 24/7 1/1 7/6 7/2 1/1 2/1 39/11 1/2 1/0 71/20 0/1 1/1 103/29 1/1 32/9 1/1 1/0 25/7 1/0 68/19 1/2 2/3 43/12 1/1 18/5 1/1 1/0 29/8 1/2 1/1 69/19 1/1 109/30 1/1 11/10 40/11 1/1 5/4 11/3 3/2 1/0 26/7 1/0 15/4 1/1 2/1 34/9 8/1 1/0 87/23 1/0 140/37 -26/1 1/0 53/14 -9/1 1/0 19/5 1/0 23/6 -1/1 0/1 27/7 1/2 1/0 31/8 1/1 1/0 35/9 1/0 4/1 0/1 1/0 17/4 -3/1 1/0 13/3 1/0 9/2 0/1 23/5 1/4 60/13 0/1 1/2 217/47 0/1 157/34 0/1 1/5 97/21 1/4 1/2 37/8 0/1 1/3 51/11 1/4 1/2 14/3 1/3 1/2 33/7 1/2 19/4 1/3 1/2 24/5 1/2 2/3 29/6 2/3 1/1 34/7 1/2 1/1 73/15 1/1 39/8 0/1 1/1 5/1 1/2 1/0 21/4 -1/3 0/1 37/7 0/1 53/10 0/1 1/11 16/3 0/1 1/4 11/2 0/1 1/3 28/5 1/2 17/3 1/2 6/1 1/2 1/1 19/3 1/1 32/5 1/1 5/4 13/2 1/1 2/1 7/1 1/0 15/2 0/1 1/2 23/3 -1/2 1/0 31/4 -1/3 0/1 39/5 0/1 8/1 0/1 1/2 9/1 1/2 1/0 10/1 0/1 1/0 0/1 1/1 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(1,0,2,1) Matrix(415,194,246,115) -> Matrix(1,0,-4,1) Matrix(249,116,-908,-423) -> Matrix(7,-2,18,-5) Matrix(893,410,734,337) -> Matrix(9,-4,16,-7) Matrix(647,296,-2188,-1001) -> Matrix(1,0,0,1) Matrix(1445,654,886,401) -> Matrix(3,-2,2,-1) Matrix(719,324,-1600,-721) -> Matrix(1,0,4,1) Matrix(4951,2222,1914,859) -> Matrix(1,0,-6,1) Matrix(157,70,-554,-247) -> Matrix(1,0,0,1) Matrix(549,242,946,417) -> Matrix(1,0,-2,1) Matrix(783,344,-2588,-1137) -> Matrix(1,0,-2,1) Matrix(1801,790,2510,1101) -> Matrix(1,0,0,1) Matrix(4703,2062,1722,755) -> Matrix(1,0,0,1) Matrix(545,238,158,69) -> Matrix(13,-4,10,-3) Matrix(853,370,-2174,-943) -> Matrix(5,-2,8,-3) Matrix(79,34,230,99) -> Matrix(5,-2,8,-3) Matrix(75,32,232,99) -> Matrix(1,0,0,1) Matrix(1453,616,1144,485) -> Matrix(9,-2,14,-3) Matrix(607,256,-1444,-609) -> Matrix(1,0,6,1) Matrix(2577,1082,1822,765) -> Matrix(27,-4,34,-5) Matrix(225,94,-754,-315) -> Matrix(1,0,-4,1) Matrix(829,344,976,405) -> Matrix(17,-4,30,-7) Matrix(449,186,-1726,-715) -> Matrix(1,0,-2,1) Matrix(223,92,-972,-401) -> Matrix(7,-2,32,-9) Matrix(371,152,-1340,-549) -> Matrix(7,-2,18,-5) Matrix(519,212,448,183) -> Matrix(7,-2,18,-5) Matrix(521,212,-1708,-695) -> Matrix(7,-2,4,-1) Matrix(361,142,-1594,-627) -> Matrix(1,0,2,1) Matrix(2607,1022,-7094,-2781) -> Matrix(3,-2,8,-5) Matrix(215,84,796,311) -> Matrix(1,0,0,1) Matrix(289,112,1076,417) -> Matrix(1,0,-4,1) Matrix(1361,526,1938,749) -> Matrix(1,0,2,1) Matrix(503,194,70,27) -> Matrix(1,0,-4,1) Matrix(73,28,-644,-247) -> Matrix(1,0,-2,1) Matrix(1709,654,358,137) -> Matrix(7,-2,18,-5) Matrix(283,108,-1208,-461) -> Matrix(7,-2,32,-9) Matrix(495,188,-1772,-673) -> Matrix(5,-2,18,-7) Matrix(707,268,1844,699) -> Matrix(7,-2,4,-1) Matrix(69,26,-422,-159) -> Matrix(1,0,0,1) Matrix(209,78,142,53) -> Matrix(7,-2,4,-1) Matrix(557,206,630,233) -> Matrix(17,-6,20,-7) Matrix(2095,774,766,283) -> Matrix(11,-4,36,-13) Matrix(4735,1742,2922,1075) -> Matrix(21,-8,8,-3) Matrix(10925,4016,2364,869) -> Matrix(5,-2,18,-7) Matrix(207,76,-1528,-561) -> Matrix(21,-8,50,-19) Matrix(137,50,-622,-227) -> Matrix(5,-2,18,-7) Matrix(343,124,-1928,-697) -> Matrix(11,-4,36,-13) Matrix(621,224,-2204,-795) -> Matrix(5,-2,28,-11) Matrix(345,124,-1444,-519) -> Matrix(5,-2,48,-19) Matrix(1717,616,616,221) -> Matrix(5,-2,-2,1) Matrix(1641,584,340,121) -> Matrix(9,-4,16,-7) Matrix(3891,1382,2182,775) -> Matrix(9,-4,34,-15) Matrix(1157,410,206,73) -> Matrix(9,-4,16,-7) Matrix(747,262,134,47) -> Matrix(3,-2,8,-5) Matrix(607,212,272,95) -> Matrix(3,-2,2,-1) Matrix(645,206,454,145) -> Matrix(17,-6,20,-7) Matrix(1093,344,448,141) -> Matrix(9,-4,-2,1) Matrix(1403,436,576,179) -> Matrix(7,-4,2,-1) Matrix(2293,710,830,257) -> Matrix(7,-4,16,-9) Matrix(317,98,1530,473) -> Matrix(13,-8,18,-11) Matrix(569,174,1586,485) -> Matrix(3,-2,2,-1) Matrix(1775,542,822,251) -> Matrix(11,-10,10,-9) Matrix(191,58,-1202,-365) -> Matrix(1,0,2,1) Matrix(503,152,-2836,-857) -> Matrix(3,-2,8,-5) Matrix(4633,1376,1000,297) -> Matrix(1,0,2,1) Matrix(2563,760,1440,427) -> Matrix(1,0,4,1) Matrix(311,92,-2248,-665) -> Matrix(7,-2,18,-5) Matrix(623,184,-3308,-977) -> Matrix(1,0,0,1) Matrix(2681,790,750,221) -> Matrix(1,0,0,1) Matrix(997,292,2612,765) -> Matrix(1,2,0,1) Matrix(1801,526,1058,309) -> Matrix(1,0,2,1) Matrix(433,126,622,181) -> Matrix(1,0,12,1) Matrix(1833,514,674,189) -> Matrix(7,-2,32,-9) Matrix(1649,460,1036,289) -> Matrix(25,-8,22,-7) Matrix(3465,958,2738,757) -> Matrix(9,-2,14,-3) Matrix(2795,772,3892,1075) -> Matrix(5,-2,18,-7) Matrix(305,84,1456,401) -> Matrix(11,-4,14,-5) Matrix(1943,534,302,83) -> Matrix(7,-2,4,-1) Matrix(59,16,424,115) -> Matrix(1,0,0,1) Matrix(1629,440,1144,309) -> Matrix(17,-6,20,-7) Matrix(901,242,242,65) -> Matrix(1,0,-2,1) Matrix(659,174,178,47) -> Matrix(3,-2,2,-1) Matrix(237,62,-1250,-327) -> Matrix(1,0,0,1) Matrix(475,122,1242,319) -> Matrix(3,-2,2,-1) Matrix(815,198,638,155) -> Matrix(15,2,22,3) Matrix(347,82,402,95) -> Matrix(13,-2,20,-3) Matrix(2637,614,1894,441) -> Matrix(5,-2,8,-3) Matrix(517,120,56,13) -> Matrix(1,0,-4,1) Matrix(1769,404,740,169) -> Matrix(17,-4,-4,1) Matrix(5117,1158,1878,425) -> Matrix(9,-2,32,-7) Matrix(967,218,794,179) -> Matrix(9,-2,14,-3) Matrix(1409,308,2420,529) -> Matrix(9,-2,14,-3) Matrix(3433,748,2024,441) -> Matrix(7,-2,4,-1) Matrix(167,36,-784,-169) -> Matrix(13,-4,36,-11) Matrix(1397,296,892,189) -> Matrix(5,-2,8,-3) Matrix(833,174,1058,221) -> Matrix(7,-2,18,-5) Matrix(167,34,54,11) -> Matrix(5,-2,8,-3) Matrix(763,146,162,31) -> Matrix(1,0,0,1) Matrix(2171,410,2494,471) -> Matrix(5,-2,8,-3) Matrix(161,30,542,101) -> Matrix(1,0,2,1) Matrix(1557,280,4076,733) -> Matrix(7,-2,4,-1) Matrix(1717,308,1232,221) -> Matrix(5,-2,8,-3) Matrix(7385,1312,2032,361) -> Matrix(25,-8,22,-7) Matrix(479,84,268,47) -> Matrix(1,0,0,1) Matrix(103,16,-676,-105) -> Matrix(25,-8,72,-23) Matrix(2693,406,1970,297) -> Matrix(11,-4,36,-13) Matrix(671,100,208,31) -> Matrix(11,-4,14,-5) Matrix(1889,260,356,49) -> Matrix(5,-2,38,-15) Matrix(303,40,356,47) -> Matrix(13,-6,24,-11) Matrix(903,110,550,67) -> Matrix(13,-6,-2,1) Matrix(147,16,248,27) -> Matrix(1,0,0,1) Matrix(197,-24,156,-19) -> Matrix(5,-2,8,-3) Matrix(1207,-158,466,-61) -> Matrix(1,0,-4,1) Matrix(191,-28,116,-17) -> Matrix(1,0,-2,1) Matrix(187,-32,76,-13) -> Matrix(3,-2,2,-1) Matrix(409,-76,296,-55) -> Matrix(13,-8,18,-11) Matrix(1533,-316,4012,-827) -> Matrix(5,-4,4,-3) Matrix(217,-46,618,-131) -> Matrix(3,-2,2,-1) Matrix(73,-16,324,-71) -> Matrix(9,-8,8,-7) Matrix(1827,-416,1076,-245) -> Matrix(3,-4,-2,3) Matrix(715,-164,824,-189) -> Matrix(3,-4,4,-5) Matrix(107,-26,70,-17) -> Matrix(1,0,0,1) Matrix(557,-146,454,-119) -> Matrix(1,-4,2,-7) Matrix(1077,-286,418,-111) -> Matrix(1,0,0,1) Matrix(449,-124,344,-95) -> Matrix(3,-4,4,-5) Matrix(1171,-326,722,-201) -> Matrix(1,2,0,1) Matrix(585,-164,824,-231) -> Matrix(1,0,4,1) Matrix(171,-50,578,-169) -> Matrix(1,0,6,1) Matrix(203,-62,370,-113) -> Matrix(1,0,0,1) Matrix(873,-272,536,-167) -> Matrix(3,-2,2,-1) Matrix(1271,-400,1808,-569) -> Matrix(1,0,6,1) Matrix(455,-162,778,-277) -> Matrix(1,0,0,1) Matrix(2461,-884,1456,-523) -> Matrix(1,0,-2,1) Matrix(2425,-874,874,-315) -> Matrix(1,0,0,1) Matrix(2651,-958,1486,-537) -> Matrix(1,0,2,1) Matrix(97,-36,256,-95) -> Matrix(5,-4,4,-3) Matrix(4967,-1898,1018,-389) -> Matrix(1,-2,2,-3) Matrix(9865,-3776,5536,-2119) -> Matrix(1,0,4,1) Matrix(127,-50,94,-37) -> Matrix(1,-2,2,-3) Matrix(187,-76,32,-13) -> Matrix(1,-2,2,-3) Matrix(343,-142,186,-77) -> Matrix(1,0,2,1) Matrix(217,-92,92,-39) -> Matrix(1,2,0,1) Matrix(245,-108,152,-67) -> Matrix(1,2,0,1) Matrix(1033,-464,728,-327) -> Matrix(13,4,16,5) Matrix(1879,-848,2608,-1177) -> Matrix(1,0,4,1) Matrix(2363,-1068,1728,-781) -> Matrix(5,2,12,5) Matrix(271,-124,212,-97) -> Matrix(11,2,16,3) Matrix(343,-186,142,-77) -> Matrix(1,0,-2,1) Matrix(737,-406,1022,-563) -> Matrix(1,0,0,1) Matrix(113,-64,196,-111) -> Matrix(5,-2,8,-3) Matrix(3005,-1746,1086,-631) -> Matrix(1,0,0,1) Matrix(9849,-5728,3616,-2103) -> Matrix(9,-4,34,-15) Matrix(2663,-1560,944,-553) -> Matrix(1,0,2,1) Matrix(249,-146,278,-163) -> Matrix(1,0,0,1) Matrix(1413,-832,304,-179) -> Matrix(1,0,2,1) Matrix(3237,-1910,1910,-1127) -> Matrix(1,0,0,1) Matrix(2461,-1456,884,-523) -> Matrix(1,0,-2,1) Matrix(191,-116,28,-17) -> Matrix(3,-2,2,-1) Matrix(709,-434,874,-535) -> Matrix(7,-4,16,-9) Matrix(873,-536,272,-167) -> Matrix(1,0,0,1) Matrix(245,-152,108,-67) -> Matrix(3,-2,2,-1) Matrix(297,-188,188,-119) -> Matrix(1,-2,2,-3) Matrix(1289,-824,912,-583) -> Matrix(3,-10,4,-13) Matrix(403,-258,214,-137) -> Matrix(1,-4,2,-7) Matrix(107,-70,26,-17) -> Matrix(1,0,0,1) Matrix(235,-162,338,-233) -> Matrix(1,0,16,1) Matrix(3617,-2544,1136,-799) -> Matrix(13,-2,20,-3) Matrix(1033,-728,464,-327) -> Matrix(11,-2,6,-1) Matrix(1289,-912,824,-583) -> Matrix(1,0,-4,1) Matrix(747,-530,926,-657) -> Matrix(7,-2,18,-5) Matrix(1843,-1326,1458,-1049) -> Matrix(9,-4,16,-7) Matrix(4961,-3576,1508,-1087) -> Matrix(5,-2,8,-3) Matrix(409,-296,76,-55) -> Matrix(1,0,0,1) Matrix(127,-94,50,-37) -> Matrix(1,0,-4,1) 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(7,-2,4,-1) Matrix(1723,-1358,1402,-1105) -> Matrix(27,-10,46,-17) Matrix(197,-156,24,-19) -> Matrix(5,-2,8,-3) Matrix(2505,-2026,706,-571) -> Matrix(5,-2,-2,1) Matrix(557,-454,146,-119) -> Matrix(9,-4,-2,1) Matrix(121,-100,144,-119) -> Matrix(17,-8,32,-15) Matrix(5643,-4918,1222,-1065) -> Matrix(3,-2,14,-9) Matrix(249,-278,146,-163) -> Matrix(1,0,-2,1) Matrix(941,-1084,204,-235) -> Matrix(1,0,0,1) Matrix(121,-144,100,-119) -> Matrix(13,-6,24,-11) Matrix(1679,-2062,434,-533) -> Matrix(7,-4,2,-1) Matrix(709,-874,434,-535) -> Matrix(11,-6,2,-1) Matrix(1047,-1328,272,-345) -> Matrix(3,-2,8,-5) Matrix(2147,-2738,1682,-2145) -> Matrix(157,-104,234,-155) Matrix(249,-322,58,-75) -> Matrix(3,-2,-4,3) Matrix(553,-724,152,-199) -> Matrix(7,-6,6,-5) Matrix(855,-1168,112,-153) -> Matrix(1,0,-2,1) Matrix(557,-764,148,-203) -> Matrix(7,-4,2,-1) Matrix(481,-664,92,-127) -> Matrix(3,-2,-4,3) Matrix(609,-844,184,-255) -> Matrix(1,0,0,1) Matrix(203,-282,18,-25) -> Matrix(3,-2,2,-1) Matrix(585,-824,164,-231) -> Matrix(5,-4,4,-3) Matrix(1271,-1808,400,-569) -> Matrix(5,-4,4,-3) Matrix(235,-338,162,-233) -> Matrix(17,-16,16,-15) Matrix(997,-1556,412,-643) -> Matrix(1,0,0,1) Matrix(919,-1458,578,-917) -> Matrix(15,-14,14,-13) Matrix(2017,-3262,1194,-1931) -> Matrix(1,-2,0,1) Matrix(2857,-4624,1764,-2855) -> Matrix(5,-8,2,-3) Matrix(1303,-2128,368,-601) -> Matrix(1,-2,0,1) Matrix(2051,-3362,1250,-2049) -> Matrix(1,-14,0,1) Matrix(899,-1522,114,-193) -> Matrix(1,0,4,1) Matrix(2923,-4952,376,-637) -> Matrix(1,0,-6,1) Matrix(455,-778,162,-277) -> Matrix(1,0,4,1) Matrix(113,-196,64,-111) -> Matrix(1,0,4,1) Matrix(6249,-11132,2420,-4311) -> Matrix(1,0,-6,1) Matrix(203,-370,62,-113) -> Matrix(5,-2,8,-3) Matrix(523,-974,138,-257) -> Matrix(5,-2,-2,1) Matrix(211,-450,98,-209) -> Matrix(15,-14,14,-13) Matrix(1205,-2666,466,-1031) -> Matrix(1,-2,0,1) Matrix(1081,-2396,328,-727) -> Matrix(3,-4,4,-5) Matrix(481,-1102,134,-307) -> Matrix(1,0,0,1) Matrix(1239,-2854,346,-797) -> Matrix(3,-4,4,-5) Matrix(517,-1198,186,-431) -> Matrix(1,-2,2,-3) Matrix(807,-1922,338,-805) -> Matrix(1,-10,0,1) Matrix(1491,-3614,578,-1401) -> Matrix(1,-2,0,1) 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(1,0,6,1) Matrix(5011,-13644,1324,-3605) -> Matrix(57,-14,-4,1) Matrix(1203,-3284,248,-677) -> Matrix(1,0,-2,1) Matrix(595,-1648,152,-421) -> Matrix(1,0,-2,1) Matrix(1855,-5142,478,-1325) -> Matrix(3,-2,2,-1) Matrix(1507,-4256,472,-1333) -> Matrix(1,0,-2,1) Matrix(1575,-4454,494,-1397) -> Matrix(11,-4,14,-5) Matrix(217,-618,46,-131) -> Matrix(1,0,0,1) Matrix(11645,-38338,2522,-8303) -> Matrix(3,-2,20,-13) Matrix(6149,-20252,1332,-4387) -> Matrix(3,-2,2,-1) Matrix(171,-578,50,-169) -> Matrix(11,-10,10,-9) Matrix(2591,-9200,532,-1889) -> Matrix(1,0,0,1) Matrix(1643,-5838,338,-1201) -> Matrix(1,-2,2,-3) Matrix(2623,-9522,722,-2621) -> Matrix(13,-12,12,-11) Matrix(4003,-15138,1058,-4001) -> Matrix(1,-34,0,1) Matrix(73,-324,16,-71) -> Matrix(1,0,4,1) Matrix(519,-2738,98,-517) -> Matrix(1,0,14,1) Matrix(115,-722,18,-113) -> Matrix(7,-6,6,-5) 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): 56 Degree of the the map X: 56 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- 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 0/1 1 1 0/1 (0/1,1/2) 0 22 1/8 (0/1,1/1) 0 22 1/7 1/2 1 11 1/6 (1/2,3/5) 0 22 2/11 (1/2,3/5) 0 22 1/5 0 11 4/19 (3/4,1/1) 0 22 3/14 (3/4,4/5) 0 22 2/9 1/1 4 2 5/22 (5/4,4/3) 0 22 8/35 (3/2,8/5) 0 22 3/13 1/0 1 11 1/4 (1/1,1/0) 0 22 5/19 1/0 1 11 4/15 (0/1,1/0) 0 22 3/11 0 11 5/18 (-1/1,1/0) 0 22 7/25 1/0 1 11 2/7 (0/1,1/0) 0 22 5/17 0/1 3 1 3/10 (0/1,1/3) 0 22 4/13 (1/2,1/1) 0 22 5/16 (1/2,1/1) 0 22 1/3 1/2 1 11 6/17 (1/2,1/1) 0 22 5/14 (2/3,1/1) 0 22 9/25 0 11 13/36 (1/2,1/1) 0 22 4/11 (1/2,2/3) 0 22 3/8 1/1 2 2 8/21 (3/2,2/1) 0 22 13/34 (1/1,2/1) 0 22 5/13 0 11 2/5 (1/1,1/0) 0 22 7/17 1/0 1 11 5/12 (2/1,1/0) 0 22 3/7 0 11 4/9 (-1/1,-1/2) 0 22 9/20 (-1/3,0/1) 0 22 14/31 (-2/3,-1/2) 0 22 5/11 -1/4 1 11 1/2 (0/1,1/3) 0 22 6/11 (1/2,1/1) 0 22 11/20 (0/1,1/3) 0 22 5/9 0 11 4/7 1/2 1 2 11/19 0 11 7/12 (2/3,1/1) 0 22 24/41 (1/2,1/1) 0 22 17/29 0 11 10/17 (1/1,1/0) 0 22 23/39 0 11 13/22 (0/1,1/3) 0 22 3/5 1/2 1 11 11/18 (0/1,1/1) 0 22 19/31 0 11 8/13 (1/2,1/1) 0 22 5/8 (2/3,1/1) 0 22 7/11 0 11 16/25 (3/1,1/0) 0 22 9/14 (-3/1,1/0) 0 22 2/3 (0/1,1/0) 0 22 9/13 0/1 8 1 7/10 (0/1,1/8) 0 22 19/27 0 11 12/17 (0/1,1/6) 0 22 17/24 (0/1,1/5) 0 22 22/31 (0/1,1/4) 0 22 5/7 1/4 1 11 23/32 1/3 2 2 18/25 (2/5,1/2) 0 22 49/68 (0/1,1/1) 0 22 31/43 0 11 13/18 (0/1,1/3) 0 22 8/11 (0/1,1/4) 0 22 3/4 (1/4,1/3) 0 22 10/13 (1/3,1/2) 0 22 7/9 1/2 1 11 11/14 (1/3,4/11) 0 22 15/19 0 11 4/5 (2/5,1/2) 0 22 21/26 (2/5,3/7) 0 22 17/21 0 11 13/16 (3/7,4/9) 0 22 9/11 1/2 1 11 5/6 1/2 4 2 11/13 1/2 1 11 6/7 (1/2,3/5) 0 22 7/8 (2/3,1/1) 0 22 1/1 0 11 8/7 (0/1,1/2) 0 22 7/6 (1/3,2/5) 0 22 6/5 1/2 3 2 17/14 (5/9,4/7) 0 22 11/9 1/2 1 11 27/22 (1/2,3/5) 0 22 16/13 (1/2,2/3) 0 22 5/4 (3/5,2/3) 0 22 24/19 (1/2,2/3) 0 22 19/15 0 11 14/11 (9/14,2/3) 0 22 37/29 2/3 13 1 23/18 (2/3,17/25) 0 22 9/7 3/4 1 11 13/10 (3/4,7/9) 0 22 17/13 0 11 4/3 (1/2,1/1) 0 22 15/11 0 11 41/30 (0/1,1/4) 0 22 26/19 (4/9,1/2) 0 22 11/8 (3/5,2/3) 0 22 29/21 0 11 18/13 (3/4,1/1) 0 22 25/18 (2/3,1/1) 0 22 32/23 2/3 1 2 7/5 3/4 1 11 24/17 (3/4,1/1) 0 22 17/12 (4/5,1/1) 0 22 27/19 0 11 10/7 (7/8,1/1) 0 22 13/9 1/1 8 1 3/2 (1/1,1/0) 0 22 17/11 1/0 1 11 14/9 (1/1,1/0) 0 22 25/16 (0/1,1/1) 0 22 11/7 0 11 19/12 (4/5,1/1) 0 22 27/17 1/1 7 1 8/5 (1/1,3/2) 0 22 21/13 0 11 55/34 (1/1,2/1) 0 22 34/21 2/1 1 2 47/29 1/0 1 11 13/8 (1/1,1/0) 0 22 31/19 0 11 49/30 (3/1,4/1) 0 22 18/11 (4/1,1/0) 0 22 41/25 1/0 7 1 23/14 (-3/1,1/0) 0 22 5/3 1/0 1 11 22/13 (-1/2,0/1) 0 22 83/49 0/1 5 1 61/36 (0/1,1/3) 0 22 39/23 0 11 17/10 (-1/2,0/1) 0 22 29/17 0 11 12/7 (0/1,1/0) 0 22 7/4 0/1 2 2 16/9 (0/1,1/4) 0 22 9/5 0 11 11/6 (2/5,1/2) 0 22 13/7 1/2 1 11 15/8 (1/2,7/13) 0 22 2/1 (1/2,1/1) 0 22 15/7 1/1 7 1 13/6 (1/1,6/5) 0 22 11/5 3/2 1 11 31/14 (1/1,2/1) 0 22 20/9 (2/1,1/0) 0 22 9/4 (0/1,1/1) 0 22 16/7 (1/1,1/0) 0 22 23/10 1/1 2 2 30/13 (3/2,2/1) 0 22 7/3 0 11 19/8 (4/1,1/0) 0 22 31/13 1/0 5 1 12/5 (-1/1,1/0) 0 22 29/12 (0/1,1/1) 0 22 46/19 (1/1,1/0) 0 22 17/7 1/0 1 11 22/9 (-1/1,1/0) 0 22 5/2 (-1/1,1/0) 0 22 18/7 (0/1,1/0) 0 22 49/19 1/0 1 11 80/31 (-1/1,1/0) 0 22 111/43 -1/1 1 1 31/12 (-1/1,0/1) 0 22 44/17 (-1/1,1/0) 0 22 13/5 0 11 8/3 0/1 3 2 19/7 0 11 30/11 (1/4,1/3) 0 22 11/4 (0/1,1/3) 0 22 36/13 (0/1,1/2) 0 22 97/35 1/2 1 1 61/22 (1/2,1/1) 0 22 25/9 0 11 14/5 (0/1,1/4) 0 22 31/11 0 11 48/17 (1/4,1/3) 0 22 65/23 1/3 2 1 17/6 (1/3,1/2) 0 22 3/1 1/2 1 11 16/5 (1/2,1/1) 0 22 13/4 (0/1,1/2) 0 22 23/7 0 11 79/24 (3/5,2/3) 0 22 135/41 2/3 3 1 56/17 (2/3,3/4) 0 22 33/10 (2/3,1/1) 0 22 10/3 (3/4,1/1) 0 22 17/5 1/1 5 1 7/2 (1/1,2/1) 0 22 39/11 0 11 71/20 (0/1,1/1) 0 22 103/29 1/1 1 1 32/9 (1/1,1/0) 0 22 25/7 1/0 1 11 43/12 1/1 2 2 18/5 (1/1,1/0) 0 22 29/8 (1/2,1/1) 0 22 69/19 1/1 6 1 40/11 (1/1,5/4) 0 22 11/3 0 11 15/4 (1/1,2/1) 0 22 34/9 (8/1,1/0) 0 22 87/23 1/0 17 1 53/14 (-9/1,1/0) 0 22 19/5 1/0 1 11 23/6 (-1/1,0/1) 0 22 4/1 (0/1,1/0) 0 22 17/4 (-3/1,1/0) 0 22 13/3 1/0 1 11 9/2 0/1 2 2 23/5 1/4 1 11 37/8 (0/1,1/3) 0 22 14/3 (1/3,1/2) 0 22 19/4 (1/3,1/2) 0 22 5/1 0 11 21/4 (-1/3,0/1) 0 22 37/7 0/1 7 1 16/3 (0/1,1/4) 0 22 11/2 (0/1,1/3) 0 22 17/3 1/2 1 11 6/1 (1/2,1/1) 0 22 19/3 1/1 3 1 13/2 (1/1,2/1) 0 22 7/1 1/0 1 11 8/1 (0/1,1/2) 0 22 9/1 0 11 1/0 (0/1,1/1) 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(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(197,-24,156,-19) (0/1,1/8) -> (5/4,24/19) Hyperbolic Matrix(115,-16,194,-27) (1/8,1/7) -> (13/22,3/5) Glide Reflection 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(401,-84,654,-137) (1/5,4/19) -> (19/31,8/13) Glide Reflection Matrix(471,-100,146,-31) (4/19,3/14) -> (16/5,13/4) Glide Reflection Matrix(73,-16,324,-71) (3/14,2/9) -> (2/9,5/22) Parabolic Matrix(2007,-458,1468,-335) (5/22,8/35) -> (41/30,26/19) Glide Reflection Matrix(357,-82,788,-181) (8/35,3/13) -> (14/31,5/11) Glide Reflection 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(311,-84,174,-47) (4/15,3/11) -> (16/9,9/5) Glide Reflection 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(69,-20,238,-69) (2/7,5/17) -> (2/7,5/17) Reflection Matrix(101,-30,340,-101) (5/17,3/10) -> (5/17,3/10) Reflection Matrix(203,-62,370,-113) (3/10,4/13) -> (6/11,11/20) Hyperbolic Matrix(471,-146,100,-31) (4/13,5/16) -> (14/3,19/4) Glide Reflection Matrix(99,-32,34,-11) (5/16,1/3) -> (17/6,3/1) Glide Reflection Matrix(99,-34,32,-11) (1/3,6/17) -> (3/1,16/5) Glide Reflection Matrix(455,-162,778,-277) (6/17,5/14) -> (7/12,24/41) Hyperbolic Matrix(485,-174,616,-221) (5/14,9/25) -> (11/14,15/19) Glide Reflection Matrix(2425,-874,874,-315) (9/25,13/36) -> (61/22,25/9) Hyperbolic Matrix(873,-316,710,-257) (13/36,4/11) -> (27/22,16/13) Glide Reflection Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(765,-292,1082,-413) (8/21,13/34) -> (12/17,17/24) Glide Reflection Matrix(699,-268,446,-171) (13/34,5/13) -> (25/16,11/7) Glide Reflection 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(183,-82,212,-95) (4/9,9/20) -> (6/7,7/8) Glide Reflection Matrix(1879,-848,2608,-1177) (9/20,14/31) -> (18/25,49/68) 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(417,-242,112,-65) (11/19,7/12) -> (11/3,15/4) Glide Reflection Matrix(2663,-1560,944,-553) (24/41,17/29) -> (31/11,48/17) Hyperbolic Matrix(749,-440,526,-309) (17/29,10/17) -> (27/19,10/7) Glide Reflection Matrix(1937,-1142,748,-441) (10/17,23/39) -> (44/17,13/5) Glide Reflection Matrix(3237,-1910,1910,-1127) (23/39,13/22) -> (61/36,39/23) 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(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(805,-514,296,-189) (7/11,16/25) -> (19/7,30/11) Glide Reflection 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(53,-36,78,-53) (2/3,9/13) -> (2/3,9/13) Reflection Matrix(181,-126,260,-181) (9/13,7/10) -> (9/13,7/10) Reflection Matrix(749,-526,440,-309) (7/10,19/27) -> (17/10,29/17) Glide Reflection Matrix(233,-164,206,-145) (19/27,12/17) -> (1/1,8/7) Glide Reflection Matrix(747,-530,926,-657) (17/24,22/31) -> (4/5,21/26) Hyperbolic Matrix(1101,-790,308,-221) (5/7,23/32) -> (25/7,43/12) Glide Reflection Matrix(1535,-1104,666,-479) (23/32,18/25) -> (23/10,30/13) Glide Reflection 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(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(405,-344,166,-141) (11/13,6/7) -> (17/7,22/9) Glide Reflection Matrix(233,-206,164,-145) (7/8,1/1) -> (17/12,27/19) Glide Reflection 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(709,-874,434,-535) (16/13,5/4) -> (49/30,18/11) Hyperbolic Matrix(583,-738,252,-319) (24/19,19/15) -> (30/13,7/3) Glide Reflection Matrix(485,-616,174,-221) (19/15,14/11) -> (25/9,14/5) Glide Reflection Matrix(813,-1036,638,-813) (14/11,37/29) -> (14/11,37/29) Reflection Matrix(1333,-1702,1044,-1333) (37/29,23/18) -> (37/29,23/18) Reflection 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(1357,-1854,800,-1093) (15/11,41/30) -> (39/23,17/10) Glide Reflection 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(1877,-2610,1160,-1613) (25/18,32/23) -> (55/34,34/21) Glide Reflection Matrix(1251,-1742,772,-1075) (32/23,7/5) -> (34/21,47/29) Glide Reflection 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(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(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(647,-1026,408,-647) (19/12,27/17) -> (19/12,27/17) Reflection Matrix(271,-432,170,-271) (27/17,8/5) -> (27/17,8/5) Reflection Matrix(319,-516,34,-55) (21/13,55/34) -> (9/1,1/0) 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(901,-1476,550,-901) (18/11,41/25) -> (18/11,41/25) Reflection Matrix(1149,-1886,700,-1149) (41/25,23/14) -> (41/25,23/14) 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(5977,-10126,3528,-5977) (83/49,61/36) -> (83/49,61/36) Reflection 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(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(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(495,-1178,208,-495) (19/8,31/13) -> (19/8,31/13) Reflection Matrix(311,-744,130,-311) (31/13,12/5) -> (31/13,12/5) Reflection Matrix(1491,-3614,578,-1401) (46/19,17/7) -> (49/19,80/31) Hyperbolic Matrix(6881,-17760,2666,-6881) (80/31,111/43) -> (80/31,111/43) Reflection Matrix(2665,-6882,1032,-2665) (111/43,31/12) -> (111/43,31/12) 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(4269,-11834,1540,-4269) (97/35,61/22) -> (97/35,61/22) Reflection Matrix(2209,-6240,782,-2209) (48/17,65/23) -> (48/17,65/23) Reflection Matrix(781,-2210,276,-781) (65/23,17/6) -> (65/23,17/6) Reflection Matrix(6479,-21330,1968,-6479) (79/24,135/41) -> (79/24,135/41) 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(4119,-14626,1160,-4119) (71/20,103/29) -> (71/20,103/29) 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(1519,-5520,418,-1519) (69/19,40/11) -> (69/19,40/11) 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(295,-1554,56,-295) (21/4,37/7) -> (21/4,37/7) 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) -> (0/1,1/1) Matrix(-1,0,2,1) -> Matrix(1,0,4,-1) (-1/1,0/1) -> (0/1,1/2) Matrix(197,-24,156,-19) -> Matrix(5,-2,8,-3) 1/2 Matrix(115,-16,194,-27) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(191,-28,116,-17) -> Matrix(1,0,-2,1) 0/1 Matrix(187,-32,76,-13) -> Matrix(3,-2,2,-1) 1/1 Matrix(409,-76,296,-55) -> Matrix(13,-8,18,-11) 2/3 Matrix(401,-84,654,-137) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(471,-100,146,-31) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(73,-16,324,-71) -> Matrix(9,-8,8,-7) 1/1 Matrix(2007,-458,1468,-335) -> Matrix(3,-4,8,-11) Matrix(357,-82,788,-181) -> Matrix(1,-2,-4,7) Matrix(107,-26,70,-17) -> Matrix(1,0,0,1) Matrix(557,-146,454,-119) -> Matrix(1,-4,2,-7) Matrix(1077,-286,418,-111) -> Matrix(1,0,0,1) Matrix(311,-84,174,-47) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(449,-124,344,-95) -> Matrix(3,-4,4,-5) 1/1 Matrix(1171,-326,722,-201) -> Matrix(1,2,0,1) 1/0 Matrix(585,-164,824,-231) -> Matrix(1,0,4,1) 0/1 Matrix(69,-20,238,-69) -> Matrix(1,0,0,-1) (2/7,5/17) -> (0/1,1/0) Matrix(101,-30,340,-101) -> Matrix(1,0,6,-1) (5/17,3/10) -> (0/1,1/3) Matrix(203,-62,370,-113) -> Matrix(1,0,0,1) Matrix(471,-146,100,-31) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(99,-32,34,-11) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(99,-34,32,-11) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(455,-162,778,-277) -> Matrix(1,0,0,1) Matrix(485,-174,616,-221) -> Matrix(1,-2,2,-5) Matrix(2425,-874,874,-315) -> Matrix(1,0,0,1) Matrix(873,-316,710,-257) -> Matrix(7,-4,12,-7) *** -> (1/2,2/3) Matrix(97,-36,256,-95) -> Matrix(5,-4,4,-3) 1/1 Matrix(765,-292,1082,-413) -> Matrix(1,-2,4,-9) Matrix(699,-268,446,-171) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(127,-50,94,-37) -> Matrix(1,-2,2,-3) 1/1 Matrix(187,-76,32,-13) -> Matrix(1,-2,2,-3) 1/1 Matrix(343,-142,186,-77) -> Matrix(1,0,2,1) 0/1 Matrix(217,-92,92,-39) -> Matrix(1,2,0,1) 1/0 Matrix(245,-108,152,-67) -> Matrix(1,2,0,1) 1/0 Matrix(183,-82,212,-95) -> Matrix(5,2,8,3) Matrix(1879,-848,2608,-1177) -> Matrix(1,0,4,1) 0/1 Matrix(271,-124,212,-97) -> Matrix(11,2,16,3) Matrix(343,-186,142,-77) -> Matrix(1,0,-2,1) 0/1 Matrix(737,-406,1022,-563) -> Matrix(1,0,0,1) Matrix(113,-64,196,-111) -> Matrix(5,-2,8,-3) 1/2 Matrix(417,-242,112,-65) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(2663,-1560,944,-553) -> Matrix(1,0,2,1) 0/1 Matrix(749,-440,526,-309) -> Matrix(7,-6,8,-7) *** -> (3/4,1/1) Matrix(1937,-1142,748,-441) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(3237,-1910,1910,-1127) -> Matrix(1,0,0,1) Matrix(191,-116,28,-17) -> Matrix(3,-2,2,-1) 1/1 Matrix(709,-434,874,-535) -> Matrix(7,-4,16,-9) 1/2 Matrix(245,-152,108,-67) -> Matrix(3,-2,2,-1) 1/1 Matrix(297,-188,188,-119) -> Matrix(1,-2,2,-3) 1/1 Matrix(805,-514,296,-189) -> Matrix(1,-2,4,-9) Matrix(403,-258,214,-137) -> Matrix(1,-4,2,-7) Matrix(107,-70,26,-17) -> Matrix(1,0,0,1) Matrix(53,-36,78,-53) -> Matrix(1,0,0,-1) (2/3,9/13) -> (0/1,1/0) Matrix(181,-126,260,-181) -> Matrix(1,0,16,-1) (9/13,7/10) -> (0/1,1/8) Matrix(749,-526,440,-309) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(233,-164,206,-145) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(747,-530,926,-657) -> Matrix(7,-2,18,-5) 1/3 Matrix(1101,-790,308,-221) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1535,-1104,666,-479) -> Matrix(11,-4,8,-3) Matrix(4961,-3576,1508,-1087) -> Matrix(5,-2,8,-3) 1/2 Matrix(409,-296,76,-55) -> Matrix(1,0,0,1) Matrix(127,-94,50,-37) -> Matrix(1,0,-4,1) 0/1 Matrix(449,-344,124,-95) -> Matrix(1,0,-2,1) 0/1 Matrix(347,-268,224,-173) -> Matrix(1,0,-2,1) 0/1 Matrix(271,-212,124,-97) -> Matrix(7,-2,4,-1) Matrix(197,-156,24,-19) -> Matrix(5,-2,8,-3) 1/2 Matrix(2505,-2026,706,-571) -> Matrix(5,-2,-2,1) Matrix(557,-454,146,-119) -> Matrix(9,-4,-2,1) Matrix(121,-100,144,-119) -> Matrix(17,-8,32,-15) 1/2 Matrix(405,-344,166,-141) -> Matrix(7,-4,-2,1) Matrix(233,-206,164,-145) -> Matrix(7,-6,8,-7) *** -> (3/4,1/1) Matrix(183,-212,82,-95) -> Matrix(5,-2,2,-1) Matrix(121,-144,100,-119) -> Matrix(13,-6,24,-11) 1/2 Matrix(337,-410,60,-73) -> Matrix(7,-4,12,-7) *** -> (1/2,2/3) Matrix(709,-874,434,-535) -> Matrix(11,-6,2,-1) Matrix(583,-738,252,-319) -> Matrix(13,-8,8,-5) Matrix(485,-616,174,-221) -> Matrix(3,-2,-2,1) Matrix(813,-1036,638,-813) -> Matrix(55,-36,84,-55) (14/11,37/29) -> (9/14,2/3) Matrix(1333,-1702,1044,-1333) -> Matrix(101,-68,150,-101) (37/29,23/18) -> (2/3,17/25) Matrix(249,-322,58,-75) -> Matrix(3,-2,-4,3) Matrix(553,-724,152,-199) -> Matrix(7,-6,6,-5) 1/1 Matrix(1357,-1854,800,-1093) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(557,-764,148,-203) -> Matrix(7,-4,2,-1) Matrix(481,-664,92,-127) -> Matrix(3,-2,-4,3) Matrix(609,-844,184,-255) -> Matrix(1,0,0,1) Matrix(1877,-2610,1160,-1613) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1251,-1742,772,-1075) -> Matrix(11,-8,4,-3) Matrix(585,-824,164,-231) -> Matrix(5,-4,4,-3) 1/1 Matrix(547,-774,200,-283) -> Matrix(5,-4,16,-13) Matrix(181,-260,126,-181) -> Matrix(15,-14,16,-15) (10/7,13/9) -> (7/8,1/1) Matrix(53,-78,36,-53) -> Matrix(-1,2,0,1) (13/9,3/2) -> (1/1,1/0) Matrix(997,-1556,412,-643) -> Matrix(1,0,0,1) Matrix(647,-1026,408,-647) -> Matrix(9,-8,10,-9) (19/12,27/17) -> (4/5,1/1) Matrix(271,-432,170,-271) -> Matrix(5,-6,4,-5) (27/17,8/5) -> (1/1,3/2) Matrix(319,-516,34,-55) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(401,-654,84,-137) -> Matrix(1,-2,2,-5) Matrix(1303,-2128,368,-601) -> Matrix(1,-2,0,1) 1/0 Matrix(901,-1476,550,-901) -> Matrix(-1,8,0,1) (18/11,41/25) -> (4/1,1/0) Matrix(1149,-1886,700,-1149) -> Matrix(1,6,0,-1) (41/25,23/14) -> (-3/1,1/0) Matrix(115,-194,16,-27) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2157,-3652,1274,-2157) -> Matrix(-1,0,4,1) (22/13,83/49) -> (-1/2,0/1) Matrix(5977,-10126,3528,-5977) -> Matrix(1,0,6,-1) (83/49,61/36) -> (0/1,1/3) Matrix(455,-778,162,-277) -> Matrix(1,0,4,1) 0/1 Matrix(113,-196,64,-111) -> Matrix(1,0,4,1) 0/1 Matrix(203,-370,62,-113) -> Matrix(5,-2,8,-3) 1/2 Matrix(523,-974,138,-257) -> Matrix(5,-2,-2,1) Matrix(29,-60,14,-29) -> Matrix(3,-2,4,-3) (2/1,15/7) -> (1/2,1/1) Matrix(181,-390,84,-181) -> Matrix(11,-12,10,-11) (15/7,13/6) -> (1/1,6/5) Matrix(507,-1120,110,-243) -> Matrix(1,-2,2,-5) Matrix(1081,-2396,328,-727) -> Matrix(3,-4,4,-5) 1/1 Matrix(481,-1102,134,-307) -> Matrix(1,0,0,1) Matrix(495,-1178,208,-495) -> Matrix(-1,8,0,1) (19/8,31/13) -> (4/1,1/0) Matrix(311,-744,130,-311) -> Matrix(1,2,0,-1) (31/13,12/5) -> (-1/1,1/0) Matrix(1491,-3614,578,-1401) -> Matrix(1,-2,0,1) 1/0 Matrix(6881,-17760,2666,-6881) -> Matrix(1,2,0,-1) (80/31,111/43) -> (-1/1,1/0) Matrix(2665,-6882,1032,-2665) -> Matrix(-1,0,2,1) (111/43,31/12) -> (-1/1,0/1) Matrix(797,-2062,172,-445) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(97,-256,36,-95) -> Matrix(1,0,6,1) 0/1 Matrix(315,-872,82,-227) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(2521,-6984,910,-2521) -> Matrix(1,0,4,-1) (36/13,97/35) -> (0/1,1/2) Matrix(4269,-11834,1540,-4269) -> Matrix(3,-2,4,-3) (97/35,61/22) -> (1/2,1/1) Matrix(2209,-6240,782,-2209) -> Matrix(7,-2,24,-7) (48/17,65/23) -> (1/4,1/3) Matrix(781,-2210,276,-781) -> Matrix(5,-2,12,-5) (65/23,17/6) -> (1/3,1/2) Matrix(6479,-21330,1968,-6479) -> Matrix(19,-12,30,-19) (79/24,135/41) -> (3/5,2/3) Matrix(4591,-15120,1394,-4591) -> Matrix(17,-12,24,-17) (135/41,56/17) -> (2/3,3/4) Matrix(101,-340,30,-101) -> Matrix(7,-6,8,-7) (10/3,17/5) -> (3/4,1/1) Matrix(69,-238,20,-69) -> Matrix(3,-4,2,-3) (17/5,7/2) -> (1/1,2/1) Matrix(4119,-14626,1160,-4119) -> Matrix(1,0,2,-1) (71/20,103/29) -> (0/1,1/1) Matrix(1855,-6592,522,-1855) -> Matrix(-1,2,0,1) (103/29,32/9) -> (1/1,1/0) Matrix(1103,-4002,304,-1103) -> Matrix(3,-2,4,-3) (29/8,69/19) -> (1/2,1/1) Matrix(1519,-5520,418,-1519) -> Matrix(9,-10,8,-9) (69/19,40/11) -> (1/1,5/4) Matrix(1565,-5916,414,-1565) -> Matrix(-1,16,0,1) (34/9,87/23) -> (8/1,1/0) Matrix(2437,-9222,644,-2437) -> Matrix(1,18,0,-1) (87/23,53/14) -> (-9/1,1/0) Matrix(73,-324,16,-71) -> Matrix(1,0,4,1) 0/1 Matrix(295,-1554,56,-295) -> Matrix(-1,0,6,1) (21/4,37/7) -> (-1/3,0/1) Matrix(223,-1184,42,-223) -> Matrix(1,0,8,-1) (37/7,16/3) -> (0/1,1/4) Matrix(37,-228,6,-37) -> Matrix(3,-2,4,-3) (6/1,19/3) -> (1/2,1/1) Matrix(77,-494,12,-77) -> Matrix(3,-4,2,-3) (19/3,13/2) -> (1/1,2/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.