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 1/21 -7/15 3/55 1/18 -6/13 1/18 4/71 -11/24 3/53 -5/11 1/17 -14/31 4/69 1/17 -9/20 1/17 -22/49 1/17 6/101 -13/29 1/17 3/50 -4/9 1/17 2/33 -11/25 1/17 -18/41 0/1 1/16 -25/57 1/17 1/16 -7/16 3/49 -10/23 1/16 4/63 -13/30 1/15 -3/7 1/16 1/15 -14/33 2/31 1/15 -11/26 3/47 -8/19 1/15 -21/50 5/73 -13/31 1/15 -5/12 1/15 -17/41 1/15 1/14 -12/29 0/1 1/13 -7/17 1/15 -9/22 1/15 -11/27 1/15 1/14 -2/5 0/1 1/14 -11/28 1/15 -20/51 1/14 2/27 -9/23 1/15 -7/18 1/14 -12/31 2/27 1/13 -17/44 1/13 -5/13 1/14 1/13 -18/47 0/1 1/13 -13/34 1/13 -8/21 0/1 1/12 -11/29 1/15 -14/37 1/14 4/55 -3/8 1/13 -10/27 1/13 4/51 -17/46 3/37 -7/19 1/13 1/12 -25/68 11/141 -43/117 7/89 -18/49 3/38 2/25 -11/30 3/37 -4/11 0/1 1/12 -13/36 1/13 -9/25 1/13 1/12 -14/39 1/13 4/51 -5/14 3/37 -16/45 3/37 4/49 -11/31 3/37 1/12 -6/17 1/12 -7/20 3/35 -1/3 1/11 -6/19 4/41 1/10 -5/16 1/10 -9/29 1/10 5/49 -13/42 1/9 -4/13 3/29 2/19 -11/36 1/9 -18/59 1/10 2/19 -7/23 1/10 1/9 -10/33 1/10 4/39 -13/43 3/29 -3/10 1/9 -11/37 1/9 -19/64 5/51 -8/27 3/29 2/19 -21/71 5/47 -13/44 1/9 -18/61 2/19 1/9 -5/17 3/28 1/9 -12/41 7/65 4/37 -7/24 1/9 -2/7 1/9 2/17 -11/39 1/9 3/26 -9/32 1/9 -7/25 1/9 -12/43 7/60 2/17 -5/18 3/25 -13/47 3/25 -21/76 1/8 -8/29 2/17 1/8 -11/40 7/57 -14/51 1/8 6/47 -3/11 1/9 1/8 -10/37 2/17 3/25 -7/26 3/25 -4/15 1/8 -5/19 3/23 -6/23 0/1 1/7 -7/27 1/9 1/8 -1/4 1/7 -6/25 1/7 6/41 -5/21 1/7 3/20 -4/17 0/1 1/6 -7/30 1/7 -10/43 1/7 -3/13 1/7 -8/35 5/33 2/13 -5/22 3/19 -12/53 2/13 1/6 -7/31 3/19 1/6 -2/9 0/1 1/6 -7/32 3/19 -12/55 1/7 2/13 -5/23 3/19 -3/14 1/6 -7/33 3/17 -4/19 2/11 1/5 -5/24 1/5 -1/5 1/6 1/5 -4/21 0/1 1/5 -7/37 3/17 -10/53 2/11 1/5 -3/16 1/5 -2/11 1/5 2/9 -7/39 1/6 1/5 -5/28 1/5 -8/45 3/14 2/9 -11/62 3/13 -3/17 1/5 -1/6 1/5 -4/25 1/4 2/7 -3/19 1/5 1/4 -2/13 1/4 -5/33 1/4 3/11 -3/20 1/3 -1/7 1/3 -4/29 -1/1 0/1 -3/22 1/7 -2/15 0/1 1/4 -1/8 1/3 -2/17 1/3 2/5 -1/9 1/3 1/2 0/1 0/1 1/1 1/8 -1/3 2/15 0/1 1/1 1/7 -1/1 1/0 1/6 -1/1 2/11 -1/2 0/1 1/5 -1/1 6/29 -3/5 -4/7 5/24 -5/9 4/19 -1/2 0/1 3/14 -1/1 2/9 -1/2 5/22 -3/7 8/35 -3/7 -2/5 3/13 -1/2 -1/3 1/4 -1/3 5/19 -1/1 -1/2 4/15 -2/5 -1/3 7/26 -1/2 3/11 -1/3 5/18 -1/3 7/25 -1/3 -1/4 2/7 -2/5 -1/3 5/17 -1/3 8/27 -1/3 -8/25 3/10 -1/3 4/13 -1/3 0/1 5/16 -1/3 6/19 -1/3 0/1 1/3 -1/3 -1/4 7/20 -1/3 6/17 -1/4 0/1 5/14 -1/3 14/39 -1/5 0/1 9/25 -1/3 13/36 -3/11 4/11 -1/3 -2/7 3/8 -1/4 8/21 -5/21 -4/17 21/55 -1/4 -3/13 34/89 -3/13 -8/35 47/123 -7/31 13/34 -1/5 31/81 -1/3 -1/4 18/47 -1/4 -8/33 5/13 -3/13 2/5 -1/4 0/1 7/17 -1/4 -3/13 5/12 -3/13 3/7 -1/5 4/9 -1/4 0/1 9/20 -7/31 14/31 -2/9 -5/23 5/11 -3/14 -1/5 1/2 -1/5 6/11 -1/5 0/1 11/20 -1/5 5/9 -3/17 4/7 -1/6 11/19 -5/31 18/31 -5/31 -4/25 25/43 -1/6 -5/31 32/55 -5/31 -4/25 7/12 -3/19 24/41 -1/6 -4/25 17/29 -3/19 10/17 -3/19 -2/13 23/39 -7/45 13/22 -5/33 16/27 -3/19 -2/13 3/5 -1/6 -1/7 11/18 -7/43 19/31 -3/19 8/13 -1/6 -2/13 5/8 -3/19 7/11 -1/7 16/25 -2/13 -3/20 9/14 -1/7 2/3 -2/13 -1/7 9/13 -1/7 16/23 -1/7 -16/113 7/10 -1/7 26/37 -1/7 -4/29 45/64 -1/7 19/27 -1/7 12/17 -4/29 -7/51 17/24 -5/37 22/31 -1/7 0/1 5/7 -1/7 -3/22 28/39 -3/22 -2/15 23/32 -3/22 18/25 -1/7 -2/15 49/68 -13/97 31/43 -3/23 13/18 -1/7 8/11 -2/15 -3/23 3/4 -1/7 10/13 -4/31 -1/8 7/9 -1/7 -1/8 11/14 -1/7 26/33 -1/7 0/1 15/19 -1/7 4/5 -2/15 -3/23 21/26 -11/85 17/21 -5/39 13/16 -1/7 9/11 -5/39 -1/8 5/6 -1/8 11/13 -1/8 -5/41 17/20 -5/41 6/7 -1/8 -4/33 13/15 -3/25 -5/42 20/23 -7/59 -2/17 27/31 -11/93 7/8 -5/43 8/9 -1/9 0/1 1/1 -1/9 8/7 -5/47 -2/19 15/13 -3/29 -1/10 7/6 -3/29 6/5 -1/10 17/14 -5/51 28/23 -1/10 -6/61 11/9 -1/10 -3/31 27/22 -5/51 43/35 -3/31 16/13 -4/41 -3/31 5/4 -3/31 24/19 -2/21 -5/53 43/34 -3/32 19/15 -1/11 33/26 -7/75 14/11 -4/43 -1/11 37/29 -1/11 60/47 -1/11 -10/111 23/18 -1/11 9/7 -1/10 -1/11 13/10 -1/11 17/13 -1/11 4/3 -1/10 0/1 15/11 -3/31 41/30 -1/11 67/49 -1/10 -3/31 26/19 -2/21 -1/11 11/8 -3/31 29/21 -5/53 18/13 -2/21 -3/32 25/18 -11/119 32/23 -1/11 39/28 -1/11 7/5 -1/10 -1/11 24/17 -2/21 -3/32 41/29 -1/11 17/12 -3/31 44/31 -8/85 -3/32 27/19 -1/11 37/26 -1/11 10/7 -4/43 -1/11 13/9 -1/11 16/11 -1/11 -6/67 3/2 -1/11 17/11 -1/11 -1/12 14/9 -4/47 -1/12 25/16 -3/37 36/23 -1/11 0/1 11/7 -1/13 19/12 -1/15 27/17 0/1 35/22 -1/5 8/5 -1/10 0/1 21/13 -1/11 55/34 -13/141 34/21 -1/11 81/50 -19/211 47/29 -1/11 -5/56 13/8 -1/11 44/27 -1/11 0/1 31/19 -1/11 49/30 -1/11 18/11 -1/11 0/1 41/25 -1/11 64/39 -1/11 -6/67 23/14 -1/11 5/3 -1/11 -1/12 27/16 -5/63 49/29 -1/13 22/13 -1/15 0/1 83/49 0/1 61/36 -1/3 39/23 -1/9 56/33 -1/11 0/1 17/10 -1/11 46/27 -5/57 -2/23 29/17 -1/11 12/7 -1/11 -2/23 7/4 -1/12 16/9 -1/13 0/1 57/32 -7/83 98/55 -1/12 -12/145 41/23 -1/12 -3/37 66/37 -3/37 -2/25 25/14 -1/13 9/5 -1/13 11/6 -1/13 13/7 -1/12 -1/13 15/8 -1/13 2/1 -1/12 0/1 15/7 -1/12 28/13 -1/12 -2/25 13/6 -1/13 11/5 -1/12 -1/13 31/14 -3/43 20/9 -1/9 0/1 29/13 -1/11 9/4 -1/13 16/7 -1/12 0/1 23/10 -1/12 30/13 -3/37 -2/25 7/3 -1/13 19/8 -1/15 31/13 0/1 43/18 -1/7 12/5 -1/11 0/1 29/12 -1/11 46/19 -8/95 -1/12 17/7 -1/12 -1/13 39/16 -1/12 22/9 -1/12 -2/25 5/2 -1/13 18/7 -1/11 0/1 49/19 -3/35 -1/12 80/31 -12/143 -1/12 111/43 -1/12 142/55 -1/12 -26/313 31/12 -7/85 75/29 -7/86 -3/37 44/17 -3/37 -2/25 57/22 -11/137 13/5 -1/13 8/3 -1/13 19/7 -1/13 49/18 -1/13 128/47 -1/13 -4/53 79/29 -1/13 -3/40 30/11 -3/40 -2/27 71/26 -3/41 41/15 -1/13 -1/14 11/4 -3/41 47/17 -1/14 -1/15 36/13 -1/15 0/1 97/35 0/1 61/22 -1/11 25/9 -1/13 64/23 -1/15 0/1 39/14 -1/11 14/5 -1/13 -2/27 31/11 -1/13 48/17 -1/14 0/1 65/23 0/1 17/6 -1/13 3/1 -1/13 -1/14 19/6 -1/13 35/11 -1/13 51/16 -1/13 67/21 -2/27 16/5 -2/27 -1/14 29/9 -1/13 13/4 -1/13 23/7 -1/13 79/24 -17/229 135/41 -2/27 56/17 -2/27 -15/203 33/10 -13/177 10/3 -4/55 -1/14 17/5 -1/14 24/7 -1/14 -10/141 7/2 -3/43 39/11 -3/43 71/20 -11/159 103/29 -2/29 32/9 -2/29 -3/44 25/7 -1/14 -1/15 68/19 -1/15 0/1 43/12 -1/14 18/5 -1/14 0/1 29/8 -3/43 69/19 -2/29 109/30 -9/131 40/11 -2/29 -3/44 11/3 -1/15 26/7 -1/14 15/4 -3/43 34/9 -2/29 -1/15 87/23 -1/15 140/37 -1/15 0/1 53/14 -1/15 19/5 -1/14 -1/15 23/6 -5/71 27/7 -3/43 31/8 -7/101 35/9 -2/29 4/1 -2/29 -1/15 17/4 -1/15 13/3 -3/44 -1/15 9/2 -1/15 23/5 -1/15 -7/106 60/13 -25/379 -6/91 217/47 -6/91 157/34 -71/1077 97/21 -23/349 37/8 -21/319 51/11 -9/137 14/3 -1/15 -4/61 33/7 -1/15 -3/46 19/4 -1/15 24/5 -1/15 -4/61 29/6 -1/15 34/7 -7/108 -2/31 73/15 -2/31 39/8 -7/109 5/1 -1/15 21/4 -9/139 37/7 -2/31 53/10 -23/357 16/3 -2/31 -7/109 11/2 -3/47 28/5 -1/16 17/3 -1/15 -1/16 6/1 -4/63 -1/16 19/3 -1/16 32/5 -1/16 -22/353 13/2 -9/145 7/1 -1/16 -3/49 15/2 -3/49 23/3 -7/115 31/4 -19/313 39/5 -2/33 8/1 -2/33 -5/83 9/1 -1/17 10/1 -1/17 1/0 -1/19 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(1,0,40,1) Matrix(415,194,246,115) -> Matrix(37,-2,-462,25) Matrix(249,116,-908,-423) -> Matrix(37,-2,278,-15) Matrix(893,410,734,337) -> Matrix(37,-2,-388,21) Matrix(647,296,-2188,-1001) -> Matrix(141,-8,1322,-75) Matrix(1445,654,886,401) -> Matrix(69,-4,-776,45) Matrix(719,324,-1600,-721) -> Matrix(171,-10,2890,-169) Matrix(4951,2222,1914,859) -> Matrix(269,-16,-3312,197) Matrix(157,70,-554,-247) -> Matrix(1,0,-8,1) Matrix(549,242,946,417) -> Matrix(97,-6,-598,37) Matrix(783,344,-2588,-1137) -> Matrix(65,-4,634,-39) Matrix(1801,790,2510,1101) -> Matrix(35,-2,-262,15) Matrix(4703,2062,1722,755) -> Matrix(1,0,-30,1) Matrix(545,238,158,69) -> Matrix(97,-6,-1374,85) Matrix(853,370,-2174,-943) -> Matrix(31,-2,450,-29) Matrix(79,34,230,99) -> Matrix(31,-2,-108,7) Matrix(75,32,232,99) -> Matrix(31,-2,-108,7) Matrix(1453,616,1144,485) -> Matrix(29,-2,-304,21) Matrix(607,256,-1444,-609) -> Matrix(61,-4,900,-59) Matrix(2577,1082,1822,765) -> Matrix(59,-4,-634,43) Matrix(225,94,-754,-315) -> Matrix(29,-2,276,-19) Matrix(829,344,976,405) -> Matrix(85,-6,-694,49) Matrix(449,186,-1726,-715) -> Matrix(1,0,-6,1) Matrix(223,92,-972,-401) -> Matrix(31,-2,202,-13) Matrix(371,152,-1340,-549) -> Matrix(27,-2,230,-17) Matrix(519,212,448,183) -> Matrix(27,-2,-256,19) Matrix(521,212,-1708,-695) -> Matrix(29,-2,276,-19) Matrix(361,142,-1594,-627) -> Matrix(27,-2,176,-13) Matrix(2607,1022,-7094,-2781) -> Matrix(53,-4,676,-51) Matrix(215,84,796,311) -> Matrix(29,-2,-72,5) Matrix(289,112,1076,417) -> Matrix(1,0,-16,1) Matrix(1361,526,1938,749) -> Matrix(79,-6,-566,43) Matrix(503,194,70,27) -> Matrix(29,-2,-478,33) Matrix(73,28,-644,-247) -> Matrix(27,-2,68,-5) Matrix(1709,654,358,137) -> Matrix(53,-4,-808,61) Matrix(283,108,-1208,-461) -> Matrix(1,0,-6,1) Matrix(495,188,-1772,-673) -> Matrix(31,-2,264,-17) Matrix(707,268,1844,699) -> Matrix(57,-4,-242,17) Matrix(69,26,-422,-159) -> Matrix(27,-2,122,-9) Matrix(209,78,142,53) -> Matrix(27,-2,-310,23) Matrix(557,206,630,233) -> Matrix(51,-4,-446,35) Matrix(2095,774,766,283) -> Matrix(1,0,-26,1) Matrix(4735,1742,2922,1075) -> Matrix(53,-4,-596,45) Matrix(10925,4016,2364,869) -> Matrix(639,-50,-9700,759) Matrix(207,76,-1528,-561) -> Matrix(25,-2,138,-11) Matrix(137,50,-622,-227) -> Matrix(1,0,-6,1) Matrix(343,124,-1928,-697) -> Matrix(27,-2,122,-9) Matrix(621,224,-2204,-795) -> Matrix(27,-2,230,-17) Matrix(345,124,-1444,-519) -> Matrix(27,-2,176,-13) Matrix(1717,616,616,221) -> Matrix(25,-2,-312,25) Matrix(1641,584,340,121) -> Matrix(99,-8,-1522,123) Matrix(3891,1382,2182,775) -> Matrix(73,-6,-888,73) Matrix(1157,410,206,73) -> Matrix(25,-2,-412,33) Matrix(747,262,134,47) -> Matrix(71,-6,-1124,95) Matrix(607,212,272,95) -> Matrix(23,-2,-264,23) Matrix(645,206,454,145) -> Matrix(43,-4,-462,43) Matrix(1093,344,448,141) -> Matrix(61,-6,-742,73) Matrix(1403,436,576,179) -> Matrix(39,-4,-458,47) Matrix(2293,710,830,257) -> Matrix(39,-4,-536,55) Matrix(317,98,1530,473) -> Matrix(59,-6,-108,11) Matrix(569,174,1586,485) -> Matrix(19,-2,-66,7) Matrix(1775,542,822,251) -> Matrix(1,0,-22,1) Matrix(191,58,-1202,-365) -> Matrix(19,-2,86,-9) Matrix(503,152,-2836,-857) -> Matrix(39,-4,166,-17) Matrix(4633,1376,1000,297) -> Matrix(45,-4,-686,61) Matrix(2563,760,1440,427) -> Matrix(19,-2,-218,23) Matrix(311,92,-2248,-665) -> Matrix(19,-2,10,-1) Matrix(623,184,-3308,-977) -> Matrix(1,0,-4,1) Matrix(2681,790,750,221) -> Matrix(19,-2,-294,31) Matrix(997,292,2612,765) -> Matrix(75,-8,-328,35) Matrix(1801,526,1058,309) -> Matrix(55,-6,-614,67) Matrix(433,126,622,181) -> Matrix(127,-14,-898,99) Matrix(1833,514,674,189) -> Matrix(1,0,-22,1) Matrix(1649,460,1036,289) -> Matrix(17,-2,-110,13) Matrix(3465,958,2738,757) -> Matrix(83,-10,-888,107) Matrix(2795,772,3892,1075) -> Matrix(67,-8,-494,59) Matrix(305,84,1456,401) -> Matrix(17,-2,-42,5) Matrix(1943,534,302,83) -> Matrix(129,-16,-2072,257) Matrix(59,16,424,115) -> Matrix(17,-2,-8,1) Matrix(1629,440,1144,309) -> Matrix(83,-10,-888,107) Matrix(901,242,242,65) -> Matrix(49,-6,-694,85) Matrix(659,174,178,47) -> Matrix(15,-2,-202,27) Matrix(237,62,-1250,-327) -> Matrix(1,0,-2,1) Matrix(475,122,1242,319) -> Matrix(1,0,-12,1) Matrix(815,198,638,155) -> Matrix(29,-4,-326,45) Matrix(347,82,402,95) -> Matrix(25,-4,-206,33) Matrix(2637,614,1894,441) -> Matrix(29,-4,-326,45) Matrix(517,120,56,13) -> Matrix(41,-6,-690,101) Matrix(1769,404,740,169) -> Matrix(13,-2,-110,17) Matrix(5117,1158,1878,425) -> Matrix(51,-8,-682,107) Matrix(967,218,794,179) -> Matrix(37,-6,-376,61) Matrix(1409,308,2420,529) -> Matrix(37,-6,-228,37) Matrix(3433,748,2024,441) -> Matrix(13,-2,-136,21) Matrix(167,36,-784,-169) -> Matrix(37,-6,216,-35) Matrix(1397,296,892,189) -> Matrix(11,-2,-126,23) Matrix(833,174,1058,221) -> Matrix(11,-2,-82,15) Matrix(167,34,54,11) -> Matrix(11,-2,-148,27) Matrix(763,146,162,31) -> Matrix(21,-4,-320,61) Matrix(2171,410,2494,471) -> Matrix(87,-16,-734,135) Matrix(161,30,542,101) -> Matrix(31,-6,-98,19) Matrix(1557,280,4076,733) -> Matrix(13,-2,-58,9) Matrix(1717,308,1232,221) -> Matrix(1,0,-16,1) Matrix(7385,1312,2032,361) -> Matrix(55,-12,-802,175) Matrix(479,84,268,47) -> Matrix(9,-2,-112,25) Matrix(103,16,-676,-105) -> Matrix(17,-4,64,-15) Matrix(2693,406,1970,297) -> Matrix(1,0,-14,1) Matrix(671,100,208,31) -> Matrix(7,-2,-94,27) Matrix(1889,260,356,49) -> Matrix(9,2,-140,-31) Matrix(303,40,356,47) -> Matrix(17,-4,-140,33) Matrix(903,110,550,67) -> Matrix(13,-4,-146,45) Matrix(147,16,248,27) -> Matrix(5,-2,-32,13) Matrix(197,-24,156,-19) -> Matrix(3,2,-32,-21) Matrix(1207,-158,466,-61) -> Matrix(5,-2,-62,25) Matrix(191,-28,116,-17) -> Matrix(1,2,-12,-23) Matrix(187,-32,76,-13) -> Matrix(3,2,-38,-25) Matrix(409,-76,296,-55) -> Matrix(7,2,-74,-21) Matrix(1533,-316,4012,-827) -> Matrix(19,12,-84,-53) Matrix(217,-46,618,-131) -> Matrix(1,0,-2,1) Matrix(73,-16,324,-71) -> Matrix(7,4,-16,-9) Matrix(1827,-416,1076,-245) -> Matrix(5,2,-48,-19) Matrix(715,-164,824,-189) -> Matrix(21,8,-176,-67) Matrix(107,-26,70,-17) -> Matrix(5,2,-58,-23) Matrix(557,-146,454,-119) -> Matrix(7,4,-72,-41) Matrix(1077,-286,418,-111) -> Matrix(5,2,-58,-23) Matrix(449,-124,344,-95) -> Matrix(5,2,-58,-23) Matrix(1171,-326,722,-201) -> Matrix(11,4,-124,-45) Matrix(585,-164,824,-231) -> Matrix(5,2,-38,-15) Matrix(171,-50,578,-169) -> Matrix(29,10,-90,-31) Matrix(203,-62,370,-113) -> Matrix(1,0,-2,1) Matrix(873,-272,536,-167) -> Matrix(1,0,-8,1) Matrix(1271,-400,1808,-569) -> Matrix(11,4,-80,-29) Matrix(455,-162,778,-277) -> Matrix(15,4,-94,-25) Matrix(2461,-884,1456,-523) -> Matrix(1,0,-10,1) Matrix(2425,-874,874,-315) -> Matrix(7,2,-88,-25) Matrix(2651,-958,1486,-537) -> Matrix(15,4,-184,-49) Matrix(97,-36,256,-95) -> Matrix(23,6,-96,-25) Matrix(4967,-1898,1018,-389) -> Matrix(53,12,-826,-187) Matrix(9865,-3776,5536,-2119) -> Matrix(15,4,-184,-49) Matrix(127,-50,94,-37) -> Matrix(1,0,-6,1) Matrix(187,-76,32,-13) -> Matrix(17,4,-268,-63) Matrix(343,-142,186,-77) -> Matrix(9,2,-104,-23) Matrix(217,-92,92,-39) -> Matrix(9,2,-122,-27) Matrix(245,-108,152,-67) -> Matrix(1,0,-6,1) Matrix(1033,-464,728,-327) -> Matrix(35,8,-372,-85) Matrix(1879,-848,2608,-1177) -> Matrix(55,12,-408,-89) Matrix(2363,-1068,1728,-781) -> Matrix(37,8,-384,-83) Matrix(271,-124,212,-97) -> Matrix(9,2,-104,-23) Matrix(343,-186,142,-77) -> Matrix(1,0,-6,1) Matrix(737,-406,1022,-563) -> Matrix(1,0,-2,1) Matrix(113,-64,196,-111) -> Matrix(47,8,-288,-49) Matrix(3005,-1746,1086,-631) -> Matrix(25,4,-344,-55) Matrix(9849,-5728,3616,-2103) -> Matrix(99,16,-1318,-213) Matrix(2663,-1560,944,-553) -> Matrix(25,4,-344,-55) Matrix(249,-146,278,-163) -> Matrix(13,2,-98,-15) Matrix(1413,-832,304,-179) -> Matrix(63,10,-964,-153) Matrix(3237,-1910,1910,-1127) -> Matrix(13,2,-72,-11) Matrix(2461,-1456,884,-523) -> Matrix(13,2,-176,-27) Matrix(191,-116,28,-17) -> Matrix(11,2,-182,-33) Matrix(709,-434,874,-535) -> Matrix(49,8,-386,-63) Matrix(873,-536,272,-167) -> Matrix(25,4,-344,-55) Matrix(245,-152,108,-67) -> Matrix(13,2,-150,-23) Matrix(297,-188,188,-119) -> Matrix(13,2,-176,-27) Matrix(1289,-824,912,-583) -> Matrix(1,0,-4,1) Matrix(403,-258,214,-137) -> Matrix(13,2,-176,-27) Matrix(107,-70,26,-17) -> Matrix(1,0,-8,1) Matrix(235,-162,338,-233) -> Matrix(125,18,-882,-127) Matrix(3617,-2544,1136,-799) -> Matrix(29,4,-370,-51) Matrix(1033,-728,464,-327) -> Matrix(29,4,-312,-43) Matrix(1289,-912,824,-583) -> Matrix(29,4,-370,-51) Matrix(747,-530,926,-657) -> Matrix(17,2,-128,-15) Matrix(1843,-1326,1458,-1049) -> Matrix(89,12,-942,-127) Matrix(4961,-3576,1508,-1087) -> Matrix(61,8,-816,-107) Matrix(409,-296,76,-55) -> Matrix(59,8,-922,-125) Matrix(127,-94,50,-37) -> Matrix(15,2,-188,-25) Matrix(449,-344,124,-95) -> Matrix(31,4,-442,-57) Matrix(347,-268,224,-173) -> Matrix(1,0,-4,1) Matrix(271,-212,124,-97) -> Matrix(15,2,-188,-25) Matrix(1723,-1358,1402,-1105) -> Matrix(31,4,-318,-41) Matrix(197,-156,24,-19) -> Matrix(29,4,-486,-67) Matrix(2505,-2026,706,-571) -> Matrix(171,22,-2464,-317) Matrix(557,-454,146,-119) -> Matrix(47,6,-666,-85) Matrix(121,-100,144,-119) -> Matrix(79,10,-640,-81) Matrix(5643,-4918,1222,-1065) -> Matrix(949,112,-14396,-1699) Matrix(249,-278,146,-163) -> Matrix(1,0,-2,1) Matrix(941,-1084,204,-235) -> Matrix(193,20,-2924,-303) Matrix(121,-144,100,-119) -> Matrix(79,8,-800,-81) Matrix(1679,-2062,434,-533) -> Matrix(185,18,-2662,-259) Matrix(709,-874,434,-535) -> Matrix(41,4,-482,-47) Matrix(1047,-1328,272,-345) -> Matrix(85,8,-1222,-115) Matrix(2147,-2738,1682,-2145) -> Matrix(153,14,-1694,-155) Matrix(249,-322,58,-75) -> Matrix(23,2,-334,-29) Matrix(553,-724,152,-199) -> Matrix(23,2,-334,-29) Matrix(855,-1168,112,-153) -> Matrix(85,8,-1392,-131) Matrix(557,-764,148,-203) -> Matrix(1,0,-4,1) Matrix(481,-664,92,-127) -> Matrix(127,12,-1958,-185) Matrix(609,-844,184,-255) -> Matrix(107,10,-1466,-137) Matrix(203,-282,18,-25) -> Matrix(65,6,-1116,-103) Matrix(585,-824,164,-231) -> Matrix(1,0,-4,1) Matrix(1271,-1808,400,-569) -> Matrix(43,4,-570,-53) Matrix(235,-338,162,-233) -> Matrix(109,10,-1210,-111) Matrix(997,-1556,412,-643) -> Matrix(49,4,-576,-47) Matrix(919,-1458,578,-917) -> Matrix(1,0,10,1) Matrix(2017,-3262,1194,-1931) -> Matrix(43,4,-570,-53) Matrix(2857,-4624,1764,-2855) -> Matrix(175,16,-1936,-177) Matrix(1303,-2128,368,-601) -> Matrix(47,4,-670,-57) Matrix(2051,-3362,1250,-2049) -> Matrix(65,6,-726,-67) Matrix(899,-1522,114,-193) -> Matrix(35,2,-578,-33) Matrix(2923,-4952,376,-637) -> Matrix(13,-2,-214,33) Matrix(455,-778,162,-277) -> Matrix(1,0,-2,1) Matrix(113,-196,64,-111) -> Matrix(23,2,-288,-25) Matrix(6249,-11132,2420,-4311) -> Matrix(167,14,-2016,-169) Matrix(203,-370,62,-113) -> Matrix(25,2,-338,-27) Matrix(523,-974,138,-257) -> Matrix(1,0,-2,1) Matrix(211,-450,98,-209) -> Matrix(23,2,-288,-25) Matrix(1205,-2666,466,-1031) -> Matrix(55,4,-674,-49) Matrix(1081,-2396,328,-727) -> Matrix(33,2,-446,-27) Matrix(481,-1102,134,-307) -> Matrix(1,0,-2,1) Matrix(1239,-2854,346,-797) -> Matrix(25,2,-338,-27) Matrix(517,-1198,186,-431) -> Matrix(25,2,-338,-27) Matrix(807,-1922,338,-805) -> Matrix(1,0,8,1) Matrix(1491,-3614,578,-1401) -> Matrix(49,4,-576,-47) Matrix(9547,-24642,3698,-9545) -> Matrix(455,38,-5472,-457) Matrix(661,-1714,86,-223) -> Matrix(201,16,-3304,-263) Matrix(97,-256,36,-95) -> Matrix(51,4,-676,-53) Matrix(5011,-13644,1324,-3605) -> Matrix(53,4,-782,-59) Matrix(1203,-3284,248,-677) -> Matrix(109,8,-1676,-123) Matrix(595,-1648,152,-421) -> Matrix(31,2,-450,-29) Matrix(1855,-5142,478,-1325) -> Matrix(15,2,-218,-29) Matrix(1507,-4256,472,-1333) -> Matrix(29,2,-392,-27) Matrix(1575,-4454,494,-1397) -> Matrix(25,2,-338,-27) Matrix(217,-618,46,-131) -> Matrix(25,2,-388,-31) Matrix(11645,-38338,2522,-8303) -> Matrix(3291,244,-49918,-3701) Matrix(6149,-20252,1332,-4387) -> Matrix(1893,140,-28706,-2123) Matrix(171,-578,50,-169) -> Matrix(195,14,-2744,-197) Matrix(2591,-9200,532,-1889) -> Matrix(521,36,-8090,-559) Matrix(1643,-5838,338,-1201) -> Matrix(291,20,-4496,-309) Matrix(2623,-9522,722,-2621) -> Matrix(347,24,-5046,-349) Matrix(4003,-15138,1058,-4001) -> Matrix(29,2,-450,-31) Matrix(73,-324,16,-71) -> Matrix(149,10,-2250,-151) Matrix(519,-2738,98,-517) -> Matrix(991,64,-15376,-993) Matrix(115,-722,18,-113) -> Matrix(415,26,-6656,-417) 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): 80 Degree of the the map X: 80 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 20 1 0/1 (0/1,1/1) 0 22 1/8 -1/3 1 22 1/7 0 11 1/6 -1/1 1 22 2/11 (-1/2,0/1) 0 22 1/5 -1/1 1 11 4/19 (-1/2,0/1) 0 22 3/14 -1/1 1 22 2/9 -1/2 2 2 5/22 -3/7 1 22 8/35 (-3/7,-2/5) 0 22 3/13 0 11 1/4 -1/3 1 22 5/19 0 11 4/15 (-2/5,-1/3) 0 22 3/11 -1/3 1 11 5/18 -1/3 1 22 7/25 0 11 2/7 (-2/5,-1/3) 0 22 5/17 -1/3 5 1 3/10 -1/3 1 22 4/13 (-1/3,0/1) 0 22 5/16 -1/3 1 22 1/3 0 11 6/17 (-1/4,0/1) 0 22 5/14 -1/3 1 22 9/25 -1/3 1 11 13/36 -3/11 1 22 4/11 (-1/3,-2/7) 0 22 3/8 -1/4 3 2 8/21 (-5/21,-4/17) 0 22 13/34 -1/5 1 22 5/13 -3/13 1 11 2/5 (-1/4,0/1) 0 22 7/17 0 11 5/12 -3/13 1 22 3/7 -1/5 1 11 4/9 (-1/4,0/1) 0 22 9/20 -7/31 1 22 14/31 (-2/9,-5/23) 0 22 5/11 0 11 1/2 -1/5 1 22 6/11 (-1/5,0/1) 0 22 11/20 -1/5 1 22 5/9 -3/17 1 11 4/7 -1/6 4 2 11/19 -5/31 1 11 7/12 -3/19 1 22 24/41 (-1/6,-4/25) 0 22 17/29 -3/19 1 11 10/17 (-3/19,-2/13) 0 22 23/39 -7/45 1 11 13/22 -5/33 1 22 3/5 0 11 11/18 -7/43 1 22 19/31 -3/19 1 11 8/13 (-1/6,-2/13) 0 22 5/8 -3/19 1 22 7/11 -1/7 1 11 16/25 (-2/13,-3/20) 0 22 9/14 -1/7 1 22 2/3 (-2/13,-1/7) 0 22 9/13 -1/7 9 1 7/10 -1/7 1 22 19/27 -1/7 1 11 12/17 (-4/29,-7/51) 0 22 17/24 -5/37 1 22 22/31 (-1/7,0/1) 0 22 5/7 0 11 23/32 -3/22 1 2 18/25 (-1/7,-2/15) 0 22 49/68 -13/97 1 22 31/43 -3/23 1 11 13/18 -1/7 1 22 8/11 (-2/15,-3/23) 0 22 3/4 -1/7 1 22 10/13 (-4/31,-1/8) 0 22 7/9 0 11 11/14 -1/7 1 22 15/19 -1/7 1 11 4/5 (-2/15,-3/23) 0 22 21/26 -11/85 1 22 17/21 -5/39 1 11 13/16 -1/7 1 22 9/11 0 11 5/6 -1/8 5 2 11/13 0 11 6/7 (-1/8,-4/33) 0 22 7/8 -5/43 1 22 1/1 -1/9 1 11 8/7 (-5/47,-2/19) 0 22 7/6 -3/29 1 22 6/5 -1/10 4 2 17/14 -5/51 1 22 11/9 0 11 27/22 -5/51 1 22 16/13 (-4/41,-3/31) 0 22 5/4 -3/31 1 22 24/19 (-2/21,-5/53) 0 22 19/15 -1/11 1 11 14/11 (-4/43,-1/11) 0 22 37/29 -1/11 7 1 23/18 -1/11 1 22 9/7 0 11 13/10 -1/11 1 22 17/13 -1/11 1 11 4/3 (-1/10,0/1) 0 22 15/11 -3/31 1 11 41/30 -1/11 1 22 26/19 (-2/21,-1/11) 0 22 11/8 -3/31 1 22 29/21 -5/53 1 11 18/13 (-2/21,-3/32) 0 22 25/18 -11/119 1 22 32/23 -1/11 8 2 7/5 0 11 24/17 (-2/21,-3/32) 0 22 17/12 -3/31 1 22 27/19 -1/11 1 11 10/7 (-4/43,-1/11) 0 22 13/9 -1/11 5 1 3/2 -1/11 1 22 17/11 0 11 14/9 (-4/47,-1/12) 0 22 25/16 -3/37 1 22 11/7 -1/13 1 11 19/12 -1/15 1 22 27/17 0/1 5 1 8/5 (-1/10,0/1) 0 22 21/13 -1/11 1 11 55/34 -13/141 1 22 34/21 -1/11 8 2 47/29 0 11 13/8 -1/11 1 22 31/19 -1/11 1 11 49/30 -1/11 1 22 18/11 (-1/11,0/1) 0 22 41/25 -1/11 3 1 23/14 -1/11 1 22 5/3 0 11 22/13 (-1/15,0/1) 0 22 83/49 0/1 12 1 61/36 -1/3 1 22 39/23 -1/9 1 11 17/10 -1/11 1 22 29/17 -1/11 1 11 12/7 (-1/11,-2/23) 0 22 7/4 -1/12 1 2 16/9 (-1/13,0/1) 0 22 9/5 -1/13 1 11 11/6 -1/13 1 22 13/7 0 11 15/8 -1/13 1 22 2/1 (-1/12,0/1) 0 22 15/7 -1/12 1 1 13/6 -1/13 1 22 11/5 0 11 31/14 -3/43 1 22 20/9 (-1/9,0/1) 0 22 9/4 -1/13 1 22 16/7 (-1/12,0/1) 0 22 23/10 -1/12 1 2 30/13 (-3/37,-2/25) 0 22 7/3 -1/13 1 11 19/8 -1/15 1 22 31/13 0/1 4 1 12/5 (-1/11,0/1) 0 22 29/12 -1/11 1 22 46/19 (-8/95,-1/12) 0 22 17/7 0 11 22/9 (-1/12,-2/25) 0 22 5/2 -1/13 1 22 18/7 (-1/11,0/1) 0 22 49/19 0 11 80/31 (-12/143,-1/12) 0 22 111/43 -1/12 19 1 31/12 -7/85 1 22 44/17 (-3/37,-2/25) 0 22 13/5 -1/13 1 11 8/3 -1/13 2 2 19/7 -1/13 1 11 30/11 (-3/40,-2/27) 0 22 11/4 -3/41 1 22 36/13 (-1/15,0/1) 0 22 97/35 0/1 4 1 61/22 -1/11 1 22 25/9 -1/13 1 11 14/5 (-1/13,-2/27) 0 22 31/11 -1/13 1 11 48/17 (-1/14,0/1) 0 22 65/23 0/1 1 1 17/6 -1/13 1 22 3/1 0 11 16/5 (-2/27,-1/14) 0 22 13/4 -1/13 1 22 23/7 -1/13 1 11 79/24 -17/229 1 22 135/41 -2/27 16 1 56/17 (-2/27,-15/203) 0 22 33/10 -13/177 1 22 10/3 (-4/55,-1/14) 0 22 17/5 -1/14 7 1 7/2 -3/43 1 22 39/11 -3/43 1 11 71/20 -11/159 1 22 103/29 -2/29 7 1 32/9 (-2/29,-3/44) 0 22 25/7 0 11 43/12 -1/14 1 2 18/5 (-1/14,0/1) 0 22 29/8 -3/43 1 22 69/19 -2/29 3 1 40/11 (-2/29,-3/44) 0 22 11/3 -1/15 1 11 15/4 -3/43 1 22 34/9 (-2/29,-1/15) 0 22 87/23 -1/15 1 1 53/14 -1/15 1 22 19/5 0 11 23/6 -5/71 1 22 4/1 (-2/29,-1/15) 0 22 17/4 -1/15 1 22 13/3 0 11 9/2 -1/15 5 2 23/5 0 11 37/8 -21/319 1 22 14/3 (-1/15,-4/61) 0 22 19/4 -1/15 1 22 5/1 -1/15 1 11 21/4 -9/139 1 22 37/7 -2/31 8 1 16/3 (-2/31,-7/109) 0 22 11/2 -3/47 1 22 17/3 0 11 6/1 (-4/63,-1/16) 0 22 19/3 -1/16 13 1 13/2 -9/145 1 22 7/1 0 11 8/1 (-2/33,-5/83) 0 22 9/1 -1/17 1 11 1/0 -1/19 1 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(-1,0,38,1) (-1/1,1/0) -> (-1/19,0/1) Matrix(-1,0,2,1) -> Matrix(1,0,2,-1) (-1/1,0/1) -> (0/1,1/1) Matrix(197,-24,156,-19) -> Matrix(3,2,-32,-21) Matrix(115,-16,194,-27) -> Matrix(1,2,-6,-13) Matrix(191,-28,116,-17) -> Matrix(1,2,-12,-23) Matrix(187,-32,76,-13) -> Matrix(3,2,-38,-25) Matrix(409,-76,296,-55) -> Matrix(7,2,-74,-21) Matrix(401,-84,654,-137) -> Matrix(5,2,-32,-13) Matrix(471,-100,146,-31) -> Matrix(3,2,-40,-27) Matrix(73,-16,324,-71) -> Matrix(7,4,-16,-9) -1/2 Matrix(2007,-458,1468,-335) -> Matrix(9,4,-92,-41) Matrix(357,-82,788,-181) -> Matrix(11,4,-52,-19) Matrix(107,-26,70,-17) -> Matrix(5,2,-58,-23) Matrix(557,-146,454,-119) -> Matrix(7,4,-72,-41) Matrix(1077,-286,418,-111) -> Matrix(5,2,-58,-23) Matrix(311,-84,174,-47) -> Matrix(5,2,-62,-25) Matrix(449,-124,344,-95) -> Matrix(5,2,-58,-23) Matrix(1171,-326,722,-201) -> Matrix(11,4,-124,-45) Matrix(585,-164,824,-231) -> Matrix(5,2,-38,-15) Matrix(69,-20,238,-69) -> Matrix(11,4,-30,-11) (2/7,5/17) -> (-2/5,-1/3) Matrix(101,-30,340,-101) -> Matrix(19,6,-60,-19) (5/17,3/10) -> (-1/3,-3/10) Matrix(203,-62,370,-113) -> Matrix(1,0,-2,1) 0/1 Matrix(471,-146,100,-31) -> Matrix(13,4,-198,-61) Matrix(99,-32,34,-11) -> Matrix(7,2,-94,-27) Matrix(99,-34,32,-11) -> Matrix(7,2,-94,-27) Matrix(455,-162,778,-277) -> Matrix(15,4,-94,-25) Matrix(485,-174,616,-221) -> Matrix(7,2,-52,-15) Matrix(2425,-874,874,-315) -> Matrix(7,2,-88,-25) Matrix(873,-316,710,-257) -> Matrix(9,2,-94,-21) Matrix(97,-36,256,-95) -> Matrix(23,6,-96,-25) -1/4 Matrix(765,-292,1082,-413) -> Matrix(35,8,-258,-59) Matrix(699,-268,446,-171) -> Matrix(17,4,-208,-49) Matrix(127,-50,94,-37) -> Matrix(1,0,-6,1) 0/1 Matrix(187,-76,32,-13) -> Matrix(17,4,-268,-63) Matrix(343,-142,186,-77) -> Matrix(9,2,-104,-23) Matrix(217,-92,92,-39) -> Matrix(9,2,-122,-27) Matrix(245,-108,152,-67) -> Matrix(1,0,-6,1) 0/1 Matrix(183,-82,212,-95) -> Matrix(17,4,-140,-33) Matrix(1879,-848,2608,-1177) -> Matrix(55,12,-408,-89) Matrix(271,-124,212,-97) -> Matrix(9,2,-104,-23) Matrix(343,-186,142,-77) -> Matrix(1,0,-6,1) 0/1 Matrix(737,-406,1022,-563) -> Matrix(1,0,-2,1) 0/1 Matrix(113,-64,196,-111) -> Matrix(47,8,-288,-49) -1/6 Matrix(417,-242,112,-65) -> Matrix(37,6,-524,-85) Matrix(2663,-1560,944,-553) -> Matrix(25,4,-344,-55) Matrix(749,-440,526,-309) -> Matrix(63,10,-674,-107) Matrix(1937,-1142,748,-441) -> Matrix(77,12,-956,-149) Matrix(3237,-1910,1910,-1127) -> Matrix(13,2,-72,-11) -1/6 Matrix(191,-116,28,-17) -> Matrix(11,2,-182,-33) Matrix(709,-434,874,-535) -> Matrix(49,8,-386,-63) Matrix(245,-152,108,-67) -> Matrix(13,2,-150,-23) Matrix(297,-188,188,-119) -> Matrix(13,2,-176,-27) Matrix(805,-514,296,-189) -> Matrix(-1,0,20,1) *** -> (-1/10,0/1) Matrix(403,-258,214,-137) -> Matrix(13,2,-176,-27) Matrix(107,-70,26,-17) -> Matrix(1,0,-8,1) 0/1 Matrix(53,-36,78,-53) -> Matrix(27,4,-182,-27) (2/3,9/13) -> (-2/13,-1/7) Matrix(181,-126,260,-181) -> Matrix(99,14,-700,-99) (9/13,7/10) -> (-1/7,-7/50) Matrix(749,-526,440,-309) -> Matrix(43,6,-480,-67) Matrix(233,-164,206,-145) -> Matrix(43,6,-394,-55) Matrix(747,-530,926,-657) -> Matrix(17,2,-128,-15) -1/8 Matrix(1101,-790,308,-221) -> Matrix(15,2,-232,-31) Matrix(1535,-1104,666,-479) -> Matrix(59,8,-730,-99) Matrix(4961,-3576,1508,-1087) -> Matrix(61,8,-816,-107) Matrix(409,-296,76,-55) -> Matrix(59,8,-922,-125) Matrix(127,-94,50,-37) -> Matrix(15,2,-188,-25) Matrix(449,-344,124,-95) -> Matrix(31,4,-442,-57) Matrix(347,-268,224,-173) -> Matrix(1,0,-4,1) 0/1 Matrix(271,-212,124,-97) -> Matrix(15,2,-188,-25) Matrix(197,-156,24,-19) -> Matrix(29,4,-486,-67) Matrix(2505,-2026,706,-571) -> Matrix(171,22,-2464,-317) Matrix(557,-454,146,-119) -> Matrix(47,6,-666,-85) Matrix(121,-100,144,-119) -> Matrix(79,10,-640,-81) -1/8 Matrix(405,-344,166,-141) -> Matrix(49,6,-596,-73) Matrix(233,-206,164,-145) -> Matrix(35,4,-376,-43) Matrix(183,-212,82,-95) -> Matrix(19,2,-218,-23) Matrix(121,-144,100,-119) -> Matrix(79,8,-800,-81) -1/10 Matrix(337,-410,60,-73) -> Matrix(21,2,-346,-33) Matrix(709,-874,434,-535) -> Matrix(41,4,-482,-47) Matrix(583,-738,252,-319) -> Matrix(43,4,-548,-51) Matrix(485,-616,174,-221) -> Matrix(21,2,-262,-25) Matrix(813,-1036,638,-813) -> Matrix(87,8,-946,-87) (14/11,37/29) -> (-4/43,-1/11) Matrix(1333,-1702,1044,-1333) -> Matrix(67,6,-748,-67) (37/29,23/18) -> (-1/11,-3/34) Matrix(249,-322,58,-75) -> Matrix(23,2,-334,-29) Matrix(553,-724,152,-199) -> Matrix(23,2,-334,-29) Matrix(1357,-1854,800,-1093) -> Matrix(21,2,-220,-21) *** -> (-1/10,-1/11) Matrix(557,-764,148,-203) -> Matrix(1,0,-4,1) 0/1 Matrix(481,-664,92,-127) -> Matrix(127,12,-1958,-185) Matrix(609,-844,184,-255) -> Matrix(107,10,-1466,-137) Matrix(1877,-2610,1160,-1613) -> Matrix(131,12,-1430,-131) *** -> (-6/65,-1/11) Matrix(1251,-1742,772,-1075) -> Matrix(45,4,-506,-45) *** -> (-1/11,-2/23) Matrix(585,-824,164,-231) -> Matrix(1,0,-4,1) 0/1 Matrix(547,-774,200,-283) -> Matrix(-1,0,24,1) *** -> (-1/12,0/1) Matrix(181,-260,126,-181) -> Matrix(87,8,-946,-87) (10/7,13/9) -> (-4/43,-1/11) Matrix(53,-78,36,-53) -> Matrix(23,2,-264,-23) (13/9,3/2) -> (-1/11,-1/12) Matrix(997,-1556,412,-643) -> Matrix(49,4,-576,-47) -1/12 Matrix(647,-1026,408,-647) -> Matrix(-1,0,30,1) (19/12,27/17) -> (-1/15,0/1) Matrix(271,-432,170,-271) -> Matrix(-1,0,20,1) (27/17,8/5) -> (-1/10,0/1) Matrix(319,-516,34,-55) -> Matrix(65,6,-1094,-101) Matrix(401,-654,84,-137) -> Matrix(45,4,-686,-61) Matrix(1303,-2128,368,-601) -> Matrix(47,4,-670,-57) Matrix(901,-1476,550,-901) -> Matrix(-1,0,22,1) (18/11,41/25) -> (-1/11,0/1) Matrix(1149,-1886,700,-1149) -> Matrix(67,6,-748,-67) (41/25,23/14) -> (-1/11,-3/34) Matrix(115,-194,16,-27) -> Matrix(25,2,-412,-33) Matrix(2157,-3652,1274,-2157) -> Matrix(-1,0,30,1) (22/13,83/49) -> (-1/15,0/1) Matrix(5977,-10126,3528,-5977) -> Matrix(-1,0,6,1) (83/49,61/36) -> (-1/3,0/1) Matrix(455,-778,162,-277) -> Matrix(1,0,-2,1) 0/1 Matrix(113,-196,64,-111) -> Matrix(23,2,-288,-25) -1/12 Matrix(203,-370,62,-113) -> Matrix(25,2,-338,-27) -1/13 Matrix(523,-974,138,-257) -> Matrix(1,0,-2,1) 0/1 Matrix(29,-60,14,-29) -> Matrix(-1,0,24,1) (2/1,15/7) -> (-1/12,0/1) Matrix(181,-390,84,-181) -> Matrix(25,2,-312,-25) (15/7,13/6) -> (-1/12,-1/13) Matrix(507,-1120,110,-243) -> Matrix(79,6,-1198,-91) Matrix(1081,-2396,328,-727) -> Matrix(33,2,-446,-27) Matrix(481,-1102,134,-307) -> Matrix(1,0,-2,1) 0/1 Matrix(495,-1178,208,-495) -> Matrix(-1,0,30,1) (19/8,31/13) -> (-1/15,0/1) Matrix(311,-744,130,-311) -> Matrix(-1,0,22,1) (31/13,12/5) -> (-1/11,0/1) Matrix(1491,-3614,578,-1401) -> Matrix(49,4,-576,-47) -1/12 Matrix(6881,-17760,2666,-6881) -> Matrix(287,24,-3432,-287) (80/31,111/43) -> (-12/143,-1/12) Matrix(2665,-6882,1032,-2665) -> Matrix(169,14,-2040,-169) (111/43,31/12) -> (-1/12,-7/85) Matrix(797,-2062,172,-445) -> Matrix(173,14,-2632,-213) Matrix(97,-256,36,-95) -> Matrix(51,4,-676,-53) -1/13 Matrix(315,-872,82,-227) -> Matrix(29,2,-420,-29) *** -> (-1/14,-1/15) Matrix(2521,-6984,910,-2521) -> Matrix(-1,0,30,1) (36/13,97/35) -> (-1/15,0/1) Matrix(4269,-11834,1540,-4269) -> Matrix(-1,0,22,1) (97/35,61/22) -> (-1/11,0/1) Matrix(2209,-6240,782,-2209) -> Matrix(-1,0,28,1) (48/17,65/23) -> (-1/14,0/1) Matrix(781,-2210,276,-781) -> Matrix(-1,0,26,1) (65/23,17/6) -> (-1/13,0/1) Matrix(6479,-21330,1968,-6479) -> Matrix(917,68,-12366,-917) (79/24,135/41) -> (-17/229,-2/27) Matrix(4591,-15120,1394,-4591) -> Matrix(811,60,-10962,-811) (135/41,56/17) -> (-2/27,-15/203) Matrix(101,-340,30,-101) -> Matrix(111,8,-1540,-111) (10/3,17/5) -> (-4/55,-1/14) Matrix(69,-238,20,-69) -> Matrix(85,6,-1204,-85) (17/5,7/2) -> (-1/14,-3/43) Matrix(4119,-14626,1160,-4119) -> Matrix(637,44,-9222,-637) (71/20,103/29) -> (-11/159,-2/29) Matrix(1855,-6592,522,-1855) -> Matrix(175,12,-2552,-175) (103/29,32/9) -> (-2/29,-3/44) Matrix(1103,-4002,304,-1103) -> Matrix(173,12,-2494,-173) (29/8,69/19) -> (-3/43,-2/29) Matrix(1519,-5520,418,-1519) -> Matrix(175,12,-2552,-175) (69/19,40/11) -> (-2/29,-3/44) Matrix(1565,-5916,414,-1565) -> Matrix(59,4,-870,-59) (34/9,87/23) -> (-2/29,-1/15) Matrix(2437,-9222,644,-2437) -> Matrix(29,2,-420,-29) (87/23,53/14) -> (-1/14,-1/15) Matrix(73,-324,16,-71) -> Matrix(149,10,-2250,-151) -1/15 Matrix(295,-1554,56,-295) -> Matrix(557,36,-8618,-557) (21/4,37/7) -> (-9/139,-2/31) Matrix(223,-1184,42,-223) -> Matrix(435,28,-6758,-435) (37/7,16/3) -> (-2/31,-7/109) Matrix(37,-228,6,-37) -> Matrix(127,8,-2016,-127) (6/1,19/3) -> (-4/63,-1/16) Matrix(77,-494,12,-77) -> Matrix(289,18,-4640,-289) (19/3,13/2) -> (-1/16,-9/145) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.