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): 1584 Minimal number of generators: 265 Number of equivalence classes of cusps: 66 Genus: 100 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 0/1 3/20 4/19 5/18 6/17 7/16 1/2 8/15 9/14 10/13 1/1 13/10 7/5 27/19 3/2 14/9 71/44 29/17 44/25 15/8 2/1 16/7 97/41 81/34 5/2 33/13 116/45 13/5 101/37 17/6 3/1 35/11 16/5 141/43 10/3 71/21 107/31 7/2 18/5 11/3 15/4 4/1 93/22 17/4 13/3 9/2 14/3 19/4 5/1 26/5 58/11 16/3 11/2 39/7 17/3 6/1 19/3 13/2 20/3 7/1 15/2 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 1/2 -7/15 1/1 -6/13 0/1 -11/24 1/4 -5/11 3/7 -9/20 9/16 -4/9 2/3 -15/34 1/2 -11/25 1/1 -7/16 1/0 -17/39 1/1 -10/23 2/1 -13/30 1/2 -3/7 1/3 -11/26 1/2 -8/19 8/13 -13/31 1/1 -18/43 2/3 -5/12 3/4 -12/29 0/1 -31/75 1/1 -19/46 1/2 -26/63 2/3 -7/17 1/1 -9/22 3/2 -11/27 1/1 -2/5 0/1 -11/28 7/12 -20/51 2/3 -9/23 3/5 -25/64 3/4 -16/41 2/3 -23/59 3/5 -7/18 7/10 -12/31 4/5 -5/13 1/1 -18/47 0/1 -13/34 7/10 -21/55 17/23 -29/76 3/4 -8/21 4/5 -19/50 5/6 -11/29 1/1 -3/8 1/0 -10/27 4/5 -7/19 3/1 -11/30 1/2 -26/71 0/1 -15/41 1/1 -19/52 1/4 -4/11 0/1 -9/25 3/5 -14/39 2/3 -5/14 1/2 -6/17 6/7 -7/20 1/0 -1/3 1/1 -7/22 1/2 -6/19 0/1 -11/35 1/1 -5/16 5/4 -4/13 0/1 -15/49 3/7 -11/36 3/4 -7/23 1/1 -3/10 3/2 -11/37 3/1 -19/64 1/0 -8/27 4/1 -5/17 1/3 -12/41 6/7 -7/24 5/4 -2/7 2/1 -7/25 -3/1 -12/43 -2/1 -17/61 -1/1 -5/18 -1/2 -18/65 0/1 -13/47 1/5 -21/76 1/0 -8/29 0/1 -19/69 1/5 -11/40 1/4 -3/11 1/1 -10/37 2/3 -7/26 3/2 -4/15 4/1 -13/49 -3/1 -9/34 -1/2 -5/19 1/1 -11/42 1/2 -17/65 1/1 -6/23 2/1 -1/4 1/0 -5/21 1/1 -9/38 5/2 -4/17 4/1 -3/13 -3/1 -11/48 1/0 -8/35 -4/3 -13/57 -1/1 -18/79 0/1 -5/22 -3/2 -2/9 0/1 -11/50 1/6 -9/41 1/3 -7/32 1/0 -5/23 1/1 -3/14 -3/2 -4/19 0/1 -1/5 1/1 -6/31 0/1 -5/26 1/6 -4/21 2/5 -7/37 1/1 -3/16 1/0 -8/43 6/7 -13/70 11/10 -5/27 1/1 -2/11 2/1 -3/17 -3/1 -4/23 -2/1 -1/6 -1/2 -2/13 -2/5 -1/7 1/3 -2/15 0/1 -5/38 1/6 -3/23 1/3 -1/8 1/0 -1/9 -1/1 0/1 0/1 1/8 1/4 1/7 1/3 3/20 1/2 2/13 2/3 1/6 1/2 2/11 0/1 5/27 1/1 3/16 1/0 7/37 1/1 4/21 0/1 1/5 -1/1 4/19 0/1 3/14 1/10 11/51 1/7 8/37 0/1 5/23 1/7 2/9 2/9 5/22 1/2 8/35 0/1 3/13 1/3 1/4 1/4 4/15 2/5 11/41 7/19 7/26 1/2 3/11 3/7 5/18 1/2 7/25 7/13 2/7 2/3 9/31 3/5 7/24 3/4 5/17 1/1 3/10 1/2 4/13 -2/1 1/3 1/1 6/17 0/1 5/14 1/6 9/25 3/13 4/11 0/1 19/52 3/8 15/41 1/1 11/30 1/6 7/19 1/5 10/27 2/7 3/8 3/8 11/29 9/19 8/21 6/11 13/34 1/2 5/13 1/1 12/31 0/1 19/49 1/1 7/18 1/2 2/5 0/1 11/27 1/3 9/22 1/2 25/61 1/5 16/39 0/1 7/17 1/3 26/63 0/1 19/46 1/2 12/29 0/1 5/12 3/8 13/31 1/3 34/81 1/3 21/50 9/26 29/69 11/31 8/19 4/11 19/45 5/13 11/26 1/2 14/33 2/5 3/7 3/7 7/16 1/2 11/25 11/21 4/9 4/7 5/11 1/1 1/2 1/2 8/15 1/1 7/13 1/1 6/11 2/3 11/20 1/0 16/29 0/1 5/9 1/1 14/25 0/1 9/16 1/4 22/39 2/5 13/23 3/7 17/30 1/2 21/37 15/31 4/7 4/7 15/26 1/2 26/45 2/3 11/19 1/1 7/12 3/4 3/5 1/1 17/28 1/0 31/51 -1/1 14/23 0/1 11/18 -1/2 8/13 0/1 13/21 -1/3 44/71 0/1 31/50 1/14 49/79 1/9 18/29 0/1 59/95 1/5 41/66 1/6 23/37 1/5 5/8 1/4 12/19 2/5 31/49 5/11 50/79 2/5 69/109 3/7 19/30 1/2 26/41 2/5 7/11 3/7 9/14 1/2 11/17 7/13 2/3 2/3 9/13 1/1 16/23 2/3 7/10 5/6 5/7 -1/1 18/25 0/1 31/43 1/3 13/18 1/2 21/29 7/15 8/11 4/7 35/48 5/8 27/37 1/1 19/26 1/2 30/41 2/3 11/15 3/5 14/19 2/3 3/4 3/4 10/13 1/1 17/22 11/10 7/9 1/1 11/14 3/2 4/5 0/1 13/16 1/4 22/27 4/9 9/11 3/5 32/39 2/3 23/28 5/8 37/45 5/7 14/17 2/3 5/6 5/6 6/7 0/1 1/1 1/1 8/7 2/1 7/6 1/2 13/11 1/1 6/5 6/5 17/14 3/2 28/23 2/1 11/9 1/1 38/31 1/1 27/22 3/2 16/13 4/3 21/17 1/1 5/4 1/0 24/19 2/1 19/15 9/5 14/11 2/1 51/40 1/0 37/29 3/1 23/18 5/2 9/7 3/1 13/10 1/0 17/13 -3/1 4/3 0/1 15/11 1/1 41/30 1/2 67/49 1/1 93/68 1/0 26/19 0/1 11/8 1/0 40/29 0/1 29/21 1/5 18/13 0/1 25/18 1/2 7/5 3/5 17/12 7/8 27/19 1/1 37/26 15/14 10/7 4/3 23/16 1/0 13/9 1/1 16/11 2/1 3/2 1/2 14/9 1/1 25/16 17/16 11/7 1/1 41/26 7/6 30/19 6/5 19/12 5/4 27/17 1/1 8/5 4/3 29/18 3/2 50/31 40/27 71/44 3/2 92/57 74/49 21/13 17/11 55/34 3/2 89/55 11/7 34/21 8/5 13/8 7/4 31/19 3/1 18/11 0/1 23/14 3/2 28/17 2/1 5/3 1/1 17/10 1/2 29/17 1/1 41/24 9/8 12/7 4/3 43/25 1/1 117/68 5/4 74/43 4/3 31/18 3/2 19/11 1/1 45/26 3/2 71/41 1/1 26/15 4/3 7/4 7/4 44/25 2/1 37/21 27/13 30/17 2/1 53/30 5/2 23/13 3/1 85/48 7/4 62/35 2/1 39/22 5/2 55/31 1/1 16/9 2/1 9/5 3/1 38/21 4/1 29/16 1/0 20/11 2/1 31/17 3/1 11/6 7/2 24/13 4/1 13/7 7/1 15/8 1/0 17/9 -7/1 2/1 0/1 13/6 1/2 11/5 1/1 42/19 0/1 31/14 1/2 20/9 4/7 9/4 3/4 16/7 1/1 23/10 11/10 7/3 1/1 26/11 2/1 97/41 2/1 71/30 5/2 45/19 1/1 64/27 2/1 19/8 1/0 50/21 2/1 81/34 1/0 112/47 0/1 31/13 1/1 43/18 3/2 12/5 0/1 29/12 5/4 46/19 2/1 17/7 1/1 39/16 5/4 61/25 7/5 83/34 7/6 22/9 4/3 49/20 3/2 27/11 5/3 5/2 3/2 33/13 2/1 61/24 25/12 28/11 2/1 23/9 3/1 18/7 2/1 67/26 5/2 116/45 3/1 165/64 1/0 49/19 3/1 31/12 1/0 44/17 2/1 13/5 1/1 73/28 7/4 133/51 2/1 60/23 2/1 47/18 3/2 34/13 2/1 21/8 7/4 50/19 2/1 29/11 15/7 8/3 8/3 27/10 7/2 46/17 2/1 19/7 3/1 30/11 4/1 101/37 4/1 172/63 4/1 71/26 25/6 41/15 5/1 52/19 4/1 11/4 1/0 36/13 6/1 133/48 1/0 97/35 7/1 61/22 11/2 25/9 19/3 14/5 10/1 17/6 1/0 20/7 -12/1 3/1 -1/1 19/6 -1/6 35/11 0/1 51/16 1/16 16/5 0/1 13/4 1/0 36/11 0/1 59/18 1/2 141/43 0/1 82/25 0/1 23/7 1/3 10/3 2/3 27/8 7/8 71/21 1/1 115/34 27/26 44/13 10/9 17/5 1/1 41/12 1/0 24/7 0/1 31/9 -1/1 69/20 1/0 107/31 0/1 145/42 1/2 38/11 0/1 7/2 1/2 18/5 1/1 29/8 9/8 11/3 1/1 48/13 4/3 37/10 3/2 26/7 2/1 41/11 3/1 97/26 3/2 56/15 2/1 15/4 1/0 34/9 2/1 53/14 3/2 19/5 1/1 4/1 2/1 21/5 3/1 38/9 2/1 93/22 5/2 55/13 3/1 17/4 1/0 13/3 3/1 35/8 1/0 57/13 3/1 22/5 2/1 9/2 9/2 23/5 7/1 60/13 10/1 37/8 1/0 88/19 8/1 227/49 8/1 139/30 17/2 51/11 9/1 14/3 12/1 19/4 1/0 24/5 -18/1 5/1 -3/1 26/5 -2/1 21/4 -5/4 58/11 -1/1 37/7 -1/1 16/3 0/1 27/5 -1/3 38/7 0/1 11/2 -1/2 39/7 0/1 67/12 1/12 28/5 0/1 17/3 1/1 6/1 0/1 19/3 1/1 13/2 1/2 20/3 1/1 27/4 5/4 7/1 1/1 15/2 5/2 8/1 2/1 9/1 3/1 10/1 10/1 1/0 1/0 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(261,122,430,201) (-1/2,-7/15) -> (3/5,17/28) Hyperbolic Matrix(173,80,426,197) (-7/15,-6/13) -> (2/5,11/27) Hyperbolic Matrix(343,158,-940,-433) (-6/13,-11/24) -> (-19/52,-4/11) Hyperbolic Matrix(341,156,1270,581) (-11/24,-5/11) -> (11/41,7/26) Hyperbolic Matrix(253,114,668,301) (-5/11,-9/20) -> (3/8,11/29) Hyperbolic Matrix(583,262,336,151) (-9/20,-4/9) -> (26/15,7/4) Hyperbolic Matrix(579,256,1400,619) (-4/9,-15/34) -> (19/46,12/29) Hyperbolic Matrix(245,108,1318,581) (-15/34,-11/25) -> (5/27,3/16) Hyperbolic Matrix(901,396,248,109) (-11/25,-7/16) -> (29/8,11/3) Hyperbolic Matrix(1793,782,736,321) (-7/16,-17/39) -> (17/7,39/16) Hyperbolic Matrix(487,212,-1546,-673) (-17/39,-10/23) -> (-6/19,-11/35) Hyperbolic Matrix(327,142,-1384,-601) (-10/23,-13/30) -> (-9/38,-4/17) Hyperbolic Matrix(647,280,-2350,-1017) (-13/30,-3/7) -> (-19/69,-11/40) Hyperbolic Matrix(637,270,880,373) (-3/7,-11/26) -> (13/18,21/29) Hyperbolic Matrix(479,202,396,167) (-11/26,-8/19) -> (6/5,17/14) Hyperbolic Matrix(157,66,716,301) (-8/19,-13/31) -> (5/23,2/9) Hyperbolic Matrix(1107,464,1744,731) (-13/31,-18/43) -> (26/41,7/11) Hyperbolic Matrix(1267,530,-3244,-1357) (-18/43,-5/12) -> (-25/64,-16/41) Hyperbolic Matrix(787,326,548,227) (-5/12,-12/29) -> (10/7,23/16) Hyperbolic Matrix(943,390,-3610,-1493) (-12/29,-31/75) -> (-17/65,-6/23) Hyperbolic Matrix(547,226,2902,1199) (-31/75,-19/46) -> (3/16,7/37) Hyperbolic Matrix(5721,2362,2192,905) (-19/46,-26/63) -> (60/23,47/18) Hyperbolic Matrix(2191,904,3604,1487) (-26/63,-7/17) -> (31/51,14/23) Hyperbolic Matrix(545,224,236,97) (-7/17,-9/22) -> (23/10,7/3) Hyperbolic Matrix(235,96,-1246,-509) (-9/22,-11/27) -> (-7/37,-3/16) Hyperbolic Matrix(231,94,1010,411) (-11/27,-2/5) -> (8/35,3/13) Hyperbolic Matrix(681,268,836,329) (-2/5,-11/28) -> (13/16,22/27) Hyperbolic Matrix(759,298,-3334,-1309) (-11/28,-20/51) -> (-18/79,-5/22) Hyperbolic Matrix(1665,652,452,177) (-20/51,-9/23) -> (11/3,48/13) Hyperbolic Matrix(829,324,-3774,-1475) (-9/23,-25/64) -> (-11/50,-9/41) Hyperbolic Matrix(4749,1852,1736,677) (-16/41,-23/59) -> (41/15,52/19) Hyperbolic Matrix(2711,1056,4372,1703) (-23/59,-7/18) -> (31/50,49/79) Hyperbolic Matrix(675,262,152,59) (-7/18,-12/31) -> (22/5,9/2) Hyperbolic Matrix(223,86,-822,-317) (-12/31,-5/13) -> (-3/11,-10/37) Hyperbolic Matrix(1195,458,968,371) (-5/13,-18/47) -> (16/13,21/17) Hyperbolic Matrix(371,142,-1936,-741) (-18/47,-13/34) -> (-5/26,-4/21) Hyperbolic Matrix(1115,426,-3646,-1393) (-13/34,-21/55) -> (-15/49,-11/36) Hyperbolic Matrix(2531,966,4462,1703) (-21/55,-29/76) -> (17/30,21/37) Hyperbolic Matrix(3497,1334,1932,737) (-29/76,-8/21) -> (38/21,29/16) Hyperbolic Matrix(447,170,-1412,-537) (-8/21,-19/50) -> (-7/22,-6/19) Hyperbolic Matrix(1927,732,2672,1015) (-19/50,-11/29) -> (31/43,13/18) Hyperbolic Matrix(813,308,520,197) (-11/29,-3/8) -> (25/16,11/7) Hyperbolic Matrix(879,326,364,135) (-3/8,-10/27) -> (12/5,29/12) Hyperbolic Matrix(363,134,-1238,-457) (-10/27,-7/19) -> (-5/17,-12/41) Hyperbolic Matrix(365,134,1016,373) (-7/19,-11/30) -> (5/14,9/25) Hyperbolic Matrix(3269,1198,1378,505) (-11/30,-26/71) -> (64/27,19/8) Hyperbolic Matrix(3049,1116,724,265) (-26/71,-15/41) -> (21/5,38/9) Hyperbolic Matrix(361,132,-2754,-1007) (-15/41,-19/52) -> (-5/38,-3/23) Hyperbolic Matrix(287,104,218,79) (-4/11,-9/25) -> (17/13,4/3) Hyperbolic Matrix(1079,388,1866,671) (-9/25,-14/39) -> (26/45,11/19) Hyperbolic Matrix(931,334,-3370,-1209) (-14/39,-5/14) -> (-21/76,-8/29) Hyperbolic Matrix(571,202,212,75) (-5/14,-6/17) -> (8/3,27/10) Hyperbolic Matrix(211,74,-1132,-397) (-6/17,-7/20) -> (-3/16,-8/43) Hyperbolic Matrix(355,124,-1274,-445) (-7/20,-1/3) -> (-17/61,-5/18) Hyperbolic Matrix(407,130,-1556,-497) (-1/3,-7/22) -> (-11/42,-17/65) Hyperbolic Matrix(535,168,-2882,-905) (-11/35,-5/16) -> (-13/70,-5/27) Hyperbolic Matrix(199,62,536,167) (-5/16,-4/13) -> (10/27,3/8) Hyperbolic Matrix(2853,874,4508,1381) (-4/13,-15/49) -> (31/49,50/79) Hyperbolic Matrix(1719,524,994,303) (-11/36,-7/23) -> (19/11,45/26) Hyperbolic Matrix(461,140,596,181) (-7/23,-3/10) -> (17/22,7/9) Hyperbolic Matrix(67,20,-526,-157) (-3/10,-11/37) -> (-3/23,-1/8) Hyperbolic Matrix(4255,1264,3336,991) (-11/37,-19/64) -> (51/40,37/29) Hyperbolic Matrix(4839,1436,1048,311) (-19/64,-8/27) -> (60/13,37/8) Hyperbolic Matrix(913,270,328,97) (-8/27,-5/17) -> (25/9,14/5) Hyperbolic Matrix(1757,514,1234,361) (-12/41,-7/24) -> (37/26,10/7) Hyperbolic Matrix(323,94,780,227) (-7/24,-2/7) -> (12/29,5/12) Hyperbolic Matrix(127,36,194,55) (-2/7,-7/25) -> (11/17,2/3) Hyperbolic Matrix(1659,464,640,179) (-7/25,-12/43) -> (44/17,13/5) Hyperbolic Matrix(1657,462,-7270,-2027) (-12/43,-17/61) -> (-13/57,-18/79) Hyperbolic Matrix(1399,388,256,71) (-5/18,-18/65) -> (38/7,11/2) Hyperbolic Matrix(3815,1056,2164,599) (-18/65,-13/47) -> (37/21,30/17) Hyperbolic Matrix(4767,1318,1718,475) (-13/47,-21/76) -> (61/22,25/9) Hyperbolic Matrix(443,122,-2284,-629) (-8/29,-19/69) -> (-1/5,-6/31) Hyperbolic Matrix(445,122,62,17) (-11/40,-3/11) -> (7/1,15/2) Hyperbolic Matrix(1829,494,1070,289) (-10/37,-7/26) -> (41/24,12/7) Hyperbolic Matrix(127,34,564,151) (-7/26,-4/15) -> (2/9,5/22) Hyperbolic Matrix(625,166,64,17) (-4/15,-13/49) -> (9/1,10/1) Hyperbolic Matrix(1441,382,3942,1045) (-13/49,-9/34) -> (19/52,15/41) Hyperbolic Matrix(439,116,-2002,-529) (-9/34,-5/19) -> (-9/41,-7/32) Hyperbolic Matrix(1745,458,2808,737) (-5/19,-11/42) -> (41/66,23/37) Hyperbolic Matrix(685,178,558,145) (-6/23,-1/4) -> (27/22,16/13) Hyperbolic Matrix(787,188,180,43) (-1/4,-5/21) -> (13/3,35/8) Hyperbolic Matrix(481,114,2232,529) (-5/21,-9/38) -> (3/14,11/51) Hyperbolic Matrix(239,56,542,127) (-4/17,-3/13) -> (11/25,4/9) Hyperbolic Matrix(1793,412,1014,233) (-3/13,-11/48) -> (53/30,23/13) Hyperbolic Matrix(1609,368,2208,505) (-11/48,-8/35) -> (8/11,35/48) Hyperbolic Matrix(2207,504,416,95) (-8/35,-13/57) -> (37/7,16/3) Hyperbolic Matrix(415,94,596,135) (-5/22,-2/9) -> (16/23,7/10) Hyperbolic Matrix(1949,430,766,169) (-2/9,-11/50) -> (61/24,28/11) Hyperbolic Matrix(1295,282,822,179) (-7/32,-5/23) -> (11/7,41/26) Hyperbolic Matrix(529,114,116,25) (-5/23,-3/14) -> (9/2,23/5) Hyperbolic Matrix(291,62,352,75) (-3/14,-4/19) -> (14/17,5/6) Hyperbolic Matrix(641,134,464,97) (-4/19,-1/5) -> (29/21,18/13) Hyperbolic Matrix(1997,386,626,121) (-6/31,-5/26) -> (51/16,16/5) Hyperbolic Matrix(1589,302,342,65) (-4/21,-7/37) -> (51/11,14/3) Hyperbolic Matrix(8025,1492,2372,441) (-8/43,-13/70) -> (115/34,44/13) Hyperbolic Matrix(509,94,1240,229) (-5/27,-2/11) -> (16/39,7/17) Hyperbolic Matrix(111,20,394,71) (-2/11,-3/17) -> (7/25,2/7) Hyperbolic Matrix(893,156,166,29) (-3/17,-4/23) -> (16/3,27/5) Hyperbolic Matrix(943,162,390,67) (-4/23,-1/6) -> (29/12,46/19) Hyperbolic Matrix(219,34,380,59) (-1/6,-2/13) -> (4/7,15/26) Hyperbolic Matrix(433,66,164,25) (-2/13,-1/7) -> (29/11,8/3) Hyperbolic Matrix(797,108,214,29) (-1/7,-2/15) -> (26/7,41/11) Hyperbolic Matrix(2069,274,370,49) (-2/15,-5/38) -> (67/12,28/5) Hyperbolic Matrix(261,32,106,13) (-1/8,-1/9) -> (27/11,5/2) Hyperbolic Matrix(257,28,156,17) (-1/9,0/1) -> (28/17,5/3) Hyperbolic Matrix(123,-14,290,-33) (0/1,1/8) -> (11/26,14/33) Hyperbolic Matrix(203,-26,164,-21) (1/8,1/7) -> (21/17,5/4) Hyperbolic Matrix(883,-130,360,-53) (1/7,3/20) -> (49/20,27/11) Hyperbolic Matrix(1077,-164,440,-67) (3/20,2/13) -> (22/9,49/20) Hyperbolic Matrix(677,-106,198,-31) (2/13,1/6) -> (41/12,24/7) Hyperbolic Matrix(117,-20,158,-27) (1/6,2/11) -> (14/19,3/4) Hyperbolic Matrix(1125,-208,622,-115) (2/11,5/27) -> (9/5,38/21) Hyperbolic Matrix(4795,-908,2012,-381) (7/37,4/21) -> (112/47,31/13) Hyperbolic Matrix(1235,-236,696,-133) (4/21,1/5) -> (55/31,16/9) Hyperbolic Matrix(801,-166,304,-63) (1/5,4/19) -> (50/19,29/11) Hyperbolic Matrix(1099,-234,418,-89) (4/19,3/14) -> (21/8,50/19) Hyperbolic Matrix(3101,-670,4994,-1079) (11/51,8/37) -> (18/29,59/95) Hyperbolic Matrix(3137,-680,1324,-287) (8/37,5/23) -> (45/19,64/27) Hyperbolic Matrix(1237,-282,2996,-683) (5/22,8/35) -> (26/63,19/46) Hyperbolic Matrix(335,-78,262,-61) (3/13,1/4) -> (23/18,9/7) Hyperbolic Matrix(109,-28,74,-19) (1/4,4/15) -> (16/11,3/2) Hyperbolic Matrix(763,-204,1814,-485) (4/15,11/41) -> (29/69,8/19) Hyperbolic Matrix(653,-176,1050,-283) (7/26,3/11) -> (23/37,5/8) Hyperbolic Matrix(181,-50,648,-179) (3/11,5/18) -> (5/18,7/25) Parabolic Matrix(1677,-484,1036,-299) (2/7,9/31) -> (89/55,34/21) Hyperbolic Matrix(2529,-736,1426,-415) (9/31,7/24) -> (39/22,55/31) Hyperbolic Matrix(677,-198,106,-31) (7/24,5/17) -> (19/3,13/2) Hyperbolic Matrix(249,-74,212,-63) (5/17,3/10) -> (7/6,13/11) Hyperbolic Matrix(317,-96,142,-43) (3/10,4/13) -> (20/9,9/4) Hyperbolic Matrix(457,-142,280,-87) (4/13,1/3) -> (31/19,18/11) Hyperbolic Matrix(613,-214,444,-155) (1/3,6/17) -> (40/29,29/21) Hyperbolic Matrix(747,-266,542,-193) (6/17,5/14) -> (11/8,40/29) Hyperbolic Matrix(641,-232,1014,-367) (9/25,4/11) -> (12/19,31/49) Hyperbolic Matrix(2057,-750,842,-307) (4/11,19/52) -> (83/34,22/9) Hyperbolic Matrix(4141,-1516,1516,-555) (15/41,11/30) -> (71/26,41/15) Hyperbolic Matrix(1547,-568,1212,-445) (11/30,7/19) -> (37/29,23/18) Hyperbolic Matrix(807,-298,436,-161) (7/19,10/27) -> (24/13,13/7) Hyperbolic Matrix(801,-304,166,-63) (11/29,8/21) -> (24/5,5/1) Hyperbolic Matrix(1331,-508,600,-229) (8/21,13/34) -> (31/14,20/9) Hyperbolic Matrix(1165,-446,1596,-611) (13/34,5/13) -> (27/37,19/26) Hyperbolic Matrix(1195,-462,1658,-641) (5/13,12/31) -> (18/25,31/43) Hyperbolic Matrix(1491,-578,3614,-1401) (12/31,19/49) -> (7/17,26/63) Hyperbolic Matrix(3215,-1248,2352,-913) (19/49,7/18) -> (41/30,67/49) Hyperbolic Matrix(297,-116,530,-207) (7/18,2/5) -> (14/25,9/16) Hyperbolic Matrix(883,-360,130,-53) (11/27,9/22) -> (27/4,7/1) Hyperbolic Matrix(6819,-2794,1828,-749) (9/22,25/61) -> (41/11,97/26) Hyperbolic Matrix(5741,-2354,9070,-3719) (25/61,16/39) -> (50/79,69/109) Hyperbolic Matrix(713,-298,390,-163) (5/12,13/31) -> (31/17,11/6) Hyperbolic Matrix(4795,-2012,908,-381) (13/31,34/81) -> (58/11,37/7) Hyperbolic Matrix(4601,-1932,874,-367) (34/81,21/50) -> (21/4,58/11) Hyperbolic Matrix(8777,-3688,3596,-1511) (21/50,29/69) -> (61/25,83/34) Hyperbolic Matrix(3137,-1324,680,-287) (8/19,19/45) -> (23/5,60/13) Hyperbolic Matrix(4365,-1844,1844,-779) (19/45,11/26) -> (71/30,45/19) Hyperbolic Matrix(1743,-740,2810,-1193) (14/33,3/7) -> (49/79,18/29) Hyperbolic Matrix(225,-98,512,-223) (3/7,7/16) -> (7/16,11/25) Parabolic Matrix(317,-142,96,-43) (4/9,5/11) -> (23/7,10/3) Hyperbolic Matrix(379,-174,220,-101) (5/11,1/2) -> (31/18,19/11) Hyperbolic Matrix(481,-254,392,-207) (1/2,8/15) -> (38/31,27/22) Hyperbolic Matrix(659,-354,538,-289) (8/15,7/13) -> (11/9,38/31) Hyperbolic Matrix(807,-436,298,-161) (7/13,6/11) -> (46/17,19/7) Hyperbolic Matrix(713,-390,298,-163) (6/11,11/20) -> (43/18,12/5) Hyperbolic Matrix(2431,-1340,742,-409) (11/20,16/29) -> (36/11,59/18) Hyperbolic Matrix(1125,-622,208,-115) (16/29,5/9) -> (27/5,38/7) Hyperbolic Matrix(827,-462,324,-181) (5/9,14/25) -> (28/11,23/9) Hyperbolic Matrix(1235,-696,236,-133) (9/16,22/39) -> (26/5,21/4) Hyperbolic Matrix(1765,-996,2146,-1211) (22/39,13/23) -> (37/45,14/17) Hyperbolic Matrix(1321,-748,2174,-1231) (13/23,17/30) -> (17/28,31/51) Hyperbolic Matrix(3551,-2016,2200,-1249) (21/37,4/7) -> (92/57,21/13) Hyperbolic Matrix(1867,-1078,2274,-1313) (15/26,26/45) -> (32/39,23/28) Hyperbolic Matrix(379,-220,174,-101) (11/19,7/12) -> (13/6,11/5) Hyperbolic Matrix(145,-86,86,-51) (7/12,3/5) -> (5/3,17/10) Hyperbolic Matrix(685,-418,372,-227) (14/23,11/18) -> (11/6,24/13) Hyperbolic Matrix(457,-280,142,-87) (11/18,8/13) -> (16/5,13/4) Hyperbolic Matrix(541,-334,426,-263) (8/13,13/21) -> (19/15,14/11) Hyperbolic Matrix(3551,-2200,2016,-1249) (13/21,44/71) -> (44/25,37/21) Hyperbolic Matrix(2697,-1672,1534,-951) (44/71,31/50) -> (7/4,44/25) Hyperbolic Matrix(16571,-10292,3576,-2221) (59/95,41/66) -> (139/30,51/11) Hyperbolic Matrix(197,-124,170,-107) (5/8,12/19) -> (8/7,7/6) Hyperbolic Matrix(17407,-11020,6282,-3977) (69/109,19/30) -> (133/48,97/35) Hyperbolic Matrix(3491,-2212,2028,-1285) (19/30,26/41) -> (74/43,31/18) Hyperbolic Matrix(253,-162,392,-251) (7/11,9/14) -> (9/14,11/17) Parabolic Matrix(109,-74,28,-19) (2/3,9/13) -> (19/5,4/1) Hyperbolic Matrix(515,-358,82,-57) (9/13,16/23) -> (6/1,19/3) Hyperbolic Matrix(189,-134,134,-95) (7/10,5/7) -> (7/5,17/12) Hyperbolic Matrix(643,-462,508,-365) (5/7,18/25) -> (24/19,19/15) Hyperbolic Matrix(613,-444,214,-155) (21/29,8/11) -> (20/7,3/1) Hyperbolic Matrix(3325,-2426,1276,-931) (35/48,27/37) -> (13/5,73/28) Hyperbolic Matrix(3215,-2352,1248,-913) (19/26,30/41) -> (18/7,67/26) Hyperbolic Matrix(849,-622,1036,-759) (30/41,11/15) -> (9/11,32/39) Hyperbolic Matrix(743,-546,132,-97) (11/15,14/19) -> (28/5,17/3) Hyperbolic Matrix(261,-200,338,-259) (3/4,10/13) -> (10/13,17/22) Parabolic Matrix(335,-262,78,-61) (7/9,11/14) -> (17/4,13/3) Hyperbolic Matrix(541,-426,334,-263) (11/14,4/5) -> (34/21,13/8) Hyperbolic Matrix(203,-164,26,-21) (4/5,13/16) -> (15/2,8/1) Hyperbolic Matrix(481,-392,254,-207) (22/27,9/11) -> (17/9,2/1) Hyperbolic Matrix(4469,-3674,2524,-2075) (23/28,37/45) -> (23/13,85/48) Hyperbolic Matrix(249,-212,74,-63) (5/6,6/7) -> (10/3,27/8) Hyperbolic Matrix(197,-170,124,-107) (6/7,1/1) -> (27/17,8/5) Hyperbolic Matrix(237,-268,130,-147) (1/1,8/7) -> (20/11,31/17) Hyperbolic Matrix(569,-674,168,-199) (13/11,6/5) -> (44/13,17/5) Hyperbolic Matrix(1765,-2146,996,-1211) (17/14,28/23) -> (62/35,39/22) Hyperbolic Matrix(1867,-2274,1078,-1313) (28/23,11/9) -> (71/41,26/15) Hyperbolic Matrix(285,-358,82,-103) (5/4,24/19) -> (38/11,7/2) Hyperbolic Matrix(4247,-5412,2468,-3145) (14/11,51/40) -> (117/68,74/43) Hyperbolic Matrix(261,-338,200,-259) (9/7,13/10) -> (13/10,17/13) Parabolic Matrix(117,-158,20,-27) (4/3,15/11) -> (17/3,6/1) Hyperbolic Matrix(2625,-3586,1516,-2071) (15/11,41/30) -> (45/26,71/41) Hyperbolic Matrix(8297,-11346,1962,-2683) (67/49,93/68) -> (93/22,55/13) Hyperbolic Matrix(4351,-5952,1030,-1409) (93/68,26/19) -> (38/9,93/22) Hyperbolic Matrix(1165,-1596,446,-611) (26/19,11/8) -> (47/18,34/13) Hyperbolic Matrix(1195,-1658,462,-641) (18/13,25/18) -> (31/12,44/17) Hyperbolic Matrix(653,-910,404,-563) (25/18,7/5) -> (21/13,55/34) Hyperbolic Matrix(1027,-1458,722,-1025) (17/12,27/19) -> (27/19,37/26) Parabolic Matrix(641,-924,188,-271) (23/16,13/9) -> (17/5,41/12) Hyperbolic Matrix(581,-844,338,-491) (13/9,16/11) -> (12/7,43/25) Hyperbolic Matrix(253,-392,162,-251) (3/2,14/9) -> (14/9,25/16) Parabolic Matrix(1891,-2984,500,-789) (41/26,30/19) -> (34/9,53/14) Hyperbolic Matrix(641,-1014,232,-367) (30/19,19/12) -> (11/4,36/13) Hyperbolic Matrix(1103,-1750,462,-733) (19/12,27/17) -> (31/13,43/18) Hyperbolic Matrix(653,-1050,176,-283) (8/5,29/18) -> (37/10,26/7) Hyperbolic Matrix(211,-340,18,-29) (29/18,50/31) -> (10/1,1/0) Hyperbolic Matrix(6249,-10082,3872,-6247) (50/31,71/44) -> (71/44,92/57) Parabolic Matrix(4849,-7846,1406,-2275) (55/34,89/55) -> (31/9,69/20) Hyperbolic Matrix(385,-628,122,-199) (13/8,31/19) -> (3/1,19/6) Hyperbolic Matrix(941,-1544,348,-571) (18/11,23/14) -> (27/10,46/17) Hyperbolic Matrix(1321,-2174,748,-1231) (23/14,28/17) -> (30/17,53/30) Hyperbolic Matrix(987,-1682,578,-985) (17/10,29/17) -> (29/17,41/24) Parabolic Matrix(7457,-12828,2892,-4975) (43/25,117/68) -> (165/64,49/19) Hyperbolic Matrix(10741,-19022,3934,-6967) (85/48,62/35) -> (172/63,71/26) Hyperbolic Matrix(297,-530,116,-207) (16/9,9/5) -> (23/9,18/7) Hyperbolic Matrix(1013,-1838,458,-831) (29/16,20/11) -> (42/19,31/14) Hyperbolic Matrix(241,-450,128,-239) (13/7,15/8) -> (15/8,17/9) Parabolic Matrix(219,-472,58,-125) (2/1,13/6) -> (15/4,34/9) Hyperbolic Matrix(847,-1868,258,-569) (11/5,42/19) -> (82/25,23/7) Hyperbolic Matrix(225,-512,98,-223) (9/4,16/7) -> (16/7,23/10) Parabolic Matrix(123,-290,14,-33) (7/3,26/11) -> (8/1,9/1) Hyperbolic Matrix(3923,-9278,1504,-3557) (26/11,97/41) -> (133/51,60/23) Hyperbolic Matrix(6983,-16524,2678,-6337) (97/41,71/30) -> (73/28,133/51) Hyperbolic Matrix(763,-1814,204,-485) (19/8,50/21) -> (56/15,15/4) Hyperbolic Matrix(5509,-13122,2312,-5507) (50/21,81/34) -> (81/34,112/47) Parabolic Matrix(1237,-2996,282,-683) (46/19,17/7) -> (57/13,22/5) Hyperbolic Matrix(3077,-7504,1110,-2707) (39/16,61/25) -> (97/35,61/22) Hyperbolic Matrix(859,-2178,338,-857) (5/2,33/13) -> (33/13,61/24) Parabolic Matrix(10441,-26912,4050,-10439) (67/26,116/45) -> (116/45,165/64) Parabolic Matrix(1349,-3482,308,-795) (49/19,31/12) -> (35/8,57/13) Hyperbolic Matrix(457,-1198,140,-367) (34/13,21/8) -> (13/4,36/11) Hyperbolic Matrix(259,-706,62,-169) (19/7,30/11) -> (4/1,21/5) Hyperbolic Matrix(7475,-20402,2738,-7473) (30/11,101/37) -> (101/37,172/63) Parabolic Matrix(2067,-5660,554,-1517) (52/19,11/4) -> (97/26,56/15) Hyperbolic Matrix(3709,-10274,1074,-2975) (36/13,133/48) -> (145/42,38/11) Hyperbolic Matrix(205,-578,72,-203) (14/5,17/6) -> (17/6,20/7) Parabolic Matrix(771,-2450,242,-769) (19/6,35/11) -> (35/11,51/16) Parabolic Matrix(10063,-32992,2172,-7121) (59/18,141/43) -> (227/49,139/30) Hyperbolic Matrix(9459,-31022,2042,-6697) (141/43,82/25) -> (88/19,227/49) Hyperbolic Matrix(2983,-10082,882,-2981) (27/8,71/21) -> (71/21,115/34) Parabolic Matrix(269,-926,52,-179) (24/7,31/9) -> (5/1,26/5) Hyperbolic Matrix(6635,-22898,1922,-6633) (69/20,107/31) -> (107/31,145/42) Parabolic Matrix(181,-648,50,-179) (7/2,18/5) -> (18/5,29/8) Parabolic Matrix(1361,-5032,294,-1087) (48/13,37/10) -> (37/8,88/19) Hyperbolic Matrix(855,-3238,202,-765) (53/14,19/5) -> (55/13,17/4) Hyperbolic Matrix(153,-722,32,-151) (14/3,19/4) -> (19/4,24/5) Parabolic Matrix(547,-3042,98,-545) (11/2,39/7) -> (39/7,67/12) Parabolic Matrix(121,-800,18,-119) (13/2,20/3) -> (20/3,27/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(261,122,430,201) -> Matrix(3,-2,2,-1) Matrix(173,80,426,197) -> Matrix(1,0,2,1) Matrix(343,158,-940,-433) -> Matrix(1,0,0,1) Matrix(341,156,1270,581) -> Matrix(7,-2,18,-5) Matrix(253,114,668,301) -> Matrix(11,-6,24,-13) Matrix(583,262,336,151) -> Matrix(17,-10,12,-7) Matrix(579,256,1400,619) -> Matrix(3,-2,8,-5) Matrix(245,108,1318,581) -> Matrix(3,-2,2,-1) Matrix(901,396,248,109) -> Matrix(9,-8,8,-7) Matrix(1793,782,736,321) -> Matrix(5,-4,4,-3) Matrix(487,212,-1546,-673) -> Matrix(1,-2,2,-3) Matrix(327,142,-1384,-601) -> Matrix(1,2,0,1) Matrix(647,280,-2350,-1017) -> Matrix(1,0,2,1) Matrix(637,270,880,373) -> Matrix(11,-6,24,-13) Matrix(479,202,396,167) -> Matrix(17,-10,12,-7) Matrix(157,66,716,301) -> Matrix(3,-2,20,-13) Matrix(1107,464,1744,731) -> Matrix(7,-4,16,-9) Matrix(1267,530,-3244,-1357) -> Matrix(1,0,0,1) Matrix(787,326,548,227) -> Matrix(5,-4,4,-3) Matrix(943,390,-3610,-1493) -> Matrix(3,-2,2,-1) Matrix(547,226,2902,1199) -> Matrix(3,-2,2,-1) Matrix(5721,2362,2192,905) -> Matrix(5,-4,4,-3) Matrix(2191,904,3604,1487) -> Matrix(3,-2,-4,3) Matrix(545,224,236,97) -> Matrix(9,-8,8,-7) Matrix(235,96,-1246,-509) -> Matrix(1,-2,2,-3) Matrix(231,94,1010,411) -> Matrix(1,0,2,1) Matrix(681,268,836,329) -> Matrix(7,-4,16,-9) Matrix(759,298,-3334,-1309) -> Matrix(3,-2,2,-1) Matrix(1665,652,452,177) -> Matrix(17,-10,12,-7) Matrix(829,324,-3774,-1475) -> Matrix(3,-2,14,-9) Matrix(4749,1852,1736,677) -> Matrix(35,-22,8,-5) Matrix(2711,1056,4372,1703) -> Matrix(3,-2,32,-21) Matrix(675,262,152,59) -> Matrix(13,-10,4,-3) Matrix(223,86,-822,-317) -> Matrix(3,-2,2,-1) Matrix(1195,458,968,371) -> Matrix(5,-4,4,-3) Matrix(371,142,-1936,-741) -> Matrix(3,-2,8,-5) Matrix(1115,426,-3646,-1393) -> Matrix(11,-8,18,-13) Matrix(2531,966,4462,1703) -> Matrix(37,-28,78,-59) Matrix(3497,1334,1932,737) -> Matrix(21,-16,4,-3) Matrix(447,170,-1412,-537) -> Matrix(5,-4,4,-3) Matrix(1927,732,2672,1015) -> Matrix(7,-6,20,-17) Matrix(813,308,520,197) -> Matrix(17,-16,16,-15) Matrix(879,326,364,135) -> Matrix(5,-4,4,-3) Matrix(363,134,-1238,-457) -> Matrix(1,-2,2,-3) Matrix(365,134,1016,373) -> Matrix(1,0,4,1) Matrix(3269,1198,1378,505) -> Matrix(3,-2,2,-1) Matrix(3049,1116,724,265) -> Matrix(1,2,0,1) Matrix(361,132,-2754,-1007) -> Matrix(1,0,2,1) Matrix(287,104,218,79) -> Matrix(1,0,-2,1) Matrix(1079,388,1866,671) -> Matrix(13,-8,18,-11) Matrix(931,334,-3370,-1209) -> Matrix(3,-2,2,-1) Matrix(571,202,212,75) -> Matrix(13,-10,4,-3) Matrix(211,74,-1132,-397) -> Matrix(1,0,0,1) Matrix(355,124,-1274,-445) -> Matrix(1,0,-2,1) Matrix(407,130,-1556,-497) -> Matrix(1,0,0,1) Matrix(535,168,-2882,-905) -> Matrix(7,-6,6,-5) Matrix(199,62,536,167) -> Matrix(1,-2,4,-7) Matrix(2853,874,4508,1381) -> Matrix(3,-2,8,-5) Matrix(1719,524,994,303) -> Matrix(7,-6,6,-5) Matrix(461,140,596,181) -> Matrix(9,-8,8,-7) Matrix(67,20,-526,-157) -> Matrix(1,-2,2,-3) Matrix(4255,1264,3336,991) -> Matrix(1,0,0,1) Matrix(4839,1436,1048,311) -> Matrix(1,6,0,1) Matrix(913,270,328,97) -> Matrix(1,6,0,1) Matrix(1757,514,1234,361) -> Matrix(11,-10,10,-9) Matrix(323,94,780,227) -> Matrix(1,-2,4,-7) Matrix(127,36,194,55) -> Matrix(1,-4,2,-7) Matrix(1659,464,640,179) -> Matrix(1,4,0,1) Matrix(1657,462,-7270,-2027) -> Matrix(1,2,-2,-3) Matrix(1399,388,256,71) -> Matrix(1,0,0,1) Matrix(3815,1056,2164,599) -> Matrix(17,2,8,1) Matrix(4767,1318,1718,475) -> Matrix(11,-6,2,-1) Matrix(443,122,-2284,-629) -> Matrix(1,0,-4,1) Matrix(445,122,62,17) -> Matrix(3,-2,2,-1) Matrix(1829,494,1070,289) -> Matrix(7,-6,6,-5) Matrix(127,34,564,151) -> Matrix(1,-2,4,-7) Matrix(625,166,64,17) -> Matrix(1,6,0,1) Matrix(1441,382,3942,1045) -> Matrix(1,2,2,5) Matrix(439,116,-2002,-529) -> Matrix(1,0,2,1) Matrix(1745,458,2808,737) -> Matrix(1,0,4,1) Matrix(685,178,558,145) -> Matrix(3,-2,2,-1) Matrix(787,188,180,43) -> Matrix(1,2,0,1) Matrix(481,114,2232,529) -> Matrix(1,-2,8,-15) Matrix(239,56,542,127) -> Matrix(1,-8,2,-15) Matrix(1793,412,1014,233) -> Matrix(5,12,2,5) Matrix(1609,368,2208,505) -> Matrix(5,8,8,13) Matrix(2207,504,416,95) -> Matrix(3,4,-4,-5) Matrix(415,94,596,135) -> Matrix(3,2,4,3) Matrix(1949,430,766,169) -> Matrix(13,2,6,1) Matrix(1295,282,822,179) -> Matrix(7,-6,6,-5) Matrix(529,114,116,25) -> Matrix(1,6,0,1) Matrix(291,62,352,75) -> Matrix(3,2,4,3) Matrix(641,134,464,97) -> Matrix(1,0,4,1) Matrix(1997,386,626,121) -> Matrix(1,0,10,1) Matrix(1589,302,342,65) -> Matrix(19,-10,2,-1) Matrix(8025,1492,2372,441) -> Matrix(17,-16,16,-15) Matrix(509,94,1240,229) -> Matrix(1,-2,4,-7) Matrix(111,20,394,71) -> Matrix(1,-4,2,-7) Matrix(893,156,166,29) -> Matrix(1,2,-2,-3) Matrix(943,162,390,67) -> Matrix(3,4,2,3) Matrix(219,34,380,59) -> Matrix(3,2,4,3) Matrix(433,66,164,25) -> Matrix(9,2,4,1) Matrix(797,108,214,29) -> Matrix(3,-2,2,-1) Matrix(2069,274,370,49) -> Matrix(1,0,6,1) Matrix(261,32,106,13) -> Matrix(3,-2,2,-1) Matrix(257,28,156,17) -> Matrix(1,2,0,1) Matrix(123,-14,290,-33) -> Matrix(7,-2,18,-5) Matrix(203,-26,164,-21) -> Matrix(7,-2,4,-1) Matrix(883,-130,360,-53) -> Matrix(19,-8,12,-5) Matrix(1077,-164,440,-67) -> Matrix(17,-10,12,-7) Matrix(677,-106,198,-31) -> Matrix(3,-2,2,-1) Matrix(117,-20,158,-27) -> Matrix(1,-2,2,-3) Matrix(1125,-208,622,-115) -> Matrix(7,-4,2,-1) Matrix(4795,-908,2012,-381) -> Matrix(1,0,0,1) Matrix(1235,-236,696,-133) -> Matrix(1,2,0,1) Matrix(801,-166,304,-63) -> Matrix(17,2,8,1) Matrix(1099,-234,418,-89) -> Matrix(27,-2,14,-1) Matrix(3101,-670,4994,-1079) -> Matrix(1,0,-2,1) Matrix(3137,-680,1324,-287) -> Matrix(15,-2,8,-1) Matrix(1237,-282,2996,-683) -> Matrix(1,0,0,1) Matrix(335,-78,262,-61) -> Matrix(3,-2,2,-1) Matrix(109,-28,74,-19) -> Matrix(1,0,-2,1) Matrix(763,-204,1814,-485) -> Matrix(7,-2,18,-5) Matrix(653,-176,1050,-283) -> Matrix(5,-2,18,-7) Matrix(181,-50,648,-179) -> Matrix(21,-10,40,-19) Matrix(1677,-484,1036,-299) -> Matrix(7,-2,4,-1) Matrix(2529,-736,1426,-415) -> Matrix(7,-4,2,-1) Matrix(677,-198,106,-31) -> Matrix(3,-2,2,-1) Matrix(249,-74,212,-63) -> Matrix(1,0,0,1) Matrix(317,-96,142,-43) -> Matrix(1,-2,2,-3) Matrix(457,-142,280,-87) -> Matrix(1,2,0,1) Matrix(613,-214,444,-155) -> Matrix(1,0,4,1) Matrix(747,-266,542,-193) -> Matrix(1,0,-6,1) Matrix(641,-232,1014,-367) -> Matrix(7,-2,18,-5) Matrix(2057,-750,842,-307) -> Matrix(13,-4,10,-3) Matrix(4141,-1516,1516,-555) -> Matrix(1,4,0,1) Matrix(1547,-568,1212,-445) -> Matrix(7,-2,4,-1) Matrix(807,-298,436,-161) -> Matrix(23,-6,4,-1) Matrix(801,-304,166,-63) -> Matrix(25,-12,-2,1) Matrix(1331,-508,600,-229) -> Matrix(3,-2,8,-5) Matrix(1165,-446,1596,-611) -> Matrix(1,0,0,1) Matrix(1195,-462,1658,-641) -> Matrix(1,0,2,1) Matrix(1491,-578,3614,-1401) -> Matrix(1,0,2,1) Matrix(3215,-1248,2352,-913) -> Matrix(1,0,0,1) Matrix(297,-116,530,-207) -> Matrix(1,0,2,1) Matrix(883,-360,130,-53) -> Matrix(13,-4,10,-3) Matrix(6819,-2794,1828,-749) -> Matrix(7,-2,4,-1) Matrix(5741,-2354,9070,-3719) -> Matrix(7,-2,18,-5) Matrix(713,-298,390,-163) -> Matrix(3,-2,2,-1) Matrix(4795,-2012,908,-381) -> Matrix(25,-8,-28,9) Matrix(4601,-1932,874,-367) -> Matrix(41,-14,-38,13) Matrix(8777,-3688,3596,-1511) -> Matrix(5,-2,8,-3) Matrix(3137,-1324,680,-287) -> Matrix(69,-26,8,-3) Matrix(4365,-1844,1844,-779) -> Matrix(21,-8,8,-3) Matrix(1743,-740,2810,-1193) -> Matrix(5,-2,38,-15) Matrix(225,-98,512,-223) -> Matrix(29,-14,56,-27) Matrix(317,-142,96,-43) -> Matrix(3,-2,8,-5) Matrix(379,-174,220,-101) -> Matrix(5,-4,4,-3) Matrix(481,-254,392,-207) -> Matrix(5,-4,4,-3) Matrix(659,-354,538,-289) -> Matrix(3,-2,2,-1) Matrix(807,-436,298,-161) -> Matrix(7,-4,2,-1) Matrix(713,-390,298,-163) -> Matrix(3,-2,2,-1) Matrix(2431,-1340,742,-409) -> Matrix(1,0,2,1) Matrix(1125,-622,208,-115) -> Matrix(1,0,-4,1) Matrix(827,-462,324,-181) -> Matrix(1,2,0,1) Matrix(1235,-696,236,-133) -> Matrix(11,-4,-8,3) Matrix(1765,-996,2146,-1211) -> Matrix(11,-4,14,-5) Matrix(1321,-748,2174,-1231) -> Matrix(9,-4,-2,1) Matrix(3551,-2016,2200,-1249) -> Matrix(127,-62,84,-41) Matrix(1867,-1078,2274,-1313) -> Matrix(11,-8,18,-13) Matrix(379,-220,174,-101) -> Matrix(3,-2,2,-1) Matrix(145,-86,86,-51) -> Matrix(3,-2,2,-1) Matrix(685,-418,372,-227) -> Matrix(1,4,0,1) Matrix(457,-280,142,-87) -> Matrix(1,0,2,1) Matrix(541,-334,426,-263) -> Matrix(3,-2,2,-1) Matrix(3551,-2200,2016,-1249) -> Matrix(33,2,16,1) Matrix(2697,-1672,1534,-951) -> Matrix(35,-2,18,-1) Matrix(16571,-10292,3576,-2221) -> Matrix(31,-8,4,-1) Matrix(197,-124,170,-107) -> Matrix(1,0,-2,1) Matrix(17407,-11020,6282,-3977) -> Matrix(7,-4,2,-1) Matrix(3491,-2212,2028,-1285) -> Matrix(7,-2,4,-1) Matrix(253,-162,392,-251) -> Matrix(21,-10,40,-19) Matrix(109,-74,28,-19) -> Matrix(5,-4,4,-3) Matrix(515,-358,82,-57) -> Matrix(3,-2,2,-1) Matrix(189,-134,134,-95) -> Matrix(1,-2,2,-3) Matrix(643,-462,508,-365) -> Matrix(7,-2,4,-1) Matrix(613,-444,214,-155) -> Matrix(17,-8,-2,1) Matrix(3325,-2426,1276,-931) -> Matrix(5,-4,4,-3) Matrix(3215,-2352,1248,-913) -> Matrix(19,-12,8,-5) Matrix(849,-622,1036,-759) -> Matrix(1,0,0,1) Matrix(743,-546,132,-97) -> Matrix(3,-2,8,-5) Matrix(261,-200,338,-259) -> Matrix(15,-14,14,-13) Matrix(335,-262,78,-61) -> Matrix(5,-8,2,-3) Matrix(541,-426,334,-263) -> Matrix(3,-8,2,-5) Matrix(203,-164,26,-21) -> Matrix(3,-2,2,-1) Matrix(481,-392,254,-207) -> Matrix(9,-4,-2,1) Matrix(4469,-3674,2524,-2075) -> Matrix(5,-4,4,-3) Matrix(249,-212,74,-63) -> Matrix(1,-2,2,-3) Matrix(197,-170,124,-107) -> Matrix(5,-4,4,-3) Matrix(237,-268,130,-147) -> Matrix(5,-8,2,-3) Matrix(569,-674,168,-199) -> Matrix(5,-4,4,-3) Matrix(1765,-2146,996,-1211) -> Matrix(9,-16,4,-7) Matrix(1867,-2274,1078,-1313) -> Matrix(3,-2,2,-1) Matrix(285,-358,82,-103) -> Matrix(1,-2,2,-3) Matrix(4247,-5412,2468,-3145) -> Matrix(5,-14,4,-11) Matrix(261,-338,200,-259) -> Matrix(1,-6,0,1) Matrix(117,-158,20,-27) -> Matrix(1,0,0,1) Matrix(2625,-3586,1516,-2071) -> Matrix(5,-4,4,-3) Matrix(8297,-11346,1962,-2683) -> Matrix(5,-8,2,-3) Matrix(4351,-5952,1030,-1409) -> Matrix(5,2,2,1) Matrix(1165,-1596,446,-611) -> Matrix(3,-2,2,-1) Matrix(1195,-1658,462,-641) -> Matrix(3,-2,2,-1) Matrix(653,-910,404,-563) -> Matrix(19,-8,12,-5) Matrix(1027,-1458,722,-1025) -> Matrix(23,-22,22,-21) Matrix(641,-924,188,-271) -> Matrix(1,0,0,1) Matrix(581,-844,338,-491) -> Matrix(3,-2,2,-1) Matrix(253,-392,162,-251) -> Matrix(19,-18,18,-17) Matrix(1891,-2984,500,-789) -> Matrix(3,-4,4,-5) Matrix(641,-1014,232,-367) -> Matrix(19,-24,4,-5) Matrix(1103,-1750,462,-733) -> Matrix(1,-2,2,-3) Matrix(653,-1050,176,-283) -> Matrix(13,-18,8,-11) Matrix(211,-340,18,-29) -> Matrix(7,-10,-2,3) Matrix(6249,-10082,3872,-6247) -> Matrix(229,-342,152,-227) Matrix(4849,-7846,1406,-2275) -> Matrix(5,-8,2,-3) Matrix(385,-628,122,-199) -> Matrix(1,-2,-2,5) Matrix(941,-1544,348,-571) -> Matrix(1,2,0,1) Matrix(1321,-2174,748,-1231) -> Matrix(9,-16,4,-7) Matrix(987,-1682,578,-985) -> Matrix(11,-10,10,-9) Matrix(7457,-12828,2892,-4975) -> Matrix(11,-14,4,-5) Matrix(10741,-19022,3934,-6967) -> Matrix(41,-78,10,-19) Matrix(297,-530,116,-207) -> Matrix(1,0,0,1) Matrix(1013,-1838,458,-831) -> Matrix(1,-2,2,-3) Matrix(241,-450,128,-239) -> Matrix(1,-14,0,1) Matrix(219,-472,58,-125) -> Matrix(3,-2,2,-1) Matrix(847,-1868,258,-569) -> Matrix(1,0,2,1) Matrix(225,-512,98,-223) -> Matrix(15,-14,14,-13) Matrix(123,-290,14,-33) -> Matrix(5,-8,2,-3) Matrix(3923,-9278,1504,-3557) -> Matrix(9,-16,4,-7) Matrix(6983,-16524,2678,-6337) -> Matrix(11,-24,6,-13) Matrix(763,-1814,204,-485) -> Matrix(1,0,0,1) Matrix(5509,-13122,2312,-5507) -> Matrix(1,-2,0,1) Matrix(1237,-2996,282,-683) -> Matrix(5,-8,2,-3) Matrix(3077,-7504,1110,-2707) -> Matrix(9,-14,2,-3) Matrix(859,-2178,338,-857) -> Matrix(29,-56,14,-27) Matrix(10441,-26912,4050,-10439) -> Matrix(7,-18,2,-5) Matrix(1349,-3482,308,-795) -> Matrix(1,0,0,1) Matrix(457,-1198,140,-367) -> Matrix(1,-2,4,-7) Matrix(259,-706,62,-169) -> Matrix(5,-18,2,-7) Matrix(7475,-20402,2738,-7473) -> Matrix(73,-288,18,-71) Matrix(2067,-5660,554,-1517) -> Matrix(3,-14,2,-9) Matrix(3709,-10274,1074,-2975) -> Matrix(1,-6,2,-11) Matrix(205,-578,72,-203) -> Matrix(1,-22,0,1) Matrix(771,-2450,242,-769) -> Matrix(1,0,22,1) Matrix(10063,-32992,2172,-7121) -> Matrix(1,8,0,1) Matrix(9459,-31022,2042,-6697) -> Matrix(47,-8,6,-1) Matrix(2983,-10082,882,-2981) -> Matrix(35,-34,34,-33) Matrix(269,-926,52,-179) -> Matrix(1,-2,0,1) Matrix(6635,-22898,1922,-6633) -> Matrix(1,0,2,1) Matrix(181,-648,50,-179) -> Matrix(11,-10,10,-9) Matrix(1361,-5032,294,-1087) -> Matrix(13,-20,2,-3) Matrix(855,-3238,202,-765) -> Matrix(5,-8,2,-3) Matrix(153,-722,32,-151) -> Matrix(1,-30,0,1) Matrix(547,-3042,98,-545) -> Matrix(1,0,14,1) Matrix(121,-800,18,-119) -> 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): 88 Degree of the the map X: 88 Degree of the the map Y: 264 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 792 Minimal number of generators: 133 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 44 Genus: 45 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 0/1 3/20 4/19 5/18 6/17 7/16 1/2 8/15 9/14 10/13 1/1 13/10 93/68 3/2 14/9 71/44 15/8 2/1 16/7 81/34 5/2 17/6 3/1 19/6 35/11 13/4 71/21 7/2 18/5 15/4 4/1 9/2 19/4 5/1 11/2 6/1 13/2 20/3 7/1 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 1/2 -7/15 1/1 -6/13 0/1 -11/24 1/4 -5/11 3/7 -4/9 2/3 -11/25 1/1 -7/16 1/0 -3/7 1/3 -8/19 8/13 -5/12 3/4 -12/29 0/1 -7/17 1/1 -9/22 3/2 -11/27 1/1 -2/5 0/1 -5/13 1/1 -18/47 0/1 -13/34 7/10 -21/55 17/23 -8/21 4/5 -11/29 1/1 -3/8 1/0 -4/11 0/1 -1/3 1/1 -6/19 0/1 -5/16 5/4 -4/13 0/1 -11/36 3/4 -7/23 1/1 -3/10 3/2 -5/17 1/3 -2/7 2/1 -3/11 1/1 -4/15 4/1 -9/34 -1/2 -5/19 1/1 -6/23 2/1 -1/4 1/0 -2/9 0/1 -1/5 1/1 -1/6 -1/2 0/1 0/1 1/8 1/4 1/7 1/3 3/20 1/2 2/13 2/3 1/6 1/2 1/5 -1/1 4/19 0/1 3/14 1/10 5/23 1/7 2/9 2/9 5/22 1/2 8/35 0/1 3/13 1/3 1/4 1/4 4/15 2/5 11/41 7/19 7/26 1/2 3/11 3/7 5/18 1/2 2/7 2/3 7/24 3/4 5/17 1/1 3/10 1/2 4/13 -2/1 1/3 1/1 6/17 0/1 5/14 1/6 9/25 3/13 4/11 0/1 7/19 1/5 10/27 2/7 3/8 3/8 5/13 1/1 12/31 0/1 19/49 1/1 7/18 1/2 2/5 0/1 11/27 1/3 9/22 1/2 25/61 1/5 16/39 0/1 7/17 1/3 26/63 0/1 19/46 1/2 12/29 0/1 5/12 3/8 13/31 1/3 34/81 1/3 21/50 9/26 29/69 11/31 8/19 4/11 11/26 1/2 14/33 2/5 3/7 3/7 7/16 1/2 4/9 4/7 5/11 1/1 1/2 1/2 8/15 1/1 7/13 1/1 6/11 2/3 11/20 1/0 5/9 1/1 9/16 1/4 4/7 4/7 7/12 3/4 3/5 1/1 17/28 1/0 14/23 0/1 11/18 -1/2 8/13 0/1 13/21 -1/3 44/71 0/1 31/50 1/14 49/79 1/9 18/29 0/1 23/37 1/5 5/8 1/4 12/19 2/5 7/11 3/7 9/14 1/2 2/3 2/3 9/13 1/1 16/23 2/3 7/10 5/6 5/7 -1/1 3/4 3/4 10/13 1/1 17/22 11/10 7/9 1/1 11/14 3/2 4/5 0/1 5/6 5/6 6/7 0/1 1/1 1/1 8/7 2/1 7/6 1/2 13/11 1/1 6/5 6/5 17/14 3/2 11/9 1/1 38/31 1/1 27/22 3/2 16/13 4/3 21/17 1/1 5/4 1/0 19/15 9/5 14/11 2/1 9/7 3/1 13/10 1/0 4/3 0/1 15/11 1/1 41/30 1/2 67/49 1/1 93/68 1/0 26/19 0/1 11/8 1/0 7/5 3/5 17/12 7/8 27/19 1/1 10/7 4/3 23/16 1/0 13/9 1/1 3/2 1/2 14/9 1/1 25/16 17/16 11/7 1/1 41/26 7/6 30/19 6/5 19/12 5/4 27/17 1/1 8/5 4/3 29/18 3/2 50/31 40/27 71/44 3/2 21/13 17/11 13/8 7/4 31/19 3/1 18/11 0/1 23/14 3/2 5/3 1/1 17/10 1/2 29/17 1/1 12/7 4/3 19/11 1/1 45/26 3/2 26/15 4/3 7/4 7/4 9/5 3/1 20/11 2/1 31/17 3/1 11/6 7/2 24/13 4/1 13/7 7/1 15/8 1/0 2/1 0/1 11/5 1/1 9/4 3/4 16/7 1/1 23/10 11/10 7/3 1/1 26/11 2/1 45/19 1/1 19/8 1/0 50/21 2/1 81/34 1/0 31/13 1/1 43/18 3/2 12/5 0/1 5/2 3/2 8/3 8/3 27/10 7/2 46/17 2/1 19/7 3/1 30/11 4/1 41/15 5/1 52/19 4/1 11/4 1/0 25/9 19/3 14/5 10/1 17/6 1/0 3/1 -1/1 19/6 -1/6 35/11 0/1 16/5 0/1 13/4 1/0 23/7 1/3 10/3 2/3 27/8 7/8 71/21 1/1 44/13 10/9 17/5 1/1 41/12 1/0 24/7 0/1 7/2 1/2 18/5 1/1 29/8 9/8 11/3 1/1 37/10 3/2 26/7 2/1 41/11 3/1 97/26 3/2 56/15 2/1 15/4 1/0 19/5 1/1 4/1 2/1 9/2 9/2 23/5 7/1 14/3 12/1 19/4 1/0 5/1 -3/1 11/2 -1/2 6/1 0/1 19/3 1/1 13/2 1/2 20/3 1/1 27/4 5/4 7/1 1/1 8/1 2/1 9/1 3/1 10/1 10/1 1/0 1/0 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(261,122,430,201) (-1/2,-7/15) -> (3/5,17/28) Hyperbolic Matrix(173,80,426,197) (-7/15,-6/13) -> (2/5,11/27) Hyperbolic Matrix(381,175,-934,-429) (-6/13,-11/24) -> (-9/22,-11/27) Hyperbolic Matrix(341,156,1270,581) (-11/24,-5/11) -> (11/41,7/26) Hyperbolic Matrix(379,171,82,37) (-5/11,-4/9) -> (23/5,14/3) Hyperbolic Matrix(1359,599,574,253) (-4/9,-11/25) -> (26/11,45/19) Hyperbolic Matrix(901,396,248,109) (-11/25,-7/16) -> (29/8,11/3) Hyperbolic Matrix(205,89,486,211) (-7/16,-3/7) -> (8/19,11/26) Hyperbolic Matrix(441,187,158,67) (-3/7,-8/19) -> (25/9,14/5) Hyperbolic Matrix(117,49,-394,-165) (-8/19,-5/12) -> (-3/10,-5/17) Hyperbolic Matrix(787,326,548,227) (-5/12,-12/29) -> (10/7,23/16) Hyperbolic Matrix(1451,599,390,161) (-12/29,-7/17) -> (26/7,41/11) Hyperbolic Matrix(545,224,236,97) (-7/17,-9/22) -> (23/10,7/3) Hyperbolic Matrix(231,94,1010,411) (-11/27,-2/5) -> (8/35,3/13) Hyperbolic Matrix(111,43,302,117) (-2/5,-5/13) -> (4/11,7/19) Hyperbolic Matrix(1195,458,968,371) (-5/13,-18/47) -> (16/13,21/17) Hyperbolic Matrix(1973,755,4696,1797) (-18/47,-13/34) -> (21/50,29/69) Hyperbolic Matrix(631,241,-2380,-909) (-13/34,-21/55) -> (-4/15,-9/34) Hyperbolic Matrix(705,269,76,29) (-21/55,-8/21) -> (9/1,10/1) Hyperbolic Matrix(1819,691,666,253) (-8/21,-11/29) -> (30/11,41/15) Hyperbolic Matrix(813,308,520,197) (-11/29,-3/8) -> (25/16,11/7) Hyperbolic Matrix(35,13,148,55) (-3/8,-4/11) -> (3/13,1/4) Hyperbolic Matrix(181,65,142,51) (-4/11,-1/3) -> (14/11,9/7) Hyperbolic Matrix(1111,353,406,129) (-1/3,-6/19) -> (41/15,52/19) Hyperbolic Matrix(1373,431,2214,695) (-6/19,-5/16) -> (31/50,49/79) Hyperbolic Matrix(199,62,536,167) (-5/16,-4/13) -> (10/27,3/8) Hyperbolic Matrix(297,91,-1126,-345) (-4/13,-11/36) -> (-9/34,-5/19) Hyperbolic Matrix(1719,524,994,303) (-11/36,-7/23) -> (19/11,45/26) Hyperbolic Matrix(461,140,596,181) (-7/23,-3/10) -> (17/22,7/9) Hyperbolic Matrix(99,29,454,133) (-5/17,-2/7) -> (5/23,2/9) Hyperbolic Matrix(161,45,254,71) (-2/7,-3/11) -> (12/19,7/11) Hyperbolic Matrix(159,43,440,119) (-3/11,-4/15) -> (9/25,4/11) Hyperbolic Matrix(843,221,2056,539) (-5/19,-6/23) -> (25/61,16/39) Hyperbolic Matrix(685,178,558,145) (-6/23,-1/4) -> (27/22,16/13) Hyperbolic Matrix(29,7,62,15) (-1/4,-2/9) -> (5/11,1/2) Hyperbolic Matrix(203,43,118,25) (-2/9,-1/5) -> (12/7,19/11) Hyperbolic Matrix(29,5,110,19) (-1/5,-1/6) -> (1/4,4/15) Hyperbolic Matrix(81,13,56,9) (-1/6,0/1) -> (13/9,3/2) Hyperbolic Matrix(123,-14,290,-33) (0/1,1/8) -> (11/26,14/33) Hyperbolic Matrix(203,-26,164,-21) (1/8,1/7) -> (21/17,5/4) Hyperbolic Matrix(61,-9,400,-59) (1/7,3/20) -> (3/20,2/13) Parabolic Matrix(677,-106,198,-31) (2/13,1/6) -> (41/12,24/7) Hyperbolic Matrix(97,-17,40,-7) (1/6,1/5) -> (12/5,5/2) Hyperbolic Matrix(325,-67,228,-47) (1/5,4/19) -> (27/19,10/7) Hyperbolic Matrix(701,-149,494,-105) (4/19,3/14) -> (17/12,27/19) Hyperbolic Matrix(283,-61,682,-147) (3/14,5/23) -> (12/29,5/12) Hyperbolic Matrix(243,-55,676,-153) (2/9,5/22) -> (5/14,9/25) Hyperbolic Matrix(1237,-282,2996,-683) (5/22,8/35) -> (26/63,19/46) Hyperbolic Matrix(763,-204,1814,-485) (4/15,11/41) -> (29/69,8/19) Hyperbolic Matrix(653,-176,1050,-283) (7/26,3/11) -> (23/37,5/8) Hyperbolic Matrix(91,-25,324,-89) (3/11,5/18) -> (5/18,2/7) Parabolic Matrix(197,-57,356,-103) (2/7,7/24) -> (11/20,5/9) Hyperbolic Matrix(677,-198,106,-31) (7/24,5/17) -> (19/3,13/2) Hyperbolic Matrix(249,-74,212,-63) (5/17,3/10) -> (7/6,13/11) Hyperbolic Matrix(193,-59,36,-11) (3/10,4/13) -> (5/1,11/2) Hyperbolic Matrix(457,-142,280,-87) (4/13,1/3) -> (31/19,18/11) Hyperbolic Matrix(291,-101,170,-59) (1/3,6/17) -> (29/17,12/7) Hyperbolic Matrix(695,-247,408,-145) (6/17,5/14) -> (17/10,29/17) Hyperbolic Matrix(807,-298,436,-161) (7/19,10/27) -> (24/13,13/7) Hyperbolic Matrix(149,-57,34,-13) (3/8,5/13) -> (4/1,9/2) Hyperbolic Matrix(1177,-455,432,-167) (5/13,12/31) -> (19/7,30/11) Hyperbolic Matrix(1491,-578,3614,-1401) (12/31,19/49) -> (7/17,26/63) Hyperbolic Matrix(3215,-1248,2352,-913) (19/49,7/18) -> (41/30,67/49) Hyperbolic Matrix(181,-71,232,-91) (7/18,2/5) -> (7/9,11/14) Hyperbolic Matrix(883,-360,130,-53) (11/27,9/22) -> (27/4,7/1) Hyperbolic Matrix(6819,-2794,1828,-749) (9/22,25/61) -> (41/11,97/26) Hyperbolic Matrix(1093,-449,1760,-723) (16/39,7/17) -> (18/29,23/37) Hyperbolic Matrix(2621,-1083,1106,-457) (19/46,12/29) -> (45/19,19/8) Hyperbolic Matrix(713,-298,390,-163) (5/12,13/31) -> (31/17,11/6) Hyperbolic Matrix(2381,-999,746,-313) (13/31,34/81) -> (35/11,16/5) Hyperbolic Matrix(3289,-1381,1036,-435) (34/81,21/50) -> (19/6,35/11) Hyperbolic Matrix(1743,-740,2810,-1193) (14/33,3/7) -> (49/79,18/29) Hyperbolic Matrix(113,-49,256,-111) (3/7,7/16) -> (7/16,4/9) Parabolic Matrix(317,-142,96,-43) (4/9,5/11) -> (23/7,10/3) Hyperbolic Matrix(481,-254,392,-207) (1/2,8/15) -> (38/31,27/22) Hyperbolic Matrix(659,-354,538,-289) (8/15,7/13) -> (11/9,38/31) Hyperbolic Matrix(807,-436,298,-161) (7/13,6/11) -> (46/17,19/7) Hyperbolic Matrix(713,-390,298,-163) (6/11,11/20) -> (43/18,12/5) Hyperbolic Matrix(163,-91,206,-115) (5/9,9/16) -> (11/14,4/5) Hyperbolic Matrix(427,-241,264,-149) (9/16,4/7) -> (21/13,13/8) Hyperbolic Matrix(161,-93,116,-67) (4/7,7/12) -> (11/8,7/5) Hyperbolic Matrix(145,-86,86,-51) (7/12,3/5) -> (5/3,17/10) Hyperbolic Matrix(1159,-705,314,-191) (17/28,14/23) -> (11/3,37/10) Hyperbolic Matrix(685,-418,372,-227) (14/23,11/18) -> (11/6,24/13) Hyperbolic Matrix(457,-280,142,-87) (11/18,8/13) -> (16/5,13/4) Hyperbolic Matrix(541,-334,426,-263) (8/13,13/21) -> (19/15,14/11) Hyperbolic Matrix(4615,-2859,1364,-845) (13/21,44/71) -> (71/21,44/13) Hyperbolic Matrix(5467,-3389,1618,-1003) (44/71,31/50) -> (27/8,71/21) Hyperbolic Matrix(197,-124,170,-107) (5/8,12/19) -> (8/7,7/6) Hyperbolic Matrix(127,-81,196,-125) (7/11,9/14) -> (9/14,2/3) Parabolic Matrix(109,-74,28,-19) (2/3,9/13) -> (19/5,4/1) Hyperbolic Matrix(515,-358,82,-57) (9/13,16/23) -> (6/1,19/3) Hyperbolic Matrix(529,-369,162,-113) (16/23,7/10) -> (13/4,23/7) Hyperbolic Matrix(189,-134,134,-95) (7/10,5/7) -> (7/5,17/12) Hyperbolic Matrix(67,-49,26,-19) (5/7,3/4) -> (5/2,8/3) Hyperbolic Matrix(261,-200,338,-259) (3/4,10/13) -> (10/13,17/22) Parabolic Matrix(89,-73,50,-41) (4/5,5/6) -> (7/4,9/5) Hyperbolic Matrix(249,-212,74,-63) (5/6,6/7) -> (10/3,27/8) Hyperbolic Matrix(197,-170,124,-107) (6/7,1/1) -> (27/17,8/5) Hyperbolic Matrix(237,-268,130,-147) (1/1,8/7) -> (20/11,31/17) Hyperbolic Matrix(569,-674,168,-199) (13/11,6/5) -> (44/13,17/5) Hyperbolic Matrix(405,-491,146,-177) (6/5,17/14) -> (11/4,25/9) Hyperbolic Matrix(591,-719,374,-455) (17/14,11/9) -> (30/19,19/12) Hyperbolic Matrix(437,-553,162,-205) (5/4,19/15) -> (8/3,27/10) Hyperbolic Matrix(131,-169,100,-129) (9/7,13/10) -> (13/10,4/3) Parabolic Matrix(127,-173,58,-79) (4/3,15/11) -> (2/1,11/5) Hyperbolic Matrix(1351,-1845,856,-1169) (15/11,41/30) -> (41/26,30/19) Hyperbolic Matrix(6325,-8649,4624,-6323) (67/49,93/68) -> (93/68,26/19) Parabolic Matrix(437,-599,116,-159) (26/19,11/8) -> (15/4,19/5) Hyperbolic Matrix(641,-924,188,-271) (23/16,13/9) -> (17/5,41/12) Hyperbolic Matrix(253,-392,162,-251) (3/2,14/9) -> (14/9,25/16) Parabolic Matrix(991,-1561,572,-901) (11/7,41/26) -> (45/26,26/15) Hyperbolic Matrix(1103,-1750,462,-733) (19/12,27/17) -> (31/13,43/18) Hyperbolic Matrix(653,-1050,176,-283) (8/5,29/18) -> (37/10,26/7) Hyperbolic Matrix(211,-340,18,-29) (29/18,50/31) -> (10/1,1/0) Hyperbolic Matrix(3125,-5041,1936,-3123) (50/31,71/44) -> (71/44,21/13) Parabolic Matrix(385,-628,122,-199) (13/8,31/19) -> (3/1,19/6) Hyperbolic Matrix(941,-1544,348,-571) (18/11,23/14) -> (27/10,46/17) Hyperbolic Matrix(357,-587,104,-171) (23/14,5/3) -> (24/7,7/2) Hyperbolic Matrix(227,-395,50,-87) (26/15,7/4) -> (9/2,23/5) Hyperbolic Matrix(123,-223,16,-29) (9/5,20/11) -> (7/1,8/1) Hyperbolic Matrix(121,-225,64,-119) (13/7,15/8) -> (15/8,2/1) Parabolic Matrix(79,-175,14,-31) (11/5,9/4) -> (11/2,6/1) Hyperbolic Matrix(225,-512,98,-223) (9/4,16/7) -> (16/7,23/10) Parabolic Matrix(123,-290,14,-33) (7/3,26/11) -> (8/1,9/1) Hyperbolic Matrix(763,-1814,204,-485) (19/8,50/21) -> (56/15,15/4) Hyperbolic Matrix(2755,-6561,1156,-2753) (50/21,81/34) -> (81/34,31/13) Parabolic Matrix(2067,-5660,554,-1517) (52/19,11/4) -> (97/26,56/15) Hyperbolic Matrix(103,-289,36,-101) (14/5,17/6) -> (17/6,3/1) Parabolic Matrix(181,-648,50,-179) (7/2,18/5) -> (18/5,29/8) Parabolic Matrix(77,-361,16,-75) (14/3,19/4) -> (19/4,5/1) Parabolic Matrix(121,-800,18,-119) (13/2,20/3) -> (20/3,27/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(261,122,430,201) -> Matrix(3,-2,2,-1) Matrix(173,80,426,197) -> Matrix(1,0,2,1) Matrix(381,175,-934,-429) -> Matrix(1,-1,2,-1) Matrix(341,156,1270,581) -> Matrix(7,-2,18,-5) Matrix(379,171,82,37) -> Matrix(17,-9,2,-1) Matrix(1359,599,574,253) -> Matrix(5,-3,2,-1) Matrix(901,396,248,109) -> Matrix(9,-8,8,-7) Matrix(205,89,486,211) -> Matrix(1,1,2,3) Matrix(441,187,158,67) -> Matrix(17,-9,2,-1) Matrix(117,49,-394,-165) -> Matrix(5,-3,2,-1) Matrix(787,326,548,227) -> Matrix(5,-4,4,-3) Matrix(1451,599,390,161) -> Matrix(5,-3,2,-1) Matrix(545,224,236,97) -> Matrix(9,-8,8,-7) Matrix(231,94,1010,411) -> Matrix(1,0,2,1) Matrix(111,43,302,117) -> Matrix(1,-1,6,-5) Matrix(1195,458,968,371) -> Matrix(5,-4,4,-3) Matrix(1973,755,4696,1797) -> Matrix(17,-11,48,-31) Matrix(631,241,-2380,-909) -> Matrix(7,-5,-4,3) Matrix(705,269,76,29) -> Matrix(17,-13,4,-3) Matrix(1819,691,666,253) -> Matrix(25,-21,6,-5) Matrix(813,308,520,197) -> Matrix(17,-16,16,-15) Matrix(35,13,148,55) -> Matrix(1,-1,4,-3) Matrix(181,65,142,51) -> Matrix(5,-3,2,-1) Matrix(1111,353,406,129) -> Matrix(9,-5,2,-1) Matrix(1373,431,2214,695) -> Matrix(1,-1,10,-9) Matrix(199,62,536,167) -> Matrix(1,-2,4,-7) Matrix(297,91,-1126,-345) -> Matrix(1,-1,2,-1) Matrix(1719,524,994,303) -> Matrix(7,-6,6,-5) Matrix(461,140,596,181) -> Matrix(9,-8,8,-7) Matrix(99,29,454,133) -> Matrix(1,-1,6,-5) Matrix(161,45,254,71) -> Matrix(1,1,2,3) Matrix(159,43,440,119) -> Matrix(1,-1,4,-3) Matrix(843,221,2056,539) -> Matrix(1,-1,4,-3) Matrix(685,178,558,145) -> Matrix(3,-2,2,-1) Matrix(29,7,62,15) -> Matrix(1,-1,2,-1) Matrix(203,43,118,25) -> Matrix(3,1,2,1) Matrix(29,5,110,19) -> Matrix(1,1,2,3) Matrix(81,13,56,9) -> Matrix(1,1,0,1) Matrix(123,-14,290,-33) -> Matrix(7,-2,18,-5) Matrix(203,-26,164,-21) -> Matrix(7,-2,4,-1) Matrix(61,-9,400,-59) -> Matrix(7,-3,12,-5) Matrix(677,-106,198,-31) -> Matrix(3,-2,2,-1) Matrix(97,-17,40,-7) -> Matrix(1,1,0,1) Matrix(325,-67,228,-47) -> Matrix(5,1,4,1) Matrix(701,-149,494,-105) -> Matrix(17,-1,18,-1) Matrix(283,-61,682,-147) -> Matrix(7,-1,22,-3) Matrix(243,-55,676,-153) -> Matrix(3,-1,16,-5) Matrix(1237,-282,2996,-683) -> Matrix(1,0,0,1) Matrix(763,-204,1814,-485) -> Matrix(7,-2,18,-5) Matrix(653,-176,1050,-283) -> Matrix(5,-2,18,-7) Matrix(91,-25,324,-89) -> Matrix(11,-5,20,-9) Matrix(197,-57,356,-103) -> Matrix(1,-1,4,-3) Matrix(677,-198,106,-31) -> Matrix(3,-2,2,-1) Matrix(249,-74,212,-63) -> Matrix(1,0,0,1) Matrix(193,-59,36,-11) -> Matrix(1,-1,0,1) Matrix(457,-142,280,-87) -> Matrix(1,2,0,1) Matrix(291,-101,170,-59) -> Matrix(3,1,2,1) Matrix(695,-247,408,-145) -> Matrix(7,-1,8,-1) Matrix(807,-298,436,-161) -> Matrix(23,-6,4,-1) Matrix(149,-57,34,-13) -> Matrix(5,-3,2,-1) Matrix(1177,-455,432,-167) -> Matrix(1,3,0,1) Matrix(1491,-578,3614,-1401) -> Matrix(1,0,2,1) Matrix(3215,-1248,2352,-913) -> Matrix(1,0,0,1) Matrix(181,-71,232,-91) -> Matrix(1,1,0,1) Matrix(883,-360,130,-53) -> Matrix(13,-4,10,-3) Matrix(6819,-2794,1828,-749) -> Matrix(7,-2,4,-1) Matrix(1093,-449,1760,-723) -> Matrix(3,-1,16,-5) Matrix(2621,-1083,1106,-457) -> Matrix(1,-1,2,-1) Matrix(713,-298,390,-163) -> Matrix(3,-2,2,-1) Matrix(2381,-999,746,-313) -> Matrix(3,-1,22,-7) Matrix(3289,-1381,1036,-435) -> Matrix(3,-1,-44,15) Matrix(1743,-740,2810,-1193) -> Matrix(5,-2,38,-15) Matrix(113,-49,256,-111) -> Matrix(15,-7,28,-13) Matrix(317,-142,96,-43) -> Matrix(3,-2,8,-5) Matrix(481,-254,392,-207) -> Matrix(5,-4,4,-3) Matrix(659,-354,538,-289) -> Matrix(3,-2,2,-1) Matrix(807,-436,298,-161) -> Matrix(7,-4,2,-1) Matrix(713,-390,298,-163) -> Matrix(3,-2,2,-1) Matrix(163,-91,206,-115) -> Matrix(1,-1,2,-1) Matrix(427,-241,264,-149) -> Matrix(13,-5,8,-3) Matrix(161,-93,116,-67) -> Matrix(1,-1,4,-3) Matrix(145,-86,86,-51) -> Matrix(3,-2,2,-1) Matrix(1159,-705,314,-191) -> Matrix(3,1,2,1) Matrix(685,-418,372,-227) -> Matrix(1,4,0,1) Matrix(457,-280,142,-87) -> Matrix(1,0,2,1) Matrix(541,-334,426,-263) -> Matrix(3,-2,2,-1) Matrix(4615,-2859,1364,-845) -> Matrix(13,1,12,1) Matrix(5467,-3389,1618,-1003) -> Matrix(21,-1,22,-1) Matrix(197,-124,170,-107) -> Matrix(1,0,-2,1) Matrix(127,-81,196,-125) -> Matrix(11,-5,20,-9) Matrix(109,-74,28,-19) -> Matrix(5,-4,4,-3) Matrix(515,-358,82,-57) -> Matrix(3,-2,2,-1) Matrix(529,-369,162,-113) -> Matrix(1,-1,6,-5) Matrix(189,-134,134,-95) -> Matrix(1,-2,2,-3) Matrix(67,-49,26,-19) -> Matrix(5,-3,2,-1) Matrix(261,-200,338,-259) -> Matrix(15,-14,14,-13) Matrix(89,-73,50,-41) -> Matrix(5,-3,2,-1) Matrix(249,-212,74,-63) -> Matrix(1,-2,2,-3) Matrix(197,-170,124,-107) -> Matrix(5,-4,4,-3) Matrix(237,-268,130,-147) -> Matrix(5,-8,2,-3) Matrix(569,-674,168,-199) -> Matrix(5,-4,4,-3) Matrix(405,-491,146,-177) -> Matrix(11,-17,2,-3) Matrix(591,-719,374,-455) -> Matrix(7,-13,6,-11) Matrix(437,-553,162,-205) -> Matrix(7,-11,2,-3) Matrix(131,-169,100,-129) -> Matrix(1,-3,0,1) Matrix(127,-173,58,-79) -> Matrix(1,-1,2,-1) Matrix(1351,-1845,856,-1169) -> Matrix(5,1,4,1) Matrix(6325,-8649,4624,-6323) -> Matrix(1,-1,0,1) Matrix(437,-599,116,-159) -> Matrix(1,1,0,1) Matrix(641,-924,188,-271) -> Matrix(1,0,0,1) Matrix(253,-392,162,-251) -> Matrix(19,-18,18,-17) Matrix(991,-1561,572,-901) -> Matrix(21,-25,16,-19) Matrix(1103,-1750,462,-733) -> Matrix(1,-2,2,-3) Matrix(653,-1050,176,-283) -> Matrix(13,-18,8,-11) Matrix(211,-340,18,-29) -> Matrix(7,-10,-2,3) Matrix(3125,-5041,1936,-3123) -> Matrix(115,-171,76,-113) Matrix(385,-628,122,-199) -> Matrix(1,-2,-2,5) Matrix(941,-1544,348,-571) -> Matrix(1,2,0,1) Matrix(357,-587,104,-171) -> Matrix(1,-1,0,1) Matrix(227,-395,50,-87) -> Matrix(11,-17,2,-3) Matrix(123,-223,16,-29) -> Matrix(1,-1,0,1) Matrix(121,-225,64,-119) -> Matrix(1,-7,0,1) Matrix(79,-175,14,-31) -> Matrix(1,-1,2,-1) Matrix(225,-512,98,-223) -> Matrix(15,-14,14,-13) Matrix(123,-290,14,-33) -> Matrix(5,-8,2,-3) Matrix(763,-1814,204,-485) -> Matrix(1,0,0,1) Matrix(2755,-6561,1156,-2753) -> Matrix(1,-1,0,1) Matrix(2067,-5660,554,-1517) -> Matrix(3,-14,2,-9) Matrix(103,-289,36,-101) -> Matrix(1,-11,0,1) Matrix(181,-648,50,-179) -> Matrix(11,-10,10,-9) Matrix(77,-361,16,-75) -> Matrix(1,-15,0,1) Matrix(121,-800,18,-119) -> Matrix(7,-6,6,-5) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 88 ----------------------------------------------------------------------- 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 23 1/7 1/3 1 23 3/20 1/2 3 1 1/6 1/2 1 23 1/5 -1/1 1 23 1/4 1/4 1 23 5/18 1/2 5 1 2/7 2/3 1 23 7/24 3/4 1 23 5/17 1/1 1 23 3/10 1/2 1 23 4/13 -2/1 1 23 1/3 1/1 1 23 3/8 3/8 1 23 5/13 1/1 1 23 12/31 0/1 1 23 7/18 1/2 1 23 2/5 0/1 1 23 9/22 1/2 1 23 7/17 1/3 1 23 5/12 3/8 1 23 3/7 3/7 1 23 7/16 1/2 7 1 1/2 1/2 1 23 8/15 1/1 1 1 7/13 1/1 1 23 6/11 2/3 1 23 11/20 1/0 1 23 5/9 1/1 1 23 9/16 1/4 1 23 4/7 4/7 1 23 7/12 3/4 1 23 3/5 1/1 1 23 11/18 -1/2 1 23 8/13 0/1 1 23 5/8 1/4 1 23 9/14 1/2 5 1 2/3 2/3 1 23 9/13 1/1 1 23 7/10 5/6 1 23 5/7 -1/1 1 23 3/4 3/4 1 23 10/13 1/1 7 1 7/9 1/1 1 23 11/14 3/2 1 23 4/5 0/1 1 23 5/6 5/6 1 23 6/7 0/1 1 23 1/1 1/1 1 23 7/6 1/2 1 23 13/11 1/1 1 23 6/5 6/5 1 23 11/9 1/1 1 23 16/13 4/3 1 23 5/4 1/0 1 23 13/10 1/0 3 1 4/3 0/1 1 23 15/11 1/1 1 23 41/30 1/2 1 23 93/68 1/0 1 1 26/19 0/1 1 23 11/8 1/0 1 23 7/5 3/5 1 23 17/12 7/8 1 23 27/19 1/1 11 1 10/7 4/3 1 23 3/2 1/2 1 23 14/9 1/1 9 1 11/7 1/1 1 23 19/12 5/4 1 23 27/17 1/1 1 23 8/5 4/3 1 23 29/18 3/2 1 23 71/44 3/2 19 1 21/13 17/11 1 23 13/8 7/4 1 23 31/19 3/1 1 23 18/11 0/1 1 23 23/14 3/2 1 23 5/3 1/1 1 23 17/10 1/2 1 23 29/17 1/1 5 1 12/7 4/3 1 23 7/4 7/4 1 23 9/5 3/1 1 23 20/11 2/1 1 23 11/6 7/2 1 23 15/8 1/0 7 1 2/1 0/1 1 23 11/5 1/1 1 23 9/4 3/4 1 23 16/7 1/1 7 1 7/3 1/1 1 23 19/8 1/0 1 23 81/34 1/0 1 1 31/13 1/1 1 23 43/18 3/2 1 23 12/5 0/1 1 23 5/2 3/2 1 23 8/3 8/3 1 23 19/7 3/1 1 23 30/11 4/1 1 23 11/4 1/0 1 23 17/6 1/0 11 1 3/1 -1/1 1 23 19/6 -1/6 1 23 35/11 0/1 11 1 16/5 0/1 1 23 13/4 1/0 1 23 10/3 2/3 1 23 27/8 7/8 1 23 71/21 1/1 17 1 44/13 10/9 1 23 17/5 1/1 1 23 24/7 0/1 1 23 7/2 1/2 1 23 18/5 1/1 5 1 11/3 1/1 1 23 26/7 2/1 1 23 15/4 1/0 1 23 19/5 1/1 1 23 4/1 2/1 1 23 9/2 9/2 1 23 19/4 1/0 15 1 5/1 -3/1 1 23 11/2 -1/2 1 23 6/1 0/1 1 23 13/2 1/2 1 23 20/3 1/1 3 1 7/1 1/1 1 23 8/1 2/1 1 23 9/1 3/1 1 23 1/0 1/0 1 23 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(143,-17,42,-5) (0/1,1/7) -> (17/5,24/7) Glide Reflection Matrix(41,-6,280,-41) (1/7,3/20) -> (1/7,3/20) Reflection Matrix(19,-3,120,-19) (3/20,1/6) -> (3/20,1/6) Reflection Matrix(97,-17,40,-7) (1/6,1/5) -> (12/5,5/2) Hyperbolic Matrix(55,-13,38,-9) (1/5,1/4) -> (10/7,3/2) Glide Reflection Matrix(19,-5,72,-19) (1/4,5/18) -> (1/4,5/18) Reflection Matrix(71,-20,252,-71) (5/18,2/7) -> (5/18,2/7) Reflection Matrix(197,-57,356,-103) (2/7,7/24) -> (11/20,5/9) Hyperbolic Matrix(321,-94,782,-229) (7/24,5/17) -> (9/22,7/17) Glide Reflection Matrix(249,-74,212,-63) (5/17,3/10) -> (7/6,13/11) Hyperbolic Matrix(193,-59,36,-11) (3/10,4/13) -> (5/1,11/2) Hyperbolic Matrix(457,-142,280,-87) (4/13,1/3) -> (31/19,18/11) Hyperbolic Matrix(117,-43,68,-25) (1/3,3/8) -> (12/7,7/4) Glide Reflection Matrix(149,-57,34,-13) (3/8,5/13) -> (4/1,9/2) Hyperbolic Matrix(1177,-455,432,-167) (5/13,12/31) -> (19/7,30/11) Hyperbolic Matrix(1541,-597,1128,-437) (12/31,7/18) -> (15/11,41/30) Glide Reflection Matrix(181,-71,232,-91) (7/18,2/5) -> (7/9,11/14) Hyperbolic Matrix(197,-80,32,-13) (2/5,9/22) -> (6/1,13/2) Glide Reflection Matrix(227,-94,326,-135) (7/17,5/12) -> (9/13,7/10) Glide Reflection Matrix(211,-89,64,-27) (5/12,3/7) -> (13/4,10/3) Glide Reflection Matrix(97,-42,224,-97) (3/7,7/16) -> (3/7,7/16) Reflection Matrix(15,-7,32,-15) (7/16,1/2) -> (7/16,1/2) Reflection Matrix(31,-16,60,-31) (1/2,8/15) -> (1/2,8/15) Reflection Matrix(209,-112,390,-209) (8/15,7/13) -> (8/15,7/13) Reflection Matrix(329,-178,268,-145) (7/13,6/11) -> (11/9,16/13) Glide Reflection Matrix(713,-390,298,-163) (6/11,11/20) -> (43/18,12/5) Hyperbolic Matrix(163,-91,206,-115) (5/9,9/16) -> (11/14,4/5) Hyperbolic Matrix(427,-241,264,-149) (9/16,4/7) -> (21/13,13/8) Hyperbolic Matrix(161,-93,116,-67) (4/7,7/12) -> (11/8,7/5) Hyperbolic Matrix(145,-86,86,-51) (7/12,3/5) -> (5/3,17/10) Hyperbolic Matrix(415,-253,228,-139) (3/5,11/18) -> (20/11,11/6) Glide Reflection Matrix(457,-280,142,-87) (11/18,8/13) -> (16/5,13/4) Hyperbolic Matrix(99,-61,86,-53) (8/13,5/8) -> (1/1,7/6) Glide Reflection Matrix(71,-45,112,-71) (5/8,9/14) -> (5/8,9/14) Reflection Matrix(55,-36,84,-55) (9/14,2/3) -> (9/14,2/3) Reflection Matrix(109,-74,28,-19) (2/3,9/13) -> (19/5,4/1) Hyperbolic Matrix(189,-134,134,-95) (7/10,5/7) -> (7/5,17/12) Hyperbolic Matrix(67,-49,26,-19) (5/7,3/4) -> (5/2,8/3) Hyperbolic Matrix(79,-60,104,-79) (3/4,10/13) -> (3/4,10/13) Reflection Matrix(181,-140,234,-181) (10/13,7/9) -> (10/13,7/9) Reflection Matrix(89,-73,50,-41) (4/5,5/6) -> (7/4,9/5) Hyperbolic Matrix(249,-212,74,-63) (5/6,6/7) -> (10/3,27/8) Hyperbolic Matrix(197,-170,124,-107) (6/7,1/1) -> (27/17,8/5) Hyperbolic Matrix(569,-674,168,-199) (13/11,6/5) -> (44/13,17/5) Hyperbolic Matrix(167,-202,62,-75) (6/5,11/9) -> (8/3,19/7) Glide Reflection Matrix(371,-458,226,-279) (16/13,5/4) -> (18/11,23/14) Glide Reflection Matrix(51,-65,40,-51) (5/4,13/10) -> (5/4,13/10) Reflection Matrix(79,-104,60,-79) (13/10,4/3) -> (13/10,4/3) Reflection Matrix(127,-173,58,-79) (4/3,15/11) -> (2/1,11/5) Hyperbolic Matrix(2789,-3813,2040,-2789) (41/30,93/68) -> (41/30,93/68) Reflection Matrix(3535,-4836,2584,-3535) (93/68,26/19) -> (93/68,26/19) Reflection Matrix(437,-599,116,-159) (26/19,11/8) -> (15/4,19/5) Hyperbolic Matrix(647,-918,456,-647) (17/12,27/19) -> (17/12,27/19) Reflection Matrix(379,-540,266,-379) (27/19,10/7) -> (27/19,10/7) Reflection Matrix(55,-84,36,-55) (3/2,14/9) -> (3/2,14/9) Reflection Matrix(197,-308,126,-197) (14/9,11/7) -> (14/9,11/7) Reflection Matrix(437,-691,160,-253) (11/7,19/12) -> (30/11,11/4) Glide Reflection Matrix(1103,-1750,462,-733) (19/12,27/17) -> (31/13,43/18) Hyperbolic Matrix(167,-269,18,-29) (8/5,29/18) -> (9/1,1/0) Glide Reflection Matrix(1277,-2059,792,-1277) (29/18,71/44) -> (29/18,71/44) Reflection Matrix(1847,-2982,1144,-1847) (71/44,21/13) -> (71/44,21/13) Reflection Matrix(385,-628,122,-199) (13/8,31/19) -> (3/1,19/6) Hyperbolic Matrix(357,-587,104,-171) (23/14,5/3) -> (24/7,7/2) Hyperbolic Matrix(579,-986,340,-579) (17/10,29/17) -> (17/10,29/17) Reflection Matrix(407,-696,238,-407) (29/17,12/7) -> (29/17,12/7) Reflection Matrix(123,-223,16,-29) (9/5,20/11) -> (7/1,8/1) Hyperbolic Matrix(89,-165,48,-89) (11/6,15/8) -> (11/6,15/8) Reflection Matrix(31,-60,16,-31) (15/8,2/1) -> (15/8,2/1) Reflection Matrix(79,-175,14,-31) (11/5,9/4) -> (11/2,6/1) Hyperbolic Matrix(127,-288,56,-127) (9/4,16/7) -> (9/4,16/7) Reflection Matrix(97,-224,42,-97) (16/7,7/3) -> (16/7,7/3) Reflection Matrix(253,-599,68,-161) (7/3,19/8) -> (26/7,15/4) Glide Reflection Matrix(647,-1539,272,-647) (19/8,81/34) -> (19/8,81/34) Reflection Matrix(2107,-5022,884,-2107) (81/34,31/13) -> (81/34,31/13) Reflection Matrix(67,-187,24,-67) (11/4,17/6) -> (11/4,17/6) Reflection Matrix(35,-102,12,-35) (17/6,3/1) -> (17/6,3/1) Reflection Matrix(419,-1330,132,-419) (19/6,35/11) -> (19/6,35/11) Reflection Matrix(351,-1120,110,-351) (35/11,16/5) -> (35/11,16/5) Reflection Matrix(1135,-3834,336,-1135) (27/8,71/21) -> (27/8,71/21) Reflection Matrix(1847,-6248,546,-1847) (71/21,44/13) -> (71/21,44/13) Reflection Matrix(71,-252,20,-71) (7/2,18/5) -> (7/2,18/5) Reflection Matrix(109,-396,30,-109) (18/5,11/3) -> (18/5,11/3) Reflection Matrix(83,-307,10,-37) (11/3,26/7) -> (8/1,9/1) Glide Reflection Matrix(37,-171,8,-37) (9/2,19/4) -> (9/2,19/4) Reflection Matrix(39,-190,8,-39) (19/4,5/1) -> (19/4,5/1) Reflection Matrix(79,-520,12,-79) (13/2,20/3) -> (13/2,20/3) Reflection Matrix(41,-280,6,-41) (20/3,7/1) -> (20/3,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,2,-1) (-1/1,0/1) -> (0/1,1/1) Matrix(143,-17,42,-5) -> Matrix(3,-1,2,-1) Matrix(41,-6,280,-41) -> Matrix(5,-2,12,-5) (1/7,3/20) -> (1/3,1/2) Matrix(19,-3,120,-19) -> Matrix(-1,1,0,1) (3/20,1/6) -> (1/2,1/0) Matrix(97,-17,40,-7) -> Matrix(1,1,0,1) 1/0 Matrix(55,-13,38,-9) -> Matrix(3,-1,2,-1) Matrix(19,-5,72,-19) -> Matrix(3,-1,8,-3) (1/4,5/18) -> (1/4,1/2) Matrix(71,-20,252,-71) -> Matrix(7,-4,12,-7) (5/18,2/7) -> (1/2,2/3) Matrix(197,-57,356,-103) -> Matrix(1,-1,4,-3) 1/2 Matrix(321,-94,782,-229) -> Matrix(3,-2,10,-7) Matrix(249,-74,212,-63) -> Matrix(1,0,0,1) Matrix(193,-59,36,-11) -> Matrix(1,-1,0,1) 1/0 Matrix(457,-142,280,-87) -> Matrix(1,2,0,1) 1/0 Matrix(117,-43,68,-25) -> Matrix(5,-1,4,-1) Matrix(149,-57,34,-13) -> Matrix(5,-3,2,-1) Matrix(1177,-455,432,-167) -> Matrix(1,3,0,1) 1/0 Matrix(1541,-597,1128,-437) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(181,-71,232,-91) -> Matrix(1,1,0,1) 1/0 Matrix(197,-80,32,-13) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(227,-94,326,-135) -> Matrix(7,-2,10,-3) Matrix(211,-89,64,-27) -> Matrix(3,-1,8,-3) *** -> (1/4,1/2) Matrix(97,-42,224,-97) -> Matrix(13,-6,28,-13) (3/7,7/16) -> (3/7,1/2) Matrix(15,-7,32,-15) -> Matrix(-1,1,0,1) (7/16,1/2) -> (1/2,1/0) Matrix(31,-16,60,-31) -> Matrix(3,-2,4,-3) (1/2,8/15) -> (1/2,1/1) Matrix(209,-112,390,-209) -> Matrix(1,0,2,-1) (8/15,7/13) -> (0/1,1/1) Matrix(329,-178,268,-145) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(713,-390,298,-163) -> Matrix(3,-2,2,-1) 1/1 Matrix(163,-91,206,-115) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(427,-241,264,-149) -> Matrix(13,-5,8,-3) Matrix(161,-93,116,-67) -> Matrix(1,-1,4,-3) 1/2 Matrix(145,-86,86,-51) -> Matrix(3,-2,2,-1) 1/1 Matrix(415,-253,228,-139) -> Matrix(-1,3,0,1) *** -> (3/2,1/0) Matrix(457,-280,142,-87) -> Matrix(1,0,2,1) 0/1 Matrix(99,-61,86,-53) -> Matrix(3,-1,2,-1) Matrix(71,-45,112,-71) -> Matrix(3,-1,8,-3) (5/8,9/14) -> (1/4,1/2) Matrix(55,-36,84,-55) -> Matrix(7,-4,12,-7) (9/14,2/3) -> (1/2,2/3) Matrix(109,-74,28,-19) -> Matrix(5,-4,4,-3) 1/1 Matrix(189,-134,134,-95) -> Matrix(1,-2,2,-3) 1/1 Matrix(67,-49,26,-19) -> Matrix(5,-3,2,-1) Matrix(79,-60,104,-79) -> Matrix(7,-6,8,-7) (3/4,10/13) -> (3/4,1/1) Matrix(181,-140,234,-181) -> Matrix(7,-8,6,-7) (10/13,7/9) -> (1/1,4/3) Matrix(89,-73,50,-41) -> Matrix(5,-3,2,-1) Matrix(249,-212,74,-63) -> Matrix(1,-2,2,-3) 1/1 Matrix(197,-170,124,-107) -> Matrix(5,-4,4,-3) 1/1 Matrix(569,-674,168,-199) -> Matrix(5,-4,4,-3) 1/1 Matrix(167,-202,62,-75) -> Matrix(7,-10,2,-3) Matrix(371,-458,226,-279) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(51,-65,40,-51) -> Matrix(-1,3,0,1) (5/4,13/10) -> (3/2,1/0) Matrix(79,-104,60,-79) -> Matrix(1,0,0,-1) (13/10,4/3) -> (0/1,1/0) Matrix(127,-173,58,-79) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(2789,-3813,2040,-2789) -> Matrix(-1,1,0,1) (41/30,93/68) -> (1/2,1/0) Matrix(3535,-4836,2584,-3535) -> Matrix(1,0,0,-1) (93/68,26/19) -> (0/1,1/0) Matrix(437,-599,116,-159) -> Matrix(1,1,0,1) 1/0 Matrix(647,-918,456,-647) -> Matrix(15,-14,16,-15) (17/12,27/19) -> (7/8,1/1) Matrix(379,-540,266,-379) -> Matrix(7,-8,6,-7) (27/19,10/7) -> (1/1,4/3) Matrix(55,-84,36,-55) -> Matrix(3,-2,4,-3) (3/2,14/9) -> (1/2,1/1) Matrix(197,-308,126,-197) -> Matrix(15,-16,14,-15) (14/9,11/7) -> (1/1,8/7) Matrix(437,-691,160,-253) -> Matrix(17,-21,4,-5) Matrix(1103,-1750,462,-733) -> Matrix(1,-2,2,-3) 1/1 Matrix(167,-269,18,-29) -> Matrix(9,-13,2,-3) Matrix(1277,-2059,792,-1277) -> Matrix(47,-69,32,-47) (29/18,71/44) -> (23/16,3/2) Matrix(1847,-2982,1144,-1847) -> Matrix(67,-102,44,-67) (71/44,21/13) -> (3/2,17/11) Matrix(385,-628,122,-199) -> Matrix(1,-2,-2,5) Matrix(357,-587,104,-171) -> Matrix(1,-1,0,1) 1/0 Matrix(579,-986,340,-579) -> Matrix(3,-2,4,-3) (17/10,29/17) -> (1/2,1/1) Matrix(407,-696,238,-407) -> Matrix(7,-8,6,-7) (29/17,12/7) -> (1/1,4/3) Matrix(123,-223,16,-29) -> Matrix(1,-1,0,1) 1/0 Matrix(89,-165,48,-89) -> Matrix(-1,7,0,1) (11/6,15/8) -> (7/2,1/0) Matrix(31,-60,16,-31) -> Matrix(1,0,0,-1) (15/8,2/1) -> (0/1,1/0) Matrix(79,-175,14,-31) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(127,-288,56,-127) -> Matrix(7,-6,8,-7) (9/4,16/7) -> (3/4,1/1) Matrix(97,-224,42,-97) -> Matrix(7,-8,6,-7) (16/7,7/3) -> (1/1,4/3) Matrix(253,-599,68,-161) -> Matrix(-1,3,0,1) *** -> (3/2,1/0) Matrix(647,-1539,272,-647) -> Matrix(-1,3,0,1) (19/8,81/34) -> (3/2,1/0) Matrix(2107,-5022,884,-2107) -> Matrix(-1,2,0,1) (81/34,31/13) -> (1/1,1/0) Matrix(67,-187,24,-67) -> Matrix(-1,9,0,1) (11/4,17/6) -> (9/2,1/0) Matrix(35,-102,12,-35) -> Matrix(1,2,0,-1) (17/6,3/1) -> (-1/1,1/0) Matrix(419,-1330,132,-419) -> Matrix(-1,0,12,1) (19/6,35/11) -> (-1/6,0/1) Matrix(351,-1120,110,-351) -> Matrix(1,0,10,-1) (35/11,16/5) -> (0/1,1/5) Matrix(1135,-3834,336,-1135) -> Matrix(15,-14,16,-15) (27/8,71/21) -> (7/8,1/1) Matrix(1847,-6248,546,-1847) -> Matrix(19,-20,18,-19) (71/21,44/13) -> (1/1,10/9) Matrix(71,-252,20,-71) -> Matrix(3,-2,4,-3) (7/2,18/5) -> (1/2,1/1) Matrix(109,-396,30,-109) -> Matrix(7,-8,6,-7) (18/5,11/3) -> (1/1,4/3) Matrix(83,-307,10,-37) -> Matrix(5,-7,2,-3) Matrix(37,-171,8,-37) -> Matrix(-1,9,0,1) (9/2,19/4) -> (9/2,1/0) Matrix(39,-190,8,-39) -> Matrix(1,6,0,-1) (19/4,5/1) -> (-3/1,1/0) Matrix(79,-520,12,-79) -> Matrix(3,-2,4,-3) (13/2,20/3) -> (1/2,1/1) Matrix(41,-280,6,-41) -> Matrix(3,-4,2,-3) (20/3,7/1) -> (1/1,2/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.