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 -1/1 1/1 -1/2 0/1 -7/15 1/1 -6/13 1/0 -11/24 0/1 -5/11 -1/1 -9/20 2/5 -4/9 1/2 -15/34 0/1 -11/25 1/1 -7/16 2/1 -17/39 1/1 -10/23 1/0 -13/30 0/1 -3/7 1/1 -11/26 0/1 -8/19 3/2 -13/31 1/1 -18/43 1/0 -5/12 0/1 -12/29 3/2 -31/75 5/1 -19/46 0/1 -26/63 1/0 -7/17 1/1 -9/22 2/1 -11/27 3/1 -2/5 1/0 -11/28 -4/1 -20/51 1/0 -9/23 -1/1 -25/64 0/1 -16/41 1/0 -23/59 1/1 -7/18 -4/1 -12/31 -3/2 -5/13 -1/1 -18/47 -1/2 -13/34 0/1 -21/55 -1/5 -29/76 0/1 -8/21 1/0 -19/50 0/1 -11/29 -1/3 -3/8 0/1 -10/27 3/4 -7/19 5/3 -11/30 2/1 -26/71 1/0 -15/41 3/1 -19/52 2/1 -4/11 1/0 -9/25 -7/1 -14/39 1/0 -5/14 -2/1 -6/17 -5/4 -7/20 -2/3 -1/3 1/1 -7/22 -2/1 -6/19 -3/2 -11/35 -1/1 -5/16 -4/5 -4/13 -1/2 -15/49 -1/7 -11/36 0/1 -7/23 -1/7 -3/10 0/1 -11/37 1/3 -19/64 0/1 -8/27 1/2 -5/17 3/5 -12/41 7/8 -7/24 4/3 -2/7 1/0 -7/25 -3/1 -12/43 1/0 -17/61 -5/3 -5/18 0/1 -18/65 1/0 -13/47 -5/1 -21/76 0/1 -8/29 1/0 -19/69 -1/1 -11/40 -2/1 -3/11 -1/1 -10/37 -3/2 -7/26 -2/3 -4/15 -1/4 -13/49 1/1 -9/34 0/1 -5/19 -1/1 -11/42 0/1 -17/65 -3/5 -6/23 -1/4 -1/4 0/1 -5/21 1/3 -9/38 2/3 -4/17 1/2 -3/13 1/1 -11/48 0/1 -8/35 1/0 -13/57 1/5 -18/79 1/2 -5/22 2/3 -2/9 1/0 -11/50 0/1 -9/41 -1/1 -7/32 0/1 -5/23 1/1 -3/14 2/3 -4/19 1/0 -1/5 1/1 -6/31 1/0 -5/26 0/1 -4/21 1/0 -7/37 1/3 -3/16 0/1 -8/43 7/8 -13/70 10/9 -5/27 1/1 -2/11 1/2 -3/17 1/1 -4/23 1/0 -1/6 2/1 -2/13 5/2 -1/7 -1/1 -2/15 1/0 -5/38 0/1 -3/23 1/1 -1/8 0/1 -1/9 1/1 0/1 1/0 1/8 -2/1 1/7 -1/1 3/20 -1/1 2/13 -1/2 1/6 0/1 2/11 1/0 5/27 1/1 3/16 2/1 7/37 7/1 4/21 1/0 1/5 1/1 4/19 1/0 3/14 -6/1 11/51 -3/1 8/37 1/0 5/23 -3/1 2/9 -5/2 5/22 0/1 8/35 1/0 3/13 1/1 1/4 -2/1 4/15 1/0 11/41 -1/1 7/26 -2/1 3/11 -1/1 5/18 -1/1 7/25 -1/1 2/7 -1/2 9/31 1/1 7/24 -2/1 5/17 -1/1 3/10 0/1 4/13 1/0 1/3 -1/1 6/17 0/1 5/14 0/1 9/25 -1/3 4/11 1/0 19/52 0/1 15/41 1/1 11/30 0/1 7/19 1/1 10/27 1/0 3/8 -2/3 11/29 -1/5 8/21 1/2 13/34 0/1 5/13 -1/1 12/31 1/0 19/49 -1/1 7/18 0/1 2/5 1/0 11/27 -1/1 9/22 0/1 25/61 -3/1 16/39 -3/2 7/17 -1/1 26/63 1/0 19/46 0/1 12/29 1/0 5/12 -2/3 13/31 -1/5 34/81 0/1 21/50 0/1 29/69 1/1 8/19 1/0 19/45 1/1 11/26 0/1 14/33 1/0 3/7 -1/1 7/16 -1/1 11/25 -1/1 4/9 -1/2 5/11 -1/3 1/2 0/1 8/15 0/1 7/13 1/7 6/11 1/4 11/20 0/1 16/29 1/2 5/9 1/1 14/25 1/0 9/16 0/1 22/39 1/0 13/23 -1/1 17/30 0/1 21/37 -1/11 4/7 1/4 15/26 0/1 26/45 1/2 11/19 3/5 7/12 2/3 3/5 1/1 17/28 2/1 31/51 3/1 14/23 1/0 11/18 2/1 8/13 1/0 13/21 5/1 44/71 1/0 31/50 -10/1 49/79 -5/1 18/29 1/0 59/95 -1/1 41/66 -2/1 23/37 -1/1 5/8 0/1 12/19 1/0 31/49 5/3 50/79 5/2 69/109 1/1 19/30 2/1 26/41 1/0 7/11 3/1 9/14 1/0 11/17 -5/1 2/3 1/0 9/13 -1/1 16/23 1/0 7/10 -4/3 5/7 -3/5 18/25 -1/2 31/43 -1/3 13/18 0/1 21/29 -1/1 8/11 -1/2 35/48 0/1 27/37 -1/3 19/26 0/1 30/41 -1/2 11/15 -1/3 14/19 -1/2 3/4 0/1 10/13 0/1 17/22 0/1 7/9 1/7 11/14 0/1 4/5 1/2 13/16 0/1 22/27 1/2 9/11 3/5 32/39 1/2 23/28 2/3 37/45 3/5 14/17 1/2 5/6 4/5 6/7 3/2 1/1 -1/1 8/7 1/2 7/6 2/3 13/11 1/1 6/5 5/4 17/14 2/1 28/23 3/2 11/9 5/3 38/31 2/1 27/22 2/1 16/13 1/0 21/17 3/1 5/4 2/1 24/19 1/0 19/15 7/1 14/11 1/0 51/40 4/1 37/29 5/1 23/18 4/1 9/7 7/1 13/10 1/0 17/13 -13/1 4/3 1/0 15/11 -3/1 41/30 -2/1 67/49 -1/1 93/68 -1/1 26/19 1/0 11/8 -2/1 40/29 -2/1 29/21 -1/1 18/13 1/0 25/18 -2/1 7/5 -5/3 17/12 -8/7 27/19 -1/1 37/26 -14/15 10/7 -3/4 23/16 0/1 13/9 -1/1 16/11 -1/2 3/2 0/1 14/9 0/1 25/16 0/1 11/7 1/3 41/26 0/1 30/19 1/2 19/12 0/1 27/17 3/5 8/5 1/0 29/18 0/1 50/31 -1/10 71/44 0/1 92/57 1/20 21/13 1/5 55/34 0/1 89/55 1/3 34/21 1/0 13/8 0/1 31/19 1/1 18/11 1/2 23/14 0/1 28/17 1/2 5/3 1/1 17/10 2/3 29/17 1/1 41/24 8/7 12/7 3/2 43/25 1/1 117/68 4/3 74/43 3/2 31/18 2/1 19/11 5/3 45/26 2/1 71/41 1/1 26/15 1/0 7/4 4/1 44/25 1/0 37/21 -11/1 30/17 1/0 53/30 -2/1 23/13 -1/1 85/48 0/1 62/35 1/0 39/22 0/1 55/31 3/1 16/9 1/0 9/5 1/1 38/21 3/2 29/16 2/1 20/11 1/0 31/17 5/3 11/6 4/1 24/13 1/0 13/7 7/1 15/8 1/0 17/9 -9/1 2/1 1/0 13/6 -2/1 11/5 -3/1 42/19 1/0 31/14 -2/1 20/9 -3/2 9/4 -2/1 16/7 -1/1 23/10 -2/3 7/3 -1/1 26/11 1/0 97/41 -1/1 1/1 71/30 0/1 45/19 1/1 64/27 1/0 19/8 0/1 50/21 1/0 81/34 1/0 112/47 1/0 31/13 -5/1 43/18 -2/1 12/5 -3/2 29/12 0/1 46/19 1/0 17/7 -1/1 39/16 -2/3 61/25 -1/3 83/34 0/1 22/9 1/0 49/20 -1/1 27/11 -1/1 5/2 0/1 33/13 -1/1 1/1 61/24 0/1 28/11 1/0 23/9 1/1 18/7 1/0 67/26 -2/1 116/45 -1/1 165/64 0/1 49/19 -1/1 31/12 0/1 44/17 1/0 13/5 -1/1 73/28 0/1 133/51 -1/1 1/1 60/23 1/0 47/18 0/1 34/13 1/0 21/8 2/1 50/19 1/0 29/11 -5/1 8/3 -3/2 27/10 0/1 46/17 -1/2 19/7 1/1 30/11 1/0 101/37 -1/1 1/1 172/63 1/0 71/26 0/1 41/15 1/1 52/19 1/0 11/4 0/1 36/13 1/0 133/48 0/1 97/35 -1/1 61/22 2/1 25/9 -3/1 14/5 1/0 17/6 1/0 20/7 1/0 3/1 -1/1 19/6 0/1 35/11 -1/1 1/1 51/16 0/1 16/5 1/0 13/4 0/1 36/11 1/0 59/18 -2/1 141/43 -3/1 -1/1 82/25 1/0 23/7 -3/1 10/3 1/0 27/8 -8/7 71/21 -1/1 115/34 -26/27 44/13 -9/10 17/5 -1/1 41/12 0/1 24/7 -1/2 31/9 1/1 69/20 0/1 107/31 -1/1 1/1 145/42 0/1 38/11 1/0 7/2 -2/1 18/5 -1/1 29/8 -8/9 11/3 -1/1 48/13 -3/4 37/10 -2/3 26/7 -1/2 41/11 -1/1 97/26 -4/7 56/15 -1/2 15/4 0/1 34/9 -1/2 53/14 0/1 19/5 -1/1 4/1 -1/2 21/5 -1/1 38/9 -1/2 93/22 -1/3 55/13 -1/3 17/4 0/1 13/3 1/1 35/8 0/1 57/13 -1/1 22/5 1/0 9/2 -2/5 23/5 -1/3 60/13 -1/4 37/8 0/1 88/19 -1/4 227/49 -1/3 -1/5 139/30 0/1 51/11 -1/3 14/3 -1/6 19/4 0/1 24/5 1/8 5/1 1/1 26/5 -1/2 21/4 0/1 58/11 0/1 37/7 1/7 16/3 1/2 27/5 1/1 38/7 1/0 11/2 0/1 39/7 -1/1 1/1 67/12 0/1 28/5 1/0 17/3 -1/1 6/1 1/0 19/3 -1/1 13/2 -2/1 20/3 -1/1 27/4 -4/5 7/1 -1/1 15/2 0/1 8/1 -1/2 9/1 -1/3 10/1 -1/8 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(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(1,0,0,1) Matrix(261,122,430,201) -> Matrix(3,-2,2,-1) Matrix(173,80,426,197) -> Matrix(1,-2,0,1) Matrix(343,158,-940,-433) -> Matrix(1,2,0,1) Matrix(341,156,1270,581) -> Matrix(3,2,-2,-1) Matrix(253,114,668,301) -> Matrix(1,0,-4,1) Matrix(583,262,336,151) -> Matrix(3,-2,2,-1) Matrix(579,256,1400,619) -> Matrix(1,0,-2,1) Matrix(245,108,1318,581) -> Matrix(3,-2,2,-1) Matrix(901,396,248,109) -> Matrix(7,-6,-8,7) Matrix(1793,782,736,321) -> Matrix(1,0,-2,1) Matrix(487,212,-1546,-673) -> Matrix(3,-4,-2,3) Matrix(327,142,-1384,-601) -> Matrix(1,-2,2,-3) Matrix(647,280,-2350,-1017) -> Matrix(1,-2,0,1) Matrix(637,270,880,373) -> Matrix(1,0,-2,1) Matrix(479,202,396,167) -> Matrix(3,-2,2,-1) Matrix(157,66,716,301) -> Matrix(1,-4,0,1) Matrix(1107,464,1744,731) -> Matrix(1,2,0,1) Matrix(1267,530,-3244,-1357) -> Matrix(1,0,0,1) Matrix(787,326,548,227) -> Matrix(1,0,-2,1) Matrix(943,390,-3610,-1493) -> Matrix(1,-2,-2,5) Matrix(547,226,2902,1199) -> Matrix(1,2,0,1) Matrix(5721,2362,2192,905) -> Matrix(1,0,0,1) Matrix(2191,904,3604,1487) -> Matrix(1,2,0,1) Matrix(545,224,236,97) -> Matrix(1,0,-2,1) Matrix(235,96,-1246,-509) -> Matrix(1,-2,2,-3) Matrix(231,94,1010,411) -> Matrix(1,-2,0,1) Matrix(681,268,836,329) -> Matrix(1,4,2,9) Matrix(759,298,-3334,-1309) -> Matrix(1,2,2,5) Matrix(1665,652,452,177) -> Matrix(3,4,-4,-5) Matrix(829,324,-3774,-1475) -> Matrix(1,0,0,1) Matrix(4749,1852,1736,677) -> Matrix(1,0,0,1) Matrix(2711,1056,4372,1703) -> Matrix(1,-6,0,1) Matrix(675,262,152,59) -> Matrix(1,2,-2,-3) Matrix(223,86,-822,-317) -> Matrix(1,0,0,1) Matrix(1195,458,968,371) -> Matrix(5,2,2,1) Matrix(371,142,-1936,-741) -> Matrix(1,0,2,1) Matrix(1115,426,-3646,-1393) -> Matrix(1,0,-2,1) Matrix(2531,966,4462,1703) -> Matrix(1,0,-6,1) Matrix(3497,1334,1932,737) -> Matrix(3,-2,2,-1) Matrix(447,170,-1412,-537) -> Matrix(3,2,-2,-1) Matrix(1927,732,2672,1015) -> Matrix(1,0,0,1) Matrix(813,308,520,197) -> Matrix(1,0,6,1) Matrix(879,326,364,135) -> Matrix(1,0,-2,1) Matrix(363,134,-1238,-457) -> Matrix(3,-4,4,-5) Matrix(365,134,1016,373) -> Matrix(1,-2,0,1) Matrix(3269,1198,1378,505) -> Matrix(1,-2,0,1) Matrix(3049,1116,724,265) -> Matrix(1,-2,-2,5) Matrix(361,132,-2754,-1007) -> Matrix(1,-2,0,1) Matrix(287,104,218,79) -> Matrix(1,-6,0,1) Matrix(1079,388,1866,671) -> Matrix(1,4,2,9) Matrix(931,334,-3370,-1209) -> Matrix(1,2,0,1) Matrix(571,202,212,75) -> Matrix(1,2,-2,-3) Matrix(211,74,-1132,-397) -> Matrix(3,2,4,3) Matrix(355,124,-1274,-445) -> Matrix(3,2,-2,-1) Matrix(407,130,-1556,-497) -> Matrix(1,2,-2,-3) Matrix(535,168,-2882,-905) -> Matrix(5,6,4,5) Matrix(199,62,536,167) -> Matrix(3,2,-2,-1) Matrix(2853,874,4508,1381) -> Matrix(9,2,4,1) Matrix(1719,524,994,303) -> Matrix(9,2,4,1) Matrix(461,140,596,181) -> Matrix(1,0,14,1) Matrix(67,20,-526,-157) -> Matrix(1,0,-2,1) Matrix(4255,1264,3336,991) -> Matrix(7,-4,2,-1) Matrix(4839,1436,1048,311) -> Matrix(1,0,-6,1) Matrix(913,270,328,97) -> Matrix(1,0,-2,1) Matrix(1757,514,1234,361) -> Matrix(11,-10,-12,11) Matrix(323,94,780,227) -> Matrix(1,-2,0,1) Matrix(127,36,194,55) -> Matrix(1,-2,0,1) Matrix(1659,464,640,179) -> Matrix(1,2,0,1) Matrix(1657,462,-7270,-2027) -> Matrix(1,2,2,5) Matrix(1399,388,256,71) -> Matrix(1,0,0,1) Matrix(3815,1056,2164,599) -> Matrix(1,-6,0,1) Matrix(4767,1318,1718,475) -> Matrix(1,2,0,1) Matrix(443,122,-2284,-629) -> Matrix(1,2,0,1) Matrix(445,122,62,17) -> Matrix(1,2,-2,-3) Matrix(1829,494,1070,289) -> Matrix(5,6,4,5) Matrix(127,34,564,151) -> Matrix(3,2,-2,-1) Matrix(625,166,64,17) -> Matrix(1,0,-4,1) Matrix(1441,382,3942,1045) -> Matrix(1,0,0,1) Matrix(439,116,-2002,-529) -> Matrix(1,0,0,1) Matrix(1745,458,2808,737) -> Matrix(3,2,-2,-1) Matrix(685,178,558,145) -> Matrix(9,2,4,1) Matrix(787,188,180,43) -> Matrix(1,0,-2,1) Matrix(481,114,2232,529) -> Matrix(9,-4,-2,1) Matrix(239,56,542,127) -> Matrix(3,-2,-4,3) Matrix(1793,412,1014,233) -> Matrix(1,-2,0,1) Matrix(1609,368,2208,505) -> Matrix(1,0,-2,1) Matrix(2207,504,416,95) -> Matrix(1,0,2,1) Matrix(415,94,596,135) -> Matrix(1,-2,0,1) Matrix(1949,430,766,169) -> Matrix(1,0,0,1) Matrix(1295,282,822,179) -> Matrix(1,0,2,1) Matrix(529,114,116,25) -> Matrix(1,0,-4,1) Matrix(291,62,352,75) -> Matrix(1,-2,2,-3) Matrix(641,134,464,97) -> Matrix(1,-2,0,1) Matrix(1997,386,626,121) -> Matrix(1,0,0,1) Matrix(1589,302,342,65) -> Matrix(1,0,-6,1) Matrix(8025,1492,2372,441) -> Matrix(17,-16,-18,17) Matrix(509,94,1240,229) -> Matrix(1,-2,0,1) Matrix(111,20,394,71) -> Matrix(3,-2,-4,3) Matrix(893,156,166,29) -> Matrix(1,-2,2,-3) Matrix(943,162,390,67) -> Matrix(1,-2,0,1) Matrix(219,34,380,59) -> Matrix(1,-2,2,-3) Matrix(433,66,164,25) -> Matrix(1,-4,0,1) Matrix(797,108,214,29) -> Matrix(1,2,-2,-3) Matrix(2069,274,370,49) -> Matrix(1,0,0,1) Matrix(261,32,106,13) -> Matrix(1,0,-2,1) Matrix(257,28,156,17) -> Matrix(1,-2,2,-3) Matrix(123,-14,290,-33) -> Matrix(1,2,0,1) Matrix(203,-26,164,-21) -> Matrix(1,4,0,1) Matrix(883,-130,360,-53) -> Matrix(3,4,-4,-5) Matrix(1077,-164,440,-67) -> Matrix(3,2,-2,-1) Matrix(677,-106,198,-31) -> Matrix(1,0,0,1) Matrix(117,-20,158,-27) -> Matrix(1,0,-2,1) Matrix(1125,-208,622,-115) -> Matrix(3,-2,2,-1) Matrix(4795,-908,2012,-381) -> Matrix(1,-12,0,1) Matrix(1235,-236,696,-133) -> Matrix(1,2,0,1) Matrix(801,-166,304,-63) -> Matrix(1,-6,0,1) Matrix(1099,-234,418,-89) -> Matrix(1,8,0,1) Matrix(3101,-670,4994,-1079) -> Matrix(1,2,0,1) Matrix(3137,-680,1324,-287) -> Matrix(1,4,0,1) Matrix(1237,-282,2996,-683) -> Matrix(1,0,0,1) Matrix(335,-78,262,-61) -> Matrix(1,6,0,1) Matrix(109,-28,74,-19) -> Matrix(1,2,-2,-3) Matrix(763,-204,1814,-485) -> Matrix(1,2,0,1) Matrix(653,-176,1050,-283) -> Matrix(1,2,-2,-3) Matrix(181,-50,648,-179) -> Matrix(9,10,-10,-11) Matrix(1677,-484,1036,-299) -> Matrix(1,0,2,1) Matrix(2529,-736,1426,-415) -> Matrix(1,2,0,1) Matrix(677,-198,106,-31) -> Matrix(1,0,0,1) Matrix(249,-74,212,-63) -> Matrix(3,2,4,3) Matrix(317,-96,142,-43) -> Matrix(3,2,-2,-1) Matrix(457,-142,280,-87) -> Matrix(1,0,2,1) Matrix(613,-214,444,-155) -> Matrix(3,2,-2,-1) Matrix(747,-266,542,-193) -> Matrix(1,-2,0,1) Matrix(641,-232,1014,-367) -> Matrix(1,2,0,1) Matrix(2057,-750,842,-307) -> Matrix(1,0,0,1) Matrix(4141,-1516,1516,-555) -> Matrix(1,0,0,1) Matrix(1547,-568,1212,-445) -> Matrix(1,4,0,1) Matrix(807,-298,436,-161) -> Matrix(1,6,0,1) Matrix(801,-304,166,-63) -> Matrix(1,0,6,1) Matrix(1331,-508,600,-229) -> Matrix(1,-2,0,1) Matrix(1165,-446,1596,-611) -> Matrix(1,0,-2,1) Matrix(1195,-462,1658,-641) -> Matrix(1,0,-2,1) Matrix(1491,-578,3614,-1401) -> Matrix(1,0,0,1) Matrix(3215,-1248,2352,-913) -> Matrix(3,2,-2,-1) Matrix(297,-116,530,-207) -> Matrix(1,0,0,1) Matrix(883,-360,130,-53) -> Matrix(3,4,-4,-5) Matrix(6819,-2794,1828,-749) -> Matrix(1,4,-2,-7) Matrix(5741,-2354,9070,-3719) -> Matrix(1,4,0,1) Matrix(713,-298,390,-163) -> Matrix(5,2,2,1) Matrix(4795,-2012,908,-381) -> Matrix(1,0,12,1) Matrix(4601,-1932,874,-367) -> Matrix(1,0,-8,1) Matrix(8777,-3688,3596,-1511) -> Matrix(1,0,-4,1) Matrix(3137,-1324,680,-287) -> Matrix(1,0,-4,1) Matrix(4365,-1844,1844,-779) -> Matrix(1,0,0,1) Matrix(1743,-740,2810,-1193) -> Matrix(1,-4,0,1) Matrix(225,-98,512,-223) -> Matrix(3,4,-4,-5) Matrix(317,-142,96,-43) -> Matrix(3,2,-2,-1) Matrix(379,-174,220,-101) -> Matrix(1,2,0,1) Matrix(481,-254,392,-207) -> Matrix(13,2,6,1) Matrix(659,-354,538,-289) -> Matrix(19,-2,10,-1) Matrix(807,-436,298,-161) -> Matrix(1,0,-6,1) Matrix(713,-390,298,-163) -> Matrix(5,-2,-2,1) Matrix(2431,-1340,742,-409) -> Matrix(5,-2,-2,1) Matrix(1125,-622,208,-115) -> Matrix(3,-2,2,-1) Matrix(827,-462,324,-181) -> Matrix(1,0,0,1) Matrix(1235,-696,236,-133) -> Matrix(1,0,-2,1) Matrix(1765,-996,2146,-1211) -> Matrix(1,-2,2,-3) Matrix(1321,-748,2174,-1231) -> Matrix(5,2,2,1) Matrix(3551,-2016,2200,-1249) -> Matrix(1,0,16,1) Matrix(1867,-1078,2274,-1313) -> Matrix(5,-2,8,-3) Matrix(379,-220,174,-101) -> Matrix(1,0,-2,1) Matrix(145,-86,86,-51) -> Matrix(1,0,0,1) Matrix(685,-418,372,-227) -> Matrix(1,2,0,1) Matrix(457,-280,142,-87) -> Matrix(1,-2,0,1) Matrix(541,-334,426,-263) -> Matrix(1,2,0,1) Matrix(3551,-2200,2016,-1249) -> Matrix(1,-16,0,1) Matrix(2697,-1672,1534,-951) -> Matrix(1,14,0,1) Matrix(16571,-10292,3576,-2221) -> Matrix(1,2,-4,-7) Matrix(197,-124,170,-107) -> Matrix(1,-2,2,-3) Matrix(17407,-11020,6282,-3977) -> Matrix(1,-2,0,1) Matrix(3491,-2212,2028,-1285) -> Matrix(3,-8,2,-5) Matrix(253,-162,392,-251) -> Matrix(1,-8,0,1) Matrix(109,-74,28,-19) -> Matrix(1,2,-2,-3) Matrix(515,-358,82,-57) -> Matrix(1,0,0,1) Matrix(189,-134,134,-95) -> Matrix(5,4,-4,-3) Matrix(643,-462,508,-365) -> Matrix(9,4,2,1) Matrix(613,-444,214,-155) -> Matrix(3,2,-2,-1) Matrix(3325,-2426,1276,-931) -> Matrix(1,0,2,1) Matrix(3215,-2352,1248,-913) -> Matrix(3,2,-2,-1) Matrix(849,-622,1036,-759) -> Matrix(3,2,4,3) Matrix(743,-546,132,-97) -> Matrix(1,0,2,1) Matrix(261,-200,338,-259) -> Matrix(1,0,20,1) Matrix(335,-262,78,-61) -> Matrix(1,0,-6,1) Matrix(541,-426,334,-263) -> Matrix(1,0,-2,1) Matrix(203,-164,26,-21) -> Matrix(1,0,-4,1) Matrix(481,-392,254,-207) -> Matrix(13,-6,-2,1) Matrix(4469,-3674,2524,-2075) -> Matrix(3,-2,2,-1) Matrix(249,-212,74,-63) -> Matrix(3,-4,-2,3) Matrix(197,-170,124,-107) -> Matrix(1,-2,2,-3) Matrix(237,-268,130,-147) -> Matrix(3,-2,2,-1) Matrix(569,-674,168,-199) -> Matrix(5,-4,-6,5) Matrix(1765,-2146,996,-1211) -> Matrix(1,-2,2,-3) Matrix(1867,-2274,1078,-1313) -> Matrix(5,-8,2,-3) Matrix(285,-358,82,-103) -> Matrix(1,-4,0,1) Matrix(4247,-5412,2468,-3145) -> Matrix(3,-8,2,-5) Matrix(261,-338,200,-259) -> Matrix(1,-20,0,1) Matrix(117,-158,20,-27) -> Matrix(1,2,0,1) Matrix(2625,-3586,1516,-2071) -> Matrix(1,4,0,1) Matrix(8297,-11346,1962,-2683) -> Matrix(1,2,-4,-7) Matrix(4351,-5952,1030,-1409) -> Matrix(1,0,-2,1) Matrix(1165,-1596,446,-611) -> Matrix(1,2,0,1) Matrix(1195,-1658,462,-641) -> Matrix(1,2,0,1) Matrix(653,-910,404,-563) -> Matrix(1,2,2,5) Matrix(1027,-1458,722,-1025) -> Matrix(21,22,-22,-23) Matrix(641,-924,188,-271) -> Matrix(1,0,0,1) Matrix(581,-844,338,-491) -> Matrix(1,2,0,1) Matrix(253,-392,162,-251) -> Matrix(1,0,8,1) Matrix(1891,-2984,500,-789) -> Matrix(1,0,-4,1) Matrix(641,-1014,232,-367) -> Matrix(1,0,-2,1) Matrix(1103,-1750,462,-733) -> Matrix(5,-2,-2,1) Matrix(653,-1050,176,-283) -> Matrix(1,2,-2,-3) Matrix(211,-340,18,-29) -> Matrix(1,0,2,1) Matrix(6249,-10082,3872,-6247) -> Matrix(1,0,30,1) Matrix(4849,-7846,1406,-2275) -> Matrix(1,0,-2,1) Matrix(385,-628,122,-199) -> Matrix(1,0,-2,1) Matrix(941,-1544,348,-571) -> Matrix(1,0,-4,1) Matrix(1321,-2174,748,-1231) -> Matrix(5,-2,-2,1) Matrix(987,-1682,578,-985) -> Matrix(11,-10,10,-9) Matrix(7457,-12828,2892,-4975) -> Matrix(3,-4,-2,3) Matrix(10741,-19022,3934,-6967) -> Matrix(1,0,0,1) Matrix(297,-530,116,-207) -> Matrix(1,0,0,1) Matrix(1013,-1838,458,-831) -> Matrix(1,-4,0,1) Matrix(241,-450,128,-239) -> Matrix(1,-16,0,1) Matrix(219,-472,58,-125) -> Matrix(1,2,-2,-3) Matrix(847,-1868,258,-569) -> Matrix(1,0,0,1) Matrix(225,-512,98,-223) -> Matrix(3,4,-4,-5) Matrix(123,-290,14,-33) -> Matrix(1,0,-2,1) Matrix(3923,-9278,1504,-3557) -> Matrix(1,0,0,1) Matrix(6983,-16524,2678,-6337) -> Matrix(1,0,0,1) Matrix(763,-1814,204,-485) -> Matrix(1,0,-2,1) Matrix(5509,-13122,2312,-5507) -> Matrix(1,-20,0,1) Matrix(1237,-2996,282,-683) -> Matrix(1,0,0,1) Matrix(3077,-7504,1110,-2707) -> Matrix(1,0,2,1) Matrix(859,-2178,338,-857) -> Matrix(1,0,0,1) Matrix(10441,-26912,4050,-10439) -> Matrix(1,2,-2,-3) Matrix(1349,-3482,308,-795) -> Matrix(1,0,0,1) Matrix(457,-1198,140,-367) -> Matrix(1,-2,0,1) Matrix(259,-706,62,-169) -> Matrix(1,0,-2,1) Matrix(7475,-20402,2738,-7473) -> Matrix(1,0,0,1) Matrix(2067,-5660,554,-1517) -> Matrix(1,4,-2,-7) Matrix(3709,-10274,1074,-2975) -> Matrix(1,0,0,1) Matrix(205,-578,72,-203) -> Matrix(1,-2,0,1) Matrix(771,-2450,242,-769) -> Matrix(1,0,0,1) Matrix(10063,-32992,2172,-7121) -> Matrix(1,2,-4,-7) Matrix(9459,-31022,2042,-6697) -> Matrix(1,2,-4,-7) Matrix(2983,-10082,882,-2981) -> Matrix(33,34,-34,-35) Matrix(269,-926,52,-179) -> Matrix(1,0,0,1) Matrix(6635,-22898,1922,-6633) -> Matrix(1,0,0,1) Matrix(181,-648,50,-179) -> Matrix(9,10,-10,-11) Matrix(1361,-5032,294,-1087) -> Matrix(3,2,-8,-5) Matrix(855,-3238,202,-765) -> Matrix(1,0,-2,1) Matrix(153,-722,32,-151) -> Matrix(1,0,14,1) Matrix(547,-3042,98,-545) -> Matrix(1,0,0,1) Matrix(121,-800,18,-119) -> Matrix(5,6,-6,-7) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 66 Degree of the the map X: 66 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 1/1 13/10 7/5 27/19 14/9 71/44 29/17 15/8 2/1 16/7 97/41 81/34 33/13 116/45 13/5 101/37 17/6 3/1 35/11 141/43 71/21 17/5 107/31 18/5 11/3 4/1 17/4 13/3 9/2 14/3 19/4 5/1 16/3 11/2 39/7 17/3 6/1 13/2 20/3 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/1 1/1 0/1 1/0 1/8 -2/1 1/7 -1/1 3/20 -1/1 2/13 -1/2 1/6 0/1 2/11 1/0 3/16 2/1 4/21 1/0 1/5 1/1 4/19 1/0 3/14 -6/1 2/9 -5/2 3/13 1/1 1/4 -2/1 4/15 1/0 7/26 -2/1 3/11 -1/1 5/18 -1/1 2/7 -1/2 9/31 1/1 7/24 -2/1 5/17 -1/1 3/10 0/1 4/13 1/0 1/3 -1/1 6/17 0/1 5/14 0/1 4/11 1/0 15/41 1/1 11/30 0/1 7/19 1/1 3/8 -2/3 8/21 1/2 13/34 0/1 5/13 -1/1 12/31 1/0 19/49 -1/1 7/18 0/1 2/5 1/0 9/22 0/1 7/17 -1/1 5/12 -2/3 13/31 -1/5 34/81 0/1 21/50 0/1 8/19 1/0 19/45 1/1 11/26 0/1 14/33 1/0 3/7 -1/1 7/16 -1/1 4/9 -1/2 5/11 -1/3 1/2 0/1 8/15 0/1 7/13 1/7 6/11 1/4 11/20 0/1 16/29 1/2 5/9 1/1 14/25 1/0 9/16 0/1 22/39 1/0 13/23 -1/1 17/30 0/1 4/7 1/4 11/19 3/5 7/12 2/3 3/5 1/1 14/23 1/0 11/18 2/1 8/13 1/0 13/21 5/1 44/71 1/0 31/50 -10/1 18/29 1/0 23/37 -1/1 5/8 0/1 12/19 1/0 19/30 2/1 7/11 3/1 9/14 1/0 2/3 1/0 9/13 -1/1 7/10 -4/3 5/7 -3/5 18/25 -1/2 13/18 0/1 8/11 -1/2 27/37 -1/3 19/26 0/1 30/41 -1/2 11/15 -1/3 14/19 -1/2 3/4 0/1 10/13 0/1 7/9 1/7 11/14 0/1 4/5 1/2 13/16 0/1 9/11 3/5 5/6 4/5 6/7 3/2 1/1 -1/1 8/7 1/2 7/6 2/3 13/11 1/1 6/5 5/4 11/9 5/3 16/13 1/0 5/4 2/1 24/19 1/0 19/15 7/1 14/11 1/0 37/29 5/1 23/18 4/1 9/7 7/1 13/10 1/0 4/3 1/0 15/11 -3/1 41/30 -2/1 67/49 -1/1 93/68 -1/1 26/19 1/0 11/8 -2/1 18/13 1/0 25/18 -2/1 7/5 -5/3 17/12 -8/7 27/19 -1/1 10/7 -3/4 13/9 -1/1 16/11 -1/2 3/2 0/1 14/9 0/1 11/7 1/3 30/19 1/2 19/12 0/1 27/17 3/5 8/5 1/0 29/18 0/1 50/31 -1/10 71/44 0/1 21/13 1/5 55/34 0/1 89/55 1/3 34/21 1/0 13/8 0/1 31/19 1/1 18/11 1/2 23/14 0/1 5/3 1/1 17/10 2/3 29/17 1/1 12/7 3/2 43/25 1/1 31/18 2/1 19/11 5/3 7/4 4/1 30/17 1/0 23/13 -1/1 39/22 0/1 55/31 3/1 16/9 1/0 9/5 1/1 29/16 2/1 20/11 1/0 31/17 5/3 11/6 4/1 13/7 7/1 15/8 1/0 2/1 1/0 13/6 -2/1 11/5 -3/1 42/19 1/0 31/14 -2/1 20/9 -3/2 9/4 -2/1 16/7 -1/1 7/3 -1/1 26/11 1/0 97/41 -1/1 1/1 71/30 0/1 45/19 1/1 19/8 0/1 50/21 1/0 81/34 1/0 31/13 -5/1 43/18 -2/1 12/5 -3/2 17/7 -1/1 22/9 1/0 5/2 0/1 33/13 -1/1 1/1 28/11 1/0 23/9 1/1 18/7 1/0 67/26 -2/1 116/45 -1/1 49/19 -1/1 31/12 0/1 13/5 -1/1 47/18 0/1 34/13 1/0 21/8 2/1 8/3 -3/2 19/7 1/1 30/11 1/0 101/37 -1/1 1/1 71/26 0/1 41/15 1/1 11/4 0/1 14/5 1/0 17/6 1/0 3/1 -1/1 19/6 0/1 35/11 -1/1 1/1 16/5 1/0 13/4 0/1 36/11 1/0 59/18 -2/1 141/43 -3/1 -1/1 82/25 1/0 23/7 -3/1 10/3 1/0 27/8 -8/7 71/21 -1/1 44/13 -9/10 17/5 -1/1 24/7 -1/2 31/9 1/1 69/20 0/1 107/31 -1/1 1/1 38/11 1/0 7/2 -2/1 18/5 -1/1 11/3 -1/1 37/10 -2/3 26/7 -1/2 15/4 0/1 34/9 -1/2 19/5 -1/1 4/1 -1/2 21/5 -1/1 17/4 0/1 13/3 1/1 9/2 -2/5 14/3 -1/6 19/4 0/1 5/1 1/1 26/5 -1/2 21/4 0/1 16/3 1/2 11/2 0/1 39/7 -1/1 1/1 28/5 1/0 17/3 -1/1 6/1 1/0 13/2 -2/1 20/3 -1/1 7/1 -1/1 8/1 -1/2 9/1 -1/3 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(123,-14,290,-33) (0/1,1/8) -> (11/26,14/33) Hyperbolic Matrix(122,-17,201,-28) (1/8,1/7) -> (3/5,14/23) Hyperbolic Matrix(280,-41,41,-6) (1/7,3/20) -> (20/3,7/1) Hyperbolic Matrix(520,-79,79,-12) (3/20,2/13) -> (13/2,20/3) Hyperbolic Matrix(80,-13,197,-32) (2/13,1/6) -> (2/5,9/22) Hyperbolic Matrix(117,-20,158,-27) (1/6,2/11) -> (14/19,3/4) Hyperbolic Matrix(156,-29,581,-108) (2/11,3/16) -> (4/15,7/26) Hyperbolic Matrix(504,-95,1199,-226) (3/16,4/21) -> (21/50,8/19) Hyperbolic Matrix(1235,-236,696,-133) (4/21,1/5) -> (55/31,16/9) Hyperbolic Matrix(190,-39,39,-8) (1/5,4/19) -> (19/4,5/1) Hyperbolic Matrix(532,-113,113,-24) (4/19,3/14) -> (14/3,19/4) Hyperbolic Matrix(114,-25,301,-66) (3/14,2/9) -> (3/8,8/21) Hyperbolic Matrix(262,-59,151,-34) (2/9,3/13) -> (19/11,7/4) 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(653,-176,1050,-283) (7/26,3/11) -> (23/37,5/8) Hyperbolic Matrix(396,-109,109,-30) (3/11,5/18) -> (18/5,11/3) Hyperbolic Matrix(252,-71,71,-20) (5/18,2/7) -> (7/2,18/5) Hyperbolic 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(782,-229,321,-94) (7/24,5/17) -> (17/7,22/9) 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(102,-35,35,-12) (1/3,6/17) -> (17/6,3/1) Hyperbolic Matrix(476,-169,169,-60) (6/17,5/14) -> (14/5,17/6) Hyperbolic Matrix(270,-97,373,-134) (5/14,4/11) -> (13/18,8/11) Hyperbolic Matrix(1852,-677,1045,-382) (4/11,15/41) -> (23/13,39/22) 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(202,-75,167,-62) (7/19,3/8) -> (6/5,11/9) 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(464,-179,731,-282) (5/13,12/31) -> (19/30,7/11) Hyperbolic Matrix(2852,-1105,1657,-642) (12/31,19/49) -> (43/25,31/18) 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(782,-321,229,-94) (9/22,7/17) -> (17/5,24/7) Hyperbolic Matrix(326,-135,227,-94) (7/17,5/12) -> (10/7,13/9) Hyperbolic Matrix(713,-298,390,-163) (5/12,13/31) -> (31/17,11/6) Hyperbolic Matrix(5022,-2107,2107,-884) (13/31,34/81) -> (81/34,31/13) Hyperbolic Matrix(8100,-3401,3401,-1428) (34/81,21/50) -> (50/21,81/34) Hyperbolic Matrix(2362,-997,905,-382) (8/19,19/45) -> (13/5,47/18) Hyperbolic Matrix(4365,-1844,1844,-779) (19/45,11/26) -> (71/30,45/19) Hyperbolic Matrix(548,-233,969,-412) (14/33,3/7) -> (13/23,17/30) Hyperbolic Matrix(224,-97,97,-42) (3/7,7/16) -> (16/7,7/3) Hyperbolic Matrix(288,-127,127,-56) (7/16,4/9) -> (9/4,16/7) Hyperbolic 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(60,-31,31,-16) (1/2,8/15) -> (15/8,2/1) Hyperbolic Matrix(390,-209,209,-112) (8/15,7/13) -> (13/7,15/8) Hyperbolic Matrix(268,-145,329,-178) (7/13,6/11) -> (13/16,9/11) 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(652,-361,177,-98) (16/29,5/9) -> (11/3,37/10) 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(1852,-1045,677,-382) (22/39,13/23) -> (41/15,11/4) Hyperbolic Matrix(1056,-599,1703,-966) (17/30,4/7) -> (31/50,18/29) Hyperbolic Matrix(262,-151,59,-34) (4/7,11/19) -> (13/3,9/2) 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(458,-279,371,-226) (14/23,11/18) -> (16/13,5/4) 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(2982,-1847,1847,-1144) (13/21,44/71) -> (71/44,21/13) Hyperbolic Matrix(7100,-4401,4401,-2728) (44/71,31/50) -> (50/31,71/44) Hyperbolic Matrix(1334,-829,737,-458) (18/29,23/37) -> (9/5,29/16) Hyperbolic Matrix(197,-124,170,-107) (5/8,12/19) -> (8/7,7/6) Hyperbolic Matrix(732,-463,1015,-642) (12/19,19/30) -> (18/25,13/18) Hyperbolic Matrix(308,-197,197,-126) (7/11,9/14) -> (14/9,11/7) Hyperbolic Matrix(84,-55,55,-36) (9/14,2/3) -> (3/2,14/9) Hyperbolic Matrix(109,-74,28,-19) (2/3,9/13) -> (19/5,4/1) Hyperbolic Matrix(326,-227,135,-94) (9/13,7/10) -> (12/5,17/7) 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(1198,-873,505,-368) (8/11,27/37) -> (45/19,19/8) Hyperbolic Matrix(3215,-2352,1248,-913) (19/26,30/41) -> (18/7,67/26) Hyperbolic Matrix(1116,-817,265,-194) (30/41,11/15) -> (21/5,17/4) Hyperbolic Matrix(743,-546,132,-97) (11/15,14/19) -> (28/5,17/3) Hyperbolic Matrix(104,-79,79,-60) (3/4,10/13) -> (13/10,4/3) Hyperbolic Matrix(234,-181,181,-140) (10/13,7/9) -> (9/7,13/10) Hyperbolic 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(458,-371,279,-226) (4/5,13/16) -> (18/11,23/14) Hyperbolic Matrix(202,-167,75,-62) (9/11,5/6) -> (8/3,19/7) 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(268,-329,145,-178) (11/9,16/13) -> (11/6,13/7) Hyperbolic Matrix(285,-358,82,-103) (5/4,24/19) -> (38/11,7/2) Hyperbolic Matrix(1354,-1727,991,-1264) (14/11,37/29) -> (15/11,41/30) Hyperbolic Matrix(117,-158,20,-27) (4/3,15/11) -> (17/3,6/1) Hyperbolic Matrix(9016,-12329,3497,-4782) (67/49,93/68) -> (116/45,49/19) Hyperbolic Matrix(6760,-9247,2623,-3588) (93/68,26/19) -> (67/26,116/45) Hyperbolic Matrix(1165,-1596,446,-611) (26/19,11/8) -> (47/18,34/13) Hyperbolic Matrix(270,-373,97,-134) (11/8,18/13) -> (11/4,14/5) Hyperbolic Matrix(732,-1015,463,-642) (18/13,25/18) -> (30/19,19/12) Hyperbolic Matrix(653,-910,404,-563) (25/18,7/5) -> (21/13,55/34) Hyperbolic Matrix(514,-729,361,-512) (17/12,27/19) -> (27/19,10/7) Parabolic Matrix(581,-844,338,-491) (13/9,16/11) -> (12/7,43/25) Hyperbolic Matrix(464,-731,179,-282) (11/7,30/19) -> (31/12,13/5) 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(1056,-1703,599,-966) (29/18,50/31) -> (7/4,30/17) Hyperbolic 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(122,-201,17,-28) (23/14,5/3) -> (7/1,8/1) Hyperbolic Matrix(494,-841,289,-492) (17/10,29/17) -> (29/17,12/7) Parabolic Matrix(166,-293,17,-30) (30/17,23/13) -> (9/1,1/0) 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(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(123,-290,14,-33) (7/3,26/11) -> (8/1,9/1) Hyperbolic Matrix(3978,-9409,1681,-3976) (26/11,97/41) -> (97/41,71/30) Parabolic Matrix(504,-1199,95,-226) (19/8,50/21) -> (21/4,16/3) Hyperbolic Matrix(80,-197,13,-32) (22/9,5/2) -> (6/1,13/2) Hyperbolic Matrix(430,-1089,169,-428) (5/2,33/13) -> (33/13,28/11) Parabolic Matrix(874,-2255,231,-596) (49/19,31/12) -> (34/9,19/5) Hyperbolic Matrix(457,-1198,140,-367) (34/13,21/8) -> (13/4,36/11) Hyperbolic Matrix(114,-301,25,-66) (21/8,8/3) -> (9/2,14/3) Hyperbolic Matrix(259,-706,62,-169) (19/7,30/11) -> (4/1,21/5) Hyperbolic Matrix(3738,-10201,1369,-3736) (30/11,101/37) -> (101/37,71/26) Parabolic Matrix(386,-1225,121,-384) (19/6,35/11) -> (35/11,16/5) Parabolic Matrix(6064,-19881,1849,-6062) (59/18,141/43) -> (141/43,82/25) Parabolic Matrix(1492,-5041,441,-1490) (27/8,71/21) -> (71/21,44/13) Parabolic Matrix(269,-926,52,-179) (24/7,31/9) -> (5/1,26/5) Hyperbolic Matrix(3318,-11449,961,-3316) (69/20,107/31) -> (107/31,38/11) Parabolic Matrix(156,-581,29,-108) (26/7,15/4) -> (16/3,11/2) Hyperbolic Matrix(274,-1521,49,-272) (11/2,39/7) -> (39/7,28/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(0,-1,1,0) Matrix(123,-14,290,-33) -> Matrix(1,2,0,1) Matrix(122,-17,201,-28) -> Matrix(2,3,1,2) Matrix(280,-41,41,-6) -> Matrix(2,3,-3,-4) Matrix(520,-79,79,-12) -> Matrix(4,3,-3,-2) Matrix(80,-13,197,-32) -> Matrix(2,1,-1,0) Matrix(117,-20,158,-27) -> Matrix(1,0,-2,1) Matrix(156,-29,581,-108) -> Matrix(2,-3,-1,2) Matrix(504,-95,1199,-226) -> Matrix(0,1,-1,2) Matrix(1235,-236,696,-133) -> Matrix(1,2,0,1) Matrix(190,-39,39,-8) -> Matrix(0,1,-1,2) Matrix(532,-113,113,-24) -> Matrix(0,-1,1,12) Matrix(114,-25,301,-66) -> Matrix(0,-1,1,4) Matrix(262,-59,151,-34) -> Matrix(2,3,1,2) Matrix(335,-78,262,-61) -> Matrix(1,6,0,1) Matrix(109,-28,74,-19) -> Matrix(1,2,-2,-3) Matrix(653,-176,1050,-283) -> Matrix(1,2,-2,-3) Matrix(396,-109,109,-30) -> Matrix(6,7,-7,-8) Matrix(252,-71,71,-20) -> Matrix(4,3,-3,-2) Matrix(1677,-484,1036,-299) -> Matrix(1,0,2,1) Matrix(2529,-736,1426,-415) -> Matrix(1,2,0,1) Matrix(782,-229,321,-94) -> Matrix(0,-1,1,2) Matrix(249,-74,212,-63) -> Matrix(3,2,4,3) Matrix(317,-96,142,-43) -> Matrix(3,2,-2,-1) Matrix(457,-142,280,-87) -> Matrix(1,0,2,1) Matrix(102,-35,35,-12) -> Matrix(2,1,-1,0) Matrix(476,-169,169,-60) -> Matrix(0,-1,1,0) Matrix(270,-97,373,-134) -> Matrix(0,-1,1,2) Matrix(1852,-677,1045,-382) -> Matrix(0,-1,1,0) Matrix(4141,-1516,1516,-555) -> Matrix(1,0,0,1) Matrix(1547,-568,1212,-445) -> Matrix(1,4,0,1) Matrix(202,-75,167,-62) -> Matrix(2,3,1,2) Matrix(1331,-508,600,-229) -> Matrix(1,-2,0,1) Matrix(1165,-446,1596,-611) -> Matrix(1,0,-2,1) Matrix(464,-179,731,-282) -> Matrix(2,-1,1,0) Matrix(2852,-1105,1657,-642) -> Matrix(2,3,1,2) Matrix(3215,-1248,2352,-913) -> Matrix(3,2,-2,-1) Matrix(297,-116,530,-207) -> Matrix(1,0,0,1) Matrix(782,-321,229,-94) -> Matrix(0,-1,1,2) Matrix(326,-135,227,-94) -> Matrix(0,-1,1,2) Matrix(713,-298,390,-163) -> Matrix(5,2,2,1) Matrix(5022,-2107,2107,-884) -> Matrix(10,1,-1,0) Matrix(8100,-3401,3401,-1428) -> Matrix(10,-1,1,0) Matrix(2362,-997,905,-382) -> Matrix(0,-1,1,0) Matrix(4365,-1844,1844,-779) -> Matrix(1,0,0,1) Matrix(548,-233,969,-412) -> Matrix(0,-1,1,2) Matrix(224,-97,97,-42) -> Matrix(0,-1,1,2) Matrix(288,-127,127,-56) -> Matrix(4,3,-3,-2) Matrix(317,-142,96,-43) -> Matrix(3,2,-2,-1) Matrix(379,-174,220,-101) -> Matrix(1,2,0,1) Matrix(60,-31,31,-16) -> Matrix(2,1,-1,0) Matrix(390,-209,209,-112) -> Matrix(14,-1,1,0) Matrix(268,-145,329,-178) -> Matrix(4,-1,9,-2) Matrix(713,-390,298,-163) -> Matrix(5,-2,-2,1) Matrix(2431,-1340,742,-409) -> Matrix(5,-2,-2,1) Matrix(652,-361,177,-98) -> Matrix(4,-3,-5,4) Matrix(827,-462,324,-181) -> Matrix(1,0,0,1) Matrix(1235,-696,236,-133) -> Matrix(1,0,-2,1) Matrix(1852,-1045,677,-382) -> Matrix(0,-1,1,0) Matrix(1056,-599,1703,-966) -> Matrix(6,1,-1,0) Matrix(262,-151,59,-34) -> Matrix(2,-1,-3,2) Matrix(379,-220,174,-101) -> Matrix(1,0,-2,1) Matrix(145,-86,86,-51) -> Matrix(1,0,0,1) Matrix(458,-279,371,-226) -> Matrix(2,-5,1,-2) Matrix(457,-280,142,-87) -> Matrix(1,-2,0,1) Matrix(541,-334,426,-263) -> Matrix(1,2,0,1) Matrix(2982,-1847,1847,-1144) -> Matrix(0,1,-1,10) Matrix(7100,-4401,4401,-2728) -> Matrix(0,-1,1,20) Matrix(1334,-829,737,-458) -> Matrix(2,3,1,2) Matrix(197,-124,170,-107) -> Matrix(1,-2,2,-3) Matrix(732,-463,1015,-642) -> Matrix(0,-1,1,0) Matrix(308,-197,197,-126) -> Matrix(0,1,-1,6) Matrix(84,-55,55,-36) -> Matrix(0,-1,1,2) Matrix(109,-74,28,-19) -> Matrix(1,2,-2,-3) Matrix(326,-227,135,-94) -> Matrix(0,-1,1,2) Matrix(189,-134,134,-95) -> Matrix(5,4,-4,-3) Matrix(643,-462,508,-365) -> Matrix(9,4,2,1) Matrix(1198,-873,505,-368) -> Matrix(2,1,-1,0) Matrix(3215,-2352,1248,-913) -> Matrix(3,2,-2,-1) Matrix(1116,-817,265,-194) -> Matrix(2,1,-5,-2) Matrix(743,-546,132,-97) -> Matrix(1,0,2,1) Matrix(104,-79,79,-60) -> Matrix(6,1,-1,0) Matrix(234,-181,181,-140) -> Matrix(14,-1,1,0) Matrix(335,-262,78,-61) -> Matrix(1,0,-6,1) Matrix(541,-426,334,-263) -> Matrix(1,0,-2,1) Matrix(458,-371,279,-226) -> Matrix(2,-1,5,-2) Matrix(202,-167,75,-62) -> Matrix(2,-1,-3,2) Matrix(249,-212,74,-63) -> Matrix(3,-4,-2,3) Matrix(197,-170,124,-107) -> Matrix(1,-2,2,-3) Matrix(237,-268,130,-147) -> Matrix(3,-2,2,-1) Matrix(569,-674,168,-199) -> Matrix(5,-4,-6,5) Matrix(268,-329,145,-178) -> Matrix(4,-9,1,-2) Matrix(285,-358,82,-103) -> Matrix(1,-4,0,1) Matrix(1354,-1727,991,-1264) -> Matrix(2,-7,-1,4) Matrix(117,-158,20,-27) -> Matrix(1,2,0,1) Matrix(9016,-12329,3497,-4782) -> Matrix(0,-1,1,2) Matrix(6760,-9247,2623,-3588) -> Matrix(2,1,-1,0) Matrix(1165,-1596,446,-611) -> Matrix(1,2,0,1) Matrix(270,-373,97,-134) -> Matrix(0,-1,1,2) Matrix(732,-1015,463,-642) -> Matrix(0,-1,1,0) Matrix(653,-910,404,-563) -> Matrix(1,2,2,5) Matrix(514,-729,361,-512) -> Matrix(10,11,-11,-12) Matrix(581,-844,338,-491) -> Matrix(1,2,0,1) Matrix(464,-731,179,-282) -> Matrix(2,-1,1,0) Matrix(1103,-1750,462,-733) -> Matrix(5,-2,-2,1) Matrix(653,-1050,176,-283) -> Matrix(1,2,-2,-3) Matrix(1056,-1703,599,-966) -> Matrix(6,1,-1,0) Matrix(4849,-7846,1406,-2275) -> Matrix(1,0,-2,1) Matrix(385,-628,122,-199) -> Matrix(1,0,-2,1) Matrix(122,-201,17,-28) -> Matrix(2,-1,-3,2) Matrix(494,-841,289,-492) -> Matrix(6,-5,5,-4) Matrix(166,-293,17,-30) -> Matrix(0,-1,1,4) Matrix(297,-530,116,-207) -> Matrix(1,0,0,1) Matrix(1013,-1838,458,-831) -> Matrix(1,-4,0,1) Matrix(219,-472,58,-125) -> Matrix(1,2,-2,-3) Matrix(847,-1868,258,-569) -> Matrix(1,0,0,1) Matrix(123,-290,14,-33) -> Matrix(1,0,-2,1) Matrix(3978,-9409,1681,-3976) -> Matrix(0,-1,1,0) Matrix(504,-1199,95,-226) -> Matrix(0,1,-1,2) Matrix(80,-197,13,-32) -> Matrix(2,1,-1,0) Matrix(430,-1089,169,-428) -> Matrix(0,-1,1,0) Matrix(874,-2255,231,-596) -> Matrix(0,-1,1,2) Matrix(457,-1198,140,-367) -> Matrix(1,-2,0,1) Matrix(114,-301,25,-66) -> Matrix(0,-1,1,4) Matrix(259,-706,62,-169) -> Matrix(1,0,-2,1) Matrix(3738,-10201,1369,-3736) -> Matrix(0,-1,1,0) Matrix(386,-1225,121,-384) -> Matrix(0,-1,1,0) Matrix(6064,-19881,1849,-6062) -> Matrix(2,5,-1,-2) Matrix(1492,-5041,441,-1490) -> Matrix(16,17,-17,-18) Matrix(269,-926,52,-179) -> Matrix(1,0,0,1) Matrix(3318,-11449,961,-3316) -> Matrix(0,-1,1,0) Matrix(156,-581,29,-108) -> Matrix(2,1,3,2) Matrix(274,-1521,49,-272) -> Matrix(0,-1,1,0) 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): 66 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 (-1/1,1/1).(0/1,1/0) 0 1 1/1 -1/1 1 23 7/6 2/3 1 23 6/5 5/4 1 23 11/9 5/3 1 23 16/13 1/0 1 23 5/4 2/1 1 23 14/11 1/0 1 23 9/7 7/1 1 23 13/10 1/0 10 1 4/3 1/0 1 23 15/11 -3/1 1 23 41/30 -2/1 1 23 26/19 1/0 1 23 11/8 -2/1 1 23 18/13 1/0 1 23 25/18 -2/1 1 23 7/5 -5/3 1 23 27/19 -1/1 11 1 10/7 -3/4 1 23 13/9 -1/1 1 23 3/2 0/1 1 23 14/9 0/1 4 1 11/7 1/3 1 23 30/19 1/2 1 23 19/12 0/1 1 23 27/17 3/5 1 23 8/5 1/0 1 23 29/18 0/1 1 23 50/31 -1/10 1 23 71/44 0/1 15 1 21/13 1/5 1 23 55/34 0/1 1 23 34/21 1/0 1 23 13/8 0/1 1 23 18/11 1/2 1 23 23/14 0/1 1 23 5/3 1/1 1 23 29/17 1/1 5 1 12/7 3/2 1 23 19/11 5/3 1 23 7/4 4/1 1 23 30/17 1/0 1 23 23/13 -1/1 1 23 39/22 0/1 1 23 16/9 1/0 1 23 9/5 1/1 1 23 29/16 2/1 1 23 20/11 1/0 1 23 11/6 4/1 1 23 13/7 7/1 1 23 15/8 1/0 8 1 2/1 1/0 1 23 13/6 -2/1 1 23 11/5 -3/1 1 23 9/4 -2/1 1 23 16/7 -1/1 2 1 7/3 -1/1 1 23 26/11 1/0 1 23 97/41 (-1/1,1/1).(0/1,1/0) 0 1 45/19 1/1 1 23 19/8 0/1 1 23 50/21 1/0 1 23 81/34 1/0 10 1 31/13 -5/1 1 23 43/18 -2/1 1 23 12/5 -3/2 1 23 17/7 -1/1 1 23 22/9 1/0 1 23 5/2 0/1 1 23 33/13 (-1/1,1/1).(0/1,1/0) 0 1 23/9 1/1 1 23 18/7 1/0 1 23 67/26 -2/1 1 23 116/45 -1/1 1 1 49/19 -1/1 1 23 31/12 0/1 1 23 13/5 -1/1 1 23 47/18 0/1 1 23 34/13 1/0 1 23 21/8 2/1 1 23 8/3 -3/2 1 23 19/7 1/1 1 23 30/11 1/0 1 23 101/37 (-1/1,1/1).(0/1,1/0) 0 1 41/15 1/1 1 23 11/4 0/1 1 23 14/5 1/0 1 23 17/6 1/0 1 1 3/1 -1/1 1 23 35/11 (-1/1,1/1).(0/1,1/0) 0 1 16/5 1/0 1 23 13/4 0/1 1 23 36/11 1/0 1 23 59/18 -2/1 1 23 141/43 (-3/1,-1/1).(-2/1,1/0) 0 1 23/7 -3/1 1 23 10/3 1/0 1 23 27/8 -8/7 1 23 71/21 -1/1 17 1 17/5 -1/1 1 23 24/7 -1/2 1 23 31/9 1/1 1 23 107/31 (-1/1,1/1).(0/1,1/0) 0 1 38/11 1/0 1 23 7/2 -2/1 1 23 18/5 -1/1 5 1 11/3 -1/1 1 23 37/10 -2/3 1 23 26/7 -1/2 1 23 15/4 0/1 1 23 34/9 -1/2 1 23 19/5 -1/1 1 23 4/1 -1/2 1 23 21/5 -1/1 1 23 17/4 0/1 1 23 13/3 1/1 1 23 9/2 -2/5 1 23 14/3 -1/6 1 23 19/4 0/1 7 1 5/1 1/1 1 23 26/5 -1/2 1 23 21/4 0/1 1 23 16/3 1/2 1 23 11/2 0/1 1 23 39/7 (-1/1,1/1).(0/1,1/0) 0 1 17/3 -1/1 1 23 6/1 1/0 1 23 13/2 -2/1 1 23 20/3 -1/1 3 1 7/1 -1/1 1 23 8/1 -1/2 1 23 9/1 -1/3 1 23 1/0 0/1 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(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(170,-197,107,-124) (1/1,7/6) -> (27/17,8/5) Glide Reflection Matrix(212,-249,63,-74) (7/6,6/5) -> (10/3,27/8) Glide Reflection Matrix(167,-202,62,-75) (6/5,11/9) -> (8/3,19/7) Glide Reflection Matrix(268,-329,145,-178) (11/9,16/13) -> (11/6,13/7) Hyperbolic Matrix(371,-458,226,-279) (16/13,5/4) -> (18/11,23/14) Glide Reflection Matrix(426,-541,263,-334) (5/4,14/11) -> (34/21,13/8) Glide Reflection Matrix(262,-335,61,-78) (14/11,9/7) -> (17/4,13/3) Glide Reflection Matrix(181,-234,140,-181) (9/7,13/10) -> (9/7,13/10) Reflection Matrix(79,-104,60,-79) (13/10,4/3) -> (13/10,4/3) Reflection Matrix(117,-158,20,-27) (4/3,15/11) -> (17/3,6/1) Hyperbolic Matrix(817,-1116,194,-265) (15/11,41/30) -> (21/5,17/4) Glide Reflection Matrix(2352,-3215,913,-1248) (41/30,26/19) -> (18/7,67/26) Glide Reflection Matrix(1165,-1596,446,-611) (26/19,11/8) -> (47/18,34/13) Hyperbolic Matrix(270,-373,97,-134) (11/8,18/13) -> (11/4,14/5) Hyperbolic Matrix(732,-1015,463,-642) (18/13,25/18) -> (30/19,19/12) Hyperbolic Matrix(653,-910,404,-563) (25/18,7/5) -> (21/13,55/34) Hyperbolic Matrix(134,-189,95,-134) (7/5,27/19) -> (7/5,27/19) Reflection Matrix(379,-540,266,-379) (27/19,10/7) -> (27/19,10/7) Reflection Matrix(227,-326,94,-135) (10/7,13/9) -> (12/5,17/7) Glide Reflection Matrix(74,-109,19,-28) (13/9,3/2) -> (19/5,4/1) Glide 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(464,-731,179,-282) (11/7,30/19) -> (31/12,13/5) 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(1056,-1703,599,-966) (29/18,50/31) -> (7/4,30/17) Hyperbolic Matrix(4401,-7100,2728,-4401) (50/31,71/44) -> (50/31,71/44) Reflection Matrix(1847,-2982,1144,-1847) (71/44,21/13) -> (71/44,21/13) Reflection Matrix(1036,-1677,299,-484) (55/34,34/21) -> (38/11,7/2) Glide Reflection Matrix(280,-457,87,-142) (13/8,18/11) -> (16/5,13/4) Glide Reflection Matrix(122,-201,17,-28) (23/14,5/3) -> (7/1,8/1) Hyperbolic Matrix(86,-145,51,-86) (5/3,29/17) -> (5/3,29/17) Reflection Matrix(407,-696,238,-407) (29/17,12/7) -> (29/17,12/7) Reflection Matrix(220,-379,101,-174) (12/7,19/11) -> (13/6,11/5) Glide Reflection Matrix(151,-262,34,-59) (19/11,7/4) -> (13/3,9/2) Glide Reflection Matrix(166,-293,17,-30) (30/17,23/13) -> (9/1,1/0) Hyperbolic Matrix(1045,-1852,382,-677) (23/13,39/22) -> (41/15,11/4) Glide Reflection Matrix(696,-1235,133,-236) (39/22,16/9) -> (26/5,21/4) Glide Reflection Matrix(297,-530,116,-207) (16/9,9/5) -> (23/9,18/7) Hyperbolic Matrix(361,-652,98,-177) (9/5,29/16) -> (11/3,37/10) Glide Reflection Matrix(1340,-2431,409,-742) (29/16,20/11) -> (36/11,59/18) Glide Reflection Matrix(390,-713,163,-298) (20/11,11/6) -> (43/18,12/5) Glide Reflection Matrix(209,-390,112,-209) (13/7,15/8) -> (13/7,15/8) Reflection Matrix(31,-60,16,-31) (15/8,2/1) -> (15/8,2/1) Reflection Matrix(219,-472,58,-125) (2/1,13/6) -> (15/4,34/9) Hyperbolic Matrix(142,-317,43,-96) (11/5,9/4) -> (23/7,10/3) Glide Reflection 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(123,-290,14,-33) (7/3,26/11) -> (8/1,9/1) Hyperbolic Matrix(2133,-5044,902,-2133) (26/11,97/41) -> (26/11,97/41) Reflection Matrix(1844,-4365,779,-1844) (97/41,45/19) -> (97/41,45/19) Reflection Matrix(997,-2362,382,-905) (45/19,19/8) -> (13/5,47/18) Glide Reflection Matrix(504,-1199,95,-226) (19/8,50/21) -> (21/4,16/3) Hyperbolic Matrix(3401,-8100,1428,-3401) (50/21,81/34) -> (50/21,81/34) Reflection Matrix(2107,-5022,884,-2107) (81/34,31/13) -> (81/34,31/13) Reflection Matrix(321,-782,94,-229) (17/7,22/9) -> (17/5,24/7) Glide Reflection Matrix(80,-197,13,-32) (22/9,5/2) -> (6/1,13/2) Hyperbolic Matrix(131,-330,52,-131) (5/2,33/13) -> (5/2,33/13) Reflection Matrix(298,-759,117,-298) (33/13,23/9) -> (33/13,23/9) Reflection Matrix(6031,-15544,2340,-6031) (67/26,116/45) -> (67/26,116/45) Reflection Matrix(4409,-11368,1710,-4409) (116/45,49/19) -> (116/45,49/19) Reflection Matrix(874,-2255,231,-596) (49/19,31/12) -> (34/9,19/5) Hyperbolic Matrix(457,-1198,140,-367) (34/13,21/8) -> (13/4,36/11) Hyperbolic Matrix(114,-301,25,-66) (21/8,8/3) -> (9/2,14/3) Hyperbolic Matrix(259,-706,62,-169) (19/7,30/11) -> (4/1,21/5) Hyperbolic Matrix(2221,-6060,814,-2221) (30/11,101/37) -> (30/11,101/37) Reflection Matrix(1516,-4141,555,-1516) (101/37,41/15) -> (101/37,41/15) Reflection Matrix(169,-476,60,-169) (14/5,17/6) -> (14/5,17/6) Reflection Matrix(35,-102,12,-35) (17/6,3/1) -> (17/6,3/1) Reflection Matrix(34,-105,11,-34) (3/1,35/11) -> (3/1,35/11) Reflection Matrix(351,-1120,110,-351) (35/11,16/5) -> (35/11,16/5) Reflection Matrix(5075,-16638,1548,-5075) (59/18,141/43) -> (59/18,141/43) Reflection Matrix(988,-3243,301,-988) (141/43,23/7) -> (141/43,23/7) Reflection Matrix(1135,-3834,336,-1135) (27/8,71/21) -> (27/8,71/21) Reflection Matrix(356,-1207,105,-356) (71/21,17/5) -> (71/21,17/5) Reflection Matrix(269,-926,52,-179) (24/7,31/9) -> (5/1,26/5) Hyperbolic Matrix(962,-3317,279,-962) (31/9,107/31) -> (31/9,107/31) Reflection Matrix(2355,-8132,682,-2355) (107/31,38/11) -> (107/31,38/11) 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(156,-581,29,-108) (26/7,15/4) -> (16/3,11/2) Hyperbolic Matrix(113,-532,24,-113) (14/3,19/4) -> (14/3,19/4) Reflection Matrix(39,-190,8,-39) (19/4,5/1) -> (19/4,5/1) Reflection Matrix(155,-858,28,-155) (11/2,39/7) -> (11/2,39/7) Reflection Matrix(118,-663,21,-118) (39/7,17/3) -> (39/7,17/3) 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(0,1,1,0) -> Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Matrix(170,-197,107,-124) -> Matrix(2,-1,3,-2) *** -> (1/3,1/1) Matrix(212,-249,63,-74) -> Matrix(4,-3,-3,2) Matrix(167,-202,62,-75) -> Matrix(1,-2,-2,3) Matrix(268,-329,145,-178) -> Matrix(4,-9,1,-2) 3/1 Matrix(371,-458,226,-279) -> Matrix(1,-2,2,-5) Matrix(426,-541,263,-334) -> Matrix(0,1,1,-2) Matrix(262,-335,61,-78) -> Matrix(0,1,1,-6) Matrix(181,-234,140,-181) -> Matrix(-1,14,0,1) (9/7,13/10) -> (7/1,1/0) Matrix(79,-104,60,-79) -> Matrix(1,6,0,-1) (13/10,4/3) -> (-3/1,1/0) Matrix(117,-158,20,-27) -> Matrix(1,2,0,1) 1/0 Matrix(817,-1116,194,-265) -> Matrix(1,2,-2,-5) Matrix(2352,-3215,913,-1248) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(1165,-1596,446,-611) -> Matrix(1,2,0,1) 1/0 Matrix(270,-373,97,-134) -> Matrix(0,-1,1,2) -1/1 Matrix(732,-1015,463,-642) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(653,-910,404,-563) -> Matrix(1,2,2,5) Matrix(134,-189,95,-134) -> Matrix(4,5,-3,-4) (7/5,27/19) -> (-5/3,-1/1) Matrix(379,-540,266,-379) -> Matrix(7,6,-8,-7) (27/19,10/7) -> (-1/1,-3/4) Matrix(227,-326,94,-135) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(74,-109,19,-28) -> Matrix(2,1,-3,-2) *** -> (-1/1,-1/3) Matrix(55,-84,36,-55) -> Matrix(-1,0,2,1) (3/2,14/9) -> (-1/1,0/1) Matrix(197,-308,126,-197) -> Matrix(1,0,6,-1) (14/9,11/7) -> (0/1,1/3) Matrix(464,-731,179,-282) -> Matrix(2,-1,1,0) 1/1 Matrix(1103,-1750,462,-733) -> Matrix(5,-2,-2,1) Matrix(653,-1050,176,-283) -> Matrix(1,2,-2,-3) -1/1 Matrix(1056,-1703,599,-966) -> Matrix(6,1,-1,0) Matrix(4401,-7100,2728,-4401) -> Matrix(-1,0,20,1) (50/31,71/44) -> (-1/10,0/1) Matrix(1847,-2982,1144,-1847) -> Matrix(1,0,10,-1) (71/44,21/13) -> (0/1,1/5) Matrix(1036,-1677,299,-484) -> Matrix(-2,1,1,0) Matrix(280,-457,87,-142) -> Matrix(-2,1,1,0) Matrix(122,-201,17,-28) -> Matrix(2,-1,-3,2) Matrix(86,-145,51,-86) -> Matrix(0,1,1,0) (5/3,29/17) -> (-1/1,1/1) Matrix(407,-696,238,-407) -> Matrix(5,-6,4,-5) (29/17,12/7) -> (1/1,3/2) Matrix(220,-379,101,-174) -> Matrix(0,1,1,-2) Matrix(151,-262,34,-59) -> Matrix(1,-2,-2,3) Matrix(166,-293,17,-30) -> Matrix(0,-1,1,4) Matrix(1045,-1852,382,-677) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(696,-1235,133,-236) -> Matrix(0,1,1,-2) Matrix(297,-530,116,-207) -> Matrix(1,0,0,1) Matrix(361,-652,98,-177) -> Matrix(3,-4,-4,5) Matrix(1340,-2431,409,-742) -> Matrix(2,-5,-1,2) Matrix(390,-713,163,-298) -> Matrix(2,-5,-1,2) Matrix(209,-390,112,-209) -> Matrix(-1,14,0,1) (13/7,15/8) -> (7/1,1/0) Matrix(31,-60,16,-31) -> Matrix(1,2,0,-1) (15/8,2/1) -> (-1/1,1/0) Matrix(219,-472,58,-125) -> Matrix(1,2,-2,-3) -1/1 Matrix(142,-317,43,-96) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(127,-288,56,-127) -> Matrix(3,4,-2,-3) (9/4,16/7) -> (-2/1,-1/1) Matrix(97,-224,42,-97) -> Matrix(-1,0,2,1) (16/7,7/3) -> (-1/1,0/1) Matrix(123,-290,14,-33) -> Matrix(1,0,-2,1) 0/1 Matrix(2133,-5044,902,-2133) -> Matrix(1,0,0,-1) (26/11,97/41) -> (0/1,1/0) Matrix(1844,-4365,779,-1844) -> Matrix(0,1,1,0) (97/41,45/19) -> (-1/1,1/1) Matrix(997,-2362,382,-905) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(504,-1199,95,-226) -> Matrix(0,1,-1,2) 1/1 Matrix(3401,-8100,1428,-3401) -> Matrix(-1,10,0,1) (50/21,81/34) -> (5/1,1/0) Matrix(2107,-5022,884,-2107) -> Matrix(1,10,0,-1) (81/34,31/13) -> (-5/1,1/0) Matrix(321,-782,94,-229) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(80,-197,13,-32) -> Matrix(2,1,-1,0) -1/1 Matrix(131,-330,52,-131) -> Matrix(1,0,0,-1) (5/2,33/13) -> (0/1,1/0) Matrix(298,-759,117,-298) -> Matrix(0,1,1,0) (33/13,23/9) -> (-1/1,1/1) Matrix(6031,-15544,2340,-6031) -> Matrix(3,4,-2,-3) (67/26,116/45) -> (-2/1,-1/1) Matrix(4409,-11368,1710,-4409) -> Matrix(1,2,0,-1) (116/45,49/19) -> (-1/1,1/0) Matrix(874,-2255,231,-596) -> Matrix(0,-1,1,2) -1/1 Matrix(457,-1198,140,-367) -> Matrix(1,-2,0,1) 1/0 Matrix(114,-301,25,-66) -> Matrix(0,-1,1,4) Matrix(259,-706,62,-169) -> Matrix(1,0,-2,1) 0/1 Matrix(2221,-6060,814,-2221) -> Matrix(1,0,0,-1) (30/11,101/37) -> (0/1,1/0) Matrix(1516,-4141,555,-1516) -> Matrix(0,1,1,0) (101/37,41/15) -> (-1/1,1/1) Matrix(169,-476,60,-169) -> Matrix(1,0,0,-1) (14/5,17/6) -> (0/1,1/0) Matrix(35,-102,12,-35) -> Matrix(1,2,0,-1) (17/6,3/1) -> (-1/1,1/0) Matrix(34,-105,11,-34) -> Matrix(0,1,1,0) (3/1,35/11) -> (-1/1,1/1) Matrix(351,-1120,110,-351) -> Matrix(1,0,0,-1) (35/11,16/5) -> (0/1,1/0) Matrix(5075,-16638,1548,-5075) -> Matrix(1,4,0,-1) (59/18,141/43) -> (-2/1,1/0) Matrix(988,-3243,301,-988) -> Matrix(2,3,-1,-2) (141/43,23/7) -> (-3/1,-1/1) Matrix(1135,-3834,336,-1135) -> Matrix(15,16,-14,-15) (27/8,71/21) -> (-8/7,-1/1) Matrix(356,-1207,105,-356) -> Matrix(2,1,-3,-2) (71/21,17/5) -> (-1/1,-1/3) Matrix(269,-926,52,-179) -> Matrix(1,0,0,1) Matrix(962,-3317,279,-962) -> Matrix(0,1,1,0) (31/9,107/31) -> (-1/1,1/1) Matrix(2355,-8132,682,-2355) -> Matrix(1,0,0,-1) (107/31,38/11) -> (0/1,1/0) Matrix(71,-252,20,-71) -> Matrix(3,4,-2,-3) (7/2,18/5) -> (-2/1,-1/1) Matrix(109,-396,30,-109) -> Matrix(7,6,-8,-7) (18/5,11/3) -> (-1/1,-3/4) Matrix(156,-581,29,-108) -> Matrix(2,1,3,2) Matrix(113,-532,24,-113) -> Matrix(-1,0,12,1) (14/3,19/4) -> (-1/6,0/1) Matrix(39,-190,8,-39) -> Matrix(1,0,2,-1) (19/4,5/1) -> (0/1,1/1) Matrix(155,-858,28,-155) -> Matrix(1,0,0,-1) (11/2,39/7) -> (0/1,1/0) Matrix(118,-663,21,-118) -> Matrix(0,1,1,0) (39/7,17/3) -> (-1/1,1/1) Matrix(79,-520,12,-79) -> Matrix(3,4,-2,-3) (13/2,20/3) -> (-2/1,-1/1) Matrix(41,-280,6,-41) -> Matrix(3,2,-4,-3) (20/3,7/1) -> (-1/1,-1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.