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 1/42 -7/15 6/235 -6/13 1/39 -11/24 5/192 -5/11 4/153 -9/20 7/264 -4/9 1/37 -15/34 5/186 -11/25 8/297 -7/16 5/184 -17/39 12/439 -10/23 3/109 -13/30 3/110 -3/7 2/73 -11/26 7/250 -8/19 5/177 -13/31 0/1 -18/43 1/35 -5/12 1/36 -12/29 5/177 -31/75 2/71 -19/46 3/106 -26/63 9/319 -7/17 4/141 -9/22 5/174 -11/27 2/69 -2/5 1/35 -11/28 5/168 -20/51 7/235 -9/23 0/1 -25/64 3/100 -16/41 1/33 -23/59 2/67 -7/18 3/98 -12/31 1/29 -5/13 2/69 -18/47 1/35 -13/34 1/34 -21/55 4/137 -29/76 11/372 -8/21 1/33 -19/50 7/234 -11/29 4/133 -3/8 1/32 -10/27 1/27 -7/19 2/69 -11/30 3/98 -26/71 7/225 -15/41 0/1 -19/52 1/36 -4/11 1/33 -9/25 2/63 -14/39 1/31 -5/14 1/30 -6/17 1/27 -7/20 1/32 -1/3 0/1 -7/22 1/34 -6/19 1/31 -11/35 2/53 -5/16 1/36 -4/13 1/33 -15/49 4/129 -11/36 1/32 -7/23 2/63 -3/10 1/30 -11/37 0/1 -19/64 7/216 -8/27 3/91 -5/17 2/57 -12/41 1/21 -7/24 1/36 -2/7 1/31 -7/25 4/119 -12/43 7/207 -17/61 2/59 -5/18 1/30 -18/65 11/321 -13/47 4/115 -21/76 1/28 -8/29 1/29 -19/69 0/1 -11/40 1/28 -3/11 2/57 -10/37 1/23 -7/26 1/34 -4/15 3/91 -13/49 2/59 -9/34 1/30 -5/19 0/1 -11/42 7/206 -17/65 2/59 -6/23 5/147 -1/4 1/28 -5/21 2/57 -9/38 7/198 -4/17 5/141 -3/13 4/111 -11/48 9/248 -8/35 3/83 -13/57 2/55 -18/79 7/193 -5/22 5/138 -2/9 1/27 -11/50 1/30 -9/41 2/57 -7/32 1/28 -5/23 0/1 -3/14 5/138 -4/19 7/191 -1/5 2/53 -6/31 1/27 -5/26 1/26 -4/21 3/79 -7/37 0/1 -3/16 3/80 -8/43 13/345 -13/70 25/662 -5/27 12/317 -2/11 5/131 -3/17 8/207 -4/23 5/129 -1/6 1/26 -2/13 7/177 -1/7 4/99 -2/15 5/123 -5/38 13/318 -3/23 2/49 -1/8 1/24 -1/9 6/143 0/1 1/21 1/8 5/92 1/7 6/109 3/20 1/18 2/13 11/197 1/6 1/18 2/11 5/87 5/27 6/103 3/16 3/52 7/37 2/35 4/21 1/17 1/5 4/69 4/19 1/17 3/14 11/186 11/51 8/135 8/37 29/489 5/23 6/101 2/9 7/117 5/22 5/82 8/35 1/17 3/13 2/33 1/4 1/16 4/15 5/81 11/41 6/97 7/26 9/146 3/11 8/129 5/18 1/16 7/25 18/287 2/7 5/79 9/31 10/157 7/24 13/204 5/17 12/187 3/10 3/46 4/13 3/47 1/3 2/31 6/17 1/15 5/14 9/134 9/25 16/237 4/11 7/103 19/52 3/44 15/41 2/29 11/30 1/14 7/19 4/59 10/27 1/15 3/8 5/72 11/29 10/141 8/21 5/69 13/34 5/66 5/13 0/1 12/31 3/43 19/49 10/141 7/18 1/14 2/5 1/15 11/27 8/121 9/22 9/134 25/61 8/119 16/39 11/163 7/17 10/147 26/63 11/161 19/46 13/190 12/29 5/73 5/12 5/72 13/31 2/29 34/81 3/43 21/50 1/14 29/69 4/57 8/19 3/43 19/45 2/29 11/26 9/130 14/33 19/273 3/7 4/57 7/16 1/14 11/25 14/195 4/9 5/69 5/11 2/27 1/2 1/14 8/15 1/13 7/13 6/77 6/11 5/63 11/20 7/88 16/29 13/161 5/9 0/1 14/25 3/37 9/16 1/12 22/39 1/11 13/23 2/25 17/30 13/158 21/37 16/193 4/7 3/35 15/26 1/10 26/45 1/11 11/19 0/1 7/12 1/8 3/5 2/27 17/28 11/140 31/51 8/101 14/23 3/37 11/18 1/14 8/13 1/13 13/21 4/53 44/71 1/13 31/50 15/194 49/79 10/129 18/29 11/141 59/95 4/51 41/66 19/242 23/37 10/127 5/8 1/12 12/19 7/87 31/49 6/73 50/79 3/37 69/109 4/51 19/30 5/62 26/41 3/37 7/11 4/49 9/14 1/12 11/17 6/71 2/3 1/11 9/13 4/39 16/23 1/9 7/10 1/6 5/7 2/27 18/25 3/37 31/43 0/1 13/18 5/62 21/29 8/97 8/11 3/35 35/48 9/104 27/37 2/23 19/26 7/78 30/41 1/11 11/15 0/1 14/19 1/15 3/4 1/12 10/13 1/11 17/22 5/54 7/9 2/21 11/14 1/10 4/5 1/9 13/16 3/32 22/27 5/51 9/11 2/19 32/39 1/9 23/28 1/8 37/45 0/1 14/17 3/29 5/6 1/6 6/7 1/11 1/1 0/1 8/7 1/13 7/6 1/10 13/11 2/11 6/5 1/15 17/14 3/34 28/23 1/13 11/9 2/23 38/31 1/11 27/22 5/54 16/13 3/31 21/17 4/41 5/4 1/12 24/19 1/13 19/15 4/45 14/11 1/11 51/40 11/120 37/29 4/43 23/18 1/10 9/7 2/21 13/10 1/10 17/13 4/39 4/3 1/9 15/11 0/1 41/30 1/10 67/49 14/141 93/68 1/10 26/19 7/69 11/8 3/28 40/29 1/9 29/21 8/71 18/13 5/43 25/18 3/26 7/5 2/15 17/12 1/0 27/19 0/1 37/26 1/30 10/7 1/15 23/16 1/12 13/9 4/45 16/11 3/31 3/2 1/10 14/9 1/9 25/16 9/80 11/7 4/35 41/26 3/26 30/19 5/43 19/12 7/60 27/17 2/17 8/5 1/9 29/18 11/90 50/31 15/121 71/44 1/8 92/57 23/183 21/13 4/31 55/34 1/6 89/55 2/19 34/21 1/7 13/8 1/8 31/19 0/1 18/11 1/7 23/14 3/26 28/17 11/91 5/3 2/15 17/10 1/2 29/17 0/1 41/24 1/24 12/7 1/13 43/25 6/67 117/68 15/164 74/43 1/11 31/18 1/10 19/11 0/1 45/26 1/10 71/41 2/19 26/15 1/11 7/4 3/28 44/25 1/9 37/21 16/143 30/17 13/115 53/30 13/114 23/13 2/17 85/48 7/60 62/35 3/25 39/22 1/10 55/31 0/1 16/9 1/9 9/5 0/1 38/21 7/61 29/16 13/112 20/11 7/59 31/17 2/17 11/6 5/42 24/13 5/41 13/7 6/49 15/8 1/8 17/9 8/63 2/1 1/7 13/6 5/38 11/5 2/15 42/19 17/127 31/14 17/126 20/9 7/51 9/4 5/36 16/7 1/7 23/10 13/90 7/3 4/27 26/11 9/59 97/41 2/13 71/30 17/110 45/19 2/13 64/27 7/43 19/8 3/20 50/21 1/7 81/34 3/20 112/47 5/33 31/13 2/13 43/18 7/46 12/5 5/33 29/12 5/32 46/19 13/83 17/7 10/63 39/16 11/68 61/25 8/49 83/34 1/6 22/9 9/55 49/20 1/6 27/11 8/47 5/2 1/6 33/13 0/1 61/24 1/12 28/11 1/9 23/9 2/15 18/7 1/7 67/26 11/78 116/45 1/7 165/64 31/216 49/19 10/69 31/12 3/20 44/17 5/33 13/5 0/1 73/28 1/0 133/51 0/1 60/23 1/13 47/18 1/10 34/13 5/39 21/8 5/36 50/19 1/7 29/11 10/69 8/3 5/33 27/10 1/6 46/17 13/83 19/7 4/25 30/11 1/7 101/37 2/13 172/63 19/123 71/26 9/58 41/15 2/13 52/19 3/19 11/4 7/44 36/13 3/19 133/48 25/156 97/35 22/137 61/22 1/6 25/9 16/99 14/5 9/55 17/6 1/6 20/7 13/77 3/1 2/11 19/6 1/6 35/11 2/11 51/16 3/16 16/5 1/5 13/4 3/16 36/11 3/11 59/18 -1/2 141/43 0/1 82/25 1/15 23/7 0/1 10/3 3/17 27/8 13/72 71/21 2/11 115/34 63/346 44/13 25/137 17/5 12/65 41/12 3/16 24/7 13/69 31/9 10/53 69/20 19/100 107/31 4/21 145/42 37/194 38/11 9/47 7/2 5/26 18/5 1/5 29/8 21/104 11/3 8/39 48/13 25/121 37/10 27/130 26/7 9/43 41/11 6/29 97/26 7/34 56/15 1/5 15/4 5/24 34/9 7/33 53/14 3/14 19/5 14/65 4/1 1/5 21/5 4/17 38/9 11/45 93/22 1/4 55/13 10/39 17/4 1/4 13/3 2/9 35/8 1/4 57/13 8/39 22/5 5/23 9/2 7/30 23/5 6/25 60/13 19/79 37/8 29/120 88/19 55/227 227/49 8/33 139/30 81/334 51/11 8/33 14/3 11/45 19/4 1/4 24/5 19/75 5/1 4/15 26/5 5/19 21/4 1/4 58/11 3/11 37/7 2/7 16/3 3/11 27/5 6/23 38/7 17/63 11/2 5/18 39/7 2/7 67/12 31/108 28/5 13/45 17/3 2/7 6/1 1/3 19/3 16/51 13/2 11/34 20/3 1/3 27/4 23/68 7/1 6/17 15/2 5/14 8/1 5/13 9/1 4/9 10/1 9/19 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(1,0,42,1) Matrix(261,122,430,201) -> Matrix(157,-4,2002,-51) Matrix(173,80,426,197) -> Matrix(77,-2,1194,-31) Matrix(343,158,-940,-433) -> Matrix(77,-2,2580,-67) Matrix(341,156,1270,581) -> Matrix(75,-2,1238,-33) Matrix(253,114,668,301) -> Matrix(227,-6,3216,-85) Matrix(583,262,336,151) -> Matrix(75,-2,788,-21) Matrix(579,256,1400,619) -> Matrix(449,-12,6548,-175) Matrix(245,108,1318,581) -> Matrix(75,-2,1238,-33) Matrix(901,396,248,109) -> Matrix(593,-16,2928,-79) Matrix(1793,782,736,321) -> Matrix(513,-14,3188,-87) Matrix(487,212,-1546,-673) -> Matrix(73,-2,2154,-59) Matrix(327,142,-1384,-601) -> Matrix(71,-2,2024,-57) Matrix(647,280,-2350,-1017) -> Matrix(73,-2,2154,-59) Matrix(637,270,880,373) -> Matrix(215,-6,2616,-73) Matrix(479,202,396,167) -> Matrix(71,-2,888,-25) Matrix(157,66,716,301) -> Matrix(211,-6,3552,-101) Matrix(1107,464,1744,731) -> Matrix(143,-4,1752,-49) Matrix(1267,530,-3244,-1357) -> Matrix(69,-2,2312,-67) Matrix(787,326,548,227) -> Matrix(71,-2,888,-25) Matrix(943,390,-3610,-1493) -> Matrix(1,0,-6,1) Matrix(547,226,2902,1199) -> Matrix(1,0,-18,1) Matrix(5721,2362,2192,905) -> Matrix(71,-2,604,-17) Matrix(2191,904,3604,1487) -> Matrix(425,-12,5348,-151) Matrix(545,224,236,97) -> Matrix(281,-8,1932,-55) Matrix(235,96,-1246,-509) -> Matrix(69,-2,1898,-55) Matrix(231,94,1010,411) -> Matrix(1,0,-18,1) Matrix(681,268,836,329) -> Matrix(135,-4,1384,-41) Matrix(759,298,-3334,-1309) -> Matrix(1,0,-6,1) Matrix(1665,652,452,177) -> Matrix(265,-8,1292,-39) Matrix(829,324,-3774,-1475) -> Matrix(67,-2,1910,-57) Matrix(4749,1852,1736,677) -> Matrix(135,-4,844,-25) Matrix(2711,1056,4372,1703) -> Matrix(397,-12,5128,-155) Matrix(675,262,152,59) -> Matrix(63,-2,284,-9) Matrix(223,86,-822,-317) -> Matrix(1,0,-6,1) Matrix(1195,458,968,371) -> Matrix(67,-2,704,-21) Matrix(371,142,-1936,-741) -> Matrix(67,-2,1776,-53) Matrix(1115,426,-3646,-1393) -> Matrix(1,0,-2,1) Matrix(2531,966,4462,1703) -> Matrix(407,-12,4918,-145) Matrix(3497,1334,1932,737) -> Matrix(337,-10,2932,-87) Matrix(447,170,-1412,-537) -> Matrix(67,-2,2044,-61) Matrix(1927,732,2672,1015) -> Matrix(133,-4,1696,-51) Matrix(813,308,520,197) -> Matrix(265,-8,2352,-71) Matrix(879,326,364,135) -> Matrix(59,-2,384,-13) Matrix(363,134,-1238,-457) -> Matrix(1,0,-6,1) Matrix(365,134,1016,373) -> Matrix(199,-6,2952,-89) Matrix(3269,1198,1378,505) -> Matrix(1,0,-26,1) Matrix(3049,1116,724,265) -> Matrix(127,-4,540,-17) Matrix(361,132,-2754,-1007) -> Matrix(59,-2,1446,-49) Matrix(287,104,218,79) -> Matrix(65,-2,618,-19) Matrix(1079,388,1866,671) -> Matrix(63,-2,662,-21) Matrix(931,334,-3370,-1209) -> Matrix(1,0,-2,1) Matrix(571,202,212,75) -> Matrix(59,-2,384,-13) Matrix(211,74,-1132,-397) -> Matrix(67,-2,1776,-53) Matrix(355,124,-1274,-445) -> Matrix(65,-2,1918,-59) Matrix(407,130,-1556,-497) -> Matrix(61,-2,1800,-59) Matrix(535,168,-2882,-905) -> Matrix(47,-2,1246,-53) Matrix(199,62,536,167) -> Matrix(67,-2,972,-29) Matrix(2853,874,4508,1381) -> Matrix(63,-2,788,-25) Matrix(1719,524,994,303) -> Matrix(63,-2,662,-21) Matrix(461,140,596,181) -> Matrix(125,-4,1344,-43) Matrix(67,20,-526,-157) -> Matrix(59,-2,1446,-49) Matrix(4255,1264,3336,991) -> Matrix(125,-4,1344,-43) Matrix(4839,1436,1048,311) -> Matrix(613,-20,2544,-83) Matrix(913,270,328,97) -> Matrix(179,-6,1104,-37) Matrix(1757,514,1234,361) -> Matrix(1,0,-6,1) Matrix(323,94,780,227) -> Matrix(67,-2,972,-29) Matrix(127,36,194,55) -> Matrix(61,-2,702,-23) Matrix(1659,464,640,179) -> Matrix(119,-4,744,-25) Matrix(1657,462,-7270,-2027) -> Matrix(1,0,-2,1) Matrix(1399,388,256,71) -> Matrix(235,-8,852,-29) Matrix(3815,1056,2164,599) -> Matrix(349,-12,3112,-107) Matrix(4767,1318,1718,475) -> Matrix(111,-4,694,-25) Matrix(443,122,-2284,-629) -> Matrix(59,-2,1564,-53) Matrix(445,122,62,17) -> Matrix(117,-4,322,-11) Matrix(1829,494,1070,289) -> Matrix(1,0,-10,1) Matrix(127,34,564,151) -> Matrix(63,-2,1040,-33) Matrix(625,166,64,17) -> Matrix(179,-6,388,-13) Matrix(1441,382,3942,1045) -> Matrix(117,-4,1726,-59) Matrix(439,116,-2002,-529) -> Matrix(59,-2,1682,-57) Matrix(1745,458,2808,737) -> Matrix(297,-10,3772,-127) Matrix(685,178,558,145) -> Matrix(117,-4,1258,-43) Matrix(787,188,180,43) -> Matrix(1,0,-24,1) Matrix(481,114,2232,529) -> Matrix(737,-26,12444,-439) Matrix(239,56,542,127) -> Matrix(281,-10,3906,-139) Matrix(1793,412,1014,233) -> Matrix(277,-10,2410,-87) Matrix(1609,368,2208,505) -> Matrix(1,0,-16,1) Matrix(2207,504,416,95) -> Matrix(1,0,-24,1) Matrix(415,94,596,135) -> Matrix(55,-2,468,-17) Matrix(1949,430,766,169) -> Matrix(1,0,-18,1) Matrix(1295,282,822,179) -> Matrix(109,-4,954,-35) Matrix(529,114,116,25) -> Matrix(167,-6,696,-25) Matrix(291,62,352,75) -> Matrix(55,-2,468,-17) Matrix(641,134,464,97) -> Matrix(163,-6,1440,-53) Matrix(1997,386,626,121) -> Matrix(107,-4,562,-21) Matrix(1589,302,342,65) -> Matrix(207,-8,854,-33) Matrix(8025,1492,2372,441) -> Matrix(2015,-76,11056,-417) Matrix(509,94,1240,229) -> Matrix(369,-14,5456,-207) Matrix(111,20,394,71) -> Matrix(261,-10,4150,-159) Matrix(893,156,166,29) -> Matrix(51,-2,230,-9) Matrix(943,162,390,67) -> Matrix(307,-12,1970,-77) Matrix(219,34,380,59) -> Matrix(51,-2,536,-21) Matrix(433,66,164,25) -> Matrix(151,-6,1032,-41) Matrix(797,108,214,29) -> Matrix(51,-2,230,-9) Matrix(2069,274,370,49) -> Matrix(883,-36,3066,-125) Matrix(261,32,106,13) -> Matrix(49,-2,270,-11) Matrix(257,28,156,17) -> Matrix(95,-4,784,-33) Matrix(123,-14,290,-33) -> Matrix(149,-8,2142,-115) Matrix(203,-26,164,-21) -> Matrix(37,-2,352,-19) Matrix(883,-130,360,-53) -> Matrix(253,-14,1500,-83) Matrix(1077,-164,440,-67) -> Matrix(359,-20,2172,-121) Matrix(677,-106,198,-31) -> Matrix(357,-20,1910,-107) Matrix(117,-20,158,-27) -> Matrix(35,-2,438,-25) Matrix(1125,-208,622,-115) -> Matrix(103,-6,910,-53) Matrix(4795,-908,2012,-381) -> Matrix(209,-12,1376,-79) Matrix(1235,-236,696,-133) -> Matrix(69,-4,604,-35) Matrix(801,-166,304,-63) -> Matrix(239,-14,1656,-97) Matrix(1099,-234,418,-89) -> Matrix(271,-16,1914,-113) Matrix(3101,-670,4994,-1079) -> Matrix(1147,-68,14658,-869) Matrix(3137,-680,1324,-287) -> Matrix(337,-20,2140,-127) Matrix(1237,-282,2996,-683) -> Matrix(227,-14,3324,-205) Matrix(335,-78,262,-61) -> Matrix(1,0,-6,1) Matrix(109,-28,74,-19) -> Matrix(33,-2,314,-19) Matrix(763,-204,1814,-485) -> Matrix(33,-2,446,-27) Matrix(653,-176,1050,-283) -> Matrix(227,-14,2870,-177) Matrix(181,-50,648,-179) -> Matrix(417,-26,6656,-415) Matrix(1677,-484,1036,-299) -> Matrix(63,-4,520,-33) Matrix(2529,-736,1426,-415) -> Matrix(157,-10,1366,-87) Matrix(677,-198,106,-31) -> Matrix(313,-20,986,-63) Matrix(249,-74,212,-63) -> Matrix(31,-2,264,-17) Matrix(317,-96,142,-43) -> Matrix(29,-2,218,-15) Matrix(457,-142,280,-87) -> Matrix(31,-2,264,-17) Matrix(613,-214,444,-155) -> Matrix(151,-10,1344,-89) Matrix(747,-266,542,-193) -> Matrix(179,-12,1626,-109) Matrix(641,-232,1014,-367) -> Matrix(207,-14,2558,-173) Matrix(2057,-750,842,-307) -> Matrix(293,-20,1802,-123) Matrix(4141,-1516,1516,-555) -> Matrix(233,-16,1500,-103) Matrix(1547,-568,1212,-445) -> Matrix(1,0,-4,1) Matrix(807,-298,436,-161) -> Matrix(205,-14,1684,-115) Matrix(801,-304,166,-63) -> Matrix(197,-14,774,-55) Matrix(1331,-508,600,-229) -> Matrix(109,-8,804,-59) Matrix(1165,-446,1596,-611) -> Matrix(25,-2,288,-23) Matrix(1195,-462,1658,-641) -> Matrix(1,0,-2,1) Matrix(1491,-578,3614,-1401) -> Matrix(283,-20,4146,-293) Matrix(3215,-1248,2352,-913) -> Matrix(55,-4,564,-41) Matrix(297,-116,530,-207) -> Matrix(27,-2,338,-25) Matrix(883,-360,130,-53) -> Matrix(211,-14,618,-41) Matrix(6819,-2794,1828,-749) -> Matrix(29,-2,160,-11) Matrix(5741,-2354,9070,-3719) -> Matrix(59,-4,782,-53) Matrix(713,-298,390,-163) -> Matrix(1,0,-6,1) Matrix(4795,-2012,908,-381) -> Matrix(173,-12,620,-43) Matrix(4601,-1932,874,-367) -> Matrix(85,-6,326,-23) Matrix(8777,-3688,3596,-1511) -> Matrix(55,-4,344,-25) Matrix(3137,-1324,680,-287) -> Matrix(293,-20,1216,-83) Matrix(4365,-1844,1844,-779) -> Matrix(233,-16,1500,-103) Matrix(1743,-740,2810,-1193) -> Matrix(373,-26,4806,-335) Matrix(225,-98,512,-223) -> Matrix(253,-18,3528,-251) Matrix(317,-142,96,-43) -> Matrix(27,-2,176,-13) Matrix(379,-174,220,-101) -> Matrix(27,-2,284,-21) Matrix(481,-254,392,-207) -> Matrix(79,-6,856,-65) Matrix(659,-354,538,-289) -> Matrix(103,-8,1146,-89) Matrix(807,-436,298,-161) -> Matrix(179,-14,1138,-89) Matrix(713,-390,298,-163) -> Matrix(1,0,-6,1) Matrix(2431,-1340,742,-409) -> Matrix(25,-2,38,-3) Matrix(1125,-622,208,-115) -> Matrix(73,-6,280,-23) Matrix(827,-462,324,-181) -> Matrix(25,-2,188,-15) Matrix(1235,-696,236,-133) -> Matrix(49,-4,184,-15) Matrix(1765,-996,2146,-1211) -> Matrix(25,-2,238,-19) Matrix(1321,-748,2174,-1231) -> Matrix(171,-14,2162,-177) Matrix(3551,-2016,2200,-1249) -> Matrix(241,-20,1916,-159) Matrix(1867,-1078,2274,-1313) -> Matrix(1,0,-2,1) Matrix(379,-220,174,-101) -> Matrix(21,-2,158,-15) Matrix(145,-86,86,-51) -> Matrix(1,0,-6,1) Matrix(685,-418,372,-227) -> Matrix(23,-2,196,-17) Matrix(457,-280,142,-87) -> Matrix(25,-2,138,-11) Matrix(541,-334,426,-263) -> Matrix(1,0,-2,1) Matrix(3551,-2200,2016,-1249) -> Matrix(261,-20,2336,-179) Matrix(2697,-1672,1534,-951) -> Matrix(233,-18,2110,-163) Matrix(16571,-10292,3576,-2221) -> Matrix(2195,-172,9048,-709) Matrix(197,-124,170,-107) -> Matrix(25,-2,238,-19) Matrix(17407,-11020,6282,-3977) -> Matrix(377,-30,2350,-187) Matrix(3491,-2212,2028,-1285) -> Matrix(99,-8,1052,-85) Matrix(253,-162,392,-251) -> Matrix(121,-10,1440,-119) Matrix(109,-74,28,-19) -> Matrix(23,-2,104,-9) Matrix(515,-358,82,-57) -> Matrix(35,-4,114,-13) Matrix(189,-134,134,-95) -> Matrix(1,0,-6,1) Matrix(643,-462,508,-365) -> Matrix(25,-2,288,-23) Matrix(613,-444,214,-155) -> Matrix(121,-10,714,-59) Matrix(3325,-2426,1276,-931) -> Matrix(23,-2,104,-9) Matrix(3215,-2352,1248,-913) -> Matrix(43,-4,312,-29) Matrix(849,-622,1036,-759) -> Matrix(21,-2,200,-19) Matrix(743,-546,132,-97) -> Matrix(17,-2,60,-7) Matrix(261,-200,338,-259) -> Matrix(67,-6,726,-65) 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(23,-2,58,-5) Matrix(481,-392,254,-207) -> Matrix(61,-6,478,-47) Matrix(4469,-3674,2524,-2075) -> Matrix(23,-2,196,-17) Matrix(249,-212,74,-63) -> Matrix(25,-2,138,-11) Matrix(197,-170,124,-107) -> Matrix(23,-2,196,-17) Matrix(237,-268,130,-147) -> Matrix(19,-2,162,-17) Matrix(569,-674,168,-199) -> Matrix(5,-2,28,-11) Matrix(1765,-2146,996,-1211) -> Matrix(23,-2,196,-17) Matrix(1867,-2274,1078,-1313) -> Matrix(1,0,-2,1) Matrix(285,-358,82,-103) -> Matrix(43,-4,226,-21) Matrix(4247,-5412,2468,-3145) -> Matrix(45,-4,484,-43) Matrix(261,-338,200,-259) -> Matrix(61,-6,600,-59) Matrix(117,-158,20,-27) -> Matrix(17,-2,60,-7) Matrix(2625,-3586,1516,-2071) -> Matrix(21,-2,200,-19) Matrix(8297,-11346,1962,-2683) -> Matrix(241,-24,954,-95) Matrix(4351,-5952,1030,-1409) -> Matrix(179,-18,726,-73) Matrix(1165,-1596,446,-611) -> Matrix(19,-2,162,-17) Matrix(1195,-1658,462,-641) -> Matrix(1,0,-2,1) Matrix(653,-910,404,-563) -> Matrix(17,-2,128,-15) Matrix(1027,-1458,722,-1025) -> Matrix(1,0,30,1) Matrix(641,-924,188,-271) -> Matrix(93,-8,500,-43) Matrix(581,-844,338,-491) -> Matrix(21,-2,242,-23) Matrix(253,-392,162,-251) -> Matrix(91,-10,810,-89) Matrix(1891,-2984,500,-789) -> Matrix(311,-36,1460,-169) Matrix(641,-1014,232,-367) -> Matrix(121,-14,752,-87) Matrix(1103,-1750,462,-733) -> Matrix(1,0,-2,1) Matrix(653,-1050,176,-283) -> Matrix(117,-14,560,-67) Matrix(211,-340,18,-29) -> Matrix(49,-6,90,-11) Matrix(6249,-10082,3872,-6247) -> Matrix(305,-38,2432,-303) Matrix(4849,-7846,1406,-2275) -> Matrix(43,-4,226,-21) Matrix(385,-628,122,-199) -> Matrix(17,-2,94,-11) Matrix(941,-1544,348,-571) -> Matrix(69,-8,440,-51) Matrix(1321,-2174,748,-1231) -> Matrix(117,-14,1028,-123) Matrix(987,-1682,578,-985) -> Matrix(1,0,22,1) Matrix(7457,-12828,2892,-4975) -> Matrix(177,-16,1228,-111) Matrix(10741,-19022,3934,-6967) -> Matrix(273,-32,1766,-207) Matrix(297,-530,116,-207) -> Matrix(17,-2,128,-15) Matrix(1013,-1838,458,-831) -> Matrix(171,-20,1274,-149) Matrix(241,-450,128,-239) -> Matrix(113,-14,896,-111) Matrix(219,-472,58,-125) -> Matrix(77,-10,362,-47) Matrix(847,-1868,258,-569) -> Matrix(15,-2,98,-13) Matrix(225,-512,98,-223) -> Matrix(127,-18,882,-125) Matrix(123,-290,14,-33) -> Matrix(53,-8,126,-19) Matrix(3923,-9278,1504,-3557) -> Matrix(13,-2,228,-35) Matrix(6983,-16524,2678,-6337) -> Matrix(13,-2,-110,17) Matrix(763,-1814,204,-485) -> Matrix(15,-2,68,-9) Matrix(5509,-13122,2312,-5507) -> Matrix(121,-18,800,-119) Matrix(1237,-2996,282,-683) -> Matrix(89,-14,426,-67) Matrix(3077,-7504,1110,-2707) -> Matrix(309,-50,1922,-311) Matrix(859,-2178,338,-857) -> Matrix(1,0,6,1) Matrix(10441,-26912,4050,-10439) -> Matrix(295,-42,2058,-293) Matrix(1349,-3482,308,-795) -> Matrix(13,-2,72,-11) Matrix(457,-1198,140,-367) -> Matrix(15,-2,68,-9) Matrix(259,-706,62,-169) -> Matrix(1,0,-2,1) Matrix(7475,-20402,2738,-7473) -> Matrix(261,-40,1690,-259) Matrix(2067,-5660,554,-1517) -> Matrix(89,-14,426,-67) Matrix(3709,-10274,1074,-2975) -> Matrix(301,-48,1574,-251) Matrix(205,-578,72,-203) -> Matrix(133,-22,792,-131) Matrix(771,-2450,242,-769) -> Matrix(45,-8,242,-43) Matrix(10063,-32992,2172,-7121) -> Matrix(97,8,400,33) Matrix(9459,-31022,2042,-6697) -> Matrix(175,-8,722,-33) Matrix(2983,-10082,882,-2981) -> Matrix(837,-152,4598,-835) Matrix(269,-926,52,-179) -> Matrix(11,-2,28,-5) Matrix(6635,-22898,1922,-6633) -> Matrix(1177,-224,6174,-1175) Matrix(181,-648,50,-179) -> Matrix(131,-26,650,-129) Matrix(1361,-5032,294,-1087) -> Matrix(627,-130,2590,-537) Matrix(855,-3238,202,-765) -> Matrix(75,-16,286,-61) Matrix(153,-722,32,-151) -> Matrix(121,-30,480,-119) Matrix(547,-3042,98,-545) -> Matrix(253,-72,882,-251) Matrix(121,-800,18,-119) -> Matrix(103,-34,306,-101) 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): 132 Degree of the the map X: 132 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): 264 Minimal number of generators: 45 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: 22 Genus: 12 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/1 13/10 14/9 15/8 2/1 16/7 7/3 17/6 3/1 35/11 71/21 18/5 4/1 9/2 19/4 5/1 6/1 20/3 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 1/21 1/7 6/109 1/6 1/18 1/5 4/69 1/4 1/16 2/7 5/79 7/24 13/204 5/17 12/187 3/10 3/46 1/3 2/31 3/8 5/72 2/5 1/15 5/12 5/72 8/19 3/43 3/7 4/57 1/2 1/14 6/11 5/63 5/9 0/1 4/7 3/35 7/12 1/8 3/5 2/27 14/23 3/37 11/18 1/14 8/13 1/13 5/8 1/12 2/3 1/11 7/10 1/6 5/7 2/27 3/4 1/12 4/5 1/9 5/6 1/6 6/7 1/11 1/1 0/1 6/5 1/15 5/4 1/12 9/7 2/21 13/10 1/10 4/3 1/9 7/5 2/15 3/2 1/10 14/9 1/9 11/7 4/35 8/5 1/9 29/18 11/90 21/13 4/31 13/8 1/8 31/19 0/1 18/11 1/7 5/3 2/15 7/4 3/28 9/5 0/1 20/11 7/59 11/6 5/42 13/7 6/49 15/8 1/8 2/1 1/7 9/4 5/36 16/7 1/7 7/3 4/27 12/5 5/33 5/2 1/6 8/3 5/33 11/4 7/44 14/5 9/55 17/6 1/6 3/1 2/11 19/6 1/6 35/11 2/11 16/5 1/5 13/4 3/16 10/3 3/17 27/8 13/72 71/21 2/11 44/13 25/137 17/5 12/65 7/2 5/26 18/5 1/5 11/3 8/39 4/1 1/5 9/2 7/30 14/3 11/45 19/4 1/4 5/1 4/15 6/1 1/3 13/2 11/34 20/3 1/3 7/1 6/17 8/1 5/13 1/0 1/0 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(42,-5,143,-17) (0/1,1/7) -> (7/24,5/17) Hyperbolic Matrix(120,-19,19,-3) (1/7,1/6) -> (6/1,13/2) Hyperbolic Matrix(97,-17,40,-7) (1/6,1/5) -> (12/5,5/2) Hyperbolic Matrix(38,-9,55,-13) (1/5,1/4) -> (2/3,7/10) Hyperbolic Matrix(72,-19,19,-5) (1/4,2/7) -> (11/3,4/1) Hyperbolic Matrix(357,-104,587,-171) (2/7,7/24) -> (3/5,14/23) Hyperbolic Matrix(426,-127,265,-79) (5/17,3/10) -> (8/5,29/18) Hyperbolic Matrix(89,-27,211,-64) (3/10,1/3) -> (8/19,3/7) Hyperbolic Matrix(68,-25,117,-43) (1/3,3/8) -> (4/7,7/12) Hyperbolic Matrix(67,-26,49,-19) (3/8,2/5) -> (4/3,7/5) Hyperbolic Matrix(97,-40,17,-7) (2/5,5/12) -> (5/1,6/1) Hyperbolic Matrix(714,-299,437,-183) (5/12,8/19) -> (31/19,18/11) Hyperbolic Matrix(32,-15,15,-7) (3/7,1/2) -> (2/1,9/4) Hyperbolic Matrix(165,-89,89,-48) (1/2,6/11) -> (11/6,13/7) Hyperbolic Matrix(253,-139,415,-228) (6/11,5/9) -> (14/23,11/18) Hyperbolic Matrix(89,-50,73,-41) (5/9,4/7) -> (6/5,5/4) Hyperbolic Matrix(202,-119,73,-43) (7/12,3/5) -> (11/4,14/5) Hyperbolic Matrix(457,-280,142,-87) (11/18,8/13) -> (16/5,13/4) Hyperbolic Matrix(86,-53,99,-61) (8/13,5/8) -> (6/7,1/1) Hyperbolic Matrix(112,-71,71,-45) (5/8,2/3) -> (11/7,8/5) Hyperbolic Matrix(188,-133,41,-29) (7/10,5/7) -> (9/2,14/3) Hyperbolic Matrix(67,-49,26,-19) (5/7,3/4) -> (5/2,8/3) Hyperbolic Matrix(65,-51,51,-40) (3/4,4/5) -> (5/4,9/7) Hyperbolic 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(86,-99,53,-61) (1/1,6/5) -> (21/13,13/8) Hyperbolic Matrix(131,-169,100,-129) (9/7,13/10) -> (13/10,4/3) Parabolic Matrix(38,-55,9,-13) (7/5,3/2) -> (4/1,9/2) Hyperbolic Matrix(127,-196,81,-125) (3/2,14/9) -> (14/9,11/7) Parabolic Matrix(1013,-1633,299,-482) (29/18,21/13) -> (44/13,17/5) Hyperbolic Matrix(385,-628,122,-199) (13/8,31/19) -> (3/1,19/6) Hyperbolic Matrix(253,-415,139,-228) (18/11,5/3) -> (20/11,11/6) Hyperbolic Matrix(68,-117,25,-43) (5/3,7/4) -> (8/3,11/4) 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(113,-256,49,-111) (9/4,16/7) -> (16/7,7/3) Parabolic Matrix(89,-211,27,-64) (7/3,12/5) -> (13/4,10/3) Hyperbolic Matrix(103,-289,36,-101) (14/5,17/6) -> (17/6,3/1) Parabolic Matrix(386,-1225,121,-384) (19/6,35/11) -> (35/11,16/5) Parabolic Matrix(1492,-5041,441,-1490) (27/8,71/21) -> (71/21,44/13) Parabolic Matrix(42,-143,5,-17) (17/5,7/2) -> (8/1,1/0) Hyperbolic Matrix(91,-324,25,-89) (7/2,18/5) -> (18/5,11/3) Parabolic Matrix(77,-361,16,-75) (14/3,19/4) -> (19/4,5/1) Parabolic Matrix(61,-400,9,-59) (13/2,20/3) -> (20/3,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,21,1) Matrix(42,-5,143,-17) -> Matrix(93,-5,1451,-78) Matrix(120,-19,19,-3) -> Matrix(89,-5,285,-16) Matrix(97,-17,40,-7) -> Matrix(53,-3,336,-19) Matrix(38,-9,55,-13) -> Matrix(17,-1,171,-10) Matrix(72,-19,19,-5) -> Matrix(49,-3,229,-14) Matrix(357,-104,587,-171) -> Matrix(110,-7,1383,-88) Matrix(426,-127,265,-79) -> Matrix(77,-5,647,-42) Matrix(89,-27,211,-64) -> Matrix(14,-1,211,-15) Matrix(68,-25,117,-43) -> Matrix(15,-1,151,-10) Matrix(67,-26,49,-19) -> Matrix(14,-1,141,-10) Matrix(97,-40,17,-7) -> Matrix(44,-3,147,-10) Matrix(714,-299,437,-183) -> Matrix(43,-3,373,-26) Matrix(32,-15,15,-7) -> Matrix(13,-1,105,-8) Matrix(165,-89,89,-48) -> Matrix(64,-5,525,-41) Matrix(253,-139,415,-228) -> Matrix(38,-3,469,-37) Matrix(89,-50,73,-41) -> Matrix(12,-1,145,-12) Matrix(202,-119,73,-43) -> Matrix(17,-1,103,-6) Matrix(457,-280,142,-87) -> Matrix(25,-2,138,-11) Matrix(86,-53,99,-61) -> Matrix(13,-1,131,-10) Matrix(112,-71,71,-45) -> Matrix(37,-3,321,-26) Matrix(188,-133,41,-29) -> Matrix(17,-1,69,-4) Matrix(67,-49,26,-19) -> Matrix(11,-1,78,-7) Matrix(65,-51,51,-40) -> Matrix(10,-1,111,-11) Matrix(89,-73,50,-41) -> Matrix(9,-1,82,-9) Matrix(249,-212,74,-63) -> Matrix(25,-2,138,-11) Matrix(86,-99,53,-61) -> Matrix(11,-1,89,-8) Matrix(131,-169,100,-129) -> Matrix(31,-3,300,-29) Matrix(38,-55,9,-13) -> Matrix(11,-1,45,-4) Matrix(127,-196,81,-125) -> Matrix(46,-5,405,-44) Matrix(1013,-1633,299,-482) -> Matrix(138,-17,755,-93) Matrix(385,-628,122,-199) -> Matrix(17,-2,94,-11) Matrix(253,-415,139,-228) -> Matrix(26,-3,217,-25) Matrix(68,-117,25,-43) -> Matrix(11,-1,67,-6) Matrix(123,-223,16,-29) -> Matrix(43,-5,112,-13) Matrix(121,-225,64,-119) -> Matrix(57,-7,448,-55) Matrix(113,-256,49,-111) -> Matrix(64,-9,441,-62) Matrix(89,-211,27,-64) -> Matrix(6,-1,43,-7) Matrix(103,-289,36,-101) -> Matrix(67,-11,396,-65) Matrix(386,-1225,121,-384) -> Matrix(23,-4,121,-21) Matrix(1492,-5041,441,-1490) -> Matrix(419,-76,2299,-417) Matrix(42,-143,5,-17) -> Matrix(27,-5,65,-12) Matrix(91,-324,25,-89) -> Matrix(66,-13,325,-64) Matrix(77,-361,16,-75) -> Matrix(61,-15,240,-59) Matrix(61,-400,9,-59) -> Matrix(52,-17,153,-50) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 1 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: 1 Number of equivalence classes of cusps: 1 Genus: 0 Degree of H/liftables -> H/(image of liftables): 132 ----------------------------------------------------------------------- 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 21 1 1/1 0/1 1 23 6/5 1/15 1 23 5/4 1/12 1 23 13/10 1/10 3 1 4/3 1/9 1 23 7/5 2/15 1 23 3/2 1/10 1 23 14/9 1/9 5 1 8/5 1/9 1 23 21/13 4/31 1 23 13/8 1/8 1 23 18/11 1/7 1 23 5/3 2/15 1 23 7/4 3/28 1 23 9/5 0/1 1 23 20/11 7/59 1 23 11/6 5/42 1 23 15/8 1/8 7 1 2/1 1/7 1 23 16/7 1/7 9 1 7/3 4/27 1 23 12/5 5/33 1 23 5/2 1/6 1 23 8/3 5/33 1 23 11/4 7/44 1 23 17/6 1/6 11 1 3/1 2/11 1 23 35/11 2/11 1 1 16/5 1/5 1 23 13/4 3/16 1 23 10/3 3/17 1 23 27/8 13/72 1 23 71/21 2/11 19 1 17/5 12/65 1 23 7/2 5/26 1 23 18/5 1/5 13 1 4/1 1/5 1 23 9/2 7/30 1 23 19/4 1/4 15 1 5/1 4/15 1 23 6/1 1/3 1 23 20/3 1/3 17 1 7/1 6/17 1 23 8/1 5/13 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(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(86,-99,53,-61) (1/1,6/5) -> (21/13,13/8) Hyperbolic Matrix(73,-89,41,-50) (6/5,5/4) -> (7/4,9/5) 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(49,-67,19,-26) (4/3,7/5) -> (5/2,8/3) Glide Reflection Matrix(38,-55,9,-13) (7/5,3/2) -> (4/1,9/2) Hyperbolic Matrix(55,-84,36,-55) (3/2,14/9) -> (3/2,14/9) Reflection Matrix(71,-112,45,-71) (14/9,8/5) -> (14/9,8/5) Reflection Matrix(265,-426,79,-127) (8/5,21/13) -> (10/3,27/8) Glide Reflection Matrix(280,-457,87,-142) (13/8,18/11) -> (16/5,13/4) Glide Reflection Matrix(253,-415,139,-228) (18/11,5/3) -> (20/11,11/6) Hyperbolic Matrix(68,-117,25,-43) (5/3,7/4) -> (8/3,11/4) Hyperbolic 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(15,-32,7,-15) (2/1,16/7) -> (2/1,16/7) Reflection Matrix(97,-224,42,-97) (16/7,7/3) -> (16/7,7/3) Reflection Matrix(89,-211,27,-64) (7/3,12/5) -> (13/4,10/3) Hyperbolic Matrix(40,-97,7,-17) (12/5,5/2) -> (5/1,6/1) Glide 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(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(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(42,-143,5,-17) (17/5,7/2) -> (8/1,1/0) Hyperbolic Matrix(71,-252,20,-71) (7/2,18/5) -> (7/2,18/5) Reflection Matrix(19,-72,5,-19) (18/5,4/1) -> (18/5,4/1) 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(19,-120,3,-19) (6/1,20/3) -> (6/1,20/3) 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(1,0,21,-1) (-1/1,1/1) -> (0/1,2/21) Matrix(86,-99,53,-61) -> Matrix(11,-1,89,-8) Matrix(73,-89,41,-50) -> Matrix(12,-1,107,-9) Matrix(51,-65,40,-51) -> Matrix(11,-1,120,-11) (5/4,13/10) -> (1/12,1/10) Matrix(79,-104,60,-79) -> Matrix(19,-2,180,-19) (13/10,4/3) -> (1/10,1/9) Matrix(49,-67,19,-26) -> Matrix(10,-1,69,-7) Matrix(38,-55,9,-13) -> Matrix(11,-1,45,-4) Matrix(55,-84,36,-55) -> Matrix(19,-2,180,-19) (3/2,14/9) -> (1/10,1/9) Matrix(71,-112,45,-71) -> Matrix(26,-3,225,-26) (14/9,8/5) -> (1/9,3/25) Matrix(265,-426,79,-127) -> Matrix(42,-5,235,-28) Matrix(280,-457,87,-142) -> Matrix(17,-2,93,-11) Matrix(253,-415,139,-228) -> Matrix(26,-3,217,-25) (0/1,2/17).(1/9,3/25).(3/26,1/8) Matrix(68,-117,25,-43) -> Matrix(11,-1,67,-6) Matrix(123,-223,16,-29) -> Matrix(43,-5,112,-13) Matrix(89,-165,48,-89) -> Matrix(41,-5,336,-41) (11/6,15/8) -> (5/42,1/8) Matrix(31,-60,16,-31) -> Matrix(15,-2,112,-15) (15/8,2/1) -> (1/8,1/7) Matrix(15,-32,7,-15) -> Matrix(8,-1,63,-8) (2/1,16/7) -> (1/9,1/7) Matrix(97,-224,42,-97) -> Matrix(55,-8,378,-55) (16/7,7/3) -> (1/7,4/27) Matrix(89,-211,27,-64) -> Matrix(6,-1,43,-7) (1/7,1/5).(0/1,2/13).(1/8,1/6) Matrix(40,-97,7,-17) -> Matrix(19,-3,63,-10) Matrix(67,-187,24,-67) -> Matrix(43,-7,264,-43) (11/4,17/6) -> (7/44,1/6) Matrix(35,-102,12,-35) -> Matrix(23,-4,132,-23) (17/6,3/1) -> (1/6,2/11) Matrix(34,-105,11,-34) -> Matrix(1,0,11,-1) (3/1,35/11) -> (0/1,2/11) Matrix(351,-1120,110,-351) -> Matrix(21,-4,110,-21) (35/11,16/5) -> (2/11,1/5) Matrix(1135,-3834,336,-1135) -> Matrix(287,-52,1584,-287) (27/8,71/21) -> (13/72,2/11) Matrix(356,-1207,105,-356) -> Matrix(131,-24,715,-131) (71/21,17/5) -> (2/11,12/65) Matrix(42,-143,5,-17) -> Matrix(27,-5,65,-12) Matrix(71,-252,20,-71) -> Matrix(51,-10,260,-51) (7/2,18/5) -> (5/26,1/5) Matrix(19,-72,5,-19) -> Matrix(14,-3,65,-14) (18/5,4/1) -> (1/5,3/13) Matrix(37,-171,8,-37) -> Matrix(29,-7,120,-29) (9/2,19/4) -> (7/30,1/4) Matrix(39,-190,8,-39) -> Matrix(31,-8,120,-31) (19/4,5/1) -> (1/4,4/15) Matrix(19,-120,3,-19) -> Matrix(16,-5,51,-16) (6/1,20/3) -> (5/17,1/3) Matrix(41,-280,6,-41) -> Matrix(35,-12,102,-35) (20/3,7/1) -> (1/3,6/17) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.