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): 1080 Minimal number of generators: 181 Number of equivalence classes of cusps: 54 Genus: 64 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -57/37 -19/17 0/1 1/1 19/16 19/15 19/14 19/13 3/2 19/12 19/11 2/1 19/8 12/5 5/2 19/7 57/20 3/1 19/6 95/29 76/23 38/11 7/2 18/5 76/21 11/3 152/41 19/5 4/1 38/9 17/4 13/3 9/2 114/25 14/3 19/4 5/1 16/3 38/7 11/2 17/3 57/10 6/1 19/3 13/2 7/1 15/2 38/5 23/3 8/1 9/1 19/2 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 -4/9 -7/1 -1/3 -13/2 -5/14 -19/3 -1/3 -6/1 -2/7 -23/4 -3/8 -17/3 -1/3 -11/2 -3/10 -16/3 -4/15 -5/1 -1/3 -19/4 -1/4 -14/3 -2/9 -37/8 -5/24 -23/5 -1/3 -32/7 -4/17 -9/2 -1/6 -13/3 -1/3 -4/1 0/1 -19/5 -1/4 -15/4 -1/4 -41/11 -3/13 -26/7 -2/11 -37/10 -3/10 -11/3 -1/5 -18/5 -2/5 -7/2 -1/4 -24/7 -4/19 -17/5 -1/5 -27/8 -1/4 -37/11 -7/33 -10/3 -2/11 -23/7 -1/3 -13/4 -3/14 -16/5 -4/19 -19/6 -1/5 -3/1 -1/5 -20/7 -8/47 -17/6 -1/6 -14/5 -2/11 -39/14 -5/26 -64/23 -12/65 -25/9 -7/39 -11/4 -1/6 -19/7 -1/6 -8/3 -4/25 -37/14 -1/4 -29/11 -5/31 -21/8 -1/6 -34/13 -2/13 -13/5 -1/7 -31/12 -1/6 -18/7 -10/63 -41/16 -11/70 -23/9 -3/19 -28/11 -16/103 -5/2 -3/20 -22/9 -6/41 -39/16 -11/76 -17/7 -1/7 -29/12 -1/6 -70/29 -10/67 -41/17 -9/61 -12/5 -8/55 -19/8 -1/7 -7/3 -1/7 -30/13 -14/101 -23/10 -11/80 -39/17 -19/139 -16/7 -4/29 -25/11 -1/7 -9/4 -7/52 -20/9 -16/121 -11/5 -3/23 -13/6 -9/70 -15/7 -7/55 -2/1 -2/17 -13/7 -9/83 -11/6 -3/28 -9/5 -7/67 -16/9 -4/39 -39/22 -19/184 -23/13 -11/107 -7/4 -1/10 -19/11 -1/10 -12/7 -8/81 -41/24 -9/92 -29/17 -1/11 -17/10 -1/10 -56/33 -4/39 -95/56 -1/10 -39/23 -11/111 -22/13 -6/61 -5/3 -3/31 -23/14 -3/32 -41/25 -11/117 -18/11 -10/107 -13/8 -1/10 -21/13 -1/11 -29/18 -5/54 -8/5 -4/43 -19/12 -1/11 -11/7 -1/11 -25/16 -7/80 -39/25 -5/59 -14/9 -2/23 -17/11 -1/11 -37/24 -7/76 -57/37 -1/11 -20/13 -8/89 -3/2 -1/12 -19/13 -1/12 -16/11 -4/49 -13/9 -3/37 -36/25 -8/103 -95/66 -1/13 -59/41 -1/13 -23/16 -1/14 -33/23 -1/17 -76/53 0/1 -43/30 -1/6 -10/7 -2/23 -57/40 -1/12 -47/33 -9/109 -37/26 -7/86 -27/19 -1/13 -17/12 -1/12 -24/17 -4/49 -31/22 -5/62 -38/27 -2/25 -7/5 -1/13 -25/18 -3/40 -18/13 -2/29 -47/34 -1/22 -76/55 0/1 -29/21 -1/7 -11/8 -1/12 -37/27 -3/41 -63/46 -1/18 -152/111 0/1 -89/65 -1/5 -26/19 -2/23 -41/30 -3/38 -15/11 -1/13 -19/14 -1/13 -4/3 0/1 -21/16 -1/12 -38/29 -2/25 -17/13 -1/13 -13/10 -1/14 -22/17 -2/27 -9/7 -1/11 -41/32 -5/62 -114/89 -2/25 -73/57 -9/113 -32/25 -4/51 -23/18 -1/14 -37/29 -5/61 -14/11 -2/25 -19/15 -1/13 -5/4 -1/14 -16/13 -4/53 -27/22 -7/94 -38/31 -2/27 -11/9 -3/41 -17/14 -1/14 -57/47 -1/14 -40/33 -12/169 -23/19 -3/43 -6/5 -2/27 -19/16 -1/14 -13/11 -5/71 -7/6 -1/14 -15/13 -7/101 -38/33 -2/29 -23/20 -11/160 -8/7 -4/59 -9/8 -5/74 -19/17 -1/15 -10/9 -6/91 -1/1 -1/17 0/1 0/1 1/1 1/17 8/7 4/59 7/6 1/14 13/11 5/71 19/16 1/14 6/5 2/27 23/19 3/43 17/14 1/14 11/9 3/41 16/13 4/53 5/4 1/14 19/15 1/13 14/11 2/25 37/29 5/61 23/18 1/14 32/25 4/51 9/7 1/11 13/10 1/14 4/3 0/1 19/14 1/13 15/11 1/13 41/30 3/38 26/19 2/23 37/27 3/41 11/8 1/12 18/13 2/29 7/5 1/13 24/17 4/49 17/12 1/12 27/19 1/13 37/26 7/86 10/7 2/23 23/16 1/14 13/9 3/37 16/11 4/49 19/13 1/12 3/2 1/12 20/13 8/89 17/11 1/11 14/9 2/23 39/25 5/59 64/41 12/139 25/16 7/80 11/7 1/11 19/12 1/11 8/5 4/43 37/23 1/13 29/18 5/54 21/13 1/11 34/21 2/21 13/8 1/10 31/19 1/11 18/11 10/107 41/25 11/117 23/14 3/32 28/17 16/169 5/3 3/31 22/13 6/61 39/23 11/111 17/10 1/10 29/17 1/11 70/41 10/103 41/24 9/92 12/7 8/81 19/11 1/10 7/4 1/10 30/17 14/137 23/13 11/107 39/22 19/184 16/9 4/39 25/14 1/10 9/5 7/67 20/11 16/151 11/6 3/28 13/7 9/83 15/8 7/64 2/1 2/17 13/6 9/70 11/5 3/23 9/4 7/52 16/7 4/29 39/17 19/139 23/10 11/80 7/3 1/7 19/8 1/7 12/5 8/55 41/17 9/61 29/12 1/6 17/7 1/7 56/23 4/29 95/39 1/7 39/16 11/76 22/9 6/41 5/2 3/20 23/9 3/19 41/16 11/70 18/7 10/63 13/5 1/7 21/8 1/6 29/11 5/31 8/3 4/25 19/7 1/6 11/4 1/6 25/9 7/39 39/14 5/26 14/5 2/11 17/6 1/6 37/13 7/43 57/20 1/6 20/7 8/47 3/1 1/5 19/6 1/5 16/5 4/19 13/4 3/14 36/11 8/33 95/29 1/4 59/18 1/4 23/7 1/3 33/10 1/0 76/23 0/1 43/13 1/11 10/3 2/11 57/17 1/5 47/14 9/44 37/11 7/33 27/8 1/4 17/5 1/5 24/7 4/19 31/9 5/23 38/11 2/9 7/2 1/4 25/7 3/11 18/5 2/5 47/13 -1/5 76/21 0/1 29/8 1/10 11/3 1/5 37/10 3/10 63/17 -1/1 152/41 0/1 89/24 1/12 26/7 2/11 41/11 3/13 15/4 1/4 19/5 1/4 4/1 0/1 21/5 1/5 38/9 2/9 17/4 1/4 13/3 1/3 22/5 2/7 9/2 1/6 41/9 5/23 114/25 2/9 73/16 9/40 32/7 4/17 23/5 1/3 37/8 5/24 14/3 2/9 19/4 1/4 5/1 1/3 16/3 4/15 27/5 7/25 38/7 2/7 11/2 3/10 17/3 1/3 57/10 1/3 40/7 12/35 23/4 3/8 6/1 2/7 19/3 1/3 13/2 5/14 7/1 1/3 15/2 7/18 38/5 2/5 23/3 11/27 8/1 4/9 9/1 5/11 19/2 1/2 10/1 6/11 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(37,304,-14,-115) (-8/1,1/0) -> (-8/3,-37/14) Hyperbolic Matrix(37,266,-16,-115) (-8/1,-7/1) -> (-7/3,-30/13) Hyperbolic Matrix(75,494,46,303) (-7/1,-13/2) -> (13/8,31/19) Hyperbolic Matrix(77,494,12,77) (-13/2,-19/3) -> (19/3,13/2) Hyperbolic Matrix(37,228,6,37) (-19/3,-6/1) -> (6/1,19/3) Hyperbolic Matrix(151,874,118,683) (-6/1,-23/4) -> (23/18,32/25) Hyperbolic Matrix(305,1748,-212,-1215) (-23/4,-17/3) -> (-59/41,-23/16) Hyperbolic Matrix(115,646,34,191) (-17/3,-11/2) -> (27/8,17/5) Hyperbolic Matrix(113,608,-92,-495) (-11/2,-16/3) -> (-16/13,-27/22) Hyperbolic Matrix(37,190,22,113) (-16/3,-5/1) -> (5/3,22/13) Hyperbolic Matrix(39,190,8,39) (-5/1,-19/4) -> (19/4,5/1) Hyperbolic Matrix(113,532,24,113) (-19/4,-14/3) -> (14/3,19/4) Hyperbolic Matrix(229,1064,82,381) (-14/3,-37/8) -> (39/14,14/5) Hyperbolic Matrix(379,1748,214,987) (-37/8,-23/5) -> (23/13,39/22) Hyperbolic Matrix(191,874,158,723) (-23/5,-32/7) -> (6/5,23/19) Hyperbolic Matrix(343,1558,-142,-645) (-32/7,-9/2) -> (-29/12,-70/29) Hyperbolic Matrix(77,342,-34,-151) (-9/2,-13/3) -> (-25/11,-9/4) Hyperbolic Matrix(115,494,-44,-189) (-13/3,-4/1) -> (-34/13,-13/5) Hyperbolic Matrix(39,152,10,39) (-4/1,-19/5) -> (19/5,4/1) Hyperbolic Matrix(151,570,40,151) (-19/5,-15/4) -> (15/4,19/5) Hyperbolic Matrix(417,1558,254,949) (-15/4,-41/11) -> (41/25,23/14) Hyperbolic Matrix(419,1558,174,647) (-41/11,-26/7) -> (12/5,41/17) Hyperbolic Matrix(913,3382,-328,-1215) (-26/7,-37/10) -> (-39/14,-64/23) Hyperbolic Matrix(381,1406,268,989) (-37/10,-11/3) -> (27/19,37/26) Hyperbolic Matrix(115,418,-52,-189) (-11/3,-18/5) -> (-20/9,-11/5) Hyperbolic Matrix(191,684,-74,-265) (-18/5,-7/2) -> (-31/12,-18/7) Hyperbolic Matrix(265,912,-188,-647) (-7/2,-24/7) -> (-24/17,-31/22) Hyperbolic Matrix(189,646,122,417) (-24/7,-17/5) -> (17/11,14/9) Hyperbolic Matrix(191,646,34,115) (-17/5,-27/8) -> (11/2,17/3) Hyperbolic Matrix(417,1406,304,1025) (-27/8,-37/11) -> (37/27,11/8) Hyperbolic Matrix(113,380,-102,-343) (-37/11,-10/3) -> (-10/9,-1/1) Hyperbolic Matrix(265,874,-104,-343) (-10/3,-23/7) -> (-23/9,-28/11) Hyperbolic Matrix(151,494,-70,-229) (-23/7,-13/4) -> (-13/6,-15/7) Hyperbolic Matrix(189,608,106,341) (-13/4,-16/5) -> (16/9,25/14) Hyperbolic Matrix(191,608,60,191) (-16/5,-19/6) -> (19/6,16/5) Hyperbolic Matrix(37,114,12,37) (-19/6,-3/1) -> (3/1,19/6) Hyperbolic Matrix(305,874,186,533) (-3/1,-20/7) -> (18/11,41/25) Hyperbolic Matrix(455,1292,-268,-761) (-20/7,-17/6) -> (-17/10,-56/33) Hyperbolic Matrix(229,646,162,457) (-17/6,-14/5) -> (24/17,17/12) Hyperbolic Matrix(381,1064,82,229) (-14/5,-39/14) -> (37/8,14/3) Hyperbolic Matrix(2281,6346,-1666,-4635) (-64/23,-25/9) -> (-89/65,-26/19) Hyperbolic Matrix(151,418,82,227) (-25/9,-11/4) -> (11/6,13/7) Hyperbolic Matrix(153,418,56,153) (-11/4,-19/7) -> (19/7,11/4) Hyperbolic Matrix(113,304,42,113) (-19/7,-8/3) -> (8/3,19/7) Hyperbolic Matrix(1065,2812,-748,-1975) (-37/14,-29/11) -> (-47/33,-37/26) Hyperbolic Matrix(419,1102,246,647) (-29/11,-21/8) -> (17/10,29/17) Hyperbolic Matrix(305,798,-232,-607) (-21/8,-34/13) -> (-4/3,-21/16) Hyperbolic Matrix(191,494,162,419) (-13/5,-31/12) -> (7/6,13/11) Hyperbolic Matrix(341,874,222,569) (-18/7,-41/16) -> (3/2,20/13) Hyperbolic Matrix(609,1558,446,1141) (-41/16,-23/9) -> (15/11,41/30) Hyperbolic Matrix(493,1254,-344,-875) (-28/11,-5/2) -> (-43/30,-10/7) Hyperbolic Matrix(77,190,62,153) (-5/2,-22/9) -> (16/13,5/4) Hyperbolic Matrix(607,1482,342,835) (-22/9,-39/16) -> (39/22,16/9) Hyperbolic Matrix(531,1292,-344,-837) (-39/16,-17/7) -> (-17/11,-37/24) Hyperbolic Matrix(455,1102,282,683) (-17/7,-29/12) -> (29/18,21/13) Hyperbolic Matrix(2661,6422,-2078,-5015) (-70/29,-41/17) -> (-73/57,-32/25) Hyperbolic Matrix(647,1558,174,419) (-41/17,-12/5) -> (26/7,41/11) Hyperbolic Matrix(191,456,80,191) (-12/5,-19/8) -> (19/8,12/5) Hyperbolic Matrix(113,266,48,113) (-19/8,-7/3) -> (7/3,19/8) Hyperbolic Matrix(379,874,-330,-761) (-30/13,-23/10) -> (-23/20,-8/7) Hyperbolic Matrix(761,1748,596,1369) (-23/10,-39/17) -> (37/29,23/18) Hyperbolic Matrix(647,1482,382,875) (-39/17,-16/7) -> (22/13,39/23) Hyperbolic Matrix(267,608,184,419) (-16/7,-25/11) -> (13/9,16/11) Hyperbolic Matrix(495,1102,-358,-797) (-9/4,-20/9) -> (-18/13,-47/34) Hyperbolic Matrix(191,418,122,267) (-11/5,-13/6) -> (25/16,11/7) Hyperbolic Matrix(303,646,-250,-533) (-15/7,-2/1) -> (-40/33,-23/19) Hyperbolic Matrix(265,494,-184,-343) (-2/1,-13/7) -> (-13/9,-36/25) Hyperbolic Matrix(227,418,82,151) (-13/7,-11/6) -> (11/4,25/9) Hyperbolic Matrix(229,418,-166,-303) (-11/6,-9/5) -> (-29/21,-11/8) Hyperbolic Matrix(191,342,-148,-265) (-9/5,-16/9) -> (-22/17,-9/7) Hyperbolic Matrix(835,1482,342,607) (-16/9,-39/22) -> (39/16,22/9) Hyperbolic Matrix(987,1748,214,379) (-39/22,-23/13) -> (23/5,37/8) Hyperbolic Matrix(151,266,-130,-229) (-23/13,-7/4) -> (-7/6,-15/13) Hyperbolic Matrix(153,266,88,153) (-7/4,-19/11) -> (19/11,7/4) Hyperbolic Matrix(265,456,154,265) (-19/11,-12/7) -> (12/7,19/11) Hyperbolic Matrix(911,1558,666,1139) (-12/7,-41/24) -> (41/30,26/19) Hyperbolic Matrix(913,1558,-712,-1215) (-41/24,-29/17) -> (-9/7,-41/32) Hyperbolic Matrix(647,1102,246,419) (-29/17,-17/10) -> (21/8,29/11) Hyperbolic Matrix(3001,5092,1052,1785) (-56/33,-95/56) -> (57/20,20/7) Hyperbolic Matrix(3383,5738,1188,2015) (-95/56,-39/23) -> (37/13,57/20) Hyperbolic Matrix(875,1482,382,647) (-39/23,-22/13) -> (16/7,39/17) Hyperbolic Matrix(113,190,22,37) (-22/13,-5/3) -> (5/1,16/3) Hyperbolic Matrix(531,874,-370,-609) (-5/3,-23/14) -> (-23/16,-33/23) Hyperbolic Matrix(949,1558,254,417) (-23/14,-41/25) -> (41/11,15/4) Hyperbolic Matrix(533,874,186,305) (-41/25,-18/11) -> (20/7,3/1) Hyperbolic Matrix(419,684,-302,-493) (-18/11,-13/8) -> (-25/18,-18/13) Hyperbolic Matrix(305,494,-234,-379) (-13/8,-21/13) -> (-17/13,-13/10) Hyperbolic Matrix(683,1102,282,455) (-21/13,-29/18) -> (29/12,17/7) Hyperbolic Matrix(189,304,-166,-267) (-29/18,-8/5) -> (-8/7,-9/8) Hyperbolic Matrix(191,304,120,191) (-8/5,-19/12) -> (19/12,8/5) Hyperbolic Matrix(265,418,168,265) (-19/12,-11/7) -> (11/7,19/12) Hyperbolic Matrix(267,418,122,191) (-11/7,-25/16) -> (13/6,11/5) Hyperbolic Matrix(2167,3382,-1582,-2469) (-25/16,-39/25) -> (-37/27,-63/46) Hyperbolic Matrix(683,1064,536,835) (-39/25,-14/9) -> (14/11,37/29) Hyperbolic Matrix(417,646,122,189) (-14/9,-17/11) -> (17/5,24/7) Hyperbolic Matrix(3723,5738,1528,2355) (-37/24,-57/37) -> (95/39,39/16) Hyperbolic Matrix(3307,5092,1358,2091) (-57/37,-20/13) -> (56/23,95/39) Hyperbolic Matrix(569,874,222,341) (-20/13,-3/2) -> (41/16,18/7) Hyperbolic Matrix(77,114,52,77) (-3/2,-19/13) -> (19/13,3/2) Hyperbolic Matrix(417,608,286,417) (-19/13,-16/11) -> (16/11,19/13) Hyperbolic Matrix(341,494,78,113) (-16/11,-13/9) -> (13/3,22/5) Hyperbolic Matrix(4065,5852,712,1025) (-36/25,-95/66) -> (57/10,40/7) Hyperbolic Matrix(3459,4978,608,875) (-95/66,-59/41) -> (17/3,57/10) Hyperbolic Matrix(4027,5776,1218,1747) (-33/23,-76/53) -> (76/23,43/13) Hyperbolic Matrix(4029,5776,1220,1749) (-76/53,-43/30) -> (33/10,76/23) Hyperbolic Matrix(533,760,54,77) (-10/7,-57/40) -> (19/2,10/1) Hyperbolic Matrix(987,1406,106,151) (-57/40,-47/33) -> (9/1,19/2) Hyperbolic Matrix(989,1406,268,381) (-37/26,-27/19) -> (11/3,37/10) Hyperbolic Matrix(455,646,374,531) (-27/19,-17/12) -> (17/14,11/9) Hyperbolic Matrix(457,646,162,229) (-17/12,-24/17) -> (14/5,17/6) Hyperbolic Matrix(1025,1444,296,417) (-31/22,-38/27) -> (38/11,7/2) Hyperbolic Matrix(1027,1444,298,419) (-38/27,-7/5) -> (31/9,38/11) Hyperbolic Matrix(191,266,28,39) (-7/5,-25/18) -> (13/2,7/1) Hyperbolic Matrix(4179,5776,1154,1595) (-47/34,-76/55) -> (76/21,29/8) Hyperbolic Matrix(4181,5776,1156,1597) (-76/55,-29/21) -> (47/13,76/21) Hyperbolic Matrix(1025,1406,304,417) (-11/8,-37/27) -> (37/11,27/8) Hyperbolic Matrix(16871,23104,4550,6231) (-63/46,-152/111) -> (152/41,89/24) Hyperbolic Matrix(16873,23104,4552,6233) (-152/111,-89/65) -> (63/17,152/41) Hyperbolic Matrix(1139,1558,666,911) (-26/19,-41/30) -> (41/24,12/7) Hyperbolic Matrix(1141,1558,446,609) (-41/30,-15/11) -> (23/9,41/16) Hyperbolic Matrix(419,570,308,419) (-15/11,-19/14) -> (19/14,15/11) Hyperbolic Matrix(113,152,84,113) (-19/14,-4/3) -> (4/3,19/14) Hyperbolic Matrix(1101,1444,260,341) (-21/16,-38/29) -> (38/9,17/4) Hyperbolic Matrix(1103,1444,262,343) (-38/29,-17/13) -> (21/5,38/9) Hyperbolic Matrix(381,494,118,153) (-13/10,-22/17) -> (16/5,13/4) Hyperbolic Matrix(10145,12996,2224,2849) (-41/32,-114/89) -> (114/25,73/16) Hyperbolic Matrix(10147,12996,2226,2851) (-114/89,-73/57) -> (41/9,114/25) Hyperbolic Matrix(683,874,118,151) (-32/25,-23/18) -> (23/4,6/1) Hyperbolic Matrix(1369,1748,596,761) (-23/18,-37/29) -> (39/17,23/10) Hyperbolic Matrix(835,1064,536,683) (-37/29,-14/11) -> (14/9,39/25) Hyperbolic Matrix(419,532,330,419) (-14/11,-19/15) -> (19/15,14/11) Hyperbolic Matrix(151,190,120,151) (-19/15,-5/4) -> (5/4,19/15) Hyperbolic Matrix(153,190,62,77) (-5/4,-16/13) -> (22/9,5/2) Hyperbolic Matrix(1177,1444,216,265) (-27/22,-38/31) -> (38/7,11/2) Hyperbolic Matrix(1179,1444,218,267) (-38/31,-11/9) -> (27/5,38/7) Hyperbolic Matrix(531,646,374,455) (-11/9,-17/14) -> (17/12,27/19) Hyperbolic Matrix(4103,4978,1252,1519) (-17/14,-57/47) -> (95/29,59/18) Hyperbolic Matrix(4827,5852,1474,1787) (-57/47,-40/33) -> (36/11,95/29) Hyperbolic Matrix(723,874,158,191) (-23/19,-6/5) -> (32/7,23/5) Hyperbolic Matrix(191,228,160,191) (-6/5,-19/16) -> (19/16,6/5) Hyperbolic Matrix(417,494,352,417) (-19/16,-13/11) -> (13/11,19/16) Hyperbolic Matrix(227,266,64,75) (-13/11,-7/6) -> (7/2,25/7) Hyperbolic Matrix(1253,1444,164,189) (-15/13,-38/33) -> (38/5,23/3) Hyperbolic Matrix(1255,1444,166,191) (-38/33,-23/20) -> (15/2,38/5) Hyperbolic Matrix(1255,1406,374,419) (-9/8,-19/17) -> (57/17,47/14) Hyperbolic Matrix(683,760,204,227) (-19/17,-10/9) -> (10/3,57/17) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(267,-304,166,-189) (1/1,8/7) -> (8/5,37/23) Hyperbolic Matrix(229,-266,130,-151) (8/7,7/6) -> (7/4,30/17) Hyperbolic Matrix(1443,-1748,440,-533) (23/19,17/14) -> (59/18,23/7) Hyperbolic Matrix(495,-608,92,-113) (11/9,16/13) -> (16/3,27/5) Hyperbolic Matrix(1215,-1558,712,-913) (32/25,9/7) -> (29/17,70/41) Hyperbolic Matrix(265,-342,148,-191) (9/7,13/10) -> (25/14,9/5) Hyperbolic Matrix(379,-494,234,-305) (13/10,4/3) -> (34/21,13/8) Hyperbolic Matrix(2469,-3382,1582,-2167) (26/19,37/27) -> (39/25,64/41) Hyperbolic Matrix(303,-418,166,-229) (11/8,18/13) -> (20/11,11/6) Hyperbolic Matrix(493,-684,302,-419) (18/13,7/5) -> (31/19,18/11) Hyperbolic Matrix(647,-912,188,-265) (7/5,24/17) -> (24/7,31/9) Hyperbolic Matrix(267,-380,26,-37) (37/26,10/7) -> (10/1,1/0) Hyperbolic Matrix(609,-874,370,-531) (10/7,23/16) -> (23/14,28/17) Hyperbolic Matrix(343,-494,184,-265) (23/16,13/9) -> (13/7,15/8) Hyperbolic Matrix(837,-1292,344,-531) (20/13,17/11) -> (17/7,56/23) Hyperbolic Matrix(4065,-6346,1096,-1711) (64/41,25/16) -> (89/24,26/7) Hyperbolic Matrix(1747,-2812,520,-837) (37/23,29/18) -> (47/14,37/11) Hyperbolic Matrix(493,-798,118,-191) (21/13,34/21) -> (4/1,21/5) Hyperbolic Matrix(761,-1254,230,-379) (28/17,5/3) -> (43/13,10/3) Hyperbolic Matrix(761,-1292,268,-455) (39/23,17/10) -> (17/6,37/13) Hyperbolic Matrix(3761,-6422,824,-1407) (70/41,41/24) -> (73/16,32/7) Hyperbolic Matrix(495,-874,64,-113) (30/17,23/13) -> (23/3,8/1) Hyperbolic Matrix(607,-1102,168,-305) (9/5,20/11) -> (18/5,47/13) Hyperbolic Matrix(343,-646,60,-113) (15/8,2/1) -> (40/7,23/4) Hyperbolic Matrix(229,-494,70,-151) (2/1,13/6) -> (13/4,36/11) Hyperbolic Matrix(189,-418,52,-115) (11/5,9/4) -> (29/8,11/3) Hyperbolic Matrix(151,-342,34,-77) (9/4,16/7) -> (22/5,9/2) Hyperbolic Matrix(115,-266,16,-37) (23/10,7/3) -> (7/1,15/2) Hyperbolic Matrix(645,-1558,142,-343) (41/17,29/12) -> (9/2,41/9) Hyperbolic Matrix(343,-874,104,-265) (5/2,23/9) -> (23/7,33/10) Hyperbolic Matrix(265,-684,74,-191) (18/7,13/5) -> (25/7,18/5) Hyperbolic Matrix(189,-494,44,-115) (13/5,21/8) -> (17/4,13/3) Hyperbolic Matrix(115,-304,14,-37) (29/11,8/3) -> (8/1,9/1) Hyperbolic Matrix(1215,-3382,328,-913) (25/9,39/14) -> (37/10,63/17) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(37,304,-14,-115) -> Matrix(1,0,-4,1) Matrix(37,266,-16,-115) -> Matrix(17,6,-122,-43) Matrix(75,494,46,303) -> Matrix(17,6,184,65) Matrix(77,494,12,77) -> Matrix(29,10,84,29) Matrix(37,228,6,37) -> Matrix(13,4,42,13) Matrix(151,874,118,683) -> Matrix(5,2,62,25) Matrix(305,1748,-212,-1215) -> Matrix(11,4,-146,-53) Matrix(115,646,34,191) -> Matrix(7,2,38,11) Matrix(113,608,-92,-495) -> Matrix(29,8,-388,-107) Matrix(37,190,22,113) -> Matrix(9,2,94,21) Matrix(39,190,8,39) -> Matrix(7,2,24,7) Matrix(113,532,24,113) -> Matrix(17,4,72,17) Matrix(229,1064,82,381) -> Matrix(1,0,10,1) Matrix(379,1748,214,987) -> Matrix(23,4,224,39) Matrix(191,874,158,723) -> Matrix(9,2,130,29) Matrix(343,1558,-142,-645) -> Matrix(11,2,-72,-13) Matrix(77,342,-34,-151) -> Matrix(5,2,-38,-15) Matrix(115,494,-44,-189) -> Matrix(7,2,-46,-13) Matrix(39,152,10,39) -> Matrix(1,0,8,1) Matrix(151,570,40,151) -> Matrix(9,2,40,9) Matrix(417,1558,254,949) -> Matrix(5,2,52,21) Matrix(419,1558,174,647) -> Matrix(29,6,198,41) Matrix(913,3382,-328,-1215) -> Matrix(5,2,-28,-11) Matrix(381,1406,268,989) -> Matrix(9,2,112,25) Matrix(115,418,-52,-189) -> Matrix(13,2,-98,-15) Matrix(191,684,-74,-265) -> Matrix(15,4,-94,-25) Matrix(265,912,-188,-647) -> Matrix(37,8,-458,-99) Matrix(189,646,122,417) -> Matrix(9,2,94,21) Matrix(191,646,34,115) -> Matrix(11,2,38,7) Matrix(417,1406,304,1025) -> Matrix(9,2,112,25) Matrix(113,380,-102,-343) -> Matrix(19,4,-290,-61) Matrix(265,874,-104,-343) -> Matrix(3,2,-20,-13) Matrix(151,494,-70,-229) -> Matrix(25,6,-196,-47) Matrix(189,608,106,341) -> Matrix(37,8,356,77) Matrix(191,608,60,191) -> Matrix(39,8,190,39) Matrix(37,114,12,37) -> Matrix(11,2,60,11) Matrix(305,874,186,533) -> Matrix(81,14,862,149) Matrix(455,1292,-268,-761) -> Matrix(23,4,-236,-41) Matrix(229,646,162,457) -> Matrix(13,2,162,25) Matrix(381,1064,82,229) -> Matrix(1,0,10,1) Matrix(2281,6346,-1666,-4635) -> Matrix(11,2,-94,-17) Matrix(151,418,82,227) -> Matrix(57,10,530,93) Matrix(153,418,56,153) -> Matrix(59,10,348,59) Matrix(113,304,42,113) -> Matrix(49,8,300,49) Matrix(1065,2812,-748,-1975) -> Matrix(23,4,-282,-49) Matrix(419,1102,246,647) -> Matrix(37,6,376,61) Matrix(305,798,-232,-607) -> Matrix(13,2,-150,-23) Matrix(191,494,162,419) -> Matrix(37,6,524,85) Matrix(341,874,222,569) -> Matrix(89,14,998,157) Matrix(609,1558,446,1141) -> Matrix(13,2,188,29) Matrix(493,1254,-344,-875) -> Matrix(13,2,-98,-15) Matrix(77,190,62,153) -> Matrix(13,2,162,25) Matrix(607,1482,342,835) -> Matrix(95,14,916,135) Matrix(531,1292,-344,-837) -> Matrix(27,4,-304,-45) Matrix(455,1102,282,683) -> Matrix(41,6,444,65) Matrix(2661,6422,-2078,-5015) -> Matrix(121,18,-1526,-227) Matrix(647,1558,174,419) -> Matrix(41,6,198,29) Matrix(191,456,80,191) -> Matrix(111,16,770,111) Matrix(113,266,48,113) -> Matrix(71,10,504,71) Matrix(379,874,-330,-761) -> Matrix(159,22,-2320,-321) Matrix(761,1748,596,1369) -> Matrix(29,4,326,45) Matrix(647,1482,382,875) -> Matrix(103,14,1052,143) Matrix(267,608,184,419) -> Matrix(59,8,730,99) Matrix(495,1102,-358,-797) -> Matrix(15,2,-278,-37) Matrix(191,418,122,267) -> Matrix(77,10,870,113) Matrix(303,646,-250,-533) -> Matrix(79,10,-1114,-141) Matrix(265,494,-184,-343) -> Matrix(55,6,-706,-77) Matrix(227,418,82,151) -> Matrix(93,10,530,57) Matrix(229,418,-166,-303) -> Matrix(19,2,-200,-21) Matrix(191,342,-148,-265) -> Matrix(19,2,-276,-29) Matrix(835,1482,342,607) -> Matrix(135,14,916,95) Matrix(987,1748,214,379) -> Matrix(39,4,224,23) Matrix(151,266,-130,-229) -> Matrix(59,6,-836,-85) Matrix(153,266,88,153) -> Matrix(99,10,980,99) Matrix(265,456,154,265) -> Matrix(161,16,1620,161) Matrix(911,1558,666,1139) -> Matrix(61,6,742,73) Matrix(913,1558,-712,-1215) -> Matrix(21,2,-242,-23) Matrix(647,1102,246,419) -> Matrix(61,6,376,37) Matrix(3001,5092,1052,1785) -> Matrix(119,12,704,71) Matrix(3383,5738,1188,2015) -> Matrix(181,18,1096,109) Matrix(875,1482,382,647) -> Matrix(143,14,1052,103) Matrix(113,190,22,37) -> Matrix(21,2,94,9) Matrix(531,874,-370,-609) -> Matrix(21,2,-326,-31) Matrix(949,1558,254,417) -> Matrix(21,2,52,5) Matrix(533,874,186,305) -> Matrix(149,14,862,81) Matrix(419,684,-302,-493) -> Matrix(43,4,-570,-53) Matrix(305,494,-234,-379) -> Matrix(21,2,-284,-27) Matrix(683,1102,282,455) -> Matrix(65,6,444,41) Matrix(189,304,-166,-267) -> Matrix(1,0,-4,1) Matrix(191,304,120,191) -> Matrix(87,8,946,87) Matrix(265,418,168,265) -> Matrix(111,10,1232,111) Matrix(267,418,122,191) -> Matrix(113,10,870,77) Matrix(2167,3382,-1582,-2469) -> Matrix(23,2,-334,-29) Matrix(683,1064,536,835) -> Matrix(1,0,24,1) Matrix(417,646,122,189) -> Matrix(21,2,94,9) Matrix(3723,5738,1528,2355) -> Matrix(197,18,1368,125) Matrix(3307,5092,1358,2091) -> Matrix(133,12,942,85) Matrix(569,874,222,341) -> Matrix(157,14,998,89) Matrix(77,114,52,77) -> Matrix(23,2,264,23) Matrix(417,608,286,417) -> Matrix(97,8,1176,97) Matrix(341,494,78,113) -> Matrix(25,2,112,9) Matrix(4065,5852,712,1025) -> Matrix(259,20,764,59) Matrix(3459,4978,608,875) -> Matrix(183,14,562,43) Matrix(4027,5776,1218,1747) -> Matrix(1,0,28,1) Matrix(4029,5776,1220,1749) -> Matrix(1,0,6,1) Matrix(533,760,54,77) -> Matrix(95,8,178,15) Matrix(987,1406,106,151) -> Matrix(169,14,350,29) Matrix(989,1406,268,381) -> Matrix(25,2,112,9) Matrix(455,646,374,531) -> Matrix(23,2,310,27) Matrix(457,646,162,229) -> Matrix(25,2,162,13) Matrix(1025,1444,296,417) -> Matrix(149,12,658,53) Matrix(1027,1444,298,419) -> Matrix(151,12,692,55) Matrix(191,266,28,39) -> Matrix(25,2,62,5) Matrix(4179,5776,1154,1595) -> Matrix(1,0,32,1) Matrix(4181,5776,1156,1597) -> Matrix(1,0,2,1) Matrix(1025,1406,304,417) -> Matrix(25,2,112,9) Matrix(16871,23104,4550,6231) -> Matrix(1,0,30,1) Matrix(16873,23104,4552,6233) -> Matrix(1,0,4,1) Matrix(1139,1558,666,911) -> Matrix(73,6,742,61) Matrix(1141,1558,446,609) -> Matrix(29,2,188,13) Matrix(419,570,308,419) -> Matrix(25,2,312,25) Matrix(113,152,84,113) -> Matrix(1,0,26,1) Matrix(1101,1444,260,341) -> Matrix(49,4,208,17) Matrix(1103,1444,262,343) -> Matrix(51,4,242,19) Matrix(381,494,118,153) -> Matrix(25,2,112,9) Matrix(10145,12996,2224,2849) -> Matrix(349,28,1558,125) Matrix(10147,12996,2226,2851) -> Matrix(351,28,1592,127) Matrix(683,874,118,151) -> Matrix(25,2,62,5) Matrix(1369,1748,596,761) -> Matrix(45,4,326,29) Matrix(835,1064,536,683) -> Matrix(1,0,24,1) Matrix(419,532,330,419) -> Matrix(51,4,650,51) Matrix(151,190,120,151) -> Matrix(27,2,364,27) Matrix(153,190,62,77) -> Matrix(25,2,162,13) Matrix(1177,1444,216,265) -> Matrix(269,20,928,69) Matrix(1179,1444,218,267) -> Matrix(271,20,962,71) Matrix(531,646,374,455) -> Matrix(27,2,310,23) Matrix(4103,4978,1252,1519) -> Matrix(195,14,766,55) Matrix(4827,5852,1474,1787) -> Matrix(281,20,1138,81) Matrix(723,874,158,191) -> Matrix(29,2,130,9) Matrix(191,228,160,191) -> Matrix(55,4,756,55) Matrix(417,494,352,417) -> Matrix(141,10,1988,141) Matrix(227,266,64,75) -> Matrix(29,2,130,9) Matrix(1253,1444,164,189) -> Matrix(521,36,1288,89) Matrix(1255,1444,166,191) -> Matrix(523,36,1322,91) Matrix(1255,1406,374,419) -> Matrix(209,14,1030,69) Matrix(683,760,204,227) -> Matrix(121,8,620,41) Matrix(1,0,2,1) -> Matrix(1,0,34,1) Matrix(267,-304,166,-189) -> Matrix(1,0,-4,1) Matrix(229,-266,130,-151) -> Matrix(85,-6,836,-59) Matrix(1443,-1748,440,-533) -> Matrix(57,-4,214,-15) Matrix(495,-608,92,-113) -> Matrix(107,-8,388,-29) Matrix(1215,-1558,712,-913) -> Matrix(23,-2,242,-21) Matrix(265,-342,148,-191) -> Matrix(29,-2,276,-19) Matrix(379,-494,234,-305) -> Matrix(27,-2,284,-21) Matrix(2469,-3382,1582,-2167) -> Matrix(29,-2,334,-23) Matrix(303,-418,166,-229) -> Matrix(21,-2,200,-19) Matrix(493,-684,302,-419) -> Matrix(53,-4,570,-43) Matrix(647,-912,188,-265) -> Matrix(99,-8,458,-37) Matrix(267,-380,26,-37) -> Matrix(49,-4,86,-7) Matrix(609,-874,370,-531) -> Matrix(31,-2,326,-21) Matrix(343,-494,184,-265) -> Matrix(77,-6,706,-55) Matrix(837,-1292,344,-531) -> Matrix(45,-4,304,-27) Matrix(4065,-6346,1096,-1711) -> Matrix(23,-2,196,-17) Matrix(1747,-2812,520,-837) -> Matrix(45,-4,214,-19) Matrix(493,-798,118,-191) -> Matrix(21,-2,116,-11) Matrix(761,-1254,230,-379) -> Matrix(21,-2,200,-19) Matrix(761,-1292,268,-455) -> Matrix(41,-4,236,-23) Matrix(3761,-6422,824,-1407) -> Matrix(185,-18,812,-79) Matrix(495,-874,64,-113) -> Matrix(215,-22,518,-53) Matrix(607,-1102,168,-305) -> Matrix(19,-2,-28,3) Matrix(343,-646,60,-113) -> Matrix(91,-10,264,-29) Matrix(229,-494,70,-151) -> Matrix(47,-6,196,-25) Matrix(189,-418,52,-115) -> Matrix(15,-2,98,-13) Matrix(151,-342,34,-77) -> Matrix(15,-2,38,-5) Matrix(115,-266,16,-37) -> Matrix(43,-6,122,-17) Matrix(645,-1558,142,-343) -> Matrix(13,-2,72,-11) Matrix(343,-874,104,-265) -> Matrix(13,-2,20,-3) Matrix(265,-684,74,-191) -> Matrix(25,-4,94,-15) Matrix(189,-494,44,-115) -> Matrix(13,-2,46,-7) Matrix(115,-304,14,-37) -> Matrix(1,0,-4,1) Matrix(1215,-3382,328,-913) -> Matrix(11,-2,28,-5) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 90 Degree of the the map X: 90 Degree of the the map Y: 180 ----------------------------------------------------------------------- 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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): 540 Minimal number of generators: 91 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: 36 Genus: 28 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 19/8 12/5 19/7 57/20 3/1 19/6 76/23 38/11 18/5 76/21 152/41 19/5 4/1 38/9 114/25 14/3 19/4 5/1 16/3 38/7 11/2 17/3 57/10 6/1 19/3 13/2 7/1 15/2 38/5 8/1 9/1 19/2 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/17 8/7 4/59 7/6 1/14 13/11 5/71 19/16 1/14 6/5 2/27 23/19 3/43 17/14 1/14 11/9 3/41 16/13 4/53 5/4 1/14 19/15 1/13 14/11 2/25 37/29 5/61 23/18 1/14 32/25 4/51 9/7 1/11 13/10 1/14 4/3 0/1 19/14 1/13 15/11 1/13 41/30 3/38 26/19 2/23 37/27 3/41 11/8 1/12 18/13 2/29 7/5 1/13 24/17 4/49 17/12 1/12 27/19 1/13 37/26 7/86 10/7 2/23 23/16 1/14 13/9 3/37 16/11 4/49 19/13 1/12 3/2 1/12 20/13 8/89 17/11 1/11 14/9 2/23 39/25 5/59 64/41 12/139 25/16 7/80 11/7 1/11 19/12 1/11 8/5 4/43 37/23 1/13 29/18 5/54 21/13 1/11 34/21 2/21 13/8 1/10 31/19 1/11 18/11 10/107 41/25 11/117 23/14 3/32 28/17 16/169 5/3 3/31 22/13 6/61 39/23 11/111 17/10 1/10 29/17 1/11 70/41 10/103 41/24 9/92 12/7 8/81 19/11 1/10 7/4 1/10 30/17 14/137 23/13 11/107 39/22 19/184 16/9 4/39 25/14 1/10 9/5 7/67 20/11 16/151 11/6 3/28 13/7 9/83 15/8 7/64 2/1 2/17 13/6 9/70 11/5 3/23 9/4 7/52 16/7 4/29 39/17 19/139 23/10 11/80 7/3 1/7 19/8 1/7 12/5 8/55 41/17 9/61 29/12 1/6 17/7 1/7 56/23 4/29 95/39 1/7 39/16 11/76 22/9 6/41 5/2 3/20 23/9 3/19 41/16 11/70 18/7 10/63 13/5 1/7 21/8 1/6 29/11 5/31 8/3 4/25 19/7 1/6 11/4 1/6 25/9 7/39 39/14 5/26 14/5 2/11 17/6 1/6 37/13 7/43 57/20 1/6 20/7 8/47 3/1 1/5 19/6 1/5 16/5 4/19 13/4 3/14 36/11 8/33 95/29 1/4 59/18 1/4 23/7 1/3 33/10 1/0 76/23 0/1 43/13 1/11 10/3 2/11 57/17 1/5 47/14 9/44 37/11 7/33 27/8 1/4 17/5 1/5 24/7 4/19 31/9 5/23 38/11 2/9 7/2 1/4 25/7 3/11 18/5 2/5 47/13 -1/5 76/21 0/1 29/8 1/10 11/3 1/5 37/10 3/10 63/17 -1/1 152/41 0/1 89/24 1/12 26/7 2/11 41/11 3/13 15/4 1/4 19/5 1/4 4/1 0/1 21/5 1/5 38/9 2/9 17/4 1/4 13/3 1/3 22/5 2/7 9/2 1/6 41/9 5/23 114/25 2/9 73/16 9/40 32/7 4/17 23/5 1/3 37/8 5/24 14/3 2/9 19/4 1/4 5/1 1/3 16/3 4/15 27/5 7/25 38/7 2/7 11/2 3/10 17/3 1/3 57/10 1/3 40/7 12/35 23/4 3/8 6/1 2/7 19/3 1/3 13/2 5/14 7/1 1/3 15/2 7/18 38/5 2/5 23/3 11/27 8/1 4/9 9/1 5/11 19/2 1/2 10/1 6/11 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(267,-304,166,-189) (1/1,8/7) -> (8/5,37/23) Hyperbolic Matrix(229,-266,130,-151) (8/7,7/6) -> (7/4,30/17) Hyperbolic Matrix(419,-494,257,-303) (7/6,13/11) -> (13/8,31/19) Hyperbolic Matrix(417,-494,65,-77) (13/11,19/16) -> (19/3,13/2) Hyperbolic Matrix(191,-228,31,-37) (19/16,6/5) -> (6/1,19/3) Hyperbolic Matrix(723,-874,565,-683) (6/5,23/19) -> (23/18,32/25) Hyperbolic Matrix(1443,-1748,440,-533) (23/19,17/14) -> (59/18,23/7) Hyperbolic Matrix(531,-646,157,-191) (17/14,11/9) -> (27/8,17/5) Hyperbolic Matrix(495,-608,92,-113) (11/9,16/13) -> (16/3,27/5) Hyperbolic Matrix(153,-190,91,-113) (16/13,5/4) -> (5/3,22/13) Hyperbolic Matrix(151,-190,31,-39) (5/4,19/15) -> (19/4,5/1) Hyperbolic Matrix(419,-532,89,-113) (19/15,14/11) -> (14/3,19/4) Hyperbolic Matrix(835,-1064,299,-381) (14/11,37/29) -> (39/14,14/5) Hyperbolic Matrix(1369,-1748,773,-987) (37/29,23/18) -> (23/13,39/22) Hyperbolic Matrix(1215,-1558,712,-913) (32/25,9/7) -> (29/17,70/41) Hyperbolic Matrix(265,-342,148,-191) (9/7,13/10) -> (25/14,9/5) Hyperbolic Matrix(379,-494,234,-305) (13/10,4/3) -> (34/21,13/8) Hyperbolic Matrix(113,-152,29,-39) (4/3,19/14) -> (19/5,4/1) Hyperbolic Matrix(419,-570,111,-151) (19/14,15/11) -> (15/4,19/5) Hyperbolic Matrix(1141,-1558,695,-949) (15/11,41/30) -> (41/25,23/14) Hyperbolic Matrix(1139,-1558,473,-647) (41/30,26/19) -> (12/5,41/17) Hyperbolic Matrix(2469,-3382,1582,-2167) (26/19,37/27) -> (39/25,64/41) Hyperbolic Matrix(1025,-1406,721,-989) (37/27,11/8) -> (27/19,37/26) Hyperbolic Matrix(303,-418,166,-229) (11/8,18/13) -> (20/11,11/6) Hyperbolic Matrix(493,-684,302,-419) (18/13,7/5) -> (31/19,18/11) Hyperbolic Matrix(647,-912,188,-265) (7/5,24/17) -> (24/7,31/9) Hyperbolic Matrix(457,-646,295,-417) (24/17,17/12) -> (17/11,14/9) Hyperbolic Matrix(455,-646,81,-115) (17/12,27/19) -> (11/2,17/3) Hyperbolic Matrix(267,-380,26,-37) (37/26,10/7) -> (10/1,1/0) Hyperbolic Matrix(609,-874,370,-531) (10/7,23/16) -> (23/14,28/17) Hyperbolic Matrix(343,-494,184,-265) (23/16,13/9) -> (13/7,15/8) Hyperbolic Matrix(419,-608,235,-341) (13/9,16/11) -> (16/9,25/14) Hyperbolic Matrix(417,-608,131,-191) (16/11,19/13) -> (19/6,16/5) Hyperbolic Matrix(77,-114,25,-37) (19/13,3/2) -> (3/1,19/6) Hyperbolic Matrix(569,-874,347,-533) (3/2,20/13) -> (18/11,41/25) Hyperbolic Matrix(837,-1292,344,-531) (20/13,17/11) -> (17/7,56/23) Hyperbolic Matrix(683,-1064,147,-229) (14/9,39/25) -> (37/8,14/3) Hyperbolic Matrix(4065,-6346,1096,-1711) (64/41,25/16) -> (89/24,26/7) Hyperbolic Matrix(267,-418,145,-227) (25/16,11/7) -> (11/6,13/7) Hyperbolic Matrix(265,-418,97,-153) (11/7,19/12) -> (19/7,11/4) Hyperbolic Matrix(191,-304,71,-113) (19/12,8/5) -> (8/3,19/7) Hyperbolic Matrix(1747,-2812,520,-837) (37/23,29/18) -> (47/14,37/11) Hyperbolic Matrix(683,-1102,401,-647) (29/18,21/13) -> (17/10,29/17) Hyperbolic Matrix(493,-798,118,-191) (21/13,34/21) -> (4/1,21/5) Hyperbolic Matrix(761,-1254,230,-379) (28/17,5/3) -> (43/13,10/3) Hyperbolic Matrix(875,-1482,493,-835) (22/13,39/23) -> (39/22,16/9) Hyperbolic Matrix(761,-1292,268,-455) (39/23,17/10) -> (17/6,37/13) Hyperbolic Matrix(3761,-6422,824,-1407) (70/41,41/24) -> (73/16,32/7) Hyperbolic Matrix(911,-1558,245,-419) (41/24,12/7) -> (26/7,41/11) Hyperbolic Matrix(265,-456,111,-191) (12/7,19/11) -> (19/8,12/5) Hyperbolic Matrix(153,-266,65,-113) (19/11,7/4) -> (7/3,19/8) Hyperbolic Matrix(495,-874,64,-113) (30/17,23/13) -> (23/3,8/1) Hyperbolic Matrix(607,-1102,168,-305) (9/5,20/11) -> (18/5,47/13) Hyperbolic Matrix(343,-646,60,-113) (15/8,2/1) -> (40/7,23/4) Hyperbolic Matrix(229,-494,70,-151) (2/1,13/6) -> (13/4,36/11) Hyperbolic Matrix(191,-418,69,-151) (13/6,11/5) -> (11/4,25/9) Hyperbolic Matrix(189,-418,52,-115) (11/5,9/4) -> (29/8,11/3) Hyperbolic Matrix(151,-342,34,-77) (9/4,16/7) -> (22/5,9/2) Hyperbolic Matrix(647,-1482,265,-607) (16/7,39/17) -> (39/16,22/9) Hyperbolic Matrix(761,-1748,165,-379) (39/17,23/10) -> (23/5,37/8) Hyperbolic Matrix(115,-266,16,-37) (23/10,7/3) -> (7/1,15/2) Hyperbolic Matrix(645,-1558,142,-343) (41/17,29/12) -> (9/2,41/9) Hyperbolic Matrix(455,-1102,173,-419) (29/12,17/7) -> (21/8,29/11) Hyperbolic Matrix(2091,-5092,733,-1785) (56/23,95/39) -> (57/20,20/7) Hyperbolic Matrix(2355,-5738,827,-2015) (95/39,39/16) -> (37/13,57/20) Hyperbolic Matrix(77,-190,15,-37) (22/9,5/2) -> (5/1,16/3) Hyperbolic Matrix(343,-874,104,-265) (5/2,23/9) -> (23/7,33/10) Hyperbolic Matrix(609,-1558,163,-417) (23/9,41/16) -> (41/11,15/4) Hyperbolic Matrix(341,-874,119,-305) (41/16,18/7) -> (20/7,3/1) Hyperbolic Matrix(265,-684,74,-191) (18/7,13/5) -> (25/7,18/5) Hyperbolic Matrix(189,-494,44,-115) (13/5,21/8) -> (17/4,13/3) Hyperbolic Matrix(115,-304,14,-37) (29/11,8/3) -> (8/1,9/1) Hyperbolic Matrix(1215,-3382,328,-913) (25/9,39/14) -> (37/10,63/17) Hyperbolic Matrix(229,-646,67,-189) (14/5,17/6) -> (17/5,24/7) Hyperbolic Matrix(153,-494,35,-113) (16/5,13/4) -> (13/3,22/5) Hyperbolic Matrix(1787,-5852,313,-1025) (36/11,95/29) -> (57/10,40/7) Hyperbolic Matrix(1519,-4978,267,-875) (95/29,59/18) -> (17/3,57/10) Hyperbolic Matrix(1749,-5776,529,-1747) (33/10,76/23) -> (76/23,43/13) Parabolic Matrix(227,-760,23,-77) (10/3,57/17) -> (19/2,10/1) Hyperbolic Matrix(419,-1406,45,-151) (57/17,47/14) -> (9/1,19/2) Hyperbolic Matrix(417,-1406,113,-381) (37/11,27/8) -> (11/3,37/10) Hyperbolic Matrix(419,-1444,121,-417) (31/9,38/11) -> (38/11,7/2) Parabolic Matrix(75,-266,11,-39) (7/2,25/7) -> (13/2,7/1) Hyperbolic Matrix(1597,-5776,441,-1595) (47/13,76/21) -> (76/21,29/8) Parabolic Matrix(6233,-23104,1681,-6231) (63/17,152/41) -> (152/41,89/24) Parabolic Matrix(343,-1444,81,-341) (21/5,38/9) -> (38/9,17/4) Parabolic Matrix(2851,-12996,625,-2849) (41/9,114/25) -> (114/25,73/16) Parabolic Matrix(191,-874,33,-151) (32/7,23/5) -> (23/4,6/1) Hyperbolic Matrix(267,-1444,49,-265) (27/5,38/7) -> (38/7,11/2) Parabolic Matrix(191,-1444,25,-189) (15/2,38/5) -> (38/5,23/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,17,1) Matrix(267,-304,166,-189) -> Matrix(1,0,-4,1) Matrix(229,-266,130,-151) -> Matrix(85,-6,836,-59) Matrix(419,-494,257,-303) -> Matrix(85,-6,921,-65) Matrix(417,-494,65,-77) -> Matrix(141,-10,409,-29) Matrix(191,-228,31,-37) -> Matrix(55,-4,179,-13) Matrix(723,-874,565,-683) -> Matrix(29,-2,363,-25) Matrix(1443,-1748,440,-533) -> Matrix(57,-4,214,-15) Matrix(531,-646,157,-191) -> Matrix(27,-2,149,-11) Matrix(495,-608,92,-113) -> Matrix(107,-8,388,-29) Matrix(153,-190,91,-113) -> Matrix(25,-2,263,-21) Matrix(151,-190,31,-39) -> Matrix(27,-2,95,-7) Matrix(419,-532,89,-113) -> Matrix(51,-4,217,-17) Matrix(835,-1064,299,-381) -> Matrix(1,0,-7,1) Matrix(1369,-1748,773,-987) -> Matrix(45,-4,439,-39) Matrix(1215,-1558,712,-913) -> Matrix(23,-2,242,-21) Matrix(265,-342,148,-191) -> Matrix(29,-2,276,-19) Matrix(379,-494,234,-305) -> Matrix(27,-2,284,-21) Matrix(113,-152,29,-39) -> Matrix(1,0,-9,1) Matrix(419,-570,111,-151) -> Matrix(25,-2,113,-9) Matrix(1141,-1558,695,-949) -> Matrix(29,-2,305,-21) Matrix(1139,-1558,473,-647) -> Matrix(73,-6,499,-41) Matrix(2469,-3382,1582,-2167) -> Matrix(29,-2,334,-23) Matrix(1025,-1406,721,-989) -> Matrix(25,-2,313,-25) Matrix(303,-418,166,-229) -> Matrix(21,-2,200,-19) Matrix(493,-684,302,-419) -> Matrix(53,-4,570,-43) Matrix(647,-912,188,-265) -> Matrix(99,-8,458,-37) Matrix(457,-646,295,-417) -> Matrix(25,-2,263,-21) Matrix(455,-646,81,-115) -> Matrix(23,-2,81,-7) Matrix(267,-380,26,-37) -> Matrix(49,-4,86,-7) Matrix(609,-874,370,-531) -> Matrix(31,-2,326,-21) Matrix(343,-494,184,-265) -> Matrix(77,-6,706,-55) Matrix(419,-608,235,-341) -> Matrix(99,-8,953,-77) Matrix(417,-608,131,-191) -> Matrix(97,-8,473,-39) Matrix(77,-114,25,-37) -> Matrix(23,-2,127,-11) Matrix(569,-874,347,-533) -> Matrix(157,-14,1671,-149) Matrix(837,-1292,344,-531) -> Matrix(45,-4,304,-27) Matrix(683,-1064,147,-229) -> Matrix(1,0,-7,1) Matrix(4065,-6346,1096,-1711) -> Matrix(23,-2,196,-17) Matrix(267,-418,145,-227) -> Matrix(113,-10,1051,-93) Matrix(265,-418,97,-153) -> Matrix(111,-10,655,-59) Matrix(191,-304,71,-113) -> Matrix(87,-8,533,-49) Matrix(1747,-2812,520,-837) -> Matrix(45,-4,214,-19) Matrix(683,-1102,401,-647) -> Matrix(65,-6,661,-61) Matrix(493,-798,118,-191) -> Matrix(21,-2,116,-11) Matrix(761,-1254,230,-379) -> Matrix(21,-2,200,-19) Matrix(875,-1482,493,-835) -> Matrix(143,-14,1379,-135) Matrix(761,-1292,268,-455) -> Matrix(41,-4,236,-23) Matrix(3761,-6422,824,-1407) -> Matrix(185,-18,812,-79) Matrix(911,-1558,245,-419) -> Matrix(61,-6,295,-29) Matrix(265,-456,111,-191) -> Matrix(161,-16,1117,-111) Matrix(153,-266,65,-113) -> Matrix(99,-10,703,-71) Matrix(495,-874,64,-113) -> Matrix(215,-22,518,-53) Matrix(607,-1102,168,-305) -> Matrix(19,-2,-28,3) Matrix(343,-646,60,-113) -> Matrix(91,-10,264,-29) Matrix(229,-494,70,-151) -> Matrix(47,-6,196,-25) Matrix(191,-418,69,-151) -> Matrix(77,-10,439,-57) Matrix(189,-418,52,-115) -> Matrix(15,-2,98,-13) Matrix(151,-342,34,-77) -> Matrix(15,-2,38,-5) Matrix(647,-1482,265,-607) -> Matrix(103,-14,699,-95) Matrix(761,-1748,165,-379) -> Matrix(29,-4,167,-23) Matrix(115,-266,16,-37) -> Matrix(43,-6,122,-17) Matrix(645,-1558,142,-343) -> Matrix(13,-2,72,-11) Matrix(455,-1102,173,-419) -> Matrix(41,-6,253,-37) Matrix(2091,-5092,733,-1785) -> Matrix(85,-12,503,-71) Matrix(2355,-5738,827,-2015) -> Matrix(125,-18,757,-109) Matrix(77,-190,15,-37) -> Matrix(13,-2,59,-9) Matrix(343,-874,104,-265) -> Matrix(13,-2,20,-3) Matrix(609,-1558,163,-417) -> Matrix(13,-2,33,-5) Matrix(341,-874,119,-305) -> Matrix(89,-14,515,-81) Matrix(265,-684,74,-191) -> Matrix(25,-4,94,-15) Matrix(189,-494,44,-115) -> Matrix(13,-2,46,-7) Matrix(115,-304,14,-37) -> Matrix(1,0,-4,1) Matrix(1215,-3382,328,-913) -> Matrix(11,-2,28,-5) Matrix(229,-646,67,-189) -> Matrix(13,-2,59,-9) Matrix(153,-494,35,-113) -> Matrix(9,-2,41,-9) Matrix(1787,-5852,313,-1025) -> Matrix(81,-20,239,-59) Matrix(1519,-4978,267,-875) -> Matrix(55,-14,169,-43) Matrix(1749,-5776,529,-1747) -> Matrix(1,0,11,1) Matrix(227,-760,23,-77) -> Matrix(41,-8,77,-15) Matrix(419,-1406,45,-151) -> Matrix(69,-14,143,-29) Matrix(417,-1406,113,-381) -> Matrix(9,-2,41,-9) Matrix(419,-1444,121,-417) -> Matrix(55,-12,243,-53) Matrix(75,-266,11,-39) -> Matrix(9,-2,23,-5) Matrix(1597,-5776,441,-1595) -> Matrix(1,0,15,1) Matrix(6233,-23104,1681,-6231) -> Matrix(1,0,13,1) Matrix(343,-1444,81,-341) -> Matrix(19,-4,81,-17) Matrix(2851,-12996,625,-2849) -> Matrix(127,-28,567,-125) Matrix(191,-874,33,-151) -> Matrix(9,-2,23,-5) Matrix(267,-1444,49,-265) -> Matrix(71,-20,245,-69) Matrix(191,-1444,25,-189) -> Matrix(91,-36,225,-89) 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): 90 ----------------------------------------------------------------------- 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 0/1 0/1 17 1 2/1 2/17 1 19 13/6 9/70 1 19 11/5 3/23 1 19 9/4 7/52 1 19 16/7 4/29 1 19 39/17 19/139 1 19 23/10 11/80 1 19 7/3 1/7 1 19 19/8 1/7 13 1 12/5 8/55 1 19 41/17 9/61 1 19 29/12 1/6 1 19 17/7 1/7 1 19 39/16 11/76 1 19 22/9 6/41 1 19 5/2 3/20 1 19 23/9 3/19 1 19 41/16 11/70 1 19 18/7 10/63 1 19 13/5 1/7 1 19 21/8 1/6 1 19 29/11 5/31 1 19 8/3 4/25 1 19 19/7 1/6 9 1 11/4 1/6 1 19 25/9 7/39 1 19 39/14 5/26 1 19 14/5 2/11 1 19 17/6 1/6 1 19 37/13 7/43 1 19 57/20 1/6 15 1 20/7 8/47 1 19 3/1 1/5 1 19 19/6 1/5 5 1 16/5 4/19 1 19 13/4 3/14 1 19 36/11 8/33 1 19 23/7 1/3 1 19 33/10 1/0 1 19 76/23 0/1 11 1 10/3 2/11 1 19 37/11 7/33 1 19 27/8 1/4 1 19 17/5 1/5 1 19 24/7 4/19 1 19 38/11 2/9 3 1 7/2 1/4 1 19 25/7 3/11 1 19 18/5 2/5 1 19 76/21 0/1 15 1 29/8 1/10 1 19 11/3 1/5 1 19 37/10 3/10 1 19 63/17 -1/1 1 19 152/41 0/1 13 1 26/7 2/11 1 19 41/11 3/13 1 19 15/4 1/4 1 19 19/5 1/4 1 1 4/1 0/1 1 19 38/9 2/9 1 1 17/4 1/4 1 19 13/3 1/3 1 19 22/5 2/7 1 19 9/2 1/6 1 19 41/9 5/23 1 19 114/25 2/9 7 1 32/7 4/17 1 19 23/5 1/3 1 19 37/8 5/24 1 19 14/3 2/9 1 19 19/4 1/4 3 1 5/1 1/3 1 19 16/3 4/15 1 19 38/7 2/7 5 1 11/2 3/10 1 19 17/3 1/3 1 19 57/10 1/3 17 1 40/7 12/35 1 19 23/4 3/8 1 19 6/1 2/7 1 19 19/3 1/3 7 1 13/2 5/14 1 19 7/1 1/3 1 19 15/2 7/18 1 19 38/5 2/5 9 1 8/1 4/9 1 19 9/1 5/11 1 19 19/2 1/2 11 1 10/1 6/11 1 19 1/0 1/0 1 19 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(229,-494,70,-151) (2/1,13/6) -> (13/4,36/11) Hyperbolic Matrix(191,-418,69,-151) (13/6,11/5) -> (11/4,25/9) Hyperbolic Matrix(189,-418,52,-115) (11/5,9/4) -> (29/8,11/3) Hyperbolic Matrix(151,-342,34,-77) (9/4,16/7) -> (22/5,9/2) Hyperbolic Matrix(647,-1482,265,-607) (16/7,39/17) -> (39/16,22/9) Hyperbolic Matrix(761,-1748,165,-379) (39/17,23/10) -> (23/5,37/8) Hyperbolic Matrix(115,-266,16,-37) (23/10,7/3) -> (7/1,15/2) Hyperbolic Matrix(113,-266,48,-113) (7/3,19/8) -> (7/3,19/8) Reflection Matrix(191,-456,80,-191) (19/8,12/5) -> (19/8,12/5) Reflection Matrix(647,-1558,174,-419) (12/5,41/17) -> (26/7,41/11) Glide Reflection Matrix(645,-1558,142,-343) (41/17,29/12) -> (9/2,41/9) Hyperbolic Matrix(455,-1102,173,-419) (29/12,17/7) -> (21/8,29/11) Hyperbolic Matrix(531,-1292,187,-455) (17/7,39/16) -> (17/6,37/13) Glide Reflection Matrix(77,-190,15,-37) (22/9,5/2) -> (5/1,16/3) Hyperbolic Matrix(343,-874,104,-265) (5/2,23/9) -> (23/7,33/10) Hyperbolic Matrix(609,-1558,163,-417) (23/9,41/16) -> (41/11,15/4) Hyperbolic Matrix(341,-874,119,-305) (41/16,18/7) -> (20/7,3/1) Hyperbolic Matrix(265,-684,74,-191) (18/7,13/5) -> (25/7,18/5) Hyperbolic Matrix(189,-494,44,-115) (13/5,21/8) -> (17/4,13/3) Hyperbolic Matrix(115,-304,14,-37) (29/11,8/3) -> (8/1,9/1) Hyperbolic Matrix(113,-304,42,-113) (8/3,19/7) -> (8/3,19/7) Reflection Matrix(153,-418,56,-153) (19/7,11/4) -> (19/7,11/4) Reflection Matrix(1215,-3382,328,-913) (25/9,39/14) -> (37/10,63/17) Hyperbolic Matrix(381,-1064,82,-229) (39/14,14/5) -> (37/8,14/3) Glide Reflection Matrix(229,-646,67,-189) (14/5,17/6) -> (17/5,24/7) Hyperbolic Matrix(1481,-4218,520,-1481) (37/13,57/20) -> (37/13,57/20) Reflection Matrix(799,-2280,280,-799) (57/20,20/7) -> (57/20,20/7) Reflection Matrix(37,-114,12,-37) (3/1,19/6) -> (3/1,19/6) Reflection Matrix(191,-608,60,-191) (19/6,16/5) -> (19/6,16/5) Reflection Matrix(153,-494,35,-113) (16/5,13/4) -> (13/3,22/5) Hyperbolic Matrix(533,-1748,93,-305) (36/11,23/7) -> (40/7,23/4) Glide Reflection Matrix(1519,-5016,460,-1519) (33/10,76/23) -> (33/10,76/23) Reflection Matrix(229,-760,69,-229) (76/23,10/3) -> (76/23,10/3) Reflection Matrix(113,-380,11,-37) (10/3,37/11) -> (10/1,1/0) Glide Reflection Matrix(417,-1406,113,-381) (37/11,27/8) -> (11/3,37/10) Hyperbolic Matrix(191,-646,34,-115) (27/8,17/5) -> (11/2,17/3) Glide Reflection Matrix(265,-912,77,-265) (24/7,38/11) -> (24/7,38/11) Reflection Matrix(153,-532,44,-153) (38/11,7/2) -> (38/11,7/2) Reflection Matrix(75,-266,11,-39) (7/2,25/7) -> (13/2,7/1) Hyperbolic Matrix(379,-1368,105,-379) (18/5,76/21) -> (18/5,76/21) Reflection Matrix(1217,-4408,336,-1217) (76/21,29/8) -> (76/21,29/8) Reflection Matrix(5167,-19152,1394,-5167) (63/17,152/41) -> (63/17,152/41) Reflection Matrix(1065,-3952,287,-1065) (152/41,26/7) -> (152/41,26/7) Reflection Matrix(151,-570,40,-151) (15/4,19/5) -> (15/4,19/5) Reflection Matrix(39,-152,10,-39) (19/5,4/1) -> (19/5,4/1) Reflection Matrix(37,-152,9,-37) (4/1,38/9) -> (4/1,38/9) Reflection Matrix(305,-1292,72,-305) (38/9,17/4) -> (38/9,17/4) Reflection Matrix(2051,-9348,450,-2051) (41/9,114/25) -> (41/9,114/25) Reflection Matrix(799,-3648,175,-799) (114/25,32/7) -> (114/25,32/7) Reflection Matrix(191,-874,33,-151) (32/7,23/5) -> (23/4,6/1) 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(113,-608,21,-113) (16/3,38/7) -> (16/3,38/7) Reflection Matrix(153,-836,28,-153) (38/7,11/2) -> (38/7,11/2) Reflection Matrix(341,-1938,60,-341) (17/3,57/10) -> (17/3,57/10) Reflection Matrix(799,-4560,140,-799) (57/10,40/7) -> (57/10,40/7) Reflection Matrix(37,-228,6,-37) (6/1,19/3) -> (6/1,19/3) Reflection Matrix(77,-494,12,-77) (19/3,13/2) -> (19/3,13/2) Reflection Matrix(151,-1140,20,-151) (15/2,38/5) -> (15/2,38/5) Reflection Matrix(39,-304,5,-39) (38/5,8/1) -> (38/5,8/1) Reflection Matrix(37,-342,4,-37) (9/1,19/2) -> (9/1,19/2) Reflection Matrix(39,-380,4,-39) (19/2,10/1) -> (19/2,10/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,0,17,-1) (0/1,2/1) -> (0/1,2/17) Matrix(229,-494,70,-151) -> Matrix(47,-6,196,-25) Matrix(191,-418,69,-151) -> Matrix(77,-10,439,-57) Matrix(189,-418,52,-115) -> Matrix(15,-2,98,-13) 1/7 Matrix(151,-342,34,-77) -> Matrix(15,-2,38,-5) Matrix(647,-1482,265,-607) -> Matrix(103,-14,699,-95) Matrix(761,-1748,165,-379) -> Matrix(29,-4,167,-23) Matrix(115,-266,16,-37) -> Matrix(43,-6,122,-17) Matrix(113,-266,48,-113) -> Matrix(71,-10,504,-71) (7/3,19/8) -> (5/36,1/7) Matrix(191,-456,80,-191) -> Matrix(111,-16,770,-111) (19/8,12/5) -> (1/7,8/55) Matrix(647,-1558,174,-419) -> Matrix(41,-6,198,-29) Matrix(645,-1558,142,-343) -> Matrix(13,-2,72,-11) 1/6 Matrix(455,-1102,173,-419) -> Matrix(41,-6,253,-37) Matrix(531,-1292,187,-455) -> Matrix(27,-4,155,-23) Matrix(77,-190,15,-37) -> Matrix(13,-2,59,-9) Matrix(343,-874,104,-265) -> Matrix(13,-2,20,-3) Matrix(609,-1558,163,-417) -> Matrix(13,-2,33,-5) Matrix(341,-874,119,-305) -> Matrix(89,-14,515,-81) Matrix(265,-684,74,-191) -> Matrix(25,-4,94,-15) Matrix(189,-494,44,-115) -> Matrix(13,-2,46,-7) Matrix(115,-304,14,-37) -> Matrix(1,0,-4,1) 0/1 Matrix(113,-304,42,-113) -> Matrix(49,-8,300,-49) (8/3,19/7) -> (4/25,1/6) Matrix(153,-418,56,-153) -> Matrix(59,-10,348,-59) (19/7,11/4) -> (1/6,5/29) Matrix(1215,-3382,328,-913) -> Matrix(11,-2,28,-5) Matrix(381,-1064,82,-229) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(229,-646,67,-189) -> Matrix(13,-2,59,-9) Matrix(1481,-4218,520,-1481) -> Matrix(85,-14,516,-85) (37/13,57/20) -> (7/43,1/6) Matrix(799,-2280,280,-799) -> Matrix(95,-16,564,-95) (57/20,20/7) -> (1/6,8/47) Matrix(37,-114,12,-37) -> Matrix(11,-2,60,-11) (3/1,19/6) -> (1/6,1/5) Matrix(191,-608,60,-191) -> Matrix(39,-8,190,-39) (19/6,16/5) -> (1/5,4/19) Matrix(153,-494,35,-113) -> Matrix(9,-2,41,-9) (0/1,2/9).(1/5,1/4) Matrix(533,-1748,93,-305) -> Matrix(15,-4,41,-11) Matrix(1519,-5016,460,-1519) -> Matrix(1,0,0,-1) (33/10,76/23) -> (0/1,1/0) Matrix(229,-760,69,-229) -> Matrix(1,0,11,-1) (76/23,10/3) -> (0/1,2/11) Matrix(113,-380,11,-37) -> Matrix(19,-4,33,-7) Matrix(417,-1406,113,-381) -> Matrix(9,-2,41,-9) (0/1,2/9).(1/5,1/4) Matrix(191,-646,34,-115) -> Matrix(11,-2,38,-7) Matrix(265,-912,77,-265) -> Matrix(37,-8,171,-37) (24/7,38/11) -> (4/19,2/9) Matrix(153,-532,44,-153) -> Matrix(17,-4,72,-17) (38/11,7/2) -> (2/9,1/4) Matrix(75,-266,11,-39) -> Matrix(9,-2,23,-5) Matrix(379,-1368,105,-379) -> Matrix(1,0,5,-1) (18/5,76/21) -> (0/1,2/5) Matrix(1217,-4408,336,-1217) -> Matrix(1,0,20,-1) (76/21,29/8) -> (0/1,1/10) Matrix(5167,-19152,1394,-5167) -> Matrix(-1,0,2,1) (63/17,152/41) -> (-1/1,0/1) Matrix(1065,-3952,287,-1065) -> Matrix(1,0,11,-1) (152/41,26/7) -> (0/1,2/11) Matrix(151,-570,40,-151) -> Matrix(9,-2,40,-9) (15/4,19/5) -> (1/5,1/4) Matrix(39,-152,10,-39) -> Matrix(1,0,8,-1) (19/5,4/1) -> (0/1,1/4) Matrix(37,-152,9,-37) -> Matrix(1,0,9,-1) (4/1,38/9) -> (0/1,2/9) Matrix(305,-1292,72,-305) -> Matrix(17,-4,72,-17) (38/9,17/4) -> (2/9,1/4) Matrix(2051,-9348,450,-2051) -> Matrix(91,-20,414,-91) (41/9,114/25) -> (5/23,2/9) Matrix(799,-3648,175,-799) -> Matrix(35,-8,153,-35) (114/25,32/7) -> (2/9,4/17) Matrix(191,-874,33,-151) -> Matrix(9,-2,23,-5) Matrix(113,-532,24,-113) -> Matrix(17,-4,72,-17) (14/3,19/4) -> (2/9,1/4) Matrix(39,-190,8,-39) -> Matrix(7,-2,24,-7) (19/4,5/1) -> (1/4,1/3) Matrix(113,-608,21,-113) -> Matrix(29,-8,105,-29) (16/3,38/7) -> (4/15,2/7) Matrix(153,-836,28,-153) -> Matrix(41,-12,140,-41) (38/7,11/2) -> (2/7,3/10) Matrix(341,-1938,60,-341) -> Matrix(31,-10,96,-31) (17/3,57/10) -> (5/16,1/3) Matrix(799,-4560,140,-799) -> Matrix(71,-24,210,-71) (57/10,40/7) -> (1/3,12/35) Matrix(37,-228,6,-37) -> Matrix(13,-4,42,-13) (6/1,19/3) -> (2/7,1/3) Matrix(77,-494,12,-77) -> Matrix(29,-10,84,-29) (19/3,13/2) -> (1/3,5/14) Matrix(151,-1140,20,-151) -> Matrix(71,-28,180,-71) (15/2,38/5) -> (7/18,2/5) Matrix(39,-304,5,-39) -> Matrix(19,-8,45,-19) (38/5,8/1) -> (2/5,4/9) Matrix(37,-342,4,-37) -> Matrix(21,-10,44,-21) (9/1,19/2) -> (5/11,1/2) Matrix(39,-380,4,-39) -> Matrix(23,-12,44,-23) (19/2,10/1) -> (1/2,6/11) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.