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 -1/1 -2/3 -7/1 -1/1 -13/2 -1/1 0/1 -19/3 -1/1 -6/1 -1/1 -1/2 -23/4 -1/2 -1/3 -17/3 -1/1 -11/2 -3/5 -1/2 -16/3 -2/5 -1/3 -5/1 -1/3 -19/4 0/1 -14/3 0/1 1/2 -37/8 2/3 1/1 -23/5 -1/1 -32/7 1/1 1/0 -9/2 -1/1 0/1 -13/3 -1/1 -4/1 -1/1 0/1 -19/5 -1/1 -15/4 -1/1 -1/2 -41/11 -3/5 -26/7 -1/1 0/1 -37/10 -1/1 -2/3 -11/3 -1/3 -18/5 -1/1 1/0 -7/2 -1/1 -1/2 -24/7 -1/2 -2/5 -17/5 -1/3 -27/8 -1/2 -3/7 -37/11 -1/3 -10/3 -1/3 -1/4 -23/7 -1/3 -13/4 -1/5 0/1 -16/5 -1/11 0/1 -19/6 0/1 -3/1 1/1 -20/7 -1/1 1/0 -17/6 -1/1 1/0 -14/5 -2/1 1/0 -39/14 -1/1 0/1 -64/23 -2/1 -1/1 -25/9 -1/1 -11/4 -3/2 -1/1 -19/7 -1/1 -8/3 -1/1 -2/3 -37/14 -1/1 0/1 -29/11 -1/1 -21/8 -1/1 -1/2 -34/13 -1/1 0/1 -13/5 -1/1 -31/12 -1/1 -1/2 -18/7 -1/1 1/0 -41/16 -7/9 -3/4 -23/9 -3/5 -28/11 -3/5 -1/2 -5/2 -1/2 0/1 -22/9 -3/7 -2/5 -39/16 -6/17 -1/3 -17/7 -1/3 -29/12 -1/3 -2/7 -70/29 -3/11 -1/4 -41/17 -3/13 -12/5 -1/5 0/1 -19/8 0/1 -7/3 1/1 -30/13 1/1 2/1 -23/10 -3/1 1/0 -39/17 -1/1 -16/7 -2/1 -1/1 -25/11 -1/1 -9/4 -1/1 0/1 -20/9 -1/1 1/0 -11/5 -1/3 -13/6 -1/1 0/1 -15/7 1/1 -2/1 -1/1 0/1 -13/7 -1/1 -11/6 -1/1 -1/2 -9/5 -1/1 -16/9 0/1 1/3 -39/22 1/1 4/3 -23/13 3/1 -7/4 -1/1 1/0 -19/11 -1/1 -12/7 -1/1 -2/3 -41/24 -5/9 -1/2 -29/17 -1/1 -17/10 -1/1 -1/2 -56/33 -1/1 -1/2 -95/56 -2/3 0/1 -39/23 -1/1 -22/13 -1/1 -2/3 -5/3 -1/1 -23/14 -1/2 -1/3 -41/25 -3/7 -18/11 -1/2 -1/3 -13/8 -1/3 0/1 -21/13 -1/3 -29/18 -2/5 -1/3 -8/5 -1/5 0/1 -19/12 0/1 -11/7 1/5 -25/16 0/1 1/3 -39/25 1/3 -14/9 0/1 1/2 -17/11 1/1 -37/24 8/9 1/1 -57/37 1/1 -20/13 1/1 5/4 -3/2 -1/1 1/0 -19/13 -1/1 -16/11 -1/1 -4/5 -13/9 -1/1 -36/25 -1/1 -2/3 -95/66 -2/3 -59/41 -3/5 -23/16 -1/1 -1/2 -33/23 -3/5 -76/53 -1/2 -43/30 -1/2 -2/5 -10/7 -1/1 -1/2 -57/40 -2/3 0/1 -47/33 -1/1 -37/26 -1/1 0/1 -27/19 -3/5 -17/12 -1/1 -1/2 -24/17 -2/3 -1/2 -31/22 -5/9 -1/2 -38/27 -1/2 -7/5 -1/3 -25/18 -1/3 0/1 -18/13 -1/2 -1/3 -47/34 -1/3 0/1 -76/55 -1/2 -1/4 -29/21 -1/3 -11/8 -1/3 -1/4 -37/27 -1/5 -63/46 -1/5 0/1 -152/111 -1/4 -1/6 -89/65 -1/5 -26/19 -1/5 0/1 -41/30 -1/6 -3/19 -15/11 -1/9 -19/14 0/1 -4/3 0/1 1/1 -21/16 1/1 1/0 -38/29 1/0 -17/13 -1/1 -13/10 -1/1 0/1 -22/17 0/1 1/5 -9/7 1/1 -41/32 5/1 1/0 -114/89 1/0 -73/57 -7/1 -32/25 -1/1 1/0 -23/18 1/1 1/0 -37/29 -1/1 -14/11 0/1 1/0 -19/15 -1/1 1/1 -5/4 0/1 1/0 -16/13 2/1 3/1 -27/22 7/1 1/0 -38/31 1/0 -11/9 -3/1 -17/14 -1/1 1/0 -57/47 -1/1 -40/33 -1/1 0/1 -23/19 1/1 -6/5 -1/1 1/0 -19/16 -2/1 0/1 -13/11 -1/1 -7/6 -1/1 1/0 -15/13 3/1 -38/33 1/0 -23/20 -7/1 1/0 -8/7 -3/1 -2/1 -9/8 -4/3 -1/1 -19/17 -1/1 -10/9 -1/1 -3/4 -1/1 -1/1 0/1 -1/2 1/0 1/1 -1/1 8/7 -2/3 -3/5 7/6 -1/1 -1/2 13/11 -1/1 19/16 -2/3 0/1 6/5 -1/1 -1/2 23/19 -1/3 17/14 -1/1 -1/2 11/9 -3/5 16/13 -3/7 -2/5 5/4 -1/2 0/1 19/15 -1/1 -1/3 14/11 -1/2 0/1 37/29 -1/1 23/18 -1/2 -1/3 32/25 -1/1 -1/2 9/7 -1/3 13/10 -1/1 0/1 4/3 -1/3 0/1 19/14 0/1 15/11 1/7 41/30 3/13 1/4 26/19 0/1 1/3 37/27 1/3 11/8 1/2 1/1 18/13 1/1 1/0 7/5 1/1 24/17 -2/1 1/0 17/12 -1/1 1/0 27/19 -3/1 37/26 -1/1 0/1 10/7 -1/1 1/0 23/16 -1/1 1/0 13/9 -1/1 16/11 -4/3 -1/1 19/13 -1/1 3/2 -1/1 -1/2 20/13 -5/14 -1/3 17/11 -1/3 14/9 -1/4 0/1 39/25 -1/5 64/41 -1/5 0/1 25/16 -1/5 0/1 11/7 -1/7 19/12 0/1 8/5 0/1 1/3 37/23 1/1 29/18 1/1 2/1 21/13 1/1 34/21 -1/1 0/1 13/8 0/1 1/1 31/19 1/1 18/11 1/1 1/0 41/25 3/1 23/14 1/1 1/0 28/17 1/1 1/0 5/3 -1/1 22/13 -2/1 -1/1 39/23 -1/1 17/10 -1/1 1/0 29/17 -1/1 70/41 1/1 1/0 41/24 -5/1 1/0 12/7 -2/1 -1/1 19/11 -1/1 7/4 -1/1 -1/2 30/17 -2/3 -3/5 23/13 -3/7 39/22 -4/11 -1/3 16/9 -1/5 0/1 25/14 0/1 1/1 9/5 -1/1 20/11 -1/1 -1/2 11/6 -1/1 1/0 13/7 -1/1 15/8 -1/1 -1/2 2/1 -1/1 0/1 13/6 -1/1 0/1 11/5 1/1 9/4 -1/1 0/1 16/7 -1/1 -2/3 39/17 -1/1 23/10 -3/5 -1/2 7/3 -1/3 19/8 0/1 12/5 0/1 1/3 41/17 3/7 29/12 2/3 1/1 17/7 1/1 56/23 7/8 1/1 95/39 1/1 39/16 1/1 6/5 22/9 2/1 3/1 5/2 0/1 1/0 23/9 -3/1 41/16 -3/2 -7/5 18/7 -1/1 -1/2 13/5 -1/1 21/8 -1/1 1/0 29/11 -1/1 8/3 -2/1 -1/1 19/7 -1/1 11/4 -1/1 -3/4 25/9 -1/1 39/14 -1/1 0/1 14/5 -2/3 -1/2 17/6 -1/1 -1/2 37/13 -1/1 57/20 -2/3 0/1 20/7 -1/1 -1/2 3/1 -1/3 19/6 0/1 16/5 0/1 1/9 13/4 0/1 1/3 36/11 0/1 1/3 95/29 1/3 59/18 1/3 1/2 23/7 1/1 33/10 2/5 1/2 76/23 1/2 43/13 3/5 10/3 1/2 1/1 57/17 1/1 47/14 1/1 6/5 37/11 1/1 27/8 3/1 1/0 17/5 1/1 24/7 2/1 1/0 31/9 5/1 38/11 1/0 7/2 -1/1 1/0 25/7 -1/1 18/5 -1/1 -1/2 47/13 -1/1 76/21 -1/2 1/0 29/8 -1/1 0/1 11/3 1/1 37/10 -2/1 -1/1 63/17 -1/1 152/41 -1/2 1/0 89/24 -1/1 0/1 26/7 -1/1 0/1 41/11 -3/1 15/4 -1/1 1/0 19/5 -1/1 4/1 -1/1 0/1 21/5 1/1 38/9 1/0 17/4 -1/1 1/0 13/3 -1/1 22/5 -1/1 -2/3 9/2 -1/1 0/1 41/9 -5/9 114/25 -1/2 73/16 -1/2 -7/15 32/7 -1/2 -1/3 23/5 -1/1 37/8 -1/3 -2/7 14/3 -1/4 0/1 19/4 0/1 5/1 1/1 16/3 1/1 2/1 27/5 7/1 38/7 1/0 11/2 -3/1 1/0 17/3 -1/1 57/10 0/1 40/7 0/1 1/1 23/4 1/1 1/0 6/1 -1/1 1/0 19/3 -1/1 13/2 -1/1 0/1 7/1 -1/1 15/2 3/1 1/0 38/5 1/0 23/3 -7/1 8/1 -2/1 -1/1 9/1 -1/1 19/2 -2/1 0/1 10/1 -1/1 1/0 1/0 -1/1 0/1 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(1,0,0,1) Matrix(37,266,-16,-115) -> Matrix(1,0,2,1) Matrix(75,494,46,303) -> Matrix(1,0,2,1) Matrix(77,494,12,77) -> Matrix(1,0,0,1) Matrix(37,228,6,37) -> Matrix(3,2,-2,-1) Matrix(151,874,118,683) -> Matrix(1,0,0,1) Matrix(305,1748,-212,-1215) -> Matrix(5,2,-8,-3) Matrix(115,646,34,191) -> Matrix(1,0,2,1) Matrix(113,608,-92,-495) -> Matrix(9,4,2,1) Matrix(37,190,22,113) -> Matrix(1,0,2,1) Matrix(39,190,8,39) -> Matrix(1,0,4,1) Matrix(113,532,24,113) -> Matrix(1,0,-6,1) Matrix(229,1064,82,381) -> Matrix(3,-2,-4,3) Matrix(379,1748,214,987) -> Matrix(1,-2,-2,5) Matrix(191,874,158,723) -> Matrix(1,0,-2,1) Matrix(343,1558,-142,-645) -> Matrix(1,2,-4,-7) Matrix(77,342,-34,-151) -> Matrix(1,0,0,1) Matrix(115,494,-44,-189) -> Matrix(1,0,0,1) Matrix(39,152,10,39) -> Matrix(1,0,0,1) Matrix(151,570,40,151) -> Matrix(3,2,-2,-1) Matrix(417,1558,254,949) -> Matrix(1,0,2,1) Matrix(419,1558,174,647) -> Matrix(1,0,4,1) Matrix(913,3382,-328,-1215) -> Matrix(3,2,-2,-1) Matrix(381,1406,268,989) -> Matrix(3,2,-2,-1) Matrix(115,418,-52,-189) -> Matrix(1,0,0,1) Matrix(191,684,-74,-265) -> Matrix(1,0,0,1) Matrix(265,912,-188,-647) -> Matrix(9,4,-16,-7) Matrix(189,646,122,417) -> Matrix(5,2,-18,-7) Matrix(191,646,34,115) -> Matrix(1,0,2,1) Matrix(417,1406,304,1025) -> Matrix(5,2,12,5) Matrix(113,380,-102,-343) -> Matrix(5,2,-8,-3) Matrix(265,874,-104,-343) -> Matrix(9,2,-14,-3) Matrix(151,494,-70,-229) -> Matrix(1,0,4,1) Matrix(189,608,106,341) -> Matrix(1,0,6,1) Matrix(191,608,60,191) -> Matrix(1,0,20,1) Matrix(37,114,12,37) -> Matrix(1,0,-4,1) Matrix(305,874,186,533) -> Matrix(1,2,0,1) Matrix(455,1292,-268,-761) -> Matrix(1,2,-2,-3) Matrix(229,646,162,457) -> Matrix(1,0,0,1) Matrix(381,1064,82,229) -> Matrix(1,2,-4,-7) Matrix(2281,6346,-1666,-4635) -> Matrix(1,2,-6,-11) Matrix(151,418,82,227) -> Matrix(1,2,-2,-3) Matrix(153,418,56,153) -> Matrix(5,6,-6,-7) Matrix(113,304,42,113) -> Matrix(5,4,-4,-3) Matrix(1065,2812,-748,-1975) -> Matrix(1,0,0,1) Matrix(419,1102,246,647) -> Matrix(3,2,-2,-1) Matrix(305,798,-232,-607) -> Matrix(1,0,2,1) Matrix(191,494,162,419) -> Matrix(1,0,0,1) Matrix(341,874,222,569) -> Matrix(5,4,-14,-11) Matrix(609,1558,446,1141) -> Matrix(3,2,16,11) Matrix(493,1254,-344,-875) -> Matrix(3,2,-8,-5) Matrix(77,190,62,153) -> Matrix(1,0,0,1) Matrix(607,1482,342,835) -> Matrix(5,2,-18,-7) Matrix(531,1292,-344,-837) -> Matrix(7,2,10,3) Matrix(455,1102,282,683) -> Matrix(1,0,4,1) Matrix(2661,6422,-2078,-5015) -> Matrix(15,4,-4,-1) Matrix(647,1558,174,419) -> Matrix(1,0,4,1) Matrix(191,456,80,191) -> Matrix(1,0,8,1) Matrix(113,266,48,113) -> Matrix(1,0,-4,1) Matrix(379,874,-330,-761) -> Matrix(1,-4,0,1) Matrix(761,1748,596,1369) -> Matrix(1,2,-2,-3) Matrix(647,1482,382,875) -> Matrix(1,0,0,1) Matrix(267,608,184,419) -> Matrix(3,2,-2,-1) Matrix(495,1102,-358,-797) -> Matrix(1,0,-2,1) Matrix(191,418,122,267) -> Matrix(1,0,-4,1) Matrix(303,646,-250,-533) -> Matrix(1,0,0,1) Matrix(265,494,-184,-343) -> Matrix(1,2,-2,-3) Matrix(227,418,82,151) -> Matrix(1,2,-2,-3) Matrix(229,418,-166,-303) -> Matrix(1,0,-2,1) Matrix(191,342,-148,-265) -> Matrix(1,0,2,1) Matrix(835,1482,342,607) -> Matrix(3,-2,2,-1) Matrix(987,1748,214,379) -> Matrix(1,-2,-2,5) Matrix(151,266,-130,-229) -> Matrix(1,0,0,1) Matrix(153,266,88,153) -> Matrix(1,2,-2,-3) Matrix(265,456,154,265) -> Matrix(5,4,-4,-3) Matrix(911,1558,666,1139) -> Matrix(3,2,10,7) Matrix(913,1558,-712,-1215) -> Matrix(1,0,2,1) Matrix(647,1102,246,419) -> Matrix(3,2,-2,-1) Matrix(3001,5092,1052,1785) -> Matrix(1,0,0,1) Matrix(3383,5738,1188,2015) -> Matrix(1,0,0,1) Matrix(875,1482,382,647) -> Matrix(1,0,0,1) Matrix(113,190,22,37) -> Matrix(1,0,2,1) Matrix(531,874,-370,-609) -> Matrix(5,2,-8,-3) Matrix(949,1558,254,417) -> Matrix(1,0,2,1) Matrix(533,874,186,305) -> Matrix(5,2,-8,-3) Matrix(419,684,-302,-493) -> Matrix(1,0,0,1) Matrix(305,494,-234,-379) -> Matrix(1,0,2,1) Matrix(683,1102,282,455) -> Matrix(1,0,4,1) Matrix(189,304,-166,-267) -> Matrix(7,2,-4,-1) Matrix(191,304,120,191) -> Matrix(1,0,8,1) Matrix(265,418,168,265) -> Matrix(1,0,-12,1) Matrix(267,418,122,191) -> Matrix(1,0,-4,1) Matrix(2167,3382,-1582,-2469) -> Matrix(1,0,-8,1) Matrix(683,1064,536,835) -> Matrix(1,0,-4,1) Matrix(417,646,122,189) -> Matrix(3,-2,2,-1) Matrix(3723,5738,1528,2355) -> Matrix(15,-14,14,-13) Matrix(3307,5092,1358,2091) -> Matrix(11,-12,12,-13) Matrix(569,874,222,341) -> Matrix(3,-4,-2,3) Matrix(77,114,52,77) -> Matrix(1,2,-2,-3) Matrix(417,608,286,417) -> Matrix(9,8,-8,-7) Matrix(341,494,78,113) -> Matrix(3,2,-2,-1) Matrix(4065,5852,712,1025) -> Matrix(3,2,4,3) Matrix(3459,4978,608,875) -> Matrix(3,2,-8,-5) Matrix(4027,5776,1218,1747) -> Matrix(11,6,20,11) Matrix(4029,5776,1220,1749) -> Matrix(9,4,20,9) Matrix(533,760,54,77) -> Matrix(3,2,-2,-1) Matrix(987,1406,106,151) -> Matrix(3,2,-2,-1) Matrix(989,1406,268,381) -> Matrix(3,2,-2,-1) Matrix(455,646,374,531) -> Matrix(1,0,0,1) Matrix(457,646,162,229) -> Matrix(1,0,0,1) Matrix(1025,1444,296,417) -> Matrix(11,6,-2,-1) Matrix(1027,1444,298,419) -> Matrix(13,6,2,1) Matrix(191,266,28,39) -> Matrix(1,0,2,1) Matrix(4179,5776,1154,1595) -> Matrix(1,0,2,1) Matrix(4181,5776,1156,1597) -> Matrix(1,0,2,1) Matrix(1025,1406,304,417) -> Matrix(9,2,4,1) Matrix(16871,23104,4550,6231) -> Matrix(1,0,4,1) Matrix(16873,23104,4552,6233) -> Matrix(1,0,4,1) Matrix(1139,1558,666,911) -> Matrix(11,2,-6,-1) Matrix(1141,1558,446,609) -> Matrix(15,2,-8,-1) Matrix(419,570,308,419) -> Matrix(1,0,16,1) Matrix(113,152,84,113) -> Matrix(1,0,-4,1) Matrix(1101,1444,260,341) -> Matrix(1,-2,0,1) Matrix(1103,1444,262,343) -> Matrix(1,2,0,1) Matrix(381,494,118,153) -> Matrix(1,0,4,1) Matrix(10145,12996,2224,2849) -> Matrix(1,-12,-2,25) Matrix(10147,12996,2226,2851) -> Matrix(1,12,-2,-23) Matrix(683,874,118,151) -> Matrix(1,0,0,1) Matrix(1369,1748,596,761) -> Matrix(1,2,-2,-3) Matrix(835,1064,536,683) -> Matrix(1,0,-4,1) Matrix(419,532,330,419) -> Matrix(1,0,-2,1) Matrix(151,190,120,151) -> Matrix(1,0,-2,1) Matrix(153,190,62,77) -> Matrix(1,0,0,1) Matrix(1177,1444,216,265) -> Matrix(1,-10,0,1) Matrix(1179,1444,218,267) -> Matrix(1,10,0,1) Matrix(531,646,374,455) -> Matrix(1,0,0,1) Matrix(4103,4978,1252,1519) -> Matrix(1,2,2,5) Matrix(4827,5852,1474,1787) -> Matrix(1,0,4,1) Matrix(723,874,158,191) -> Matrix(1,0,-2,1) Matrix(191,228,160,191) -> Matrix(1,2,-2,-3) Matrix(417,494,352,417) -> Matrix(1,2,-2,-3) Matrix(227,266,64,75) -> Matrix(1,0,0,1) Matrix(1253,1444,164,189) -> Matrix(1,-10,0,1) Matrix(1255,1444,166,191) -> Matrix(1,10,0,1) Matrix(1255,1406,374,419) -> Matrix(9,10,8,9) Matrix(683,760,204,227) -> Matrix(5,4,6,5) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(267,-304,166,-189) -> Matrix(3,2,4,3) Matrix(229,-266,130,-151) -> Matrix(1,0,0,1) Matrix(1443,-1748,440,-533) -> Matrix(1,0,4,1) Matrix(495,-608,92,-113) -> Matrix(9,4,2,1) Matrix(1215,-1558,712,-913) -> Matrix(1,0,2,1) Matrix(265,-342,148,-191) -> Matrix(1,0,2,1) Matrix(379,-494,234,-305) -> Matrix(1,0,2,1) Matrix(2469,-3382,1582,-2167) -> Matrix(1,0,-8,1) Matrix(303,-418,166,-229) -> Matrix(1,0,-2,1) Matrix(493,-684,302,-419) -> Matrix(1,0,0,1) Matrix(647,-912,188,-265) -> Matrix(1,4,0,1) Matrix(267,-380,26,-37) -> Matrix(1,0,0,1) Matrix(609,-874,370,-531) -> Matrix(1,2,0,1) Matrix(343,-494,184,-265) -> Matrix(1,2,-2,-3) Matrix(837,-1292,344,-531) -> Matrix(7,2,10,3) Matrix(4065,-6346,1096,-1711) -> Matrix(1,0,4,1) Matrix(1747,-2812,520,-837) -> Matrix(5,-4,4,-3) Matrix(493,-798,118,-191) -> Matrix(1,0,0,1) Matrix(761,-1254,230,-379) -> Matrix(1,-2,2,-3) Matrix(761,-1292,268,-455) -> Matrix(1,2,-2,-3) Matrix(3761,-6422,824,-1407) -> Matrix(1,-2,-2,5) Matrix(495,-874,64,-113) -> Matrix(7,4,-2,-1) Matrix(607,-1102,168,-305) -> Matrix(1,0,0,1) Matrix(343,-646,60,-113) -> Matrix(1,0,2,1) Matrix(229,-494,70,-151) -> Matrix(1,0,4,1) Matrix(189,-418,52,-115) -> Matrix(1,0,0,1) Matrix(151,-342,34,-77) -> Matrix(1,0,0,1) Matrix(115,-266,16,-37) -> Matrix(1,0,2,1) Matrix(645,-1558,142,-343) -> Matrix(3,-2,-4,3) Matrix(343,-874,104,-265) -> Matrix(1,2,2,5) Matrix(265,-684,74,-191) -> Matrix(1,0,0,1) Matrix(189,-494,44,-115) -> Matrix(1,0,0,1) Matrix(115,-304,14,-37) -> Matrix(1,0,0,1) Matrix(1215,-3382,328,-913) -> Matrix(3,2,-2,-1) 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): 45 Degree of the the map X: 45 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 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): 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 1/1 19/16 19/15 19/14 19/13 3/2 19/12 19/11 9/5 2/1 19/8 95/39 5/2 8/3 19/7 3/1 19/6 95/29 57/17 17/5 7/2 76/21 11/3 19/5 4/1 38/9 13/3 9/2 23/5 19/4 5/1 6/1 19/3 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -1/1 -6/1 -1/1 -1/2 -5/1 -1/3 -19/4 0/1 -14/3 0/1 1/2 -23/5 -1/1 -9/2 -1/1 0/1 -13/3 -1/1 -4/1 -1/1 0/1 -11/3 -1/3 -18/5 -1/1 1/0 -7/2 -1/1 -1/2 -17/5 -1/3 -10/3 -1/3 -1/4 -23/7 -1/3 -13/4 -1/5 0/1 -16/5 -1/11 0/1 -19/6 0/1 -3/1 1/1 -8/3 -1/1 -2/3 -21/8 -1/1 -1/2 -34/13 -1/1 0/1 -13/5 -1/1 -31/12 -1/1 -1/2 -18/7 -1/1 1/0 -23/9 -3/5 -5/2 -1/2 0/1 -17/7 -1/3 -12/5 -1/5 0/1 -19/8 0/1 -7/3 1/1 -9/4 -1/1 0/1 -20/9 -1/1 1/0 -11/5 -1/3 -2/1 -1/1 0/1 -11/6 -1/1 -1/2 -9/5 -1/1 -16/9 0/1 1/3 -23/13 3/1 -7/4 -1/1 1/0 -5/3 -1/1 -13/8 -1/3 0/1 -21/13 -1/3 -8/5 -1/5 0/1 -19/12 0/1 -11/7 1/5 -14/9 0/1 1/2 -3/2 -1/1 1/0 -13/9 -1/1 -10/7 -1/1 -1/2 -7/5 -1/3 -18/13 -1/2 -1/3 -47/34 -1/3 0/1 -76/55 -1/2 -1/4 -29/21 -1/3 -11/8 -1/3 -1/4 -26/19 -1/5 0/1 -15/11 -1/9 -19/14 0/1 -4/3 0/1 1/1 -21/16 1/1 1/0 -38/29 1/0 -17/13 -1/1 -13/10 -1/1 0/1 -22/17 0/1 1/5 -9/7 1/1 -5/4 0/1 1/0 -11/9 -3/1 -6/5 -1/1 1/0 -19/16 -2/1 0/1 -13/11 -1/1 -7/6 -1/1 1/0 -8/7 -3/1 -2/1 -1/1 -1/1 0/1 -1/2 1/0 1/1 -1/1 8/7 -2/3 -3/5 7/6 -1/1 -1/2 13/11 -1/1 19/16 -2/3 0/1 6/5 -1/1 -1/2 23/19 -1/3 17/14 -1/1 -1/2 11/9 -3/5 5/4 -1/2 0/1 19/15 -1/1 -1/3 14/11 -1/2 0/1 9/7 -1/3 13/10 -1/1 0/1 4/3 -1/3 0/1 19/14 0/1 15/11 1/7 26/19 0/1 1/3 11/8 1/2 1/1 18/13 1/1 1/0 7/5 1/1 10/7 -1/1 1/0 13/9 -1/1 16/11 -4/3 -1/1 19/13 -1/1 3/2 -1/1 -1/2 20/13 -5/14 -1/3 17/11 -1/3 14/9 -1/4 0/1 11/7 -1/7 19/12 0/1 8/5 0/1 1/3 37/23 1/1 29/18 1/1 2/1 21/13 1/1 34/21 -1/1 0/1 13/8 0/1 1/1 5/3 -1/1 12/7 -2/1 -1/1 19/11 -1/1 7/4 -1/1 -1/2 23/13 -3/7 39/22 -4/11 -1/3 16/9 -1/5 0/1 25/14 0/1 1/1 9/5 -1/1 20/11 -1/1 -1/2 11/6 -1/1 1/0 2/1 -1/1 0/1 13/6 -1/1 0/1 11/5 1/1 9/4 -1/1 0/1 7/3 -1/3 19/8 0/1 12/5 0/1 1/3 17/7 1/1 56/23 7/8 1/1 95/39 1/1 39/16 1/1 6/5 22/9 2/1 3/1 5/2 0/1 1/0 23/9 -3/1 41/16 -3/2 -7/5 18/7 -1/1 -1/2 13/5 -1/1 21/8 -1/1 1/0 8/3 -2/1 -1/1 19/7 -1/1 11/4 -1/1 -3/4 3/1 -1/3 19/6 0/1 16/5 0/1 1/9 13/4 0/1 1/3 36/11 0/1 1/3 95/29 1/3 59/18 1/3 1/2 23/7 1/1 10/3 1/2 1/1 57/17 1/1 47/14 1/1 6/5 37/11 1/1 27/8 3/1 1/0 17/5 1/1 7/2 -1/1 1/0 25/7 -1/1 18/5 -1/1 -1/2 47/13 -1/1 76/21 -1/2 1/0 29/8 -1/1 0/1 11/3 1/1 15/4 -1/1 1/0 19/5 -1/1 4/1 -1/1 0/1 21/5 1/1 38/9 1/0 17/4 -1/1 1/0 13/3 -1/1 9/2 -1/1 0/1 23/5 -1/1 14/3 -1/4 0/1 19/4 0/1 5/1 1/1 6/1 -1/1 1/0 19/3 -1/1 13/2 -1/1 0/1 7/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(18,133,-13,-96) (-7/1,1/0) -> (-7/5,-18/13) Hyperbolic Matrix(20,133,3,20) (-7/1,-6/1) -> (13/2,7/1) Hyperbolic Matrix(18,95,-11,-58) (-6/1,-5/1) -> (-5/3,-13/8) 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(94,437,-37,-172) (-14/3,-23/5) -> (-23/9,-5/2) Hyperbolic Matrix(96,437,-29,-132) (-23/5,-9/2) -> (-10/3,-23/7) Hyperbolic Matrix(56,247,-39,-172) (-9/2,-13/3) -> (-13/9,-10/7) Hyperbolic Matrix(115,494,-44,-189) (-13/3,-4/1) -> (-34/13,-13/5) Hyperbolic Matrix(56,209,15,56) (-4/1,-11/3) -> (11/3,15/4) 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(94,323,-39,-134) (-7/2,-17/5) -> (-17/7,-12/5) Hyperbolic Matrix(208,703,129,436) (-17/5,-10/3) -> (29/18,21/13) Hyperbolic Matrix(134,437,111,362) (-23/7,-13/4) -> (6/5,23/19) 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(20,57,7,20) (-3/1,-8/3) -> (11/4,3/1) Hyperbolic Matrix(94,247,-51,-134) (-8/3,-21/8) -> (-2/1,-11/6) 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(512,1311,289,740) (-18/7,-23/9) -> (23/13,39/22) Hyperbolic Matrix(132,323,85,208) (-5/2,-17/7) -> (17/11,14/9) 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(58,133,-41,-94) (-7/3,-9/4) -> (-10/7,-7/5) Hyperbolic Matrix(495,1102,-358,-797) (-9/4,-20/9) -> (-18/13,-47/34) Hyperbolic Matrix(96,209,79,172) (-11/5,-2/1) -> (17/14,11/9) 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(740,1311,289,512) (-16/9,-23/13) -> (23/9,41/16) Hyperbolic Matrix(398,703,-291,-514) (-23/13,-7/4) -> (-26/19,-15/11) Hyperbolic Matrix(56,95,33,56) (-7/4,-5/3) -> (5/3,12/7) Hyperbolic Matrix(305,494,-234,-379) (-13/8,-21/13) -> (-17/13,-13/10) Hyperbolic Matrix(436,703,129,208) (-21/13,-8/5) -> (27/8,17/5) 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(134,209,-109,-170) (-11/7,-14/9) -> (-5/4,-11/9) Hyperbolic Matrix(208,323,85,132) (-14/9,-3/2) -> (22/9,5/2) Hyperbolic Matrix(170,247,117,170) (-3/2,-13/9) -> (13/9,16/11) 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(208,285,-181,-248) (-11/8,-26/19) -> (-7/6,-8/7) 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(134,171,105,134) (-9/7,-5/4) -> (14/11,9/7) Hyperbolic Matrix(172,209,79,96) (-11/9,-6/5) -> (13/6,11/5) 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(286,323,85,96) (-8/7,-1/1) -> (37/11,27/8) 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(248,-285,181,-208) (8/7,7/6) -> (26/19,11/8) Hyperbolic Matrix(1443,-1748,440,-533) (23/19,17/14) -> (59/18,23/7) Hyperbolic Matrix(170,-209,109,-134) (11/9,5/4) -> (14/9,11/7) Hyperbolic Matrix(286,-361,225,-284) (5/4,19/15) -> (19/15,14/11) Parabolic 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(514,-703,291,-398) (15/11,26/19) -> (7/4,23/13) Hyperbolic Matrix(303,-418,166,-229) (11/8,18/13) -> (20/11,11/6) Hyperbolic Matrix(96,-133,13,-18) (18/13,7/5) -> (7/1,1/0) Hyperbolic Matrix(94,-133,41,-58) (7/5,10/7) -> (9/4,7/3) Hyperbolic Matrix(172,-247,39,-56) (10/7,13/9) -> (13/3,9/2) Hyperbolic Matrix(248,-361,169,-246) (16/11,19/13) -> (19/13,3/2) Parabolic Matrix(286,-437,161,-246) (3/2,20/13) -> (39/22,16/9) Hyperbolic Matrix(837,-1292,344,-531) (20/13,17/11) -> (17/7,56/23) 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(58,-95,11,-18) (13/8,5/3) -> (5/1,6/1) Hyperbolic Matrix(210,-361,121,-208) (12/7,19/11) -> (19/11,7/4) Parabolic Matrix(607,-1102,168,-305) (9/5,20/11) -> (18/5,47/13) Hyperbolic Matrix(134,-247,51,-94) (11/6,2/1) -> (21/8,8/3) 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(134,-323,39,-94) (12/5,17/7) -> (17/5,7/2) Hyperbolic Matrix(3706,-9025,1521,-3704) (56/23,95/39) -> (95/39,39/16) Parabolic Matrix(818,-1995,319,-778) (39/16,22/9) -> (41/16,18/7) Hyperbolic Matrix(172,-437,37,-94) (5/2,23/9) -> (23/5,14/3) 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(134,-361,49,-132) (8/3,19/7) -> (19/7,11/4) Parabolic Matrix(2756,-9025,841,-2754) (36/11,95/29) -> (95/29,59/18) Parabolic Matrix(132,-437,29,-96) (23/7,10/3) -> (9/2,23/5) Hyperbolic Matrix(970,-3249,289,-968) (10/3,57/17) -> (57/17,47/14) Parabolic Matrix(96,-361,25,-94) (15/4,19/5) -> (19/5,4/1) Parabolic Matrix(58,-361,9,-56) (6/1,19/3) -> (19/3,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(18,133,-13,-96) -> Matrix(2,1,-5,-2) Matrix(20,133,3,20) -> Matrix(2,1,-1,0) Matrix(18,95,-11,-58) -> Matrix(2,1,-5,-2) Matrix(39,190,8,39) -> Matrix(1,0,4,1) Matrix(113,532,24,113) -> Matrix(1,0,-6,1) Matrix(94,437,-37,-172) -> Matrix(2,-1,-3,2) Matrix(96,437,-29,-132) -> Matrix(0,-1,1,4) Matrix(56,247,-39,-172) -> Matrix(0,-1,1,2) Matrix(115,494,-44,-189) -> Matrix(1,0,0,1) Matrix(56,209,15,56) -> Matrix(2,1,-1,0) Matrix(115,418,-52,-189) -> Matrix(1,0,0,1) Matrix(191,684,-74,-265) -> Matrix(1,0,0,1) Matrix(94,323,-39,-134) -> Matrix(2,1,-9,-4) Matrix(208,703,129,436) -> Matrix(2,1,-1,0) Matrix(134,437,111,362) -> Matrix(4,1,-9,-2) Matrix(189,608,106,341) -> Matrix(1,0,6,1) Matrix(191,608,60,191) -> Matrix(1,0,20,1) Matrix(37,114,12,37) -> Matrix(1,0,-4,1) Matrix(20,57,7,20) -> Matrix(0,-1,1,2) Matrix(94,247,-51,-134) -> Matrix(2,1,-1,0) Matrix(305,798,-232,-607) -> Matrix(1,0,2,1) Matrix(191,494,162,419) -> Matrix(1,0,0,1) Matrix(512,1311,289,740) -> Matrix(4,3,-11,-8) Matrix(132,323,85,208) -> Matrix(2,1,-9,-4) Matrix(191,456,80,191) -> Matrix(1,0,8,1) Matrix(113,266,48,113) -> Matrix(1,0,-4,1) Matrix(58,133,-41,-94) -> Matrix(0,-1,1,2) Matrix(495,1102,-358,-797) -> Matrix(1,0,-2,1) Matrix(96,209,79,172) -> Matrix(0,-1,1,2) Matrix(229,418,-166,-303) -> Matrix(1,0,-2,1) Matrix(191,342,-148,-265) -> Matrix(1,0,2,1) Matrix(740,1311,289,512) -> Matrix(2,-3,-1,2) Matrix(398,703,-291,-514) -> Matrix(0,-1,1,6) Matrix(56,95,33,56) -> Matrix(2,1,-1,0) Matrix(305,494,-234,-379) -> Matrix(1,0,2,1) Matrix(436,703,129,208) -> Matrix(2,1,-1,0) Matrix(191,304,120,191) -> Matrix(1,0,8,1) Matrix(265,418,168,265) -> Matrix(1,0,-12,1) Matrix(134,209,-109,-170) -> Matrix(2,-1,1,0) Matrix(208,323,85,132) -> Matrix(2,-1,1,0) Matrix(170,247,117,170) -> Matrix(4,3,-3,-2) Matrix(4179,5776,1154,1595) -> Matrix(1,0,2,1) Matrix(4181,5776,1156,1597) -> Matrix(1,0,2,1) Matrix(208,285,-181,-248) -> Matrix(6,1,-1,0) Matrix(419,570,308,419) -> Matrix(1,0,16,1) Matrix(113,152,84,113) -> Matrix(1,0,-4,1) Matrix(1101,1444,260,341) -> Matrix(1,-2,0,1) Matrix(1103,1444,262,343) -> Matrix(1,2,0,1) Matrix(381,494,118,153) -> Matrix(1,0,4,1) Matrix(134,171,105,134) -> Matrix(0,-1,1,2) Matrix(172,209,79,96) -> Matrix(0,-1,1,2) Matrix(191,228,160,191) -> Matrix(1,2,-2,-3) Matrix(417,494,352,417) -> Matrix(1,2,-2,-3) Matrix(227,266,64,75) -> Matrix(1,0,0,1) Matrix(286,323,85,96) -> Matrix(2,3,1,2) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(267,-304,166,-189) -> Matrix(3,2,4,3) Matrix(248,-285,181,-208) -> Matrix(2,1,7,4) Matrix(1443,-1748,440,-533) -> Matrix(1,0,4,1) Matrix(170,-209,109,-134) -> Matrix(2,1,-9,-4) Matrix(286,-361,225,-284) -> Matrix(2,1,-5,-2) Matrix(265,-342,148,-191) -> Matrix(1,0,2,1) Matrix(379,-494,234,-305) -> Matrix(1,0,2,1) Matrix(514,-703,291,-398) -> Matrix(4,-1,-7,2) Matrix(303,-418,166,-229) -> Matrix(1,0,-2,1) Matrix(96,-133,13,-18) -> Matrix(0,-1,1,0) Matrix(94,-133,41,-58) -> Matrix(0,-1,1,2) Matrix(172,-247,39,-56) -> Matrix(0,-1,1,2) Matrix(248,-361,169,-246) -> Matrix(4,5,-5,-6) Matrix(286,-437,161,-246) -> Matrix(2,1,-9,-4) Matrix(837,-1292,344,-531) -> Matrix(7,2,10,3) Matrix(1747,-2812,520,-837) -> Matrix(5,-4,4,-3) Matrix(493,-798,118,-191) -> Matrix(1,0,0,1) Matrix(58,-95,11,-18) -> Matrix(0,-1,1,0) Matrix(210,-361,121,-208) -> Matrix(2,3,-3,-4) Matrix(607,-1102,168,-305) -> Matrix(1,0,0,1) Matrix(134,-247,51,-94) -> Matrix(2,1,-1,0) Matrix(229,-494,70,-151) -> Matrix(1,0,4,1) Matrix(189,-418,52,-115) -> Matrix(1,0,0,1) Matrix(134,-323,39,-94) -> Matrix(2,-1,1,0) Matrix(3706,-9025,1521,-3704) -> Matrix(14,-13,13,-12) Matrix(818,-1995,319,-778) -> Matrix(4,-5,-3,4) Matrix(172,-437,37,-94) -> Matrix(0,-1,1,4) Matrix(265,-684,74,-191) -> Matrix(1,0,0,1) Matrix(189,-494,44,-115) -> Matrix(1,0,0,1) Matrix(134,-361,49,-132) -> Matrix(4,5,-5,-6) Matrix(2756,-9025,841,-2754) -> Matrix(4,-1,9,-2) Matrix(132,-437,29,-96) -> Matrix(2,-1,-3,2) Matrix(970,-3249,289,-968) -> Matrix(8,-7,7,-6) Matrix(96,-361,25,-94) -> Matrix(0,-1,1,2) Matrix(58,-361,9,-56) -> Matrix(0,-1,1,2) 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): 45 ----------------------------------------------------------------------- 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 (-1/1,0/1) 0 1 1/1 -1/1 1 19 8/7 (-2/3,-3/5) 0 19 7/6 (-1/1,-1/2) 0 19 13/11 -1/1 1 19 19/16 (-1/1,-1/2) 0 1 6/5 (-1/1,-1/2) 0 19 11/9 -3/5 1 19 5/4 (-1/2,0/1) 0 19 19/15 (-1/1,-1/3).(-1/2,0/1) 0 1 9/7 -1/3 1 19 13/10 (-1/1,0/1) 0 19 4/3 (-1/3,0/1) 0 19 19/14 0/1 10 1 15/11 1/7 1 19 26/19 (0/1,1/3) 0 19 11/8 (1/2,1/1) 0 19 18/13 (1/1,1/0) 0 19 7/5 1/1 1 19 10/7 (-1/1,1/0) 0 19 13/9 -1/1 1 19 19/13 -1/1 5 1 3/2 (-1/1,-1/2) 0 19 14/9 (-1/4,0/1) 0 19 11/7 -1/7 1 19 19/12 0/1 10 1 8/5 (0/1,1/3) 0 19 21/13 1/1 1 19 34/21 (-1/1,0/1) 0 19 13/8 (0/1,1/1) 0 19 5/3 -1/1 1 19 19/11 -1/1 3 1 7/4 (-1/1,-1/2) 0 19 23/13 -3/7 1 19 16/9 (-1/5,0/1) 0 19 25/14 (0/1,1/1) 0 19 9/5 -1/1 1 19 20/11 (-1/1,-1/2) 0 19 11/6 (-1/1,1/0) 0 19 2/1 (-1/1,0/1) 0 19 13/6 (-1/1,0/1) 0 19 11/5 1/1 1 19 9/4 (-1/1,0/1) 0 19 7/3 -1/3 1 19 19/8 0/1 6 1 12/5 (0/1,1/3) 0 19 17/7 1/1 1 19 95/39 1/1 13 1 39/16 (1/1,6/5) 0 19 22/9 (2/1,3/1) 0 19 5/2 (0/1,1/0) 0 19 23/9 -3/1 1 19 41/16 (-3/2,-7/5) 0 19 18/7 (-1/1,-1/2) 0 19 13/5 -1/1 1 19 21/8 (-1/1,1/0) 0 19 8/3 (-2/1,-1/1) 0 19 19/7 -1/1 5 1 3/1 -1/3 1 19 19/6 0/1 12 1 16/5 (0/1,1/9) 0 19 13/4 (0/1,1/3) 0 19 36/11 (0/1,1/3) 0 19 95/29 1/3 1 1 23/7 1/1 1 19 10/3 (1/2,1/1) 0 19 57/17 1/1 7 1 37/11 1/1 1 19 27/8 (3/1,1/0) 0 19 17/5 1/1 1 19 7/2 (-1/1,1/0) 0 19 25/7 -1/1 1 19 18/5 (-1/1,-1/2) 0 19 47/13 -1/1 1 19 76/21 (-1/1,0/1) 0 1 29/8 (-1/1,0/1) 0 19 11/3 1/1 1 19 19/5 -1/1 1 1 4/1 (-1/1,0/1) 0 19 21/5 1/1 1 19 38/9 1/0 2 1 17/4 (-1/1,1/0) 0 19 13/3 -1/1 1 19 9/2 (-1/1,0/1) 0 19 23/5 -1/1 1 19 14/3 (-1/4,0/1) 0 19 19/4 0/1 5 1 5/1 1/1 1 19 6/1 (-1/1,1/0) 0 19 19/3 -1/1 1 1 7/1 -1/1 1 19 1/0 (-1/1,0/1) 0 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(286,-323,85,-96) (1/1,8/7) -> (37/11,27/8) Glide Reflection Matrix(248,-285,181,-208) (8/7,7/6) -> (26/19,11/8) Hyperbolic Matrix(227,-266,64,-75) (7/6,13/11) -> (7/2,25/7) Glide Reflection Matrix(417,-494,352,-417) (13/11,19/16) -> (13/11,19/16) Reflection Matrix(191,-228,160,-191) (19/16,6/5) -> (19/16,6/5) Reflection Matrix(172,-209,79,-96) (6/5,11/9) -> (13/6,11/5) Glide Reflection Matrix(170,-209,109,-134) (11/9,5/4) -> (14/9,11/7) Hyperbolic Matrix(151,-190,120,-151) (5/4,19/15) -> (5/4,19/15) Reflection Matrix(134,-171,105,-134) (19/15,9/7) -> (19/15,9/7) Reflection 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,-152,84,-113) (4/3,19/14) -> (4/3,19/14) Reflection Matrix(419,-570,308,-419) (19/14,15/11) -> (19/14,15/11) Reflection Matrix(514,-703,291,-398) (15/11,26/19) -> (7/4,23/13) Hyperbolic Matrix(303,-418,166,-229) (11/8,18/13) -> (20/11,11/6) Hyperbolic Matrix(96,-133,13,-18) (18/13,7/5) -> (7/1,1/0) Hyperbolic Matrix(94,-133,41,-58) (7/5,10/7) -> (9/4,7/3) Hyperbolic Matrix(172,-247,39,-56) (10/7,13/9) -> (13/3,9/2) Hyperbolic Matrix(170,-247,117,-170) (13/9,19/13) -> (13/9,19/13) Reflection Matrix(77,-114,52,-77) (19/13,3/2) -> (19/13,3/2) Reflection Matrix(208,-323,85,-132) (3/2,14/9) -> (22/9,5/2) Glide Reflection Matrix(265,-418,168,-265) (11/7,19/12) -> (11/7,19/12) Reflection Matrix(191,-304,120,-191) (19/12,8/5) -> (19/12,8/5) Reflection Matrix(436,-703,129,-208) (8/5,21/13) -> (27/8,17/5) Glide Reflection Matrix(493,-798,118,-191) (21/13,34/21) -> (4/1,21/5) Hyperbolic Matrix(58,-95,11,-18) (13/8,5/3) -> (5/1,6/1) Hyperbolic Matrix(56,-95,33,-56) (5/3,19/11) -> (5/3,19/11) Reflection Matrix(153,-266,88,-153) (19/11,7/4) -> (19/11,7/4) Reflection Matrix(740,-1311,289,-512) (23/13,16/9) -> (23/9,41/16) Glide Reflection Matrix(341,-608,106,-189) (16/9,25/14) -> (16/5,13/4) Glide Reflection Matrix(607,-1102,168,-305) (9/5,20/11) -> (18/5,47/13) Hyperbolic Matrix(134,-247,51,-94) (11/6,2/1) -> (21/8,8/3) 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(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(134,-323,39,-94) (12/5,17/7) -> (17/5,7/2) Hyperbolic Matrix(664,-1615,273,-664) (17/7,95/39) -> (17/7,95/39) Reflection Matrix(3041,-7410,1248,-3041) (95/39,39/16) -> (95/39,39/16) Reflection Matrix(818,-1995,319,-778) (39/16,22/9) -> (41/16,18/7) Hyperbolic Matrix(172,-437,37,-94) (5/2,23/9) -> (23/5,14/3) 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(113,-304,42,-113) (8/3,19/7) -> (8/3,19/7) Reflection Matrix(20,-57,7,-20) (19/7,3/1) -> (19/7,3/1) 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(2089,-6840,638,-2089) (36/11,95/29) -> (36/11,95/29) Reflection Matrix(666,-2185,203,-666) (95/29,23/7) -> (95/29,23/7) Reflection Matrix(132,-437,29,-96) (23/7,10/3) -> (9/2,23/5) Hyperbolic Matrix(341,-1140,102,-341) (10/3,57/17) -> (10/3,57/17) Reflection Matrix(628,-2109,187,-628) (57/17,37/11) -> (57/17,37/11) Reflection Matrix(1975,-7144,546,-1975) (47/13,76/21) -> (47/13,76/21) Reflection Matrix(1217,-4408,336,-1217) (76/21,29/8) -> (76/21,29/8) Reflection Matrix(56,-209,15,-56) (11/3,19/5) -> (11/3,19/5) Reflection Matrix(39,-152,10,-39) (19/5,4/1) -> (19/5,4/1) Reflection Matrix(379,-1596,90,-379) (21/5,38/9) -> (21/5,38/9) Reflection Matrix(305,-1292,72,-305) (38/9,17/4) -> (38/9,17/4) Reflection 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(37,-228,6,-37) (6/1,19/3) -> (6/1,19/3) Reflection Matrix(20,-133,3,-20) (19/3,7/1) -> (19/3,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(-1,0,2,1) (0/1,1/1) -> (-1/1,0/1) Matrix(286,-323,85,-96) -> Matrix(4,3,3,2) Matrix(248,-285,181,-208) -> Matrix(2,1,7,4) Matrix(227,-266,64,-75) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(417,-494,352,-417) -> Matrix(3,2,-4,-3) (13/11,19/16) -> (-1/1,-1/2) Matrix(191,-228,160,-191) -> Matrix(3,2,-4,-3) (19/16,6/5) -> (-1/1,-1/2) Matrix(172,-209,79,-96) -> Matrix(2,1,-3,-2) *** -> (-1/1,-1/3) Matrix(170,-209,109,-134) -> Matrix(2,1,-9,-4) -1/3 Matrix(151,-190,120,-151) -> Matrix(-1,0,4,1) (5/4,19/15) -> (-1/2,0/1) Matrix(134,-171,105,-134) -> Matrix(2,1,-3,-2) (19/15,9/7) -> (-1/1,-1/3) Matrix(265,-342,148,-191) -> Matrix(1,0,2,1) 0/1 Matrix(379,-494,234,-305) -> Matrix(1,0,2,1) 0/1 Matrix(113,-152,84,-113) -> Matrix(-1,0,6,1) (4/3,19/14) -> (-1/3,0/1) Matrix(419,-570,308,-419) -> Matrix(1,0,14,-1) (19/14,15/11) -> (0/1,1/7) Matrix(514,-703,291,-398) -> Matrix(4,-1,-7,2) Matrix(303,-418,166,-229) -> Matrix(1,0,-2,1) 0/1 Matrix(96,-133,13,-18) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(94,-133,41,-58) -> Matrix(0,-1,1,2) -1/1 Matrix(172,-247,39,-56) -> Matrix(0,-1,1,2) -1/1 Matrix(170,-247,117,-170) -> Matrix(2,3,-1,-2) (13/9,19/13) -> (-3/1,-1/1) Matrix(77,-114,52,-77) -> Matrix(3,2,-4,-3) (19/13,3/2) -> (-1/1,-1/2) Matrix(208,-323,85,-132) -> Matrix(4,1,1,0) Matrix(265,-418,168,-265) -> Matrix(-1,0,14,1) (11/7,19/12) -> (-1/7,0/1) Matrix(191,-304,120,-191) -> Matrix(1,0,6,-1) (19/12,8/5) -> (0/1,1/3) Matrix(436,-703,129,-208) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(493,-798,118,-191) -> Matrix(1,0,0,1) Matrix(58,-95,11,-18) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(56,-95,33,-56) -> Matrix(0,1,1,0) (5/3,19/11) -> (-1/1,1/1) Matrix(153,-266,88,-153) -> Matrix(3,2,-4,-3) (19/11,7/4) -> (-1/1,-1/2) Matrix(740,-1311,289,-512) -> Matrix(8,3,-5,-2) Matrix(341,-608,106,-189) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(607,-1102,168,-305) -> Matrix(1,0,0,1) Matrix(134,-247,51,-94) -> Matrix(2,1,-1,0) -1/1 Matrix(229,-494,70,-151) -> Matrix(1,0,4,1) 0/1 Matrix(189,-418,52,-115) -> Matrix(1,0,0,1) Matrix(113,-266,48,-113) -> Matrix(-1,0,6,1) (7/3,19/8) -> (-1/3,0/1) Matrix(191,-456,80,-191) -> Matrix(1,0,6,-1) (19/8,12/5) -> (0/1,1/3) Matrix(134,-323,39,-94) -> Matrix(2,-1,1,0) 1/1 Matrix(664,-1615,273,-664) -> Matrix(2,-1,3,-2) (17/7,95/39) -> (1/3,1/1) Matrix(3041,-7410,1248,-3041) -> Matrix(11,-12,10,-11) (95/39,39/16) -> (1/1,6/5) Matrix(818,-1995,319,-778) -> Matrix(4,-5,-3,4) Matrix(172,-437,37,-94) -> Matrix(0,-1,1,4) Matrix(265,-684,74,-191) -> Matrix(1,0,0,1) Matrix(189,-494,44,-115) -> Matrix(1,0,0,1) Matrix(113,-304,42,-113) -> Matrix(3,4,-2,-3) (8/3,19/7) -> (-2/1,-1/1) Matrix(20,-57,7,-20) -> Matrix(2,1,-3,-2) (19/7,3/1) -> (-1/1,-1/3) Matrix(37,-114,12,-37) -> Matrix(-1,0,6,1) (3/1,19/6) -> (-1/3,0/1) Matrix(191,-608,60,-191) -> Matrix(1,0,18,-1) (19/6,16/5) -> (0/1,1/9) Matrix(2089,-6840,638,-2089) -> Matrix(1,0,6,-1) (36/11,95/29) -> (0/1,1/3) Matrix(666,-2185,203,-666) -> Matrix(2,-1,3,-2) (95/29,23/7) -> (1/3,1/1) Matrix(132,-437,29,-96) -> Matrix(2,-1,-3,2) Matrix(341,-1140,102,-341) -> Matrix(3,-2,4,-3) (10/3,57/17) -> (1/2,1/1) Matrix(628,-2109,187,-628) -> Matrix(4,-5,3,-4) (57/17,37/11) -> (1/1,5/3) Matrix(1975,-7144,546,-1975) -> Matrix(-1,0,2,1) (47/13,76/21) -> (-1/1,0/1) Matrix(1217,-4408,336,-1217) -> Matrix(-1,0,2,1) (76/21,29/8) -> (-1/1,0/1) Matrix(56,-209,15,-56) -> Matrix(0,1,1,0) (11/3,19/5) -> (-1/1,1/1) Matrix(39,-152,10,-39) -> Matrix(-1,0,2,1) (19/5,4/1) -> (-1/1,0/1) Matrix(379,-1596,90,-379) -> Matrix(-1,2,0,1) (21/5,38/9) -> (1/1,1/0) Matrix(305,-1292,72,-305) -> Matrix(1,2,0,-1) (38/9,17/4) -> (-1/1,1/0) Matrix(113,-532,24,-113) -> Matrix(-1,0,8,1) (14/3,19/4) -> (-1/4,0/1) Matrix(39,-190,8,-39) -> Matrix(1,0,2,-1) (19/4,5/1) -> (0/1,1/1) Matrix(37,-228,6,-37) -> Matrix(1,2,0,-1) (6/1,19/3) -> (-1/1,1/0) Matrix(20,-133,3,-20) -> Matrix(0,1,1,0) (19/3,7/1) -> (-1/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.