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 -20/57 -23/76 -11/38 -21/76 -41/152 -9/38 -4/17 -25/114 -7/38 -10/57 -2/15 -5/38 -1/9 -2/19 -1/10 0/1 1/8 1/7 2/13 3/19 1/6 3/17 2/11 3/16 1/5 4/19 3/14 2/9 3/13 1/4 5/19 3/11 5/18 2/7 6/19 1/3 7/19 2/5 5/12 8/19 7/15 1/2 11/19 12/19 37/57 2/3 13/19 14/19 15/19 47/57 16/19 17/19 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -7/8 -5/2 -6/7 -2/1 -1/1 -11/13 -5/4 -16/19 -1/1 -5/6 -1/2 -19/23 -1/2 -14/17 0/1 1/1 -9/11 -1/2 -13/16 1/2 -4/5 1/1 1/0 -15/19 1/0 -11/14 1/0 -29/37 1/0 -18/23 -4/1 -3/1 -25/32 1/0 -7/9 1/0 -10/13 -3/1 -2/1 -3/4 -3/2 -14/19 -1/1 -11/15 -7/8 -30/41 -1/1 -5/6 -19/26 -3/4 -27/37 -3/4 -8/11 -1/1 -2/3 -13/18 -1/2 -5/7 -1/2 -17/24 1/0 -12/17 -1/1 0/1 -19/27 1/2 -26/37 0/1 1/1 -7/10 1/0 -16/23 -2/1 -1/1 -9/13 1/0 -11/16 1/0 -13/19 1/0 -2/3 -1/1 1/0 -13/20 1/0 -11/17 -3/2 -9/14 -3/2 -25/39 -3/2 -41/64 -3/2 -16/25 -4/3 -1/1 -7/11 -7/6 -12/19 -1/1 -5/8 -5/6 -23/37 -3/4 -18/29 -3/4 -11/15 -13/21 -7/10 -21/34 -5/8 -8/13 -1/1 -2/3 -19/31 -1/2 -11/18 -1/2 -25/41 -1/2 -14/23 -2/3 -3/5 -17/28 -1/2 -3/5 -1/2 -13/22 -1/2 -23/39 -1/2 -10/17 -1/3 0/1 -17/29 -1/2 -41/70 -1/2 -24/41 -1/2 -1/3 -7/12 -1/4 -11/19 0/1 -4/7 0/1 1/1 -17/30 -1/2 -13/23 1/2 -22/39 0/1 1/1 -9/16 1/2 -14/25 1/1 2/1 -5/9 1/0 -11/20 1/0 -6/11 -3/1 -2/1 -7/13 -3/2 -8/15 -4/3 -1/1 -1/2 -1/2 -6/13 0/1 1/1 -5/11 3/2 -4/9 -3/1 1/0 -7/16 1/0 -17/39 1/0 -10/23 -3/1 -2/1 -3/7 -3/2 -8/19 -1/1 -5/12 -5/6 -17/41 -3/4 -12/29 -7/9 -3/4 -7/17 -1/2 -23/56 -3/4 -39/95 -2/3 -16/39 -1/1 -2/3 -9/22 -3/4 -2/5 -1/1 -1/2 -9/23 -3/8 -16/41 -1/2 -1/3 -7/18 -1/2 -5/13 -1/4 -8/21 -1/1 0/1 -11/29 -1/2 -3/8 -1/4 -7/19 0/1 -4/11 0/1 1/3 -9/25 1/0 -14/39 0/1 1/1 -5/14 1/0 -6/17 0/1 1/1 -13/37 1/2 -20/57 1/1 -7/20 1/0 -1/3 1/0 -6/19 -1/1 -5/16 -5/6 -4/13 -1/1 -2/3 -11/36 -7/10 -29/95 -2/3 -18/59 -2/3 -11/17 -7/23 -5/8 -10/33 -5/9 -1/2 -23/76 -1/2 -13/43 -1/2 -3/10 -1/2 -17/57 -1/2 -14/47 -1/2 -11/23 -11/37 -1/2 -8/27 -3/7 -2/5 -5/17 -1/4 -7/24 -1/4 -9/31 -1/6 -11/38 0/1 -2/7 -1/1 0/1 -7/25 -3/4 -5/18 -1/2 -13/47 -1/2 -21/76 -1/2 -8/29 -1/2 -5/11 -3/11 -1/4 -10/37 -1/3 0/1 -17/63 -1/4 -41/152 0/1 -24/89 -1/1 0/1 -7/26 -1/2 -11/41 -1/4 -4/15 -1/5 0/1 -5/19 0/1 -1/4 1/0 -5/21 -1/6 -9/38 0/1 -4/17 0/1 1/3 -3/13 1/0 -5/22 1/0 -2/9 -1/1 1/0 -9/41 1/0 -25/114 1/0 -16/73 -3/1 1/0 -7/32 1/0 -5/23 1/0 -8/37 -2/1 -1/1 -3/14 -3/2 -4/19 -1/1 -1/5 -1/2 -3/16 -1/2 -5/27 -1/6 -7/38 0/1 -2/11 0/1 1/1 -3/17 -3/2 -10/57 -1/1 -7/40 -7/8 -4/23 -1/1 -2/3 -1/6 -1/2 -3/19 0/1 -2/13 0/1 1/1 -1/7 1/0 -2/15 -1/3 0/1 -5/38 0/1 -3/23 1/2 -1/8 -1/2 -1/9 1/0 -2/19 -1/1 -1/10 -1/2 0/1 -1/1 0/1 1/8 1/0 1/7 -1/2 2/13 -1/3 0/1 3/19 0/1 1/6 1/0 4/23 -2/1 -1/1 3/17 -3/4 2/11 -1/3 0/1 3/16 1/0 1/5 1/0 4/19 -1/1 3/14 -3/4 8/37 -1/1 -2/3 5/23 -1/2 7/32 -1/2 2/9 -1/1 -1/2 3/13 -1/2 1/4 -1/2 5/19 0/1 4/15 0/1 1/3 11/41 1/2 7/26 1/0 10/37 0/1 1/1 3/11 1/2 5/18 1/0 2/7 -1/1 0/1 7/24 1/2 5/17 1/2 8/27 2/1 3/1 11/37 1/0 3/10 1/0 7/23 -5/2 4/13 -2/1 -1/1 5/16 -5/4 6/19 -1/1 1/3 -1/2 7/20 -1/2 6/17 -1/3 0/1 5/14 -1/2 14/39 -1/3 0/1 23/64 -1/4 9/25 -1/2 4/11 -1/5 0/1 7/19 0/1 3/8 1/2 14/37 0/1 1/1 11/29 1/0 8/21 -1/1 0/1 13/34 1/2 5/13 1/2 12/31 1/1 2/1 7/18 1/0 16/41 1/1 1/0 9/23 3/2 11/28 1/0 2/5 -1/1 1/0 9/22 -3/2 16/39 -2/1 -1/1 7/17 1/0 12/29 -3/2 -7/5 29/70 -3/2 17/41 -3/2 5/12 -5/4 8/19 -1/1 3/7 -3/4 13/30 -1/2 10/23 -2/3 -3/5 17/39 -1/2 7/16 -1/2 11/25 -1/2 4/9 -3/5 -1/2 9/20 -1/2 5/11 -3/8 6/13 -1/3 0/1 7/15 -1/6 1/2 1/0 7/13 -3/4 6/11 -2/3 -3/5 5/9 -1/2 9/16 -1/4 22/39 -1/3 0/1 13/23 -1/4 4/7 -1/3 0/1 11/19 0/1 7/12 1/2 24/41 1/1 1/0 17/29 1/0 10/17 0/1 1/1 33/56 1/2 56/95 1/1 23/39 1/0 13/22 1/0 3/5 1/0 14/23 -3/1 -2/1 25/41 1/0 11/18 1/0 8/13 -2/1 -1/1 13/21 -7/4 18/29 -11/7 -3/2 5/8 -5/4 12/19 -1/1 7/11 -7/8 16/25 -1/1 -4/5 25/39 -3/4 9/14 -3/4 11/17 -3/4 24/37 -1/1 -2/3 37/57 -2/3 13/20 -1/2 2/3 -1/1 -1/2 13/19 -1/2 11/16 -1/2 9/13 -1/2 25/36 -3/2 66/95 -1/1 41/59 -7/8 16/23 -1/1 -2/3 23/33 -1/2 53/76 -1/2 30/43 -1/2 -3/7 7/10 -1/2 40/57 -1/3 33/47 -1/4 26/37 -1/3 0/1 19/27 -1/4 12/17 -1/1 0/1 17/24 -1/2 22/31 -1/5 0/1 27/38 0/1 5/7 1/0 18/25 0/1 1/1 13/18 1/0 34/47 7/1 1/0 55/76 1/0 21/29 1/0 8/11 -2/1 -1/1 27/37 -3/2 46/63 -7/5 -4/3 111/152 -4/3 65/89 -5/4 19/26 -3/2 30/41 -5/4 -1/1 11/15 -7/6 14/19 -1/1 3/4 -3/4 16/21 -9/13 -2/3 29/38 -2/3 13/17 -9/14 10/13 -2/3 -3/5 17/22 -7/12 7/9 -1/2 32/41 -3/5 -1/2 89/114 -1/2 57/73 -1/2 25/32 -1/2 18/23 -3/5 -4/7 29/37 -1/2 11/14 -1/2 15/19 -1/2 4/5 -1/2 -1/3 13/16 -1/4 22/27 -1/7 0/1 31/38 0/1 9/11 1/0 14/17 -1/3 0/1 47/57 0/1 33/40 1/6 19/23 1/0 5/6 1/0 16/19 -1/1 11/13 -5/6 6/7 -1/1 -2/3 13/15 -3/4 33/38 -2/3 20/23 -2/3 -7/11 7/8 -5/8 8/9 -7/13 -1/2 17/19 -1/2 9/10 -1/2 1/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(189,166,-304,-267) (-1/1,-7/8) -> (-5/8,-23/37) Hyperbolic Matrix(151,130,-266,-229) (-7/8,-6/7) -> (-4/7,-17/30) Hyperbolic Matrix(191,162,494,419) (-6/7,-11/13) -> (5/13,12/31) Hyperbolic Matrix(417,352,494,417) (-11/13,-16/19) -> (16/19,11/13) Hyperbolic Matrix(191,160,228,191) (-16/19,-5/6) -> (5/6,16/19) Hyperbolic Matrix(191,158,874,723) (-5/6,-19/23) -> (5/23,7/32) Hyperbolic Matrix(533,440,-1748,-1443) (-19/23,-14/17) -> (-18/59,-7/23) Hyperbolic Matrix(455,374,646,531) (-14/17,-9/11) -> (19/27,12/17) Hyperbolic Matrix(113,92,-608,-495) (-9/11,-13/16) -> (-3/16,-5/27) Hyperbolic Matrix(77,62,190,153) (-13/16,-4/5) -> (2/5,9/22) Hyperbolic Matrix(151,120,190,151) (-4/5,-15/19) -> (15/19,4/5) Hyperbolic Matrix(419,330,532,419) (-15/19,-11/14) -> (11/14,15/19) Hyperbolic Matrix(683,536,1064,835) (-11/14,-29/37) -> (25/39,9/14) Hyperbolic Matrix(761,596,1748,1369) (-29/37,-18/23) -> (10/23,17/39) Hyperbolic Matrix(151,118,874,683) (-18/23,-25/32) -> (1/6,4/23) Hyperbolic Matrix(913,712,-1558,-1215) (-25/32,-7/9) -> (-17/29,-41/70) Hyperbolic Matrix(191,148,-342,-265) (-7/9,-10/13) -> (-14/25,-5/9) Hyperbolic Matrix(305,234,-494,-379) (-10/13,-3/4) -> (-21/34,-8/13) Hyperbolic Matrix(113,84,152,113) (-3/4,-14/19) -> (14/19,3/4) Hyperbolic Matrix(419,308,570,419) (-14/19,-11/15) -> (11/15,14/19) Hyperbolic Matrix(609,446,1558,1141) (-11/15,-30/41) -> (16/41,9/23) Hyperbolic Matrix(911,666,1558,1139) (-30/41,-19/26) -> (7/12,24/41) Hyperbolic Matrix(2167,1582,-3382,-2469) (-19/26,-27/37) -> (-25/39,-41/64) Hyperbolic Matrix(417,304,1406,1025) (-27/37,-8/11) -> (8/27,11/37) Hyperbolic Matrix(229,166,-418,-303) (-8/11,-13/18) -> (-11/20,-6/11) Hyperbolic Matrix(419,302,-684,-493) (-13/18,-5/7) -> (-19/31,-11/18) Hyperbolic Matrix(265,188,-912,-647) (-5/7,-17/24) -> (-7/24,-9/31) Hyperbolic Matrix(229,162,646,457) (-17/24,-12/17) -> (6/17,5/14) Hyperbolic Matrix(531,374,646,455) (-12/17,-19/27) -> (9/11,14/17) Hyperbolic Matrix(381,268,1406,989) (-19/27,-26/37) -> (10/37,3/11) Hyperbolic Matrix(37,26,-380,-267) (-26/37,-7/10) -> (-1/10,0/1) Hyperbolic Matrix(531,370,-874,-609) (-7/10,-16/23) -> (-14/23,-17/28) Hyperbolic Matrix(265,184,-494,-343) (-16/23,-9/13) -> (-7/13,-8/15) Hyperbolic Matrix(267,184,608,419) (-9/13,-11/16) -> (7/16,11/25) Hyperbolic Matrix(417,286,608,417) (-11/16,-13/19) -> (13/19,11/16) Hyperbolic Matrix(77,52,114,77) (-13/19,-2/3) -> (2/3,13/19) Hyperbolic Matrix(341,222,874,569) (-2/3,-13/20) -> (7/18,16/41) Hyperbolic Matrix(531,344,-1292,-837) (-13/20,-11/17) -> (-7/17,-23/56) Hyperbolic Matrix(189,122,646,417) (-11/17,-9/14) -> (7/24,5/17) Hyperbolic Matrix(835,536,1064,683) (-9/14,-25/39) -> (29/37,11/14) Hyperbolic Matrix(1711,1096,-6346,-4065) (-41/64,-16/25) -> (-24/89,-7/26) Hyperbolic Matrix(191,122,418,267) (-16/25,-7/11) -> (5/11,6/13) Hyperbolic Matrix(265,168,418,265) (-7/11,-12/19) -> (12/19,7/11) Hyperbolic Matrix(191,120,304,191) (-12/19,-5/8) -> (5/8,12/19) Hyperbolic Matrix(837,520,-2812,-1747) (-23/37,-18/29) -> (-14/47,-11/37) Hyperbolic Matrix(455,282,1102,683) (-18/29,-13/21) -> (7/17,12/29) Hyperbolic Matrix(191,118,-798,-493) (-13/21,-21/34) -> (-1/4,-5/21) Hyperbolic Matrix(75,46,494,303) (-8/13,-19/31) -> (1/7,2/13) Hyperbolic Matrix(305,186,874,533) (-11/18,-25/41) -> (1/3,7/20) Hyperbolic Matrix(417,254,1558,949) (-25/41,-14/23) -> (4/15,11/41) Hyperbolic Matrix(379,230,-1254,-761) (-17/28,-3/5) -> (-13/43,-3/10) Hyperbolic Matrix(37,22,190,113) (-3/5,-13/22) -> (3/16,1/5) Hyperbolic Matrix(647,382,1482,875) (-13/22,-23/39) -> (17/39,7/16) Hyperbolic Matrix(455,268,-1292,-761) (-23/39,-10/17) -> (-6/17,-13/37) Hyperbolic Matrix(419,246,1102,647) (-10/17,-17/29) -> (11/29,8/21) Hyperbolic Matrix(1407,824,-6422,-3761) (-41/70,-24/41) -> (-16/73,-7/32) Hyperbolic Matrix(1139,666,1558,911) (-24/41,-7/12) -> (19/26,30/41) Hyperbolic Matrix(265,154,456,265) (-7/12,-11/19) -> (11/19,7/12) Hyperbolic Matrix(153,88,266,153) (-11/19,-4/7) -> (4/7,11/19) Hyperbolic Matrix(113,64,-874,-495) (-17/30,-13/23) -> (-3/23,-1/8) Hyperbolic Matrix(379,214,1748,987) (-13/23,-22/39) -> (8/37,5/23) Hyperbolic Matrix(607,342,1482,835) (-22/39,-9/16) -> (9/22,16/39) Hyperbolic Matrix(189,106,608,341) (-9/16,-14/25) -> (4/13,5/16) Hyperbolic Matrix(305,168,-1102,-607) (-5/9,-11/20) -> (-5/18,-13/47) Hyperbolic Matrix(151,82,418,227) (-6/11,-7/13) -> (9/25,4/11) Hyperbolic Matrix(113,60,-646,-343) (-8/15,-1/2) -> (-7/40,-4/23) Hyperbolic Matrix(151,70,-494,-229) (-1/2,-6/13) -> (-4/13,-11/36) Hyperbolic Matrix(267,122,418,191) (-6/13,-5/11) -> (7/11,16/25) Hyperbolic Matrix(115,52,-418,-189) (-5/11,-4/9) -> (-8/29,-3/11) Hyperbolic Matrix(77,34,-342,-151) (-4/9,-7/16) -> (-5/22,-2/9) Hyperbolic Matrix(875,382,1482,647) (-7/16,-17/39) -> (23/39,13/22) Hyperbolic Matrix(1369,596,1748,761) (-17/39,-10/23) -> (18/23,29/37) Hyperbolic Matrix(37,16,-266,-115) (-10/23,-3/7) -> (-1/7,-2/15) Hyperbolic Matrix(113,48,266,113) (-3/7,-8/19) -> (8/19,3/7) Hyperbolic Matrix(191,80,456,191) (-8/19,-5/12) -> (5/12,8/19) Hyperbolic Matrix(419,174,1558,647) (-5/12,-17/41) -> (11/41,7/26) Hyperbolic Matrix(343,142,-1558,-645) (-17/41,-12/29) -> (-2/9,-9/41) Hyperbolic Matrix(683,282,1102,455) (-12/29,-7/17) -> (13/21,18/29) Hyperbolic Matrix(3307,1358,5092,2091) (-23/56,-39/95) -> (37/57,13/20) Hyperbolic Matrix(3723,1528,5738,2355) (-39/95,-16/39) -> (24/37,37/57) Hyperbolic Matrix(835,342,1482,607) (-16/39,-9/22) -> (9/16,22/39) Hyperbolic Matrix(153,62,190,77) (-9/22,-2/5) -> (4/5,13/16) Hyperbolic Matrix(265,104,-874,-343) (-2/5,-9/23) -> (-7/23,-10/33) Hyperbolic Matrix(1141,446,1558,609) (-9/23,-16/41) -> (30/41,11/15) Hyperbolic Matrix(569,222,874,341) (-16/41,-7/18) -> (13/20,2/3) Hyperbolic Matrix(191,74,-684,-265) (-7/18,-5/13) -> (-7/25,-5/18) Hyperbolic Matrix(115,44,-494,-189) (-5/13,-8/21) -> (-4/17,-3/13) Hyperbolic Matrix(647,246,1102,419) (-8/21,-11/29) -> (17/29,10/17) Hyperbolic Matrix(37,14,-304,-115) (-11/29,-3/8) -> (-1/8,-1/9) Hyperbolic Matrix(113,42,304,113) (-3/8,-7/19) -> (7/19,3/8) Hyperbolic Matrix(153,56,418,153) (-7/19,-4/11) -> (4/11,7/19) Hyperbolic Matrix(227,82,418,151) (-4/11,-9/25) -> (7/13,6/11) Hyperbolic Matrix(913,328,-3382,-1215) (-9/25,-14/39) -> (-10/37,-17/63) Hyperbolic Matrix(229,82,1064,381) (-14/39,-5/14) -> (3/14,8/37) Hyperbolic Matrix(457,162,646,229) (-5/14,-6/17) -> (12/17,17/24) Hyperbolic Matrix(3383,1188,5738,2015) (-13/37,-20/57) -> (56/95,23/39) Hyperbolic Matrix(3001,1052,5092,1785) (-20/57,-7/20) -> (33/56,56/95) Hyperbolic Matrix(533,186,874,305) (-7/20,-1/3) -> (25/41,11/18) Hyperbolic Matrix(37,12,114,37) (-1/3,-6/19) -> (6/19,1/3) Hyperbolic Matrix(191,60,608,191) (-6/19,-5/16) -> (5/16,6/19) Hyperbolic Matrix(381,118,494,153) (-5/16,-4/13) -> (10/13,17/22) Hyperbolic Matrix(4827,1474,5852,1787) (-11/36,-29/95) -> (47/57,33/40) Hyperbolic Matrix(4103,1252,4978,1519) (-29/95,-18/59) -> (14/17,47/57) Hyperbolic Matrix(4029,1220,5776,1749) (-10/33,-23/76) -> (53/76,30/43) Hyperbolic Matrix(4027,1218,5776,1747) (-23/76,-13/43) -> (23/33,53/76) Hyperbolic Matrix(683,204,760,227) (-3/10,-17/57) -> (17/19,9/10) Hyperbolic Matrix(1255,374,1406,419) (-17/57,-14/47) -> (8/9,17/19) Hyperbolic Matrix(1025,304,1406,417) (-11/37,-8/27) -> (8/11,27/37) Hyperbolic Matrix(115,34,646,191) (-8/27,-5/17) -> (3/17,2/11) Hyperbolic Matrix(417,122,646,189) (-5/17,-7/24) -> (9/14,11/17) Hyperbolic Matrix(1027,298,1444,419) (-9/31,-11/38) -> (27/38,5/7) Hyperbolic Matrix(1025,296,1444,417) (-11/38,-2/7) -> (22/31,27/38) Hyperbolic Matrix(227,64,266,75) (-2/7,-7/25) -> (11/13,6/7) Hyperbolic Matrix(4181,1156,5776,1597) (-13/47,-21/76) -> (55/76,21/29) Hyperbolic Matrix(4179,1154,5776,1595) (-21/76,-8/29) -> (34/47,55/76) Hyperbolic Matrix(989,268,1406,381) (-3/11,-10/37) -> (26/37,19/27) Hyperbolic Matrix(16873,4552,23104,6233) (-17/63,-41/152) -> (111/152,65/89) Hyperbolic Matrix(16871,4550,23104,6231) (-41/152,-24/89) -> (46/63,111/152) Hyperbolic Matrix(647,174,1558,419) (-7/26,-11/41) -> (17/41,5/12) Hyperbolic Matrix(949,254,1558,417) (-11/41,-4/15) -> (14/23,25/41) Hyperbolic Matrix(151,40,570,151) (-4/15,-5/19) -> (5/19,4/15) Hyperbolic Matrix(39,10,152,39) (-5/19,-1/4) -> (1/4,5/19) Hyperbolic Matrix(1103,262,1444,343) (-5/21,-9/38) -> (29/38,13/17) Hyperbolic Matrix(1101,260,1444,341) (-9/38,-4/17) -> (16/21,29/38) Hyperbolic Matrix(341,78,494,113) (-3/13,-5/22) -> (11/16,9/13) Hyperbolic Matrix(10147,2226,12996,2851) (-9/41,-25/114) -> (89/114,57/73) Hyperbolic Matrix(10145,2224,12996,2849) (-25/114,-16/73) -> (32/41,89/114) Hyperbolic Matrix(723,158,874,191) (-7/32,-5/23) -> (19/23,5/6) Hyperbolic Matrix(987,214,1748,379) (-5/23,-8/37) -> (22/39,13/23) Hyperbolic Matrix(381,82,1064,229) (-8/37,-3/14) -> (5/14,14/39) Hyperbolic Matrix(113,24,532,113) (-3/14,-4/19) -> (4/19,3/14) Hyperbolic Matrix(39,8,190,39) (-4/19,-1/5) -> (1/5,4/19) Hyperbolic Matrix(113,22,190,37) (-1/5,-3/16) -> (13/22,3/5) Hyperbolic Matrix(1179,218,1444,267) (-5/27,-7/38) -> (31/38,9/11) Hyperbolic Matrix(1177,216,1444,265) (-7/38,-2/11) -> (22/27,31/38) Hyperbolic Matrix(191,34,646,115) (-2/11,-3/17) -> (5/17,8/27) Hyperbolic Matrix(3459,608,4978,875) (-3/17,-10/57) -> (66/95,41/59) Hyperbolic Matrix(4065,712,5852,1025) (-10/57,-7/40) -> (25/36,66/95) Hyperbolic Matrix(683,118,874,151) (-4/23,-1/6) -> (25/32,18/23) Hyperbolic Matrix(37,6,228,37) (-1/6,-3/19) -> (3/19,1/6) Hyperbolic Matrix(77,12,494,77) (-3/19,-2/13) -> (2/13,3/19) Hyperbolic Matrix(191,28,266,39) (-2/13,-1/7) -> (5/7,18/25) Hyperbolic Matrix(1255,166,1444,191) (-2/15,-5/38) -> (33/38,20/23) Hyperbolic Matrix(1253,164,1444,189) (-5/38,-3/23) -> (13/15,33/38) Hyperbolic Matrix(987,106,1406,151) (-1/9,-2/19) -> (40/57,33/47) Hyperbolic Matrix(533,54,760,77) (-2/19,-1/10) -> (7/10,40/57) Hyperbolic Matrix(115,-14,304,-37) (0/1,1/8) -> (3/8,14/37) Hyperbolic Matrix(115,-16,266,-37) (1/8,1/7) -> (3/7,13/30) Hyperbolic Matrix(1215,-212,1748,-305) (4/23,3/17) -> (41/59,16/23) Hyperbolic Matrix(495,-92,608,-113) (2/11,3/16) -> (13/16,22/27) Hyperbolic Matrix(645,-142,1558,-343) (7/32,2/9) -> (12/29,29/70) Hyperbolic Matrix(151,-34,342,-77) (2/9,3/13) -> (11/25,4/9) Hyperbolic Matrix(189,-44,494,-115) (3/13,1/4) -> (13/34,5/13) Hyperbolic Matrix(1215,-328,3382,-913) (7/26,10/37) -> (14/39,23/64) Hyperbolic Matrix(189,-52,418,-115) (3/11,5/18) -> (9/20,5/11) Hyperbolic Matrix(265,-74,684,-191) (5/18,2/7) -> (12/31,7/18) Hyperbolic Matrix(647,-188,912,-265) (2/7,7/24) -> (17/24,22/31) Hyperbolic Matrix(343,-102,380,-113) (11/37,3/10) -> (9/10,1/1) Hyperbolic Matrix(343,-104,874,-265) (3/10,7/23) -> (9/23,11/28) Hyperbolic Matrix(229,-70,494,-151) (7/23,4/13) -> (6/13,7/15) Hyperbolic Matrix(761,-268,1292,-455) (7/20,6/17) -> (10/17,33/56) Hyperbolic Matrix(4635,-1666,6346,-2281) (23/64,9/25) -> (65/89,19/26) Hyperbolic Matrix(1975,-748,2812,-1065) (14/37,11/29) -> (33/47,26/37) Hyperbolic Matrix(607,-232,798,-305) (8/21,13/34) -> (3/4,16/21) Hyperbolic Matrix(875,-344,1254,-493) (11/28,2/5) -> (30/43,7/10) Hyperbolic Matrix(837,-344,1292,-531) (16/39,7/17) -> (11/17,24/37) Hyperbolic Matrix(5015,-2078,6422,-2661) (29/70,17/41) -> (57/73,25/32) Hyperbolic Matrix(761,-330,874,-379) (13/30,10/23) -> (20/23,7/8) Hyperbolic Matrix(797,-358,1102,-495) (4/9,9/20) -> (13/18,34/47) Hyperbolic Matrix(533,-250,646,-303) (7/15,1/2) -> (33/40,19/23) Hyperbolic Matrix(343,-184,494,-265) (1/2,7/13) -> (9/13,25/36) Hyperbolic Matrix(303,-166,418,-229) (6/11,5/9) -> (21/29,8/11) Hyperbolic Matrix(265,-148,342,-191) (5/9,9/16) -> (17/22,7/9) Hyperbolic Matrix(229,-130,266,-151) (13/23,4/7) -> (6/7,13/15) Hyperbolic Matrix(1215,-712,1558,-913) (24/41,17/29) -> (7/9,32/41) Hyperbolic Matrix(609,-370,874,-531) (3/5,14/23) -> (16/23,23/33) Hyperbolic Matrix(493,-302,684,-419) (11/18,8/13) -> (18/25,13/18) Hyperbolic Matrix(379,-234,494,-305) (8/13,13/21) -> (13/17,10/13) Hyperbolic Matrix(267,-166,304,-189) (18/29,5/8) -> (7/8,8/9) Hyperbolic Matrix(2469,-1582,3382,-2167) (16/25,25/39) -> (27/37,46/63) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(189,166,-304,-267) -> Matrix(3,10,-4,-13) Matrix(151,130,-266,-229) -> Matrix(1,2,0,1) Matrix(191,162,494,419) -> Matrix(3,4,2,3) Matrix(417,352,494,417) -> Matrix(9,10,-10,-11) Matrix(191,160,228,191) -> Matrix(3,2,-2,-1) Matrix(191,158,874,723) -> Matrix(5,2,-8,-3) Matrix(533,440,-1748,-1443) -> Matrix(9,2,-14,-3) Matrix(455,374,646,531) -> Matrix(1,0,-2,1) Matrix(113,92,-608,-495) -> Matrix(1,0,-4,1) Matrix(77,62,190,153) -> Matrix(1,-2,0,1) Matrix(151,120,190,151) -> Matrix(1,-2,-2,5) Matrix(419,330,532,419) -> Matrix(1,12,-2,-23) Matrix(683,536,1064,835) -> Matrix(3,16,-4,-21) Matrix(761,596,1748,1369) -> Matrix(1,6,-2,-11) Matrix(151,118,874,683) -> Matrix(1,2,0,1) Matrix(913,712,-1558,-1215) -> Matrix(1,2,-2,-3) Matrix(191,148,-342,-265) -> Matrix(1,4,0,1) Matrix(305,234,-494,-379) -> Matrix(1,4,-2,-7) Matrix(113,84,152,113) -> Matrix(5,6,-6,-7) Matrix(419,308,570,419) -> Matrix(15,14,-14,-13) Matrix(609,446,1558,1141) -> Matrix(5,4,6,5) Matrix(911,666,1558,1139) -> Matrix(5,4,6,5) Matrix(2167,1582,-3382,-2469) -> Matrix(31,24,-22,-17) Matrix(417,304,1406,1025) -> Matrix(11,8,4,3) Matrix(229,166,-418,-303) -> Matrix(7,4,-2,-1) Matrix(419,302,-684,-493) -> Matrix(5,2,-8,-3) Matrix(265,188,-912,-647) -> Matrix(1,0,-4,1) Matrix(229,162,646,457) -> Matrix(1,0,-2,1) Matrix(531,374,646,455) -> Matrix(1,0,-2,1) Matrix(381,268,1406,989) -> Matrix(1,0,0,1) Matrix(37,26,-380,-267) -> Matrix(1,0,-2,1) Matrix(531,370,-874,-609) -> Matrix(1,4,-2,-7) Matrix(265,184,-494,-343) -> Matrix(3,2,-2,-1) Matrix(267,184,608,419) -> Matrix(1,2,-2,-3) Matrix(417,286,608,417) -> Matrix(1,0,-2,1) Matrix(77,52,114,77) -> Matrix(1,2,-2,-3) Matrix(341,222,874,569) -> Matrix(1,2,0,1) Matrix(531,344,-1292,-837) -> Matrix(3,4,-4,-5) Matrix(189,122,646,417) -> Matrix(1,2,0,1) Matrix(835,536,1064,683) -> Matrix(11,16,-20,-29) Matrix(1711,1096,-6346,-4065) -> Matrix(3,4,-4,-5) Matrix(191,122,418,267) -> Matrix(3,4,-10,-13) Matrix(265,168,418,265) -> Matrix(13,14,-14,-15) Matrix(191,120,304,191) -> Matrix(11,10,-10,-9) Matrix(837,520,-2812,-1747) -> Matrix(29,22,-62,-47) Matrix(455,282,1102,683) -> Matrix(17,12,-10,-7) Matrix(191,118,-798,-493) -> Matrix(3,2,-8,-5) Matrix(75,46,494,303) -> Matrix(3,2,-8,-5) Matrix(305,186,874,533) -> Matrix(3,2,-8,-5) Matrix(417,254,1558,949) -> Matrix(3,2,4,3) Matrix(379,230,-1254,-761) -> Matrix(3,2,-8,-5) Matrix(37,22,190,113) -> Matrix(1,0,2,1) Matrix(647,382,1482,875) -> Matrix(5,2,-8,-3) Matrix(455,268,-1292,-761) -> Matrix(1,0,4,1) Matrix(419,246,1102,647) -> Matrix(1,0,2,1) Matrix(1407,824,-6422,-3761) -> Matrix(3,2,-2,-1) Matrix(1139,666,1558,911) -> Matrix(13,4,-10,-3) Matrix(265,154,456,265) -> Matrix(1,0,6,1) Matrix(153,88,266,153) -> Matrix(1,0,-4,1) Matrix(113,64,-874,-495) -> Matrix(1,0,0,1) Matrix(379,214,1748,987) -> Matrix(3,-2,-4,3) Matrix(607,342,1482,835) -> Matrix(1,-2,0,1) Matrix(189,106,608,341) -> Matrix(3,-4,-2,3) Matrix(305,168,-1102,-607) -> Matrix(1,6,-2,-11) Matrix(151,82,418,227) -> Matrix(1,2,-4,-7) Matrix(113,60,-646,-343) -> Matrix(5,6,-6,-7) Matrix(151,70,-494,-229) -> Matrix(3,-2,-4,3) Matrix(267,122,418,191) -> Matrix(5,-4,-6,5) Matrix(115,52,-418,-189) -> Matrix(1,-2,-2,5) Matrix(77,34,-342,-151) -> Matrix(1,2,0,1) Matrix(875,382,1482,647) -> Matrix(1,2,0,1) Matrix(1369,596,1748,761) -> Matrix(1,6,-2,-11) Matrix(37,16,-266,-115) -> Matrix(1,2,-2,-3) Matrix(113,48,266,113) -> Matrix(5,6,-6,-7) Matrix(191,80,456,191) -> Matrix(11,10,-10,-9) Matrix(419,174,1558,647) -> Matrix(5,4,6,5) Matrix(343,142,-1558,-645) -> Matrix(13,10,-4,-3) Matrix(683,282,1102,455) -> Matrix(17,12,-10,-7) Matrix(3307,1358,5092,2091) -> Matrix(11,8,-18,-13) Matrix(3723,1528,5738,2355) -> Matrix(1,0,0,1) Matrix(835,342,1482,607) -> Matrix(3,2,-8,-5) Matrix(153,62,190,77) -> Matrix(3,2,-8,-5) Matrix(265,104,-874,-343) -> Matrix(9,4,-16,-7) Matrix(1141,446,1558,609) -> Matrix(13,4,-10,-3) Matrix(569,222,874,341) -> Matrix(5,2,-8,-3) Matrix(191,74,-684,-265) -> Matrix(5,2,-8,-3) Matrix(115,44,-494,-189) -> Matrix(1,0,4,1) Matrix(647,246,1102,419) -> Matrix(1,0,2,1) Matrix(37,14,-304,-115) -> Matrix(1,0,2,1) Matrix(113,42,304,113) -> Matrix(1,0,6,1) Matrix(153,56,418,153) -> Matrix(1,0,-8,1) Matrix(227,82,418,151) -> Matrix(3,-2,-4,3) Matrix(913,328,-3382,-1215) -> Matrix(1,0,-4,1) Matrix(229,82,1064,381) -> Matrix(3,-2,-4,3) Matrix(457,162,646,229) -> Matrix(1,0,-2,1) Matrix(3383,1188,5738,2015) -> Matrix(3,-2,2,-1) Matrix(3001,1052,5092,1785) -> Matrix(1,-2,2,-3) Matrix(533,186,874,305) -> Matrix(1,-2,0,1) Matrix(37,12,114,37) -> Matrix(1,2,-2,-3) Matrix(191,60,608,191) -> Matrix(11,10,-10,-9) Matrix(381,118,494,153) -> Matrix(11,8,-18,-13) Matrix(4827,1474,5852,1787) -> Matrix(3,2,28,19) Matrix(4103,1252,4978,1519) -> Matrix(3,2,-26,-17) Matrix(4029,1220,5776,1749) -> Matrix(15,8,-32,-17) Matrix(4027,1218,5776,1747) -> Matrix(13,6,-24,-11) Matrix(683,204,760,227) -> Matrix(15,8,-32,-17) Matrix(1255,374,1406,419) -> Matrix(37,18,-72,-35) Matrix(1025,304,1406,417) -> Matrix(19,8,-12,-5) Matrix(115,34,646,191) -> Matrix(5,2,-8,-3) Matrix(417,122,646,189) -> Matrix(5,2,-8,-3) Matrix(1027,298,1444,419) -> Matrix(1,0,6,1) Matrix(1025,296,1444,417) -> Matrix(1,0,-4,1) Matrix(227,64,266,75) -> Matrix(1,2,-2,-3) Matrix(4181,1156,5776,1597) -> Matrix(27,14,-2,-1) Matrix(4179,1154,5776,1595) -> Matrix(25,12,2,1) Matrix(989,268,1406,381) -> Matrix(1,0,0,1) Matrix(16873,4552,23104,6233) -> Matrix(21,4,-16,-3) Matrix(16871,4550,23104,6231) -> Matrix(3,-4,-2,3) Matrix(647,174,1558,419) -> Matrix(13,4,-10,-3) Matrix(949,254,1558,417) -> Matrix(7,2,-4,-1) Matrix(151,40,570,151) -> Matrix(1,0,8,1) Matrix(39,10,152,39) -> Matrix(1,0,-2,1) Matrix(1103,262,1444,343) -> Matrix(21,2,-32,-3) Matrix(1101,260,1444,341) -> Matrix(15,-2,-22,3) Matrix(341,78,494,113) -> Matrix(1,0,-2,1) Matrix(10147,2226,12996,2851) -> Matrix(1,4,-2,-7) Matrix(10145,2224,12996,2849) -> Matrix(1,6,-2,-11) Matrix(723,158,874,191) -> Matrix(1,2,0,1) Matrix(987,214,1748,379) -> Matrix(1,2,-4,-7) Matrix(381,82,1064,229) -> Matrix(1,2,-4,-7) Matrix(113,24,532,113) -> Matrix(5,6,-6,-7) Matrix(39,8,190,39) -> Matrix(3,2,-2,-1) Matrix(113,22,190,37) -> Matrix(1,0,2,1) Matrix(1179,218,1444,267) -> Matrix(1,0,6,1) Matrix(1177,216,1444,265) -> Matrix(1,0,-8,1) Matrix(191,34,646,115) -> Matrix(1,2,0,1) Matrix(3459,608,4978,875) -> Matrix(9,10,-10,-11) Matrix(4065,712,5852,1025) -> Matrix(11,10,-10,-9) Matrix(683,118,874,151) -> Matrix(5,2,-8,-3) Matrix(37,6,228,37) -> Matrix(1,0,2,1) Matrix(77,12,494,77) -> Matrix(1,0,-4,1) Matrix(191,28,266,39) -> Matrix(1,0,0,1) Matrix(1255,166,1444,191) -> Matrix(13,2,-20,-3) Matrix(1253,164,1444,189) -> Matrix(7,-2,-10,3) Matrix(987,106,1406,151) -> Matrix(1,2,-4,-7) Matrix(533,54,760,77) -> Matrix(3,2,-8,-5) Matrix(115,-14,304,-37) -> Matrix(1,0,2,1) Matrix(115,-16,266,-37) -> Matrix(1,2,-2,-3) Matrix(1215,-212,1748,-305) -> Matrix(3,4,-4,-5) Matrix(495,-92,608,-113) -> Matrix(1,0,-4,1) Matrix(645,-142,1558,-343) -> Matrix(17,10,-12,-7) Matrix(151,-34,342,-77) -> Matrix(5,2,-8,-3) Matrix(189,-44,494,-115) -> Matrix(1,0,4,1) Matrix(1215,-328,3382,-913) -> Matrix(1,0,-4,1) Matrix(189,-52,418,-115) -> Matrix(1,-2,-2,5) Matrix(265,-74,684,-191) -> Matrix(1,2,0,1) Matrix(647,-188,912,-265) -> Matrix(1,0,-4,1) Matrix(343,-102,380,-113) -> Matrix(1,-4,-2,9) Matrix(343,-104,874,-265) -> Matrix(1,4,0,1) Matrix(229,-70,494,-151) -> Matrix(1,2,-4,-7) Matrix(761,-268,1292,-455) -> Matrix(1,0,4,1) Matrix(4635,-1666,6346,-2281) -> Matrix(13,4,-10,-3) Matrix(1975,-748,2812,-1065) -> Matrix(1,0,-4,1) Matrix(607,-232,798,-305) -> Matrix(7,-2,-10,3) Matrix(875,-344,1254,-493) -> Matrix(1,-2,-2,5) Matrix(837,-344,1292,-531) -> Matrix(3,4,-4,-5) Matrix(5015,-2078,6422,-2661) -> Matrix(7,10,-12,-17) Matrix(761,-330,874,-379) -> Matrix(11,8,-18,-13) Matrix(797,-358,1102,-495) -> Matrix(9,4,2,1) Matrix(533,-250,646,-303) -> Matrix(1,0,6,1) Matrix(343,-184,494,-265) -> Matrix(3,2,-2,-1) Matrix(303,-166,418,-229) -> Matrix(7,4,-2,-1) Matrix(265,-148,342,-191) -> Matrix(9,4,-16,-7) Matrix(229,-130,266,-151) -> Matrix(5,2,-8,-3) Matrix(1215,-712,1558,-913) -> Matrix(1,2,-2,-3) Matrix(609,-370,874,-531) -> Matrix(1,4,-2,-7) Matrix(493,-302,684,-419) -> Matrix(1,2,0,1) Matrix(379,-234,494,-305) -> Matrix(1,4,-2,-7) Matrix(267,-166,304,-189) -> Matrix(7,10,-12,-17) Matrix(2469,-1582,3382,-2167) -> Matrix(31,24,-22,-17) 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): 60 Degree of the the map X: 60 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 -21/76 -9/38 -4/17 0/1 1/8 1/7 2/13 3/19 1/6 2/11 1/5 4/19 2/9 1/4 5/19 4/15 2/7 6/19 1/3 7/19 2/5 8/19 1/2 5/9 11/19 56/95 12/19 2/3 13/19 66/95 40/57 14/19 15/19 16/19 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -6/7 -2/1 -1/1 -5/6 -1/2 -4/5 1/1 1/0 -15/19 1/0 -11/14 1/0 -18/23 -4/1 -3/1 -7/9 1/0 -10/13 -3/1 -2/1 -3/4 -3/2 -8/11 -1/1 -2/3 -13/18 -1/2 -5/7 -1/2 -12/17 -1/1 0/1 -7/10 1/0 -16/23 -2/1 -1/1 -9/13 1/0 -11/16 1/0 -13/19 1/0 -2/3 -1/1 1/0 -5/8 -5/6 -13/21 -7/10 -21/34 -5/8 -8/13 -1/1 -2/3 -19/31 -1/2 -11/18 -1/2 -14/23 -2/3 -3/5 -3/5 -1/2 -10/17 -1/3 0/1 -7/12 -1/4 -11/19 0/1 -4/7 0/1 1/1 -5/9 1/0 -11/20 1/0 -6/11 -3/1 -2/1 -1/2 -1/2 -5/11 3/2 -4/9 -3/1 1/0 -7/16 1/0 -10/23 -3/1 -2/1 -3/7 -3/2 -2/5 -1/1 -1/2 -5/13 -1/4 -8/21 -1/1 0/1 -3/8 -1/4 -7/19 0/1 -4/11 0/1 1/3 -5/14 1/0 -1/3 1/0 -4/13 -1/1 -2/3 -3/10 -1/2 -2/7 -1/1 0/1 -5/18 -1/2 -13/47 -1/2 -21/76 -1/2 -8/29 -1/2 -5/11 -3/11 -1/4 -7/26 -1/2 -4/15 -1/5 0/1 -5/19 0/1 -1/4 1/0 -5/21 -1/6 -9/38 0/1 -4/17 0/1 1/3 -3/13 1/0 -5/22 1/0 -2/9 -1/1 1/0 -1/5 -1/2 -2/11 0/1 1/1 -1/6 -1/2 -3/19 0/1 -2/13 0/1 1/1 -1/7 1/0 -1/8 -1/2 0/1 -1/1 0/1 1/8 1/0 1/7 -1/2 2/13 -1/3 0/1 3/19 0/1 1/6 1/0 4/23 -2/1 -1/1 3/17 -3/4 2/11 -1/3 0/1 1/5 1/0 4/19 -1/1 3/14 -3/4 2/9 -1/1 -1/2 3/13 -1/2 1/4 -1/2 5/19 0/1 4/15 0/1 1/3 7/26 1/0 3/11 1/2 5/18 1/0 2/7 -1/1 0/1 3/10 1/0 4/13 -2/1 -1/1 5/16 -5/4 6/19 -1/1 1/3 -1/2 7/20 -1/2 6/17 -1/3 0/1 5/14 -1/2 4/11 -1/5 0/1 7/19 0/1 3/8 1/2 14/37 0/1 1/1 11/29 1/0 8/21 -1/1 0/1 13/34 1/2 5/13 1/2 2/5 -1/1 1/0 5/12 -5/4 8/19 -1/1 3/7 -3/4 10/23 -2/3 -3/5 17/39 -1/2 7/16 -1/2 11/25 -1/2 4/9 -3/5 -1/2 9/20 -1/2 5/11 -3/8 1/2 1/0 7/13 -3/4 6/11 -2/3 -3/5 5/9 -1/2 4/7 -1/3 0/1 11/19 0/1 7/12 1/2 10/17 0/1 1/1 33/56 1/2 56/95 1/1 23/39 1/0 13/22 1/0 3/5 1/0 14/23 -3/1 -2/1 25/41 1/0 11/18 1/0 8/13 -2/1 -1/1 13/21 -7/4 5/8 -5/4 12/19 -1/1 7/11 -7/8 2/3 -1/1 -1/2 13/19 -1/2 11/16 -1/2 9/13 -1/2 25/36 -3/2 66/95 -1/1 41/59 -7/8 16/23 -1/1 -2/3 7/10 -1/2 40/57 -1/3 33/47 -1/4 26/37 -1/3 0/1 19/27 -1/4 12/17 -1/1 0/1 5/7 1/0 18/25 0/1 1/1 13/18 1/0 34/47 7/1 1/0 55/76 1/0 21/29 1/0 8/11 -2/1 -1/1 11/15 -7/6 14/19 -1/1 3/4 -3/4 16/21 -9/13 -2/3 29/38 -2/3 13/17 -9/14 10/13 -2/3 -3/5 7/9 -1/2 18/23 -3/5 -4/7 11/14 -1/2 15/19 -1/2 4/5 -1/2 -1/3 5/6 1/0 16/19 -1/1 11/13 -5/6 6/7 -1/1 -2/3 1/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(37,32,-133,-115) (-1/1,-6/7) -> (-2/7,-5/18) Hyperbolic Matrix(113,96,133,113) (-6/7,-5/6) -> (11/13,6/7) Hyperbolic Matrix(37,30,-95,-77) (-5/6,-4/5) -> (-2/5,-5/13) Hyperbolic Matrix(151,120,190,151) (-4/5,-15/19) -> (15/19,4/5) Hyperbolic Matrix(419,330,532,419) (-15/19,-11/14) -> (11/14,15/19) Hyperbolic Matrix(265,208,-437,-343) (-11/14,-18/23) -> (-14/23,-3/5) Hyperbolic Matrix(305,238,-437,-341) (-18/23,-7/9) -> (-7/10,-16/23) Hyperbolic Matrix(75,58,-247,-191) (-7/9,-10/13) -> (-4/13,-3/10) Hyperbolic Matrix(305,234,-494,-379) (-10/13,-3/4) -> (-21/34,-8/13) Hyperbolic Matrix(153,112,209,153) (-3/4,-8/11) -> (8/11,11/15) Hyperbolic Matrix(229,166,-418,-303) (-8/11,-13/18) -> (-11/20,-6/11) Hyperbolic Matrix(419,302,-684,-493) (-13/18,-5/7) -> (-19/31,-11/18) Hyperbolic Matrix(189,134,-323,-229) (-5/7,-12/17) -> (-10/17,-7/12) Hyperbolic Matrix(267,188,703,495) (-12/17,-7/10) -> (11/29,8/21) Hyperbolic Matrix(75,52,437,303) (-16/23,-9/13) -> (1/6,4/23) Hyperbolic Matrix(267,184,608,419) (-9/13,-11/16) -> (7/16,11/25) Hyperbolic Matrix(417,286,608,417) (-11/16,-13/19) -> (13/19,11/16) Hyperbolic Matrix(77,52,114,77) (-13/19,-2/3) -> (2/3,13/19) Hyperbolic Matrix(37,24,57,37) (-2/3,-5/8) -> (7/11,2/3) Hyperbolic Matrix(113,70,-247,-153) (-5/8,-13/21) -> (-1/2,-5/11) Hyperbolic Matrix(191,118,-798,-493) (-13/21,-21/34) -> (-1/4,-5/21) Hyperbolic Matrix(75,46,494,303) (-8/13,-19/31) -> (1/7,2/13) Hyperbolic Matrix(571,348,1311,799) (-11/18,-14/23) -> (10/23,17/39) Hyperbolic Matrix(115,68,323,191) (-3/5,-10/17) -> (6/17,5/14) Hyperbolic Matrix(265,154,456,265) (-7/12,-11/19) -> (11/19,7/12) Hyperbolic Matrix(153,88,266,153) (-11/19,-4/7) -> (4/7,11/19) Hyperbolic Matrix(39,22,-133,-75) (-4/7,-5/9) -> (-3/10,-2/7) Hyperbolic Matrix(305,168,-1102,-607) (-5/9,-11/20) -> (-5/18,-13/47) Hyperbolic Matrix(37,20,209,113) (-6/11,-1/2) -> (3/17,2/11) Hyperbolic Matrix(115,52,-418,-189) (-5/11,-4/9) -> (-8/29,-3/11) Hyperbolic Matrix(77,34,-342,-151) (-4/9,-7/16) -> (-5/22,-2/9) Hyperbolic Matrix(799,348,1311,571) (-7/16,-10/23) -> (14/23,25/41) Hyperbolic Matrix(189,82,-703,-305) (-10/23,-3/7) -> (-7/26,-4/15) Hyperbolic Matrix(39,16,95,39) (-3/7,-2/5) -> (2/5,5/12) Hyperbolic Matrix(115,44,-494,-189) (-5/13,-8/21) -> (-4/17,-3/13) Hyperbolic Matrix(495,188,703,267) (-8/21,-3/8) -> (19/27,12/17) Hyperbolic Matrix(113,42,304,113) (-3/8,-7/19) -> (7/19,3/8) Hyperbolic Matrix(153,56,418,153) (-7/19,-4/11) -> (4/11,7/19) Hyperbolic Matrix(39,14,-209,-75) (-4/11,-5/14) -> (-1/5,-2/11) Hyperbolic Matrix(191,68,323,115) (-5/14,-1/3) -> (13/22,3/5) Hyperbolic Matrix(77,24,247,77) (-1/3,-4/13) -> (4/13,5/16) Hyperbolic Matrix(4181,1156,5776,1597) (-13/47,-21/76) -> (55/76,21/29) Hyperbolic Matrix(4179,1154,5776,1595) (-21/76,-8/29) -> (34/47,55/76) Hyperbolic Matrix(37,10,-285,-77) (-3/11,-7/26) -> (-1/7,-1/8) Hyperbolic Matrix(151,40,570,151) (-4/15,-5/19) -> (5/19,4/15) Hyperbolic Matrix(39,10,152,39) (-5/19,-1/4) -> (1/4,5/19) Hyperbolic Matrix(1103,262,1444,343) (-5/21,-9/38) -> (29/38,13/17) Hyperbolic Matrix(1101,260,1444,341) (-9/38,-4/17) -> (16/21,29/38) Hyperbolic Matrix(341,78,494,113) (-3/13,-5/22) -> (11/16,9/13) Hyperbolic Matrix(37,8,171,37) (-2/9,-1/5) -> (3/14,2/9) Hyperbolic Matrix(113,20,209,37) (-2/11,-1/6) -> (7/13,6/11) Hyperbolic Matrix(37,6,228,37) (-1/6,-3/19) -> (3/19,1/6) Hyperbolic Matrix(77,12,494,77) (-3/19,-2/13) -> (2/13,3/19) Hyperbolic Matrix(191,28,266,39) (-2/13,-1/7) -> (5/7,18/25) Hyperbolic Matrix(227,26,323,37) (-1/8,0/1) -> (26/37,19/27) Hyperbolic Matrix(115,-14,304,-37) (0/1,1/8) -> (3/8,14/37) Hyperbolic Matrix(77,-10,285,-37) (1/8,1/7) -> (7/26,3/11) Hyperbolic Matrix(1215,-212,1748,-305) (4/23,3/17) -> (41/59,16/23) Hyperbolic Matrix(75,-14,209,-39) (2/11,1/5) -> (5/14,4/11) Hyperbolic Matrix(77,-16,361,-75) (1/5,4/19) -> (4/19,3/14) Parabolic Matrix(151,-34,342,-77) (2/9,3/13) -> (11/25,4/9) Hyperbolic Matrix(189,-44,494,-115) (3/13,1/4) -> (13/34,5/13) Hyperbolic Matrix(305,-82,703,-189) (4/15,7/26) -> (3/7,10/23) Hyperbolic Matrix(189,-52,418,-115) (3/11,5/18) -> (9/20,5/11) Hyperbolic Matrix(115,-32,133,-37) (5/18,2/7) -> (6/7,1/1) Hyperbolic Matrix(75,-22,133,-39) (2/7,3/10) -> (5/9,4/7) Hyperbolic Matrix(191,-58,247,-75) (3/10,4/13) -> (10/13,7/9) Hyperbolic Matrix(115,-36,361,-113) (5/16,6/19) -> (6/19,1/3) Parabolic Matrix(191,-66,437,-151) (1/3,7/20) -> (17/39,7/16) Hyperbolic Matrix(761,-268,1292,-455) (7/20,6/17) -> (10/17,33/56) Hyperbolic Matrix(1975,-748,2812,-1065) (14/37,11/29) -> (33/47,26/37) Hyperbolic Matrix(607,-232,798,-305) (8/21,13/34) -> (3/4,16/21) Hyperbolic Matrix(77,-30,95,-37) (5/13,2/5) -> (4/5,5/6) Hyperbolic Matrix(153,-64,361,-151) (5/12,8/19) -> (8/19,3/7) Parabolic Matrix(797,-358,1102,-495) (4/9,9/20) -> (13/18,34/47) Hyperbolic Matrix(153,-70,247,-113) (5/11,1/2) -> (13/21,5/8) Hyperbolic Matrix(343,-184,494,-265) (1/2,7/13) -> (9/13,25/36) Hyperbolic Matrix(303,-166,418,-229) (6/11,5/9) -> (21/29,8/11) Hyperbolic Matrix(229,-134,323,-189) (7/12,10/17) -> (12/17,5/7) Hyperbolic Matrix(5321,-3136,9025,-5319) (33/56,56/95) -> (56/95,23/39) Parabolic Matrix(1217,-718,1995,-1177) (23/39,13/22) -> (25/41,11/18) Hyperbolic Matrix(343,-208,437,-265) (3/5,14/23) -> (18/23,11/14) Hyperbolic Matrix(493,-302,684,-419) (11/18,8/13) -> (18/25,13/18) Hyperbolic Matrix(379,-234,494,-305) (8/13,13/21) -> (13/17,10/13) Hyperbolic Matrix(229,-144,361,-227) (5/8,12/19) -> (12/19,7/11) Parabolic Matrix(6271,-4356,9025,-6269) (25/36,66/95) -> (66/95,41/59) Parabolic Matrix(341,-238,437,-305) (16/23,7/10) -> (7/9,18/23) Hyperbolic Matrix(2281,-1600,3249,-2279) (7/10,40/57) -> (40/57,33/47) Parabolic Matrix(267,-196,361,-265) (11/15,14/19) -> (14/19,3/4) Parabolic Matrix(305,-256,361,-303) (5/6,16/19) -> (16/19,11/13) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(37,32,-133,-115) -> Matrix(1,2,-2,-3) Matrix(113,96,133,113) -> Matrix(3,4,-4,-5) Matrix(37,30,-95,-77) -> Matrix(1,0,-2,1) Matrix(151,120,190,151) -> Matrix(1,-2,-2,5) Matrix(419,330,532,419) -> Matrix(1,12,-2,-23) Matrix(265,208,-437,-343) -> Matrix(1,6,-2,-11) Matrix(305,238,-437,-341) -> Matrix(1,2,0,1) Matrix(75,58,-247,-191) -> Matrix(1,4,-2,-7) Matrix(305,234,-494,-379) -> Matrix(1,4,-2,-7) Matrix(153,112,209,153) -> Matrix(5,4,-4,-3) Matrix(229,166,-418,-303) -> Matrix(7,4,-2,-1) Matrix(419,302,-684,-493) -> Matrix(5,2,-8,-3) Matrix(189,134,-323,-229) -> Matrix(1,0,-2,1) Matrix(267,188,703,495) -> Matrix(1,0,0,1) Matrix(75,52,437,303) -> Matrix(1,0,0,1) Matrix(267,184,608,419) -> Matrix(1,2,-2,-3) Matrix(417,286,608,417) -> Matrix(1,0,-2,1) Matrix(77,52,114,77) -> Matrix(1,2,-2,-3) Matrix(37,24,57,37) -> Matrix(1,2,-2,-3) Matrix(113,70,-247,-153) -> Matrix(3,2,4,3) Matrix(191,118,-798,-493) -> Matrix(3,2,-8,-5) Matrix(75,46,494,303) -> Matrix(3,2,-8,-5) Matrix(571,348,1311,799) -> Matrix(1,0,0,1) Matrix(115,68,323,191) -> Matrix(1,0,0,1) Matrix(265,154,456,265) -> Matrix(1,0,6,1) Matrix(153,88,266,153) -> Matrix(1,0,-4,1) Matrix(39,22,-133,-75) -> Matrix(1,0,-2,1) Matrix(305,168,-1102,-607) -> Matrix(1,6,-2,-11) Matrix(37,20,209,113) -> Matrix(1,2,-2,-3) Matrix(115,52,-418,-189) -> Matrix(1,-2,-2,5) Matrix(77,34,-342,-151) -> Matrix(1,2,0,1) Matrix(799,348,1311,571) -> Matrix(1,0,0,1) Matrix(189,82,-703,-305) -> Matrix(1,2,-4,-7) Matrix(39,16,95,39) -> Matrix(3,2,-2,-1) Matrix(115,44,-494,-189) -> Matrix(1,0,4,1) Matrix(495,188,703,267) -> Matrix(1,0,0,1) Matrix(113,42,304,113) -> Matrix(1,0,6,1) Matrix(153,56,418,153) -> Matrix(1,0,-8,1) Matrix(39,14,-209,-75) -> Matrix(1,0,-2,1) Matrix(191,68,323,115) -> Matrix(1,0,0,1) Matrix(77,24,247,77) -> Matrix(5,4,-4,-3) Matrix(4181,1156,5776,1597) -> Matrix(27,14,-2,-1) Matrix(4179,1154,5776,1595) -> Matrix(25,12,2,1) Matrix(37,10,-285,-77) -> Matrix(1,0,2,1) Matrix(151,40,570,151) -> Matrix(1,0,8,1) Matrix(39,10,152,39) -> Matrix(1,0,-2,1) Matrix(1103,262,1444,343) -> Matrix(21,2,-32,-3) Matrix(1101,260,1444,341) -> Matrix(15,-2,-22,3) Matrix(341,78,494,113) -> Matrix(1,0,-2,1) Matrix(37,8,171,37) -> Matrix(1,2,-2,-3) Matrix(113,20,209,37) -> Matrix(1,2,-2,-3) Matrix(37,6,228,37) -> Matrix(1,0,2,1) Matrix(77,12,494,77) -> Matrix(1,0,-4,1) Matrix(191,28,266,39) -> Matrix(1,0,0,1) Matrix(227,26,323,37) -> Matrix(1,0,-2,1) Matrix(115,-14,304,-37) -> Matrix(1,0,2,1) Matrix(77,-10,285,-37) -> Matrix(1,0,2,1) Matrix(1215,-212,1748,-305) -> Matrix(3,4,-4,-5) Matrix(75,-14,209,-39) -> Matrix(1,0,-2,1) Matrix(77,-16,361,-75) -> Matrix(3,4,-4,-5) Matrix(151,-34,342,-77) -> Matrix(5,2,-8,-3) Matrix(189,-44,494,-115) -> Matrix(1,0,4,1) Matrix(305,-82,703,-189) -> Matrix(3,-2,-4,3) Matrix(189,-52,418,-115) -> Matrix(1,-2,-2,5) Matrix(115,-32,133,-37) -> Matrix(1,2,-2,-3) Matrix(75,-22,133,-39) -> Matrix(1,0,-2,1) Matrix(191,-58,247,-75) -> Matrix(1,4,-2,-7) Matrix(115,-36,361,-113) -> Matrix(5,6,-6,-7) Matrix(191,-66,437,-151) -> Matrix(5,2,-8,-3) Matrix(761,-268,1292,-455) -> Matrix(1,0,4,1) Matrix(1975,-748,2812,-1065) -> Matrix(1,0,-4,1) Matrix(607,-232,798,-305) -> Matrix(7,-2,-10,3) Matrix(77,-30,95,-37) -> Matrix(1,0,-2,1) Matrix(153,-64,361,-151) -> Matrix(7,8,-8,-9) Matrix(797,-358,1102,-495) -> Matrix(9,4,2,1) Matrix(153,-70,247,-113) -> Matrix(7,2,-4,-1) Matrix(343,-184,494,-265) -> Matrix(3,2,-2,-1) Matrix(303,-166,418,-229) -> Matrix(7,4,-2,-1) Matrix(229,-134,323,-189) -> Matrix(1,0,-2,1) Matrix(5321,-3136,9025,-5319) -> Matrix(3,-2,2,-1) Matrix(1217,-718,1995,-1177) -> Matrix(1,-2,0,1) Matrix(343,-208,437,-265) -> Matrix(1,6,-2,-11) Matrix(493,-302,684,-419) -> Matrix(1,2,0,1) Matrix(379,-234,494,-305) -> Matrix(1,4,-2,-7) Matrix(229,-144,361,-227) -> Matrix(11,12,-12,-13) Matrix(6271,-4356,9025,-6269) -> Matrix(9,10,-10,-11) Matrix(341,-238,437,-305) -> Matrix(5,2,-8,-3) Matrix(2281,-1600,3249,-2279) -> Matrix(5,2,-18,-7) Matrix(267,-196,361,-265) -> Matrix(9,10,-10,-11) Matrix(305,-256,361,-303) -> Matrix(5,6,-6,-7) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 30 ----------------------------------------------------------------------- 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 19 1/8 1/0 1 19 1/7 -1/2 1 19 2/13 (-1/3,0/1) 0 19 3/19 0/1 3 1 1/6 1/0 1 19 2/11 (-1/3,0/1) 0 19 1/5 1/0 1 19 4/19 -1/1 4 1 2/9 (-1/1,-1/2) 0 19 3/13 -1/2 1 19 1/4 -1/2 1 19 5/19 0/1 5 1 4/15 (0/1,1/3) 0 19 7/26 1/0 1 19 3/11 1/2 1 19 5/18 1/0 1 19 2/7 (-1/1,0/1) 0 19 3/10 1/0 1 19 4/13 (-2/1,-1/1) 0 19 6/19 -1/1 6 1 1/3 -1/2 1 19 5/14 -1/2 1 19 4/11 (-1/5,0/1) 0 19 7/19 0/1 7 1 3/8 1/2 1 19 8/21 (-1/1,0/1) 0 19 13/34 1/2 1 19 5/13 1/2 1 19 2/5 (-1/1,1/0) 0 19 8/19 -1/1 8 1 3/7 -3/4 1 19 10/23 (-2/3,-3/5) 0 19 7/16 -1/2 1 19 11/25 -1/2 1 19 4/9 (-3/5,-1/2) 0 19 9/20 -1/2 1 19 5/11 -3/8 1 19 1/2 1/0 1 19 7/13 -3/4 1 19 6/11 (-2/3,-3/5) 0 19 5/9 -1/2 1 19 4/7 (-1/3,0/1) 0 19 11/19 0/1 5 1 7/12 1/2 1 19 10/17 (0/1,1/1) 0 19 56/95 1/1 2 1 23/39 1/0 1 19 13/22 1/0 1 19 3/5 1/0 1 19 14/23 (-3/1,-2/1) 0 19 25/41 1/0 1 19 11/18 1/0 1 19 8/13 (-2/1,-1/1) 0 19 13/21 -7/4 1 19 5/8 -5/4 1 19 12/19 -1/1 12 1 2/3 (-1/1,-1/2) 0 19 13/19 -1/2 1 1 11/16 -1/2 1 19 9/13 -1/2 1 19 25/36 -3/2 1 19 66/95 -1/1 10 1 16/23 (-1/1,-2/3) 0 19 7/10 -1/2 1 19 40/57 -1/3 2 1 26/37 (-1/3,0/1) 0 19 19/27 -1/4 1 19 12/17 (-1/1,0/1) 0 19 5/7 1/0 1 19 18/25 (0/1,1/1) 0 19 13/18 1/0 1 19 34/47 (7/1,1/0) 0 19 55/76 1/0 13 1 21/29 1/0 1 19 8/11 (-2/1,-1/1) 0 19 14/19 -1/1 10 1 3/4 -3/4 1 19 16/21 (-9/13,-2/3) 0 19 29/38 -2/3 9 1 13/17 -9/14 1 19 10/13 (-2/3,-3/5) 0 19 7/9 -1/2 1 19 18/23 (-3/5,-4/7) 0 19 11/14 -1/2 1 19 15/19 -1/2 7 1 4/5 (-1/2,-1/3) 0 19 5/6 1/0 1 19 16/19 -1/1 6 1 6/7 (-1/1,-2/3) 0 19 1/1 -1/2 1 19 1/0 0/1 1 1 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(227,-26,323,-37) (0/1,1/8) -> (26/37,19/27) Glide Reflection Matrix(77,-10,285,-37) (1/8,1/7) -> (7/26,3/11) Hyperbolic Matrix(191,-28,266,-39) (1/7,2/13) -> (5/7,18/25) Glide Reflection Matrix(77,-12,494,-77) (2/13,3/19) -> (2/13,3/19) Reflection Matrix(37,-6,228,-37) (3/19,1/6) -> (3/19,1/6) Reflection Matrix(113,-20,209,-37) (1/6,2/11) -> (7/13,6/11) Glide Reflection Matrix(75,-14,209,-39) (2/11,1/5) -> (5/14,4/11) Hyperbolic Matrix(39,-8,190,-39) (1/5,4/19) -> (1/5,4/19) Reflection Matrix(37,-8,171,-37) (4/19,2/9) -> (4/19,2/9) Reflection Matrix(151,-34,342,-77) (2/9,3/13) -> (11/25,4/9) Hyperbolic Matrix(189,-44,494,-115) (3/13,1/4) -> (13/34,5/13) Hyperbolic Matrix(39,-10,152,-39) (1/4,5/19) -> (1/4,5/19) Reflection Matrix(151,-40,570,-151) (5/19,4/15) -> (5/19,4/15) Reflection Matrix(305,-82,703,-189) (4/15,7/26) -> (3/7,10/23) Hyperbolic Matrix(189,-52,418,-115) (3/11,5/18) -> (9/20,5/11) Hyperbolic Matrix(115,-32,133,-37) (5/18,2/7) -> (6/7,1/1) Hyperbolic Matrix(75,-22,133,-39) (2/7,3/10) -> (5/9,4/7) Hyperbolic Matrix(191,-58,247,-75) (3/10,4/13) -> (10/13,7/9) Hyperbolic Matrix(77,-24,247,-77) (4/13,6/19) -> (4/13,6/19) Reflection Matrix(37,-12,114,-37) (6/19,1/3) -> (6/19,1/3) Reflection Matrix(191,-68,323,-115) (1/3,5/14) -> (13/22,3/5) Glide Reflection Matrix(153,-56,418,-153) (4/11,7/19) -> (4/11,7/19) Reflection Matrix(113,-42,304,-113) (7/19,3/8) -> (7/19,3/8) Reflection Matrix(495,-188,703,-267) (3/8,8/21) -> (19/27,12/17) Glide Reflection Matrix(607,-232,798,-305) (8/21,13/34) -> (3/4,16/21) Hyperbolic Matrix(77,-30,95,-37) (5/13,2/5) -> (4/5,5/6) Hyperbolic Matrix(39,-16,95,-39) (2/5,8/19) -> (2/5,8/19) Reflection Matrix(113,-48,266,-113) (8/19,3/7) -> (8/19,3/7) Reflection Matrix(799,-348,1311,-571) (10/23,7/16) -> (14/23,25/41) Glide Reflection Matrix(419,-184,608,-267) (7/16,11/25) -> (11/16,9/13) Glide Reflection Matrix(797,-358,1102,-495) (4/9,9/20) -> (13/18,34/47) Hyperbolic Matrix(153,-70,247,-113) (5/11,1/2) -> (13/21,5/8) Hyperbolic Matrix(343,-184,494,-265) (1/2,7/13) -> (9/13,25/36) Hyperbolic Matrix(303,-166,418,-229) (6/11,5/9) -> (21/29,8/11) Hyperbolic Matrix(153,-88,266,-153) (4/7,11/19) -> (4/7,11/19) Reflection Matrix(265,-154,456,-265) (11/19,7/12) -> (11/19,7/12) Reflection Matrix(229,-134,323,-189) (7/12,10/17) -> (12/17,5/7) Hyperbolic Matrix(951,-560,1615,-951) (10/17,56/95) -> (10/17,56/95) Reflection Matrix(4369,-2576,7410,-4369) (56/95,23/39) -> (56/95,23/39) Reflection Matrix(1217,-718,1995,-1177) (23/39,13/22) -> (25/41,11/18) Hyperbolic Matrix(343,-208,437,-265) (3/5,14/23) -> (18/23,11/14) Hyperbolic Matrix(493,-302,684,-419) (11/18,8/13) -> (18/25,13/18) Hyperbolic Matrix(379,-234,494,-305) (8/13,13/21) -> (13/17,10/13) Hyperbolic Matrix(191,-120,304,-191) (5/8,12/19) -> (5/8,12/19) Reflection Matrix(37,-24,57,-37) (12/19,2/3) -> (12/19,2/3) Reflection Matrix(77,-52,114,-77) (2/3,13/19) -> (2/3,13/19) Reflection Matrix(417,-286,608,-417) (13/19,11/16) -> (13/19,11/16) Reflection Matrix(4751,-3300,6840,-4751) (25/36,66/95) -> (25/36,66/95) Reflection Matrix(1519,-1056,2185,-1519) (66/95,16/23) -> (66/95,16/23) Reflection Matrix(341,-238,437,-305) (16/23,7/10) -> (7/9,18/23) Hyperbolic Matrix(799,-560,1140,-799) (7/10,40/57) -> (7/10,40/57) Reflection Matrix(1481,-1040,2109,-1481) (40/57,26/37) -> (40/57,26/37) Reflection Matrix(5169,-3740,7144,-5169) (34/47,55/76) -> (34/47,55/76) Reflection Matrix(3191,-2310,4408,-3191) (55/76,21/29) -> (55/76,21/29) Reflection Matrix(153,-112,209,-153) (8/11,14/19) -> (8/11,14/19) Reflection Matrix(113,-84,152,-113) (14/19,3/4) -> (14/19,3/4) Reflection Matrix(1217,-928,1596,-1217) (16/21,29/38) -> (16/21,29/38) Reflection Matrix(987,-754,1292,-987) (29/38,13/17) -> (29/38,13/17) Reflection Matrix(419,-330,532,-419) (11/14,15/19) -> (11/14,15/19) Reflection Matrix(151,-120,190,-151) (15/19,4/5) -> (15/19,4/5) Reflection Matrix(191,-160,228,-191) (5/6,16/19) -> (5/6,16/19) Reflection Matrix(113,-96,133,-113) (16/19,6/7) -> (16/19,6/7) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) 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(227,-26,323,-37) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(77,-10,285,-37) -> Matrix(1,0,2,1) 0/1 Matrix(191,-28,266,-39) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(77,-12,494,-77) -> Matrix(-1,0,6,1) (2/13,3/19) -> (-1/3,0/1) Matrix(37,-6,228,-37) -> Matrix(1,0,0,-1) (3/19,1/6) -> (0/1,1/0) Matrix(113,-20,209,-37) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(75,-14,209,-39) -> Matrix(1,0,-2,1) 0/1 Matrix(39,-8,190,-39) -> Matrix(1,2,0,-1) (1/5,4/19) -> (-1/1,1/0) Matrix(37,-8,171,-37) -> Matrix(3,2,-4,-3) (4/19,2/9) -> (-1/1,-1/2) Matrix(151,-34,342,-77) -> Matrix(5,2,-8,-3) -1/2 Matrix(189,-44,494,-115) -> Matrix(1,0,4,1) 0/1 Matrix(39,-10,152,-39) -> Matrix(-1,0,4,1) (1/4,5/19) -> (-1/2,0/1) Matrix(151,-40,570,-151) -> Matrix(1,0,6,-1) (5/19,4/15) -> (0/1,1/3) Matrix(305,-82,703,-189) -> Matrix(3,-2,-4,3) Matrix(189,-52,418,-115) -> Matrix(1,-2,-2,5) Matrix(115,-32,133,-37) -> Matrix(1,2,-2,-3) -1/1 Matrix(75,-22,133,-39) -> Matrix(1,0,-2,1) 0/1 Matrix(191,-58,247,-75) -> Matrix(1,4,-2,-7) Matrix(77,-24,247,-77) -> Matrix(3,4,-2,-3) (4/13,6/19) -> (-2/1,-1/1) Matrix(37,-12,114,-37) -> Matrix(3,2,-4,-3) (6/19,1/3) -> (-1/1,-1/2) Matrix(191,-68,323,-115) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(153,-56,418,-153) -> Matrix(-1,0,10,1) (4/11,7/19) -> (-1/5,0/1) Matrix(113,-42,304,-113) -> Matrix(1,0,4,-1) (7/19,3/8) -> (0/1,1/2) Matrix(495,-188,703,-267) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(607,-232,798,-305) -> Matrix(7,-2,-10,3) Matrix(77,-30,95,-37) -> Matrix(1,0,-2,1) 0/1 Matrix(39,-16,95,-39) -> Matrix(1,2,0,-1) (2/5,8/19) -> (-1/1,1/0) Matrix(113,-48,266,-113) -> Matrix(7,6,-8,-7) (8/19,3/7) -> (-1/1,-3/4) Matrix(799,-348,1311,-571) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(419,-184,608,-267) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(797,-358,1102,-495) -> Matrix(9,4,2,1) Matrix(153,-70,247,-113) -> Matrix(7,2,-4,-1) Matrix(343,-184,494,-265) -> Matrix(3,2,-2,-1) -1/1 Matrix(303,-166,418,-229) -> Matrix(7,4,-2,-1) Matrix(153,-88,266,-153) -> Matrix(-1,0,6,1) (4/7,11/19) -> (-1/3,0/1) Matrix(265,-154,456,-265) -> Matrix(1,0,4,-1) (11/19,7/12) -> (0/1,1/2) Matrix(229,-134,323,-189) -> Matrix(1,0,-2,1) 0/1 Matrix(951,-560,1615,-951) -> Matrix(1,0,2,-1) (10/17,56/95) -> (0/1,1/1) Matrix(4369,-2576,7410,-4369) -> Matrix(-1,2,0,1) (56/95,23/39) -> (1/1,1/0) Matrix(1217,-718,1995,-1177) -> Matrix(1,-2,0,1) 1/0 Matrix(343,-208,437,-265) -> Matrix(1,6,-2,-11) Matrix(493,-302,684,-419) -> Matrix(1,2,0,1) 1/0 Matrix(379,-234,494,-305) -> Matrix(1,4,-2,-7) Matrix(191,-120,304,-191) -> Matrix(9,10,-8,-9) (5/8,12/19) -> (-5/4,-1/1) Matrix(37,-24,57,-37) -> Matrix(3,2,-4,-3) (12/19,2/3) -> (-1/1,-1/2) Matrix(77,-52,114,-77) -> Matrix(3,2,-4,-3) (2/3,13/19) -> (-1/1,-1/2) Matrix(417,-286,608,-417) -> Matrix(-1,0,4,1) (13/19,11/16) -> (-1/2,0/1) Matrix(4751,-3300,6840,-4751) -> Matrix(5,6,-4,-5) (25/36,66/95) -> (-3/2,-1/1) Matrix(1519,-1056,2185,-1519) -> Matrix(5,4,-6,-5) (66/95,16/23) -> (-1/1,-2/3) Matrix(341,-238,437,-305) -> Matrix(5,2,-8,-3) -1/2 Matrix(799,-560,1140,-799) -> Matrix(5,2,-12,-5) (7/10,40/57) -> (-1/2,-1/3) Matrix(1481,-1040,2109,-1481) -> Matrix(-1,0,6,1) (40/57,26/37) -> (-1/3,0/1) Matrix(5169,-3740,7144,-5169) -> Matrix(-1,14,0,1) (34/47,55/76) -> (7/1,1/0) Matrix(3191,-2310,4408,-3191) -> Matrix(1,12,0,-1) (55/76,21/29) -> (-6/1,1/0) Matrix(153,-112,209,-153) -> Matrix(3,4,-2,-3) (8/11,14/19) -> (-2/1,-1/1) Matrix(113,-84,152,-113) -> Matrix(7,6,-8,-7) (14/19,3/4) -> (-1/1,-3/4) Matrix(1217,-928,1596,-1217) -> Matrix(53,36,-78,-53) (16/21,29/38) -> (-9/13,-2/3) Matrix(987,-754,1292,-987) -> Matrix(55,36,-84,-55) (29/38,13/17) -> (-2/3,-9/14) Matrix(419,-330,532,-419) -> Matrix(23,12,-44,-23) (11/14,15/19) -> (-6/11,-1/2) Matrix(151,-120,190,-151) -> Matrix(5,2,-12,-5) (15/19,4/5) -> (-1/2,-1/3) Matrix(191,-160,228,-191) -> Matrix(1,2,0,-1) (5/6,16/19) -> (-1/1,1/0) Matrix(113,-96,133,-113) -> Matrix(5,4,-6,-5) (16/19,6/7) -> (-1/1,-2/3) Matrix(-1,2,0,1) -> Matrix(-1,0,4,1) (1/1,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.