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 0/1 1/2 -7/8 1/1 -6/7 0/1 1/2 -11/13 2/5 1/2 -16/19 1/2 -5/6 1/1 -19/23 0/1 1/2 -14/17 0/1 1/0 -9/11 -1/2 0/1 -13/16 1/5 -4/5 1/3 1/2 -15/19 1/2 -11/14 3/5 -29/37 1/2 2/3 -18/23 2/3 3/4 -25/32 1/1 -7/9 3/4 1/1 -10/13 0/1 1/0 -3/4 1/3 -14/19 1/2 -11/15 1/2 4/7 -30/41 1/2 3/5 -19/26 3/5 -27/37 1/2 2/3 -8/11 2/3 3/4 -13/18 1/1 -5/7 0/1 1/0 -17/24 1/5 -12/17 0/1 1/4 -19/27 0/1 1/6 -26/37 0/1 1/4 -7/10 1/3 -16/23 3/8 2/5 -9/13 2/5 1/2 -11/16 5/11 -13/19 1/2 -2/3 1/2 1/1 -13/20 1/1 -11/17 0/1 1/2 -9/14 1/3 -25/39 0/1 1/2 -41/64 1/1 -16/25 0/1 1/4 -7/11 2/5 1/2 -12/19 1/2 -5/8 3/5 -23/37 1/2 2/3 -18/29 1/2 3/5 -13/21 9/14 2/3 -21/34 9/13 -8/13 2/3 3/4 -19/31 3/4 4/5 -11/18 1/1 -25/41 3/4 1/1 -14/23 3/4 4/5 -17/28 1/1 -3/5 1/1 1/0 -13/22 1/3 -23/39 0/1 1/2 -10/17 0/1 1/0 -17/29 1/4 1/3 -41/70 1/3 -24/41 1/3 1/2 -7/12 1/3 -11/19 1/2 -4/7 1/2 2/3 -17/30 3/5 -13/23 2/3 7/10 -22/39 2/3 3/4 -9/16 5/7 -14/25 3/4 4/5 -5/9 7/8 1/1 -11/20 1/1 -6/11 2/1 1/0 -7/13 0/1 1/2 -8/15 0/1 1/0 -1/2 1/1 -6/13 0/1 1/0 -5/11 1/2 2/3 -4/9 1/1 7/6 -7/16 5/3 -17/39 3/2 2/1 -10/23 7/4 2/1 -3/7 2/1 1/0 -8/19 1/0 -5/12 -1/1 -17/41 -1/1 1/0 -12/29 -1/1 -1/2 -7/17 0/1 1/2 -23/56 1/1 -39/95 1/0 -16/39 0/1 1/0 -9/22 -1/1 -2/5 1/2 1/1 -9/23 4/3 3/2 -16/41 1/1 3/2 -7/18 1/1 -5/13 3/2 2/1 -8/21 2/1 9/4 -11/29 3/1 1/0 -3/8 3/1 -7/19 1/0 -4/11 -2/1 1/0 -9/25 -1/2 0/1 -14/39 0/1 1/0 -5/14 -1/1 -6/17 0/1 1/0 -13/37 0/1 1/2 -20/57 1/2 -7/20 1/1 -1/3 1/1 1/0 -6/19 1/0 -5/16 -5/1 -4/13 -2/1 1/0 -11/36 -1/1 -29/95 1/0 -18/59 -2/1 1/0 -7/23 -2/1 -3/2 -10/33 -7/6 -1/1 -23/76 -1/1 -13/43 -1/1 -7/8 -3/10 -1/1 -17/57 -1/2 -14/47 -1/2 -1/3 -11/37 -1/2 0/1 -8/27 -1/4 0/1 -5/17 -1/2 0/1 -7/24 -1/3 -9/31 -1/8 0/1 -11/38 0/1 -2/7 0/1 1/2 -7/25 1/2 2/3 -5/18 1/1 -13/47 15/16 1/1 -21/76 1/1 -8/29 1/1 11/10 -3/11 3/2 2/1 -10/37 2/1 1/0 -17/63 3/2 2/1 -41/152 2/1 -24/89 2/1 9/4 -7/26 3/1 -11/41 3/1 1/0 -4/15 4/1 1/0 -5/19 1/0 -1/4 -1/1 -5/21 -1/10 0/1 -9/38 0/1 -4/17 0/1 1/8 -3/13 0/1 1/2 -5/22 3/5 -2/9 1/1 3/2 -9/41 1/1 1/0 -25/114 1/1 -16/73 1/1 3/2 -7/32 1/1 -5/23 3/2 2/1 -8/37 2/1 1/0 -3/14 3/1 -4/19 1/0 -1/5 -1/1 1/0 -3/16 -1/3 -5/27 -1/10 0/1 -7/38 0/1 -2/11 0/1 1/4 -3/17 0/1 1/2 -10/57 1/2 -7/40 1/1 -4/23 0/1 1/0 -1/6 1/1 -3/19 1/0 -2/13 -2/1 1/0 -1/7 0/1 1/0 -2/15 -1/4 0/1 -5/38 0/1 -3/23 0/1 1/6 -1/8 1/1 -1/9 1/1 1/0 -2/19 1/0 -1/10 -1/1 0/1 0/1 1/0 1/8 -1/1 1/7 0/1 1/0 2/13 2/1 1/0 3/19 1/0 1/6 -1/1 4/23 0/1 1/0 3/17 -1/2 0/1 2/11 -1/4 0/1 3/16 1/3 1/5 1/1 1/0 4/19 1/0 3/14 -3/1 8/37 -2/1 1/0 5/23 -2/1 -3/2 7/32 -1/1 2/9 -3/2 -1/1 3/13 -1/2 0/1 1/4 1/1 5/19 1/0 4/15 -4/1 1/0 11/41 -3/1 1/0 7/26 -3/1 10/37 -2/1 1/0 3/11 -2/1 -3/2 5/18 -1/1 2/7 -1/2 0/1 7/24 1/3 5/17 0/1 1/2 8/27 0/1 1/4 11/37 0/1 1/2 3/10 1/1 7/23 3/2 2/1 4/13 2/1 1/0 5/16 5/1 6/19 1/0 1/3 -1/1 1/0 7/20 -1/1 6/17 0/1 1/0 5/14 1/1 14/39 0/1 1/0 23/64 -1/1 9/25 0/1 1/2 4/11 2/1 1/0 7/19 1/0 3/8 -3/1 14/37 -2/1 1/0 11/29 -3/1 1/0 8/21 -9/4 -2/1 13/34 -9/5 5/13 -2/1 -3/2 12/31 -3/2 -4/3 7/18 -1/1 16/41 -3/2 -1/1 9/23 -3/2 -4/3 11/28 -1/1 2/5 -1/1 -1/2 9/22 1/1 16/39 0/1 1/0 7/17 -1/2 0/1 12/29 1/2 1/1 29/70 1/1 17/41 1/1 1/0 5/12 1/1 8/19 1/0 3/7 -2/1 1/0 13/30 -3/1 10/23 -2/1 -7/4 17/39 -2/1 -3/2 7/16 -5/3 11/25 -3/2 -4/3 4/9 -7/6 -1/1 9/20 -1/1 5/11 -2/3 -1/2 6/13 0/1 1/0 7/15 -1/2 0/1 1/2 -1/1 7/13 -1/2 0/1 6/11 -2/1 1/0 5/9 -1/1 -7/8 9/16 -5/7 22/39 -3/4 -2/3 13/23 -7/10 -2/3 4/7 -2/3 -1/2 11/19 -1/2 7/12 -1/3 24/41 -1/2 -1/3 17/29 -1/3 -1/4 10/17 0/1 1/0 33/56 -1/1 56/95 -1/2 23/39 -1/2 0/1 13/22 -1/3 3/5 -1/1 1/0 14/23 -4/5 -3/4 25/41 -1/1 -3/4 11/18 -1/1 8/13 -3/4 -2/3 13/21 -2/3 -9/14 18/29 -3/5 -1/2 5/8 -3/5 12/19 -1/2 7/11 -1/2 -2/5 16/25 -1/4 0/1 25/39 -1/2 0/1 9/14 -1/3 11/17 -1/2 0/1 24/37 0/1 1/0 37/57 1/0 13/20 -1/1 2/3 -1/1 -1/2 13/19 -1/2 11/16 -5/11 9/13 -1/2 -2/5 25/36 -1/3 66/95 -1/2 41/59 -1/2 -2/5 16/23 -2/5 -3/8 23/33 -7/20 -1/3 53/76 -1/3 30/43 -1/3 -7/22 7/10 -1/3 40/57 -1/4 33/47 -1/4 -1/5 26/37 -1/4 0/1 19/27 -1/6 0/1 12/17 -1/4 0/1 17/24 -1/5 22/31 -1/10 0/1 27/38 0/1 5/7 0/1 1/0 18/25 -2/1 1/0 13/18 -1/1 34/47 -15/14 -1/1 55/76 -1/1 21/29 -1/1 -11/12 8/11 -3/4 -2/3 27/37 -2/3 -1/2 46/63 -3/4 -2/3 111/152 -2/3 65/89 -2/3 -9/14 19/26 -3/5 30/41 -3/5 -1/2 11/15 -4/7 -1/2 14/19 -1/2 3/4 -1/3 16/21 -1/12 0/1 29/38 0/1 13/17 0/1 1/6 10/13 0/1 1/0 17/22 -3/1 7/9 -1/1 -3/4 32/41 -1/1 -1/2 89/114 -1/1 57/73 -1/1 -3/4 25/32 -1/1 18/23 -3/4 -2/3 29/37 -2/3 -1/2 11/14 -3/5 15/19 -1/2 4/5 -1/2 -1/3 13/16 -1/5 22/27 -1/12 0/1 31/38 0/1 9/11 0/1 1/2 14/17 0/1 1/0 47/57 1/0 33/40 -1/1 19/23 -1/2 0/1 5/6 -1/1 16/19 -1/2 11/13 -1/2 -2/5 6/7 -1/2 0/1 13/15 -1/6 0/1 33/38 0/1 20/23 0/1 1/4 7/8 -1/1 8/9 -1/1 -1/2 17/19 -1/2 9/10 -1/3 1/1 -1/2 0/1 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,-4,1) Matrix(189,166,-304,-267) -> Matrix(5,-2,8,-3) Matrix(151,130,-266,-229) -> Matrix(5,-2,8,-3) Matrix(191,162,494,419) -> Matrix(11,-4,-8,3) Matrix(417,352,494,417) -> Matrix(9,-4,-20,9) Matrix(191,160,228,191) -> Matrix(3,-2,-4,3) Matrix(191,158,874,723) -> Matrix(1,-2,0,1) Matrix(533,440,-1748,-1443) -> Matrix(1,-2,0,1) Matrix(455,374,646,531) -> Matrix(1,0,-4,1) Matrix(113,92,-608,-495) -> Matrix(1,0,-8,1) Matrix(77,62,190,153) -> Matrix(1,0,-4,1) Matrix(151,120,190,151) -> Matrix(5,-2,-12,5) Matrix(419,330,532,419) -> Matrix(11,-6,-20,11) Matrix(683,536,1064,835) -> Matrix(3,-2,-4,3) Matrix(761,596,1748,1369) -> Matrix(13,-8,-8,5) Matrix(151,118,874,683) -> Matrix(3,-2,-4,3) Matrix(913,712,-1558,-1215) -> Matrix(3,-2,8,-5) Matrix(191,148,-342,-265) -> Matrix(3,-4,4,-5) Matrix(305,234,-494,-379) -> Matrix(3,2,4,3) Matrix(113,84,152,113) -> Matrix(5,-2,-12,5) Matrix(419,308,570,419) -> Matrix(15,-8,-28,15) Matrix(609,446,1558,1141) -> Matrix(13,-8,-8,5) Matrix(911,666,1558,1139) -> Matrix(3,-2,-4,3) Matrix(2167,1582,-3382,-2469) -> Matrix(3,-2,8,-5) Matrix(417,304,1406,1025) -> Matrix(3,-2,8,-5) Matrix(229,166,-418,-303) -> Matrix(5,-4,4,-3) Matrix(419,302,-684,-493) -> Matrix(3,-4,4,-5) Matrix(265,188,-912,-647) -> Matrix(1,0,-8,1) Matrix(229,162,646,457) -> Matrix(1,0,-4,1) Matrix(531,374,646,455) -> Matrix(1,0,-4,1) Matrix(381,268,1406,989) -> Matrix(9,-2,-4,1) Matrix(37,26,-380,-267) -> Matrix(1,0,-4,1) Matrix(531,370,-874,-609) -> Matrix(17,-6,20,-7) Matrix(265,184,-494,-343) -> Matrix(5,-2,8,-3) Matrix(267,184,608,419) -> Matrix(23,-10,-16,7) Matrix(417,286,608,417) -> Matrix(21,-10,-44,21) Matrix(77,52,114,77) -> Matrix(3,-2,-4,3) Matrix(341,222,874,569) -> Matrix(1,-2,0,1) Matrix(531,344,-1292,-837) -> Matrix(1,0,0,1) Matrix(189,122,646,417) -> Matrix(1,0,0,1) Matrix(835,536,1064,683) -> Matrix(3,-2,-4,3) Matrix(1711,1096,-6346,-4065) -> Matrix(1,2,0,1) Matrix(191,122,418,267) -> Matrix(1,0,-4,1) Matrix(265,168,418,265) -> Matrix(9,-4,-20,9) Matrix(191,120,304,191) -> Matrix(11,-6,-20,11) Matrix(837,520,-2812,-1747) -> Matrix(3,-2,-4,3) Matrix(455,282,1102,683) -> Matrix(3,-2,8,-5) Matrix(191,118,-798,-493) -> Matrix(3,-2,-16,11) Matrix(75,46,494,303) -> Matrix(5,-4,4,-3) Matrix(305,186,874,533) -> Matrix(3,-2,-4,3) Matrix(417,254,1558,949) -> Matrix(11,-8,-4,3) Matrix(379,230,-1254,-761) -> Matrix(7,-6,-8,7) Matrix(37,22,190,113) -> Matrix(1,0,0,1) Matrix(647,382,1482,875) -> Matrix(1,-2,0,1) Matrix(455,268,-1292,-761) -> Matrix(1,0,0,1) Matrix(419,246,1102,647) -> Matrix(9,-2,-4,1) Matrix(1407,824,-6422,-3761) -> Matrix(7,-2,4,-1) Matrix(1139,666,1558,911) -> Matrix(3,-2,-4,3) Matrix(265,154,456,265) -> Matrix(5,-2,-12,5) Matrix(153,88,266,153) -> Matrix(7,-4,-12,7) Matrix(113,64,-874,-495) -> Matrix(3,-2,8,-5) Matrix(379,214,1748,987) -> Matrix(11,-8,-4,3) Matrix(607,342,1482,835) -> Matrix(3,-2,-4,3) Matrix(189,106,608,341) -> Matrix(13,-10,4,-3) Matrix(305,168,-1102,-607) -> Matrix(7,-8,8,-9) Matrix(151,82,418,227) -> Matrix(1,0,0,1) Matrix(113,60,-646,-343) -> Matrix(1,0,0,1) Matrix(151,70,-494,-229) -> Matrix(1,-2,0,1) Matrix(267,122,418,191) -> Matrix(1,0,-4,1) Matrix(115,52,-418,-189) -> Matrix(5,-4,4,-3) Matrix(77,34,-342,-151) -> Matrix(3,-4,4,-5) Matrix(875,382,1482,647) -> Matrix(1,-2,0,1) Matrix(1369,596,1748,761) -> Matrix(5,-8,-8,13) Matrix(37,16,-266,-115) -> Matrix(1,-2,0,1) Matrix(113,48,266,113) -> Matrix(1,-4,0,1) Matrix(191,80,456,191) -> Matrix(1,2,0,1) Matrix(419,174,1558,647) -> Matrix(1,-2,0,1) Matrix(343,142,-1558,-645) -> Matrix(1,2,0,1) Matrix(683,282,1102,455) -> Matrix(5,2,-8,-3) Matrix(3307,1358,5092,2091) -> Matrix(1,-2,0,1) Matrix(3723,1528,5738,2355) -> Matrix(1,0,0,1) Matrix(835,342,1482,607) -> Matrix(3,-2,-4,3) Matrix(153,62,190,77) -> Matrix(1,0,-4,1) Matrix(265,104,-874,-343) -> Matrix(5,-6,-4,5) Matrix(1141,446,1558,609) -> Matrix(5,-8,-8,13) Matrix(569,222,874,341) -> Matrix(1,-2,0,1) Matrix(191,74,-684,-265) -> Matrix(3,-4,4,-5) Matrix(115,44,-494,-189) -> Matrix(1,-2,4,-7) Matrix(647,246,1102,419) -> Matrix(1,-2,-4,9) Matrix(37,14,-304,-115) -> Matrix(1,-2,0,1) Matrix(113,42,304,113) -> Matrix(1,-6,0,1) Matrix(153,56,418,153) -> Matrix(1,4,0,1) Matrix(227,82,418,151) -> Matrix(1,0,0,1) Matrix(913,328,-3382,-1215) -> Matrix(1,2,0,1) Matrix(229,82,1064,381) -> Matrix(1,-2,0,1) Matrix(457,162,646,229) -> Matrix(1,0,-4,1) Matrix(3383,1188,5738,2015) -> Matrix(1,0,-4,1) Matrix(3001,1052,5092,1785) -> Matrix(3,-2,-4,3) Matrix(533,186,874,305) -> Matrix(3,-2,-4,3) Matrix(37,12,114,37) -> Matrix(1,-2,0,1) Matrix(191,60,608,191) -> Matrix(1,10,0,1) Matrix(381,118,494,153) -> Matrix(1,2,0,1) Matrix(4827,1474,5852,1787) -> Matrix(1,0,0,1) Matrix(4103,1252,4978,1519) -> Matrix(1,2,0,1) Matrix(4029,1220,5776,1749) -> Matrix(13,14,-40,-43) Matrix(4027,1218,5776,1747) -> Matrix(15,14,-44,-41) Matrix(683,204,760,227) -> Matrix(3,2,-8,-5) Matrix(1255,374,1406,419) -> Matrix(5,2,-8,-3) Matrix(1025,304,1406,417) -> Matrix(5,2,-8,-3) Matrix(115,34,646,191) -> Matrix(1,0,0,1) Matrix(417,122,646,189) -> Matrix(1,0,0,1) Matrix(1027,298,1444,419) -> Matrix(1,0,8,1) Matrix(1025,296,1444,417) -> Matrix(1,0,-12,1) Matrix(227,64,266,75) -> Matrix(1,0,-4,1) Matrix(4181,1156,5776,1597) -> Matrix(27,-26,-28,27) Matrix(4179,1154,5776,1595) -> Matrix(25,-26,-24,25) Matrix(989,268,1406,381) -> Matrix(1,-2,-4,9) Matrix(16873,4552,23104,6233) -> Matrix(13,-24,-20,37) Matrix(16871,4550,23104,6231) -> Matrix(11,-24,-16,35) Matrix(647,174,1558,419) -> Matrix(1,-2,0,1) Matrix(949,254,1558,417) -> Matrix(3,-8,-4,11) Matrix(151,40,570,151) -> Matrix(1,-8,0,1) Matrix(39,10,152,39) -> Matrix(1,2,0,1) Matrix(1103,262,1444,343) -> Matrix(1,0,16,1) Matrix(1101,260,1444,341) -> Matrix(1,0,-20,1) Matrix(341,78,494,113) -> Matrix(5,-2,-12,5) Matrix(10147,2226,12996,2851) -> Matrix(3,-2,-4,3) Matrix(10145,2224,12996,2849) -> Matrix(1,-2,0,1) Matrix(723,158,874,191) -> Matrix(1,-2,0,1) Matrix(987,214,1748,379) -> Matrix(3,-8,-4,11) Matrix(381,82,1064,229) -> Matrix(1,-2,0,1) Matrix(113,24,532,113) -> Matrix(1,-6,0,1) Matrix(39,8,190,39) -> Matrix(1,2,0,1) Matrix(113,22,190,37) -> Matrix(1,0,0,1) Matrix(1179,218,1444,267) -> Matrix(1,0,12,1) Matrix(1177,216,1444,265) -> Matrix(1,0,-16,1) Matrix(191,34,646,115) -> Matrix(1,0,0,1) Matrix(3459,608,4978,875) -> Matrix(5,-2,-12,5) Matrix(4065,712,5852,1025) -> Matrix(1,0,-4,1) Matrix(683,118,874,151) -> Matrix(3,-2,-4,3) Matrix(37,6,228,37) -> Matrix(1,-2,0,1) Matrix(77,12,494,77) -> Matrix(1,4,0,1) Matrix(191,28,266,39) -> Matrix(1,0,0,1) Matrix(1255,166,1444,191) -> Matrix(1,0,8,1) Matrix(1253,164,1444,189) -> Matrix(1,0,-12,1) Matrix(987,106,1406,151) -> Matrix(1,-2,-4,9) Matrix(533,54,760,77) -> Matrix(1,2,-4,-7) Matrix(115,-14,304,-37) -> Matrix(1,-2,0,1) Matrix(115,-16,266,-37) -> Matrix(1,-2,0,1) Matrix(1215,-212,1748,-305) -> Matrix(3,2,-8,-5) Matrix(495,-92,608,-113) -> Matrix(1,0,-8,1) Matrix(645,-142,1558,-343) -> Matrix(1,2,0,1) Matrix(151,-34,342,-77) -> Matrix(5,4,-4,-3) Matrix(189,-44,494,-115) -> Matrix(7,2,-4,-1) Matrix(1215,-328,3382,-913) -> Matrix(1,2,0,1) Matrix(189,-52,418,-115) -> Matrix(3,4,-4,-5) Matrix(265,-74,684,-191) -> Matrix(5,4,-4,-3) Matrix(647,-188,912,-265) -> Matrix(1,0,-8,1) Matrix(343,-102,380,-113) -> Matrix(1,0,-4,1) Matrix(343,-104,874,-265) -> Matrix(5,-6,-4,5) Matrix(229,-70,494,-151) -> Matrix(1,-2,0,1) Matrix(761,-268,1292,-455) -> Matrix(1,0,0,1) Matrix(4635,-1666,6346,-2281) -> Matrix(5,2,-8,-3) Matrix(1975,-748,2812,-1065) -> Matrix(1,2,-4,-7) Matrix(607,-232,798,-305) -> Matrix(1,2,-8,-15) Matrix(875,-344,1254,-493) -> Matrix(5,6,-16,-19) Matrix(837,-344,1292,-531) -> Matrix(1,0,0,1) Matrix(5015,-2078,6422,-2661) -> Matrix(3,-2,-4,3) Matrix(761,-330,874,-379) -> Matrix(1,2,0,1) Matrix(797,-358,1102,-495) -> Matrix(9,8,-8,-7) Matrix(533,-250,646,-303) -> Matrix(1,0,0,1) Matrix(343,-184,494,-265) -> Matrix(3,2,-8,-5) Matrix(303,-166,418,-229) -> Matrix(3,4,-4,-5) Matrix(265,-148,342,-191) -> Matrix(5,4,-4,-3) Matrix(229,-130,266,-151) -> Matrix(3,2,-8,-5) Matrix(1215,-712,1558,-913) -> Matrix(5,2,-8,-3) Matrix(609,-370,874,-531) -> Matrix(7,6,-20,-17) Matrix(493,-302,684,-419) -> Matrix(5,4,-4,-3) Matrix(379,-234,494,-305) -> Matrix(3,2,4,3) Matrix(267,-166,304,-189) -> Matrix(3,2,-8,-5) Matrix(2469,-1582,3382,-2167) -> Matrix(5,2,-8,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 30 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 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 1/4 5/19 4/15 5/18 3/10 6/19 1/3 7/19 5/12 8/19 1/2 37/57 53/76 27/38 55/76 111/152 29/38 89/114 31/38 47/57 33/38 17/19 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/0 1/8 -1/1 1/7 0/1 1/0 2/13 2/1 1/0 3/19 1/0 1/6 -1/1 4/23 0/1 1/0 3/17 -1/2 0/1 2/11 -1/4 0/1 3/16 1/3 1/5 1/1 1/0 4/19 1/0 3/14 -3/1 8/37 -2/1 1/0 5/23 -2/1 -3/2 7/32 -1/1 2/9 -3/2 -1/1 3/13 -1/2 0/1 1/4 1/1 5/19 1/0 4/15 -4/1 1/0 11/41 -3/1 1/0 7/26 -3/1 10/37 -2/1 1/0 3/11 -2/1 -3/2 5/18 -1/1 2/7 -1/2 0/1 7/24 1/3 5/17 0/1 1/2 8/27 0/1 1/4 11/37 0/1 1/2 3/10 1/1 7/23 3/2 2/1 4/13 2/1 1/0 5/16 5/1 6/19 1/0 1/3 -1/1 1/0 7/20 -1/1 6/17 0/1 1/0 5/14 1/1 14/39 0/1 1/0 23/64 -1/1 9/25 0/1 1/2 4/11 2/1 1/0 7/19 1/0 3/8 -3/1 14/37 -2/1 1/0 11/29 -3/1 1/0 8/21 -9/4 -2/1 13/34 -9/5 5/13 -2/1 -3/2 12/31 -3/2 -4/3 7/18 -1/1 16/41 -3/2 -1/1 9/23 -3/2 -4/3 11/28 -1/1 2/5 -1/1 -1/2 9/22 1/1 16/39 0/1 1/0 7/17 -1/2 0/1 12/29 1/2 1/1 29/70 1/1 17/41 1/1 1/0 5/12 1/1 8/19 1/0 3/7 -2/1 1/0 13/30 -3/1 10/23 -2/1 -7/4 17/39 -2/1 -3/2 7/16 -5/3 11/25 -3/2 -4/3 4/9 -7/6 -1/1 9/20 -1/1 5/11 -2/3 -1/2 6/13 0/1 1/0 7/15 -1/2 0/1 1/2 -1/1 7/13 -1/2 0/1 6/11 -2/1 1/0 5/9 -1/1 -7/8 9/16 -5/7 22/39 -3/4 -2/3 13/23 -7/10 -2/3 4/7 -2/3 -1/2 11/19 -1/2 7/12 -1/3 24/41 -1/2 -1/3 17/29 -1/3 -1/4 10/17 0/1 1/0 33/56 -1/1 56/95 -1/2 23/39 -1/2 0/1 13/22 -1/3 3/5 -1/1 1/0 14/23 -4/5 -3/4 25/41 -1/1 -3/4 11/18 -1/1 8/13 -3/4 -2/3 13/21 -2/3 -9/14 18/29 -3/5 -1/2 5/8 -3/5 12/19 -1/2 7/11 -1/2 -2/5 16/25 -1/4 0/1 25/39 -1/2 0/1 9/14 -1/3 11/17 -1/2 0/1 24/37 0/1 1/0 37/57 1/0 13/20 -1/1 2/3 -1/1 -1/2 13/19 -1/2 11/16 -5/11 9/13 -1/2 -2/5 25/36 -1/3 66/95 -1/2 41/59 -1/2 -2/5 16/23 -2/5 -3/8 23/33 -7/20 -1/3 53/76 -1/3 30/43 -1/3 -7/22 7/10 -1/3 40/57 -1/4 33/47 -1/4 -1/5 26/37 -1/4 0/1 19/27 -1/6 0/1 12/17 -1/4 0/1 17/24 -1/5 22/31 -1/10 0/1 27/38 0/1 5/7 0/1 1/0 18/25 -2/1 1/0 13/18 -1/1 34/47 -15/14 -1/1 55/76 -1/1 21/29 -1/1 -11/12 8/11 -3/4 -2/3 27/37 -2/3 -1/2 46/63 -3/4 -2/3 111/152 -2/3 65/89 -2/3 -9/14 19/26 -3/5 30/41 -3/5 -1/2 11/15 -4/7 -1/2 14/19 -1/2 3/4 -1/3 16/21 -1/12 0/1 29/38 0/1 13/17 0/1 1/6 10/13 0/1 1/0 17/22 -3/1 7/9 -1/1 -3/4 32/41 -1/1 -1/2 89/114 -1/1 57/73 -1/1 -3/4 25/32 -1/1 18/23 -3/4 -2/3 29/37 -2/3 -1/2 11/14 -3/5 15/19 -1/2 4/5 -1/2 -1/3 13/16 -1/5 22/27 -1/12 0/1 31/38 0/1 9/11 0/1 1/2 14/17 0/1 1/0 47/57 1/0 33/40 -1/1 19/23 -1/2 0/1 5/6 -1/1 16/19 -1/2 11/13 -1/2 -2/5 6/7 -1/2 0/1 13/15 -1/6 0/1 33/38 0/1 20/23 0/1 1/4 7/8 -1/1 8/9 -1/1 -1/2 17/19 -1/2 9/10 -1/3 1/1 -1/2 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic 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(191,-29,494,-75) (1/7,2/13) -> (5/13,12/31) Hyperbolic Matrix(417,-65,494,-77) (2/13,3/19) -> (16/19,11/13) Hyperbolic Matrix(191,-31,228,-37) (3/19,1/6) -> (5/6,16/19) Hyperbolic Matrix(191,-33,874,-151) (1/6,4/23) -> (5/23,7/32) Hyperbolic Matrix(1215,-212,1748,-305) (4/23,3/17) -> (41/59,16/23) Hyperbolic Matrix(455,-81,646,-115) (3/17,2/11) -> (19/27,12/17) Hyperbolic Matrix(495,-92,608,-113) (2/11,3/16) -> (13/16,22/27) Hyperbolic Matrix(77,-15,190,-37) (3/16,1/5) -> (2/5,9/22) Hyperbolic Matrix(151,-31,190,-39) (1/5,4/19) -> (15/19,4/5) Hyperbolic Matrix(419,-89,532,-113) (4/19,3/14) -> (11/14,15/19) Hyperbolic Matrix(683,-147,1064,-229) (3/14,8/37) -> (25/39,9/14) Hyperbolic Matrix(761,-165,1748,-379) (8/37,5/23) -> (10/23,17/39) 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(113,-29,152,-39) (1/4,5/19) -> (14/19,3/4) Hyperbolic Matrix(419,-111,570,-151) (5/19,4/15) -> (11/15,14/19) Hyperbolic Matrix(609,-163,1558,-417) (4/15,11/41) -> (16/41,9/23) Hyperbolic Matrix(911,-245,1558,-419) (11/41,7/26) -> (7/12,24/41) Hyperbolic Matrix(1215,-328,3382,-913) (7/26,10/37) -> (14/39,23/64) Hyperbolic Matrix(417,-113,1406,-381) (10/37,3/11) -> (8/27,11/37) 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(229,-67,646,-189) (7/24,5/17) -> (6/17,5/14) Hyperbolic Matrix(531,-157,646,-191) (5/17,8/27) -> (9/11,14/17) 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(267,-83,608,-189) (4/13,5/16) -> (7/16,11/25) Hyperbolic Matrix(417,-131,608,-191) (5/16,6/19) -> (13/19,11/16) Hyperbolic Matrix(77,-25,114,-37) (6/19,1/3) -> (2/3,13/19) Hyperbolic Matrix(341,-119,874,-305) (1/3,7/20) -> (7/18,16/41) Hyperbolic Matrix(761,-268,1292,-455) (7/20,6/17) -> (10/17,33/56) Hyperbolic Matrix(835,-299,1064,-381) (5/14,14/39) -> (29/37,11/14) Hyperbolic Matrix(4635,-1666,6346,-2281) (23/64,9/25) -> (65/89,19/26) Hyperbolic Matrix(191,-69,418,-151) (9/25,4/11) -> (5/11,6/13) Hyperbolic Matrix(265,-97,418,-153) (4/11,7/19) -> (12/19,7/11) Hyperbolic Matrix(191,-71,304,-113) (7/19,3/8) -> (5/8,12/19) Hyperbolic Matrix(1975,-748,2812,-1065) (14/37,11/29) -> (33/47,26/37) Hyperbolic Matrix(455,-173,1102,-419) (11/29,8/21) -> (7/17,12/29) 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(647,-265,1482,-607) (9/22,16/39) -> (17/39,7/16) 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(1139,-473,1558,-647) (17/41,5/12) -> (19/26,30/41) Hyperbolic Matrix(265,-111,456,-191) (5/12,8/19) -> (11/19,7/12) Hyperbolic Matrix(153,-65,266,-113) (8/19,3/7) -> (4/7,11/19) 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(267,-145,418,-227) (7/13,6/11) -> (7/11,16/25) 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(875,-493,1482,-835) (9/16,22/39) -> (23/39,13/22) Hyperbolic Matrix(1369,-773,1748,-987) (22/39,13/23) -> (18/23,29/37) 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(683,-401,1102,-647) (17/29,10/17) -> (13/21,18/29) Hyperbolic Matrix(3307,-1949,5092,-3001) (33/56,56/95) -> (37/57,13/20) Hyperbolic Matrix(3723,-2195,5738,-3383) (56/95,23/39) -> (24/37,37/57) Hyperbolic Matrix(153,-91,190,-113) (13/22,3/5) -> (4/5,13/16) Hyperbolic Matrix(609,-370,874,-531) (3/5,14/23) -> (16/23,23/33) Hyperbolic Matrix(1141,-695,1558,-949) (14/23,25/41) -> (30/41,11/15) Hyperbolic Matrix(569,-347,874,-533) (25/41,11/18) -> (13/20,2/3) 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 Matrix(457,-295,646,-417) (9/14,11/17) -> (12/17,17/24) Hyperbolic Matrix(381,-263,494,-341) (11/16,9/13) -> (10/13,17/22) Hyperbolic Matrix(4827,-3353,5852,-4065) (25/36,66/95) -> (47/57,33/40) Hyperbolic Matrix(4103,-2851,4978,-3459) (66/95,41/59) -> (14/17,47/57) Hyperbolic Matrix(4029,-2809,5776,-4027) (23/33,53/76) -> (53/76,30/43) Parabolic Matrix(683,-479,760,-533) (7/10,40/57) -> (17/19,9/10) Hyperbolic Matrix(1255,-881,1406,-987) (40/57,33/47) -> (8/9,17/19) Hyperbolic Matrix(1025,-721,1406,-989) (26/37,19/27) -> (8/11,27/37) Hyperbolic Matrix(1027,-729,1444,-1025) (22/31,27/38) -> (27/38,5/7) Parabolic Matrix(227,-163,266,-191) (5/7,18/25) -> (11/13,6/7) Hyperbolic Matrix(4181,-3025,5776,-4179) (34/47,55/76) -> (55/76,21/29) Parabolic Matrix(16873,-12321,23104,-16871) (46/63,111/152) -> (111/152,65/89) Parabolic Matrix(1103,-841,1444,-1101) (16/21,29/38) -> (29/38,13/17) Parabolic Matrix(10147,-7921,12996,-10145) (32/41,89/114) -> (89/114,57/73) Parabolic Matrix(723,-565,874,-683) (25/32,18/23) -> (19/23,5/6) Hyperbolic Matrix(1179,-961,1444,-1177) (22/27,31/38) -> (31/38,9/11) Parabolic Matrix(1255,-1089,1444,-1253) (13/15,33/38) -> (33/38,20/23) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-2,1) Matrix(115,-14,304,-37) -> Matrix(1,-2,0,1) Matrix(115,-16,266,-37) -> Matrix(1,-2,0,1) Matrix(191,-29,494,-75) -> Matrix(3,-4,-2,3) Matrix(417,-65,494,-77) -> Matrix(1,-4,-2,9) Matrix(191,-31,228,-37) -> Matrix(1,2,-2,-3) Matrix(191,-33,874,-151) -> Matrix(3,2,-2,-1) Matrix(1215,-212,1748,-305) -> Matrix(3,2,-8,-5) Matrix(455,-81,646,-115) -> Matrix(1,0,-2,1) Matrix(495,-92,608,-113) -> Matrix(1,0,-8,1) Matrix(77,-15,190,-37) -> Matrix(1,0,-2,1) Matrix(151,-31,190,-39) -> Matrix(1,-2,-2,5) Matrix(419,-89,532,-113) -> Matrix(1,6,-2,-11) Matrix(683,-147,1064,-229) -> Matrix(1,2,-2,-3) Matrix(761,-165,1748,-379) -> Matrix(3,8,-2,-5) Matrix(645,-142,1558,-343) -> Matrix(1,2,0,1) Matrix(151,-34,342,-77) -> Matrix(5,4,-4,-3) Matrix(189,-44,494,-115) -> Matrix(7,2,-4,-1) Matrix(113,-29,152,-39) -> Matrix(1,-2,-2,5) Matrix(419,-111,570,-151) -> Matrix(1,8,-2,-15) Matrix(609,-163,1558,-417) -> Matrix(3,8,-2,-5) Matrix(911,-245,1558,-419) -> Matrix(1,2,-2,-3) Matrix(1215,-328,3382,-913) -> Matrix(1,2,0,1) Matrix(417,-113,1406,-381) -> Matrix(1,2,2,5) Matrix(189,-52,418,-115) -> Matrix(3,4,-4,-5) Matrix(265,-74,684,-191) -> Matrix(5,4,-4,-3) Matrix(647,-188,912,-265) -> Matrix(1,0,-8,1) Matrix(229,-67,646,-189) -> Matrix(1,0,-2,1) Matrix(531,-157,646,-191) -> Matrix(1,0,-2,1) Matrix(343,-102,380,-113) -> Matrix(1,0,-4,1) Matrix(343,-104,874,-265) -> Matrix(5,-6,-4,5) Matrix(229,-70,494,-151) -> Matrix(1,-2,0,1) Matrix(267,-83,608,-189) -> Matrix(3,-10,-2,7) Matrix(417,-131,608,-191) -> Matrix(1,-10,-2,21) Matrix(77,-25,114,-37) -> Matrix(1,2,-2,-3) Matrix(341,-119,874,-305) -> Matrix(3,2,-2,-1) Matrix(761,-268,1292,-455) -> Matrix(1,0,0,1) Matrix(835,-299,1064,-381) -> Matrix(1,2,-2,-3) Matrix(4635,-1666,6346,-2281) -> Matrix(5,2,-8,-3) Matrix(191,-69,418,-151) -> Matrix(1,0,-2,1) Matrix(265,-97,418,-153) -> Matrix(1,-4,-2,9) Matrix(191,-71,304,-113) -> Matrix(1,6,-2,-11) Matrix(1975,-748,2812,-1065) -> Matrix(1,2,-4,-7) Matrix(455,-173,1102,-419) -> Matrix(1,2,2,5) Matrix(607,-232,798,-305) -> Matrix(1,2,-8,-15) Matrix(875,-344,1254,-493) -> Matrix(5,6,-16,-19) Matrix(647,-265,1482,-607) -> Matrix(3,2,-2,-1) Matrix(837,-344,1292,-531) -> Matrix(1,0,0,1) Matrix(5015,-2078,6422,-2661) -> Matrix(3,-2,-4,3) Matrix(1139,-473,1558,-647) -> Matrix(1,2,-2,-3) Matrix(265,-111,456,-191) -> Matrix(1,-2,-2,5) Matrix(153,-65,266,-113) -> Matrix(1,4,-2,-7) Matrix(761,-330,874,-379) -> Matrix(1,2,0,1) Matrix(797,-358,1102,-495) -> Matrix(9,8,-8,-7) Matrix(533,-250,646,-303) -> Matrix(1,0,0,1) Matrix(343,-184,494,-265) -> Matrix(3,2,-8,-5) Matrix(267,-145,418,-227) -> Matrix(1,0,-2,1) Matrix(303,-166,418,-229) -> Matrix(3,4,-4,-5) Matrix(265,-148,342,-191) -> Matrix(5,4,-4,-3) Matrix(875,-493,1482,-835) -> Matrix(3,2,-2,-1) Matrix(1369,-773,1748,-987) -> Matrix(11,8,-18,-13) Matrix(229,-130,266,-151) -> Matrix(3,2,-8,-5) Matrix(1215,-712,1558,-913) -> Matrix(5,2,-8,-3) Matrix(683,-401,1102,-647) -> Matrix(9,2,-14,-3) Matrix(3307,-1949,5092,-3001) -> Matrix(3,2,-2,-1) Matrix(3723,-2195,5738,-3383) -> Matrix(1,0,2,1) Matrix(153,-91,190,-113) -> Matrix(1,0,-2,1) Matrix(609,-370,874,-531) -> Matrix(7,6,-20,-17) Matrix(1141,-695,1558,-949) -> Matrix(11,8,-18,-13) Matrix(569,-347,874,-533) -> Matrix(3,2,-2,-1) Matrix(493,-302,684,-419) -> Matrix(5,4,-4,-3) Matrix(379,-234,494,-305) -> Matrix(3,2,4,3) Matrix(267,-166,304,-189) -> Matrix(3,2,-8,-5) Matrix(2469,-1582,3382,-2167) -> Matrix(5,2,-8,-3) Matrix(457,-295,646,-417) -> Matrix(1,0,-2,1) Matrix(381,-263,494,-341) -> Matrix(5,2,2,1) Matrix(4827,-3353,5852,-4065) -> Matrix(1,0,2,1) Matrix(4103,-2851,4978,-3459) -> Matrix(5,2,2,1) Matrix(4029,-2809,5776,-4027) -> Matrix(41,14,-126,-43) Matrix(683,-479,760,-533) -> Matrix(7,2,-18,-5) Matrix(1255,-881,1406,-987) -> Matrix(9,2,-14,-3) Matrix(1025,-721,1406,-989) -> Matrix(9,2,-14,-3) Matrix(1027,-729,1444,-1025) -> Matrix(1,0,10,1) Matrix(227,-163,266,-191) -> Matrix(1,0,-2,1) Matrix(4181,-3025,5776,-4179) -> Matrix(25,26,-26,-27) Matrix(16873,-12321,23104,-16871) -> Matrix(35,24,-54,-37) Matrix(1103,-841,1444,-1101) -> Matrix(1,0,18,1) Matrix(10147,-7921,12996,-10145) -> Matrix(1,2,-2,-3) Matrix(723,-565,874,-683) -> Matrix(3,2,-2,-1) Matrix(1179,-961,1444,-1177) -> Matrix(1,0,14,1) Matrix(1255,-1089,1444,-1253) -> Matrix(1,0,10,1) 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 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 (0/1,1/0) 0 38 1/8 -1/1 2 19 1/7 (0/1,1/0) 0 38 2/13 (2/1,1/0) 0 38 3/19 1/0 6 2 1/6 -1/1 2 19 4/23 (0/1,1/0) 0 38 3/17 (-1/2,0/1) 0 38 2/11 (-1/4,0/1) 0 38 7/38 0/1 14 1 3/16 1/3 2 19 1/5 (1/1,1/0) 0 38 4/19 1/0 8 2 3/14 -3/1 2 19 8/37 (-2/1,1/0) 0 38 5/23 (-2/1,-3/2) 0 38 7/32 -1/1 2 19 2/9 (-3/2,-1/1) 0 38 3/13 (-1/2,0/1) 0 38 1/4 1/1 2 19 5/19 1/0 10 2 4/15 (-4/1,1/0) 0 38 11/41 (-3/1,1/0) 0 38 7/26 -3/1 2 19 10/37 (-2/1,1/0) 0 38 3/11 (-2/1,-3/2) 0 38 5/18 -1/1 2 19 2/7 (-1/2,0/1) 0 38 11/38 0/1 10 1 7/24 1/3 2 19 5/17 (0/1,1/2) 0 38 8/27 (0/1,1/4) 0 38 11/37 (0/1,1/2) 0 38 3/10 1/1 2 19 7/23 (3/2,2/1) 0 38 4/13 (2/1,1/0) 0 38 5/16 5/1 2 19 6/19 1/0 12 2 1/3 (-1/1,1/0) 0 38 7/20 -1/1 2 19 6/17 (0/1,1/0) 0 38 5/14 1/1 2 19 14/39 (0/1,1/0) 0 38 23/64 -1/1 2 19 41/114 0/1 6 1 9/25 (0/1,1/2) 0 38 4/11 (2/1,1/0) 0 38 7/19 1/0 10 2 3/8 -3/1 2 19 14/37 (-2/1,1/0) 0 38 25/66 -1/1 2 19 36/95 1/0 4 2 11/29 (-3/1,1/0) 0 38 8/21 (-9/4,-2/1) 0 38 29/76 -2/1 18 1 13/34 -9/5 2 19 5/13 (-2/1,-3/2) 0 38 12/31 (-3/2,-4/3) 0 38 7/18 -1/1 2 19 16/41 (-3/2,-1/1) 0 38 9/23 (-3/2,-4/3) 0 38 11/28 -1/1 2 19 15/38 -1/1 14 1 2/5 (-1/1,-1/2) 0 38 9/22 1/1 2 19 16/39 (0/1,1/0) 0 38 39/95 1/0 2 2 23/56 -1/1 2 19 7/17 (-1/2,0/1) 0 38 12/29 (1/2,1/1) 0 38 29/70 1/1 2 19 63/152 1/1 2 1 17/41 (1/1,1/0) 0 38 5/12 1/1 2 19 8/19 1/0 6 2 3/7 (-2/1,1/0) 0 38 13/30 -3/1 2 19 33/76 -2/1 10 1 10/23 (-2/1,-7/4) 0 38 17/39 (-2/1,-3/2) 0 38 7/16 -5/3 2 19 11/25 (-3/2,-4/3) 0 38 4/9 (-7/6,-1/1) 0 38 17/38 -1/1 26 1 9/20 -1/1 2 19 5/11 (-2/3,-1/2) 0 38 6/13 (0/1,1/0) 0 38 7/15 (-1/2,0/1) 0 38 8/17 (0/1,1/0) 0 38 9/19 1/0 2 2 1/2 -1/1 2 19 1/0 0/1 2 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(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(191,-29,494,-75) (1/7,2/13) -> (5/13,12/31) Hyperbolic 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(191,-33,874,-151) (1/6,4/23) -> (5/23,7/32) Hyperbolic Matrix(303,-53,646,-113) (4/23,3/17) -> (7/15,8/17) Glide Reflection Matrix(191,-34,646,-115) (3/17,2/11) -> (5/17,8/27) Glide Reflection Matrix(153,-28,836,-153) (2/11,7/38) -> (2/11,7/38) Reflection Matrix(113,-21,608,-113) (7/38,3/16) -> (7/38,3/16) Reflection Matrix(77,-15,190,-37) (3/16,1/5) -> (2/5,9/22) Hyperbolic Matrix(39,-8,190,-39) (1/5,4/19) -> (1/5,4/19) Reflection Matrix(113,-24,532,-113) (4/19,3/14) -> (4/19,3/14) Reflection Matrix(381,-82,1064,-229) (3/14,8/37) -> (5/14,14/39) Glide Reflection Matrix(761,-165,1748,-379) (8/37,5/23) -> (10/23,17/39) 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(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(609,-163,1558,-417) (4/15,11/41) -> (16/41,9/23) Hyperbolic Matrix(647,-174,1558,-419) (11/41,7/26) -> (17/41,5/12) Glide Reflection Matrix(1215,-328,3382,-913) (7/26,10/37) -> (14/39,23/64) Hyperbolic Matrix(417,-113,1406,-381) (10/37,3/11) -> (8/27,11/37) 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(153,-44,532,-153) (2/7,11/38) -> (2/7,11/38) Reflection Matrix(265,-77,912,-265) (11/38,7/24) -> (11/38,7/24) Reflection Matrix(229,-67,646,-189) (7/24,5/17) -> (6/17,5/14) Hyperbolic Matrix(1065,-317,2812,-837) (11/37,3/10) -> (14/37,25/66) Glide Reflection 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(267,-83,608,-189) (4/13,5/16) -> (7/16,11/25) Hyperbolic Matrix(191,-60,608,-191) (5/16,6/19) -> (5/16,6/19) Reflection Matrix(37,-12,114,-37) (6/19,1/3) -> (6/19,1/3) Reflection Matrix(341,-119,874,-305) (1/3,7/20) -> (7/18,16/41) Hyperbolic Matrix(531,-187,1292,-455) (7/20,6/17) -> (23/56,7/17) Glide Reflection Matrix(2623,-943,7296,-2623) (23/64,41/114) -> (23/64,41/114) Reflection Matrix(2051,-738,5700,-2051) (41/114,9/25) -> (41/114,9/25) Reflection Matrix(191,-69,418,-151) (9/25,4/11) -> (5/11,6/13) Hyperbolic 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(4751,-1800,12540,-4751) (25/66,36/95) -> (25/66,36/95) Reflection Matrix(2089,-792,5510,-2089) (36/95,11/29) -> (36/95,11/29) Reflection Matrix(455,-173,1102,-419) (11/29,8/21) -> (7/17,12/29) Hyperbolic Matrix(1217,-464,3192,-1217) (8/21,29/76) -> (8/21,29/76) Reflection Matrix(987,-377,2584,-987) (29/76,13/34) -> (29/76,13/34) Reflection Matrix(419,-165,1064,-419) (11/28,15/38) -> (11/28,15/38) Reflection Matrix(151,-60,380,-151) (15/38,2/5) -> (15/38,2/5) Reflection Matrix(647,-265,1482,-607) (9/22,16/39) -> (17/39,7/16) Hyperbolic Matrix(3041,-1248,7410,-3041) (16/39,39/95) -> (16/39,39/95) Reflection Matrix(4369,-1794,10640,-4369) (39/95,23/56) -> (39/95,23/56) Reflection Matrix(4409,-1827,10640,-4409) (29/70,63/152) -> (29/70,63/152) Reflection Matrix(5167,-2142,12464,-5167) (63/152,17/41) -> (63/152,17/41) Reflection Matrix(191,-80,456,-191) (5/12,8/19) -> (5/12,8/19) Reflection Matrix(113,-48,266,-113) (8/19,3/7) -> (8/19,3/7) Reflection Matrix(989,-429,2280,-989) (13/30,33/76) -> (13/30,33/76) Reflection Matrix(1519,-660,3496,-1519) (33/76,10/23) -> (33/76,10/23) Reflection Matrix(305,-136,684,-305) (4/9,17/38) -> (4/9,17/38) Reflection Matrix(341,-153,760,-341) (17/38,9/20) -> (17/38,9/20) Reflection Matrix(305,-144,646,-305) (8/17,9/19) -> (8/17,9/19) Reflection Matrix(37,-18,76,-37) (9/19,1/2) -> (9/19,1/2) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(115,-14,304,-37) -> Matrix(1,-2,0,1) 1/0 Matrix(115,-16,266,-37) -> Matrix(1,-2,0,1) 1/0 Matrix(191,-29,494,-75) -> Matrix(3,-4,-2,3) Matrix(77,-12,494,-77) -> Matrix(-1,4,0,1) (2/13,3/19) -> (2/1,1/0) Matrix(37,-6,228,-37) -> Matrix(1,2,0,-1) (3/19,1/6) -> (-1/1,1/0) Matrix(191,-33,874,-151) -> Matrix(3,2,-2,-1) -1/1 Matrix(303,-53,646,-113) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(191,-34,646,-115) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(153,-28,836,-153) -> Matrix(-1,0,8,1) (2/11,7/38) -> (-1/4,0/1) Matrix(113,-21,608,-113) -> Matrix(1,0,6,-1) (7/38,3/16) -> (0/1,1/3) Matrix(77,-15,190,-37) -> 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(113,-24,532,-113) -> Matrix(1,6,0,-1) (4/19,3/14) -> (-3/1,1/0) Matrix(381,-82,1064,-229) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(761,-165,1748,-379) -> Matrix(3,8,-2,-5) -2/1 Matrix(645,-142,1558,-343) -> Matrix(1,2,0,1) 1/0 Matrix(151,-34,342,-77) -> Matrix(5,4,-4,-3) -1/1 Matrix(189,-44,494,-115) -> Matrix(7,2,-4,-1) Matrix(39,-10,152,-39) -> Matrix(-1,2,0,1) (1/4,5/19) -> (1/1,1/0) Matrix(151,-40,570,-151) -> Matrix(1,8,0,-1) (5/19,4/15) -> (-4/1,1/0) Matrix(609,-163,1558,-417) -> Matrix(3,8,-2,-5) -2/1 Matrix(647,-174,1558,-419) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(1215,-328,3382,-913) -> Matrix(1,2,0,1) 1/0 Matrix(417,-113,1406,-381) -> Matrix(1,2,2,5) Matrix(189,-52,418,-115) -> Matrix(3,4,-4,-5) -1/1 Matrix(265,-74,684,-191) -> Matrix(5,4,-4,-3) -1/1 Matrix(153,-44,532,-153) -> Matrix(-1,0,4,1) (2/7,11/38) -> (-1/2,0/1) Matrix(265,-77,912,-265) -> Matrix(1,0,6,-1) (11/38,7/24) -> (0/1,1/3) Matrix(229,-67,646,-189) -> Matrix(1,0,-2,1) 0/1 Matrix(1065,-317,2812,-837) -> Matrix(3,-2,-2,1) Matrix(343,-104,874,-265) -> Matrix(5,-6,-4,5) Matrix(229,-70,494,-151) -> Matrix(1,-2,0,1) 1/0 Matrix(267,-83,608,-189) -> Matrix(3,-10,-2,7) Matrix(191,-60,608,-191) -> Matrix(-1,10,0,1) (5/16,6/19) -> (5/1,1/0) Matrix(37,-12,114,-37) -> Matrix(1,2,0,-1) (6/19,1/3) -> (-1/1,1/0) Matrix(341,-119,874,-305) -> Matrix(3,2,-2,-1) -1/1 Matrix(531,-187,1292,-455) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(2623,-943,7296,-2623) -> Matrix(-1,0,2,1) (23/64,41/114) -> (-1/1,0/1) Matrix(2051,-738,5700,-2051) -> Matrix(1,0,4,-1) (41/114,9/25) -> (0/1,1/2) Matrix(191,-69,418,-151) -> Matrix(1,0,-2,1) 0/1 Matrix(153,-56,418,-153) -> Matrix(-1,4,0,1) (4/11,7/19) -> (2/1,1/0) Matrix(113,-42,304,-113) -> Matrix(1,6,0,-1) (7/19,3/8) -> (-3/1,1/0) Matrix(4751,-1800,12540,-4751) -> Matrix(1,2,0,-1) (25/66,36/95) -> (-1/1,1/0) Matrix(2089,-792,5510,-2089) -> Matrix(1,6,0,-1) (36/95,11/29) -> (-3/1,1/0) Matrix(455,-173,1102,-419) -> Matrix(1,2,2,5) Matrix(1217,-464,3192,-1217) -> Matrix(17,36,-8,-17) (8/21,29/76) -> (-9/4,-2/1) Matrix(987,-377,2584,-987) -> Matrix(19,36,-10,-19) (29/76,13/34) -> (-2/1,-9/5) Matrix(419,-165,1064,-419) -> Matrix(11,12,-10,-11) (11/28,15/38) -> (-6/5,-1/1) Matrix(151,-60,380,-151) -> Matrix(3,2,-4,-3) (15/38,2/5) -> (-1/1,-1/2) Matrix(647,-265,1482,-607) -> Matrix(3,2,-2,-1) -1/1 Matrix(3041,-1248,7410,-3041) -> Matrix(1,0,0,-1) (16/39,39/95) -> (0/1,1/0) Matrix(4369,-1794,10640,-4369) -> Matrix(1,2,0,-1) (39/95,23/56) -> (-1/1,1/0) Matrix(4409,-1827,10640,-4409) -> Matrix(1,0,2,-1) (29/70,63/152) -> (0/1,1/1) Matrix(5167,-2142,12464,-5167) -> Matrix(-1,2,0,1) (63/152,17/41) -> (1/1,1/0) Matrix(191,-80,456,-191) -> Matrix(-1,2,0,1) (5/12,8/19) -> (1/1,1/0) Matrix(113,-48,266,-113) -> Matrix(1,4,0,-1) (8/19,3/7) -> (-2/1,1/0) Matrix(989,-429,2280,-989) -> Matrix(5,12,-2,-5) (13/30,33/76) -> (-3/1,-2/1) Matrix(1519,-660,3496,-1519) -> Matrix(15,28,-8,-15) (33/76,10/23) -> (-2/1,-7/4) Matrix(305,-136,684,-305) -> Matrix(13,14,-12,-13) (4/9,17/38) -> (-7/6,-1/1) Matrix(341,-153,760,-341) -> Matrix(13,12,-14,-13) (17/38,9/20) -> (-1/1,-6/7) Matrix(305,-144,646,-305) -> Matrix(1,0,0,-1) (8/17,9/19) -> (0/1,1/0) Matrix(37,-18,76,-37) -> Matrix(1,2,0,-1) (9/19,1/2) -> (-1/1,1/0) Matrix(-1,1,0,1) -> Matrix(-1,0,2,1) (1/2,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.