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): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -6/13 -5/12 -2/5 -4/11 -3/10 -1/4 -2/9 -1/8 0/1 1/6 1/5 4/17 3/11 5/16 4/11 2/5 1/2 8/13 5/7 3/4 4/5 1/1 15/13 23/19 5/4 4/3 7/5 3/2 64/41 13/8 40/23 9/5 2/1 29/13 59/25 5/2 13/5 11/4 31/11 3/1 16/5 43/13 10/3 7/2 11/3 15/4 83/22 19/5 4/1 17/4 13/3 22/5 9/2 23/5 14/3 52/11 5/1 53/10 16/3 11/2 17/3 6/1 13/2 7/1 37/5 15/2 8/1 9/1 19/2 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 -7/15 1/3 -6/13 1/2 -11/24 0/1 -5/11 0/1 -9/20 -2/1 -4/9 1/4 -11/25 0/1 -7/16 1/3 -10/23 1/2 -3/7 1/1 -11/26 1/3 -8/19 3/4 -13/31 0/1 -5/12 0/1 -17/41 0/1 -12/29 1/4 -19/46 1/3 -7/17 3/7 -16/39 3/4 -9/22 0/1 -11/27 1/1 -2/5 1/2 -9/23 1/1 -7/18 2/5 -12/31 5/8 -5/13 1/1 -8/21 1/0 -11/29 0/1 -3/8 2/3 -13/35 1/1 -10/27 1/2 -7/19 0/1 -11/30 0/1 -4/11 1/2 -13/36 2/3 -22/61 1/2 -9/25 3/5 -14/39 1/2 -5/14 1/1 -6/17 3/2 -1/3 1/1 -5/16 4/5 -4/13 1/0 -11/36 0/1 -7/23 3/5 -3/10 1/1 -11/37 9/7 -8/27 5/4 -13/44 16/11 -5/17 2/1 -7/24 0/1 -9/31 1/1 -2/7 3/2 -7/25 2/1 -5/18 4/1 -3/11 -1/1 -7/26 0/1 -11/41 0/1 -4/15 1/4 -5/19 1/1 -1/4 1/1 -6/25 3/2 -5/21 5/3 -9/38 2/1 -4/17 1/0 -7/30 2/1 -3/13 7/3 -8/35 1/0 -5/22 4/1 -2/9 1/0 -7/32 -2/1 -5/23 -2/1 -3/14 -2/3 -4/19 1/0 -1/5 1/1 -3/16 2/1 -2/11 3/2 -3/17 2/1 -1/6 4/1 -2/13 -5/2 -1/7 0/1 -2/15 1/2 -1/8 1/1 -1/9 1/1 0/1 1/0 1/8 -3/1 2/15 -5/2 1/7 -1/1 1/6 -1/1 2/11 -1/2 1/5 0/1 5/24 0/1 4/19 3/4 3/14 2/1 2/9 5/2 5/22 5/1 3/13 9/1 4/17 1/0 1/4 -4/1 5/19 -2/1 4/15 1/0 11/41 -23/9 7/26 -7/3 3/11 -2/1 5/18 -2/1 2/7 -3/2 7/24 -8/7 5/17 -1/1 3/10 -2/1 7/23 -4/3 4/13 -5/4 5/16 -1/1 1/3 -1/1 5/14 0/1 9/25 1/1 13/36 1/1 4/11 1/0 15/41 0/1 11/30 0/1 7/19 -1/3 10/27 1/6 3/8 2/3 5/13 2/1 2/5 1/0 7/17 -4/1 12/29 1/0 5/12 -4/1 18/43 -19/6 31/74 -3/1 13/31 -3/1 8/19 1/0 19/45 -3/1 11/26 -10/3 3/7 -7/3 10/23 -3/2 7/16 -2/1 11/25 -2/1 4/9 1/0 5/11 -5/3 1/2 -1/1 6/11 -1/2 5/9 -1/1 14/25 -1/2 23/41 -1/1 9/16 0/1 13/23 -2/3 4/7 -1/4 7/12 0/1 17/29 1/3 10/17 1/2 13/22 1/1 3/5 1/1 8/13 1/0 13/21 -9/1 5/8 -4/1 7/11 -2/1 16/25 1/0 41/64 -3/1 25/39 -3/1 34/53 -5/2 9/14 -2/1 11/17 -2/1 2/3 -3/2 13/19 -3/5 11/16 -1/1 9/13 -1/1 7/10 0/1 19/27 -5/1 12/17 1/0 29/41 -2/1 17/24 -2/1 22/31 -11/6 5/7 -2/1 8/11 -5/4 3/4 -1/1 10/13 -1/2 17/22 -1/1 7/9 -3/5 25/32 -1/3 18/23 -1/2 29/37 0/1 11/14 0/1 15/19 -1/1 19/24 0/1 4/5 1/0 13/16 -2/1 22/27 -3/2 9/11 -1/1 5/6 -4/5 11/13 0/1 6/7 -1/2 13/15 0/1 7/8 -1/1 8/9 1/0 1/1 -1/1 9/8 -4/5 8/7 -3/4 15/13 -2/3 7/6 -2/3 13/11 0/1 6/5 -3/2 23/19 -1/1 17/14 -12/13 11/9 -1/1 38/31 -5/6 27/22 -1/1 16/13 -3/4 5/4 -1/1 24/19 -3/4 19/15 -5/7 33/26 -2/3 47/37 -2/3 14/11 -1/2 23/18 -2/3 9/7 -3/5 4/3 -1/2 15/11 -1/1 11/8 0/1 18/13 -1/6 61/44 0/1 43/31 1/9 25/18 0/1 7/5 0/1 31/22 6/1 24/17 1/0 65/46 -3/1 41/29 -2/1 17/12 -2/1 27/19 -1/1 37/26 -1/1 10/7 -1/2 23/16 -1/1 36/25 1/0 13/9 -1/1 16/11 1/0 19/13 -5/3 22/15 -7/6 3/2 -2/3 14/9 -1/2 39/25 -1/1 64/41 -1/2 25/16 0/1 36/23 1/0 11/7 0/1 19/12 -4/3 27/17 -1/1 8/5 1/0 13/8 -1/1 18/11 -5/6 5/3 -1/1 17/10 -1/1 29/17 -5/7 41/24 -2/3 12/7 -5/8 19/11 -4/7 45/26 -6/11 26/15 -1/2 59/34 -9/17 33/19 -15/29 40/23 -1/2 7/4 -2/5 23/13 0/1 39/22 0/1 55/31 -1/1 16/9 1/0 41/23 -1/1 66/37 -1/2 25/14 -1/1 9/5 -1/1 20/11 -5/8 11/6 -2/3 13/7 -1/1 2/1 -1/2 15/7 -1/3 13/6 0/1 11/5 -1/1 20/9 -1/4 29/13 0/1 38/17 1/2 9/4 0/1 16/7 -3/4 7/3 -3/7 33/14 -6/17 59/25 -1/3 85/36 -12/37 26/11 -3/10 45/19 -1/3 19/8 -1/3 50/21 -1/2 31/13 -1/3 12/5 -1/4 5/2 0/1 18/7 -1/2 49/19 -1/3 31/12 0/1 106/41 1/0 75/29 -1/1 44/17 1/0 13/5 0/1 21/8 -2/1 71/27 -2/1 50/19 -3/2 29/11 -1/1 8/3 -3/4 27/10 -8/15 46/17 -1/2 19/7 -5/11 49/18 -2/5 30/11 -1/2 71/26 -2/5 41/15 -2/5 52/19 -3/8 11/4 -1/3 47/17 -1/3 36/13 -1/4 25/9 -1/3 14/5 -1/6 31/11 0/1 48/17 1/12 17/6 0/1 3/1 -1/1 16/5 -1/2 29/9 -9/19 13/4 -4/9 23/7 -2/5 33/10 -2/5 43/13 -2/5 10/3 -1/2 27/8 -1/3 44/13 -3/8 17/5 -1/3 41/12 -10/29 65/19 -1/3 24/7 -5/16 7/2 -1/3 32/9 -1/4 57/16 -12/47 82/23 -1/4 25/7 -5/21 18/5 -1/6 29/8 -2/11 11/3 0/1 26/7 -1/2 67/18 0/1 41/11 1/3 15/4 0/1 49/13 -1/1 83/22 -1/1 34/9 -1/2 19/5 0/1 4/1 -1/4 17/4 0/1 30/7 1/14 13/3 1/5 35/8 0/1 57/13 0/1 22/5 1/2 9/2 2/1 23/5 -1/1 14/3 -1/2 33/7 -1/1 52/11 -1/2 71/15 -1/3 19/4 0/1 24/5 1/0 5/1 0/1 21/4 -2/1 37/7 -1/1 53/10 -1/1 16/3 -3/4 11/2 0/1 17/3 -1/1 6/1 -1/2 19/3 -1/3 13/2 -1/3 7/1 -1/3 22/3 -1/6 37/5 0/1 15/2 0/1 8/1 -1/4 9/1 -1/9 19/2 0/1 10/1 1/6 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(315,148,398,187) (-1/2,-7/15) -> (15/19,19/24) Hyperbolic Matrix(865,402,312,145) (-7/15,-6/13) -> (36/13,25/9) Hyperbolic Matrix(697,320,856,393) (-6/13,-11/24) -> (13/16,22/27) Hyperbolic Matrix(79,36,384,175) (-11/24,-5/11) -> (1/5,5/24) Hyperbolic Matrix(537,242,304,137) (-5/11,-9/20) -> (7/4,23/13) Hyperbolic Matrix(227,102,612,275) (-9/20,-4/9) -> (10/27,3/8) Hyperbolic Matrix(149,66,228,101) (-4/9,-11/25) -> (11/17,2/3) Hyperbolic Matrix(223,98,826,363) (-11/25,-7/16) -> (7/26,3/11) Hyperbolic Matrix(371,162,300,131) (-7/16,-10/23) -> (16/13,5/4) Hyperbolic Matrix(521,226,740,321) (-10/23,-3/7) -> (19/27,12/17) Hyperbolic Matrix(873,370,512,217) (-3/7,-11/26) -> (17/10,29/17) Hyperbolic Matrix(147,62,652,275) (-11/26,-8/19) -> (2/9,5/22) Hyperbolic Matrix(433,182,364,153) (-8/19,-13/31) -> (13/11,6/5) Hyperbolic Matrix(359,150,-864,-361) (-13/31,-5/12) -> (-5/12,-17/41) Parabolic Matrix(1795,744,1146,475) (-17/41,-12/29) -> (36/23,11/7) Hyperbolic Matrix(571,236,646,267) (-12/29,-19/46) -> (7/8,8/9) Hyperbolic Matrix(785,324,1146,473) (-19/46,-7/17) -> (13/19,11/16) Hyperbolic Matrix(497,204,1854,761) (-7/17,-16/39) -> (4/15,11/41) Hyperbolic Matrix(283,116,1354,555) (-16/39,-9/22) -> (5/24,4/19) Hyperbolic Matrix(353,144,-1488,-607) (-9/22,-11/27) -> (-5/21,-9/38) Hyperbolic Matrix(639,260,-1772,-721) (-11/27,-2/5) -> (-22/61,-9/25) Hyperbolic Matrix(347,136,620,243) (-2/5,-9/23) -> (5/9,14/25) Hyperbolic Matrix(621,242,136,53) (-9/23,-7/18) -> (9/2,23/5) Hyperbolic Matrix(547,212,-1850,-717) (-7/18,-12/31) -> (-8/27,-13/44) Hyperbolic Matrix(957,370,344,133) (-12/31,-5/13) -> (25/9,14/5) Hyperbolic Matrix(339,130,206,79) (-5/13,-8/21) -> (18/11,5/3) Hyperbolic Matrix(405,154,476,181) (-8/21,-11/29) -> (11/13,6/7) Hyperbolic Matrix(69,26,268,101) (-11/29,-3/8) -> (1/4,5/19) Hyperbolic Matrix(537,200,1270,473) (-3/8,-13/35) -> (19/45,11/26) Hyperbolic Matrix(1667,618,936,347) (-13/35,-10/27) -> (16/9,41/23) Hyperbolic Matrix(265,98,868,321) (-10/27,-7/19) -> (7/23,4/13) Hyperbolic Matrix(463,170,-1724,-633) (-7/19,-11/30) -> (-7/26,-11/41) Hyperbolic Matrix(263,96,-726,-265) (-11/30,-4/11) -> (-4/11,-13/36) Parabolic Matrix(1773,640,2762,997) (-13/36,-22/61) -> (34/53,9/14) Hyperbolic Matrix(2361,848,916,329) (-9/25,-14/39) -> (18/7,49/19) Hyperbolic Matrix(67,24,522,187) (-14/39,-5/14) -> (1/8,2/15) Hyperbolic Matrix(455,162,132,47) (-5/14,-6/17) -> (24/7,7/2) Hyperbolic Matrix(517,182,196,69) (-6/17,-1/3) -> (29/11,8/3) Hyperbolic Matrix(489,154,308,97) (-1/3,-5/16) -> (19/12,27/17) Hyperbolic Matrix(123,38,424,131) (-5/16,-4/13) -> (2/7,7/24) Hyperbolic Matrix(483,148,62,19) (-4/13,-11/36) -> (15/2,8/1) Hyperbolic Matrix(1811,552,666,203) (-11/36,-7/23) -> (19/7,49/18) Hyperbolic Matrix(179,54,-600,-181) (-7/23,-3/10) -> (-3/10,-11/37) Parabolic Matrix(357,106,-1492,-443) (-11/37,-8/27) -> (-6/25,-5/21) Hyperbolic Matrix(835,246,594,175) (-13/44,-5/17) -> (7/5,31/22) Hyperbolic Matrix(773,226,236,69) (-5/17,-7/24) -> (13/4,23/7) Hyperbolic Matrix(831,242,1480,431) (-7/24,-9/31) -> (23/41,9/16) Hyperbolic Matrix(1121,324,474,137) (-9/31,-2/7) -> (26/11,45/19) Hyperbolic Matrix(233,66,60,17) (-2/7,-7/25) -> (19/5,4/1) Hyperbolic Matrix(409,114,348,97) (-7/25,-5/18) -> (7/6,13/11) Hyperbolic Matrix(289,80,466,129) (-5/18,-3/11) -> (13/21,5/8) Hyperbolic Matrix(289,78,804,217) (-3/11,-7/26) -> (5/14,9/25) Hyperbolic Matrix(977,262,1376,369) (-11/41,-4/15) -> (22/31,5/7) Hyperbolic Matrix(515,136,284,75) (-4/15,-5/19) -> (9/5,20/11) Hyperbolic Matrix(511,134,286,75) (-5/19,-1/4) -> (25/14,9/5) Hyperbolic Matrix(889,216,498,121) (-1/4,-6/25) -> (66/37,25/14) Hyperbolic Matrix(1597,378,714,169) (-9/38,-4/17) -> (38/17,9/4) Hyperbolic Matrix(1043,244,218,51) (-4/17,-7/30) -> (19/4,24/5) Hyperbolic Matrix(1425,332,382,89) (-7/30,-3/13) -> (41/11,15/4) Hyperbolic Matrix(873,200,598,137) (-3/13,-8/35) -> (16/11,19/13) Hyperbolic Matrix(491,112,434,99) (-8/35,-5/22) -> (9/8,8/7) Hyperbolic Matrix(107,24,-486,-109) (-5/22,-2/9) -> (-2/9,-7/32) Parabolic Matrix(1181,258,1506,329) (-7/32,-5/23) -> (29/37,11/14) Hyperbolic Matrix(269,58,320,69) (-5/23,-3/14) -> (5/6,11/13) Hyperbolic Matrix(479,102,108,23) (-3/14,-4/19) -> (22/5,9/2) Hyperbolic Matrix(373,78,636,133) (-4/19,-1/5) -> (17/29,10/17) Hyperbolic Matrix(517,98,364,69) (-1/5,-3/16) -> (17/12,27/19) Hyperbolic Matrix(207,38,256,47) (-3/16,-2/11) -> (4/5,13/16) Hyperbolic Matrix(563,100,152,27) (-2/11,-3/17) -> (11/3,26/7) Hyperbolic Matrix(559,98,154,27) (-3/17,-1/6) -> (29/8,11/3) Hyperbolic Matrix(399,62,148,23) (-1/6,-2/13) -> (8/3,27/10) Hyperbolic Matrix(197,30,348,53) (-2/13,-1/7) -> (13/23,4/7) Hyperbolic Matrix(243,34,50,7) (-1/7,-2/15) -> (24/5,5/1) Hyperbolic Matrix(533,70,434,57) (-2/15,-1/8) -> (27/22,16/13) Hyperbolic Matrix(189,22,524,61) (-1/8,-1/9) -> (9/25,13/36) Hyperbolic Matrix(235,24,186,19) (-1/9,0/1) -> (24/19,19/15) Hyperbolic Matrix(263,-32,74,-9) (0/1,1/8) -> (7/2,32/9) Hyperbolic Matrix(259,-36,36,-5) (2/15,1/7) -> (7/1,22/3) Hyperbolic Matrix(109,-16,184,-27) (1/7,1/6) -> (13/22,3/5) Hyperbolic Matrix(357,-64,106,-19) (1/6,2/11) -> (10/3,27/8) Hyperbolic Matrix(141,-26,320,-59) (2/11,1/5) -> (11/25,4/9) Hyperbolic Matrix(347,-74,830,-177) (4/19,3/14) -> (5/12,18/43) Hyperbolic Matrix(379,-82,208,-45) (3/14,2/9) -> (20/11,11/6) Hyperbolic Matrix(479,-110,614,-141) (5/22,3/13) -> (7/9,25/32) Hyperbolic Matrix(921,-214,340,-79) (3/13,4/17) -> (46/17,19/7) Hyperbolic Matrix(643,-154,238,-57) (4/17,1/4) -> (27/10,46/17) Hyperbolic Matrix(1031,-272,398,-105) (5/19,4/15) -> (44/17,13/5) Hyperbolic Matrix(3277,-880,1888,-507) (11/41,7/26) -> (59/34,33/19) Hyperbolic Matrix(297,-82,460,-127) (3/11,5/18) -> (9/14,11/17) Hyperbolic Matrix(229,-64,526,-147) (5/18,2/7) -> (10/23,7/16) Hyperbolic Matrix(1105,-324,324,-95) (7/24,5/17) -> (17/5,41/12) Hyperbolic Matrix(357,-106,64,-19) (5/17,3/10) -> (11/2,17/3) Hyperbolic Matrix(1225,-372,708,-215) (3/10,7/23) -> (19/11,45/26) Hyperbolic Matrix(641,-198,450,-139) (4/13,5/16) -> (37/26,10/7) Hyperbolic Matrix(543,-172,382,-121) (5/16,1/3) -> (27/19,37/26) Hyperbolic Matrix(93,-32,32,-11) (1/3,5/14) -> (17/6,3/1) Hyperbolic Matrix(1665,-602,1358,-491) (13/36,4/11) -> (38/31,27/22) Hyperbolic Matrix(2831,-1034,1076,-393) (4/11,15/41) -> (71/27,50/19) Hyperbolic Matrix(2643,-968,800,-293) (15/41,11/30) -> (33/10,43/13) Hyperbolic Matrix(2059,-756,798,-293) (11/30,7/19) -> (49/19,31/12) Hyperbolic Matrix(921,-340,214,-79) (7/19,10/27) -> (30/7,13/3) Hyperbolic Matrix(335,-128,212,-81) (3/8,5/13) -> (11/7,19/12) Hyperbolic Matrix(61,-24,150,-59) (5/13,2/5) -> (2/5,7/17) Parabolic Matrix(1129,-466,298,-123) (7/17,12/29) -> (34/9,19/5) Hyperbolic Matrix(1781,-738,654,-271) (12/29,5/12) -> (49/18,30/11) Hyperbolic Matrix(3463,-1450,652,-273) (18/43,31/74) -> (53/10,16/3) Hyperbolic Matrix(4381,-1836,828,-347) (31/74,13/31) -> (37/7,53/10) Hyperbolic Matrix(2101,-882,798,-335) (13/31,8/19) -> (50/19,29/11) Hyperbolic Matrix(1919,-810,1566,-661) (8/19,19/45) -> (11/9,38/31) Hyperbolic Matrix(413,-176,176,-75) (11/26,3/7) -> (7/3,33/14) Hyperbolic Matrix(263,-114,30,-13) (3/7,10/23) -> (8/1,9/1) Hyperbolic Matrix(1343,-590,758,-333) (7/16,11/25) -> (23/13,39/22) Hyperbolic Matrix(319,-144,144,-65) (4/9,5/11) -> (11/5,20/9) Hyperbolic Matrix(201,-92,260,-119) (5/11,1/2) -> (17/22,7/9) Hyperbolic Matrix(273,-148,190,-103) (1/2,6/11) -> (10/7,23/16) Hyperbolic Matrix(379,-208,82,-45) (6/11,5/9) -> (23/5,14/3) Hyperbolic Matrix(2019,-1132,3148,-1765) (14/25,23/41) -> (25/39,34/53) Hyperbolic Matrix(563,-318,108,-61) (9/16,13/23) -> (5/1,21/4) Hyperbolic Matrix(293,-170,212,-123) (4/7,7/12) -> (11/8,18/13) Hyperbolic Matrix(1537,-900,900,-527) (7/12,17/29) -> (29/17,41/24) Hyperbolic Matrix(1427,-842,422,-249) (10/17,13/22) -> (27/8,44/13) Hyperbolic Matrix(209,-128,338,-207) (3/5,8/13) -> (8/13,13/21) Parabolic Matrix(335,-212,128,-81) (5/8,7/11) -> (13/5,21/8) Hyperbolic Matrix(923,-590,1178,-753) (7/11,16/25) -> (18/23,29/37) Hyperbolic Matrix(4251,-2722,1126,-721) (16/25,41/64) -> (83/22,34/9) Hyperbolic Matrix(6373,-4084,1690,-1083) (41/64,25/39) -> (49/13,83/22) Hyperbolic Matrix(475,-324,324,-221) (2/3,13/19) -> (19/13,22/15) Hyperbolic Matrix(473,-326,74,-51) (11/16,9/13) -> (19/3,13/2) Hyperbolic Matrix(273,-190,148,-103) (9/13,7/10) -> (11/6,13/7) Hyperbolic Matrix(641,-450,198,-139) (7/10,19/27) -> (29/9,13/4) Hyperbolic Matrix(2829,-2000,1034,-731) (12/17,29/41) -> (41/15,52/19) Hyperbolic Matrix(2803,-1984,640,-453) (29/41,17/24) -> (35/8,57/13) Hyperbolic Matrix(271,-192,24,-17) (17/24,22/31) -> (10/1,1/0) Hyperbolic Matrix(293,-212,170,-123) (5/7,8/11) -> (12/7,19/11) Hyperbolic Matrix(73,-54,96,-71) (8/11,3/4) -> (3/4,10/13) Parabolic Matrix(1091,-842,758,-585) (10/13,17/22) -> (23/16,36/25) Hyperbolic Matrix(2263,-1770,1602,-1253) (25/32,18/23) -> (24/17,65/46) Hyperbolic Matrix(893,-704,704,-555) (11/14,15/19) -> (19/15,33/26) Hyperbolic Matrix(959,-762,258,-205) (19/24,4/5) -> (26/7,67/18) Hyperbolic Matrix(1665,-1358,602,-491) (22/27,9/11) -> (47/17,36/13) Hyperbolic Matrix(253,-208,208,-171) (9/11,5/6) -> (17/14,11/9) Hyperbolic Matrix(451,-388,136,-117) (6/7,13/15) -> (43/13,10/3) Hyperbolic Matrix(1303,-1132,922,-801) (13/15,7/8) -> (65/46,41/29) Hyperbolic Matrix(511,-456,288,-257) (8/9,1/1) -> (55/31,16/9) Hyperbolic Matrix(317,-354,60,-67) (1/1,9/8) -> (21/4,37/7) Hyperbolic Matrix(685,-786,156,-179) (8/7,15/13) -> (57/13,22/5) Hyperbolic Matrix(1169,-1352,428,-495) (15/13,7/6) -> (71/26,41/15) Hyperbolic Matrix(781,-942,228,-275) (6/5,23/19) -> (65/19,24/7) Hyperbolic Matrix(1689,-2048,494,-599) (23/19,17/14) -> (41/12,65/19) Hyperbolic Matrix(1225,-1546,706,-891) (5/4,24/19) -> (26/15,59/34) Hyperbolic Matrix(1517,-1926,204,-259) (33/26,47/37) -> (37/5,15/2) Hyperbolic Matrix(1221,-1552,166,-211) (47/37,14/11) -> (22/3,37/5) Hyperbolic Matrix(923,-1178,590,-753) (14/11,23/18) -> (25/16,36/23) Hyperbolic Matrix(479,-614,110,-141) (23/18,9/7) -> (13/3,35/8) Hyperbolic Matrix(73,-96,54,-71) (9/7,4/3) -> (4/3,15/11) Parabolic Matrix(231,-316,106,-145) (15/11,11/8) -> (13/6,11/5) Hyperbolic Matrix(687,-952,70,-97) (18/13,61/44) -> (19/2,10/1) Hyperbolic Matrix(985,-1366,106,-147) (61/44,43/31) -> (9/1,19/2) Hyperbolic Matrix(2815,-3906,756,-1049) (43/31,25/18) -> (67/18,41/11) Hyperbolic Matrix(579,-806,176,-245) (25/18,7/5) -> (23/7,33/10) Hyperbolic Matrix(1673,-2360,470,-663) (31/22,24/17) -> (32/9,57/16) Hyperbolic Matrix(1461,-2068,556,-787) (41/29,17/12) -> (21/8,71/27) Hyperbolic Matrix(2271,-3272,878,-1265) (36/25,13/9) -> (75/29,44/17) Hyperbolic Matrix(583,-844,172,-249) (13/9,16/11) -> (44/13,17/5) Hyperbolic Matrix(1327,-1948,562,-825) (22/15,3/2) -> (85/36,26/11) Hyperbolic Matrix(297,-460,82,-127) (3/2,14/9) -> (18/5,29/8) Hyperbolic Matrix(2019,-3148,1132,-1765) (14/9,39/25) -> (41/23,66/37) Hyperbolic Matrix(5725,-8934,2214,-3455) (39/25,64/41) -> (106/41,75/29) Hyperbolic Matrix(2967,-4634,1148,-1793) (64/41,25/16) -> (31/12,106/41) Hyperbolic Matrix(1005,-1598,422,-671) (27/17,8/5) -> (50/21,31/13) Hyperbolic Matrix(209,-338,128,-207) (8/5,13/8) -> (13/8,18/11) Parabolic Matrix(109,-184,16,-27) (5/3,17/10) -> (13/2,7/1) Hyperbolic Matrix(1271,-2172,450,-769) (41/24,12/7) -> (48/17,17/6) Hyperbolic Matrix(1845,-3196,676,-1171) (45/26,26/15) -> (30/11,71/26) Hyperbolic Matrix(2133,-3706,598,-1039) (33/19,40/23) -> (82/23,25/7) Hyperbolic Matrix(1639,-2854,460,-801) (40/23,7/4) -> (57/16,82/23) Hyperbolic Matrix(2151,-3814,454,-805) (39/22,55/31) -> (71/15,19/4) Hyperbolic Matrix(29,-56,14,-27) (13/7,2/1) -> (2/1,15/7) Parabolic Matrix(399,-862,106,-229) (15/7,13/6) -> (15/4,49/13) Hyperbolic Matrix(755,-1682,338,-753) (20/9,29/13) -> (29/13,38/17) Parabolic Matrix(141,-320,26,-59) (9/4,16/7) -> (16/3,11/2) Hyperbolic Matrix(229,-526,64,-147) (16/7,7/3) -> (25/7,18/5) Hyperbolic Matrix(2951,-6962,1250,-2949) (33/14,59/25) -> (59/25,85/36) Parabolic Matrix(585,-1388,212,-503) (45/19,19/8) -> (11/4,47/17) Hyperbolic Matrix(647,-1538,236,-561) (19/8,50/21) -> (52/19,11/4) Hyperbolic Matrix(347,-830,74,-177) (31/13,12/5) -> (14/3,33/7) Hyperbolic Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(683,-1922,242,-681) (14/5,31/11) -> (31/11,48/17) Parabolic Matrix(161,-512,50,-159) (3/1,16/5) -> (16/5,29/9) Parabolic Matrix(137,-578,32,-135) (4/1,17/4) -> (17/4,30/7) Parabolic Matrix(1145,-5408,242,-1143) (33/7,52/11) -> (52/11,71/15) Parabolic Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(315,148,398,187) -> Matrix(1,0,-4,1) Matrix(865,402,312,145) -> Matrix(1,0,-6,1) Matrix(697,320,856,393) -> Matrix(1,-2,0,1) Matrix(79,36,384,175) -> Matrix(1,0,0,1) Matrix(537,242,304,137) -> Matrix(1,0,-2,1) Matrix(227,102,612,275) -> Matrix(1,0,2,1) Matrix(149,66,228,101) -> Matrix(5,-2,-2,1) Matrix(223,98,826,363) -> Matrix(13,-2,-6,1) Matrix(371,162,300,131) -> Matrix(7,-2,-10,3) Matrix(521,226,740,321) -> Matrix(9,-4,-2,1) Matrix(873,370,512,217) -> Matrix(7,-2,-10,3) Matrix(147,62,652,275) -> Matrix(7,-4,2,-1) Matrix(433,182,364,153) -> Matrix(1,0,-2,1) Matrix(359,150,-864,-361) -> Matrix(1,0,2,1) Matrix(1795,744,1146,475) -> Matrix(1,0,-4,1) Matrix(571,236,646,267) -> Matrix(1,0,-4,1) Matrix(785,324,1146,473) -> Matrix(1,0,-4,1) Matrix(497,204,1854,761) -> Matrix(11,-8,-4,3) Matrix(283,116,1354,555) -> Matrix(1,0,0,1) Matrix(353,144,-1488,-607) -> Matrix(7,-2,4,-1) Matrix(639,260,-1772,-721) -> Matrix(5,-2,8,-3) Matrix(347,136,620,243) -> Matrix(3,-2,-4,3) Matrix(621,242,136,53) -> Matrix(1,0,-2,1) Matrix(547,212,-1850,-717) -> Matrix(17,-10,12,-7) Matrix(957,370,344,133) -> Matrix(3,-2,-10,7) Matrix(339,130,206,79) -> Matrix(5,-4,-6,5) Matrix(405,154,476,181) -> Matrix(1,0,-2,1) Matrix(69,26,268,101) -> Matrix(5,-2,-2,1) Matrix(537,200,1270,473) -> Matrix(1,-4,0,1) Matrix(1667,618,936,347) -> Matrix(1,0,-2,1) Matrix(265,98,868,321) -> Matrix(3,-4,-2,3) Matrix(463,170,-1724,-633) -> Matrix(1,0,-2,1) Matrix(263,96,-726,-265) -> Matrix(5,-2,8,-3) Matrix(1773,640,2762,997) -> Matrix(11,-8,-4,3) Matrix(2361,848,916,329) -> Matrix(3,-2,-4,3) Matrix(67,24,522,187) -> Matrix(11,-8,-4,3) Matrix(455,162,132,47) -> Matrix(3,-2,-10,7) Matrix(517,182,196,69) -> Matrix(1,0,-2,1) Matrix(489,154,308,97) -> Matrix(1,0,-2,1) Matrix(123,38,424,131) -> Matrix(3,-4,-2,3) Matrix(483,148,62,19) -> Matrix(1,0,-4,1) Matrix(1811,552,666,203) -> Matrix(5,-2,-12,5) Matrix(179,54,-600,-181) -> Matrix(7,-6,6,-5) Matrix(357,106,-1492,-443) -> Matrix(1,-2,2,-3) Matrix(835,246,594,175) -> Matrix(1,-2,2,-3) Matrix(773,226,236,69) -> Matrix(1,-4,-2,9) Matrix(831,242,1480,431) -> Matrix(1,0,-2,1) Matrix(1121,324,474,137) -> Matrix(1,0,-4,1) Matrix(233,66,60,17) -> Matrix(1,-2,-2,5) Matrix(409,114,348,97) -> Matrix(1,-2,-2,5) Matrix(289,80,466,129) -> Matrix(1,-8,0,1) Matrix(289,78,804,217) -> Matrix(1,0,2,1) Matrix(977,262,1376,369) -> Matrix(3,2,-2,-1) Matrix(515,136,284,75) -> Matrix(3,-2,-4,3) Matrix(511,134,286,75) -> Matrix(1,0,-2,1) Matrix(889,216,498,121) -> Matrix(1,-2,0,1) Matrix(1597,378,714,169) -> Matrix(1,-2,2,-3) Matrix(1043,244,218,51) -> Matrix(1,-2,0,1) Matrix(1425,332,382,89) -> Matrix(1,-2,0,1) Matrix(873,200,598,137) -> Matrix(1,-4,0,1) Matrix(491,112,434,99) -> Matrix(3,-8,-4,11) Matrix(107,24,-486,-109) -> Matrix(1,-6,0,1) Matrix(1181,258,1506,329) -> Matrix(1,2,-2,-3) Matrix(269,58,320,69) -> Matrix(1,2,-2,-3) Matrix(479,102,108,23) -> Matrix(1,0,2,1) Matrix(373,78,636,133) -> Matrix(1,0,2,1) Matrix(517,98,364,69) -> Matrix(3,-4,-2,3) Matrix(207,38,256,47) -> Matrix(3,-4,-2,3) Matrix(563,100,152,27) -> Matrix(1,-2,0,1) Matrix(559,98,154,27) -> Matrix(1,-2,-6,13) Matrix(399,62,148,23) -> Matrix(1,4,-2,-7) Matrix(197,30,348,53) -> Matrix(1,2,-2,-3) Matrix(243,34,50,7) -> Matrix(1,0,-2,1) Matrix(533,70,434,57) -> Matrix(5,-4,-6,5) Matrix(189,22,524,61) -> Matrix(1,-2,2,-3) Matrix(235,24,186,19) -> Matrix(3,-8,-4,11) Matrix(263,-32,74,-9) -> Matrix(1,4,-4,-15) Matrix(259,-36,36,-5) -> Matrix(1,2,-4,-7) Matrix(109,-16,184,-27) -> Matrix(1,2,0,1) Matrix(357,-64,106,-19) -> Matrix(3,2,-8,-5) Matrix(141,-26,320,-59) -> Matrix(3,2,-2,-1) Matrix(347,-74,830,-177) -> Matrix(7,-10,-2,3) Matrix(379,-82,208,-45) -> Matrix(1,0,-2,1) Matrix(479,-110,614,-141) -> Matrix(1,-6,-2,13) Matrix(921,-214,340,-79) -> Matrix(1,-14,-2,29) Matrix(643,-154,238,-57) -> Matrix(1,12,-2,-23) Matrix(1031,-272,398,-105) -> Matrix(1,2,0,1) Matrix(3277,-880,1888,-507) -> Matrix(21,52,-40,-99) Matrix(297,-82,460,-127) -> Matrix(5,8,-2,-3) Matrix(229,-64,526,-147) -> Matrix(1,0,0,1) Matrix(1105,-324,324,-95) -> Matrix(3,2,-8,-5) Matrix(357,-106,64,-19) -> Matrix(1,2,-2,-3) Matrix(1225,-372,708,-215) -> Matrix(11,16,-20,-29) Matrix(641,-198,450,-139) -> Matrix(5,6,-6,-7) Matrix(543,-172,382,-121) -> Matrix(5,4,-4,-3) Matrix(93,-32,32,-11) -> Matrix(1,0,0,1) Matrix(1665,-602,1358,-491) -> Matrix(5,-4,-6,5) Matrix(2831,-1034,1076,-393) -> Matrix(3,2,-2,-1) Matrix(2643,-968,800,-293) -> Matrix(3,2,-8,-5) Matrix(2059,-756,798,-293) -> Matrix(1,0,0,1) Matrix(921,-340,214,-79) -> Matrix(1,0,8,1) Matrix(335,-128,212,-81) -> Matrix(1,-2,0,1) Matrix(61,-24,150,-59) -> Matrix(1,-6,0,1) Matrix(1129,-466,298,-123) -> Matrix(1,4,-2,-7) Matrix(1781,-738,654,-271) -> Matrix(1,2,-2,-3) Matrix(3463,-1450,652,-273) -> Matrix(9,28,-10,-31) Matrix(4381,-1836,828,-347) -> Matrix(9,26,-8,-23) Matrix(2101,-882,798,-335) -> Matrix(3,8,-2,-5) Matrix(1919,-810,1566,-661) -> Matrix(5,16,-6,-19) Matrix(413,-176,176,-75) -> Matrix(3,8,-8,-21) Matrix(263,-114,30,-13) -> Matrix(1,2,-6,-11) Matrix(1343,-590,758,-333) -> Matrix(1,2,-2,-3) Matrix(319,-144,144,-65) -> Matrix(1,2,-4,-7) Matrix(201,-92,260,-119) -> Matrix(3,4,-4,-5) Matrix(273,-148,190,-103) -> Matrix(1,0,0,1) Matrix(379,-208,82,-45) -> Matrix(1,0,0,1) Matrix(2019,-1132,3148,-1765) -> Matrix(1,-2,0,1) Matrix(563,-318,108,-61) -> Matrix(3,2,-2,-1) Matrix(293,-170,212,-123) -> Matrix(1,0,-2,1) Matrix(1537,-900,900,-527) -> Matrix(11,-2,-16,3) Matrix(1427,-842,422,-249) -> Matrix(1,-2,-2,5) Matrix(209,-128,338,-207) -> Matrix(1,-10,0,1) Matrix(335,-212,128,-81) -> Matrix(1,2,0,1) Matrix(923,-590,1178,-753) -> Matrix(1,2,-2,-3) Matrix(4251,-2722,1126,-721) -> Matrix(1,4,-2,-7) Matrix(6373,-4084,1690,-1083) -> Matrix(1,2,0,1) Matrix(475,-324,324,-221) -> Matrix(5,4,-4,-3) Matrix(473,-326,74,-51) -> Matrix(1,0,-2,1) Matrix(273,-190,148,-103) -> Matrix(1,2,-2,-3) Matrix(641,-450,198,-139) -> Matrix(1,-4,-2,9) Matrix(2829,-2000,1034,-731) -> Matrix(3,8,-8,-21) Matrix(2803,-1984,640,-453) -> Matrix(1,2,4,9) Matrix(271,-192,24,-17) -> Matrix(1,2,0,1) Matrix(293,-212,170,-123) -> Matrix(7,10,-12,-17) Matrix(73,-54,96,-71) -> Matrix(5,6,-6,-7) Matrix(1091,-842,758,-585) -> Matrix(3,2,-2,-1) Matrix(2263,-1770,1602,-1253) -> Matrix(3,2,-2,-1) Matrix(893,-704,704,-555) -> Matrix(3,-2,-4,3) Matrix(959,-762,258,-205) -> Matrix(1,0,-2,1) Matrix(1665,-1358,602,-491) -> Matrix(3,4,-10,-13) Matrix(253,-208,208,-171) -> Matrix(7,8,-8,-9) Matrix(451,-388,136,-117) -> Matrix(3,2,-8,-5) Matrix(1303,-1132,922,-801) -> Matrix(1,-2,0,1) Matrix(511,-456,288,-257) -> Matrix(1,0,0,1) Matrix(317,-354,60,-67) -> Matrix(7,6,-6,-5) Matrix(685,-786,156,-179) -> Matrix(3,2,10,7) Matrix(1169,-1352,428,-495) -> Matrix(7,4,-16,-9) Matrix(781,-942,228,-275) -> Matrix(7,8,-22,-25) Matrix(1689,-2048,494,-599) -> Matrix(23,22,-68,-65) Matrix(1225,-1546,706,-891) -> Matrix(35,26,-66,-49) Matrix(1517,-1926,204,-259) -> Matrix(3,2,10,7) Matrix(1221,-1552,166,-211) -> Matrix(3,2,-20,-13) Matrix(923,-1178,590,-753) -> Matrix(3,2,-2,-1) Matrix(479,-614,110,-141) -> Matrix(3,2,10,7) Matrix(73,-96,54,-71) -> Matrix(3,2,-8,-5) Matrix(231,-316,106,-145) -> Matrix(1,0,0,1) Matrix(687,-952,70,-97) -> Matrix(1,0,12,1) Matrix(985,-1366,106,-147) -> Matrix(1,0,-18,1) Matrix(2815,-3906,756,-1049) -> Matrix(1,0,-6,1) Matrix(579,-806,176,-245) -> Matrix(1,-2,-2,5) Matrix(1673,-2360,470,-663) -> Matrix(1,6,-4,-23) Matrix(1461,-2068,556,-787) -> Matrix(1,0,0,1) Matrix(2271,-3272,878,-1265) -> Matrix(1,0,0,1) Matrix(583,-844,172,-249) -> Matrix(3,2,-8,-5) Matrix(1327,-1948,562,-825) -> Matrix(9,10,-28,-31) Matrix(297,-460,82,-127) -> Matrix(1,0,-4,1) Matrix(2019,-3148,1132,-1765) -> Matrix(1,0,0,1) Matrix(5725,-8934,2214,-3455) -> Matrix(3,2,-2,-1) Matrix(2967,-4634,1148,-1793) -> Matrix(1,0,2,1) Matrix(1005,-1598,422,-671) -> Matrix(1,0,-2,1) Matrix(209,-338,128,-207) -> Matrix(5,6,-6,-7) Matrix(109,-184,16,-27) -> Matrix(3,2,-8,-5) Matrix(1271,-2172,450,-769) -> Matrix(3,2,28,19) Matrix(1845,-3196,676,-1171) -> Matrix(15,8,-32,-17) Matrix(2133,-3706,598,-1039) -> Matrix(39,20,-158,-81) Matrix(1639,-2854,460,-801) -> Matrix(29,14,-114,-55) Matrix(2151,-3814,454,-805) -> Matrix(1,0,-2,1) Matrix(29,-56,14,-27) -> Matrix(3,2,-8,-5) Matrix(399,-862,106,-229) -> Matrix(1,0,2,1) Matrix(755,-1682,338,-753) -> Matrix(1,0,6,1) Matrix(141,-320,26,-59) -> Matrix(1,0,0,1) Matrix(229,-526,64,-147) -> Matrix(3,2,-14,-9) Matrix(2951,-6962,1250,-2949) -> Matrix(53,18,-162,-55) Matrix(585,-1388,212,-503) -> Matrix(1,0,0,1) Matrix(647,-1538,236,-561) -> Matrix(7,2,-18,-5) Matrix(347,-830,74,-177) -> Matrix(1,0,2,1) Matrix(61,-150,24,-59) -> Matrix(1,0,2,1) Matrix(683,-1922,242,-681) -> Matrix(1,0,18,1) Matrix(161,-512,50,-159) -> Matrix(19,10,-40,-21) Matrix(137,-578,32,-135) -> Matrix(1,0,18,1) Matrix(1145,-5408,242,-1143) -> Matrix(3,2,-8,-5) Matrix(37,-216,6,-35) -> Matrix(3,2,-8,-5) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 Degree of the the map X: 64 Degree of the the map Y: 192 ----------------------------------------------------------------------- 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): 576 Minimal number of generators: 97 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: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -6/13 -2/5 -4/11 -3/10 -1/4 -2/9 -1/8 0/1 1/6 4/17 2/7 5/16 4/11 2/5 1/2 8/13 3/4 4/5 1/1 23/19 5/4 4/3 3/2 64/41 13/8 40/23 2/1 5/2 8/3 11/4 14/5 31/11 3/1 16/5 10/3 7/2 4/1 17/4 22/5 9/2 23/5 14/3 52/11 5/1 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 -6/13 1/2 -5/11 0/1 -4/9 1/4 -7/16 1/3 -3/7 1/1 -5/12 0/1 -7/17 3/7 -2/5 1/2 -7/18 2/5 -12/31 5/8 -5/13 1/1 -8/21 1/0 -11/29 0/1 -3/8 2/3 -10/27 1/2 -7/19 0/1 -4/11 1/2 -5/14 1/1 -6/17 3/2 -1/3 1/1 -3/10 1/1 -5/17 2/1 -2/7 3/2 -1/4 1/1 -3/13 7/3 -2/9 1/0 -3/14 -2/3 -4/19 1/0 -1/5 1/1 -1/6 4/1 -1/7 0/1 -1/8 1/1 0/1 1/0 1/8 -3/1 1/7 -1/1 1/6 -1/1 2/11 -1/2 1/5 0/1 2/9 5/2 5/22 5/1 3/13 9/1 4/17 1/0 1/4 -4/1 5/19 -2/1 4/15 1/0 11/41 -23/9 7/26 -7/3 3/11 -2/1 5/18 -2/1 2/7 -3/2 7/24 -8/7 5/17 -1/1 3/10 -2/1 7/23 -4/3 4/13 -5/4 5/16 -1/1 1/3 -1/1 5/14 0/1 9/25 1/1 13/36 1/1 4/11 1/0 15/41 0/1 11/30 0/1 7/19 -1/3 10/27 1/6 3/8 2/3 2/5 1/0 3/7 -7/3 10/23 -3/2 7/16 -2/1 11/25 -2/1 4/9 1/0 1/2 -1/1 6/11 -1/2 5/9 -1/1 9/16 0/1 13/23 -2/3 4/7 -1/4 7/12 0/1 17/29 1/3 10/17 1/2 13/22 1/1 3/5 1/1 8/13 1/0 5/8 -4/1 7/11 -2/1 2/3 -3/2 5/7 -2/1 8/11 -5/4 3/4 -1/1 10/13 -1/2 7/9 -3/5 11/14 0/1 15/19 -1/1 4/5 1/0 13/16 -2/1 22/27 -3/2 9/11 -1/1 5/6 -4/5 11/13 0/1 6/7 -1/2 13/15 0/1 7/8 -1/1 1/1 -1/1 6/5 -3/2 23/19 -1/1 17/14 -12/13 11/9 -1/1 27/22 -1/1 16/13 -3/4 5/4 -1/1 4/3 -1/2 7/5 0/1 31/22 6/1 24/17 1/0 41/29 -2/1 17/12 -2/1 27/19 -1/1 37/26 -1/1 10/7 -1/2 23/16 -1/1 13/9 -1/1 16/11 1/0 3/2 -2/3 14/9 -1/2 39/25 -1/1 64/41 -1/2 25/16 0/1 11/7 0/1 8/5 1/0 13/8 -1/1 18/11 -5/6 5/3 -1/1 17/10 -1/1 29/17 -5/7 41/24 -2/3 12/7 -5/8 19/11 -4/7 26/15 -1/2 33/19 -15/29 40/23 -1/2 7/4 -2/5 2/1 -1/2 7/3 -3/7 26/11 -3/10 19/8 -1/3 31/13 -1/3 12/5 -1/4 5/2 0/1 18/7 -1/2 49/19 -1/3 31/12 0/1 44/17 1/0 13/5 0/1 21/8 -2/1 29/11 -1/1 8/3 -3/4 11/4 -1/3 36/13 -1/4 25/9 -1/3 14/5 -1/6 31/11 0/1 48/17 1/12 17/6 0/1 3/1 -1/1 16/5 -1/2 13/4 -4/9 23/7 -2/5 10/3 -1/2 27/8 -1/3 44/13 -3/8 17/5 -1/3 41/12 -10/29 65/19 -1/3 24/7 -5/16 7/2 -1/3 4/1 -1/4 17/4 0/1 30/7 1/14 13/3 1/5 22/5 1/2 9/2 2/1 23/5 -1/1 14/3 -1/2 33/7 -1/1 52/11 -1/2 19/4 0/1 5/1 0/1 11/2 0/1 6/1 -1/2 7/1 -1/3 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(161,76,197,93) (-1/2,-6/13) -> (22/27,9/11) Hyperbolic Matrix(539,246,195,89) (-6/13,-5/11) -> (11/4,36/13) Hyperbolic Matrix(457,206,193,87) (-5/11,-4/9) -> (26/11,19/8) Hyperbolic Matrix(77,34,-265,-117) (-4/9,-7/16) -> (-5/17,-2/7) Hyperbolic Matrix(369,160,113,49) (-7/16,-3/7) -> (13/4,23/7) Hyperbolic Matrix(143,60,255,107) (-3/7,-5/12) -> (5/9,9/16) Hyperbolic Matrix(499,206,109,45) (-5/12,-7/17) -> (9/2,23/5) Hyperbolic Matrix(69,28,-175,-71) (-7/17,-2/5) -> (-2/5,-7/18) Parabolic Matrix(413,160,1541,597) (-7/18,-12/31) -> (4/15,11/41) Hyperbolic Matrix(957,370,344,133) (-12/31,-5/13) -> (25/9,14/5) Hyperbolic Matrix(339,130,206,79) (-5/13,-8/21) -> (18/11,5/3) Hyperbolic Matrix(405,154,476,181) (-8/21,-11/29) -> (11/13,6/7) Hyperbolic Matrix(69,26,268,101) (-11/29,-3/8) -> (1/4,5/19) Hyperbolic Matrix(1467,544,569,211) (-3/8,-10/27) -> (18/7,49/19) Hyperbolic Matrix(265,98,868,321) (-10/27,-7/19) -> (7/23,4/13) Hyperbolic Matrix(131,48,-363,-133) (-7/19,-4/11) -> (-4/11,-5/14) Parabolic Matrix(455,162,132,47) (-5/14,-6/17) -> (24/7,7/2) Hyperbolic Matrix(517,182,196,69) (-6/17,-1/3) -> (29/11,8/3) Hyperbolic Matrix(59,18,213,65) (-1/3,-3/10) -> (3/11,5/18) Hyperbolic Matrix(121,36,447,133) (-3/10,-5/17) -> (7/26,3/11) Hyperbolic Matrix(57,16,89,25) (-2/7,-1/4) -> (7/11,2/3) Hyperbolic Matrix(163,38,193,45) (-1/4,-3/13) -> (5/6,11/13) Hyperbolic Matrix(53,12,-243,-55) (-3/13,-2/9) -> (-2/9,-3/14) Parabolic Matrix(479,102,108,23) (-3/14,-4/19) -> (22/5,9/2) Hyperbolic Matrix(373,78,636,133) (-4/19,-1/5) -> (17/29,10/17) Hyperbolic Matrix(101,18,129,23) (-1/5,-1/6) -> (7/9,11/14) Hyperbolic Matrix(51,8,223,35) (-1/6,-1/7) -> (5/22,3/13) Hyperbolic Matrix(147,20,169,23) (-1/7,-1/8) -> (13/15,7/8) Hyperbolic Matrix(233,24,165,17) (-1/8,0/1) -> (24/17,41/29) Hyperbolic Matrix(227,-26,131,-15) (0/1,1/8) -> (19/11,26/15) Hyperbolic Matrix(73,-10,241,-33) (1/8,1/7) -> (3/10,7/23) Hyperbolic Matrix(109,-16,184,-27) (1/7,1/6) -> (13/22,3/5) Hyperbolic Matrix(357,-64,106,-19) (1/6,2/11) -> (10/3,27/8) Hyperbolic Matrix(141,-26,320,-59) (2/11,1/5) -> (11/25,4/9) Hyperbolic Matrix(139,-30,51,-11) (1/5,2/9) -> (8/3,11/4) Hyperbolic Matrix(205,-46,361,-81) (2/9,5/22) -> (13/23,4/7) Hyperbolic Matrix(69,-16,289,-67) (3/13,4/17) -> (4/17,1/4) Parabolic Matrix(1031,-272,398,-105) (5/19,4/15) -> (44/17,13/5) Hyperbolic Matrix(1093,-294,777,-209) (11/41,7/26) -> (7/5,31/22) Hyperbolic Matrix(229,-64,526,-147) (5/18,2/7) -> (10/23,7/16) Hyperbolic Matrix(261,-76,601,-175) (2/7,7/24) -> (3/7,10/23) Hyperbolic Matrix(1105,-324,324,-95) (7/24,5/17) -> (17/5,41/12) Hyperbolic Matrix(129,-38,17,-5) (5/17,3/10) -> (7/1,1/0) Hyperbolic Matrix(641,-198,450,-139) (4/13,5/16) -> (37/26,10/7) Hyperbolic Matrix(543,-172,382,-121) (5/16,1/3) -> (27/19,37/26) Hyperbolic Matrix(93,-32,32,-11) (1/3,5/14) -> (17/6,3/1) Hyperbolic Matrix(1019,-366,387,-139) (5/14,9/25) -> (21/8,29/11) Hyperbolic Matrix(1637,-590,1157,-417) (9/25,13/36) -> (41/29,17/12) Hyperbolic Matrix(309,-112,847,-307) (13/36,4/11) -> (4/11,15/41) Parabolic Matrix(1261,-462,1029,-377) (15/41,11/30) -> (11/9,27/22) Hyperbolic Matrix(2059,-756,798,-293) (11/30,7/19) -> (49/19,31/12) Hyperbolic Matrix(921,-340,214,-79) (7/19,10/27) -> (30/7,13/3) Hyperbolic Matrix(397,-148,169,-63) (10/27,3/8) -> (7/3,26/11) Hyperbolic Matrix(31,-12,75,-29) (3/8,2/5) -> (2/5,3/7) Parabolic Matrix(1079,-474,453,-199) (7/16,11/25) -> (19/8,31/13) Hyperbolic Matrix(115,-52,73,-33) (4/9,1/2) -> (11/7,8/5) Hyperbolic Matrix(273,-148,190,-103) (1/2,6/11) -> (10/7,23/16) Hyperbolic Matrix(379,-208,82,-45) (6/11,5/9) -> (23/5,14/3) Hyperbolic Matrix(939,-530,551,-311) (9/16,13/23) -> (17/10,29/17) Hyperbolic Matrix(79,-46,67,-39) (4/7,7/12) -> (1/1,6/5) Hyperbolic Matrix(1537,-900,900,-527) (7/12,17/29) -> (29/17,41/24) Hyperbolic Matrix(1427,-842,422,-249) (10/17,13/22) -> (27/8,44/13) Hyperbolic Matrix(105,-64,169,-103) (3/5,8/13) -> (8/13,5/8) Parabolic Matrix(335,-212,128,-81) (5/8,7/11) -> (13/5,21/8) Hyperbolic Matrix(49,-34,13,-9) (2/3,5/7) -> (7/2,4/1) Hyperbolic Matrix(293,-212,170,-123) (5/7,8/11) -> (12/7,19/11) Hyperbolic Matrix(73,-54,96,-71) (8/11,3/4) -> (3/4,10/13) Parabolic Matrix(165,-128,107,-83) (10/13,7/9) -> (3/2,14/9) Hyperbolic Matrix(751,-592,529,-417) (11/14,15/19) -> (17/12,27/19) Hyperbolic Matrix(141,-112,175,-139) (15/19,4/5) -> (4/5,13/16) Parabolic Matrix(1251,-1018,451,-367) (13/16,22/27) -> (36/13,25/9) Hyperbolic Matrix(253,-208,208,-171) (9/11,5/6) -> (17/14,11/9) Hyperbolic Matrix(429,-370,349,-301) (6/7,13/15) -> (27/22,16/13) Hyperbolic Matrix(157,-138,33,-29) (7/8,1/1) -> (19/4,5/1) Hyperbolic Matrix(781,-942,228,-275) (6/5,23/19) -> (65/19,24/7) Hyperbolic Matrix(1689,-2048,494,-599) (23/19,17/14) -> (41/12,65/19) Hyperbolic Matrix(339,-418,103,-127) (16/13,5/4) -> (23/7,10/3) Hyperbolic Matrix(37,-48,27,-35) (5/4,4/3) -> (4/3,7/5) Parabolic Matrix(1133,-1598,653,-921) (31/22,24/17) -> (26/15,33/19) Hyperbolic Matrix(499,-718,319,-459) (23/16,13/9) -> (25/16,11/7) Hyperbolic Matrix(583,-844,172,-249) (13/9,16/11) -> (44/13,17/5) Hyperbolic Matrix(187,-274,43,-63) (16/11,3/2) -> (13/3,22/5) Hyperbolic Matrix(1379,-2150,533,-831) (14/9,39/25) -> (31/12,44/17) Hyperbolic Matrix(2625,-4096,1681,-2623) (39/25,64/41) -> (64/41,25/16) Parabolic Matrix(209,-338,128,-207) (8/5,13/8) -> (13/8,18/11) Parabolic Matrix(125,-212,23,-39) (5/3,17/10) -> (5/1,11/2) Hyperbolic Matrix(1271,-2172,450,-769) (41/24,12/7) -> (48/17,17/6) Hyperbolic Matrix(921,-1600,529,-919) (33/19,40/23) -> (40/23,7/4) Parabolic Matrix(15,-28,7,-13) (7/4,2/1) -> (2/1,7/3) Parabolic Matrix(347,-830,74,-177) (31/13,12/5) -> (14/3,33/7) Hyperbolic Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(683,-1922,242,-681) (14/5,31/11) -> (31/11,48/17) Parabolic Matrix(81,-256,25,-79) (3/1,16/5) -> (16/5,13/4) Parabolic Matrix(137,-578,32,-135) (4/1,17/4) -> (17/4,30/7) Parabolic Matrix(573,-2704,121,-571) (33/7,52/11) -> (52/11,19/4) Parabolic Matrix(19,-108,3,-17) (11/2,6/1) -> (6/1,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(161,76,197,93) -> Matrix(5,-1,-4,1) Matrix(539,246,195,89) -> Matrix(1,-1,-2,3) Matrix(457,206,193,87) -> Matrix(1,-1,-2,3) Matrix(77,34,-265,-117) -> Matrix(1,-1,2,-1) Matrix(369,160,113,49) -> Matrix(7,-3,-16,7) Matrix(143,60,255,107) -> Matrix(1,-1,0,1) Matrix(499,206,109,45) -> Matrix(3,-1,-2,1) Matrix(69,28,-175,-71) -> Matrix(3,-1,4,-1) Matrix(413,160,1541,597) -> Matrix(21,-13,-8,5) Matrix(957,370,344,133) -> Matrix(3,-2,-10,7) Matrix(339,130,206,79) -> Matrix(5,-4,-6,5) Matrix(405,154,476,181) -> Matrix(1,0,-2,1) Matrix(69,26,268,101) -> Matrix(5,-2,-2,1) Matrix(1467,544,569,211) -> Matrix(1,-1,0,1) Matrix(265,98,868,321) -> Matrix(3,-4,-2,3) Matrix(131,48,-363,-133) -> Matrix(3,-1,4,-1) Matrix(455,162,132,47) -> Matrix(3,-2,-10,7) Matrix(517,182,196,69) -> Matrix(1,0,-2,1) Matrix(59,18,213,65) -> Matrix(3,-1,-2,1) Matrix(121,36,447,133) -> Matrix(9,-11,-4,5) Matrix(57,16,89,25) -> Matrix(1,-3,0,1) Matrix(163,38,193,45) -> Matrix(1,-1,-2,3) Matrix(53,12,-243,-55) -> Matrix(1,-3,0,1) Matrix(479,102,108,23) -> Matrix(1,0,2,1) Matrix(373,78,636,133) -> Matrix(1,0,2,1) Matrix(101,18,129,23) -> Matrix(1,-1,-2,3) Matrix(51,8,223,35) -> Matrix(1,5,0,1) Matrix(147,20,169,23) -> Matrix(1,-1,0,1) Matrix(233,24,165,17) -> Matrix(1,-3,0,1) Matrix(227,-26,131,-15) -> Matrix(1,7,-2,-13) Matrix(73,-10,241,-33) -> Matrix(3,5,-2,-3) Matrix(109,-16,184,-27) -> Matrix(1,2,0,1) Matrix(357,-64,106,-19) -> Matrix(3,2,-8,-5) Matrix(141,-26,320,-59) -> Matrix(3,2,-2,-1) Matrix(139,-30,51,-11) -> Matrix(1,-1,-2,3) Matrix(205,-46,361,-81) -> Matrix(1,-3,-2,7) Matrix(69,-16,289,-67) -> Matrix(1,-13,0,1) Matrix(1031,-272,398,-105) -> Matrix(1,2,0,1) Matrix(1093,-294,777,-209) -> Matrix(3,7,2,5) Matrix(229,-64,526,-147) -> Matrix(1,0,0,1) Matrix(261,-76,601,-175) -> Matrix(7,9,-4,-5) Matrix(1105,-324,324,-95) -> Matrix(3,2,-8,-5) Matrix(129,-38,17,-5) -> Matrix(1,1,-2,-1) Matrix(641,-198,450,-139) -> Matrix(5,6,-6,-7) Matrix(543,-172,382,-121) -> Matrix(5,4,-4,-3) Matrix(93,-32,32,-11) -> Matrix(1,0,0,1) Matrix(1019,-366,387,-139) -> Matrix(3,-1,-2,1) Matrix(1637,-590,1157,-417) -> Matrix(3,-1,-2,1) Matrix(309,-112,847,-307) -> Matrix(1,-1,0,1) Matrix(1261,-462,1029,-377) -> Matrix(5,1,-6,-1) Matrix(2059,-756,798,-293) -> Matrix(1,0,0,1) Matrix(921,-340,214,-79) -> Matrix(1,0,8,1) Matrix(397,-148,169,-63) -> Matrix(3,-1,-8,3) Matrix(31,-12,75,-29) -> Matrix(1,-3,0,1) Matrix(1079,-474,453,-199) -> Matrix(1,1,-2,-1) Matrix(115,-52,73,-33) -> Matrix(1,1,0,1) Matrix(273,-148,190,-103) -> Matrix(1,0,0,1) Matrix(379,-208,82,-45) -> Matrix(1,0,0,1) Matrix(939,-530,551,-311) -> Matrix(7,5,-10,-7) Matrix(79,-46,67,-39) -> Matrix(1,1,-2,-1) Matrix(1537,-900,900,-527) -> Matrix(11,-2,-16,3) Matrix(1427,-842,422,-249) -> Matrix(1,-2,-2,5) Matrix(105,-64,169,-103) -> Matrix(1,-5,0,1) Matrix(335,-212,128,-81) -> Matrix(1,2,0,1) Matrix(49,-34,13,-9) -> Matrix(1,1,-2,-1) Matrix(293,-212,170,-123) -> Matrix(7,10,-12,-17) Matrix(73,-54,96,-71) -> Matrix(5,6,-6,-7) Matrix(165,-128,107,-83) -> Matrix(1,1,-4,-3) Matrix(751,-592,529,-417) -> Matrix(1,-1,0,1) Matrix(141,-112,175,-139) -> Matrix(1,-1,0,1) Matrix(1251,-1018,451,-367) -> Matrix(1,1,-2,-1) Matrix(253,-208,208,-171) -> Matrix(7,8,-8,-9) Matrix(429,-370,349,-301) -> Matrix(5,1,-6,-1) Matrix(157,-138,33,-29) -> Matrix(1,1,-2,-1) Matrix(781,-942,228,-275) -> Matrix(7,8,-22,-25) Matrix(1689,-2048,494,-599) -> Matrix(23,22,-68,-65) Matrix(339,-418,103,-127) -> Matrix(9,7,-22,-17) Matrix(37,-48,27,-35) -> Matrix(1,1,-4,-3) Matrix(1133,-1598,653,-921) -> Matrix(1,9,-2,-17) Matrix(499,-718,319,-459) -> Matrix(1,1,-2,-1) Matrix(583,-844,172,-249) -> Matrix(3,2,-8,-5) Matrix(187,-274,43,-63) -> Matrix(1,1,2,3) Matrix(1379,-2150,533,-831) -> Matrix(1,1,-2,-1) Matrix(2625,-4096,1681,-2623) -> Matrix(1,1,-4,-3) Matrix(209,-338,128,-207) -> Matrix(5,6,-6,-7) Matrix(125,-212,23,-39) -> Matrix(1,1,-4,-3) Matrix(1271,-2172,450,-769) -> Matrix(3,2,28,19) Matrix(921,-1600,529,-919) -> Matrix(33,17,-68,-35) Matrix(15,-28,7,-13) -> Matrix(1,1,-4,-3) Matrix(347,-830,74,-177) -> Matrix(1,0,2,1) Matrix(61,-150,24,-59) -> Matrix(1,0,2,1) Matrix(683,-1922,242,-681) -> Matrix(1,0,18,1) Matrix(81,-256,25,-79) -> Matrix(9,5,-20,-11) Matrix(137,-578,32,-135) -> Matrix(1,0,18,1) Matrix(573,-2704,121,-571) -> Matrix(1,1,-4,-3) Matrix(19,-108,3,-17) -> Matrix(1,1,-4,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 1 1 0/1 1/0 1 21 1/7 -1/1 1 21 1/6 -1/1 1 3 2/11 -1/2 1 21 1/5 0/1 1 7 2/9 5/2 1 21 4/17 1/0 13 1 1/4 -4/1 1 21 2/7 -3/2 1 7 5/17 -1/1 1 21 3/10 -2/1 1 21 4/13 -5/4 1 21 5/16 -1/1 5 1 1/3 -1/1 1 21 5/14 0/1 1 21 4/11 1/0 1 7 7/19 -1/3 1 21 3/8 2/3 1 21 2/5 1/0 3 3 3/7 -7/3 1 21 4/9 1/0 1 21 1/2 -1/1 1 7 4/7 -1/4 1 21 7/12 0/1 1 21 10/17 1/2 1 7 13/22 1/1 1 3 3/5 1/1 1 21 8/13 1/0 5 1 2/3 -3/2 1 21 5/7 -2/1 1 7 8/11 -5/4 1 21 3/4 -1/1 3 3 10/13 -1/2 1 21 7/9 -3/5 1 21 4/5 1/0 1 7 9/11 -1/1 1 21 5/6 -4/5 1 21 6/7 -1/2 1 21 7/8 -1/1 1 7 1/1 -1/1 1 21 6/5 -3/2 1 21 23/19 -1/1 15 1 17/14 -12/13 1 21 11/9 -1/1 1 21 5/4 -1/1 1 7 4/3 -1/2 1 3 7/5 0/1 1 7 24/17 1/0 1 21 17/12 -2/1 1 21 10/7 -1/2 1 21 13/9 -1/1 1 21 16/11 1/0 1 7 3/2 -2/3 1 21 14/9 -1/2 1 21 64/41 -1/2 1 1 25/16 0/1 1 21 11/7 0/1 1 7 8/5 1/0 1 21 13/8 -1/1 3 1 5/3 -1/1 1 21 17/10 -1/1 1 7 12/7 -5/8 1 21 19/11 -4/7 1 7 26/15 -1/2 1 21 40/23 -1/2 17 1 7/4 -2/5 1 21 2/1 -1/2 1 7 7/3 -3/7 1 21 12/5 -1/4 1 21 5/2 0/1 1 3 18/7 -1/2 1 21 31/12 0/1 1 21 13/5 0/1 1 7 8/3 -3/4 1 21 11/4 -1/3 1 7 14/5 -1/6 1 21 31/11 0/1 9 1 17/6 0/1 1 21 3/1 -1/1 1 21 16/5 -1/2 5 1 10/3 -1/2 1 21 27/8 -1/3 1 3 44/13 -3/8 1 7 17/5 -1/3 1 21 7/2 -1/3 1 7 4/1 -1/4 1 21 17/4 0/1 9 1 13/3 1/5 1 21 9/2 2/1 1 21 14/3 -1/2 1 21 52/11 -1/2 1 1 19/4 0/1 1 21 5/1 0/1 1 7 11/2 0/1 1 21 6/1 -1/2 1 3 7/1 -1/3 1 21 1/0 0/1 1 21 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(185,-24,131,-17) (0/1,1/7) -> (24/17,17/12) Glide Reflection Matrix(109,-16,184,-27) (1/7,1/6) -> (13/22,3/5) Hyperbolic Matrix(357,-64,106,-19) (1/6,2/11) -> (10/3,27/8) Hyperbolic Matrix(107,-20,123,-23) (2/11,1/5) -> (6/7,7/8) Glide Reflection Matrix(139,-30,51,-11) (1/5,2/9) -> (8/3,11/4) Hyperbolic Matrix(35,-8,153,-35) (2/9,4/17) -> (2/9,4/17) Reflection Matrix(33,-8,136,-33) (4/17,1/4) -> (4/17,1/4) Reflection Matrix(65,-18,83,-23) (1/4,2/7) -> (7/9,4/5) Glide Reflection Matrix(131,-38,162,-47) (2/7,5/17) -> (4/5,9/11) Glide Reflection Matrix(129,-38,17,-5) (5/17,3/10) -> (7/1,1/0) Hyperbolic Matrix(321,-98,226,-69) (3/10,4/13) -> (17/12,10/7) Glide Reflection Matrix(129,-40,416,-129) (4/13,5/16) -> (4/13,5/16) Reflection Matrix(31,-10,96,-31) (5/16,1/3) -> (5/16,1/3) Reflection Matrix(93,-32,32,-11) (1/3,5/14) -> (17/6,3/1) Hyperbolic Matrix(217,-78,370,-133) (5/14,4/11) -> (7/12,10/17) Glide Reflection Matrix(337,-124,231,-85) (4/11,7/19) -> (16/11,3/2) Glide Reflection Matrix(275,-102,62,-23) (7/19,3/8) -> (13/3,9/2) Glide Reflection Matrix(31,-12,75,-29) (3/8,2/5) -> (2/5,3/7) Parabolic Matrix(87,-38,103,-45) (3/7,4/9) -> (5/6,6/7) Glide Reflection Matrix(115,-52,73,-33) (4/9,1/2) -> (11/7,8/5) Hyperbolic Matrix(107,-60,41,-23) (1/2,4/7) -> (13/5,8/3) Glide Reflection Matrix(79,-46,67,-39) (4/7,7/12) -> (1/1,6/5) Hyperbolic Matrix(1427,-842,422,-249) (10/17,13/22) -> (27/8,44/13) Hyperbolic Matrix(79,-48,130,-79) (3/5,8/13) -> (3/5,8/13) Reflection Matrix(25,-16,39,-25) (8/13,2/3) -> (8/13,2/3) Reflection Matrix(49,-34,13,-9) (2/3,5/7) -> (7/2,4/1) Hyperbolic Matrix(293,-212,170,-123) (5/7,8/11) -> (12/7,19/11) Hyperbolic Matrix(73,-54,96,-71) (8/11,3/4) -> (3/4,10/13) Parabolic Matrix(165,-128,107,-83) (10/13,7/9) -> (3/2,14/9) Hyperbolic Matrix(253,-208,208,-171) (9/11,5/6) -> (17/14,11/9) Hyperbolic Matrix(157,-138,33,-29) (7/8,1/1) -> (19/4,5/1) Hyperbolic Matrix(229,-276,190,-229) (6/5,23/19) -> (6/5,23/19) Reflection Matrix(645,-782,532,-645) (23/19,17/14) -> (23/19,17/14) Reflection Matrix(131,-162,38,-47) (11/9,5/4) -> (17/5,7/2) Glide Reflection Matrix(37,-48,27,-35) (5/4,4/3) -> (4/3,7/5) Parabolic Matrix(453,-638,262,-369) (7/5,24/17) -> (19/11,26/15) Glide Reflection Matrix(379,-544,147,-211) (10/7,13/9) -> (18/7,31/12) Glide Reflection Matrix(583,-844,172,-249) (13/9,16/11) -> (44/13,17/5) Hyperbolic Matrix(575,-896,369,-575) (14/9,64/41) -> (14/9,64/41) Reflection Matrix(2049,-3200,1312,-2049) (64/41,25/16) -> (64/41,25/16) Reflection Matrix(425,-666,164,-257) (25/16,11/7) -> (31/12,13/5) Glide Reflection Matrix(129,-208,80,-129) (8/5,13/8) -> (8/5,13/8) Reflection Matrix(79,-130,48,-79) (13/8,5/3) -> (13/8,5/3) Reflection Matrix(125,-212,23,-39) (5/3,17/10) -> (5/1,11/2) Hyperbolic Matrix(217,-370,78,-133) (17/10,12/7) -> (11/4,14/5) Glide Reflection Matrix(599,-1040,345,-599) (26/15,40/23) -> (26/15,40/23) Reflection Matrix(321,-560,184,-321) (40/23,7/4) -> (40/23,7/4) Reflection Matrix(15,-28,7,-13) (7/4,2/1) -> (2/1,7/3) Parabolic Matrix(87,-206,19,-45) (7/3,12/5) -> (9/2,14/3) Glide Reflection Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(309,-868,110,-309) (14/5,31/11) -> (14/5,31/11) Reflection Matrix(373,-1054,132,-373) (31/11,17/6) -> (31/11,17/6) Reflection Matrix(31,-96,10,-31) (3/1,16/5) -> (3/1,16/5) Reflection Matrix(49,-160,15,-49) (16/5,10/3) -> (16/5,10/3) Reflection Matrix(33,-136,8,-33) (4/1,17/4) -> (4/1,17/4) Reflection Matrix(103,-442,24,-103) (17/4,13/3) -> (17/4,13/3) Reflection Matrix(155,-728,33,-155) (14/3,52/11) -> (14/3,52/11) Reflection Matrix(417,-1976,88,-417) (52/11,19/4) -> (52/11,19/4) Reflection Matrix(19,-108,3,-17) (11/2,6/1) -> (6/1,7/1) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(1,0,0,-1) (-1/1,0/1) -> (0/1,1/0) Matrix(185,-24,131,-17) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(109,-16,184,-27) -> Matrix(1,2,0,1) 1/0 Matrix(357,-64,106,-19) -> Matrix(3,2,-8,-5) -1/2 Matrix(107,-20,123,-23) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(139,-30,51,-11) -> Matrix(1,-1,-2,3) Matrix(35,-8,153,-35) -> Matrix(-1,5,0,1) (2/9,4/17) -> (5/2,1/0) Matrix(33,-8,136,-33) -> Matrix(1,8,0,-1) (4/17,1/4) -> (-4/1,1/0) Matrix(65,-18,83,-23) -> Matrix(1,1,-2,-3) Matrix(131,-38,162,-47) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(129,-38,17,-5) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(321,-98,226,-69) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(129,-40,416,-129) -> Matrix(9,10,-8,-9) (4/13,5/16) -> (-5/4,-1/1) Matrix(31,-10,96,-31) -> Matrix(-1,0,2,1) (5/16,1/3) -> (-1/1,0/1) Matrix(93,-32,32,-11) -> Matrix(1,0,0,1) Matrix(217,-78,370,-133) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(337,-124,231,-85) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(275,-102,62,-23) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(31,-12,75,-29) -> Matrix(1,-3,0,1) 1/0 Matrix(87,-38,103,-45) -> Matrix(1,1,-2,-3) Matrix(115,-52,73,-33) -> Matrix(1,1,0,1) 1/0 Matrix(107,-60,41,-23) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(79,-46,67,-39) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(1427,-842,422,-249) -> Matrix(1,-2,-2,5) Matrix(79,-48,130,-79) -> Matrix(-1,2,0,1) (3/5,8/13) -> (1/1,1/0) Matrix(25,-16,39,-25) -> Matrix(1,3,0,-1) (8/13,2/3) -> (-3/2,1/0) Matrix(49,-34,13,-9) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(293,-212,170,-123) -> Matrix(7,10,-12,-17) Matrix(73,-54,96,-71) -> Matrix(5,6,-6,-7) -1/1 Matrix(165,-128,107,-83) -> Matrix(1,1,-4,-3) -1/2 Matrix(253,-208,208,-171) -> Matrix(7,8,-8,-9) -1/1 Matrix(157,-138,33,-29) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(229,-276,190,-229) -> Matrix(5,6,-4,-5) (6/5,23/19) -> (-3/2,-1/1) Matrix(645,-782,532,-645) -> Matrix(25,24,-26,-25) (23/19,17/14) -> (-1/1,-12/13) Matrix(131,-162,38,-47) -> Matrix(3,2,-10,-7) Matrix(37,-48,27,-35) -> Matrix(1,1,-4,-3) -1/2 Matrix(453,-638,262,-369) -> Matrix(1,-4,-2,7) Matrix(379,-544,147,-211) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(583,-844,172,-249) -> Matrix(3,2,-8,-5) -1/2 Matrix(575,-896,369,-575) -> Matrix(1,1,0,-1) (14/9,64/41) -> (-1/2,1/0) Matrix(2049,-3200,1312,-2049) -> Matrix(-1,0,4,1) (64/41,25/16) -> (-1/2,0/1) Matrix(425,-666,164,-257) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(129,-208,80,-129) -> Matrix(1,2,0,-1) (8/5,13/8) -> (-1/1,1/0) Matrix(79,-130,48,-79) -> Matrix(5,4,-6,-5) (13/8,5/3) -> (-1/1,-2/3) Matrix(125,-212,23,-39) -> Matrix(1,1,-4,-3) -1/2 Matrix(217,-370,78,-133) -> Matrix(3,2,-10,-7) Matrix(599,-1040,345,-599) -> Matrix(25,13,-48,-25) (26/15,40/23) -> (-13/24,-1/2) Matrix(321,-560,184,-321) -> Matrix(9,4,-20,-9) (40/23,7/4) -> (-1/2,-2/5) Matrix(15,-28,7,-13) -> Matrix(1,1,-4,-3) -1/2 Matrix(87,-206,19,-45) -> Matrix(3,1,-2,-1) Matrix(61,-150,24,-59) -> Matrix(1,0,2,1) 0/1 Matrix(309,-868,110,-309) -> Matrix(-1,0,12,1) (14/5,31/11) -> (-1/6,0/1) Matrix(373,-1054,132,-373) -> Matrix(1,0,6,-1) (31/11,17/6) -> (0/1,1/3) Matrix(31,-96,10,-31) -> Matrix(3,2,-4,-3) (3/1,16/5) -> (-1/1,-1/2) Matrix(49,-160,15,-49) -> Matrix(7,3,-16,-7) (16/5,10/3) -> (-1/2,-3/8) Matrix(33,-136,8,-33) -> Matrix(-1,0,8,1) (4/1,17/4) -> (-1/4,0/1) Matrix(103,-442,24,-103) -> Matrix(1,0,10,-1) (17/4,13/3) -> (0/1,1/5) Matrix(155,-728,33,-155) -> Matrix(1,1,0,-1) (14/3,52/11) -> (-1/2,1/0) Matrix(417,-1976,88,-417) -> Matrix(-1,0,4,1) (52/11,19/4) -> (-1/2,0/1) Matrix(19,-108,3,-17) -> Matrix(1,1,-4,-3) -1/2 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.