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): 720 Minimal number of generators: 121 Number of equivalence classes of cusps: 40 Genus: 41 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 0/1 2/9 3/8 1/2 4/7 5/6 1/1 6/5 7/5 13/9 3/2 27/17 34/21 7/4 2/1 15/7 23/10 7/3 31/13 5/2 13/5 8/3 3/1 10/3 17/5 7/2 69/19 11/3 87/23 4/1 13/3 9/2 5/1 37/7 17/3 6/1 19/3 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 1/41 -6/13 1/39 2/77 -11/24 2/75 1/37 -5/11 1/39 -4/9 0/1 1/37 -11/25 3/113 -18/41 2/75 1/37 -7/16 4/149 1/37 -3/7 1/37 1/36 -5/12 2/71 1/35 -17/41 1/36 3/107 -12/29 3/107 2/71 -7/17 1/35 -9/22 2/71 5/177 -2/5 1/35 2/69 -5/13 1/34 3/101 -18/47 3/101 8/269 -13/34 2/67 1/33 -8/21 7/235 2/67 -11/29 5/167 -14/37 2/67 1/33 -3/8 4/133 1/33 -7/19 1/33 5/164 -18/49 1/33 6/197 -11/30 4/131 7/229 -4/11 5/163 2/65 -13/36 2/65 7/227 -9/25 5/162 3/97 -14/39 3/97 16/517 -5/14 4/129 5/161 -1/3 1/31 -4/13 5/149 4/119 -7/23 3/89 5/148 -10/33 7/207 2/59 -13/43 11/325 -3/10 2/59 5/147 -8/27 7/205 4/117 -21/71 9/263 -13/44 6/175 1/29 -18/61 4/117 1/29 -5/17 5/146 1/29 -7/24 14/407 1/29 -2/7 1/29 4/115 -9/32 1/29 2/57 -7/25 5/143 -12/43 17/485 2/57 -5/18 2/57 7/199 -13/47 3/85 -8/29 1/29 2/57 -3/11 3/85 1/28 -1/4 2/55 1/27 -6/25 1/27 12/323 -5/21 1/27 5/134 -4/17 5/133 2/53 -7/30 2/53 3/79 -3/13 1/27 -8/35 5/133 2/53 -5/22 2/53 3/79 -7/31 3/79 1/26 -2/9 1/27 2/53 -1/5 1/26 1/25 -3/16 6/151 1/25 -2/11 1/25 4/99 -7/39 1/25 3/74 -5/28 1/25 2/49 -8/45 13/319 2/49 -11/62 2/49 19/465 -3/17 3/73 -1/6 0/1 1/25 -1/7 1/23 -4/29 0/1 1/19 -3/22 0/1 1/27 -2/15 1/25 2/49 -1/8 2/47 1/23 -2/17 1/23 4/91 -1/9 1/23 1/22 0/1 0/1 1/21 1/6 1/19 2/37 2/11 2/35 1/17 1/5 1/19 3/14 2/37 3/55 2/9 1/18 5/22 6/107 5/89 8/35 5/89 4/71 3/13 1/18 3/53 1/4 0/1 1/17 3/11 3/53 5/18 2/35 1/17 2/7 4/69 1/17 1/3 1/17 1/16 4/11 3/49 4/65 3/8 1/16 8/21 9/143 8/127 13/34 6/95 5/79 18/47 7/111 6/95 5/13 5/79 2/5 2/31 1/15 7/17 1/16 3/47 5/12 3/47 2/31 3/7 1/15 4/9 2/31 5/77 1/2 1/15 2/29 5/9 5/71 4/7 1/14 11/19 11/153 18/31 9/125 8/111 25/43 1/14 9/125 32/55 9/125 8/111 7/12 8/111 7/97 3/5 1/14 3/41 11/18 3/41 8/109 8/13 2/27 1/13 5/8 7/95 2/27 7/11 5/67 9/14 2/27 1/13 2/3 4/53 1/13 5/7 1/13 5/64 13/18 1/13 6/77 8/11 4/51 7/89 3/4 5/63 2/25 10/13 2/25 7/87 7/9 5/62 3/37 11/14 3/37 16/197 4/5 4/49 5/61 9/11 9/109 1/12 5/6 1/12 11/13 1/12 11/131 17/20 10/119 9/107 6/7 7/83 6/71 1/1 1/11 7/6 6/61 7/71 6/5 1/10 17/14 14/139 13/129 28/23 11/109 10/99 11/9 1/10 9/89 5/4 5/49 4/39 9/7 3/29 5/48 13/10 7/67 2/19 17/13 11/105 4/3 2/19 5/47 15/11 7/65 11/8 7/65 4/37 29/21 9/83 18/13 6/55 1/9 25/18 4/37 1/9 7/5 5/46 1/9 10/7 14/127 1/9 13/9 1/9 16/11 1/9 22/197 3/2 1/9 4/35 17/11 3/26 5/43 14/9 1/9 2/17 25/16 5/43 2/17 11/7 5/43 19/12 17/145 2/17 27/17 2/17 35/22 2/17 31/263 8/5 2/17 7/59 21/13 3/25 55/34 4/33 5/41 34/21 1/8 81/50 0/1 1/9 47/29 1/9 1/8 13/8 1/9 2/17 5/3 3/25 1/8 12/7 7/57 8/65 7/4 1/8 16/9 9/71 8/63 41/23 1/8 7/55 25/14 8/63 7/55 9/5 5/39 11/6 3/23 2/15 13/7 1/8 3/23 2/1 2/15 1/7 15/7 1/7 28/13 1/7 26/181 13/6 1/7 12/83 11/5 1/7 5/34 9/4 5/33 2/13 16/7 2/13 3/19 23/10 1/6 30/13 0/1 1/5 7/3 1/7 19/8 5/33 2/13 31/13 2/13 43/18 2/13 11/71 12/5 2/13 3/19 17/7 3/19 1/6 22/9 2/11 1/5 5/2 1/7 2/13 18/7 4/25 5/31 49/19 3/19 1/6 31/12 3/19 4/25 13/5 5/31 8/3 1/6 19/7 7/41 49/18 6/35 5/29 128/47 5/29 4/23 79/29 1/6 5/29 30/11 7/41 6/35 11/4 4/23 3/17 3/1 1/6 1/5 10/3 6/31 1/5 17/5 1/5 24/7 1/5 14/69 7/2 1/5 4/19 25/7 1/5 3/14 68/19 1/5 4/19 43/12 3/14 18/5 1/5 2/9 29/8 13/59 2/9 69/19 2/9 109/30 2/9 51/229 40/11 2/9 19/85 11/3 3/13 15/4 0/1 1/3 34/9 0/1 1/5 87/23 1/5 140/37 1/5 4/19 53/14 1/5 2/9 19/5 1/5 1/4 4/1 0/1 1/5 17/4 1/5 2/9 13/3 3/13 1/4 9/2 1/4 23/5 1/4 5/19 37/8 4/15 3/11 14/3 3/11 2/7 5/1 1/3 21/4 -1/1 0/1 37/7 0/1 53/10 0/1 1/15 16/3 0/1 1/7 11/2 1/5 2/9 17/3 1/4 3/11 6/1 2/7 1/3 19/3 1/3 32/5 1/3 10/29 13/2 1/3 4/11 7/1 1/3 1/2 1/0 0/1 1/1 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(205,96,-536,-251) (-1/2,-6/13) -> (-18/47,-13/34) Hyperbolic Matrix(893,410,734,337) (-6/13,-11/24) -> (17/14,28/23) Hyperbolic Matrix(647,296,-2188,-1001) (-11/24,-5/11) -> (-21/71,-13/44) Hyperbolic Matrix(199,90,42,19) (-5/11,-4/9) -> (14/3,5/1) Hyperbolic Matrix(549,242,946,417) (-4/9,-11/25) -> (11/19,18/31) Hyperbolic Matrix(783,344,-2588,-1137) (-11/25,-18/41) -> (-10/33,-13/43) Hyperbolic Matrix(821,360,-2780,-1219) (-18/41,-7/16) -> (-13/44,-18/61) Hyperbolic Matrix(37,16,-192,-83) (-7/16,-3/7) -> (-1/5,-3/16) Hyperbolic Matrix(113,48,40,17) (-3/7,-5/12) -> (11/4,3/1) Hyperbolic Matrix(829,344,976,405) (-5/12,-17/41) -> (11/13,17/20) Hyperbolic Matrix(1463,606,2518,1043) (-17/41,-12/29) -> (18/31,25/43) Hyperbolic Matrix(223,92,-972,-401) (-12/29,-7/17) -> (-3/13,-8/35) Hyperbolic Matrix(371,152,-1340,-549) (-7/17,-9/22) -> (-5/18,-13/47) Hyperbolic Matrix(333,136,-928,-379) (-9/22,-2/5) -> (-14/39,-5/14) Hyperbolic Matrix(181,70,106,41) (-2/5,-5/13) -> (5/3,12/7) Hyperbolic Matrix(73,28,-644,-247) (-5/13,-18/47) -> (-2/17,-1/9) Hyperbolic Matrix(283,108,-1208,-461) (-13/34,-8/21) -> (-4/17,-7/30) Hyperbolic Matrix(495,188,-1772,-673) (-8/21,-11/29) -> (-7/25,-12/43) Hyperbolic Matrix(707,268,1844,699) (-11/29,-14/37) -> (18/47,5/13) Hyperbolic Matrix(249,94,1094,413) (-14/37,-3/8) -> (5/22,8/35) Hyperbolic Matrix(173,64,-592,-219) (-3/8,-7/19) -> (-5/17,-7/24) Hyperbolic Matrix(381,140,-2120,-779) (-7/19,-18/49) -> (-2/11,-7/39) Hyperbolic Matrix(207,76,-1528,-561) (-18/49,-11/30) -> (-3/22,-2/15) Hyperbolic Matrix(383,140,1004,367) (-11/30,-4/11) -> (8/21,13/34) Hyperbolic Matrix(343,124,-1928,-697) (-4/11,-13/36) -> (-5/28,-8/45) Hyperbolic Matrix(1753,632,380,137) (-13/36,-9/25) -> (23/5,37/8) Hyperbolic Matrix(345,124,-1444,-519) (-9/25,-14/39) -> (-6/25,-5/21) Hyperbolic Matrix(35,12,32,11) (-5/14,-1/3) -> (1/1,7/6) Hyperbolic Matrix(31,10,34,11) (-1/3,-4/13) -> (6/7,1/1) Hyperbolic Matrix(157,48,-664,-203) (-4/13,-7/23) -> (-5/21,-4/17) Hyperbolic Matrix(283,86,1234,375) (-7/23,-10/33) -> (8/35,3/13) Hyperbolic Matrix(503,152,-2836,-857) (-13/43,-3/10) -> (-11/62,-3/17) Hyperbolic Matrix(597,178,218,65) (-3/10,-8/27) -> (30/11,11/4) Hyperbolic Matrix(311,92,-2248,-665) (-8/27,-21/71) -> (-1/7,-4/29) Hyperbolic Matrix(2681,790,750,221) (-18/61,-5/17) -> (25/7,68/19) Hyperbolic Matrix(405,118,278,81) (-7/24,-2/7) -> (16/11,3/2) Hyperbolic Matrix(707,200,152,43) (-2/7,-9/32) -> (37/8,14/3) Hyperbolic Matrix(1833,514,674,189) (-9/32,-7/25) -> (19/7,49/18) Hyperbolic Matrix(1649,460,1036,289) (-12/43,-5/18) -> (35/22,8/5) Hyperbolic Matrix(1613,446,698,193) (-13/47,-8/29) -> (30/13,7/3) Hyperbolic Matrix(29,8,-272,-75) (-8/29,-3/11) -> (-1/9,0/1) Hyperbolic Matrix(89,24,152,41) (-3/11,-1/4) -> (7/12,3/5) Hyperbolic Matrix(437,106,202,49) (-1/4,-6/25) -> (28/13,13/6) Hyperbolic Matrix(1345,312,832,193) (-7/30,-3/13) -> (21/13,55/34) Hyperbolic Matrix(1769,404,740,169) (-8/35,-5/22) -> (43/18,12/5) Hyperbolic Matrix(1677,380,940,213) (-5/22,-7/31) -> (41/23,25/14) Hyperbolic Matrix(967,218,794,179) (-7/31,-2/9) -> (28/23,11/9) Hyperbolic Matrix(29,6,82,17) (-2/9,-1/5) -> (1/3,4/11) Hyperbolic Matrix(461,86,134,25) (-3/16,-2/11) -> (24/7,7/2) Hyperbolic Matrix(4475,802,2762,495) (-7/39,-5/28) -> (81/50,47/29) Hyperbolic Matrix(7385,1312,2032,361) (-8/45,-11/62) -> (109/30,40/11) Hyperbolic Matrix(479,84,268,47) (-3/17,-1/6) -> (25/14,9/5) Hyperbolic Matrix(27,4,128,19) (-1/6,-1/7) -> (1/5,3/14) Hyperbolic Matrix(1889,260,356,49) (-4/29,-3/22) -> (53/10,16/3) Hyperbolic Matrix(303,40,356,47) (-2/15,-1/8) -> (17/20,6/7) Hyperbolic Matrix(477,58,74,9) (-1/8,-2/17) -> (32/5,13/2) Hyperbolic Matrix(59,-8,96,-13) (0/1,1/6) -> (11/18,8/13) Hyperbolic Matrix(187,-32,76,-13) (1/6,2/11) -> (22/9,5/2) Hyperbolic Matrix(409,-76,296,-55) (2/11,1/5) -> (29/21,18/13) Hyperbolic Matrix(73,-16,324,-71) (3/14,2/9) -> (2/9,5/22) Parabolic Matrix(107,-26,70,-17) (3/13,1/4) -> (3/2,17/11) Hyperbolic Matrix(157,-42,86,-23) (1/4,3/11) -> (9/5,11/6) Hyperbolic Matrix(449,-124,344,-95) (3/11,5/18) -> (13/10,17/13) Hyperbolic Matrix(499,-140,360,-101) (5/18,2/7) -> (18/13,25/18) Hyperbolic Matrix(51,-16,16,-5) (2/7,1/3) -> (3/1,10/3) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(1417,-542,2434,-931) (13/34,18/47) -> (32/55,7/12) Hyperbolic Matrix(127,-50,94,-37) (5/13,2/5) -> (4/3,15/11) Hyperbolic Matrix(187,-76,32,-13) (2/5,7/17) -> (17/3,6/1) Hyperbolic Matrix(343,-142,186,-77) (7/17,5/12) -> (11/6,13/7) Hyperbolic Matrix(217,-92,92,-39) (5/12,3/7) -> (7/3,19/8) Hyperbolic Matrix(245,-108,152,-67) (3/7,4/9) -> (8/5,21/13) Hyperbolic Matrix(107,-48,136,-61) (4/9,1/2) -> (11/14,4/5) Hyperbolic Matrix(157,-86,42,-23) (1/2,5/9) -> (11/3,15/4) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(9849,-5728,3616,-2103) (25/43,32/55) -> (128/47,79/29) Hyperbolic Matrix(191,-116,28,-17) (3/5,11/18) -> (13/2,7/1) Hyperbolic Matrix(245,-152,108,-67) (8/13,5/8) -> (9/4,16/7) Hyperbolic Matrix(297,-188,188,-119) (5/8,7/11) -> (11/7,19/12) Hyperbolic Matrix(523,-334,202,-129) (7/11,9/14) -> (31/12,13/5) Hyperbolic Matrix(107,-70,26,-17) (9/14,2/3) -> (4/1,17/4) Hyperbolic Matrix(91,-64,64,-45) (2/3,5/7) -> (7/5,10/7) Hyperbolic Matrix(499,-360,140,-101) (5/7,13/18) -> (7/2,25/7) Hyperbolic Matrix(409,-296,76,-55) (13/18,8/11) -> (16/3,11/2) Hyperbolic Matrix(127,-94,50,-37) (8/11,3/4) -> (5/2,18/7) Hyperbolic Matrix(449,-344,124,-95) (3/4,10/13) -> (18/5,29/8) Hyperbolic Matrix(347,-268,224,-173) (10/13,7/9) -> (17/11,14/9) Hyperbolic Matrix(271,-212,124,-97) (7/9,11/14) -> (13/6,11/5) Hyperbolic Matrix(327,-266,134,-109) (4/5,9/11) -> (17/7,22/9) Hyperbolic Matrix(121,-100,144,-119) (9/11,5/6) -> (5/6,11/13) Parabolic Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(167,-206,30,-37) (11/9,5/4) -> (11/2,17/3) Hyperbolic Matrix(107,-136,48,-61) (5/4,9/7) -> (11/5,9/4) Hyperbolic Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(553,-724,152,-199) (17/13,4/3) -> (40/11,11/3) Hyperbolic Matrix(363,-496,232,-317) (15/11,11/8) -> (25/16,11/7) Hyperbolic Matrix(481,-664,92,-127) (11/8,29/21) -> (5/1,21/4) Hyperbolic Matrix(911,-1266,562,-781) (25/18,7/5) -> (47/29,13/8) Hyperbolic Matrix(235,-338,162,-233) (10/7,13/9) -> (13/9,16/11) Parabolic Matrix(679,-1060,180,-281) (14/9,25/16) -> (15/4,34/9) Hyperbolic Matrix(919,-1458,578,-917) (19/12,27/17) -> (27/17,35/22) Parabolic Matrix(2857,-4624,1764,-2855) (55/34,34/21) -> (34/21,81/50) Parabolic Matrix(59,-96,8,-13) (13/8,5/3) -> (7/1,1/0) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(1401,-2494,514,-915) (16/9,41/23) -> (79/29,30/11) Hyperbolic Matrix(175,-332,68,-129) (13/7,2/1) -> (18/7,49/19) Hyperbolic Matrix(211,-450,98,-209) (2/1,15/7) -> (15/7,28/13) Parabolic Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(1239,-2854,346,-797) (23/10,30/13) -> (68/19,43/12) Hyperbolic Matrix(807,-1922,338,-805) (19/8,31/13) -> (31/13,43/18) Parabolic Matrix(123,-296,32,-77) (12/5,17/7) -> (19/5,4/1) Hyperbolic Matrix(1235,-3186,326,-841) (49/19,31/12) -> (53/14,19/5) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(5011,-13644,1324,-3605) (49/18,128/47) -> (140/37,53/14) Hyperbolic Matrix(171,-578,50,-169) (10/3,17/5) -> (17/5,24/7) Parabolic Matrix(2623,-9522,722,-2621) (29/8,69/19) -> (69/19,109/30) Parabolic Matrix(4003,-15138,1058,-4001) (34/9,87/23) -> (87/23,140/37) Parabolic Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(519,-2738,98,-517) (21/4,37/7) -> (37/7,53/10) Parabolic Matrix(115,-722,18,-113) (6/1,19/3) -> (19/3,32/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,40,1) Matrix(205,96,-536,-251) -> Matrix(81,-2,2714,-67) Matrix(893,410,734,337) -> Matrix(457,-12,4532,-119) Matrix(647,296,-2188,-1001) -> Matrix(147,-4,4300,-117) Matrix(199,90,42,19) -> Matrix(77,-2,270,-7) Matrix(549,242,946,417) -> Matrix(305,-8,4232,-111) Matrix(783,344,-2588,-1137) -> Matrix(599,-16,17708,-473) Matrix(821,360,-2780,-1219) -> Matrix(73,-2,2154,-59) Matrix(37,16,-192,-83) -> Matrix(73,-2,1862,-51) Matrix(113,48,40,17) -> Matrix(73,-2,402,-11) Matrix(829,344,976,405) -> Matrix(289,-8,3432,-95) Matrix(1463,606,2518,1043) -> Matrix(217,-6,3002,-83) Matrix(223,92,-972,-401) -> Matrix(141,-4,3772,-107) Matrix(371,152,-1340,-549) -> Matrix(143,-4,4040,-113) Matrix(333,136,-928,-379) -> Matrix(353,-10,11402,-323) Matrix(181,70,106,41) -> Matrix(203,-6,1658,-49) Matrix(73,28,-644,-247) -> Matrix(135,-4,3004,-89) Matrix(283,108,-1208,-461) -> Matrix(135,-4,3544,-105) Matrix(495,188,-1772,-673) -> Matrix(669,-20,19100,-571) Matrix(707,268,1844,699) -> Matrix(667,-20,10572,-317) Matrix(249,94,1094,413) -> Matrix(467,-14,8306,-249) Matrix(173,64,-592,-219) -> Matrix(329,-10,9574,-291) Matrix(381,140,-2120,-779) -> Matrix(65,-2,1658,-51) Matrix(207,76,-1528,-561) -> Matrix(131,-4,3308,-101) Matrix(383,140,1004,367) -> Matrix(719,-22,11406,-349) Matrix(343,124,-1928,-697) -> Matrix(519,-16,12748,-393) Matrix(1753,632,380,137) -> Matrix(713,-22,2690,-83) Matrix(345,124,-1444,-519) -> Matrix(647,-20,17372,-537) Matrix(35,12,32,11) -> Matrix(63,-2,662,-21) Matrix(31,10,34,11) -> Matrix(61,-2,702,-23) Matrix(157,48,-664,-203) -> Matrix(297,-10,7930,-267) Matrix(283,86,1234,375) -> Matrix(533,-18,9446,-319) Matrix(503,152,-2836,-857) -> Matrix(827,-28,20232,-685) Matrix(597,178,218,65) -> Matrix(411,-14,2378,-81) Matrix(311,92,-2248,-665) -> Matrix(117,-4,2428,-83) Matrix(2681,790,750,221) -> Matrix(233,-8,1136,-39) Matrix(405,118,278,81) -> Matrix(523,-18,4678,-161) Matrix(707,200,152,43) -> Matrix(287,-10,1062,-37) Matrix(1833,514,674,189) -> Matrix(459,-16,2668,-93) Matrix(1649,460,1036,289) -> Matrix(1369,-48,11608,-407) Matrix(1613,446,698,193) -> Matrix(57,-2,314,-11) Matrix(29,8,-272,-75) -> Matrix(57,-2,1226,-43) Matrix(89,24,152,41) -> Matrix(169,-6,2338,-83) Matrix(437,106,202,49) -> Matrix(379,-14,2626,-97) Matrix(1345,312,832,193) -> Matrix(51,-2,434,-17) Matrix(1769,404,740,169) -> Matrix(425,-16,2736,-103) Matrix(1677,380,940,213) -> Matrix(261,-10,2062,-79) Matrix(967,218,794,179) -> Matrix(313,-12,3104,-119) Matrix(29,6,82,17) -> Matrix(51,-2,842,-33) Matrix(461,86,134,25) -> Matrix(251,-10,1230,-49) Matrix(4475,802,2762,495) -> Matrix(49,-2,466,-19) Matrix(7385,1312,2032,361) -> Matrix(1569,-64,7036,-287) Matrix(479,84,268,47) -> Matrix(193,-8,1520,-63) Matrix(27,4,128,19) -> Matrix(47,-2,870,-37) Matrix(1889,260,356,49) -> Matrix(1,0,-12,1) Matrix(303,40,356,47) -> Matrix(193,-8,2292,-95) Matrix(477,58,74,9) -> Matrix(139,-6,394,-17) Matrix(59,-8,96,-13) -> Matrix(41,-2,554,-27) Matrix(187,-32,76,-13) -> Matrix(1,0,-12,1) Matrix(409,-76,296,-55) -> Matrix(67,-4,620,-37) Matrix(73,-16,324,-71) -> Matrix(145,-8,2592,-143) Matrix(107,-26,70,-17) -> Matrix(69,-4,604,-35) Matrix(157,-42,86,-23) -> Matrix(37,-2,278,-15) Matrix(449,-124,344,-95) -> Matrix(279,-16,2668,-153) Matrix(499,-140,360,-101) -> Matrix(33,-2,314,-19) Matrix(51,-16,16,-5) -> Matrix(33,-2,182,-11) Matrix(97,-36,256,-95) -> Matrix(193,-12,3072,-191) Matrix(1417,-542,2434,-931) -> Matrix(33,-2,446,-27) Matrix(127,-50,94,-37) -> Matrix(125,-8,1172,-75) Matrix(187,-76,32,-13) -> Matrix(1,0,-12,1) Matrix(343,-142,186,-77) -> Matrix(1,0,-8,1) Matrix(217,-92,92,-39) -> Matrix(61,-4,412,-27) Matrix(245,-108,152,-67) -> Matrix(63,-4,520,-33) Matrix(107,-48,136,-61) -> Matrix(153,-10,1882,-123) Matrix(157,-86,42,-23) -> Matrix(29,-2,102,-7) Matrix(113,-64,196,-111) -> Matrix(225,-16,3136,-223) Matrix(9849,-5728,3616,-2103) -> Matrix(55,-4,344,-25) Matrix(191,-116,28,-17) -> Matrix(55,-4,124,-9) Matrix(245,-152,108,-67) -> Matrix(55,-4,344,-25) Matrix(297,-188,188,-119) -> Matrix(269,-20,2300,-171) Matrix(523,-334,202,-129) -> Matrix(133,-10,838,-63) Matrix(107,-70,26,-17) -> Matrix(53,-4,252,-19) Matrix(91,-64,64,-45) -> Matrix(129,-10,1174,-91) Matrix(499,-360,140,-101) -> Matrix(25,-2,138,-11) Matrix(409,-296,76,-55) -> Matrix(51,-4,268,-21) Matrix(127,-94,50,-37) -> Matrix(101,-8,644,-51) Matrix(449,-344,124,-95) -> Matrix(199,-16,908,-73) Matrix(347,-268,224,-173) -> Matrix(199,-16,1704,-137) Matrix(271,-212,124,-97) -> Matrix(247,-20,1692,-137) Matrix(327,-266,134,-109) -> Matrix(73,-6,426,-35) Matrix(121,-100,144,-119) -> Matrix(241,-20,2880,-239) Matrix(121,-144,100,-119) -> Matrix(201,-20,2000,-199) Matrix(167,-206,30,-37) -> Matrix(59,-6,246,-25) Matrix(107,-136,48,-61) -> Matrix(97,-10,650,-67) Matrix(249,-322,58,-75) -> Matrix(115,-12,508,-53) Matrix(553,-724,152,-199) -> Matrix(267,-28,1192,-125) Matrix(363,-496,232,-317) -> Matrix(55,-6,486,-53) Matrix(481,-664,92,-127) -> Matrix(37,-4,28,-3) Matrix(911,-1266,562,-781) -> Matrix(55,-6,486,-53) Matrix(235,-338,162,-233) -> Matrix(325,-36,2916,-323) Matrix(679,-1060,180,-281) -> Matrix(17,-2,94,-11) Matrix(919,-1458,578,-917) -> Matrix(817,-96,6936,-815) Matrix(2857,-4624,1764,-2855) -> Matrix(33,-4,256,-31) Matrix(59,-96,8,-13) -> Matrix(17,-2,26,-3) Matrix(113,-196,64,-111) -> Matrix(129,-16,1024,-127) Matrix(1401,-2494,514,-915) -> Matrix(15,-2,98,-13) Matrix(175,-332,68,-129) -> Matrix(47,-6,290,-37) Matrix(211,-450,98,-209) -> Matrix(197,-28,1372,-195) Matrix(481,-1102,134,-307) -> Matrix(51,-8,236,-37) Matrix(1239,-2854,346,-797) -> Matrix(21,-4,100,-19) Matrix(807,-1922,338,-805) -> Matrix(209,-32,1352,-207) Matrix(123,-296,32,-77) -> Matrix(13,-2,46,-7) Matrix(1235,-3186,326,-841) -> Matrix(13,-2,46,-7) Matrix(97,-256,36,-95) -> Matrix(73,-12,432,-71) Matrix(5011,-13644,1324,-3605) -> Matrix(93,-16,436,-75) Matrix(171,-578,50,-169) -> Matrix(101,-20,500,-99) Matrix(2623,-9522,722,-2621) -> Matrix(577,-128,2592,-575) Matrix(4003,-15138,1058,-4001) -> Matrix(21,-4,100,-19) Matrix(73,-324,16,-71) -> Matrix(33,-8,128,-31) Matrix(519,-2738,98,-517) -> Matrix(1,0,16,1) Matrix(115,-722,18,-113) -> Matrix(37,-12,108,-35) 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: 120 ----------------------------------------------------------------------- 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): 360 Minimal number of generators: 61 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: 30 Genus: 16 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/1 6/5 7/5 13/9 27/17 7/4 2/1 15/7 23/10 7/3 31/13 13/5 8/3 3/1 17/5 7/2 69/19 11/3 87/23 4/1 13/3 9/2 5/1 37/7 17/3 6/1 19/3 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 0/1 1/21 1/6 1/19 2/37 2/11 2/35 1/17 1/5 1/19 2/9 1/18 3/13 1/18 3/53 1/4 0/1 1/17 3/11 3/53 5/18 2/35 1/17 2/7 4/69 1/17 1/3 1/17 1/16 3/8 1/16 5/13 5/79 2/5 2/31 1/15 7/17 1/16 3/47 5/12 3/47 2/31 3/7 1/15 4/9 2/31 5/77 1/2 1/15 2/29 5/9 5/71 4/7 1/14 3/5 1/14 3/41 11/18 3/41 8/109 8/13 2/27 1/13 5/8 7/95 2/27 7/11 5/67 9/14 2/27 1/13 2/3 4/53 1/13 5/7 1/13 5/64 13/18 1/13 6/77 8/11 4/51 7/89 3/4 5/63 2/25 10/13 2/25 7/87 7/9 5/62 3/37 11/14 3/37 16/197 4/5 4/49 5/61 9/11 9/109 1/12 5/6 1/12 1/1 1/11 6/5 1/10 11/9 1/10 9/89 5/4 5/49 4/39 9/7 3/29 5/48 13/10 7/67 2/19 17/13 11/105 4/3 2/19 5/47 15/11 7/65 11/8 7/65 4/37 29/21 9/83 18/13 6/55 1/9 25/18 4/37 1/9 7/5 5/46 1/9 10/7 14/127 1/9 13/9 1/9 3/2 1/9 4/35 17/11 3/26 5/43 14/9 1/9 2/17 25/16 5/43 2/17 11/7 5/43 19/12 17/145 2/17 27/17 2/17 8/5 2/17 7/59 21/13 3/25 34/21 1/8 47/29 1/9 1/8 13/8 1/9 2/17 5/3 3/25 1/8 7/4 1/8 9/5 5/39 11/6 3/23 2/15 13/7 1/8 3/23 2/1 2/15 1/7 15/7 1/7 13/6 1/7 12/83 11/5 1/7 5/34 9/4 5/33 2/13 16/7 2/13 3/19 23/10 1/6 7/3 1/7 19/8 5/33 2/13 31/13 2/13 12/5 2/13 3/19 17/7 3/19 1/6 22/9 2/11 1/5 5/2 1/7 2/13 18/7 4/25 5/31 49/19 3/19 1/6 31/12 3/19 4/25 13/5 5/31 8/3 1/6 3/1 1/6 1/5 10/3 6/31 1/5 17/5 1/5 7/2 1/5 4/19 25/7 1/5 3/14 43/12 3/14 18/5 1/5 2/9 29/8 13/59 2/9 69/19 2/9 40/11 2/9 19/85 11/3 3/13 15/4 0/1 1/3 34/9 0/1 1/5 87/23 1/5 53/14 1/5 2/9 19/5 1/5 1/4 4/1 0/1 1/5 17/4 1/5 2/9 13/3 3/13 1/4 9/2 1/4 5/1 1/3 21/4 -1/1 0/1 37/7 0/1 16/3 0/1 1/7 11/2 1/5 2/9 17/3 1/4 3/11 6/1 2/7 1/3 19/3 1/3 13/2 1/3 4/11 7/1 1/3 1/2 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(59,-8,96,-13) (0/1,1/6) -> (11/18,8/13) Hyperbolic Matrix(187,-32,76,-13) (1/6,2/11) -> (22/9,5/2) Hyperbolic Matrix(409,-76,296,-55) (2/11,1/5) -> (29/21,18/13) Hyperbolic Matrix(90,-19,19,-4) (1/5,2/9) -> (9/2,5/1) Hyperbolic Matrix(234,-53,53,-12) (2/9,3/13) -> (13/3,9/2) Hyperbolic Matrix(107,-26,70,-17) (3/13,1/4) -> (3/2,17/11) Hyperbolic Matrix(157,-42,86,-23) (1/4,3/11) -> (9/5,11/6) Hyperbolic Matrix(449,-124,344,-95) (3/11,5/18) -> (13/10,17/13) Hyperbolic Matrix(499,-140,360,-101) (5/18,2/7) -> (18/13,25/18) Hyperbolic Matrix(51,-16,16,-5) (2/7,1/3) -> (3/1,10/3) Hyperbolic Matrix(48,-17,17,-6) (1/3,3/8) -> (8/3,3/1) Hyperbolic Matrix(208,-79,79,-30) (3/8,5/13) -> (13/5,8/3) Hyperbolic Matrix(127,-50,94,-37) (5/13,2/5) -> (4/3,15/11) Hyperbolic Matrix(187,-76,32,-13) (2/5,7/17) -> (17/3,6/1) Hyperbolic Matrix(343,-142,186,-77) (7/17,5/12) -> (11/6,13/7) Hyperbolic Matrix(217,-92,92,-39) (5/12,3/7) -> (7/3,19/8) Hyperbolic Matrix(245,-108,152,-67) (3/7,4/9) -> (8/5,21/13) Hyperbolic Matrix(107,-48,136,-61) (4/9,1/2) -> (11/14,4/5) Hyperbolic Matrix(157,-86,42,-23) (1/2,5/9) -> (11/3,15/4) Hyperbolic Matrix(126,-71,71,-40) (5/9,4/7) -> (7/4,9/5) Hyperbolic Matrix(70,-41,41,-24) (4/7,3/5) -> (5/3,7/4) Hyperbolic Matrix(191,-116,28,-17) (3/5,11/18) -> (13/2,7/1) Hyperbolic Matrix(245,-152,108,-67) (8/13,5/8) -> (9/4,16/7) Hyperbolic Matrix(297,-188,188,-119) (5/8,7/11) -> (11/7,19/12) Hyperbolic Matrix(523,-334,202,-129) (7/11,9/14) -> (31/12,13/5) Hyperbolic Matrix(107,-70,26,-17) (9/14,2/3) -> (4/1,17/4) Hyperbolic Matrix(91,-64,64,-45) (2/3,5/7) -> (7/5,10/7) Hyperbolic Matrix(499,-360,140,-101) (5/7,13/18) -> (7/2,25/7) Hyperbolic Matrix(409,-296,76,-55) (13/18,8/11) -> (16/3,11/2) Hyperbolic Matrix(127,-94,50,-37) (8/11,3/4) -> (5/2,18/7) Hyperbolic Matrix(449,-344,124,-95) (3/4,10/13) -> (18/5,29/8) Hyperbolic Matrix(347,-268,224,-173) (10/13,7/9) -> (17/11,14/9) Hyperbolic Matrix(271,-212,124,-97) (7/9,11/14) -> (13/6,11/5) Hyperbolic Matrix(327,-266,134,-109) (4/5,9/11) -> (17/7,22/9) Hyperbolic Matrix(132,-109,109,-90) (9/11,5/6) -> (6/5,11/9) Hyperbolic Matrix(12,-11,11,-10) (5/6,1/1) -> (1/1,6/5) Parabolic Matrix(167,-206,30,-37) (11/9,5/4) -> (11/2,17/3) Hyperbolic Matrix(107,-136,48,-61) (5/4,9/7) -> (11/5,9/4) Hyperbolic Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(553,-724,152,-199) (17/13,4/3) -> (40/11,11/3) Hyperbolic Matrix(363,-496,232,-317) (15/11,11/8) -> (25/16,11/7) Hyperbolic Matrix(481,-664,92,-127) (11/8,29/21) -> (5/1,21/4) Hyperbolic Matrix(911,-1266,562,-781) (25/18,7/5) -> (47/29,13/8) Hyperbolic Matrix(118,-169,81,-116) (10/7,13/9) -> (13/9,3/2) Parabolic Matrix(679,-1060,180,-281) (14/9,25/16) -> (15/4,34/9) Hyperbolic Matrix(460,-729,289,-458) (19/12,27/17) -> (27/17,8/5) Parabolic Matrix(446,-721,193,-312) (21/13,34/21) -> (23/10,7/3) Hyperbolic Matrix(1772,-2871,495,-802) (34/21,47/29) -> (25/7,43/12) Hyperbolic Matrix(59,-96,8,-13) (13/8,5/3) -> (7/1,1/0) Hyperbolic Matrix(175,-332,68,-129) (13/7,2/1) -> (18/7,49/19) Hyperbolic Matrix(106,-225,49,-104) (2/1,15/7) -> (15/7,13/6) Parabolic Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(404,-961,169,-402) (19/8,31/13) -> (31/13,12/5) Parabolic Matrix(123,-296,32,-77) (12/5,17/7) -> (19/5,4/1) Hyperbolic Matrix(1235,-3186,326,-841) (49/19,31/12) -> (53/14,19/5) Hyperbolic Matrix(86,-289,25,-84) (10/3,17/5) -> (17/5,7/2) Parabolic Matrix(1312,-4761,361,-1310) (29/8,69/19) -> (69/19,40/11) Parabolic Matrix(2002,-7569,529,-2000) (34/9,87/23) -> (87/23,53/14) Parabolic Matrix(260,-1369,49,-258) (21/4,37/7) -> (37/7,16/3) Parabolic Matrix(58,-361,9,-56) (6/1,19/3) -> (19/3,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,20,1) Matrix(59,-8,96,-13) -> Matrix(41,-2,554,-27) Matrix(187,-32,76,-13) -> Matrix(1,0,-12,1) Matrix(409,-76,296,-55) -> Matrix(67,-4,620,-37) Matrix(90,-19,19,-4) -> Matrix(37,-2,130,-7) Matrix(234,-53,53,-12) -> Matrix(107,-6,446,-25) Matrix(107,-26,70,-17) -> Matrix(69,-4,604,-35) Matrix(157,-42,86,-23) -> Matrix(37,-2,278,-15) Matrix(449,-124,344,-95) -> Matrix(279,-16,2668,-153) Matrix(499,-140,360,-101) -> Matrix(33,-2,314,-19) Matrix(51,-16,16,-5) -> Matrix(33,-2,182,-11) Matrix(48,-17,17,-6) -> Matrix(33,-2,182,-11) Matrix(208,-79,79,-30) -> Matrix(159,-10,970,-61) Matrix(127,-50,94,-37) -> Matrix(125,-8,1172,-75) Matrix(187,-76,32,-13) -> Matrix(1,0,-12,1) Matrix(343,-142,186,-77) -> Matrix(1,0,-8,1) Matrix(217,-92,92,-39) -> Matrix(61,-4,412,-27) Matrix(245,-108,152,-67) -> Matrix(63,-4,520,-33) Matrix(107,-48,136,-61) -> Matrix(153,-10,1882,-123) Matrix(157,-86,42,-23) -> Matrix(29,-2,102,-7) Matrix(126,-71,71,-40) -> Matrix(141,-10,1114,-79) Matrix(70,-41,41,-24) -> Matrix(83,-6,678,-49) Matrix(191,-116,28,-17) -> Matrix(55,-4,124,-9) Matrix(245,-152,108,-67) -> Matrix(55,-4,344,-25) Matrix(297,-188,188,-119) -> Matrix(269,-20,2300,-171) Matrix(523,-334,202,-129) -> Matrix(133,-10,838,-63) Matrix(107,-70,26,-17) -> Matrix(53,-4,252,-19) Matrix(91,-64,64,-45) -> Matrix(129,-10,1174,-91) Matrix(499,-360,140,-101) -> Matrix(25,-2,138,-11) Matrix(409,-296,76,-55) -> Matrix(51,-4,268,-21) Matrix(127,-94,50,-37) -> Matrix(101,-8,644,-51) Matrix(449,-344,124,-95) -> Matrix(199,-16,908,-73) Matrix(347,-268,224,-173) -> Matrix(199,-16,1704,-137) Matrix(271,-212,124,-97) -> Matrix(247,-20,1692,-137) Matrix(327,-266,134,-109) -> Matrix(73,-6,426,-35) Matrix(132,-109,109,-90) -> Matrix(217,-18,2158,-179) Matrix(12,-11,11,-10) -> Matrix(23,-2,242,-21) Matrix(167,-206,30,-37) -> Matrix(59,-6,246,-25) Matrix(107,-136,48,-61) -> Matrix(97,-10,650,-67) Matrix(249,-322,58,-75) -> Matrix(115,-12,508,-53) Matrix(553,-724,152,-199) -> Matrix(267,-28,1192,-125) Matrix(363,-496,232,-317) -> Matrix(55,-6,486,-53) Matrix(481,-664,92,-127) -> Matrix(37,-4,28,-3) Matrix(911,-1266,562,-781) -> Matrix(55,-6,486,-53) Matrix(118,-169,81,-116) -> Matrix(163,-18,1458,-161) Matrix(679,-1060,180,-281) -> Matrix(17,-2,94,-11) Matrix(460,-729,289,-458) -> Matrix(409,-48,3468,-407) Matrix(446,-721,193,-312) -> Matrix(17,-2,94,-11) Matrix(1772,-2871,495,-802) -> Matrix(19,-2,86,-9) Matrix(59,-96,8,-13) -> Matrix(17,-2,26,-3) Matrix(175,-332,68,-129) -> Matrix(47,-6,290,-37) Matrix(106,-225,49,-104) -> Matrix(99,-14,686,-97) Matrix(481,-1102,134,-307) -> Matrix(51,-8,236,-37) Matrix(404,-961,169,-402) -> Matrix(105,-16,676,-103) Matrix(123,-296,32,-77) -> Matrix(13,-2,46,-7) Matrix(1235,-3186,326,-841) -> Matrix(13,-2,46,-7) Matrix(86,-289,25,-84) -> Matrix(51,-10,250,-49) Matrix(1312,-4761,361,-1310) -> Matrix(289,-64,1296,-287) Matrix(2002,-7569,529,-2000) -> Matrix(11,-2,50,-9) Matrix(260,-1369,49,-258) -> Matrix(1,0,8,1) Matrix(58,-361,9,-56) -> Matrix(19,-6,54,-17) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 15 ----------------------------------------------------------------------- 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 20 1 1/1 1/11 2 11 6/5 1/10 10 2 11/9 (1/10,9/89) 0 11 5/4 (5/49,4/39) 0 22 9/7 (3/29,5/48) 0 11 13/10 (7/67,2/19) 0 22 4/3 (2/19,5/47) 0 22 11/8 (7/65,4/37) 0 22 18/13 (6/55,1/9) 0 22 7/5 (5/46,1/9) 0 11 13/9 1/9 18 1 3/2 (1/9,4/35) 0 22 14/9 (1/9,2/17) 0 22 11/7 5/43 2 11 27/17 2/17 12 1 8/5 (2/17,7/59) 0 22 13/8 (1/9,2/17) 0 22 5/3 (3/25,1/8) 0 11 7/4 1/8 8 2 9/5 5/39 2 11 2/1 (2/15,1/7) 0 22 15/7 1/7 14 1 11/5 (1/7,5/34) 0 11 9/4 (5/33,2/13) 0 22 16/7 (2/13,3/19) 0 22 23/10 1/6 2 2 7/3 1/7 2 11 31/13 2/13 4 1 12/5 (2/13,3/19) 0 22 17/7 (3/19,1/6) 0 11 5/2 (1/7,2/13) 0 22 18/7 (4/25,5/31) 0 22 31/12 (3/19,4/25) 0 22 13/5 5/31 2 11 8/3 1/6 6 2 3/1 (1/6,1/5) 0 11 17/5 1/5 10 1 7/2 (1/5,4/19) 0 22 25/7 (1/5,3/14) 0 11 43/12 3/14 2 2 18/5 (1/5,2/9) 0 22 29/8 (13/59,2/9) 0 22 69/19 2/9 16 1 11/3 3/13 2 11 15/4 (0/1,1/3) 0 22 34/9 (0/1,1/5) 0 22 87/23 1/5 2 1 19/5 (1/5,1/4) 0 11 4/1 (0/1,1/5) 0 22 17/4 (1/5,2/9) 0 22 13/3 (3/13,1/4) 0 11 9/2 1/4 4 2 5/1 1/3 2 11 37/7 0/1 8 1 16/3 (0/1,1/7) 0 22 11/2 (1/5,2/9) 0 22 17/3 (1/4,3/11) 0 11 6/1 (2/7,1/3) 0 22 19/3 1/3 6 1 7/1 (1/3,1/2) 0 11 1/0 (0/1,1/1) 0 22 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(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(11,-12,10,-11) (1/1,6/5) -> (1/1,6/5) Reflection Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(167,-206,30,-37) (11/9,5/4) -> (11/2,17/3) Hyperbolic Matrix(107,-136,48,-61) (5/4,9/7) -> (11/5,9/4) Hyperbolic Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(344,-449,95,-124) (13/10,4/3) -> (18/5,29/8) Glide Reflection Matrix(94,-127,37,-50) (4/3,11/8) -> (5/2,18/7) Glide Reflection Matrix(296,-409,55,-76) (11/8,18/13) -> (16/3,11/2) Glide Reflection Matrix(360,-499,101,-140) (18/13,7/5) -> (7/2,25/7) Glide Reflection Matrix(64,-91,45,-64) (7/5,13/9) -> (7/5,13/9) Reflection Matrix(53,-78,36,-53) (13/9,3/2) -> (13/9,3/2) Reflection Matrix(70,-107,17,-26) (3/2,14/9) -> (4/1,17/4) Glide Reflection Matrix(334,-523,129,-202) (14/9,11/7) -> (31/12,13/5) Glide Reflection Matrix(188,-297,119,-188) (11/7,27/17) -> (11/7,27/17) Reflection Matrix(271,-432,170,-271) (27/17,8/5) -> (27/17,8/5) Reflection Matrix(152,-245,67,-108) (8/5,13/8) -> (9/4,16/7) Glide Reflection Matrix(59,-96,8,-13) (13/8,5/3) -> (7/1,1/0) Hyperbolic Matrix(41,-70,24,-41) (5/3,7/4) -> (5/3,7/4) Reflection Matrix(71,-126,40,-71) (7/4,9/5) -> (7/4,9/5) Reflection Matrix(86,-157,23,-42) (9/5,2/1) -> (11/3,15/4) Glide Reflection Matrix(29,-60,14,-29) (2/1,15/7) -> (2/1,15/7) Reflection Matrix(76,-165,35,-76) (15/7,11/5) -> (15/7,11/5) Reflection Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(139,-322,60,-139) (23/10,7/3) -> (23/10,7/3) Reflection Matrix(92,-217,39,-92) (7/3,31/13) -> (7/3,31/13) Reflection Matrix(311,-744,130,-311) (31/13,12/5) -> (31/13,12/5) Reflection Matrix(123,-296,32,-77) (12/5,17/7) -> (19/5,4/1) Hyperbolic Matrix(76,-187,13,-32) (17/7,5/2) -> (17/3,6/1) Glide Reflection Matrix(418,-1077,111,-286) (18/7,31/12) -> (15/4,34/9) Glide Reflection Matrix(79,-208,30,-79) (13/5,8/3) -> (13/5,8/3) Reflection Matrix(17,-48,6,-17) (8/3,3/1) -> (8/3,3/1) Reflection Matrix(16,-51,5,-16) (3/1,17/5) -> (3/1,17/5) Reflection Matrix(69,-238,20,-69) (17/5,7/2) -> (17/5,7/2) Reflection Matrix(601,-2150,168,-601) (25/7,43/12) -> (25/7,43/12) Reflection Matrix(1103,-4002,304,-1103) (29/8,69/19) -> (29/8,69/19) Reflection Matrix(208,-759,57,-208) (69/19,11/3) -> (69/19,11/3) Reflection Matrix(1565,-5916,414,-1565) (34/9,87/23) -> (34/9,87/23) Reflection Matrix(436,-1653,115,-436) (87/23,19/5) -> (87/23,19/5) Reflection Matrix(53,-234,12,-53) (13/3,9/2) -> (13/3,9/2) Reflection Matrix(19,-90,4,-19) (9/2,5/1) -> (9/2,5/1) Reflection Matrix(36,-185,7,-36) (5/1,37/7) -> (5/1,37/7) Reflection Matrix(223,-1184,42,-223) (37/7,16/3) -> (37/7,16/3) Reflection Matrix(37,-228,6,-37) (6/1,19/3) -> (6/1,19/3) Reflection Matrix(20,-133,3,-20) (19/3,7/1) -> (19/3,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,2,-1) (-1/1,1/0) -> (0/1,1/1) Matrix(0,1,1,0) -> Matrix(1,0,22,-1) (-1/1,1/1) -> (0/1,1/11) Matrix(11,-12,10,-11) -> Matrix(21,-2,220,-21) (1/1,6/5) -> (1/11,1/10) Matrix(109,-132,90,-109) -> Matrix(179,-18,1780,-179) (6/5,11/9) -> (1/10,9/89) Matrix(167,-206,30,-37) -> Matrix(59,-6,246,-25) Matrix(107,-136,48,-61) -> Matrix(97,-10,650,-67) Matrix(249,-322,58,-75) -> Matrix(115,-12,508,-53) Matrix(344,-449,95,-124) -> Matrix(153,-16,698,-73) Matrix(94,-127,37,-50) -> Matrix(75,-8,478,-51) Matrix(296,-409,55,-76) -> Matrix(37,-4,194,-21) Matrix(360,-499,101,-140) -> Matrix(19,-2,104,-11) Matrix(64,-91,45,-64) -> Matrix(91,-10,828,-91) (7/5,13/9) -> (5/46,1/9) Matrix(53,-78,36,-53) -> Matrix(71,-8,630,-71) (13/9,3/2) -> (1/9,4/35) Matrix(70,-107,17,-26) -> Matrix(35,-4,166,-19) Matrix(334,-523,129,-202) -> Matrix(87,-10,548,-63) Matrix(188,-297,119,-188) -> Matrix(171,-20,1462,-171) (11/7,27/17) -> (5/43,2/17) Matrix(271,-432,170,-271) -> Matrix(237,-28,2006,-237) (27/17,8/5) -> (2/17,7/59) Matrix(152,-245,67,-108) -> Matrix(33,-4,206,-25) Matrix(59,-96,8,-13) -> Matrix(17,-2,26,-3) Matrix(41,-70,24,-41) -> Matrix(49,-6,400,-49) (5/3,7/4) -> (3/25,1/8) Matrix(71,-126,40,-71) -> Matrix(79,-10,624,-79) (7/4,9/5) -> (1/8,5/39) Matrix(86,-157,23,-42) -> Matrix(15,-2,52,-7) Matrix(29,-60,14,-29) -> Matrix(29,-4,210,-29) (2/1,15/7) -> (2/15,1/7) Matrix(76,-165,35,-76) -> Matrix(69,-10,476,-69) (15/7,11/5) -> (1/7,5/34) Matrix(481,-1102,134,-307) -> Matrix(51,-8,236,-37) Matrix(139,-322,60,-139) -> Matrix(13,-2,84,-13) (23/10,7/3) -> (1/7,1/6) Matrix(92,-217,39,-92) -> Matrix(27,-4,182,-27) (7/3,31/13) -> (1/7,2/13) Matrix(311,-744,130,-311) -> Matrix(77,-12,494,-77) (31/13,12/5) -> (2/13,3/19) Matrix(123,-296,32,-77) -> Matrix(13,-2,46,-7) Matrix(76,-187,13,-32) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(418,-1077,111,-286) -> Matrix(25,-4,106,-17) Matrix(79,-208,30,-79) -> Matrix(61,-10,372,-61) (13/5,8/3) -> (5/31,1/6) Matrix(17,-48,6,-17) -> Matrix(11,-2,60,-11) (8/3,3/1) -> (1/6,1/5) Matrix(16,-51,5,-16) -> Matrix(11,-2,60,-11) (3/1,17/5) -> (1/6,1/5) Matrix(69,-238,20,-69) -> Matrix(39,-8,190,-39) (17/5,7/2) -> (1/5,4/19) Matrix(601,-2150,168,-601) -> Matrix(29,-6,140,-29) (25/7,43/12) -> (1/5,3/14) Matrix(1103,-4002,304,-1103) -> Matrix(235,-52,1062,-235) (29/8,69/19) -> (13/59,2/9) Matrix(208,-759,57,-208) -> Matrix(53,-12,234,-53) (69/19,11/3) -> (2/9,3/13) Matrix(1565,-5916,414,-1565) -> Matrix(1,0,10,-1) (34/9,87/23) -> (0/1,1/5) Matrix(436,-1653,115,-436) -> Matrix(9,-2,40,-9) (87/23,19/5) -> (1/5,1/4) Matrix(53,-234,12,-53) -> Matrix(25,-6,104,-25) (13/3,9/2) -> (3/13,1/4) Matrix(19,-90,4,-19) -> Matrix(7,-2,24,-7) (9/2,5/1) -> (1/4,1/3) Matrix(36,-185,7,-36) -> Matrix(1,0,6,-1) (5/1,37/7) -> (0/1,1/3) Matrix(223,-1184,42,-223) -> Matrix(1,0,14,-1) (37/7,16/3) -> (0/1,1/7) Matrix(37,-228,6,-37) -> Matrix(13,-4,42,-13) (6/1,19/3) -> (2/7,1/3) Matrix(20,-133,3,-20) -> Matrix(5,-2,12,-5) (19/3,7/1) -> (1/3,1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.