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 -1/2 1/0 -1/2 -1/1 0/1 -6/13 -1/1 -4/5 -11/24 -1/1 -2/3 -5/11 -2/3 -4/9 -1/1 0/1 -11/25 0/1 -18/41 -1/1 -2/3 -7/16 -1/1 0/1 -3/7 -1/1 -1/2 -5/12 -2/5 -1/3 -17/41 -1/2 -1/3 -12/29 -1/3 0/1 -7/17 0/1 -9/22 -1/3 0/1 -2/5 -1/1 0/1 -5/13 -1/2 -1/3 -18/47 -1/3 -4/13 -13/34 -1/3 0/1 -8/21 -1/3 0/1 -11/29 0/1 -14/37 -1/3 -4/13 -3/8 -1/5 0/1 -7/19 0/1 1/2 -18/49 0/1 1/1 -11/30 0/1 1/1 -4/11 -1/1 0/1 -13/36 -2/1 -1/1 -9/25 -1/2 0/1 -14/39 0/1 1/1 -5/14 -1/1 0/1 -1/3 0/1 -4/13 -1/1 0/1 -7/23 0/1 1/0 -10/33 -1/1 -2/3 -13/43 0/1 -3/10 -1/1 0/1 -8/27 -1/3 0/1 -21/71 0/1 -13/44 -1/3 0/1 -18/61 -1/3 -2/7 -5/17 -1/4 0/1 -7/24 -1/11 0/1 -2/7 0/1 1/3 -9/32 4/5 1/1 -7/25 0/1 -12/43 0/1 1/1 -5/18 0/1 1/1 -13/47 0/1 -8/29 0/1 1/1 -3/11 1/1 1/0 -1/4 -1/1 0/1 -6/25 0/1 1/5 -5/21 0/1 1/2 -4/17 0/1 1/1 -7/30 0/1 1/1 -3/13 0/1 -8/35 0/1 1/1 -5/22 0/1 1/1 -7/31 1/1 1/0 -2/9 1/1 2/1 -1/5 -1/1 1/0 -3/16 -2/1 -1/1 -2/11 -1/1 0/1 -7/39 0/1 1/0 -5/28 -2/1 -1/1 -8/45 -1/1 0/1 -11/62 -1/1 0/1 -3/17 0/1 -1/6 -1/1 0/1 -1/7 -2/1 -4/29 -2/1 -1/1 -3/22 -2/1 -1/1 -2/15 -2/1 -1/1 -1/8 -4/3 -1/1 -2/17 -1/1 -6/7 -1/9 -1/1 -1/2 0/1 -1/1 0/1 1/6 -1/1 -4/5 2/11 -1/1 -2/3 1/5 -2/3 3/14 -3/5 -4/7 2/9 -1/2 5/22 -5/11 -4/9 8/35 -3/7 -8/19 3/13 -1/2 -2/5 1/4 -1/1 0/1 3/11 0/1 5/18 -1/1 -2/3 2/7 -1/1 0/1 1/3 -1/1 -1/2 4/11 -3/5 -4/7 3/8 -1/2 8/21 -7/15 -6/13 13/34 -6/13 -5/11 18/47 -5/11 -24/53 5/13 -4/9 2/5 -2/5 -1/3 7/17 -1/2 -1/3 5/12 -1/3 0/1 3/7 0/1 4/9 -1/3 0/1 1/2 -1/1 0/1 5/9 -2/3 4/7 -1/2 11/19 -4/9 18/31 -4/9 -3/7 25/43 -7/16 -3/7 32/55 -3/7 -20/47 7/12 -3/7 -2/5 3/5 -1/2 -1/3 11/18 -1/3 -4/13 8/13 -1/3 0/1 5/8 -1/3 0/1 7/11 0/1 9/14 -1/3 -4/13 2/3 -1/5 0/1 5/7 0/1 1/2 13/18 0/1 1/1 8/11 0/1 1/1 3/4 -1/1 0/1 10/13 -2/1 -1/1 7/9 -1/2 0/1 11/14 0/1 1/1 4/5 -1/1 0/1 9/11 -1/1 -1/2 5/6 -1/2 11/13 -1/2 -1/3 17/20 -2/5 -1/3 6/7 -1/3 0/1 1/1 0/1 7/6 0/1 1/1 6/5 1/0 17/14 -2/1 -1/1 28/23 -1/1 0/1 11/9 -1/1 1/0 5/4 -1/1 0/1 9/7 0/1 1/0 13/10 -1/1 -2/3 17/13 0/1 4/3 -1/1 0/1 15/11 -2/5 11/8 -1/3 0/1 29/21 0/1 18/13 -1/3 0/1 25/18 -1/3 -2/7 7/5 -1/4 0/1 10/7 -1/11 0/1 13/9 0/1 16/11 0/1 1/17 3/2 0/1 1/3 17/11 1/2 2/3 14/9 4/5 1/1 25/16 1/1 2/1 11/7 0/1 19/12 0/1 1/1 27/17 1/2 1/0 35/22 0/1 1/1 8/5 0/1 1/1 21/13 0/1 55/34 0/1 1/3 34/21 1/2 81/50 4/7 3/5 47/29 1/2 2/3 13/8 0/1 1/1 5/3 1/1 1/0 12/7 2/1 3/1 7/4 1/0 16/9 -4/1 -3/1 41/23 -3/1 -5/2 25/14 -3/1 -2/1 9/5 -2/1 11/6 -2/1 -1/1 13/7 -3/2 -1/1 2/1 -1/1 0/1 15/7 0/1 28/13 0/1 1/11 13/6 0/1 1/5 11/5 0/1 1/2 9/4 0/1 1/1 16/7 0/1 1/1 23/10 1/0 30/13 -1/1 0/1 7/3 0/1 19/8 0/1 1/1 31/13 1/2 1/0 43/18 0/1 1/1 12/5 0/1 1/1 17/7 1/1 1/0 22/9 0/1 1/1 5/2 1/1 2/1 18/7 2/1 3/1 49/19 11/4 3/1 31/12 3/1 16/5 13/5 4/1 8/3 1/0 19/7 -6/1 49/18 -26/5 -5/1 128/47 -5/1 -64/13 79/29 -5/1 -19/4 30/11 -5/1 -4/1 11/4 -4/1 -3/1 3/1 -1/1 1/0 10/3 -2/1 -1/1 17/5 -1/1 24/7 -1/1 -2/3 7/2 -1/1 0/1 25/7 0/1 1/0 68/19 1/1 2/1 43/12 1/0 18/5 -2/1 -1/1 29/8 -1/1 0/1 69/19 -1/2 1/0 109/30 -1/1 0/1 40/11 -1/1 0/1 11/3 0/1 15/4 -2/1 -1/1 34/9 -8/7 -1/1 87/23 -1/1 140/37 -1/1 -28/29 53/14 -1/1 -10/11 19/5 -1/1 -1/2 4/1 -1/1 0/1 17/4 1/1 4/3 13/3 2/1 1/0 9/2 1/0 23/5 -6/1 1/0 37/8 -16/3 -5/1 14/3 -4/1 -3/1 5/1 -2/1 21/4 -2/1 -1/1 37/7 -3/2 1/0 53/10 -2/1 -1/1 16/3 -2/1 -1/1 11/2 -2/1 -1/1 17/3 -3/2 -1/1 6/1 -4/3 -1/1 19/3 -1/1 32/5 -1/1 -16/17 13/2 -1/1 -6/7 7/1 -1/1 -1/2 1/0 -1/1 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(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(1,0,0,1) Matrix(205,96,-536,-251) -> Matrix(1,0,-2,1) Matrix(893,410,734,337) -> Matrix(5,4,-4,-3) Matrix(647,296,-2188,-1001) -> Matrix(3,2,-8,-5) Matrix(199,90,42,19) -> Matrix(7,4,-2,-1) Matrix(549,242,946,417) -> Matrix(7,4,-16,-9) Matrix(783,344,-2588,-1137) -> Matrix(1,0,0,1) Matrix(821,360,-2780,-1219) -> Matrix(1,0,-2,1) Matrix(37,16,-192,-83) -> Matrix(3,2,-2,-1) Matrix(113,48,40,17) -> Matrix(3,2,-2,-1) Matrix(829,344,976,405) -> Matrix(1,0,0,1) Matrix(1463,606,2518,1043) -> Matrix(15,4,-34,-9) Matrix(223,92,-972,-401) -> Matrix(1,0,4,1) Matrix(371,152,-1340,-549) -> Matrix(1,0,4,1) Matrix(333,136,-928,-379) -> Matrix(1,0,2,1) Matrix(181,70,106,41) -> Matrix(5,2,2,1) Matrix(73,28,-644,-247) -> Matrix(5,2,-8,-3) Matrix(283,108,-1208,-461) -> Matrix(1,0,4,1) Matrix(495,188,-1772,-673) -> Matrix(1,0,4,1) Matrix(707,268,1844,699) -> Matrix(7,4,-16,-9) Matrix(249,94,1094,413) -> Matrix(15,4,-34,-9) Matrix(173,64,-592,-219) -> Matrix(1,0,-6,1) Matrix(381,140,-2120,-779) -> Matrix(1,0,-2,1) Matrix(207,76,-1528,-561) -> Matrix(1,-2,0,1) Matrix(383,140,1004,367) -> Matrix(1,-6,-2,13) Matrix(343,124,-1928,-697) -> Matrix(1,0,0,1) Matrix(1753,632,380,137) -> Matrix(11,6,-2,-1) Matrix(345,124,-1444,-519) -> Matrix(1,0,4,1) Matrix(35,12,32,11) -> Matrix(1,0,2,1) Matrix(31,10,34,11) -> Matrix(1,0,-2,1) Matrix(157,48,-664,-203) -> Matrix(1,0,2,1) Matrix(283,86,1234,375) -> Matrix(1,-2,-2,5) Matrix(503,152,-2836,-857) -> Matrix(1,0,0,1) Matrix(597,178,218,65) -> Matrix(7,4,-2,-1) Matrix(311,92,-2248,-665) -> Matrix(7,2,-4,-1) Matrix(2681,790,750,221) -> Matrix(1,0,4,1) Matrix(405,118,278,81) -> Matrix(1,0,14,1) Matrix(707,200,152,43) -> Matrix(9,-4,-2,1) Matrix(1833,514,674,189) -> Matrix(1,-6,0,1) Matrix(1649,460,1036,289) -> Matrix(1,0,0,1) Matrix(1613,446,698,193) -> Matrix(1,0,-2,1) Matrix(29,8,-272,-75) -> Matrix(1,0,-2,1) Matrix(89,24,152,41) -> Matrix(1,-2,-2,5) Matrix(437,106,202,49) -> Matrix(1,0,6,1) Matrix(1345,312,832,193) -> Matrix(1,0,2,1) Matrix(1769,404,740,169) -> Matrix(1,0,0,1) Matrix(1677,380,940,213) -> Matrix(5,-2,-2,1) Matrix(967,218,794,179) -> Matrix(1,-2,0,1) Matrix(29,6,82,17) -> Matrix(1,2,-2,-3) Matrix(461,86,134,25) -> Matrix(1,2,-2,-3) Matrix(4475,802,2762,495) -> Matrix(1,-2,2,-3) Matrix(7385,1312,2032,361) -> Matrix(1,0,0,1) Matrix(479,84,268,47) -> Matrix(1,-2,0,1) Matrix(27,4,128,19) -> Matrix(1,4,-2,-7) Matrix(1889,260,356,49) -> Matrix(1,0,0,1) Matrix(303,40,356,47) -> Matrix(1,2,-4,-7) Matrix(477,58,74,9) -> Matrix(9,10,-10,-11) Matrix(59,-8,96,-13) -> Matrix(1,0,-2,1) Matrix(187,-32,76,-13) -> Matrix(3,2,4,3) Matrix(409,-76,296,-55) -> Matrix(3,2,-8,-5) Matrix(73,-16,324,-71) -> Matrix(15,8,-32,-17) Matrix(107,-26,70,-17) -> Matrix(1,0,4,1) Matrix(157,-42,86,-23) -> Matrix(3,2,-2,-1) Matrix(449,-124,344,-95) -> Matrix(1,0,0,1) Matrix(499,-140,360,-101) -> Matrix(1,0,-2,1) Matrix(51,-16,16,-5) -> Matrix(3,2,-2,-1) Matrix(97,-36,256,-95) -> Matrix(19,10,-40,-21) Matrix(1417,-542,2434,-931) -> Matrix(61,28,-146,-67) Matrix(127,-50,94,-37) -> Matrix(5,2,-8,-3) Matrix(187,-76,32,-13) -> Matrix(7,2,-4,-1) Matrix(343,-142,186,-77) -> Matrix(7,2,-4,-1) Matrix(217,-92,92,-39) -> Matrix(1,0,4,1) Matrix(245,-108,152,-67) -> Matrix(1,0,4,1) Matrix(107,-48,136,-61) -> Matrix(1,0,2,1) Matrix(157,-86,42,-23) -> Matrix(3,2,-2,-1) Matrix(113,-64,196,-111) -> Matrix(11,6,-24,-13) Matrix(9849,-5728,3616,-2103) -> Matrix(213,92,-44,-19) Matrix(191,-116,28,-17) -> Matrix(5,2,-8,-3) Matrix(245,-152,108,-67) -> Matrix(1,0,4,1) Matrix(297,-188,188,-119) -> Matrix(1,0,4,1) Matrix(523,-334,202,-129) -> Matrix(9,4,2,1) Matrix(107,-70,26,-17) -> Matrix(1,0,4,1) Matrix(91,-64,64,-45) -> Matrix(1,0,-6,1) Matrix(499,-360,140,-101) -> Matrix(1,0,-2,1) Matrix(409,-296,76,-55) -> Matrix(1,-2,0,1) Matrix(127,-94,50,-37) -> Matrix(1,2,0,1) Matrix(449,-344,124,-95) -> Matrix(1,0,0,1) Matrix(347,-268,224,-173) -> Matrix(3,2,4,3) Matrix(271,-212,124,-97) -> Matrix(1,0,4,1) Matrix(327,-266,134,-109) -> Matrix(1,0,2,1) Matrix(121,-100,144,-119) -> Matrix(3,2,-8,-5) Matrix(121,-144,100,-119) -> Matrix(1,-2,0,1) Matrix(167,-206,30,-37) -> Matrix(3,2,-2,-1) Matrix(107,-136,48,-61) -> Matrix(1,0,2,1) Matrix(249,-322,58,-75) -> Matrix(1,2,0,1) Matrix(553,-724,152,-199) -> Matrix(1,0,0,1) Matrix(363,-496,232,-317) -> Matrix(5,2,2,1) Matrix(481,-664,92,-127) -> Matrix(7,2,-4,-1) Matrix(911,-1266,562,-781) -> Matrix(7,2,10,3) Matrix(235,-338,162,-233) -> Matrix(1,0,28,1) Matrix(679,-1060,180,-281) -> Matrix(3,-4,-2,3) Matrix(919,-1458,578,-917) -> Matrix(1,0,0,1) Matrix(2857,-4624,1764,-2855) -> Matrix(9,-4,16,-7) Matrix(59,-96,8,-13) -> Matrix(1,0,-2,1) Matrix(113,-196,64,-111) -> Matrix(1,-6,0,1) Matrix(1401,-2494,514,-915) -> Matrix(9,32,-2,-7) Matrix(175,-332,68,-129) -> Matrix(5,2,2,1) Matrix(211,-450,98,-209) -> Matrix(1,0,12,1) Matrix(481,-1102,134,-307) -> Matrix(1,-2,0,1) Matrix(1239,-2854,346,-797) -> Matrix(1,2,0,1) Matrix(807,-1922,338,-805) -> Matrix(1,0,0,1) Matrix(123,-296,32,-77) -> Matrix(1,0,-2,1) Matrix(1235,-3186,326,-841) -> Matrix(5,-14,-6,17) Matrix(97,-256,36,-95) -> Matrix(1,-10,0,1) Matrix(5011,-13644,1324,-3605) -> Matrix(15,76,-16,-81) Matrix(171,-578,50,-169) -> Matrix(3,4,-4,-5) Matrix(2623,-9522,722,-2621) -> Matrix(1,0,0,1) Matrix(4003,-15138,1058,-4001) -> Matrix(35,36,-36,-37) Matrix(73,-324,16,-71) -> Matrix(1,-8,0,1) Matrix(519,-2738,98,-517) -> Matrix(1,0,0,1) Matrix(115,-722,18,-113) -> Matrix(19,20,-20,-21) 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): 30 Degree of the the map X: 30 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 -1/2 1/0 0/1 -1/1 0/1 1/6 -1/1 -4/5 2/11 -1/1 -2/3 1/5 -2/3 2/9 -1/2 3/13 -1/2 -2/5 1/4 -1/1 0/1 3/11 0/1 5/18 -1/1 -2/3 2/7 -1/1 0/1 1/3 -1/1 -1/2 3/8 -1/2 5/13 -4/9 2/5 -2/5 -1/3 7/17 -1/2 -1/3 5/12 -1/3 0/1 3/7 0/1 4/9 -1/3 0/1 1/2 -1/1 0/1 5/9 -2/3 4/7 -1/2 3/5 -1/2 -1/3 11/18 -1/3 -4/13 8/13 -1/3 0/1 5/8 -1/3 0/1 7/11 0/1 9/14 -1/3 -4/13 2/3 -1/5 0/1 5/7 0/1 1/2 13/18 0/1 1/1 8/11 0/1 1/1 3/4 -1/1 0/1 10/13 -2/1 -1/1 7/9 -1/2 0/1 11/14 0/1 1/1 4/5 -1/1 0/1 9/11 -1/1 -1/2 5/6 -1/2 1/1 0/1 6/5 1/0 11/9 -1/1 1/0 5/4 -1/1 0/1 9/7 0/1 1/0 13/10 -1/1 -2/3 17/13 0/1 4/3 -1/1 0/1 15/11 -2/5 11/8 -1/3 0/1 29/21 0/1 18/13 -1/3 0/1 25/18 -1/3 -2/7 7/5 -1/4 0/1 10/7 -1/11 0/1 13/9 0/1 3/2 0/1 1/3 17/11 1/2 2/3 14/9 4/5 1/1 25/16 1/1 2/1 11/7 0/1 19/12 0/1 1/1 27/17 1/2 1/0 8/5 0/1 1/1 21/13 0/1 34/21 1/2 47/29 1/2 2/3 13/8 0/1 1/1 5/3 1/1 1/0 7/4 1/0 9/5 -2/1 11/6 -2/1 -1/1 13/7 -3/2 -1/1 2/1 -1/1 0/1 15/7 0/1 13/6 0/1 1/5 11/5 0/1 1/2 9/4 0/1 1/1 16/7 0/1 1/1 23/10 1/0 7/3 0/1 19/8 0/1 1/1 31/13 1/2 1/0 12/5 0/1 1/1 17/7 1/1 1/0 22/9 0/1 1/1 5/2 1/1 2/1 18/7 2/1 3/1 49/19 11/4 3/1 31/12 3/1 16/5 13/5 4/1 8/3 1/0 3/1 -1/1 1/0 10/3 -2/1 -1/1 17/5 -1/1 7/2 -1/1 0/1 25/7 0/1 1/0 43/12 1/0 18/5 -2/1 -1/1 29/8 -1/1 0/1 69/19 -1/2 1/0 40/11 -1/1 0/1 11/3 0/1 15/4 -2/1 -1/1 34/9 -8/7 -1/1 87/23 -1/1 53/14 -1/1 -10/11 19/5 -1/1 -1/2 4/1 -1/1 0/1 17/4 1/1 4/3 13/3 2/1 1/0 9/2 1/0 5/1 -2/1 21/4 -2/1 -1/1 37/7 -3/2 1/0 16/3 -2/1 -1/1 11/2 -2/1 -1/1 17/3 -3/2 -1/1 6/1 -4/3 -1/1 19/3 -1/1 13/2 -1/1 -6/7 7/1 -1/1 -1/2 1/0 -1/1 0/1 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(1,0,0,1) Matrix(59,-8,96,-13) -> Matrix(1,0,-2,1) Matrix(187,-32,76,-13) -> Matrix(3,2,4,3) Matrix(409,-76,296,-55) -> Matrix(3,2,-8,-5) Matrix(90,-19,19,-4) -> Matrix(7,4,-2,-1) Matrix(234,-53,53,-12) -> Matrix(9,4,2,1) Matrix(107,-26,70,-17) -> Matrix(1,0,4,1) Matrix(157,-42,86,-23) -> Matrix(3,2,-2,-1) Matrix(449,-124,344,-95) -> Matrix(1,0,0,1) Matrix(499,-140,360,-101) -> Matrix(1,0,-2,1) Matrix(51,-16,16,-5) -> Matrix(3,2,-2,-1) Matrix(48,-17,17,-6) -> Matrix(3,2,-2,-1) Matrix(208,-79,79,-30) -> Matrix(17,8,2,1) Matrix(127,-50,94,-37) -> Matrix(5,2,-8,-3) Matrix(187,-76,32,-13) -> Matrix(7,2,-4,-1) Matrix(343,-142,186,-77) -> Matrix(7,2,-4,-1) Matrix(217,-92,92,-39) -> Matrix(1,0,4,1) Matrix(245,-108,152,-67) -> Matrix(1,0,4,1) Matrix(107,-48,136,-61) -> Matrix(1,0,2,1) Matrix(157,-86,42,-23) -> Matrix(3,2,-2,-1) Matrix(126,-71,71,-40) -> Matrix(7,4,-2,-1) Matrix(70,-41,41,-24) -> Matrix(5,2,2,1) Matrix(191,-116,28,-17) -> Matrix(5,2,-8,-3) Matrix(245,-152,108,-67) -> Matrix(1,0,4,1) Matrix(297,-188,188,-119) -> Matrix(1,0,4,1) Matrix(523,-334,202,-129) -> Matrix(9,4,2,1) Matrix(107,-70,26,-17) -> Matrix(1,0,4,1) Matrix(91,-64,64,-45) -> Matrix(1,0,-6,1) Matrix(499,-360,140,-101) -> Matrix(1,0,-2,1) Matrix(409,-296,76,-55) -> Matrix(1,-2,0,1) Matrix(127,-94,50,-37) -> Matrix(1,2,0,1) Matrix(449,-344,124,-95) -> Matrix(1,0,0,1) Matrix(347,-268,224,-173) -> Matrix(3,2,4,3) Matrix(271,-212,124,-97) -> Matrix(1,0,4,1) Matrix(327,-266,134,-109) -> Matrix(1,0,2,1) Matrix(132,-109,109,-90) -> Matrix(3,2,-2,-1) Matrix(12,-11,11,-10) -> Matrix(1,0,2,1) Matrix(167,-206,30,-37) -> Matrix(3,2,-2,-1) Matrix(107,-136,48,-61) -> Matrix(1,0,2,1) Matrix(249,-322,58,-75) -> Matrix(1,2,0,1) Matrix(553,-724,152,-199) -> Matrix(1,0,0,1) Matrix(363,-496,232,-317) -> Matrix(5,2,2,1) Matrix(481,-664,92,-127) -> Matrix(7,2,-4,-1) Matrix(911,-1266,562,-781) -> Matrix(7,2,10,3) Matrix(118,-169,81,-116) -> Matrix(1,0,14,1) Matrix(679,-1060,180,-281) -> Matrix(3,-4,-2,3) Matrix(460,-729,289,-458) -> Matrix(1,0,0,1) Matrix(446,-721,193,-312) -> Matrix(1,0,-2,1) Matrix(1772,-2871,495,-802) -> Matrix(3,-2,2,-1) Matrix(59,-96,8,-13) -> Matrix(1,0,-2,1) Matrix(175,-332,68,-129) -> Matrix(5,2,2,1) Matrix(106,-225,49,-104) -> Matrix(1,0,6,1) Matrix(481,-1102,134,-307) -> Matrix(1,-2,0,1) Matrix(404,-961,169,-402) -> Matrix(1,0,0,1) Matrix(123,-296,32,-77) -> Matrix(1,0,-2,1) Matrix(1235,-3186,326,-841) -> Matrix(5,-14,-6,17) Matrix(86,-289,25,-84) -> Matrix(1,2,-2,-3) Matrix(1312,-4761,361,-1310) -> Matrix(1,0,0,1) Matrix(2002,-7569,529,-2000) -> Matrix(17,18,-18,-19) Matrix(260,-1369,49,-258) -> Matrix(1,0,0,1) Matrix(58,-361,9,-56) -> Matrix(9,10,-10,-11) 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): 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 (-1/1,0/1) 0 1 1/1 0/1 2 11 6/5 1/0 1 2 11/9 (-1/1,1/0) 0 11 5/4 (-1/1,0/1) 0 22 9/7 (0/1,1/0) 0 11 13/10 (-1/1,-2/3) 0 22 4/3 (-1/1,0/1) 0 22 11/8 (-1/3,0/1) 0 22 18/13 (-1/3,0/1) 0 22 7/5 (-1/4,0/1) 0 11 13/9 0/1 14 1 3/2 (0/1,1/3) 0 22 14/9 (4/5,1/1) 0 22 11/7 0/1 2 11 27/17 (0/1,1/1) 0 1 8/5 (0/1,1/1) 0 22 13/8 (0/1,1/1) 0 22 5/3 (1/1,1/0) 0 11 7/4 1/0 3 2 9/5 -2/1 2 11 2/1 (-1/1,0/1) 0 22 15/7 0/1 6 1 11/5 (0/1,1/2) 0 11 9/4 (0/1,1/1) 0 22 16/7 (0/1,1/1) 0 22 23/10 1/0 2 2 7/3 0/1 2 11 31/13 (0/1,1/1) 0 1 12/5 (0/1,1/1) 0 22 17/7 (1/1,1/0) 0 11 5/2 (1/1,2/1) 0 22 18/7 (2/1,3/1) 0 22 31/12 (3/1,16/5) 0 22 13/5 4/1 2 11 8/3 1/0 5 2 3/1 (-1/1,1/0) 0 11 17/5 -1/1 2 1 7/2 (-1/1,0/1) 0 22 25/7 (0/1,1/0) 0 11 43/12 1/0 2 2 18/5 (-2/1,-1/1) 0 22 29/8 (-1/1,0/1) 0 22 69/19 (-1/1,0/1) 0 1 11/3 0/1 2 11 15/4 (-2/1,-1/1) 0 22 34/9 (-8/7,-1/1) 0 22 87/23 -1/1 18 1 19/5 (-1/1,-1/2) 0 11 4/1 (-1/1,0/1) 0 22 17/4 (1/1,4/3) 0 22 13/3 (2/1,1/0) 0 11 9/2 1/0 4 2 5/1 -2/1 2 11 37/7 (-2/1,-1/1) 0 1 16/3 (-2/1,-1/1) 0 22 11/2 (-2/1,-1/1) 0 22 17/3 (-3/2,-1/1) 0 11 6/1 (-4/3,-1/1) 0 22 19/3 -1/1 10 1 7/1 (-1/1,-1/2) 0 11 1/0 (-1/1,0/1) 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) -> (-1/1,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,2,1) (-1/1,1/1) -> (-1/1,0/1) Matrix(11,-12,10,-11) -> Matrix(1,0,0,-1) (1/1,6/5) -> (0/1,1/0) Matrix(109,-132,90,-109) -> Matrix(1,2,0,-1) (6/5,11/9) -> (-1/1,1/0) Matrix(167,-206,30,-37) -> Matrix(3,2,-2,-1) -1/1 Matrix(107,-136,48,-61) -> Matrix(1,0,2,1) 0/1 Matrix(249,-322,58,-75) -> Matrix(1,2,0,1) 1/0 Matrix(344,-449,95,-124) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(94,-127,37,-50) -> Matrix(3,2,2,1) Matrix(296,-409,55,-76) -> Matrix(5,2,-2,-1) Matrix(360,-499,101,-140) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(64,-91,45,-64) -> Matrix(-1,0,8,1) (7/5,13/9) -> (-1/4,0/1) Matrix(53,-78,36,-53) -> Matrix(1,0,6,-1) (13/9,3/2) -> (0/1,1/3) Matrix(70,-107,17,-26) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(334,-523,129,-202) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(188,-297,119,-188) -> Matrix(1,0,2,-1) (11/7,27/17) -> (0/1,1/1) Matrix(271,-432,170,-271) -> Matrix(1,0,2,-1) (27/17,8/5) -> (0/1,1/1) Matrix(152,-245,67,-108) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(59,-96,8,-13) -> Matrix(1,0,-2,1) 0/1 Matrix(41,-70,24,-41) -> Matrix(-1,2,0,1) (5/3,7/4) -> (1/1,1/0) Matrix(71,-126,40,-71) -> Matrix(1,4,0,-1) (7/4,9/5) -> (-2/1,1/0) Matrix(86,-157,23,-42) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(29,-60,14,-29) -> Matrix(-1,0,2,1) (2/1,15/7) -> (-1/1,0/1) Matrix(76,-165,35,-76) -> Matrix(1,0,4,-1) (15/7,11/5) -> (0/1,1/2) Matrix(481,-1102,134,-307) -> Matrix(1,-2,0,1) 1/0 Matrix(139,-322,60,-139) -> Matrix(1,0,0,-1) (23/10,7/3) -> (0/1,1/0) Matrix(92,-217,39,-92) -> Matrix(1,0,2,-1) (7/3,31/13) -> (0/1,1/1) Matrix(311,-744,130,-311) -> Matrix(1,0,2,-1) (31/13,12/5) -> (0/1,1/1) Matrix(123,-296,32,-77) -> Matrix(1,0,-2,1) 0/1 Matrix(76,-187,13,-32) -> Matrix(3,-2,-2,1) Matrix(418,-1077,111,-286) -> Matrix(3,-8,-2,5) Matrix(79,-208,30,-79) -> Matrix(-1,8,0,1) (13/5,8/3) -> (4/1,1/0) Matrix(17,-48,6,-17) -> Matrix(1,2,0,-1) (8/3,3/1) -> (-1/1,1/0) Matrix(16,-51,5,-16) -> Matrix(1,2,0,-1) (3/1,17/5) -> (-1/1,1/0) Matrix(69,-238,20,-69) -> Matrix(-1,0,2,1) (17/5,7/2) -> (-1/1,0/1) Matrix(601,-2150,168,-601) -> Matrix(1,0,0,-1) (25/7,43/12) -> (0/1,1/0) Matrix(1103,-4002,304,-1103) -> Matrix(-1,0,2,1) (29/8,69/19) -> (-1/1,0/1) Matrix(208,-759,57,-208) -> Matrix(-1,0,2,1) (69/19,11/3) -> (-1/1,0/1) Matrix(1565,-5916,414,-1565) -> Matrix(15,16,-14,-15) (34/9,87/23) -> (-8/7,-1/1) Matrix(436,-1653,115,-436) -> Matrix(3,2,-4,-3) (87/23,19/5) -> (-1/1,-1/2) Matrix(53,-234,12,-53) -> Matrix(-1,4,0,1) (13/3,9/2) -> (2/1,1/0) Matrix(19,-90,4,-19) -> Matrix(1,4,0,-1) (9/2,5/1) -> (-2/1,1/0) Matrix(36,-185,7,-36) -> Matrix(3,4,-2,-3) (5/1,37/7) -> (-2/1,-1/1) Matrix(223,-1184,42,-223) -> Matrix(3,4,-2,-3) (37/7,16/3) -> (-2/1,-1/1) Matrix(37,-228,6,-37) -> Matrix(7,8,-6,-7) (6/1,19/3) -> (-4/3,-1/1) Matrix(20,-133,3,-20) -> Matrix(3,2,-4,-3) (19/3,7/1) -> (-1/1,-1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.