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 1/19 -6/13 1/17 2/33 -11/24 2/31 1/15 -5/11 1/17 -4/9 0/1 1/15 -11/25 3/47 -18/41 2/31 1/15 -7/16 4/61 1/15 -3/7 1/15 1/14 -5/12 2/27 1/13 -17/41 1/14 3/41 -12/29 3/41 2/27 -7/17 1/13 -9/22 2/27 5/67 -2/5 1/13 2/25 -5/13 1/12 3/35 -18/47 3/35 8/93 -13/34 2/23 1/11 -8/21 7/81 2/23 -11/29 5/57 -14/37 2/23 1/11 -3/8 4/45 1/11 -7/19 1/11 5/54 -18/49 1/11 6/65 -11/30 4/43 7/75 -4/11 5/53 2/21 -13/36 2/21 7/73 -9/25 5/52 3/31 -14/39 3/31 16/165 -5/14 4/41 5/51 -1/3 1/9 -4/13 5/39 4/31 -7/23 3/23 5/38 -10/33 7/53 2/15 -13/43 11/83 -3/10 2/15 5/37 -8/27 7/51 4/29 -21/71 9/65 -13/44 6/43 1/7 -18/61 4/29 1/7 -5/17 5/36 1/7 -7/24 14/99 1/7 -2/7 1/7 4/27 -9/32 1/7 2/13 -7/25 5/33 -12/43 17/111 2/13 -5/18 2/13 7/45 -13/47 3/19 -8/29 1/7 2/13 -3/11 3/19 1/6 -1/4 2/11 1/5 -6/25 1/5 12/59 -5/21 1/5 5/24 -4/17 5/23 2/9 -7/30 2/9 3/13 -3/13 1/5 -8/35 5/23 2/9 -5/22 2/9 3/13 -7/31 3/13 1/4 -2/9 1/5 2/9 -1/5 1/4 1/3 -3/16 6/19 1/3 -2/11 1/3 4/11 -7/39 1/3 3/8 -5/28 1/3 2/5 -8/45 13/33 2/5 -11/62 2/5 19/47 -3/17 3/7 -1/6 0/1 1/3 -1/7 1/1 -4/29 -1/3 0/1 -3/22 0/1 1/5 -2/15 1/3 2/5 -1/8 2/3 1/1 -2/17 1/1 4/3 -1/9 1/1 1/0 0/1 -1/1 0/1 1/6 -1/3 -2/7 2/11 -2/9 -1/5 1/5 -1/3 3/14 -2/7 -3/11 2/9 -1/4 5/22 -6/25 -5/21 8/35 -5/21 -4/17 3/13 -1/4 -3/13 1/4 -1/5 0/1 3/11 -3/13 5/18 -2/9 -1/5 2/7 -4/19 -1/5 1/3 -1/5 -1/6 4/11 -3/17 -4/23 3/8 -1/6 8/21 -9/55 -8/49 13/34 -6/37 -5/31 18/47 -7/43 -6/37 5/13 -5/31 2/5 -2/13 -1/7 7/17 -1/6 -3/19 5/12 -3/19 -2/13 3/7 -1/7 4/9 -2/13 -5/33 1/2 -1/7 -2/15 5/9 -5/39 4/7 -1/8 11/19 -11/89 18/31 -9/73 -8/65 25/43 -1/8 -9/73 32/55 -9/73 -8/65 7/12 -8/65 -7/57 3/5 -1/8 -3/25 11/18 -3/25 -8/67 8/13 -2/17 -1/9 5/8 -7/59 -2/17 7/11 -5/43 9/14 -2/17 -1/9 2/3 -4/35 -1/9 5/7 -1/9 -5/46 13/18 -1/9 -6/55 8/11 -4/37 -7/65 3/4 -5/47 -2/19 10/13 -2/19 -7/67 7/9 -5/48 -3/29 11/14 -3/29 -16/155 4/5 -4/39 -5/49 9/11 -9/89 -1/10 5/6 -1/10 11/13 -1/10 -11/111 17/20 -10/101 -9/91 6/7 -7/71 -6/61 1/1 -1/11 7/6 -6/71 -7/83 6/5 -1/12 17/14 -14/169 -13/157 28/23 -11/133 -10/121 11/9 -1/12 -9/109 5/4 -5/61 -4/49 9/7 -3/37 -5/62 13/10 -7/87 -2/25 17/13 -11/137 4/3 -2/25 -5/63 15/11 -7/89 11/8 -7/89 -4/51 29/21 -9/115 18/13 -6/77 -1/13 25/18 -4/51 -1/13 7/5 -5/64 -1/13 10/7 -14/181 -1/13 13/9 -1/13 16/11 -1/13 -22/287 3/2 -1/13 -4/53 17/11 -3/40 -5/67 14/9 -1/13 -2/27 25/16 -5/67 -2/27 11/7 -5/67 19/12 -17/229 -2/27 27/17 -2/27 35/22 -2/27 -31/419 8/5 -2/27 -7/95 21/13 -3/41 55/34 -4/55 -5/69 34/21 -1/14 81/50 -1/13 0/1 47/29 -1/13 -1/14 13/8 -1/13 -2/27 5/3 -3/41 -1/14 12/7 -7/97 -8/111 7/4 -1/14 16/9 -9/127 -8/113 41/23 -1/14 -7/99 25/14 -8/113 -7/99 9/5 -5/71 11/6 -3/43 -2/29 13/7 -1/14 -3/43 2/1 -2/29 -1/15 15/7 -1/15 28/13 -1/15 -26/391 13/6 -1/15 -12/181 11/5 -1/15 -5/76 9/4 -5/77 -2/31 16/7 -2/31 -3/47 23/10 -1/16 30/13 -1/17 0/1 7/3 -1/15 19/8 -5/77 -2/31 31/13 -2/31 43/18 -2/31 -11/171 12/5 -2/31 -3/47 17/7 -3/47 -1/16 22/9 -2/33 -1/17 5/2 -1/15 -2/31 18/7 -4/63 -5/79 49/19 -3/47 -1/16 31/12 -3/47 -4/63 13/5 -5/79 8/3 -1/16 19/7 -7/113 49/18 -6/97 -5/81 128/47 -5/81 -4/65 79/29 -1/16 -5/81 30/11 -7/113 -6/97 11/4 -4/65 -3/49 3/1 -1/16 -1/17 10/3 -6/101 -1/17 17/5 -1/17 24/7 -1/17 -14/239 7/2 -1/17 -4/69 25/7 -1/17 -3/52 68/19 -1/17 -4/69 43/12 -3/52 18/5 -1/17 -2/35 29/8 -13/227 -2/35 69/19 -2/35 109/30 -2/35 -51/893 40/11 -2/35 -19/333 11/3 -3/53 15/4 -1/19 0/1 34/9 -1/17 0/1 87/23 -1/17 140/37 -1/17 -4/69 53/14 -1/17 -2/35 19/5 -1/17 -1/18 4/1 -1/17 0/1 17/4 -1/17 -2/35 13/3 -3/53 -1/18 9/2 -1/18 23/5 -1/18 -5/91 37/8 -4/73 -3/55 14/3 -3/55 -2/37 5/1 -1/19 21/4 -1/23 0/1 37/7 0/1 53/10 -1/7 0/1 16/3 -1/15 0/1 11/2 -1/17 -2/35 17/3 -1/18 -3/55 6/1 -2/37 -1/19 19/3 -1/19 32/5 -1/19 -10/191 13/2 -1/19 -4/77 7/1 -1/19 -1/20 1/0 -1/21 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(1,0,40,1) Matrix(205,96,-536,-251) -> Matrix(37,-2,426,-23) Matrix(893,410,734,337) -> Matrix(193,-12,-2332,145) Matrix(647,296,-2188,-1001) -> Matrix(59,-4,428,-29) Matrix(199,90,42,19) -> Matrix(33,-2,-610,37) Matrix(549,242,946,417) -> Matrix(129,-8,-1048,65) Matrix(783,344,-2588,-1137) -> Matrix(247,-16,1868,-121) Matrix(821,360,-2780,-1219) -> Matrix(29,-2,218,-15) Matrix(37,16,-192,-83) -> Matrix(29,-2,102,-7) Matrix(113,48,40,17) -> Matrix(29,-2,-478,33) Matrix(829,344,976,405) -> Matrix(113,-8,-1144,81) Matrix(1463,606,2518,1043) -> Matrix(85,-6,-694,49) Matrix(223,92,-972,-401) -> Matrix(53,-4,252,-19) Matrix(371,152,-1340,-549) -> Matrix(55,-4,344,-25) Matrix(333,136,-928,-379) -> Matrix(133,-10,1370,-103) Matrix(181,70,106,41) -> Matrix(71,-6,-982,83) Matrix(73,28,-644,-247) -> Matrix(47,-4,12,-1) Matrix(283,108,-1208,-461) -> Matrix(47,-4,200,-17) Matrix(495,188,-1772,-673) -> Matrix(229,-20,1500,-131) Matrix(707,268,1844,699) -> Matrix(227,-20,-1396,123) Matrix(249,94,1094,413) -> Matrix(159,-14,-670,59) Matrix(173,64,-592,-219) -> Matrix(109,-10,774,-71) Matrix(381,140,-2120,-779) -> Matrix(21,-2,74,-7) Matrix(207,76,-1528,-561) -> Matrix(43,-4,140,-13) Matrix(383,140,1004,367) -> Matrix(235,-22,-1442,135) Matrix(343,124,-1928,-697) -> Matrix(167,-16,428,-41) Matrix(1753,632,380,137) -> Matrix(229,-22,-4174,401) Matrix(345,124,-1444,-519) -> Matrix(207,-20,1004,-97) Matrix(35,12,32,11) -> Matrix(19,-2,-218,23) Matrix(31,10,34,11) -> Matrix(17,-2,-178,21) Matrix(157,48,-664,-203) -> Matrix(77,-10,362,-47) Matrix(283,86,1234,375) -> Matrix(137,-18,-586,77) Matrix(503,152,-2836,-857) -> Matrix(211,-28,520,-69) Matrix(597,178,218,65) -> Matrix(103,-14,-1670,227) Matrix(311,92,-2248,-665) -> Matrix(29,-4,-36,5) Matrix(2681,790,750,221) -> Matrix(57,-8,-976,137) Matrix(405,118,278,81) -> Matrix(127,-18,-1658,235) Matrix(707,200,152,43) -> Matrix(67,-10,-1226,183) Matrix(1833,514,674,189) -> Matrix(107,-16,-1732,259) Matrix(1649,460,1036,289) -> Matrix(313,-48,-4232,649) Matrix(1613,446,698,193) -> Matrix(13,-2,-214,33) Matrix(29,8,-272,-75) -> Matrix(13,-2,-6,1) Matrix(89,24,152,41) -> Matrix(37,-6,-302,49) Matrix(437,106,202,49) -> Matrix(71,-14,-1070,211) Matrix(1345,312,832,193) -> Matrix(7,-2,-94,27) Matrix(1769,404,740,169) -> Matrix(73,-16,-1136,249) Matrix(1677,380,940,213) -> Matrix(41,-10,-578,141) Matrix(967,218,794,179) -> Matrix(49,-12,-592,145) Matrix(29,6,82,17) -> Matrix(7,-2,-38,11) Matrix(461,86,134,25) -> Matrix(31,-10,-530,171) Matrix(4475,802,2762,495) -> Matrix(5,-2,-62,25) Matrix(7385,1312,2032,361) -> Matrix(161,-64,-2820,1121) Matrix(479,84,268,47) -> Matrix(17,-8,-240,113) Matrix(27,4,128,19) -> Matrix(3,-2,-10,7) Matrix(1889,260,356,49) -> Matrix(1,0,-12,1) Matrix(303,40,356,47) -> Matrix(17,-8,-172,81) Matrix(477,58,74,9) -> Matrix(7,-6,-134,115) Matrix(59,-8,96,-13) -> Matrix(3,2,-26,-17) Matrix(187,-32,76,-13) -> Matrix(1,0,-12,1) Matrix(409,-76,296,-55) -> Matrix(21,4,-268,-51) Matrix(73,-16,324,-71) -> Matrix(31,8,-128,-33) Matrix(107,-26,70,-17) -> Matrix(19,4,-252,-53) Matrix(157,-42,86,-23) -> Matrix(7,2,-102,-29) Matrix(449,-124,344,-95) -> Matrix(73,16,-908,-199) Matrix(499,-140,360,-101) -> Matrix(11,2,-138,-25) Matrix(51,-16,16,-5) -> Matrix(11,2,-182,-33) Matrix(97,-36,256,-95) -> Matrix(71,12,-432,-73) Matrix(1417,-542,2434,-931) -> Matrix(11,2,-94,-17) Matrix(127,-50,94,-37) -> Matrix(51,8,-644,-101) 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(27,4,-412,-61) Matrix(245,-108,152,-67) -> Matrix(25,4,-344,-55) Matrix(107,-48,136,-61) -> Matrix(67,10,-650,-97) Matrix(157,-86,42,-23) -> Matrix(15,2,-278,-37) Matrix(113,-64,196,-111) -> Matrix(127,16,-1024,-129) Matrix(9849,-5728,3616,-2103) -> Matrix(33,4,-520,-63) Matrix(191,-116,28,-17) -> Matrix(33,4,-652,-79) Matrix(245,-152,108,-67) -> Matrix(33,4,-520,-63) Matrix(297,-188,188,-119) -> Matrix(171,20,-2300,-269) Matrix(523,-334,202,-129) -> Matrix(87,10,-1366,-157) Matrix(107,-70,26,-17) -> Matrix(35,4,-604,-69) Matrix(91,-64,64,-45) -> Matrix(91,10,-1174,-129) Matrix(499,-360,140,-101) -> Matrix(19,2,-314,-33) Matrix(409,-296,76,-55) -> Matrix(37,4,-620,-67) Matrix(127,-94,50,-37) -> Matrix(75,8,-1172,-125) Matrix(449,-344,124,-95) -> Matrix(153,16,-2668,-279) Matrix(347,-268,224,-173) -> Matrix(153,16,-2056,-215) Matrix(271,-212,124,-97) -> Matrix(193,20,-2924,-303) Matrix(327,-266,134,-109) -> Matrix(59,6,-954,-97) Matrix(121,-100,144,-119) -> Matrix(199,20,-2000,-201) Matrix(121,-144,100,-119) -> Matrix(239,20,-2880,-241) Matrix(167,-206,30,-37) -> Matrix(73,6,-1302,-107) Matrix(107,-136,48,-61) -> Matrix(123,10,-1882,-153) Matrix(249,-322,58,-75) -> Matrix(149,12,-2620,-211) Matrix(553,-724,152,-199) -> Matrix(349,28,-6120,-491) Matrix(363,-496,232,-317) -> Matrix(77,6,-1014,-79) Matrix(481,-664,92,-127) -> Matrix(51,4,-1084,-85) Matrix(911,-1266,562,-781) -> Matrix(77,6,-1014,-79) Matrix(235,-338,162,-233) -> Matrix(467,36,-6084,-469) Matrix(679,-1060,180,-281) -> Matrix(27,2,-446,-33) Matrix(919,-1458,578,-917) -> Matrix(1295,96,-17496,-1297) Matrix(2857,-4624,1764,-2855) -> Matrix(55,4,-784,-57) Matrix(59,-96,8,-13) -> Matrix(27,2,-554,-41) Matrix(113,-196,64,-111) -> Matrix(223,16,-3136,-225) Matrix(1401,-2494,514,-915) -> Matrix(29,2,-450,-31) Matrix(175,-332,68,-129) -> Matrix(85,6,-1346,-95) Matrix(211,-450,98,-209) -> Matrix(419,28,-6300,-421) Matrix(481,-1102,134,-307) -> Matrix(125,8,-2172,-139) Matrix(1239,-2854,346,-797) -> Matrix(67,4,-1156,-69) Matrix(807,-1922,338,-805) -> Matrix(495,32,-7688,-497) Matrix(123,-296,32,-77) -> Matrix(31,2,-574,-37) Matrix(1235,-3186,326,-841) -> Matrix(31,2,-574,-37) Matrix(97,-256,36,-95) -> Matrix(191,12,-3072,-193) Matrix(5011,-13644,1324,-3605) -> Matrix(259,16,-4484,-277) Matrix(171,-578,50,-169) -> Matrix(339,20,-5780,-341) Matrix(2623,-9522,722,-2621) -> Matrix(2239,128,-39200,-2241) Matrix(4003,-15138,1058,-4001) -> Matrix(67,4,-1156,-69) Matrix(73,-324,16,-71) -> Matrix(143,8,-2592,-145) Matrix(519,-2738,98,-517) -> Matrix(1,0,16,1) Matrix(115,-722,18,-113) -> Matrix(227,12,-4332,-229) 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 -1/1 0/1 1/6 -1/3 -2/7 2/11 -2/9 -1/5 1/5 -1/3 2/9 -1/4 3/13 -1/4 -3/13 1/4 -1/5 0/1 3/11 -3/13 5/18 -2/9 -1/5 2/7 -4/19 -1/5 1/3 -1/5 -1/6 3/8 -1/6 5/13 -5/31 2/5 -2/13 -1/7 7/17 -1/6 -3/19 5/12 -3/19 -2/13 3/7 -1/7 4/9 -2/13 -5/33 1/2 -1/7 -2/15 5/9 -5/39 4/7 -1/8 3/5 -1/8 -3/25 11/18 -3/25 -8/67 8/13 -2/17 -1/9 5/8 -7/59 -2/17 7/11 -5/43 9/14 -2/17 -1/9 2/3 -4/35 -1/9 5/7 -1/9 -5/46 13/18 -1/9 -6/55 8/11 -4/37 -7/65 3/4 -5/47 -2/19 10/13 -2/19 -7/67 7/9 -5/48 -3/29 11/14 -3/29 -16/155 4/5 -4/39 -5/49 9/11 -9/89 -1/10 5/6 -1/10 1/1 -1/11 6/5 -1/12 11/9 -1/12 -9/109 5/4 -5/61 -4/49 9/7 -3/37 -5/62 13/10 -7/87 -2/25 17/13 -11/137 4/3 -2/25 -5/63 15/11 -7/89 11/8 -7/89 -4/51 29/21 -9/115 18/13 -6/77 -1/13 25/18 -4/51 -1/13 7/5 -5/64 -1/13 10/7 -14/181 -1/13 13/9 -1/13 3/2 -1/13 -4/53 17/11 -3/40 -5/67 14/9 -1/13 -2/27 25/16 -5/67 -2/27 11/7 -5/67 19/12 -17/229 -2/27 27/17 -2/27 8/5 -2/27 -7/95 21/13 -3/41 34/21 -1/14 47/29 -1/13 -1/14 13/8 -1/13 -2/27 5/3 -3/41 -1/14 7/4 -1/14 9/5 -5/71 11/6 -3/43 -2/29 13/7 -1/14 -3/43 2/1 -2/29 -1/15 15/7 -1/15 13/6 -1/15 -12/181 11/5 -1/15 -5/76 9/4 -5/77 -2/31 16/7 -2/31 -3/47 23/10 -1/16 7/3 -1/15 19/8 -5/77 -2/31 31/13 -2/31 12/5 -2/31 -3/47 17/7 -3/47 -1/16 22/9 -2/33 -1/17 5/2 -1/15 -2/31 18/7 -4/63 -5/79 49/19 -3/47 -1/16 31/12 -3/47 -4/63 13/5 -5/79 8/3 -1/16 3/1 -1/16 -1/17 10/3 -6/101 -1/17 17/5 -1/17 7/2 -1/17 -4/69 25/7 -1/17 -3/52 43/12 -3/52 18/5 -1/17 -2/35 29/8 -13/227 -2/35 69/19 -2/35 40/11 -2/35 -19/333 11/3 -3/53 15/4 -1/19 0/1 34/9 -1/17 0/1 87/23 -1/17 53/14 -1/17 -2/35 19/5 -1/17 -1/18 4/1 -1/17 0/1 17/4 -1/17 -2/35 13/3 -3/53 -1/18 9/2 -1/18 5/1 -1/19 21/4 -1/23 0/1 37/7 0/1 16/3 -1/15 0/1 11/2 -1/17 -2/35 17/3 -1/18 -3/55 6/1 -2/37 -1/19 19/3 -1/19 13/2 -1/19 -4/77 7/1 -1/19 -1/20 1/0 -1/21 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(1,0,20,1) Matrix(59,-8,96,-13) -> Matrix(3,2,-26,-17) Matrix(187,-32,76,-13) -> Matrix(1,0,-12,1) Matrix(409,-76,296,-55) -> Matrix(21,4,-268,-51) Matrix(90,-19,19,-4) -> Matrix(7,2,-130,-37) Matrix(234,-53,53,-12) -> Matrix(25,6,-446,-107) Matrix(107,-26,70,-17) -> Matrix(19,4,-252,-53) Matrix(157,-42,86,-23) -> Matrix(7,2,-102,-29) Matrix(449,-124,344,-95) -> Matrix(73,16,-908,-199) Matrix(499,-140,360,-101) -> Matrix(11,2,-138,-25) Matrix(51,-16,16,-5) -> Matrix(11,2,-182,-33) Matrix(48,-17,17,-6) -> Matrix(11,2,-182,-33) Matrix(208,-79,79,-30) -> Matrix(61,10,-970,-159) Matrix(127,-50,94,-37) -> Matrix(51,8,-644,-101) 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(27,4,-412,-61) Matrix(245,-108,152,-67) -> Matrix(25,4,-344,-55) Matrix(107,-48,136,-61) -> Matrix(67,10,-650,-97) Matrix(157,-86,42,-23) -> Matrix(15,2,-278,-37) Matrix(126,-71,71,-40) -> Matrix(79,10,-1114,-141) Matrix(70,-41,41,-24) -> Matrix(49,6,-678,-83) Matrix(191,-116,28,-17) -> Matrix(33,4,-652,-79) Matrix(245,-152,108,-67) -> Matrix(33,4,-520,-63) Matrix(297,-188,188,-119) -> Matrix(171,20,-2300,-269) Matrix(523,-334,202,-129) -> Matrix(87,10,-1366,-157) Matrix(107,-70,26,-17) -> Matrix(35,4,-604,-69) Matrix(91,-64,64,-45) -> Matrix(91,10,-1174,-129) Matrix(499,-360,140,-101) -> Matrix(19,2,-314,-33) Matrix(409,-296,76,-55) -> Matrix(37,4,-620,-67) Matrix(127,-94,50,-37) -> Matrix(75,8,-1172,-125) Matrix(449,-344,124,-95) -> Matrix(153,16,-2668,-279) Matrix(347,-268,224,-173) -> Matrix(153,16,-2056,-215) Matrix(271,-212,124,-97) -> Matrix(193,20,-2924,-303) Matrix(327,-266,134,-109) -> Matrix(59,6,-954,-97) Matrix(132,-109,109,-90) -> Matrix(179,18,-2158,-217) Matrix(12,-11,11,-10) -> Matrix(21,2,-242,-23) Matrix(167,-206,30,-37) -> Matrix(73,6,-1302,-107) Matrix(107,-136,48,-61) -> Matrix(123,10,-1882,-153) Matrix(249,-322,58,-75) -> Matrix(149,12,-2620,-211) Matrix(553,-724,152,-199) -> Matrix(349,28,-6120,-491) Matrix(363,-496,232,-317) -> Matrix(77,6,-1014,-79) Matrix(481,-664,92,-127) -> Matrix(51,4,-1084,-85) Matrix(911,-1266,562,-781) -> Matrix(77,6,-1014,-79) Matrix(118,-169,81,-116) -> Matrix(233,18,-3042,-235) Matrix(679,-1060,180,-281) -> Matrix(27,2,-446,-33) Matrix(460,-729,289,-458) -> Matrix(647,48,-8748,-649) Matrix(446,-721,193,-312) -> Matrix(27,2,-446,-33) Matrix(1772,-2871,495,-802) -> Matrix(25,2,-438,-35) Matrix(59,-96,8,-13) -> Matrix(27,2,-554,-41) Matrix(175,-332,68,-129) -> Matrix(85,6,-1346,-95) Matrix(106,-225,49,-104) -> Matrix(209,14,-3150,-211) Matrix(481,-1102,134,-307) -> Matrix(125,8,-2172,-139) Matrix(404,-961,169,-402) -> Matrix(247,16,-3844,-249) Matrix(123,-296,32,-77) -> Matrix(31,2,-574,-37) Matrix(1235,-3186,326,-841) -> Matrix(31,2,-574,-37) Matrix(86,-289,25,-84) -> Matrix(169,10,-2890,-171) Matrix(1312,-4761,361,-1310) -> Matrix(1119,64,-19600,-1121) Matrix(2002,-7569,529,-2000) -> Matrix(33,2,-578,-35) Matrix(260,-1369,49,-258) -> Matrix(1,0,8,1) Matrix(58,-361,9,-56) -> Matrix(113,6,-2166,-115) 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 -1/12 10 2 11/9 (-1/12,-9/109) 0 11 5/4 (-5/61,-4/49) 0 22 9/7 (-3/37,-5/62) 0 11 13/10 (-7/87,-2/25) 0 22 4/3 (-2/25,-5/63) 0 22 11/8 (-7/89,-4/51) 0 22 18/13 (-6/77,-1/13) 0 22 7/5 (-5/64,-1/13) 0 11 13/9 -1/13 18 1 3/2 (-1/13,-4/53) 0 22 14/9 (-1/13,-2/27) 0 22 11/7 -5/67 2 11 27/17 -2/27 12 1 8/5 (-2/27,-7/95) 0 22 13/8 (-1/13,-2/27) 0 22 5/3 (-3/41,-1/14) 0 11 7/4 -1/14 8 2 9/5 -5/71 2 11 2/1 (-2/29,-1/15) 0 22 15/7 -1/15 14 1 11/5 (-1/15,-5/76) 0 11 9/4 (-5/77,-2/31) 0 22 16/7 (-2/31,-3/47) 0 22 23/10 -1/16 2 2 7/3 -1/15 2 11 31/13 -2/31 4 1 12/5 (-2/31,-3/47) 0 22 17/7 (-3/47,-1/16) 0 11 5/2 (-1/15,-2/31) 0 22 18/7 (-4/63,-5/79) 0 22 31/12 (-3/47,-4/63) 0 22 13/5 -5/79 2 11 8/3 -1/16 6 2 3/1 (-1/16,-1/17) 0 11 17/5 -1/17 10 1 7/2 (-1/17,-4/69) 0 22 25/7 (-1/17,-3/52) 0 11 43/12 -3/52 2 2 18/5 (-1/17,-2/35) 0 22 29/8 (-13/227,-2/35) 0 22 69/19 -2/35 16 1 11/3 -3/53 2 11 15/4 (-1/19,0/1) 0 22 34/9 (-1/17,0/1) 0 22 87/23 -1/17 2 1 19/5 (-1/17,-1/18) 0 11 4/1 (-1/17,0/1) 0 22 17/4 (-1/17,-2/35) 0 22 13/3 (-3/53,-1/18) 0 11 9/2 -1/18 4 2 5/1 -1/19 2 11 37/7 0/1 8 1 16/3 (-1/15,0/1) 0 22 11/2 (-1/17,-2/35) 0 22 17/3 (-1/18,-3/55) 0 11 6/1 (-2/37,-1/19) 0 22 19/3 -1/19 6 1 7/1 (-1/19,-1/20) 0 11 1/0 (-1/21,0/1) 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(-1,0,42,1) (-1/1,1/0) -> (-1/21,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,22,1) (-1/1,1/1) -> (-1/11,0/1) Matrix(11,-12,10,-11) -> Matrix(23,2,-264,-23) (1/1,6/5) -> (-1/11,-1/12) Matrix(109,-132,90,-109) -> Matrix(217,18,-2616,-217) (6/5,11/9) -> (-1/12,-9/109) Matrix(167,-206,30,-37) -> Matrix(73,6,-1302,-107) Matrix(107,-136,48,-61) -> Matrix(123,10,-1882,-153) Matrix(249,-322,58,-75) -> Matrix(149,12,-2620,-211) Matrix(344,-449,95,-124) -> Matrix(199,16,-3470,-279) Matrix(94,-127,37,-50) -> Matrix(101,8,-1578,-125) Matrix(296,-409,55,-76) -> Matrix(51,4,-854,-67) Matrix(360,-499,101,-140) -> Matrix(25,2,-412,-33) Matrix(64,-91,45,-64) -> Matrix(129,10,-1664,-129) (7/5,13/9) -> (-5/64,-1/13) Matrix(53,-78,36,-53) -> Matrix(105,8,-1378,-105) (13/9,3/2) -> (-1/13,-4/53) Matrix(70,-107,17,-26) -> Matrix(53,4,-914,-69) Matrix(334,-523,129,-202) -> Matrix(133,10,-2088,-157) Matrix(188,-297,119,-188) -> Matrix(269,20,-3618,-269) (11/7,27/17) -> (-5/67,-2/27) Matrix(271,-432,170,-271) -> Matrix(379,28,-5130,-379) (27/17,8/5) -> (-2/27,-7/95) Matrix(152,-245,67,-108) -> Matrix(55,4,-866,-63) Matrix(59,-96,8,-13) -> Matrix(27,2,-554,-41) Matrix(41,-70,24,-41) -> Matrix(83,6,-1148,-83) (5/3,7/4) -> (-3/41,-1/14) Matrix(71,-126,40,-71) -> Matrix(141,10,-1988,-141) (7/4,9/5) -> (-1/14,-5/71) Matrix(86,-157,23,-42) -> Matrix(29,2,-536,-37) Matrix(29,-60,14,-29) -> Matrix(59,4,-870,-59) (2/1,15/7) -> (-2/29,-1/15) Matrix(76,-165,35,-76) -> Matrix(151,10,-2280,-151) (15/7,11/5) -> (-1/15,-5/76) Matrix(481,-1102,134,-307) -> Matrix(125,8,-2172,-139) Matrix(139,-322,60,-139) -> Matrix(31,2,-480,-31) (23/10,7/3) -> (-1/15,-1/16) Matrix(92,-217,39,-92) -> Matrix(61,4,-930,-61) (7/3,31/13) -> (-1/15,-2/31) Matrix(311,-744,130,-311) -> Matrix(187,12,-2914,-187) (31/13,12/5) -> (-2/31,-3/47) Matrix(123,-296,32,-77) -> Matrix(31,2,-574,-37) Matrix(76,-187,13,-32) -> Matrix(-1,0,34,1) *** -> (-1/17,0/1) Matrix(418,-1077,111,-286) -> Matrix(63,4,-1118,-71) Matrix(79,-208,30,-79) -> Matrix(159,10,-2528,-159) (13/5,8/3) -> (-5/79,-1/16) Matrix(17,-48,6,-17) -> Matrix(33,2,-544,-33) (8/3,3/1) -> (-1/16,-1/17) Matrix(16,-51,5,-16) -> Matrix(33,2,-544,-33) (3/1,17/5) -> (-1/16,-1/17) Matrix(69,-238,20,-69) -> Matrix(137,8,-2346,-137) (17/5,7/2) -> (-1/17,-4/69) Matrix(601,-2150,168,-601) -> Matrix(103,6,-1768,-103) (25/7,43/12) -> (-1/17,-3/52) Matrix(1103,-4002,304,-1103) -> Matrix(909,52,-15890,-909) (29/8,69/19) -> (-13/227,-2/35) Matrix(208,-759,57,-208) -> Matrix(211,12,-3710,-211) (69/19,11/3) -> (-2/35,-3/53) Matrix(1565,-5916,414,-1565) -> Matrix(-1,0,34,1) (34/9,87/23) -> (-1/17,0/1) Matrix(436,-1653,115,-436) -> Matrix(35,2,-612,-35) (87/23,19/5) -> (-1/17,-1/18) Matrix(53,-234,12,-53) -> Matrix(107,6,-1908,-107) (13/3,9/2) -> (-3/53,-1/18) Matrix(19,-90,4,-19) -> Matrix(37,2,-684,-37) (9/2,5/1) -> (-1/18,-1/19) Matrix(36,-185,7,-36) -> Matrix(-1,0,38,1) (5/1,37/7) -> (-1/19,0/1) Matrix(223,-1184,42,-223) -> Matrix(-1,0,30,1) (37/7,16/3) -> (-1/15,0/1) Matrix(37,-228,6,-37) -> Matrix(75,4,-1406,-75) (6/1,19/3) -> (-2/37,-1/19) Matrix(20,-133,3,-20) -> Matrix(39,2,-760,-39) (19/3,7/1) -> (-1/19,-1/20) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.