INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -6/13 -3/7 -5/12 -4/11 -1/3 -3/10 -2/9 -1/5 -4/25 -1/8 0/1 1/7 1/6 5/23 3/11 1/3 4/11 2/5 1/2 5/9 3/5 8/13 11/17 3/4 7/9 16/19 1/1 4/3 7/5 3/2 17/11 5/3 22/13 9/5 2/1 19/9 24/11 11/5 29/13 7/3 59/25 5/2 141/55 71/27 8/3 41/15 3/1 16/5 43/13 10/3 17/5 7/2 11/3 4/1 13/3 22/5 9/2 23/5 14/3 5/1 26/5 47/9 16/3 11/2 6/1 20/3 7/1 8/1 25/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/2 -7/15 2/3 -6/13 1/2 -11/24 1/2 -5/11 1/2 3/4 -4/9 2/3 1/1 -7/16 1/2 -10/23 1/2 2/3 -3/7 1/1 -14/33 2/3 1/1 -11/26 3/4 -8/19 2/3 1/1 -21/50 3/4 -13/31 3/4 11/14 -5/12 1/1 -12/29 0/1 1/2 -7/17 1/2 3/4 -9/22 1/2 -11/27 1/1 -13/32 5/6 -2/5 0/1 1/1 -7/18 3/2 -12/31 1/1 2/1 -5/13 1/1 -13/34 0/1 -8/21 0/1 1/2 -3/8 3/2 -10/27 0/1 1/0 -7/19 0/1 -4/11 1/1 -9/25 2/1 -14/39 5/3 2/1 -5/14 1/0 -1/3 1/2 1/0 -5/16 1/2 -9/29 2/1 -4/13 -2/1 1/0 -11/36 -5/6 -7/23 0/1 -10/33 -1/1 1/0 -3/10 0/1 -8/27 0/1 1/1 -5/17 1/1 -2/7 -1/1 0/1 -9/32 1/10 -16/57 1/7 1/6 -7/25 1/6 1/4 -5/18 1/2 -8/29 1/2 -3/11 1/1 -4/15 -1/1 0/1 -1/4 1/0 -3/13 3/2 1/0 -2/9 0/1 -5/23 3/8 1/2 -3/14 1/2 -4/19 1/1 1/0 -9/43 1/2 3/4 -5/24 1/0 -1/5 0/1 -3/16 1/2 -2/11 0/1 1/0 -1/6 1/0 -5/31 1/2 5/8 -4/25 1/1 -7/44 1/2 -3/19 1/1 -2/13 -1/1 0/1 -3/20 1/4 -1/7 1/2 1/0 -1/8 0/1 -2/17 1/1 1/0 -1/9 0/1 -1/10 1/0 0/1 0/1 1/1 1/9 1/2 1/0 1/8 1/2 1/7 0/1 2/13 1/2 1/1 1/6 0/1 1/5 1/2 1/0 4/19 -1/1 1/0 7/33 0/1 3/14 -1/2 5/23 0/1 7/32 1/8 2/9 0/1 1/3 3/13 1/1 4/17 1/1 5/21 5/2 1/0 1/4 1/2 4/15 -1/1 0/1 3/11 0/1 8/29 0/1 1/5 13/47 1/5 5/18 1/2 2/7 0/1 1/2 5/17 3/2 1/0 8/27 1/0 3/10 1/0 7/23 1/4 1/2 11/36 1/0 4/13 0/1 1/2 5/16 1/1 1/3 0/1 5/14 1/2 9/25 3/2 1/0 4/11 1/2 1/1 7/19 3/2 1/0 3/8 1/0 2/5 0/1 5/12 1/2 8/19 2/5 1/2 3/7 1/2 3/4 7/16 5/4 4/9 2/1 1/0 13/29 1/0 9/20 1/0 14/31 -3/1 -2/1 5/11 -1/1 6/13 -1/1 0/1 1/2 1/2 7/13 0/1 13/24 1/0 6/11 -1/2 0/1 5/9 0/1 14/25 0/1 1/8 37/66 1/6 23/41 0/1 9/16 1/4 4/7 0/1 1/3 15/26 1/4 11/19 1/4 1/2 7/12 1/2 17/29 1/2 7/12 10/17 0/1 1/2 13/22 2/3 3/5 1/1 14/23 1/1 2/1 11/18 1/0 8/13 1/0 21/34 1/0 34/55 -3/1 1/0 13/21 -3/2 1/0 31/50 -7/8 18/29 -1/2 0/1 5/8 1/0 12/19 0/1 1/1 31/49 -2/1 19/30 -1/1 7/11 -1/2 -1/4 16/25 -1/4 -1/5 25/39 0/1 9/14 -1/8 11/17 0/1 13/20 1/14 2/3 0/1 1/3 9/13 1/4 1/2 7/10 1/2 19/27 3/8 1/2 12/17 1/2 2/3 5/7 1/1 13/18 -1/2 21/29 1/4 1/2 29/40 1/2 8/11 0/1 1/1 19/26 1/0 11/15 3/2 1/0 3/4 0/1 13/17 3/14 1/4 36/47 1/4 10/39 23/30 5/18 10/13 1/3 1/2 27/35 1/2 1/0 17/22 1/4 24/31 0/1 1/3 7/9 0/1 18/23 1/4 3/11 29/37 1/4 3/10 11/14 5/16 37/47 1/3 26/33 1/3 12/35 41/52 7/20 15/19 5/14 3/8 4/5 2/5 1/2 9/11 2/3 5/6 1/0 21/25 1/2 1/0 16/19 0/1 27/32 3/8 11/13 1/1 6/7 0/1 1/0 13/15 0/1 7/8 1/4 1/1 1/2 1/0 6/5 0/1 1/1 11/9 1/3 5/4 1/2 4/3 1/1 11/8 1/0 18/13 0/1 1/3 25/18 1/2 32/23 0/1 1/1 39/28 1/0 7/5 0/1 31/22 5/14 86/61 2/5 55/39 3/8 1/2 24/17 3/7 1/2 41/29 1/2 17/12 1/2 44/31 3/5 2/3 71/50 3/4 27/19 1/2 3/4 10/7 0/1 1/2 23/16 1/2 13/9 1/2 3/4 42/29 1/1 1/0 29/20 0/1 16/11 2/5 1/2 3/2 3/4 17/11 1/1 14/9 1/1 9/8 25/16 5/4 11/7 5/4 3/2 19/12 3/2 27/17 3/1 8/5 0/1 1/0 29/18 1/0 50/31 -1/3 0/1 21/13 1/2 1/0 13/8 0/1 44/27 1/4 1/3 31/19 3/8 1/2 18/11 1/2 2/3 41/25 3/8 1/2 23/14 1/2 5/3 1/1 22/13 1/2 39/23 1/2 1/0 17/10 1/2 12/7 2/3 1/1 31/18 2/3 50/29 7/10 5/7 19/11 3/4 5/6 45/26 5/6 26/15 1/2 1/1 7/4 3/4 23/13 6/7 62/35 5/6 1/1 39/22 19/22 55/31 47/54 7/8 16/9 8/9 1/1 9/5 1/1 20/11 1/1 8/7 51/28 19/16 31/17 6/5 11/6 3/2 2/1 0/1 1/1 19/9 1/1 17/8 17/16 15/7 9/8 7/6 13/6 5/4 37/17 11/8 3/2 24/11 1/1 11/5 1/1 20/9 3/2 2/1 29/13 2/1 38/17 1/1 2/1 9/4 1/0 34/15 1/0 25/11 0/1 41/18 1/4 57/25 1/2 7/12 16/7 3/4 1/1 39/17 1/1 23/10 9/8 7/3 3/2 1/0 47/20 3/2 40/17 1/1 2/1 33/14 3/2 59/25 2/1 85/36 9/4 26/11 2/1 3/1 19/8 1/0 69/29 1/0 50/21 -3/1 1/0 31/13 0/1 12/5 0/1 1/0 53/22 1/2 94/39 1/1 41/17 -1/2 1/0 29/12 1/2 17/7 0/1 5/2 1/1 23/9 6/5 41/16 5/4 141/55 5/4 100/39 5/4 84/67 59/23 5/4 53/42 77/30 33/26 18/7 9/7 4/3 49/19 4/3 80/31 1/1 4/3 31/12 5/4 13/5 11/8 3/2 47/18 3/2 81/31 3/2 34/13 3/2 14/9 55/21 2/1 21/8 3/2 71/27 3/2 50/19 3/2 14/9 29/11 5/3 8/3 1/1 2/1 19/7 3/2 1/0 30/11 1/2 1/1 41/15 1/1 52/19 1/1 7/6 11/4 3/2 14/5 1/1 2/1 17/6 5/2 20/7 6/1 1/0 3/1 1/1 22/7 16/11 3/2 41/13 3/2 37/24 19/6 13/8 16/5 2/1 45/14 1/2 29/9 3/2 1/0 42/13 1/1 2/1 13/4 1/0 23/7 3/2 1/0 33/10 7/4 43/13 2/1 10/3 2/1 1/0 27/8 2/1 17/5 3/2 1/0 41/12 11/6 65/19 2/1 24/7 2/1 7/3 7/2 1/0 25/7 2/1 68/19 4/1 5/1 111/31 17/2 1/0 154/43 20/1 1/0 197/55 1/0 43/12 1/0 61/17 -1/2 1/0 18/5 1/1 1/0 11/3 1/1 26/7 1/1 3/2 67/18 3/2 41/11 2/1 15/4 3/2 4/1 1/1 2/1 13/3 3/1 35/8 7/2 92/21 3/1 4/1 57/13 4/1 22/5 4/1 1/0 9/2 1/0 23/5 1/0 37/8 1/0 14/3 0/1 1/0 19/4 3/2 43/9 3/1 67/14 11/2 24/5 -2/1 1/0 5/1 3/2 1/0 26/5 9/5 2/1 47/9 2/1 21/4 9/4 16/3 2/1 3/1 11/2 1/0 6/1 1/0 13/2 1/0 20/3 1/1 5/4 27/4 7/4 7/1 2/1 8/1 6/1 1/0 25/3 1/0 17/2 1/0 9/1 -1/2 1/0 1/0 1/0 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(425,202,162,77) (-1/2,-7/15) -> (55/21,21/8) Hyperbolic Matrix(835,388,368,171) (-7/15,-6/13) -> (34/15,25/11) Hyperbolic Matrix(933,428,412,189) (-6/13,-11/24) -> (9/4,34/15) Hyperbolic Matrix(823,376,1136,519) (-11/24,-5/11) -> (21/29,29/40) Hyperbolic Matrix(103,46,150,67) (-5/11,-4/9) -> (2/3,9/13) Hyperbolic Matrix(199,88,52,23) (-4/9,-7/16) -> (15/4,4/1) Hyperbolic Matrix(795,346,494,215) (-7/16,-10/23) -> (8/5,29/18) Hyperbolic Matrix(295,128,348,151) (-10/23,-3/7) -> (11/13,6/7) Hyperbolic Matrix(485,206,1754,745) (-3/7,-14/33) -> (8/29,13/47) Hyperbolic Matrix(1165,494,1606,681) (-14/33,-11/26) -> (29/40,8/11) Hyperbolic Matrix(389,164,676,285) (-11/26,-8/19) -> (4/7,15/26) Hyperbolic Matrix(871,366,1930,811) (-8/19,-21/50) -> (9/20,14/31) Hyperbolic Matrix(481,202,50,21) (-21/50,-13/31) -> (9/1,1/0) Hyperbolic Matrix(673,282,1062,445) (-13/31,-5/12) -> (19/30,7/11) Hyperbolic Matrix(193,80,620,257) (-5/12,-12/29) -> (4/13,5/16) Hyperbolic Matrix(953,394,670,277) (-12/29,-7/17) -> (27/19,10/7) Hyperbolic Matrix(667,274,426,175) (-7/17,-9/22) -> (25/16,11/7) Hyperbolic Matrix(1231,502,282,115) (-9/22,-11/27) -> (13/3,35/8) Hyperbolic Matrix(285,116,-1796,-731) (-11/27,-13/32) -> (-7/44,-3/19) Hyperbolic Matrix(1037,420,1316,533) (-13/32,-2/5) -> (26/33,41/52) Hyperbolic Matrix(91,36,48,19) (-2/5,-7/18) -> (11/6,2/1) Hyperbolic Matrix(733,284,1004,389) (-7/18,-12/31) -> (8/11,19/26) Hyperbolic Matrix(275,106,454,175) (-12/31,-5/13) -> (3/5,14/23) Hyperbolic Matrix(271,104,456,175) (-5/13,-13/34) -> (13/22,3/5) Hyperbolic Matrix(907,346,270,103) (-13/34,-8/21) -> (10/3,27/8) Hyperbolic Matrix(179,68,408,155) (-8/21,-3/8) -> (7/16,4/9) Hyperbolic Matrix(625,232,132,49) (-3/8,-10/27) -> (14/3,19/4) Hyperbolic Matrix(1065,394,446,165) (-10/27,-7/19) -> (31/13,12/5) Hyperbolic Matrix(175,64,-484,-177) (-7/19,-4/11) -> (-4/11,-9/25) Parabolic Matrix(2361,848,916,329) (-9/25,-14/39) -> (18/7,49/19) Hyperbolic Matrix(1831,656,1136,407) (-14/39,-5/14) -> (29/18,50/31) Hyperbolic Matrix(175,62,302,107) (-5/14,-1/3) -> (11/19,7/12) Hyperbolic Matrix(407,128,124,39) (-1/3,-5/16) -> (13/4,23/7) Hyperbolic Matrix(815,254,446,139) (-5/16,-9/29) -> (31/17,11/6) Hyperbolic Matrix(1701,526,650,201) (-9/29,-4/13) -> (34/13,55/21) Hyperbolic Matrix(1051,322,1694,519) (-4/13,-11/36) -> (31/50,18/29) Hyperbolic Matrix(965,294,686,209) (-11/36,-7/23) -> (7/5,31/22) Hyperbolic Matrix(323,98,1526,463) (-7/23,-10/33) -> (4/19,7/33) Hyperbolic Matrix(1523,460,884,267) (-10/33,-3/10) -> (31/18,50/29) Hyperbolic Matrix(957,284,556,165) (-3/10,-8/27) -> (12/7,31/18) Hyperbolic Matrix(237,70,518,153) (-8/27,-5/17) -> (5/11,6/13) Hyperbolic Matrix(159,46,38,11) (-5/17,-2/7) -> (4/1,13/3) Hyperbolic Matrix(155,44,236,67) (-2/7,-9/32) -> (13/20,2/3) Hyperbolic Matrix(4207,1182,2374,667) (-9/32,-16/57) -> (62/35,39/22) Hyperbolic Matrix(3735,1048,2648,743) (-16/57,-7/25) -> (55/39,24/17) Hyperbolic Matrix(1009,282,390,109) (-7/25,-5/18) -> (31/12,13/5) Hyperbolic Matrix(231,64,776,215) (-5/18,-8/29) -> (8/27,3/10) Hyperbolic Matrix(387,106,230,63) (-8/29,-3/11) -> (5/3,22/13) Hyperbolic Matrix(231,62,190,51) (-3/11,-4/15) -> (6/5,11/9) Hyperbolic Matrix(151,40,268,71) (-4/15,-1/4) -> (9/16,4/7) Hyperbolic Matrix(291,68,184,43) (-1/4,-3/13) -> (11/7,19/12) Hyperbolic Matrix(71,16,-324,-73) (-3/13,-2/9) -> (-2/9,-5/23) Parabolic Matrix(427,92,608,131) (-5/23,-3/14) -> (7/10,19/27) Hyperbolic Matrix(497,106,286,61) (-3/14,-4/19) -> (26/15,7/4) Hyperbolic Matrix(2053,430,1418,297) (-4/19,-9/43) -> (13/9,42/29) Hyperbolic Matrix(2123,444,2692,563) (-9/43,-5/24) -> (41/52,15/19) Hyperbolic Matrix(1059,220,284,59) (-5/24,-1/5) -> (41/11,15/4) Hyperbolic Matrix(417,80,172,33) (-1/5,-3/16) -> (29/12,17/7) Hyperbolic Matrix(343,64,552,103) (-3/16,-2/11) -> (18/29,5/8) Hyperbolic Matrix(67,12,240,43) (-2/11,-1/6) -> (5/18,2/7) Hyperbolic Matrix(2741,444,1068,173) (-1/6,-5/31) -> (59/23,77/30) Hyperbolic Matrix(3939,634,1634,263) (-5/31,-4/25) -> (94/39,41/17) Hyperbolic Matrix(5461,870,2266,361) (-4/25,-7/44) -> (53/22,94/39) Hyperbolic Matrix(331,52,732,115) (-3/19,-2/13) -> (14/31,5/11) Hyperbolic Matrix(131,20,596,91) (-2/13,-3/20) -> (7/32,2/9) Hyperbolic Matrix(659,98,854,127) (-3/20,-1/7) -> (27/35,17/22) Hyperbolic Matrix(325,44,96,13) (-1/7,-1/8) -> (27/8,17/5) Hyperbolic Matrix(829,100,572,69) (-1/8,-2/17) -> (42/29,29/20) Hyperbolic Matrix(949,108,536,61) (-2/17,-1/9) -> (23/13,62/35) Hyperbolic Matrix(563,60,1004,107) (-1/9,-1/10) -> (37/66,23/41) Hyperbolic Matrix(433,40,184,17) (-1/10,0/1) -> (40/17,33/14) Hyperbolic Matrix(407,-42,126,-13) (0/1,1/9) -> (29/9,42/13) Hyperbolic Matrix(855,-98,602,-69) (1/9,1/8) -> (71/50,27/19) Hyperbolic Matrix(147,-20,272,-37) (1/8,1/7) -> (7/13,13/24) Hyperbolic Matrix(437,-66,682,-103) (1/7,2/13) -> (16/25,25/39) Hyperbolic Matrix(433,-70,266,-43) (2/13,1/6) -> (13/8,44/27) Hyperbolic Matrix(191,-34,118,-21) (1/6,1/5) -> (21/13,13/8) Hyperbolic Matrix(417,-86,674,-139) (1/5,4/19) -> (34/55,13/21) Hyperbolic Matrix(1385,-294,994,-211) (7/33,3/14) -> (39/28,7/5) Hyperbolic Matrix(231,-50,1058,-229) (3/14,5/23) -> (5/23,7/32) Parabolic Matrix(365,-82,138,-31) (2/9,3/13) -> (29/11,8/3) Hyperbolic Matrix(499,-116,228,-53) (3/13,4/17) -> (24/11,11/5) Hyperbolic Matrix(1133,-268,520,-123) (4/17,5/21) -> (37/17,24/11) Hyperbolic Matrix(1039,-250,586,-141) (5/21,1/4) -> (39/22,55/31) Hyperbolic Matrix(311,-82,110,-29) (1/4,4/15) -> (14/5,17/6) Hyperbolic Matrix(133,-36,484,-131) (4/15,3/11) -> (3/11,8/29) Parabolic Matrix(1667,-462,350,-97) (13/47,5/18) -> (19/4,43/9) Hyperbolic Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(1427,-422,842,-249) (5/17,8/27) -> (22/13,39/23) Hyperbolic Matrix(989,-300,300,-91) (3/10,7/23) -> (23/7,33/10) Hyperbolic Matrix(1631,-498,750,-229) (7/23,11/36) -> (13/6,37/17) Hyperbolic Matrix(985,-302,1758,-539) (11/36,4/13) -> (14/25,37/66) Hyperbolic Matrix(553,-174,874,-275) (5/16,1/3) -> (31/49,19/30) Hyperbolic Matrix(371,-132,104,-37) (1/3,5/14) -> (7/2,25/7) Hyperbolic Matrix(535,-192,248,-89) (5/14,9/25) -> (15/7,13/6) Hyperbolic Matrix(1441,-520,884,-319) (9/25,4/11) -> (44/27,31/19) Hyperbolic Matrix(779,-286,286,-105) (4/11,7/19) -> (19/7,30/11) Hyperbolic Matrix(449,-166,614,-227) (7/19,3/8) -> (19/26,11/15) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(435,-182,98,-41) (5/12,8/19) -> (22/5,9/2) Hyperbolic Matrix(393,-166,670,-283) (8/19,3/7) -> (17/29,10/17) Hyperbolic Matrix(273,-118,118,-51) (3/7,7/16) -> (23/10,7/3) Hyperbolic Matrix(2089,-934,794,-355) (4/9,13/29) -> (71/27,50/19) Hyperbolic Matrix(1931,-868,812,-365) (13/29,9/20) -> (19/8,69/29) Hyperbolic Matrix(305,-142,58,-27) (6/13,1/2) -> (21/4,16/3) Hyperbolic Matrix(583,-312,256,-137) (1/2,7/13) -> (25/11,41/18) Hyperbolic Matrix(871,-474,362,-197) (13/24,6/11) -> (12/5,53/22) Hyperbolic Matrix(181,-100,324,-179) (6/11,5/9) -> (5/9,14/25) Parabolic Matrix(1219,-684,180,-101) (23/41,9/16) -> (27/4,7/1) Hyperbolic Matrix(1349,-780,780,-451) (15/26,11/19) -> (19/11,45/26) Hyperbolic Matrix(1519,-890,582,-341) (7/12,17/29) -> (13/5,47/18) Hyperbolic Matrix(845,-498,582,-343) (10/17,13/22) -> (29/20,16/11) Hyperbolic Matrix(1183,-722,834,-509) (14/23,11/18) -> (17/12,44/31) Hyperbolic Matrix(417,-256,676,-415) (11/18,8/13) -> (8/13,21/34) Parabolic Matrix(4569,-2824,1228,-759) (21/34,34/55) -> (26/7,67/18) Hyperbolic Matrix(1107,-686,518,-321) (13/21,31/50) -> (17/8,15/7) Hyperbolic Matrix(619,-390,446,-281) (5/8,12/19) -> (18/13,25/18) Hyperbolic Matrix(3807,-2408,1064,-673) (12/19,31/49) -> (25/7,68/19) Hyperbolic Matrix(923,-590,1178,-753) (7/11,16/25) -> (18/23,29/37) Hyperbolic Matrix(2423,-1554,1330,-853) (25/39,9/14) -> (51/28,31/17) Hyperbolic Matrix(375,-242,578,-373) (9/14,11/17) -> (11/17,13/20) Parabolic Matrix(429,-298,298,-207) (9/13,7/10) -> (23/16,13/9) Hyperbolic Matrix(1183,-834,722,-509) (19/27,12/17) -> (18/11,41/25) Hyperbolic Matrix(327,-232,148,-105) (12/17,5/7) -> (11/5,20/9) Hyperbolic Matrix(619,-446,390,-281) (5/7,13/18) -> (19/12,27/17) Hyperbolic Matrix(1495,-1082,438,-317) (13/18,21/29) -> (17/5,41/12) Hyperbolic Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(4473,-3424,1744,-1335) (13/17,36/47) -> (100/39,59/23) Hyperbolic Matrix(3869,-2964,808,-619) (36/47,23/30) -> (67/14,24/5) Hyperbolic Matrix(951,-730,142,-109) (23/30,10/13) -> (20/3,27/4) Hyperbolic Matrix(1423,-1096,396,-305) (10/13,27/35) -> (61/17,18/5) Hyperbolic Matrix(1327,-1026,410,-317) (17/22,24/31) -> (42/13,13/4) Hyperbolic Matrix(2239,-1736,868,-673) (24/31,7/9) -> (49/19,80/31) Hyperbolic Matrix(1163,-908,488,-381) (7/9,18/23) -> (50/21,31/13) Hyperbolic Matrix(2071,-1624,644,-505) (29/37,11/14) -> (45/14,29/9) Hyperbolic Matrix(1065,-838,502,-395) (11/14,37/47) -> (19/9,17/8) Hyperbolic Matrix(721,-568,344,-271) (37/47,26/33) -> (2/1,19/9) Hyperbolic Matrix(123,-100,16,-13) (4/5,9/11) -> (7/1,8/1) Hyperbolic Matrix(215,-178,122,-101) (9/11,5/6) -> (7/4,23/13) Hyperbolic Matrix(1217,-1022,518,-435) (5/6,21/25) -> (7/3,47/20) Hyperbolic Matrix(3195,-2686,2266,-1905) (21/25,16/19) -> (86/61,55/39) Hyperbolic Matrix(3341,-2818,2370,-1999) (16/19,27/32) -> (31/22,86/61) Hyperbolic Matrix(2247,-1898,470,-397) (27/32,11/13) -> (43/9,67/14) Hyperbolic Matrix(451,-388,136,-117) (6/7,13/15) -> (43/13,10/3) Hyperbolic Matrix(839,-730,254,-221) (13/15,7/8) -> (33/10,43/13) Hyperbolic Matrix(357,-316,148,-131) (7/8,1/1) -> (41/17,29/12) Hyperbolic Matrix(103,-122,38,-45) (1/1,6/5) -> (8/3,19/7) Hyperbolic Matrix(227,-278,138,-169) (11/9,5/4) -> (23/14,5/3) Hyperbolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(283,-390,82,-113) (11/8,18/13) -> (24/7,7/2) Hyperbolic Matrix(891,-1238,398,-553) (25/18,32/23) -> (38/17,9/4) Hyperbolic Matrix(2201,-3064,936,-1303) (32/23,39/28) -> (47/20,40/17) Hyperbolic Matrix(2623,-3706,1102,-1557) (24/17,41/29) -> (69/29,50/21) Hyperbolic Matrix(1461,-2068,556,-787) (41/29,17/12) -> (21/8,71/27) Hyperbolic Matrix(3935,-5586,1666,-2365) (44/31,71/50) -> (85/36,26/11) Hyperbolic Matrix(483,-692,104,-149) (10/7,23/16) -> (37/8,14/3) Hyperbolic Matrix(227,-332,80,-117) (16/11,3/2) -> (17/6,20/7) Hyperbolic Matrix(331,-508,144,-221) (3/2,17/11) -> (39/17,23/10) Hyperbolic Matrix(527,-818,230,-357) (17/11,14/9) -> (16/7,39/17) Hyperbolic Matrix(437,-682,66,-103) (14/9,25/16) -> (13/2,20/3) Hyperbolic Matrix(995,-1582,378,-601) (27/17,8/5) -> (50/19,29/11) Hyperbolic Matrix(493,-796,96,-155) (50/31,21/13) -> (5/1,26/5) Hyperbolic Matrix(511,-834,106,-173) (31/19,18/11) -> (24/5,5/1) Hyperbolic Matrix(551,-904,64,-105) (41/25,23/14) -> (17/2,9/1) Hyperbolic Matrix(1599,-2714,446,-757) (39/23,17/10) -> (43/12,61/17) Hyperbolic Matrix(393,-670,166,-283) (17/10,12/7) -> (26/11,19/8) Hyperbolic Matrix(1829,-3154,802,-1383) (50/29,19/11) -> (57/25,16/7) Hyperbolic Matrix(1517,-2626,554,-959) (45/26,26/15) -> (52/19,11/4) Hyperbolic Matrix(3107,-5516,868,-1541) (55/31,16/9) -> (68/19,111/31) Hyperbolic Matrix(181,-324,100,-179) (16/9,9/5) -> (9/5,20/11) Parabolic Matrix(1351,-2458,526,-957) (20/11,51/28) -> (77/30,18/7) Hyperbolic Matrix(799,-1778,182,-405) (20/9,29/13) -> (57/13,22/5) Hyperbolic Matrix(2165,-4834,494,-1103) (29/13,38/17) -> (92/21,57/13) Hyperbolic Matrix(1213,-2764,384,-875) (41/18,57/25) -> (41/13,19/6) Hyperbolic Matrix(2951,-6962,1250,-2949) (33/14,59/25) -> (59/25,85/36) Parabolic Matrix(81,-200,32,-79) (17/7,5/2) -> (5/2,23/9) Parabolic Matrix(1259,-3222,338,-865) (23/9,41/16) -> (67/18,41/11) Hyperbolic Matrix(5517,-14140,1540,-3947) (41/16,141/55) -> (197/55,43/12) Hyperbolic Matrix(16153,-41414,4510,-11563) (141/55,100/39) -> (154/43,197/55) Hyperbolic Matrix(2189,-5652,500,-1291) (80/31,31/12) -> (35/8,92/21) Hyperbolic Matrix(977,-2552,116,-303) (47/18,81/31) -> (25/3,17/2) Hyperbolic Matrix(573,-1498,70,-183) (81/31,34/13) -> (8/1,25/3) Hyperbolic Matrix(1231,-3362,450,-1229) (30/11,41/15) -> (41/15,52/19) Parabolic Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(43,-126,14,-41) (20/7,3/1) -> (3/1,22/7) Parabolic Matrix(2779,-8756,776,-2445) (22/7,41/13) -> (111/31,154/43) Hyperbolic Matrix(321,-1024,100,-319) (19/6,16/5) -> (16/5,45/14) Parabolic Matrix(963,-3292,184,-629) (41/12,65/19) -> (47/9,21/4) Hyperbolic Matrix(823,-2818,158,-541) (65/19,24/7) -> (26/5,47/9) Hyperbolic Matrix(133,-484,36,-131) (18/5,11/3) -> (11/3,26/7) Parabolic Matrix(231,-1058,50,-229) (9/2,23/5) -> (23/5,37/8) Parabolic Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(425,202,162,77) -> Matrix(5,-4,4,-3) Matrix(835,388,368,171) -> Matrix(3,-2,2,-1) Matrix(933,428,412,189) -> Matrix(7,-4,2,-1) Matrix(823,376,1136,519) -> Matrix(3,-2,8,-5) Matrix(103,46,150,67) -> Matrix(3,-2,8,-5) Matrix(199,88,52,23) -> Matrix(5,-4,4,-3) Matrix(795,346,494,215) -> Matrix(3,-2,2,-1) Matrix(295,128,348,151) -> Matrix(3,-2,2,-1) Matrix(485,206,1754,745) -> Matrix(3,-2,14,-9) Matrix(1165,494,1606,681) -> Matrix(3,-2,2,-1) Matrix(389,164,676,285) -> Matrix(3,-2,8,-5) Matrix(871,366,1930,811) -> Matrix(11,-8,-4,3) Matrix(481,202,50,21) -> Matrix(5,-4,4,-3) Matrix(673,282,1062,445) -> Matrix(5,-4,-6,5) Matrix(193,80,620,257) -> Matrix(1,0,0,1) Matrix(953,394,670,277) -> Matrix(1,0,0,1) Matrix(667,274,426,175) -> Matrix(7,-6,6,-5) Matrix(1231,502,282,115) -> Matrix(13,-10,4,-3) Matrix(285,116,-1796,-731) -> Matrix(5,-4,4,-3) Matrix(1037,420,1316,533) -> Matrix(13,-12,38,-35) Matrix(91,36,48,19) -> Matrix(1,0,0,1) Matrix(733,284,1004,389) -> Matrix(1,-2,2,-3) Matrix(275,106,454,175) -> Matrix(1,0,0,1) Matrix(271,104,456,175) -> Matrix(1,-2,2,-3) Matrix(907,346,270,103) -> Matrix(3,-2,2,-1) Matrix(179,68,408,155) -> Matrix(3,-2,2,-1) Matrix(625,232,132,49) -> Matrix(1,0,0,1) Matrix(1065,394,446,165) -> Matrix(1,0,0,1) Matrix(175,64,-484,-177) -> Matrix(3,-2,2,-1) Matrix(2361,848,916,329) -> Matrix(3,-2,2,-1) Matrix(1831,656,1136,407) -> Matrix(1,-2,0,1) Matrix(175,62,302,107) -> Matrix(1,0,2,1) Matrix(407,128,124,39) -> Matrix(3,-2,2,-1) Matrix(815,254,446,139) -> Matrix(5,-4,4,-3) Matrix(1701,526,650,201) -> Matrix(3,-8,2,-5) Matrix(1051,322,1694,519) -> Matrix(1,2,-2,-3) Matrix(965,294,686,209) -> Matrix(1,0,4,1) Matrix(323,98,1526,463) -> Matrix(1,0,0,1) Matrix(1523,460,884,267) -> Matrix(7,2,10,3) Matrix(957,284,556,165) -> Matrix(1,-2,2,-3) Matrix(237,70,518,153) -> Matrix(1,0,-2,1) Matrix(159,46,38,11) -> Matrix(1,2,0,1) Matrix(155,44,236,67) -> Matrix(1,0,4,1) Matrix(4207,1182,2374,667) -> Matrix(41,-6,48,-7) Matrix(3735,1048,2648,743) -> Matrix(11,-2,28,-5) Matrix(1009,282,390,109) -> Matrix(13,-4,10,-3) Matrix(231,64,776,215) -> Matrix(1,0,-2,1) Matrix(387,106,230,63) -> Matrix(1,0,0,1) Matrix(231,62,190,51) -> Matrix(1,0,2,1) Matrix(151,40,268,71) -> Matrix(1,0,4,1) Matrix(291,68,184,43) -> Matrix(3,-2,2,-1) Matrix(71,16,-324,-73) -> Matrix(1,0,2,1) Matrix(427,92,608,131) -> Matrix(1,0,0,1) Matrix(497,106,286,61) -> Matrix(1,-2,2,-3) Matrix(2053,430,1418,297) -> Matrix(1,0,0,1) Matrix(2123,444,2692,563) -> Matrix(7,-6,20,-17) Matrix(1059,220,284,59) -> Matrix(3,-2,2,-1) Matrix(417,80,172,33) -> Matrix(1,0,0,1) Matrix(343,64,552,103) -> Matrix(1,0,-2,1) Matrix(67,12,240,43) -> Matrix(1,0,2,1) Matrix(2741,444,1068,173) -> Matrix(33,-14,26,-11) Matrix(3939,634,1634,263) -> Matrix(3,-2,2,-1) Matrix(5461,870,2266,361) -> Matrix(1,0,0,1) Matrix(331,52,732,115) -> Matrix(1,-2,0,1) Matrix(131,20,596,91) -> Matrix(1,0,4,1) Matrix(659,98,854,127) -> Matrix(1,0,0,1) Matrix(325,44,96,13) -> Matrix(3,-2,2,-1) Matrix(829,100,572,69) -> Matrix(1,0,0,1) Matrix(949,108,536,61) -> Matrix(5,-6,6,-7) Matrix(563,60,1004,107) -> Matrix(1,0,6,1) Matrix(433,40,184,17) -> Matrix(3,-2,2,-1) Matrix(407,-42,126,-13) -> Matrix(3,-2,2,-1) Matrix(855,-98,602,-69) -> Matrix(1,-2,2,-3) Matrix(147,-20,272,-37) -> Matrix(1,0,-2,1) Matrix(437,-66,682,-103) -> Matrix(1,0,-6,1) Matrix(433,-70,266,-43) -> Matrix(1,0,2,1) Matrix(191,-34,118,-21) -> Matrix(1,0,0,1) Matrix(417,-86,674,-139) -> Matrix(1,-2,0,1) Matrix(1385,-294,994,-211) -> Matrix(1,0,2,1) Matrix(231,-50,1058,-229) -> Matrix(1,0,10,1) Matrix(365,-82,138,-31) -> Matrix(7,-2,4,-1) Matrix(499,-116,228,-53) -> Matrix(5,-4,4,-3) Matrix(1133,-268,520,-123) -> Matrix(3,-2,2,-1) Matrix(1039,-250,586,-141) -> Matrix(7,6,8,7) Matrix(311,-82,110,-29) -> Matrix(1,2,0,1) Matrix(133,-36,484,-131) -> Matrix(1,0,6,1) Matrix(1667,-462,350,-97) -> Matrix(7,-2,4,-1) Matrix(173,-50,218,-63) -> Matrix(3,-2,8,-5) Matrix(1427,-422,842,-249) -> Matrix(1,-2,2,-3) Matrix(989,-300,300,-91) -> Matrix(7,-2,4,-1) Matrix(1631,-498,750,-229) -> Matrix(5,-4,4,-3) Matrix(985,-302,1758,-539) -> Matrix(1,0,6,1) Matrix(553,-174,874,-275) -> Matrix(1,-2,0,1) Matrix(371,-132,104,-37) -> Matrix(3,-2,2,-1) Matrix(535,-192,248,-89) -> Matrix(7,-6,6,-5) Matrix(1441,-520,884,-319) -> Matrix(1,0,2,1) Matrix(779,-286,286,-105) -> Matrix(1,0,0,1) Matrix(449,-166,614,-227) -> Matrix(1,0,0,1) Matrix(41,-16,100,-39) -> Matrix(1,0,2,1) Matrix(435,-182,98,-41) -> Matrix(3,-2,2,-1) Matrix(393,-166,670,-283) -> Matrix(5,-2,8,-3) Matrix(273,-118,118,-51) -> Matrix(5,-4,4,-3) Matrix(2089,-934,794,-355) -> Matrix(3,-20,2,-13) Matrix(1931,-868,812,-365) -> Matrix(1,4,0,1) Matrix(305,-142,58,-27) -> Matrix(5,2,2,1) Matrix(583,-312,256,-137) -> Matrix(1,0,2,1) Matrix(871,-474,362,-197) -> Matrix(1,0,2,1) Matrix(181,-100,324,-179) -> Matrix(1,0,10,1) Matrix(1219,-684,180,-101) -> Matrix(15,-2,8,-1) Matrix(1349,-780,780,-451) -> Matrix(11,-4,14,-5) Matrix(1519,-890,582,-341) -> Matrix(29,-16,20,-11) Matrix(845,-498,582,-343) -> Matrix(3,-2,8,-5) Matrix(1183,-722,834,-509) -> Matrix(1,-4,2,-7) Matrix(417,-256,676,-415) -> Matrix(1,-2,0,1) Matrix(4569,-2824,1228,-759) -> Matrix(3,10,2,7) Matrix(1107,-686,518,-321) -> Matrix(9,10,8,9) Matrix(619,-390,446,-281) -> Matrix(1,0,2,1) Matrix(3807,-2408,1064,-673) -> Matrix(1,4,0,1) Matrix(923,-590,1178,-753) -> Matrix(7,2,24,7) Matrix(2423,-1554,1330,-853) -> Matrix(29,6,24,5) Matrix(375,-242,578,-373) -> Matrix(1,0,22,1) Matrix(429,-298,298,-207) -> Matrix(5,-2,8,-3) Matrix(1183,-834,722,-509) -> Matrix(1,0,0,1) Matrix(327,-232,148,-105) -> Matrix(5,-4,4,-3) Matrix(619,-446,390,-281) -> Matrix(1,2,0,1) Matrix(1495,-1082,438,-317) -> Matrix(7,-2,4,-1) Matrix(97,-72,128,-95) -> Matrix(1,0,4,1) Matrix(4473,-3424,1744,-1335) -> Matrix(141,-34,112,-27) Matrix(3869,-2964,808,-619) -> Matrix(31,-8,4,-1) Matrix(951,-730,142,-109) -> Matrix(13,-4,10,-3) Matrix(1423,-1096,396,-305) -> Matrix(1,0,-2,1) Matrix(1327,-1026,410,-317) -> Matrix(7,-2,4,-1) Matrix(2239,-1736,868,-673) -> Matrix(13,-4,10,-3) Matrix(1163,-908,488,-381) -> Matrix(1,0,-4,1) Matrix(2071,-1624,644,-505) -> Matrix(13,-4,10,-3) Matrix(1065,-838,502,-395) -> Matrix(67,-22,64,-21) Matrix(721,-568,344,-271) -> Matrix(35,-12,38,-13) Matrix(123,-100,16,-13) -> Matrix(7,-4,2,-1) Matrix(215,-178,122,-101) -> Matrix(3,-4,4,-5) Matrix(1217,-1022,518,-435) -> Matrix(3,-2,2,-1) Matrix(3195,-2686,2266,-1905) -> Matrix(3,-2,8,-5) Matrix(3341,-2818,2370,-1999) -> Matrix(7,-2,18,-5) Matrix(2247,-1898,470,-397) -> Matrix(7,-4,2,-1) Matrix(451,-388,136,-117) -> Matrix(1,2,0,1) Matrix(839,-730,254,-221) -> Matrix(15,-2,8,-1) Matrix(357,-316,148,-131) -> Matrix(1,0,-2,1) Matrix(103,-122,38,-45) -> Matrix(3,-2,2,-1) Matrix(227,-278,138,-169) -> Matrix(5,-2,8,-3) Matrix(49,-64,36,-47) -> Matrix(3,-2,2,-1) Matrix(283,-390,82,-113) -> Matrix(1,2,0,1) Matrix(891,-1238,398,-553) -> Matrix(3,-2,2,-1) Matrix(2201,-3064,936,-1303) -> Matrix(3,-2,2,-1) Matrix(2623,-3706,1102,-1557) -> Matrix(13,-6,-2,1) Matrix(1461,-2068,556,-787) -> Matrix(5,-4,4,-3) Matrix(3935,-5586,1666,-2365) -> Matrix(19,-12,8,-5) Matrix(483,-692,104,-149) -> Matrix(1,0,-2,1) Matrix(227,-332,80,-117) -> Matrix(7,-4,2,-1) Matrix(331,-508,144,-221) -> Matrix(13,-12,12,-11) Matrix(527,-818,230,-357) -> Matrix(11,-12,12,-13) Matrix(437,-682,66,-103) -> Matrix(3,-4,4,-5) Matrix(995,-1582,378,-601) -> Matrix(3,-14,2,-9) Matrix(493,-796,96,-155) -> Matrix(3,-2,2,-1) Matrix(511,-834,106,-173) -> Matrix(1,0,-2,1) Matrix(551,-904,64,-105) -> Matrix(5,-2,-2,1) Matrix(1599,-2714,446,-757) -> Matrix(1,0,-2,1) Matrix(393,-670,166,-283) -> Matrix(7,-4,2,-1) Matrix(1829,-3154,802,-1383) -> Matrix(11,-8,18,-13) Matrix(1517,-2626,554,-959) -> Matrix(9,-8,8,-7) Matrix(3107,-5516,868,-1541) -> Matrix(41,-36,8,-7) Matrix(181,-324,100,-179) -> Matrix(17,-16,16,-15) Matrix(1351,-2458,526,-957) -> Matrix(59,-68,46,-53) Matrix(799,-1778,182,-405) -> Matrix(9,-14,2,-3) Matrix(2165,-4834,494,-1103) -> Matrix(1,2,0,1) Matrix(1213,-2764,384,-875) -> Matrix(19,-8,12,-5) Matrix(2951,-6962,1250,-2949) -> Matrix(13,-24,6,-11) Matrix(81,-200,32,-79) -> Matrix(7,-6,6,-5) Matrix(1259,-3222,338,-865) -> Matrix(23,-28,14,-17) Matrix(5517,-14140,1540,-3947) -> Matrix(37,-46,-4,5) Matrix(16153,-41414,4510,-11563) -> Matrix(147,-184,4,-5) Matrix(2189,-5652,500,-1291) -> Matrix(5,-8,2,-3) Matrix(977,-2552,116,-303) -> Matrix(31,-46,-2,3) Matrix(573,-1498,70,-183) -> Matrix(21,-32,2,-3) Matrix(1231,-3362,450,-1229) -> Matrix(9,-8,8,-7) Matrix(119,-330,22,-61) -> Matrix(5,-8,2,-3) Matrix(43,-126,14,-41) -> Matrix(3,-2,2,-1) Matrix(2779,-8756,776,-2445) -> Matrix(29,-44,2,-3) Matrix(321,-1024,100,-319) -> Matrix(5,-8,2,-3) Matrix(963,-3292,184,-629) -> Matrix(21,-40,10,-19) Matrix(823,-2818,158,-541) -> Matrix(15,-32,8,-17) Matrix(133,-484,36,-131) -> Matrix(3,-2,2,-1) Matrix(231,-1058,50,-229) -> Matrix(1,-6,0,1) Matrix(25,-144,4,-23) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 58 Degree of the the map X: 58 Degree of the the map Y: 192 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 1 1 0/1 (0/1,1/1) 0 28 1/9 0 14 1/8 1/2 1 28 1/7 0/1 1 7 2/13 (1/2,1/1) 0 28 1/6 0/1 1 4 1/5 0 14 4/19 (-1/1,1/0) 0 28 3/14 -1/2 1 28 5/23 0/1 5 1 2/9 (0/1,1/3) 0 28 3/13 1/1 1 7 4/17 1/1 2 4 5/21 0 14 1/4 1/2 1 28 4/15 (-1/1,0/1) 0 28 3/11 0/1 3 2 2/7 (0/1,1/2) 0 28 5/17 0 14 3/10 1/0 1 28 7/23 0 14 11/36 1/0 1 28 4/13 (0/1,1/2) 0 28 1/3 0/1 1 7 5/14 1/2 1 28 9/25 0 14 4/11 (1/2,1/1) 0 28 7/19 0 14 3/8 1/0 1 28 2/5 0/1 2 4 5/12 1/2 1 28 8/19 (2/5,1/2) 0 28 3/7 0 14 4/9 (2/1,1/0) 0 28 13/29 1/0 9 2 9/20 1/0 1 28 5/11 -1/1 1 7 1/2 1/2 1 28 7/13 0/1 1 7 13/24 1/0 1 28 6/11 (-1/2,0/1) 0 28 5/9 0/1 5 2 4/7 (0/1,1/3) 0 28 7/12 1/2 1 28 17/29 0 14 10/17 (0/1,1/2) 0 28 3/5 1/1 1 7 11/18 1/0 1 28 8/13 1/0 2 4 21/34 1/0 1 28 34/55 (-3/1,1/0) 0 28 13/21 0 14 5/8 1/0 1 28 12/19 (0/1,1/1) 0 28 7/11 0 14 16/25 (-1/4,-1/5) 0 28 25/39 0/1 1 7 9/14 -1/8 1 28 11/17 0/1 11 1 2/3 (0/1,1/3) 0 28 7/10 1/2 1 28 12/17 (1/2,2/3) 0 28 5/7 1/1 1 7 13/18 -1/2 1 28 21/29 0 14 8/11 (0/1,1/1) 0 28 11/15 0 14 3/4 0/1 2 4 13/17 0 14 36/47 (1/4,10/39) 0 28 23/30 5/18 1 28 10/13 (1/3,1/2) 0 28 17/22 1/4 1 28 24/31 (0/1,1/3) 0 28 7/9 0/1 1 7 18/23 (1/4,3/11) 0 28 29/37 0 14 11/14 5/16 1 28 37/47 1/3 17 1 26/33 (1/3,12/35) 0 28 15/19 0 14 4/5 (2/5,1/2) 0 28 9/11 2/3 1 7 5/6 1/0 1 28 6/7 (0/1,1/0) 0 28 13/15 0/1 4 1 7/8 1/4 1 28 1/1 0 14 6/5 (0/1,1/1) 0 28 5/4 1/2 1 28 4/3 1/1 2 4 11/8 1/0 1 28 18/13 (0/1,1/3) 0 28 25/18 1/2 1 28 32/23 (0/1,1/1) 0 28 7/5 0/1 1 7 24/17 (3/7,1/2) 0 28 41/29 1/2 9 2 17/12 1/2 1 28 10/7 (0/1,1/2) 0 28 13/9 0 14 16/11 (2/5,1/2) 0 28 3/2 3/4 1 28 17/11 1/1 12 1 14/9 (1/1,9/8) 0 28 11/7 0 14 8/5 (0/1,1/0) 0 28 21/13 0 14 13/8 0/1 1 4 44/27 (1/4,1/3) 0 28 31/19 0 14 18/11 (1/2,2/3) 0 28 5/3 1/1 1 7 17/10 1/2 1 28 12/7 (2/3,1/1) 0 28 19/11 0 14 7/4 3/4 1 28 23/13 6/7 1 7 39/22 19/22 1 28 55/31 0 14 16/9 (8/9,1/1) 0 28 9/5 1/1 8 2 2/1 (0/1,1/1) 0 28 15/7 0 14 13/6 5/4 1 28 37/17 0 14 24/11 1/1 2 4 11/5 1/1 1 7 20/9 (3/2,2/1) 0 28 29/13 2/1 1 2 38/17 (1/1,2/1) 0 28 9/4 1/0 1 28 25/11 0/1 1 7 41/18 1/4 1 28 16/7 (3/4,1/1) 0 28 7/3 0 14 33/14 3/2 1 28 59/25 2/1 3 1 26/11 (2/1,3/1) 0 28 19/8 1/0 1 28 12/5 (0/1,1/0) 0 28 17/7 0/1 1 7 5/2 1/1 3 4 23/9 6/5 1 7 41/16 5/4 1 28 141/55 5/4 23 1 100/39 (5/4,84/67) 0 28 59/23 0 14 18/7 (9/7,4/3) 0 28 13/5 0 14 47/18 3/2 1 28 81/31 3/2 13 1 34/13 (3/2,14/9) 0 28 21/8 3/2 1 28 29/11 5/3 1 7 8/3 (1/1,2/1) 0 28 19/7 0 14 30/11 (1/2,1/1) 0 28 41/15 1/1 4 1 11/4 3/2 1 28 14/5 (1/1,2/1) 0 28 17/6 5/2 1 28 20/7 (6/1,1/0) 0 28 3/1 1/1 1 7 22/7 (16/11,3/2) 0 28 19/6 13/8 1 28 16/5 2/1 2 4 45/14 1/2 1 28 29/9 0 14 42/13 (1/1,2/1) 0 28 13/4 1/0 1 28 10/3 (2/1,1/0) 0 28 17/5 0 14 41/12 11/6 1 28 65/19 2/1 9 1 24/7 (2/1,7/3) 0 28 7/2 1/0 1 28 25/7 2/1 1 7 43/12 1/0 1 28 18/5 (1/1,1/0) 0 28 11/3 1/1 1 2 4/1 (1/1,2/1) 0 28 9/2 1/0 1 28 23/5 1/0 3 1 14/3 (0/1,1/0) 0 28 5/1 0 14 16/3 (2/1,3/1) 0 28 11/2 1/0 1 28 6/1 1/0 2 4 13/2 1/0 1 28 7/1 2/1 1 7 8/1 (6/1,1/0) 0 28 1/0 1/0 1 28 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(407,-42,126,-13) (0/1,1/9) -> (29/9,42/13) Hyperbolic Matrix(353,-40,150,-17) (1/9,1/8) -> (7/3,33/14) Glide Reflection Matrix(147,-20,272,-37) (1/8,1/7) -> (7/13,13/24) Hyperbolic Matrix(437,-66,682,-103) (1/7,2/13) -> (16/25,25/39) Hyperbolic Matrix(433,-70,266,-43) (2/13,1/6) -> (13/8,44/27) Hyperbolic Matrix(191,-34,118,-21) (1/6,1/5) -> (21/13,13/8) Hyperbolic Matrix(417,-86,674,-139) (1/5,4/19) -> (34/55,13/21) Hyperbolic Matrix(463,-98,600,-127) (4/19,3/14) -> (10/13,17/22) Glide Reflection Matrix(139,-30,644,-139) (3/14,5/23) -> (3/14,5/23) Reflection Matrix(91,-20,414,-91) (5/23,2/9) -> (5/23,2/9) Reflection Matrix(365,-82,138,-31) (2/9,3/13) -> (29/11,8/3) Hyperbolic Matrix(499,-116,228,-53) (3/13,4/17) -> (24/11,11/5) Hyperbolic Matrix(1133,-268,520,-123) (4/17,5/21) -> (37/17,24/11) Hyperbolic Matrix(1039,-250,586,-141) (5/21,1/4) -> (39/22,55/31) Hyperbolic Matrix(311,-82,110,-29) (1/4,4/15) -> (14/5,17/6) Hyperbolic Matrix(89,-24,330,-89) (4/15,3/11) -> (4/15,3/11) Reflection Matrix(43,-12,154,-43) (3/11,2/7) -> (3/11,2/7) Reflection Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(215,-64,346,-103) (5/17,3/10) -> (13/21,5/8) Glide Reflection Matrix(171,-52,194,-59) (3/10,7/23) -> (7/8,1/1) Glide Reflection Matrix(1631,-498,750,-229) (7/23,11/36) -> (13/6,37/17) Hyperbolic Matrix(385,-118,708,-217) (11/36,4/13) -> (13/24,6/11) Glide Reflection Matrix(257,-80,106,-33) (4/13,1/3) -> (12/5,17/7) Glide Reflection Matrix(371,-132,104,-37) (1/3,5/14) -> (7/2,25/7) Hyperbolic Matrix(535,-192,248,-89) (5/14,9/25) -> (15/7,13/6) Hyperbolic Matrix(1441,-520,884,-319) (9/25,4/11) -> (44/27,31/19) Hyperbolic Matrix(779,-286,286,-105) (4/11,7/19) -> (19/7,30/11) Hyperbolic Matrix(285,-106,164,-61) (7/19,3/8) -> (19/11,7/4) Glide Reflection Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(277,-116,394,-165) (5/12,8/19) -> (7/10,12/17) Glide Reflection Matrix(393,-166,670,-283) (8/19,3/7) -> (17/29,10/17) Hyperbolic Matrix(155,-68,98,-43) (3/7,4/9) -> (11/7,8/5) Glide Reflection Matrix(233,-104,522,-233) (4/9,13/29) -> (4/9,13/29) Reflection Matrix(1313,-590,928,-417) (13/29,9/20) -> (41/29,17/12) Glide Reflection Matrix(811,-366,308,-139) (9/20,5/11) -> (21/8,29/11) Glide Reflection Matrix(153,-70,212,-97) (5/11,1/2) -> (5/7,13/18) Glide Reflection Matrix(583,-312,256,-137) (1/2,7/13) -> (25/11,41/18) Hyperbolic Matrix(109,-60,198,-109) (6/11,5/9) -> (6/11,5/9) Reflection Matrix(71,-40,126,-71) (5/9,4/7) -> (5/9,4/7) Reflection Matrix(107,-62,88,-51) (4/7,7/12) -> (6/5,5/4) Glide Reflection Matrix(1519,-890,582,-341) (7/12,17/29) -> (13/5,47/18) Hyperbolic Matrix(175,-104,106,-63) (10/17,3/5) -> (18/11,5/3) Glide Reflection Matrix(175,-106,104,-63) (3/5,11/18) -> (5/3,17/10) Glide Reflection Matrix(417,-256,676,-415) (11/18,8/13) -> (8/13,21/34) Parabolic Matrix(2977,-1840,830,-513) (21/34,34/55) -> (43/12,18/5) Glide Reflection Matrix(619,-390,446,-281) (5/8,12/19) -> (18/13,25/18) Hyperbolic Matrix(445,-282,172,-109) (12/19,7/11) -> (18/7,13/5) Glide Reflection Matrix(923,-590,1178,-753) (7/11,16/25) -> (18/23,29/37) Hyperbolic Matrix(1843,-1182,1040,-667) (25/39,9/14) -> (23/13,39/22) Glide Reflection Matrix(307,-198,476,-307) (9/14,11/17) -> (9/14,11/17) Reflection Matrix(67,-44,102,-67) (11/17,2/3) -> (11/17,2/3) Reflection Matrix(67,-46,16,-11) (2/3,7/10) -> (4/1,9/2) Glide Reflection Matrix(327,-232,148,-105) (12/17,5/7) -> (11/5,20/9) Hyperbolic Matrix(1495,-1082,438,-317) (13/18,21/29) -> (17/5,41/12) Hyperbolic Matrix(519,-376,98,-71) (21/29,8/11) -> (5/1,16/3) Glide Reflection Matrix(389,-284,226,-165) (8/11,11/15) -> (12/7,19/11) Glide Reflection Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(4473,-3424,1744,-1335) (13/17,36/47) -> (100/39,59/23) Hyperbolic Matrix(1553,-1190,492,-377) (36/47,23/30) -> (22/7,19/6) Glide Reflection Matrix(1013,-778,444,-341) (23/30,10/13) -> (41/18,16/7) Glide Reflection Matrix(1327,-1026,410,-317) (17/22,24/31) -> (42/13,13/4) Hyperbolic Matrix(505,-392,362,-281) (24/31,7/9) -> (32/23,7/5) Glide Reflection Matrix(377,-294,268,-209) (7/9,18/23) -> (7/5,24/17) Glide Reflection Matrix(2071,-1624,644,-505) (29/37,11/14) -> (45/14,29/9) Hyperbolic Matrix(1035,-814,1316,-1035) (11/14,37/47) -> (11/14,37/47) Reflection Matrix(2443,-1924,3102,-2443) (37/47,26/33) -> (37/47,26/33) Reflection Matrix(533,-420,250,-197) (26/33,15/19) -> (2/1,15/7) Glide Reflection Matrix(123,-100,16,-13) (4/5,9/11) -> (7/1,8/1) Hyperbolic Matrix(215,-178,122,-101) (9/11,5/6) -> (7/4,23/13) Hyperbolic Matrix(151,-128,46,-39) (5/6,6/7) -> (13/4,10/3) Glide Reflection Matrix(181,-156,210,-181) (6/7,13/15) -> (6/7,13/15) Reflection Matrix(209,-182,240,-209) (13/15,7/8) -> (13/15,7/8) Reflection Matrix(103,-122,38,-45) (1/1,6/5) -> (8/3,19/7) Hyperbolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(283,-390,82,-113) (11/8,18/13) -> (24/7,7/2) Hyperbolic Matrix(891,-1238,398,-553) (25/18,32/23) -> (38/17,9/4) Hyperbolic Matrix(1393,-1968,986,-1393) (24/17,41/29) -> (24/17,41/29) Reflection Matrix(277,-394,116,-165) (17/12,10/7) -> (19/8,12/5) Glide Reflection Matrix(161,-232,34,-49) (10/7,13/9) -> (14/3,5/1) Glide Reflection Matrix(503,-730,308,-447) (13/9,16/11) -> (31/19,18/11) Glide Reflection Matrix(227,-332,80,-117) (16/11,3/2) -> (17/6,20/7) Hyperbolic Matrix(67,-102,44,-67) (3/2,17/11) -> (3/2,17/11) Reflection Matrix(307,-476,198,-307) (17/11,14/9) -> (17/11,14/9) Reflection Matrix(175,-274,76,-119) (14/9,11/7) -> (16/7,7/3) Glide Reflection Matrix(215,-346,64,-103) (8/5,21/13) -> (10/3,17/5) Glide Reflection Matrix(393,-670,166,-283) (17/10,12/7) -> (26/11,19/8) Hyperbolic Matrix(1089,-1934,424,-753) (55/31,16/9) -> (59/23,18/7) Glide Reflection Matrix(161,-288,90,-161) (16/9,9/5) -> (16/9,9/5) Reflection Matrix(19,-36,10,-19) (9/5,2/1) -> (9/5,2/1) Reflection Matrix(521,-1160,234,-521) (20/9,29/13) -> (20/9,29/13) Reflection Matrix(987,-2204,442,-987) (29/13,38/17) -> (29/13,38/17) Reflection Matrix(171,-388,26,-59) (9/4,25/11) -> (13/2,7/1) Glide Reflection Matrix(1651,-3894,700,-1651) (33/14,59/25) -> (33/14,59/25) Reflection Matrix(1299,-3068,550,-1299) (59/25,26/11) -> (59/25,26/11) Reflection Matrix(81,-200,32,-79) (17/7,5/2) -> (5/2,23/9) Parabolic Matrix(787,-2014,220,-563) (23/9,41/16) -> (25/7,43/12) Glide Reflection Matrix(4511,-11562,1760,-4511) (41/16,141/55) -> (41/16,141/55) Reflection Matrix(10999,-28200,4290,-10999) (141/55,100/39) -> (141/55,100/39) Reflection Matrix(2915,-7614,1116,-2915) (47/18,81/31) -> (47/18,81/31) Reflection Matrix(2107,-5508,806,-2107) (81/31,34/13) -> (81/31,34/13) Reflection Matrix(77,-202,8,-21) (34/13,21/8) -> (8/1,1/0) Glide Reflection Matrix(901,-2460,330,-901) (30/11,41/15) -> (30/11,41/15) Reflection Matrix(329,-902,120,-329) (41/15,11/4) -> (41/15,11/4) Reflection Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(43,-126,14,-41) (20/7,3/1) -> (3/1,22/7) Parabolic Matrix(321,-1024,100,-319) (19/6,16/5) -> (16/5,45/14) Parabolic Matrix(1559,-5330,456,-1559) (41/12,65/19) -> (41/12,65/19) Reflection Matrix(911,-3120,266,-911) (65/19,24/7) -> (65/19,24/7) Reflection Matrix(109,-396,30,-109) (18/5,11/3) -> (18/5,11/3) Reflection Matrix(23,-88,6,-23) (11/3,4/1) -> (11/3,4/1) Reflection Matrix(91,-414,20,-91) (9/2,23/5) -> (9/2,23/5) Reflection Matrix(139,-644,30,-139) (23/5,14/3) -> (23/5,14/3) Reflection Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,2,-1) (-1/1,0/1) -> (0/1,1/1) Matrix(407,-42,126,-13) -> Matrix(3,-2,2,-1) 1/1 Matrix(353,-40,150,-17) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(147,-20,272,-37) -> Matrix(1,0,-2,1) 0/1 Matrix(437,-66,682,-103) -> Matrix(1,0,-6,1) 0/1 Matrix(433,-70,266,-43) -> Matrix(1,0,2,1) 0/1 Matrix(191,-34,118,-21) -> Matrix(1,0,0,1) Matrix(417,-86,674,-139) -> Matrix(1,-2,0,1) 1/0 Matrix(463,-98,600,-127) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(139,-30,644,-139) -> Matrix(-1,0,4,1) (3/14,5/23) -> (-1/2,0/1) Matrix(91,-20,414,-91) -> Matrix(1,0,6,-1) (5/23,2/9) -> (0/1,1/3) Matrix(365,-82,138,-31) -> Matrix(7,-2,4,-1) Matrix(499,-116,228,-53) -> Matrix(5,-4,4,-3) 1/1 Matrix(1133,-268,520,-123) -> Matrix(3,-2,2,-1) 1/1 Matrix(1039,-250,586,-141) -> Matrix(7,6,8,7) Matrix(311,-82,110,-29) -> Matrix(1,2,0,1) 1/0 Matrix(89,-24,330,-89) -> Matrix(-1,0,2,1) (4/15,3/11) -> (-1/1,0/1) Matrix(43,-12,154,-43) -> Matrix(1,0,4,-1) (3/11,2/7) -> (0/1,1/2) Matrix(173,-50,218,-63) -> Matrix(3,-2,8,-5) 1/2 Matrix(215,-64,346,-103) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(171,-52,194,-59) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1631,-498,750,-229) -> Matrix(5,-4,4,-3) 1/1 Matrix(385,-118,708,-217) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(257,-80,106,-33) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(371,-132,104,-37) -> Matrix(3,-2,2,-1) 1/1 Matrix(535,-192,248,-89) -> Matrix(7,-6,6,-5) 1/1 Matrix(1441,-520,884,-319) -> Matrix(1,0,2,1) 0/1 Matrix(779,-286,286,-105) -> Matrix(1,0,0,1) Matrix(285,-106,164,-61) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(41,-16,100,-39) -> Matrix(1,0,2,1) 0/1 Matrix(277,-116,394,-165) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(393,-166,670,-283) -> Matrix(5,-2,8,-3) 1/2 Matrix(155,-68,98,-43) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(233,-104,522,-233) -> Matrix(-1,4,0,1) (4/9,13/29) -> (2/1,1/0) Matrix(1313,-590,928,-417) -> Matrix(1,4,2,7) Matrix(811,-366,308,-139) -> Matrix(3,8,2,5) Matrix(153,-70,212,-97) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(583,-312,256,-137) -> Matrix(1,0,2,1) 0/1 Matrix(109,-60,198,-109) -> Matrix(-1,0,4,1) (6/11,5/9) -> (-1/2,0/1) Matrix(71,-40,126,-71) -> Matrix(1,0,6,-1) (5/9,4/7) -> (0/1,1/3) Matrix(107,-62,88,-51) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1519,-890,582,-341) -> Matrix(29,-16,20,-11) Matrix(175,-104,106,-63) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(175,-106,104,-63) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(417,-256,676,-415) -> Matrix(1,-2,0,1) 1/0 Matrix(2977,-1840,830,-513) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(619,-390,446,-281) -> Matrix(1,0,2,1) 0/1 Matrix(445,-282,172,-109) -> Matrix(5,4,4,3) Matrix(923,-590,1178,-753) -> Matrix(7,2,24,7) Matrix(1843,-1182,1040,-667) -> Matrix(29,6,34,7) Matrix(307,-198,476,-307) -> Matrix(-1,0,16,1) (9/14,11/17) -> (-1/8,0/1) Matrix(67,-44,102,-67) -> Matrix(1,0,6,-1) (11/17,2/3) -> (0/1,1/3) Matrix(67,-46,16,-11) -> Matrix(5,-2,2,-1) Matrix(327,-232,148,-105) -> Matrix(5,-4,4,-3) 1/1 Matrix(1495,-1082,438,-317) -> Matrix(7,-2,4,-1) Matrix(519,-376,98,-71) -> Matrix(5,-2,2,-1) Matrix(389,-284,226,-165) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(97,-72,128,-95) -> Matrix(1,0,4,1) 0/1 Matrix(4473,-3424,1744,-1335) -> Matrix(141,-34,112,-27) Matrix(1553,-1190,492,-377) -> Matrix(53,-14,34,-9) Matrix(1013,-778,444,-341) -> Matrix(7,-2,10,-3) Matrix(1327,-1026,410,-317) -> Matrix(7,-2,4,-1) Matrix(505,-392,362,-281) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(377,-294,268,-209) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(2071,-1624,644,-505) -> Matrix(13,-4,10,-3) Matrix(1035,-814,1316,-1035) -> Matrix(31,-10,96,-31) (11/14,37/47) -> (5/16,1/3) Matrix(2443,-1924,3102,-2443) -> Matrix(71,-24,210,-71) (37/47,26/33) -> (1/3,12/35) Matrix(533,-420,250,-197) -> Matrix(35,-12,32,-11) Matrix(123,-100,16,-13) -> Matrix(7,-4,2,-1) Matrix(215,-178,122,-101) -> Matrix(3,-4,4,-5) 1/1 Matrix(151,-128,46,-39) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(181,-156,210,-181) -> Matrix(1,0,0,-1) (6/7,13/15) -> (0/1,1/0) Matrix(209,-182,240,-209) -> Matrix(1,0,8,-1) (13/15,7/8) -> (0/1,1/4) Matrix(103,-122,38,-45) -> Matrix(3,-2,2,-1) 1/1 Matrix(49,-64,36,-47) -> Matrix(3,-2,2,-1) 1/1 Matrix(283,-390,82,-113) -> Matrix(1,2,0,1) 1/0 Matrix(891,-1238,398,-553) -> Matrix(3,-2,2,-1) 1/1 Matrix(1393,-1968,986,-1393) -> Matrix(13,-6,28,-13) (24/17,41/29) -> (3/7,1/2) Matrix(277,-394,116,-165) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(161,-232,34,-49) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(503,-730,308,-447) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(227,-332,80,-117) -> Matrix(7,-4,2,-1) Matrix(67,-102,44,-67) -> Matrix(7,-6,8,-7) (3/2,17/11) -> (3/4,1/1) Matrix(307,-476,198,-307) -> Matrix(17,-18,16,-17) (17/11,14/9) -> (1/1,9/8) Matrix(175,-274,76,-119) -> Matrix(5,-6,4,-5) *** -> (1/1,3/2) Matrix(215,-346,64,-103) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(393,-670,166,-283) -> Matrix(7,-4,2,-1) Matrix(1089,-1934,424,-753) -> Matrix(77,-68,60,-53) Matrix(161,-288,90,-161) -> Matrix(17,-16,18,-17) (16/9,9/5) -> (8/9,1/1) Matrix(19,-36,10,-19) -> Matrix(1,0,2,-1) (9/5,2/1) -> (0/1,1/1) Matrix(521,-1160,234,-521) -> Matrix(7,-12,4,-7) (20/9,29/13) -> (3/2,2/1) Matrix(987,-2204,442,-987) -> Matrix(3,-4,2,-3) (29/13,38/17) -> (1/1,2/1) Matrix(171,-388,26,-59) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1651,-3894,700,-1651) -> Matrix(7,-12,4,-7) (33/14,59/25) -> (3/2,2/1) Matrix(1299,-3068,550,-1299) -> Matrix(5,-12,2,-5) (59/25,26/11) -> (2/1,3/1) Matrix(81,-200,32,-79) -> Matrix(7,-6,6,-5) 1/1 Matrix(787,-2014,220,-563) -> Matrix(13,-16,4,-5) Matrix(4511,-11562,1760,-4511) -> Matrix(249,-310,200,-249) (41/16,141/55) -> (31/25,5/4) Matrix(10999,-28200,4290,-10999) -> Matrix(671,-840,536,-671) (141/55,100/39) -> (5/4,84/67) Matrix(2915,-7614,1116,-2915) -> Matrix(101,-150,68,-101) (47/18,81/31) -> (25/17,3/2) Matrix(2107,-5508,806,-2107) -> Matrix(55,-84,36,-55) (81/31,34/13) -> (3/2,14/9) Matrix(77,-202,8,-21) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(901,-2460,330,-901) -> Matrix(3,-2,4,-3) (30/11,41/15) -> (1/2,1/1) Matrix(329,-902,120,-329) -> Matrix(5,-6,4,-5) (41/15,11/4) -> (1/1,3/2) Matrix(119,-330,22,-61) -> Matrix(5,-8,2,-3) 2/1 Matrix(43,-126,14,-41) -> Matrix(3,-2,2,-1) 1/1 Matrix(321,-1024,100,-319) -> Matrix(5,-8,2,-3) 2/1 Matrix(1559,-5330,456,-1559) -> Matrix(23,-44,12,-23) (41/12,65/19) -> (11/6,2/1) Matrix(911,-3120,266,-911) -> Matrix(13,-28,6,-13) (65/19,24/7) -> (2/1,7/3) Matrix(109,-396,30,-109) -> Matrix(-1,2,0,1) (18/5,11/3) -> (1/1,1/0) Matrix(23,-88,6,-23) -> Matrix(3,-4,2,-3) (11/3,4/1) -> (1/1,2/1) Matrix(91,-414,20,-91) -> Matrix(-1,6,0,1) (9/2,23/5) -> (3/1,1/0) Matrix(139,-644,30,-139) -> Matrix(1,0,0,-1) (23/5,14/3) -> (0/1,1/0) Matrix(25,-144,4,-23) -> Matrix(1,-2,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.