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 -1/5 -1/8 0/1 1/7 1/6 5/23 3/11 5/16 1/3 2/5 1/2 5/9 3/5 11/17 5/7 3/4 1/1 15/13 19/16 9/7 4/3 3/2 17/11 43/27 13/8 5/3 9/5 2/1 11/5 29/13 7/3 5/2 81/31 41/15 3/1 16/5 10/3 27/8 17/5 65/19 7/2 11/3 23/6 4/1 113/27 17/4 13/3 9/2 23/5 19/4 5/1 47/9 21/4 11/2 6/1 13/2 7/1 15/2 31/4 8/1 25/3 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/2 -8/17 1/3 -7/15 0/1 -13/28 0/1 1/3 -6/13 1/2 -5/11 1/3 1/1 -14/31 -1/1 -9/20 0/1 1/4 -13/29 1/2 -17/38 0/1 -21/47 1/3 1/1 -4/9 1/3 -7/16 1/2 1/1 -10/23 1/1 -3/7 0/1 -14/33 1/3 -25/59 1/5 1/3 -11/26 2/7 1/3 -8/19 3/7 -5/12 1/2 -12/29 1/3 -7/17 3/5 1/1 -2/5 1/3 -7/18 1/2 2/3 -5/13 1/2 -13/34 1/1 -8/21 1/1 -11/29 1/3 1/1 -25/66 0/1 1/1 -14/37 1/1 -3/8 0/1 1/2 -7/19 1/2 -11/30 0/1 1/2 -4/11 1/2 -13/36 3/5 2/3 -9/25 2/3 -14/39 1/1 -5/14 1/2 1/1 -11/31 2/3 -6/17 1/1 -1/3 1/3 1/1 -4/13 -1/1 -3/10 0/1 -8/27 1/1 -13/44 0/1 1/4 -5/17 0/1 -7/24 3/7 1/2 -2/7 1/1 -5/18 1/1 1/0 -8/29 1/0 -3/11 1/0 -7/26 0/1 1/0 -4/15 -1/3 -1/4 0/1 1/2 -6/25 1/1 -11/46 0/1 -5/21 1/2 -4/17 1/1 -3/13 -1/1 1/1 -5/22 -1/1 1/0 -2/9 0/1 -5/23 1/5 1/3 -8/37 1/3 -3/14 0/1 1/4 -4/19 1/3 -5/24 2/5 1/2 -1/5 1/2 -3/16 1/1 1/0 -2/11 1/1 -1/6 0/1 1/2 -1/7 3/5 1/1 -2/15 1/1 -1/8 1/1 -1/9 0/1 0/1 1/1 1/7 0/1 1/6 1/1 3/17 2/1 2/11 1/1 1/5 1/1 3/1 4/19 3/1 3/14 7/1 1/0 5/23 1/0 2/9 -3/1 3/13 1/0 1/4 0/1 1/0 4/15 -1/1 3/11 0/1 8/29 1/1 13/47 0/1 5/18 0/1 1/1 2/7 1/1 5/17 1/3 1/1 8/27 1/2 3/10 1/2 1/1 7/23 1/1 7/5 4/13 1/1 9/29 1/1 3/1 5/16 1/0 6/19 1/1 1/3 1/0 5/14 -2/1 1/0 9/25 -5/3 -1/1 4/11 -1/1 3/8 -1/2 0/1 8/21 -1/1 21/55 -2/3 13/34 -3/5 -1/2 5/13 -1/1 -1/3 12/31 -1/3 19/49 0/1 7/18 -1/2 0/1 2/5 0/1 9/22 0/1 1/4 25/61 1/5 1/3 16/39 1/3 7/17 0/1 12/29 1/3 5/12 1/3 1/2 13/31 2/3 8/19 1/1 3/7 1/3 1/1 7/16 1/1 2/1 11/25 0/1 15/34 1/1 4/9 1/1 5/11 1/0 6/13 1/1 1/2 0/1 1/0 6/11 -1/5 5/9 0/1 14/25 1/11 23/41 0/1 9/16 0/1 1/8 4/7 1/5 15/26 4/13 1/3 11/19 1/3 3/7 29/50 1/3 2/5 18/31 1/2 7/12 0/1 1/2 31/53 0/1 24/41 1/5 41/70 0/1 1/4 17/29 1/5 1/3 10/17 1/3 13/22 1/3 3/5 1/2 11/18 1/2 1/1 30/49 1/1 19/31 3/5 1/1 8/13 1/2 5/8 1/2 1/1 12/19 1/3 7/11 3/5 1/1 16/25 1/1 25/39 2/3 9/14 4/5 1/1 11/17 1/1 2/3 1/1 11/16 1/1 1/0 9/13 1/1 3/1 7/10 -3/1 1/0 19/27 -3/1 -1/1 12/17 -1/1 29/41 -1/1 17/24 -1/1 -2/3 39/55 -1/1 -3/5 22/31 -1/1 5/7 0/1 3/4 0/1 7/9 0/1 11/14 0/1 1/0 15/19 1/5 1/3 4/5 1/3 13/16 1/2 1/1 9/11 1/2 5/6 1/2 2/3 6/7 1/1 1/1 -1/1 1/1 9/8 1/2 1/1 8/7 1/1 15/13 1/1 7/6 1/1 5/4 13/11 3/2 32/27 1/1 19/16 3/2 44/37 5/3 25/21 1/1 5/3 6/5 1/1 17/14 2/1 5/2 28/23 3/1 39/32 2/1 3/1 11/9 2/1 16/13 3/1 21/17 3/1 5/1 5/4 1/1 1/0 14/11 1/1 23/18 0/1 1/1 32/25 1/1 9/7 2/1 40/31 3/1 31/24 2/1 1/0 22/17 1/1 35/27 7/3 3/1 13/10 2/1 3/1 4/3 1/0 19/14 -2/1 -1/1 34/25 -1/1 49/36 -1/1 1/0 113/83 1/0 64/47 -3/1 15/11 -3/1 -1/1 11/8 0/1 1/0 40/29 -1/1 29/21 -1/1 -1/3 47/34 -1/6 0/1 65/47 0/1 18/13 1/3 25/18 1/2 1/1 7/5 1/0 24/17 1/1 41/29 1/0 17/12 1/1 1/0 44/31 3/1 71/50 -3/1 1/0 27/19 -1/1 1/1 10/7 3/1 33/23 1/0 23/16 -7/1 1/0 13/9 -3/1 -1/1 3/2 0/1 1/0 17/11 0/1 31/20 0/1 1/2 14/9 1/1 25/16 0/1 1/1 36/23 1/1 47/30 1/0 11/7 -1/1 1/1 30/19 0/1 19/12 0/1 1/0 27/17 0/1 35/22 0/1 1/2 43/27 1/2 8/5 1/1 29/18 1/1 1/0 50/31 1/1 21/13 -1/1 1/1 13/8 1/1 31/19 1/1 5/3 18/11 1/1 41/25 1/1 5/3 23/14 2/1 1/0 5/3 1/0 22/13 1/0 61/36 0/1 1/1 39/23 1/1 3/1 17/10 1/1 1/0 12/7 -1/1 19/11 1/3 1/1 45/26 6/7 1/1 26/15 1/1 7/4 2/1 1/0 16/9 5/1 9/5 1/0 20/11 -5/1 51/28 -6/1 -5/1 31/17 -4/1 11/6 -3/1 1/0 13/7 -2/1 15/8 -1/1 0/1 17/9 -1/1 1/1 2/1 -1/1 15/7 1/5 1/3 13/6 0/1 1/2 11/5 1/2 31/14 2/3 3/4 20/9 1/1 49/22 8/9 1/1 29/13 1/1 9/4 1/1 1/0 16/7 1/1 39/17 1/1 23/10 1/1 4/3 7/3 1/1 3/1 5/2 1/0 13/5 -1/1 1/1 47/18 3/1 1/0 81/31 1/0 115/44 -9/1 1/0 34/13 -3/1 21/8 -1/1 1/0 71/27 1/0 121/46 -2/1 1/0 50/19 -1/1 29/11 1/0 8/3 -3/1 27/10 -2/1 -3/2 19/7 -7/5 -1/1 30/11 -1/1 41/15 -1/1 52/19 -1/1 11/4 -1/1 -2/3 25/9 -1/1 -1/3 64/23 -1/1 39/14 -1/2 0/1 14/5 -1/1 17/6 -1/1 0/1 20/7 -1/1 3/1 0/1 22/7 1/1 19/6 0/1 1/0 16/5 0/1 13/4 1/2 1/1 49/15 2/3 36/11 1/1 23/7 5/7 1/1 33/10 7/8 1/1 43/13 1/1 10/3 1/1 27/8 1/1 44/13 1/1 61/18 1/1 2/1 17/5 1/1 3/1 58/17 1/1 41/12 2/1 1/0 65/19 1/0 89/26 0/1 1/0 24/7 1/1 7/2 1/1 1/0 18/5 3/1 11/3 1/0 26/7 -3/1 67/18 -3/1 1/0 108/29 -3/1 41/11 1/0 15/4 -2/1 1/0 19/5 1/0 42/11 -1/1 65/17 -1/1 1/1 23/6 -1/1 1/0 4/1 -1/1 25/6 0/1 1/0 46/11 1/1 113/27 1/0 67/16 -1/1 1/0 21/5 -1/1 1/1 17/4 0/1 47/11 1/3 1/1 30/7 1/1 13/3 1/0 35/8 -3/2 -1/1 57/13 -1/1 22/5 -1/1 9/2 -1/2 0/1 23/5 0/1 37/8 0/1 1/8 14/3 1/3 61/13 1/3 1/1 47/10 0/1 1/2 33/7 0/1 19/4 0/1 1/1 43/9 0/1 24/5 1/1 5/1 -1/1 1/1 26/5 -1/5 47/9 0/1 21/4 0/1 1/4 16/3 1/1 11/2 1/1 1/0 6/1 1/0 19/3 -3/1 -1/1 13/2 -1/1 0/1 20/3 -1/1 47/7 -1/1 -1/3 27/4 -1/2 0/1 7/1 0/1 15/2 -1/1 1/0 23/3 -1/1 -1/3 31/4 0/1 8/1 -1/1 25/3 0/1 17/2 0/1 1/2 9/1 -1/1 1/1 10/1 -1/1 1/0 0/1 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(745,352,1272,601) (-1/2,-8/17) -> (24/41,41/70) Hyperbolic Matrix(1373,644,420,197) (-8/17,-7/15) -> (49/15,36/11) Hyperbolic Matrix(893,416,732,341) (-7/15,-13/28) -> (39/32,11/9) Hyperbolic Matrix(1409,652,832,385) (-13/28,-6/13) -> (22/13,61/36) Hyperbolic Matrix(153,70,518,237) (-6/13,-5/11) -> (5/17,8/27) Hyperbolic Matrix(1327,600,1024,463) (-5/11,-14/31) -> (22/17,35/27) Hyperbolic Matrix(1427,644,308,139) (-14/31,-9/20) -> (37/8,14/3) Hyperbolic Matrix(1119,502,506,227) (-9/20,-13/29) -> (11/5,31/14) Hyperbolic Matrix(509,228,-2132,-955) (-13/29,-17/38) -> (-11/46,-5/21) Hyperbolic Matrix(2331,1042,302,135) (-17/38,-21/47) -> (23/3,31/4) Hyperbolic Matrix(1363,608,204,91) (-21/47,-4/9) -> (20/3,47/7) Hyperbolic Matrix(351,154,98,43) (-4/9,-7/16) -> (7/2,18/5) Hyperbolic Matrix(795,346,494,215) (-7/16,-10/23) -> (8/5,29/18) Hyperbolic Matrix(245,106,594,257) (-10/23,-3/7) -> (7/17,12/29) Hyperbolic Matrix(485,206,1754,745) (-3/7,-14/33) -> (8/29,13/47) Hyperbolic Matrix(3983,1688,1168,495) (-14/33,-25/59) -> (17/5,58/17) Hyperbolic Matrix(4613,1954,2722,1153) (-25/59,-11/26) -> (61/36,39/23) Hyperbolic Matrix(389,164,676,285) (-11/26,-8/19) -> (4/7,15/26) Hyperbolic Matrix(239,100,-576,-241) (-8/19,-5/12) -> (-5/12,-12/29) Parabolic Matrix(953,394,670,277) (-12/29,-7/17) -> (27/19,10/7) Hyperbolic Matrix(239,98,378,155) (-7/17,-2/5) -> (12/19,7/11) Hyperbolic Matrix(323,126,182,71) (-2/5,-7/18) -> (7/4,16/9) Hyperbolic Matrix(227,88,276,107) (-7/18,-5/13) -> (9/11,5/6) 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(453,172,1172,445) (-8/21,-11/29) -> (5/13,12/31) Hyperbolic Matrix(3067,1162,4326,1639) (-11/29,-25/66) -> (17/24,39/55) Hyperbolic Matrix(3291,1246,2702,1023) (-25/66,-14/37) -> (28/23,39/32) Hyperbolic Matrix(1259,476,812,307) (-14/37,-3/8) -> (31/20,14/9) Hyperbolic Matrix(43,16,180,67) (-3/8,-7/19) -> (3/13,1/4) Hyperbolic Matrix(577,212,264,97) (-7/19,-11/30) -> (13/6,11/5) Hyperbolic Matrix(617,226,1062,389) (-11/30,-4/11) -> (18/31,7/12) Hyperbolic Matrix(967,350,1666,603) (-4/11,-13/36) -> (29/50,18/31) Hyperbolic Matrix(1663,600,352,127) (-13/36,-9/25) -> (33/7,19/4) Hyperbolic Matrix(745,268,1048,377) (-9/25,-14/39) -> (22/31,5/7) Hyperbolic Matrix(1831,656,1136,407) (-14/39,-5/14) -> (29/18,50/31) Hyperbolic Matrix(697,248,1824,649) (-5/14,-11/31) -> (21/55,13/34) Hyperbolic Matrix(825,292,1472,521) (-11/31,-6/17) -> (14/25,23/41) Hyperbolic Matrix(131,46,430,151) (-6/17,-1/3) -> (7/23,4/13) Hyperbolic Matrix(283,88,164,51) (-1/3,-4/13) -> (12/7,19/11) Hyperbolic Matrix(119,36,-400,-121) (-4/13,-3/10) -> (-3/10,-8/27) Parabolic Matrix(1271,376,240,71) (-8/27,-13/44) -> (21/4,16/3) Hyperbolic Matrix(955,282,2462,727) (-13/44,-5/17) -> (19/49,7/18) Hyperbolic Matrix(397,116,948,277) (-5/17,-7/24) -> (5/12,13/31) Hyperbolic Matrix(117,34,554,161) (-7/24,-2/7) -> (4/19,3/14) Hyperbolic Matrix(351,98,154,43) (-2/7,-5/18) -> (9/4,16/7) 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(383,104,232,63) (-3/11,-7/26) -> (23/14,5/3) Hyperbolic Matrix(613,164,228,61) (-7/26,-4/15) -> (8/3,27/10) Hyperbolic Matrix(39,10,74,19) (-4/15,-1/4) -> (1/2,6/11) Hyperbolic Matrix(1257,304,368,89) (-1/4,-6/25) -> (58/17,41/12) Hyperbolic Matrix(1143,274,146,35) (-6/25,-11/46) -> (31/4,8/1) Hyperbolic Matrix(1543,366,586,139) (-5/21,-4/17) -> (50/19,29/11) Hyperbolic Matrix(327,76,512,119) (-4/17,-3/13) -> (7/11,16/25) Hyperbolic Matrix(509,116,724,165) (-3/13,-5/22) -> (7/10,19/27) Hyperbolic Matrix(469,106,146,33) (-5/22,-2/9) -> (16/5,13/4) Hyperbolic Matrix(789,172,500,109) (-2/9,-5/23) -> (11/7,30/19) Hyperbolic Matrix(1145,248,928,201) (-5/23,-8/37) -> (16/13,21/17) Hyperbolic Matrix(1427,308,644,139) (-8/37,-3/14) -> (31/14,20/9) Hyperbolic Matrix(497,106,286,61) (-3/14,-4/19) -> (26/15,7/4) Hyperbolic Matrix(1169,244,848,177) (-4/19,-5/24) -> (11/8,40/29) Hyperbolic Matrix(1059,220,284,59) (-5/24,-1/5) -> (41/11,15/4) Hyperbolic Matrix(243,46,206,39) (-1/5,-3/16) -> (7/6,13/11) Hyperbolic Matrix(377,70,70,13) (-3/16,-2/11) -> (16/3,11/2) Hyperbolic Matrix(35,6,134,23) (-2/11,-1/6) -> (1/4,4/15) Hyperbolic Matrix(99,16,68,11) (-1/6,-1/7) -> (13/9,3/2) Hyperbolic Matrix(715,98,518,71) (-1/7,-2/15) -> (40/29,29/21) Hyperbolic Matrix(257,34,582,77) (-2/15,-1/8) -> (15/34,4/9) Hyperbolic Matrix(223,26,506,59) (-1/8,-1/9) -> (11/25,15/34) Hyperbolic Matrix(93,8,244,21) (-1/9,0/1) -> (8/21,21/55) Hyperbolic Matrix(123,-16,100,-13) (0/1,1/7) -> (11/9,16/13) Hyperbolic Matrix(25,-4,144,-23) (1/7,1/6) -> (1/6,3/17) Parabolic Matrix(547,-98,854,-153) (3/17,2/11) -> (16/25,25/39) Hyperbolic Matrix(119,-22,330,-61) (2/11,1/5) -> (9/25,4/11) Hyperbolic Matrix(511,-106,834,-173) (1/5,4/19) -> (30/49,19/31) Hyperbolic Matrix(991,-214,690,-149) (3/14,5/23) -> (33/23,23/16) Hyperbolic Matrix(527,-116,368,-81) (5/23,2/9) -> (10/7,33/23) Hyperbolic Matrix(365,-82,138,-31) (2/9,3/13) -> (29/11,8/3) 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(371,-104,132,-37) (5/18,2/7) -> (14/5,17/6) Hyperbolic Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(989,-300,300,-91) (3/10,7/23) -> (23/7,33/10) Hyperbolic Matrix(407,-126,42,-13) (4/13,9/29) -> (9/1,10/1) Hyperbolic Matrix(1539,-478,982,-305) (9/29,5/16) -> (47/30,11/7) Hyperbolic Matrix(1469,-462,938,-295) (5/16,6/19) -> (36/23,47/30) Hyperbolic Matrix(487,-156,128,-41) (6/19,1/3) -> (19/5,42/11) Hyperbolic Matrix(311,-110,82,-29) (1/3,5/14) -> (15/4,19/5) Hyperbolic Matrix(535,-192,248,-89) (5/14,9/25) -> (15/7,13/6) Hyperbolic Matrix(103,-38,122,-45) (4/11,3/8) -> (5/6,6/7) Hyperbolic Matrix(365,-138,82,-31) (3/8,8/21) -> (22/5,9/2) Hyperbolic Matrix(1053,-404,404,-155) (13/34,5/13) -> (13/5,47/18) Hyperbolic Matrix(2239,-868,1736,-673) (12/31,19/49) -> (9/7,40/31) Hyperbolic Matrix(81,-32,200,-79) (7/18,2/5) -> (2/5,9/22) Parabolic Matrix(2681,-1098,398,-163) (9/22,25/61) -> (47/7,27/4) Hyperbolic Matrix(4489,-1840,3296,-1351) (25/61,16/39) -> (64/47,15/11) Hyperbolic Matrix(2085,-856,436,-179) (16/39,7/17) -> (43/9,24/5) Hyperbolic Matrix(357,-148,316,-131) (12/29,5/12) -> (9/8,8/7) Hyperbolic Matrix(1163,-488,908,-381) (13/31,8/19) -> (32/25,9/7) 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(583,-256,312,-137) (7/16,11/25) -> (13/7,15/8) Hyperbolic Matrix(327,-148,232,-105) (4/9,5/11) -> (7/5,24/17) Hyperbolic Matrix(499,-228,116,-53) (5/11,6/13) -> (30/7,13/3) Hyperbolic Matrix(535,-248,192,-89) (6/13,1/2) -> (39/14,14/5) 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(215,-122,178,-101) (9/16,4/7) -> (6/5,17/14) Hyperbolic Matrix(1349,-780,780,-451) (15/26,11/19) -> (19/11,45/26) Hyperbolic Matrix(1135,-658,602,-349) (11/19,29/50) -> (15/8,17/9) Hyperbolic Matrix(1201,-702,142,-83) (7/12,31/53) -> (25/3,17/2) Hyperbolic Matrix(1449,-848,176,-103) (31/53,24/41) -> (8/1,25/3) Hyperbolic Matrix(5633,-3300,1200,-703) (41/70,17/29) -> (61/13,47/10) Hyperbolic Matrix(1427,-842,422,-249) (10/17,13/22) -> (27/8,44/13) Hyperbolic Matrix(227,-138,278,-169) (3/5,11/18) -> (13/16,9/11) Hyperbolic Matrix(3751,-2296,1008,-617) (11/18,30/49) -> (26/7,67/18) Hyperbolic Matrix(433,-266,70,-43) (19/31,8/13) -> (6/1,19/3) Hyperbolic Matrix(191,-118,34,-21) (8/13,5/8) -> (11/2,6/1) Hyperbolic Matrix(619,-390,446,-281) (5/8,12/19) -> (18/13,25/18) Hyperbolic Matrix(2423,-1554,1330,-853) (25/39,9/14) -> (51/28,31/17) Hyperbolic Matrix(937,-604,408,-263) (9/14,11/17) -> (39/17,23/10) Hyperbolic Matrix(389,-254,170,-111) (11/17,2/3) -> (16/7,39/17) Hyperbolic Matrix(133,-90,34,-23) (2/3,11/16) -> (23/6,4/1) Hyperbolic Matrix(845,-582,498,-343) (11/16,9/13) -> (39/23,17/10) Hyperbolic 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(1871,-1322,426,-301) (12/17,29/41) -> (57/13,22/5) Hyperbolic Matrix(2705,-1914,1214,-859) (29/41,17/24) -> (49/22,29/13) Hyperbolic Matrix(3195,-2266,2686,-1905) (39/55,22/31) -> (44/37,25/21) Hyperbolic Matrix(49,-36,64,-47) (5/7,3/4) -> (3/4,7/9) Parabolic Matrix(549,-430,346,-271) (7/9,11/14) -> (19/12,27/17) Hyperbolic Matrix(1299,-1024,940,-741) (11/14,15/19) -> (29/21,47/34) Hyperbolic Matrix(789,-640,556,-451) (4/5,13/16) -> (17/12,44/31) Hyperbolic Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(199,-222,26,-29) (1/1,9/8) -> (15/2,23/3) Hyperbolic Matrix(431,-494,130,-149) (8/7,15/13) -> (43/13,10/3) Hyperbolic Matrix(687,-796,208,-241) (15/13,7/6) -> (33/10,43/13) Hyperbolic Matrix(2295,-2716,616,-729) (13/11,32/27) -> (108/29,41/11) Hyperbolic Matrix(1217,-1444,1024,-1215) (32/27,19/16) -> (19/16,44/37) Parabolic Matrix(599,-716,128,-153) (25/21,6/5) -> (14/3,61/13) Hyperbolic Matrix(631,-768,152,-185) (17/14,28/23) -> (4/1,25/6) Hyperbolic Matrix(1315,-1626,926,-1145) (21/17,5/4) -> (71/50,27/19) Hyperbolic Matrix(173,-218,50,-63) (5/4,14/11) -> (24/7,7/2) Hyperbolic Matrix(923,-1178,590,-753) (14/11,23/18) -> (25/16,36/23) Hyperbolic Matrix(1585,-2028,712,-911) (23/18,32/25) -> (20/9,49/22) Hyperbolic Matrix(4951,-6390,1882,-2429) (40/31,31/24) -> (121/46,50/19) Hyperbolic Matrix(257,-332,24,-31) (31/24,22/17) -> (10/1,1/0) Hyperbolic Matrix(1817,-2356,536,-695) (35/27,13/10) -> (61/18,17/5) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(1555,-2114,854,-1161) (19/14,34/25) -> (20/11,51/28) Hyperbolic Matrix(5563,-7570,1494,-2033) (34/25,49/36) -> (67/18,108/29) Hyperbolic Matrix(9629,-13108,2300,-3131) (49/36,113/83) -> (113/27,67/16) Hyperbolic Matrix(9129,-12430,2182,-2971) (113/83,64/47) -> (46/11,113/27) Hyperbolic Matrix(449,-614,166,-227) (15/11,11/8) -> (27/10,19/7) Hyperbolic Matrix(2585,-3574,494,-683) (47/34,65/47) -> (47/9,21/4) Hyperbolic Matrix(1833,-2536,352,-487) (65/47,18/13) -> (26/5,47/9) Hyperbolic Matrix(409,-570,94,-131) (25/18,7/5) -> (13/3,35/8) Hyperbolic Matrix(963,-1360,604,-853) (24/17,41/29) -> (43/27,8/5) Hyperbolic Matrix(1461,-2068,556,-787) (41/29,17/12) -> (21/8,71/27) Hyperbolic Matrix(5265,-7474,2014,-2859) (44/31,71/50) -> (115/44,34/13) Hyperbolic Matrix(375,-578,242,-373) (3/2,17/11) -> (17/11,31/20) Parabolic Matrix(437,-682,66,-103) (14/9,25/16) -> (13/2,20/3) Hyperbolic Matrix(553,-874,174,-275) (30/19,19/12) -> (19/6,16/5) Hyperbolic Matrix(1525,-2424,324,-515) (27/17,35/22) -> (47/10,33/7) Hyperbolic Matrix(4829,-7688,1836,-2923) (35/22,43/27) -> (71/27,121/46) Hyperbolic Matrix(1607,-2594,578,-933) (50/31,21/13) -> (25/9,64/23) Hyperbolic Matrix(417,-676,256,-415) (21/13,13/8) -> (13/8,31/19) Parabolic 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(487,-830,186,-317) (17/10,12/7) -> (34/13,21/8) Hyperbolic Matrix(1517,-2626,554,-959) (45/26,26/15) -> (52/19,11/4) Hyperbolic Matrix(181,-324,100,-179) (16/9,9/5) -> (9/5,20/11) Parabolic Matrix(515,-942,158,-289) (31/17,11/6) -> (13/4,49/15) Hyperbolic Matrix(147,-272,20,-37) (11/6,13/7) -> (7/1,15/2) Hyperbolic Matrix(443,-844,116,-221) (17/9,2/1) -> (42/11,65/17) Hyperbolic Matrix(187,-400,36,-77) (2/1,15/7) -> (5/1,26/5) Hyperbolic Matrix(683,-1528,156,-349) (29/13,9/4) -> (35/8,57/13) Hyperbolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(5023,-13122,1922,-5021) (47/18,81/31) -> (81/31,115/44) Parabolic Matrix(1231,-3362,450,-1229) (30/11,41/15) -> (41/15,52/19) Parabolic Matrix(193,-534,30,-83) (11/4,25/9) -> (19/3,13/2) Hyperbolic Matrix(2383,-6632,696,-1937) (64/23,39/14) -> (89/26,24/7) Hyperbolic Matrix(691,-1968,204,-581) (17/6,20/7) -> (44/13,61/18) Hyperbolic Matrix(43,-126,14,-41) (20/7,3/1) -> (3/1,22/7) Parabolic Matrix(451,-1424,108,-341) (22/7,19/6) -> (25/6,46/11) Hyperbolic Matrix(727,-2382,170,-557) (36/11,23/7) -> (47/11,30/7) Hyperbolic Matrix(2471,-8450,722,-2469) (41/12,65/19) -> (65/19,89/26) Parabolic Matrix(133,-484,36,-131) (18/5,11/3) -> (11/3,26/7) Parabolic Matrix(1265,-4838,302,-1155) (65/17,23/6) -> (67/16,21/5) Hyperbolic Matrix(273,-1156,64,-271) (21/5,17/4) -> (17/4,47/11) Parabolic Matrix(231,-1058,50,-229) (9/2,23/5) -> (23/5,37/8) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(745,352,1272,601) -> Matrix(1,0,2,1) Matrix(1373,644,420,197) -> Matrix(5,-2,8,-3) Matrix(893,416,732,341) -> Matrix(3,-2,2,-1) Matrix(1409,652,832,385) -> Matrix(1,0,-2,1) Matrix(153,70,518,237) -> Matrix(1,0,0,1) Matrix(1327,600,1024,463) -> Matrix(1,2,0,1) Matrix(1427,644,308,139) -> Matrix(1,0,4,1) Matrix(1119,502,506,227) -> Matrix(5,-2,8,-3) Matrix(509,228,-2132,-955) -> Matrix(1,0,0,1) Matrix(2331,1042,302,135) -> Matrix(1,0,-4,1) Matrix(1363,608,204,91) -> Matrix(1,0,-4,1) Matrix(351,154,98,43) -> Matrix(3,-2,2,-1) Matrix(795,346,494,215) -> Matrix(3,-2,2,-1) Matrix(245,106,594,257) -> Matrix(1,0,2,1) Matrix(485,206,1754,745) -> Matrix(1,0,-2,1) Matrix(3983,1688,1168,495) -> Matrix(7,-2,4,-1) Matrix(4613,1954,2722,1153) -> Matrix(7,-2,4,-1) Matrix(389,164,676,285) -> Matrix(5,-2,18,-7) Matrix(239,100,-576,-241) -> Matrix(5,-2,8,-3) Matrix(953,394,670,277) -> Matrix(3,-2,2,-1) Matrix(239,98,378,155) -> Matrix(1,0,0,1) Matrix(323,126,182,71) -> Matrix(7,-4,2,-1) Matrix(227,88,276,107) -> Matrix(1,0,0,1) Matrix(271,104,456,175) -> Matrix(3,-2,8,-5) Matrix(907,346,270,103) -> Matrix(3,-2,2,-1) Matrix(453,172,1172,445) -> Matrix(1,0,-4,1) Matrix(3067,1162,4326,1639) -> Matrix(3,-2,-4,3) Matrix(3291,1246,2702,1023) -> Matrix(1,2,0,1) Matrix(1259,476,812,307) -> Matrix(1,0,0,1) Matrix(43,16,180,67) -> Matrix(1,0,-2,1) Matrix(577,212,264,97) -> Matrix(1,0,0,1) Matrix(617,226,1062,389) -> Matrix(1,0,0,1) Matrix(967,350,1666,603) -> Matrix(7,-4,16,-9) Matrix(1663,600,352,127) -> Matrix(3,-2,8,-5) Matrix(745,268,1048,377) -> Matrix(3,-2,-4,3) Matrix(1831,656,1136,407) -> Matrix(3,-2,2,-1) Matrix(697,248,1824,649) -> Matrix(7,-4,-12,7) Matrix(825,292,1472,521) -> Matrix(3,-2,32,-21) Matrix(131,46,430,151) -> Matrix(5,-4,4,-3) Matrix(283,88,164,51) -> Matrix(1,0,0,1) Matrix(119,36,-400,-121) -> Matrix(1,0,2,1) Matrix(1271,376,240,71) -> Matrix(1,0,0,1) Matrix(955,282,2462,727) -> Matrix(1,0,-6,1) Matrix(397,116,948,277) -> Matrix(5,-2,8,-3) Matrix(117,34,554,161) -> Matrix(7,-4,2,-1) Matrix(351,98,154,43) -> Matrix(1,0,0,1) Matrix(231,64,776,215) -> Matrix(1,-2,2,-3) Matrix(387,106,230,63) -> Matrix(1,0,0,1) Matrix(383,104,232,63) -> Matrix(1,2,0,1) Matrix(613,164,228,61) -> Matrix(3,2,-2,-1) Matrix(39,10,74,19) -> Matrix(1,0,-2,1) Matrix(1257,304,368,89) -> Matrix(3,-2,2,-1) Matrix(1143,274,146,35) -> Matrix(1,0,-2,1) Matrix(1543,366,586,139) -> Matrix(1,0,-2,1) Matrix(327,76,512,119) -> Matrix(1,-2,2,-3) Matrix(509,116,724,165) -> Matrix(1,-2,0,1) Matrix(469,106,146,33) -> Matrix(1,0,2,1) Matrix(789,172,500,109) -> Matrix(1,0,-4,1) Matrix(1145,248,928,201) -> Matrix(15,-4,4,-1) Matrix(1427,308,644,139) -> Matrix(5,-2,8,-3) Matrix(497,106,286,61) -> Matrix(7,-2,4,-1) Matrix(1169,244,848,177) -> Matrix(5,-2,-2,1) Matrix(1059,220,284,59) -> Matrix(9,-4,-2,1) Matrix(243,46,206,39) -> Matrix(5,-4,4,-3) Matrix(377,70,70,13) -> Matrix(1,0,0,1) Matrix(35,6,134,23) -> Matrix(1,0,-2,1) Matrix(99,16,68,11) -> Matrix(1,0,-2,1) Matrix(715,98,518,71) -> Matrix(3,-2,-4,3) Matrix(257,34,582,77) -> Matrix(3,-2,2,-1) Matrix(223,26,506,59) -> Matrix(1,0,0,1) Matrix(93,8,244,21) -> Matrix(3,-2,-4,3) Matrix(123,-16,100,-13) -> Matrix(1,2,0,1) Matrix(25,-4,144,-23) -> Matrix(3,-2,2,-1) Matrix(547,-98,854,-153) -> Matrix(3,-4,4,-5) Matrix(119,-22,330,-61) -> Matrix(3,-4,-2,3) Matrix(511,-106,834,-173) -> Matrix(1,-4,2,-7) Matrix(991,-214,690,-149) -> Matrix(1,-14,0,1) Matrix(527,-116,368,-81) -> Matrix(1,6,0,1) Matrix(365,-82,138,-31) -> Matrix(1,0,0,1) Matrix(133,-36,484,-131) -> Matrix(1,0,2,1) Matrix(1667,-462,350,-97) -> Matrix(1,0,0,1) Matrix(371,-104,132,-37) -> Matrix(1,0,-2,1) Matrix(173,-50,218,-63) -> Matrix(1,0,2,1) Matrix(989,-300,300,-91) -> Matrix(5,-6,6,-7) Matrix(407,-126,42,-13) -> Matrix(1,-2,0,1) Matrix(1539,-478,982,-305) -> Matrix(1,-2,0,1) Matrix(1469,-462,938,-295) -> Matrix(1,0,0,1) Matrix(487,-156,128,-41) -> Matrix(1,-2,0,1) Matrix(311,-110,82,-29) -> Matrix(1,0,0,1) Matrix(535,-192,248,-89) -> Matrix(1,2,2,5) Matrix(103,-38,122,-45) -> Matrix(3,2,4,3) Matrix(365,-138,82,-31) -> Matrix(1,0,0,1) Matrix(1053,-404,404,-155) -> Matrix(1,0,2,1) Matrix(2239,-868,1736,-673) -> Matrix(9,2,4,1) Matrix(81,-32,200,-79) -> Matrix(1,0,6,1) Matrix(2681,-1098,398,-163) -> Matrix(1,0,-6,1) Matrix(4489,-1840,3296,-1351) -> Matrix(9,-2,-4,1) Matrix(2085,-856,436,-179) -> Matrix(1,0,-2,1) Matrix(357,-148,316,-131) -> Matrix(5,-2,8,-3) Matrix(1163,-488,908,-381) -> Matrix(5,-4,4,-3) Matrix(393,-166,670,-283) -> Matrix(1,0,2,1) Matrix(273,-118,118,-51) -> Matrix(3,-2,2,-1) Matrix(583,-256,312,-137) -> Matrix(1,-2,0,1) Matrix(327,-148,232,-105) -> Matrix(1,0,0,1) Matrix(499,-228,116,-53) -> Matrix(1,0,0,1) Matrix(535,-248,192,-89) -> Matrix(1,0,-2,1) Matrix(181,-100,324,-179) -> Matrix(1,0,16,1) Matrix(1219,-684,180,-101) -> Matrix(1,0,-10,1) Matrix(215,-122,178,-101) -> Matrix(11,-2,6,-1) Matrix(1349,-780,780,-451) -> Matrix(5,-2,8,-3) Matrix(1135,-658,602,-349) -> Matrix(5,-2,-2,1) Matrix(1201,-702,142,-83) -> Matrix(1,0,0,1) Matrix(1449,-848,176,-103) -> Matrix(1,0,-6,1) Matrix(5633,-3300,1200,-703) -> Matrix(1,0,-2,1) Matrix(1427,-842,422,-249) -> Matrix(7,-2,4,-1) Matrix(227,-138,278,-169) -> Matrix(1,0,0,1) Matrix(3751,-2296,1008,-617) -> Matrix(5,-2,-2,1) Matrix(433,-266,70,-43) -> Matrix(1,0,-2,1) Matrix(191,-118,34,-21) -> Matrix(3,-2,2,-1) Matrix(619,-390,446,-281) -> Matrix(1,0,0,1) Matrix(2423,-1554,1330,-853) -> Matrix(19,-14,-4,3) Matrix(937,-604,408,-263) -> Matrix(9,-8,8,-7) Matrix(389,-254,170,-111) -> Matrix(1,-2,2,-3) Matrix(133,-90,34,-23) -> Matrix(1,-2,0,1) Matrix(845,-582,498,-343) -> Matrix(1,0,0,1) Matrix(429,-298,298,-207) -> Matrix(1,-4,0,1) Matrix(1183,-834,722,-509) -> Matrix(3,4,2,3) Matrix(1871,-1322,426,-301) -> Matrix(3,4,-4,-5) Matrix(2705,-1914,1214,-859) -> Matrix(11,10,12,11) Matrix(3195,-2266,2686,-1905) -> Matrix(13,8,8,5) Matrix(49,-36,64,-47) -> Matrix(1,0,2,1) Matrix(549,-430,346,-271) -> Matrix(1,0,0,1) Matrix(1299,-1024,940,-741) -> Matrix(1,0,-6,1) Matrix(789,-640,556,-451) -> Matrix(3,-2,2,-1) Matrix(163,-144,60,-53) -> Matrix(3,-4,-2,3) Matrix(199,-222,26,-29) -> Matrix(1,0,-2,1) Matrix(431,-494,130,-149) -> Matrix(7,-6,6,-5) Matrix(687,-796,208,-241) -> Matrix(11,-12,12,-13) Matrix(2295,-2716,616,-729) -> Matrix(7,-10,-2,3) Matrix(1217,-1444,1024,-1215) -> Matrix(13,-18,8,-11) Matrix(599,-716,128,-153) -> Matrix(1,-2,4,-7) Matrix(631,-768,152,-185) -> Matrix(1,-2,-2,5) Matrix(1315,-1626,926,-1145) -> Matrix(1,-4,0,1) Matrix(173,-218,50,-63) -> Matrix(1,0,0,1) Matrix(923,-1178,590,-753) -> Matrix(1,0,0,1) Matrix(1585,-2028,712,-911) -> Matrix(7,-8,8,-9) Matrix(4951,-6390,1882,-2429) -> Matrix(1,-4,0,1) Matrix(257,-332,24,-31) -> Matrix(1,-2,0,1) Matrix(1817,-2356,536,-695) -> Matrix(3,-8,2,-5) Matrix(97,-128,72,-95) -> Matrix(1,-4,0,1) Matrix(1555,-2114,854,-1161) -> Matrix(1,-4,0,1) Matrix(5563,-7570,1494,-2033) -> Matrix(1,-2,0,1) Matrix(9629,-13108,2300,-3131) -> Matrix(1,0,0,1) Matrix(9129,-12430,2182,-2971) -> Matrix(1,4,0,1) Matrix(449,-614,166,-227) -> Matrix(3,2,-2,-1) Matrix(2585,-3574,494,-683) -> Matrix(1,0,10,1) Matrix(1833,-2536,352,-487) -> Matrix(1,0,-8,1) Matrix(409,-570,94,-131) -> Matrix(1,-2,0,1) Matrix(963,-1360,604,-853) -> Matrix(1,-2,2,-3) Matrix(1461,-2068,556,-787) -> Matrix(1,-2,0,1) Matrix(5265,-7474,2014,-2859) -> Matrix(1,-6,0,1) Matrix(375,-578,242,-373) -> Matrix(1,0,2,1) Matrix(437,-682,66,-103) -> Matrix(1,0,-2,1) Matrix(553,-874,174,-275) -> Matrix(1,0,0,1) Matrix(1525,-2424,324,-515) -> Matrix(1,0,0,1) Matrix(4829,-7688,1836,-2923) -> Matrix(5,-2,-2,1) Matrix(1607,-2594,578,-933) -> Matrix(1,0,-2,1) Matrix(417,-676,256,-415) -> Matrix(3,-2,2,-1) Matrix(511,-834,106,-173) -> Matrix(1,-2,2,-3) Matrix(551,-904,64,-105) -> Matrix(1,-2,2,-3) Matrix(487,-830,186,-317) -> Matrix(1,-2,0,1) Matrix(1517,-2626,554,-959) -> Matrix(9,-8,-10,9) Matrix(181,-324,100,-179) -> Matrix(1,-10,0,1) Matrix(515,-942,158,-289) -> Matrix(1,2,2,5) Matrix(147,-272,20,-37) -> Matrix(1,2,0,1) Matrix(443,-844,116,-221) -> Matrix(1,0,0,1) Matrix(187,-400,36,-77) -> Matrix(1,0,-4,1) Matrix(683,-1528,156,-349) -> Matrix(3,-4,-2,3) Matrix(41,-100,16,-39) -> Matrix(1,-2,0,1) Matrix(5023,-13122,1922,-5021) -> Matrix(1,-12,0,1) Matrix(1231,-3362,450,-1229) -> Matrix(21,22,-22,-23) Matrix(193,-534,30,-83) -> Matrix(3,2,-2,-1) Matrix(2383,-6632,696,-1937) -> Matrix(1,0,2,1) Matrix(691,-1968,204,-581) -> Matrix(1,2,0,1) Matrix(43,-126,14,-41) -> Matrix(1,0,2,1) Matrix(451,-1424,108,-341) -> Matrix(1,0,0,1) Matrix(727,-2382,170,-557) -> Matrix(3,-2,2,-1) Matrix(2471,-8450,722,-2469) -> Matrix(1,-2,0,1) Matrix(133,-484,36,-131) -> Matrix(1,-6,0,1) Matrix(1265,-4838,302,-1155) -> Matrix(1,0,0,1) Matrix(273,-1156,64,-271) -> Matrix(1,0,2,1) Matrix(231,-1058,50,-229) -> Matrix(1,0,10,1) 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): 44 Degree of the the map X: 44 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 1/1 1 28 1/7 0/1 1 7 1/6 1/1 2 4 3/17 2/1 1 7 2/11 1/1 1 28 1/5 0 14 3/14 (7/1,1/0) 0 28 5/23 1/0 10 1 2/9 -3/1 1 28 1/4 (0/1,1/0) 0 28 3/11 0/1 1 2 5/18 (0/1,1/1) 0 28 2/7 1/1 1 28 5/17 0 14 3/10 (1/2,1/1) 0 28 4/13 1/1 1 28 9/29 0 14 5/16 1/0 2 4 6/19 1/1 1 28 1/3 1/0 1 7 5/14 (-2/1,1/0) 0 28 9/25 0 14 4/11 -1/1 1 28 3/8 (-1/2,0/1) 0 28 8/21 -1/1 1 28 13/34 (-3/5,-1/2) 0 28 5/13 0 14 7/18 (-1/2,0/1) 0 28 2/5 0/1 3 4 9/22 (0/1,1/4) 0 28 25/61 0 14 16/39 1/3 1 28 7/17 0/1 1 7 5/12 (1/3,1/2) 0 28 8/19 1/1 1 28 3/7 0 14 7/16 (1/1,2/1) 0 28 11/25 0/1 1 7 4/9 1/1 1 28 5/11 1/0 1 7 6/13 1/1 1 28 1/2 (0/1,1/0) 0 28 5/9 0/1 8 2 9/16 (0/1,1/8) 0 28 4/7 1/5 1 28 11/19 0 14 7/12 (0/1,1/2) 0 28 31/53 0/1 3 1 24/41 1/5 1 28 17/29 0 14 10/17 1/3 1 28 3/5 1/2 1 7 11/18 (1/2,1/1) 0 28 19/31 0 14 8/13 1/2 1 4 5/8 (1/2,1/1) 0 28 7/11 0 14 9/14 (4/5,1/1) 0 28 11/17 1/1 5 1 2/3 1/1 1 28 11/16 (1/1,1/0) 0 28 9/13 0 14 7/10 (-3/1,1/0) 0 28 12/17 -1/1 1 28 29/41 -1/1 9 2 17/24 (-1/1,-2/3) 0 28 5/7 0/1 1 7 3/4 0/1 2 4 7/9 0/1 1 7 11/14 (0/1,1/0) 0 28 15/19 0 14 4/5 1/3 1 28 5/6 (1/2,2/3) 0 28 6/7 1/1 1 28 1/1 0 14 8/7 1/1 1 28 15/13 1/1 9 1 7/6 (1/1,5/4) 0 28 6/5 1/1 1 28 17/14 (2/1,5/2) 0 28 28/23 3/1 1 28 11/9 2/1 1 7 16/13 3/1 1 28 5/4 (1/1,1/0) 0 28 14/11 1/1 1 28 23/18 (0/1,1/1) 0 28 9/7 2/1 1 7 31/24 (2/1,1/0) 0 28 22/17 1/1 1 28 13/10 (2/1,3/1) 0 28 4/3 1/0 2 4 19/14 (-2/1,-1/1) 0 28 34/25 -1/1 1 28 49/36 (-1/1,1/0) 0 28 113/83 1/0 2 1 64/47 -3/1 1 28 15/11 0 14 11/8 (0/1,1/0) 0 28 29/21 0 14 47/34 (-1/6,0/1) 0 28 65/47 0/1 9 1 18/13 1/3 1 28 7/5 1/0 1 7 24/17 1/1 1 28 41/29 1/0 1 2 17/12 (1/1,1/0) 0 28 10/7 3/1 1 28 3/2 (0/1,1/0) 0 28 17/11 0/1 1 1 14/9 1/1 1 28 25/16 (0/1,1/1) 0 28 36/23 1/1 1 28 47/30 1/0 2 4 11/7 0 14 19/12 (0/1,1/0) 0 28 27/17 0/1 1 7 35/22 (0/1,1/2) 0 28 43/27 1/2 1 2 8/5 1/1 1 28 21/13 0 14 13/8 1/1 2 4 31/19 0 14 18/11 1/1 1 28 5/3 1/0 1 7 17/10 (1/1,1/0) 0 28 12/7 -1/1 1 28 7/4 (2/1,1/0) 0 28 9/5 1/0 5 2 11/6 (-3/1,1/0) 0 28 13/7 -2/1 1 7 15/8 (-1/1,0/1) 0 28 2/1 -1/1 1 28 11/5 1/2 1 7 20/9 1/1 1 28 29/13 1/1 9 2 9/4 (1/1,1/0) 0 28 7/3 0 14 5/2 1/0 2 4 13/5 0 14 47/18 (3/1,1/0) 0 28 81/31 1/0 6 1 34/13 -3/1 1 28 21/8 (-1/1,1/0) 0 28 8/3 -3/1 1 28 19/7 0 14 30/11 -1/1 1 28 41/15 -1/1 11 1 11/4 (-1/1,-2/3) 0 28 25/9 0 14 39/14 (-1/2,0/1) 0 28 14/5 -1/1 1 28 17/6 (-1/1,0/1) 0 28 20/7 -1/1 1 28 3/1 0/1 1 7 13/4 (1/2,1/1) 0 28 36/11 1/1 1 28 23/7 0 14 10/3 1/1 1 28 17/5 0 14 41/12 (2/1,1/0) 0 28 65/19 1/0 1 1 24/7 1/1 1 28 7/2 (1/1,1/0) 0 28 11/3 1/0 3 2 15/4 (-2/1,1/0) 0 28 19/5 1/0 1 7 42/11 -1/1 1 28 23/6 (-1/1,1/0) 0 28 4/1 -1/1 1 28 25/6 (0/1,1/0) 0 28 21/5 0 14 17/4 0/1 2 4 47/11 0 14 30/7 1/1 1 28 13/3 1/0 1 7 22/5 -1/1 1 28 9/2 (-1/2,0/1) 0 28 23/5 0/1 5 1 14/3 1/3 1 28 19/4 (0/1,1/1) 0 28 24/5 1/1 1 28 5/1 0 14 11/2 (1/1,1/0) 0 28 6/1 1/0 1 4 19/3 0 14 13/2 (-1/1,0/1) 0 28 20/3 -1/1 1 28 7/1 0/1 1 7 15/2 (-1/1,1/0) 0 28 8/1 -1/1 1 28 9/1 0 14 10/1 -1/1 1 28 1/0 (0/1,1/0) 0 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(123,-16,100,-13) (0/1,1/7) -> (11/9,16/13) Hyperbolic Matrix(25,-4,144,-23) (1/7,1/6) -> (1/6,3/17) Parabolic Matrix(189,-34,428,-77) (3/17,2/11) -> (11/25,4/9) Glide Reflection Matrix(119,-22,330,-61) (2/11,1/5) -> (9/25,4/11) Hyperbolic Matrix(161,-34,232,-49) (1/5,3/14) -> (9/13,7/10) 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(67,-16,46,-11) (2/9,1/4) -> (10/7,3/2) Glide Reflection Matrix(23,-6,88,-23) (1/4,3/11) -> (1/4,3/11) Reflection Matrix(109,-30,396,-109) (3/11,5/18) -> (3/11,5/18) Reflection Matrix(371,-104,132,-37) (5/18,2/7) -> (14/5,17/6) Hyperbolic Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(237,-70,44,-13) (5/17,3/10) -> (5/1,11/2) Glide Reflection Matrix(151,-46,128,-39) (3/10,4/13) -> (7/6,6/5) Glide Reflection Matrix(407,-126,42,-13) (4/13,9/29) -> (9/1,10/1) Hyperbolic Matrix(1539,-478,982,-305) (9/29,5/16) -> (47/30,11/7) Hyperbolic Matrix(1469,-462,938,-295) (5/16,6/19) -> (36/23,47/30) Hyperbolic Matrix(487,-156,128,-41) (6/19,1/3) -> (19/5,42/11) Hyperbolic Matrix(311,-110,82,-29) (1/3,5/14) -> (15/4,19/5) Hyperbolic Matrix(681,-244,494,-177) (5/14,9/25) -> (11/8,29/21) Glide Reflection Matrix(103,-38,122,-45) (4/11,3/8) -> (5/6,6/7) Hyperbolic Matrix(365,-138,82,-31) (3/8,8/21) -> (22/5,9/2) Hyperbolic Matrix(649,-248,526,-201) (8/21,13/34) -> (16/13,5/4) Glide Reflection Matrix(1053,-404,404,-155) (13/34,5/13) -> (13/5,47/18) Hyperbolic Matrix(445,-172,282,-109) (5/13,7/18) -> (11/7,19/12) Glide Reflection Matrix(81,-32,200,-79) (7/18,2/5) -> (2/5,9/22) Parabolic Matrix(1987,-814,476,-195) (9/22,25/61) -> (25/6,21/5) Glide Reflection Matrix(4489,-1840,3296,-1351) (25/61,16/39) -> (64/47,15/11) Hyperbolic Matrix(457,-188,158,-65) (16/39,7/17) -> (20/7,3/1) Glide Reflection Matrix(257,-106,80,-33) (7/17,5/12) -> (3/1,13/4) Glide Reflection 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(175,-76,274,-119) (3/7,7/16) -> (7/11,9/14) Glide Reflection Matrix(583,-256,312,-137) (7/16,11/25) -> (13/7,15/8) Hyperbolic Matrix(327,-148,232,-105) (4/9,5/11) -> (7/5,24/17) Hyperbolic Matrix(499,-228,116,-53) (5/11,6/13) -> (30/7,13/3) Hyperbolic Matrix(535,-248,192,-89) (6/13,1/2) -> (39/14,14/5) Hyperbolic Matrix(19,-10,36,-19) (1/2,5/9) -> (1/2,5/9) Reflection Matrix(161,-90,288,-161) (5/9,9/16) -> (5/9,9/16) Reflection Matrix(215,-122,178,-101) (9/16,4/7) -> (6/5,17/14) Hyperbolic Matrix(285,-164,106,-61) (4/7,11/19) -> (8/3,19/7) Glide Reflection Matrix(389,-226,284,-165) (11/19,7/12) -> (15/11,11/8) Glide Reflection Matrix(743,-434,1272,-743) (7/12,31/53) -> (7/12,31/53) Reflection Matrix(2543,-1488,4346,-2543) (31/53,24/41) -> (31/53,24/41) Reflection Matrix(601,-352,70,-41) (24/41,17/29) -> (8/1,9/1) Glide Reflection 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(503,-308,730,-447) (11/18,19/31) -> (11/16,9/13) Glide Reflection Matrix(433,-266,70,-43) (19/31,8/13) -> (6/1,19/3) Hyperbolic Matrix(191,-118,34,-21) (8/13,5/8) -> (11/2,6/1) Hyperbolic Matrix(155,-98,68,-43) (5/8,7/11) -> (9/4,7/3) 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(133,-90,34,-23) (2/3,11/16) -> (23/6,4/1) Hyperbolic Matrix(1313,-928,590,-417) (12/17,29/41) -> (20/9,29/13) Glide Reflection Matrix(1393,-986,1968,-1393) (29/41,17/24) -> (29/41,17/24) Reflection Matrix(377,-268,294,-209) (17/24,5/7) -> (23/18,9/7) Glide Reflection Matrix(49,-36,64,-47) (5/7,3/4) -> (3/4,7/9) Parabolic Matrix(549,-430,346,-271) (7/9,11/14) -> (19/12,27/17) Hyperbolic Matrix(1299,-1024,940,-741) (11/14,15/19) -> (29/21,47/34) Hyperbolic Matrix(107,-88,62,-51) (4/5,5/6) -> (12/7,7/4) Glide Reflection Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(171,-194,52,-59) (1/1,8/7) -> (23/7,10/3) Glide Reflection Matrix(209,-240,182,-209) (8/7,15/13) -> (8/7,15/13) Reflection Matrix(181,-210,156,-181) (15/13,7/6) -> (15/13,7/6) Reflection Matrix(631,-768,152,-185) (17/14,28/23) -> (4/1,25/6) Hyperbolic Matrix(341,-416,50,-61) (28/23,11/9) -> (20/3,7/1) Glide Reflection Matrix(173,-218,50,-63) (5/4,14/11) -> (24/7,7/2) Hyperbolic Matrix(923,-1178,590,-753) (14/11,23/18) -> (25/16,36/23) Hyperbolic Matrix(893,-1152,562,-725) (9/7,31/24) -> (27/17,35/22) Glide Reflection Matrix(257,-332,24,-31) (31/24,22/17) -> (10/1,1/0) Hyperbolic Matrix(463,-600,98,-127) (22/17,13/10) -> (14/3,19/4) Glide Reflection Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(403,-548,214,-291) (19/14,34/25) -> (15/8,2/1) Glide Reflection Matrix(2087,-2840,546,-743) (34/25,49/36) -> (42/11,23/6) Glide Reflection Matrix(8135,-11074,5976,-8135) (49/36,113/83) -> (49/36,113/83) Reflection Matrix(10623,-14464,7802,-10623) (113/83,64/47) -> (113/83,64/47) Reflection Matrix(4419,-6110,3196,-4419) (47/34,65/47) -> (47/34,65/47) Reflection Matrix(1691,-2340,1222,-1691) (65/47,18/13) -> (65/47,18/13) Reflection Matrix(153,-212,70,-97) (18/13,7/5) -> (2/1,11/5) Glide Reflection Matrix(963,-1360,604,-853) (24/17,41/29) -> (43/27,8/5) Hyperbolic Matrix(985,-1394,696,-985) (41/29,17/12) -> (41/29,17/12) Reflection Matrix(243,-346,92,-131) (17/12,10/7) -> (21/8,8/3) Glide Reflection 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(437,-682,66,-103) (14/9,25/16) -> (13/2,20/3) Hyperbolic Matrix(1891,-3010,1188,-1891) (35/22,43/27) -> (35/22,43/27) Reflection Matrix(215,-346,64,-103) (8/5,21/13) -> (10/3,17/5) Glide Reflection Matrix(417,-676,256,-415) (21/13,13/8) -> (13/8,31/19) Parabolic Matrix(511,-834,106,-173) (31/19,18/11) -> (24/5,5/1) Hyperbolic Matrix(487,-830,186,-317) (17/10,12/7) -> (34/13,21/8) Hyperbolic Matrix(71,-126,40,-71) (7/4,9/5) -> (7/4,9/5) Reflection Matrix(109,-198,60,-109) (9/5,11/6) -> (9/5,11/6) Reflection Matrix(147,-272,20,-37) (11/6,13/7) -> (7/1,15/2) Hyperbolic Matrix(227,-502,52,-115) (11/5,20/9) -> (13/3,22/5) Glide Reflection Matrix(233,-522,104,-233) (29/13,9/4) -> (29/13,9/4) Reflection Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic 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(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(193,-534,30,-83) (11/4,25/9) -> (19/3,13/2) Hyperbolic Matrix(607,-1688,178,-495) (25/9,39/14) -> (17/5,41/12) Glide Reflection Matrix(277,-788,58,-165) (17/6,20/7) -> (19/4,24/5) Glide Reflection Matrix(197,-644,26,-85) (13/4,36/11) -> (15/2,8/1) Glide Reflection Matrix(727,-2382,170,-557) (36/11,23/7) -> (47/11,30/7) Hyperbolic 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(43,-154,12,-43) (7/2,11/3) -> (7/2,11/3) Reflection Matrix(89,-330,24,-89) (11/3,15/4) -> (11/3,15/4) Reflection Matrix(273,-1156,64,-271) (21/5,17/4) -> (17/4,47/11) Parabolic 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 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(123,-16,100,-13) -> Matrix(1,2,0,1) 1/0 Matrix(25,-4,144,-23) -> Matrix(3,-2,2,-1) 1/1 Matrix(189,-34,428,-77) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(119,-22,330,-61) -> Matrix(3,-4,-2,3) Matrix(161,-34,232,-49) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(139,-30,644,-139) -> Matrix(-1,14,0,1) (3/14,5/23) -> (7/1,1/0) Matrix(91,-20,414,-91) -> Matrix(1,6,0,-1) (5/23,2/9) -> (-3/1,1/0) Matrix(67,-16,46,-11) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(23,-6,88,-23) -> Matrix(1,0,0,-1) (1/4,3/11) -> (0/1,1/0) Matrix(109,-30,396,-109) -> Matrix(1,0,2,-1) (3/11,5/18) -> (0/1,1/1) Matrix(371,-104,132,-37) -> Matrix(1,0,-2,1) 0/1 Matrix(173,-50,218,-63) -> Matrix(1,0,2,1) 0/1 Matrix(237,-70,44,-13) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(151,-46,128,-39) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(407,-126,42,-13) -> Matrix(1,-2,0,1) 1/0 Matrix(1539,-478,982,-305) -> Matrix(1,-2,0,1) 1/0 Matrix(1469,-462,938,-295) -> Matrix(1,0,0,1) Matrix(487,-156,128,-41) -> Matrix(1,-2,0,1) 1/0 Matrix(311,-110,82,-29) -> Matrix(1,0,0,1) Matrix(681,-244,494,-177) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(103,-38,122,-45) -> Matrix(3,2,4,3) Matrix(365,-138,82,-31) -> Matrix(1,0,0,1) Matrix(649,-248,526,-201) -> Matrix(7,4,2,1) Matrix(1053,-404,404,-155) -> Matrix(1,0,2,1) 0/1 Matrix(445,-172,282,-109) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(81,-32,200,-79) -> Matrix(1,0,6,1) 0/1 Matrix(1987,-814,476,-195) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(4489,-1840,3296,-1351) -> Matrix(9,-2,-4,1) Matrix(457,-188,158,-65) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(257,-106,80,-33) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(277,-116,394,-165) -> Matrix(3,-2,-2,1) Matrix(393,-166,670,-283) -> Matrix(1,0,2,1) 0/1 Matrix(175,-76,274,-119) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(583,-256,312,-137) -> Matrix(1,-2,0,1) 1/0 Matrix(327,-148,232,-105) -> Matrix(1,0,0,1) Matrix(499,-228,116,-53) -> Matrix(1,0,0,1) Matrix(535,-248,192,-89) -> Matrix(1,0,-2,1) 0/1 Matrix(19,-10,36,-19) -> Matrix(1,0,0,-1) (1/2,5/9) -> (0/1,1/0) Matrix(161,-90,288,-161) -> Matrix(1,0,16,-1) (5/9,9/16) -> (0/1,1/8) Matrix(215,-122,178,-101) -> Matrix(11,-2,6,-1) Matrix(285,-164,106,-61) -> Matrix(7,-2,-4,1) Matrix(389,-226,284,-165) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(743,-434,1272,-743) -> Matrix(1,0,4,-1) (7/12,31/53) -> (0/1,1/2) Matrix(2543,-1488,4346,-2543) -> Matrix(1,0,10,-1) (31/53,24/41) -> (0/1,1/5) Matrix(601,-352,70,-41) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(175,-104,106,-63) -> Matrix(5,-2,2,-1) Matrix(175,-106,104,-63) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(503,-308,730,-447) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(433,-266,70,-43) -> Matrix(1,0,-2,1) 0/1 Matrix(191,-118,34,-21) -> Matrix(3,-2,2,-1) 1/1 Matrix(155,-98,68,-43) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(307,-198,476,-307) -> Matrix(9,-8,10,-9) (9/14,11/17) -> (4/5,1/1) Matrix(67,-44,102,-67) -> Matrix(-1,2,0,1) (11/17,2/3) -> (1/1,1/0) Matrix(133,-90,34,-23) -> Matrix(1,-2,0,1) 1/0 Matrix(1313,-928,590,-417) -> Matrix(5,6,6,7) Matrix(1393,-986,1968,-1393) -> Matrix(5,4,-6,-5) (29/41,17/24) -> (-1/1,-2/3) Matrix(377,-268,294,-209) -> Matrix(3,2,2,1) Matrix(49,-36,64,-47) -> Matrix(1,0,2,1) 0/1 Matrix(549,-430,346,-271) -> Matrix(1,0,0,1) Matrix(1299,-1024,940,-741) -> Matrix(1,0,-6,1) 0/1 Matrix(107,-88,62,-51) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(163,-144,60,-53) -> Matrix(3,-4,-2,3) Matrix(171,-194,52,-59) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(209,-240,182,-209) -> Matrix(9,-8,10,-9) (8/7,15/13) -> (4/5,1/1) Matrix(181,-210,156,-181) -> Matrix(9,-10,8,-9) (15/13,7/6) -> (1/1,5/4) Matrix(631,-768,152,-185) -> Matrix(1,-2,-2,5) Matrix(341,-416,50,-61) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(173,-218,50,-63) -> Matrix(1,0,0,1) Matrix(923,-1178,590,-753) -> Matrix(1,0,0,1) Matrix(893,-1152,562,-725) -> Matrix(1,-2,2,-5) Matrix(257,-332,24,-31) -> Matrix(1,-2,0,1) 1/0 Matrix(463,-600,98,-127) -> Matrix(1,-2,2,-5) Matrix(97,-128,72,-95) -> Matrix(1,-4,0,1) 1/0 Matrix(403,-548,214,-291) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(2087,-2840,546,-743) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(8135,-11074,5976,-8135) -> Matrix(1,2,0,-1) (49/36,113/83) -> (-1/1,1/0) Matrix(10623,-14464,7802,-10623) -> Matrix(1,6,0,-1) (113/83,64/47) -> (-3/1,1/0) Matrix(4419,-6110,3196,-4419) -> Matrix(-1,0,12,1) (47/34,65/47) -> (-1/6,0/1) Matrix(1691,-2340,1222,-1691) -> Matrix(1,0,6,-1) (65/47,18/13) -> (0/1,1/3) Matrix(153,-212,70,-97) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(963,-1360,604,-853) -> Matrix(1,-2,2,-3) 1/1 Matrix(985,-1394,696,-985) -> Matrix(-1,2,0,1) (41/29,17/12) -> (1/1,1/0) Matrix(243,-346,92,-131) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(67,-102,44,-67) -> Matrix(1,0,0,-1) (3/2,17/11) -> (0/1,1/0) Matrix(307,-476,198,-307) -> Matrix(1,0,2,-1) (17/11,14/9) -> (0/1,1/1) Matrix(437,-682,66,-103) -> Matrix(1,0,-2,1) 0/1 Matrix(1891,-3010,1188,-1891) -> Matrix(1,0,4,-1) (35/22,43/27) -> (0/1,1/2) Matrix(215,-346,64,-103) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(417,-676,256,-415) -> Matrix(3,-2,2,-1) 1/1 Matrix(511,-834,106,-173) -> Matrix(1,-2,2,-3) 1/1 Matrix(487,-830,186,-317) -> Matrix(1,-2,0,1) 1/0 Matrix(71,-126,40,-71) -> Matrix(-1,4,0,1) (7/4,9/5) -> (2/1,1/0) Matrix(109,-198,60,-109) -> Matrix(1,6,0,-1) (9/5,11/6) -> (-3/1,1/0) Matrix(147,-272,20,-37) -> Matrix(1,2,0,1) 1/0 Matrix(227,-502,52,-115) -> Matrix(3,-2,-2,1) Matrix(233,-522,104,-233) -> Matrix(-1,2,0,1) (29/13,9/4) -> (1/1,1/0) Matrix(41,-100,16,-39) -> Matrix(1,-2,0,1) 1/0 Matrix(2915,-7614,1116,-2915) -> Matrix(-1,6,0,1) (47/18,81/31) -> (3/1,1/0) Matrix(2107,-5508,806,-2107) -> Matrix(1,6,0,-1) (81/31,34/13) -> (-3/1,1/0) Matrix(901,-2460,330,-901) -> Matrix(17,18,-16,-17) (30/11,41/15) -> (-9/8,-1/1) Matrix(329,-902,120,-329) -> Matrix(5,4,-6,-5) (41/15,11/4) -> (-1/1,-2/3) Matrix(193,-534,30,-83) -> Matrix(3,2,-2,-1) -1/1 Matrix(607,-1688,178,-495) -> Matrix(3,2,2,1) Matrix(277,-788,58,-165) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(197,-644,26,-85) -> Matrix(3,-2,-2,1) Matrix(727,-2382,170,-557) -> Matrix(3,-2,2,-1) 1/1 Matrix(1559,-5330,456,-1559) -> Matrix(-1,4,0,1) (41/12,65/19) -> (2/1,1/0) Matrix(911,-3120,266,-911) -> Matrix(-1,2,0,1) (65/19,24/7) -> (1/1,1/0) Matrix(43,-154,12,-43) -> Matrix(-1,2,0,1) (7/2,11/3) -> (1/1,1/0) Matrix(89,-330,24,-89) -> Matrix(1,4,0,-1) (11/3,15/4) -> (-2/1,1/0) Matrix(273,-1156,64,-271) -> Matrix(1,0,2,1) 0/1 Matrix(91,-414,20,-91) -> Matrix(-1,0,4,1) (9/2,23/5) -> (-1/2,0/1) Matrix(139,-644,30,-139) -> Matrix(1,0,6,-1) (23/5,14/3) -> (0/1,1/3) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.