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: 50 Genus: 36 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -6/1 -11/2 -4/1 -10/3 -11/4 -2/1 -11/6 -55/34 -22/15 -11/8 -22/19 0/1 1/1 11/9 22/17 11/8 3/2 11/7 22/13 11/6 2/1 11/5 22/9 5/2 55/21 11/4 3/1 22/7 33/10 10/3 7/2 11/3 4/1 17/4 22/5 9/2 19/4 110/23 5/1 11/2 23/4 6/1 13/2 7/1 22/3 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 0/1 1/0 -8/1 1/0 -7/1 -1/1 0/1 -13/2 -1/1 -1/2 -6/1 -1/2 -11/2 0/1 -16/3 1/2 -5/1 -1/1 0/1 -14/3 -1/2 -23/5 -1/1 0/1 -32/7 -1/2 -9/2 -1/3 0/1 -22/5 0/1 -13/3 0/1 1/0 -17/4 -1/1 0/1 -21/5 -1/1 0/1 -4/1 -1/2 -19/5 -2/5 -1/3 -15/4 -1/2 -1/3 -11/3 -1/3 -7/2 -1/3 0/1 -10/3 -1/4 -13/4 -1/4 -1/5 -16/5 -1/4 -3/1 -1/3 0/1 -11/4 -1/4 -19/7 -2/9 -1/5 -27/10 -1/5 0/1 -35/13 -1/4 0/1 -8/3 -1/4 -29/11 -1/5 0/1 -21/8 -1/5 0/1 -13/5 -2/7 -1/4 -5/2 -1/4 -1/5 -22/9 -1/5 -17/7 -1/5 -2/11 -46/19 -1/6 -29/12 -1/5 -1/6 -41/17 -1/5 0/1 -12/5 -1/6 -43/18 -1/4 0/1 -31/13 -1/4 0/1 -19/8 -1/4 0/1 -7/3 -1/5 0/1 -23/10 -1/5 0/1 -16/7 -1/4 -25/11 -1/5 -2/11 -34/15 -1/6 -9/4 -1/5 0/1 -11/5 -1/5 -13/6 -1/5 -1/6 -2/1 -1/6 -11/6 -1/7 -20/11 -1/8 -29/16 -1/7 -1/8 -9/5 -1/8 0/1 -25/14 -1/8 0/1 -66/37 0/1 -41/23 -1/5 0/1 -16/9 -1/6 -7/4 -1/7 0/1 -12/7 -1/6 -17/10 -4/27 -1/7 -22/13 -1/7 -5/3 -1/7 -2/15 -28/17 -5/38 -23/14 -2/15 -3/23 -41/25 -2/15 -3/23 -18/11 -1/8 -13/8 -1/8 -1/9 -34/21 -1/8 -55/34 -1/8 -76/47 -1/8 -21/13 -1/7 0/1 -50/31 -1/8 -29/18 -1/7 -1/8 -66/41 -1/7 -37/23 -1/7 -2/15 -8/5 -1/8 -27/17 -2/15 -3/23 -46/29 -1/8 -19/12 -4/31 -1/8 -11/7 -1/8 -3/2 -1/8 -1/9 -22/15 -1/9 -19/13 -1/9 -4/37 -16/11 -1/10 -29/20 -1/9 -1/10 -13/9 -2/19 -1/10 -23/16 -1/11 0/1 -33/23 0/1 -43/30 -1/6 0/1 -10/7 -1/8 -17/12 -1/9 -2/19 -41/29 -1/9 0/1 -65/46 -1/9 0/1 -24/17 -1/10 -31/22 -1/9 -1/10 -7/5 -1/9 0/1 -11/8 -1/9 -15/11 -1/9 -2/19 -19/14 -2/19 -1/10 -42/31 -1/10 -65/48 -1/9 0/1 -88/65 -1/9 -23/17 -1/9 -2/19 -4/3 -1/10 -13/10 -5/49 -1/10 -22/17 -1/10 -9/7 -1/10 -4/41 -5/4 -1/10 -1/11 -11/9 -1/11 -17/14 -1/11 -2/23 -23/19 -1/11 -2/23 -6/5 -1/12 -7/6 -1/11 0/1 -22/19 -1/11 -15/13 -1/11 -2/23 -8/7 -1/12 -1/1 -1/13 0/1 0/1 0/1 1/1 0/1 1/13 8/7 1/12 7/6 0/1 1/11 6/5 1/12 23/19 2/23 1/11 17/14 2/23 1/11 11/9 1/11 5/4 1/11 1/10 9/7 4/41 1/10 22/17 1/10 13/10 1/10 5/49 4/3 1/10 11/8 1/9 18/13 1/8 7/5 0/1 1/9 24/17 1/10 17/12 2/19 1/9 10/7 1/8 13/9 1/10 2/19 29/20 1/10 1/9 16/11 1/10 3/2 1/9 1/8 11/7 1/8 19/12 1/8 4/31 8/5 1/8 29/18 1/8 1/7 50/31 1/8 21/13 0/1 1/7 13/8 1/9 1/8 18/11 1/8 23/14 3/23 2/15 5/3 2/15 1/7 22/13 1/7 17/10 1/7 4/27 12/7 1/6 7/4 0/1 1/7 16/9 1/6 25/14 0/1 1/8 9/5 0/1 1/8 11/6 1/7 13/7 2/13 1/6 15/8 1/7 1/6 2/1 1/6 13/6 1/6 1/5 11/5 1/5 9/4 0/1 1/5 34/15 1/6 25/11 2/11 1/5 66/29 1/5 41/18 1/5 3/14 16/7 1/4 23/10 0/1 1/5 7/3 0/1 1/5 26/11 1/4 45/19 0/1 1/5 19/8 0/1 1/4 31/13 0/1 1/4 43/18 0/1 1/4 12/5 1/6 29/12 1/6 1/5 46/19 1/6 17/7 2/11 1/5 22/9 1/5 5/2 1/5 1/4 13/5 1/4 2/7 34/13 1/2 89/34 0/1 1/0 55/21 0/1 21/8 0/1 1/5 29/11 0/1 1/5 66/25 1/5 37/14 1/5 2/9 8/3 1/4 11/4 1/4 14/5 1/4 17/6 2/7 1/3 20/7 1/4 3/1 0/1 1/3 22/7 0/1 19/6 0/1 1/6 16/5 1/4 13/4 1/5 1/4 23/7 0/1 1/3 33/10 1/4 10/3 1/4 7/2 0/1 1/3 11/3 1/3 15/4 1/3 1/2 34/9 1/2 19/5 1/3 2/5 42/11 1/2 23/6 1/3 2/5 4/1 1/2 21/5 0/1 1/1 17/4 0/1 1/1 30/7 1/0 13/3 0/1 1/0 22/5 0/1 9/2 0/1 1/3 32/7 1/2 55/12 1/2 23/5 0/1 1/1 14/3 1/2 19/4 1/2 2/3 43/9 2/3 1/1 110/23 1/1 67/14 0/1 1/1 24/5 1/2 5/1 0/1 1/1 11/2 0/1 17/3 0/1 1/5 23/4 0/1 1/3 6/1 1/2 13/2 1/2 1/1 20/3 1/2 7/1 0/1 1/1 22/3 1/1 15/2 1/1 1/0 8/1 1/0 9/1 0/1 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(43,418,18,175) (-9/1,1/0) -> (31/13,43/18) Hyperbolic Matrix(43,374,10,87) (-9/1,-8/1) -> (30/7,13/3) Hyperbolic Matrix(45,352,-28,-219) (-8/1,-7/1) -> (-37/23,-8/5) Hyperbolic Matrix(45,308,-32,-219) (-7/1,-13/2) -> (-31/22,-7/5) Hyperbolic Matrix(45,286,14,89) (-13/2,-6/1) -> (16/5,13/4) Hyperbolic Matrix(43,242,-8,-45) (-6/1,-11/2) -> (-11/2,-16/3) Parabolic Matrix(43,220,-26,-133) (-16/3,-5/1) -> (-5/3,-28/17) Hyperbolic Matrix(89,418,-56,-263) (-5/1,-14/3) -> (-8/5,-27/17) Hyperbolic Matrix(43,198,38,175) (-14/3,-23/5) -> (1/1,8/7) Hyperbolic Matrix(527,2420,-326,-1497) (-23/5,-32/7) -> (-76/47,-21/13) Hyperbolic Matrix(131,594,58,263) (-32/7,-9/2) -> (9/4,34/15) Hyperbolic Matrix(89,396,20,89) (-9/2,-22/5) -> (22/5,9/2) Hyperbolic Matrix(131,572,30,131) (-22/5,-13/3) -> (13/3,22/5) Hyperbolic Matrix(221,946,-82,-351) (-13/3,-17/4) -> (-27/10,-35/13) Hyperbolic Matrix(177,748,146,617) (-17/4,-21/5) -> (23/19,17/14) Hyperbolic Matrix(175,726,74,307) (-21/5,-4/1) -> (26/11,45/19) Hyperbolic Matrix(131,506,-80,-309) (-4/1,-19/5) -> (-41/25,-18/11) Hyperbolic Matrix(309,1166,-128,-483) (-19/5,-15/4) -> (-29/12,-41/17) Hyperbolic Matrix(89,330,24,89) (-15/4,-11/3) -> (11/3,15/4) Hyperbolic Matrix(43,154,12,43) (-11/3,-7/2) -> (7/2,11/3) Hyperbolic Matrix(45,154,26,89) (-7/2,-10/3) -> (12/7,7/4) Hyperbolic Matrix(175,572,-108,-353) (-10/3,-13/4) -> (-13/8,-34/21) Hyperbolic Matrix(89,286,14,45) (-13/4,-16/5) -> (6/1,13/2) Hyperbolic Matrix(221,704,-124,-395) (-16/5,-3/1) -> (-41/23,-16/9) Hyperbolic Matrix(87,242,-32,-89) (-3/1,-11/4) -> (-11/4,-19/7) Parabolic Matrix(529,1430,-374,-1011) (-19/7,-27/10) -> (-17/12,-41/29) Hyperbolic Matrix(131,352,16,43) (-35/13,-8/3) -> (8/1,9/1) Hyperbolic Matrix(133,352,-116,-307) (-8/3,-29/11) -> (-15/13,-8/7) Hyperbolic Matrix(309,814,134,353) (-29/11,-21/8) -> (23/10,7/3) Hyperbolic Matrix(219,572,-152,-397) (-21/8,-13/5) -> (-13/9,-23/16) Hyperbolic Matrix(43,110,34,87) (-13/5,-5/2) -> (5/4,9/7) Hyperbolic Matrix(89,220,36,89) (-5/2,-22/9) -> (22/9,5/2) Hyperbolic Matrix(307,748,126,307) (-22/9,-17/7) -> (17/7,22/9) Hyperbolic Matrix(263,638,54,131) (-17/7,-46/19) -> (24/5,5/1) Hyperbolic Matrix(309,748,164,397) (-46/19,-29/12) -> (15/8,2/1) Hyperbolic Matrix(703,1694,310,747) (-41/17,-12/5) -> (34/15,25/11) Hyperbolic Matrix(395,946,-276,-661) (-12/5,-43/18) -> (-43/30,-10/7) Hyperbolic Matrix(175,418,18,43) (-43/18,-31/13) -> (9/1,1/0) Hyperbolic Matrix(397,946,222,529) (-31/13,-19/8) -> (25/14,9/5) Hyperbolic Matrix(177,418,-130,-307) (-19/8,-7/3) -> (-15/11,-19/14) Hyperbolic Matrix(353,814,134,309) (-7/3,-23/10) -> (21/8,29/11) Hyperbolic Matrix(441,1012,-268,-615) (-23/10,-16/7) -> (-28/17,-23/14) Hyperbolic Matrix(309,704,-212,-483) (-16/7,-25/11) -> (-19/13,-16/11) Hyperbolic Matrix(659,1496,174,395) (-25/11,-34/15) -> (34/9,19/5) Hyperbolic Matrix(263,594,58,131) (-34/15,-9/4) -> (9/2,32/7) Hyperbolic Matrix(89,198,40,89) (-9/4,-11/5) -> (11/5,9/4) Hyperbolic Matrix(131,286,60,131) (-11/5,-13/6) -> (13/6,11/5) Hyperbolic Matrix(175,374,-124,-265) (-13/6,-2/1) -> (-24/17,-31/22) Hyperbolic Matrix(131,242,-72,-133) (-2/1,-11/6) -> (-11/6,-20/11) Parabolic Matrix(1055,1914,436,791) (-20/11,-29/16) -> (29/12,46/19) Hyperbolic Matrix(353,638,244,441) (-29/16,-9/5) -> (13/9,29/20) Hyperbolic Matrix(529,946,222,397) (-9/5,-25/14) -> (19/8,31/13) Hyperbolic Matrix(1011,1804,320,571) (-25/14,-66/37) -> (22/7,19/6) Hyperbolic Matrix(617,1100,198,353) (-66/37,-41/23) -> (3/1,22/7) Hyperbolic Matrix(87,154,74,131) (-16/9,-7/4) -> (7/6,6/5) Hyperbolic Matrix(89,154,26,45) (-7/4,-12/7) -> (10/3,7/2) Hyperbolic Matrix(219,374,154,263) (-12/7,-17/10) -> (17/12,10/7) Hyperbolic Matrix(441,748,260,441) (-17/10,-22/13) -> (22/13,17/10) Hyperbolic Matrix(131,220,78,131) (-22/13,-5/3) -> (5/3,22/13) Hyperbolic Matrix(2199,3608,-1556,-2553) (-23/14,-41/25) -> (-41/29,-65/46) Hyperbolic Matrix(175,286,134,219) (-18/11,-13/8) -> (13/10,4/3) Hyperbolic Matrix(3739,6050,-2312,-3741) (-34/21,-55/34) -> (-55/34,-76/47) Parabolic Matrix(791,1276,654,1055) (-21/13,-50/31) -> (6/5,23/19) Hyperbolic Matrix(1187,1914,818,1319) (-50/31,-29/18) -> (29/20,16/11) Hyperbolic Matrix(1011,1628,136,219) (-29/18,-66/41) -> (22/3,15/2) Hyperbolic Matrix(793,1276,110,177) (-66/41,-37/23) -> (7/1,22/3) Hyperbolic Matrix(1275,2024,526,835) (-27/17,-46/29) -> (46/19,17/7) Hyperbolic Matrix(1055,1672,-778,-1233) (-46/29,-19/12) -> (-19/14,-42/31) Hyperbolic Matrix(265,418,168,265) (-19/12,-11/7) -> (11/7,19/12) Hyperbolic Matrix(43,66,28,43) (-11/7,-3/2) -> (3/2,11/7) Hyperbolic Matrix(747,1100,328,483) (-3/2,-22/15) -> (66/29,41/18) Hyperbolic Matrix(1233,1804,542,793) (-22/15,-19/13) -> (25/11,66/29) Hyperbolic Matrix(1319,1914,818,1187) (-16/11,-29/20) -> (29/18,50/31) Hyperbolic Matrix(395,572,212,307) (-29/20,-13/9) -> (13/7,15/8) Hyperbolic Matrix(1363,1958,520,747) (-23/16,-33/23) -> (55/21,21/8) Hyperbolic Matrix(3697,5302,1412,2025) (-33/23,-43/30) -> (89/34,55/21) Hyperbolic Matrix(263,374,154,219) (-10/7,-17/12) -> (17/10,12/7) Hyperbolic Matrix(3037,4290,-2242,-3167) (-65/46,-24/17) -> (-42/31,-65/48) Hyperbolic Matrix(175,242,-128,-177) (-7/5,-11/8) -> (-11/8,-15/11) Parabolic Matrix(9635,13046,2014,2727) (-65/48,-88/65) -> (110/23,67/14) Hyperbolic Matrix(4665,6314,976,1321) (-88/65,-23/17) -> (43/9,110/23) Hyperbolic Matrix(131,176,32,43) (-23/17,-4/3) -> (4/1,21/5) Hyperbolic Matrix(219,286,134,175) (-4/3,-13/10) -> (13/8,18/11) Hyperbolic Matrix(441,572,340,441) (-13/10,-22/17) -> (22/17,13/10) Hyperbolic Matrix(307,396,238,307) (-22/17,-9/7) -> (9/7,22/17) Hyperbolic Matrix(87,110,34,43) (-9/7,-5/4) -> (5/2,13/5) Hyperbolic Matrix(89,110,72,89) (-5/4,-11/9) -> (11/9,5/4) Hyperbolic Matrix(307,374,252,307) (-11/9,-17/14) -> (17/14,11/9) Hyperbolic Matrix(617,748,146,177) (-17/14,-23/19) -> (21/5,17/4) Hyperbolic Matrix(1055,1276,654,791) (-23/19,-6/5) -> (50/31,21/13) Hyperbolic Matrix(131,154,74,87) (-6/5,-7/6) -> (7/4,16/9) Hyperbolic Matrix(1099,1276,416,483) (-7/6,-22/19) -> (66/25,37/14) Hyperbolic Matrix(1409,1628,534,617) (-22/19,-15/13) -> (29/11,66/25) Hyperbolic Matrix(175,198,38,43) (-8/7,-1/1) -> (23/5,14/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(307,-352,116,-133) (8/7,7/6) -> (37/14,8/3) Hyperbolic Matrix(177,-242,128,-175) (4/3,11/8) -> (11/8,18/13) Parabolic Matrix(221,-308,94,-131) (18/13,7/5) -> (7/3,26/11) Hyperbolic Matrix(219,-308,32,-45) (7/5,24/17) -> (20/3,7/1) Hyperbolic Matrix(529,-748,186,-263) (24/17,17/12) -> (17/6,20/7) Hyperbolic Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(483,-704,212,-309) (16/11,3/2) -> (41/18,16/7) Hyperbolic Matrix(263,-418,56,-89) (19/12,8/5) -> (14/3,19/4) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(309,-506,80,-131) (18/11,23/14) -> (23/6,4/1) Hyperbolic Matrix(307,-506,54,-89) (23/14,5/3) -> (17/3,23/4) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(133,-242,72,-131) (9/5,11/6) -> (11/6,13/7) Parabolic Matrix(133,-286,20,-43) (2/1,13/6) -> (13/2,20/3) Hyperbolic Matrix(221,-506,38,-87) (16/7,23/10) -> (23/4,6/1) Hyperbolic Matrix(705,-1672,148,-351) (45/19,19/8) -> (19/4,43/9) Hyperbolic Matrix(1057,-2530,404,-967) (43/18,12/5) -> (34/13,89/34) Hyperbolic Matrix(483,-1166,128,-309) (12/5,29/12) -> (15/4,34/9) Hyperbolic Matrix(89,-242,32,-87) (8/3,11/4) -> (11/4,14/5) Parabolic Matrix(265,-748,62,-175) (14/5,17/6) -> (17/4,30/7) Hyperbolic Matrix(175,-506,46,-133) (20/7,3/1) -> (19/5,42/11) Hyperbolic Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(485,-1606,106,-351) (33/10,10/3) -> (32/7,55/12) Hyperbolic Matrix(881,-3366,184,-703) (42/11,23/6) -> (67/14,24/5) Hyperbolic Matrix(45,-242,8,-43) (5/1,11/2) -> (11/2,17/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(43,418,18,175) -> Matrix(1,0,4,1) Matrix(43,374,10,87) -> Matrix(1,0,0,1) Matrix(45,352,-28,-219) -> Matrix(1,2,-8,-15) Matrix(45,308,-32,-219) -> Matrix(1,0,-8,1) Matrix(45,286,14,89) -> Matrix(1,0,6,1) Matrix(43,242,-8,-45) -> Matrix(1,0,4,1) Matrix(43,220,-26,-133) -> Matrix(1,2,-8,-15) Matrix(89,418,-56,-263) -> Matrix(5,2,-38,-15) Matrix(43,198,38,175) -> Matrix(1,0,14,1) Matrix(527,2420,-326,-1497) -> Matrix(1,0,-6,1) Matrix(131,594,58,263) -> Matrix(1,0,8,1) Matrix(89,396,20,89) -> Matrix(1,0,6,1) Matrix(131,572,30,131) -> Matrix(1,0,0,1) Matrix(221,946,-82,-351) -> Matrix(1,0,-4,1) Matrix(177,748,146,617) -> Matrix(3,2,34,23) Matrix(175,726,74,307) -> Matrix(1,0,6,1) Matrix(131,506,-80,-309) -> Matrix(9,4,-70,-31) Matrix(309,1166,-128,-483) -> Matrix(5,2,-28,-11) Matrix(89,330,24,89) -> Matrix(5,2,12,5) Matrix(43,154,12,43) -> Matrix(1,0,6,1) Matrix(45,154,26,89) -> Matrix(1,0,10,1) Matrix(175,572,-108,-353) -> Matrix(1,0,-4,1) Matrix(89,286,14,45) -> Matrix(1,0,6,1) Matrix(221,704,-124,-395) -> Matrix(1,0,-2,1) Matrix(87,242,-32,-89) -> Matrix(7,2,-32,-9) Matrix(529,1430,-374,-1011) -> Matrix(9,2,-86,-19) Matrix(131,352,16,43) -> Matrix(1,0,4,1) Matrix(133,352,-116,-307) -> Matrix(9,2,-104,-23) Matrix(309,814,134,353) -> Matrix(1,0,10,1) Matrix(219,572,-152,-397) -> Matrix(1,0,-6,1) Matrix(43,110,34,87) -> Matrix(9,2,94,21) Matrix(89,220,36,89) -> Matrix(9,2,40,9) Matrix(307,748,126,307) -> Matrix(21,4,110,21) Matrix(263,638,54,131) -> Matrix(11,2,16,3) Matrix(309,748,164,397) -> Matrix(1,0,12,1) Matrix(703,1694,310,747) -> Matrix(11,2,60,11) Matrix(395,946,-276,-661) -> Matrix(1,0,-2,1) Matrix(175,418,18,43) -> Matrix(1,0,4,1) Matrix(397,946,222,529) -> Matrix(1,0,12,1) Matrix(177,418,-130,-307) -> Matrix(9,2,-86,-19) Matrix(353,814,134,309) -> Matrix(1,0,10,1) Matrix(441,1012,-268,-615) -> Matrix(13,2,-98,-15) Matrix(309,704,-212,-483) -> Matrix(9,2,-86,-19) Matrix(659,1496,174,395) -> Matrix(1,0,8,1) Matrix(263,594,58,131) -> Matrix(1,0,8,1) Matrix(89,198,40,89) -> Matrix(1,0,10,1) Matrix(131,286,60,131) -> Matrix(11,2,60,11) Matrix(175,374,-124,-265) -> Matrix(1,0,-4,1) Matrix(131,242,-72,-133) -> Matrix(13,2,-98,-15) Matrix(1055,1914,436,791) -> Matrix(15,2,82,11) Matrix(353,638,244,441) -> Matrix(15,2,142,19) Matrix(529,946,222,397) -> Matrix(1,0,12,1) Matrix(1011,1804,320,571) -> Matrix(1,0,14,1) Matrix(617,1100,198,353) -> Matrix(1,0,8,1) Matrix(87,154,74,131) -> Matrix(1,0,18,1) Matrix(89,154,26,45) -> Matrix(1,0,10,1) Matrix(219,374,154,263) -> Matrix(13,2,110,17) Matrix(441,748,260,441) -> Matrix(55,8,378,55) Matrix(131,220,78,131) -> Matrix(29,4,210,29) Matrix(2199,3608,-1556,-2553) -> Matrix(15,2,-158,-21) Matrix(175,286,134,219) -> Matrix(31,4,302,39) Matrix(3739,6050,-2312,-3741) -> Matrix(15,2,-128,-17) Matrix(791,1276,654,1055) -> Matrix(15,2,172,23) Matrix(1187,1914,818,1319) -> Matrix(15,2,142,19) Matrix(1011,1628,136,219) -> Matrix(1,0,8,1) Matrix(793,1276,110,177) -> Matrix(15,2,22,3) Matrix(1275,2024,526,835) -> Matrix(31,4,178,23) Matrix(1055,1672,-778,-1233) -> Matrix(15,2,-158,-21) Matrix(265,418,168,265) -> Matrix(63,8,496,63) Matrix(43,66,28,43) -> Matrix(17,2,144,17) Matrix(747,1100,328,483) -> Matrix(35,4,166,19) Matrix(1233,1804,542,793) -> Matrix(55,6,284,31) Matrix(1319,1914,818,1187) -> Matrix(19,2,142,15) Matrix(395,572,212,307) -> Matrix(1,0,16,1) Matrix(1363,1958,520,747) -> Matrix(1,0,16,1) Matrix(3697,5302,1412,2025) -> Matrix(1,0,6,1) Matrix(263,374,154,219) -> Matrix(17,2,110,13) Matrix(3037,4290,-2242,-3167) -> Matrix(1,0,0,1) Matrix(175,242,-128,-177) -> Matrix(17,2,-162,-19) Matrix(9635,13046,2014,2727) -> Matrix(1,0,10,1) Matrix(4665,6314,976,1321) -> Matrix(37,4,46,5) Matrix(131,176,32,43) -> Matrix(19,2,28,3) Matrix(219,286,134,175) -> Matrix(39,4,302,31) Matrix(441,572,340,441) -> Matrix(99,10,980,99) Matrix(307,396,238,307) -> Matrix(81,8,820,81) Matrix(87,110,34,43) -> Matrix(21,2,94,9) Matrix(89,110,72,89) -> Matrix(21,2,220,21) Matrix(307,374,252,307) -> Matrix(45,4,506,45) Matrix(617,748,146,177) -> Matrix(23,2,34,3) Matrix(1055,1276,654,791) -> Matrix(23,2,172,15) Matrix(131,154,74,87) -> Matrix(1,0,18,1) Matrix(1099,1276,416,483) -> Matrix(21,2,94,9) Matrix(1409,1628,534,617) -> Matrix(23,2,126,11) Matrix(175,198,38,43) -> Matrix(1,0,14,1) Matrix(1,0,2,1) -> Matrix(1,0,26,1) Matrix(307,-352,116,-133) -> Matrix(23,-2,104,-9) Matrix(177,-242,128,-175) -> Matrix(19,-2,162,-17) Matrix(221,-308,94,-131) -> Matrix(1,0,-4,1) Matrix(219,-308,32,-45) -> Matrix(1,0,-8,1) Matrix(529,-748,186,-263) -> Matrix(1,0,-6,1) Matrix(397,-572,152,-219) -> Matrix(1,0,-6,1) Matrix(483,-704,212,-309) -> Matrix(19,-2,86,-9) Matrix(263,-418,56,-89) -> Matrix(15,-2,38,-5) Matrix(219,-352,28,-45) -> Matrix(15,-2,8,-1) Matrix(353,-572,108,-175) -> Matrix(1,0,-4,1) Matrix(309,-506,80,-131) -> Matrix(31,-4,70,-9) Matrix(307,-506,54,-89) -> Matrix(15,-2,68,-9) Matrix(395,-704,124,-221) -> Matrix(1,0,-2,1) Matrix(133,-242,72,-131) -> Matrix(15,-2,98,-13) Matrix(133,-286,20,-43) -> Matrix(1,0,-4,1) Matrix(221,-506,38,-87) -> Matrix(1,0,-2,1) Matrix(705,-1672,148,-351) -> Matrix(9,-2,14,-3) Matrix(1057,-2530,404,-967) -> Matrix(1,0,-4,1) Matrix(483,-1166,128,-309) -> Matrix(11,-2,28,-5) Matrix(89,-242,32,-87) -> Matrix(9,-2,32,-7) Matrix(265,-748,62,-175) -> Matrix(7,-2,4,-1) Matrix(175,-506,46,-133) -> Matrix(7,-2,18,-5) Matrix(615,-2024,134,-441) -> Matrix(1,0,-2,1) Matrix(485,-1606,106,-351) -> Matrix(7,-2,18,-5) Matrix(881,-3366,184,-703) -> Matrix(5,-2,8,-3) Matrix(45,-242,8,-43) -> Matrix(1,0,4,1) 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): 28 Degree of the the map X: 28 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. ----------------------------------------------------------------------- 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 0/1 0/1 13 1 1/1 (0/1,1/13) 0 22 8/7 1/12 1 11 7/6 (0/1,1/11) 0 22 6/5 1/12 1 11 23/19 (2/23,1/11) 0 22 17/14 (2/23,1/11) 0 22 11/9 1/11 3 2 5/4 (1/11,1/10) 0 22 9/7 (4/41,1/10) 0 22 22/17 1/10 9 1 13/10 (1/10,5/49) 0 22 4/3 1/10 1 11 11/8 1/9 2 2 18/13 1/8 1 11 7/5 (0/1,1/9) 0 22 24/17 1/10 1 11 17/12 (2/19,1/9) 0 22 10/7 1/8 1 11 13/9 (1/10,2/19) 0 22 29/20 (1/10,1/9) 0 22 16/11 1/10 1 11 3/2 (1/9,1/8) 0 22 11/7 1/8 5 2 19/12 (1/8,4/31) 0 22 8/5 1/8 1 11 29/18 (1/8,1/7) 0 22 50/31 1/8 1 11 21/13 (0/1,1/7) 0 22 13/8 (1/9,1/8) 0 22 18/11 1/8 1 11 23/14 (3/23,2/15) 0 22 5/3 (2/15,1/7) 0 22 22/13 1/7 6 1 17/10 (1/7,4/27) 0 22 12/7 1/6 1 11 7/4 (0/1,1/7) 0 22 16/9 1/6 1 11 25/14 (0/1,1/8) 0 22 9/5 (0/1,1/8) 0 22 11/6 1/7 2 2 13/7 (2/13,1/6) 0 22 15/8 (1/7,1/6) 0 22 2/1 1/6 1 11 13/6 (1/6,1/5) 0 22 11/5 1/5 1 2 9/4 (0/1,1/5) 0 22 34/15 1/6 1 11 25/11 (2/11,1/5) 0 22 66/29 1/5 5 1 41/18 (1/5,3/14) 0 22 16/7 1/4 1 11 23/10 (0/1,1/5) 0 22 7/3 (0/1,1/5) 0 22 26/11 1/4 1 11 45/19 (0/1,1/5) 0 22 19/8 (0/1,1/4) 0 22 31/13 (0/1,1/4) 0 22 43/18 (0/1,1/4) 0 22 12/5 1/6 1 11 29/12 (1/6,1/5) 0 22 46/19 1/6 1 11 17/7 (2/11,1/5) 0 22 22/9 1/5 3 1 5/2 (1/5,1/4) 0 22 13/5 (1/4,2/7) 0 22 34/13 1/2 1 11 89/34 (0/1,1/0) 0 22 55/21 0/1 5 2 21/8 (0/1,1/5) 0 22 29/11 (0/1,1/5) 0 22 66/25 1/5 2 1 37/14 (1/5,2/9) 0 22 8/3 1/4 1 11 11/4 1/4 2 2 14/5 1/4 1 11 17/6 (2/7,1/3) 0 22 20/7 1/4 1 11 3/1 (0/1,1/3) 0 22 22/7 0/1 3 1 19/6 (0/1,1/6) 0 22 16/5 1/4 1 11 13/4 (1/5,1/4) 0 22 23/7 (0/1,1/3) 0 22 33/10 1/4 2 2 10/3 1/4 1 11 7/2 (0/1,1/3) 0 22 11/3 1/3 1 2 15/4 (1/3,1/2) 0 22 34/9 1/2 1 11 19/5 (1/3,2/5) 0 22 42/11 1/2 1 11 23/6 (1/3,2/5) 0 22 4/1 1/2 1 11 21/5 (0/1,1/1) 0 22 17/4 (0/1,1/1) 0 22 30/7 1/0 1 11 13/3 (0/1,1/0) 0 22 22/5 0/1 3 1 9/2 (0/1,1/3) 0 22 32/7 1/2 1 11 55/12 1/2 2 2 23/5 (0/1,1/1) 0 22 14/3 1/2 1 11 19/4 (1/2,2/3) 0 22 43/9 (2/3,1/1) 0 22 110/23 1/1 2 1 67/14 (0/1,1/1) 0 22 24/5 1/2 1 11 5/1 (0/1,1/1) 0 22 11/2 0/1 4 2 17/3 (0/1,1/5) 0 22 23/4 (0/1,1/3) 0 22 6/1 1/2 1 11 13/2 (1/2,1/1) 0 22 20/3 1/2 1 11 7/1 (0/1,1/1) 0 22 22/3 1/1 1 1 15/2 (1/1,1/0) 0 22 8/1 1/0 1 11 9/1 (0/1,1/0) 0 22 1/0 (0/1,1/0) 0 22 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(175,-198,38,-43) (1/1,8/7) -> (23/5,14/3) Glide Reflection Matrix(307,-352,116,-133) (8/7,7/6) -> (37/14,8/3) Hyperbolic Matrix(131,-154,74,-87) (7/6,6/5) -> (7/4,16/9) Glide Reflection Matrix(1055,-1276,654,-791) (6/5,23/19) -> (50/31,21/13) Glide Reflection Matrix(617,-748,146,-177) (23/19,17/14) -> (21/5,17/4) Glide Reflection Matrix(307,-374,252,-307) (17/14,11/9) -> (17/14,11/9) Reflection Matrix(89,-110,72,-89) (11/9,5/4) -> (11/9,5/4) Reflection Matrix(87,-110,34,-43) (5/4,9/7) -> (5/2,13/5) Glide Reflection Matrix(307,-396,238,-307) (9/7,22/17) -> (9/7,22/17) Reflection Matrix(441,-572,340,-441) (22/17,13/10) -> (22/17,13/10) Reflection Matrix(219,-286,134,-175) (13/10,4/3) -> (13/8,18/11) Glide Reflection Matrix(177,-242,128,-175) (4/3,11/8) -> (11/8,18/13) Parabolic Matrix(221,-308,94,-131) (18/13,7/5) -> (7/3,26/11) Hyperbolic Matrix(219,-308,32,-45) (7/5,24/17) -> (20/3,7/1) Hyperbolic Matrix(529,-748,186,-263) (24/17,17/12) -> (17/6,20/7) Hyperbolic Matrix(263,-374,154,-219) (17/12,10/7) -> (17/10,12/7) Glide Reflection Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(395,-572,212,-307) (13/9,29/20) -> (13/7,15/8) Glide Reflection Matrix(1319,-1914,818,-1187) (29/20,16/11) -> (29/18,50/31) Glide Reflection Matrix(483,-704,212,-309) (16/11,3/2) -> (41/18,16/7) Hyperbolic Matrix(43,-66,28,-43) (3/2,11/7) -> (3/2,11/7) Reflection Matrix(265,-418,168,-265) (11/7,19/12) -> (11/7,19/12) Reflection Matrix(263,-418,56,-89) (19/12,8/5) -> (14/3,19/4) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(309,-506,80,-131) (18/11,23/14) -> (23/6,4/1) Hyperbolic Matrix(307,-506,54,-89) (23/14,5/3) -> (17/3,23/4) Hyperbolic Matrix(131,-220,78,-131) (5/3,22/13) -> (5/3,22/13) Reflection Matrix(441,-748,260,-441) (22/13,17/10) -> (22/13,17/10) Reflection Matrix(89,-154,26,-45) (12/7,7/4) -> (10/3,7/2) Glide Reflection Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(529,-946,222,-397) (25/14,9/5) -> (19/8,31/13) Glide Reflection Matrix(133,-242,72,-131) (9/5,11/6) -> (11/6,13/7) Parabolic Matrix(397,-748,164,-309) (15/8,2/1) -> (29/12,46/19) Glide Reflection Matrix(133,-286,20,-43) (2/1,13/6) -> (13/2,20/3) Hyperbolic Matrix(131,-286,60,-131) (13/6,11/5) -> (13/6,11/5) Reflection Matrix(89,-198,40,-89) (11/5,9/4) -> (11/5,9/4) Reflection Matrix(263,-594,58,-131) (9/4,34/15) -> (9/2,32/7) Glide Reflection Matrix(659,-1496,174,-395) (34/15,25/11) -> (34/9,19/5) Glide Reflection Matrix(1451,-3300,638,-1451) (25/11,66/29) -> (25/11,66/29) Reflection Matrix(2377,-5412,1044,-2377) (66/29,41/18) -> (66/29,41/18) Reflection Matrix(221,-506,38,-87) (16/7,23/10) -> (23/4,6/1) Hyperbolic Matrix(353,-814,134,-309) (23/10,7/3) -> (21/8,29/11) Glide Reflection Matrix(307,-726,74,-175) (26/11,45/19) -> (4/1,21/5) Glide Reflection Matrix(705,-1672,148,-351) (45/19,19/8) -> (19/4,43/9) Hyperbolic Matrix(175,-418,18,-43) (31/13,43/18) -> (9/1,1/0) Glide Reflection Matrix(1057,-2530,404,-967) (43/18,12/5) -> (34/13,89/34) Hyperbolic Matrix(483,-1166,128,-309) (12/5,29/12) -> (15/4,34/9) Hyperbolic Matrix(263,-638,54,-131) (46/19,17/7) -> (24/5,5/1) Glide Reflection Matrix(307,-748,126,-307) (17/7,22/9) -> (17/7,22/9) Reflection Matrix(89,-220,36,-89) (22/9,5/2) -> (22/9,5/2) Reflection Matrix(3739,-9790,1428,-3739) (89/34,55/21) -> (89/34,55/21) Reflection Matrix(881,-2310,336,-881) (55/21,21/8) -> (55/21,21/8) Reflection Matrix(1451,-3828,550,-1451) (29/11,66/25) -> (29/11,66/25) Reflection Matrix(1849,-4884,700,-1849) (66/25,37/14) -> (66/25,37/14) Reflection Matrix(89,-242,32,-87) (8/3,11/4) -> (11/4,14/5) Parabolic Matrix(265,-748,62,-175) (14/5,17/6) -> (17/4,30/7) Hyperbolic Matrix(175,-506,46,-133) (20/7,3/1) -> (19/5,42/11) Hyperbolic Matrix(43,-132,14,-43) (3/1,22/7) -> (3/1,22/7) Reflection Matrix(265,-836,84,-265) (22/7,19/6) -> (22/7,19/6) Reflection Matrix(89,-286,14,-45) (16/5,13/4) -> (6/1,13/2) Glide Reflection Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(485,-1606,106,-351) (33/10,10/3) -> (32/7,55/12) Hyperbolic 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(881,-3366,184,-703) (42/11,23/6) -> (67/14,24/5) Hyperbolic Matrix(87,-374,10,-43) (30/7,13/3) -> (8/1,9/1) Glide Reflection Matrix(131,-572,30,-131) (13/3,22/5) -> (13/3,22/5) Reflection Matrix(89,-396,20,-89) (22/5,9/2) -> (22/5,9/2) Reflection Matrix(1979,-9460,414,-1979) (43/9,110/23) -> (43/9,110/23) Reflection Matrix(3081,-14740,644,-3081) (110/23,67/14) -> (110/23,67/14) Reflection Matrix(45,-242,8,-43) (5/1,11/2) -> (11/2,17/3) Parabolic Matrix(43,-308,6,-43) (7/1,22/3) -> (7/1,22/3) Reflection Matrix(89,-660,12,-89) (22/3,15/2) -> (22/3,15/2) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,26,-1) (0/1,1/1) -> (0/1,1/13) Matrix(175,-198,38,-43) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(307,-352,116,-133) -> Matrix(23,-2,104,-9) Matrix(131,-154,74,-87) -> Matrix(1,0,18,-1) *** -> (0/1,1/9) Matrix(1055,-1276,654,-791) -> Matrix(23,-2,172,-15) Matrix(617,-748,146,-177) -> Matrix(23,-2,34,-3) Matrix(307,-374,252,-307) -> Matrix(45,-4,506,-45) (17/14,11/9) -> (2/23,1/11) Matrix(89,-110,72,-89) -> Matrix(21,-2,220,-21) (11/9,5/4) -> (1/11,1/10) Matrix(87,-110,34,-43) -> Matrix(21,-2,94,-9) Matrix(307,-396,238,-307) -> Matrix(81,-8,820,-81) (9/7,22/17) -> (4/41,1/10) Matrix(441,-572,340,-441) -> Matrix(99,-10,980,-99) (22/17,13/10) -> (1/10,5/49) Matrix(219,-286,134,-175) -> Matrix(39,-4,302,-31) Matrix(177,-242,128,-175) -> Matrix(19,-2,162,-17) 1/9 Matrix(221,-308,94,-131) -> Matrix(1,0,-4,1) 0/1 Matrix(219,-308,32,-45) -> Matrix(1,0,-8,1) 0/1 Matrix(529,-748,186,-263) -> Matrix(1,0,-6,1) 0/1 Matrix(263,-374,154,-219) -> Matrix(17,-2,110,-13) Matrix(397,-572,152,-219) -> Matrix(1,0,-6,1) 0/1 Matrix(395,-572,212,-307) -> Matrix(1,0,16,-1) *** -> (0/1,1/8) Matrix(1319,-1914,818,-1187) -> Matrix(19,-2,142,-15) Matrix(483,-704,212,-309) -> Matrix(19,-2,86,-9) Matrix(43,-66,28,-43) -> Matrix(17,-2,144,-17) (3/2,11/7) -> (1/9,1/8) Matrix(265,-418,168,-265) -> Matrix(63,-8,496,-63) (11/7,19/12) -> (1/8,4/31) Matrix(263,-418,56,-89) -> Matrix(15,-2,38,-5) Matrix(219,-352,28,-45) -> Matrix(15,-2,8,-1) Matrix(353,-572,108,-175) -> Matrix(1,0,-4,1) 0/1 Matrix(309,-506,80,-131) -> Matrix(31,-4,70,-9) Matrix(307,-506,54,-89) -> Matrix(15,-2,68,-9) Matrix(131,-220,78,-131) -> Matrix(29,-4,210,-29) (5/3,22/13) -> (2/15,1/7) Matrix(441,-748,260,-441) -> Matrix(55,-8,378,-55) (22/13,17/10) -> (1/7,4/27) Matrix(89,-154,26,-45) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(395,-704,124,-221) -> Matrix(1,0,-2,1) 0/1 Matrix(529,-946,222,-397) -> Matrix(1,0,12,-1) *** -> (0/1,1/6) Matrix(133,-242,72,-131) -> Matrix(15,-2,98,-13) 1/7 Matrix(397,-748,164,-309) -> Matrix(1,0,12,-1) *** -> (0/1,1/6) Matrix(133,-286,20,-43) -> Matrix(1,0,-4,1) 0/1 Matrix(131,-286,60,-131) -> Matrix(11,-2,60,-11) (13/6,11/5) -> (1/6,1/5) Matrix(89,-198,40,-89) -> Matrix(1,0,10,-1) (11/5,9/4) -> (0/1,1/5) Matrix(263,-594,58,-131) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(659,-1496,174,-395) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(1451,-3300,638,-1451) -> Matrix(21,-4,110,-21) (25/11,66/29) -> (2/11,1/5) Matrix(2377,-5412,1044,-2377) -> Matrix(29,-6,140,-29) (66/29,41/18) -> (1/5,3/14) Matrix(221,-506,38,-87) -> Matrix(1,0,-2,1) 0/1 Matrix(353,-814,134,-309) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(307,-726,74,-175) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(705,-1672,148,-351) -> Matrix(9,-2,14,-3) Matrix(175,-418,18,-43) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1057,-2530,404,-967) -> Matrix(1,0,-4,1) 0/1 Matrix(483,-1166,128,-309) -> Matrix(11,-2,28,-5) Matrix(263,-638,54,-131) -> Matrix(11,-2,16,-3) Matrix(307,-748,126,-307) -> Matrix(21,-4,110,-21) (17/7,22/9) -> (2/11,1/5) Matrix(89,-220,36,-89) -> Matrix(9,-2,40,-9) (22/9,5/2) -> (1/5,1/4) Matrix(3739,-9790,1428,-3739) -> Matrix(1,0,0,-1) (89/34,55/21) -> (0/1,1/0) Matrix(881,-2310,336,-881) -> Matrix(1,0,10,-1) (55/21,21/8) -> (0/1,1/5) Matrix(1451,-3828,550,-1451) -> Matrix(1,0,10,-1) (29/11,66/25) -> (0/1,1/5) Matrix(1849,-4884,700,-1849) -> Matrix(19,-4,90,-19) (66/25,37/14) -> (1/5,2/9) Matrix(89,-242,32,-87) -> Matrix(9,-2,32,-7) 1/4 Matrix(265,-748,62,-175) -> Matrix(7,-2,4,-1) Matrix(175,-506,46,-133) -> Matrix(7,-2,18,-5) 1/3 Matrix(43,-132,14,-43) -> Matrix(1,0,6,-1) (3/1,22/7) -> (0/1,1/3) Matrix(265,-836,84,-265) -> Matrix(1,0,12,-1) (22/7,19/6) -> (0/1,1/6) Matrix(89,-286,14,-45) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(615,-2024,134,-441) -> Matrix(1,0,-2,1) 0/1 Matrix(485,-1606,106,-351) -> Matrix(7,-2,18,-5) 1/3 Matrix(43,-154,12,-43) -> Matrix(1,0,6,-1) (7/2,11/3) -> (0/1,1/3) Matrix(89,-330,24,-89) -> Matrix(5,-2,12,-5) (11/3,15/4) -> (1/3,1/2) Matrix(881,-3366,184,-703) -> Matrix(5,-2,8,-3) 1/2 Matrix(87,-374,10,-43) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(131,-572,30,-131) -> Matrix(1,0,0,-1) (13/3,22/5) -> (0/1,1/0) Matrix(89,-396,20,-89) -> Matrix(1,0,6,-1) (22/5,9/2) -> (0/1,1/3) Matrix(1979,-9460,414,-1979) -> Matrix(5,-4,6,-5) (43/9,110/23) -> (2/3,1/1) Matrix(3081,-14740,644,-3081) -> Matrix(1,0,2,-1) (110/23,67/14) -> (0/1,1/1) Matrix(45,-242,8,-43) -> Matrix(1,0,4,1) 0/1 Matrix(43,-308,6,-43) -> Matrix(1,0,2,-1) (7/1,22/3) -> (0/1,1/1) Matrix(89,-660,12,-89) -> Matrix(-1,2,0,1) (22/3,15/2) -> (1/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.