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): 768 Minimal number of generators: 129 Number of equivalence classes of cusps: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/1 -6/1 -5/1 -14/3 -13/3 -4/1 -11/3 -3/1 -14/5 -13/5 -7/3 -2/1 -1/1 -1/2 -3/7 -1/3 -1/4 -1/5 0/1 1/7 3/13 1/4 1/3 5/11 1/2 3/5 5/7 3/4 1/1 9/7 4/3 7/5 3/2 8/5 5/3 2/1 11/5 7/3 12/5 17/7 5/2 8/3 41/15 3/1 49/15 10/3 25/7 11/3 4/1 13/3 14/3 5/1 6/1 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -2/1 -13/2 1/0 -6/1 -2/1 1/0 -5/1 -1/1 -19/4 1/0 -14/3 -2/1 -1/1 -9/2 1/0 -22/5 -2/1 -3/2 -13/3 -1/1 -17/4 -5/4 -4/1 -1/1 1/0 -11/3 -1/1 -18/5 -1/1 -4/5 -7/2 -1/2 -10/3 -1/1 1/0 -13/4 -1/2 -3/1 -1/1 -14/5 -1/2 0/1 -11/4 1/0 -8/3 -1/1 1/0 -13/5 -1/1 -18/7 -1/1 -2/3 -5/2 -1/2 -22/9 0/1 1/1 -17/7 0/1 -29/12 1/0 -41/17 1/0 -12/5 -1/1 1/0 -7/3 -1/1 -23/10 1/0 -16/7 -1/2 0/1 -9/4 -1/2 -20/9 0/1 1/0 -11/5 -1/1 -13/6 1/0 -2/1 -1/1 0/1 -1/1 0/1 -2/3 0/1 1/1 -11/17 1/1 -9/14 1/2 -7/11 1/1 -5/8 1/2 -18/29 2/3 1/1 -13/21 1/1 -8/13 1/1 1/0 -3/5 1/1 -7/12 1/2 -18/31 4/5 1/1 -11/19 1/1 -4/7 1/1 1/0 -13/23 1/1 -9/16 1/0 -5/9 1/1 -1/2 1/0 -5/11 -1/1 -9/20 1/0 -4/9 -1/1 1/0 -7/16 1/0 -10/23 0/1 1/1 -3/7 1/0 -14/33 -2/1 -1/1 -11/26 1/0 -19/45 -3/1 -8/19 -2/1 1/0 -5/12 1/0 -12/29 -1/1 1/0 -7/17 -2/1 -16/39 -3/2 -4/3 -9/22 -5/4 -2/5 -1/1 0/1 -3/8 1/0 -13/35 -1/1 -10/27 0/1 1/0 -7/19 -1/1 -4/11 -1/1 1/0 -5/14 -1/2 -6/17 -1/1 0/1 -7/20 -1/2 -1/3 0/1 -7/22 1/0 -6/19 -2/1 -1/1 -5/16 -1/2 -4/13 -1/2 0/1 -3/10 1/0 -8/27 0/1 1/0 -5/17 -1/1 -2/7 -1/2 0/1 -1/4 1/0 -4/17 0/1 1/2 -7/30 1/2 -3/13 1/1 -5/22 1/0 -2/9 -1/1 1/0 -3/14 -1/2 -7/33 0/1 -4/19 -1/1 -1/2 -1/5 0/1 -4/21 1/3 1/2 -11/58 1/2 -7/37 2/3 -3/16 1/2 -5/27 1/1 -7/38 1/0 -2/11 0/1 1/0 -1/6 1/0 -2/13 0/1 1/1 -3/20 1/0 -1/7 0/1 -2/15 0/1 1/1 -1/8 1/0 0/1 0/1 1/0 1/8 1/0 1/7 0/1 2/13 0/1 1/2 1/6 1/0 1/5 0/1 3/14 1/0 2/9 -1/1 0/1 5/22 -1/2 3/13 0/1 4/17 0/1 1/2 1/4 1/0 3/11 -1/1 2/7 0/1 1/0 5/17 -1/1 8/27 -3/2 -1/1 3/10 -1/2 1/3 0/1 5/14 1/2 4/11 1/2 1/1 3/8 1/2 5/13 1/1 2/5 1/1 1/0 3/7 -1/1 4/9 -1/2 0/1 9/20 -1/4 5/11 0/1 6/13 0/1 1/3 1/2 1/0 7/13 -1/1 6/11 -2/3 -1/2 5/9 -1/3 9/16 -1/4 4/7 -1/4 0/1 3/5 0/1 8/13 0/1 1/8 5/8 1/4 2/3 0/1 1/2 9/13 0/1 7/10 1/2 5/7 1/1 13/18 1/0 8/11 0/1 1/0 11/15 1/1 14/19 0/1 1/1 3/4 1/0 10/13 -1/2 0/1 7/9 0/1 11/14 1/4 4/5 0/1 1/2 9/11 1/1 5/6 1/2 6/7 1/1 2/1 1/1 0/1 8/7 1/2 3/5 7/6 1/2 6/5 0/1 1/1 17/14 1/2 11/9 1/1 5/4 1/2 14/11 3/4 1/1 9/7 1/1 13/10 3/2 4/3 1/1 1/0 23/17 1/0 19/14 1/0 15/11 0/1 11/8 1/2 7/5 1/1 17/12 3/2 10/7 0/1 1/0 3/2 1/0 14/9 0/1 1/0 11/7 1/1 30/19 4/1 1/0 49/31 1/0 19/12 1/0 27/17 -1/1 8/5 0/1 1/0 5/3 0/1 12/7 0/1 1/2 31/18 1/2 19/11 1/1 7/4 1/2 2/1 0/1 1/1 13/6 5/6 11/5 1/1 31/14 13/12 20/9 1/1 9/8 9/4 5/4 25/11 1/1 16/7 4/3 3/2 23/10 3/2 7/3 2/1 26/11 2/1 1/0 19/8 1/0 12/5 1/1 1/0 29/12 1/0 17/7 1/1 39/16 3/2 22/9 1/1 2/1 5/2 1/0 23/9 1/1 18/7 1/1 3/2 13/5 1/1 47/18 3/2 81/31 3/2 34/13 3/2 8/5 21/8 7/4 8/3 2/1 1/0 35/13 2/1 27/10 5/2 19/7 3/1 30/11 4/1 1/0 71/26 1/0 41/15 1/0 11/4 1/0 3/1 1/0 13/4 1/0 49/15 1/0 85/26 1/0 36/11 -5/1 1/0 23/7 -2/1 10/3 -1/1 0/1 37/11 0/1 27/8 1/2 17/5 0/1 7/2 1/0 25/7 0/1 18/5 0/1 1/2 11/3 1/1 4/1 1/1 1/0 17/4 1/0 13/3 1/0 35/8 1/0 22/5 0/1 1/0 9/2 1/0 14/3 0/1 1/0 33/7 0/1 19/4 1/2 5/1 1/1 6/1 3/1 1/0 13/2 1/0 7/1 1/0 15/2 1/0 8/1 -2/1 1/0 9/1 0/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(29,220,-12,-91) (-7/1,1/0) -> (-17/7,-29/12) Hyperbolic Matrix(17,112,-80,-527) (-7/1,-13/2) -> (-3/14,-7/33) Hyperbolic Matrix(53,340,12,77) (-13/2,-6/1) -> (22/5,9/2) Hyperbolic Matrix(7,40,-24,-137) (-6/1,-5/1) -> (-5/17,-2/7) Hyperbolic Matrix(127,608,80,383) (-5/1,-19/4) -> (19/12,27/17) Hyperbolic Matrix(17,80,-112,-527) (-19/4,-14/3) -> (-2/13,-3/20) Hyperbolic Matrix(27,124,-76,-349) (-14/3,-9/2) -> (-5/14,-6/17) Hyperbolic Matrix(9,40,56,249) (-9/2,-22/5) -> (2/13,1/6) Hyperbolic Matrix(95,416,-256,-1121) (-22/5,-13/3) -> (-13/35,-10/27) Hyperbolic Matrix(29,124,-156,-667) (-13/3,-17/4) -> (-3/16,-5/27) Hyperbolic Matrix(89,376,40,169) (-17/4,-4/1) -> (20/9,9/4) Hyperbolic Matrix(23,88,-40,-153) (-4/1,-11/3) -> (-11/19,-4/7) Hyperbolic Matrix(109,396,-188,-683) (-11/3,-18/5) -> (-18/31,-11/19) Hyperbolic Matrix(37,132,44,157) (-18/5,-7/2) -> (5/6,6/7) Hyperbolic Matrix(13,44,-60,-203) (-7/2,-10/3) -> (-2/9,-3/14) Hyperbolic Matrix(71,232,56,183) (-10/3,-13/4) -> (5/4,14/11) Hyperbolic Matrix(29,92,52,165) (-13/4,-3/1) -> (5/9,9/16) Hyperbolic Matrix(69,196,44,125) (-3/1,-14/5) -> (14/9,11/7) Hyperbolic Matrix(55,152,72,199) (-14/5,-11/4) -> (3/4,10/13) Hyperbolic Matrix(37,100,-84,-227) (-11/4,-8/3) -> (-4/9,-7/16) Hyperbolic Matrix(79,208,-128,-337) (-8/3,-13/5) -> (-13/21,-8/13) Hyperbolic Matrix(181,468,-292,-755) (-13/5,-18/7) -> (-18/29,-13/21) Hyperbolic Matrix(61,156,52,133) (-18/7,-5/2) -> (7/6,6/5) Hyperbolic Matrix(21,52,44,109) (-5/2,-22/9) -> (6/13,1/2) Hyperbolic Matrix(23,56,-168,-409) (-22/9,-17/7) -> (-1/7,-2/15) Hyperbolic Matrix(679,1640,248,599) (-29/12,-41/17) -> (41/15,11/4) Hyperbolic Matrix(183,440,136,327) (-41/17,-12/5) -> (4/3,23/17) Hyperbolic Matrix(47,112,-128,-305) (-12/5,-7/3) -> (-7/19,-4/11) Hyperbolic Matrix(73,168,136,313) (-7/3,-23/10) -> (1/2,7/13) Hyperbolic Matrix(223,512,-544,-1249) (-23/10,-16/7) -> (-16/39,-9/22) Hyperbolic Matrix(51,116,-164,-373) (-16/7,-9/4) -> (-5/16,-4/13) Hyperbolic Matrix(25,56,104,233) (-9/4,-20/9) -> (4/17,1/4) Hyperbolic Matrix(211,468,-500,-1109) (-20/9,-11/5) -> (-19/45,-8/19) Hyperbolic Matrix(53,116,-228,-499) (-11/5,-13/6) -> (-7/30,-3/13) Hyperbolic Matrix(137,296,56,121) (-13/6,-2/1) -> (22/9,5/2) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(271,176,368,239) (-2/3,-11/17) -> (11/15,14/19) Hyperbolic Matrix(725,468,268,173) (-11/17,-9/14) -> (27/10,19/7) Hyperbolic Matrix(181,116,220,141) (-9/14,-7/11) -> (9/11,5/6) Hyperbolic Matrix(177,112,128,81) (-7/11,-5/8) -> (11/8,7/5) Hyperbolic Matrix(251,156,-716,-445) (-5/8,-18/29) -> (-6/17,-7/20) Hyperbolic Matrix(163,100,44,27) (-8/13,-3/5) -> (11/3,4/1) Hyperbolic Matrix(75,44,196,115) (-3/5,-7/12) -> (3/8,5/13) Hyperbolic Matrix(227,132,-724,-421) (-7/12,-18/31) -> (-6/19,-5/16) Hyperbolic Matrix(219,124,740,419) (-4/7,-13/23) -> (5/17,8/27) Hyperbolic Matrix(517,292,108,61) (-13/23,-9/16) -> (19/4,5/1) Hyperbolic Matrix(221,124,180,101) (-9/16,-5/9) -> (11/9,5/4) Hyperbolic Matrix(73,40,104,57) (-5/9,-1/2) -> (7/10,5/7) Hyperbolic Matrix(61,28,-268,-123) (-1/2,-5/11) -> (-3/13,-5/22) Hyperbolic Matrix(293,132,-788,-355) (-5/11,-9/20) -> (-3/8,-13/35) Hyperbolic Matrix(233,104,56,25) (-9/20,-4/9) -> (4/1,17/4) Hyperbolic Matrix(55,24,-424,-185) (-7/16,-10/23) -> (-2/15,-1/8) Hyperbolic Matrix(167,72,-392,-169) (-10/23,-3/7) -> (-3/7,-14/33) Parabolic Matrix(387,164,-1220,-517) (-14/33,-11/26) -> (-7/22,-6/19) Hyperbolic Matrix(445,188,-2412,-1019) (-11/26,-19/45) -> (-5/27,-7/38) Hyperbolic Matrix(219,92,388,163) (-8/19,-5/12) -> (9/16,4/7) Hyperbolic Matrix(985,408,408,169) (-5/12,-12/29) -> (12/5,29/12) Hyperbolic Matrix(271,112,-1280,-529) (-12/29,-7/17) -> (-7/33,-4/19) Hyperbolic Matrix(487,200,56,23) (-7/17,-16/39) -> (8/1,9/1) Hyperbolic Matrix(109,44,52,21) (-9/22,-2/5) -> (2/1,13/6) Hyperbolic Matrix(51,20,28,11) (-2/5,-3/8) -> (7/4,2/1) Hyperbolic Matrix(303,112,560,207) (-10/27,-7/19) -> (7/13,6/11) Hyperbolic Matrix(199,72,152,55) (-4/11,-5/14) -> (13/10,4/3) Hyperbolic Matrix(149,52,-788,-275) (-7/20,-1/3) -> (-7/37,-3/16) Hyperbolic Matrix(187,60,-988,-317) (-1/3,-7/22) -> (-11/58,-7/37) Hyperbolic Matrix(183,56,232,71) (-4/13,-3/10) -> (11/14,4/5) Hyperbolic Matrix(229,68,-980,-291) (-3/10,-8/27) -> (-4/17,-7/30) Hyperbolic Matrix(865,256,544,161) (-8/27,-5/17) -> (27/17,8/5) Hyperbolic Matrix(43,12,68,19) (-2/7,-1/4) -> (5/8,2/3) Hyperbolic Matrix(169,40,376,89) (-1/4,-4/17) -> (4/9,9/20) Hyperbolic Matrix(249,56,40,9) (-5/22,-2/9) -> (6/1,13/2) Hyperbolic Matrix(39,8,-200,-41) (-4/19,-1/5) -> (-1/5,-4/21) Parabolic Matrix(3873,736,1184,225) (-4/21,-11/58) -> (85/26,36/11) Hyperbolic Matrix(1921,352,704,129) (-7/38,-2/11) -> (30/11,71/26) Hyperbolic Matrix(117,20,76,13) (-2/11,-1/6) -> (3/2,14/9) Hyperbolic Matrix(77,12,340,53) (-1/6,-2/13) -> (2/9,5/22) Hyperbolic Matrix(187,28,20,3) (-3/20,-1/7) -> (9/1,1/0) Hyperbolic Matrix(1,0,16,1) (-1/8,0/1) -> (0/1,1/8) Parabolic Matrix(397,-52,84,-11) (1/8,1/7) -> (33/7,19/4) Hyperbolic Matrix(527,-80,112,-17) (1/7,2/13) -> (14/3,33/7) Hyperbolic Matrix(137,-24,40,-7) (1/6,1/5) -> (17/5,7/2) Hyperbolic Matrix(213,-44,92,-19) (1/5,3/14) -> (23/10,7/3) Hyperbolic Matrix(237,-52,196,-43) (3/14,2/9) -> (6/5,17/14) Hyperbolic Matrix(1121,-256,416,-95) (5/22,3/13) -> (35/13,27/10) Hyperbolic Matrix(699,-164,260,-61) (3/13,4/17) -> (8/3,35/13) Hyperbolic Matrix(153,-40,88,-23) (1/4,3/11) -> (19/11,7/4) Hyperbolic Matrix(275,-76,76,-21) (3/11,2/7) -> (18/5,11/3) Hyperbolic Matrix(643,-188,236,-69) (2/7,5/17) -> (19/7,30/11) Hyperbolic Matrix(1037,-308,468,-139) (8/27,3/10) -> (31/14,20/9) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(189,-68,164,-59) (5/14,4/11) -> (8/7,7/6) Hyperbolic Matrix(305,-112,128,-47) (4/11,3/8) -> (19/8,12/5) Hyperbolic Matrix(299,-116,116,-45) (5/13,2/5) -> (18/7,13/5) Hyperbolic Matrix(67,-28,12,-5) (2/5,3/7) -> (5/1,6/1) Hyperbolic Matrix(155,-68,212,-93) (3/7,4/9) -> (8/11,11/15) Hyperbolic Matrix(1037,-468,308,-139) (9/20,5/11) -> (37/11,27/8) Hyperbolic Matrix(591,-272,176,-81) (5/11,6/13) -> (10/3,37/11) Hyperbolic Matrix(391,-216,248,-137) (6/11,5/9) -> (11/7,30/19) Hyperbolic Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(337,-208,128,-79) (8/13,5/8) -> (21/8,8/3) Hyperbolic Matrix(359,-248,152,-105) (2/3,9/13) -> (7/3,26/11) Hyperbolic Matrix(397,-276,292,-203) (9/13,7/10) -> (19/14,15/11) Hyperbolic Matrix(317,-228,260,-187) (5/7,13/18) -> (17/14,11/9) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(829,-612,340,-251) (14/19,3/4) -> (39/16,22/9) Hyperbolic Matrix(487,-376,136,-105) (10/13,7/9) -> (25/7,18/5) Hyperbolic Matrix(413,-324,116,-91) (7/9,11/14) -> (7/2,25/7) Hyperbolic Matrix(301,-244,132,-107) (4/5,9/11) -> (25/11,16/7) Hyperbolic Matrix(171,-148,52,-45) (6/7,1/1) -> (23/7,10/3) Hyperbolic Matrix(197,-220,60,-67) (1/1,8/7) -> (36/11,23/7) Hyperbolic Matrix(379,-484,148,-189) (14/11,9/7) -> (23/9,18/7) Hyperbolic Matrix(265,-344,104,-135) (9/7,13/10) -> (5/2,23/9) Hyperbolic Matrix(1781,-2412,652,-883) (23/17,19/14) -> (71/26,41/15) Hyperbolic Matrix(433,-592,128,-175) (15/11,11/8) -> (27/8,17/5) Hyperbolic Matrix(345,-488,152,-215) (7/5,17/12) -> (9/4,25/11) Hyperbolic Matrix(555,-788,212,-301) (17/12,10/7) -> (34/13,21/8) Hyperbolic Matrix(91,-132,20,-29) (10/7,3/2) -> (9/2,14/3) Hyperbolic Matrix(2593,-4096,992,-1567) (30/19,49/31) -> (81/31,34/13) Hyperbolic Matrix(991,-1568,304,-481) (49/31,19/12) -> (13/4,49/15) Hyperbolic Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(751,-1296,288,-497) (31/18,19/11) -> (13/5,47/18) Hyperbolic Matrix(221,-484,100,-219) (13/6,11/5) -> (11/5,31/14) Parabolic Matrix(185,-424,24,-55) (16/7,23/10) -> (15/2,8/1) Hyperbolic Matrix(561,-1328,128,-303) (26/11,19/8) -> (35/8,22/5) Hyperbolic Matrix(477,-1156,196,-475) (29/12,17/7) -> (17/7,39/16) Parabolic Matrix(3517,-9188,1076,-2811) (47/18,81/31) -> (49/15,85/26) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) Parabolic Matrix(29,-196,4,-27) (13/2,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(29,220,-12,-91) -> Matrix(1,2,0,1) Matrix(17,112,-80,-527) -> Matrix(1,2,-2,-3) Matrix(53,340,12,77) -> Matrix(1,2,0,1) Matrix(7,40,-24,-137) -> Matrix(1,2,-2,-3) Matrix(127,608,80,383) -> Matrix(1,0,0,1) Matrix(17,80,-112,-527) -> Matrix(1,2,0,1) Matrix(27,124,-76,-349) -> Matrix(1,2,-2,-3) Matrix(9,40,56,249) -> Matrix(1,2,0,1) Matrix(95,416,-256,-1121) -> Matrix(1,2,-2,-3) Matrix(29,124,-156,-667) -> Matrix(3,4,2,3) Matrix(89,376,40,169) -> Matrix(9,10,8,9) Matrix(23,88,-40,-153) -> Matrix(1,2,0,1) Matrix(109,396,-188,-683) -> Matrix(9,8,10,9) Matrix(37,132,44,157) -> Matrix(3,2,4,3) Matrix(13,44,-60,-203) -> Matrix(1,0,0,1) Matrix(71,232,56,183) -> Matrix(3,2,4,3) Matrix(29,92,52,165) -> Matrix(1,0,-2,1) Matrix(69,196,44,125) -> Matrix(1,0,2,1) Matrix(55,152,72,199) -> Matrix(1,0,0,1) Matrix(37,100,-84,-227) -> Matrix(1,0,0,1) Matrix(79,208,-128,-337) -> Matrix(1,2,0,1) Matrix(181,468,-292,-755) -> Matrix(5,4,6,5) Matrix(61,156,52,133) -> Matrix(3,2,4,3) Matrix(21,52,44,109) -> Matrix(1,0,2,1) Matrix(23,56,-168,-409) -> Matrix(1,0,0,1) Matrix(679,1640,248,599) -> Matrix(1,2,0,1) Matrix(183,440,136,327) -> Matrix(1,2,0,1) Matrix(47,112,-128,-305) -> Matrix(1,0,0,1) Matrix(73,168,136,313) -> Matrix(1,0,0,1) Matrix(223,512,-544,-1249) -> Matrix(5,4,-4,-3) Matrix(51,116,-164,-373) -> Matrix(1,0,0,1) Matrix(25,56,104,233) -> Matrix(1,0,2,1) Matrix(211,468,-500,-1109) -> Matrix(1,-2,0,1) Matrix(53,116,-228,-499) -> Matrix(1,0,2,1) Matrix(137,296,56,121) -> Matrix(1,2,0,1) Matrix(3,4,-4,-5) -> Matrix(1,0,2,1) Matrix(271,176,368,239) -> Matrix(1,0,0,1) Matrix(725,468,268,173) -> Matrix(1,2,0,1) Matrix(181,116,220,141) -> Matrix(1,0,0,1) Matrix(177,112,128,81) -> Matrix(1,0,0,1) Matrix(251,156,-716,-445) -> Matrix(3,-2,-4,3) Matrix(163,100,44,27) -> Matrix(1,0,0,1) Matrix(75,44,196,115) -> Matrix(1,0,0,1) Matrix(227,132,-724,-421) -> Matrix(3,-2,-4,3) Matrix(219,124,740,419) -> Matrix(3,-4,-2,3) Matrix(517,292,108,61) -> Matrix(1,-2,2,-3) Matrix(221,124,180,101) -> Matrix(1,-2,2,-3) Matrix(73,40,104,57) -> Matrix(1,-2,2,-3) Matrix(61,28,-268,-123) -> Matrix(1,2,0,1) Matrix(293,132,-788,-355) -> Matrix(1,0,0,1) Matrix(233,104,56,25) -> Matrix(1,2,0,1) Matrix(55,24,-424,-185) -> Matrix(1,0,0,1) Matrix(167,72,-392,-169) -> Matrix(1,-2,0,1) Matrix(387,164,-1220,-517) -> Matrix(1,0,0,1) Matrix(445,188,-2412,-1019) -> Matrix(1,4,0,1) Matrix(219,92,388,163) -> Matrix(1,2,-4,-7) Matrix(985,408,408,169) -> Matrix(1,2,0,1) Matrix(271,112,-1280,-529) -> Matrix(1,2,-2,-3) Matrix(487,200,56,23) -> Matrix(1,2,-2,-3) Matrix(109,44,52,21) -> Matrix(1,0,2,1) Matrix(51,20,28,11) -> Matrix(1,0,2,1) Matrix(303,112,560,207) -> Matrix(1,2,-2,-3) Matrix(199,72,152,55) -> Matrix(1,2,0,1) Matrix(149,52,-788,-275) -> Matrix(3,2,4,3) Matrix(187,60,-988,-317) -> Matrix(1,-2,2,-3) Matrix(183,56,232,71) -> Matrix(1,0,4,1) Matrix(229,68,-980,-291) -> Matrix(1,0,2,1) Matrix(865,256,544,161) -> Matrix(1,0,0,1) Matrix(43,12,68,19) -> Matrix(1,0,4,1) Matrix(169,40,376,89) -> Matrix(1,0,-4,1) Matrix(249,56,40,9) -> Matrix(1,4,0,1) Matrix(39,8,-200,-41) -> Matrix(1,0,4,1) Matrix(3873,736,1184,225) -> Matrix(13,-6,-2,1) Matrix(1921,352,704,129) -> Matrix(1,4,0,1) Matrix(117,20,76,13) -> Matrix(1,0,0,1) Matrix(77,12,340,53) -> Matrix(1,0,-2,1) Matrix(187,28,20,3) -> Matrix(1,0,0,1) Matrix(1,0,16,1) -> Matrix(1,0,0,1) Matrix(397,-52,84,-11) -> Matrix(1,0,2,1) Matrix(527,-80,112,-17) -> Matrix(1,0,-2,1) Matrix(137,-24,40,-7) -> Matrix(1,0,0,1) Matrix(213,-44,92,-19) -> Matrix(3,-2,2,-1) Matrix(237,-52,196,-43) -> Matrix(1,0,2,1) Matrix(1121,-256,416,-95) -> Matrix(9,2,4,1) Matrix(699,-164,260,-61) -> Matrix(3,-2,2,-1) Matrix(153,-40,88,-23) -> Matrix(1,0,2,1) Matrix(275,-76,76,-21) -> Matrix(1,0,2,1) Matrix(643,-188,236,-69) -> Matrix(1,4,0,1) Matrix(1037,-308,468,-139) -> Matrix(11,12,10,11) Matrix(25,-8,72,-23) -> Matrix(1,0,4,1) Matrix(189,-68,164,-59) -> Matrix(5,-2,8,-3) Matrix(305,-112,128,-47) -> Matrix(3,-2,2,-1) Matrix(299,-116,116,-45) -> Matrix(3,-2,2,-1) Matrix(67,-28,12,-5) -> Matrix(1,2,0,1) Matrix(155,-68,212,-93) -> Matrix(1,0,2,1) Matrix(1037,-468,308,-139) -> Matrix(1,0,6,1) Matrix(591,-272,176,-81) -> Matrix(1,0,-4,1) Matrix(391,-216,248,-137) -> Matrix(5,2,2,1) Matrix(61,-36,100,-59) -> Matrix(1,0,12,1) Matrix(337,-208,128,-79) -> Matrix(15,-2,8,-1) Matrix(359,-248,152,-105) -> Matrix(3,-2,2,-1) Matrix(397,-276,292,-203) -> Matrix(1,0,-2,1) Matrix(317,-228,260,-187) -> Matrix(1,-2,2,-3) Matrix(557,-404,324,-235) -> Matrix(1,0,2,1) Matrix(829,-612,340,-251) -> Matrix(3,-2,2,-1) Matrix(487,-376,136,-105) -> Matrix(1,0,4,1) Matrix(413,-324,116,-91) -> Matrix(1,0,-4,1) Matrix(301,-244,132,-107) -> Matrix(5,-4,4,-3) Matrix(171,-148,52,-45) -> Matrix(1,-2,0,1) Matrix(197,-220,60,-67) -> Matrix(5,-2,-2,1) Matrix(379,-484,148,-189) -> Matrix(7,-6,6,-5) Matrix(265,-344,104,-135) -> Matrix(1,-2,2,-3) Matrix(1781,-2412,652,-883) -> Matrix(1,6,0,1) Matrix(433,-592,128,-175) -> Matrix(1,0,0,1) Matrix(345,-488,152,-215) -> Matrix(3,-2,2,-1) Matrix(555,-788,212,-301) -> Matrix(3,-8,2,-5) Matrix(91,-132,20,-29) -> Matrix(1,0,0,1) Matrix(2593,-4096,992,-1567) -> Matrix(3,-20,2,-13) Matrix(991,-1568,304,-481) -> Matrix(1,2,0,1) Matrix(61,-100,36,-59) -> Matrix(1,0,2,1) Matrix(751,-1296,288,-497) -> Matrix(5,-4,4,-3) Matrix(221,-484,100,-219) -> Matrix(19,-18,18,-17) Matrix(185,-424,24,-55) -> Matrix(7,-10,-2,3) Matrix(561,-1328,128,-303) -> Matrix(1,-2,0,1) Matrix(477,-1156,196,-475) -> Matrix(3,-2,2,-1) Matrix(3517,-9188,1076,-2811) -> Matrix(27,-40,-2,3) Matrix(25,-72,8,-23) -> Matrix(1,-2,0,1) Matrix(157,-676,36,-155) -> Matrix(1,-2,0,1) Matrix(29,-196,4,-27) -> Matrix(1,-10,0,1) 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): 30 Degree of the the map X: 30 Degree of the the map Y: 128 ----------------------------------------------------------------------- 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 -5/1 -1/1 1 4 -9/2 1/0 1 16 -13/3 -1/1 1 8 -4/1 (-1/1,1/0) 0 16 -11/3 -1/1 5 2 -18/5 (-1/1,-4/5) 0 16 -7/2 -1/2 1 16 -3/1 -1/1 1 8 -8/3 (-1/1,1/0) 0 16 -13/5 -1/1 3 2 -18/7 (-1/1,-2/3) 0 16 -5/2 -1/2 1 16 -7/3 -1/1 1 4 -9/4 -1/2 1 16 -11/5 -1/1 1 8 -2/1 (-1/1,0/1) 0 16 -1/1 0/1 1 2 0/1 (0/1,1/0) 0 16 1/7 0/1 2 2 2/13 (0/1,1/2) 0 16 1/6 1/0 1 16 1/5 0/1 1 8 3/14 1/0 1 16 2/9 (-1/1,0/1) 0 16 3/13 0/1 3 2 4/17 (0/1,1/2) 0 16 1/4 1/0 1 16 3/11 -1/1 1 8 2/7 (0/1,1/0) 0 16 5/17 -1/1 1 8 8/27 (-3/2,-1/1) 0 16 3/10 -1/2 1 16 1/3 0/1 2 4 5/14 1/2 1 16 4/11 (1/2,1/1) 0 16 3/8 1/2 1 16 5/13 1/1 1 8 2/5 (1/1,1/0) 0 16 3/7 -1/1 1 8 4/9 (-1/2,0/1) 0 16 5/11 0/1 5 2 6/13 (0/1,1/3) 0 16 1/2 1/0 1 16 6/11 (-2/3,-1/2) 0 16 5/9 -1/3 1 8 4/7 (-1/4,0/1) 0 16 3/5 0/1 6 2 2/3 (0/1,1/2) 0 16 9/13 0/1 1 8 7/10 1/2 1 16 5/7 1/1 1 4 13/18 1/0 1 16 8/11 (0/1,1/0) 0 16 11/15 1/1 1 8 14/19 (0/1,1/1) 0 16 3/4 1/0 1 16 10/13 (-1/2,0/1) 0 16 7/9 0/1 4 2 4/5 (0/1,1/2) 0 16 9/11 1/1 1 4 5/6 1/2 1 16 6/7 (1/1,2/1) 0 16 1/1 0/1 1 8 8/7 (1/2,3/5) 0 16 7/6 1/2 1 16 6/5 (0/1,1/1) 0 16 17/14 1/2 1 16 11/9 1/1 1 4 5/4 1/2 1 16 14/11 (3/4,1/1) 0 16 9/7 1/1 4 2 4/3 (1/1,1/0) 0 16 23/17 1/0 3 2 19/14 1/0 1 16 15/11 0/1 1 8 11/8 1/2 1 16 7/5 1/1 1 4 17/12 3/2 1 16 10/7 (0/1,1/0) 0 16 3/2 1/0 1 16 11/7 1/1 1 8 30/19 (4/1,1/0) 0 16 49/31 1/0 11 2 19/12 1/0 1 16 8/5 (0/1,1/0) 0 16 5/3 0/1 1 2 2/1 (0/1,1/1) 0 16 11/5 1/1 9 2 20/9 (1/1,9/8) 0 16 9/4 5/4 1 16 25/11 1/1 1 4 16/7 (4/3,3/2) 0 16 23/10 3/2 1 16 7/3 2/1 1 8 26/11 (2/1,1/0) 0 16 19/8 1/0 1 16 12/5 (1/1,1/0) 0 16 17/7 1/1 1 2 22/9 (1/1,2/1) 0 16 5/2 1/0 1 16 18/7 (1/1,3/2) 0 16 13/5 1/1 1 8 8/3 (2/1,1/0) 0 16 27/10 5/2 1 16 19/7 3/1 1 8 30/11 (4/1,1/0) 0 16 41/15 1/0 3 2 11/4 1/0 1 16 3/1 1/0 1 4 13/4 1/0 1 16 49/15 1/0 11 2 36/11 (-5/1,1/0) 0 16 23/7 -2/1 1 8 10/3 (-1/1,0/1) 0 16 27/8 1/2 1 16 17/5 0/1 1 8 7/2 1/0 1 16 18/5 (0/1,1/2) 0 16 11/3 1/1 1 8 4/1 (1/1,1/0) 0 16 13/3 1/0 1 2 22/5 (0/1,1/0) 0 16 9/2 1/0 1 16 14/3 (0/1,1/0) 0 16 19/4 1/2 1 16 5/1 1/1 1 8 6/1 (3/1,1/0) 0 16 7/1 1/0 5 2 8/1 (-2/1,1/0) 0 16 1/0 1/0 1 16 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(7,40,10,57) (-5/1,1/0) -> (7/10,5/7) Glide Reflection Matrix(27,124,22,101) (-5/1,-9/2) -> (11/9,5/4) Glide Reflection Matrix(67,292,14,61) (-9/2,-13/3) -> (19/4,5/1) Glide Reflection Matrix(29,124,98,419) (-13/3,-4/1) -> (5/17,8/27) Glide Reflection Matrix(23,88,-6,-23) (-4/1,-11/3) -> (-4/1,-11/3) Reflection Matrix(109,396,-30,-109) (-11/3,-18/5) -> (-11/3,-18/5) Reflection Matrix(37,132,44,157) (-18/5,-7/2) -> (5/6,6/7) Hyperbolic Matrix(13,44,34,115) (-7/2,-3/1) -> (3/8,5/13) Glide Reflection Matrix(37,100,10,27) (-3/1,-8/3) -> (11/3,4/1) Glide Reflection Matrix(79,208,-30,-79) (-8/3,-13/5) -> (-8/3,-13/5) Reflection Matrix(181,468,-70,-181) (-13/5,-18/7) -> (-13/5,-18/7) Reflection Matrix(61,156,52,133) (-18/7,-5/2) -> (7/6,6/5) Hyperbolic Matrix(47,112,34,81) (-5/2,-7/3) -> (11/8,7/5) Glide Reflection Matrix(51,116,62,141) (-7/3,-9/4) -> (9/11,5/6) Glide Reflection Matrix(211,468,78,173) (-9/4,-11/5) -> (27/10,19/7) Glide Reflection Matrix(81,176,110,239) (-11/5,-2/1) -> (11/15,14/19) Glide Reflection Matrix(3,4,-2,-3) (-2/1,-1/1) -> (-2/1,-1/1) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(1,0,14,-1) (0/1,1/7) -> (0/1,1/7) Reflection Matrix(27,-4,182,-27) (1/7,2/13) -> (1/7,2/13) Reflection Matrix(331,-52,70,-11) (2/13,1/6) -> (14/3,19/4) Glide Reflection Matrix(137,-24,40,-7) (1/6,1/5) -> (17/5,7/2) Hyperbolic Matrix(213,-44,92,-19) (1/5,3/14) -> (23/10,7/3) Hyperbolic Matrix(237,-52,196,-43) (3/14,2/9) -> (6/5,17/14) Hyperbolic Matrix(53,-12,234,-53) (2/9,3/13) -> (2/9,3/13) Reflection Matrix(103,-24,442,-103) (3/13,4/17) -> (3/13,4/17) Reflection Matrix(491,-116,182,-43) (4/17,1/4) -> (8/3,27/10) Glide Reflection Matrix(77,-20,50,-13) (1/4,3/11) -> (3/2,11/7) Glide Reflection Matrix(275,-76,76,-21) (3/11,2/7) -> (18/5,11/3) Hyperbolic Matrix(643,-188,236,-69) (2/7,5/17) -> (19/7,30/11) Hyperbolic Matrix(443,-132,198,-59) (8/27,3/10) -> (20/9,9/4) Glide Reflection Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(189,-68,164,-59) (5/14,4/11) -> (8/7,7/6) Hyperbolic Matrix(305,-112,128,-47) (4/11,3/8) -> (19/8,12/5) Hyperbolic Matrix(299,-116,116,-45) (5/13,2/5) -> (18/7,13/5) Hyperbolic Matrix(67,-28,12,-5) (2/5,3/7) -> (5/1,6/1) Hyperbolic Matrix(155,-68,212,-93) (3/7,4/9) -> (8/11,11/15) Hyperbolic Matrix(89,-40,198,-89) (4/9,5/11) -> (4/9,5/11) Reflection Matrix(131,-60,286,-131) (5/11,6/13) -> (5/11,6/13) Reflection Matrix(371,-172,110,-51) (6/13,1/2) -> (10/3,27/8) Glide Reflection Matrix(207,-112,146,-79) (1/2,6/11) -> (17/12,10/7) Glide Reflection Matrix(391,-216,248,-137) (6/11,5/9) -> (11/7,30/19) Hyperbolic Matrix(163,-92,62,-35) (5/9,4/7) -> (13/5,8/3) Glide Reflection Matrix(41,-24,70,-41) (4/7,3/5) -> (4/7,3/5) Reflection Matrix(19,-12,30,-19) (3/5,2/3) -> (3/5,2/3) Reflection Matrix(359,-248,152,-105) (2/3,9/13) -> (7/3,26/11) Hyperbolic Matrix(397,-276,292,-203) (9/13,7/10) -> (19/14,15/11) Hyperbolic Matrix(317,-228,260,-187) (5/7,13/18) -> (17/14,11/9) Hyperbolic Matrix(353,-256,222,-161) (13/18,8/11) -> (19/12,8/5) Glide Reflection Matrix(183,-136,74,-55) (14/19,3/4) -> (22/9,5/2) Glide Reflection Matrix(163,-124,46,-35) (3/4,10/13) -> (7/2,18/5) Glide Reflection Matrix(181,-140,234,-181) (10/13,7/9) -> (10/13,7/9) Reflection Matrix(71,-56,90,-71) (7/9,4/5) -> (7/9,4/5) Reflection Matrix(301,-244,132,-107) (4/5,9/11) -> (25/11,16/7) Hyperbolic Matrix(171,-148,52,-45) (6/7,1/1) -> (23/7,10/3) Hyperbolic Matrix(197,-220,60,-67) (1/1,8/7) -> (36/11,23/7) Hyperbolic Matrix(127,-160,50,-63) (5/4,14/11) -> (5/2,18/7) Glide Reflection Matrix(197,-252,154,-197) (14/11,9/7) -> (14/11,9/7) Reflection Matrix(55,-72,42,-55) (9/7,4/3) -> (9/7,4/3) Reflection Matrix(137,-184,102,-137) (4/3,23/17) -> (4/3,23/17) Reflection Matrix(761,-1032,278,-377) (23/17,19/14) -> (41/15,11/4) Glide Reflection Matrix(433,-592,128,-175) (15/11,11/8) -> (27/8,17/5) Hyperbolic Matrix(345,-488,152,-215) (7/5,17/12) -> (9/4,25/11) Hyperbolic Matrix(91,-132,20,-29) (10/7,3/2) -> (9/2,14/3) Hyperbolic Matrix(1861,-2940,1178,-1861) (30/19,49/31) -> (30/19,49/31) Reflection Matrix(991,-1568,304,-481) (49/31,19/12) -> (13/4,49/15) Hyperbolic Matrix(49,-80,30,-49) (8/5,5/3) -> (8/5,5/3) Reflection Matrix(11,-20,6,-11) (5/3,2/1) -> (5/3,2/1) Reflection Matrix(21,-44,10,-21) (2/1,11/5) -> (2/1,11/5) Reflection Matrix(199,-440,90,-199) (11/5,20/9) -> (11/5,20/9) Reflection Matrix(87,-200,10,-23) (16/7,23/10) -> (8/1,1/0) Glide Reflection Matrix(275,-652,62,-147) (26/11,19/8) -> (22/5,9/2) Glide Reflection Matrix(169,-408,70,-169) (12/5,17/7) -> (12/5,17/7) Reflection Matrix(307,-748,126,-307) (17/7,22/9) -> (17/7,22/9) Reflection Matrix(901,-2460,330,-901) (30/11,41/15) -> (30/11,41/15) Reflection Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(1079,-3528,330,-1079) (49/15,36/11) -> (49/15,36/11) Reflection Matrix(25,-104,6,-25) (4/1,13/3) -> (4/1,13/3) Reflection Matrix(131,-572,30,-131) (13/3,22/5) -> (13/3,22/5) Reflection Matrix(13,-84,2,-13) (6/1,7/1) -> (6/1,7/1) Reflection Matrix(15,-112,2,-15) (7/1,8/1) -> (7/1,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(7,40,10,57) -> Matrix(1,2,2,3) Matrix(27,124,22,101) -> Matrix(1,2,2,3) Matrix(67,292,14,61) -> Matrix(1,2,2,3) Matrix(29,124,98,419) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(23,88,-6,-23) -> Matrix(1,2,0,-1) (-4/1,-11/3) -> (-1/1,1/0) Matrix(109,396,-30,-109) -> Matrix(9,8,-10,-9) (-11/3,-18/5) -> (-1/1,-4/5) Matrix(37,132,44,157) -> Matrix(3,2,4,3) Matrix(13,44,34,115) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(37,100,10,27) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(79,208,-30,-79) -> Matrix(1,2,0,-1) (-8/3,-13/5) -> (-1/1,1/0) Matrix(181,468,-70,-181) -> Matrix(5,4,-6,-5) (-13/5,-18/7) -> (-1/1,-2/3) Matrix(61,156,52,133) -> Matrix(3,2,4,3) Matrix(47,112,34,81) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(51,116,62,141) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(211,468,78,173) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(81,176,110,239) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(3,4,-2,-3) -> Matrix(-1,0,2,1) (-2/1,-1/1) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(1,0,0,-1) (-1/1,0/1) -> (0/1,1/0) Matrix(1,0,14,-1) -> Matrix(1,0,0,-1) (0/1,1/7) -> (0/1,1/0) Matrix(27,-4,182,-27) -> Matrix(1,0,4,-1) (1/7,2/13) -> (0/1,1/2) Matrix(331,-52,70,-11) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(137,-24,40,-7) -> Matrix(1,0,0,1) Matrix(213,-44,92,-19) -> Matrix(3,-2,2,-1) 1/1 Matrix(237,-52,196,-43) -> Matrix(1,0,2,1) 0/1 Matrix(53,-12,234,-53) -> Matrix(-1,0,2,1) (2/9,3/13) -> (-1/1,0/1) Matrix(103,-24,442,-103) -> Matrix(1,0,4,-1) (3/13,4/17) -> (0/1,1/2) Matrix(491,-116,182,-43) -> Matrix(5,-2,2,-1) Matrix(77,-20,50,-13) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(275,-76,76,-21) -> Matrix(1,0,2,1) 0/1 Matrix(643,-188,236,-69) -> Matrix(1,4,0,1) 1/0 Matrix(443,-132,198,-59) -> Matrix(7,6,6,5) Matrix(25,-8,72,-23) -> Matrix(1,0,4,1) 0/1 Matrix(189,-68,164,-59) -> Matrix(5,-2,8,-3) 1/2 Matrix(305,-112,128,-47) -> Matrix(3,-2,2,-1) 1/1 Matrix(299,-116,116,-45) -> Matrix(3,-2,2,-1) 1/1 Matrix(67,-28,12,-5) -> Matrix(1,2,0,1) 1/0 Matrix(155,-68,212,-93) -> Matrix(1,0,2,1) 0/1 Matrix(89,-40,198,-89) -> Matrix(-1,0,4,1) (4/9,5/11) -> (-1/2,0/1) Matrix(131,-60,286,-131) -> Matrix(1,0,6,-1) (5/11,6/13) -> (0/1,1/3) Matrix(371,-172,110,-51) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(207,-112,146,-79) -> Matrix(3,2,2,1) Matrix(391,-216,248,-137) -> Matrix(5,2,2,1) Matrix(163,-92,62,-35) -> Matrix(7,2,4,1) Matrix(41,-24,70,-41) -> Matrix(-1,0,8,1) (4/7,3/5) -> (-1/4,0/1) Matrix(19,-12,30,-19) -> Matrix(1,0,4,-1) (3/5,2/3) -> (0/1,1/2) Matrix(359,-248,152,-105) -> Matrix(3,-2,2,-1) 1/1 Matrix(397,-276,292,-203) -> Matrix(1,0,-2,1) 0/1 Matrix(317,-228,260,-187) -> Matrix(1,-2,2,-3) 1/1 Matrix(353,-256,222,-161) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(183,-136,74,-55) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(163,-124,46,-35) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(181,-140,234,-181) -> Matrix(-1,0,4,1) (10/13,7/9) -> (-1/2,0/1) Matrix(71,-56,90,-71) -> Matrix(1,0,4,-1) (7/9,4/5) -> (0/1,1/2) Matrix(301,-244,132,-107) -> Matrix(5,-4,4,-3) 1/1 Matrix(171,-148,52,-45) -> Matrix(1,-2,0,1) 1/0 Matrix(197,-220,60,-67) -> Matrix(5,-2,-2,1) Matrix(127,-160,50,-63) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(197,-252,154,-197) -> Matrix(7,-6,8,-7) (14/11,9/7) -> (3/4,1/1) Matrix(55,-72,42,-55) -> Matrix(-1,2,0,1) (9/7,4/3) -> (1/1,1/0) Matrix(137,-184,102,-137) -> Matrix(-1,2,0,1) (4/3,23/17) -> (1/1,1/0) Matrix(761,-1032,278,-377) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(433,-592,128,-175) -> Matrix(1,0,0,1) Matrix(345,-488,152,-215) -> Matrix(3,-2,2,-1) 1/1 Matrix(91,-132,20,-29) -> Matrix(1,0,0,1) Matrix(1861,-2940,1178,-1861) -> Matrix(-1,8,0,1) (30/19,49/31) -> (4/1,1/0) Matrix(991,-1568,304,-481) -> Matrix(1,2,0,1) 1/0 Matrix(49,-80,30,-49) -> Matrix(1,0,0,-1) (8/5,5/3) -> (0/1,1/0) Matrix(11,-20,6,-11) -> Matrix(1,0,2,-1) (5/3,2/1) -> (0/1,1/1) Matrix(21,-44,10,-21) -> Matrix(1,0,2,-1) (2/1,11/5) -> (0/1,1/1) Matrix(199,-440,90,-199) -> Matrix(17,-18,16,-17) (11/5,20/9) -> (1/1,9/8) Matrix(87,-200,10,-23) -> Matrix(1,-2,-2,3) Matrix(275,-652,62,-147) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(169,-408,70,-169) -> Matrix(-1,2,0,1) (12/5,17/7) -> (1/1,1/0) Matrix(307,-748,126,-307) -> Matrix(3,-4,2,-3) (17/7,22/9) -> (1/1,2/1) Matrix(901,-2460,330,-901) -> Matrix(-1,8,0,1) (30/11,41/15) -> (4/1,1/0) Matrix(25,-72,8,-23) -> Matrix(1,-2,0,1) 1/0 Matrix(1079,-3528,330,-1079) -> Matrix(1,10,0,-1) (49/15,36/11) -> (-5/1,1/0) Matrix(25,-104,6,-25) -> Matrix(-1,2,0,1) (4/1,13/3) -> (1/1,1/0) Matrix(131,-572,30,-131) -> Matrix(1,0,0,-1) (13/3,22/5) -> (0/1,1/0) Matrix(13,-84,2,-13) -> Matrix(-1,6,0,1) (6/1,7/1) -> (3/1,1/0) Matrix(15,-112,2,-15) -> Matrix(1,4,0,-1) (7/1,8/1) -> (-2/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.