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 -1/1 -8/19 -6/17 -1/3 -4/15 -2/13 0/1 2/9 5/17 1/3 3/8 1/2 4/7 9/13 5/6 1/1 6/5 13/9 3/2 34/21 41/25 5/3 7/4 2/1 15/7 23/10 7/3 5/2 8/3 3/1 67/21 16/5 10/3 17/5 7/2 4/1 13/3 9/2 14/3 24/5 5/1 37/7 16/3 6/1 19/3 7/1 8/1 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 1/2 -5/11 1/2 3/4 -4/9 1/2 2/3 -3/7 1/2 3/4 -8/19 1/1 -13/31 3/2 1/0 -5/12 1/2 -7/17 1/2 3/4 -9/22 3/4 -11/27 5/6 7/8 -2/5 0/1 1/1 -5/13 3/2 1/0 -18/47 2/1 3/1 -13/34 1/0 -8/21 0/1 1/1 -3/8 1/2 -4/11 2/1 1/0 -5/14 1/2 -6/17 1/1 -7/20 1/0 -1/3 1/2 1/0 -4/13 0/1 1/1 -11/36 5/6 -18/59 1/1 8/7 -7/23 3/2 1/0 -3/10 1/0 -11/37 -3/4 -1/2 -8/27 -1/3 0/1 -5/17 -1/2 1/0 -12/41 -1/3 0/1 -7/24 -1/6 -2/7 0/1 1/2 -3/11 -1/2 1/0 -4/15 0/1 -5/19 1/4 1/2 -6/23 1/4 1/3 -1/4 1/0 -2/9 0/1 1/0 -1/5 1/2 1/0 -4/21 -1/1 1/0 -3/16 -1/2 -2/11 0/1 1/3 -3/17 1/2 3/4 -1/6 1/2 -2/13 0/1 -3/20 1/4 -1/7 1/2 1/0 -1/8 1/0 -2/17 0/1 1/3 -1/9 1/2 1/0 0/1 0/1 1/1 1/8 1/0 2/15 1/2 1/1 1/7 1/2 1/0 1/6 1/2 2/11 0/1 1/1 1/5 1/2 1/0 2/9 0/1 3/13 1/4 1/2 1/4 1/0 3/11 3/2 1/0 5/18 1/0 7/25 -5/2 1/0 2/7 -1/1 0/1 5/17 0/1 8/27 0/1 1/9 3/10 1/4 4/13 1/3 1/2 5/16 1/2 6/19 3/5 2/3 1/3 1/2 1/0 5/14 -3/2 4/11 -1/1 0/1 3/8 0/1 8/21 0/1 1/5 13/34 3/14 5/13 1/4 1/2 2/5 0/1 1/2 5/12 3/4 3/7 3/2 1/0 4/9 -1/1 0/1 9/20 -1/2 5/11 -1/2 1/0 1/2 1/2 4/7 0/1 7/12 1/6 10/17 1/3 1/2 13/22 1/4 3/5 1/4 1/2 11/18 1/2 19/31 1/2 1/0 8/13 1/2 2/3 5/8 1/2 7/11 1/2 1/0 2/3 0/1 1/0 9/13 0/1 16/23 0/1 1/16 7/10 1/8 19/27 1/6 3/16 12/17 0/1 1/5 17/24 3/16 22/31 1/5 2/9 5/7 1/4 1/2 18/25 0/1 1/3 31/43 1/4 1/2 13/18 1/4 8/11 0/1 1/5 3/4 1/2 10/13 0/1 1/2 7/9 1/2 3/4 11/14 5/4 26/33 1/1 2/1 15/19 5/2 1/0 4/5 0/1 1/1 9/11 1/2 1/0 5/6 0/1 11/13 1/6 1/4 6/7 0/1 1/3 1/1 1/2 1/0 6/5 1/1 11/9 3/2 1/0 16/13 0/1 1/1 5/4 1/0 24/19 0/1 1/1 19/15 1/2 1/0 14/11 -1/1 0/1 37/29 0/1 23/18 1/6 9/7 1/4 1/2 13/10 1/2 17/13 3/8 1/2 4/3 1/2 2/3 11/8 1/2 29/21 7/10 3/4 18/13 2/3 5/7 25/18 3/4 32/23 3/4 7/5 3/4 5/6 17/12 3/4 44/31 4/5 1/1 27/19 13/16 5/6 37/26 17/20 10/7 7/8 1/1 13/9 1/1 3/2 1/0 17/11 1/4 1/2 14/9 2/5 1/2 25/16 7/12 11/7 1/2 3/4 19/12 3/4 8/5 0/1 1/1 21/13 3/8 1/2 34/21 1/2 47/29 1/2 9/16 13/8 1/2 31/19 1/2 7/12 49/30 5/8 18/11 3/5 2/3 41/25 2/3 64/39 2/3 9/13 23/14 3/4 5/3 1/2 3/4 17/10 3/4 46/27 4/5 9/11 29/17 23/28 5/6 12/7 6/7 1/1 7/4 1/1 16/9 1/1 6/5 57/32 5/4 41/23 5/4 23/18 25/14 3/2 9/5 3/2 1/0 2/1 0/1 1/1 15/7 1/1 28/13 1/1 26/25 13/6 13/12 11/5 7/6 5/4 20/9 1/1 4/3 29/13 3/2 1/0 9/4 3/2 16/7 3/2 2/1 23/10 2/1 30/13 1/1 2/1 7/3 3/2 1/0 19/8 3/4 31/13 1/1 12/5 1/1 5/4 29/12 11/8 46/19 22/15 3/2 17/7 3/2 7/4 22/9 1/1 2/1 5/2 1/0 8/3 1/1 11/4 5/4 14/5 4/3 7/5 31/11 29/20 3/2 48/17 40/27 3/2 65/23 3/2 17/6 3/2 3/1 3/2 1/0 19/6 7/2 35/11 13/2 1/0 51/16 1/0 67/21 1/0 16/5 -2/1 1/0 29/9 -1/2 1/0 13/4 1/2 10/3 0/1 1/1 17/5 1/1 24/7 1/1 6/5 7/2 3/2 25/7 5/4 3/2 68/19 1/1 4/3 43/12 4/3 18/5 4/3 3/2 29/8 3/2 40/11 3/2 14/9 11/3 3/2 7/4 4/1 2/1 1/0 13/3 5/2 1/0 9/2 1/0 23/5 1/2 1/0 37/8 1/0 14/3 1/1 1/0 33/7 5/2 1/0 19/4 1/0 24/5 0/1 1/1 5/1 3/2 1/0 21/4 7/4 37/7 2/1 16/3 2/1 7/3 11/2 5/2 6/1 4/1 1/0 19/3 1/0 32/5 -10/1 1/0 13/2 1/0 7/1 1/2 1/0 8/1 2/1 3/1 9/1 9/2 1/0 10/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(161,74,124,57) (-1/2,-5/11) -> (9/7,13/10) Hyperbolic Matrix(161,72,38,17) (-5/11,-4/9) -> (4/1,13/3) Hyperbolic Matrix(77,34,120,53) (-4/9,-3/7) -> (7/11,2/3) Hyperbolic Matrix(303,128,-722,-305) (-3/7,-8/19) -> (-8/19,-13/31) Parabolic Matrix(225,94,-754,-315) (-13/31,-5/12) -> (-3/10,-11/37) Hyperbolic Matrix(373,154,264,109) (-5/12,-7/17) -> (7/5,17/12) Hyperbolic Matrix(669,274,188,77) (-7/17,-9/22) -> (7/2,25/7) Hyperbolic Matrix(2005,818,1228,501) (-9/22,-11/27) -> (31/19,49/30) Hyperbolic Matrix(521,212,-1708,-695) (-11/27,-2/5) -> (-18/59,-7/23) Hyperbolic Matrix(71,28,38,15) (-2/5,-5/13) -> (9/5,2/1) Hyperbolic Matrix(73,28,-644,-247) (-5/13,-18/47) -> (-2/17,-1/9) Hyperbolic Matrix(1709,654,358,137) (-18/47,-13/34) -> (19/4,24/5) Hyperbolic Matrix(1137,434,820,313) (-13/34,-8/21) -> (18/13,25/18) Hyperbolic Matrix(353,134,108,41) (-8/21,-3/8) -> (13/4,10/3) Hyperbolic Matrix(71,26,172,63) (-3/8,-4/11) -> (2/5,5/12) Hyperbolic Matrix(205,74,36,13) (-4/11,-5/14) -> (11/2,6/1) Hyperbolic Matrix(203,72,-578,-205) (-5/14,-6/17) -> (-6/17,-7/20) Parabolic Matrix(607,212,272,95) (-7/20,-1/3) -> (29/13,9/4) Hyperbolic Matrix(129,40,158,49) (-1/3,-4/13) -> (4/5,9/11) Hyperbolic Matrix(1013,310,1428,437) (-4/13,-11/36) -> (17/24,22/31) Hyperbolic Matrix(1775,542,822,251) (-11/36,-18/59) -> (28/13,13/6) Hyperbolic Matrix(443,134,724,219) (-7/23,-3/10) -> (11/18,19/31) Hyperbolic Matrix(249,74,784,233) (-11/37,-8/27) -> (6/19,1/3) Hyperbolic Matrix(751,222,592,175) (-8/27,-5/17) -> (19/15,14/11) Hyperbolic Matrix(1057,310,1340,393) (-5/17,-12/41) -> (26/33,15/19) Hyperbolic Matrix(1801,526,1058,309) (-12/41,-7/24) -> (17/10,46/27) Hyperbolic Matrix(433,126,622,181) (-7/24,-2/7) -> (16/23,7/10) Hyperbolic Matrix(121,34,32,9) (-2/7,-3/11) -> (11/3,4/1) Hyperbolic Matrix(119,32,-450,-121) (-3/11,-4/15) -> (-4/15,-5/19) Parabolic Matrix(61,16,446,117) (-5/19,-6/23) -> (2/15,1/7) Hyperbolic Matrix(891,232,626,163) (-6/23,-1/4) -> (37/26,10/7) Hyperbolic Matrix(115,26,84,19) (-1/4,-2/9) -> (4/3,11/8) Hyperbolic Matrix(55,12,142,31) (-2/9,-1/5) -> (5/13,2/5) Hyperbolic Matrix(763,146,162,31) (-1/5,-4/21) -> (14/3,33/7) Hyperbolic Matrix(53,10,408,77) (-4/21,-3/16) -> (1/8,2/15) Hyperbolic Matrix(161,30,542,101) (-3/16,-2/11) -> (8/27,3/10) Hyperbolic Matrix(213,38,28,5) (-2/11,-3/17) -> (7/1,8/1) Hyperbolic Matrix(479,84,268,47) (-3/17,-1/6) -> (25/14,9/5) Hyperbolic Matrix(51,8,-338,-53) (-1/6,-2/13) -> (-2/13,-3/20) Parabolic Matrix(671,100,208,31) (-3/20,-1/7) -> (29/9,13/4) Hyperbolic Matrix(103,14,228,31) (-1/7,-1/8) -> (9/20,5/11) Hyperbolic Matrix(903,110,550,67) (-1/8,-2/17) -> (64/39,23/14) Hyperbolic Matrix(193,18,268,25) (-1/9,0/1) -> (18/25,31/43) Hyperbolic Matrix(197,-24,156,-19) (0/1,1/8) -> (5/4,24/19) Hyperbolic Matrix(191,-28,116,-17) (1/7,1/6) -> (23/14,5/3) Hyperbolic Matrix(187,-32,76,-13) (1/6,2/11) -> (22/9,5/2) Hyperbolic Matrix(409,-76,296,-55) (2/11,1/5) -> (29/21,18/13) Hyperbolic Matrix(37,-8,162,-35) (1/5,2/9) -> (2/9,3/13) Parabolic Matrix(107,-26,70,-17) (3/13,1/4) -> (3/2,17/11) Hyperbolic Matrix(207,-56,122,-33) (1/4,3/11) -> (5/3,17/10) Hyperbolic Matrix(449,-124,344,-95) (3/11,5/18) -> (13/10,17/13) Hyperbolic Matrix(1171,-326,722,-201) (5/18,7/25) -> (47/29,13/8) Hyperbolic Matrix(585,-164,824,-231) (7/25,2/7) -> (22/31,5/7) Hyperbolic Matrix(171,-50,578,-169) (2/7,5/17) -> (5/17,8/27) Parabolic Matrix(269,-82,456,-139) (3/10,4/13) -> (10/17,13/22) Hyperbolic Matrix(705,-218,152,-47) (4/13,5/16) -> (37/8,14/3) Hyperbolic Matrix(1339,-422,752,-237) (5/16,6/19) -> (16/9,57/32) Hyperbolic Matrix(229,-80,146,-51) (1/3,5/14) -> (25/16,11/7) Hyperbolic Matrix(355,-128,502,-181) (5/14,4/11) -> (12/17,17/24) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(1115,-426,1416,-541) (8/21,13/34) -> (11/14,26/33) Hyperbolic Matrix(349,-134,112,-43) (13/34,5/13) -> (3/1,19/6) Hyperbolic Matrix(217,-92,92,-39) (5/12,3/7) -> (7/3,19/8) Hyperbolic Matrix(245,-108,152,-67) (3/7,4/9) -> (8/5,21/13) Hyperbolic Matrix(1033,-464,728,-327) (4/9,9/20) -> (17/12,44/31) Hyperbolic Matrix(271,-124,212,-97) (5/11,1/2) -> (23/18,9/7) Hyperbolic Matrix(57,-32,98,-55) (1/2,4/7) -> (4/7,7/12) Parabolic Matrix(637,-374,264,-155) (7/12,10/17) -> (12/5,29/12) Hyperbolic Matrix(747,-442,1036,-613) (13/22,3/5) -> (31/43,13/18) Hyperbolic Matrix(191,-116,28,-17) (3/5,11/18) -> (13/2,7/1) Hyperbolic Matrix(873,-536,272,-167) (19/31,8/13) -> (16/5,29/9) Hyperbolic Matrix(245,-152,108,-67) (8/13,5/8) -> (9/4,16/7) Hyperbolic Matrix(297,-188,188,-119) (5/8,7/11) -> (11/7,19/12) Hyperbolic Matrix(235,-162,338,-233) (2/3,9/13) -> (9/13,16/23) Parabolic Matrix(1085,-762,608,-427) (7/10,19/27) -> (41/23,25/14) Hyperbolic Matrix(1033,-728,464,-327) (19/27,12/17) -> (20/9,29/13) Hyperbolic Matrix(385,-276,166,-119) (5/7,18/25) -> (30/13,7/3) Hyperbolic Matrix(409,-296,76,-55) (13/18,8/11) -> (16/3,11/2) Hyperbolic Matrix(177,-130,64,-47) (8/11,3/4) -> (11/4,14/5) Hyperbolic Matrix(449,-344,124,-95) (3/4,10/13) -> (18/5,29/8) Hyperbolic Matrix(347,-268,224,-173) (10/13,7/9) -> (17/11,14/9) Hyperbolic Matrix(271,-212,124,-97) (7/9,11/14) -> (13/6,11/5) Hyperbolic Matrix(197,-156,24,-19) (15/19,4/5) -> (8/1,9/1) Hyperbolic Matrix(121,-100,144,-119) (9/11,5/6) -> (5/6,11/13) Parabolic Matrix(761,-646,536,-455) (11/13,6/7) -> (44/31,27/19) Hyperbolic Matrix(141,-124,58,-51) (6/7,1/1) -> (17/7,22/9) Hyperbolic Matrix(61,-72,50,-59) (1/1,6/5) -> (6/5,11/9) Parabolic Matrix(791,-970,464,-569) (11/9,16/13) -> (46/27,29/17) Hyperbolic Matrix(709,-874,434,-535) (16/13,5/4) -> (49/30,18/11) Hyperbolic Matrix(1495,-1892,418,-529) (24/19,19/15) -> (25/7,68/19) Hyperbolic Matrix(871,-1110,164,-209) (14/11,37/29) -> (37/7,16/3) Hyperbolic Matrix(1275,-1628,242,-309) (37/29,23/18) -> (21/4,37/7) Hyperbolic Matrix(553,-724,152,-199) (17/13,4/3) -> (40/11,11/3) Hyperbolic Matrix(481,-664,92,-127) (11/8,29/21) -> (5/1,21/4) Hyperbolic Matrix(203,-282,18,-25) (25/18,32/23) -> (10/1,1/0) Hyperbolic Matrix(257,-358,28,-39) (32/23,7/5) -> (9/1,10/1) Hyperbolic Matrix(1271,-1808,400,-569) (27/19,37/26) -> (19/6,35/11) Hyperbolic Matrix(325,-466,136,-195) (10/7,13/9) -> (31/13,12/5) Hyperbolic Matrix(233,-340,98,-143) (13/9,3/2) -> (19/8,31/13) Hyperbolic Matrix(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(323,-512,94,-149) (19/12,8/5) -> (24/7,7/2) Hyperbolic Matrix(1429,-2312,882,-1427) (21/13,34/21) -> (34/21,47/29) Parabolic Matrix(887,-1446,192,-313) (13/8,31/19) -> (23/5,37/8) Hyperbolic Matrix(2051,-3362,1250,-2049) (18/11,41/25) -> (41/25,64/39) Parabolic Matrix(455,-778,162,-277) (29/17,12/7) -> (14/5,31/11) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(2293,-4086,720,-1283) (57/32,41/23) -> (35/11,51/16) Hyperbolic Matrix(211,-450,98,-209) (2/1,15/7) -> (15/7,28/13) Parabolic Matrix(165,-364,34,-75) (11/5,20/9) -> (24/5,5/1) Hyperbolic Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(1239,-2854,346,-797) (23/10,30/13) -> (68/19,43/12) Hyperbolic Matrix(925,-2242,328,-795) (46/19,17/7) -> (31/11,48/17) Hyperbolic Matrix(49,-128,18,-47) (5/2,8/3) -> (8/3,11/4) Parabolic Matrix(1507,-4256,472,-1333) (48/17,65/23) -> (67/21,16/5) Hyperbolic Matrix(1575,-4454,494,-1397) (65/23,17/6) -> (51/16,67/21) Hyperbolic Matrix(217,-618,46,-131) (17/6,3/1) -> (33/7,19/4) Hyperbolic Matrix(171,-578,50,-169) (10/3,17/5) -> (17/5,24/7) Parabolic Matrix(399,-1448,62,-225) (29/8,40/11) -> (32/5,13/2) Hyperbolic Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(115,-722,18,-113) (6/1,19/3) -> (19/3,32/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(161,74,124,57) -> Matrix(3,-2,8,-5) Matrix(161,72,38,17) -> Matrix(7,-4,2,-1) Matrix(77,34,120,53) -> Matrix(3,-2,2,-1) Matrix(303,128,-722,-305) -> Matrix(5,-4,4,-3) Matrix(225,94,-754,-315) -> Matrix(1,0,-2,1) Matrix(373,154,264,109) -> Matrix(1,-2,2,-3) Matrix(669,274,188,77) -> Matrix(7,-6,6,-5) Matrix(2005,818,1228,501) -> Matrix(17,-14,28,-23) Matrix(521,212,-1708,-695) -> Matrix(9,-8,8,-7) Matrix(71,28,38,15) -> Matrix(1,0,0,1) Matrix(73,28,-644,-247) -> Matrix(1,-2,2,-3) Matrix(1709,654,358,137) -> Matrix(1,-2,0,1) Matrix(1137,434,820,313) -> Matrix(3,2,4,3) Matrix(353,134,108,41) -> Matrix(1,0,0,1) Matrix(71,26,172,63) -> Matrix(1,-2,2,-3) Matrix(205,74,36,13) -> Matrix(1,2,0,1) Matrix(203,72,-578,-205) -> Matrix(3,-2,2,-1) Matrix(607,212,272,95) -> Matrix(3,-2,2,-1) Matrix(129,40,158,49) -> Matrix(1,0,0,1) Matrix(1013,310,1428,437) -> Matrix(3,-2,14,-9) Matrix(1775,542,822,251) -> Matrix(19,-18,18,-17) Matrix(443,134,724,219) -> Matrix(1,-2,2,-3) Matrix(249,74,784,233) -> Matrix(3,2,4,3) Matrix(751,222,592,175) -> Matrix(1,0,2,1) Matrix(1057,310,1340,393) -> Matrix(5,2,2,1) Matrix(1801,526,1058,309) -> Matrix(21,4,26,5) Matrix(433,126,622,181) -> Matrix(1,0,14,1) Matrix(121,34,32,9) -> Matrix(3,-2,2,-1) Matrix(119,32,-450,-121) -> Matrix(1,0,4,1) Matrix(61,16,446,117) -> Matrix(1,0,-2,1) Matrix(891,232,626,163) -> Matrix(17,-6,20,-7) Matrix(115,26,84,19) -> Matrix(1,-2,2,-3) Matrix(55,12,142,31) -> Matrix(1,0,2,1) Matrix(763,146,162,31) -> Matrix(1,2,0,1) Matrix(53,10,408,77) -> Matrix(1,0,2,1) Matrix(161,30,542,101) -> Matrix(1,0,6,1) Matrix(213,38,28,5) -> Matrix(3,-2,2,-1) Matrix(479,84,268,47) -> Matrix(5,-4,4,-3) Matrix(51,8,-338,-53) -> Matrix(1,0,2,1) Matrix(671,100,208,31) -> Matrix(1,0,-2,1) Matrix(103,14,228,31) -> Matrix(1,0,-2,1) Matrix(903,110,550,67) -> Matrix(3,2,4,3) Matrix(193,18,268,25) -> Matrix(1,0,2,1) Matrix(197,-24,156,-19) -> Matrix(1,0,0,1) Matrix(191,-28,116,-17) -> Matrix(1,-2,2,-3) Matrix(187,-32,76,-13) -> Matrix(3,-2,2,-1) Matrix(409,-76,296,-55) -> Matrix(3,2,4,3) Matrix(37,-8,162,-35) -> Matrix(1,0,2,1) Matrix(107,-26,70,-17) -> Matrix(1,0,0,1) Matrix(207,-56,122,-33) -> Matrix(3,-4,4,-5) Matrix(449,-124,344,-95) -> Matrix(1,0,2,1) Matrix(1171,-326,722,-201) -> Matrix(1,-2,2,-3) Matrix(585,-164,824,-231) -> Matrix(1,2,4,9) Matrix(171,-50,578,-169) -> Matrix(1,0,10,1) Matrix(269,-82,456,-139) -> Matrix(1,0,0,1) Matrix(705,-218,152,-47) -> Matrix(1,0,-2,1) Matrix(1339,-422,752,-237) -> Matrix(27,-16,22,-13) Matrix(229,-80,146,-51) -> Matrix(1,-2,2,-3) Matrix(355,-128,502,-181) -> Matrix(1,0,6,1) Matrix(97,-36,256,-95) -> Matrix(1,0,6,1) Matrix(1115,-426,1416,-541) -> Matrix(11,-2,6,-1) Matrix(349,-134,112,-43) -> Matrix(7,-2,4,-1) Matrix(217,-92,92,-39) -> Matrix(1,0,0,1) Matrix(245,-108,152,-67) -> Matrix(1,0,2,1) Matrix(1033,-464,728,-327) -> Matrix(5,4,6,5) Matrix(271,-124,212,-97) -> Matrix(1,0,4,1) Matrix(57,-32,98,-55) -> Matrix(1,0,4,1) Matrix(637,-374,264,-155) -> Matrix(13,-4,10,-3) Matrix(747,-442,1036,-613) -> Matrix(1,0,0,1) Matrix(191,-116,28,-17) -> Matrix(1,0,-2,1) Matrix(873,-536,272,-167) -> Matrix(1,0,-2,1) Matrix(245,-152,108,-67) -> Matrix(5,-4,4,-3) Matrix(297,-188,188,-119) -> Matrix(1,-2,2,-3) Matrix(235,-162,338,-233) -> Matrix(1,0,16,1) Matrix(1085,-762,608,-427) -> Matrix(29,-4,22,-3) Matrix(1033,-728,464,-327) -> Matrix(21,-4,16,-3) Matrix(385,-276,166,-119) -> Matrix(7,-2,4,-1) Matrix(409,-296,76,-55) -> Matrix(3,-2,2,-1) Matrix(177,-130,64,-47) -> Matrix(13,-4,10,-3) Matrix(449,-344,124,-95) -> Matrix(5,-4,4,-3) Matrix(347,-268,224,-173) -> Matrix(3,-2,8,-5) Matrix(271,-212,124,-97) -> Matrix(9,-8,8,-7) Matrix(197,-156,24,-19) -> Matrix(1,2,0,1) Matrix(121,-100,144,-119) -> Matrix(1,0,4,1) Matrix(761,-646,536,-455) -> Matrix(11,-4,14,-5) Matrix(141,-124,58,-51) -> Matrix(7,-2,4,-1) Matrix(61,-72,50,-59) -> Matrix(3,-2,2,-1) Matrix(791,-970,464,-569) -> Matrix(5,4,6,5) Matrix(709,-874,434,-535) -> Matrix(5,-2,8,-3) Matrix(1495,-1892,418,-529) -> Matrix(5,-4,4,-3) Matrix(871,-1110,164,-209) -> Matrix(9,2,4,1) Matrix(1275,-1628,242,-309) -> Matrix(19,-2,10,-1) Matrix(553,-724,152,-199) -> Matrix(19,-8,12,-5) Matrix(481,-664,92,-127) -> Matrix(17,-12,10,-7) Matrix(203,-282,18,-25) -> Matrix(3,-2,-4,3) Matrix(257,-358,28,-39) -> Matrix(21,-16,4,-3) Matrix(1271,-1808,400,-569) -> Matrix(31,-26,6,-5) Matrix(325,-466,136,-195) -> Matrix(13,-12,12,-11) Matrix(233,-340,98,-143) -> Matrix(3,-4,4,-5) Matrix(997,-1556,412,-643) -> Matrix(29,-16,20,-11) Matrix(323,-512,94,-149) -> Matrix(7,-6,6,-5) Matrix(1429,-2312,882,-1427) -> Matrix(13,-6,24,-11) Matrix(887,-1446,192,-313) -> Matrix(7,-4,2,-1) Matrix(2051,-3362,1250,-2049) -> Matrix(37,-24,54,-35) Matrix(455,-778,162,-277) -> Matrix(45,-38,32,-27) Matrix(113,-196,64,-111) -> Matrix(13,-12,12,-11) Matrix(2293,-4086,720,-1283) -> Matrix(35,-44,4,-5) Matrix(211,-450,98,-209) -> Matrix(27,-26,26,-25) Matrix(165,-364,34,-75) -> Matrix(3,-4,4,-5) Matrix(481,-1102,134,-307) -> Matrix(11,-18,8,-13) Matrix(1239,-2854,346,-797) -> Matrix(3,-2,2,-1) Matrix(925,-2242,328,-795) -> Matrix(35,-54,24,-37) Matrix(49,-128,18,-47) -> Matrix(5,-4,4,-3) Matrix(1507,-4256,472,-1333) -> Matrix(31,-46,-2,3) Matrix(1575,-4454,494,-1397) -> Matrix(37,-56,2,-3) Matrix(217,-618,46,-131) -> Matrix(5,-8,2,-3) Matrix(171,-578,50,-169) -> Matrix(7,-6,6,-5) Matrix(399,-1448,62,-225) -> Matrix(11,-16,-2,3) Matrix(73,-324,16,-71) -> Matrix(1,-2,0,1) Matrix(115,-722,18,-113) -> Matrix(1,-14,0,1) 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): 36 Degree of the the map X: 36 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 -1/1 0/1 1 1 0/1 (0/1,1/1) 0 22 1/8 1/0 1 22 1/7 0 11 1/6 1/2 1 22 2/11 (0/1,1/1) 0 22 1/5 0 11 2/9 0/1 2 2 3/13 0 11 1/4 1/0 1 22 3/11 0 11 5/18 1/0 1 22 7/25 0 11 2/7 (-1/1,0/1) 0 22 5/17 0/1 5 1 3/10 1/4 1 22 4/13 (1/3,1/2) 0 22 5/16 1/2 1 22 1/3 0 11 5/14 -3/2 1 22 4/11 (-1/1,0/1) 0 22 3/8 0/1 3 2 2/5 (0/1,1/2) 0 22 3/7 0 11 4/9 (-1/1,0/1) 0 22 5/11 0 11 1/2 1/2 1 22 4/7 0/1 4 2 7/12 1/6 1 22 10/17 (1/3,1/2) 0 22 13/22 1/4 1 22 3/5 0 11 11/18 1/2 1 22 8/13 (1/2,2/3) 0 22 5/8 1/2 1 22 2/3 (0/1,1/0) 0 22 9/13 0/1 8 1 7/10 1/8 1 22 19/27 0 11 12/17 (0/1,1/5) 0 22 17/24 3/16 1 22 5/7 0 11 18/25 (0/1,1/3) 0 22 13/18 1/4 1 22 8/11 (0/1,1/5) 0 22 3/4 1/2 1 22 10/13 (0/1,1/2) 0 22 7/9 0 11 11/14 5/4 1 22 15/19 0 11 4/5 (0/1,1/1) 0 22 5/6 0/1 2 2 6/7 (0/1,1/3) 0 22 1/1 0 11 6/5 1/1 2 2 11/9 0 11 16/13 (0/1,1/1) 0 22 5/4 1/0 1 22 14/11 (-1/1,0/1) 0 22 37/29 0/1 7 1 23/18 1/6 1 22 9/7 0 11 4/3 (1/2,2/3) 0 22 7/5 0 11 10/7 (7/8,1/1) 0 22 13/9 1/1 8 1 3/2 1/0 1 22 17/11 0 11 14/9 (2/5,1/2) 0 22 25/16 7/12 1 22 11/7 0 11 8/5 (0/1,1/1) 0 22 21/13 0 11 34/21 1/2 6 2 47/29 0 11 13/8 1/2 1 22 31/19 0 11 18/11 (3/5,2/3) 0 22 41/25 2/3 3 1 23/14 3/4 1 22 5/3 0 11 17/10 3/4 1 22 29/17 0 11 12/7 (6/7,1/1) 0 22 7/4 1/1 6 2 2/1 (0/1,1/1) 0 22 15/7 1/1 13 1 13/6 13/12 1 22 11/5 0 11 20/9 (1/1,4/3) 0 22 9/4 3/2 1 22 16/7 (3/2,2/1) 0 22 23/10 2/1 1 2 30/13 (1/1,2/1) 0 22 7/3 0 11 12/5 (1/1,5/4) 0 22 29/12 11/8 1 22 46/19 (22/15,3/2) 0 22 17/7 0 11 22/9 (1/1,2/1) 0 22 5/2 1/0 1 22 8/3 1/1 4 2 11/4 5/4 1 22 14/5 (4/3,7/5) 0 22 31/11 0 11 48/17 (40/27,3/2) 0 22 65/23 3/2 17 1 17/6 3/2 1 22 3/1 0 11 10/3 (0/1,1/1) 0 22 17/5 1/1 3 1 7/2 3/2 1 22 4/1 (2/1,1/0) 0 22 9/2 1/0 1 2 14/3 (1/1,1/0) 0 22 19/4 1/0 1 22 5/1 0 11 6/1 (4/1,1/0) 0 22 19/3 1/0 7 1 13/2 1/0 1 22 7/1 0 11 1/0 1/0 1 22 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(157,-18,218,-25) (0/1,1/8) -> (18/25,13/18) Glide Reflection Matrix(115,-16,194,-27) (1/8,1/7) -> (13/22,3/5) Glide Reflection Matrix(191,-28,116,-17) (1/7,1/6) -> (23/14,5/3) Hyperbolic Matrix(187,-32,76,-13) (1/6,2/11) -> (22/9,5/2) Hyperbolic Matrix(75,-14,166,-31) (2/11,1/5) -> (4/9,5/11) Glide Reflection Matrix(37,-8,162,-35) (1/5,2/9) -> (2/9,3/13) Parabolic Matrix(107,-26,70,-17) (3/13,1/4) -> (3/2,17/11) Hyperbolic Matrix(207,-56,122,-33) (1/4,3/11) -> (5/3,17/10) Hyperbolic Matrix(137,-38,18,-5) (3/11,5/18) -> (7/1,1/0) Glide Reflection Matrix(1171,-326,722,-201) (5/18,7/25) -> (47/29,13/8) Hyperbolic Matrix(205,-58,258,-73) (7/25,2/7) -> (15/19,4/5) Glide Reflection Matrix(69,-20,238,-69) (2/7,5/17) -> (2/7,5/17) Reflection Matrix(101,-30,340,-101) (5/17,3/10) -> (5/17,3/10) Reflection Matrix(269,-82,456,-139) (3/10,4/13) -> (10/17,13/22) Hyperbolic Matrix(471,-146,100,-31) (4/13,5/16) -> (14/3,19/4) Glide Reflection Matrix(99,-32,34,-11) (5/16,1/3) -> (17/6,3/1) Glide Reflection Matrix(229,-80,146,-51) (1/3,5/14) -> (25/16,11/7) Hyperbolic Matrix(355,-128,502,-181) (5/14,4/11) -> (12/17,17/24) Hyperbolic Matrix(65,-24,176,-65) (4/11,3/8) -> (4/11,3/8) Reflection Matrix(31,-12,80,-31) (3/8,2/5) -> (3/8,2/5) Reflection Matrix(63,-26,46,-19) (2/5,3/7) -> (4/3,7/5) Glide Reflection Matrix(245,-108,152,-67) (3/7,4/9) -> (8/5,21/13) Hyperbolic Matrix(271,-124,212,-97) (5/11,1/2) -> (23/18,9/7) Hyperbolic Matrix(57,-32,98,-55) (1/2,4/7) -> (4/7,7/12) Parabolic Matrix(637,-374,264,-155) (7/12,10/17) -> (12/5,29/12) Hyperbolic Matrix(191,-116,28,-17) (3/5,11/18) -> (13/2,7/1) Hyperbolic Matrix(219,-134,286,-175) (11/18,8/13) -> (3/4,10/13) Glide Reflection Matrix(245,-152,108,-67) (8/13,5/8) -> (9/4,16/7) Hyperbolic Matrix(53,-34,14,-9) (5/8,2/3) -> (7/2,4/1) Glide Reflection Matrix(53,-36,78,-53) (2/3,9/13) -> (2/3,9/13) Reflection Matrix(181,-126,260,-181) (9/13,7/10) -> (9/13,7/10) Reflection Matrix(749,-526,440,-309) (7/10,19/27) -> (17/10,29/17) Glide Reflection Matrix(619,-436,504,-355) (19/27,12/17) -> (11/9,16/13) Glide Reflection Matrix(437,-310,554,-393) (17/24,5/7) -> (11/14,15/19) Glide Reflection Matrix(385,-276,166,-119) (5/7,18/25) -> (30/13,7/3) Hyperbolic Matrix(307,-222,242,-175) (13/18,8/11) -> (5/4,14/11) Glide Reflection Matrix(177,-130,64,-47) (8/11,3/4) -> (11/4,14/5) Hyperbolic Matrix(347,-268,224,-173) (10/13,7/9) -> (17/11,14/9) Hyperbolic Matrix(271,-212,124,-97) (7/9,11/14) -> (13/6,11/5) Hyperbolic Matrix(49,-40,60,-49) (4/5,5/6) -> (4/5,5/6) Reflection Matrix(71,-60,84,-71) (5/6,6/7) -> (5/6,6/7) Reflection Matrix(141,-124,58,-51) (6/7,1/1) -> (17/7,22/9) Hyperbolic Matrix(61,-72,50,-59) (1/1,6/5) -> (6/5,11/9) Parabolic Matrix(197,-244,88,-109) (16/13,5/4) -> (20/9,9/4) Glide Reflection Matrix(813,-1036,638,-813) (14/11,37/29) -> (14/11,37/29) Reflection Matrix(1333,-1702,1044,-1333) (37/29,23/18) -> (37/29,23/18) Reflection Matrix(57,-74,10,-13) (9/7,4/3) -> (5/1,6/1) Glide Reflection Matrix(109,-154,46,-65) (7/5,10/7) -> (7/3,12/5) Glide Reflection Matrix(181,-260,126,-181) (10/7,13/9) -> (10/7,13/9) Reflection Matrix(53,-78,36,-53) (13/9,3/2) -> (13/9,3/2) Reflection Matrix(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(85,-134,26,-41) (11/7,8/5) -> (3/1,10/3) Glide Reflection Matrix(1429,-2312,882,-1427) (21/13,34/21) -> (34/21,47/29) Parabolic Matrix(401,-654,84,-137) (13/8,31/19) -> (19/4,5/1) Glide Reflection Matrix(501,-818,226,-369) (31/19,18/11) -> (11/5,20/9) Glide Reflection Matrix(901,-1476,550,-901) (18/11,41/25) -> (18/11,41/25) Reflection Matrix(1149,-1886,700,-1149) (41/25,23/14) -> (41/25,23/14) Reflection Matrix(455,-778,162,-277) (29/17,12/7) -> (14/5,31/11) Hyperbolic Matrix(97,-168,56,-97) (12/7,7/4) -> (12/7,7/4) Reflection Matrix(15,-28,8,-15) (7/4,2/1) -> (7/4,2/1) Reflection Matrix(29,-60,14,-29) (2/1,15/7) -> (2/1,15/7) Reflection Matrix(181,-390,84,-181) (15/7,13/6) -> (15/7,13/6) Reflection Matrix(321,-736,140,-321) (16/7,23/10) -> (16/7,23/10) Reflection Matrix(599,-1380,260,-599) (23/10,30/13) -> (23/10,30/13) Reflection Matrix(925,-2242,328,-795) (46/19,17/7) -> (31/11,48/17) Hyperbolic Matrix(49,-128,18,-47) (5/2,8/3) -> (8/3,11/4) Parabolic Matrix(2209,-6240,782,-2209) (48/17,65/23) -> (48/17,65/23) Reflection Matrix(781,-2210,276,-781) (65/23,17/6) -> (65/23,17/6) Reflection Matrix(101,-340,30,-101) (10/3,17/5) -> (10/3,17/5) Reflection Matrix(69,-238,20,-69) (17/5,7/2) -> (17/5,7/2) Reflection Matrix(17,-72,4,-17) (4/1,9/2) -> (4/1,9/2) Reflection Matrix(55,-252,12,-55) (9/2,14/3) -> (9/2,14/3) Reflection Matrix(37,-228,6,-37) (6/1,19/3) -> (6/1,19/3) Reflection Matrix(77,-494,12,-77) (19/3,13/2) -> (19/3,13/2) 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(157,-18,218,-25) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(115,-16,194,-27) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(191,-28,116,-17) -> Matrix(1,-2,2,-3) 1/1 Matrix(187,-32,76,-13) -> Matrix(3,-2,2,-1) 1/1 Matrix(75,-14,166,-31) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(37,-8,162,-35) -> Matrix(1,0,2,1) 0/1 Matrix(107,-26,70,-17) -> Matrix(1,0,0,1) Matrix(207,-56,122,-33) -> Matrix(3,-4,4,-5) 1/1 Matrix(137,-38,18,-5) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1171,-326,722,-201) -> Matrix(1,-2,2,-3) 1/1 Matrix(205,-58,258,-73) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(69,-20,238,-69) -> Matrix(-1,0,2,1) (2/7,5/17) -> (-1/1,0/1) Matrix(101,-30,340,-101) -> Matrix(1,0,8,-1) (5/17,3/10) -> (0/1,1/4) Matrix(269,-82,456,-139) -> Matrix(1,0,0,1) Matrix(471,-146,100,-31) -> Matrix(5,-2,2,-1) Matrix(99,-32,34,-11) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(229,-80,146,-51) -> Matrix(1,-2,2,-3) 1/1 Matrix(355,-128,502,-181) -> Matrix(1,0,6,1) 0/1 Matrix(65,-24,176,-65) -> Matrix(-1,0,2,1) (4/11,3/8) -> (-1/1,0/1) Matrix(31,-12,80,-31) -> Matrix(1,0,4,-1) (3/8,2/5) -> (0/1,1/2) Matrix(63,-26,46,-19) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(245,-108,152,-67) -> Matrix(1,0,2,1) 0/1 Matrix(271,-124,212,-97) -> Matrix(1,0,4,1) 0/1 Matrix(57,-32,98,-55) -> Matrix(1,0,4,1) 0/1 Matrix(637,-374,264,-155) -> Matrix(13,-4,10,-3) Matrix(191,-116,28,-17) -> Matrix(1,0,-2,1) 0/1 Matrix(219,-134,286,-175) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(245,-152,108,-67) -> Matrix(5,-4,4,-3) 1/1 Matrix(53,-34,14,-9) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(53,-36,78,-53) -> Matrix(1,0,0,-1) (2/3,9/13) -> (0/1,1/0) Matrix(181,-126,260,-181) -> Matrix(1,0,16,-1) (9/13,7/10) -> (0/1,1/8) Matrix(749,-526,440,-309) -> Matrix(29,-4,36,-5) Matrix(619,-436,504,-355) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(437,-310,554,-393) -> Matrix(9,-2,4,-1) Matrix(385,-276,166,-119) -> Matrix(7,-2,4,-1) Matrix(307,-222,242,-175) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(177,-130,64,-47) -> Matrix(13,-4,10,-3) Matrix(347,-268,224,-173) -> Matrix(3,-2,8,-5) 1/2 Matrix(271,-212,124,-97) -> Matrix(9,-8,8,-7) 1/1 Matrix(49,-40,60,-49) -> Matrix(1,0,2,-1) (4/5,5/6) -> (0/1,1/1) Matrix(71,-60,84,-71) -> Matrix(1,0,6,-1) (5/6,6/7) -> (0/1,1/3) Matrix(141,-124,58,-51) -> Matrix(7,-2,4,-1) Matrix(61,-72,50,-59) -> Matrix(3,-2,2,-1) 1/1 Matrix(197,-244,88,-109) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(813,-1036,638,-813) -> Matrix(-1,0,2,1) (14/11,37/29) -> (-1/1,0/1) Matrix(1333,-1702,1044,-1333) -> Matrix(1,0,12,-1) (37/29,23/18) -> (0/1,1/6) Matrix(57,-74,10,-13) -> Matrix(5,-2,2,-1) Matrix(109,-154,46,-65) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(181,-260,126,-181) -> Matrix(15,-14,16,-15) (10/7,13/9) -> (7/8,1/1) Matrix(53,-78,36,-53) -> Matrix(-1,2,0,1) (13/9,3/2) -> (1/1,1/0) Matrix(997,-1556,412,-643) -> Matrix(29,-16,20,-11) Matrix(85,-134,26,-41) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1429,-2312,882,-1427) -> Matrix(13,-6,24,-11) 1/2 Matrix(401,-654,84,-137) -> Matrix(3,-2,-2,1) Matrix(501,-818,226,-369) -> Matrix(23,-14,18,-11) Matrix(901,-1476,550,-901) -> Matrix(19,-12,30,-19) (18/11,41/25) -> (3/5,2/3) Matrix(1149,-1886,700,-1149) -> Matrix(17,-12,24,-17) (41/25,23/14) -> (2/3,3/4) Matrix(455,-778,162,-277) -> Matrix(45,-38,32,-27) Matrix(97,-168,56,-97) -> Matrix(13,-12,14,-13) (12/7,7/4) -> (6/7,1/1) Matrix(15,-28,8,-15) -> Matrix(1,0,2,-1) (7/4,2/1) -> (0/1,1/1) Matrix(29,-60,14,-29) -> Matrix(1,0,2,-1) (2/1,15/7) -> (0/1,1/1) Matrix(181,-390,84,-181) -> Matrix(25,-26,24,-25) (15/7,13/6) -> (1/1,13/12) Matrix(321,-736,140,-321) -> Matrix(7,-12,4,-7) (16/7,23/10) -> (3/2,2/1) Matrix(599,-1380,260,-599) -> Matrix(3,-4,2,-3) (23/10,30/13) -> (1/1,2/1) Matrix(925,-2242,328,-795) -> Matrix(35,-54,24,-37) 3/2 Matrix(49,-128,18,-47) -> Matrix(5,-4,4,-3) 1/1 Matrix(2209,-6240,782,-2209) -> Matrix(161,-240,108,-161) (48/17,65/23) -> (40/27,3/2) Matrix(781,-2210,276,-781) -> Matrix(43,-66,28,-43) (65/23,17/6) -> (3/2,11/7) Matrix(101,-340,30,-101) -> Matrix(1,0,2,-1) (10/3,17/5) -> (0/1,1/1) Matrix(69,-238,20,-69) -> Matrix(5,-6,4,-5) (17/5,7/2) -> (1/1,3/2) Matrix(17,-72,4,-17) -> Matrix(-1,4,0,1) (4/1,9/2) -> (2/1,1/0) Matrix(55,-252,12,-55) -> Matrix(-1,2,0,1) (9/2,14/3) -> (1/1,1/0) Matrix(37,-228,6,-37) -> Matrix(-1,8,0,1) (6/1,19/3) -> (4/1,1/0) Matrix(77,-494,12,-77) -> Matrix(1,6,0,-1) (19/3,13/2) -> (-3/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.