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 -6/1 -5/1 -13/3 -4/1 -11/3 -10/3 -3/1 -8/3 -2/1 -9/5 -8/5 -48/31 -4/3 -8/7 -1/1 -4/5 -2/3 -4/7 -8/15 0/1 1/2 4/7 2/3 3/4 4/5 1/1 8/7 16/13 5/4 4/3 16/11 3/2 8/5 7/4 16/9 2/1 16/7 7/3 5/2 8/3 3/1 16/5 10/3 17/5 7/2 11/3 4/1 13/3 5/1 16/3 17/3 6/1 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -6/1 -1/2 -11/2 -1/3 -16/3 0/1 -5/1 0/1 1/0 -9/2 -1/1 -13/3 -3/2 -4/1 -1/1 -19/5 -3/4 -15/4 -1/1 -26/7 -3/4 -11/3 -1/1 -2/3 -18/5 -3/4 -7/2 -3/5 -24/7 -1/2 -17/5 -1/2 -4/9 -10/3 -1/3 -23/7 -1/3 -2/7 -13/4 -1/5 -16/5 0/1 -3/1 1/0 -8/3 -1/1 -13/5 -1/1 -4/5 -31/12 -1/1 -18/7 -3/4 -5/2 -1/1 -22/9 -1/2 -17/7 -1/2 -29/12 -3/5 -12/5 -1/2 -7/3 -1/3 0/1 -16/7 0/1 -9/4 1/1 -11/5 1/0 -2/1 -1/1 -11/6 -1/1 -9/5 -1/3 0/1 -16/9 0/1 -7/4 1/1 -19/11 -2/1 -1/1 -31/18 -1/1 -12/7 -1/1 -5/3 1/0 -8/5 -1/1 -11/7 -1/1 -2/3 -14/9 -1/2 -31/20 -1/1 -48/31 -2/3 -17/11 -1/2 -3/2 -1/1 -16/11 0/1 -13/9 0/1 1/1 -23/16 3/1 -10/7 1/0 -17/12 -1/1 -41/29 -6/5 -1/1 -24/17 -1/1 -7/5 -1/2 -11/8 -1/1 -26/19 1/1 -15/11 -2/1 1/0 -4/3 -1/1 -17/13 -1/2 0/1 -13/10 -1/3 -22/17 1/0 -31/24 -1/1 -9/7 -1/2 -14/11 1/0 -5/4 -1/1 -16/13 0/1 -11/9 1/0 -17/14 -1/1 -23/19 -1/1 -2/3 -6/5 -1/1 -13/11 1/0 -7/6 -1/1 -8/7 -1/1 -1/1 -1/1 0/1 -8/9 -1/1 -7/8 -1/1 -6/7 -1/1 -11/13 -1/2 -16/19 0/1 -5/6 -1/1 -9/11 1/0 -13/16 1/1 -4/5 -1/1 -7/9 1/0 -10/13 -1/2 -13/17 -1/3 0/1 -16/21 0/1 -3/4 -1/1 -17/23 1/0 -14/19 1/0 -11/15 -2/1 -1/1 -8/11 -1/1 -5/7 -1/2 -7/10 -1/3 -16/23 0/1 -9/13 0/1 1/1 -2/3 -1/1 -9/14 -1/3 -16/25 0/1 -7/11 0/1 1/1 -5/8 -1/1 -18/29 -3/2 -49/79 -3/2 -80/129 -4/3 -31/50 -1/1 -13/21 -4/3 -1/1 -8/13 -1/1 -3/5 -1/2 -16/27 0/1 -13/22 1/3 -10/17 1/1 -17/29 4/1 1/0 -24/41 1/0 -7/12 -3/1 -11/19 -2/1 -1/1 -15/26 -1/1 -4/7 -1/1 -5/9 -1/2 0/1 -16/29 0/1 -11/20 1/1 -6/11 1/0 -7/13 -3/2 -8/15 -1/1 -9/17 -1/1 -4/5 -1/2 -1/1 0/1 0/1 1/2 1/1 6/11 1/1 11/20 5/3 5/9 1/0 4/7 1/1 15/26 1/1 11/19 3/2 7/12 1/1 17/29 3/2 10/17 3/2 13/22 9/5 3/5 2/1 1/0 5/8 1/1 7/11 3/2 9/14 7/3 2/3 1/0 9/13 3/2 7/10 3/1 5/7 4/1 1/0 3/4 1/1 13/17 5/2 10/13 3/1 17/22 3/1 7/9 3/1 4/1 4/5 1/0 13/16 -3/1 9/11 -1/1 0/1 5/6 1/1 11/13 2/1 3/1 6/7 1/0 7/8 7/1 1/1 1/0 9/8 5/1 8/7 1/0 7/6 -7/1 6/5 1/0 17/14 -3/1 11/9 -3/1 -2/1 27/22 -7/3 16/13 -2/1 5/4 -1/1 14/11 -1/1 9/7 0/1 1/1 22/17 1/1 13/10 3/1 4/3 1/0 19/14 -7/1 15/11 1/0 11/8 -5/1 7/5 -4/1 -3/1 10/7 -3/1 13/9 -5/2 29/20 -11/5 16/11 -2/1 3/2 -1/1 17/11 0/1 1/0 14/9 1/1 11/7 1/0 8/5 1/0 21/13 1/0 13/8 -7/1 5/3 -4/1 1/0 12/7 -3/1 31/18 -3/1 19/11 -5/2 26/15 -3/1 7/4 -3/1 16/9 -2/1 25/14 -9/5 9/5 -3/2 11/6 -1/1 2/1 1/0 11/5 -3/1 -2/1 9/4 -7/3 16/7 -2/1 23/10 -13/7 7/3 -3/2 12/5 -1/1 29/12 1/1 17/7 0/1 1/0 5/2 -1/1 18/7 -1/1 49/19 -2/1 1/0 80/31 -2/1 31/12 -1/1 13/5 1/0 8/3 1/0 19/7 1/0 49/18 -3/1 30/11 -3/1 11/4 -3/1 3/1 -2/1 1/0 19/6 -11/5 16/5 -2/1 13/4 -9/5 23/7 -7/4 33/10 -5/3 10/3 -3/2 27/8 -5/3 17/5 -3/2 41/12 -1/1 24/7 -1/1 7/2 -1/1 18/5 -5/3 65/18 -5/3 112/31 -8/5 47/13 -8/5 -3/2 29/8 -11/7 11/3 -3/2 26/7 -1/1 41/11 -6/5 -1/1 15/4 -1/1 4/1 -1/1 17/4 -1/1 13/3 -1/1 0/1 22/5 1/0 9/2 -3/1 5/1 1/0 21/4 -7/3 16/3 -2/1 11/2 -5/3 17/3 -8/5 -3/2 6/1 -1/1 7/1 -4/3 -1/1 15/2 -1/1 8/1 -1/1 17/2 -1/1 9/1 -1/2 1/0 -1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(17,112,-12,-79) (-6/1,1/0) -> (-10/7,-17/12) Hyperbolic Matrix(49,272,-20,-111) (-6/1,-11/2) -> (-5/2,-22/9) Hyperbolic Matrix(65,352,12,65) (-11/2,-16/3) -> (16/3,11/2) Hyperbolic Matrix(31,160,-56,-289) (-16/3,-5/1) -> (-5/9,-16/29) Hyperbolic Matrix(17,80,24,113) (-5/1,-9/2) -> (7/10,5/7) Hyperbolic Matrix(47,208,-40,-177) (-9/2,-13/3) -> (-13/11,-7/6) Hyperbolic Matrix(31,128,-8,-33) (-13/3,-4/1) -> (-4/1,-19/5) Parabolic Matrix(207,784,80,303) (-19/5,-15/4) -> (31/12,13/5) Hyperbolic Matrix(305,1136,-236,-879) (-15/4,-26/7) -> (-22/17,-31/24) Hyperbolic Matrix(95,352,112,415) (-26/7,-11/3) -> (11/13,6/7) Hyperbolic Matrix(97,352,-132,-479) (-11/3,-18/5) -> (-14/19,-11/15) Hyperbolic Matrix(49,176,76,273) (-18/5,-7/2) -> (9/14,2/3) Hyperbolic Matrix(65,224,56,193) (-7/2,-24/7) -> (8/7,7/6) Hyperbolic Matrix(239,816,-408,-1393) (-24/7,-17/5) -> (-17/29,-24/41) Hyperbolic Matrix(175,592,-128,-433) (-17/5,-10/3) -> (-26/19,-15/11) Hyperbolic Matrix(111,368,-92,-305) (-10/3,-23/7) -> (-23/19,-6/5) Hyperbolic Matrix(127,416,156,511) (-23/7,-13/4) -> (13/16,9/11) Hyperbolic Matrix(129,416,40,129) (-13/4,-16/5) -> (16/5,13/4) Hyperbolic Matrix(31,96,-52,-161) (-16/5,-3/1) -> (-3/5,-16/27) Hyperbolic Matrix(17,48,-28,-79) (-3/1,-8/3) -> (-8/13,-3/5) Hyperbolic Matrix(79,208,-128,-337) (-8/3,-13/5) -> (-13/21,-8/13) Hyperbolic Matrix(241,624,56,145) (-13/5,-31/12) -> (17/4,13/3) Hyperbolic Matrix(385,992,-248,-639) (-31/12,-18/7) -> (-14/9,-31/20) Hyperbolic Matrix(81,208,44,113) (-18/7,-5/2) -> (11/6,2/1) Hyperbolic Matrix(223,544,380,927) (-22/9,-17/7) -> (17/29,10/17) Hyperbolic Matrix(225,544,-304,-735) (-17/7,-29/12) -> (-3/4,-17/23) Hyperbolic Matrix(113,272,140,337) (-29/12,-12/5) -> (4/5,13/16) Hyperbolic Matrix(47,112,60,143) (-12/5,-7/3) -> (7/9,4/5) Hyperbolic Matrix(97,224,-152,-351) (-7/3,-16/7) -> (-16/25,-7/11) Hyperbolic Matrix(127,288,56,127) (-16/7,-9/4) -> (9/4,16/7) Hyperbolic Matrix(79,176,136,303) (-9/4,-11/5) -> (11/19,7/12) Hyperbolic Matrix(81,176,52,113) (-11/5,-2/1) -> (14/9,11/7) Hyperbolic Matrix(113,208,44,81) (-2/1,-11/6) -> (5/2,18/7) Hyperbolic Matrix(79,144,96,175) (-11/6,-9/5) -> (9/11,5/6) Hyperbolic Matrix(161,288,-232,-415) (-9/5,-16/9) -> (-16/23,-9/13) Hyperbolic Matrix(127,224,72,127) (-16/9,-7/4) -> (7/4,16/9) Hyperbolic Matrix(305,528,-212,-367) (-7/4,-19/11) -> (-13/9,-23/16) Hyperbolic Matrix(575,992,-928,-1601) (-19/11,-31/18) -> (-31/50,-13/21) Hyperbolic Matrix(177,304,308,529) (-31/18,-12/7) -> (4/7,15/26) Hyperbolic Matrix(47,80,84,143) (-12/7,-5/3) -> (5/9,4/7) Hyperbolic Matrix(49,80,-68,-111) (-5/3,-8/5) -> (-8/11,-5/7) Hyperbolic Matrix(111,176,-152,-241) (-8/5,-11/7) -> (-11/15,-8/11) Hyperbolic Matrix(113,176,52,81) (-11/7,-14/9) -> (2/1,11/5) Hyperbolic Matrix(2561,3968,992,1537) (-31/20,-48/31) -> (80/31,31/12) Hyperbolic Matrix(2399,3712,-3868,-5985) (-48/31,-17/11) -> (-49/79,-80/129) Hyperbolic Matrix(239,368,176,271) (-17/11,-3/2) -> (19/14,15/11) Hyperbolic Matrix(65,96,44,65) (-3/2,-16/11) -> (16/11,3/2) Hyperbolic Matrix(287,416,-376,-545) (-16/11,-13/9) -> (-13/17,-16/21) Hyperbolic Matrix(145,208,168,241) (-23/16,-10/7) -> (6/7,7/8) Hyperbolic Matrix(927,1312,248,351) (-17/12,-41/29) -> (41/11,15/4) Hyperbolic Matrix(385,544,-724,-1023) (-41/29,-24/17) -> (-8/15,-9/17) Hyperbolic Matrix(159,224,-296,-417) (-24/17,-7/5) -> (-7/13,-8/15) Hyperbolic Matrix(81,112,128,177) (-7/5,-11/8) -> (5/8,7/11) Hyperbolic Matrix(257,352,468,641) (-11/8,-26/19) -> (6/11,11/20) Hyperbolic Matrix(95,128,-72,-97) (-15/11,-4/3) -> (-4/3,-17/13) Parabolic Matrix(209,272,136,177) (-17/13,-13/10) -> (3/2,17/11) Hyperbolic Matrix(321,416,544,705) (-13/10,-22/17) -> (10/17,13/22) Hyperbolic Matrix(223,288,24,31) (-31/24,-9/7) -> (9/1,1/0) Hyperbolic Matrix(113,144,164,209) (-9/7,-14/11) -> (2/3,9/13) Hyperbolic Matrix(127,160,-204,-257) (-14/11,-5/4) -> (-5/8,-18/29) Hyperbolic Matrix(129,160,104,129) (-5/4,-16/13) -> (16/13,5/4) Hyperbolic Matrix(287,352,-340,-417) (-16/13,-11/9) -> (-11/13,-16/19) Hyperbolic Matrix(289,352,500,609) (-11/9,-17/14) -> (15/26,11/19) Hyperbolic Matrix(145,176,-276,-335) (-17/14,-23/19) -> (-9/17,-1/2) Hyperbolic Matrix(175,208,228,271) (-6/5,-13/11) -> (13/17,10/13) Hyperbolic Matrix(193,224,56,65) (-7/6,-8/7) -> (24/7,7/2) Hyperbolic Matrix(15,16,-16,-17) (-8/7,-1/1) -> (-1/1,-8/9) Parabolic Matrix(561,496,164,145) (-8/9,-7/8) -> (41/12,24/7) Hyperbolic Matrix(257,224,148,129) (-7/8,-6/7) -> (26/15,7/4) Hyperbolic Matrix(415,352,112,95) (-6/7,-11/13) -> (11/3,26/7) Hyperbolic Matrix(609,512,496,417) (-16/19,-5/6) -> (27/22,16/13) Hyperbolic Matrix(175,144,96,79) (-5/6,-9/11) -> (9/5,11/6) Hyperbolic Matrix(511,416,156,127) (-9/11,-13/16) -> (13/4,23/7) Hyperbolic Matrix(337,272,140,113) (-13/16,-4/5) -> (12/5,29/12) Hyperbolic Matrix(143,112,60,47) (-4/5,-7/9) -> (7/3,12/5) Hyperbolic Matrix(145,112,-268,-207) (-7/9,-10/13) -> (-6/11,-7/13) Hyperbolic Matrix(543,416,124,95) (-10/13,-13/17) -> (13/3,22/5) Hyperbolic Matrix(673,512,464,353) (-16/21,-3/4) -> (29/20,16/11) Hyperbolic Matrix(1345,992,-2168,-1599) (-17/23,-14/19) -> (-18/29,-49/79) Hyperbolic Matrix(113,80,24,17) (-5/7,-7/10) -> (9/2,5/1) Hyperbolic Matrix(735,512,412,287) (-7/10,-16/23) -> (16/9,25/14) Hyperbolic Matrix(209,144,164,113) (-9/13,-2/3) -> (14/11,9/7) Hyperbolic Matrix(273,176,76,49) (-2/3,-9/14) -> (7/2,18/5) Hyperbolic Matrix(799,512,348,223) (-9/14,-16/25) -> (16/7,23/10) Hyperbolic Matrix(177,112,128,81) (-7/11,-5/8) -> (11/8,7/5) Hyperbolic Matrix(13985,8672,3872,2401) (-80/129,-31/50) -> (65/18,112/31) Hyperbolic Matrix(865,512,272,161) (-16/27,-13/22) -> (19/6,16/5) Hyperbolic Matrix(705,416,544,321) (-13/22,-10/17) -> (22/17,13/10) Hyperbolic Matrix(463,272,80,47) (-10/17,-17/29) -> (17/3,6/1) Hyperbolic Matrix(465,272,412,241) (-24/41,-7/12) -> (9/8,8/7) Hyperbolic Matrix(303,176,136,79) (-7/12,-11/19) -> (11/5,9/4) Hyperbolic Matrix(609,352,500,289) (-11/19,-15/26) -> (17/14,11/9) Hyperbolic Matrix(529,304,308,177) (-15/26,-4/7) -> (12/7,31/18) Hyperbolic Matrix(143,80,84,47) (-4/7,-5/9) -> (5/3,12/7) Hyperbolic Matrix(929,512,176,97) (-16/29,-11/20) -> (21/4,16/3) Hyperbolic Matrix(497,272,148,81) (-11/20,-6/11) -> (10/3,27/8) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(207,-112,268,-145) (1/2,6/11) -> (10/13,17/22) Hyperbolic Matrix(289,-160,56,-31) (11/20,5/9) -> (5/1,21/4) Hyperbolic Matrix(1393,-816,408,-239) (7/12,17/29) -> (17/5,41/12) Hyperbolic Matrix(161,-96,52,-31) (13/22,3/5) -> (3/1,19/6) Hyperbolic Matrix(79,-48,28,-17) (3/5,5/8) -> (11/4,3/1) Hyperbolic Matrix(351,-224,152,-97) (7/11,9/14) -> (23/10,7/3) Hyperbolic Matrix(415,-288,232,-161) (9/13,7/10) -> (25/14,9/5) Hyperbolic Matrix(111,-80,68,-49) (5/7,3/4) -> (13/8,5/3) Hyperbolic Matrix(545,-416,376,-287) (3/4,13/17) -> (13/9,29/20) Hyperbolic Matrix(289,-224,40,-31) (17/22,7/9) -> (7/1,15/2) Hyperbolic Matrix(417,-352,340,-287) (5/6,11/13) -> (11/9,27/22) Hyperbolic Matrix(17,-16,16,-15) (7/8,1/1) -> (1/1,9/8) Parabolic Matrix(177,-208,40,-47) (7/6,6/5) -> (22/5,9/2) Hyperbolic Matrix(305,-368,92,-111) (6/5,17/14) -> (33/10,10/3) Hyperbolic Matrix(241,-304,88,-111) (5/4,14/11) -> (30/11,11/4) Hyperbolic Matrix(879,-1136,236,-305) (9/7,22/17) -> (26/7,41/11) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(433,-592,128,-175) (15/11,11/8) -> (27/8,17/5) Hyperbolic Matrix(79,-112,12,-17) (7/5,10/7) -> (6/1,7/1) Hyperbolic Matrix(367,-528,212,-305) (10/7,13/9) -> (19/11,26/15) Hyperbolic Matrix(639,-992,248,-385) (17/11,14/9) -> (18/7,49/19) Hyperbolic Matrix(161,-256,100,-159) (11/7,8/5) -> (8/5,21/13) Parabolic Matrix(465,-752,128,-207) (21/13,13/8) -> (29/8,11/3) Hyperbolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic Matrix(767,-1856,212,-513) (29/12,17/7) -> (47/13,29/8) Hyperbolic Matrix(111,-272,20,-49) (17/7,5/2) -> (11/2,17/3) Hyperbolic Matrix(3585,-9248,992,-2559) (49/19,80/31) -> (112/31,47/13) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(1039,-2832,288,-785) (49/18,30/11) -> (18/5,65/18) Hyperbolic Matrix(209,-688,24,-79) (23/7,33/10) -> (17/2,9/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(33,-256,4,-31) (15/2,8/1) -> (8/1,17/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(17,112,-12,-79) -> Matrix(3,2,-2,-1) Matrix(49,272,-20,-111) -> Matrix(5,2,-8,-3) Matrix(65,352,12,65) -> Matrix(11,2,-6,-1) Matrix(31,160,-56,-289) -> Matrix(1,0,-2,1) Matrix(17,80,24,113) -> Matrix(1,4,0,1) Matrix(47,208,-40,-177) -> Matrix(1,2,-2,-3) Matrix(31,128,-8,-33) -> Matrix(5,6,-6,-7) Matrix(207,784,80,303) -> Matrix(5,4,-4,-3) Matrix(305,1136,-236,-879) -> Matrix(5,4,-4,-3) Matrix(95,352,112,415) -> Matrix(11,8,4,3) Matrix(97,352,-132,-479) -> Matrix(5,4,-4,-3) Matrix(49,176,76,273) -> Matrix(11,8,4,3) Matrix(65,224,56,193) -> Matrix(19,10,-2,-1) Matrix(239,816,-408,-1393) -> Matrix(17,8,2,1) Matrix(175,592,-128,-433) -> Matrix(5,2,2,1) Matrix(111,368,-92,-305) -> Matrix(1,0,2,1) Matrix(127,416,156,511) -> Matrix(7,2,-4,-1) Matrix(129,416,40,129) -> Matrix(19,2,-10,-1) Matrix(31,96,-52,-161) -> Matrix(1,0,-2,1) Matrix(17,48,-28,-79) -> Matrix(1,2,-2,-3) Matrix(79,208,-128,-337) -> Matrix(9,8,-8,-7) Matrix(241,624,56,145) -> Matrix(5,4,-4,-3) Matrix(385,992,-248,-639) -> Matrix(3,2,-2,-1) Matrix(81,208,44,113) -> Matrix(5,4,-4,-3) Matrix(223,544,380,927) -> Matrix(13,8,8,5) Matrix(225,544,-304,-735) -> Matrix(7,4,-2,-1) Matrix(113,272,140,337) -> Matrix(11,6,-2,-1) Matrix(47,112,60,143) -> Matrix(9,4,2,1) Matrix(97,224,-152,-351) -> Matrix(1,0,4,1) Matrix(127,288,56,127) -> Matrix(9,-2,-4,1) Matrix(79,176,136,303) -> Matrix(3,-2,2,-1) Matrix(81,176,52,113) -> Matrix(1,2,0,1) Matrix(113,208,44,81) -> Matrix(3,2,-2,-1) Matrix(79,144,96,175) -> Matrix(1,0,2,1) Matrix(161,288,-232,-415) -> Matrix(1,0,4,1) Matrix(127,224,72,127) -> Matrix(5,-2,-2,1) Matrix(305,528,-212,-367) -> Matrix(1,2,0,1) Matrix(575,992,-928,-1601) -> Matrix(3,2,-2,-1) Matrix(177,304,308,529) -> Matrix(3,4,2,3) Matrix(47,80,84,143) -> Matrix(1,2,0,1) Matrix(49,80,-68,-111) -> Matrix(1,2,-2,-3) Matrix(111,176,-152,-241) -> Matrix(5,4,-4,-3) Matrix(113,176,52,81) -> Matrix(7,4,-2,-1) Matrix(2561,3968,992,1537) -> Matrix(5,4,-4,-3) Matrix(2399,3712,-3868,-5985) -> Matrix(17,10,-12,-7) Matrix(239,368,176,271) -> Matrix(15,8,-2,-1) Matrix(65,96,44,65) -> Matrix(3,2,-2,-1) Matrix(287,416,-376,-545) -> Matrix(1,0,-4,1) Matrix(145,208,168,241) -> Matrix(1,4,0,1) Matrix(927,1312,248,351) -> Matrix(1,0,0,1) Matrix(385,544,-724,-1023) -> Matrix(9,10,-10,-11) Matrix(159,224,-296,-417) -> Matrix(5,4,-4,-3) Matrix(81,112,128,177) -> Matrix(1,2,0,1) Matrix(257,352,468,641) -> Matrix(3,-2,2,-1) Matrix(95,128,-72,-97) -> Matrix(1,2,-2,-3) Matrix(209,272,136,177) -> Matrix(1,0,2,1) Matrix(321,416,544,705) -> Matrix(3,-2,2,-1) Matrix(223,288,24,31) -> Matrix(1,0,0,1) Matrix(113,144,164,209) -> Matrix(1,2,0,1) Matrix(127,160,-204,-257) -> Matrix(3,2,-2,-1) Matrix(129,160,104,129) -> Matrix(3,2,-2,-1) Matrix(287,352,-340,-417) -> Matrix(1,0,-2,1) Matrix(289,352,500,609) -> Matrix(3,4,2,3) Matrix(145,176,-276,-335) -> Matrix(1,2,-2,-3) Matrix(175,208,228,271) -> Matrix(5,2,2,1) Matrix(193,224,56,65) -> Matrix(3,2,-2,-1) Matrix(15,16,-16,-17) -> Matrix(1,0,0,1) Matrix(561,496,164,145) -> Matrix(5,4,-4,-3) Matrix(257,224,148,129) -> Matrix(1,-2,0,1) Matrix(415,352,112,95) -> Matrix(5,4,-4,-3) Matrix(609,512,496,417) -> Matrix(5,-2,-2,1) Matrix(175,144,96,79) -> Matrix(3,2,-2,-1) Matrix(511,416,156,127) -> Matrix(7,2,-4,-1) Matrix(337,272,140,113) -> Matrix(1,0,0,1) Matrix(143,112,60,47) -> Matrix(3,2,-2,-1) Matrix(145,112,-268,-207) -> Matrix(3,2,-2,-1) Matrix(543,416,124,95) -> Matrix(1,0,2,1) Matrix(673,512,464,353) -> Matrix(9,-2,-4,1) Matrix(1345,992,-2168,-1599) -> Matrix(3,2,-2,-1) Matrix(113,80,24,17) -> Matrix(3,2,-2,-1) Matrix(735,512,412,287) -> Matrix(15,2,-8,-1) Matrix(209,144,164,113) -> Matrix(1,0,0,1) Matrix(273,176,76,49) -> Matrix(7,2,-4,-1) Matrix(799,512,348,223) -> Matrix(19,2,-10,-1) Matrix(177,112,128,81) -> Matrix(1,-4,0,1) Matrix(13985,8672,3872,2401) -> Matrix(23,28,-14,-17) Matrix(865,512,272,161) -> Matrix(17,-2,-8,1) Matrix(705,416,544,321) -> Matrix(3,-2,2,-1) Matrix(463,272,80,47) -> Matrix(3,-4,-2,3) Matrix(465,272,412,241) -> Matrix(1,8,0,1) Matrix(303,176,136,79) -> Matrix(5,8,-2,-3) Matrix(609,352,500,289) -> Matrix(5,8,-2,-3) Matrix(529,304,308,177) -> Matrix(11,14,-4,-5) Matrix(143,80,84,47) -> Matrix(7,4,-2,-1) Matrix(929,512,176,97) -> Matrix(9,-2,-4,1) Matrix(497,272,148,81) -> Matrix(3,2,-2,-1) Matrix(1,0,4,1) -> Matrix(1,0,2,1) Matrix(207,-112,268,-145) -> Matrix(5,-8,2,-3) Matrix(289,-160,56,-31) -> Matrix(1,-4,0,1) Matrix(1393,-816,408,-239) -> Matrix(5,-6,-4,5) Matrix(161,-96,52,-31) -> Matrix(1,-4,0,1) Matrix(79,-48,28,-17) -> Matrix(1,-4,0,1) Matrix(351,-224,152,-97) -> Matrix(7,-12,-4,7) Matrix(415,-288,232,-161) -> Matrix(7,-12,-4,7) Matrix(111,-80,68,-49) -> Matrix(1,-8,0,1) Matrix(545,-416,376,-287) -> Matrix(9,-20,-4,9) Matrix(289,-224,40,-31) -> Matrix(5,-16,-4,13) Matrix(417,-352,340,-287) -> Matrix(5,-12,-2,5) Matrix(17,-16,16,-15) -> Matrix(1,-2,0,1) Matrix(177,-208,40,-47) -> Matrix(1,4,0,1) Matrix(305,-368,92,-111) -> Matrix(3,14,-2,-9) Matrix(241,-304,88,-111) -> Matrix(1,-2,0,1) Matrix(879,-1136,236,-305) -> Matrix(5,-6,-4,5) Matrix(97,-128,72,-95) -> Matrix(1,-10,0,1) Matrix(433,-592,128,-175) -> Matrix(3,20,-2,-13) Matrix(79,-112,12,-17) -> Matrix(3,8,-2,-5) Matrix(367,-528,212,-305) -> Matrix(1,0,0,1) Matrix(639,-992,248,-385) -> Matrix(1,-2,0,1) Matrix(161,-256,100,-159) -> Matrix(1,-14,0,1) Matrix(465,-752,128,-207) -> Matrix(3,32,-2,-21) Matrix(881,-1520,324,-559) -> Matrix(7,18,-2,-5) Matrix(767,-1856,212,-513) -> Matrix(3,8,-2,-5) Matrix(111,-272,20,-49) -> Matrix(3,8,-2,-5) Matrix(3585,-9248,992,-2559) -> Matrix(3,14,-2,-9) Matrix(97,-256,36,-95) -> Matrix(1,-2,0,1) Matrix(1039,-2832,288,-785) -> Matrix(3,14,-2,-9) Matrix(209,-688,24,-79) -> Matrix(7,12,-10,-17) Matrix(33,-128,8,-31) -> Matrix(1,2,-2,-3) Matrix(33,-256,4,-31) -> Matrix(9,10,-10,-11) 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): 43 Degree of the the map X: 43 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 -6/1 -1/2 1 8 -11/2 -1/3 1 16 -16/3 0/1 6 2 -5/1 (0/1,1/0) 0 16 -4/1 -1/1 3 4 -15/4 -1/1 1 16 -11/3 (-1/1,-2/3) 0 16 -7/2 -3/5 1 16 -24/7 -1/2 13 2 -17/5 (-1/2,-4/9) 0 16 -10/3 -1/3 1 8 -13/4 -1/5 1 16 -16/5 0/1 10 2 -3/1 1/0 2 16 -8/3 -1/1 5 2 -13/5 (-1/1,-4/5) 0 16 -31/12 -1/1 1 16 -18/7 -3/4 1 8 -5/2 -1/1 1 16 -7/3 (-1/3,0/1) 0 16 -16/7 0/1 9 2 -9/4 1/1 1 16 -2/1 -1/1 1 8 -9/5 (-1/3,0/1) 0 16 -16/9 0/1 7 2 -7/4 1/1 1 16 -5/3 1/0 2 16 -8/5 -1/1 3 2 -11/7 (-1/1,-2/3) 0 16 -14/9 -1/2 1 8 -31/20 -1/1 1 16 -48/31 -2/3 2 2 -17/11 -1/2 2 16 -3/2 -1/1 1 16 -16/11 0/1 5 2 -13/9 (0/1,1/1) 0 16 -10/7 1/0 1 8 -17/12 -1/1 1 16 -41/29 (-6/5,-1/1) 0 16 -24/17 -1/1 7 2 -7/5 -1/2 2 16 -4/3 -1/1 1 4 -13/10 -1/3 1 16 -9/7 -1/2 2 16 -5/4 -1/1 1 16 -16/13 0/1 3 2 -11/9 1/0 2 16 -6/5 -1/1 1 8 -7/6 -1/1 1 16 -8/7 -1/1 1 2 -1/1 (-1/1,0/1) 0 16 0/1 0/1 1 2 1/1 1/0 2 16 8/7 1/0 13 2 7/6 -7/1 1 16 6/5 1/0 1 8 17/14 -3/1 1 16 11/9 (-3/1,-2/1) 0 16 16/13 -2/1 3 2 5/4 -1/1 1 16 14/11 -1/1 1 8 9/7 (0/1,1/1) 0 16 22/17 1/1 1 8 13/10 3/1 1 16 4/3 1/0 5 4 19/14 -7/1 1 16 15/11 1/0 2 16 11/8 -5/1 1 16 7/5 (-4/1,-3/1) 0 16 10/7 -3/1 1 8 13/9 -5/2 2 16 16/11 -2/1 5 2 3/2 -1/1 1 16 17/11 (0/1,1/0) 0 16 14/9 1/1 1 8 11/7 1/0 2 16 8/5 1/0 7 2 5/3 (-4/1,1/0) 0 16 12/7 -3/1 3 4 31/18 -3/1 1 16 19/11 -5/2 2 16 26/15 -3/1 1 8 7/4 -3/1 1 16 16/9 -2/1 7 2 9/5 -3/2 2 16 11/6 -1/1 1 16 2/1 1/0 1 8 11/5 (-3/1,-2/1) 0 16 9/4 -7/3 1 16 16/7 -2/1 9 2 7/3 -3/2 2 16 12/5 -1/1 1 4 29/12 1/1 1 16 17/7 (0/1,1/0) 0 16 5/2 -1/1 1 16 18/7 -1/1 1 8 49/19 (-2/1,1/0) 0 16 80/31 -2/1 2 2 31/12 -1/1 1 16 13/5 1/0 2 16 8/3 1/0 1 2 3/1 (-2/1,1/0) 0 16 16/5 -2/1 10 2 13/4 -9/5 1 16 23/7 -7/4 2 16 33/10 -5/3 1 16 10/3 -3/2 1 8 27/8 -5/3 1 16 17/5 -3/2 2 16 24/7 -1/1 1 2 7/2 -1/1 1 16 18/5 -5/3 1 8 11/3 -3/2 2 16 26/7 -1/1 1 8 41/11 (-6/5,-1/1) 0 16 15/4 -1/1 1 16 4/1 -1/1 1 4 17/4 -1/1 1 16 13/3 (-1/1,0/1) 0 16 22/5 1/0 1 8 9/2 -3/1 1 16 5/1 1/0 2 16 16/3 -2/1 6 2 11/2 -5/3 1 16 17/3 (-8/5,-3/2) 0 16 6/1 -1/1 1 8 7/1 (-4/3,-1/1) 0 16 8/1 -1/1 5 2 9/1 -1/2 2 16 1/0 -1/1 1 16 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(17,112,-12,-79) (-6/1,1/0) -> (-10/7,-17/12) Hyperbolic Matrix(47,272,14,81) (-6/1,-11/2) -> (10/3,27/8) Glide Reflection Matrix(65,352,12,65) (-11/2,-16/3) -> (16/3,11/2) Hyperbolic Matrix(31,160,-6,-31) (-16/3,-5/1) -> (-16/3,-5/1) Reflection Matrix(17,80,10,47) (-5/1,-4/1) -> (5/3,12/7) Glide Reflection Matrix(79,304,46,177) (-4/1,-15/4) -> (12/7,31/18) Glide Reflection Matrix(95,352,78,289) (-15/4,-11/3) -> (17/14,11/9) Glide Reflection Matrix(49,176,22,79) (-11/3,-7/2) -> (11/5,9/4) Glide Reflection Matrix(65,224,56,193) (-7/2,-24/7) -> (8/7,7/6) Hyperbolic Matrix(239,816,-70,-239) (-24/7,-17/5) -> (-24/7,-17/5) Reflection Matrix(81,272,14,47) (-17/5,-10/3) -> (17/3,6/1) Glide Reflection Matrix(127,416,98,321) (-10/3,-13/4) -> (22/17,13/10) Glide Reflection Matrix(129,416,40,129) (-13/4,-16/5) -> (16/5,13/4) Hyperbolic Matrix(31,96,-10,-31) (-16/5,-3/1) -> (-16/5,-3/1) Reflection Matrix(17,48,-6,-17) (-3/1,-8/3) -> (-3/1,-8/3) Reflection Matrix(79,208,-30,-79) (-8/3,-13/5) -> (-8/3,-13/5) Reflection Matrix(241,624,56,145) (-13/5,-31/12) -> (17/4,13/3) Hyperbolic Matrix(385,992,-248,-639) (-31/12,-18/7) -> (-14/9,-31/20) Hyperbolic Matrix(81,208,44,113) (-18/7,-5/2) -> (11/6,2/1) Hyperbolic Matrix(47,112,34,81) (-5/2,-7/3) -> (11/8,7/5) Glide Reflection Matrix(97,224,-42,-97) (-7/3,-16/7) -> (-7/3,-16/7) Reflection Matrix(127,288,56,127) (-16/7,-9/4) -> (9/4,16/7) Hyperbolic Matrix(79,176,22,49) (-9/4,-2/1) -> (7/2,18/5) Glide Reflection Matrix(79,144,62,113) (-2/1,-9/5) -> (14/11,9/7) Glide Reflection Matrix(161,288,-90,-161) (-9/5,-16/9) -> (-9/5,-16/9) Reflection Matrix(127,224,72,127) (-16/9,-7/4) -> (7/4,16/9) Hyperbolic Matrix(47,80,10,17) (-7/4,-5/3) -> (9/2,5/1) Glide Reflection Matrix(49,80,-30,-49) (-5/3,-8/5) -> (-5/3,-8/5) Reflection Matrix(111,176,-70,-111) (-8/5,-11/7) -> (-8/5,-11/7) Reflection Matrix(113,176,52,81) (-11/7,-14/9) -> (2/1,11/5) Hyperbolic Matrix(2561,3968,992,1537) (-31/20,-48/31) -> (80/31,31/12) Hyperbolic Matrix(1055,1632,-682,-1055) (-48/31,-17/11) -> (-48/31,-17/11) Reflection Matrix(239,368,176,271) (-17/11,-3/2) -> (19/14,15/11) Hyperbolic Matrix(65,96,44,65) (-3/2,-16/11) -> (16/11,3/2) Hyperbolic Matrix(287,416,-198,-287) (-16/11,-13/9) -> (-16/11,-13/9) Reflection Matrix(289,416,66,95) (-13/9,-10/7) -> (13/3,22/5) Glide Reflection Matrix(927,1312,248,351) (-17/12,-41/29) -> (41/11,15/4) Hyperbolic Matrix(1393,1968,-986,-1393) (-41/29,-24/17) -> (-41/29,-24/17) Reflection Matrix(239,336,-170,-239) (-24/17,-7/5) -> (-24/17,-7/5) Reflection Matrix(81,112,34,47) (-7/5,-4/3) -> (7/3,12/5) Glide Reflection Matrix(207,272,86,113) (-4/3,-13/10) -> (12/5,29/12) Glide Reflection Matrix(321,416,98,127) (-13/10,-9/7) -> (13/4,23/7) Glide Reflection Matrix(113,144,62,79) (-9/7,-5/4) -> (9/5,11/6) Glide Reflection Matrix(129,160,104,129) (-5/4,-16/13) -> (16/13,5/4) Hyperbolic Matrix(287,352,-234,-287) (-16/13,-11/9) -> (-16/13,-11/9) Reflection Matrix(289,352,78,95) (-11/9,-6/5) -> (11/3,26/7) Glide Reflection Matrix(191,224,110,129) (-6/5,-7/6) -> (26/15,7/4) Glide Reflection Matrix(193,224,56,65) (-7/6,-8/7) -> (24/7,7/2) Hyperbolic Matrix(15,16,-14,-15) (-8/7,-1/1) -> (-8/7,-1/1) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(15,-16,14,-15) (1/1,8/7) -> (1/1,8/7) Reflection Matrix(177,-208,40,-47) (7/6,6/5) -> (22/5,9/2) Hyperbolic Matrix(305,-368,92,-111) (6/5,17/14) -> (33/10,10/3) Hyperbolic Matrix(287,-352,234,-287) (11/9,16/13) -> (11/9,16/13) Reflection Matrix(127,-160,50,-63) (5/4,14/11) -> (5/2,18/7) Glide Reflection Matrix(879,-1136,236,-305) (9/7,22/17) -> (26/7,41/11) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(433,-592,128,-175) (15/11,11/8) -> (27/8,17/5) Hyperbolic Matrix(79,-112,12,-17) (7/5,10/7) -> (6/1,7/1) Hyperbolic Matrix(367,-528,212,-305) (10/7,13/9) -> (19/11,26/15) Hyperbolic Matrix(287,-416,198,-287) (13/9,16/11) -> (13/9,16/11) Reflection Matrix(353,-544,146,-225) (3/2,17/11) -> (29/12,17/7) Glide Reflection Matrix(639,-992,248,-385) (17/11,14/9) -> (18/7,49/19) Hyperbolic Matrix(225,-352,62,-97) (14/9,11/7) -> (18/5,11/3) Glide Reflection Matrix(111,-176,70,-111) (11/7,8/5) -> (11/7,8/5) Reflection Matrix(49,-80,30,-49) (8/5,5/3) -> (8/5,5/3) Reflection Matrix(575,-992,222,-383) (31/18,19/11) -> (31/12,13/5) Glide Reflection Matrix(161,-288,90,-161) (16/9,9/5) -> (16/9,9/5) Reflection Matrix(97,-224,42,-97) (16/7,7/3) -> (16/7,7/3) Reflection Matrix(111,-272,20,-49) (17/7,5/2) -> (11/2,17/3) Hyperbolic Matrix(3039,-7840,1178,-3039) (49/19,80/31) -> (49/19,80/31) Reflection Matrix(79,-208,30,-79) (13/5,8/3) -> (13/5,8/3) Reflection Matrix(17,-48,6,-17) (8/3,3/1) -> (8/3,3/1) Reflection Matrix(31,-96,10,-31) (3/1,16/5) -> (3/1,16/5) Reflection Matrix(97,-320,10,-33) (23/7,33/10) -> (9/1,1/0) Glide Reflection Matrix(239,-816,70,-239) (17/5,24/7) -> (17/5,24/7) Reflection Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(31,-160,6,-31) (5/1,16/3) -> (5/1,16/3) Reflection Matrix(15,-112,2,-15) (7/1,8/1) -> (7/1,8/1) Reflection Matrix(17,-144,2,-17) (8/1,9/1) -> (8/1,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(17,112,-12,-79) -> Matrix(3,2,-2,-1) -1/1 Matrix(47,272,14,81) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(65,352,12,65) -> Matrix(11,2,-6,-1) Matrix(31,160,-6,-31) -> Matrix(1,0,0,-1) (-16/3,-5/1) -> (0/1,1/0) Matrix(17,80,10,47) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(79,304,46,177) -> Matrix(17,14,-6,-5) Matrix(95,352,78,289) -> Matrix(11,8,-4,-3) Matrix(49,176,22,79) -> Matrix(11,8,-4,-3) Matrix(65,224,56,193) -> Matrix(19,10,-2,-1) Matrix(239,816,-70,-239) -> Matrix(17,8,-36,-17) (-24/7,-17/5) -> (-1/2,-4/9) Matrix(81,272,14,47) -> Matrix(11,4,-8,-3) Matrix(127,416,98,321) -> Matrix(7,2,4,1) Matrix(129,416,40,129) -> Matrix(19,2,-10,-1) Matrix(31,96,-10,-31) -> Matrix(1,0,0,-1) (-16/5,-3/1) -> (0/1,1/0) Matrix(17,48,-6,-17) -> Matrix(1,2,0,-1) (-3/1,-8/3) -> (-1/1,1/0) Matrix(79,208,-30,-79) -> Matrix(9,8,-10,-9) (-8/3,-13/5) -> (-1/1,-4/5) Matrix(241,624,56,145) -> Matrix(5,4,-4,-3) -1/1 Matrix(385,992,-248,-639) -> Matrix(3,2,-2,-1) -1/1 Matrix(81,208,44,113) -> Matrix(5,4,-4,-3) -1/1 Matrix(47,112,34,81) -> Matrix(9,4,-2,-1) Matrix(97,224,-42,-97) -> Matrix(-1,0,6,1) (-7/3,-16/7) -> (-1/3,0/1) Matrix(127,288,56,127) -> Matrix(9,-2,-4,1) Matrix(79,176,22,49) -> Matrix(3,-2,-2,1) Matrix(79,144,62,113) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(161,288,-90,-161) -> Matrix(-1,0,6,1) (-9/5,-16/9) -> (-1/3,0/1) Matrix(127,224,72,127) -> Matrix(5,-2,-2,1) Matrix(47,80,10,17) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(49,80,-30,-49) -> Matrix(1,2,0,-1) (-5/3,-8/5) -> (-1/1,1/0) Matrix(111,176,-70,-111) -> Matrix(5,4,-6,-5) (-8/5,-11/7) -> (-1/1,-2/3) Matrix(113,176,52,81) -> Matrix(7,4,-2,-1) Matrix(2561,3968,992,1537) -> Matrix(5,4,-4,-3) -1/1 Matrix(1055,1632,-682,-1055) -> Matrix(7,4,-12,-7) (-48/31,-17/11) -> (-2/3,-1/2) Matrix(239,368,176,271) -> Matrix(15,8,-2,-1) Matrix(65,96,44,65) -> Matrix(3,2,-2,-1) -1/1 Matrix(287,416,-198,-287) -> Matrix(1,0,2,-1) (-16/11,-13/9) -> (0/1,1/1) Matrix(289,416,66,95) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(927,1312,248,351) -> Matrix(1,0,0,1) Matrix(1393,1968,-986,-1393) -> Matrix(11,12,-10,-11) (-41/29,-24/17) -> (-6/5,-1/1) Matrix(239,336,-170,-239) -> Matrix(3,2,-4,-3) (-24/17,-7/5) -> (-1/1,-1/2) Matrix(81,112,34,47) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(207,272,86,113) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(321,416,98,127) -> Matrix(3,-2,-2,1) Matrix(113,144,62,79) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(129,160,104,129) -> Matrix(3,2,-2,-1) -1/1 Matrix(287,352,-234,-287) -> Matrix(1,0,0,-1) (-16/13,-11/9) -> (0/1,1/0) Matrix(289,352,78,95) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(191,224,110,129) -> Matrix(5,2,-2,-1) Matrix(193,224,56,65) -> Matrix(3,2,-2,-1) -1/1 Matrix(15,16,-14,-15) -> Matrix(-1,0,2,1) (-8/7,-1/1) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(1,0,0,-1) (0/1,1/1) -> (0/1,1/0) Matrix(15,-16,14,-15) -> Matrix(1,2,0,-1) (1/1,8/7) -> (-1/1,1/0) Matrix(177,-208,40,-47) -> Matrix(1,4,0,1) 1/0 Matrix(305,-368,92,-111) -> Matrix(3,14,-2,-9) Matrix(287,-352,234,-287) -> Matrix(5,12,-2,-5) (11/9,16/13) -> (-3/1,-2/1) Matrix(127,-160,50,-63) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(879,-1136,236,-305) -> Matrix(5,-6,-4,5) Matrix(97,-128,72,-95) -> Matrix(1,-10,0,1) 1/0 Matrix(433,-592,128,-175) -> Matrix(3,20,-2,-13) Matrix(79,-112,12,-17) -> Matrix(3,8,-2,-5) -2/1 Matrix(367,-528,212,-305) -> Matrix(1,0,0,1) Matrix(287,-416,198,-287) -> Matrix(9,20,-4,-9) (13/9,16/11) -> (-5/2,-2/1) Matrix(353,-544,146,-225) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(639,-992,248,-385) -> Matrix(1,-2,0,1) 1/0 Matrix(225,-352,62,-97) -> Matrix(3,-8,-2,5) Matrix(111,-176,70,-111) -> Matrix(-1,6,0,1) (11/7,8/5) -> (3/1,1/0) Matrix(49,-80,30,-49) -> Matrix(1,8,0,-1) (8/5,5/3) -> (-4/1,1/0) Matrix(575,-992,222,-383) -> Matrix(1,2,-2,-5) Matrix(161,-288,90,-161) -> Matrix(7,12,-4,-7) (16/9,9/5) -> (-2/1,-3/2) Matrix(97,-224,42,-97) -> Matrix(7,12,-4,-7) (16/7,7/3) -> (-2/1,-3/2) Matrix(111,-272,20,-49) -> Matrix(3,8,-2,-5) -2/1 Matrix(3039,-7840,1178,-3039) -> Matrix(1,4,0,-1) (49/19,80/31) -> (-2/1,1/0) Matrix(79,-208,30,-79) -> Matrix(1,2,0,-1) (13/5,8/3) -> (-1/1,1/0) Matrix(17,-48,6,-17) -> Matrix(1,4,0,-1) (8/3,3/1) -> (-2/1,1/0) Matrix(31,-96,10,-31) -> Matrix(1,4,0,-1) (3/1,16/5) -> (-2/1,1/0) Matrix(97,-320,10,-33) -> Matrix(1,2,2,3) Matrix(239,-816,70,-239) -> Matrix(5,6,-4,-5) (17/5,24/7) -> (-3/2,-1/1) Matrix(33,-128,8,-31) -> Matrix(1,2,-2,-3) -1/1 Matrix(31,-160,6,-31) -> Matrix(1,4,0,-1) (5/1,16/3) -> (-2/1,1/0) Matrix(15,-112,2,-15) -> Matrix(7,8,-6,-7) (7/1,8/1) -> (-4/3,-1/1) Matrix(17,-144,2,-17) -> Matrix(3,2,-4,-3) (8/1,9/1) -> (-1/1,-1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.