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 -7/4 -3/2 -5/4 -1/1 -7/8 -5/6 -3/4 -11/15 -5/8 -1/2 -3/7 -3/8 -1/3 -3/11 -1/4 -3/13 -1/5 -1/6 -1/7 -1/8 -1/9 0/1 1/6 3/16 1/5 3/13 1/4 3/11 2/7 5/16 1/3 3/8 2/5 7/16 1/2 5/9 9/16 4/7 5/8 31/48 2/3 11/16 11/15 3/4 4/5 13/16 5/6 7/8 1/1 5/4 4/3 3/2 7/4 15/8 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 0/1 -11/6 -1/1 1/1 -20/11 0/1 -9/5 0/1 1/0 -7/4 0/1 -26/15 0/1 -19/11 0/1 1/1 -12/7 2/1 -29/17 -4/1 1/0 -17/10 -1/1 -22/13 0/1 -5/3 1/0 -8/5 0/1 -11/7 -2/1 -1/1 -14/9 0/1 -3/2 -1/1 -13/9 -2/1 -1/1 -10/7 -2/3 -7/5 1/0 -4/3 0/1 -17/13 -1/1 -2/3 -13/10 -1/1 -1/3 -22/17 0/1 -9/7 1/0 -5/4 -1/1 -16/13 0/1 -11/9 1/0 -6/5 0/1 -13/11 -1/2 -7/6 -1/1 -8/7 0/1 -1/1 -1/1 0/1 -8/9 0/1 -7/8 -1/1 -6/7 0/1 -5/6 -1/1 -14/17 0/1 -9/11 1/0 -22/27 -2/1 -13/16 -1/1 -4/5 0/1 -11/14 -1/1 1/1 -7/9 -1/2 -17/22 -1/1 1/1 -10/13 0/1 -3/4 -1/1 -14/19 -2/3 -11/15 -2/3 -1/2 -8/11 0/1 -5/7 -1/2 -7/10 -1/1 1/1 -9/13 -2/1 -1/1 -20/29 -4/3 -11/16 -1/1 -2/3 0/1 -11/17 1/0 -9/14 -3/1 -1/1 -7/11 -2/1 -1/1 -5/8 -1/1 -13/21 -1/1 -4/5 -8/13 -2/3 -3/5 -1/2 -7/12 0/1 -18/31 0/1 -11/19 0/1 1/1 -15/26 1/1 3/1 -4/7 -2/1 -9/16 -1/1 -14/25 -6/7 -5/9 -1/1 -2/3 -6/11 0/1 -1/2 -1/1 -5/11 -1/2 -4/9 0/1 -7/16 -1/1 -10/23 -4/5 -3/7 -1/1 -2/3 -5/12 -1/2 -12/29 -2/5 -7/17 -1/2 -2/5 0/1 -7/18 -1/1 -1/3 -19/49 -1/2 -31/80 -1/1 -1/3 -12/31 0/1 -5/13 -1/1 0/1 -3/8 -1/1 -7/19 -1/1 -2/3 -18/49 -2/3 -11/30 -1/1 -3/5 -4/11 -2/3 -1/3 -1/2 -6/19 0/1 -5/16 -1/1 -1/3 -4/13 0/1 -7/23 -1/3 0/1 -10/33 0/1 -3/10 -1/1 -8/27 -2/3 -5/17 -4/7 -1/2 -12/41 -10/19 -7/24 -1/2 -2/7 -2/5 -5/18 -1/1 -1/3 -18/65 0/1 -31/112 -1/1 -1/3 -13/47 -1/2 -8/29 -2/5 -3/11 -1/3 0/1 -7/26 -1/3 -1/5 -11/41 -1/6 -4/15 0/1 -1/4 0/1 -4/17 0/1 -3/13 1/0 -5/22 -1/1 -2/9 0/1 -1/5 -1/2 0/1 -4/21 0/1 -3/16 -1/1 -1/3 -2/11 0/1 -3/17 -1/2 -1/6 -1/1 -1/3 -1/7 -1/4 -2/15 0/1 -1/8 0/1 -2/17 0/1 -1/9 0/1 1/1 0/1 0/1 1/6 1/1 2/11 0/1 3/16 -1/1 1/1 1/5 1/0 2/9 -2/3 3/13 -1/3 0/1 1/4 0/1 5/19 0/1 1/3 4/15 0/1 7/26 1/3 3/11 1/2 5/18 1/1 2/7 0/1 7/24 1/1 5/17 1/0 3/10 -1/1 1/1 7/23 1/2 4/13 0/1 5/16 -1/1 1/1 1/3 0/1 1/0 3/8 0/1 5/13 1/4 12/31 0/1 7/18 1/3 2/5 0/1 9/22 1/3 7/17 1/2 2/3 12/29 2/3 5/12 1/1 3/7 1/2 7/16 1/1 4/9 2/1 5/11 0/1 1/1 1/2 -1/1 1/1 6/11 0/1 5/9 1/2 9/16 1/1 4/7 2/1 11/19 3/2 18/31 2/1 7/12 2/1 3/5 2/1 1/0 5/8 1/0 7/11 1/0 9/14 -1/1 20/31 0/1 31/48 -1/1 1/1 11/17 0/1 1/0 2/3 0/1 11/16 1/1 9/13 3/2 16/23 2/1 7/10 1/1 12/17 2/1 29/41 11/6 17/24 2/1 5/7 2/1 3/1 8/11 4/1 19/26 3/1 5/1 11/15 1/0 3/4 1/0 13/17 1/0 10/13 -2/1 17/22 -3/1 24/31 -2/1 7/9 -2/1 -1/1 11/14 -1/1 4/5 0/1 13/16 1/1 9/11 1/1 2/1 14/17 2/1 19/23 5/2 5/6 1/1 3/1 11/13 3/1 4/1 6/7 6/1 7/8 1/0 1/1 1/0 9/8 1/0 8/7 -8/1 7/6 -5/1 -3/1 13/11 -4/1 -3/1 19/16 -3/1 6/5 -2/1 11/9 -1/1 0/1 16/13 0/1 5/4 1/0 9/7 -5/1 -4/1 13/10 -3/1 17/13 -7/2 21/16 -3/1 4/3 -2/1 23/17 -2/1 1/0 19/14 -1/1 15/11 1/0 11/8 1/0 7/5 -4/1 1/0 10/7 -4/1 23/16 -3/1 13/9 -5/2 3/2 -3/1 -1/1 14/9 -4/1 25/16 -3/1 11/7 -5/2 8/5 -2/1 29/18 -7/3 79/49 -9/4 -2/1 129/80 -7/3 -11/5 50/31 -2/1 21/13 -9/4 13/8 -2/1 5/3 -2/1 1/0 27/16 -3/1 -1/1 22/13 -2/1 17/10 -3/1 -1/1 29/17 1/0 41/24 -3/1 12/7 -2/1 19/11 -5/2 26/15 -2/1 7/4 -2/1 9/5 1/0 29/16 -3/1 -1/1 20/11 -2/1 11/6 -3/1 13/7 -7/3 -2/1 15/8 -2/1 17/9 -7/4 2/1 -2/1 1/0 -1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(145,268,-112,-207) (-2/1,-11/6) -> (-13/10,-22/17) Hyperbolic Matrix(257,468,352,641) (-11/6,-20/11) -> (8/11,19/26) Hyperbolic Matrix(31,56,-160,-289) (-20/11,-9/5) -> (-1/5,-4/21) Hyperbolic Matrix(47,84,80,143) (-9/5,-7/4) -> (7/12,3/5) Hyperbolic Matrix(177,308,304,529) (-7/4,-26/15) -> (18/31,7/12) Hyperbolic Matrix(289,500,352,609) (-26/15,-19/11) -> (9/11,14/17) Hyperbolic Matrix(79,136,176,303) (-19/11,-12/7) -> (4/9,5/11) Hyperbolic Matrix(239,408,-816,-1393) (-12/7,-29/17) -> (-5/17,-12/41) Hyperbolic Matrix(223,380,544,927) (-29/17,-17/10) -> (9/22,7/17) Hyperbolic Matrix(321,544,416,705) (-17/10,-22/13) -> (10/13,17/22) Hyperbolic Matrix(31,52,-96,-161) (-22/13,-5/3) -> (-1/3,-6/19) Hyperbolic Matrix(17,28,-48,-79) (-5/3,-8/5) -> (-4/11,-1/3) Hyperbolic Matrix(81,128,112,177) (-8/5,-11/7) -> (5/7,8/11) Hyperbolic Matrix(97,152,-224,-351) (-11/7,-14/9) -> (-10/23,-3/7) Hyperbolic Matrix(49,76,176,273) (-14/9,-3/2) -> (5/18,2/7) Hyperbolic Matrix(113,164,144,209) (-3/2,-13/9) -> (7/9,11/14) Hyperbolic Matrix(161,232,-288,-415) (-13/9,-10/7) -> (-14/25,-5/9) Hyperbolic Matrix(17,24,80,113) (-10/7,-7/5) -> (1/5,2/9) Hyperbolic Matrix(49,68,-80,-111) (-7/5,-4/3) -> (-8/13,-3/5) Hyperbolic Matrix(287,376,-416,-545) (-4/3,-17/13) -> (-9/13,-20/29) Hyperbolic Matrix(175,228,208,271) (-17/13,-13/10) -> (5/6,11/13) Hyperbolic Matrix(31,40,-224,-289) (-22/17,-9/7) -> (-1/7,-2/15) Hyperbolic Matrix(47,60,112,143) (-9/7,-5/4) -> (5/12,3/7) Hyperbolic Matrix(113,140,272,337) (-5/4,-16/13) -> (12/29,5/12) Hyperbolic Matrix(127,156,416,511) (-16/13,-11/9) -> (7/23,4/13) Hyperbolic Matrix(79,96,144,175) (-11/9,-6/5) -> (6/11,5/9) Hyperbolic Matrix(287,340,-352,-417) (-6/5,-13/11) -> (-9/11,-22/27) Hyperbolic Matrix(95,112,352,415) (-13/11,-7/6) -> (7/26,3/11) Hyperbolic Matrix(145,168,208,241) (-7/6,-8/7) -> (16/23,7/10) Hyperbolic Matrix(15,16,-16,-17) (-8/7,-1/1) -> (-1/1,-8/9) Parabolic Matrix(465,412,272,241) (-8/9,-7/8) -> (41/24,12/7) Hyperbolic Matrix(65,56,224,193) (-7/8,-6/7) -> (2/7,7/24) Hyperbolic Matrix(47,40,-208,-177) (-6/7,-5/6) -> (-5/22,-2/9) Hyperbolic Matrix(111,92,-368,-305) (-5/6,-14/17) -> (-10/33,-3/10) Hyperbolic Matrix(609,500,352,289) (-14/17,-9/11) -> (19/11,26/15) Hyperbolic Matrix(609,496,512,417) (-22/27,-13/16) -> (19/16,6/5) Hyperbolic Matrix(129,104,160,129) (-13/16,-4/5) -> (4/5,13/16) Hyperbolic Matrix(111,88,-304,-241) (-4/5,-11/14) -> (-11/30,-4/11) Hyperbolic Matrix(209,164,144,113) (-11/14,-7/9) -> (13/9,3/2) Hyperbolic Matrix(305,236,-1136,-879) (-7/9,-17/22) -> (-7/26,-11/41) Hyperbolic Matrix(705,544,416,321) (-17/22,-10/13) -> (22/13,17/10) Hyperbolic Matrix(95,72,-128,-97) (-10/13,-3/4) -> (-3/4,-14/19) Parabolic Matrix(239,176,368,271) (-14/19,-11/15) -> (11/17,2/3) Hyperbolic Matrix(175,128,-592,-433) (-11/15,-8/11) -> (-8/27,-5/17) Hyperbolic Matrix(177,128,112,81) (-8/11,-5/7) -> (11/7,8/5) Hyperbolic Matrix(17,12,-112,-79) (-5/7,-7/10) -> (-1/6,-1/7) Hyperbolic Matrix(305,212,-528,-367) (-7/10,-9/13) -> (-11/19,-15/26) Hyperbolic Matrix(673,464,512,353) (-20/29,-11/16) -> (21/16,4/3) Hyperbolic Matrix(65,44,96,65) (-11/16,-2/3) -> (2/3,11/16) Hyperbolic Matrix(209,136,272,177) (-2/3,-11/17) -> (13/17,10/13) Hyperbolic Matrix(385,248,-992,-639) (-11/17,-9/14) -> (-7/18,-19/49) Hyperbolic Matrix(81,52,176,113) (-9/14,-7/11) -> (5/11,1/2) Hyperbolic Matrix(159,100,-256,-161) (-7/11,-5/8) -> (-5/8,-13/21) Parabolic Matrix(207,128,-752,-465) (-13/21,-8/13) -> (-8/29,-3/11) Hyperbolic Matrix(143,84,80,47) (-3/5,-7/12) -> (7/4,9/5) Hyperbolic Matrix(529,308,304,177) (-7/12,-18/31) -> (26/15,7/4) Hyperbolic Matrix(559,324,-1520,-881) (-18/31,-11/19) -> (-7/19,-18/49) Hyperbolic Matrix(257,148,224,129) (-15/26,-4/7) -> (8/7,7/6) Hyperbolic Matrix(127,72,224,127) (-4/7,-9/16) -> (9/16,4/7) Hyperbolic Matrix(735,412,512,287) (-9/16,-14/25) -> (10/7,23/16) Hyperbolic Matrix(175,96,144,79) (-5/9,-6/11) -> (6/5,11/9) Hyperbolic Matrix(81,44,208,113) (-6/11,-1/2) -> (7/18,2/5) Hyperbolic Matrix(113,52,176,81) (-1/2,-5/11) -> (7/11,9/14) Hyperbolic Matrix(303,136,176,79) (-5/11,-4/9) -> (12/7,19/11) Hyperbolic Matrix(127,56,288,127) (-4/9,-7/16) -> (7/16,4/9) Hyperbolic Matrix(799,348,512,223) (-7/16,-10/23) -> (14/9,25/16) Hyperbolic Matrix(143,60,112,47) (-3/7,-5/12) -> (5/4,9/7) Hyperbolic Matrix(337,140,272,113) (-5/12,-12/29) -> (16/13,5/4) Hyperbolic Matrix(513,212,-1856,-767) (-12/29,-7/17) -> (-13/47,-8/29) Hyperbolic Matrix(49,20,-272,-111) (-7/17,-2/5) -> (-2/11,-3/17) Hyperbolic Matrix(113,44,208,81) (-2/5,-7/18) -> (1/2,6/11) Hyperbolic Matrix(2559,992,-9248,-3585) (-19/49,-31/80) -> (-31/112,-13/47) Hyperbolic Matrix(2561,992,3968,1537) (-31/80,-12/31) -> (20/31,31/48) Hyperbolic Matrix(207,80,784,303) (-12/31,-5/13) -> (5/19,4/15) Hyperbolic Matrix(95,36,-256,-97) (-5/13,-3/8) -> (-3/8,-7/19) Parabolic Matrix(785,288,-2832,-1039) (-18/49,-11/30) -> (-5/18,-18/65) Hyperbolic Matrix(865,272,512,161) (-6/19,-5/16) -> (27/16,22/13) Hyperbolic Matrix(129,40,416,129) (-5/16,-4/13) -> (4/13,5/16) Hyperbolic Matrix(511,156,416,127) (-4/13,-7/23) -> (11/9,16/13) Hyperbolic Matrix(79,24,-688,-209) (-7/23,-10/33) -> (-2/17,-1/9) Hyperbolic Matrix(497,148,272,81) (-3/10,-8/27) -> (20/11,11/6) Hyperbolic Matrix(561,164,496,145) (-12/41,-7/24) -> (9/8,8/7) Hyperbolic Matrix(193,56,224,65) (-7/24,-2/7) -> (6/7,7/8) Hyperbolic Matrix(273,76,176,49) (-2/7,-5/18) -> (3/2,14/9) Hyperbolic Matrix(13985,3872,8672,2401) (-18/65,-31/112) -> (129/80,50/31) Hyperbolic Matrix(415,112,352,95) (-3/11,-7/26) -> (7/6,13/11) Hyperbolic Matrix(927,248,1312,351) (-11/41,-4/15) -> (12/17,29/41) Hyperbolic Matrix(31,8,-128,-33) (-4/15,-1/4) -> (-1/4,-4/17) Parabolic Matrix(241,56,624,145) (-4/17,-3/13) -> (5/13,12/31) Hyperbolic Matrix(543,124,416,95) (-3/13,-5/22) -> (13/10,17/13) Hyperbolic Matrix(113,24,80,17) (-2/9,-1/5) -> (7/5,10/7) Hyperbolic Matrix(929,176,512,97) (-4/21,-3/16) -> (29/16,20/11) Hyperbolic Matrix(65,12,352,65) (-3/16,-2/11) -> (2/11,3/16) Hyperbolic Matrix(463,80,272,47) (-3/17,-1/6) -> (17/10,29/17) Hyperbolic Matrix(31,4,-256,-33) (-2/15,-1/8) -> (-1/8,-2/17) Parabolic Matrix(223,24,288,31) (-1/9,0/1) -> (24/31,7/9) Hyperbolic Matrix(79,-12,112,-17) (0/1,1/6) -> (7/10,12/17) Hyperbolic Matrix(111,-20,272,-49) (1/6,2/11) -> (2/5,9/22) Hyperbolic Matrix(289,-56,160,-31) (3/16,1/5) -> (9/5,29/16) Hyperbolic Matrix(177,-40,208,-47) (2/9,3/13) -> (11/13,6/7) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(879,-236,1136,-305) (4/15,7/26) -> (17/22,24/31) Hyperbolic Matrix(479,-132,352,-97) (3/11,5/18) -> (19/14,15/11) Hyperbolic Matrix(1393,-408,816,-239) (7/24,5/17) -> (29/17,41/24) Hyperbolic Matrix(433,-128,592,-175) (5/17,3/10) -> (19/26,11/15) Hyperbolic Matrix(305,-92,368,-111) (3/10,7/23) -> (19/23,5/6) Hyperbolic Matrix(161,-52,96,-31) (5/16,1/3) -> (5/3,27/16) Hyperbolic Matrix(79,-28,48,-17) (1/3,3/8) -> (13/8,5/3) Hyperbolic Matrix(337,-128,208,-79) (3/8,5/13) -> (21/13,13/8) Hyperbolic Matrix(639,-248,992,-385) (12/31,7/18) -> (9/14,20/31) Hyperbolic Matrix(735,-304,544,-225) (7/17,12/29) -> (4/3,23/17) Hyperbolic Matrix(351,-152,224,-97) (3/7,7/16) -> (25/16,11/7) Hyperbolic Matrix(415,-232,288,-161) (5/9,9/16) -> (23/16,13/9) Hyperbolic Matrix(367,-212,528,-305) (4/7,11/19) -> (9/13,16/23) Hyperbolic Matrix(1601,-928,992,-575) (11/19,18/31) -> (50/31,21/13) Hyperbolic Matrix(111,-68,80,-49) (3/5,5/8) -> (11/8,7/5) Hyperbolic Matrix(241,-152,176,-111) (5/8,7/11) -> (15/11,11/8) Hyperbolic Matrix(5985,-3868,3712,-2399) (31/48,11/17) -> (79/49,129/80) Hyperbolic Matrix(545,-376,416,-287) (11/16,9/13) -> (17/13,21/16) Hyperbolic Matrix(1023,-724,544,-385) (29/41,17/24) -> (15/8,17/9) Hyperbolic Matrix(417,-296,224,-159) (17/24,5/7) -> (13/7,15/8) Hyperbolic Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(257,-204,160,-127) (11/14,4/5) -> (8/5,29/18) Hyperbolic Matrix(417,-340,352,-287) (13/16,9/11) -> (13/11,19/16) Hyperbolic Matrix(335,-276,176,-145) (14/17,19/23) -> (17/9,2/1) Hyperbolic Matrix(17,-16,16,-15) (7/8,1/1) -> (1/1,9/8) Parabolic Matrix(207,-268,112,-145) (9/7,13/10) -> (11/6,13/7) Hyperbolic Matrix(1599,-2168,992,-1345) (23/17,19/14) -> (29/18,79/49) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(3,2,-2,-1) Matrix(145,268,-112,-207) -> Matrix(1,0,-2,1) Matrix(257,468,352,641) -> Matrix(1,4,0,1) Matrix(31,56,-160,-289) -> Matrix(1,0,-2,1) Matrix(47,84,80,143) -> Matrix(1,2,0,1) Matrix(177,308,304,529) -> Matrix(3,-2,2,-1) Matrix(289,500,352,609) -> Matrix(3,-2,2,-1) Matrix(79,136,176,303) -> Matrix(1,0,0,1) Matrix(239,408,-816,-1393) -> Matrix(1,8,-2,-15) Matrix(223,380,544,927) -> Matrix(1,2,2,5) Matrix(321,544,416,705) -> Matrix(1,-2,0,1) Matrix(31,52,-96,-161) -> Matrix(1,0,-2,1) Matrix(17,28,-48,-79) -> Matrix(1,2,-2,-3) Matrix(81,128,112,177) -> Matrix(1,4,0,1) Matrix(97,152,-224,-351) -> Matrix(3,4,-4,-5) Matrix(49,76,176,273) -> Matrix(1,0,2,1) Matrix(113,164,144,209) -> Matrix(1,0,0,1) Matrix(161,232,-288,-415) -> Matrix(3,4,-4,-5) Matrix(17,24,80,113) -> Matrix(1,0,0,1) Matrix(49,68,-80,-111) -> Matrix(1,2,-2,-3) Matrix(287,376,-416,-545) -> Matrix(5,4,-4,-3) Matrix(175,228,208,271) -> Matrix(5,2,2,1) Matrix(31,40,-224,-289) -> Matrix(1,0,-4,1) Matrix(47,60,112,143) -> Matrix(1,0,2,1) Matrix(113,140,272,337) -> Matrix(3,2,4,3) Matrix(127,156,416,511) -> Matrix(1,0,2,1) Matrix(79,96,144,175) -> Matrix(1,0,2,1) Matrix(287,340,-352,-417) -> Matrix(3,2,-2,-1) Matrix(95,112,352,415) -> Matrix(1,0,4,1) Matrix(145,168,208,241) -> Matrix(1,2,0,1) Matrix(15,16,-16,-17) -> Matrix(1,0,0,1) Matrix(465,412,272,241) -> Matrix(1,-2,0,1) Matrix(65,56,224,193) -> Matrix(1,0,2,1) Matrix(47,40,-208,-177) -> Matrix(1,0,0,1) Matrix(111,92,-368,-305) -> Matrix(1,0,0,1) Matrix(609,500,352,289) -> Matrix(5,-2,-2,1) Matrix(609,496,512,417) -> Matrix(5,8,-2,-3) Matrix(129,104,160,129) -> Matrix(1,0,2,1) Matrix(111,88,-304,-241) -> Matrix(1,2,-2,-3) Matrix(209,164,144,113) -> Matrix(1,-2,0,1) Matrix(305,236,-1136,-879) -> Matrix(1,0,-4,1) Matrix(705,544,416,321) -> Matrix(1,-2,0,1) Matrix(95,72,-128,-97) -> Matrix(1,2,-2,-3) Matrix(239,176,368,271) -> Matrix(3,2,-2,-1) Matrix(175,128,-592,-433) -> Matrix(5,2,-8,-3) Matrix(177,128,112,81) -> Matrix(1,-2,0,1) Matrix(17,12,-112,-79) -> Matrix(1,0,-2,1) Matrix(305,212,-528,-367) -> Matrix(1,2,0,1) Matrix(673,464,512,353) -> Matrix(11,14,-4,-5) Matrix(65,44,96,65) -> Matrix(1,0,2,1) Matrix(209,136,272,177) -> Matrix(1,-2,0,1) Matrix(385,248,-992,-639) -> Matrix(1,2,-2,-3) Matrix(81,52,176,113) -> Matrix(1,2,0,1) Matrix(159,100,-256,-161) -> Matrix(5,6,-6,-7) Matrix(207,128,-752,-465) -> Matrix(5,4,-14,-11) Matrix(143,84,80,47) -> Matrix(3,2,-2,-1) Matrix(529,308,304,177) -> Matrix(9,-2,-4,1) Matrix(559,324,-1520,-881) -> Matrix(3,-2,-4,3) Matrix(257,148,224,129) -> Matrix(1,-6,0,1) Matrix(127,72,224,127) -> Matrix(3,4,2,3) Matrix(735,412,512,287) -> Matrix(25,22,-8,-7) Matrix(175,96,144,79) -> Matrix(3,2,-2,-1) Matrix(81,44,208,113) -> Matrix(1,0,4,1) Matrix(113,52,176,81) -> Matrix(3,2,-2,-1) Matrix(303,136,176,79) -> Matrix(1,-2,0,1) Matrix(127,56,288,127) -> Matrix(1,2,0,1) Matrix(799,348,512,223) -> Matrix(19,16,-6,-5) Matrix(143,60,112,47) -> Matrix(11,6,-2,-1) Matrix(337,140,272,113) -> Matrix(5,2,2,1) Matrix(513,212,-1856,-767) -> Matrix(1,0,0,1) Matrix(49,20,-272,-111) -> Matrix(1,0,0,1) Matrix(113,44,208,81) -> Matrix(1,0,2,1) Matrix(2559,992,-9248,-3585) -> Matrix(1,0,0,1) Matrix(2561,992,3968,1537) -> Matrix(1,0,2,1) Matrix(207,80,784,303) -> Matrix(1,0,4,1) Matrix(95,36,-256,-97) -> Matrix(1,2,-2,-3) Matrix(785,288,-2832,-1039) -> Matrix(3,2,-8,-5) Matrix(865,272,512,161) -> Matrix(3,2,-2,-1) Matrix(129,40,416,129) -> Matrix(1,0,2,1) Matrix(511,156,416,127) -> Matrix(1,0,2,1) Matrix(79,24,-688,-209) -> Matrix(1,0,4,1) Matrix(497,148,272,81) -> Matrix(7,4,-2,-1) Matrix(561,164,496,145) -> Matrix(35,18,-2,-1) Matrix(193,56,224,65) -> Matrix(17,8,2,1) Matrix(273,76,176,49) -> Matrix(3,2,-2,-1) Matrix(13985,3872,8672,2401) -> Matrix(5,-2,-2,1) Matrix(415,112,352,95) -> Matrix(15,4,-4,-1) Matrix(927,248,1312,351) -> Matrix(1,2,0,1) Matrix(31,8,-128,-33) -> Matrix(1,0,2,1) Matrix(241,56,624,145) -> Matrix(1,0,4,1) Matrix(543,124,416,95) -> Matrix(7,4,-2,-1) Matrix(113,24,80,17) -> Matrix(7,4,-2,-1) Matrix(929,176,512,97) -> Matrix(3,2,-2,-1) Matrix(65,12,352,65) -> Matrix(1,0,2,1) Matrix(463,80,272,47) -> Matrix(3,2,-2,-1) Matrix(31,4,-256,-33) -> Matrix(1,0,10,1) Matrix(223,24,288,31) -> Matrix(1,-2,0,1) Matrix(79,-12,112,-17) -> Matrix(3,-2,2,-1) Matrix(111,-20,272,-49) -> Matrix(1,0,2,1) Matrix(289,-56,160,-31) -> Matrix(1,-2,0,1) Matrix(177,-40,208,-47) -> Matrix(9,4,2,1) Matrix(33,-8,128,-31) -> Matrix(1,0,6,1) Matrix(879,-236,1136,-305) -> Matrix(9,-2,-4,1) Matrix(479,-132,352,-97) -> Matrix(1,0,-2,1) Matrix(1393,-408,816,-239) -> Matrix(1,-4,0,1) Matrix(433,-128,592,-175) -> Matrix(1,4,0,1) Matrix(305,-92,368,-111) -> Matrix(1,2,0,1) Matrix(161,-52,96,-31) -> Matrix(1,-2,0,1) Matrix(79,-28,48,-17) -> Matrix(1,-2,0,1) Matrix(337,-128,208,-79) -> Matrix(17,-2,-8,1) Matrix(639,-248,992,-385) -> Matrix(1,0,-4,1) Matrix(735,-304,544,-225) -> Matrix(1,0,-2,1) Matrix(351,-152,224,-97) -> Matrix(11,-8,-4,3) Matrix(415,-232,288,-161) -> Matrix(11,-8,-4,3) Matrix(367,-212,528,-305) -> Matrix(1,0,0,1) Matrix(1601,-928,992,-575) -> Matrix(5,-12,-2,5) Matrix(111,-68,80,-49) -> Matrix(1,-6,0,1) Matrix(241,-152,176,-111) -> Matrix(1,2,0,1) Matrix(5985,-3868,3712,-2399) -> Matrix(9,-2,-4,1) Matrix(545,-376,416,-287) -> Matrix(13,-16,-4,5) Matrix(1023,-724,544,-385) -> Matrix(19,-36,-10,19) Matrix(417,-296,224,-159) -> Matrix(9,-20,-4,9) Matrix(97,-72,128,-95) -> Matrix(1,-8,0,1) Matrix(257,-204,160,-127) -> Matrix(5,-2,-2,1) Matrix(417,-340,352,-287) -> Matrix(7,-10,-2,3) Matrix(335,-276,176,-145) -> Matrix(3,-4,-2,3) Matrix(17,-16,16,-15) -> Matrix(1,-2,0,1) Matrix(207,-268,112,-145) -> Matrix(5,18,-2,-7) Matrix(1599,-2168,992,-1345) -> Matrix(9,16,-4,-7) 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): 32 Degree of the the map X: 32 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 -1/1 (-1/1,0/1) 0 16 -7/8 -1/1 1 2 -6/7 0/1 1 16 -5/6 -1/1 1 8 -9/11 1/0 2 16 -13/16 -1/1 3 2 -4/5 0/1 1 16 -7/9 -1/2 2 16 -10/13 0/1 1 16 -3/4 -1/1 1 4 -5/7 -1/2 2 16 -7/10 0 8 -9/13 (-2/1,-1/1) 0 16 -11/16 -1/1 5 2 -2/3 0/1 1 16 -11/17 1/0 2 16 -9/14 0 8 -7/11 (-2/1,-1/1) 0 16 -5/8 -1/1 3 2 -3/5 -1/2 2 16 -4/7 -2/1 1 16 -9/16 -1/1 7 2 -5/9 (-1/1,-2/3) 0 16 -1/2 -1/1 1 8 -4/9 0/1 1 16 -7/16 -1/1 5 2 -3/7 (-1/1,-2/3) 0 16 -2/5 0/1 1 16 -7/18 0 8 -19/49 -1/2 2 16 -31/80 (-1/2,0/1) 0 2 -12/31 0/1 1 16 -5/13 (-1/1,0/1) 0 16 -3/8 -1/1 1 2 -1/3 -1/2 2 16 -5/16 (-1/2,0/1) 0 2 -4/13 0/1 1 16 -3/10 -1/1 1 8 -5/17 (-4/7,-1/2) 0 16 -7/24 -1/2 12 2 -2/7 -2/5 1 16 -3/11 (-1/3,0/1) 0 16 -4/15 0/1 1 16 -1/4 0/1 1 4 -1/5 (-1/2,0/1) 0 16 -3/16 (-1/2,0/1) 0 2 -2/11 0/1 1 16 -1/6 0 8 -1/7 -1/4 2 16 -1/8 0/1 5 2 -1/9 (0/1,1/1) 0 16 0/1 0/1 1 16 1/6 1/1 1 8 2/11 0/1 1 16 3/16 (0/1,1/0) 0 2 1/5 1/0 2 16 2/9 -2/3 1 16 3/13 (-1/3,0/1) 0 16 1/4 0/1 3 4 5/19 (0/1,1/3) 0 16 4/15 0/1 1 16 7/26 1/3 1 8 3/11 1/2 2 16 5/18 1/1 1 8 2/7 0/1 1 16 7/24 1/1 1 2 5/17 1/0 2 16 3/10 0 8 7/23 1/2 2 16 4/13 0/1 1 16 5/16 (0/1,1/0) 0 2 1/3 (0/1,1/0) 0 16 3/8 0/1 4 2 5/13 1/4 2 16 12/31 0/1 1 16 7/18 1/3 1 8 2/5 0/1 1 16 9/22 1/3 1 8 7/17 (1/2,2/3) 0 16 12/29 2/3 1 16 5/12 1/1 1 4 3/7 1/2 2 16 7/16 1/1 5 2 4/9 2/1 1 16 5/11 (0/1,1/1) 0 16 1/2 0 8 6/11 0/1 1 16 5/9 1/2 2 16 9/16 1/1 7 2 4/7 2/1 1 16 11/19 3/2 2 16 18/31 2/1 1 16 7/12 2/1 1 4 3/5 (2/1,1/0) 0 16 5/8 1/0 4 2 7/11 1/0 2 16 9/14 -1/1 1 8 20/31 0/1 1 16 31/48 (0/1,1/0) 0 2 11/17 (0/1,1/0) 0 16 2/3 0/1 1 16 11/16 1/1 5 2 9/13 3/2 2 16 16/23 2/1 1 16 7/10 1/1 1 8 12/17 2/1 1 16 29/41 11/6 2 16 17/24 2/1 7 2 5/7 (2/1,3/1) 0 16 8/11 4/1 1 16 19/26 0 8 11/15 1/0 2 16 3/4 1/0 4 4 13/17 1/0 2 16 10/13 -2/1 1 16 17/22 -3/1 1 8 24/31 -2/1 1 16 7/9 (-2/1,-1/1) 0 16 11/14 -1/1 1 8 4/5 0/1 1 16 13/16 1/1 3 2 9/11 (1/1,2/1) 0 16 14/17 2/1 1 16 19/23 5/2 2 16 5/6 0 8 11/13 (3/1,4/1) 0 16 6/7 6/1 1 16 7/8 1/0 12 2 1/1 1/0 2 16 1/0 -1/1 1 2 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(15,14,-16,-15) (-1/1,-7/8) -> (-1/1,-7/8) Reflection Matrix(65,56,224,193) (-7/8,-6/7) -> (2/7,7/24) Hyperbolic Matrix(145,122,208,175) (-6/7,-5/6) -> (16/23,7/10) Glide Reflection Matrix(95,78,352,289) (-5/6,-9/11) -> (7/26,3/11) Glide Reflection Matrix(287,234,-352,-287) (-9/11,-13/16) -> (-9/11,-13/16) Reflection Matrix(129,104,160,129) (-13/16,-4/5) -> (4/5,13/16) Hyperbolic Matrix(79,62,144,113) (-4/5,-7/9) -> (6/11,5/9) Glide Reflection Matrix(127,98,416,321) (-7/9,-10/13) -> (7/23,4/13) Glide Reflection Matrix(113,86,272,207) (-10/13,-3/4) -> (12/29,5/12) Glide Reflection Matrix(47,34,112,81) (-3/4,-5/7) -> (5/12,3/7) Glide Reflection Matrix(17,12,-112,-79) (-5/7,-7/10) -> (-1/6,-1/7) Hyperbolic Matrix(175,122,208,145) (-7/10,-9/13) -> (5/6,11/13) Glide Reflection Matrix(287,198,-416,-287) (-9/13,-11/16) -> (-9/13,-11/16) Reflection Matrix(65,44,96,65) (-11/16,-2/3) -> (2/3,11/16) Hyperbolic Matrix(209,136,272,177) (-2/3,-11/17) -> (13/17,10/13) Hyperbolic Matrix(385,248,-992,-639) (-11/17,-9/14) -> (-7/18,-19/49) Hyperbolic Matrix(81,52,176,113) (-9/14,-7/11) -> (5/11,1/2) Hyperbolic Matrix(111,70,-176,-111) (-7/11,-5/8) -> (-7/11,-5/8) Reflection Matrix(49,30,-80,-49) (-5/8,-3/5) -> (-5/8,-3/5) Reflection Matrix(17,10,80,47) (-3/5,-4/7) -> (1/5,2/9) Glide Reflection Matrix(127,72,224,127) (-4/7,-9/16) -> (9/16,4/7) Hyperbolic Matrix(161,90,-288,-161) (-9/16,-5/9) -> (-9/16,-5/9) Reflection Matrix(113,62,144,79) (-5/9,-1/2) -> (7/9,11/14) Glide Reflection Matrix(49,22,176,79) (-1/2,-4/9) -> (5/18,2/7) Glide Reflection Matrix(127,56,288,127) (-4/9,-7/16) -> (7/16,4/9) Hyperbolic Matrix(97,42,-224,-97) (-7/16,-3/7) -> (-7/16,-3/7) Reflection Matrix(81,34,112,47) (-3/7,-2/5) -> (5/7,8/11) Glide Reflection Matrix(113,44,208,81) (-2/5,-7/18) -> (1/2,6/11) Hyperbolic Matrix(3039,1178,-7840,-3039) (-19/49,-31/80) -> (-19/49,-31/80) Reflection Matrix(2561,992,3968,1537) (-31/80,-12/31) -> (20/31,31/48) Hyperbolic Matrix(207,80,784,303) (-12/31,-5/13) -> (5/19,4/15) Hyperbolic Matrix(79,30,-208,-79) (-5/13,-3/8) -> (-5/13,-3/8) Reflection Matrix(17,6,-48,-17) (-3/8,-1/3) -> (-3/8,-1/3) Reflection Matrix(31,10,-96,-31) (-1/3,-5/16) -> (-1/3,-5/16) Reflection Matrix(129,40,416,129) (-5/16,-4/13) -> (4/13,5/16) Hyperbolic Matrix(321,98,416,127) (-4/13,-3/10) -> (10/13,17/22) Glide Reflection Matrix(223,66,544,161) (-3/10,-5/17) -> (9/22,7/17) Glide Reflection Matrix(239,70,-816,-239) (-5/17,-7/24) -> (-5/17,-7/24) Reflection Matrix(193,56,224,65) (-7/24,-2/7) -> (6/7,7/8) Hyperbolic Matrix(79,22,176,49) (-2/7,-3/11) -> (4/9,5/11) Glide Reflection Matrix(289,78,352,95) (-3/11,-4/15) -> (9/11,14/17) Glide Reflection Matrix(177,46,304,79) (-4/15,-1/4) -> (18/31,7/12) Glide Reflection Matrix(47,10,80,17) (-1/4,-1/5) -> (7/12,3/5) Glide Reflection Matrix(31,6,-160,-31) (-1/5,-3/16) -> (-1/5,-3/16) Reflection Matrix(65,12,352,65) (-3/16,-2/11) -> (2/11,3/16) Hyperbolic Matrix(257,46,352,63) (-2/11,-1/6) -> (8/11,19/26) Glide Reflection Matrix(15,2,-112,-15) (-1/7,-1/8) -> (-1/7,-1/8) Reflection Matrix(17,2,-144,-17) (-1/8,-1/9) -> (-1/8,-1/9) Reflection Matrix(223,24,288,31) (-1/9,0/1) -> (24/31,7/9) Hyperbolic Matrix(79,-12,112,-17) (0/1,1/6) -> (7/10,12/17) Hyperbolic Matrix(111,-20,272,-49) (1/6,2/11) -> (2/5,9/22) Hyperbolic Matrix(31,-6,160,-31) (3/16,1/5) -> (3/16,1/5) Reflection Matrix(177,-40,208,-47) (2/9,3/13) -> (11/13,6/7) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(879,-236,1136,-305) (4/15,7/26) -> (17/22,24/31) Hyperbolic Matrix(225,-62,352,-97) (3/11,5/18) -> (7/11,9/14) Glide Reflection Matrix(239,-70,816,-239) (7/24,5/17) -> (7/24,5/17) Reflection Matrix(433,-128,592,-175) (5/17,3/10) -> (19/26,11/15) Hyperbolic Matrix(305,-92,368,-111) (3/10,7/23) -> (19/23,5/6) Hyperbolic Matrix(31,-10,96,-31) (5/16,1/3) -> (5/16,1/3) Reflection Matrix(17,-6,48,-17) (1/3,3/8) -> (1/3,3/8) Reflection Matrix(79,-30,208,-79) (3/8,5/13) -> (3/8,5/13) Reflection Matrix(575,-222,992,-383) (5/13,12/31) -> (11/19,18/31) Glide Reflection Matrix(639,-248,992,-385) (12/31,7/18) -> (9/14,20/31) Hyperbolic Matrix(127,-50,160,-63) (7/18,2/5) -> (11/14,4/5) Glide Reflection Matrix(353,-146,544,-225) (7/17,12/29) -> (11/17,2/3) Glide Reflection Matrix(97,-42,224,-97) (3/7,7/16) -> (3/7,7/16) Reflection Matrix(161,-90,288,-161) (5/9,9/16) -> (5/9,9/16) Reflection Matrix(367,-212,528,-305) (4/7,11/19) -> (9/13,16/23) Hyperbolic Matrix(49,-30,80,-49) (3/5,5/8) -> (3/5,5/8) Reflection Matrix(111,-70,176,-111) (5/8,7/11) -> (5/8,7/11) Reflection Matrix(1055,-682,1632,-1055) (31/48,11/17) -> (31/48,11/17) Reflection Matrix(287,-198,416,-287) (11/16,9/13) -> (11/16,9/13) Reflection Matrix(897,-634,1088,-769) (12/17,29/41) -> (14/17,19/23) Glide Reflection Matrix(1393,-986,1968,-1393) (29/41,17/24) -> (29/41,17/24) Reflection Matrix(239,-170,336,-239) (17/24,5/7) -> (17/24,5/7) Reflection Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(287,-234,352,-287) (13/16,9/11) -> (13/16,9/11) Reflection Matrix(15,-14,16,-15) (7/8,1/1) -> (7/8,1/1) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(15,14,-16,-15) -> Matrix(-1,0,2,1) (-1/1,-7/8) -> (-1/1,0/1) Matrix(65,56,224,193) -> Matrix(1,0,2,1) 0/1 Matrix(145,122,208,175) -> Matrix(3,2,2,1) Matrix(95,78,352,289) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(287,234,-352,-287) -> Matrix(1,2,0,-1) (-9/11,-13/16) -> (-1/1,1/0) Matrix(129,104,160,129) -> Matrix(1,0,2,1) 0/1 Matrix(79,62,144,113) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(127,98,416,321) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(113,86,272,207) -> Matrix(1,2,2,3) Matrix(47,34,112,81) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(17,12,-112,-79) -> Matrix(1,0,-2,1) 0/1 Matrix(175,122,208,145) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(287,198,-416,-287) -> Matrix(3,4,-2,-3) (-9/13,-11/16) -> (-2/1,-1/1) Matrix(65,44,96,65) -> Matrix(1,0,2,1) 0/1 Matrix(209,136,272,177) -> Matrix(1,-2,0,1) 1/0 Matrix(385,248,-992,-639) -> Matrix(1,2,-2,-3) -1/1 Matrix(81,52,176,113) -> Matrix(1,2,0,1) 1/0 Matrix(111,70,-176,-111) -> Matrix(3,4,-2,-3) (-7/11,-5/8) -> (-2/1,-1/1) Matrix(49,30,-80,-49) -> Matrix(3,2,-4,-3) (-5/8,-3/5) -> (-1/1,-1/2) Matrix(17,10,80,47) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(127,72,224,127) -> Matrix(3,4,2,3) Matrix(161,90,-288,-161) -> Matrix(5,4,-6,-5) (-9/16,-5/9) -> (-1/1,-2/3) Matrix(113,62,144,79) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(49,22,176,79) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(127,56,288,127) -> Matrix(1,2,0,1) 1/0 Matrix(97,42,-224,-97) -> Matrix(5,4,-6,-5) (-7/16,-3/7) -> (-1/1,-2/3) Matrix(81,34,112,47) -> Matrix(7,4,2,1) Matrix(113,44,208,81) -> Matrix(1,0,2,1) 0/1 Matrix(3039,1178,-7840,-3039) -> Matrix(-1,0,4,1) (-19/49,-31/80) -> (-1/2,0/1) Matrix(2561,992,3968,1537) -> Matrix(1,0,2,1) 0/1 Matrix(207,80,784,303) -> Matrix(1,0,4,1) 0/1 Matrix(79,30,-208,-79) -> Matrix(-1,0,2,1) (-5/13,-3/8) -> (-1/1,0/1) Matrix(17,6,-48,-17) -> Matrix(3,2,-4,-3) (-3/8,-1/3) -> (-1/1,-1/2) Matrix(31,10,-96,-31) -> Matrix(-1,0,4,1) (-1/3,-5/16) -> (-1/2,0/1) Matrix(129,40,416,129) -> Matrix(1,0,2,1) 0/1 Matrix(321,98,416,127) -> Matrix(5,2,-2,-1) Matrix(223,66,544,161) -> Matrix(3,2,8,5) Matrix(239,70,-816,-239) -> Matrix(15,8,-28,-15) (-5/17,-7/24) -> (-4/7,-1/2) Matrix(193,56,224,65) -> Matrix(17,8,2,1) Matrix(79,22,176,49) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(289,78,352,95) -> Matrix(7,2,4,1) Matrix(177,46,304,79) -> Matrix(7,2,4,1) Matrix(47,10,80,17) -> Matrix(3,2,2,1) Matrix(31,6,-160,-31) -> Matrix(-1,0,4,1) (-1/5,-3/16) -> (-1/2,0/1) Matrix(65,12,352,65) -> Matrix(1,0,2,1) 0/1 Matrix(257,46,352,63) -> Matrix(7,4,2,1) Matrix(15,2,-112,-15) -> Matrix(-1,0,8,1) (-1/7,-1/8) -> (-1/4,0/1) Matrix(17,2,-144,-17) -> Matrix(1,0,2,-1) (-1/8,-1/9) -> (0/1,1/1) Matrix(223,24,288,31) -> Matrix(1,-2,0,1) 1/0 Matrix(79,-12,112,-17) -> Matrix(3,-2,2,-1) 1/1 Matrix(111,-20,272,-49) -> Matrix(1,0,2,1) 0/1 Matrix(31,-6,160,-31) -> Matrix(1,0,0,-1) (3/16,1/5) -> (0/1,1/0) Matrix(177,-40,208,-47) -> Matrix(9,4,2,1) Matrix(33,-8,128,-31) -> Matrix(1,0,6,1) 0/1 Matrix(879,-236,1136,-305) -> Matrix(9,-2,-4,1) Matrix(225,-62,352,-97) -> Matrix(3,-2,-2,1) Matrix(239,-70,816,-239) -> Matrix(-1,2,0,1) (7/24,5/17) -> (1/1,1/0) Matrix(433,-128,592,-175) -> Matrix(1,4,0,1) 1/0 Matrix(305,-92,368,-111) -> Matrix(1,2,0,1) 1/0 Matrix(31,-10,96,-31) -> Matrix(1,0,0,-1) (5/16,1/3) -> (0/1,1/0) Matrix(17,-6,48,-17) -> Matrix(1,0,0,-1) (1/3,3/8) -> (0/1,1/0) Matrix(79,-30,208,-79) -> Matrix(1,0,8,-1) (3/8,5/13) -> (0/1,1/4) Matrix(575,-222,992,-383) -> Matrix(5,-2,2,-1) Matrix(639,-248,992,-385) -> Matrix(1,0,-4,1) 0/1 Matrix(127,-50,160,-63) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(353,-146,544,-225) -> Matrix(3,-2,-2,1) Matrix(97,-42,224,-97) -> Matrix(3,-2,4,-3) (3/7,7/16) -> (1/2,1/1) Matrix(161,-90,288,-161) -> Matrix(3,-2,4,-3) (5/9,9/16) -> (1/2,1/1) Matrix(367,-212,528,-305) -> Matrix(1,0,0,1) Matrix(49,-30,80,-49) -> Matrix(-1,4,0,1) (3/5,5/8) -> (2/1,1/0) Matrix(111,-70,176,-111) -> Matrix(1,4,0,-1) (5/8,7/11) -> (-2/1,1/0) Matrix(1055,-682,1632,-1055) -> Matrix(1,0,0,-1) (31/48,11/17) -> (0/1,1/0) Matrix(287,-198,416,-287) -> Matrix(5,-6,4,-5) (11/16,9/13) -> (1/1,3/2) Matrix(897,-634,1088,-769) -> Matrix(7,-12,4,-7) *** -> (3/2,2/1) Matrix(1393,-986,1968,-1393) -> Matrix(23,-44,12,-23) (29/41,17/24) -> (11/6,2/1) Matrix(239,-170,336,-239) -> Matrix(5,-12,2,-5) (17/24,5/7) -> (2/1,3/1) Matrix(97,-72,128,-95) -> Matrix(1,-8,0,1) 1/0 Matrix(287,-234,352,-287) -> Matrix(3,-4,2,-3) (13/16,9/11) -> (1/1,2/1) Matrix(15,-14,16,-15) -> Matrix(1,0,0,-1) (7/8,1/1) -> (0/1,1/0) Matrix(-1,2,0,1) -> Matrix(1,2,0,-1) (1/1,1/0) -> (-1/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.