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 -9/8 -1/1 -5/6 -3/4 -1/2 -17/48 -1/3 -1/4 -1/5 -1/6 -2/13 -1/7 -2/15 0/1 1/8 1/7 1/6 2/11 3/16 1/5 2/9 1/4 4/15 2/7 4/13 5/16 1/3 4/11 3/8 2/5 7/16 4/9 1/2 9/16 4/7 5/8 2/3 11/16 3/4 4/5 13/16 5/6 7/8 1/1 5/4 4/3 11/8 3/2 13/8 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 1/1 -13/7 1/1 -11/6 0/1 -20/11 1/0 -9/5 1/1 -16/9 1/2 -23/13 1/1 -7/4 0/1 -12/7 1/2 -17/10 0/1 2/1 -22/13 -1/1 0/1 -5/3 1/1 -18/11 -1/1 0/1 -13/8 0/1 -8/5 1/2 -11/7 -1/1 -14/9 0/1 1/3 -3/2 0/1 -13/9 1/1 -10/7 0/1 1/3 -7/5 1/1 -18/13 0/1 1/1 -11/8 0/1 -4/3 1/2 -17/13 1/1 -13/10 0/1 -22/17 3/7 1/2 -9/7 3/5 -14/11 2/3 1/1 -19/15 1/1 -5/4 1/1 -6/5 1/2 1/1 -13/11 1/1 -7/6 0/1 2/3 -8/7 3/4 -9/8 1/1 -1/1 1/1 -5/6 2/1 -9/11 1/1 -22/27 1/1 1/0 -13/16 0/1 2/1 -4/5 1/0 -7/9 1/3 -10/13 2/3 1/1 -3/4 1/1 -14/19 1/1 4/3 -11/15 1/1 -19/26 4/3 -8/11 3/2 -13/18 2/1 -5/7 1/1 -22/31 1/1 2/1 -17/24 2/1 -12/17 1/0 -7/10 0/1 2/1 -16/23 3/2 -9/13 1/1 -20/29 1/0 -11/16 0/1 2/1 -2/3 1/1 1/0 -5/8 1/1 -8/13 5/4 -19/31 1/1 -11/18 4/3 -3/5 1/1 -13/22 4/3 -10/17 3/2 5/3 -17/29 5/3 -7/12 2/1 -4/7 3/2 -9/16 2/1 -14/25 2/1 7/3 -5/9 3/1 -6/11 1/1 2/1 -7/13 3/1 -1/2 0/1 2/1 -7/15 1/1 -6/13 1/1 2/1 -5/11 1/1 -4/9 3/2 -7/16 2/1 -10/23 2/1 11/5 -3/7 3/1 -8/19 5/2 -13/31 3/1 -5/12 3/1 -2/5 3/1 1/0 -3/8 1/0 -4/11 1/0 -5/14 0/1 -11/31 1/1 -17/48 0/1 2/1 -6/17 1/1 1/0 -1/3 1/1 -6/19 5/3 2/1 -5/16 2/1 -4/13 5/2 -7/23 3/1 -3/10 2/1 -5/17 3/1 -12/41 17/6 -7/24 3/1 -2/7 3/1 4/1 -3/11 5/1 -7/26 4/1 6/1 -4/15 1/0 -1/4 1/0 -4/17 1/0 -15/64 -4/1 -2/1 -11/47 -3/1 -7/30 -4/1 -2/1 -3/13 -1/1 -5/22 -2/1 -7/31 -1/1 -9/40 -1/1 -2/9 -1/1 0/1 -3/14 0/1 -1/5 1/1 -4/21 3/2 -3/16 2/1 -2/11 2/1 3/1 -3/17 3/1 -4/23 7/2 -1/6 2/1 4/1 -2/13 4/1 5/1 -1/7 7/1 -2/15 13/1 1/0 -1/8 1/0 0/1 1/0 1/8 1/0 1/7 -7/1 1/6 -4/1 -2/1 3/17 -3/1 2/11 -3/1 -2/1 3/16 -2/1 1/5 -1/1 3/14 0/1 2/9 0/1 1/1 5/22 2/1 3/13 1/1 1/4 1/0 5/19 -7/1 4/15 1/0 3/11 -5/1 2/7 -4/1 -3/1 3/10 -2/1 4/13 -5/2 5/16 -2/1 1/3 -1/1 6/17 -1/1 1/0 5/14 0/1 4/11 1/0 3/8 1/0 2/5 -3/1 1/0 5/12 -3/1 13/31 -3/1 8/19 -5/2 11/26 -2/1 3/7 -3/1 7/16 -2/1 4/9 -3/2 5/11 -1/1 1/2 -2/1 0/1 6/11 -2/1 -1/1 5/9 -3/1 9/16 -2/1 4/7 -3/2 7/12 -2/1 17/29 -5/3 10/17 -5/3 -3/2 3/5 -1/1 11/18 -4/3 30/49 -5/4 -1/1 49/80 -4/3 -6/5 19/31 -1/1 8/13 -5/4 5/8 -1/1 2/3 -1/1 1/0 11/16 -2/1 0/1 9/13 -1/1 16/23 -3/2 23/33 -1/1 7/10 -2/1 0/1 19/27 -1/1 12/17 1/0 17/24 -2/1 5/7 -1/1 13/18 -2/1 8/11 -3/2 19/26 -4/3 30/41 -6/5 -1/1 11/15 -1/1 3/4 -1/1 13/17 -1/1 10/13 -1/1 -2/3 17/22 -2/3 -4/7 7/9 -1/3 4/5 1/0 13/16 -2/1 0/1 9/11 -1/1 14/17 1/1 1/0 5/6 -2/1 6/7 -4/3 -1/1 7/8 -1/1 8/9 -3/4 1/1 -1/1 7/6 -2/3 0/1 13/11 -1/1 19/16 -2/3 0/1 6/5 -1/1 -1/2 5/4 -1/1 19/15 -1/1 14/11 -1/1 -2/3 9/7 -3/5 31/24 -1/2 22/17 -1/2 -3/7 13/10 0/1 17/13 -1/1 21/16 -2/3 0/1 4/3 -1/2 11/8 0/1 18/13 -1/1 0/1 43/31 -1/1 25/18 -2/3 0/1 7/5 -1/1 10/7 -1/3 0/1 23/16 0/1 13/9 -1/1 3/2 0/1 14/9 -1/3 0/1 25/16 0/1 11/7 1/1 8/5 -1/2 13/8 0/1 18/11 0/1 1/1 23/14 0/1 2/1 51/31 1/1 79/48 0/1 2/1 28/17 1/0 5/3 -1/1 27/16 0/1 22/13 0/1 1/1 17/10 -2/1 0/1 29/17 -1/1 70/41 -4/3 -1/1 41/24 -1/1 12/7 -1/2 7/4 0/1 23/13 -1/1 16/9 -1/2 9/5 -1/1 29/16 0/1 20/11 1/0 11/6 0/1 13/7 -1/1 15/8 0/1 2/1 -1/1 0/1 1/0 0/1 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(159,296,-224,-417) (-2/1,-13/7) -> (-5/7,-22/31) Hyperbolic Matrix(95,176,224,415) (-13/7,-11/6) -> (11/26,3/7) 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(65,116,144,257) (-9/5,-16/9) -> (4/9,5/11) Hyperbolic Matrix(289,512,416,737) (-16/9,-23/13) -> (9/13,16/23) Hyperbolic Matrix(159,280,272,479) (-23/13,-7/4) -> (7/12,17/29) Hyperbolic Matrix(65,112,112,193) (-7/4,-12/7) -> (4/7,7/12) Hyperbolic Matrix(129,220,-112,-191) (-12/7,-17/10) -> (-7/6,-8/7) 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(95,156,-176,-289) (-5/3,-18/11) -> (-6/11,-7/13) Hyperbolic Matrix(287,468,176,287) (-18/11,-13/8) -> (13/8,18/11) Hyperbolic Matrix(129,208,80,129) (-13/8,-8/5) -> (8/5,13/8) Hyperbolic Matrix(63,100,80,127) (-8/5,-11/7) -> (7/9,4/5) Hyperbolic Matrix(97,152,-224,-351) (-11/7,-14/9) -> (-10/23,-3/7) Hyperbolic Matrix(31,48,144,223) (-14/9,-3/2) -> (3/14,2/9) Hyperbolic Matrix(127,184,176,255) (-3/2,-13/9) -> (5/7,13/18) Hyperbolic Matrix(161,232,-288,-415) (-13/9,-10/7) -> (-14/25,-5/9) Hyperbolic Matrix(31,44,112,159) (-10/7,-7/5) -> (3/11,2/7) Hyperbolic Matrix(95,132,-208,-289) (-7/5,-18/13) -> (-6/13,-5/11) Hyperbolic Matrix(287,396,208,287) (-18/13,-11/8) -> (11/8,18/13) Hyperbolic Matrix(65,88,48,65) (-11/8,-4/3) -> (4/3,11/8) Hyperbolic Matrix(287,376,-416,-545) (-4/3,-17/13) -> (-9/13,-20/29) Hyperbolic Matrix(95,124,416,543) (-17/13,-13/10) -> (5/22,3/13) Hyperbolic Matrix(225,292,272,353) (-13/10,-22/17) -> (14/17,5/6) Hyperbolic Matrix(31,40,-224,-289) (-22/17,-9/7) -> (-1/7,-2/15) Hyperbolic Matrix(97,124,176,225) (-9/7,-14/11) -> (6/11,5/9) Hyperbolic Matrix(63,80,352,447) (-14/11,-19/15) -> (3/17,2/11) Hyperbolic Matrix(127,160,304,383) (-19/15,-5/4) -> (5/12,13/31) Hyperbolic Matrix(33,40,80,97) (-5/4,-6/5) -> (2/5,5/12) Hyperbolic Matrix(287,340,-352,-417) (-6/5,-13/11) -> (-9/11,-22/27) Hyperbolic Matrix(191,224,272,319) (-13/11,-7/6) -> (7/10,19/27) Hyperbolic Matrix(383,436,224,255) (-8/7,-9/8) -> (41/24,12/7) Hyperbolic Matrix(65,72,-288,-319) (-9/8,-1/1) -> (-7/31,-9/40) Hyperbolic Matrix(33,28,-112,-95) (-1/1,-5/6) -> (-3/10,-5/17) Hyperbolic Matrix(161,132,-272,-223) (-5/6,-9/11) -> (-3/5,-13/22) 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(127,100,80,63) (-4/5,-7/9) -> (11/7,8/5) Hyperbolic Matrix(31,24,-208,-161) (-7/9,-10/13) -> (-2/13,-1/7) Hyperbolic Matrix(95,72,-128,-97) (-10/13,-3/4) -> (-3/4,-14/19) Parabolic Matrix(223,164,-480,-353) (-14/19,-11/15) -> (-7/15,-6/13) Hyperbolic Matrix(257,188,-1136,-831) (-11/15,-19/26) -> (-5/22,-7/31) Hyperbolic Matrix(641,468,352,257) (-19/26,-8/11) -> (20/11,11/6) Hyperbolic Matrix(127,92,352,255) (-8/11,-13/18) -> (5/14,4/11) Hyperbolic Matrix(255,184,176,127) (-13/18,-5/7) -> (13/9,3/2) Hyperbolic Matrix(513,364,272,193) (-22/31,-17/24) -> (15/8,2/1) Hyperbolic Matrix(577,408,816,577) (-17/24,-12/17) -> (12/17,17/24) Hyperbolic Matrix(159,112,-592,-417) (-12/17,-7/10) -> (-7/26,-4/15) Hyperbolic Matrix(63,44,-368,-257) (-7/10,-16/23) -> (-4/23,-1/6) Hyperbolic Matrix(737,512,416,289) (-16/23,-9/13) -> (23/13,16/9) 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(31,20,48,31) (-2/3,-5/8) -> (5/8,2/3) Hyperbolic Matrix(129,80,208,129) (-5/8,-8/13) -> (8/13,5/8) Hyperbolic Matrix(417,256,992,609) (-8/13,-19/31) -> (13/31,8/19) Hyperbolic Matrix(353,216,-992,-607) (-19/31,-11/18) -> (-5/14,-11/31) Hyperbolic Matrix(33,20,160,97) (-11/18,-3/5) -> (1/5,3/14) Hyperbolic Matrix(705,416,544,321) (-13/22,-10/17) -> (22/17,13/10) Hyperbolic Matrix(191,112,544,319) (-10/17,-17/29) -> (1/3,6/17) Hyperbolic Matrix(479,280,272,159) (-17/29,-7/12) -> (7/4,23/13) Hyperbolic Matrix(193,112,112,65) (-7/12,-4/7) -> (12/7,7/4) 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(225,124,176,97) (-5/9,-6/11) -> (14/11,9/7) Hyperbolic Matrix(97,52,-416,-223) (-7/13,-1/2) -> (-7/30,-3/13) Hyperbolic Matrix(127,60,-544,-257) (-1/2,-7/15) -> (-11/47,-7/30) Hyperbolic Matrix(257,116,144,65) (-5/11,-4/9) -> (16/9,9/5) 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(161,68,-528,-223) (-3/7,-8/19) -> (-4/13,-7/23) Hyperbolic Matrix(609,256,992,417) (-8/19,-13/31) -> (19/31,8/13) Hyperbolic Matrix(383,160,304,127) (-13/31,-5/12) -> (5/4,19/15) Hyperbolic Matrix(97,40,80,33) (-5/12,-2/5) -> (6/5,5/4) Hyperbolic Matrix(31,12,80,31) (-2/5,-3/8) -> (3/8,2/5) Hyperbolic Matrix(65,24,176,65) (-3/8,-4/11) -> (4/11,3/8) Hyperbolic Matrix(255,92,352,127) (-4/11,-5/14) -> (13/18,8/11) Hyperbolic Matrix(993,352,-4240,-1503) (-11/31,-17/48) -> (-15/64,-11/47) Hyperbolic Matrix(2273,804,3712,1313) (-17/48,-6/17) -> (30/49,49/80) Hyperbolic Matrix(319,112,544,191) (-6/17,-1/3) -> (17/29,10/17) 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(383,116,208,63) (-7/23,-3/10) -> (11/6,13/7) Hyperbolic Matrix(1215,356,1744,511) (-5/17,-12/41) -> (16/23,23/33) Hyperbolic Matrix(479,140,544,159) (-12/41,-7/24) -> (7/8,8/9) Hyperbolic Matrix(193,56,224,65) (-7/24,-2/7) -> (6/7,7/8) Hyperbolic Matrix(159,44,112,31) (-2/7,-3/11) -> (7/5,10/7) Hyperbolic Matrix(415,112,352,95) (-3/11,-7/26) -> (7/6,13/11) Hyperbolic Matrix(31,8,-128,-33) (-4/15,-1/4) -> (-1/4,-4/17) Parabolic Matrix(3135,736,1904,447) (-4/17,-15/64) -> (79/48,28/17) Hyperbolic Matrix(543,124,416,95) (-3/13,-5/22) -> (13/10,17/13) Hyperbolic Matrix(3169,712,1856,417) (-9/40,-2/9) -> (70/41,41/24) Hyperbolic Matrix(223,48,144,31) (-2/9,-3/14) -> (3/2,14/9) Hyperbolic Matrix(97,20,160,33) (-3/14,-1/5) -> (3/5,11/18) 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(447,80,352,63) (-2/11,-3/17) -> (19/15,14/11) Hyperbolic Matrix(159,28,176,31) (-3/17,-4/23) -> (8/9,1/1) Hyperbolic Matrix(353,56,208,33) (-1/6,-2/13) -> (22/13,17/10) Hyperbolic Matrix(641,84,496,65) (-2/15,-1/8) -> (31/24,22/17) Hyperbolic Matrix(1,0,16,1) (-1/8,0/1) -> (0/1,1/8) Parabolic Matrix(289,-40,224,-31) (1/8,1/7) -> (9/7,31/24) Hyperbolic Matrix(161,-24,208,-31) (1/7,1/6) -> (17/22,7/9) Hyperbolic Matrix(257,-44,368,-63) (1/6,3/17) -> (23/33,7/10) Hyperbolic Matrix(289,-56,160,-31) (3/16,1/5) -> (9/5,29/16) Hyperbolic Matrix(831,-188,1136,-257) (2/9,5/22) -> (19/26,30/41) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(607,-160,368,-97) (5/19,4/15) -> (28/17,5/3) Hyperbolic Matrix(417,-112,592,-159) (4/15,3/11) -> (19/27,12/17) Hyperbolic Matrix(95,-28,112,-33) (2/7,3/10) -> (5/6,6/7) Hyperbolic Matrix(223,-68,528,-161) (3/10,4/13) -> (8/19,11/26) Hyperbolic Matrix(161,-52,96,-31) (5/16,1/3) -> (5/3,27/16) Hyperbolic Matrix(607,-216,992,-353) (6/17,5/14) -> (11/18,30/49) Hyperbolic Matrix(351,-152,224,-97) (3/7,7/16) -> (25/16,11/7) Hyperbolic Matrix(289,-132,208,-95) (5/11,1/2) -> (25/18,7/5) Hyperbolic Matrix(289,-156,176,-95) (1/2,6/11) -> (18/11,23/14) Hyperbolic Matrix(415,-232,288,-161) (5/9,9/16) -> (23/16,13/9) Hyperbolic Matrix(223,-132,272,-161) (10/17,3/5) -> (9/11,14/17) Hyperbolic Matrix(6529,-4000,3968,-2431) (49/80,19/31) -> (51/31,79/48) Hyperbolic Matrix(545,-376,416,-287) (11/16,9/13) -> (17/13,21/16) Hyperbolic Matrix(417,-296,224,-159) (17/24,5/7) -> (13/7,15/8) Hyperbolic Matrix(2239,-1640,1312,-961) (30/41,11/15) -> (29/17,70/41) Hyperbolic Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(865,-664,624,-479) (13/17,10/13) -> (18/13,43/31) Hyperbolic Matrix(417,-340,352,-287) (13/16,9/11) -> (13/11,19/16) Hyperbolic Matrix(191,-220,112,-129) (1/1,7/6) -> (17/10,29/17) Hyperbolic Matrix(1631,-2264,992,-1377) (43/31,25/18) -> (23/14,51/31) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,0,-2,1) Matrix(159,296,-224,-417) -> Matrix(3,-2,2,-1) Matrix(95,176,224,415) -> Matrix(5,-2,-2,1) Matrix(257,468,352,641) -> Matrix(3,-4,-2,3) Matrix(31,56,-160,-289) -> Matrix(3,-2,2,-1) Matrix(65,116,144,257) -> Matrix(1,-2,0,1) Matrix(289,512,416,737) -> Matrix(1,-2,0,1) Matrix(159,280,272,479) -> Matrix(3,2,-2,-1) Matrix(65,112,112,193) -> Matrix(1,-2,0,1) Matrix(129,220,-112,-191) -> Matrix(1,-2,2,-3) Matrix(321,544,416,705) -> Matrix(1,2,-2,-3) Matrix(31,52,-96,-161) -> Matrix(3,-2,2,-1) Matrix(95,156,-176,-289) -> Matrix(1,2,0,1) Matrix(287,468,176,287) -> Matrix(1,0,2,1) Matrix(129,208,80,129) -> Matrix(1,0,-4,1) Matrix(63,100,80,127) -> Matrix(1,0,-2,1) Matrix(97,152,-224,-351) -> Matrix(5,2,2,1) Matrix(31,48,144,223) -> Matrix(1,0,-2,1) Matrix(127,184,176,255) -> Matrix(1,-2,0,1) Matrix(161,232,-288,-415) -> Matrix(1,2,0,1) Matrix(31,44,112,159) -> Matrix(9,-4,-2,1) Matrix(95,132,-208,-289) -> Matrix(3,-2,2,-1) Matrix(287,396,208,287) -> Matrix(1,0,-2,1) Matrix(65,88,48,65) -> Matrix(1,0,-4,1) Matrix(287,376,-416,-545) -> Matrix(3,-2,2,-1) Matrix(95,124,416,543) -> Matrix(3,-2,2,-1) Matrix(225,292,272,353) -> Matrix(5,-2,-2,1) Matrix(31,40,-224,-289) -> Matrix(19,-10,2,-1) Matrix(97,124,176,225) -> Matrix(1,0,-2,1) Matrix(63,80,352,447) -> Matrix(11,-8,-4,3) Matrix(127,160,304,383) -> Matrix(11,-8,-4,3) Matrix(33,40,80,97) -> Matrix(5,-2,-2,1) Matrix(287,340,-352,-417) -> Matrix(3,-2,2,-1) Matrix(191,224,272,319) -> Matrix(1,0,-2,1) Matrix(383,436,224,255) -> Matrix(5,-4,-6,5) Matrix(65,72,-288,-319) -> Matrix(1,-2,0,1) Matrix(33,28,-112,-95) -> Matrix(5,-8,2,-3) Matrix(161,132,-272,-223) -> Matrix(3,-2,2,-1) Matrix(609,496,512,417) -> Matrix(1,0,-2,1) Matrix(129,104,160,129) -> Matrix(1,-2,0,1) Matrix(127,100,80,63) -> Matrix(1,0,-2,1) Matrix(31,24,-208,-161) -> Matrix(11,-6,2,-1) Matrix(95,72,-128,-97) -> Matrix(7,-6,6,-5) Matrix(223,164,-480,-353) -> Matrix(1,-2,2,-3) Matrix(257,188,-1136,-831) -> Matrix(5,-6,-4,5) Matrix(641,468,352,257) -> Matrix(3,-4,-2,3) Matrix(127,92,352,255) -> Matrix(1,-2,2,-3) Matrix(255,184,176,127) -> Matrix(1,-2,0,1) Matrix(513,364,272,193) -> Matrix(1,-2,0,1) Matrix(577,408,816,577) -> Matrix(1,-4,0,1) Matrix(159,112,-592,-417) -> Matrix(1,4,0,1) Matrix(63,44,-368,-257) -> Matrix(1,2,0,1) Matrix(737,512,416,289) -> Matrix(1,-2,0,1) Matrix(673,464,512,353) -> Matrix(1,0,-2,1) Matrix(65,44,96,65) -> Matrix(1,-2,0,1) Matrix(31,20,48,31) -> Matrix(1,-2,0,1) Matrix(129,80,208,129) -> Matrix(9,-10,-8,9) Matrix(417,256,992,609) -> Matrix(7,-10,-2,3) Matrix(353,216,-992,-607) -> Matrix(3,-4,4,-5) Matrix(33,20,160,97) -> Matrix(3,-4,-2,3) Matrix(705,416,544,321) -> Matrix(3,-4,-8,11) Matrix(191,112,544,319) -> Matrix(1,-2,2,-3) Matrix(479,280,272,159) -> Matrix(1,-2,2,-3) Matrix(193,112,112,65) -> Matrix(1,-2,0,1) Matrix(127,72,224,127) -> Matrix(7,-12,-4,7) Matrix(735,412,512,287) -> Matrix(1,-2,-6,13) Matrix(225,124,176,97) -> Matrix(1,0,-2,1) Matrix(97,52,-416,-223) -> Matrix(1,-4,0,1) Matrix(127,60,-544,-257) -> Matrix(1,-4,0,1) Matrix(257,116,144,65) -> Matrix(1,-2,0,1) Matrix(127,56,288,127) -> Matrix(7,-12,-4,7) Matrix(799,348,512,223) -> Matrix(1,-2,-8,17) Matrix(161,68,-528,-223) -> Matrix(1,0,0,1) Matrix(609,256,992,417) -> Matrix(3,-10,-2,7) Matrix(383,160,304,127) -> Matrix(3,-8,-4,11) Matrix(97,40,80,33) -> Matrix(1,-2,-2,5) Matrix(31,12,80,31) -> Matrix(1,-6,0,1) Matrix(65,24,176,65) -> Matrix(1,2,0,1) Matrix(255,92,352,127) -> Matrix(3,2,-2,-1) Matrix(993,352,-4240,-1503) -> Matrix(1,-4,0,1) Matrix(2273,804,3712,1313) -> Matrix(5,-6,-4,5) Matrix(319,112,544,191) -> Matrix(3,2,-2,-1) Matrix(865,272,512,161) -> Matrix(1,-2,4,-7) Matrix(129,40,416,129) -> Matrix(9,-20,-4,9) Matrix(383,116,208,63) -> Matrix(1,-2,-2,5) Matrix(1215,356,1744,511) -> Matrix(3,-8,-4,11) Matrix(479,140,544,159) -> Matrix(9,-26,-10,29) Matrix(193,56,224,65) -> Matrix(5,-16,-4,13) Matrix(159,44,112,31) -> Matrix(1,-4,-2,9) Matrix(415,112,352,95) -> Matrix(1,-4,-2,9) Matrix(31,8,-128,-33) -> Matrix(1,-8,0,1) Matrix(3135,736,1904,447) -> Matrix(1,4,0,1) Matrix(543,124,416,95) -> Matrix(1,2,-2,-3) Matrix(3169,712,1856,417) -> Matrix(5,4,-4,-3) Matrix(223,48,144,31) -> Matrix(1,0,-2,1) Matrix(97,20,160,33) -> Matrix(3,-4,-2,3) Matrix(929,176,512,97) -> Matrix(1,-2,2,-3) Matrix(65,12,352,65) -> Matrix(5,-12,-2,5) Matrix(447,80,352,63) -> Matrix(3,-8,-4,11) Matrix(159,28,176,31) -> Matrix(1,-2,-2,5) Matrix(353,56,208,33) -> Matrix(1,-4,0,1) Matrix(641,84,496,65) -> Matrix(1,-16,-2,33) Matrix(1,0,16,1) -> Matrix(1,-2,0,1) Matrix(289,-40,224,-31) -> Matrix(1,10,-2,-19) Matrix(161,-24,208,-31) -> Matrix(1,6,-2,-11) Matrix(257,-44,368,-63) -> Matrix(1,2,0,1) Matrix(289,-56,160,-31) -> Matrix(1,2,-2,-3) Matrix(831,-188,1136,-257) -> Matrix(5,-6,-4,5) Matrix(33,-8,128,-31) -> Matrix(1,-8,0,1) Matrix(607,-160,368,-97) -> Matrix(1,6,0,1) Matrix(417,-112,592,-159) -> Matrix(1,4,0,1) Matrix(95,-28,112,-33) -> Matrix(3,8,-2,-5) Matrix(223,-68,528,-161) -> Matrix(1,0,0,1) Matrix(161,-52,96,-31) -> Matrix(1,2,-2,-3) Matrix(607,-216,992,-353) -> Matrix(5,4,-4,-3) Matrix(351,-152,224,-97) -> Matrix(1,2,2,5) Matrix(289,-132,208,-95) -> Matrix(1,2,-2,-3) Matrix(289,-156,176,-95) -> Matrix(1,2,0,1) Matrix(415,-232,288,-161) -> Matrix(1,2,0,1) Matrix(223,-132,272,-161) -> Matrix(1,2,-2,-3) Matrix(6529,-4000,3968,-2431) -> Matrix(5,6,4,5) Matrix(545,-376,416,-287) -> Matrix(1,2,-2,-3) Matrix(417,-296,224,-159) -> Matrix(1,2,-2,-3) Matrix(2239,-1640,1312,-961) -> Matrix(1,2,-2,-3) Matrix(97,-72,128,-95) -> Matrix(5,6,-6,-7) Matrix(865,-664,624,-479) -> Matrix(3,2,-2,-1) Matrix(417,-340,352,-287) -> Matrix(1,2,-2,-3) Matrix(191,-220,112,-129) -> Matrix(3,2,-2,-1) Matrix(1631,-2264,992,-1377) -> Matrix(1,0,2,1) 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): 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 0/1 1/0 2 16 1/8 1/0 12 2 1/7 -7/1 1 16 1/6 0 8 3/17 -3/1 1 16 2/11 (-3/1,-2/1) 0 16 3/16 -2/1 3 2 1/5 -1/1 1 16 3/14 0/1 1 8 2/9 (0/1,1/1) 0 16 5/22 2/1 1 8 3/13 1/1 1 16 1/4 1/0 4 4 5/19 -7/1 1 16 4/15 1/0 2 16 3/11 -5/1 1 16 2/7 (-4/1,-3/1) 0 16 3/10 -2/1 1 8 4/13 -5/2 2 16 5/16 -2/1 5 2 1/3 -1/1 1 16 6/17 (-1/1,1/0) 0 16 5/14 0/1 1 8 4/11 1/0 2 16 3/8 1/0 4 2 2/5 (-3/1,1/0) 0 16 5/12 -3/1 1 4 13/31 -3/1 1 16 8/19 -5/2 2 16 11/26 -2/1 1 8 3/7 -3/1 1 16 7/16 -2/1 7 2 4/9 -3/2 2 16 5/11 -1/1 1 16 1/2 0 8 6/11 (-2/1,-1/1) 0 16 5/9 -3/1 1 16 9/16 -2/1 5 2 4/7 -3/2 2 16 7/12 -2/1 1 4 17/29 -5/3 1 16 10/17 (-5/3,-3/2) 0 16 3/5 -1/1 1 16 11/18 -4/3 1 8 30/49 (-5/4,-1/1) 0 16 49/80 (-5/4,-1/1) 0 2 19/31 -1/1 1 16 8/13 -5/4 2 16 5/8 -1/1 4 2 2/3 (-1/1,1/0) 0 16 11/16 (-1/1,1/0) 0 2 9/13 -1/1 1 16 16/23 -3/2 2 16 23/33 -1/1 1 16 7/10 0 8 19/27 -1/1 1 16 12/17 1/0 2 16 17/24 -2/1 1 2 5/7 -1/1 1 16 13/18 -2/1 1 8 8/11 -3/2 2 16 19/26 -4/3 1 8 30/41 (-6/5,-1/1) 0 16 11/15 -1/1 1 16 3/4 -1/1 3 4 13/17 -1/1 1 16 10/13 (-1/1,-2/3) 0 16 17/22 0 8 7/9 -1/3 1 16 4/5 1/0 2 16 13/16 (-1/1,1/0) 0 2 9/11 -1/1 1 16 14/17 (1/1,1/0) 0 16 5/6 -2/1 1 8 6/7 (-4/3,-1/1) 0 16 7/8 -1/1 7 2 8/9 -3/4 2 16 1/1 -1/1 1 16 7/6 0 8 13/11 -1/1 1 16 19/16 (-1/1,-1/2) 0 2 6/5 (-1/1,-1/2) 0 16 5/4 -1/1 1 4 19/15 -1/1 1 16 14/11 (-1/1,-2/3) 0 16 9/7 -3/5 1 16 31/24 -1/2 12 2 22/17 (-1/2,-3/7) 0 16 13/10 0/1 1 8 17/13 -1/1 1 16 21/16 (-1/1,-1/2) 0 2 4/3 -1/2 2 16 11/8 0/1 1 2 18/13 (-1/1,0/1) 0 16 43/31 -1/1 1 16 25/18 0 8 7/5 -1/1 1 16 10/7 (-1/3,0/1) 0 16 23/16 0/1 5 2 13/9 -1/1 1 16 3/2 0/1 1 8 14/9 (-1/3,0/1) 0 16 25/16 0/1 7 2 11/7 1/1 1 16 8/5 -1/2 2 16 13/8 0/1 3 2 18/11 (0/1,1/1) 0 16 23/14 0 8 51/31 1/1 1 16 79/48 (1/1,1/0) 0 2 28/17 1/0 2 16 5/3 -1/1 1 16 27/16 0/1 5 2 22/13 (0/1,1/1) 0 16 17/10 0 8 29/17 -1/1 1 16 70/41 (-4/3,-1/1) 0 16 41/24 -1/1 5 2 12/7 -1/2 2 16 7/4 0/1 1 4 23/13 -1/1 1 16 16/9 -1/2 2 16 9/5 -1/1 1 16 29/16 0/1 3 2 20/11 1/0 2 16 11/6 0/1 1 8 13/7 -1/1 1 16 15/8 0/1 1 2 2/1 (-1/1,0/1) 0 16 1/0 0/1 1 2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,16,-1) (0/1,1/8) -> (0/1,1/8) Reflection Matrix(289,-40,224,-31) (1/8,1/7) -> (9/7,31/24) Hyperbolic Matrix(161,-24,208,-31) (1/7,1/6) -> (17/22,7/9) Hyperbolic Matrix(257,-44,368,-63) (1/6,3/17) -> (23/33,7/10) Hyperbolic Matrix(447,-80,352,-63) (3/17,2/11) -> (19/15,14/11) Glide Reflection Matrix(65,-12,352,-65) (2/11,3/16) -> (2/11,3/16) Reflection Matrix(289,-56,160,-31) (3/16,1/5) -> (9/5,29/16) Hyperbolic Matrix(97,-20,160,-33) (1/5,3/14) -> (3/5,11/18) Glide Reflection Matrix(223,-48,144,-31) (3/14,2/9) -> (3/2,14/9) Glide Reflection Matrix(831,-188,1136,-257) (2/9,5/22) -> (19/26,30/41) Hyperbolic Matrix(543,-124,416,-95) (5/22,3/13) -> (13/10,17/13) Glide Reflection Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(607,-160,368,-97) (5/19,4/15) -> (28/17,5/3) Hyperbolic Matrix(417,-112,592,-159) (4/15,3/11) -> (19/27,12/17) Hyperbolic Matrix(159,-44,112,-31) (3/11,2/7) -> (7/5,10/7) Glide Reflection Matrix(95,-28,112,-33) (2/7,3/10) -> (5/6,6/7) Hyperbolic Matrix(223,-68,528,-161) (3/10,4/13) -> (8/19,11/26) Hyperbolic Matrix(129,-40,416,-129) (4/13,5/16) -> (4/13,5/16) Reflection Matrix(161,-52,96,-31) (5/16,1/3) -> (5/3,27/16) Hyperbolic Matrix(319,-112,544,-191) (1/3,6/17) -> (17/29,10/17) Glide Reflection Matrix(607,-216,992,-353) (6/17,5/14) -> (11/18,30/49) Hyperbolic Matrix(255,-92,352,-127) (5/14,4/11) -> (13/18,8/11) Glide Reflection 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(97,-40,80,-33) (2/5,5/12) -> (6/5,5/4) Glide Reflection Matrix(383,-160,304,-127) (5/12,13/31) -> (5/4,19/15) Glide Reflection Matrix(609,-256,992,-417) (13/31,8/19) -> (19/31,8/13) Glide Reflection Matrix(415,-176,224,-95) (11/26,3/7) -> (11/6,13/7) Glide Reflection Matrix(351,-152,224,-97) (3/7,7/16) -> (25/16,11/7) Hyperbolic Matrix(127,-56,288,-127) (7/16,4/9) -> (7/16,4/9) Reflection Matrix(257,-116,144,-65) (4/9,5/11) -> (16/9,9/5) Glide Reflection Matrix(289,-132,208,-95) (5/11,1/2) -> (25/18,7/5) Hyperbolic Matrix(289,-156,176,-95) (1/2,6/11) -> (18/11,23/14) Hyperbolic Matrix(225,-124,176,-97) (6/11,5/9) -> (14/11,9/7) Glide Reflection Matrix(415,-232,288,-161) (5/9,9/16) -> (23/16,13/9) Hyperbolic Matrix(127,-72,224,-127) (9/16,4/7) -> (9/16,4/7) Reflection Matrix(193,-112,112,-65) (4/7,7/12) -> (12/7,7/4) Glide Reflection Matrix(479,-280,272,-159) (7/12,17/29) -> (7/4,23/13) Glide Reflection Matrix(223,-132,272,-161) (10/17,3/5) -> (9/11,14/17) Hyperbolic Matrix(4801,-2940,7840,-4801) (30/49,49/80) -> (30/49,49/80) Reflection Matrix(6529,-4000,3968,-2431) (49/80,19/31) -> (51/31,79/48) Hyperbolic Matrix(129,-80,208,-129) (8/13,5/8) -> (8/13,5/8) Reflection Matrix(31,-20,48,-31) (5/8,2/3) -> (5/8,2/3) Reflection Matrix(65,-44,96,-65) (2/3,11/16) -> (2/3,11/16) Reflection Matrix(545,-376,416,-287) (11/16,9/13) -> (17/13,21/16) Hyperbolic Matrix(737,-512,416,-289) (9/13,16/23) -> (23/13,16/9) Glide Reflection Matrix(287,-200,320,-223) (16/23,23/33) -> (8/9,1/1) Glide Reflection Matrix(319,-224,272,-191) (7/10,19/27) -> (7/6,13/11) Glide Reflection Matrix(577,-408,816,-577) (12/17,17/24) -> (12/17,17/24) Reflection Matrix(417,-296,224,-159) (17/24,5/7) -> (13/7,15/8) Hyperbolic Matrix(255,-184,176,-127) (5/7,13/18) -> (13/9,3/2) Glide Reflection Matrix(641,-468,352,-257) (8/11,19/26) -> (20/11,11/6) Glide Reflection Matrix(2239,-1640,1312,-961) (30/41,11/15) -> (29/17,70/41) Hyperbolic Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(865,-664,624,-479) (13/17,10/13) -> (18/13,43/31) Hyperbolic Matrix(705,-544,416,-321) (10/13,17/22) -> (22/13,17/10) Glide Reflection Matrix(127,-100,80,-63) (7/9,4/5) -> (11/7,8/5) Glide Reflection Matrix(129,-104,160,-129) (4/5,13/16) -> (4/5,13/16) Reflection Matrix(417,-340,352,-287) (13/16,9/11) -> (13/11,19/16) Hyperbolic Matrix(353,-292,272,-225) (14/17,5/6) -> (22/17,13/10) Glide Reflection Matrix(97,-84,112,-97) (6/7,7/8) -> (6/7,7/8) Reflection Matrix(127,-112,144,-127) (7/8,8/9) -> (7/8,8/9) Reflection Matrix(191,-220,112,-129) (1/1,7/6) -> (17/10,29/17) Hyperbolic Matrix(191,-228,160,-191) (19/16,6/5) -> (19/16,6/5) Reflection Matrix(1055,-1364,816,-1055) (31/24,22/17) -> (31/24,22/17) Reflection Matrix(127,-168,96,-127) (21/16,4/3) -> (21/16,4/3) Reflection Matrix(65,-88,48,-65) (4/3,11/8) -> (4/3,11/8) Reflection Matrix(287,-396,208,-287) (11/8,18/13) -> (11/8,18/13) Reflection Matrix(1631,-2264,992,-1377) (43/31,25/18) -> (23/14,51/31) Hyperbolic Matrix(321,-460,224,-321) (10/7,23/16) -> (10/7,23/16) Reflection Matrix(449,-700,288,-449) (14/9,25/16) -> (14/9,25/16) Reflection Matrix(129,-208,80,-129) (8/5,13/8) -> (8/5,13/8) Reflection Matrix(287,-468,176,-287) (13/8,18/11) -> (13/8,18/11) Reflection Matrix(2687,-4424,1632,-2687) (79/48,28/17) -> (79/48,28/17) Reflection Matrix(703,-1188,416,-703) (27/16,22/13) -> (27/16,22/13) Reflection Matrix(3361,-5740,1968,-3361) (70/41,41/24) -> (70/41,41/24) Reflection Matrix(575,-984,336,-575) (41/24,12/7) -> (41/24,12/7) Reflection Matrix(639,-1160,352,-639) (29/16,20/11) -> (29/16,20/11) Reflection Matrix(31,-60,16,-31) (15/8,2/1) -> (15/8,2/1) Reflection Matrix(-1,4,0,1) (2/1,1/0) -> (2/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,16,-1) -> Matrix(1,2,0,-1) (0/1,1/8) -> (-1/1,1/0) Matrix(289,-40,224,-31) -> Matrix(1,10,-2,-19) Matrix(161,-24,208,-31) -> Matrix(1,6,-2,-11) Matrix(257,-44,368,-63) -> Matrix(1,2,0,1) 1/0 Matrix(447,-80,352,-63) -> Matrix(3,8,-4,-11) Matrix(65,-12,352,-65) -> Matrix(5,12,-2,-5) (2/11,3/16) -> (-3/1,-2/1) Matrix(289,-56,160,-31) -> Matrix(1,2,-2,-3) -1/1 Matrix(97,-20,160,-33) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(223,-48,144,-31) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(831,-188,1136,-257) -> Matrix(5,-6,-4,5) Matrix(543,-124,416,-95) -> Matrix(1,-2,-2,3) Matrix(33,-8,128,-31) -> Matrix(1,-8,0,1) 1/0 Matrix(607,-160,368,-97) -> Matrix(1,6,0,1) 1/0 Matrix(417,-112,592,-159) -> Matrix(1,4,0,1) 1/0 Matrix(159,-44,112,-31) -> Matrix(1,4,-2,-9) Matrix(95,-28,112,-33) -> Matrix(3,8,-2,-5) -2/1 Matrix(223,-68,528,-161) -> Matrix(1,0,0,1) Matrix(129,-40,416,-129) -> Matrix(9,20,-4,-9) (4/13,5/16) -> (-5/2,-2/1) Matrix(161,-52,96,-31) -> Matrix(1,2,-2,-3) -1/1 Matrix(319,-112,544,-191) -> Matrix(3,-2,-2,1) Matrix(607,-216,992,-353) -> Matrix(5,4,-4,-3) -1/1 Matrix(255,-92,352,-127) -> Matrix(3,-2,-2,1) Matrix(65,-24,176,-65) -> Matrix(-1,2,0,1) (4/11,3/8) -> (1/1,1/0) Matrix(31,-12,80,-31) -> Matrix(1,6,0,-1) (3/8,2/5) -> (-3/1,1/0) Matrix(97,-40,80,-33) -> Matrix(1,2,-2,-5) Matrix(383,-160,304,-127) -> Matrix(3,8,-4,-11) Matrix(609,-256,992,-417) -> Matrix(3,10,-2,-7) Matrix(415,-176,224,-95) -> Matrix(1,2,-2,-5) Matrix(351,-152,224,-97) -> Matrix(1,2,2,5) Matrix(127,-56,288,-127) -> Matrix(7,12,-4,-7) (7/16,4/9) -> (-2/1,-3/2) Matrix(257,-116,144,-65) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(289,-132,208,-95) -> Matrix(1,2,-2,-3) -1/1 Matrix(289,-156,176,-95) -> Matrix(1,2,0,1) 1/0 Matrix(225,-124,176,-97) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(415,-232,288,-161) -> Matrix(1,2,0,1) 1/0 Matrix(127,-72,224,-127) -> Matrix(7,12,-4,-7) (9/16,4/7) -> (-2/1,-3/2) Matrix(193,-112,112,-65) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(479,-280,272,-159) -> Matrix(1,2,2,3) Matrix(223,-132,272,-161) -> Matrix(1,2,-2,-3) -1/1 Matrix(4801,-2940,7840,-4801) -> Matrix(9,10,-8,-9) (30/49,49/80) -> (-5/4,-1/1) Matrix(6529,-4000,3968,-2431) -> Matrix(5,6,4,5) Matrix(129,-80,208,-129) -> Matrix(9,10,-8,-9) (8/13,5/8) -> (-5/4,-1/1) Matrix(31,-20,48,-31) -> Matrix(1,2,0,-1) (5/8,2/3) -> (-1/1,1/0) Matrix(65,-44,96,-65) -> Matrix(1,2,0,-1) (2/3,11/16) -> (-1/1,1/0) Matrix(545,-376,416,-287) -> Matrix(1,2,-2,-3) -1/1 Matrix(737,-512,416,-289) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(287,-200,320,-223) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(319,-224,272,-191) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(577,-408,816,-577) -> Matrix(1,4,0,-1) (12/17,17/24) -> (-2/1,1/0) Matrix(417,-296,224,-159) -> Matrix(1,2,-2,-3) -1/1 Matrix(255,-184,176,-127) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(641,-468,352,-257) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(2239,-1640,1312,-961) -> Matrix(1,2,-2,-3) -1/1 Matrix(97,-72,128,-95) -> Matrix(5,6,-6,-7) -1/1 Matrix(865,-664,624,-479) -> Matrix(3,2,-2,-1) -1/1 Matrix(705,-544,416,-321) -> Matrix(3,2,2,1) Matrix(127,-100,80,-63) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(129,-104,160,-129) -> Matrix(1,2,0,-1) (4/5,13/16) -> (-1/1,1/0) Matrix(417,-340,352,-287) -> Matrix(1,2,-2,-3) -1/1 Matrix(353,-292,272,-225) -> Matrix(1,2,-2,-5) Matrix(97,-84,112,-97) -> Matrix(7,8,-6,-7) (6/7,7/8) -> (-4/3,-1/1) Matrix(127,-112,144,-127) -> Matrix(7,6,-8,-7) (7/8,8/9) -> (-1/1,-3/4) Matrix(191,-220,112,-129) -> Matrix(3,2,-2,-1) -1/1 Matrix(191,-228,160,-191) -> Matrix(3,2,-4,-3) (19/16,6/5) -> (-1/1,-1/2) Matrix(1055,-1364,816,-1055) -> Matrix(13,6,-28,-13) (31/24,22/17) -> (-1/2,-3/7) Matrix(127,-168,96,-127) -> Matrix(3,2,-4,-3) (21/16,4/3) -> (-1/1,-1/2) Matrix(65,-88,48,-65) -> Matrix(-1,0,4,1) (4/3,11/8) -> (-1/2,0/1) Matrix(287,-396,208,-287) -> Matrix(-1,0,2,1) (11/8,18/13) -> (-1/1,0/1) Matrix(1631,-2264,992,-1377) -> Matrix(1,0,2,1) 0/1 Matrix(321,-460,224,-321) -> Matrix(-1,0,6,1) (10/7,23/16) -> (-1/3,0/1) Matrix(449,-700,288,-449) -> Matrix(-1,0,6,1) (14/9,25/16) -> (-1/3,0/1) Matrix(129,-208,80,-129) -> Matrix(-1,0,4,1) (8/5,13/8) -> (-1/2,0/1) Matrix(287,-468,176,-287) -> Matrix(1,0,2,-1) (13/8,18/11) -> (0/1,1/1) Matrix(2687,-4424,1632,-2687) -> Matrix(-1,2,0,1) (79/48,28/17) -> (1/1,1/0) Matrix(703,-1188,416,-703) -> Matrix(1,0,2,-1) (27/16,22/13) -> (0/1,1/1) Matrix(3361,-5740,1968,-3361) -> Matrix(7,8,-6,-7) (70/41,41/24) -> (-4/3,-1/1) Matrix(575,-984,336,-575) -> Matrix(3,2,-4,-3) (41/24,12/7) -> (-1/1,-1/2) Matrix(639,-1160,352,-639) -> Matrix(1,0,0,-1) (29/16,20/11) -> (0/1,1/0) Matrix(31,-60,16,-31) -> Matrix(-1,0,2,1) (15/8,2/1) -> (-1/1,0/1) Matrix(-1,4,0,1) -> Matrix(-1,0,2,1) (2/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.