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: 64 Genus: 33 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -7/1 -6/1 -5/1 -9/2 -4/1 -11/3 -10/3 -3/1 -8/3 -9/4 -2/1 -9/5 -3/2 -10/7 -4/3 -6/5 -1/1 -6/7 -3/4 -2/3 -3/5 -6/11 0/1 1/2 6/11 3/5 2/3 3/4 9/11 6/7 1/1 6/5 5/4 4/3 10/7 3/2 36/23 12/7 7/4 9/5 2/1 24/11 9/4 12/5 5/2 8/3 11/4 3/1 36/11 10/3 24/7 7/2 11/3 4/1 9/2 24/5 5/1 11/2 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 -8/1 -2/1 -7/1 -1/1 -6/1 -2/1 0/1 -11/2 -1/2 1/0 -5/1 -1/1 1/1 -14/3 1/1 -23/5 1/1 -9/2 1/0 -13/3 1/1 -4/1 1/0 -15/4 -1/1 -11/3 -1/1 1/1 -18/5 1/0 -7/2 -1/2 1/0 -24/7 0/1 -17/5 -1/1 1/1 -10/3 0/1 -3/1 1/0 -14/5 -4/1 -25/9 -11/3 -3/1 -36/13 -3/1 -11/4 1/0 -8/3 -2/1 -13/5 -3/1 -1/1 -18/7 -2/1 -5/2 -3/2 1/0 -12/5 -1/1 -7/3 -1/1 -1/3 -23/10 1/2 1/0 -16/7 0/1 -25/11 -1/1 -9/4 0/1 -11/5 -1/1 -2/1 1/0 -13/7 -3/1 -24/13 -2/1 -11/6 -3/2 1/0 -9/5 -1/1 -25/14 -3/2 1/0 -16/9 0/1 -23/13 -1/1 -7/4 1/0 -12/7 1/0 -5/3 -3/1 -18/11 -2/1 -13/8 -3/2 -8/5 -2/1 -11/7 -5/3 -1/1 -3/2 -1/1 -13/9 -1/1 1/1 -36/25 1/0 -23/16 1/0 -10/7 -2/1 0/1 -17/12 1/0 -24/17 -2/1 -7/5 -1/1 -18/13 -1/1 -11/8 -1/2 -15/11 1/0 -4/3 -1/1 -13/10 -1/2 -1/4 -9/7 0/1 -23/18 1/2 1/0 -14/11 -1/1 -19/15 -1/1 -1/3 -24/19 0/1 -5/4 1/0 -11/9 -1/1 -6/5 -2/1 0/1 -7/6 -1/2 1/0 -8/7 -2/1 -1/1 -1/1 1/1 -7/8 1/0 -6/7 -1/1 -5/6 -1/2 1/0 -14/17 0/1 2/1 -23/28 1/0 -9/11 1/0 -4/5 -1/1 -11/14 -1/2 1/0 -18/23 -2/1 0/1 -7/9 -1/1 -10/13 -1/1 -3/4 -1/1 -14/19 -1/1 -25/34 -11/14 -3/4 -36/49 -3/4 -11/15 -1/1 -5/7 -8/11 -2/3 -13/18 -7/12 -1/2 -5/7 -1/1 -12/17 -1/2 -7/10 -1/2 -1/4 -16/23 0/1 -25/36 -1/2 -9/13 -1/2 -11/16 -1/4 -2/3 0/1 -13/20 -1/2 -24/37 0/1 -11/17 1/1 -9/14 1/0 -25/39 -1/1 -16/25 0/1 -7/11 -3/1 -1/1 -12/19 -1/1 -5/8 -1/2 -13/21 -1/1 -1/3 -8/13 0/1 -11/18 -1/2 1/0 -3/5 0/1 -13/22 1/2 1/0 -36/61 1/1 -23/39 1/1 3/1 -10/17 1/0 -7/12 1/0 -18/31 0/1 -11/19 -1/1 1/1 -4/7 1/0 -9/16 -2/1 -23/41 -1/1 -14/25 -2/1 0/1 -19/34 -5/2 1/0 -24/43 -2/1 -5/9 -5/3 -1/1 -6/11 -1/1 -7/13 -1/1 -1/2 -1/2 1/0 0/1 0/1 1/2 1/2 1/0 6/11 0/1 5/9 1/3 14/25 1/4 9/16 1/3 4/7 1/2 11/19 1/1 7/12 1/2 10/17 0/1 2/3 3/5 1/1 14/23 0/1 2/1 25/41 1/1 11/18 3/2 1/0 8/13 0/1 5/8 1/2 7/11 1/1 16/25 0/1 9/14 1/1 2/3 1/1 9/13 1/0 16/23 0/1 7/10 3/2 1/0 5/7 -1/1 1/1 13/18 -1/2 1/0 8/11 0/1 3/4 0/1 10/13 0/1 7/9 1/3 1/1 11/14 1/2 5/8 4/5 1/1 9/11 1/0 14/17 1/0 19/23 -1/1 5/6 1/2 1/0 6/7 0/1 7/8 1/2 1/1 1/1 8/7 2/1 7/6 3/2 1/0 6/5 1/0 11/9 -1/1 1/1 5/4 1/0 14/11 0/1 23/18 1/2 3/4 9/7 1/1 13/10 1/2 1/0 4/3 1/1 15/11 3/2 26/19 5/3 11/8 3/2 18/13 2/1 25/18 9/4 5/2 7/5 1/1 3/1 24/17 2/1 17/12 1/0 10/7 1/0 3/2 1/0 14/9 1/0 39/25 1/0 25/16 1/0 36/23 1/0 11/7 -1/1 19/12 1/0 8/5 0/1 13/8 1/2 18/11 1/1 5/3 1/1 3/1 17/10 7/2 1/0 12/7 1/0 7/4 1/0 23/13 -1/1 1/1 16/9 0/1 25/14 1/2 1/0 9/5 0/1 11/6 -1/2 1/0 2/1 0/1 2/1 13/6 -1/2 1/0 24/11 0/1 11/5 1/3 1/1 9/4 1/1 34/15 1/0 25/11 1/1 3/1 16/7 0/1 23/10 1/2 3/4 7/3 1/1 19/8 1/2 12/5 1/1 5/2 3/2 1/0 18/7 1/1 31/12 3/2 13/5 1/1 60/23 3/2 47/18 3/2 13/8 34/13 2/1 21/8 2/1 8/3 2/1 11/4 5/2 3/1 1/0 13/4 1/2 36/11 1/1 59/18 5/4 3/2 23/7 1/1 10/3 1/1 17/5 1/1 24/7 2/1 7/2 3/2 1/0 18/5 0/1 2/1 11/3 1/1 15/4 2/1 4/1 1/0 13/3 -1/1 1/1 48/11 0/1 35/8 1/2 22/5 1/1 9/2 1/1 32/7 2/1 23/5 1/1 3/1 14/3 2/1 19/4 3/2 24/5 2/1 29/6 9/4 5/2 5/1 3/1 11/2 11/2 1/0 6/1 1/0 13/2 -9/2 1/0 7/1 -3/1 -1/1 8/1 0/1 9/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(25,216,-36,-311) (-8/1,1/0) -> (-16/23,-25/36) Hyperbolic Matrix(23,168,36,263) (-8/1,-7/1) -> (7/11,16/25) Hyperbolic Matrix(25,168,-32,-215) (-7/1,-6/1) -> (-18/23,-7/9) Hyperbolic Matrix(47,264,-60,-337) (-6/1,-11/2) -> (-11/14,-18/23) Hyperbolic Matrix(23,120,32,167) (-11/2,-5/1) -> (5/7,13/18) Hyperbolic Matrix(71,336,-56,-265) (-5/1,-14/3) -> (-14/11,-19/15) Hyperbolic Matrix(119,552,36,167) (-14/3,-23/5) -> (23/7,10/3) Hyperbolic Matrix(95,432,-148,-673) (-23/5,-9/2) -> (-9/14,-25/39) Hyperbolic Matrix(49,216,-76,-335) (-9/2,-13/3) -> (-11/17,-9/14) Hyperbolic Matrix(23,96,40,167) (-13/3,-4/1) -> (4/7,11/19) Hyperbolic Matrix(25,96,44,169) (-4/1,-15/4) -> (9/16,4/7) Hyperbolic Matrix(71,264,32,119) (-15/4,-11/3) -> (11/5,9/4) Hyperbolic Matrix(73,264,60,217) (-11/3,-18/5) -> (6/5,11/9) Hyperbolic Matrix(47,168,40,143) (-18/5,-7/2) -> (7/6,6/5) Hyperbolic Matrix(97,336,28,97) (-7/2,-24/7) -> (24/7,7/2) Hyperbolic Matrix(169,576,120,409) (-24/7,-17/5) -> (7/5,24/17) Hyperbolic Matrix(71,240,92,311) (-17/5,-10/3) -> (10/13,7/9) Hyperbolic Matrix(23,72,-8,-25) (-10/3,-3/1) -> (-3/1,-14/5) Parabolic Matrix(241,672,52,145) (-14/5,-25/9) -> (23/5,14/3) Hyperbolic Matrix(623,1728,-1056,-2929) (-25/9,-36/13) -> (-36/61,-23/39) Hyperbolic Matrix(313,864,96,265) (-36/13,-11/4) -> (13/4,36/11) Hyperbolic Matrix(71,192,44,119) (-11/4,-8/3) -> (8/5,13/8) Hyperbolic Matrix(73,192,-100,-263) (-8/3,-13/5) -> (-11/15,-8/11) Hyperbolic Matrix(167,432,-288,-745) (-13/5,-18/7) -> (-18/31,-11/19) Hyperbolic Matrix(47,120,56,143) (-18/7,-5/2) -> (5/6,6/7) Hyperbolic Matrix(49,120,20,49) (-5/2,-12/5) -> (12/5,5/2) Hyperbolic Matrix(71,168,-112,-265) (-12/5,-7/3) -> (-7/11,-12/19) Hyperbolic Matrix(145,336,104,241) (-7/3,-23/10) -> (25/18,7/5) Hyperbolic Matrix(335,768,188,431) (-23/10,-16/7) -> (16/9,25/14) Hyperbolic Matrix(95,216,84,191) (-16/7,-25/11) -> (1/1,8/7) Hyperbolic Matrix(191,432,-340,-769) (-25/11,-9/4) -> (-9/16,-23/41) Hyperbolic Matrix(119,264,32,71) (-9/4,-11/5) -> (11/3,15/4) Hyperbolic Matrix(23,48,-12,-25) (-11/5,-2/1) -> (-2/1,-13/7) Parabolic Matrix(311,576,-480,-889) (-13/7,-24/13) -> (-24/37,-11/17) Hyperbolic Matrix(313,576,144,265) (-24/13,-11/6) -> (13/6,24/11) Hyperbolic Matrix(119,216,92,167) (-11/6,-9/5) -> (9/7,13/10) Hyperbolic Matrix(241,432,188,337) (-9/5,-25/14) -> (23/18,9/7) Hyperbolic Matrix(431,768,188,335) (-25/14,-16/9) -> (16/7,23/10) Hyperbolic Matrix(433,768,-676,-1199) (-16/9,-23/13) -> (-25/39,-16/25) Hyperbolic Matrix(95,168,108,191) (-23/13,-7/4) -> (7/8,1/1) Hyperbolic Matrix(97,168,56,97) (-7/4,-12/7) -> (12/7,7/4) Hyperbolic Matrix(71,120,-100,-169) (-12/7,-5/3) -> (-5/7,-12/17) Hyperbolic Matrix(73,120,132,217) (-5/3,-18/11) -> (6/11,5/9) Hyperbolic Matrix(265,432,192,313) (-18/11,-13/8) -> (11/8,18/13) Hyperbolic Matrix(119,192,44,71) (-13/8,-8/5) -> (8/3,11/4) Hyperbolic Matrix(121,192,-196,-311) (-8/5,-11/7) -> (-13/21,-8/13) Hyperbolic Matrix(47,72,-32,-49) (-11/7,-3/2) -> (-3/2,-13/9) Parabolic Matrix(599,864,-816,-1177) (-13/9,-36/25) -> (-36/49,-11/15) Hyperbolic Matrix(1201,1728,768,1105) (-36/25,-23/16) -> (25/16,36/23) Hyperbolic Matrix(385,552,-468,-671) (-23/16,-10/7) -> (-14/17,-23/28) Hyperbolic Matrix(169,240,288,409) (-10/7,-17/12) -> (7/12,10/17) Hyperbolic Matrix(577,816,408,577) (-17/12,-24/17) -> (24/17,17/12) Hyperbolic Matrix(409,576,120,169) (-24/17,-7/5) -> (17/5,24/7) Hyperbolic Matrix(121,168,-224,-311) (-7/5,-18/13) -> (-6/11,-7/13) Hyperbolic Matrix(313,432,192,265) (-18/13,-11/8) -> (13/8,18/11) Hyperbolic Matrix(193,264,-280,-383) (-11/8,-15/11) -> (-9/13,-11/16) Hyperbolic Matrix(71,96,88,119) (-15/11,-4/3) -> (4/5,9/11) Hyperbolic Matrix(73,96,92,121) (-4/3,-13/10) -> (11/14,4/5) Hyperbolic Matrix(167,216,92,119) (-13/10,-9/7) -> (9/5,11/6) Hyperbolic Matrix(337,432,188,241) (-9/7,-23/18) -> (25/14,9/5) Hyperbolic Matrix(527,672,-716,-913) (-23/18,-14/11) -> (-14/19,-25/34) Hyperbolic Matrix(455,576,-816,-1033) (-19/15,-24/19) -> (-24/43,-5/9) Hyperbolic Matrix(457,576,96,121) (-24/19,-5/4) -> (19/4,24/5) Hyperbolic Matrix(215,264,136,167) (-5/4,-11/9) -> (11/7,19/12) Hyperbolic Matrix(217,264,60,73) (-11/9,-6/5) -> (18/5,11/3) Hyperbolic Matrix(143,168,40,47) (-6/5,-7/6) -> (7/2,18/5) Hyperbolic Matrix(145,168,208,241) (-7/6,-8/7) -> (16/23,7/10) Hyperbolic Matrix(191,216,84,95) (-8/7,-1/1) -> (25/11,16/7) Hyperbolic Matrix(191,168,108,95) (-1/1,-7/8) -> (7/4,23/13) Hyperbolic Matrix(361,312,140,121) (-7/8,-6/7) -> (18/7,31/12) Hyperbolic Matrix(143,120,56,47) (-6/7,-5/6) -> (5/2,18/7) Hyperbolic Matrix(407,336,-728,-601) (-5/6,-14/17) -> (-14/25,-19/34) Hyperbolic Matrix(263,216,28,23) (-23/28,-9/11) -> (9/1,1/0) Hyperbolic Matrix(119,96,88,71) (-9/11,-4/5) -> (4/3,15/11) Hyperbolic Matrix(121,96,92,73) (-4/5,-11/14) -> (13/10,4/3) Hyperbolic Matrix(311,240,92,71) (-7/9,-10/13) -> (10/3,17/5) Hyperbolic Matrix(95,72,-128,-97) (-10/13,-3/4) -> (-3/4,-14/19) Parabolic Matrix(4343,3192,1664,1223) (-25/34,-36/49) -> (60/23,47/18) Hyperbolic Matrix(265,192,432,313) (-8/11,-13/18) -> (11/18,8/13) Hyperbolic Matrix(167,120,32,23) (-13/18,-5/7) -> (5/1,11/2) Hyperbolic Matrix(409,288,240,169) (-12/17,-7/10) -> (17/10,12/7) Hyperbolic Matrix(241,168,208,145) (-7/10,-16/23) -> (8/7,7/6) Hyperbolic Matrix(1729,1200,1108,769) (-25/36,-9/13) -> (39/25,25/16) Hyperbolic Matrix(71,48,-108,-73) (-11/16,-2/3) -> (-2/3,-13/20) Parabolic Matrix(2255,1464,516,335) (-13/20,-24/37) -> (48/11,35/8) Hyperbolic Matrix(263,168,36,23) (-16/25,-7/11) -> (7/1,8/1) Hyperbolic Matrix(457,288,192,121) (-12/19,-5/8) -> (19/8,12/5) Hyperbolic Matrix(193,120,156,97) (-5/8,-13/21) -> (11/9,5/4) Hyperbolic Matrix(313,192,432,265) (-8/13,-11/18) -> (13/18,8/11) Hyperbolic Matrix(119,72,-200,-121) (-11/18,-3/5) -> (-3/5,-13/22) Parabolic Matrix(4391,2592,1340,791) (-13/22,-36/61) -> (36/11,59/18) Hyperbolic Matrix(1751,1032,772,455) (-23/39,-10/17) -> (34/15,25/11) Hyperbolic Matrix(409,240,288,169) (-10/17,-7/12) -> (17/12,10/7) Hyperbolic Matrix(289,168,332,193) (-7/12,-18/31) -> (6/7,7/8) Hyperbolic Matrix(167,96,40,23) (-11/19,-4/7) -> (4/1,13/3) Hyperbolic Matrix(169,96,44,25) (-4/7,-9/16) -> (15/4,4/1) Hyperbolic Matrix(1199,672,1968,1103) (-23/41,-14/25) -> (14/23,25/41) Hyperbolic Matrix(2063,1152,428,239) (-19/34,-24/43) -> (24/5,29/6) Hyperbolic Matrix(217,120,132,73) (-5/9,-6/11) -> (18/11,5/3) Hyperbolic Matrix(313,168,136,73) (-7/13,-1/2) -> (23/10,7/3) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(311,-168,224,-121) (1/2,6/11) -> (18/13,25/18) Hyperbolic Matrix(601,-336,728,-407) (5/9,14/25) -> (14/17,19/23) Hyperbolic Matrix(769,-432,340,-191) (14/25,9/16) -> (9/4,34/15) Hyperbolic Matrix(745,-432,288,-167) (11/19,7/12) -> (31/12,13/5) Hyperbolic Matrix(121,-72,200,-119) (10/17,3/5) -> (3/5,14/23) Parabolic Matrix(2833,-1728,864,-527) (25/41,11/18) -> (59/18,23/7) Hyperbolic Matrix(311,-192,196,-121) (8/13,5/8) -> (19/12,8/5) Hyperbolic Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(673,-432,148,-95) (16/25,9/14) -> (9/2,32/7) Hyperbolic Matrix(335,-216,76,-49) (9/14,2/3) -> (22/5,9/2) Hyperbolic Matrix(383,-264,280,-193) (2/3,9/13) -> (15/11,26/19) Hyperbolic Matrix(311,-216,36,-25) (9/13,16/23) -> (8/1,9/1) Hyperbolic Matrix(169,-120,100,-71) (7/10,5/7) -> (5/3,17/10) Hyperbolic Matrix(263,-192,100,-73) (8/11,3/4) -> (21/8,8/3) Hyperbolic Matrix(409,-312,156,-119) (3/4,10/13) -> (34/13,21/8) Hyperbolic Matrix(215,-168,32,-25) (7/9,11/14) -> (13/2,7/1) Hyperbolic Matrix(817,-672,524,-431) (9/11,14/17) -> (14/9,39/25) Hyperbolic Matrix(697,-576,144,-119) (19/23,5/6) -> (29/6,5/1) Hyperbolic Matrix(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(1129,-1440,432,-551) (14/11,23/18) -> (47/18,34/13) Hyperbolic Matrix(841,-1152,192,-263) (26/19,11/8) -> (35/8,22/5) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(719,-1128,276,-433) (36/23,11/7) -> (13/5,60/23) Hyperbolic Matrix(623,-1104,136,-241) (23/13,16/9) -> (32/7,23/5) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(383,-840,88,-193) (24/11,11/5) -> (13/3,48/11) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(25,216,-36,-311) -> Matrix(1,2,-2,-3) Matrix(23,168,36,263) -> Matrix(1,2,0,1) Matrix(25,168,-32,-215) -> Matrix(1,0,0,1) Matrix(47,264,-60,-337) -> Matrix(1,0,0,1) Matrix(23,120,32,167) -> Matrix(1,0,0,1) Matrix(71,336,-56,-265) -> Matrix(1,0,-2,1) Matrix(119,552,36,167) -> Matrix(1,0,0,1) Matrix(95,432,-148,-673) -> Matrix(1,-2,0,1) Matrix(49,216,-76,-335) -> Matrix(1,0,0,1) Matrix(23,96,40,167) -> Matrix(1,-2,2,-3) Matrix(25,96,44,169) -> Matrix(1,2,2,5) Matrix(71,264,32,119) -> Matrix(1,0,2,1) Matrix(73,264,60,217) -> Matrix(1,0,0,1) Matrix(47,168,40,143) -> Matrix(1,2,0,1) Matrix(97,336,28,97) -> Matrix(1,2,0,1) Matrix(169,576,120,409) -> Matrix(1,2,0,1) Matrix(71,240,92,311) -> Matrix(1,0,2,1) Matrix(23,72,-8,-25) -> Matrix(1,-4,0,1) Matrix(241,672,52,145) -> Matrix(3,10,2,7) Matrix(623,1728,-1056,-2929) -> Matrix(3,10,2,7) Matrix(313,864,96,265) -> Matrix(1,2,2,5) Matrix(71,192,44,119) -> Matrix(1,2,2,5) Matrix(73,192,-100,-263) -> Matrix(3,4,-4,-5) Matrix(167,432,-288,-745) -> Matrix(1,2,0,1) Matrix(47,120,56,143) -> Matrix(1,2,0,1) Matrix(49,120,20,49) -> Matrix(3,4,2,3) Matrix(71,168,-112,-265) -> Matrix(3,2,-2,-1) Matrix(145,336,104,241) -> Matrix(5,2,2,1) Matrix(335,768,188,431) -> Matrix(1,0,0,1) Matrix(95,216,84,191) -> Matrix(1,2,0,1) Matrix(191,432,-340,-769) -> Matrix(3,2,-2,-1) Matrix(119,264,32,71) -> Matrix(1,2,0,1) Matrix(23,48,-12,-25) -> Matrix(1,-2,0,1) Matrix(311,576,-480,-889) -> Matrix(1,2,2,5) Matrix(313,576,144,265) -> Matrix(1,2,-2,-3) Matrix(119,216,92,167) -> Matrix(1,2,0,1) Matrix(241,432,188,337) -> Matrix(1,0,2,1) Matrix(431,768,188,335) -> Matrix(1,0,2,1) Matrix(433,768,-676,-1199) -> Matrix(1,0,0,1) Matrix(95,168,108,191) -> Matrix(1,0,2,1) Matrix(97,168,56,97) -> Matrix(1,0,0,1) Matrix(71,120,-100,-169) -> Matrix(1,4,-2,-7) Matrix(73,120,132,217) -> Matrix(1,2,4,9) Matrix(265,432,192,313) -> Matrix(7,12,4,7) Matrix(119,192,44,71) -> Matrix(1,4,0,1) Matrix(121,192,-196,-311) -> Matrix(1,2,-4,-7) Matrix(47,72,-32,-49) -> Matrix(1,2,-2,-3) Matrix(599,864,-816,-1177) -> Matrix(3,-2,-4,3) Matrix(1201,1728,768,1105) -> Matrix(1,2,0,1) Matrix(385,552,-468,-671) -> Matrix(1,2,0,1) Matrix(169,240,288,409) -> Matrix(1,0,2,1) Matrix(577,816,408,577) -> Matrix(1,4,0,1) Matrix(409,576,120,169) -> Matrix(3,4,2,3) Matrix(121,168,-224,-311) -> Matrix(3,4,-4,-5) Matrix(313,432,192,265) -> Matrix(3,2,4,3) Matrix(193,264,-280,-383) -> Matrix(1,0,-2,1) Matrix(71,96,88,119) -> Matrix(1,2,0,1) Matrix(73,96,92,121) -> Matrix(3,2,4,3) Matrix(167,216,92,119) -> Matrix(1,0,2,1) Matrix(337,432,188,241) -> Matrix(1,0,0,1) Matrix(527,672,-716,-913) -> Matrix(3,4,-4,-5) Matrix(455,576,-816,-1033) -> Matrix(7,2,-4,-1) Matrix(457,576,96,121) -> Matrix(3,-2,2,-1) Matrix(215,264,136,167) -> Matrix(1,0,0,1) Matrix(217,264,60,73) -> Matrix(1,2,0,1) Matrix(143,168,40,47) -> Matrix(1,2,0,1) Matrix(145,168,208,241) -> Matrix(1,2,0,1) Matrix(191,216,84,95) -> Matrix(1,2,0,1) Matrix(191,168,108,95) -> Matrix(1,0,0,1) Matrix(361,312,140,121) -> Matrix(3,4,2,3) Matrix(143,120,56,47) -> Matrix(1,2,0,1) Matrix(407,336,-728,-601) -> Matrix(1,-2,0,1) Matrix(263,216,28,23) -> Matrix(1,0,0,1) Matrix(119,96,88,71) -> Matrix(3,4,2,3) Matrix(121,96,92,73) -> Matrix(1,0,2,1) Matrix(311,240,92,71) -> Matrix(1,2,0,1) Matrix(95,72,-128,-97) -> Matrix(3,4,-4,-5) Matrix(4343,3192,1664,1223) -> Matrix(47,36,30,23) Matrix(265,192,432,313) -> Matrix(3,2,-2,-1) Matrix(167,120,32,23) -> Matrix(5,2,2,1) Matrix(409,288,240,169) -> Matrix(9,4,2,1) Matrix(241,168,208,145) -> Matrix(5,2,2,1) Matrix(1729,1200,1108,769) -> Matrix(1,0,2,1) Matrix(71,48,-108,-73) -> Matrix(1,0,2,1) Matrix(2255,1464,516,335) -> Matrix(1,0,4,1) Matrix(263,168,36,23) -> Matrix(1,0,0,1) Matrix(457,288,192,121) -> Matrix(3,2,4,3) Matrix(193,120,156,97) -> Matrix(1,0,2,1) Matrix(313,192,432,265) -> Matrix(1,0,0,1) Matrix(119,72,-200,-121) -> Matrix(1,0,2,1) Matrix(4391,2592,1340,791) -> Matrix(5,-4,4,-3) Matrix(1751,1032,772,455) -> Matrix(1,0,0,1) Matrix(409,240,288,169) -> Matrix(1,2,0,1) Matrix(289,168,332,193) -> Matrix(1,0,2,1) Matrix(167,96,40,23) -> Matrix(1,0,0,1) Matrix(169,96,44,25) -> Matrix(1,4,0,1) Matrix(1199,672,1968,1103) -> Matrix(1,2,0,1) Matrix(2063,1152,428,239) -> Matrix(9,20,4,9) Matrix(217,120,132,73) -> Matrix(3,4,2,3) Matrix(313,168,136,73) -> Matrix(3,2,4,3) Matrix(1,0,4,1) -> Matrix(1,0,2,1) Matrix(311,-168,224,-121) -> Matrix(5,2,2,1) Matrix(601,-336,728,-407) -> Matrix(1,0,-4,1) Matrix(769,-432,340,-191) -> Matrix(7,-2,4,-1) Matrix(745,-432,288,-167) -> Matrix(5,-4,4,-3) Matrix(121,-72,200,-119) -> Matrix(3,-2,2,-1) Matrix(2833,-1728,864,-527) -> Matrix(3,-2,2,-1) Matrix(311,-192,196,-121) -> Matrix(1,0,-2,1) Matrix(265,-168,112,-71) -> Matrix(1,0,0,1) Matrix(673,-432,148,-95) -> Matrix(3,-2,2,-1) Matrix(335,-216,76,-49) -> Matrix(1,0,0,1) Matrix(383,-264,280,-193) -> Matrix(3,-8,2,-5) Matrix(311,-216,36,-25) -> Matrix(1,0,0,1) Matrix(169,-120,100,-71) -> Matrix(1,2,0,1) Matrix(263,-192,100,-73) -> Matrix(3,-2,2,-1) Matrix(409,-312,156,-119) -> Matrix(7,-2,4,-1) Matrix(215,-168,32,-25) -> Matrix(5,-2,-2,1) Matrix(817,-672,524,-431) -> Matrix(1,0,0,1) Matrix(697,-576,144,-119) -> Matrix(5,2,2,1) Matrix(265,-336,56,-71) -> Matrix(3,-2,2,-1) Matrix(1129,-1440,432,-551) -> Matrix(7,-2,4,-1) Matrix(841,-1152,192,-263) -> Matrix(1,-2,4,-7) Matrix(49,-72,32,-47) -> Matrix(1,-2,0,1) Matrix(719,-1128,276,-433) -> Matrix(3,4,2,3) Matrix(623,-1104,136,-241) -> Matrix(1,2,0,1) Matrix(25,-48,12,-23) -> Matrix(1,0,0,1) Matrix(383,-840,88,-193) -> Matrix(1,0,-2,1) Matrix(25,-72,8,-23) -> Matrix(1,-2,0,1) Matrix(25,-144,4,-23) -> Matrix(1,-10,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 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 -8/1 -2/1 1 6 -6/1 (-2/1,0/1) 0 2 -5/1 0 12 -9/2 1/0 1 4 -4/1 1/0 2 6 -3/1 1/0 2 4 -8/3 -2/1 3 6 -18/7 -2/1 1 2 -5/2 0 12 -12/5 -1/1 4 2 -7/3 0 12 -16/7 0/1 1 6 -9/4 0/1 1 4 -2/1 1/0 1 6 -11/6 0 12 -9/5 -1/1 1 4 -16/9 0/1 1 6 -7/4 1/0 1 12 -12/7 1/0 4 2 -5/3 -3/1 1 12 -18/11 -2/1 5 2 -8/5 -2/1 3 6 -3/2 -1/1 1 4 -4/3 -1/1 2 6 -9/7 0/1 1 4 -14/11 -1/1 1 6 -19/15 0 12 -24/19 0/1 5 2 -5/4 1/0 1 12 -6/5 (-2/1,0/1) 0 2 -8/7 -2/1 1 6 -1/1 0 12 -6/7 -1/1 1 2 -5/6 0 12 -9/11 1/0 2 4 -4/5 -1/1 2 6 -3/4 -1/1 2 4 -8/11 -2/3 3 6 -5/7 -1/1 1 12 -12/17 -1/2 4 2 -7/10 0 12 -16/23 0/1 1 6 -9/13 -1/2 1 4 -2/3 0/1 1 6 -9/14 1/0 1 4 -16/25 0/1 1 6 -7/11 0 12 -12/19 -1/1 4 2 -5/8 -1/2 1 12 -8/13 0/1 3 6 -3/5 0/1 1 4 -4/7 1/0 2 6 -9/16 -2/1 1 4 -5/9 0 12 -6/11 -1/1 5 2 -1/2 0 12 0/1 0/1 1 2 1/2 0 12 3/5 1/1 1 4 5/8 1/2 1 12 7/11 1/1 1 12 16/25 0/1 1 6 9/14 1/1 1 4 2/3 1/1 1 6 9/13 1/0 2 4 7/10 0 12 5/7 0 12 8/11 0/1 3 6 3/4 0/1 1 4 4/5 1/1 2 6 5/6 0 12 6/7 0/1 1 2 1/1 1/1 1 12 7/6 0 12 6/5 1/0 1 2 5/4 1/0 1 12 14/11 0/1 1 6 9/7 1/1 1 4 4/3 1/1 2 6 15/11 3/2 2 4 26/19 5/3 1 6 11/8 3/2 1 12 18/13 2/1 5 2 7/5 0 12 3/2 1/0 1 4 11/7 -1/1 1 12 8/5 0/1 3 6 13/8 1/2 1 12 5/3 0 12 17/10 0 12 12/7 1/0 4 2 7/4 1/0 1 12 23/13 0 12 16/9 0/1 1 6 9/5 0/1 1 4 11/6 0 12 2/1 0 6 13/6 0 12 24/11 0/1 5 2 11/5 0 12 9/4 1/1 2 4 25/11 0 12 16/7 0/1 1 6 7/3 1/1 1 12 19/8 1/2 1 12 12/5 1/1 4 2 5/2 0 12 18/7 1/1 1 2 13/5 1/1 1 12 8/3 2/1 3 6 3/1 1/0 1 4 4/1 1/0 2 6 13/3 0 12 35/8 1/2 1 12 22/5 1/1 1 6 9/2 1/1 1 4 14/3 2/1 1 6 19/4 3/2 1 12 24/5 2/1 5 2 29/6 0 12 5/1 3/1 1 12 11/2 0 12 6/1 1/0 5 2 7/1 0 12 8/1 0/1 1 6 1/0 1/0 1 12 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(7,72,11,113) (-8/1,1/0) -> (7/11,16/25) Glide Reflection Matrix(7,48,-1,-7) (-8/1,-6/1) -> (-8/1,-6/1) Reflection Matrix(17,96,-3,-17) (-6/1,-16/3) -> (-6/1,-16/3) Reflection Matrix(23,120,32,167) (-11/2,-5/1) -> (5/7,13/18) Hyperbolic Matrix(31,144,-17,-79) (-5/1,-9/2) -> (-11/6,-9/5) Glide Reflection Matrix(17,72,13,55) (-9/2,-4/1) -> (9/7,4/3) Glide Reflection Matrix(7,24,-9,-31) (-4/1,-3/1) -> (-4/5,-3/4) Glide Reflection Matrix(17,48,-23,-65) (-3/1,-8/3) -> (-3/4,-8/11) Glide Reflection Matrix(55,144,-21,-55) (-8/3,-18/7) -> (-8/3,-18/7) Reflection Matrix(47,120,56,143) (-18/7,-5/2) -> (5/6,6/7) Hyperbolic Matrix(49,120,20,49) (-5/2,-12/5) -> (12/5,5/2) Hyperbolic Matrix(71,168,-112,-265) (-12/5,-7/3) -> (-7/11,-12/19) Hyperbolic Matrix(145,336,104,241) (-7/3,-23/10) -> (25/18,7/5) Hyperbolic Matrix(209,480,-91,-209) (-30/13,-16/7) -> (-30/13,-16/7) Reflection Matrix(127,288,71,161) (-16/7,-9/4) -> (16/9,9/5) Glide Reflection Matrix(65,144,-51,-113) (-9/4,-2/1) -> (-9/7,-14/11) Glide Reflection Matrix(103,192,-81,-151) (-2/1,-11/6) -> (-14/11,-19/15) Glide Reflection Matrix(161,288,-251,-449) (-9/5,-16/9) -> (-9/14,-16/25) Glide Reflection Matrix(271,480,-153,-271) (-16/9,-30/17) -> (-16/9,-30/17) Reflection Matrix(41,72,45,79) (-23/13,-7/4) -> (7/8,1/1) Glide Reflection Matrix(97,168,56,97) (-7/4,-12/7) -> (12/7,7/4) Hyperbolic Matrix(71,120,-100,-169) (-12/7,-5/3) -> (-5/7,-12/17) Hyperbolic Matrix(175,288,127,209) (-5/3,-18/11) -> (11/8,18/13) Glide Reflection Matrix(89,144,-55,-89) (-18/11,-8/5) -> (-18/11,-8/5) Reflection Matrix(31,48,11,17) (-8/5,-3/2) -> (8/3,3/1) Glide Reflection Matrix(17,24,5,7) (-3/2,-4/3) -> (3/1,4/1) Glide Reflection Matrix(55,72,-97,-127) (-4/3,-9/7) -> (-4/7,-9/16) Glide Reflection Matrix(607,768,279,353) (-19/15,-24/19) -> (13/6,24/11) Glide Reflection Matrix(457,576,96,121) (-24/19,-5/4) -> (19/4,24/5) Hyperbolic Matrix(175,216,111,137) (-5/4,-11/9) -> (11/7,19/12) Glide Reflection Matrix(79,96,-65,-79) (-16/13,-6/5) -> (-16/13,-6/5) Reflection Matrix(41,48,-35,-41) (-6/5,-8/7) -> (-6/5,-8/7) Reflection Matrix(191,216,84,95) (-8/7,-1/1) -> (25/11,16/7) Hyperbolic Matrix(55,48,47,41) (-1/1,-6/7) -> (7/6,6/5) Glide Reflection Matrix(143,120,56,47) (-6/7,-5/6) -> (5/2,18/7) Hyperbolic Matrix(175,144,79,65) (-5/6,-9/11) -> (11/5,9/4) Glide Reflection Matrix(119,96,88,71) (-9/11,-4/5) -> (4/3,15/11) Hyperbolic Matrix(199,144,123,89) (-8/11,-5/7) -> (8/5,13/8) Glide Reflection Matrix(409,288,240,169) (-12/17,-7/10) -> (17/10,12/7) Hyperbolic Matrix(689,480,389,271) (-7/10,-16/23) -> (23/13,16/9) Glide Reflection Matrix(415,288,647,449) (-16/23,-9/13) -> (16/25,9/14) Glide Reflection Matrix(209,144,45,31) (-9/13,-2/3) -> (9/2,14/3) Glide Reflection Matrix(223,144,175,113) (-2/3,-9/14) -> (14/11,9/7) Glide Reflection Matrix(263,168,36,23) (-16/25,-7/11) -> (7/1,8/1) Hyperbolic Matrix(457,288,192,121) (-12/19,-5/8) -> (19/8,12/5) Hyperbolic Matrix(233,144,89,55) (-5/8,-8/13) -> (13/5,8/3) Glide Reflection Matrix(79,48,107,65) (-8/13,-3/5) -> (8/11,3/4) Glide Reflection Matrix(41,24,53,31) (-3/5,-4/7) -> (3/4,4/5) Glide Reflection Matrix(257,144,141,79) (-9/16,-5/9) -> (9/5,11/6) Glide Reflection Matrix(175,96,31,17) (-5/9,-6/11) -> (11/2,6/1) Glide Reflection Matrix(89,48,13,7) (-6/11,-1/2) -> (6/1,7/1) Glide Reflection Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(41,-24,29,-17) (1/2,3/5) -> (7/5,3/2) Glide Reflection Matrix(79,-48,51,-31) (3/5,5/8) -> (3/2,11/7) Glide Reflection Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(335,-216,76,-49) (9/14,2/3) -> (22/5,9/2) Hyperbolic Matrix(383,-264,280,-193) (2/3,9/13) -> (15/11,26/19) Hyperbolic Matrix(415,-288,183,-127) (9/13,7/10) -> (9/4,25/11) Glide Reflection Matrix(169,-120,100,-71) (7/10,5/7) -> (5/3,17/10) Hyperbolic Matrix(199,-144,275,-199) (18/25,8/11) -> (18/25,8/11) Reflection Matrix(89,-72,21,-17) (4/5,5/6) -> (4/1,13/3) Glide Reflection Matrix(55,-48,63,-55) (6/7,8/9) -> (6/7,8/9) Reflection Matrix(65,-72,37,-41) (1/1,7/6) -> (7/4,23/13) Glide Reflection Matrix(137,-168,53,-65) (6/5,5/4) -> (18/7,13/5) Glide Reflection Matrix(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(841,-1152,192,-263) (26/19,11/8) -> (35/8,22/5) Hyperbolic Matrix(415,-576,299,-415) (18/13,32/23) -> (18/13,32/23) Reflection Matrix(151,-240,95,-151) (30/19,8/5) -> (30/19,8/5) Reflection Matrix(103,-168,19,-31) (13/8,5/3) -> (5/1,11/2) Glide Reflection Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(439,-960,91,-199) (24/11,11/5) -> (24/5,29/6) Glide Reflection Matrix(31,-72,3,-7) (16/7,7/3) -> (8/1,1/0) Glide Reflection Matrix(247,-1080,51,-223) (13/3,35/8) -> (29/6,5/1) Glide Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(7,72,11,113) -> Matrix(1,2,1,1) Matrix(7,48,-1,-7) -> Matrix(-1,0,1,1) (-8/1,-6/1) -> (-2/1,0/1) Matrix(17,96,-3,-17) -> Matrix(-1,0,1,1) (-6/1,-16/3) -> (-2/1,0/1) Matrix(23,120,32,167) -> Matrix(1,0,0,1) Matrix(31,144,-17,-79) -> Matrix(1,-2,-1,1) Matrix(17,72,13,55) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(7,24,-9,-31) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(17,48,-23,-65) -> Matrix(1,4,-1,-5) Matrix(55,144,-21,-55) -> Matrix(-1,0,1,1) (-8/3,-18/7) -> (-2/1,0/1) Matrix(47,120,56,143) -> Matrix(1,2,0,1) 1/0 Matrix(49,120,20,49) -> Matrix(3,4,2,3) Matrix(71,168,-112,-265) -> Matrix(3,2,-2,-1) -1/1 Matrix(145,336,104,241) -> Matrix(5,2,2,1) Matrix(209,480,-91,-209) -> Matrix(-1,0,1,1) (-30/13,-16/7) -> (-2/1,0/1) Matrix(127,288,71,161) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(65,144,-51,-113) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(103,192,-81,-151) -> Matrix(1,2,-1,-3) Matrix(161,288,-251,-449) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(271,480,-153,-271) -> Matrix(-1,0,1,1) (-16/9,-30/17) -> (-2/1,0/1) Matrix(41,72,45,79) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(97,168,56,97) -> Matrix(1,0,0,1) Matrix(71,120,-100,-169) -> Matrix(1,4,-2,-7) Matrix(175,288,127,209) -> Matrix(5,12,3,7) Matrix(89,144,-55,-89) -> Matrix(-1,0,1,1) (-18/11,-8/5) -> (-2/1,0/1) Matrix(31,48,11,17) -> Matrix(3,4,1,1) Matrix(17,24,5,7) -> Matrix(1,2,1,1) Matrix(55,72,-97,-127) -> Matrix(3,2,-1,-1) Matrix(607,768,279,353) -> Matrix(-1,0,3,1) *** -> (-2/3,0/1) Matrix(457,576,96,121) -> Matrix(3,-2,2,-1) 1/1 Matrix(175,216,111,137) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(79,96,-65,-79) -> Matrix(-1,0,1,1) (-16/13,-6/5) -> (-2/1,0/1) Matrix(41,48,-35,-41) -> Matrix(-1,0,1,1) (-6/5,-8/7) -> (-2/1,0/1) Matrix(191,216,84,95) -> Matrix(1,2,0,1) 1/0 Matrix(55,48,47,41) -> Matrix(1,2,1,1) Matrix(143,120,56,47) -> Matrix(1,2,0,1) 1/0 Matrix(175,144,79,65) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(119,96,88,71) -> Matrix(3,4,2,3) Matrix(199,144,123,89) -> Matrix(3,2,5,3) Matrix(409,288,240,169) -> Matrix(9,4,2,1) Matrix(689,480,389,271) -> Matrix(-1,0,3,1) *** -> (-2/3,0/1) Matrix(415,288,647,449) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(209,144,45,31) -> Matrix(5,2,3,1) Matrix(223,144,175,113) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(263,168,36,23) -> Matrix(1,0,0,1) Matrix(457,288,192,121) -> Matrix(3,2,4,3) Matrix(233,144,89,55) -> Matrix(5,2,3,1) Matrix(79,48,107,65) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(41,24,53,31) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(257,144,141,79) -> Matrix(1,2,1,1) Matrix(175,96,31,17) -> Matrix(7,8,1,1) Matrix(89,48,13,7) -> Matrix(3,2,-1,-1) Matrix(1,0,4,1) -> Matrix(1,0,2,1) 0/1 Matrix(41,-24,29,-17) -> Matrix(3,-2,1,-1) Matrix(79,-48,51,-31) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(265,-168,112,-71) -> Matrix(1,0,0,1) Matrix(335,-216,76,-49) -> Matrix(1,0,0,1) Matrix(383,-264,280,-193) -> Matrix(3,-8,2,-5) 2/1 Matrix(415,-288,183,-127) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(169,-120,100,-71) -> Matrix(1,2,0,1) 1/0 Matrix(199,-144,275,-199) -> Matrix(-1,0,1,1) (18/25,8/11) -> (-2/1,0/1) Matrix(89,-72,21,-17) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(55,-48,63,-55) -> Matrix(1,0,3,-1) (6/7,8/9) -> (0/1,2/3) Matrix(65,-72,37,-41) -> Matrix(1,-2,-1,1) Matrix(137,-168,53,-65) -> Matrix(1,2,1,1) Matrix(265,-336,56,-71) -> Matrix(3,-2,2,-1) 1/1 Matrix(841,-1152,192,-263) -> Matrix(1,-2,4,-7) Matrix(415,-576,299,-415) -> Matrix(7,-16,3,-7) (18/13,32/23) -> (2/1,8/3) Matrix(151,-240,95,-151) -> Matrix(-1,0,1,1) (30/19,8/5) -> (-2/1,0/1) Matrix(103,-168,19,-31) -> Matrix(5,-4,1,-1) Matrix(25,-48,12,-23) -> Matrix(1,0,0,1) Matrix(439,-960,91,-199) -> Matrix(11,-2,5,-1) Matrix(31,-72,3,-7) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(247,-1080,51,-223) -> Matrix(7,-2,3,-1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.