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): 864 Minimal number of generators: 145 Number of equivalence classes of cusps: 64 Genus: 41 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -16/9 -5/3 -14/9 -4/3 -1/1 -5/6 -2/3 -17/27 -1/2 -4/9 -10/27 -6/17 -1/3 -4/13 -8/27 -4/15 -19/72 -1/4 -2/9 -1/5 -1/6 -1/7 -2/15 -1/8 0/1 1/9 1/8 1/7 2/13 1/6 2/11 1/5 2/9 4/17 1/4 4/15 5/18 2/7 8/27 1/3 4/11 10/27 7/18 2/5 4/9 1/2 5/9 4/7 11/18 2/3 13/18 7/9 4/5 5/6 1/1 11/9 4/3 13/9 14/9 5/3 26/15 16/9 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 -24/13 1/2 -11/6 0/1 -20/11 1/0 -9/5 1/1 -16/9 0/1 -23/13 1/3 -7/4 0/1 -33/19 1/1 -26/15 1/1 -19/11 -1/1 -12/7 1/2 -17/10 2/1 -5/3 0/1 -18/11 1/2 1/1 -31/19 1/1 -13/8 2/1 -34/21 -1/1 -89/55 -1/1 -55/34 0/1 -21/13 -1/1 -8/5 1/2 -11/7 -1/1 -14/9 0/1 -17/11 1/3 -3/2 0/1 -19/13 1/1 -16/11 1/0 -13/9 0/1 -10/7 0/1 1/3 -17/12 0/1 2/5 -7/5 1/1 -18/13 0/1 1/3 -29/21 0/1 -11/8 2/5 -4/3 1/2 1/0 -13/10 2/5 -35/27 1/2 -22/17 1/2 5/9 -9/7 1/1 -14/11 1/2 1/1 -19/15 0/1 -5/4 2/3 -21/17 1/1 -16/13 3/4 -11/9 1/1 -6/5 0/1 1/1 -1/1 1/1 -6/7 1/1 2/1 -5/6 0/1 2/1 -9/11 -1/1 -4/5 1/2 -7/9 1/1 -10/13 1/1 6/5 -13/17 1/1 -3/4 2/1 -8/11 1/0 -13/18 0/1 2/1 -18/25 1/1 1/0 -5/7 1/1 -2/3 1/1 -7/11 1/1 -12/19 3/2 -17/27 2/1 -22/35 1/1 2/1 -5/8 2/1 -8/13 3/2 -11/18 2/1 -14/23 2/1 3/1 -3/5 1/1 -13/22 2/1 -10/17 3/1 1/0 -17/29 -1/1 -7/12 0/1 2/1 -11/19 1/1 -15/26 4/3 -4/7 1/0 -5/9 1/1 -6/11 1/1 3/2 -1/2 2/1 -4/9 1/0 -7/16 0/1 -17/39 0/1 -10/23 0/1 1/1 -3/7 1/1 -8/19 1/0 -13/31 -1/1 -5/12 0/1 2/1 -7/17 1/1 -2/5 1/1 2/1 -7/18 2/1 -12/31 13/6 -5/13 7/3 -13/34 2/1 -8/21 5/2 1/0 -3/8 2/1 -10/27 3/1 -17/46 16/5 -7/19 3/1 -11/30 4/1 -4/11 1/0 -5/14 4/1 -6/17 3/1 1/0 -1/3 1/0 -6/19 -1/1 1/0 -5/16 0/1 -9/29 1/1 -4/13 1/0 -3/10 0/1 -8/27 1/1 -13/44 8/7 -5/17 1/1 -2/7 1/1 2/1 -5/18 2/1 -8/29 9/4 -3/11 3/1 -10/37 2/1 3/1 -7/26 2/1 -4/15 5/2 1/0 -9/34 2/1 -14/53 5/2 3/1 -19/72 2/1 8/3 -5/19 3/1 -1/4 4/1 -2/9 1/0 -3/14 -6/1 -7/33 -4/1 -11/52 -4/1 -15/71 -3/1 -19/90 -4/1 -2/1 -4/19 1/0 -1/5 -1/1 -3/16 0/1 -2/11 1/1 1/0 -3/17 1/1 -4/23 3/2 -1/6 2/1 -3/19 3/1 -2/13 3/1 4/1 -1/7 3/1 -2/15 5/1 -1/8 8/1 -1/9 1/0 0/1 1/0 1/9 1/0 1/8 -8/1 1/7 -3/1 2/13 -4/1 -3/1 1/6 -2/1 4/23 -3/2 3/17 -1/1 2/11 -1/1 1/0 1/5 1/1 2/9 1/0 3/13 -9/1 4/17 1/0 1/4 -4/1 5/19 -3/1 4/15 -5/2 1/0 3/11 -3/1 5/18 -2/1 2/7 -2/1 -1/1 5/17 -1/1 8/27 -1/1 3/10 0/1 1/3 1/0 4/11 1/0 11/30 -4/1 7/19 -3/1 10/27 -3/1 3/8 -2/1 11/29 -3/1 8/21 -5/2 1/0 21/55 -3/1 13/34 -2/1 5/13 -7/3 7/18 -2/1 2/5 -2/1 -1/1 5/12 -2/1 0/1 8/19 1/0 3/7 -1/1 4/9 1/0 5/11 -3/1 6/13 -3/1 -2/1 1/2 -2/1 7/13 -5/3 6/11 -3/2 -1/1 5/9 -1/1 4/7 1/0 11/19 -1/1 7/12 -2/1 0/1 10/17 -3/1 1/0 13/22 -2/1 3/5 -1/1 11/18 -2/1 8/13 -3/2 21/34 -2/1 13/21 -3/2 5/8 -2/1 2/3 -1/1 7/10 0/1 26/37 -1/1 0/1 19/27 0/1 12/17 1/0 5/7 -1/1 13/18 -2/1 0/1 8/11 1/0 11/15 1/0 25/34 -2/1 39/53 -1/1 53/72 -2/1 0/1 14/19 -1/1 1/0 3/4 -2/1 13/17 -1/1 23/30 -4/3 10/13 -6/5 -1/1 7/9 -1/1 4/5 -1/2 5/6 -2/1 0/1 6/7 -2/1 -1/1 1/1 -1/1 7/6 -2/3 0/1 6/5 -1/1 0/1 11/9 -1/1 16/13 -3/4 21/17 -1/1 5/4 -2/3 14/11 -1/1 -1/2 23/18 -2/3 0/1 9/7 -1/1 4/3 -1/2 1/0 15/11 -1/1 26/19 -5/9 -1/2 37/27 -1/2 11/8 -2/5 18/13 -1/3 0/1 25/18 0/1 7/5 -1/1 24/17 -1/2 17/12 -2/5 0/1 10/7 -1/3 0/1 13/9 0/1 16/11 1/0 3/2 0/1 14/9 0/1 25/16 0/1 36/23 1/2 11/7 1/1 30/19 -3/1 1/0 19/12 -2/1 0/1 8/5 -1/2 29/18 0/1 21/13 1/1 55/34 0/1 34/21 1/1 13/8 -2/1 44/27 -1/1 31/19 -1/1 18/11 -1/1 -1/2 23/14 -2/3 28/17 -1/2 5/3 0/1 32/19 1/0 27/16 0/1 22/13 -1/1 0/1 17/10 -2/1 46/27 -1/1 29/17 -1/1 12/7 -1/2 31/18 0/1 19/11 1/1 45/26 -4/1 26/15 -1/1 59/34 0/1 92/53 1/0 125/72 -2/1 0/1 33/19 -1/1 7/4 0/1 16/9 0/1 25/14 0/1 9/5 -1/1 29/16 0/1 20/11 1/0 11/6 0/1 24/13 -1/2 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(73,136,-270,-503) (-2/1,-13/7) -> (-3/11,-10/37) Hyperbolic Matrix(395,732,252,467) (-13/7,-24/13) -> (36/23,11/7) Hyperbolic Matrix(37,68,216,397) (-24/13,-11/6) -> (1/6,4/23) Hyperbolic Matrix(145,264,396,721) (-11/6,-20/11) -> (4/11,11/30) Hyperbolic Matrix(289,524,-198,-359) (-20/11,-9/5) -> (-19/13,-16/11) Hyperbolic Matrix(287,512,-162,-289) (-9/5,-16/9) -> (-16/9,-23/13) Parabolic Matrix(181,320,306,541) (-23/13,-7/4) -> (13/22,3/5) Hyperbolic Matrix(179,312,144,251) (-7/4,-33/19) -> (21/17,5/4) Hyperbolic Matrix(1981,3436,-1224,-2123) (-33/19,-26/15) -> (-34/21,-89/55) Hyperbolic Matrix(37,64,-270,-467) (-26/15,-19/11) -> (-1/7,-2/15) Hyperbolic Matrix(109,188,-396,-683) (-19/11,-12/7) -> (-8/29,-3/11) Hyperbolic Matrix(145,248,-252,-431) (-12/7,-17/10) -> (-15/26,-4/7) Hyperbolic Matrix(323,548,-234,-397) (-17/10,-5/3) -> (-29/21,-11/8) Hyperbolic Matrix(251,412,-198,-325) (-5/3,-18/11) -> (-14/11,-19/15) Hyperbolic Matrix(71,116,396,647) (-18/11,-31/19) -> (3/17,2/11) Hyperbolic Matrix(287,468,-972,-1585) (-31/19,-13/8) -> (-13/44,-5/17) Hyperbolic Matrix(37,60,-288,-467) (-13/8,-34/21) -> (-2/15,-1/8) Hyperbolic Matrix(1115,1804,-5274,-8533) (-89/55,-55/34) -> (-11/52,-15/71) Hyperbolic Matrix(683,1104,378,611) (-55/34,-21/13) -> (9/5,29/16) Hyperbolic Matrix(181,292,-468,-755) (-21/13,-8/5) -> (-12/31,-5/13) Hyperbolic Matrix(73,116,-90,-143) (-8/5,-11/7) -> (-9/11,-4/5) Hyperbolic Matrix(251,392,-162,-253) (-11/7,-14/9) -> (-14/9,-17/11) Parabolic Matrix(73,112,-234,-359) (-17/11,-3/2) -> (-5/16,-9/29) Hyperbolic Matrix(757,1108,468,685) (-3/2,-19/13) -> (21/13,55/34) Hyperbolic Matrix(287,416,198,287) (-16/11,-13/9) -> (13/9,16/11) Hyperbolic Matrix(181,260,126,181) (-13/9,-10/7) -> (10/7,13/9) Hyperbolic Matrix(107,152,126,179) (-10/7,-17/12) -> (5/6,6/7) Hyperbolic Matrix(181,256,-432,-611) (-17/12,-7/5) -> (-13/31,-5/12) Hyperbolic Matrix(109,152,-180,-251) (-7/5,-18/13) -> (-14/23,-3/5) Hyperbolic Matrix(431,596,-990,-1369) (-18/13,-29/21) -> (-17/39,-10/23) Hyperbolic Matrix(71,96,-54,-73) (-11/8,-4/3) -> (-4/3,-13/10) Parabolic Matrix(37,48,306,397) (-13/10,-35/27) -> (1/9,1/8) Hyperbolic Matrix(1331,1724,972,1259) (-35/27,-22/17) -> (26/19,37/27) Hyperbolic Matrix(397,512,252,325) (-22/17,-9/7) -> (11/7,30/19) Hyperbolic Matrix(181,232,-252,-323) (-9/7,-14/11) -> (-18/25,-5/7) Hyperbolic Matrix(73,92,-342,-431) (-19/15,-5/4) -> (-3/14,-7/33) Hyperbolic Matrix(251,312,144,179) (-5/4,-21/17) -> (33/19,7/4) Hyperbolic Matrix(107,132,612,755) (-21/17,-16/13) -> (4/23,3/17) Hyperbolic Matrix(287,352,234,287) (-16/13,-11/9) -> (11/9,16/13) Hyperbolic Matrix(109,132,90,109) (-11/9,-6/5) -> (6/5,11/9) Hyperbolic Matrix(37,44,-90,-107) (-6/5,-1/1) -> (-7/17,-2/5) Hyperbolic Matrix(37,32,126,109) (-1/1,-6/7) -> (2/7,5/17) Hyperbolic Matrix(179,152,126,107) (-6/7,-5/6) -> (17/12,10/7) Hyperbolic Matrix(179,148,-306,-253) (-5/6,-9/11) -> (-17/29,-7/12) Hyperbolic Matrix(71,56,90,71) (-4/5,-7/9) -> (7/9,4/5) Hyperbolic Matrix(181,140,234,181) (-7/9,-10/13) -> (10/13,7/9) Hyperbolic Matrix(73,56,-468,-359) (-10/13,-13/17) -> (-3/19,-2/13) Hyperbolic Matrix(37,28,144,109) (-13/17,-3/4) -> (1/4,5/19) Hyperbolic Matrix(71,52,-198,-145) (-3/4,-8/11) -> (-4/11,-5/14) Hyperbolic Matrix(287,208,396,287) (-8/11,-13/18) -> (13/18,8/11) Hyperbolic Matrix(827,596,648,467) (-13/18,-18/25) -> (14/11,23/18) Hyperbolic Matrix(35,24,-54,-37) (-5/7,-2/3) -> (-2/3,-7/11) Parabolic Matrix(145,92,342,217) (-7/11,-12/19) -> (8/19,3/7) Hyperbolic Matrix(685,432,972,613) (-12/19,-17/27) -> (19/27,12/17) Hyperbolic Matrix(1367,860,1944,1223) (-17/27,-22/35) -> (26/37,19/27) Hyperbolic Matrix(541,340,288,181) (-22/35,-5/8) -> (15/8,2/1) Hyperbolic Matrix(71,44,-234,-145) (-5/8,-8/13) -> (-4/13,-3/10) Hyperbolic Matrix(287,176,468,287) (-8/13,-11/18) -> (11/18,8/13) Hyperbolic Matrix(899,548,648,395) (-11/18,-14/23) -> (18/13,25/18) Hyperbolic Matrix(323,192,180,107) (-3/5,-13/22) -> (25/14,9/5) Hyperbolic Matrix(359,212,486,287) (-13/22,-10/17) -> (14/19,3/4) Hyperbolic Matrix(1009,592,738,433) (-10/17,-17/29) -> (15/11,26/19) Hyperbolic Matrix(145,84,126,73) (-7/12,-11/19) -> (1/1,7/6) Hyperbolic Matrix(505,292,-1368,-791) (-11/19,-15/26) -> (-17/46,-7/19) Hyperbolic Matrix(71,40,126,71) (-4/7,-5/9) -> (5/9,4/7) Hyperbolic Matrix(109,60,198,109) (-5/9,-6/11) -> (6/11,5/9) Hyperbolic Matrix(37,20,-198,-107) (-6/11,-1/2) -> (-3/16,-2/11) Hyperbolic Matrix(71,32,-162,-73) (-1/2,-4/9) -> (-4/9,-7/16) Parabolic Matrix(541,236,-2556,-1115) (-7/16,-17/39) -> (-7/33,-11/52) Hyperbolic Matrix(37,16,252,109) (-10/23,-3/7) -> (1/7,2/13) Hyperbolic Matrix(179,76,252,107) (-3/7,-8/19) -> (12/17,5/7) Hyperbolic Matrix(181,76,774,325) (-8/19,-13/31) -> (3/13,4/17) Hyperbolic Matrix(251,104,432,179) (-5/12,-7/17) -> (11/19,7/12) Hyperbolic Matrix(71,28,180,71) (-2/5,-7/18) -> (7/18,2/5) Hyperbolic Matrix(1043,404,648,251) (-7/18,-12/31) -> (8/5,29/18) Hyperbolic Matrix(251,96,468,179) (-5/13,-13/34) -> (1/2,7/13) Hyperbolic Matrix(325,124,-1224,-467) (-13/34,-8/21) -> (-4/15,-9/34) Hyperbolic Matrix(179,68,-666,-253) (-8/21,-3/8) -> (-7/26,-4/15) Hyperbolic Matrix(539,200,-1458,-541) (-3/8,-10/27) -> (-10/27,-17/46) Parabolic Matrix(109,40,-684,-251) (-7/19,-11/30) -> (-1/6,-3/19) Hyperbolic Matrix(721,264,396,145) (-11/30,-4/11) -> (20/11,11/6) Hyperbolic Matrix(361,128,612,217) (-5/14,-6/17) -> (10/17,13/22) Hyperbolic Matrix(35,12,-108,-37) (-6/17,-1/3) -> (-1/3,-6/19) Parabolic Matrix(395,124,-1494,-469) (-6/19,-5/16) -> (-9/34,-14/53) Hyperbolic Matrix(865,268,468,145) (-9/29,-4/13) -> (24/13,13/7) Hyperbolic Matrix(431,128,-1458,-433) (-3/10,-8/27) -> (-8/27,-13/44) Parabolic Matrix(109,32,126,37) (-5/17,-2/7) -> (6/7,1/1) Hyperbolic Matrix(71,20,252,71) (-2/7,-5/18) -> (5/18,2/7) Hyperbolic Matrix(1115,308,648,179) (-5/18,-8/29) -> (12/7,31/18) Hyperbolic Matrix(935,252,1332,359) (-10/37,-7/26) -> (7/10,26/37) Hyperbolic Matrix(3817,1008,5184,1369) (-14/53,-19/72) -> (53/72,14/19) Hyperbolic Matrix(1441,380,-6822,-1799) (-19/72,-5/19) -> (-15/71,-19/90) Hyperbolic Matrix(109,28,144,37) (-5/19,-1/4) -> (3/4,13/17) Hyperbolic Matrix(35,8,-162,-37) (-1/4,-2/9) -> (-2/9,-3/14) Parabolic Matrix(10655,2248,6138,1295) (-19/90,-4/19) -> (92/53,125/72) Hyperbolic Matrix(253,52,180,37) (-4/19,-1/5) -> (7/5,24/17) Hyperbolic Matrix(145,28,378,73) (-1/5,-3/16) -> (13/34,5/13) Hyperbolic Matrix(647,116,396,71) (-2/11,-3/17) -> (31/19,18/11) Hyperbolic Matrix(755,132,612,107) (-3/17,-4/23) -> (16/13,21/17) Hyperbolic Matrix(397,68,216,37) (-4/23,-1/6) -> (11/6,24/13) Hyperbolic Matrix(107,16,234,35) (-2/13,-1/7) -> (5/11,6/13) Hyperbolic Matrix(395,48,288,35) (-1/8,-1/9) -> (37/27,11/8) Hyperbolic Matrix(1,0,18,1) (-1/9,0/1) -> (0/1,1/9) Parabolic Matrix(467,-64,270,-37) (1/8,1/7) -> (19/11,45/26) Hyperbolic Matrix(359,-56,468,-73) (2/13,1/6) -> (23/30,10/13) Hyperbolic Matrix(107,-20,198,-37) (2/11,1/5) -> (7/13,6/11) Hyperbolic Matrix(37,-8,162,-35) (1/5,2/9) -> (2/9,3/13) Parabolic Matrix(503,-120,306,-73) (4/17,1/4) -> (23/14,28/17) Hyperbolic Matrix(467,-124,1224,-325) (5/19,4/15) -> (8/21,21/55) Hyperbolic Matrix(253,-68,666,-179) (4/15,3/11) -> (11/29,8/21) Hyperbolic Matrix(683,-188,396,-109) (3/11,5/18) -> (31/18,19/11) Hyperbolic Matrix(1585,-468,972,-287) (5/17,8/27) -> (44/27,31/19) Hyperbolic Matrix(791,-236,486,-145) (8/27,3/10) -> (13/8,44/27) Hyperbolic Matrix(145,-44,234,-71) (3/10,1/3) -> (13/21,5/8) Hyperbolic Matrix(145,-52,198,-71) (1/3,4/11) -> (8/11,11/15) Hyperbolic Matrix(827,-304,1080,-397) (11/30,7/19) -> (13/17,23/30) Hyperbolic Matrix(1657,-612,972,-359) (7/19,10/27) -> (46/27,29/17) Hyperbolic Matrix(827,-308,486,-181) (10/27,3/8) -> (17/10,46/27) Hyperbolic Matrix(539,-204,288,-109) (3/8,11/29) -> (13/7,15/8) Hyperbolic Matrix(2701,-1032,3672,-1403) (21/55,13/34) -> (25/34,39/53) Hyperbolic Matrix(755,-292,468,-181) (5/13,7/18) -> (29/18,21/13) Hyperbolic Matrix(107,-44,90,-37) (2/5,5/12) -> (7/6,6/5) Hyperbolic Matrix(611,-256,432,-181) (5/12,8/19) -> (24/17,17/12) Hyperbolic Matrix(73,-32,162,-71) (3/7,4/9) -> (4/9,5/11) Parabolic Matrix(395,-184,234,-109) (6/13,1/2) -> (27/16,22/13) Hyperbolic Matrix(431,-248,252,-145) (4/7,11/19) -> (29/17,12/7) Hyperbolic Matrix(683,-400,432,-253) (7/12,10/17) -> (30/19,19/12) Hyperbolic Matrix(251,-152,180,-109) (3/5,11/18) -> (25/18,7/5) Hyperbolic Matrix(1549,-956,990,-611) (8/13,21/34) -> (25/16,36/23) Hyperbolic Matrix(899,-556,1224,-757) (21/34,13/21) -> (11/15,25/34) Hyperbolic Matrix(37,-24,54,-35) (5/8,2/3) -> (2/3,7/10) Parabolic Matrix(323,-232,252,-181) (5/7,13/18) -> (23/18,9/7) Hyperbolic Matrix(9001,-6624,5184,-3815) (39/53,53/72) -> (125/72,33/19) Hyperbolic Matrix(143,-116,90,-73) (4/5,5/6) -> (19/12,8/5) Hyperbolic Matrix(325,-412,198,-251) (5/4,14/11) -> (18/11,23/14) Hyperbolic Matrix(73,-96,54,-71) (9/7,4/3) -> (4/3,15/11) Parabolic Matrix(397,-548,234,-323) (11/8,18/13) -> (22/13,17/10) Hyperbolic Matrix(359,-524,198,-289) (16/11,3/2) -> (29/16,20/11) Hyperbolic Matrix(253,-392,162,-251) (3/2,14/9) -> (14/9,25/16) Parabolic Matrix(2123,-3436,1224,-1981) (55/34,34/21) -> (26/15,59/34) Hyperbolic Matrix(1153,-1868,666,-1079) (34/21,13/8) -> (45/26,26/15) Hyperbolic Matrix(181,-300,108,-179) (28/17,5/3) -> (5/3,32/19) Parabolic Matrix(2593,-4372,1494,-2519) (32/19,27/16) -> (59/34,92/53) Hyperbolic Matrix(289,-512,162,-287) (7/4,16/9) -> (16/9,25/14) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,0,-2,1) Matrix(73,136,-270,-503) -> Matrix(1,2,0,1) Matrix(395,732,252,467) -> Matrix(1,0,0,1) Matrix(37,68,216,397) -> Matrix(1,-2,0,1) Matrix(145,264,396,721) -> Matrix(1,-4,0,1) Matrix(289,524,-198,-359) -> Matrix(1,0,0,1) Matrix(287,512,-162,-289) -> Matrix(1,0,2,1) Matrix(181,320,306,541) -> Matrix(5,-2,-2,1) Matrix(179,312,144,251) -> Matrix(3,-2,-4,3) Matrix(1981,3436,-1224,-2123) -> Matrix(1,0,-2,1) Matrix(37,64,-270,-467) -> Matrix(1,4,0,1) Matrix(109,188,-396,-683) -> Matrix(5,2,2,1) Matrix(145,248,-252,-431) -> Matrix(3,-2,2,-1) Matrix(323,548,-234,-397) -> Matrix(1,0,2,1) Matrix(251,412,-198,-325) -> Matrix(1,0,0,1) Matrix(71,116,396,647) -> Matrix(1,0,-2,1) Matrix(287,468,-972,-1585) -> Matrix(7,-6,6,-5) Matrix(37,60,-288,-467) -> Matrix(1,6,0,1) Matrix(1115,1804,-5274,-8533) -> Matrix(7,4,-2,-1) Matrix(683,1104,378,611) -> Matrix(1,0,0,1) Matrix(181,292,-468,-755) -> Matrix(9,2,4,1) Matrix(73,116,-90,-143) -> Matrix(1,0,0,1) Matrix(251,392,-162,-253) -> Matrix(1,0,4,1) Matrix(73,112,-234,-359) -> Matrix(1,0,-2,1) Matrix(757,1108,468,685) -> Matrix(1,0,0,1) Matrix(287,416,198,287) -> Matrix(1,0,0,1) Matrix(181,260,126,181) -> Matrix(1,0,-6,1) Matrix(107,152,126,179) -> Matrix(5,-2,-2,1) Matrix(181,256,-432,-611) -> Matrix(1,0,-2,1) Matrix(109,152,-180,-251) -> Matrix(3,-2,2,-1) Matrix(431,596,-990,-1369) -> Matrix(1,0,-2,1) Matrix(71,96,-54,-73) -> Matrix(1,0,0,1) Matrix(37,48,306,397) -> Matrix(21,-10,-2,1) Matrix(1331,1724,972,1259) -> Matrix(19,-10,-36,19) Matrix(397,512,252,325) -> Matrix(3,-2,2,-1) Matrix(181,232,-252,-323) -> Matrix(3,-2,2,-1) Matrix(73,92,-342,-431) -> Matrix(9,-4,-2,1) Matrix(251,312,144,179) -> Matrix(3,-2,-4,3) Matrix(107,132,612,755) -> Matrix(1,0,-2,1) Matrix(287,352,234,287) -> Matrix(7,-6,-8,7) Matrix(109,132,90,109) -> Matrix(1,0,-2,1) Matrix(37,44,-90,-107) -> Matrix(3,-2,2,-1) Matrix(37,32,126,109) -> Matrix(3,-4,-2,3) Matrix(179,152,126,107) -> Matrix(1,-2,-2,5) Matrix(179,148,-306,-253) -> Matrix(1,0,0,1) Matrix(71,56,90,71) -> Matrix(3,-2,-4,3) Matrix(181,140,234,181) -> Matrix(11,-12,-10,11) Matrix(73,56,-468,-359) -> Matrix(11,-14,4,-5) Matrix(37,28,144,109) -> Matrix(7,-10,-2,3) Matrix(71,52,-198,-145) -> Matrix(1,2,0,1) Matrix(287,208,396,287) -> Matrix(1,-2,0,1) Matrix(827,596,648,467) -> Matrix(1,0,-2,1) Matrix(35,24,-54,-37) -> Matrix(3,-2,2,-1) Matrix(145,92,342,217) -> Matrix(3,-4,-2,3) Matrix(685,432,972,613) -> Matrix(1,-2,2,-3) Matrix(1367,860,1944,1223) -> Matrix(1,-2,0,1) Matrix(541,340,288,181) -> Matrix(1,-2,0,1) Matrix(71,44,-234,-145) -> Matrix(1,-2,2,-3) Matrix(287,176,468,287) -> Matrix(7,-12,-4,7) Matrix(899,548,648,395) -> Matrix(1,-2,-4,9) Matrix(323,192,180,107) -> Matrix(1,-2,0,1) Matrix(359,212,486,287) -> Matrix(1,-4,0,1) Matrix(1009,592,738,433) -> Matrix(1,2,-2,-3) Matrix(145,84,126,73) -> Matrix(1,0,-2,1) Matrix(505,292,-1368,-791) -> Matrix(7,-4,2,-1) Matrix(71,40,126,71) -> Matrix(1,-2,0,1) Matrix(109,60,198,109) -> Matrix(5,-6,-4,5) Matrix(37,20,-198,-107) -> Matrix(1,-2,2,-3) Matrix(71,32,-162,-73) -> Matrix(1,-2,0,1) Matrix(541,236,-2556,-1115) -> Matrix(1,-4,0,1) Matrix(37,16,252,109) -> Matrix(1,-4,0,1) Matrix(179,76,252,107) -> Matrix(1,-2,0,1) Matrix(181,76,774,325) -> Matrix(1,-8,0,1) Matrix(251,104,432,179) -> Matrix(1,-2,0,1) Matrix(71,28,180,71) -> Matrix(3,-4,-2,3) Matrix(1043,404,648,251) -> Matrix(1,-2,-8,17) Matrix(251,96,468,179) -> Matrix(1,-4,0,1) Matrix(325,124,-1224,-467) -> Matrix(1,0,0,1) Matrix(179,68,-666,-253) -> Matrix(1,0,0,1) Matrix(539,200,-1458,-541) -> Matrix(19,-54,6,-17) Matrix(109,40,-684,-251) -> Matrix(5,-18,2,-7) Matrix(721,264,396,145) -> Matrix(1,-4,0,1) Matrix(361,128,612,217) -> Matrix(1,-6,0,1) Matrix(35,12,-108,-37) -> Matrix(1,-4,0,1) Matrix(395,124,-1494,-469) -> Matrix(5,2,2,1) Matrix(865,268,468,145) -> Matrix(1,0,-2,1) Matrix(431,128,-1458,-433) -> Matrix(9,-8,8,-7) Matrix(109,32,126,37) -> Matrix(3,-4,-2,3) Matrix(71,20,252,71) -> Matrix(3,-4,-2,3) Matrix(1115,308,648,179) -> Matrix(1,-2,-6,13) Matrix(935,252,1332,359) -> Matrix(1,-2,-2,5) Matrix(3817,1008,5184,1369) -> Matrix(1,-2,-2,5) Matrix(1441,380,-6822,-1799) -> Matrix(5,-12,-2,5) Matrix(109,28,144,37) -> Matrix(3,-10,-2,7) Matrix(35,8,-162,-37) -> Matrix(1,-10,0,1) Matrix(10655,2248,6138,1295) -> Matrix(1,2,0,1) Matrix(253,52,180,37) -> Matrix(1,2,-2,-3) Matrix(145,28,378,73) -> Matrix(5,-2,-2,1) Matrix(647,116,396,71) -> Matrix(1,0,-2,1) Matrix(755,132,612,107) -> Matrix(1,0,-2,1) Matrix(397,68,216,37) -> Matrix(1,-2,0,1) Matrix(107,16,234,35) -> Matrix(1,-6,0,1) Matrix(395,48,288,35) -> Matrix(1,-10,-2,21) Matrix(1,0,18,1) -> Matrix(1,-2,0,1) Matrix(467,-64,270,-37) -> Matrix(1,4,0,1) Matrix(359,-56,468,-73) -> Matrix(5,14,-4,-11) Matrix(107,-20,198,-37) -> Matrix(3,2,-2,-1) Matrix(37,-8,162,-35) -> Matrix(1,-10,0,1) Matrix(503,-120,306,-73) -> Matrix(1,6,-2,-11) Matrix(467,-124,1224,-325) -> Matrix(1,0,0,1) Matrix(253,-68,666,-179) -> Matrix(1,0,0,1) Matrix(683,-188,396,-109) -> Matrix(1,2,2,5) Matrix(1585,-468,972,-287) -> Matrix(5,6,-6,-7) Matrix(791,-236,486,-145) -> Matrix(3,2,-2,-1) Matrix(145,-44,234,-71) -> Matrix(3,2,-2,-1) Matrix(145,-52,198,-71) -> Matrix(1,2,0,1) Matrix(827,-304,1080,-397) -> Matrix(3,8,-2,-5) Matrix(1657,-612,972,-359) -> Matrix(3,10,-4,-13) Matrix(827,-308,486,-181) -> Matrix(3,8,-2,-5) Matrix(539,-204,288,-109) -> Matrix(1,2,0,1) Matrix(2701,-1032,3672,-1403) -> Matrix(3,8,-2,-5) Matrix(755,-292,468,-181) -> Matrix(1,2,4,9) Matrix(107,-44,90,-37) -> Matrix(1,2,-2,-3) Matrix(611,-256,432,-181) -> Matrix(1,0,-2,1) Matrix(73,-32,162,-71) -> Matrix(1,-2,0,1) Matrix(395,-184,234,-109) -> Matrix(1,2,0,1) Matrix(431,-248,252,-145) -> Matrix(1,2,-2,-3) Matrix(683,-400,432,-253) -> Matrix(1,0,0,1) Matrix(251,-152,180,-109) -> Matrix(1,2,-2,-3) Matrix(1549,-956,990,-611) -> Matrix(1,2,0,1) Matrix(899,-556,1224,-757) -> Matrix(5,8,-2,-3) Matrix(37,-24,54,-35) -> Matrix(1,2,-2,-3) Matrix(323,-232,252,-181) -> Matrix(1,2,-2,-3) Matrix(9001,-6624,5184,-3815) -> Matrix(1,0,0,1) Matrix(143,-116,90,-73) -> Matrix(1,0,0,1) Matrix(325,-412,198,-251) -> Matrix(1,0,0,1) Matrix(73,-96,54,-71) -> Matrix(1,0,0,1) Matrix(397,-548,234,-323) -> Matrix(1,0,2,1) Matrix(359,-524,198,-289) -> Matrix(1,0,0,1) Matrix(253,-392,162,-251) -> Matrix(1,0,4,1) Matrix(2123,-3436,1224,-1981) -> Matrix(1,0,-2,1) Matrix(1153,-1868,666,-1079) -> Matrix(1,-2,0,1) Matrix(181,-300,108,-179) -> Matrix(1,0,2,1) Matrix(2593,-4372,1494,-2519) -> Matrix(1,0,0,1) Matrix(289,-512,162,-287) -> 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): 36 Degree of the the map X: 36 Degree of the the map Y: 144 ----------------------------------------------------------------------- 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 18 1/9 1/0 14 2 1/8 -8/1 1 18 1/7 -3/1 1 18 2/13 (-4/1,-3/1) 0 18 1/6 -2/1 1 6 4/23 -3/2 2 18 3/17 -1/1 1 18 2/11 (-1/1,1/0) 0 18 1/5 1/1 1 18 2/9 1/0 10 2 3/13 -9/1 1 18 4/17 1/0 2 18 1/4 -4/1 1 18 5/19 -3/1 1 18 4/15 0 6 3/11 -3/1 1 18 5/18 -2/1 5 2 2/7 (-2/1,-1/1) 0 18 5/17 -1/1 1 18 8/27 -1/1 8 2 3/10 0/1 1 18 1/3 1/0 2 6 4/11 1/0 2 18 11/30 -4/1 1 6 7/19 -3/1 1 18 10/27 -3/1 6 2 3/8 -2/1 1 18 11/29 -3/1 1 18 8/21 0 6 21/55 -3/1 1 18 13/34 -2/1 1 18 5/13 -7/3 1 18 7/18 -2/1 7 2 2/5 (-2/1,-1/1) 0 18 5/12 0 6 8/19 1/0 2 18 3/7 -1/1 1 18 4/9 1/0 2 2 5/11 -3/1 1 18 6/13 (-3/1,-2/1) 0 18 1/2 -2/1 1 18 7/13 -5/3 1 18 6/11 (-3/2,-1/1) 0 18 5/9 -1/1 2 2 4/7 1/0 2 18 11/19 -1/1 1 18 7/12 0 6 10/17 (-3/1,1/0) 0 18 13/22 -2/1 1 18 3/5 -1/1 1 18 11/18 -2/1 3 2 8/13 -3/2 2 18 21/34 -2/1 1 18 13/21 -3/2 2 6 5/8 -2/1 1 18 2/3 -1/1 2 6 7/10 0/1 1 18 26/37 (-1/1,0/1) 0 18 19/27 0/1 1 2 12/17 1/0 2 18 5/7 -1/1 1 18 13/18 (-1/1,1/0) 0 2 8/11 1/0 2 18 11/15 1/0 2 6 25/34 -2/1 1 18 39/53 -1/1 1 18 53/72 (-1/1,1/0) 0 2 14/19 (-1/1,1/0) 0 18 3/4 -2/1 1 18 13/17 -1/1 1 18 23/30 -4/3 1 6 10/13 (-6/5,-1/1) 0 18 7/9 -1/1 7 2 4/5 -1/2 2 18 5/6 0 6 6/7 (-2/1,-1/1) 0 18 1/1 -1/1 1 18 7/6 0 6 6/5 (-1/1,0/1) 0 18 11/9 -1/1 3 2 16/13 -3/4 2 18 21/17 -1/1 1 18 5/4 -2/3 1 18 14/11 (-1/1,-1/2) 0 18 23/18 (-1/1,-1/2) 0 2 9/7 -1/1 1 18 4/3 0 6 15/11 -1/1 1 18 26/19 (-5/9,-1/2) 0 18 37/27 -1/2 14 2 11/8 -2/5 1 18 18/13 (-1/3,0/1) 0 18 25/18 0/1 3 2 7/5 -1/1 1 18 24/17 -1/2 2 18 17/12 0 6 10/7 (-1/3,0/1) 0 18 13/9 0/1 3 2 16/11 1/0 2 18 3/2 0/1 1 18 14/9 0/1 4 2 25/16 0/1 1 18 36/23 1/2 2 18 11/7 1/1 1 18 30/19 (-3/1,1/0) 0 18 19/12 0 6 8/5 -1/2 2 18 29/18 0/1 7 2 21/13 1/1 1 18 55/34 0/1 1 18 34/21 1/1 2 6 13/8 -2/1 1 18 44/27 -1/1 8 2 31/19 -1/1 1 18 18/11 (-1/1,-1/2) 0 18 23/14 -2/3 1 18 28/17 -1/2 2 18 5/3 0/1 1 6 32/19 1/0 2 18 27/16 0/1 1 18 22/13 (-1/1,0/1) 0 18 17/10 -2/1 1 18 46/27 -1/1 6 2 29/17 -1/1 1 18 12/7 -1/2 2 18 31/18 0/1 5 2 19/11 1/1 1 18 45/26 -4/1 1 18 26/15 -1/1 2 6 59/34 0/1 1 18 92/53 1/0 2 18 125/72 (-1/1,1/0) 0 2 33/19 -1/1 1 18 7/4 0/1 1 18 16/9 0/1 2 2 25/14 0/1 1 18 9/5 -1/1 1 18 29/16 0/1 1 18 20/11 1/0 2 18 11/6 0/1 1 6 24/13 -1/2 2 18 13/7 -1/1 1 18 15/8 0/1 1 18 2/1 (-1/1,0/1) 0 18 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(1,0,18,-1) (0/1,1/9) -> (0/1,1/9) Reflection Matrix(395,-48,288,-35) (1/9,1/8) -> (37/27,11/8) Glide Reflection Matrix(467,-64,270,-37) (1/8,1/7) -> (19/11,45/26) Hyperbolic Matrix(107,-16,234,-35) (1/7,2/13) -> (5/11,6/13) Glide Reflection Matrix(359,-56,468,-73) (2/13,1/6) -> (23/30,10/13) Hyperbolic Matrix(397,-68,216,-37) (1/6,4/23) -> (11/6,24/13) Glide Reflection Matrix(755,-132,612,-107) (4/23,3/17) -> (16/13,21/17) Glide Reflection Matrix(647,-116,396,-71) (3/17,2/11) -> (31/19,18/11) Glide Reflection Matrix(107,-20,198,-37) (2/11,1/5) -> (7/13,6/11) Hyperbolic Matrix(37,-8,162,-35) (1/5,2/9) -> (2/9,3/13) Parabolic Matrix(431,-100,306,-71) (3/13,4/17) -> (7/5,24/17) Glide Reflection Matrix(503,-120,306,-73) (4/17,1/4) -> (23/14,28/17) Hyperbolic Matrix(109,-28,144,-37) (1/4,5/19) -> (3/4,13/17) Glide Reflection Matrix(467,-124,1224,-325) (5/19,4/15) -> (8/21,21/55) Hyperbolic Matrix(253,-68,666,-179) (4/15,3/11) -> (11/29,8/21) Hyperbolic Matrix(683,-188,396,-109) (3/11,5/18) -> (31/18,19/11) Hyperbolic Matrix(71,-20,252,-71) (5/18,2/7) -> (5/18,2/7) Reflection Matrix(109,-32,126,-37) (2/7,5/17) -> (6/7,1/1) Glide Reflection Matrix(1585,-468,972,-287) (5/17,8/27) -> (44/27,31/19) Hyperbolic Matrix(791,-236,486,-145) (8/27,3/10) -> (13/8,44/27) Hyperbolic Matrix(145,-44,234,-71) (3/10,1/3) -> (13/21,5/8) Hyperbolic Matrix(145,-52,198,-71) (1/3,4/11) -> (8/11,11/15) Hyperbolic Matrix(721,-264,396,-145) (4/11,11/30) -> (20/11,11/6) Glide Reflection Matrix(827,-304,1080,-397) (11/30,7/19) -> (13/17,23/30) Hyperbolic Matrix(1657,-612,972,-359) (7/19,10/27) -> (46/27,29/17) Hyperbolic Matrix(827,-308,486,-181) (10/27,3/8) -> (17/10,46/27) Hyperbolic Matrix(539,-204,288,-109) (3/8,11/29) -> (13/7,15/8) Hyperbolic Matrix(2701,-1032,3672,-1403) (21/55,13/34) -> (25/34,39/53) Hyperbolic Matrix(251,-96,468,-179) (13/34,5/13) -> (1/2,7/13) Glide Reflection Matrix(755,-292,468,-181) (5/13,7/18) -> (29/18,21/13) Hyperbolic Matrix(71,-28,180,-71) (7/18,2/5) -> (7/18,2/5) Reflection Matrix(107,-44,90,-37) (2/5,5/12) -> (7/6,6/5) Hyperbolic Matrix(611,-256,432,-181) (5/12,8/19) -> (24/17,17/12) Hyperbolic Matrix(179,-76,252,-107) (8/19,3/7) -> (12/17,5/7) Glide Reflection Matrix(73,-32,162,-71) (3/7,4/9) -> (4/9,5/11) Parabolic Matrix(395,-184,234,-109) (6/13,1/2) -> (27/16,22/13) Hyperbolic Matrix(109,-60,198,-109) (6/11,5/9) -> (6/11,5/9) Reflection Matrix(71,-40,126,-71) (5/9,4/7) -> (5/9,4/7) Reflection Matrix(431,-248,252,-145) (4/7,11/19) -> (29/17,12/7) Hyperbolic Matrix(145,-84,126,-73) (11/19,7/12) -> (1/1,7/6) Glide Reflection Matrix(683,-400,432,-253) (7/12,10/17) -> (30/19,19/12) Hyperbolic Matrix(359,-212,486,-287) (10/17,13/22) -> (14/19,3/4) Glide Reflection Matrix(323,-192,180,-107) (13/22,3/5) -> (25/14,9/5) Glide Reflection Matrix(251,-152,180,-109) (3/5,11/18) -> (25/18,7/5) Hyperbolic Matrix(287,-176,468,-287) (11/18,8/13) -> (11/18,8/13) Reflection Matrix(1549,-956,990,-611) (8/13,21/34) -> (25/16,36/23) Hyperbolic Matrix(899,-556,1224,-757) (21/34,13/21) -> (11/15,25/34) Hyperbolic Matrix(37,-24,54,-35) (5/8,2/3) -> (2/3,7/10) Parabolic Matrix(575,-404,306,-215) (7/10,26/37) -> (15/8,2/1) Glide Reflection Matrix(1405,-988,1998,-1405) (26/37,19/27) -> (26/37,19/27) Reflection Matrix(647,-456,918,-647) (19/27,12/17) -> (19/27,12/17) Reflection Matrix(323,-232,252,-181) (5/7,13/18) -> (23/18,9/7) Hyperbolic Matrix(287,-208,396,-287) (13/18,8/11) -> (13/18,8/11) Reflection Matrix(9001,-6624,5184,-3815) (39/53,53/72) -> (125/72,33/19) Hyperbolic Matrix(2015,-1484,2736,-2015) (53/72,14/19) -> (53/72,14/19) Reflection Matrix(181,-140,234,-181) (10/13,7/9) -> (10/13,7/9) Reflection Matrix(71,-56,90,-71) (7/9,4/5) -> (7/9,4/5) Reflection Matrix(143,-116,90,-73) (4/5,5/6) -> (19/12,8/5) Hyperbolic Matrix(179,-152,126,-107) (5/6,6/7) -> (17/12,10/7) Glide Reflection Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(287,-352,234,-287) (11/9,16/13) -> (11/9,16/13) Reflection Matrix(251,-312,144,-179) (21/17,5/4) -> (33/19,7/4) Glide Reflection Matrix(325,-412,198,-251) (5/4,14/11) -> (18/11,23/14) Hyperbolic Matrix(505,-644,396,-505) (14/11,23/18) -> (14/11,23/18) Reflection Matrix(73,-96,54,-71) (9/7,4/3) -> (4/3,15/11) Parabolic Matrix(539,-736,342,-467) (15/11,26/19) -> (11/7,30/19) Glide Reflection Matrix(1405,-1924,1026,-1405) (26/19,37/27) -> (26/19,37/27) Reflection Matrix(397,-548,234,-323) (11/8,18/13) -> (22/13,17/10) Hyperbolic Matrix(649,-900,468,-649) (18/13,25/18) -> (18/13,25/18) Reflection Matrix(181,-260,126,-181) (10/7,13/9) -> (10/7,13/9) Reflection Matrix(287,-416,198,-287) (13/9,16/11) -> (13/9,16/11) Reflection Matrix(359,-524,198,-289) (16/11,3/2) -> (29/16,20/11) Hyperbolic Matrix(253,-392,162,-251) (3/2,14/9) -> (14/9,25/16) Parabolic Matrix(467,-732,252,-395) (36/23,11/7) -> (24/13,13/7) Glide Reflection Matrix(289,-464,180,-289) (8/5,29/18) -> (8/5,29/18) Reflection Matrix(683,-1104,378,-611) (21/13,55/34) -> (9/5,29/16) Glide Reflection Matrix(2123,-3436,1224,-1981) (55/34,34/21) -> (26/15,59/34) Hyperbolic Matrix(1153,-1868,666,-1079) (34/21,13/8) -> (45/26,26/15) Hyperbolic Matrix(181,-300,108,-179) (28/17,5/3) -> (5/3,32/19) Parabolic Matrix(2593,-4372,1494,-2519) (32/19,27/16) -> (59/34,92/53) Hyperbolic Matrix(433,-744,252,-433) (12/7,31/18) -> (12/7,31/18) Reflection Matrix(13249,-23000,7632,-13249) (92/53,125/72) -> (92/53,125/72) Reflection Matrix(289,-512,162,-287) (7/4,16/9) -> (16/9,25/14) Parabolic 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(1,0,18,-1) -> Matrix(1,2,0,-1) (0/1,1/9) -> (-1/1,1/0) Matrix(395,-48,288,-35) -> Matrix(1,10,-2,-21) Matrix(467,-64,270,-37) -> Matrix(1,4,0,1) 1/0 Matrix(107,-16,234,-35) -> Matrix(1,6,0,-1) *** -> (-3/1,1/0) Matrix(359,-56,468,-73) -> Matrix(5,14,-4,-11) Matrix(397,-68,216,-37) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(755,-132,612,-107) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(647,-116,396,-71) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(107,-20,198,-37) -> Matrix(3,2,-2,-1) -1/1 Matrix(37,-8,162,-35) -> Matrix(1,-10,0,1) 1/0 Matrix(431,-100,306,-71) -> Matrix(1,8,-2,-17) Matrix(503,-120,306,-73) -> Matrix(1,6,-2,-11) Matrix(109,-28,144,-37) -> Matrix(3,10,-2,-7) Matrix(467,-124,1224,-325) -> Matrix(1,0,0,1) Matrix(253,-68,666,-179) -> Matrix(1,0,0,1) Matrix(683,-188,396,-109) -> Matrix(1,2,2,5) Matrix(71,-20,252,-71) -> Matrix(3,4,-2,-3) (5/18,2/7) -> (-2/1,-1/1) Matrix(109,-32,126,-37) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(1585,-468,972,-287) -> Matrix(5,6,-6,-7) -1/1 Matrix(791,-236,486,-145) -> Matrix(3,2,-2,-1) -1/1 Matrix(145,-44,234,-71) -> Matrix(3,2,-2,-1) -1/1 Matrix(145,-52,198,-71) -> Matrix(1,2,0,1) 1/0 Matrix(721,-264,396,-145) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(827,-304,1080,-397) -> Matrix(3,8,-2,-5) -2/1 Matrix(1657,-612,972,-359) -> Matrix(3,10,-4,-13) Matrix(827,-308,486,-181) -> Matrix(3,8,-2,-5) -2/1 Matrix(539,-204,288,-109) -> Matrix(1,2,0,1) 1/0 Matrix(2701,-1032,3672,-1403) -> Matrix(3,8,-2,-5) -2/1 Matrix(251,-96,468,-179) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(755,-292,468,-181) -> Matrix(1,2,4,9) Matrix(71,-28,180,-71) -> Matrix(3,4,-2,-3) (7/18,2/5) -> (-2/1,-1/1) Matrix(107,-44,90,-37) -> Matrix(1,2,-2,-3) -1/1 Matrix(611,-256,432,-181) -> Matrix(1,0,-2,1) 0/1 Matrix(179,-76,252,-107) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(73,-32,162,-71) -> Matrix(1,-2,0,1) 1/0 Matrix(395,-184,234,-109) -> Matrix(1,2,0,1) 1/0 Matrix(109,-60,198,-109) -> Matrix(5,6,-4,-5) (6/11,5/9) -> (-3/2,-1/1) Matrix(71,-40,126,-71) -> Matrix(1,2,0,-1) (5/9,4/7) -> (-1/1,1/0) Matrix(431,-248,252,-145) -> Matrix(1,2,-2,-3) -1/1 Matrix(145,-84,126,-73) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(683,-400,432,-253) -> Matrix(1,0,0,1) Matrix(359,-212,486,-287) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(323,-192,180,-107) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(251,-152,180,-109) -> Matrix(1,2,-2,-3) -1/1 Matrix(287,-176,468,-287) -> Matrix(7,12,-4,-7) (11/18,8/13) -> (-2/1,-3/2) Matrix(1549,-956,990,-611) -> Matrix(1,2,0,1) 1/0 Matrix(899,-556,1224,-757) -> Matrix(5,8,-2,-3) -2/1 Matrix(37,-24,54,-35) -> Matrix(1,2,-2,-3) -1/1 Matrix(575,-404,306,-215) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1405,-988,1998,-1405) -> Matrix(-1,0,2,1) (26/37,19/27) -> (-1/1,0/1) Matrix(647,-456,918,-647) -> Matrix(1,0,0,-1) (19/27,12/17) -> (0/1,1/0) Matrix(323,-232,252,-181) -> Matrix(1,2,-2,-3) -1/1 Matrix(287,-208,396,-287) -> Matrix(1,2,0,-1) (13/18,8/11) -> (-1/1,1/0) Matrix(9001,-6624,5184,-3815) -> Matrix(1,0,0,1) Matrix(2015,-1484,2736,-2015) -> Matrix(1,2,0,-1) (53/72,14/19) -> (-1/1,1/0) Matrix(181,-140,234,-181) -> Matrix(11,12,-10,-11) (10/13,7/9) -> (-6/5,-1/1) Matrix(71,-56,90,-71) -> Matrix(3,2,-4,-3) (7/9,4/5) -> (-1/1,-1/2) Matrix(143,-116,90,-73) -> Matrix(1,0,0,1) Matrix(179,-152,126,-107) -> Matrix(1,2,-2,-5) Matrix(109,-132,90,-109) -> Matrix(-1,0,2,1) (6/5,11/9) -> (-1/1,0/1) Matrix(287,-352,234,-287) -> Matrix(7,6,-8,-7) (11/9,16/13) -> (-1/1,-3/4) Matrix(251,-312,144,-179) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(325,-412,198,-251) -> Matrix(1,0,0,1) Matrix(505,-644,396,-505) -> Matrix(3,2,-4,-3) (14/11,23/18) -> (-1/1,-1/2) Matrix(73,-96,54,-71) -> Matrix(1,0,0,1) Matrix(539,-736,342,-467) -> Matrix(3,2,2,1) Matrix(1405,-1924,1026,-1405) -> Matrix(19,10,-36,-19) (26/19,37/27) -> (-5/9,-1/2) Matrix(397,-548,234,-323) -> Matrix(1,0,2,1) 0/1 Matrix(649,-900,468,-649) -> Matrix(-1,0,6,1) (18/13,25/18) -> (-1/3,0/1) Matrix(181,-260,126,-181) -> Matrix(-1,0,6,1) (10/7,13/9) -> (-1/3,0/1) Matrix(287,-416,198,-287) -> Matrix(1,0,0,-1) (13/9,16/11) -> (0/1,1/0) Matrix(359,-524,198,-289) -> Matrix(1,0,0,1) Matrix(253,-392,162,-251) -> Matrix(1,0,4,1) 0/1 Matrix(467,-732,252,-395) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(289,-464,180,-289) -> Matrix(-1,0,4,1) (8/5,29/18) -> (-1/2,0/1) Matrix(683,-1104,378,-611) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2123,-3436,1224,-1981) -> Matrix(1,0,-2,1) 0/1 Matrix(1153,-1868,666,-1079) -> Matrix(1,-2,0,1) 1/0 Matrix(181,-300,108,-179) -> Matrix(1,0,2,1) 0/1 Matrix(2593,-4372,1494,-2519) -> Matrix(1,0,0,1) Matrix(433,-744,252,-433) -> Matrix(-1,0,4,1) (12/7,31/18) -> (-1/2,0/1) Matrix(13249,-23000,7632,-13249) -> Matrix(1,2,0,-1) (92/53,125/72) -> (-1/1,1/0) Matrix(289,-512,162,-287) -> Matrix(1,0,2,1) 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.