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): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -5/6 -4/5 -18/25 -7/10 -2/3 -11/18 -3/5 -14/25 -8/15 -1/2 -9/20 -5/12 -2/5 -8/21 -16/45 -1/3 -14/45 -3/10 -8/27 -4/15 -1/4 -2/9 -3/14 -6/29 -1/5 -4/21 -4/23 -1/6 -2/15 -1/8 -1/9 -1/10 -1/11 0/1 1/10 1/9 1/8 2/15 1/7 2/13 1/6 2/11 1/5 4/19 3/14 2/9 3/13 7/30 4/17 1/4 4/15 2/7 8/27 3/10 1/3 11/30 2/5 5/12 13/30 9/20 7/15 1/2 8/15 14/25 17/30 3/5 11/18 19/30 2/3 31/45 7/10 151/210 18/25 11/15 23/30 4/5 5/6 13/15 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/1 -7/8 1/1 3/1 -13/15 1/1 -6/7 1/1 2/1 -5/6 1/0 -14/17 2/1 1/0 -23/28 -1/1 1/1 -32/39 1/1 2/1 1/0 -9/11 3/1 -4/5 1/0 -15/19 1/1 -11/14 -1/1 1/1 -18/23 -3/1 1/0 -25/32 -1/1 -1/3 -32/41 0/1 1/0 -7/9 -1/1 1/1 -10/13 4/1 1/0 -23/30 1/0 -13/17 -5/1 -3/4 -1/1 1/1 -14/19 2/1 1/0 -11/15 1/0 -8/11 -1/1 1/0 -21/29 -1/1 -13/18 0/1 -44/61 0/1 1/0 -31/43 -1/1 -18/25 1/0 -23/32 -1/1 -3/5 -5/7 1/1 -22/31 2/3 1/1 -17/24 1/0 -12/17 0/1 1/0 -19/27 -1/1 1/1 -7/10 1/0 -23/33 -3/1 -1/1 -16/23 -1/1 1/0 -9/13 1/1 -2/3 0/1 1/1 1/0 -11/17 1/1 -9/14 -1/1 1/1 -16/25 1/0 -39/61 -1/1 -23/36 0/1 -7/11 -1/1 -19/30 0/1 -12/19 0/1 1/2 -17/27 1/3 1/1 -56/89 8/9 1/1 -39/62 1/1 7/5 -22/35 1/0 -5/8 -1/1 1/1 -23/37 1/1 -18/29 1/1 2/1 -13/21 1/1 3/1 -8/13 -2/1 1/0 -19/31 -1/1 -11/18 0/1 -36/59 0/1 1/0 -25/41 -1/1 -14/23 1/1 1/0 -17/28 -5/3 -1/1 -3/5 0/1 -13/22 -1/1 1/1 -23/39 -1/1 1/1 -10/17 0/1 1/2 -17/29 1/1 -7/12 1/0 -4/7 -1/1 0/1 -17/30 0/1 -13/23 1/7 -35/62 1/5 3/13 -22/39 0/1 1/5 1/4 -9/16 1/3 1/1 -14/25 1/2 -33/59 1/1 -19/34 -1/1 1/1 -5/9 1/3 1/1 -16/29 0/1 1/1 -11/20 1/1 -17/31 1/1 -6/11 1/1 1/0 -7/13 -1/1 -8/15 0/1 -9/17 1/1 -1/2 -1/1 1/1 -8/17 2/1 1/0 -7/15 1/0 -6/13 0/1 1/0 -5/11 1/1 -9/20 1/1 -13/29 1/1 -4/9 1/1 2/1 1/0 -7/16 3/1 5/1 -10/23 7/1 1/0 -13/30 1/0 -3/7 -1/1 -14/33 0/1 1/2 1/1 -25/59 1/1 -11/26 1/1 3/1 -8/19 0/1 1/0 -29/69 -1/1 1/1 -21/50 0/1 -13/31 1/1 -5/12 1/0 -2/5 1/0 -7/18 1/0 -12/31 -1/1 0/1 -29/75 0/1 -17/44 -1/1 1/1 -5/13 1/1 -13/34 -5/1 -3/1 -34/89 -3/1 -14/5 -21/55 -2/1 -8/21 -2/1 -1/1 1/0 -27/71 -3/1 -19/50 -2/1 -11/29 -1/1 -14/37 -1/1 1/0 -17/45 -1/1 -3/8 -1/1 1/1 -13/35 0/1 -23/62 5/7 1/1 -56/151 14/15 1/1 -89/240 1/1 -33/89 1/1 -10/27 1/1 2/1 1/0 -17/46 1/1 3/1 -7/19 3/1 -11/30 1/0 -4/11 -3/1 1/0 -5/14 -5/3 -1/1 -16/45 -1/1 -11/31 -1/1 -6/17 0/1 1/0 -1/3 -1/1 1/1 -5/16 -3/1 -1/1 -14/45 -1/1 -9/29 -1/1 -4/13 -1/2 0/1 -7/23 -1/1 -3/10 0/1 -11/37 1/3 -8/27 0/1 1/1 1/0 -13/44 -1/1 1/1 -31/105 0/1 -18/61 0/1 1/0 -5/17 1/1 -17/58 1/3 1/1 -12/41 0/1 1/0 -7/24 1/0 -2/7 -1/1 0/1 -5/18 1/0 -8/29 -2/1 -1/1 -11/40 -1/1 -3/11 -1/1 -4/15 0/1 -5/19 1/3 -6/23 1/2 1/1 -7/27 3/5 1/1 -8/31 1/1 6/5 -1/4 -1/1 1/1 -5/21 -1/1 -1/3 -4/17 -1/4 0/1 -7/30 0/1 -3/13 1/3 -8/35 1/2 -5/22 1/3 1/1 -7/31 1/1 -2/9 0/1 1/1 1/0 -3/14 -3/1 -1/1 -7/33 -1/1 1/1 -4/19 0/1 1/0 -5/24 1/0 -6/29 -4/3 -1/1 -1/5 0/1 -4/21 -1/1 0/1 1/0 -3/16 1/3 1/1 -2/11 -1/1 1/0 -3/17 1/1 -4/23 -1/1 1/0 -5/29 -1/1 -1/6 0/1 -3/19 1/1 -2/13 0/1 1/0 -1/7 -1/1 -2/15 0/1 -3/23 1/1 -1/8 -1/1 1/1 -1/9 -1/1 1/1 -1/10 0/1 -1/11 -1/1 0/1 0/1 1/0 1/10 0/1 1/9 -1/1 1/1 1/8 -1/1 1/1 2/15 0/1 1/7 1/1 2/13 0/1 1/0 1/6 0/1 3/17 -1/1 2/11 1/1 1/0 1/5 0/1 5/24 1/0 4/19 0/1 1/0 3/14 1/1 3/1 2/9 -1/1 0/1 1/0 5/22 -1/1 -1/3 8/35 -1/2 3/13 -1/3 7/30 0/1 4/17 0/1 1/4 5/21 1/3 1/1 1/4 -1/1 1/1 4/15 0/1 7/26 1/5 1/3 10/37 1/3 1/2 3/11 1/1 2/7 0/1 1/1 5/17 -1/1 18/61 0/1 1/0 13/44 -1/1 1/1 8/27 -1/1 0/1 1/0 3/10 0/1 10/33 0/1 1/4 1/3 7/23 1/1 4/13 0/1 1/2 5/16 1/1 3/1 1/3 -1/1 1/1 6/17 0/1 1/0 5/14 1/1 5/3 14/39 2/1 3/1 1/0 9/25 2/1 4/11 3/1 1/0 11/30 1/0 7/19 -3/1 10/27 -2/1 -1/1 1/0 3/8 -1/1 1/1 14/37 1/1 1/0 11/29 1/1 19/50 2/1 27/71 3/1 8/21 1/1 2/1 1/0 21/55 2/1 34/89 14/5 3/1 13/34 3/1 5/1 5/13 -1/1 2/5 1/0 7/17 -3/1 12/29 -2/1 -1/1 5/12 1/0 13/31 -1/1 21/50 0/1 29/69 -1/1 1/1 8/19 0/1 1/0 11/26 -3/1 -1/1 25/59 -1/1 14/33 -1/1 -1/2 0/1 3/7 1/1 13/30 1/0 10/23 -7/1 1/0 7/16 -5/1 -3/1 4/9 -2/1 -1/1 1/0 13/29 -1/1 9/20 -1/1 5/11 -1/1 11/24 0/1 6/13 0/1 1/0 7/15 1/0 1/2 -1/1 1/1 8/15 0/1 15/28 1/3 1/1 7/13 1/1 6/11 -1/1 1/0 11/20 -1/1 5/9 -1/1 -1/3 19/34 -1/1 1/1 33/59 -1/1 14/25 -1/2 9/16 -1/1 -1/3 22/39 -1/4 -1/5 0/1 13/23 -1/7 17/30 0/1 4/7 0/1 1/1 11/19 1/1 29/50 1/1 18/31 1/1 2/1 7/12 1/0 17/29 -1/1 44/75 -1/1 27/46 -1/1 -5/7 10/17 -1/2 0/1 23/39 -1/1 1/1 13/22 -1/1 1/1 16/27 -2/1 -1/1 1/0 3/5 0/1 20/33 1/2 2/3 1/1 37/61 1/1 17/28 1/1 5/3 14/23 -1/1 1/0 25/41 1/1 61/100 0/1 36/59 0/1 1/0 11/18 0/1 19/31 1/1 46/75 1/1 27/44 1/1 7/5 8/13 2/1 1/0 13/21 -3/1 -1/1 31/50 -1/1 18/29 -2/1 -1/1 23/37 -1/1 28/45 0/1 5/8 -1/1 1/1 22/35 1/0 17/27 -1/1 -1/3 29/46 -1/1 -3/5 12/19 -1/2 0/1 19/30 0/1 7/11 1/1 23/36 0/1 39/61 1/1 16/25 1/0 9/14 -1/1 1/1 2/3 -1/1 0/1 1/0 11/16 -1/1 1/1 42/61 0/1 1/0 31/45 0/1 20/29 0/1 1/1 9/13 -1/1 25/36 0/1 41/59 1/1 16/23 1/1 1/0 7/10 1/0 26/37 -1/1 1/0 45/64 -5/3 -1/1 64/91 -8/7 -1/1 19/27 -1/1 1/1 12/17 0/1 1/0 17/24 1/0 39/55 -2/1 22/31 -1/1 -2/3 5/7 -1/1 28/39 0/1 1/2 1/1 23/32 3/5 1/1 87/121 1/1 151/210 1/1 64/89 1/1 10/9 41/57 1/1 5/3 18/25 1/0 31/43 1/1 44/61 0/1 1/0 13/18 0/1 21/29 1/1 29/40 1/1 8/11 1/1 1/0 11/15 1/0 14/19 -2/1 1/0 3/4 -1/1 1/1 13/17 5/1 23/30 1/0 10/13 -4/1 1/0 7/9 -1/1 1/1 32/41 0/1 1/0 25/32 1/3 1/1 18/23 3/1 1/0 11/14 -1/1 1/1 4/5 1/0 13/16 -3/1 -1/1 22/27 -2/1 -1/1 1/0 9/11 -3/1 32/39 -2/1 -1/1 1/0 23/28 -1/1 1/1 37/45 1/0 14/17 -2/1 1/0 5/6 1/0 16/19 -2/1 1/0 27/32 -3/1 -7/3 11/13 -3/1 6/7 -2/1 -1/1 13/15 -1/1 20/23 -1/1 1/0 7/8 -3/1 -1/1 8/9 -2/1 -3/2 -1/1 1/1 -1/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(61,54,-270,-239) (-1/1,-7/8) -> (-5/22,-7/31) Hyperbolic Matrix(181,158,-480,-419) (-7/8,-13/15) -> (-17/45,-3/8) Hyperbolic Matrix(181,156,210,181) (-13/15,-6/7) -> (6/7,13/15) Hyperbolic Matrix(61,52,-210,-179) (-6/7,-5/6) -> (-7/24,-2/7) Hyperbolic Matrix(361,298,510,421) (-5/6,-14/17) -> (12/17,17/24) Hyperbolic Matrix(241,198,-510,-419) (-14/17,-23/28) -> (-1/2,-8/17) Hyperbolic Matrix(1681,1380,2340,1921) (-23/28,-32/39) -> (28/39,23/32) Hyperbolic Matrix(1141,936,3000,2461) (-32/39,-9/11) -> (27/71,8/21) Hyperbolic Matrix(119,96,-150,-121) (-9/11,-4/5) -> (-4/5,-15/19) Parabolic Matrix(421,332,-1140,-899) (-15/19,-11/14) -> (-17/46,-7/19) Hyperbolic Matrix(301,236,690,541) (-11/14,-18/23) -> (10/23,7/16) Hyperbolic Matrix(839,656,1380,1079) (-18/23,-25/32) -> (17/28,14/23) Hyperbolic Matrix(1619,1264,1920,1499) (-25/32,-32/41) -> (16/19,27/32) Hyperbolic Matrix(1261,984,3000,2341) (-32/41,-7/9) -> (29/69,8/19) Hyperbolic Matrix(241,186,390,301) (-7/9,-10/13) -> (8/13,13/21) Hyperbolic Matrix(599,460,780,599) (-10/13,-23/30) -> (23/30,10/13) Hyperbolic Matrix(781,598,1020,781) (-23/30,-13/17) -> (13/17,23/30) Hyperbolic Matrix(241,184,630,481) (-13/17,-3/4) -> (13/34,5/13) Hyperbolic Matrix(241,178,570,421) (-3/4,-14/19) -> (8/19,11/26) Hyperbolic Matrix(419,308,570,419) (-14/19,-11/15) -> (11/15,14/19) Hyperbolic Matrix(241,176,330,241) (-11/15,-8/11) -> (8/11,11/15) Hyperbolic Matrix(361,262,-660,-479) (-8/11,-21/29) -> (-17/31,-6/11) Hyperbolic Matrix(661,478,1080,781) (-21/29,-13/18) -> (11/18,19/31) Hyperbolic Matrix(1319,952,2160,1559) (-13/18,-44/61) -> (36/59,11/18) Hyperbolic Matrix(1079,778,3660,2639) (-44/61,-31/43) -> (5/17,18/61) Hyperbolic Matrix(419,302,1830,1319) (-31/43,-18/25) -> (8/35,3/13) Hyperbolic Matrix(1679,1208,-2670,-1921) (-18/25,-23/32) -> (-39/62,-22/35) Hyperbolic Matrix(661,474,-1170,-839) (-23/32,-5/7) -> (-13/23,-35/62) Hyperbolic Matrix(839,596,1350,959) (-5/7,-22/31) -> (18/29,23/37) Hyperbolic Matrix(299,212,-1440,-1021) (-22/31,-17/24) -> (-5/24,-6/29) Hyperbolic Matrix(421,298,510,361) (-17/24,-12/17) -> (14/17,5/6) Hyperbolic Matrix(179,126,510,359) (-12/17,-19/27) -> (1/3,6/17) Hyperbolic Matrix(419,294,-600,-421) (-19/27,-7/10) -> (-7/10,-23/33) Parabolic Matrix(359,250,-1380,-961) (-23/33,-16/23) -> (-6/23,-7/27) Hyperbolic Matrix(121,84,-690,-479) (-16/23,-9/13) -> (-3/17,-4/23) Hyperbolic Matrix(59,40,-90,-61) (-9/13,-2/3) -> (-2/3,-11/17) Parabolic Matrix(359,232,-930,-601) (-11/17,-9/14) -> (-17/44,-5/13) Hyperbolic Matrix(421,270,750,481) (-9/14,-16/25) -> (14/25,9/16) Hyperbolic Matrix(1679,1074,3000,1919) (-16/25,-39/61) -> (33/59,14/25) Hyperbolic Matrix(3001,1918,4320,2761) (-39/61,-23/36) -> (25/36,41/59) Hyperbolic Matrix(301,192,660,421) (-23/36,-7/11) -> (5/11,11/24) Hyperbolic Matrix(419,266,660,419) (-7/11,-19/30) -> (19/30,7/11) Hyperbolic Matrix(721,456,1140,721) (-19/30,-12/19) -> (12/19,19/30) Hyperbolic Matrix(241,152,-1140,-719) (-12/19,-17/27) -> (-7/33,-4/19) Hyperbolic Matrix(3419,2152,4860,3059) (-17/27,-56/89) -> (64/91,19/27) Hyperbolic Matrix(5519,3472,-14880,-9361) (-56/89,-39/62) -> (-23/62,-56/151) Hyperbolic Matrix(239,150,1050,659) (-22/35,-5/8) -> (5/22,8/35) Hyperbolic Matrix(61,38,-480,-299) (-5/8,-23/37) -> (-3/23,-1/8) Hyperbolic Matrix(959,596,1350,839) (-23/37,-18/29) -> (22/31,5/7) Hyperbolic Matrix(481,298,-870,-539) (-18/29,-13/21) -> (-5/9,-16/29) Hyperbolic Matrix(301,186,390,241) (-13/21,-8/13) -> (10/13,7/9) Hyperbolic Matrix(241,148,-780,-479) (-8/13,-19/31) -> (-9/29,-4/13) Hyperbolic Matrix(781,478,1080,661) (-19/31,-11/18) -> (13/18,21/29) Hyperbolic Matrix(1559,952,2160,1319) (-11/18,-36/59) -> (44/61,13/18) Hyperbolic Matrix(59,36,-690,-421) (-36/59,-25/41) -> (-1/11,0/1) Hyperbolic Matrix(479,292,1770,1079) (-25/41,-14/23) -> (10/37,3/11) Hyperbolic Matrix(1079,656,1380,839) (-14/23,-17/28) -> (25/32,18/23) Hyperbolic Matrix(479,290,-1290,-781) (-17/28,-3/5) -> (-13/35,-23/62) Hyperbolic Matrix(301,178,-810,-479) (-3/5,-13/22) -> (-3/8,-13/35) Hyperbolic Matrix(61,36,510,301) (-13/22,-23/39) -> (1/9,1/8) Hyperbolic Matrix(241,142,1020,601) (-23/39,-10/17) -> (4/17,5/21) Hyperbolic Matrix(361,212,-1020,-599) (-10/17,-17/29) -> (-11/31,-6/17) Hyperbolic Matrix(301,176,720,421) (-17/29,-7/12) -> (5/12,13/31) Hyperbolic Matrix(59,34,-210,-121) (-7/12,-4/7) -> (-2/7,-5/18) Hyperbolic Matrix(239,136,420,239) (-4/7,-17/30) -> (17/30,4/7) Hyperbolic Matrix(781,442,1380,781) (-17/30,-13/23) -> (13/23,17/30) Hyperbolic Matrix(2881,1626,3510,1981) (-35/62,-22/39) -> (32/39,23/28) Hyperbolic Matrix(419,236,1170,659) (-22/39,-9/16) -> (5/14,14/39) Hyperbolic Matrix(481,270,750,421) (-9/16,-14/25) -> (16/25,9/14) Hyperbolic Matrix(1919,1074,3000,1679) (-14/25,-33/59) -> (39/61,16/25) Hyperbolic Matrix(1499,838,3540,1979) (-33/59,-19/34) -> (11/26,25/59) Hyperbolic Matrix(179,100,750,419) (-19/34,-5/9) -> (5/21,1/4) Hyperbolic Matrix(1201,662,2070,1141) (-16/29,-11/20) -> (29/50,18/31) Hyperbolic Matrix(539,296,1200,659) (-11/20,-17/31) -> (13/29,9/20) Hyperbolic Matrix(59,32,330,179) (-6/11,-7/13) -> (3/17,2/11) Hyperbolic Matrix(239,128,-450,-241) (-7/13,-8/15) -> (-8/15,-9/17) Parabolic Matrix(481,254,570,301) (-9/17,-1/2) -> (27/32,11/13) Hyperbolic Matrix(839,394,1020,479) (-8/17,-7/15) -> (37/45,14/17) Hyperbolic Matrix(181,84,390,181) (-7/15,-6/13) -> (6/13,7/15) Hyperbolic Matrix(61,28,-390,-179) (-6/13,-5/11) -> (-3/19,-2/13) Hyperbolic Matrix(181,82,-660,-299) (-5/11,-9/20) -> (-11/40,-3/11) Hyperbolic Matrix(1261,566,1740,781) (-9/20,-13/29) -> (21/29,29/40) Hyperbolic Matrix(241,108,270,121) (-13/29,-4/9) -> (8/9,1/1) Hyperbolic Matrix(59,26,270,119) (-4/9,-7/16) -> (3/14,2/9) Hyperbolic Matrix(541,236,690,301) (-7/16,-10/23) -> (18/23,11/14) Hyperbolic Matrix(599,260,1380,599) (-10/23,-13/30) -> (13/30,10/23) Hyperbolic Matrix(181,78,420,181) (-13/30,-3/7) -> (3/7,13/30) Hyperbolic Matrix(301,128,990,421) (-3/7,-14/33) -> (10/33,7/23) Hyperbolic Matrix(1679,712,-4530,-1921) (-14/33,-25/59) -> (-33/89,-10/27) Hyperbolic Matrix(1979,838,3540,1499) (-25/59,-11/26) -> (19/34,33/59) Hyperbolic Matrix(421,178,570,241) (-11/26,-8/19) -> (14/19,3/4) Hyperbolic Matrix(2341,984,3000,1261) (-8/19,-29/69) -> (7/9,32/41) Hyperbolic Matrix(119,50,1140,479) (-29/69,-21/50) -> (1/10,1/9) Hyperbolic Matrix(1139,478,3000,1259) (-21/50,-13/31) -> (11/29,19/50) Hyperbolic Matrix(421,176,720,301) (-13/31,-5/12) -> (7/12,17/29) Hyperbolic Matrix(59,24,-150,-61) (-5/12,-2/5) -> (-2/5,-7/18) Parabolic Matrix(541,210,930,361) (-7/18,-12/31) -> (18/31,7/12) Hyperbolic Matrix(2461,952,3570,1381) (-12/31,-29/75) -> (31/45,20/29) Hyperbolic Matrix(2339,904,-7920,-3061) (-29/75,-17/44) -> (-13/44,-31/105) Hyperbolic Matrix(481,184,630,241) (-5/13,-13/34) -> (3/4,13/17) Hyperbolic Matrix(361,138,-1410,-539) (-13/34,-34/89) -> (-8/31,-1/4) Hyperbolic Matrix(4681,1788,6600,2521) (-34/89,-21/55) -> (39/55,22/31) Hyperbolic Matrix(959,366,2670,1019) (-21/55,-8/21) -> (14/39,9/25) Hyperbolic Matrix(2461,936,3000,1141) (-8/21,-27/71) -> (9/11,32/39) Hyperbolic Matrix(121,46,-1260,-479) (-27/71,-19/50) -> (-1/10,-1/11) Hyperbolic Matrix(1259,478,3000,1139) (-19/50,-11/29) -> (13/31,21/50) Hyperbolic Matrix(301,114,-1740,-659) (-11/29,-14/37) -> (-4/23,-5/29) Hyperbolic Matrix(1381,522,1590,601) (-14/37,-17/45) -> (13/15,20/23) Hyperbolic Matrix(38161,14152,53070,19681) (-56/151,-89/240) -> (151/210,64/89) Hyperbolic Matrix(34319,12726,47730,17699) (-89/240,-33/89) -> (87/121,151/210) Hyperbolic Matrix(719,266,2430,899) (-10/27,-17/46) -> (13/44,8/27) Hyperbolic Matrix(419,154,1140,419) (-7/19,-11/30) -> (11/30,7/19) Hyperbolic Matrix(241,88,660,241) (-11/30,-4/11) -> (4/11,11/30) Hyperbolic Matrix(61,22,-330,-119) (-4/11,-5/14) -> (-3/16,-2/11) Hyperbolic Matrix(1859,662,3030,1079) (-5/14,-16/45) -> (46/75,27/44) Hyperbolic Matrix(2281,810,3720,1321) (-16/45,-11/31) -> (19/31,46/75) Hyperbolic Matrix(359,126,510,179) (-6/17,-1/3) -> (19/27,12/17) Hyperbolic Matrix(121,38,-570,-179) (-1/3,-5/16) -> (-3/14,-7/33) Hyperbolic Matrix(1919,598,3270,1019) (-5/16,-14/45) -> (44/75,27/46) Hyperbolic Matrix(2041,634,3480,1081) (-14/45,-9/29) -> (17/29,44/75) Hyperbolic Matrix(59,18,390,119) (-4/13,-7/23) -> (1/7,2/13) Hyperbolic Matrix(179,54,-600,-181) (-7/23,-3/10) -> (-3/10,-11/37) Parabolic Matrix(599,178,1410,419) (-11/37,-8/27) -> (14/33,3/7) Hyperbolic Matrix(1319,390,1620,479) (-8/27,-13/44) -> (13/16,22/27) Hyperbolic Matrix(6301,1860,9150,2701) (-31/105,-18/61) -> (42/61,31/45) Hyperbolic Matrix(2639,778,3660,1079) (-18/61,-5/17) -> (31/43,44/61) Hyperbolic Matrix(661,194,1230,361) (-5/17,-17/58) -> (15/28,7/13) Hyperbolic Matrix(2881,844,3690,1081) (-17/58,-12/41) -> (32/41,25/32) Hyperbolic Matrix(301,88,1440,421) (-12/41,-7/24) -> (5/24,4/19) Hyperbolic Matrix(361,100,870,241) (-5/18,-8/29) -> (12/29,5/12) Hyperbolic Matrix(1619,446,2610,719) (-8/29,-11/40) -> (31/50,18/29) Hyperbolic Matrix(119,32,-450,-121) (-3/11,-4/15) -> (-4/15,-5/19) Parabolic Matrix(841,220,1380,361) (-5/19,-6/23) -> (14/23,25/41) Hyperbolic Matrix(2999,776,4170,1079) (-7/27,-8/31) -> (64/89,41/57) Hyperbolic Matrix(419,100,750,179) (-1/4,-5/21) -> (5/9,19/34) Hyperbolic Matrix(601,142,1020,241) (-5/21,-4/17) -> (10/17,23/39) Hyperbolic Matrix(239,56,1020,239) (-4/17,-7/30) -> (7/30,4/17) Hyperbolic Matrix(181,42,780,181) (-7/30,-3/13) -> (3/13,7/30) Hyperbolic Matrix(1319,302,1830,419) (-3/13,-8/35) -> (18/25,31/43) Hyperbolic Matrix(659,150,1050,239) (-8/35,-5/22) -> (5/8,22/35) Hyperbolic Matrix(241,54,540,121) (-7/31,-2/9) -> (4/9,13/29) Hyperbolic Matrix(119,26,270,59) (-2/9,-3/14) -> (7/16,4/9) Hyperbolic Matrix(479,100,570,119) (-4/19,-5/24) -> (5/6,16/19) Hyperbolic Matrix(779,160,2040,419) (-6/29,-1/5) -> (21/55,34/89) Hyperbolic Matrix(481,92,1260,241) (-1/5,-4/21) -> (8/21,21/55) Hyperbolic Matrix(541,102,960,181) (-4/21,-3/16) -> (9/16,22/39) Hyperbolic Matrix(179,32,330,59) (-2/11,-3/17) -> (7/13,6/11) Hyperbolic Matrix(901,154,1410,241) (-5/29,-1/6) -> (23/36,39/61) Hyperbolic Matrix(479,76,750,119) (-1/6,-3/19) -> (7/11,23/36) Hyperbolic Matrix(119,18,390,59) (-2/13,-1/7) -> (7/23,4/13) Hyperbolic Matrix(59,8,-450,-61) (-1/7,-2/15) -> (-2/15,-3/23) Parabolic Matrix(301,36,510,61) (-1/8,-1/9) -> (23/39,13/22) Hyperbolic Matrix(479,50,1140,119) (-1/9,-1/10) -> (21/50,29/69) Hyperbolic Matrix(421,-36,690,-59) (0/1,1/10) -> (61/100,36/59) Hyperbolic Matrix(299,-38,480,-61) (1/8,2/15) -> (28/45,5/8) Hyperbolic Matrix(541,-74,870,-119) (2/15,1/7) -> (23/37,28/45) Hyperbolic Matrix(179,-28,390,-61) (2/13,1/6) -> (11/24,6/13) Hyperbolic Matrix(479,-84,690,-121) (1/6,3/17) -> (9/13,25/36) Hyperbolic Matrix(119,-22,330,-61) (2/11,1/5) -> (9/25,4/11) Hyperbolic Matrix(1021,-212,1440,-299) (1/5,5/24) -> (17/24,39/55) Hyperbolic Matrix(719,-152,1140,-241) (4/19,3/14) -> (29/46,12/19) Hyperbolic Matrix(239,-54,270,-61) (2/9,5/22) -> (7/8,8/9) Hyperbolic Matrix(121,-32,450,-119) (1/4,4/15) -> (4/15,7/26) Parabolic Matrix(2341,-632,3330,-899) (7/26,10/37) -> (26/37,45/64) Hyperbolic Matrix(121,-34,210,-59) (3/11,2/7) -> (4/7,11/19) Hyperbolic Matrix(179,-52,210,-61) (2/7,5/17) -> (11/13,6/7) Hyperbolic Matrix(2519,-744,3660,-1081) (18/61,13/44) -> (11/16,42/61) Hyperbolic Matrix(181,-54,600,-179) (8/27,3/10) -> (3/10,10/33) Parabolic Matrix(479,-148,780,-241) (4/13,5/16) -> (27/44,8/13) Hyperbolic Matrix(359,-114,570,-181) (5/16,1/3) -> (17/27,29/46) Hyperbolic Matrix(599,-212,1020,-361) (6/17,5/14) -> (27/46,10/17) Hyperbolic Matrix(661,-244,810,-299) (7/19,10/27) -> (22/27,9/11) Hyperbolic Matrix(479,-178,810,-301) (10/27,3/8) -> (13/22,16/27) Hyperbolic Matrix(419,-158,480,-181) (3/8,14/37) -> (20/23,7/8) Hyperbolic Matrix(1981,-750,2850,-1079) (14/37,11/29) -> (41/59,16/23) Hyperbolic Matrix(5581,-2122,9150,-3479) (19/50,27/71) -> (25/41,61/100) Hyperbolic Matrix(6181,-2362,8790,-3359) (34/89,13/34) -> (45/64,64/91) Hyperbolic Matrix(61,-24,150,-59) (5/13,2/5) -> (2/5,7/17) Parabolic Matrix(601,-248,870,-359) (7/17,12/29) -> (20/29,9/13) Hyperbolic Matrix(2401,-1018,3960,-1679) (25/59,14/33) -> (20/33,37/61) Hyperbolic Matrix(539,-244,930,-421) (9/20,5/11) -> (11/19,29/50) Hyperbolic Matrix(419,-198,510,-241) (7/15,1/2) -> (23/28,37/45) Hyperbolic Matrix(241,-128,450,-239) (1/2,8/15) -> (8/15,15/28) Parabolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(539,-298,870,-481) (11/20,5/9) -> (13/21,31/50) Hyperbolic Matrix(839,-474,1170,-661) (22/39,13/23) -> (5/7,28/39) Hyperbolic Matrix(181,-108,300,-179) (16/27,3/5) -> (3/5,20/33) Parabolic Matrix(3839,-2330,5340,-3241) (37/61,17/28) -> (23/32,87/121) Hyperbolic Matrix(1921,-1208,2670,-1679) (22/35,17/27) -> (41/57,18/25) Hyperbolic Matrix(61,-40,90,-59) (9/14,2/3) -> (2/3,11/16) Parabolic Matrix(421,-294,600,-419) (16/23,7/10) -> (7/10,26/37) Parabolic Matrix(121,-96,150,-119) (11/14,4/5) -> (4/5,13/16) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(61,54,-270,-239) -> Matrix(1,-2,2,-3) Matrix(181,158,-480,-419) -> Matrix(1,-2,0,1) Matrix(181,156,210,181) -> Matrix(3,-4,-2,3) Matrix(61,52,-210,-179) -> Matrix(1,-2,0,1) Matrix(361,298,510,421) -> Matrix(1,-2,0,1) Matrix(241,198,-510,-419) -> Matrix(1,0,0,1) Matrix(1681,1380,2340,1921) -> Matrix(1,-2,2,-3) Matrix(1141,936,3000,2461) -> Matrix(1,0,0,1) Matrix(119,96,-150,-121) -> Matrix(1,-2,0,1) Matrix(421,332,-1140,-899) -> Matrix(1,2,0,1) Matrix(301,236,690,541) -> Matrix(1,-4,0,1) Matrix(839,656,1380,1079) -> Matrix(1,2,0,1) Matrix(1619,1264,1920,1499) -> Matrix(1,-2,0,1) Matrix(1261,984,3000,2341) -> Matrix(1,0,0,1) Matrix(241,186,390,301) -> Matrix(1,-2,0,1) Matrix(599,460,780,599) -> Matrix(1,-8,0,1) Matrix(781,598,1020,781) -> Matrix(1,10,0,1) Matrix(241,184,630,481) -> Matrix(1,4,0,1) Matrix(241,178,570,421) -> Matrix(1,-2,0,1) Matrix(419,308,570,419) -> Matrix(1,-4,0,1) Matrix(241,176,330,241) -> Matrix(1,2,0,1) Matrix(361,262,-660,-479) -> Matrix(1,2,0,1) Matrix(661,478,1080,781) -> Matrix(1,0,2,1) Matrix(1319,952,2160,1559) -> Matrix(1,0,0,1) Matrix(1079,778,3660,2639) -> Matrix(1,0,0,1) Matrix(419,302,1830,1319) -> Matrix(1,0,-2,1) Matrix(1679,1208,-2670,-1921) -> Matrix(1,2,0,1) Matrix(661,474,-1170,-839) -> Matrix(1,0,6,1) Matrix(839,596,1350,959) -> Matrix(1,0,-2,1) Matrix(299,212,-1440,-1021) -> Matrix(1,-2,0,1) Matrix(421,298,510,361) -> Matrix(1,-2,0,1) Matrix(179,126,510,359) -> Matrix(1,0,0,1) Matrix(419,294,-600,-421) -> Matrix(1,-2,0,1) Matrix(359,250,-1380,-961) -> Matrix(1,0,2,1) Matrix(121,84,-690,-479) -> Matrix(1,0,0,1) Matrix(59,40,-90,-61) -> Matrix(1,0,0,1) Matrix(359,232,-930,-601) -> Matrix(1,0,0,1) Matrix(421,270,750,481) -> Matrix(1,0,-2,1) Matrix(1679,1074,3000,1919) -> Matrix(1,2,-2,-3) Matrix(3001,1918,4320,2761) -> Matrix(1,0,2,1) Matrix(301,192,660,421) -> Matrix(1,0,0,1) Matrix(419,266,660,419) -> Matrix(1,0,2,1) Matrix(721,456,1140,721) -> Matrix(1,0,-4,1) Matrix(241,152,-1140,-719) -> Matrix(1,0,-2,1) Matrix(3419,2152,4860,3059) -> Matrix(1,0,-2,1) Matrix(5519,3472,-14880,-9361) -> Matrix(5,-6,6,-7) Matrix(239,150,1050,659) -> Matrix(1,0,-2,1) Matrix(61,38,-480,-299) -> Matrix(1,0,0,1) Matrix(959,596,1350,839) -> Matrix(1,0,-2,1) Matrix(481,298,-870,-539) -> Matrix(1,-2,2,-3) Matrix(301,186,390,241) -> Matrix(1,-2,0,1) Matrix(241,148,-780,-479) -> Matrix(1,2,-2,-3) Matrix(781,478,1080,661) -> Matrix(1,0,2,1) Matrix(1559,952,2160,1319) -> Matrix(1,0,0,1) Matrix(59,36,-690,-421) -> Matrix(1,0,0,1) Matrix(479,292,1770,1079) -> Matrix(1,0,2,1) Matrix(1079,656,1380,839) -> Matrix(1,2,0,1) Matrix(479,290,-1290,-781) -> Matrix(1,0,2,1) Matrix(301,178,-810,-479) -> Matrix(1,0,0,1) Matrix(61,36,510,301) -> Matrix(1,0,0,1) Matrix(241,142,1020,601) -> Matrix(1,0,2,1) Matrix(361,212,-1020,-599) -> Matrix(1,0,-2,1) Matrix(301,176,720,421) -> Matrix(1,-2,0,1) Matrix(59,34,-210,-121) -> Matrix(1,0,0,1) Matrix(239,136,420,239) -> Matrix(1,0,2,1) Matrix(781,442,1380,781) -> Matrix(1,0,-14,1) Matrix(2881,1626,3510,1981) -> Matrix(9,-2,-4,1) Matrix(419,236,1170,659) -> Matrix(7,-2,4,-1) Matrix(481,270,750,421) -> Matrix(1,0,-2,1) Matrix(1919,1074,3000,1679) -> Matrix(3,-2,2,-1) Matrix(1499,838,3540,1979) -> Matrix(1,-2,0,1) Matrix(179,100,750,419) -> Matrix(1,0,0,1) Matrix(1201,662,2070,1141) -> Matrix(3,-2,2,-1) Matrix(539,296,1200,659) -> Matrix(3,-4,-2,3) Matrix(59,32,330,179) -> Matrix(1,0,0,1) Matrix(239,128,-450,-241) -> Matrix(1,0,2,1) Matrix(481,254,570,301) -> Matrix(5,-2,-2,1) Matrix(839,394,1020,479) -> Matrix(1,-4,0,1) Matrix(181,84,390,181) -> Matrix(1,0,0,1) Matrix(61,28,-390,-179) -> Matrix(1,0,0,1) Matrix(181,82,-660,-299) -> Matrix(1,0,-2,1) Matrix(1261,566,1740,781) -> Matrix(1,-2,2,-3) Matrix(241,108,270,121) -> Matrix(3,-4,-2,3) Matrix(59,26,270,119) -> Matrix(1,-2,0,1) Matrix(541,236,690,301) -> Matrix(1,-4,0,1) Matrix(599,260,1380,599) -> Matrix(1,-14,0,1) Matrix(181,78,420,181) -> Matrix(1,2,0,1) Matrix(301,128,990,421) -> Matrix(1,0,2,1) Matrix(1679,712,-4530,-1921) -> Matrix(3,-2,2,-1) Matrix(1979,838,3540,1499) -> Matrix(1,-2,0,1) Matrix(421,178,570,241) -> Matrix(1,-2,0,1) Matrix(2341,984,3000,1261) -> Matrix(1,0,0,1) Matrix(119,50,1140,479) -> Matrix(1,0,0,1) Matrix(1139,478,3000,1259) -> Matrix(3,-2,2,-1) Matrix(421,176,720,301) -> Matrix(1,-2,0,1) Matrix(59,24,-150,-61) -> Matrix(1,-2,0,1) Matrix(541,210,930,361) -> Matrix(1,2,0,1) Matrix(2461,952,3570,1381) -> Matrix(1,0,2,1) Matrix(2339,904,-7920,-3061) -> Matrix(1,0,0,1) Matrix(481,184,630,241) -> Matrix(1,4,0,1) Matrix(361,138,-1410,-539) -> Matrix(1,4,0,1) Matrix(4681,1788,6600,2521) -> Matrix(3,8,-2,-5) Matrix(959,366,2670,1019) -> Matrix(1,4,0,1) Matrix(2461,936,3000,1141) -> Matrix(1,0,0,1) Matrix(121,46,-1260,-479) -> Matrix(1,2,0,1) Matrix(1259,478,3000,1139) -> Matrix(1,2,-2,-3) Matrix(301,114,-1740,-659) -> Matrix(1,0,0,1) Matrix(1381,522,1590,601) -> Matrix(1,0,0,1) Matrix(38161,14152,53070,19681) -> Matrix(25,-24,24,-23) Matrix(34319,12726,47730,17699) -> Matrix(21,-22,22,-23) Matrix(719,266,2430,899) -> Matrix(1,-2,0,1) Matrix(419,154,1140,419) -> Matrix(1,-6,0,1) Matrix(241,88,660,241) -> Matrix(1,6,0,1) Matrix(61,22,-330,-119) -> Matrix(1,2,0,1) Matrix(1859,662,3030,1079) -> Matrix(5,6,4,5) Matrix(2281,810,3720,1321) -> Matrix(3,2,4,3) Matrix(359,126,510,179) -> Matrix(1,0,0,1) Matrix(121,38,-570,-179) -> Matrix(1,0,0,1) Matrix(1919,598,3270,1019) -> Matrix(3,4,-4,-5) Matrix(2041,634,3480,1081) -> Matrix(5,4,-4,-3) Matrix(59,18,390,119) -> Matrix(1,0,2,1) Matrix(179,54,-600,-181) -> Matrix(1,0,4,1) Matrix(599,178,1410,419) -> Matrix(1,0,-2,1) Matrix(1319,390,1620,479) -> Matrix(1,-2,0,1) Matrix(6301,1860,9150,2701) -> Matrix(1,0,0,1) Matrix(2639,778,3660,1079) -> Matrix(1,0,0,1) Matrix(661,194,1230,361) -> Matrix(1,0,0,1) Matrix(2881,844,3690,1081) -> Matrix(1,0,0,1) Matrix(301,88,1440,421) -> Matrix(1,0,0,1) Matrix(361,100,870,241) -> Matrix(1,0,0,1) Matrix(1619,446,2610,719) -> Matrix(1,0,0,1) Matrix(119,32,-450,-121) -> Matrix(1,0,4,1) Matrix(841,220,1380,361) -> Matrix(1,0,-2,1) Matrix(2999,776,4170,1079) -> Matrix(5,-4,4,-3) Matrix(419,100,750,179) -> Matrix(1,0,0,1) Matrix(601,142,1020,241) -> Matrix(1,0,2,1) Matrix(239,56,1020,239) -> Matrix(1,0,8,1) Matrix(181,42,780,181) -> Matrix(1,0,-6,1) Matrix(1319,302,1830,419) -> Matrix(1,0,-2,1) Matrix(659,150,1050,239) -> Matrix(1,0,-2,1) Matrix(241,54,540,121) -> Matrix(1,-2,0,1) Matrix(119,26,270,59) -> Matrix(1,-2,0,1) Matrix(479,100,570,119) -> Matrix(1,-2,0,1) Matrix(779,160,2040,419) -> Matrix(5,2,2,1) Matrix(481,92,1260,241) -> Matrix(1,2,0,1) Matrix(541,102,960,181) -> Matrix(1,0,-4,1) Matrix(179,32,330,59) -> Matrix(1,0,0,1) Matrix(901,154,1410,241) -> Matrix(1,0,2,1) Matrix(479,76,750,119) -> Matrix(1,0,0,1) Matrix(119,18,390,59) -> Matrix(1,0,2,1) Matrix(59,8,-450,-61) -> Matrix(1,0,2,1) Matrix(301,36,510,61) -> Matrix(1,0,0,1) Matrix(479,50,1140,119) -> Matrix(1,0,0,1) Matrix(421,-36,690,-59) -> Matrix(1,0,0,1) Matrix(299,-38,480,-61) -> Matrix(1,0,0,1) Matrix(541,-74,870,-119) -> Matrix(1,0,-2,1) Matrix(179,-28,390,-61) -> Matrix(1,0,0,1) Matrix(479,-84,690,-121) -> Matrix(1,0,0,1) Matrix(119,-22,330,-61) -> Matrix(1,2,0,1) Matrix(1021,-212,1440,-299) -> Matrix(1,-2,0,1) Matrix(719,-152,1140,-241) -> Matrix(1,0,-2,1) Matrix(239,-54,270,-61) -> Matrix(3,2,-2,-1) Matrix(121,-32,450,-119) -> Matrix(1,0,4,1) Matrix(2341,-632,3330,-899) -> Matrix(5,-2,-2,1) Matrix(121,-34,210,-59) -> Matrix(1,0,0,1) Matrix(179,-52,210,-61) -> Matrix(1,-2,0,1) Matrix(2519,-744,3660,-1081) -> Matrix(1,0,0,1) Matrix(181,-54,600,-179) -> Matrix(1,0,4,1) Matrix(479,-148,780,-241) -> Matrix(3,-2,2,-1) Matrix(359,-114,570,-181) -> Matrix(1,0,-2,1) Matrix(599,-212,1020,-361) -> Matrix(1,0,-2,1) Matrix(661,-244,810,-299) -> Matrix(1,0,0,1) Matrix(479,-178,810,-301) -> Matrix(1,0,0,1) Matrix(419,-158,480,-181) -> Matrix(1,-2,0,1) Matrix(1981,-750,2850,-1079) -> Matrix(1,0,0,1) Matrix(5581,-2122,9150,-3479) -> Matrix(1,-2,0,1) Matrix(6181,-2362,8790,-3359) -> Matrix(3,-10,-2,7) Matrix(61,-24,150,-59) -> Matrix(1,-2,0,1) Matrix(601,-248,870,-359) -> Matrix(1,2,0,1) Matrix(2401,-1018,3960,-1679) -> Matrix(3,2,4,3) Matrix(539,-244,930,-421) -> Matrix(1,0,2,1) Matrix(419,-198,510,-241) -> Matrix(1,0,0,1) Matrix(241,-128,450,-239) -> Matrix(1,0,2,1) Matrix(479,-262,660,-361) -> Matrix(1,2,0,1) Matrix(539,-298,870,-481) -> Matrix(3,2,-2,-1) Matrix(839,-474,1170,-661) -> Matrix(1,0,6,1) Matrix(181,-108,300,-179) -> Matrix(1,0,2,1) Matrix(3839,-2330,5340,-3241) -> Matrix(3,-4,4,-5) Matrix(1921,-1208,2670,-1679) -> Matrix(1,2,0,1) Matrix(61,-40,90,-59) -> Matrix(1,0,0,1) Matrix(421,-294,600,-419) -> Matrix(1,-2,0,1) Matrix(121,-96,150,-119) -> Matrix(1,-2,0,1) 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): 42 Degree of the the map X: 42 Degree of the the map Y: 192 ----------------------------------------------------------------------- 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 (0/1,1/0) 0 30 1/10 0/1 1 3 1/9 0 10 1/8 0 15 2/15 0/1 2 2 1/7 1/1 1 30 2/13 (0/1,1/0) 0 30 1/6 0/1 1 5 3/17 -1/1 1 30 2/11 (1/1,1/0) 0 30 1/5 0/1 1 6 5/24 1/0 1 5 4/19 (0/1,1/0) 0 30 3/14 0 15 2/9 0 10 5/22 0 15 8/35 -1/2 2 6 3/13 -1/3 1 30 7/30 0/1 7 1 4/17 (0/1,1/4) 0 30 5/21 0 10 1/4 0 15 4/15 0/1 4 2 7/26 0 15 10/37 (1/3,1/2) 0 30 3/11 1/1 1 30 2/7 (0/1,1/1) 0 30 5/17 -1/1 1 30 18/61 (0/1,1/0) 0 30 13/44 0 15 8/27 0 10 3/10 0/1 2 3 10/33 0 10 7/23 1/1 1 30 4/13 (0/1,1/2) 0 30 5/16 0 15 1/3 0 10 6/17 (0/1,1/0) 0 30 5/14 0 15 14/39 0 10 9/25 2/1 1 6 4/11 (3/1,1/0) 0 30 11/30 1/0 6 1 7/19 -3/1 1 30 10/27 0 10 3/8 0 15 14/37 (1/1,1/0) 0 30 11/29 1/1 1 30 19/50 2/1 1 3 27/71 3/1 1 30 8/21 0 10 21/55 2/1 1 6 34/89 (14/5,3/1) 0 30 13/34 0 15 5/13 -1/1 1 30 2/5 1/0 2 6 7/17 -3/1 1 30 12/29 (-2/1,-1/1) 0 30 5/12 1/0 1 5 13/31 -1/1 1 30 21/50 0/1 1 3 29/69 0 10 8/19 (0/1,1/0) 0 30 11/26 0 15 25/59 -1/1 1 30 14/33 0 10 3/7 1/1 1 30 13/30 1/0 8 1 10/23 (-7/1,1/0) 0 30 7/16 0 15 4/9 0 10 13/29 -1/1 1 30 9/20 -1/1 3 3 5/11 -1/1 1 30 11/24 0/1 1 5 6/13 (0/1,1/0) 0 30 7/15 1/0 2 2 1/2 0 15 8/15 0/1 2 2 15/28 0 15 7/13 1/1 1 30 6/11 (-1/1,1/0) 0 30 11/20 -1/1 3 3 5/9 0 10 19/34 0 15 33/59 -1/1 1 30 14/25 -1/2 2 6 9/16 0 15 22/39 0 10 13/23 -1/7 1 30 17/30 0/1 8 1 4/7 (0/1,1/1) 0 30 11/19 1/1 1 30 29/50 1/1 3 3 18/31 (1/1,2/1) 0 30 7/12 1/0 1 5 17/29 -1/1 1 30 44/75 -1/1 8 2 27/46 0 15 10/17 (-1/2,0/1) 0 30 23/39 0 10 13/22 0 15 16/27 0 10 3/5 0/1 1 6 20/33 0 10 37/61 1/1 1 30 17/28 0 15 14/23 (-1/1,1/0) 0 30 25/41 1/1 1 30 61/100 0/1 1 3 36/59 (0/1,1/0) 0 30 11/18 0/1 1 5 19/31 1/1 1 30 46/75 1/1 8 2 27/44 0 15 8/13 (2/1,1/0) 0 30 13/21 0 10 31/50 -1/1 3 3 18/29 (-2/1,-1/1) 0 30 23/37 -1/1 1 30 28/45 0/1 2 2 5/8 0 15 22/35 1/0 2 6 17/27 0 10 29/46 0 15 12/19 (-1/2,0/1) 0 30 19/30 0/1 3 1 7/11 1/1 1 30 23/36 0/1 1 5 39/61 1/1 1 30 16/25 1/0 2 6 9/14 0 15 2/3 0 10 11/16 0 15 42/61 (0/1,1/0) 0 30 31/45 0/1 1 2 20/29 (0/1,1/1) 0 30 9/13 -1/1 1 30 25/36 0/1 1 5 41/59 1/1 1 30 16/23 (1/1,1/0) 0 30 7/10 1/0 1 3 26/37 (-1/1,1/0) 0 30 45/64 0 15 64/91 (-8/7,-1/1) 0 30 19/27 0 10 12/17 (0/1,1/0) 0 30 17/24 1/0 1 5 39/55 -2/1 1 6 22/31 (-1/1,-2/3) 0 30 5/7 -1/1 1 30 28/39 0 10 23/32 0 15 87/121 1/1 1 30 151/210 1/1 23 1 64/89 (1/1,10/9) 0 30 41/57 0 10 18/25 1/0 2 6 31/43 1/1 1 30 44/61 (0/1,1/0) 0 30 13/18 0/1 1 5 21/29 1/1 1 30 29/40 1/1 3 3 8/11 (1/1,1/0) 0 30 11/15 1/0 3 2 14/19 (-2/1,1/0) 0 30 3/4 0 15 13/17 5/1 1 30 23/30 1/0 9 1 10/13 (-4/1,1/0) 0 30 7/9 0 10 32/41 (0/1,1/0) 0 30 25/32 0 15 18/23 (3/1,1/0) 0 30 11/14 0 15 4/5 1/0 2 6 13/16 0 15 22/27 0 10 9/11 -3/1 1 30 32/39 0 10 23/28 0 15 37/45 1/0 2 2 14/17 (-2/1,1/0) 0 30 5/6 1/0 1 5 16/19 (-2/1,1/0) 0 30 27/32 0 15 11/13 -3/1 1 30 6/7 (-2/1,-1/1) 0 30 13/15 -1/1 1 2 20/23 (-1/1,1/0) 0 30 7/8 0 15 8/9 0 10 1/1 -1/1 1 30 1/0 0/1 1 1 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(421,-36,690,-59) (0/1,1/10) -> (61/100,36/59) Hyperbolic Matrix(479,-50,1140,-119) (1/10,1/9) -> (21/50,29/69) Glide Reflection Matrix(301,-36,510,-61) (1/9,1/8) -> (23/39,13/22) Glide Reflection Matrix(299,-38,480,-61) (1/8,2/15) -> (28/45,5/8) Hyperbolic Matrix(541,-74,870,-119) (2/15,1/7) -> (23/37,28/45) Hyperbolic Matrix(119,-18,390,-59) (1/7,2/13) -> (7/23,4/13) Glide Reflection Matrix(179,-28,390,-61) (2/13,1/6) -> (11/24,6/13) Hyperbolic Matrix(479,-84,690,-121) (1/6,3/17) -> (9/13,25/36) Hyperbolic Matrix(179,-32,330,-59) (3/17,2/11) -> (7/13,6/11) Glide Reflection Matrix(119,-22,330,-61) (2/11,1/5) -> (9/25,4/11) Hyperbolic Matrix(1021,-212,1440,-299) (1/5,5/24) -> (17/24,39/55) Hyperbolic Matrix(479,-100,570,-119) (5/24,4/19) -> (5/6,16/19) Glide Reflection Matrix(719,-152,1140,-241) (4/19,3/14) -> (29/46,12/19) Hyperbolic Matrix(119,-26,270,-59) (3/14,2/9) -> (7/16,4/9) Glide Reflection Matrix(239,-54,270,-61) (2/9,5/22) -> (7/8,8/9) Hyperbolic Matrix(659,-150,1050,-239) (5/22,8/35) -> (5/8,22/35) Glide Reflection Matrix(1319,-302,1830,-419) (8/35,3/13) -> (18/25,31/43) Glide Reflection Matrix(181,-42,780,-181) (3/13,7/30) -> (3/13,7/30) Reflection Matrix(239,-56,1020,-239) (7/30,4/17) -> (7/30,4/17) Reflection Matrix(601,-142,1020,-241) (4/17,5/21) -> (10/17,23/39) Glide Reflection Matrix(419,-100,750,-179) (5/21,1/4) -> (5/9,19/34) Glide Reflection Matrix(121,-32,450,-119) (1/4,4/15) -> (4/15,7/26) Parabolic Matrix(2341,-632,3330,-899) (7/26,10/37) -> (26/37,45/64) Hyperbolic Matrix(1079,-292,1770,-479) (10/37,3/11) -> (14/23,25/41) Glide Reflection Matrix(121,-34,210,-59) (3/11,2/7) -> (4/7,11/19) Hyperbolic Matrix(179,-52,210,-61) (2/7,5/17) -> (11/13,6/7) Hyperbolic Matrix(2639,-778,3660,-1079) (5/17,18/61) -> (31/43,44/61) Glide Reflection Matrix(2519,-744,3660,-1081) (18/61,13/44) -> (11/16,42/61) Hyperbolic Matrix(1319,-390,1620,-479) (13/44,8/27) -> (13/16,22/27) Glide Reflection Matrix(181,-54,600,-179) (8/27,3/10) -> (3/10,10/33) Parabolic Matrix(421,-128,990,-301) (10/33,7/23) -> (14/33,3/7) Glide Reflection Matrix(479,-148,780,-241) (4/13,5/16) -> (27/44,8/13) Hyperbolic Matrix(359,-114,570,-181) (5/16,1/3) -> (17/27,29/46) Hyperbolic Matrix(359,-126,510,-179) (1/3,6/17) -> (19/27,12/17) Glide Reflection Matrix(599,-212,1020,-361) (6/17,5/14) -> (27/46,10/17) Hyperbolic Matrix(659,-236,1170,-419) (5/14,14/39) -> (9/16,22/39) Glide Reflection Matrix(1019,-366,2670,-959) (14/39,9/25) -> (8/21,21/55) Glide Reflection Matrix(241,-88,660,-241) (4/11,11/30) -> (4/11,11/30) Reflection Matrix(419,-154,1140,-419) (11/30,7/19) -> (11/30,7/19) Reflection Matrix(661,-244,810,-299) (7/19,10/27) -> (22/27,9/11) Hyperbolic Matrix(479,-178,810,-301) (10/27,3/8) -> (13/22,16/27) Hyperbolic Matrix(419,-158,480,-181) (3/8,14/37) -> (20/23,7/8) Hyperbolic Matrix(1981,-750,2850,-1079) (14/37,11/29) -> (41/59,16/23) Hyperbolic Matrix(1259,-478,3000,-1139) (11/29,19/50) -> (13/31,21/50) Glide Reflection Matrix(5581,-2122,9150,-3479) (19/50,27/71) -> (25/41,61/100) Hyperbolic Matrix(2461,-936,3000,-1141) (27/71,8/21) -> (9/11,32/39) Glide Reflection Matrix(4681,-1788,6600,-2521) (21/55,34/89) -> (39/55,22/31) Glide Reflection Matrix(6181,-2362,8790,-3359) (34/89,13/34) -> (45/64,64/91) Hyperbolic Matrix(481,-184,630,-241) (13/34,5/13) -> (3/4,13/17) Glide Reflection Matrix(61,-24,150,-59) (5/13,2/5) -> (2/5,7/17) Parabolic Matrix(601,-248,870,-359) (7/17,12/29) -> (20/29,9/13) Hyperbolic Matrix(419,-174,720,-299) (12/29,5/12) -> (18/31,7/12) Glide Reflection Matrix(421,-176,720,-301) (5/12,13/31) -> (7/12,17/29) Glide Reflection Matrix(2341,-984,3000,-1261) (29/69,8/19) -> (7/9,32/41) Glide Reflection Matrix(421,-178,570,-241) (8/19,11/26) -> (14/19,3/4) Glide Reflection Matrix(1979,-838,3540,-1499) (11/26,25/59) -> (19/34,33/59) Glide Reflection Matrix(2401,-1018,3960,-1679) (25/59,14/33) -> (20/33,37/61) Hyperbolic Matrix(181,-78,420,-181) (3/7,13/30) -> (3/7,13/30) Reflection Matrix(599,-260,1380,-599) (13/30,10/23) -> (13/30,10/23) Reflection Matrix(541,-236,690,-301) (10/23,7/16) -> (18/23,11/14) Glide Reflection Matrix(241,-108,270,-121) (4/9,13/29) -> (8/9,1/1) Glide Reflection Matrix(1261,-566,1740,-781) (13/29,9/20) -> (21/29,29/40) Glide Reflection Matrix(539,-244,930,-421) (9/20,5/11) -> (11/19,29/50) Hyperbolic Matrix(421,-192,660,-301) (5/11,11/24) -> (7/11,23/36) Glide Reflection Matrix(181,-84,390,-181) (6/13,7/15) -> (6/13,7/15) Reflection Matrix(419,-198,510,-241) (7/15,1/2) -> (23/28,37/45) Hyperbolic Matrix(241,-128,450,-239) (1/2,8/15) -> (8/15,15/28) Parabolic Matrix(659,-354,780,-419) (15/28,7/13) -> (27/32,11/13) Glide Reflection Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(539,-298,870,-481) (11/20,5/9) -> (13/21,31/50) Hyperbolic Matrix(1919,-1074,3000,-1679) (33/59,14/25) -> (39/61,16/25) Glide Reflection Matrix(481,-270,750,-421) (14/25,9/16) -> (16/25,9/14) Glide Reflection Matrix(839,-474,1170,-661) (22/39,13/23) -> (5/7,28/39) Hyperbolic Matrix(781,-442,1380,-781) (13/23,17/30) -> (13/23,17/30) Reflection Matrix(239,-136,420,-239) (17/30,4/7) -> (17/30,4/7) Reflection Matrix(1861,-1080,3000,-1741) (29/50,18/31) -> (31/50,18/29) Glide Reflection Matrix(2759,-1618,4500,-2639) (17/29,44/75) -> (19/31,46/75) Glide Reflection Matrix(4141,-2430,6750,-3961) (44/75,27/46) -> (46/75,27/44) Glide Reflection Matrix(181,-108,300,-179) (16/27,3/5) -> (3/5,20/33) Parabolic Matrix(3839,-2330,5340,-3241) (37/61,17/28) -> (23/32,87/121) Hyperbolic Matrix(1079,-656,1380,-839) (17/28,14/23) -> (25/32,18/23) Glide Reflection Matrix(1559,-952,2160,-1319) (36/59,11/18) -> (44/61,13/18) Glide Reflection Matrix(781,-478,1080,-661) (11/18,19/31) -> (13/18,21/29) Glide Reflection Matrix(301,-186,390,-241) (8/13,13/21) -> (10/13,7/9) Glide Reflection Matrix(959,-596,1350,-839) (18/29,23/37) -> (22/31,5/7) Glide Reflection Matrix(1921,-1208,2670,-1679) (22/35,17/27) -> (41/57,18/25) Hyperbolic Matrix(721,-456,1140,-721) (12/19,19/30) -> (12/19,19/30) Reflection Matrix(419,-266,660,-419) (19/30,7/11) -> (19/30,7/11) Reflection Matrix(3001,-1918,4320,-2761) (23/36,39/61) -> (25/36,41/59) Glide Reflection Matrix(61,-40,90,-59) (9/14,2/3) -> (2/3,11/16) Parabolic Matrix(3781,-2604,5490,-3781) (42/61,31/45) -> (42/61,31/45) Reflection Matrix(1799,-1240,2610,-1799) (31/45,20/29) -> (31/45,20/29) Reflection Matrix(421,-294,600,-419) (16/23,7/10) -> (7/10,26/37) Parabolic Matrix(5459,-3840,7590,-5339) (64/91,19/27) -> (64/89,41/57) Glide Reflection Matrix(421,-298,510,-361) (12/17,17/24) -> (14/17,5/6) Glide Reflection Matrix(1921,-1380,2340,-1681) (28/39,23/32) -> (32/39,23/28) Glide Reflection Matrix(36541,-26274,50820,-36541) (87/121,151/210) -> (87/121,151/210) Reflection Matrix(26879,-19328,37380,-26879) (151/210,64/89) -> (151/210,64/89) Reflection Matrix(241,-176,330,-241) (8/11,11/15) -> (8/11,11/15) Reflection Matrix(419,-308,570,-419) (11/15,14/19) -> (11/15,14/19) Reflection Matrix(781,-598,1020,-781) (13/17,23/30) -> (13/17,23/30) Reflection Matrix(599,-460,780,-599) (23/30,10/13) -> (23/30,10/13) Reflection Matrix(1619,-1264,1920,-1499) (32/41,25/32) -> (16/19,27/32) Glide Reflection Matrix(121,-96,150,-119) (11/14,4/5) -> (4/5,13/16) Parabolic Matrix(1259,-1036,1530,-1259) (37/45,14/17) -> (37/45,14/17) Reflection Matrix(181,-156,210,-181) (6/7,13/15) -> (6/7,13/15) Reflection Matrix(599,-520,690,-599) (13/15,20/23) -> (13/15,20/23) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(421,-36,690,-59) -> Matrix(1,0,0,1) Matrix(479,-50,1140,-119) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(301,-36,510,-61) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(299,-38,480,-61) -> Matrix(1,0,0,1) Matrix(541,-74,870,-119) -> Matrix(1,0,-2,1) 0/1 Matrix(119,-18,390,-59) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(179,-28,390,-61) -> Matrix(1,0,0,1) Matrix(479,-84,690,-121) -> Matrix(1,0,0,1) Matrix(179,-32,330,-59) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(119,-22,330,-61) -> Matrix(1,2,0,1) 1/0 Matrix(1021,-212,1440,-299) -> Matrix(1,-2,0,1) 1/0 Matrix(479,-100,570,-119) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(719,-152,1140,-241) -> Matrix(1,0,-2,1) 0/1 Matrix(119,-26,270,-59) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(239,-54,270,-61) -> Matrix(3,2,-2,-1) -1/1 Matrix(659,-150,1050,-239) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1319,-302,1830,-419) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(181,-42,780,-181) -> Matrix(-1,0,6,1) (3/13,7/30) -> (-1/3,0/1) Matrix(239,-56,1020,-239) -> Matrix(1,0,8,-1) (7/30,4/17) -> (0/1,1/4) Matrix(601,-142,1020,-241) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(419,-100,750,-179) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(121,-32,450,-119) -> Matrix(1,0,4,1) 0/1 Matrix(2341,-632,3330,-899) -> Matrix(5,-2,-2,1) Matrix(1079,-292,1770,-479) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(121,-34,210,-59) -> Matrix(1,0,0,1) Matrix(179,-52,210,-61) -> Matrix(1,-2,0,1) 1/0 Matrix(2639,-778,3660,-1079) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2519,-744,3660,-1081) -> Matrix(1,0,0,1) Matrix(1319,-390,1620,-479) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(181,-54,600,-179) -> Matrix(1,0,4,1) 0/1 Matrix(421,-128,990,-301) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(479,-148,780,-241) -> Matrix(3,-2,2,-1) 1/1 Matrix(359,-114,570,-181) -> Matrix(1,0,-2,1) 0/1 Matrix(359,-126,510,-179) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(599,-212,1020,-361) -> Matrix(1,0,-2,1) 0/1 Matrix(659,-236,1170,-419) -> Matrix(1,-2,-4,7) Matrix(1019,-366,2670,-959) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(241,-88,660,-241) -> Matrix(-1,6,0,1) (4/11,11/30) -> (3/1,1/0) Matrix(419,-154,1140,-419) -> Matrix(1,6,0,-1) (11/30,7/19) -> (-3/1,1/0) Matrix(661,-244,810,-299) -> Matrix(1,0,0,1) Matrix(479,-178,810,-301) -> Matrix(1,0,0,1) Matrix(419,-158,480,-181) -> Matrix(1,-2,0,1) 1/0 Matrix(1981,-750,2850,-1079) -> Matrix(1,0,0,1) Matrix(1259,-478,3000,-1139) -> Matrix(1,-2,-2,3) Matrix(5581,-2122,9150,-3479) -> Matrix(1,-2,0,1) 1/0 Matrix(2461,-936,3000,-1141) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(4681,-1788,6600,-2521) -> Matrix(3,-8,-2,5) Matrix(6181,-2362,8790,-3359) -> Matrix(3,-10,-2,7) Matrix(481,-184,630,-241) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(61,-24,150,-59) -> Matrix(1,-2,0,1) 1/0 Matrix(601,-248,870,-359) -> Matrix(1,2,0,1) 1/0 Matrix(419,-174,720,-299) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(421,-176,720,-301) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(2341,-984,3000,-1261) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(421,-178,570,-241) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(1979,-838,3540,-1499) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(2401,-1018,3960,-1679) -> Matrix(3,2,4,3) Matrix(181,-78,420,-181) -> Matrix(-1,2,0,1) (3/7,13/30) -> (1/1,1/0) Matrix(599,-260,1380,-599) -> Matrix(1,14,0,-1) (13/30,10/23) -> (-7/1,1/0) Matrix(541,-236,690,-301) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(241,-108,270,-121) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(1261,-566,1740,-781) -> Matrix(1,2,2,3) Matrix(539,-244,930,-421) -> Matrix(1,0,2,1) 0/1 Matrix(421,-192,660,-301) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(181,-84,390,-181) -> Matrix(1,0,0,-1) (6/13,7/15) -> (0/1,1/0) Matrix(419,-198,510,-241) -> Matrix(1,0,0,1) Matrix(241,-128,450,-239) -> Matrix(1,0,2,1) 0/1 Matrix(659,-354,780,-419) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(479,-262,660,-361) -> Matrix(1,2,0,1) 1/0 Matrix(539,-298,870,-481) -> Matrix(3,2,-2,-1) -1/1 Matrix(1919,-1074,3000,-1679) -> Matrix(3,2,2,1) Matrix(481,-270,750,-421) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(839,-474,1170,-661) -> Matrix(1,0,6,1) 0/1 Matrix(781,-442,1380,-781) -> Matrix(-1,0,14,1) (13/23,17/30) -> (-1/7,0/1) Matrix(239,-136,420,-239) -> Matrix(1,0,2,-1) (17/30,4/7) -> (0/1,1/1) Matrix(1861,-1080,3000,-1741) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2759,-1618,4500,-2639) -> Matrix(1,2,2,3) Matrix(4141,-2430,6750,-3961) -> Matrix(7,6,6,5) Matrix(181,-108,300,-179) -> Matrix(1,0,2,1) 0/1 Matrix(3839,-2330,5340,-3241) -> Matrix(3,-4,4,-5) 1/1 Matrix(1079,-656,1380,-839) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1559,-952,2160,-1319) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(781,-478,1080,-661) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(301,-186,390,-241) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(959,-596,1350,-839) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1921,-1208,2670,-1679) -> Matrix(1,2,0,1) 1/0 Matrix(721,-456,1140,-721) -> Matrix(-1,0,4,1) (12/19,19/30) -> (-1/2,0/1) Matrix(419,-266,660,-419) -> Matrix(1,0,2,-1) (19/30,7/11) -> (0/1,1/1) Matrix(3001,-1918,4320,-2761) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(61,-40,90,-59) -> Matrix(1,0,0,1) Matrix(3781,-2604,5490,-3781) -> Matrix(1,0,0,-1) (42/61,31/45) -> (0/1,1/0) Matrix(1799,-1240,2610,-1799) -> Matrix(1,0,2,-1) (31/45,20/29) -> (0/1,1/1) Matrix(421,-294,600,-419) -> Matrix(1,-2,0,1) 1/0 Matrix(5459,-3840,7590,-5339) -> Matrix(3,2,2,1) Matrix(421,-298,510,-361) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(1921,-1380,2340,-1681) -> Matrix(3,-2,-2,1) Matrix(36541,-26274,50820,-36541) -> Matrix(27,-26,28,-27) (87/121,151/210) -> (13/14,1/1) Matrix(26879,-19328,37380,-26879) -> Matrix(19,-20,18,-19) (151/210,64/89) -> (1/1,10/9) Matrix(241,-176,330,-241) -> Matrix(-1,2,0,1) (8/11,11/15) -> (1/1,1/0) Matrix(419,-308,570,-419) -> Matrix(1,4,0,-1) (11/15,14/19) -> (-2/1,1/0) Matrix(781,-598,1020,-781) -> Matrix(-1,10,0,1) (13/17,23/30) -> (5/1,1/0) Matrix(599,-460,780,-599) -> Matrix(1,8,0,-1) (23/30,10/13) -> (-4/1,1/0) Matrix(1619,-1264,1920,-1499) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(121,-96,150,-119) -> Matrix(1,-2,0,1) 1/0 Matrix(1259,-1036,1530,-1259) -> Matrix(1,4,0,-1) (37/45,14/17) -> (-2/1,1/0) Matrix(181,-156,210,-181) -> Matrix(3,4,-2,-3) (6/7,13/15) -> (-2/1,-1/1) Matrix(599,-520,690,-599) -> Matrix(1,2,0,-1) (13/15,20/23) -> (-1/1,1/0) Matrix(-1,2,0,1) -> Matrix(-1,0,2,1) (1/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.