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 -10/1 -9/1 -8/1 -15/2 -6/1 -5/1 -14/3 -9/2 -35/8 -4/1 -15/4 -27/8 -10/3 -3/1 -5/2 -12/5 -20/9 -2/1 -15/8 -25/14 -5/3 -18/11 -3/2 -10/7 -5/4 -6/5 0/1 1/1 15/13 6/5 5/4 30/23 15/11 10/7 3/2 30/19 18/11 5/3 30/17 25/14 15/8 2/1 15/7 20/9 30/13 12/5 5/2 75/29 21/8 240/89 30/11 45/16 3/1 45/14 10/3 27/8 7/2 15/4 4/1 17/4 30/7 13/3 35/8 9/2 14/3 19/4 29/6 5/1 21/4 11/2 23/4 6/1 13/2 7/1 15/2 8/1 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -1/1 -9/1 0/1 -8/1 -3/2 -15/2 -1/1 -7/1 -1/1 -2/3 -13/2 -1/2 0/1 -6/1 -1/1 -17/3 -1/1 -1/2 -11/2 -1/1 0/1 -5/1 0/1 -24/5 0/1 -19/4 -1/1 0/1 -14/3 1/0 -9/2 -2/1 0/1 -22/5 1/2 -35/8 1/1 -13/3 1/1 1/0 -30/7 1/0 -17/4 -2/1 1/0 -21/5 0/1 -4/1 1/0 -15/4 1/0 -26/7 1/0 -37/10 -4/1 -3/1 -11/3 -3/1 -2/1 -7/2 -2/1 1/0 -17/5 -3/2 -1/1 -61/18 -2/1 -1/1 -44/13 -3/2 -27/8 -2/1 -4/3 -10/3 -1/1 -33/10 -2/1 0/1 -23/7 -2/1 -1/1 -13/4 0/1 1/0 -16/5 1/0 -3/1 -2/1 -17/6 -2/1 -3/2 -14/5 -3/2 -39/14 -2/1 -4/3 -25/9 -4/3 -11/4 -4/3 -1/1 -30/11 -1/1 -19/7 -1/1 0/1 -27/10 -2/1 0/1 -8/3 1/0 -37/14 -2/1 -13/7 -29/11 -7/4 -5/3 -50/19 -5/3 -71/27 -5/3 -8/5 -21/8 -2/1 -8/5 -55/21 -8/5 -89/34 -14/9 -3/2 -34/13 -3/2 -13/5 -3/2 -7/5 -5/2 -1/1 -17/7 -3/1 1/0 -29/12 -2/1 1/0 -12/5 -2/1 -31/13 -3/2 -1/1 -50/21 -1/1 -69/29 0/1 -19/8 -2/1 -1/1 -26/11 -3/2 -59/25 -5/3 -3/2 -33/14 -2/1 -4/3 -7/3 -2/1 -1/1 -30/13 -1/1 -23/10 -1/1 0/1 -16/7 1/0 -9/4 -2/1 0/1 -29/13 -1/1 1/0 -20/9 -2/1 -11/5 -2/1 -1/1 -24/11 -1/1 -13/6 -2/1 1/0 -15/7 -2/1 -2/1 -3/2 -15/8 -3/2 -28/15 -3/2 -13/7 -3/2 -7/5 -11/6 -7/5 -4/3 -20/11 -4/3 -9/5 -4/3 -34/19 -3/2 -59/33 -3/2 -7/5 -25/14 -3/2 -16/9 -3/2 -39/22 -10/7 -4/3 -23/13 -7/5 -4/3 -30/17 -4/3 -7/4 -3/2 -4/3 -19/11 -7/5 -4/3 -50/29 -4/3 -31/18 -3/2 -4/3 -12/7 -4/3 -29/17 -3/2 -1/1 -75/44 -3/2 -46/27 -3/2 -17/10 -3/2 -4/3 -39/23 -10/7 -22/13 -11/8 -27/16 -18/13 -4/3 -5/3 -4/3 -33/20 -4/3 -30/23 -61/37 -43/33 -13/10 -28/17 -13/10 -23/14 -4/3 -9/7 -41/25 -22/17 -9/7 -100/61 -9/7 -59/36 -4/3 -9/7 -18/11 -9/7 -31/19 -19/15 -5/4 -75/46 -5/4 -44/27 -5/4 -13/8 -14/11 -5/4 -21/13 -6/5 -50/31 -6/5 -29/18 -6/5 -7/6 -37/23 -10/9 -1/1 -45/28 -1/1 -8/5 -3/2 -35/22 -1/1 -27/17 -4/3 -46/29 -3/2 -19/12 -7/5 -4/3 -30/19 -4/3 -11/7 -4/3 -9/7 -36/23 -9/7 -61/39 -19/15 -5/4 -25/16 -5/4 -14/9 -5/4 -3/2 -4/3 -6/5 -16/11 -5/4 -61/42 -4/3 -1/1 -45/31 -4/3 -29/20 -4/3 -5/4 -13/9 -5/4 -1/1 -36/25 -1/1 -59/41 -3/2 -7/5 -23/16 -4/3 -9/7 -10/7 -5/4 -37/26 -6/5 -1/1 -64/45 -5/4 -91/64 -4/3 -5/4 -27/19 -6/5 -17/12 -5/4 -6/5 -24/17 -6/5 -55/39 -6/5 -31/22 -7/6 -8/7 -7/5 -4/3 -1/1 -39/28 -4/3 -6/5 -32/23 -5/4 -121/87 -19/15 -5/4 -210/151 -5/4 -89/64 -5/4 -16/13 -57/41 -6/5 -25/18 -1/1 -43/31 -5/4 -1/1 -61/44 -6/5 -1/1 -18/13 -1/1 -29/21 -3/2 -7/5 -40/29 -4/3 -11/8 -4/3 -1/1 -15/11 -4/3 -19/14 -4/3 -9/7 -4/3 -5/4 -17/13 -29/23 -5/4 -30/23 -5/4 -13/10 -5/4 -26/21 -9/7 -6/5 -41/32 -4/3 -1/1 -32/25 -5/4 -23/18 -6/5 -1/1 -14/11 -5/4 -5/4 -5/4 -16/13 -5/4 -27/22 -16/13 -6/5 -11/9 -11/9 -6/5 -39/32 -28/23 -6/5 -28/23 -17/14 -45/37 -6/5 -17/14 -5/4 -6/5 -6/5 -6/5 -19/16 -6/5 -1/1 -32/27 -5/4 -13/11 -5/4 -11/9 -7/6 -17/14 -6/5 -15/13 -6/5 -23/20 -6/5 -61/51 -8/7 -19/16 -9/8 -6/5 -8/7 -1/1 -7/6 -1/1 0/1 -1/1 1/1 -1/1 -7/8 8/7 -19/22 15/13 -6/7 7/6 -6/7 -17/20 6/5 -6/7 17/14 -6/7 -5/6 28/23 -17/20 39/32 -6/7 -28/33 11/9 -6/7 -11/13 5/4 -5/6 19/15 -1/1 -4/5 14/11 -5/6 23/18 -1/1 -6/7 32/25 -5/6 41/32 -1/1 -4/5 9/7 -6/7 13/10 -26/31 -5/6 30/23 -5/6 17/13 -5/6 -29/35 4/3 -5/6 19/14 -9/11 -4/5 15/11 -4/5 11/8 -1/1 -4/5 29/21 -7/9 -3/4 18/13 -1/1 61/44 -1/1 -6/7 43/31 -1/1 -5/6 25/18 -1/1 32/23 -5/6 7/5 -1/1 -4/5 31/22 -8/9 -7/8 24/17 -6/7 17/12 -6/7 -5/6 27/19 -6/7 10/7 -5/6 33/23 -4/5 23/16 -9/11 -4/5 13/9 -1/1 -5/6 3/2 -6/7 -4/5 17/11 -1/1 -5/6 14/9 -5/6 25/16 -5/6 61/39 -5/6 -19/23 36/23 -9/11 11/7 -9/11 -4/5 30/19 -4/5 19/12 -4/5 -7/9 27/17 -4/5 89/56 -10/13 -3/4 62/39 -3/4 35/22 -1/1 8/5 -3/4 37/23 -1/1 -10/11 29/18 -7/8 -6/7 21/13 -6/7 13/8 -5/6 -14/17 31/19 -5/6 -19/23 18/11 -9/11 59/36 -9/11 -4/5 41/25 -9/11 -22/27 23/14 -9/11 -4/5 28/17 -13/16 5/3 -4/5 22/13 -11/14 39/23 -10/13 17/10 -4/5 -3/4 29/17 -1/1 -3/4 12/7 -4/5 7/4 -4/5 -3/4 30/17 -4/5 23/13 -4/5 -7/9 62/35 -3/4 39/22 -4/5 -10/13 16/9 -3/4 25/14 -3/4 59/33 -7/9 -3/4 34/19 -3/4 9/5 -4/5 29/16 -5/6 -4/5 20/11 -4/5 31/17 -15/19 -11/14 11/6 -4/5 -7/9 13/7 -7/9 -3/4 15/8 -3/4 17/9 -3/4 -5/7 2/1 -3/4 17/8 -7/10 -2/3 15/7 -2/3 13/6 -2/3 -1/2 11/5 -1/1 -2/3 20/9 -2/3 29/13 -1/1 -1/2 9/4 -2/3 0/1 16/7 -1/2 23/10 -1/1 0/1 30/13 -1/1 7/3 -1/1 -2/3 33/14 -4/5 -2/3 59/25 -3/4 -5/7 26/11 -3/4 19/8 -1/1 -2/3 69/29 0/1 50/21 -1/1 31/13 -1/1 -3/4 12/5 -2/3 5/2 -1/1 18/7 -4/5 31/12 -4/5 -3/4 75/29 -4/5 44/17 -3/4 13/5 -7/9 -3/4 34/13 -3/4 89/34 -3/4 -14/19 55/21 -8/11 21/8 -8/11 -2/3 71/27 -8/11 -5/7 50/19 -5/7 29/11 -5/7 -7/10 37/14 -13/19 -2/3 45/17 -2/3 8/3 -1/2 35/13 -2/3 62/23 -1/2 151/56 -6/11 -1/2 240/89 -1/2 89/33 -1/2 -1/3 27/10 -2/3 0/1 46/17 -1/2 19/7 -1/1 0/1 30/11 -1/1 11/4 -1/1 -4/5 14/5 -3/4 45/16 -3/4 31/11 -3/4 -5/7 17/6 -3/4 -2/3 3/1 -2/3 16/5 -1/2 45/14 -1/2 29/9 -1/2 -1/3 13/4 -1/2 0/1 23/7 -1/1 -2/3 10/3 -1/1 37/11 -1/1 -4/5 27/8 -4/5 -2/3 44/13 -3/4 105/31 -2/3 61/18 -1/1 -2/3 17/5 -1/1 -3/4 58/17 -3/4 41/12 -5/7 -2/3 24/7 -2/3 7/2 -2/3 -1/2 18/5 -2/3 29/8 -2/3 -1/2 40/11 -2/3 11/3 -2/3 -3/5 15/4 -1/2 19/5 -1/1 0/1 23/6 -1/1 -2/3 27/7 -2/3 31/8 -1/2 0/1 4/1 -1/2 21/5 0/1 17/4 -2/3 -1/2 30/7 -1/2 13/3 -1/2 -1/3 35/8 -1/3 22/5 -1/4 31/7 -1/1 -1/2 9/2 -2/3 0/1 14/3 -1/2 33/7 0/1 19/4 -1/1 0/1 24/5 0/1 29/6 -2/3 -1/2 5/1 0/1 21/4 -2/1 0/1 16/3 1/0 11/2 -1/1 0/1 17/3 -1/1 1/0 23/4 -3/1 -2/1 29/5 -5/3 -3/2 6/1 -1/1 19/3 -1/1 0/1 13/2 0/1 1/0 7/1 -2/1 -1/1 15/2 -1/1 23/3 -1/1 -10/11 8/1 -3/4 9/1 0/1 10/1 -1/1 11/1 -1/1 -2/3 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(59,690,-36,-421) (-10/1,1/0) -> (-100/61,-59/36) Hyperbolic Matrix(119,1140,50,479) (-10/1,-9/1) -> (69/29,50/21) Hyperbolic Matrix(61,510,36,301) (-9/1,-8/1) -> (22/13,39/23) Hyperbolic Matrix(61,480,-38,-299) (-8/1,-15/2) -> (-45/28,-8/5) Hyperbolic Matrix(119,870,-74,-541) (-15/2,-7/1) -> (-37/23,-45/28) Hyperbolic Matrix(59,390,18,119) (-7/1,-13/2) -> (13/4,23/7) Hyperbolic Matrix(61,390,-28,-179) (-13/2,-6/1) -> (-24/11,-13/6) Hyperbolic Matrix(121,690,-84,-479) (-6/1,-17/3) -> (-13/9,-36/25) Hyperbolic Matrix(59,330,32,179) (-17/3,-11/2) -> (11/6,13/7) Hyperbolic Matrix(61,330,-22,-119) (-11/2,-5/1) -> (-25/9,-11/4) Hyperbolic Matrix(299,1440,-212,-1021) (-5/1,-24/5) -> (-24/17,-55/39) Hyperbolic Matrix(301,1440,88,421) (-24/5,-19/4) -> (41/12,24/7) Hyperbolic Matrix(241,1140,-152,-719) (-19/4,-14/3) -> (-46/29,-19/12) Hyperbolic Matrix(59,270,26,119) (-14/3,-9/2) -> (9/4,16/7) Hyperbolic Matrix(61,270,-54,-239) (-9/2,-22/5) -> (-8/7,-9/8) Hyperbolic Matrix(239,1050,150,659) (-22/5,-35/8) -> (35/22,8/5) Hyperbolic Matrix(419,1830,302,1319) (-35/8,-13/3) -> (43/31,25/18) Hyperbolic Matrix(181,780,42,181) (-13/3,-30/7) -> (30/7,13/3) Hyperbolic Matrix(239,1020,56,239) (-30/7,-17/4) -> (17/4,30/7) Hyperbolic Matrix(241,1020,142,601) (-17/4,-21/5) -> (39/23,17/10) Hyperbolic Matrix(179,750,100,419) (-21/5,-4/1) -> (34/19,9/5) Hyperbolic Matrix(119,450,-32,-121) (-4/1,-15/4) -> (-15/4,-26/7) Parabolic Matrix(899,3330,-632,-2341) (-26/7,-37/10) -> (-37/26,-64/45) Hyperbolic Matrix(479,1770,292,1079) (-37/10,-11/3) -> (41/25,23/14) Hyperbolic Matrix(59,210,-34,-121) (-11/3,-7/2) -> (-7/4,-19/11) Hyperbolic Matrix(61,210,-52,-179) (-7/2,-17/5) -> (-13/11,-7/6) Hyperbolic Matrix(1079,3660,778,2639) (-17/5,-61/18) -> (61/44,43/31) Hyperbolic Matrix(1081,3660,-744,-2519) (-61/18,-44/13) -> (-16/11,-61/42) Hyperbolic Matrix(719,2430,266,899) (-44/13,-27/8) -> (27/10,46/17) Hyperbolic Matrix(179,600,-54,-181) (-27/8,-10/3) -> (-10/3,-33/10) Parabolic Matrix(301,990,128,421) (-33/10,-23/7) -> (7/3,33/14) Hyperbolic Matrix(119,390,18,59) (-23/7,-13/4) -> (13/2,7/1) Hyperbolic Matrix(241,780,-148,-479) (-13/4,-16/5) -> (-44/27,-13/8) Hyperbolic Matrix(181,570,-114,-359) (-16/5,-3/1) -> (-27/17,-46/29) Hyperbolic Matrix(179,510,126,359) (-3/1,-17/6) -> (17/12,27/19) Hyperbolic Matrix(361,1020,-212,-599) (-17/6,-14/5) -> (-46/27,-17/10) Hyperbolic Matrix(419,1170,236,659) (-14/5,-39/14) -> (39/22,16/9) Hyperbolic Matrix(959,2670,366,1019) (-39/14,-25/9) -> (55/21,21/8) Hyperbolic Matrix(241,660,88,241) (-11/4,-30/11) -> (30/11,11/4) Hyperbolic Matrix(419,1140,154,419) (-30/11,-19/7) -> (19/7,30/11) Hyperbolic Matrix(299,810,-244,-661) (-19/7,-27/10) -> (-27/22,-11/9) Hyperbolic Matrix(301,810,-178,-479) (-27/10,-8/3) -> (-22/13,-27/16) Hyperbolic Matrix(181,480,-158,-419) (-8/3,-37/14) -> (-23/20,-8/7) Hyperbolic Matrix(1079,2850,-750,-1981) (-37/14,-29/11) -> (-59/41,-23/16) Hyperbolic Matrix(1139,3000,478,1259) (-29/11,-50/19) -> (50/21,31/13) Hyperbolic Matrix(3479,9150,-2122,-5581) (-50/19,-71/27) -> (-41/25,-100/61) Hyperbolic Matrix(1141,3000,936,2461) (-71/27,-21/8) -> (39/32,11/9) Hyperbolic Matrix(481,1260,92,241) (-21/8,-55/21) -> (5/1,21/4) Hyperbolic Matrix(779,2040,160,419) (-55/21,-89/34) -> (29/6,5/1) Hyperbolic Matrix(3359,8790,-2362,-6181) (-89/34,-34/13) -> (-64/45,-91/64) Hyperbolic Matrix(241,630,184,481) (-34/13,-13/5) -> (17/13,4/3) Hyperbolic Matrix(59,150,-24,-61) (-13/5,-5/2) -> (-5/2,-17/7) Parabolic Matrix(359,870,-248,-601) (-17/7,-29/12) -> (-29/20,-13/9) Hyperbolic Matrix(361,870,100,241) (-29/12,-12/5) -> (18/5,29/8) Hyperbolic Matrix(301,720,176,421) (-12/5,-31/13) -> (29/17,12/7) Hyperbolic Matrix(1259,3000,478,1139) (-31/13,-50/21) -> (50/19,29/11) Hyperbolic Matrix(479,1140,50,119) (-50/21,-69/29) -> (9/1,10/1) Hyperbolic Matrix(1261,3000,984,2341) (-69/29,-19/8) -> (41/32,9/7) Hyperbolic Matrix(241,570,178,421) (-19/8,-26/11) -> (4/3,19/14) Hyperbolic Matrix(1499,3540,838,1979) (-26/11,-59/25) -> (59/33,34/19) Hyperbolic Matrix(1679,3960,-1018,-2401) (-59/25,-33/14) -> (-33/20,-61/37) Hyperbolic Matrix(599,1410,178,419) (-33/14,-7/3) -> (37/11,27/8) Hyperbolic Matrix(181,420,78,181) (-7/3,-30/13) -> (30/13,7/3) Hyperbolic Matrix(599,1380,260,599) (-30/13,-23/10) -> (23/10,30/13) Hyperbolic Matrix(301,690,236,541) (-23/10,-16/7) -> (14/11,23/18) Hyperbolic Matrix(119,270,26,59) (-16/7,-9/4) -> (9/2,14/3) Hyperbolic Matrix(241,540,54,121) (-9/4,-29/13) -> (31/7,9/2) Hyperbolic Matrix(539,1200,296,659) (-29/13,-20/9) -> (20/11,31/17) Hyperbolic Matrix(421,930,-244,-539) (-20/9,-11/5) -> (-19/11,-50/29) Hyperbolic Matrix(301,660,192,421) (-11/5,-24/11) -> (36/23,11/7) Hyperbolic Matrix(181,390,84,181) (-13/6,-15/7) -> (15/7,13/6) Hyperbolic Matrix(241,510,-198,-419) (-15/7,-2/1) -> (-28/23,-45/37) Hyperbolic Matrix(239,450,-128,-241) (-2/1,-15/8) -> (-15/8,-28/15) Parabolic Matrix(661,1230,194,361) (-28/15,-13/7) -> (17/5,58/17) Hyperbolic Matrix(179,330,32,59) (-13/7,-11/6) -> (11/2,17/3) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(481,870,-298,-539) (-20/11,-9/5) -> (-21/13,-50/31) Hyperbolic Matrix(419,750,100,179) (-9/5,-34/19) -> (4/1,21/5) Hyperbolic Matrix(1979,3540,838,1499) (-34/19,-59/33) -> (59/25,26/11) Hyperbolic Matrix(1679,3000,1074,1919) (-59/33,-25/14) -> (25/16,61/39) Hyperbolic Matrix(421,750,270,481) (-25/14,-16/9) -> (14/9,25/16) Hyperbolic Matrix(541,960,102,181) (-16/9,-39/22) -> (21/4,16/3) Hyperbolic Matrix(661,1170,-474,-839) (-39/22,-23/13) -> (-7/5,-39/28) Hyperbolic Matrix(781,1380,442,781) (-23/13,-30/17) -> (30/17,23/13) Hyperbolic Matrix(239,420,136,239) (-30/17,-7/4) -> (7/4,30/17) Hyperbolic Matrix(1201,2070,662,1141) (-50/29,-31/18) -> (29/16,20/11) Hyperbolic Matrix(541,930,210,361) (-31/18,-12/7) -> (18/7,31/12) Hyperbolic Matrix(421,720,176,301) (-12/7,-29/17) -> (31/13,12/5) Hyperbolic Matrix(2041,3480,634,1081) (-29/17,-75/44) -> (45/14,29/9) Hyperbolic Matrix(1919,3270,598,1019) (-75/44,-46/27) -> (16/5,45/14) Hyperbolic Matrix(601,1020,142,241) (-17/10,-39/23) -> (21/5,17/4) Hyperbolic Matrix(301,510,36,61) (-39/23,-22/13) -> (8/1,9/1) Hyperbolic Matrix(179,300,-108,-181) (-27/16,-5/3) -> (-5/3,-33/20) Parabolic Matrix(3241,5340,-2330,-3839) (-61/37,-28/17) -> (-32/23,-121/87) Hyperbolic Matrix(839,1380,656,1079) (-28/17,-23/14) -> (23/18,32/25) Hyperbolic Matrix(841,1380,220,361) (-23/14,-41/25) -> (19/5,23/6) Hyperbolic Matrix(1319,2160,952,1559) (-59/36,-18/11) -> (18/13,61/44) Hyperbolic Matrix(661,1080,478,781) (-18/11,-31/19) -> (29/21,18/13) Hyperbolic Matrix(2281,3720,810,1321) (-31/19,-75/46) -> (45/16,31/11) Hyperbolic Matrix(1859,3030,662,1079) (-75/46,-44/27) -> (14/5,45/16) Hyperbolic Matrix(241,390,186,301) (-13/8,-21/13) -> (9/7,13/10) Hyperbolic Matrix(1619,2610,446,719) (-50/31,-29/18) -> (29/8,40/11) Hyperbolic Matrix(839,1350,596,959) (-29/18,-37/23) -> (7/5,31/22) Hyperbolic Matrix(659,1050,150,239) (-8/5,-35/22) -> (35/8,22/5) Hyperbolic Matrix(1679,2670,-1208,-1921) (-35/22,-27/17) -> (-57/41,-25/18) Hyperbolic Matrix(721,1140,456,721) (-19/12,-30/19) -> (30/19,19/12) Hyperbolic Matrix(419,660,266,419) (-30/19,-11/7) -> (11/7,30/19) Hyperbolic Matrix(479,750,76,119) (-11/7,-36/23) -> (6/1,19/3) Hyperbolic Matrix(901,1410,154,241) (-36/23,-61/39) -> (29/5,6/1) Hyperbolic Matrix(1919,3000,1074,1679) (-61/39,-25/16) -> (25/14,59/33) Hyperbolic Matrix(481,750,270,421) (-25/16,-14/9) -> (16/9,25/14) Hyperbolic Matrix(59,90,-40,-61) (-14/9,-3/2) -> (-3/2,-16/11) Parabolic Matrix(6301,9150,1860,2701) (-61/42,-45/31) -> (105/31,61/18) Hyperbolic Matrix(2461,3570,952,1381) (-45/31,-29/20) -> (31/12,75/29) Hyperbolic Matrix(3001,4320,1918,2761) (-36/25,-59/41) -> (61/39,36/23) Hyperbolic Matrix(419,600,-294,-421) (-23/16,-10/7) -> (-10/7,-37/26) Parabolic Matrix(3419,4860,2152,3059) (-91/64,-27/19) -> (27/17,89/56) Hyperbolic Matrix(359,510,126,179) (-27/19,-17/12) -> (17/6,3/1) Hyperbolic Matrix(361,510,298,421) (-17/12,-24/17) -> (6/5,17/14) Hyperbolic Matrix(4681,6600,1788,2521) (-55/39,-31/22) -> (89/34,55/21) Hyperbolic Matrix(959,1350,596,839) (-31/22,-7/5) -> (37/23,29/18) Hyperbolic Matrix(1681,2340,1380,1921) (-39/28,-32/23) -> (28/23,39/32) Hyperbolic Matrix(34319,47730,12726,17699) (-121/87,-210/151) -> (240/89,89/33) Hyperbolic Matrix(38161,53070,14152,19681) (-210/151,-89/64) -> (151/56,240/89) Hyperbolic Matrix(2999,4170,776,1079) (-89/64,-57/41) -> (27/7,31/8) Hyperbolic Matrix(1319,1830,302,419) (-25/18,-43/31) -> (13/3,35/8) Hyperbolic Matrix(2639,3660,778,1079) (-43/31,-61/44) -> (61/18,17/5) Hyperbolic Matrix(1559,2160,952,1319) (-61/44,-18/13) -> (18/11,59/36) Hyperbolic Matrix(781,1080,478,661) (-18/13,-29/21) -> (31/19,18/11) Hyperbolic Matrix(1261,1740,566,781) (-29/21,-40/29) -> (20/9,29/13) Hyperbolic Matrix(241,330,176,241) (-11/8,-15/11) -> (15/11,11/8) Hyperbolic Matrix(419,570,308,419) (-15/11,-19/14) -> (19/14,15/11) Hyperbolic Matrix(421,570,178,241) (-19/14,-4/3) -> (26/11,19/8) Hyperbolic Matrix(481,630,184,241) (-4/3,-17/13) -> (13/5,34/13) Hyperbolic Matrix(781,1020,598,781) (-17/13,-30/23) -> (30/23,17/13) Hyperbolic Matrix(599,780,460,599) (-30/23,-13/10) -> (13/10,30/23) Hyperbolic Matrix(301,390,186,241) (-13/10,-9/7) -> (21/13,13/8) Hyperbolic Matrix(2341,3000,984,1261) (-9/7,-41/32) -> (19/8,69/29) Hyperbolic Matrix(2881,3690,844,1081) (-41/32,-32/25) -> (58/17,41/12) Hyperbolic Matrix(1079,1380,656,839) (-32/25,-23/18) -> (23/14,28/17) Hyperbolic Matrix(541,690,236,301) (-23/18,-14/11) -> (16/7,23/10) Hyperbolic Matrix(119,150,-96,-121) (-14/11,-5/4) -> (-5/4,-16/13) Parabolic Matrix(1319,1620,390,479) (-16/13,-27/22) -> (27/8,44/13) Hyperbolic Matrix(2461,3000,936,1141) (-11/9,-39/32) -> (21/8,71/27) Hyperbolic Matrix(2881,3510,1626,1981) (-39/32,-28/23) -> (62/35,39/22) Hyperbolic Matrix(839,1020,394,479) (-45/37,-17/14) -> (17/8,15/7) Hyperbolic Matrix(421,510,298,361) (-17/14,-6/5) -> (24/17,17/12) Hyperbolic Matrix(479,570,100,119) (-6/5,-19/16) -> (19/4,24/5) Hyperbolic Matrix(1619,1920,1264,1499) (-19/16,-32/27) -> (32/25,41/32) Hyperbolic Matrix(481,570,254,301) (-32/27,-13/11) -> (17/9,2/1) Hyperbolic Matrix(181,210,156,181) (-7/6,-15/13) -> (15/13,7/6) Hyperbolic Matrix(1381,1590,522,601) (-15/13,-23/20) -> (37/14,45/17) Hyperbolic Matrix(241,270,108,121) (-9/8,-1/1) -> (29/13,9/4) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(239,-270,54,-61) (1/1,8/7) -> (22/5,31/7) Hyperbolic Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(179,-210,52,-61) (7/6,6/5) -> (24/7,7/2) Hyperbolic Matrix(419,-510,198,-241) (17/14,28/23) -> (2/1,17/8) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(1921,-2670,1208,-1679) (25/18,32/23) -> (62/39,35/22) Hyperbolic Matrix(839,-1170,474,-661) (32/23,7/5) -> (23/13,62/35) Hyperbolic Matrix(1021,-1440,212,-299) (31/22,24/17) -> (24/5,29/6) Hyperbolic Matrix(421,-600,294,-419) (27/19,10/7) -> (10/7,33/23) Parabolic Matrix(961,-1380,250,-359) (33/23,23/16) -> (23/6,27/7) Hyperbolic Matrix(479,-690,84,-121) (23/16,13/9) -> (17/3,23/4) Hyperbolic Matrix(61,-90,40,-59) (13/9,3/2) -> (3/2,17/11) Parabolic Matrix(601,-930,232,-359) (17/11,14/9) -> (44/17,13/5) Hyperbolic Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(9361,-14880,3472,-5519) (89/56,62/39) -> (62/23,151/56) Hyperbolic Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(539,-870,298,-481) (29/18,21/13) -> (9/5,29/16) Hyperbolic Matrix(479,-780,148,-241) (13/8,31/19) -> (29/9,13/4) Hyperbolic Matrix(421,-690,36,-59) (59/36,41/25) -> (11/1,1/0) Hyperbolic Matrix(781,-1290,290,-479) (28/17,5/3) -> (35/13,62/23) Hyperbolic Matrix(479,-810,178,-301) (5/3,22/13) -> (8/3,35/13) Hyperbolic Matrix(599,-1020,212,-361) (17/10,29/17) -> (31/11,17/6) Hyperbolic Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(241,-450,128,-239) (13/7,15/8) -> (15/8,17/9) Parabolic Matrix(179,-390,28,-61) (13/6,11/5) -> (19/3,13/2) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(1921,-4530,712,-1679) (33/14,59/25) -> (89/33,27/10) Hyperbolic Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(3061,-7920,904,-2339) (75/29,44/17) -> (44/13,105/31) Hyperbolic Matrix(539,-1410,138,-361) (34/13,89/34) -> (31/8,4/1) Hyperbolic Matrix(479,-1260,46,-121) (71/27,50/19) -> (10/1,11/1) Hyperbolic Matrix(659,-1740,114,-301) (29/11,37/14) -> (23/4,29/5) Hyperbolic Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(179,-570,38,-121) (3/1,16/5) -> (14/3,33/7) Hyperbolic Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(121,-450,32,-119) (11/3,15/4) -> (15/4,19/5) Parabolic Matrix(61,-450,8,-59) (7/1,15/2) -> (15/2,23/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(59,690,-36,-421) -> Matrix(13,4,-10,-3) Matrix(119,1140,50,479) -> Matrix(1,0,0,1) Matrix(61,510,36,301) -> Matrix(3,10,-4,-13) Matrix(61,480,-38,-299) -> Matrix(1,0,0,1) Matrix(119,870,-74,-541) -> Matrix(13,12,-12,-11) Matrix(59,390,18,119) -> Matrix(1,0,0,1) Matrix(61,390,-28,-179) -> Matrix(3,2,-2,-1) Matrix(121,690,-84,-479) -> Matrix(7,6,-6,-5) Matrix(59,330,32,179) -> Matrix(11,4,-14,-5) Matrix(61,330,-22,-119) -> Matrix(5,4,-4,-3) Matrix(299,1440,-212,-1021) -> Matrix(7,6,-6,-5) Matrix(301,1440,88,421) -> Matrix(3,-2,-4,3) Matrix(241,1140,-152,-719) -> Matrix(3,-4,-2,3) Matrix(59,270,26,119) -> Matrix(1,2,-2,-3) Matrix(61,270,-54,-239) -> Matrix(7,6,-6,-5) Matrix(239,1050,150,659) -> Matrix(5,-4,-6,5) Matrix(419,1830,302,1319) -> Matrix(5,-4,-6,5) Matrix(181,780,42,181) -> Matrix(1,-2,-2,5) Matrix(239,1020,56,239) -> Matrix(1,4,-2,-7) Matrix(241,1020,142,601) -> Matrix(3,10,-4,-13) Matrix(179,750,100,419) -> Matrix(3,4,-4,-5) Matrix(119,450,-32,-121) -> Matrix(1,-2,0,1) Matrix(899,3330,-632,-2341) -> Matrix(5,14,-4,-11) Matrix(479,1770,292,1079) -> Matrix(13,48,-16,-59) Matrix(59,210,-34,-121) -> Matrix(3,2,-2,-1) Matrix(61,210,-52,-179) -> Matrix(17,28,-14,-23) Matrix(1079,3660,778,2639) -> Matrix(7,8,-8,-9) Matrix(1081,3660,-744,-2519) -> Matrix(3,2,-2,-1) Matrix(719,2430,266,899) -> Matrix(3,4,-4,-5) Matrix(179,600,-54,-181) -> Matrix(1,2,-2,-3) Matrix(301,990,128,421) -> Matrix(3,4,-4,-5) Matrix(119,390,18,59) -> Matrix(1,0,0,1) Matrix(241,780,-148,-479) -> Matrix(5,14,-4,-11) Matrix(181,570,-114,-359) -> Matrix(3,2,-2,-1) Matrix(179,510,126,359) -> Matrix(7,8,-8,-9) Matrix(361,1020,-212,-599) -> Matrix(11,18,-8,-13) Matrix(419,1170,236,659) -> Matrix(17,24,-22,-31) Matrix(959,2670,366,1019) -> Matrix(7,12,-10,-17) Matrix(241,660,88,241) -> Matrix(7,8,-8,-9) Matrix(419,1140,154,419) -> Matrix(1,0,0,1) Matrix(299,810,-244,-661) -> Matrix(5,-6,-4,5) Matrix(301,810,-178,-479) -> Matrix(11,18,-8,-13) Matrix(181,480,-158,-419) -> Matrix(19,44,-16,-37) Matrix(1079,2850,-750,-1981) -> Matrix(19,34,-14,-25) Matrix(1139,3000,478,1259) -> Matrix(13,22,-16,-27) Matrix(3479,9150,-2122,-5581) -> Matrix(111,182,-86,-141) Matrix(1141,3000,936,2461) -> Matrix(73,118,-86,-139) Matrix(481,1260,92,241) -> Matrix(5,8,-2,-3) Matrix(779,2040,160,419) -> Matrix(5,8,-12,-19) Matrix(3359,8790,-2362,-6181) -> Matrix(37,58,-30,-47) Matrix(241,630,184,481) -> Matrix(33,52,-40,-63) Matrix(59,150,-24,-61) -> Matrix(1,2,-2,-3) Matrix(359,870,-248,-601) -> Matrix(5,14,-4,-11) Matrix(361,870,100,241) -> Matrix(1,4,-2,-7) Matrix(301,720,176,421) -> Matrix(5,6,-6,-7) Matrix(1259,3000,478,1139) -> Matrix(17,22,-24,-31) Matrix(479,1140,50,119) -> Matrix(1,0,0,1) Matrix(1261,3000,984,2341) -> Matrix(5,6,-6,-7) Matrix(241,570,178,421) -> Matrix(13,22,-16,-27) Matrix(1499,3540,838,1979) -> Matrix(5,6,-6,-7) Matrix(1679,3960,-1018,-2401) -> Matrix(47,64,-36,-49) Matrix(599,1410,178,419) -> Matrix(5,6,-6,-7) Matrix(181,420,78,181) -> Matrix(3,4,-4,-5) Matrix(599,1380,260,599) -> Matrix(1,0,0,1) Matrix(301,690,236,541) -> Matrix(5,6,-6,-7) Matrix(119,270,26,59) -> Matrix(1,2,-2,-3) Matrix(241,540,54,121) -> Matrix(1,2,-2,-3) Matrix(539,1200,296,659) -> Matrix(11,26,-14,-33) Matrix(421,930,-244,-539) -> Matrix(11,18,-8,-13) Matrix(301,660,192,421) -> Matrix(13,22,-16,-27) Matrix(181,390,84,181) -> Matrix(1,4,-2,-7) Matrix(241,510,-198,-419) -> Matrix(29,52,-24,-43) Matrix(239,450,-128,-241) -> Matrix(23,36,-16,-25) Matrix(661,1230,194,361) -> Matrix(17,24,-22,-31) Matrix(179,330,32,59) -> Matrix(3,4,2,3) Matrix(361,660,-262,-479) -> Matrix(23,32,-18,-25) Matrix(481,870,-298,-539) -> Matrix(3,2,-2,-1) Matrix(419,750,100,179) -> Matrix(3,4,-4,-5) Matrix(1979,3540,838,1499) -> Matrix(5,6,-6,-7) Matrix(1679,3000,1074,1919) -> Matrix(13,22,-16,-27) Matrix(421,750,270,481) -> Matrix(7,8,-8,-9) Matrix(541,960,102,181) -> Matrix(3,4,2,3) Matrix(661,1170,-474,-839) -> Matrix(23,32,-18,-25) Matrix(781,1380,442,781) -> Matrix(41,56,-52,-71) Matrix(239,420,136,239) -> Matrix(17,24,-22,-31) Matrix(1201,2070,662,1141) -> Matrix(7,8,-8,-9) Matrix(541,930,210,361) -> Matrix(17,24,-22,-31) Matrix(421,720,176,301) -> Matrix(5,6,-6,-7) Matrix(2041,3480,634,1081) -> Matrix(1,2,-4,-7) Matrix(1919,3270,598,1019) -> Matrix(11,16,-20,-29) Matrix(601,1020,142,241) -> Matrix(7,10,-12,-17) Matrix(301,510,36,61) -> Matrix(7,10,-12,-17) Matrix(179,300,-108,-181) -> Matrix(71,96,-54,-73) Matrix(3241,5340,-2330,-3839) -> Matrix(25,32,-18,-23) Matrix(839,1380,656,1079) -> Matrix(45,58,-52,-67) Matrix(841,1380,220,361) -> Matrix(17,22,-24,-31) Matrix(1319,2160,952,1559) -> Matrix(45,58,-52,-67) Matrix(661,1080,478,781) -> Matrix(17,22,-24,-31) Matrix(2281,3720,810,1321) -> Matrix(65,82,-88,-111) Matrix(1859,3030,662,1079) -> Matrix(7,8,-8,-9) Matrix(241,390,186,301) -> Matrix(49,60,-58,-71) Matrix(1619,2610,446,719) -> Matrix(7,8,-8,-9) Matrix(839,1350,596,959) -> Matrix(13,14,-14,-15) Matrix(659,1050,150,239) -> Matrix(3,4,-10,-13) Matrix(1679,2670,-1208,-1921) -> Matrix(3,2,-2,-1) Matrix(721,1140,456,721) -> Matrix(41,56,-52,-71) Matrix(419,660,266,419) -> Matrix(55,72,-68,-89) Matrix(479,750,76,119) -> Matrix(3,4,-10,-13) Matrix(901,1410,154,241) -> Matrix(25,32,-18,-23) Matrix(1919,3000,1074,1679) -> Matrix(17,22,-24,-31) Matrix(481,750,270,421) -> Matrix(7,8,-8,-9) Matrix(59,90,-40,-61) -> Matrix(1,0,0,1) Matrix(6301,9150,1860,2701) -> Matrix(5,6,-6,-7) Matrix(2461,3570,952,1381) -> Matrix(7,8,-8,-9) Matrix(3001,4320,1918,2761) -> Matrix(13,22,-16,-27) Matrix(419,600,-294,-421) -> Matrix(39,50,-32,-41) Matrix(3419,4860,2152,3059) -> Matrix(31,38,-40,-49) Matrix(359,510,126,179) -> Matrix(7,8,-8,-9) Matrix(361,510,298,421) -> Matrix(49,60,-58,-71) Matrix(4681,6600,1788,2521) -> Matrix(63,74,-86,-101) Matrix(959,1350,596,839) -> Matrix(13,14,-14,-15) Matrix(1681,2340,1380,1921) -> Matrix(27,38,-32,-45) Matrix(34319,47730,12726,17699) -> Matrix(19,24,-42,-53) Matrix(38161,53070,14152,19681) -> Matrix(37,46,-70,-87) Matrix(2999,4170,776,1079) -> Matrix(13,16,-22,-27) Matrix(1319,1830,302,419) -> Matrix(3,4,-10,-13) Matrix(2639,3660,778,1079) -> Matrix(7,8,-8,-9) Matrix(1559,2160,952,1319) -> Matrix(49,58,-60,-71) Matrix(781,1080,478,661) -> Matrix(13,22,-16,-27) Matrix(1261,1740,566,781) -> Matrix(7,10,-12,-17) Matrix(241,330,176,241) -> Matrix(7,8,-8,-9) Matrix(419,570,308,419) -> Matrix(55,72,-68,-89) Matrix(421,570,178,241) -> Matrix(17,22,-24,-31) Matrix(481,630,184,241) -> Matrix(41,52,-56,-71) Matrix(781,1020,598,781) -> Matrix(231,290,-278,-349) Matrix(599,780,460,599) -> Matrix(209,260,-250,-311) Matrix(301,390,186,241) -> Matrix(49,60,-58,-71) Matrix(2341,3000,984,1261) -> Matrix(5,6,-6,-7) Matrix(2881,3690,844,1081) -> Matrix(17,22,-24,-31) Matrix(1079,1380,656,839) -> Matrix(49,58,-60,-71) Matrix(541,690,236,301) -> Matrix(5,6,-6,-7) Matrix(119,150,-96,-121) -> Matrix(39,50,-32,-41) Matrix(1319,1620,390,479) -> Matrix(31,38,-40,-49) Matrix(2461,3000,936,1141) -> Matrix(97,118,-134,-163) Matrix(2881,3510,1626,1981) -> Matrix(71,86,-90,-109) Matrix(839,1020,394,479) -> Matrix(27,32,-38,-45) Matrix(421,510,298,361) -> Matrix(49,60,-58,-71) Matrix(479,570,100,119) -> Matrix(5,6,-6,-7) Matrix(1619,1920,1264,1499) -> Matrix(9,10,-10,-11) Matrix(481,570,254,301) -> Matrix(7,8,-8,-9) Matrix(181,210,156,181) -> Matrix(169,204,-198,-239) Matrix(1381,1590,522,601) -> Matrix(167,200,-248,-297) Matrix(241,270,108,121) -> Matrix(7,8,-8,-9) Matrix(1,0,2,1) -> Matrix(13,14,-14,-15) Matrix(239,-270,54,-61) -> Matrix(7,6,-6,-5) Matrix(419,-480,158,-181) -> Matrix(51,44,-80,-69) Matrix(179,-210,52,-61) -> Matrix(33,28,-46,-39) Matrix(419,-510,198,-241) -> Matrix(61,52,-88,-75) Matrix(121,-150,96,-119) -> Matrix(59,50,-72,-61) Matrix(899,-1140,332,-421) -> Matrix(5,4,-4,-3) Matrix(479,-660,262,-361) -> Matrix(39,32,-50,-41) Matrix(1921,-2670,1208,-1679) -> Matrix(3,2,-2,-1) Matrix(839,-1170,474,-661) -> Matrix(39,32,-50,-41) Matrix(1021,-1440,212,-299) -> Matrix(7,6,-6,-5) Matrix(421,-600,294,-419) -> Matrix(59,50,-72,-61) Matrix(961,-1380,250,-359) -> Matrix(17,14,-28,-23) Matrix(479,-690,84,-121) -> Matrix(7,6,-6,-5) Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(601,-930,232,-359) -> Matrix(39,32,-50,-41) Matrix(719,-1140,152,-241) -> Matrix(5,4,-14,-11) Matrix(9361,-14880,3472,-5519) -> Matrix(11,8,-18,-13) Matrix(299,-480,38,-61) -> Matrix(1,0,0,1) Matrix(539,-870,298,-481) -> Matrix(3,2,-2,-1) Matrix(479,-780,148,-241) -> Matrix(17,14,-28,-23) Matrix(421,-690,36,-59) -> Matrix(5,4,6,5) Matrix(781,-1290,290,-479) -> Matrix(37,30,-58,-47) Matrix(479,-810,178,-301) -> Matrix(23,18,-32,-25) Matrix(599,-1020,212,-361) -> Matrix(23,18,-32,-25) Matrix(121,-210,34,-59) -> Matrix(3,2,-2,-1) Matrix(241,-450,128,-239) -> Matrix(47,36,-64,-49) Matrix(179,-390,28,-61) -> Matrix(3,2,-2,-1) Matrix(299,-660,82,-181) -> Matrix(11,8,-18,-13) Matrix(1921,-4530,712,-1679) -> Matrix(3,2,-2,-1) Matrix(61,-150,24,-59) -> Matrix(1,2,-2,-3) Matrix(3061,-7920,904,-2339) -> Matrix(23,18,-32,-25) Matrix(539,-1410,138,-361) -> Matrix(19,14,-34,-25) Matrix(479,-1260,46,-121) -> Matrix(25,18,-32,-23) Matrix(659,-1740,114,-301) -> Matrix(29,20,-16,-11) Matrix(119,-330,22,-61) -> Matrix(5,4,-4,-3) Matrix(179,-570,38,-121) -> Matrix(3,2,-8,-5) Matrix(181,-600,54,-179) -> Matrix(1,2,-2,-3) Matrix(121,-450,32,-119) -> Matrix(3,2,-8,-5) Matrix(61,-450,8,-59) -> Matrix(11,12,-12,-13) 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): 47 Degree of the the map X: 47 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 -1/1 7 1 1/1 (-1/1,-7/8) 0 30 8/7 -19/22 1 15 15/13 -6/7 13 2 7/6 (-6/7,-17/20) 0 30 6/5 -6/7 1 5 17/14 (-6/7,-5/6) 0 30 28/23 -17/20 1 15 39/32 0 10 11/9 (-6/7,-11/13) 0 30 5/4 -5/6 2 6 19/15 (-1/1,-4/5) 0 30 14/11 -5/6 1 15 23/18 (-1/1,-6/7) 0 30 32/25 -5/6 1 15 41/32 (-1/1,-4/5) 0 30 9/7 -6/7 1 10 13/10 (-26/31,-5/6) 0 30 30/23 -5/6 11 1 17/13 (-5/6,-29/35) 0 30 4/3 -5/6 1 15 19/14 (-9/11,-4/5) 0 30 15/11 -4/5 2 2 11/8 (-1/1,-4/5) 0 30 29/21 (-7/9,-3/4) 0 30 18/13 -1/1 2 5 61/44 (-1/1,-6/7) 0 30 43/31 (-1/1,-5/6) 0 30 25/18 -1/1 2 6 32/23 -5/6 1 15 7/5 (-1/1,-4/5) 0 30 31/22 (-8/9,-7/8) 0 30 24/17 -6/7 1 5 17/12 (-6/7,-5/6) 0 30 27/19 -6/7 1 10 10/7 -5/6 1 3 33/23 -4/5 1 10 23/16 (-9/11,-4/5) 0 30 13/9 (-1/1,-5/6) 0 30 3/2 0 10 17/11 (-1/1,-5/6) 0 30 14/9 -5/6 1 15 25/16 -5/6 2 6 61/39 (-5/6,-19/23) 0 30 36/23 -9/11 2 5 11/7 (-9/11,-4/5) 0 30 30/19 -4/5 4 1 19/12 (-4/5,-7/9) 0 30 27/17 -4/5 1 10 89/56 (-10/13,-3/4) 0 30 62/39 -3/4 1 15 35/22 -1/1 2 6 8/5 -3/4 1 15 37/23 (-1/1,-10/11) 0 30 29/18 (-7/8,-6/7) 0 30 21/13 -6/7 1 10 13/8 (-5/6,-14/17) 0 30 31/19 (-5/6,-19/23) 0 30 18/11 -9/11 2 5 59/36 (-9/11,-4/5) 0 30 41/25 (-9/11,-22/27) 0 30 23/14 (-9/11,-4/5) 0 30 28/17 -13/16 1 15 5/3 -4/5 3 6 22/13 -11/14 1 15 39/23 -10/13 1 10 17/10 (-4/5,-3/4) 0 30 29/17 (-1/1,-3/4) 0 30 12/7 -4/5 1 5 7/4 (-4/5,-3/4) 0 30 30/17 -4/5 1 1 23/13 (-4/5,-7/9) 0 30 62/35 -3/4 1 15 39/22 0 10 16/9 -3/4 1 15 25/14 -3/4 2 6 59/33 (-7/9,-3/4) 0 30 34/19 -3/4 1 15 9/5 -4/5 1 10 29/16 (-5/6,-4/5) 0 30 20/11 -4/5 3 3 31/17 (-15/19,-11/14) 0 30 11/6 (-4/5,-7/9) 0 30 13/7 (-7/9,-3/4) 0 30 15/8 -3/4 4 2 17/9 (-3/4,-5/7) 0 30 2/1 -3/4 1 15 17/8 (-7/10,-2/3) 0 30 15/7 -2/3 4 2 13/6 (-2/3,-1/2) 0 30 11/5 (-1/1,-2/3) 0 30 20/9 -2/3 3 3 29/13 (-1/1,-1/2) 0 30 9/4 0 10 16/7 -1/2 1 15 23/10 (-1/1,0/1) 0 30 30/13 -1/1 2 1 7/3 (-1/1,-2/3) 0 30 33/14 0 10 59/25 (-3/4,-5/7) 0 30 26/11 -3/4 1 15 19/8 (-1/1,-2/3) 0 30 69/29 0/1 1 10 50/21 -1/1 4 3 31/13 (-1/1,-3/4) 0 30 12/5 -2/3 1 5 5/2 -1/1 2 6 18/7 -4/5 1 5 31/12 (-4/5,-3/4) 0 30 75/29 -4/5 1 2 44/17 -3/4 1 15 13/5 (-7/9,-3/4) 0 30 34/13 -3/4 1 15 89/34 (-3/4,-14/19) 0 30 55/21 -8/11 1 6 21/8 0 10 71/27 (-8/11,-5/7) 0 30 50/19 -5/7 4 3 29/11 (-5/7,-7/10) 0 30 37/14 (-13/19,-2/3) 0 30 45/17 -2/3 13 2 8/3 -1/2 1 15 35/13 -2/3 3 6 62/23 -1/2 1 15 151/56 (-6/11,-1/2) 0 30 240/89 -1/2 7 1 89/33 (-1/2,-1/3) 0 30 27/10 0 10 46/17 -1/2 1 15 19/7 (-1/1,0/1) 0 30 30/11 -1/1 4 1 11/4 (-1/1,-4/5) 0 30 14/5 -3/4 1 15 45/16 -3/4 6 2 31/11 (-3/4,-5/7) 0 30 17/6 (-3/4,-2/3) 0 30 3/1 -2/3 1 10 16/5 -1/2 1 15 45/14 -1/2 6 2 29/9 (-1/2,-1/3) 0 30 13/4 (-1/2,0/1) 0 30 23/7 (-1/1,-2/3) 0 30 10/3 -1/1 1 3 37/11 (-1/1,-4/5) 0 30 27/8 0 10 44/13 -3/4 1 15 105/31 -2/3 1 2 61/18 (-1/1,-2/3) 0 30 17/5 (-1/1,-3/4) 0 30 58/17 -3/4 1 15 41/12 (-5/7,-2/3) 0 30 24/7 -2/3 1 5 7/2 (-2/3,-1/2) 0 30 18/5 -2/3 1 5 29/8 (-2/3,-1/2) 0 30 40/11 -2/3 3 3 11/3 (-2/3,-3/5) 0 30 15/4 -1/2 2 2 19/5 (-1/1,0/1) 0 30 23/6 (-1/1,-2/3) 0 30 27/7 -2/3 1 10 31/8 (-1/2,0/1) 0 30 4/1 -1/2 1 15 21/5 0/1 1 10 17/4 (-2/3,-1/2) 0 30 30/7 -1/2 3 1 13/3 (-1/2,-1/3) 0 30 35/8 -1/3 2 6 22/5 -1/4 1 15 31/7 (-1/1,-1/2) 0 30 9/2 0 10 14/3 -1/2 1 15 33/7 0/1 1 10 19/4 (-1/1,0/1) 0 30 24/5 0/1 1 5 29/6 (-2/3,-1/2) 0 30 5/1 0/1 1 6 21/4 0 10 16/3 1/0 1 15 11/2 (-1/1,0/1) 0 30 17/3 (-1/1,1/0) 0 30 23/4 (-3/1,-2/1) 0 30 29/5 (-5/3,-3/2) 0 30 6/1 -1/1 2 5 19/3 (-1/1,0/1) 0 30 13/2 (0/1,1/0) 0 30 7/1 (-2/1,-1/1) 0 30 15/2 -1/1 12 2 23/3 (-1/1,-10/11) 0 30 8/1 -3/4 1 15 9/1 0/1 1 10 10/1 -1/1 4 3 11/1 (-1/1,-2/3) 0 30 1/0 (-1/1,0/1) 0 30 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(239,-270,54,-61) (1/1,8/7) -> (22/5,31/7) Hyperbolic Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(181,-210,156,-181) (15/13,7/6) -> (15/13,7/6) Reflection Matrix(179,-210,52,-61) (7/6,6/5) -> (24/7,7/2) Hyperbolic Matrix(421,-510,298,-361) (6/5,17/14) -> (24/17,17/12) Glide Reflection Matrix(419,-510,198,-241) (17/14,28/23) -> (2/1,17/8) Hyperbolic Matrix(2881,-3510,1626,-1981) (28/23,39/32) -> (62/35,39/22) Glide Reflection Matrix(2461,-3000,936,-1141) (39/32,11/9) -> (21/8,71/27) Glide Reflection Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(541,-690,236,-301) (14/11,23/18) -> (16/7,23/10) Glide Reflection Matrix(1079,-1380,656,-839) (23/18,32/25) -> (23/14,28/17) Glide Reflection Matrix(2881,-3690,844,-1081) (32/25,41/32) -> (58/17,41/12) Glide Reflection Matrix(2341,-3000,984,-1261) (41/32,9/7) -> (19/8,69/29) Glide Reflection Matrix(301,-390,186,-241) (9/7,13/10) -> (21/13,13/8) Glide Reflection Matrix(599,-780,460,-599) (13/10,30/23) -> (13/10,30/23) Reflection Matrix(781,-1020,598,-781) (30/23,17/13) -> (30/23,17/13) Reflection Matrix(481,-630,184,-241) (17/13,4/3) -> (13/5,34/13) Glide Reflection Matrix(421,-570,178,-241) (4/3,19/14) -> (26/11,19/8) Glide Reflection Matrix(419,-570,308,-419) (19/14,15/11) -> (19/14,15/11) Reflection Matrix(241,-330,176,-241) (15/11,11/8) -> (15/11,11/8) Reflection Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(781,-1080,478,-661) (29/21,18/13) -> (31/19,18/11) Glide Reflection Matrix(1559,-2160,952,-1319) (18/13,61/44) -> (18/11,59/36) Glide Reflection Matrix(2639,-3660,778,-1079) (61/44,43/31) -> (61/18,17/5) Glide Reflection Matrix(1319,-1830,302,-419) (43/31,25/18) -> (13/3,35/8) Glide Reflection Matrix(1921,-2670,1208,-1679) (25/18,32/23) -> (62/39,35/22) Hyperbolic Matrix(839,-1170,474,-661) (32/23,7/5) -> (23/13,62/35) Hyperbolic Matrix(959,-1350,596,-839) (7/5,31/22) -> (37/23,29/18) Glide Reflection Matrix(1021,-1440,212,-299) (31/22,24/17) -> (24/5,29/6) Hyperbolic Matrix(359,-510,126,-179) (17/12,27/19) -> (17/6,3/1) Glide Reflection Matrix(421,-600,294,-419) (27/19,10/7) -> (10/7,33/23) Parabolic Matrix(961,-1380,250,-359) (33/23,23/16) -> (23/6,27/7) Hyperbolic Matrix(479,-690,84,-121) (23/16,13/9) -> (17/3,23/4) Hyperbolic Matrix(61,-90,40,-59) (13/9,3/2) -> (3/2,17/11) Parabolic Matrix(601,-930,232,-359) (17/11,14/9) -> (44/17,13/5) Hyperbolic Matrix(481,-750,270,-421) (14/9,25/16) -> (16/9,25/14) Glide Reflection Matrix(1919,-3000,1074,-1679) (25/16,61/39) -> (25/14,59/33) Glide Reflection Matrix(901,-1410,154,-241) (61/39,36/23) -> (29/5,6/1) Glide Reflection Matrix(479,-750,76,-119) (36/23,11/7) -> (6/1,19/3) Glide Reflection Matrix(419,-660,266,-419) (11/7,30/19) -> (11/7,30/19) Reflection Matrix(721,-1140,456,-721) (30/19,19/12) -> (30/19,19/12) Reflection Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(2039,-3240,528,-839) (27/17,89/56) -> (27/7,31/8) Glide Reflection Matrix(9361,-14880,3472,-5519) (89/56,62/39) -> (62/23,151/56) Hyperbolic Matrix(659,-1050,150,-239) (35/22,8/5) -> (35/8,22/5) Glide Reflection Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(539,-870,298,-481) (29/18,21/13) -> (9/5,29/16) Hyperbolic Matrix(479,-780,148,-241) (13/8,31/19) -> (29/9,13/4) Hyperbolic Matrix(421,-690,36,-59) (59/36,41/25) -> (11/1,1/0) Hyperbolic Matrix(841,-1380,220,-361) (41/25,23/14) -> (19/5,23/6) Glide Reflection Matrix(781,-1290,290,-479) (28/17,5/3) -> (35/13,62/23) Hyperbolic Matrix(479,-810,178,-301) (5/3,22/13) -> (8/3,35/13) Hyperbolic Matrix(301,-510,36,-61) (22/13,39/23) -> (8/1,9/1) Glide Reflection Matrix(601,-1020,142,-241) (39/23,17/10) -> (21/5,17/4) Glide Reflection Matrix(599,-1020,212,-361) (17/10,29/17) -> (31/11,17/6) Hyperbolic Matrix(421,-720,176,-301) (29/17,12/7) -> (31/13,12/5) Glide Reflection Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(239,-420,136,-239) (7/4,30/17) -> (7/4,30/17) Reflection Matrix(781,-1380,442,-781) (30/17,23/13) -> (30/17,23/13) Reflection Matrix(541,-960,102,-181) (39/22,16/9) -> (21/4,16/3) Glide Reflection Matrix(1979,-3540,838,-1499) (59/33,34/19) -> (59/25,26/11) Glide Reflection Matrix(419,-750,100,-179) (34/19,9/5) -> (4/1,21/5) Glide Reflection Matrix(959,-1740,264,-479) (29/16,20/11) -> (29/8,40/11) Glide Reflection Matrix(659,-1200,296,-539) (20/11,31/17) -> (20/9,29/13) Glide Reflection Matrix(179,-330,32,-59) (11/6,13/7) -> (11/2,17/3) Glide Reflection Matrix(241,-450,128,-239) (13/7,15/8) -> (15/8,17/9) Parabolic Matrix(539,-1020,158,-299) (17/9,2/1) -> (17/5,58/17) Glide Reflection Matrix(239,-510,112,-239) (17/8,15/7) -> (17/8,15/7) Reflection Matrix(181,-390,84,-181) (15/7,13/6) -> (15/7,13/6) Reflection Matrix(179,-390,28,-61) (13/6,11/5) -> (19/3,13/2) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(241,-540,54,-121) (29/13,9/4) -> (31/7,9/2) Glide Reflection Matrix(119,-270,26,-59) (9/4,16/7) -> (9/2,14/3) Glide Reflection Matrix(599,-1380,260,-599) (23/10,30/13) -> (23/10,30/13) Reflection Matrix(181,-420,78,-181) (30/13,7/3) -> (30/13,7/3) Reflection Matrix(599,-1410,178,-419) (7/3,33/14) -> (37/11,27/8) Glide Reflection Matrix(1921,-4530,712,-1679) (33/14,59/25) -> (89/33,27/10) Hyperbolic Matrix(479,-1140,50,-119) (69/29,50/21) -> (9/1,10/1) Glide Reflection Matrix(1259,-3000,478,-1139) (50/21,31/13) -> (50/19,29/11) Glide Reflection Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(419,-1080,116,-299) (18/7,31/12) -> (18/5,29/8) Glide Reflection Matrix(1799,-4650,696,-1799) (31/12,75/29) -> (31/12,75/29) Reflection Matrix(3061,-7920,904,-2339) (75/29,44/17) -> (44/13,105/31) Hyperbolic Matrix(539,-1410,138,-361) (34/13,89/34) -> (31/8,4/1) Hyperbolic Matrix(779,-2040,160,-419) (89/34,55/21) -> (29/6,5/1) Glide Reflection Matrix(481,-1260,92,-241) (55/21,21/8) -> (5/1,21/4) Glide Reflection Matrix(479,-1260,46,-121) (71/27,50/19) -> (10/1,11/1) Hyperbolic Matrix(659,-1740,114,-301) (29/11,37/14) -> (23/4,29/5) Hyperbolic Matrix(1259,-3330,476,-1259) (37/14,45/17) -> (37/14,45/17) Reflection Matrix(26879,-72480,9968,-26879) (151/56,240/89) -> (151/56,240/89) Reflection Matrix(15841,-42720,5874,-15841) (240/89,89/33) -> (240/89,89/33) Reflection Matrix(899,-2430,266,-719) (27/10,46/17) -> (27/8,44/13) Glide Reflection Matrix(419,-1140,154,-419) (19/7,30/11) -> (19/7,30/11) Reflection Matrix(241,-660,88,-241) (30/11,11/4) -> (30/11,11/4) Reflection Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(481,-1350,150,-421) (14/5,45/16) -> (16/5,45/14) Glide Reflection Matrix(959,-2700,298,-839) (45/16,31/11) -> (45/14,29/9) Glide Reflection Matrix(179,-570,38,-121) (3/1,16/5) -> (14/3,33/7) Hyperbolic Matrix(119,-390,18,-59) (13/4,23/7) -> (13/2,7/1) Glide Reflection Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(3781,-12810,1116,-3781) (105/31,61/18) -> (105/31,61/18) Reflection Matrix(421,-1440,88,-301) (41/12,24/7) -> (19/4,24/5) Glide Reflection Matrix(121,-450,32,-119) (11/3,15/4) -> (15/4,19/5) Parabolic Matrix(239,-1020,56,-239) (17/4,30/7) -> (17/4,30/7) Reflection Matrix(181,-780,42,-181) (30/7,13/3) -> (30/7,13/3) Reflection Matrix(61,-450,8,-59) (7/1,15/2) -> (15/2,23/3) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(15,14,-16,-15) (0/1,1/1) -> (-1/1,-7/8) Matrix(239,-270,54,-61) -> Matrix(7,6,-6,-5) -1/1 Matrix(419,-480,158,-181) -> Matrix(51,44,-80,-69) Matrix(181,-210,156,-181) -> Matrix(239,204,-280,-239) (15/13,7/6) -> (-6/7,-17/20) Matrix(179,-210,52,-61) -> Matrix(33,28,-46,-39) Matrix(421,-510,298,-361) -> Matrix(71,60,-84,-71) *** -> (-6/7,-5/6) Matrix(419,-510,198,-241) -> Matrix(61,52,-88,-75) Matrix(2881,-3510,1626,-1981) -> Matrix(101,86,-128,-109) Matrix(2461,-3000,936,-1141) -> Matrix(139,118,-192,-163) Matrix(121,-150,96,-119) -> Matrix(59,50,-72,-61) -5/6 Matrix(899,-1140,332,-421) -> Matrix(5,4,-4,-3) -1/1 Matrix(541,-690,236,-301) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(1079,-1380,656,-839) -> Matrix(67,58,-82,-71) Matrix(2881,-3690,844,-1081) -> Matrix(27,22,-38,-31) Matrix(2341,-3000,984,-1261) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(301,-390,186,-241) -> Matrix(71,60,-84,-71) *** -> (-6/7,-5/6) Matrix(599,-780,460,-599) -> Matrix(311,260,-372,-311) (13/10,30/23) -> (-26/31,-5/6) Matrix(781,-1020,598,-781) -> Matrix(349,290,-420,-349) (30/23,17/13) -> (-5/6,-29/35) Matrix(481,-630,184,-241) -> Matrix(63,52,-86,-71) Matrix(421,-570,178,-241) -> Matrix(27,22,-38,-31) Matrix(419,-570,308,-419) -> Matrix(89,72,-110,-89) (19/14,15/11) -> (-9/11,-4/5) Matrix(241,-330,176,-241) -> Matrix(9,8,-10,-9) (15/11,11/8) -> (-1/1,-4/5) Matrix(479,-660,262,-361) -> Matrix(39,32,-50,-41) -4/5 Matrix(781,-1080,478,-661) -> Matrix(31,22,-38,-27) Matrix(1559,-2160,952,-1319) -> Matrix(67,58,-82,-71) Matrix(2639,-3660,778,-1079) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(1319,-1830,302,-419) -> Matrix(5,4,-16,-13) Matrix(1921,-2670,1208,-1679) -> Matrix(3,2,-2,-1) -1/1 Matrix(839,-1170,474,-661) -> Matrix(39,32,-50,-41) -4/5 Matrix(959,-1350,596,-839) -> Matrix(15,14,-16,-15) *** -> (-1/1,-7/8) Matrix(1021,-1440,212,-299) -> Matrix(7,6,-6,-5) -1/1 Matrix(359,-510,126,-179) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(421,-600,294,-419) -> Matrix(59,50,-72,-61) -5/6 Matrix(961,-1380,250,-359) -> Matrix(17,14,-28,-23) Matrix(479,-690,84,-121) -> Matrix(7,6,-6,-5) -1/1 Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(601,-930,232,-359) -> Matrix(39,32,-50,-41) -4/5 Matrix(481,-750,270,-421) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(1919,-3000,1074,-1679) -> Matrix(27,22,-38,-31) Matrix(901,-1410,154,-241) -> Matrix(39,32,-28,-23) Matrix(479,-750,76,-119) -> Matrix(5,4,-16,-13) Matrix(419,-660,266,-419) -> Matrix(89,72,-110,-89) (11/7,30/19) -> (-9/11,-4/5) Matrix(721,-1140,456,-721) -> Matrix(71,56,-90,-71) (30/19,19/12) -> (-4/5,-7/9) Matrix(719,-1140,152,-241) -> Matrix(5,4,-14,-11) Matrix(2039,-3240,528,-839) -> Matrix(13,10,-22,-17) Matrix(9361,-14880,3472,-5519) -> Matrix(11,8,-18,-13) -2/3 Matrix(659,-1050,150,-239) -> Matrix(5,4,-16,-13) Matrix(299,-480,38,-61) -> Matrix(1,0,0,1) Matrix(539,-870,298,-481) -> Matrix(3,2,-2,-1) -1/1 Matrix(479,-780,148,-241) -> Matrix(17,14,-28,-23) Matrix(421,-690,36,-59) -> Matrix(5,4,6,5) Matrix(841,-1380,220,-361) -> Matrix(27,22,-38,-31) Matrix(781,-1290,290,-479) -> Matrix(37,30,-58,-47) Matrix(479,-810,178,-301) -> Matrix(23,18,-32,-25) -3/4 Matrix(301,-510,36,-61) -> Matrix(13,10,-22,-17) Matrix(601,-1020,142,-241) -> Matrix(13,10,-22,-17) Matrix(599,-1020,212,-361) -> Matrix(23,18,-32,-25) -3/4 Matrix(421,-720,176,-301) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(121,-210,34,-59) -> Matrix(3,2,-2,-1) -1/1 Matrix(239,-420,136,-239) -> Matrix(31,24,-40,-31) (7/4,30/17) -> (-4/5,-3/4) Matrix(781,-1380,442,-781) -> Matrix(71,56,-90,-71) (30/17,23/13) -> (-4/5,-7/9) Matrix(541,-960,102,-181) -> Matrix(5,4,4,3) Matrix(1979,-3540,838,-1499) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(419,-750,100,-179) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(959,-1740,264,-479) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(659,-1200,296,-539) -> Matrix(33,26,-52,-41) Matrix(179,-330,32,-59) -> Matrix(5,4,4,3) Matrix(241,-450,128,-239) -> Matrix(47,36,-64,-49) -3/4 Matrix(539,-1020,158,-299) -> Matrix(17,12,-24,-17) *** -> (-3/4,-2/3) Matrix(239,-510,112,-239) -> Matrix(41,28,-60,-41) (17/8,15/7) -> (-7/10,-2/3) Matrix(181,-390,84,-181) -> Matrix(7,4,-12,-7) (15/7,13/6) -> (-2/3,-1/2) Matrix(179,-390,28,-61) -> Matrix(3,2,-2,-1) -1/1 Matrix(299,-660,82,-181) -> Matrix(11,8,-18,-13) -2/3 Matrix(241,-540,54,-121) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(119,-270,26,-59) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(599,-1380,260,-599) -> Matrix(-1,0,2,1) (23/10,30/13) -> (-1/1,0/1) Matrix(181,-420,78,-181) -> Matrix(5,4,-6,-5) (30/13,7/3) -> (-1/1,-2/3) Matrix(599,-1410,178,-419) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(1921,-4530,712,-1679) -> Matrix(3,2,-2,-1) -1/1 Matrix(479,-1140,50,-119) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1259,-3000,478,-1139) -> Matrix(27,22,-38,-31) Matrix(61,-150,24,-59) -> Matrix(1,2,-2,-3) -1/1 Matrix(419,-1080,116,-299) -> Matrix(13,10,-22,-17) Matrix(1799,-4650,696,-1799) -> Matrix(31,24,-40,-31) (31/12,75/29) -> (-4/5,-3/4) Matrix(3061,-7920,904,-2339) -> Matrix(23,18,-32,-25) -3/4 Matrix(539,-1410,138,-361) -> Matrix(19,14,-34,-25) Matrix(779,-2040,160,-419) -> Matrix(11,8,-26,-19) Matrix(481,-1260,92,-241) -> Matrix(11,8,-4,-3) Matrix(479,-1260,46,-121) -> Matrix(25,18,-32,-23) -3/4 Matrix(659,-1740,114,-301) -> Matrix(29,20,-16,-11) Matrix(1259,-3330,476,-1259) -> Matrix(77,52,-114,-77) (37/14,45/17) -> (-13/19,-2/3) Matrix(26879,-72480,9968,-26879) -> Matrix(23,12,-44,-23) (151/56,240/89) -> (-6/11,-1/2) Matrix(15841,-42720,5874,-15841) -> Matrix(5,2,-12,-5) (240/89,89/33) -> (-1/2,-1/3) Matrix(899,-2430,266,-719) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(419,-1140,154,-419) -> Matrix(-1,0,2,1) (19/7,30/11) -> (-1/1,0/1) Matrix(241,-660,88,-241) -> Matrix(9,8,-10,-9) (30/11,11/4) -> (-1/1,-4/5) Matrix(119,-330,22,-61) -> Matrix(5,4,-4,-3) -1/1 Matrix(481,-1350,150,-421) -> Matrix(13,10,-22,-17) Matrix(959,-2700,298,-839) -> Matrix(11,8,-26,-19) Matrix(179,-570,38,-121) -> Matrix(3,2,-8,-5) -1/2 Matrix(119,-390,18,-59) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(181,-600,54,-179) -> Matrix(1,2,-2,-3) -1/1 Matrix(3781,-12810,1116,-3781) -> Matrix(5,4,-6,-5) (105/31,61/18) -> (-1/1,-2/3) Matrix(421,-1440,88,-301) -> Matrix(3,2,-10,-7) Matrix(121,-450,32,-119) -> Matrix(3,2,-8,-5) -1/2 Matrix(239,-1020,56,-239) -> Matrix(7,4,-12,-7) (17/4,30/7) -> (-2/3,-1/2) Matrix(181,-780,42,-181) -> Matrix(5,2,-12,-5) (30/7,13/3) -> (-1/2,-1/3) Matrix(61,-450,8,-59) -> Matrix(11,12,-12,-13) -1/1 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.