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: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/1 -7/1 -6/1 -14/3 -9/2 -18/5 -7/2 -3/1 -14/5 -12/5 -7/3 -28/13 -15/7 -7/4 -63/40 -3/2 -7/5 -63/52 -7/6 0/1 1/1 7/6 21/17 21/16 7/5 3/2 21/13 105/64 7/4 2/1 15/7 28/13 42/19 84/37 7/3 12/5 5/2 105/41 21/8 63/23 14/5 3/1 42/13 84/25 7/2 18/5 11/3 15/4 42/11 4/1 21/5 17/4 13/3 9/2 14/3 19/4 5/1 21/4 16/3 11/2 17/3 63/11 6/1 19/3 13/2 20/3 7/1 15/2 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -1/1 -8/1 1/1 1/0 -7/1 -1/1 -13/2 -1/1 -2/3 -6/1 0/1 -23/4 -2/1 -1/1 -17/3 -1/2 -11/2 -1/2 0/1 -16/3 -3/5 -1/2 -21/4 -1/2 -5/1 -1/2 -19/4 -1/3 0/1 -14/3 0/1 -23/5 -1/2 -9/2 -2/5 0/1 -22/5 -1/2 -1/3 -13/3 -1/2 -17/4 -4/11 -1/3 -21/5 -1/3 -4/1 -1/3 -1/4 -19/5 -1/4 -15/4 -2/7 0/1 -56/15 -2/7 -41/11 -11/40 -26/7 -5/19 -1/4 -11/3 -1/4 -18/5 -2/7 -7/2 -1/4 -24/7 -2/9 -41/12 -3/13 -2/9 -17/5 -3/14 -61/18 -6/29 -1/5 -105/31 -1/5 -44/13 -1/5 -3/16 -27/8 -2/9 0/1 -37/11 -1/6 -10/3 -1/3 -1/4 -33/10 -4/17 -2/9 -23/7 -1/4 -36/11 -4/17 -13/4 -3/13 -2/9 -16/5 -3/14 -1/5 -3/1 -1/5 -17/6 -1/5 -4/21 -14/5 -2/11 -25/9 -1/6 -11/4 -4/23 -1/6 -19/7 -1/6 -27/10 -2/11 0/1 -35/13 -1/5 -8/3 -3/17 -1/6 -21/8 -1/6 -13/5 -1/6 -18/7 -2/13 -41/16 -2/13 -1/7 -105/41 -1/7 -64/25 -1/6 -1/7 -23/9 -1/6 -5/2 -1/6 -2/13 -27/11 -1/7 -22/9 -1/6 -1/7 -17/7 -3/20 -29/12 -1/7 0/1 -70/29 0/1 -41/17 -3/16 -12/5 -2/13 -19/8 -4/27 -1/7 -7/3 -1/7 -23/10 -1/7 -2/15 -39/17 -1/7 -16/7 -1/7 -3/22 -41/18 -1/7 -2/15 -25/11 -7/52 -34/15 -5/38 -3/23 -9/4 -2/15 0/1 -20/9 -1/7 -1/8 -11/5 -1/8 -13/6 -1/7 -2/15 -28/13 -2/15 -15/7 -3/23 -2/1 -1/8 -1/9 -15/8 -4/37 -2/19 -28/15 -2/19 -13/7 -1/10 -11/6 -1/10 0/1 -42/23 0/1 -31/17 -1/8 -20/11 -1/8 -1/9 -9/5 -1/9 -34/19 -3/28 -5/47 -59/33 -15/142 -84/47 -2/19 -25/14 -2/19 -7/67 -41/23 -13/126 -16/9 -1/9 -1/10 -7/4 -1/10 -26/15 -1/10 -3/31 -19/11 -1/10 -31/18 -2/19 -1/10 -105/61 -1/10 -74/43 -1/10 -13/131 -43/25 -11/112 -12/7 -2/21 -41/24 -2/21 -1/11 -70/41 -2/21 -29/17 -3/32 -17/10 -1/11 0/1 -39/23 -1/11 -61/36 -6/65 -1/11 -22/13 -1/11 -3/34 -27/16 -2/23 0/1 -5/3 -1/10 -23/14 -2/21 -1/11 -64/39 -11/120 -1/11 -105/64 -1/11 -41/25 -7/78 -18/11 0/1 -31/19 -1/10 -13/8 -2/21 -1/11 -21/13 -1/11 -8/5 -1/11 -1/12 -27/17 -1/11 -19/12 -1/11 0/1 -30/19 -2/23 -41/26 -1/11 -2/23 -52/33 -3/35 -1/12 -63/40 -1/12 -11/7 -1/12 -25/16 -2/25 -1/13 -14/9 0/1 -17/11 -1/10 -20/13 -1/11 -1/12 -3/2 -2/23 0/1 -22/15 -1/11 -1/12 -19/13 -1/12 -16/11 -1/12 -1/13 -29/20 -1/15 0/1 -42/29 0/1 -13/9 -1/10 -23/16 -1/11 -2/23 -10/7 -1/11 -1/12 -47/33 -1/14 -84/59 0/1 -37/26 -1/10 0/1 -27/19 -1/11 -44/31 -5/59 -1/12 -17/12 -1/13 0/1 -7/5 -1/12 -25/18 -3/37 -2/25 -43/31 -7/90 -18/13 0/1 -29/21 -1/12 -11/8 -1/12 0/1 -26/19 -1/12 -3/37 -41/30 -3/37 -2/25 -56/41 -2/25 -15/11 -1/13 -19/14 -1/13 0/1 -42/31 0/1 -23/17 -1/12 -4/3 -1/12 -1/13 -21/16 -1/13 -17/13 -5/66 -13/10 -1/13 -2/27 -35/27 -1/13 -57/44 -2/27 0/1 -22/17 -1/13 -3/40 -9/7 -1/13 -41/32 -2/27 -3/41 -32/25 -1/13 -1/14 -23/18 -1/13 -2/27 -14/11 -2/27 -19/15 -1/14 -5/4 -2/27 -1/14 -21/17 -1/14 -16/13 -1/14 -7/99 -11/9 -1/14 -17/14 -1/15 0/1 -40/33 -5/69 -1/14 -63/52 -1/14 -23/19 -1/14 -6/5 -2/29 -19/16 -1/15 0/1 -13/11 -3/44 -20/17 -3/44 -1/15 -7/6 -1/15 -22/19 -1/15 -5/76 -15/13 -1/15 -8/7 -1/15 -3/46 -9/8 -2/31 -4/63 -10/9 -7/111 -1/16 -1/1 -1/18 0/1 0/1 1/1 1/20 9/8 4/71 2/35 8/7 3/52 1/17 7/6 1/17 13/11 3/50 6/5 2/33 23/19 1/16 17/14 0/1 1/17 11/9 1/16 16/13 7/113 1/16 21/17 1/16 5/4 1/16 2/31 19/15 1/16 14/11 2/31 23/18 2/31 1/15 9/7 1/15 22/17 3/46 1/15 13/10 2/31 1/15 17/13 5/76 21/16 1/15 4/3 1/15 1/14 19/14 0/1 1/15 15/11 1/15 56/41 2/29 41/30 2/29 3/43 26/19 3/43 1/14 11/8 0/1 1/14 18/13 0/1 7/5 1/14 24/17 2/27 41/29 5/64 17/12 0/1 1/15 61/43 1/14 105/74 1/14 44/31 1/14 5/69 27/19 1/13 37/26 0/1 1/12 10/7 1/14 1/13 33/23 1/13 23/16 2/27 1/13 36/25 0/1 13/9 1/12 16/11 1/15 1/14 3/2 0/1 2/27 17/11 1/12 14/9 0/1 25/16 1/15 2/29 11/7 1/14 19/12 0/1 1/13 27/17 1/13 35/22 1/13 8/5 1/14 1/13 21/13 1/13 13/8 1/13 2/25 18/11 0/1 41/25 7/92 105/64 1/13 64/39 1/13 11/142 23/14 1/13 2/25 5/3 1/12 27/16 0/1 2/27 22/13 3/40 1/13 17/10 0/1 1/13 29/17 3/38 70/41 2/25 41/24 1/13 2/25 12/7 2/25 19/11 1/12 7/4 1/12 23/13 1/12 39/22 4/47 2/23 16/9 1/12 1/11 41/23 13/152 25/14 7/81 2/23 34/19 5/57 3/34 9/5 1/11 20/11 1/11 1/10 11/6 0/1 1/12 13/7 1/12 28/15 2/23 15/8 2/23 4/45 2/1 1/11 1/10 15/7 3/29 28/13 2/19 13/6 2/19 1/9 11/5 1/10 42/19 2/19 31/14 2/19 3/28 20/9 1/10 1/9 9/4 0/1 2/19 34/15 3/29 5/48 59/26 15/143 2/19 84/37 2/19 25/11 7/66 41/18 2/19 1/9 16/7 3/28 1/9 7/3 1/9 26/11 1/9 3/26 19/8 1/9 4/35 31/13 3/26 105/44 3/26 74/31 3/26 5/43 43/18 1/9 2/17 12/5 2/17 41/17 3/22 70/29 0/1 29/12 0/1 1/9 17/7 3/26 39/16 0/1 2/17 61/25 1/8 22/9 1/9 1/8 27/11 1/9 5/2 2/17 1/8 23/9 1/8 64/25 1/9 1/8 105/41 1/9 41/16 1/9 2/17 18/7 2/17 31/12 2/17 1/8 13/5 1/8 21/8 1/8 8/3 1/8 3/23 27/10 0/1 2/15 19/7 1/8 30/11 0/1 41/15 7/58 52/19 11/89 1/8 63/23 1/8 11/4 1/8 4/31 25/9 1/8 14/5 2/15 17/6 4/29 1/7 20/7 7/50 1/7 3/1 1/7 22/7 5/36 1/7 19/6 1/7 4/27 16/5 1/7 3/20 29/9 7/46 42/13 2/13 13/4 2/13 3/19 23/7 1/6 10/3 1/6 1/5 47/14 0/1 1/4 84/25 0/1 37/11 1/8 27/8 0/1 2/13 44/13 3/22 1/7 17/5 3/20 7/2 1/6 25/7 5/28 43/12 2/11 1/5 18/5 2/11 29/8 0/1 1/5 11/3 1/6 26/7 1/6 5/29 41/11 11/62 56/15 2/11 15/4 0/1 2/11 19/5 1/6 42/11 2/11 23/6 2/11 1/5 4/1 1/6 1/5 21/5 1/5 17/4 1/5 4/19 13/3 1/4 35/8 1/5 57/13 1/5 22/5 1/5 1/4 9/2 0/1 2/9 41/9 9/38 32/7 1/4 3/11 23/5 1/4 14/3 0/1 19/4 0/1 1/5 5/1 1/4 21/4 1/4 16/3 1/4 3/11 11/2 0/1 1/4 17/3 1/4 40/7 7/22 1/3 63/11 1/3 23/4 1/3 2/5 6/1 0/1 19/3 1/4 13/2 2/7 1/3 20/3 3/10 1/3 7/1 1/3 22/3 1/4 1/3 15/2 0/1 2/5 8/1 1/2 1/1 9/1 1/3 10/1 1/3 1/2 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(41,378,-32,-295) (-9/1,1/0) -> (-9/7,-41/32) Hyperbolic Matrix(43,378,24,211) (-9/1,-8/1) -> (34/19,9/5) Hyperbolic Matrix(43,336,-16,-125) (-8/1,-7/1) -> (-35/13,-8/3) Hyperbolic Matrix(83,546,-64,-421) (-7/1,-13/2) -> (-13/10,-35/27) Hyperbolic Matrix(85,546,-26,-167) (-13/2,-6/1) -> (-36/11,-13/4) Hyperbolic Matrix(167,966,116,671) (-6/1,-23/4) -> (23/16,36/25) Hyperbolic Matrix(251,1428,-74,-421) (-23/4,-17/3) -> (-17/5,-61/18) Hyperbolic Matrix(83,462,30,167) (-17/3,-11/2) -> (11/4,25/9) Hyperbolic Matrix(85,462,62,337) (-11/2,-16/3) -> (26/19,11/8) Hyperbolic Matrix(127,672,24,127) (-16/3,-21/4) -> (21/4,16/3) Hyperbolic Matrix(41,210,8,41) (-21/4,-5/1) -> (5/1,21/4) Hyperbolic Matrix(43,210,26,127) (-5/1,-19/4) -> (23/14,5/3) Hyperbolic Matrix(125,588,98,461) (-19/4,-14/3) -> (14/11,23/18) Hyperbolic Matrix(127,588,100,463) (-14/3,-23/5) -> (19/15,14/11) Hyperbolic Matrix(211,966,-64,-293) (-23/5,-9/2) -> (-33/10,-23/7) Hyperbolic Matrix(85,378,38,169) (-9/2,-22/5) -> (20/9,9/4) Hyperbolic Matrix(125,546,-106,-463) (-22/5,-13/3) -> (-13/11,-20/17) Hyperbolic Matrix(167,714,98,419) (-13/3,-17/4) -> (17/10,29/17) Hyperbolic Matrix(169,714,40,169) (-17/4,-21/5) -> (21/5,17/4) Hyperbolic Matrix(41,168,10,41) (-21/5,-4/1) -> (4/1,21/5) Hyperbolic Matrix(43,168,-32,-125) (-4/1,-19/5) -> (-23/17,-4/3) Hyperbolic Matrix(211,798,78,295) (-19/5,-15/4) -> (27/10,19/7) Hyperbolic Matrix(337,1260,180,673) (-15/4,-56/15) -> (28/15,15/8) Hyperbolic Matrix(1385,5166,574,2141) (-56/15,-41/11) -> (41/17,70/29) Hyperbolic Matrix(463,1722,260,967) (-41/11,-26/7) -> (16/9,41/23) Hyperbolic Matrix(125,462,102,377) (-26/7,-11/3) -> (11/9,16/13) Hyperbolic Matrix(209,756,-128,-463) (-11/3,-18/5) -> (-18/11,-31/19) Hyperbolic Matrix(83,294,-24,-85) (-18/5,-7/2) -> (-7/2,-24/7) Parabolic Matrix(503,1722,196,671) (-24/7,-41/12) -> (41/16,18/7) Hyperbolic Matrix(505,1722,222,757) (-41/12,-17/5) -> (25/11,41/18) Hyperbolic Matrix(1847,6258,322,1091) (-61/18,-105/31) -> (63/11,23/4) Hyperbolic Matrix(2059,6972,360,1219) (-105/31,-44/13) -> (40/7,63/11) Hyperbolic Matrix(211,714,112,379) (-44/13,-27/8) -> (15/8,2/1) Hyperbolic Matrix(337,1134,200,673) (-27/8,-37/11) -> (5/3,27/16) Hyperbolic Matrix(251,840,-176,-589) (-37/11,-10/3) -> (-10/7,-47/33) Hyperbolic Matrix(127,420,-114,-377) (-10/3,-33/10) -> (-9/8,-10/9) Hyperbolic Matrix(295,966,244,799) (-23/7,-36/11) -> (6/5,23/19) Hyperbolic Matrix(209,672,-144,-463) (-13/4,-16/5) -> (-16/11,-29/20) Hyperbolic Matrix(211,672,-92,-293) (-16/5,-3/1) -> (-39/17,-16/7) Hyperbolic Matrix(251,714,-148,-421) (-3/1,-17/6) -> (-17/10,-39/23) Hyperbolic Matrix(209,588,134,377) (-17/6,-14/5) -> (14/9,25/16) Hyperbolic Matrix(211,588,136,379) (-14/5,-25/9) -> (17/11,14/9) Hyperbolic Matrix(167,462,30,83) (-25/9,-11/4) -> (11/2,17/3) Hyperbolic Matrix(293,798,-170,-463) (-11/4,-19/7) -> (-19/11,-31/18) Hyperbolic Matrix(295,798,78,211) (-19/7,-27/10) -> (15/4,19/5) Hyperbolic Matrix(1091,2940,-842,-2269) (-27/10,-35/13) -> (-35/27,-57/44) Hyperbolic Matrix(127,336,48,127) (-8/3,-21/8) -> (21/8,8/3) Hyperbolic Matrix(209,546,80,209) (-21/8,-13/5) -> (13/5,21/8) Hyperbolic Matrix(293,756,-212,-547) (-13/5,-18/7) -> (-18/13,-29/21) Hyperbolic Matrix(589,1512,164,421) (-18/7,-41/16) -> (43/12,18/5) Hyperbolic Matrix(3361,8610,1312,3361) (-41/16,-105/41) -> (105/41,41/16) Hyperbolic Matrix(5249,13440,2050,5249) (-105/41,-64/25) -> (64/25,105/41) Hyperbolic Matrix(1723,4410,706,1807) (-64/25,-23/9) -> (61/25,22/9) Hyperbolic Matrix(83,210,66,167) (-23/9,-5/2) -> (5/4,19/15) Hyperbolic Matrix(461,1134,324,797) (-5/2,-27/11) -> (27/19,37/26) Hyperbolic Matrix(377,924,-326,-799) (-27/11,-22/9) -> (-22/19,-15/13) Hyperbolic Matrix(293,714,-190,-463) (-22/9,-17/7) -> (-17/11,-20/13) Hyperbolic Matrix(295,714,226,547) (-17/7,-29/12) -> (13/10,17/13) Hyperbolic Matrix(713,1722,330,797) (-29/12,-70/29) -> (28/13,13/6) Hyperbolic Matrix(2141,5166,574,1385) (-70/29,-41/17) -> (41/11,56/15) Hyperbolic Matrix(715,1722,262,631) (-41/17,-12/5) -> (30/11,41/15) Hyperbolic Matrix(335,798,-212,-505) (-12/5,-19/8) -> (-19/12,-30/19) Hyperbolic Matrix(125,294,-54,-127) (-19/8,-7/3) -> (-7/3,-23/10) Parabolic Matrix(1427,3276,-842,-1933) (-23/10,-39/17) -> (-39/23,-61/36) Hyperbolic Matrix(755,1722,552,1259) (-16/7,-41/18) -> (41/30,26/19) Hyperbolic Matrix(923,2100,258,587) (-41/18,-25/11) -> (25/7,43/12) Hyperbolic Matrix(1259,2856,-704,-1597) (-25/11,-34/15) -> (-34/19,-59/33) Hyperbolic Matrix(167,378,148,335) (-34/15,-9/4) -> (9/8,8/7) Hyperbolic Matrix(169,378,38,85) (-9/4,-20/9) -> (22/5,9/2) Hyperbolic Matrix(379,840,-208,-461) (-20/9,-11/5) -> (-31/17,-20/11) Hyperbolic Matrix(211,462,58,127) (-11/5,-13/6) -> (29/8,11/3) Hyperbolic Matrix(797,1722,330,713) (-13/6,-28/13) -> (70/29,29/12) Hyperbolic Matrix(587,1260,430,923) (-28/13,-15/7) -> (15/11,56/41) Hyperbolic Matrix(335,714,236,503) (-15/7,-2/1) -> (44/31,27/19) Hyperbolic Matrix(379,714,112,211) (-2/1,-15/8) -> (27/8,44/13) Hyperbolic Matrix(673,1260,180,337) (-15/8,-28/15) -> (56/15,15/4) Hyperbolic Matrix(925,1722,542,1009) (-28/15,-13/7) -> (29/17,70/41) Hyperbolic Matrix(295,546,114,211) (-13/7,-11/6) -> (31/12,13/5) Hyperbolic Matrix(965,1764,436,797) (-11/6,-42/23) -> (42/19,31/14) Hyperbolic Matrix(967,1764,438,799) (-42/23,-31/17) -> (11/5,42/19) Hyperbolic Matrix(209,378,162,293) (-20/11,-9/5) -> (9/7,22/17) Hyperbolic Matrix(211,378,24,43) (-9/5,-34/19) -> (8/1,9/1) Hyperbolic Matrix(3947,7056,1738,3107) (-59/33,-84/47) -> (84/37,25/11) Hyperbolic Matrix(3949,7056,1740,3109) (-84/47,-25/14) -> (59/26,84/37) Hyperbolic Matrix(965,1722,682,1217) (-25/14,-41/23) -> (41/29,17/12) Hyperbolic Matrix(967,1722,260,463) (-41/23,-16/9) -> (26/7,41/11) Hyperbolic Matrix(167,294,-96,-169) (-16/9,-7/4) -> (-7/4,-26/15) Parabolic Matrix(461,798,-316,-547) (-26/15,-19/11) -> (-19/13,-16/11) Hyperbolic Matrix(1805,3108,658,1133) (-31/18,-105/61) -> (63/23,11/4) Hyperbolic Matrix(5881,10122,2148,3697) (-105/61,-74/43) -> (52/19,63/23) Hyperbolic Matrix(2563,4410,562,967) (-74/43,-43/25) -> (41/9,32/7) Hyperbolic Matrix(587,1008,244,419) (-43/25,-12/7) -> (12/5,41/17) Hyperbolic Matrix(589,1008,246,421) (-12/7,-41/24) -> (43/18,12/5) Hyperbolic Matrix(3025,5166,2214,3781) (-41/24,-70/41) -> (56/41,41/30) Hyperbolic Matrix(1009,1722,542,925) (-70/41,-29/17) -> (13/7,28/15) Hyperbolic Matrix(419,714,98,167) (-29/17,-17/10) -> (17/4,13/3) Hyperbolic Matrix(2603,4410,1586,2687) (-61/36,-22/13) -> (64/39,23/14) Hyperbolic Matrix(1093,1848,-844,-1427) (-22/13,-27/16) -> (-57/44,-22/17) Hyperbolic Matrix(673,1134,200,337) (-27/16,-5/3) -> (37/11,27/8) Hyperbolic Matrix(127,210,26,43) (-5/3,-23/14) -> (19/4,5/1) Hyperbolic Matrix(1049,1722,332,545) (-23/14,-64/39) -> (22/7,19/6) Hyperbolic Matrix(8191,13440,4992,8191) (-64/39,-105/64) -> (105/64,64/39) Hyperbolic Matrix(5249,8610,3200,5249) (-105/64,-41/25) -> (41/25,105/64) Hyperbolic Matrix(1051,1722,744,1219) (-41/25,-18/11) -> (24/17,41/29) Hyperbolic Matrix(335,546,154,251) (-31/19,-13/8) -> (13/6,11/5) Hyperbolic Matrix(337,546,208,337) (-13/8,-21/13) -> (21/13,13/8) Hyperbolic Matrix(209,336,130,209) (-21/13,-8/5) -> (8/5,21/13) Hyperbolic Matrix(211,336,-184,-293) (-8/5,-27/17) -> (-15/13,-8/7) Hyperbolic Matrix(503,798,370,587) (-27/17,-19/12) -> (19/14,15/11) Hyperbolic Matrix(1091,1722,638,1007) (-30/19,-41/26) -> (41/24,12/7) Hyperbolic Matrix(293,462,26,41) (-41/26,-52/33) -> (10/1,1/0) Hyperbolic Matrix(6425,10122,2692,4241) (-52/33,-63/40) -> (105/44,74/31) Hyperbolic Matrix(1975,3108,828,1303) (-63/40,-11/7) -> (31/13,105/44) Hyperbolic Matrix(295,462,242,379) (-11/7,-25/16) -> (17/14,11/9) Hyperbolic Matrix(377,588,134,209) (-25/16,-14/9) -> (14/5,17/6) Hyperbolic Matrix(379,588,136,211) (-14/9,-17/11) -> (25/9,14/5) Hyperbolic Matrix(83,126,-56,-85) (-20/13,-3/2) -> (-3/2,-22/15) Parabolic Matrix(1177,1722,460,673) (-22/15,-19/13) -> (23/9,64/25) Hyperbolic Matrix(1217,1764,376,545) (-29/20,-42/29) -> (42/13,13/4) Hyperbolic Matrix(1219,1764,378,547) (-42/29,-13/9) -> (29/9,42/13) Hyperbolic Matrix(379,546,-320,-461) (-13/9,-23/16) -> (-19/16,-13/11) Hyperbolic Matrix(673,966,-526,-755) (-23/16,-10/7) -> (-32/25,-23/18) Hyperbolic Matrix(4955,7056,1474,2099) (-47/33,-84/59) -> (84/25,37/11) Hyperbolic Matrix(4957,7056,1476,2101) (-84/59,-37/26) -> (47/14,84/25) Hyperbolic Matrix(797,1134,324,461) (-37/26,-27/19) -> (27/11,5/2) Hyperbolic Matrix(503,714,236,335) (-27/19,-44/31) -> (2/1,15/7) Hyperbolic Matrix(1007,1428,-830,-1177) (-44/31,-17/12) -> (-17/14,-40/33) Hyperbolic Matrix(209,294,-150,-211) (-17/12,-7/5) -> (-7/5,-25/18) Parabolic Matrix(1513,2100,848,1177) (-25/18,-43/31) -> (41/23,25/14) Hyperbolic Matrix(1091,1512,666,923) (-43/31,-18/13) -> (18/11,41/25) Hyperbolic Matrix(335,462,182,251) (-29/21,-11/8) -> (11/6,13/7) Hyperbolic Matrix(337,462,62,85) (-11/8,-26/19) -> (16/3,11/2) Hyperbolic Matrix(1259,1722,552,755) (-26/19,-41/30) -> (41/18,16/7) Hyperbolic Matrix(3781,5166,2214,3025) (-41/30,-56/41) -> (70/41,41/24) Hyperbolic Matrix(923,1260,430,587) (-56/41,-15/11) -> (15/7,28/13) Hyperbolic Matrix(587,798,370,503) (-15/11,-19/14) -> (19/12,27/17) Hyperbolic Matrix(1301,1764,340,461) (-19/14,-42/31) -> (42/11,23/6) Hyperbolic Matrix(1303,1764,342,463) (-42/31,-23/17) -> (19/5,42/11) Hyperbolic Matrix(127,168,96,127) (-4/3,-21/16) -> (21/16,4/3) Hyperbolic Matrix(545,714,416,545) (-21/16,-17/13) -> (17/13,21/16) Hyperbolic Matrix(547,714,226,295) (-17/13,-13/10) -> (29/12,17/7) Hyperbolic Matrix(293,378,162,209) (-22/17,-9/7) -> (9/5,20/11) Hyperbolic Matrix(3443,4410,1442,1847) (-41/32,-32/25) -> (74/31,43/18) Hyperbolic Matrix(461,588,98,125) (-23/18,-14/11) -> (14/3,19/4) Hyperbolic Matrix(463,588,100,127) (-14/11,-19/15) -> (23/5,14/3) Hyperbolic Matrix(167,210,66,83) (-19/15,-5/4) -> (5/2,23/9) Hyperbolic Matrix(169,210,136,169) (-5/4,-21/17) -> (21/17,5/4) Hyperbolic Matrix(545,672,442,545) (-21/17,-16/13) -> (16/13,21/17) Hyperbolic Matrix(377,462,102,125) (-16/13,-11/9) -> (11/3,26/7) Hyperbolic Matrix(379,462,242,295) (-11/9,-17/14) -> (25/16,11/7) Hyperbolic Matrix(5753,6972,4054,4913) (-40/33,-63/52) -> (105/74,44/31) Hyperbolic Matrix(5167,6258,3642,4411) (-63/52,-23/19) -> (61/43,105/74) Hyperbolic Matrix(209,252,34,41) (-23/19,-6/5) -> (6/1,19/3) Hyperbolic Matrix(211,252,36,43) (-6/5,-19/16) -> (23/4,6/1) Hyperbolic Matrix(251,294,-216,-253) (-20/17,-7/6) -> (-7/6,-22/19) Parabolic Matrix(335,378,148,167) (-8/7,-9/8) -> (9/4,34/15) Hyperbolic Matrix(421,462,154,169) (-10/9,-1/1) -> (41/15,52/19) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(337,-378,74,-83) (1/1,9/8) -> (9/2,41/9) Hyperbolic Matrix(293,-336,184,-211) (8/7,7/6) -> (35/22,8/5) Hyperbolic Matrix(463,-546,106,-125) (7/6,13/11) -> (13/3,35/8) Hyperbolic Matrix(461,-546,320,-379) (13/11,6/5) -> (36/25,13/9) Hyperbolic Matrix(1177,-1428,830,-1007) (23/19,17/14) -> (17/12,61/43) Hyperbolic Matrix(755,-966,526,-673) (23/18,9/7) -> (33/23,23/16) Hyperbolic Matrix(421,-546,64,-83) (22/17,13/10) -> (13/2,20/3) Hyperbolic Matrix(125,-168,32,-43) (4/3,19/14) -> (23/6,4/1) Hyperbolic Matrix(547,-756,212,-293) (11/8,18/13) -> (18/7,31/12) Hyperbolic Matrix(211,-294,150,-209) (18/13,7/5) -> (7/5,24/17) Parabolic Matrix(589,-840,176,-251) (37/26,10/7) -> (10/3,47/14) Hyperbolic Matrix(293,-420,30,-43) (10/7,33/23) -> (9/1,10/1) Hyperbolic Matrix(463,-672,144,-209) (13/9,16/11) -> (16/5,29/9) Hyperbolic Matrix(461,-672,260,-379) (16/11,3/2) -> (39/22,16/9) Hyperbolic Matrix(463,-714,190,-293) (3/2,17/11) -> (17/7,39/16) Hyperbolic Matrix(505,-798,212,-335) (11/7,19/12) -> (19/8,31/13) Hyperbolic Matrix(1849,-2940,422,-671) (27/17,35/22) -> (35/8,57/13) Hyperbolic Matrix(463,-756,128,-209) (13/8,18/11) -> (18/5,29/8) Hyperbolic Matrix(547,-924,74,-125) (27/16,22/13) -> (22/3,15/2) Hyperbolic Matrix(421,-714,148,-251) (22/13,17/10) -> (17/6,20/7) Hyperbolic Matrix(463,-798,170,-293) (12/7,19/11) -> (19/7,30/11) Hyperbolic Matrix(169,-294,96,-167) (19/11,7/4) -> (7/4,23/13) Parabolic Matrix(1849,-3276,758,-1343) (23/13,39/22) -> (39/16,61/25) Hyperbolic Matrix(1597,-2856,704,-1259) (25/14,34/19) -> (34/15,59/26) Hyperbolic Matrix(461,-840,208,-379) (20/11,11/6) -> (31/14,20/9) Hyperbolic Matrix(127,-294,54,-125) (16/7,7/3) -> (7/3,26/11) Parabolic Matrix(337,-798,106,-251) (26/11,19/8) -> (19/6,16/5) Hyperbolic Matrix(755,-1848,172,-421) (22/9,27/11) -> (57/13,22/5) Hyperbolic Matrix(125,-336,16,-43) (8/3,27/10) -> (15/2,8/1) Hyperbolic Matrix(43,-126,14,-41) (20/7,3/1) -> (3/1,22/7) Parabolic Matrix(167,-546,26,-85) (13/4,23/7) -> (19/3,13/2) Hyperbolic Matrix(293,-966,64,-211) (23/7,10/3) -> (32/7,23/5) Hyperbolic Matrix(421,-1428,74,-251) (44/13,17/5) -> (17/3,40/7) Hyperbolic Matrix(85,-294,24,-83) (17/5,7/2) -> (7/2,25/7) Parabolic Matrix(43,-294,6,-41) (20/3,7/1) -> (7/1,22/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(41,378,-32,-295) -> Matrix(1,2,-14,-27) Matrix(43,378,24,211) -> Matrix(3,2,34,23) Matrix(43,336,-16,-125) -> Matrix(1,2,-6,-11) Matrix(83,546,-64,-421) -> Matrix(1,0,-12,1) Matrix(85,546,-26,-167) -> Matrix(7,4,-30,-17) Matrix(167,966,116,671) -> Matrix(1,0,14,1) Matrix(251,1428,-74,-421) -> Matrix(5,4,-24,-19) Matrix(83,462,30,167) -> Matrix(7,4,54,31) Matrix(85,462,62,337) -> Matrix(1,0,16,1) Matrix(127,672,24,127) -> Matrix(11,6,42,23) Matrix(41,210,8,41) -> Matrix(5,2,22,9) Matrix(43,210,26,127) -> Matrix(5,2,62,25) Matrix(125,588,98,461) -> Matrix(7,2,108,31) Matrix(127,588,100,463) -> Matrix(3,2,46,31) Matrix(211,966,-64,-293) -> Matrix(3,2,-14,-9) Matrix(85,378,38,169) -> Matrix(1,0,12,1) Matrix(125,546,-106,-463) -> Matrix(7,2,-102,-29) Matrix(167,714,98,419) -> Matrix(11,4,140,51) Matrix(169,714,40,169) -> Matrix(23,8,112,39) Matrix(41,168,10,41) -> Matrix(7,2,38,11) Matrix(43,168,-32,-125) -> Matrix(7,2,-88,-25) Matrix(211,798,78,295) -> Matrix(7,2,52,15) Matrix(337,1260,180,673) -> Matrix(13,4,146,45) Matrix(1385,5166,574,2141) -> Matrix(7,2,38,11) Matrix(463,1722,260,967) -> Matrix(23,6,272,71) Matrix(125,462,102,377) -> Matrix(9,2,148,33) Matrix(209,756,-128,-463) -> Matrix(7,2,-74,-21) Matrix(83,294,-24,-85) -> Matrix(15,4,-64,-17) Matrix(503,1722,196,671) -> Matrix(17,4,140,33) Matrix(505,1722,222,757) -> Matrix(35,8,328,75) Matrix(1847,6258,322,1091) -> Matrix(39,8,112,23) Matrix(2059,6972,360,1219) -> Matrix(51,10,158,31) Matrix(211,714,112,379) -> Matrix(11,2,126,23) Matrix(337,1134,200,673) -> Matrix(1,0,18,1) Matrix(251,840,-176,-589) -> Matrix(1,0,-8,1) Matrix(127,420,-114,-377) -> Matrix(25,6,-396,-95) Matrix(295,966,244,799) -> Matrix(25,6,404,97) Matrix(209,672,-144,-463) -> Matrix(9,2,-122,-27) Matrix(211,672,-92,-293) -> Matrix(29,6,-208,-43) Matrix(251,714,-148,-421) -> Matrix(21,4,-226,-43) Matrix(209,588,134,377) -> Matrix(11,2,170,31) Matrix(211,588,136,379) -> Matrix(11,2,126,23) Matrix(167,462,30,83) -> Matrix(23,4,86,15) Matrix(293,798,-170,-463) -> Matrix(11,2,-116,-21) Matrix(295,798,78,211) -> Matrix(11,2,60,11) Matrix(1091,2940,-842,-2269) -> Matrix(1,0,-8,1) Matrix(127,336,48,127) -> Matrix(35,6,274,47) Matrix(209,546,80,209) -> Matrix(61,10,494,81) Matrix(293,756,-212,-547) -> Matrix(13,2,-150,-23) Matrix(589,1512,164,421) -> Matrix(1,0,12,1) Matrix(3361,8610,1312,3361) -> Matrix(27,4,236,35) Matrix(5249,13440,2050,5249) -> Matrix(13,2,110,17) Matrix(1723,4410,706,1807) -> Matrix(13,2,110,17) Matrix(83,210,66,167) -> Matrix(1,0,22,1) Matrix(461,1134,324,797) -> Matrix(13,2,162,25) Matrix(377,924,-326,-799) -> Matrix(41,6,-622,-91) Matrix(293,714,-190,-463) -> Matrix(13,2,-150,-23) Matrix(295,714,226,547) -> Matrix(15,2,232,31) Matrix(713,1722,330,797) -> Matrix(15,2,142,19) Matrix(2141,5166,574,1385) -> Matrix(7,2,38,11) Matrix(715,1722,262,631) -> Matrix(13,2,110,17) Matrix(335,798,-212,-505) -> Matrix(27,4,-304,-45) Matrix(125,294,-54,-127) -> Matrix(41,6,-294,-43) Matrix(1427,3276,-842,-1933) -> Matrix(57,8,-620,-87) Matrix(755,1722,552,1259) -> Matrix(59,8,848,115) Matrix(923,2100,258,587) -> Matrix(29,4,152,21) Matrix(1259,2856,-704,-1597) -> Matrix(121,16,-1142,-151) Matrix(167,378,148,335) -> Matrix(31,4,550,71) Matrix(169,378,38,85) -> Matrix(1,0,12,1) Matrix(379,840,-208,-461) -> Matrix(15,2,-128,-17) Matrix(211,462,58,127) -> Matrix(15,2,82,11) Matrix(797,1722,330,713) -> Matrix(15,2,142,19) Matrix(587,1260,430,923) -> Matrix(61,8,892,117) Matrix(335,714,236,503) -> Matrix(31,4,426,55) Matrix(379,714,112,211) -> Matrix(19,2,142,15) Matrix(673,1260,180,337) -> Matrix(37,4,194,21) Matrix(925,1722,542,1009) -> Matrix(77,8,972,101) Matrix(295,546,114,211) -> Matrix(21,2,178,17) Matrix(965,1764,436,797) -> Matrix(23,2,218,19) Matrix(967,1764,438,799) -> Matrix(15,2,142,19) Matrix(209,378,162,293) -> Matrix(19,2,294,31) Matrix(211,378,24,43) -> Matrix(19,2,66,7) Matrix(3947,7056,1738,3107) -> Matrix(417,44,3952,417) Matrix(3949,7056,1740,3109) -> Matrix(419,44,3990,419) Matrix(965,1722,682,1217) -> Matrix(19,2,218,23) Matrix(967,1722,260,463) -> Matrix(59,6,344,35) Matrix(167,294,-96,-169) -> Matrix(39,4,-400,-41) Matrix(461,798,-316,-547) -> Matrix(21,2,-242,-23) Matrix(1805,3108,658,1133) -> Matrix(59,6,462,47) Matrix(5881,10122,2148,3697) -> Matrix(241,24,1938,193) Matrix(2563,4410,562,967) -> Matrix(101,10,414,41) Matrix(587,1008,244,419) -> Matrix(41,4,338,33) Matrix(589,1008,246,421) -> Matrix(43,4,376,35) Matrix(3025,5166,2214,3781) -> Matrix(41,4,584,57) Matrix(1009,1722,542,925) -> Matrix(85,8,988,93) Matrix(419,714,98,167) -> Matrix(43,4,204,19) Matrix(2603,4410,1586,2687) -> Matrix(87,8,1120,103) Matrix(1093,1848,-844,-1427) -> Matrix(1,0,-2,1) Matrix(673,1134,200,337) -> Matrix(1,0,18,1) Matrix(127,210,26,43) -> Matrix(21,2,94,9) Matrix(1049,1722,332,545) -> Matrix(65,6,444,41) Matrix(8191,13440,4992,8191) -> Matrix(241,22,3122,285) Matrix(5249,8610,3200,5249) -> Matrix(155,14,2026,183) Matrix(1051,1722,744,1219) -> Matrix(23,2,310,27) Matrix(335,546,154,251) -> Matrix(1,0,20,1) Matrix(337,546,208,337) -> Matrix(43,4,548,51) Matrix(209,336,130,209) -> Matrix(23,2,310,27) Matrix(211,336,-184,-293) -> Matrix(21,2,-326,-31) Matrix(503,798,370,587) -> Matrix(1,0,26,1) Matrix(1091,1722,638,1007) -> Matrix(1,0,24,1) Matrix(293,462,26,41) -> Matrix(23,2,34,3) Matrix(6425,10122,2692,4241) -> Matrix(165,14,1426,121) Matrix(1975,3108,828,1303) -> Matrix(21,2,178,17) Matrix(295,462,242,379) -> Matrix(25,2,412,33) Matrix(377,588,134,209) -> Matrix(27,2,202,15) Matrix(379,588,136,211) -> Matrix(19,2,142,15) Matrix(83,126,-56,-85) -> Matrix(1,0,0,1) Matrix(1177,1722,460,673) -> Matrix(1,0,20,1) Matrix(1217,1764,376,545) -> Matrix(33,2,214,13) Matrix(1219,1764,378,547) -> Matrix(13,2,84,13) Matrix(379,546,-320,-461) -> Matrix(23,2,-334,-29) Matrix(673,966,-526,-755) -> Matrix(1,0,-2,1) Matrix(4955,7056,1474,2099) -> Matrix(1,0,22,1) Matrix(4957,7056,1476,2101) -> Matrix(1,0,14,1) Matrix(797,1134,324,461) -> Matrix(21,2,178,17) Matrix(503,714,236,335) -> Matrix(47,4,458,39) Matrix(1007,1428,-830,-1177) -> Matrix(1,0,-2,1) Matrix(209,294,-150,-211) -> Matrix(23,2,-288,-25) Matrix(1513,2100,848,1177) -> Matrix(101,8,1174,93) Matrix(1091,1512,666,923) -> Matrix(1,0,26,1) Matrix(335,462,182,251) -> Matrix(1,0,24,1) Matrix(337,462,62,85) -> Matrix(1,0,16,1) Matrix(1259,1722,552,755) -> Matrix(99,8,928,75) Matrix(3781,5166,2214,3025) -> Matrix(49,4,600,49) Matrix(923,1260,430,587) -> Matrix(101,8,972,77) Matrix(587,798,370,503) -> Matrix(1,0,26,1) Matrix(1301,1764,340,461) -> Matrix(27,2,148,11) Matrix(1303,1764,342,463) -> Matrix(23,2,126,11) Matrix(127,168,96,127) -> Matrix(25,2,362,29) Matrix(545,714,416,545) -> Matrix(131,10,1978,151) Matrix(547,714,226,295) -> Matrix(27,2,256,19) Matrix(293,378,162,209) -> Matrix(27,2,310,23) Matrix(3443,4410,1442,1847) -> Matrix(109,8,940,69) Matrix(461,588,98,125) -> Matrix(27,2,148,11) Matrix(463,588,100,127) -> Matrix(27,2,94,7) Matrix(167,210,66,83) -> Matrix(1,0,22,1) Matrix(169,210,136,169) -> Matrix(55,4,866,63) Matrix(545,672,442,545) -> Matrix(197,14,3166,225) Matrix(377,462,102,125) -> Matrix(29,2,188,13) Matrix(379,462,242,295) -> Matrix(29,2,420,29) Matrix(5753,6972,4054,4913) -> Matrix(139,10,1932,139) Matrix(5167,6258,3642,4411) -> Matrix(141,10,1988,141) Matrix(209,252,34,41) -> Matrix(29,2,130,9) Matrix(211,252,36,43) -> Matrix(29,2,72,5) Matrix(251,294,-216,-253) -> Matrix(119,8,-1800,-121) Matrix(335,378,148,167) -> Matrix(63,4,614,39) Matrix(421,462,154,169) -> Matrix(65,4,536,33) Matrix(1,0,2,1) -> Matrix(1,0,38,1) Matrix(337,-378,74,-83) -> Matrix(71,-4,302,-17) Matrix(293,-336,184,-211) -> Matrix(35,-2,438,-25) Matrix(463,-546,106,-125) -> Matrix(33,-2,182,-11) Matrix(461,-546,320,-379) -> Matrix(33,-2,446,-27) Matrix(1177,-1428,830,-1007) -> Matrix(1,0,-2,1) Matrix(755,-966,526,-673) -> Matrix(1,0,-2,1) Matrix(421,-546,64,-83) -> Matrix(1,0,-12,1) Matrix(125,-168,32,-43) -> Matrix(29,-2,160,-11) Matrix(547,-756,212,-293) -> Matrix(27,-2,230,-17) Matrix(211,-294,150,-209) -> Matrix(29,-2,392,-27) Matrix(589,-840,176,-251) -> Matrix(1,0,-8,1) Matrix(293,-420,30,-43) -> Matrix(27,-2,68,-5) Matrix(463,-672,144,-209) -> Matrix(31,-2,202,-13) Matrix(461,-672,260,-379) -> Matrix(29,-2,334,-23) Matrix(463,-714,190,-293) -> Matrix(27,-2,230,-17) Matrix(505,-798,212,-335) -> Matrix(53,-4,464,-35) Matrix(1849,-2940,422,-671) -> Matrix(53,-4,252,-19) Matrix(463,-756,128,-209) -> Matrix(25,-2,138,-11) Matrix(547,-924,74,-125) -> Matrix(27,-2,68,-5) Matrix(421,-714,148,-251) -> Matrix(51,-4,370,-29) Matrix(463,-798,170,-293) -> Matrix(25,-2,188,-15) Matrix(169,-294,96,-167) -> Matrix(49,-4,576,-47) Matrix(1849,-3276,758,-1343) -> Matrix(47,-4,388,-33) Matrix(1597,-2856,704,-1259) -> Matrix(183,-16,1750,-153) Matrix(461,-840,208,-379) -> Matrix(21,-2,200,-19) Matrix(127,-294,54,-125) -> Matrix(55,-6,486,-53) Matrix(337,-798,106,-251) -> Matrix(1,0,-2,1) Matrix(755,-1848,172,-421) -> Matrix(1,0,-4,1) Matrix(125,-336,16,-43) -> Matrix(15,-2,38,-5) Matrix(43,-126,14,-41) -> Matrix(15,-2,98,-13) Matrix(167,-546,26,-85) -> Matrix(25,-4,94,-15) Matrix(293,-966,64,-211) -> Matrix(13,-2,46,-7) Matrix(421,-1428,74,-251) -> Matrix(27,-4,88,-13) Matrix(85,-294,24,-83) -> Matrix(25,-4,144,-23) Matrix(43,-294,6,-41) -> Matrix(7,-2,18,-5) 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): 64 Degree of the the map X: 64 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 19 1 1/1 1/20 1 21 9/8 0 7 8/7 (3/52,1/17) 0 21 7/6 1/17 4 3 13/11 3/50 1 21 6/5 2/33 1 7 23/19 1/16 1 21 17/14 (0/1,1/17) 0 21 11/9 1/16 1 21 16/13 (7/113,1/16) 0 21 21/17 1/16 9 1 5/4 (1/16,2/31) 0 21 19/15 1/16 1 21 14/11 2/31 1 3 23/18 (2/31,1/15) 0 21 9/7 1/15 1 7 22/17 (3/46,1/15) 0 21 13/10 (2/31,1/15) 0 21 17/13 5/76 1 21 21/16 1/15 6 1 4/3 (1/15,1/14) 0 21 19/14 (0/1,1/15) 0 21 15/11 1/15 1 7 56/41 2/29 5 3 41/30 (2/29,3/43) 0 21 26/19 (3/43,1/14) 0 21 11/8 (0/1,1/14) 0 21 18/13 0/1 1 7 7/5 1/14 1 3 24/17 2/27 1 7 41/29 5/64 1 21 17/12 (0/1,1/15) 0 21 61/43 1/14 1 21 105/74 1/14 10 1 44/31 (1/14,5/69) 0 21 27/19 1/13 1 7 37/26 (0/1,1/12) 0 21 10/7 (1/14,1/13) 0 21 33/23 1/13 1 7 23/16 (2/27,1/13) 0 21 36/25 0/1 1 7 13/9 1/12 1 21 16/11 (1/15,1/14) 0 21 3/2 0 7 17/11 1/12 1 21 14/9 0/1 2 3 25/16 (1/15,2/29) 0 21 11/7 1/14 1 21 19/12 (0/1,1/13) 0 21 27/17 1/13 1 7 35/22 1/13 4 3 8/5 (1/14,1/13) 0 21 21/13 1/13 3 1 13/8 (1/13,2/25) 0 21 18/11 0/1 1 7 41/25 7/92 1 21 105/64 1/13 18 1 64/39 (1/13,11/142) 0 21 23/14 (1/13,2/25) 0 21 5/3 1/12 1 21 27/16 0 7 22/13 (3/40,1/13) 0 21 17/10 (0/1,1/13) 0 21 29/17 3/38 1 21 70/41 2/25 5 3 41/24 (1/13,2/25) 0 21 12/7 2/25 1 7 19/11 1/12 1 21 7/4 1/12 2 3 23/13 1/12 1 21 39/22 0 7 16/9 (1/12,1/11) 0 21 41/23 13/152 1 21 25/14 (7/81,2/23) 0 21 34/19 (5/57,3/34) 0 21 9/5 1/11 1 7 20/11 (1/11,1/10) 0 21 11/6 (0/1,1/12) 0 21 13/7 1/12 1 21 28/15 2/23 5 3 15/8 0 7 2/1 (1/11,1/10) 0 21 15/7 3/29 1 7 28/13 2/19 5 3 13/6 (2/19,1/9) 0 21 11/5 1/10 1 21 42/19 2/19 2 1 31/14 (2/19,3/28) 0 21 20/9 (1/10,1/9) 0 21 9/4 0 7 34/15 (3/29,5/48) 0 21 59/26 (15/143,2/19) 0 21 84/37 2/19 11 1 25/11 7/66 1 21 41/18 (2/19,1/9) 0 21 16/7 (3/28,1/9) 0 21 7/3 1/9 3 3 26/11 (1/9,3/26) 0 21 19/8 (1/9,4/35) 0 21 31/13 3/26 1 21 105/44 3/26 2 1 74/31 (3/26,5/43) 0 21 43/18 (1/9,2/17) 0 21 12/5 2/17 1 7 41/17 3/22 1 21 70/29 0/1 5 3 29/12 (0/1,1/9) 0 21 17/7 3/26 1 21 39/16 0 7 61/25 1/8 1 21 22/9 (1/9,1/8) 0 21 27/11 1/9 1 7 5/2 (2/17,1/8) 0 21 23/9 1/8 1 21 64/25 (1/9,1/8) 0 21 105/41 1/9 1 1 41/16 (1/9,2/17) 0 21 18/7 2/17 1 7 31/12 (2/17,1/8) 0 21 13/5 1/8 1 21 21/8 1/8 8 1 8/3 (1/8,3/23) 0 21 27/10 0 7 19/7 1/8 1 21 30/11 0/1 1 7 41/15 7/58 1 21 52/19 (11/89,1/8) 0 21 63/23 1/8 15 1 11/4 (1/8,4/31) 0 21 25/9 1/8 1 21 14/5 2/15 2 3 17/6 (4/29,1/7) 0 21 20/7 (7/50,1/7) 0 21 3/1 1/7 1 7 22/7 (5/36,1/7) 0 21 19/6 (1/7,4/27) 0 21 16/5 (1/7,3/20) 0 21 29/9 7/46 1 21 42/13 2/13 5 1 13/4 (2/13,3/19) 0 21 23/7 1/6 1 21 10/3 (1/6,1/5) 0 21 47/14 (0/1,1/4) 0 21 84/25 0/1 4 1 37/11 1/8 1 21 27/8 0 7 44/13 (3/22,1/7) 0 21 17/5 3/20 1 21 7/2 1/6 2 3 25/7 5/28 1 21 43/12 (2/11,1/5) 0 21 18/5 2/11 1 7 29/8 (0/1,1/5) 0 21 11/3 1/6 1 21 26/7 (1/6,5/29) 0 21 41/11 11/62 1 21 56/15 2/11 5 3 15/4 0 7 19/5 1/6 1 21 42/11 2/11 1 1 23/6 (2/11,1/5) 0 21 4/1 (1/6,1/5) 0 21 21/5 1/5 5 1 17/4 (1/5,4/19) 0 21 13/3 1/4 1 21 35/8 1/5 4 3 57/13 1/5 1 7 22/5 (1/5,1/4) 0 21 9/2 0 7 41/9 9/38 1 21 32/7 (1/4,3/11) 0 21 23/5 1/4 1 21 14/3 0/1 1 3 19/4 (0/1,1/5) 0 21 5/1 1/4 1 21 21/4 1/4 4 1 16/3 (1/4,3/11) 0 21 11/2 (0/1,1/4) 0 21 17/3 1/4 1 21 40/7 (7/22,1/3) 0 21 63/11 1/3 9 1 23/4 (1/3,2/5) 0 21 6/1 0/1 1 7 19/3 1/4 1 21 13/2 (2/7,1/3) 0 21 20/3 (3/10,1/3) 0 21 7/1 1/3 1 3 22/3 (1/4,1/3) 0 21 15/2 0 7 8/1 (1/2,1/1) 0 21 9/1 1/3 1 7 10/1 (1/3,1/2) 0 21 1/0 (0/1,1/1) 0 21 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(337,-378,74,-83) (1/1,9/8) -> (9/2,41/9) Hyperbolic Matrix(335,-378,148,-167) (9/8,8/7) -> (9/4,34/15) Glide Reflection Matrix(293,-336,184,-211) (8/7,7/6) -> (35/22,8/5) Hyperbolic Matrix(463,-546,106,-125) (7/6,13/11) -> (13/3,35/8) Hyperbolic Matrix(461,-546,320,-379) (13/11,6/5) -> (36/25,13/9) Hyperbolic Matrix(209,-252,34,-41) (6/5,23/19) -> (6/1,19/3) Glide Reflection Matrix(1177,-1428,830,-1007) (23/19,17/14) -> (17/12,61/43) Hyperbolic Matrix(379,-462,242,-295) (17/14,11/9) -> (25/16,11/7) Glide Reflection Matrix(377,-462,102,-125) (11/9,16/13) -> (11/3,26/7) Glide Reflection Matrix(545,-672,442,-545) (16/13,21/17) -> (16/13,21/17) Reflection Matrix(169,-210,136,-169) (21/17,5/4) -> (21/17,5/4) Reflection Matrix(167,-210,66,-83) (5/4,19/15) -> (5/2,23/9) Glide Reflection Matrix(463,-588,100,-127) (19/15,14/11) -> (23/5,14/3) Glide Reflection Matrix(461,-588,98,-125) (14/11,23/18) -> (14/3,19/4) Glide Reflection Matrix(755,-966,526,-673) (23/18,9/7) -> (33/23,23/16) Hyperbolic Matrix(293,-378,162,-209) (9/7,22/17) -> (9/5,20/11) Glide Reflection Matrix(421,-546,64,-83) (22/17,13/10) -> (13/2,20/3) Hyperbolic Matrix(547,-714,226,-295) (13/10,17/13) -> (29/12,17/7) Glide Reflection Matrix(545,-714,416,-545) (17/13,21/16) -> (17/13,21/16) Reflection Matrix(127,-168,96,-127) (21/16,4/3) -> (21/16,4/3) Reflection Matrix(125,-168,32,-43) (4/3,19/14) -> (23/6,4/1) Hyperbolic Matrix(587,-798,370,-503) (19/14,15/11) -> (19/12,27/17) Glide Reflection Matrix(923,-1260,430,-587) (15/11,56/41) -> (15/7,28/13) Glide Reflection Matrix(3781,-5166,2214,-3025) (56/41,41/30) -> (70/41,41/24) Glide Reflection Matrix(1259,-1722,552,-755) (41/30,26/19) -> (41/18,16/7) Glide Reflection Matrix(337,-462,62,-85) (26/19,11/8) -> (16/3,11/2) Glide Reflection Matrix(547,-756,212,-293) (11/8,18/13) -> (18/7,31/12) Hyperbolic Matrix(211,-294,150,-209) (18/13,7/5) -> (7/5,24/17) Parabolic Matrix(1219,-1722,744,-1051) (24/17,41/29) -> (18/11,41/25) Glide Reflection Matrix(1217,-1722,682,-965) (41/29,17/12) -> (41/23,25/14) Glide Reflection Matrix(9029,-12810,6364,-9029) (61/43,105/74) -> (61/43,105/74) Reflection Matrix(6511,-9240,4588,-6511) (105/74,44/31) -> (105/74,44/31) Reflection Matrix(503,-714,236,-335) (44/31,27/19) -> (2/1,15/7) Glide Reflection Matrix(797,-1134,324,-461) (27/19,37/26) -> (27/11,5/2) Glide Reflection Matrix(589,-840,176,-251) (37/26,10/7) -> (10/3,47/14) Hyperbolic Matrix(293,-420,30,-43) (10/7,33/23) -> (9/1,10/1) Hyperbolic Matrix(671,-966,116,-167) (23/16,36/25) -> (23/4,6/1) Glide Reflection Matrix(463,-672,144,-209) (13/9,16/11) -> (16/5,29/9) Hyperbolic Matrix(461,-672,260,-379) (16/11,3/2) -> (39/22,16/9) Hyperbolic Matrix(463,-714,190,-293) (3/2,17/11) -> (17/7,39/16) Hyperbolic Matrix(379,-588,136,-211) (17/11,14/9) -> (25/9,14/5) Glide Reflection Matrix(377,-588,134,-209) (14/9,25/16) -> (14/5,17/6) Glide Reflection Matrix(505,-798,212,-335) (11/7,19/12) -> (19/8,31/13) Hyperbolic Matrix(1849,-2940,422,-671) (27/17,35/22) -> (35/8,57/13) Hyperbolic Matrix(209,-336,130,-209) (8/5,21/13) -> (8/5,21/13) Reflection Matrix(337,-546,208,-337) (21/13,13/8) -> (21/13,13/8) Reflection Matrix(463,-756,128,-209) (13/8,18/11) -> (18/5,29/8) Hyperbolic Matrix(5249,-8610,3200,-5249) (41/25,105/64) -> (41/25,105/64) Reflection Matrix(8191,-13440,4992,-8191) (105/64,64/39) -> (105/64,64/39) Reflection Matrix(1049,-1722,332,-545) (64/39,23/14) -> (22/7,19/6) Glide Reflection Matrix(127,-210,26,-43) (23/14,5/3) -> (19/4,5/1) Glide Reflection Matrix(673,-1134,200,-337) (5/3,27/16) -> (37/11,27/8) Glide Reflection Matrix(547,-924,74,-125) (27/16,22/13) -> (22/3,15/2) Hyperbolic Matrix(421,-714,148,-251) (22/13,17/10) -> (17/6,20/7) Hyperbolic Matrix(419,-714,98,-167) (17/10,29/17) -> (17/4,13/3) Glide Reflection Matrix(1009,-1722,542,-925) (29/17,70/41) -> (13/7,28/15) Glide Reflection Matrix(589,-1008,246,-421) (41/24,12/7) -> (43/18,12/5) Glide Reflection Matrix(463,-798,170,-293) (12/7,19/11) -> (19/7,30/11) Hyperbolic Matrix(169,-294,96,-167) (19/11,7/4) -> (7/4,23/13) Parabolic Matrix(1849,-3276,758,-1343) (23/13,39/22) -> (39/16,61/25) Hyperbolic Matrix(967,-1722,260,-463) (16/9,41/23) -> (26/7,41/11) Glide Reflection Matrix(1597,-2856,704,-1259) (25/14,34/19) -> (34/15,59/26) Hyperbolic Matrix(211,-378,24,-43) (34/19,9/5) -> (8/1,9/1) Glide Reflection Matrix(461,-840,208,-379) (20/11,11/6) -> (31/14,20/9) Hyperbolic Matrix(295,-546,114,-211) (11/6,13/7) -> (31/12,13/5) Glide Reflection Matrix(673,-1260,180,-337) (28/15,15/8) -> (56/15,15/4) Glide Reflection Matrix(379,-714,112,-211) (15/8,2/1) -> (27/8,44/13) Glide Reflection Matrix(797,-1722,330,-713) (28/13,13/6) -> (70/29,29/12) Glide Reflection Matrix(211,-462,58,-127) (13/6,11/5) -> (29/8,11/3) Glide Reflection Matrix(419,-924,190,-419) (11/5,42/19) -> (11/5,42/19) Reflection Matrix(1177,-2604,532,-1177) (42/19,31/14) -> (42/19,31/14) Reflection Matrix(169,-378,38,-85) (20/9,9/4) -> (22/5,9/2) Glide Reflection Matrix(4367,-9912,1924,-4367) (59/26,84/37) -> (59/26,84/37) Reflection Matrix(1849,-4200,814,-1849) (84/37,25/11) -> (84/37,25/11) Reflection Matrix(923,-2100,258,-587) (25/11,41/18) -> (25/7,43/12) Glide Reflection Matrix(127,-294,54,-125) (16/7,7/3) -> (7/3,26/11) Parabolic Matrix(337,-798,106,-251) (26/11,19/8) -> (19/6,16/5) Hyperbolic Matrix(2729,-6510,1144,-2729) (31/13,105/44) -> (31/13,105/44) Reflection Matrix(6511,-15540,2728,-6511) (105/44,74/31) -> (105/44,74/31) Reflection Matrix(211,-504,18,-43) (74/31,43/18) -> (10/1,1/0) Glide Reflection Matrix(715,-1722,262,-631) (12/5,41/17) -> (30/11,41/15) Glide Reflection Matrix(2141,-5166,574,-1385) (41/17,70/29) -> (41/11,56/15) Glide Reflection Matrix(1807,-4410,706,-1723) (61/25,22/9) -> (23/9,64/25) Glide Reflection Matrix(755,-1848,172,-421) (22/9,27/11) -> (57/13,22/5) Hyperbolic Matrix(5249,-13440,2050,-5249) (64/25,105/41) -> (64/25,105/41) Reflection Matrix(3361,-8610,1312,-3361) (105/41,41/16) -> (105/41,41/16) Reflection Matrix(589,-1512,164,-421) (41/16,18/7) -> (43/12,18/5) Glide Reflection Matrix(209,-546,80,-209) (13/5,21/8) -> (13/5,21/8) Reflection Matrix(127,-336,48,-127) (21/8,8/3) -> (21/8,8/3) Reflection Matrix(125,-336,16,-43) (8/3,27/10) -> (15/2,8/1) Hyperbolic Matrix(295,-798,78,-211) (27/10,19/7) -> (15/4,19/5) Glide Reflection Matrix(1259,-3444,276,-755) (41/15,52/19) -> (41/9,32/7) Glide Reflection Matrix(2393,-6552,874,-2393) (52/19,63/23) -> (52/19,63/23) Reflection Matrix(505,-1386,184,-505) (63/23,11/4) -> (63/23,11/4) Reflection Matrix(167,-462,30,-83) (11/4,25/9) -> (11/2,17/3) Glide Reflection Matrix(43,-126,14,-41) (20/7,3/1) -> (3/1,22/7) Parabolic Matrix(755,-2436,234,-755) (29/9,42/13) -> (29/9,42/13) Reflection Matrix(337,-1092,104,-337) (42/13,13/4) -> (42/13,13/4) Reflection Matrix(167,-546,26,-85) (13/4,23/7) -> (19/3,13/2) Hyperbolic Matrix(293,-966,64,-211) (23/7,10/3) -> (32/7,23/5) Hyperbolic Matrix(2351,-7896,700,-2351) (47/14,84/25) -> (47/14,84/25) Reflection Matrix(1849,-6216,550,-1849) (84/25,37/11) -> (84/25,37/11) Reflection Matrix(421,-1428,74,-251) (44/13,17/5) -> (17/3,40/7) Hyperbolic Matrix(85,-294,24,-83) (17/5,7/2) -> (7/2,25/7) Parabolic Matrix(419,-1596,110,-419) (19/5,42/11) -> (19/5,42/11) Reflection Matrix(505,-1932,132,-505) (42/11,23/6) -> (42/11,23/6) Reflection Matrix(41,-168,10,-41) (4/1,21/5) -> (4/1,21/5) Reflection Matrix(169,-714,40,-169) (21/5,17/4) -> (21/5,17/4) Reflection Matrix(41,-210,8,-41) (5/1,21/4) -> (5/1,21/4) Reflection Matrix(127,-672,24,-127) (21/4,16/3) -> (21/4,16/3) Reflection Matrix(881,-5040,154,-881) (40/7,63/11) -> (40/7,63/11) Reflection Matrix(505,-2898,88,-505) (63/11,23/4) -> (63/11,23/4) Reflection Matrix(43,-294,6,-41) (20/3,7/1) -> (7/1,22/3) 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) -> (0/1,1/1) Matrix(1,0,2,-1) -> Matrix(1,0,40,-1) (0/1,1/1) -> (0/1,1/20) Matrix(337,-378,74,-83) -> Matrix(71,-4,302,-17) Matrix(335,-378,148,-167) -> Matrix(71,-4,692,-39) Matrix(293,-336,184,-211) -> Matrix(35,-2,438,-25) Matrix(463,-546,106,-125) -> Matrix(33,-2,182,-11) Matrix(461,-546,320,-379) -> Matrix(33,-2,446,-27) Matrix(209,-252,34,-41) -> Matrix(33,-2,148,-9) Matrix(1177,-1428,830,-1007) -> Matrix(1,0,-2,1) 0/1 Matrix(379,-462,242,-295) -> Matrix(33,-2,478,-29) Matrix(377,-462,102,-125) -> Matrix(33,-2,214,-13) Matrix(545,-672,442,-545) -> Matrix(225,-14,3616,-225) (16/13,21/17) -> (7/113,1/16) Matrix(169,-210,136,-169) -> Matrix(63,-4,992,-63) (21/17,5/4) -> (1/16,2/31) Matrix(167,-210,66,-83) -> Matrix(1,0,24,-1) *** -> (0/1,1/12) Matrix(463,-588,100,-127) -> Matrix(31,-2,108,-7) Matrix(461,-588,98,-125) -> Matrix(31,-2,170,-11) Matrix(755,-966,526,-673) -> Matrix(1,0,-2,1) 0/1 Matrix(293,-378,162,-209) -> Matrix(31,-2,356,-23) Matrix(421,-546,64,-83) -> Matrix(1,0,-12,1) 0/1 Matrix(547,-714,226,-295) -> Matrix(31,-2,294,-19) Matrix(545,-714,416,-545) -> Matrix(151,-10,2280,-151) (17/13,21/16) -> (5/76,1/15) Matrix(127,-168,96,-127) -> Matrix(29,-2,420,-29) (21/16,4/3) -> (1/15,1/14) Matrix(125,-168,32,-43) -> Matrix(29,-2,160,-11) Matrix(587,-798,370,-503) -> Matrix(1,0,28,-1) *** -> (0/1,1/14) Matrix(923,-1260,430,-587) -> Matrix(117,-8,1126,-77) Matrix(3781,-5166,2214,-3025) -> Matrix(57,-4,698,-49) Matrix(1259,-1722,552,-755) -> Matrix(115,-8,1078,-75) Matrix(337,-462,62,-85) -> Matrix(1,0,18,-1) *** -> (0/1,1/9) Matrix(547,-756,212,-293) -> Matrix(27,-2,230,-17) Matrix(211,-294,150,-209) -> Matrix(29,-2,392,-27) 1/14 Matrix(1219,-1722,744,-1051) -> Matrix(27,-2,364,-27) *** -> (1/14,1/13) Matrix(1217,-1722,682,-965) -> Matrix(23,-2,264,-23) *** -> (1/12,1/11) Matrix(9029,-12810,6364,-9029) -> Matrix(141,-10,1988,-141) (61/43,105/74) -> (5/71,1/14) Matrix(6511,-9240,4588,-6511) -> Matrix(139,-10,1932,-139) (105/74,44/31) -> (1/14,5/69) Matrix(503,-714,236,-335) -> Matrix(55,-4,536,-39) Matrix(797,-1134,324,-461) -> Matrix(25,-2,212,-17) Matrix(589,-840,176,-251) -> Matrix(1,0,-8,1) 0/1 Matrix(293,-420,30,-43) -> Matrix(27,-2,68,-5) Matrix(671,-966,116,-167) -> Matrix(1,0,16,-1) *** -> (0/1,1/8) Matrix(463,-672,144,-209) -> Matrix(31,-2,202,-13) Matrix(461,-672,260,-379) -> Matrix(29,-2,334,-23) Matrix(463,-714,190,-293) -> Matrix(27,-2,230,-17) Matrix(379,-588,136,-211) -> Matrix(23,-2,172,-15) Matrix(377,-588,134,-209) -> Matrix(31,-2,232,-15) Matrix(505,-798,212,-335) -> Matrix(53,-4,464,-35) Matrix(1849,-2940,422,-671) -> Matrix(53,-4,252,-19) Matrix(209,-336,130,-209) -> Matrix(27,-2,364,-27) (8/5,21/13) -> (1/14,1/13) Matrix(337,-546,208,-337) -> Matrix(51,-4,650,-51) (21/13,13/8) -> (1/13,2/25) Matrix(463,-756,128,-209) -> Matrix(25,-2,138,-11) Matrix(5249,-8610,3200,-5249) -> Matrix(183,-14,2392,-183) (41/25,105/64) -> (7/92,1/13) Matrix(8191,-13440,4992,-8191) -> Matrix(285,-22,3692,-285) (105/64,64/39) -> (1/13,11/142) Matrix(1049,-1722,332,-545) -> Matrix(77,-6,526,-41) Matrix(127,-210,26,-43) -> Matrix(25,-2,112,-9) Matrix(673,-1134,200,-337) -> Matrix(1,0,20,-1) *** -> (0/1,1/10) Matrix(547,-924,74,-125) -> Matrix(27,-2,68,-5) Matrix(421,-714,148,-251) -> Matrix(51,-4,370,-29) Matrix(419,-714,98,-167) -> Matrix(51,-4,242,-19) Matrix(1009,-1722,542,-925) -> Matrix(101,-8,1174,-93) Matrix(589,-1008,246,-421) -> Matrix(51,-4,446,-35) Matrix(463,-798,170,-293) -> Matrix(25,-2,188,-15) Matrix(169,-294,96,-167) -> Matrix(49,-4,576,-47) 1/12 Matrix(1849,-3276,758,-1343) -> Matrix(47,-4,388,-33) Matrix(967,-1722,260,-463) -> Matrix(71,-6,414,-35) Matrix(1597,-2856,704,-1259) -> Matrix(183,-16,1750,-153) Matrix(211,-378,24,-43) -> Matrix(23,-2,80,-7) Matrix(461,-840,208,-379) -> Matrix(21,-2,200,-19) 1/10 Matrix(295,-546,114,-211) -> Matrix(25,-2,212,-17) Matrix(673,-1260,180,-337) -> Matrix(45,-4,236,-21) Matrix(379,-714,112,-211) -> Matrix(23,-2,172,-15) Matrix(797,-1722,330,-713) -> Matrix(19,-2,180,-19) *** -> (1/10,1/9) Matrix(211,-462,58,-127) -> Matrix(19,-2,104,-11) Matrix(419,-924,190,-419) -> Matrix(39,-4,380,-39) (11/5,42/19) -> (1/10,2/19) Matrix(1177,-2604,532,-1177) -> Matrix(113,-12,1064,-113) (42/19,31/14) -> (2/19,3/28) Matrix(169,-378,38,-85) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(4367,-9912,1924,-4367) -> Matrix(571,-60,5434,-571) (59/26,84/37) -> (15/143,2/19) Matrix(1849,-4200,814,-1849) -> Matrix(265,-28,2508,-265) (84/37,25/11) -> (2/19,7/66) Matrix(923,-2100,258,-587) -> Matrix(37,-4,194,-21) Matrix(127,-294,54,-125) -> Matrix(55,-6,486,-53) 1/9 Matrix(337,-798,106,-251) -> Matrix(1,0,-2,1) 0/1 Matrix(2729,-6510,1144,-2729) -> Matrix(53,-6,468,-53) (31/13,105/44) -> (1/9,3/26) Matrix(6511,-15540,2728,-6511) -> Matrix(259,-30,2236,-259) (105/44,74/31) -> (3/26,5/43) Matrix(211,-504,18,-43) -> Matrix(17,-2,8,-1) Matrix(715,-1722,262,-631) -> Matrix(17,-2,144,-17) *** -> (1/9,1/8) Matrix(2141,-5166,574,-1385) -> Matrix(11,-2,60,-11) *** -> (1/6,1/5) Matrix(1807,-4410,706,-1723) -> Matrix(17,-2,144,-17) *** -> (1/9,1/8) Matrix(755,-1848,172,-421) -> Matrix(1,0,-4,1) 0/1 Matrix(5249,-13440,2050,-5249) -> Matrix(17,-2,144,-17) (64/25,105/41) -> (1/9,1/8) Matrix(3361,-8610,1312,-3361) -> Matrix(35,-4,306,-35) (105/41,41/16) -> (1/9,2/17) Matrix(589,-1512,164,-421) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(209,-546,80,-209) -> Matrix(81,-10,656,-81) (13/5,21/8) -> (5/41,1/8) Matrix(127,-336,48,-127) -> Matrix(47,-6,368,-47) (21/8,8/3) -> (1/8,3/23) Matrix(125,-336,16,-43) -> Matrix(15,-2,38,-5) Matrix(295,-798,78,-211) -> Matrix(15,-2,82,-11) Matrix(1259,-3444,276,-755) -> Matrix(65,-8,268,-33) Matrix(2393,-6552,874,-2393) -> Matrix(177,-22,1424,-177) (52/19,63/23) -> (11/89,1/8) Matrix(505,-1386,184,-505) -> Matrix(63,-8,496,-63) (63/23,11/4) -> (1/8,4/31) Matrix(167,-462,30,-83) -> Matrix(31,-4,116,-15) Matrix(43,-126,14,-41) -> Matrix(15,-2,98,-13) 1/7 Matrix(755,-2436,234,-755) -> Matrix(183,-28,1196,-183) (29/9,42/13) -> (7/46,2/13) Matrix(337,-1092,104,-337) -> Matrix(77,-12,494,-77) (42/13,13/4) -> (2/13,3/19) Matrix(167,-546,26,-85) -> Matrix(25,-4,94,-15) Matrix(293,-966,64,-211) -> Matrix(13,-2,46,-7) Matrix(2351,-7896,700,-2351) -> Matrix(1,0,8,-1) (47/14,84/25) -> (0/1,1/4) Matrix(1849,-6216,550,-1849) -> Matrix(1,0,16,-1) (84/25,37/11) -> (0/1,1/8) Matrix(421,-1428,74,-251) -> Matrix(27,-4,88,-13) Matrix(85,-294,24,-83) -> Matrix(25,-4,144,-23) 1/6 Matrix(419,-1596,110,-419) -> Matrix(23,-4,132,-23) (19/5,42/11) -> (1/6,2/11) Matrix(505,-1932,132,-505) -> Matrix(21,-4,110,-21) (42/11,23/6) -> (2/11,1/5) Matrix(41,-168,10,-41) -> Matrix(11,-2,60,-11) (4/1,21/5) -> (1/6,1/5) Matrix(169,-714,40,-169) -> Matrix(39,-8,190,-39) (21/5,17/4) -> (1/5,4/19) Matrix(41,-210,8,-41) -> Matrix(9,-2,40,-9) (5/1,21/4) -> (1/5,1/4) Matrix(127,-672,24,-127) -> Matrix(23,-6,88,-23) (21/4,16/3) -> (1/4,3/11) Matrix(881,-5040,154,-881) -> Matrix(43,-14,132,-43) (40/7,63/11) -> (7/22,1/3) Matrix(505,-2898,88,-505) -> Matrix(11,-4,30,-11) (63/11,23/4) -> (1/3,2/5) Matrix(43,-294,6,-41) -> Matrix(7,-2,18,-5) 1/3 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.