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 1/3 -8/1 3/7 1/2 -7/1 1/2 -13/2 1/3 -6/1 0/1 1/2 1/1 -23/4 1/1 -17/3 0/1 1/1 -11/2 1/1 -16/3 0/1 1/0 -21/4 0/1 -5/1 0/1 1/3 -19/4 1/3 -14/3 0/1 2/5 -23/5 3/7 1/2 -9/2 1/3 1/1 -22/5 1/3 1/2 -13/3 1/3 1/2 -17/4 1/3 -21/5 1/2 -4/1 0/1 1/2 -19/5 1/3 1/2 -15/4 1/3 1/1 -56/15 0/1 -41/11 2/7 1/3 -26/7 2/5 1/2 -11/3 0/1 1/1 -18/5 0/1 1/1 1/0 -7/2 0/1 -24/7 0/1 1/5 1/4 -41/12 1/3 -17/5 0/1 1/5 -61/18 1/5 -105/31 1/5 -44/13 1/5 1/4 -27/8 1/5 1/3 -37/11 0/1 1/1 -10/3 1/5 1/4 -33/10 1/5 1/3 -23/7 3/13 1/4 -36/11 1/4 3/11 2/7 -13/4 1/3 -16/5 1/4 2/7 -3/1 1/3 -17/6 1/3 -14/5 2/5 -25/9 2/5 3/7 -11/4 3/7 -19/7 1/3 1/2 -27/10 1/3 3/7 -35/13 1/2 -8/3 3/7 1/2 -21/8 1/2 -13/5 1/2 3/5 -18/7 0/1 1/2 1/1 -41/16 1/3 -105/41 1/2 -64/25 1/2 1/1 -23/9 1/3 1/2 -5/2 1/1 -27/11 1/3 -22/9 1/3 1/2 -17/7 0/1 1/1 -29/12 1/5 -70/29 0/1 -41/17 1/5 2/9 -12/5 0/1 1/4 1/3 -19/8 1/3 -7/3 1/3 -23/10 1/3 -39/17 1/3 -16/7 3/8 2/5 -41/18 1/3 -25/11 5/13 2/5 -34/15 5/12 3/7 -9/4 1/3 3/7 -20/9 1/3 1/2 -11/5 2/5 3/7 -13/6 3/7 -28/13 4/9 -15/7 5/11 -2/1 1/2 1/1 -15/8 1/3 1/1 -28/15 0/1 -13/7 1/3 1/2 -11/6 1/1 -42/23 0/1 -31/17 0/1 1/5 -20/11 1/4 1/3 -9/5 1/3 -34/19 3/8 5/13 -59/33 13/33 2/5 -84/47 2/5 -25/14 7/17 -41/23 3/7 10/23 -16/9 2/5 1/2 -7/4 1/2 -26/15 1/2 6/11 -19/11 1/2 5/9 -31/18 3/5 -105/61 1/2 -74/43 1/2 7/13 -43/25 6/11 5/9 -12/7 1/2 4/7 3/5 -41/24 3/5 -70/41 2/3 -29/17 1/2 3/5 -17/10 3/5 -39/23 3/5 -61/36 3/5 -22/13 3/5 11/18 -27/16 3/5 7/11 -5/3 2/3 1/1 -23/14 1/1 -64/39 11/12 1/1 -105/64 1/1 -41/25 1/1 4/3 -18/11 1/2 2/3 1/1 -31/19 2/3 1/1 -13/8 1/1 -21/13 1/1 -8/5 1/1 1/0 -27/17 1/1 -19/12 1/1 -30/19 0/1 1/2 1/1 -41/26 1/1 -52/33 7/8 1/1 -63/40 1/1 -11/7 1/1 2/1 -25/16 -1/1 -14/9 0/1 -17/11 0/1 1/1 -20/13 1/3 1/2 -3/2 1/3 1/1 -22/15 1/3 1/2 -19/13 1/2 1/1 -16/11 1/2 2/3 -29/20 1/1 -42/29 0/1 2/3 -13/9 1/2 1/1 -23/16 1/1 -10/7 1/1 1/0 -47/33 -1/3 0/1 -84/59 0/1 -37/26 1/5 -27/19 1/3 -44/31 7/15 1/2 -17/12 3/5 -7/5 1/1 -25/18 -1/1 -43/31 4/5 1/1 -18/13 1/1 2/1 1/0 -29/21 -1/1 1/0 -11/8 1/1 -26/19 0/1 1/2 -41/30 1/1 -56/41 0/1 -15/11 1/1 -19/14 1/1 -42/31 0/1 2/1 -23/17 1/1 1/0 -4/3 0/1 1/0 -21/16 0/1 -17/13 0/1 1/9 -13/10 1/5 -35/27 1/4 -57/44 3/11 1/3 -22/17 1/3 1/2 -9/7 1/3 -41/32 1/3 -32/25 1/3 3/8 -23/18 1/3 -14/11 0/1 2/5 -19/15 1/2 1/1 -5/4 1/3 -21/17 1/2 -16/13 1/2 4/7 -11/9 2/3 1/1 -17/14 1/3 -40/33 11/23 1/2 -63/52 1/2 -23/19 1/2 7/13 -6/5 1/2 2/3 1/1 -19/16 1/1 -13/11 1/2 1/1 -20/17 1/2 1/1 -7/6 1/1 -22/19 1/1 1/0 -15/13 1/1 -8/7 1/1 1/0 -9/8 1/3 1/1 -10/9 1/3 1/2 -1/1 0/1 1/1 0/1 0/1 1/1 0/1 1/5 9/8 1/5 1/3 8/7 1/6 1/5 7/6 1/5 13/11 1/5 1/4 6/5 1/5 2/9 1/4 23/19 7/29 1/4 17/14 1/3 11/9 1/5 2/9 16/13 4/17 1/4 21/17 1/4 5/4 1/3 19/15 1/5 1/4 14/11 0/1 2/7 23/18 1/3 9/7 1/3 22/17 1/4 1/3 13/10 1/1 17/13 -1/3 0/1 21/16 0/1 4/3 0/1 1/6 19/14 1/5 15/11 1/5 56/41 0/1 41/30 1/5 26/19 0/1 1/4 11/8 1/5 18/13 1/6 2/11 1/5 7/5 1/5 24/17 0/1 1/5 1/4 41/29 1/5 6/29 17/12 3/13 61/43 11/45 1/4 105/74 1/4 44/31 1/4 7/27 27/19 1/3 37/26 1/1 10/7 1/6 1/5 33/23 1/5 23/16 1/5 36/25 1/5 2/9 1/4 13/9 1/5 1/4 16/11 2/9 1/4 3/2 1/5 1/3 17/11 0/1 1/5 14/9 0/1 25/16 1/7 11/7 2/11 1/5 19/12 1/5 27/17 1/5 35/22 1/5 8/5 1/6 1/5 21/13 1/5 13/8 1/5 18/11 1/5 2/9 1/4 41/25 4/21 1/5 105/64 1/5 64/39 1/5 11/54 23/14 1/5 5/3 1/5 2/9 27/16 7/31 3/13 22/13 11/48 3/13 17/10 3/13 29/17 3/13 1/4 70/41 2/9 41/24 3/13 12/7 3/13 4/17 1/4 19/11 5/21 1/4 7/4 1/4 23/13 1/4 3/11 39/22 5/19 3/11 16/9 1/4 2/7 41/23 10/37 3/11 25/14 7/25 34/19 5/17 3/10 9/5 1/3 20/11 1/3 1/2 11/6 1/5 13/7 1/4 1/3 28/15 0/1 15/8 1/5 1/3 2/1 1/5 1/4 15/7 5/19 28/13 4/15 13/6 3/11 11/5 3/11 2/7 42/19 2/7 31/14 5/17 20/9 1/4 1/3 9/4 3/11 1/3 34/15 3/11 5/18 59/26 15/53 84/37 2/7 25/11 2/7 5/17 41/18 1/3 16/7 2/7 3/10 7/3 1/3 26/11 0/1 1/4 19/8 1/3 31/13 2/7 1/3 105/44 1/3 74/31 1/3 7/20 43/18 1/3 12/5 0/1 1/3 1/2 41/17 2/3 1/1 70/29 0/1 29/12 1/1 17/7 0/1 1/5 39/16 1/5 1/3 61/25 1/5 1/4 22/9 1/4 1/3 27/11 1/3 5/2 1/5 23/9 1/4 1/3 64/25 1/5 1/4 105/41 1/4 41/16 1/3 18/7 0/1 1/5 1/4 31/12 1/5 13/5 3/13 1/4 21/8 1/4 8/3 1/4 3/11 27/10 3/11 1/3 19/7 1/4 1/3 30/11 1/4 3/11 2/7 41/15 0/1 1/3 52/19 1/5 1/4 63/23 1/4 11/4 3/11 25/9 3/11 2/7 14/5 2/7 17/6 1/3 20/7 7/22 1/3 3/1 1/3 22/7 5/16 1/3 19/6 1/3 16/5 2/5 1/2 29/9 1/3 1/2 42/13 0/1 2/5 13/4 1/3 23/7 1/2 3/5 10/3 1/2 1/1 47/14 -1/3 84/25 0/1 37/11 0/1 1/5 27/8 1/3 1/1 44/13 1/2 1/1 17/5 0/1 1/1 7/2 0/1 25/7 0/1 1/5 43/12 1/7 18/5 0/1 1/6 1/5 29/8 1/5 11/3 0/1 1/5 26/7 1/4 2/7 41/11 1/3 2/5 56/15 0/1 15/4 1/5 1/3 19/5 1/4 1/3 42/11 0/1 2/7 23/6 1/3 4/1 0/1 1/4 21/5 1/4 17/4 1/3 13/3 1/4 1/3 35/8 1/3 57/13 1/3 22/5 1/4 1/3 9/2 1/5 1/3 41/9 0/1 1/5 32/7 1/4 1/3 23/5 1/4 3/11 14/3 0/1 2/7 19/4 1/3 5/1 0/1 1/3 21/4 0/1 16/3 0/1 1/6 11/2 1/5 17/3 0/1 1/5 40/7 1/6 1/5 63/11 1/5 23/4 1/5 6/1 0/1 1/5 1/4 19/3 1/4 5/19 13/2 1/3 20/3 1/6 1/5 7/1 1/4 22/3 7/26 3/11 15/2 3/11 1/3 8/1 1/4 3/11 9/1 1/3 10/1 5/16 1/3 1/0 1/3 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(5,-2,18,-7) Matrix(43,378,24,211) -> Matrix(11,-4,36,-13) Matrix(43,336,-16,-125) -> Matrix(1,0,0,1) Matrix(83,546,-64,-421) -> Matrix(1,0,2,1) Matrix(85,546,-26,-167) -> Matrix(5,-2,18,-7) Matrix(167,966,116,671) -> Matrix(3,-2,14,-9) Matrix(251,1428,-74,-421) -> Matrix(1,0,4,1) Matrix(83,462,30,167) -> Matrix(5,-2,18,-7) Matrix(85,462,62,337) -> Matrix(1,0,4,1) Matrix(127,672,24,127) -> Matrix(1,0,6,1) Matrix(41,210,8,41) -> Matrix(1,0,0,1) Matrix(43,210,26,127) -> Matrix(7,-2,32,-9) Matrix(125,588,98,461) -> Matrix(5,-2,18,-7) Matrix(127,588,100,463) -> Matrix(5,-2,18,-7) Matrix(211,966,-64,-293) -> Matrix(1,0,2,1) Matrix(85,378,38,169) -> Matrix(5,-2,18,-7) Matrix(125,546,-106,-463) -> Matrix(5,-2,8,-3) Matrix(167,714,98,419) -> Matrix(3,-2,14,-9) Matrix(169,714,40,169) -> Matrix(5,-2,18,-7) Matrix(41,168,10,41) -> Matrix(1,0,2,1) Matrix(43,168,-32,-125) -> Matrix(1,0,-2,1) Matrix(211,798,78,295) -> Matrix(5,-2,18,-7) Matrix(337,1260,180,673) -> Matrix(1,0,2,1) Matrix(1385,5166,574,2141) -> Matrix(1,0,-2,1) Matrix(463,1722,260,967) -> Matrix(9,-4,34,-15) Matrix(125,462,102,377) -> Matrix(3,-2,14,-9) Matrix(209,756,-128,-463) -> Matrix(1,-2,2,-3) Matrix(83,294,-24,-85) -> Matrix(1,0,4,1) Matrix(503,1722,196,671) -> Matrix(1,0,0,1) Matrix(505,1722,222,757) -> Matrix(5,-2,18,-7) Matrix(1847,6258,322,1091) -> Matrix(1,0,0,1) Matrix(2059,6972,360,1219) -> Matrix(9,-2,50,-11) Matrix(211,714,112,379) -> Matrix(1,0,0,1) Matrix(337,1134,200,673) -> Matrix(3,-2,14,-9) Matrix(251,840,-176,-589) -> Matrix(1,0,-4,1) Matrix(127,420,-114,-377) -> Matrix(1,0,-2,1) Matrix(295,966,244,799) -> Matrix(15,-4,64,-17) Matrix(209,672,-144,-463) -> Matrix(1,0,-2,1) Matrix(211,672,-92,-293) -> Matrix(13,-4,36,-11) Matrix(251,714,-148,-421) -> Matrix(27,-10,46,-17) Matrix(209,588,134,377) -> Matrix(5,-2,38,-15) Matrix(211,588,136,379) -> Matrix(5,-2,18,-7) Matrix(167,462,30,83) -> Matrix(5,-2,18,-7) Matrix(293,798,-170,-463) -> Matrix(13,-6,24,-11) Matrix(295,798,78,211) -> Matrix(5,-2,18,-7) Matrix(1091,2940,-842,-2269) -> Matrix(9,-4,34,-15) Matrix(127,336,48,127) -> Matrix(13,-6,50,-23) Matrix(209,546,80,209) -> Matrix(11,-6,46,-25) Matrix(293,756,-212,-547) -> Matrix(3,-2,2,-1) Matrix(589,1512,164,421) -> Matrix(1,0,4,1) Matrix(3361,8610,1312,3361) -> Matrix(5,-2,18,-7) Matrix(5249,13440,2050,5249) -> Matrix(3,-2,14,-9) Matrix(1723,4410,706,1807) -> Matrix(1,0,2,1) Matrix(83,210,66,167) -> Matrix(1,0,2,1) Matrix(461,1134,324,797) -> Matrix(1,0,0,1) Matrix(377,924,-326,-799) -> Matrix(1,0,-2,1) Matrix(293,714,-190,-463) -> Matrix(1,0,0,1) Matrix(295,714,226,547) -> Matrix(1,0,-4,1) Matrix(713,1722,330,797) -> Matrix(17,-4,64,-15) Matrix(2141,5166,574,1385) -> Matrix(1,0,-2,1) Matrix(715,1722,262,631) -> Matrix(9,-2,32,-7) Matrix(335,798,-212,-505) -> Matrix(1,0,-2,1) Matrix(125,294,-54,-127) -> Matrix(7,-2,18,-5) Matrix(1427,3276,-842,-1933) -> Matrix(45,-16,76,-27) Matrix(755,1722,552,1259) -> Matrix(5,-2,28,-11) Matrix(923,2100,258,587) -> Matrix(5,-2,38,-15) Matrix(1259,2856,-704,-1597) -> Matrix(39,-16,100,-41) Matrix(167,378,148,335) -> Matrix(5,-2,18,-7) Matrix(169,378,38,85) -> Matrix(5,-2,18,-7) Matrix(379,840,-208,-461) -> Matrix(5,-2,18,-7) Matrix(211,462,58,127) -> Matrix(5,-2,18,-7) Matrix(797,1722,330,713) -> Matrix(9,-4,16,-7) Matrix(587,1260,430,923) -> Matrix(9,-4,34,-15) Matrix(335,714,236,503) -> Matrix(13,-6,50,-23) Matrix(379,714,112,211) -> Matrix(1,0,0,1) Matrix(673,1260,180,337) -> Matrix(1,0,2,1) Matrix(925,1722,542,1009) -> Matrix(3,-2,14,-9) Matrix(295,546,114,211) -> Matrix(3,-2,14,-9) Matrix(965,1764,436,797) -> Matrix(3,2,10,7) Matrix(967,1764,438,799) -> Matrix(13,-2,46,-7) Matrix(209,378,162,293) -> Matrix(1,0,0,1) Matrix(211,378,24,43) -> Matrix(11,-4,36,-13) Matrix(3947,7056,1738,3107) -> Matrix(91,-36,316,-125) Matrix(3949,7056,1740,3109) -> Matrix(109,-44,384,-155) Matrix(965,1722,682,1217) -> Matrix(19,-8,88,-37) Matrix(967,1722,260,463) -> Matrix(9,-4,34,-15) Matrix(167,294,-96,-169) -> Matrix(17,-8,32,-15) Matrix(461,798,-316,-547) -> Matrix(7,-4,16,-9) Matrix(1805,3108,658,1133) -> Matrix(1,0,2,1) Matrix(5881,10122,2148,3697) -> Matrix(15,-8,62,-33) Matrix(2563,4410,562,967) -> Matrix(11,-6,46,-25) Matrix(587,1008,244,419) -> Matrix(7,-4,16,-9) Matrix(589,1008,246,421) -> Matrix(7,-4,16,-9) Matrix(3025,5166,2214,3781) -> Matrix(3,-2,20,-13) Matrix(1009,1722,542,925) -> Matrix(3,-2,14,-9) Matrix(419,714,98,167) -> Matrix(3,-2,14,-9) Matrix(2603,4410,1586,2687) -> Matrix(37,-22,180,-107) Matrix(1093,1848,-844,-1427) -> Matrix(13,-8,44,-27) Matrix(673,1134,200,337) -> Matrix(3,-2,14,-9) Matrix(127,210,26,43) -> Matrix(3,-2,8,-5) Matrix(1049,1722,332,545) -> Matrix(7,-6,20,-17) Matrix(8191,13440,4992,8191) -> Matrix(23,-22,114,-109) Matrix(5249,8610,3200,5249) -> Matrix(7,-8,36,-41) Matrix(1051,1722,744,1219) -> Matrix(3,-2,14,-9) Matrix(335,546,154,251) -> Matrix(11,-8,40,-29) Matrix(337,546,208,337) -> Matrix(9,-8,44,-39) Matrix(209,336,130,209) -> Matrix(1,-2,6,-11) Matrix(211,336,-184,-293) -> Matrix(1,0,0,1) Matrix(503,798,370,587) -> Matrix(1,0,4,1) Matrix(1091,1722,638,1007) -> Matrix(7,-4,30,-17) Matrix(293,462,26,41) -> Matrix(3,-2,8,-5) Matrix(6425,10122,2692,4241) -> Matrix(15,-14,44,-41) Matrix(1975,3108,828,1303) -> Matrix(3,-4,10,-13) Matrix(295,462,242,379) -> Matrix(1,0,4,1) Matrix(377,588,134,209) -> Matrix(3,2,10,7) Matrix(379,588,136,211) -> Matrix(5,-2,18,-7) Matrix(83,126,-56,-85) -> Matrix(1,0,0,1) Matrix(1177,1722,460,673) -> Matrix(1,0,2,1) Matrix(1217,1764,376,545) -> Matrix(3,-2,8,-5) Matrix(1219,1764,378,547) -> Matrix(3,-2,8,-5) Matrix(379,546,-320,-461) -> Matrix(1,0,0,1) Matrix(673,966,-526,-755) -> Matrix(3,-2,8,-5) Matrix(4955,7056,1474,2099) -> Matrix(1,0,8,1) Matrix(4957,7056,1476,2101) -> Matrix(1,0,-8,1) Matrix(797,1134,324,461) -> Matrix(1,0,0,1) Matrix(503,714,236,335) -> Matrix(13,-6,50,-23) Matrix(1007,1428,-830,-1177) -> Matrix(7,-4,16,-9) Matrix(209,294,-150,-211) -> Matrix(3,-2,2,-1) Matrix(1513,2100,848,1177) -> Matrix(5,-2,18,-7) Matrix(1091,1512,666,923) -> Matrix(1,0,4,1) Matrix(335,462,182,251) -> Matrix(1,0,4,1) Matrix(337,462,62,85) -> Matrix(1,0,4,1) Matrix(1259,1722,552,755) -> Matrix(1,-2,4,-7) Matrix(3781,5166,2214,3025) -> Matrix(1,2,4,9) Matrix(923,1260,430,587) -> Matrix(9,-4,34,-15) Matrix(587,798,370,503) -> Matrix(1,0,4,1) Matrix(1301,1764,340,461) -> Matrix(1,-2,4,-7) Matrix(1303,1764,342,463) -> Matrix(1,-2,4,-7) Matrix(127,168,96,127) -> Matrix(1,0,6,1) Matrix(545,714,416,545) -> Matrix(1,0,-12,1) Matrix(547,714,226,295) -> Matrix(1,0,-4,1) Matrix(293,378,162,209) -> Matrix(1,0,0,1) Matrix(3443,4410,1442,1847) -> Matrix(13,-4,36,-11) Matrix(461,588,98,125) -> Matrix(5,-2,18,-7) Matrix(463,588,100,127) -> Matrix(5,-2,18,-7) Matrix(167,210,66,83) -> Matrix(1,0,2,1) Matrix(169,210,136,169) -> Matrix(5,-2,18,-7) Matrix(545,672,442,545) -> Matrix(15,-8,62,-33) Matrix(377,462,102,125) -> Matrix(3,-2,14,-9) Matrix(379,462,242,295) -> Matrix(1,0,4,1) Matrix(5753,6972,4054,4913) -> Matrix(37,-18,146,-71) Matrix(5167,6258,3642,4411) -> Matrix(35,-18,142,-73) Matrix(209,252,34,41) -> Matrix(3,-2,14,-9) Matrix(211,252,36,43) -> Matrix(3,-2,14,-9) Matrix(251,294,-216,-253) -> Matrix(3,-2,2,-1) Matrix(335,378,148,167) -> Matrix(5,-2,18,-7) Matrix(421,462,154,169) -> Matrix(1,0,2,1) Matrix(1,0,2,1) -> Matrix(1,0,4,1) Matrix(337,-378,74,-83) -> Matrix(1,0,0,1) Matrix(293,-336,184,-211) -> Matrix(1,0,0,1) Matrix(463,-546,106,-125) -> Matrix(9,-2,32,-7) Matrix(461,-546,320,-379) -> Matrix(1,0,0,1) Matrix(1177,-1428,830,-1007) -> Matrix(15,-4,64,-17) Matrix(755,-966,526,-673) -> Matrix(7,-2,32,-9) Matrix(421,-546,64,-83) -> Matrix(1,0,2,1) Matrix(125,-168,32,-43) -> Matrix(1,0,-2,1) Matrix(547,-756,212,-293) -> Matrix(11,-2,50,-9) Matrix(211,-294,150,-209) -> Matrix(11,-2,50,-9) Matrix(589,-840,176,-251) -> Matrix(1,0,-4,1) Matrix(293,-420,30,-43) -> Matrix(19,-4,62,-13) Matrix(463,-672,144,-209) -> Matrix(1,0,-2,1) Matrix(461,-672,260,-379) -> Matrix(17,-4,64,-15) Matrix(463,-714,190,-293) -> Matrix(1,0,0,1) Matrix(505,-798,212,-335) -> Matrix(1,0,-2,1) Matrix(1849,-2940,422,-671) -> Matrix(1,0,-2,1) Matrix(463,-756,128,-209) -> Matrix(9,-2,50,-11) Matrix(547,-924,74,-125) -> Matrix(53,-12,190,-43) Matrix(421,-714,148,-251) -> Matrix(43,-10,142,-33) Matrix(463,-798,170,-293) -> Matrix(25,-6,96,-23) Matrix(169,-294,96,-167) -> Matrix(33,-8,128,-31) Matrix(1849,-3276,758,-1343) -> Matrix(15,-4,64,-17) Matrix(1597,-2856,704,-1259) -> Matrix(55,-16,196,-57) Matrix(461,-840,208,-379) -> Matrix(5,-2,18,-7) Matrix(127,-294,54,-125) -> Matrix(7,-2,18,-5) Matrix(337,-798,106,-251) -> Matrix(7,-2,18,-5) Matrix(755,-1848,172,-421) -> Matrix(1,0,0,1) Matrix(125,-336,16,-43) -> Matrix(1,0,0,1) Matrix(43,-126,14,-41) -> Matrix(7,-2,18,-5) Matrix(167,-546,26,-85) -> Matrix(5,-2,18,-7) Matrix(293,-966,64,-211) -> Matrix(1,0,2,1) Matrix(421,-1428,74,-251) -> Matrix(1,0,4,1) Matrix(85,-294,24,-83) -> Matrix(1,0,4,1) Matrix(43,-294,6,-41) -> Matrix(17,-4,64,-15) 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): 48 Degree of the the map X: 48 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 2 1 1/1 (0/1,1/5) 0 21 9/8 0 7 8/7 (1/6,1/5) 0 21 7/6 1/5 1 3 13/11 (1/5,1/4) 0 21 6/5 0 7 23/19 (7/29,1/4) 0 21 17/14 1/3 1 21 11/9 (1/5,2/9) 0 21 16/13 (4/17,1/4) 0 21 21/17 1/4 5 1 5/4 1/3 1 21 19/15 (1/5,1/4) 0 21 14/11 0 3 23/18 1/3 1 21 9/7 1/3 1 7 22/17 (1/4,1/3) 0 21 13/10 1/1 1 21 17/13 (-1/3,0/1) 0 21 21/16 0/1 9 1 4/3 (0/1,1/6) 0 21 19/14 1/5 1 21 15/11 1/5 1 7 56/41 0/1 2 3 41/30 1/5 1 21 26/19 (0/1,1/4) 0 21 11/8 1/5 1 21 18/13 0 7 7/5 1/5 1 3 24/17 0 7 41/29 (1/5,6/29) 0 21 17/12 3/13 1 21 61/43 (11/45,1/4) 0 21 105/74 1/4 18 1 44/31 (1/4,7/27) 0 21 27/19 1/3 1 7 37/26 1/1 1 21 10/7 (1/6,1/5) 0 21 33/23 1/5 1 7 23/16 1/5 1 21 36/25 0 7 13/9 (1/5,1/4) 0 21 16/11 (2/9,1/4) 0 21 3/2 0 7 17/11 (0/1,1/5) 0 21 14/9 0/1 2 3 25/16 1/7 1 21 11/7 (2/11,1/5) 0 21 19/12 1/5 1 21 27/17 1/5 1 7 35/22 1/5 1 3 8/5 (1/6,1/5) 0 21 21/13 1/5 5 1 13/8 1/5 1 21 18/11 0 7 41/25 (4/21,1/5) 0 21 105/64 1/5 15 1 64/39 (1/5,11/54) 0 21 23/14 1/5 1 21 5/3 (1/5,2/9) 0 21 27/16 0 7 22/13 (11/48,3/13) 0 21 17/10 3/13 1 21 29/17 (3/13,1/4) 0 21 70/41 2/9 2 3 41/24 3/13 1 21 12/7 0 7 19/11 (5/21,1/4) 0 21 7/4 1/4 4 3 23/13 (1/4,3/11) 0 21 39/22 0 7 16/9 (1/4,2/7) 0 21 41/23 (10/37,3/11) 0 21 25/14 7/25 1 21 34/19 (5/17,3/10) 0 21 9/5 1/3 1 7 20/11 (1/3,1/2) 0 21 11/6 1/5 1 21 13/7 (1/4,1/3) 0 21 28/15 0/1 2 3 15/8 0 7 2/1 (1/5,1/4) 0 21 15/7 5/19 1 7 28/13 4/15 2 3 13/6 3/11 1 21 11/5 (3/11,2/7) 0 21 42/19 2/7 4 1 31/14 5/17 1 21 20/9 (1/4,1/3) 0 21 9/4 0 7 34/15 (3/11,5/18) 0 21 59/26 15/53 1 21 84/37 2/7 10 1 25/11 (2/7,5/17) 0 21 41/18 1/3 1 21 16/7 (2/7,3/10) 0 21 7/3 1/3 1 3 26/11 (0/1,1/4) 0 21 19/8 1/3 1 21 31/13 (2/7,1/3) 0 21 105/44 1/3 9 1 74/31 (1/3,7/20) 0 21 43/18 1/3 1 21 12/5 0 7 41/17 (2/3,1/1) 0 21 70/29 0/1 2 3 29/12 1/1 1 21 17/7 (0/1,1/5) 0 21 39/16 0 7 61/25 (1/5,1/4) 0 21 22/9 (1/4,1/3) 0 21 27/11 1/3 1 7 5/2 1/5 1 21 23/9 (1/4,1/3) 0 21 64/25 (1/5,1/4) 0 21 105/41 1/4 2 1 41/16 1/3 1 21 18/7 0 7 31/12 1/5 1 21 13/5 (3/13,1/4) 0 21 21/8 1/4 6 1 8/3 (1/4,3/11) 0 21 27/10 0 7 19/7 (1/4,1/3) 0 21 30/11 0 7 41/15 (0/1,1/3) 0 21 52/19 (1/5,1/4) 0 21 63/23 1/4 4 1 11/4 3/11 1 21 25/9 (3/11,2/7) 0 21 14/5 2/7 2 3 17/6 1/3 1 21 20/7 (7/22,1/3) 0 21 3/1 1/3 1 7 22/7 (5/16,1/3) 0 21 19/6 1/3 1 21 16/5 (2/5,1/2) 0 21 29/9 (1/3,1/2) 0 21 42/13 (1/3,1/2) 0 1 13/4 1/3 1 21 23/7 (1/2,3/5) 0 21 10/3 (1/2,1/1) 0 21 47/14 -1/3 1 21 84/25 0/1 8 1 37/11 (0/1,1/5) 0 21 27/8 0 7 44/13 (1/2,1/1) 0 21 17/5 (0/1,1/1) 0 21 7/2 0/1 2 3 25/7 (0/1,1/5) 0 21 43/12 1/7 1 21 18/5 0 7 29/8 1/5 1 21 11/3 (0/1,1/5) 0 21 26/7 (1/4,2/7) 0 21 41/11 (1/3,2/5) 0 21 56/15 0/1 2 3 15/4 0 7 19/5 (1/4,1/3) 0 21 42/11 (1/4,1/3) 0 1 23/6 1/3 1 21 4/1 (0/1,1/4) 0 21 21/5 1/4 1 1 17/4 1/3 1 21 13/3 (1/4,1/3) 0 21 35/8 1/3 1 3 57/13 1/3 1 7 22/5 (1/4,1/3) 0 21 9/2 0 7 41/9 (0/1,1/5) 0 21 32/7 (1/4,1/3) 0 21 23/5 (1/4,3/11) 0 21 14/3 0 3 19/4 1/3 1 21 5/1 (0/1,1/3) 0 21 21/4 0/1 3 1 16/3 (0/1,1/6) 0 21 11/2 1/5 1 21 17/3 (0/1,1/5) 0 21 40/7 (1/6,1/5) 0 21 63/11 1/5 1 1 23/4 1/5 1 21 6/1 0 7 19/3 (1/4,5/19) 0 21 13/2 1/3 1 21 20/3 (1/6,1/5) 0 21 7/1 1/4 2 3 22/3 (7/26,3/11) 0 21 15/2 0 7 8/1 (1/4,3/11) 0 21 9/1 1/3 1 7 10/1 (5/16,1/3) 0 21 1/0 1/3 1 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(1,0,6,-1) (0/1,1/0) -> (0/1,1/3) Matrix(1,0,2,-1) -> Matrix(1,0,10,-1) (0/1,1/1) -> (0/1,1/5) Matrix(337,-378,74,-83) -> Matrix(1,0,0,1) Matrix(335,-378,148,-167) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(293,-336,184,-211) -> Matrix(1,0,0,1) Matrix(463,-546,106,-125) -> Matrix(9,-2,32,-7) 1/4 Matrix(461,-546,320,-379) -> Matrix(1,0,0,1) Matrix(209,-252,34,-41) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(1177,-1428,830,-1007) -> Matrix(15,-4,64,-17) 1/4 Matrix(379,-462,242,-295) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(377,-462,102,-125) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(545,-672,442,-545) -> Matrix(33,-8,136,-33) (16/13,21/17) -> (4/17,1/4) Matrix(169,-210,136,-169) -> Matrix(7,-2,24,-7) (21/17,5/4) -> (1/4,1/3) Matrix(167,-210,66,-83) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(463,-588,100,-127) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(461,-588,98,-125) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(755,-966,526,-673) -> Matrix(7,-2,32,-9) 1/4 Matrix(293,-378,162,-209) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(421,-546,64,-83) -> Matrix(1,0,2,1) 0/1 Matrix(547,-714,226,-295) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(545,-714,416,-545) -> Matrix(-1,0,6,1) (17/13,21/16) -> (-1/3,0/1) Matrix(127,-168,96,-127) -> Matrix(1,0,12,-1) (21/16,4/3) -> (0/1,1/6) Matrix(125,-168,32,-43) -> Matrix(1,0,-2,1) 0/1 Matrix(587,-798,370,-503) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(923,-1260,430,-587) -> Matrix(15,-4,56,-15) *** -> (1/4,2/7) Matrix(3781,-5166,2214,-3025) -> Matrix(13,-2,58,-9) Matrix(1259,-1722,552,-755) -> Matrix(11,-2,38,-7) Matrix(337,-462,62,-85) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(547,-756,212,-293) -> Matrix(11,-2,50,-9) 1/5 Matrix(211,-294,150,-209) -> Matrix(11,-2,50,-9) 1/5 Matrix(1219,-1722,744,-1051) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(1217,-1722,682,-965) -> Matrix(37,-8,134,-29) Matrix(9029,-12810,6364,-9029) -> Matrix(89,-22,360,-89) (61/43,105/74) -> (11/45,1/4) Matrix(6511,-9240,4588,-6511) -> Matrix(55,-14,216,-55) (105/74,44/31) -> (1/4,7/27) Matrix(503,-714,236,-335) -> Matrix(23,-6,88,-23) *** -> (1/4,3/11) Matrix(797,-1134,324,-461) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(589,-840,176,-251) -> Matrix(1,0,-4,1) 0/1 Matrix(293,-420,30,-43) -> Matrix(19,-4,62,-13) Matrix(671,-966,116,-167) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(463,-672,144,-209) -> Matrix(1,0,-2,1) 0/1 Matrix(461,-672,260,-379) -> Matrix(17,-4,64,-15) 1/4 Matrix(463,-714,190,-293) -> Matrix(1,0,0,1) Matrix(379,-588,136,-211) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(377,-588,134,-209) -> Matrix(15,-2,52,-7) Matrix(505,-798,212,-335) -> Matrix(1,0,-2,1) 0/1 Matrix(1849,-2940,422,-671) -> Matrix(1,0,-2,1) 0/1 Matrix(209,-336,130,-209) -> Matrix(11,-2,60,-11) (8/5,21/13) -> (1/6,1/5) Matrix(337,-546,208,-337) -> Matrix(39,-8,190,-39) (21/13,13/8) -> (1/5,4/19) Matrix(463,-756,128,-209) -> Matrix(9,-2,50,-11) 1/5 Matrix(5249,-8610,3200,-5249) -> Matrix(41,-8,210,-41) (41/25,105/64) -> (4/21,1/5) Matrix(8191,-13440,4992,-8191) -> Matrix(109,-22,540,-109) (105/64,64/39) -> (1/5,11/54) Matrix(1049,-1722,332,-545) -> Matrix(29,-6,82,-17) Matrix(127,-210,26,-43) -> Matrix(9,-2,22,-5) Matrix(673,-1134,200,-337) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(547,-924,74,-125) -> Matrix(53,-12,190,-43) Matrix(421,-714,148,-251) -> Matrix(43,-10,142,-33) Matrix(419,-714,98,-167) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(1009,-1722,542,-925) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(589,-1008,246,-421) -> Matrix(17,-4,38,-9) Matrix(463,-798,170,-293) -> Matrix(25,-6,96,-23) 1/4 Matrix(169,-294,96,-167) -> Matrix(33,-8,128,-31) 1/4 Matrix(1849,-3276,758,-1343) -> Matrix(15,-4,64,-17) 1/4 Matrix(967,-1722,260,-463) -> Matrix(15,-4,56,-15) *** -> (1/4,2/7) Matrix(1597,-2856,704,-1259) -> Matrix(55,-16,196,-57) 2/7 Matrix(211,-378,24,-43) -> Matrix(13,-4,42,-13) *** -> (2/7,1/3) Matrix(461,-840,208,-379) -> Matrix(5,-2,18,-7) 1/3 Matrix(295,-546,114,-211) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(673,-1260,180,-337) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(379,-714,112,-211) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(797,-1722,330,-713) -> Matrix(15,-4,26,-7) Matrix(211,-462,58,-127) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(419,-924,190,-419) -> Matrix(43,-12,154,-43) (11/5,42/19) -> (3/11,2/7) Matrix(1177,-2604,532,-1177) -> Matrix(69,-20,238,-69) (42/19,31/14) -> (2/7,5/17) Matrix(169,-378,38,-85) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(4367,-9912,1924,-4367) -> Matrix(211,-60,742,-211) (59/26,84/37) -> (15/53,2/7) Matrix(1849,-4200,814,-1849) -> Matrix(69,-20,238,-69) (84/37,25/11) -> (2/7,5/17) Matrix(923,-2100,258,-587) -> Matrix(7,-2,52,-15) Matrix(127,-294,54,-125) -> Matrix(7,-2,18,-5) 1/3 Matrix(337,-798,106,-251) -> Matrix(7,-2,18,-5) 1/3 Matrix(2729,-6510,1144,-2729) -> Matrix(13,-4,42,-13) (31/13,105/44) -> (2/7,1/3) Matrix(6511,-15540,2728,-6511) -> Matrix(41,-14,120,-41) (105/44,74/31) -> (1/3,7/20) Matrix(211,-504,18,-43) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(715,-1722,262,-631) -> Matrix(3,-2,10,-7) Matrix(2141,-5166,574,-1385) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1807,-4410,706,-1723) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(755,-1848,172,-421) -> Matrix(1,0,0,1) Matrix(5249,-13440,2050,-5249) -> Matrix(9,-2,40,-9) (64/25,105/41) -> (1/5,1/4) Matrix(3361,-8610,1312,-3361) -> Matrix(7,-2,24,-7) (105/41,41/16) -> (1/4,1/3) Matrix(589,-1512,164,-421) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(209,-546,80,-209) -> Matrix(25,-6,104,-25) (13/5,21/8) -> (3/13,1/4) Matrix(127,-336,48,-127) -> Matrix(23,-6,88,-23) (21/8,8/3) -> (1/4,3/11) Matrix(125,-336,16,-43) -> Matrix(1,0,0,1) Matrix(295,-798,78,-211) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(1259,-3444,276,-755) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(2393,-6552,874,-2393) -> Matrix(9,-2,40,-9) (52/19,63/23) -> (1/5,1/4) Matrix(505,-1386,184,-505) -> Matrix(23,-6,88,-23) (63/23,11/4) -> (1/4,3/11) Matrix(167,-462,30,-83) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(43,-126,14,-41) -> Matrix(7,-2,18,-5) 1/3 Matrix(755,-2436,234,-755) -> Matrix(5,-2,12,-5) (29/9,42/13) -> (1/3,1/2) Matrix(337,-1092,104,-337) -> Matrix(5,-2,12,-5) (42/13,13/4) -> (1/3,1/2) Matrix(167,-546,26,-85) -> Matrix(5,-2,18,-7) 1/3 Matrix(293,-966,64,-211) -> Matrix(1,0,2,1) 0/1 Matrix(2351,-7896,700,-2351) -> Matrix(-1,0,6,1) (47/14,84/25) -> (-1/3,0/1) Matrix(1849,-6216,550,-1849) -> Matrix(1,0,10,-1) (84/25,37/11) -> (0/1,1/5) Matrix(421,-1428,74,-251) -> Matrix(1,0,4,1) 0/1 Matrix(85,-294,24,-83) -> Matrix(1,0,4,1) 0/1 Matrix(419,-1596,110,-419) -> Matrix(7,-2,24,-7) (19/5,42/11) -> (1/4,1/3) Matrix(505,-1932,132,-505) -> Matrix(7,-2,24,-7) (42/11,23/6) -> (1/4,1/3) Matrix(41,-168,10,-41) -> Matrix(1,0,8,-1) (4/1,21/5) -> (0/1,1/4) Matrix(169,-714,40,-169) -> Matrix(7,-2,24,-7) (21/5,17/4) -> (1/4,1/3) Matrix(41,-210,8,-41) -> Matrix(1,0,6,-1) (5/1,21/4) -> (0/1,1/3) Matrix(127,-672,24,-127) -> Matrix(1,0,12,-1) (21/4,16/3) -> (0/1,1/6) Matrix(881,-5040,154,-881) -> Matrix(11,-2,60,-11) (40/7,63/11) -> (1/6,1/5) Matrix(505,-2898,88,-505) -> Matrix(1,0,10,-1) (63/11,23/4) -> (0/1,1/5) Matrix(43,-294,6,-41) -> Matrix(17,-4,64,-15) 1/4 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.