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 1/2 -8/1 1/4 1/3 -7/1 1/2 -13/2 3/4 1/1 -6/1 1/2 1/0 -23/4 1/1 1/0 -17/3 0/1 1/0 -11/2 0/1 1/0 -16/3 -1/4 0/1 -21/4 0/1 -5/1 0/1 1/4 -19/4 1/4 1/3 -14/3 1/3 -23/5 1/3 1/2 -9/2 3/8 1/2 -22/5 2/5 1/2 -13/3 3/7 1/2 -17/4 8/17 1/2 -21/5 1/2 -4/1 1/2 2/3 -19/5 1/1 7/6 -15/4 3/2 1/0 -56/15 2/1 -41/11 2/1 1/0 -26/7 4/1 1/0 -11/3 0/1 1/0 -18/5 -1/2 1/0 -7/2 0/1 -24/7 1/4 1/2 -41/12 0/1 1/2 -17/5 0/1 1/4 -61/18 1/5 1/4 -105/31 1/4 -44/13 1/4 1/3 -27/8 1/4 1/2 -37/11 0/1 1/0 -10/3 0/1 1/4 -33/10 1/4 3/10 -23/7 3/10 1/3 -36/11 3/8 1/2 -13/4 1/4 1/3 -16/5 3/8 2/5 -3/1 1/2 -17/6 1/2 4/7 -14/5 2/3 -25/9 2/3 3/4 -11/4 2/3 3/4 -19/7 5/6 1/1 -27/10 1/2 1/0 -35/13 1/2 -8/3 3/4 1/1 -21/8 1/1 -13/5 1/1 3/2 -18/7 1/2 1/0 -41/16 0/1 1/2 -105/41 1/2 -64/25 1/2 2/3 -23/9 1/2 1/1 -5/2 0/1 1/0 -27/11 1/2 -22/9 0/1 1/2 -17/7 0/1 1/0 -29/12 1/5 1/4 -70/29 0/1 -41/17 0/1 1/4 -12/5 1/4 1/2 -19/8 1/3 3/8 -7/3 1/2 -23/10 3/5 5/8 -39/17 1/2 -16/7 5/8 2/3 -41/18 1/2 2/3 -25/11 5/8 2/3 -34/15 5/7 3/4 -9/4 1/2 3/4 -20/9 1/2 2/3 -11/5 2/3 3/4 -13/6 3/4 7/9 -28/13 4/5 -15/7 5/6 -2/1 1/1 1/0 -15/8 1/2 1/0 -28/15 0/1 -13/7 1/2 1/1 -11/6 0/1 1/0 -42/23 0/1 -31/17 0/1 1/4 -20/11 0/1 1/2 -9/5 1/2 -34/19 3/5 5/8 -59/33 13/20 2/3 -84/47 2/3 -25/14 2/3 7/10 -41/23 2/3 3/4 -16/9 3/4 4/5 -7/4 1/1 -26/15 5/4 4/3 -19/11 1/1 3/2 -31/18 6/5 5/4 -105/61 5/4 -74/43 5/4 14/11 -43/25 5/4 4/3 -12/7 5/4 3/2 -41/24 4/3 3/2 -70/41 4/3 -29/17 7/5 3/2 -17/10 3/2 8/5 -39/23 3/2 -61/36 5/3 7/4 -22/13 3/2 2/1 -27/16 3/2 7/4 -5/3 2/1 1/0 -23/14 3/1 1/0 -64/39 7/2 4/1 -105/64 4/1 -41/25 4/1 1/0 -18/11 7/2 1/0 -31/19 4/1 1/0 -13/8 7/1 1/0 -21/13 1/0 -8/5 -3/1 1/0 -27/17 -3/2 -19/12 -1/1 -3/4 -30/19 -1/2 1/0 -41/26 -1/2 0/1 -52/33 -1/4 0/1 -63/40 0/1 -11/7 0/1 1/0 -25/16 -2/3 -1/2 -14/9 0/1 -17/11 0/1 1/0 -20/13 0/1 1/2 -3/2 1/2 1/0 -22/15 0/1 1/2 -19/13 1/2 1/1 -16/11 0/1 1/0 -29/20 3/4 1/1 -42/29 1/1 -13/9 1/1 3/2 -23/16 1/1 1/0 -10/7 2/1 1/0 -47/33 7/4 2/1 -84/59 2/1 -37/26 2/1 9/4 -27/19 5/2 -44/31 23/8 3/1 -17/12 7/2 4/1 -7/5 1/0 -25/18 -9/2 -4/1 -43/31 -4/1 1/0 -18/13 -7/2 1/0 -29/21 -3/1 -5/2 -11/8 -2/1 1/0 -26/19 -2/1 -7/4 -41/30 -2/1 -3/2 -56/41 -2/1 -15/11 -3/2 -19/14 -9/8 -1/1 -42/31 -1/1 -23/17 -1/1 -9/10 -4/3 -1/2 0/1 -21/16 0/1 -17/13 0/1 1/8 -13/10 1/4 1/3 -35/27 1/2 -57/44 1/2 1/0 -22/17 0/1 1/2 -9/7 1/2 -41/32 1/2 2/3 -32/25 2/3 3/4 -23/18 3/4 1/1 -14/11 1/1 -19/15 1/1 3/2 -5/4 2/1 1/0 -21/17 1/0 -16/13 -6/1 1/0 -11/9 -2/1 1/0 -17/14 -3/2 -4/3 -40/33 -13/12 -1/1 -63/52 -1/1 -23/19 -1/1 -5/6 -6/5 -1/2 1/0 -19/16 -1/1 1/0 -13/11 -1/1 -1/2 -20/17 -1/2 0/1 -7/6 0/1 -22/19 0/1 1/2 -15/13 1/2 -8/7 -1/1 1/0 -9/8 1/2 1/0 -10/9 2/1 1/0 -1/1 0/1 1/0 0/1 0/1 1/1 0/1 1/4 9/8 1/4 1/2 8/7 1/5 1/4 7/6 0/1 13/11 1/6 1/5 6/5 1/6 1/4 23/19 5/26 1/5 17/14 4/19 3/14 11/9 2/9 1/4 16/13 6/25 1/4 21/17 1/4 5/4 1/4 2/7 19/15 3/10 1/3 14/11 1/3 23/18 1/3 3/8 9/7 1/2 22/17 0/1 1/2 13/10 1/1 1/0 17/13 -1/4 0/1 21/16 0/1 4/3 0/1 1/6 19/14 1/5 9/44 15/11 3/14 56/41 2/9 41/30 3/14 2/9 26/19 7/32 2/9 11/8 2/9 1/4 18/13 7/30 1/4 7/5 1/4 24/17 1/4 9/34 41/29 1/4 4/15 17/12 4/15 7/26 61/43 31/114 3/11 105/74 3/11 44/31 3/11 23/84 27/19 5/18 37/26 9/32 2/7 10/7 1/4 2/7 33/23 3/10 23/16 1/4 1/3 36/25 1/4 3/10 13/9 3/10 1/3 16/11 0/1 1/4 3/2 1/4 1/2 17/11 0/1 1/4 14/9 0/1 25/16 1/6 2/11 11/7 0/1 1/4 19/12 3/16 1/5 27/17 3/14 35/22 2/9 8/5 3/13 1/4 21/13 1/4 13/8 1/4 7/27 18/11 1/4 7/26 41/25 1/4 4/15 105/64 4/15 64/39 4/15 7/26 23/14 1/4 3/11 5/3 1/4 2/7 27/16 7/24 3/10 22/13 2/7 3/10 17/10 8/27 3/10 29/17 3/10 7/23 70/41 4/13 41/24 3/10 4/13 12/7 3/10 5/16 19/11 3/10 1/3 7/4 1/3 23/13 1/3 5/14 39/22 5/14 3/8 16/9 4/11 3/8 41/23 3/8 2/5 25/14 7/18 2/5 34/19 5/12 3/7 9/5 1/2 20/11 0/1 1/2 11/6 0/1 1/4 13/7 1/3 1/2 28/15 0/1 15/8 1/4 1/2 2/1 1/4 1/3 15/7 5/14 28/13 4/11 13/6 7/19 3/8 11/5 3/8 2/5 42/19 2/5 31/14 2/5 5/12 20/9 2/5 1/2 9/4 3/8 1/2 34/15 3/8 5/13 59/26 15/38 2/5 84/37 2/5 25/11 2/5 5/12 41/18 2/5 1/2 16/7 2/5 5/12 7/3 1/2 26/11 2/3 3/4 19/8 3/4 1/1 31/13 0/1 1/0 105/44 0/1 74/31 0/1 1/4 43/18 0/1 1/2 12/5 1/2 1/0 41/17 0/1 1/0 70/29 0/1 29/12 -1/1 1/0 17/7 0/1 1/4 39/16 1/4 1/2 61/25 1/3 1/2 22/9 0/1 1/2 27/11 1/2 5/2 0/1 1/4 23/9 1/3 1/2 64/25 2/5 1/2 105/41 1/2 41/16 0/1 1/2 18/7 1/4 1/2 31/12 1/4 2/7 13/5 3/10 1/3 21/8 1/3 8/3 1/3 3/8 27/10 1/4 1/2 19/7 1/3 5/14 30/11 5/14 3/8 41/15 4/11 3/8 52/19 10/27 3/8 63/23 3/8 11/4 3/8 2/5 25/9 3/8 2/5 14/5 2/5 17/6 4/9 1/2 20/7 2/5 1/2 3/1 1/2 22/7 1/2 2/3 19/6 3/4 1/1 16/5 2/3 3/4 29/9 5/6 1/1 42/13 1/1 13/4 1/1 1/0 23/7 1/1 3/2 10/3 0/1 1/0 47/14 -1/4 0/1 84/25 0/1 37/11 0/1 1/4 27/8 1/2 1/0 44/13 1/1 1/0 17/5 0/1 1/0 7/2 0/1 25/7 0/1 1/4 43/12 0/1 1/6 18/5 1/6 1/4 29/8 1/4 3/11 11/3 0/1 1/4 26/7 1/4 4/15 41/11 1/4 2/7 56/15 2/7 15/4 1/4 3/10 19/5 7/22 1/3 42/11 1/3 23/6 1/3 11/32 4/1 2/5 1/2 21/5 1/2 17/4 1/2 8/15 13/3 1/2 3/5 35/8 2/3 57/13 1/2 22/5 1/2 2/3 9/2 1/2 3/4 41/9 2/3 3/4 32/7 3/4 4/5 23/5 1/2 1/1 14/3 1/1 19/4 1/1 1/0 5/1 0/1 1/0 21/4 0/1 16/3 0/1 1/8 11/2 0/1 1/4 17/3 0/1 1/4 40/7 1/5 1/4 63/11 1/4 23/4 1/4 1/3 6/1 1/4 1/2 19/3 1/3 5/14 13/2 1/3 3/8 20/3 2/5 1/2 7/1 1/2 22/3 1/2 2/3 15/2 1/2 3/4 8/1 1/1 1/0 9/1 1/2 10/1 0/1 1/0 1/0 0/1 1/2 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,-2,8,-3) Matrix(43,378,24,211) -> Matrix(3,-2,8,-5) Matrix(43,336,-16,-125) -> Matrix(5,-2,8,-3) Matrix(83,546,-64,-421) -> Matrix(3,-2,8,-5) Matrix(85,546,-26,-167) -> Matrix(3,-2,8,-5) Matrix(167,966,116,671) -> Matrix(1,-2,4,-7) Matrix(251,1428,-74,-421) -> Matrix(1,0,4,1) Matrix(83,462,30,167) -> Matrix(3,-2,8,-5) Matrix(85,462,62,337) -> Matrix(1,2,4,9) Matrix(127,672,24,127) -> Matrix(1,0,12,1) Matrix(41,210,8,41) -> Matrix(1,0,-4,1) Matrix(43,210,26,127) -> Matrix(9,-2,32,-7) Matrix(125,588,98,461) -> Matrix(13,-4,36,-11) Matrix(127,588,100,463) -> Matrix(11,-4,36,-13) Matrix(211,966,-64,-293) -> Matrix(11,-4,36,-13) Matrix(85,378,38,169) -> Matrix(1,0,0,1) Matrix(125,546,-106,-463) -> Matrix(5,-2,-12,5) Matrix(167,714,98,419) -> Matrix(35,-16,116,-53) Matrix(169,714,40,169) -> Matrix(33,-16,64,-31) Matrix(41,168,10,41) -> Matrix(7,-4,16,-9) Matrix(43,168,-32,-125) -> Matrix(3,-2,-4,3) Matrix(211,798,78,295) -> Matrix(1,-2,4,-7) Matrix(337,1260,180,673) -> Matrix(1,-2,4,-7) Matrix(1385,5166,574,2141) -> Matrix(1,-2,0,1) Matrix(463,1722,260,967) -> Matrix(3,-8,8,-21) Matrix(125,462,102,377) -> Matrix(1,2,4,9) Matrix(209,756,-128,-463) -> Matrix(1,4,0,1) 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(3,-2,8,-5) Matrix(1847,6258,322,1091) -> Matrix(9,-2,32,-7) Matrix(2059,6972,360,1219) -> Matrix(7,-2,32,-9) Matrix(211,714,112,379) -> Matrix(1,0,0,1) Matrix(337,1134,200,673) -> Matrix(1,-2,4,-7) Matrix(251,840,-176,-589) -> Matrix(7,-2,4,-1) Matrix(127,420,-114,-377) -> Matrix(7,-2,4,-1) Matrix(295,966,244,799) -> Matrix(5,-2,28,-11) Matrix(209,672,-144,-463) -> Matrix(5,-2,8,-3) Matrix(211,672,-92,-293) -> Matrix(9,-4,16,-7) Matrix(251,714,-148,-421) -> Matrix(5,-4,4,-3) Matrix(209,588,134,377) -> Matrix(3,-2,20,-13) Matrix(211,588,136,379) -> Matrix(3,-2,8,-5) Matrix(167,462,30,83) -> Matrix(3,-2,8,-5) Matrix(293,798,-170,-463) -> Matrix(9,-8,8,-7) Matrix(295,798,78,211) -> Matrix(1,-2,4,-7) Matrix(1091,2940,-842,-2269) -> Matrix(1,0,0,1) Matrix(127,336,48,127) -> Matrix(7,-6,20,-17) Matrix(209,546,80,209) -> Matrix(5,-6,16,-19) Matrix(293,756,-212,-547) -> Matrix(1,-4,0,1) Matrix(589,1512,164,421) -> Matrix(1,0,4,1) Matrix(3361,8610,1312,3361) -> Matrix(1,0,0,1) Matrix(5249,13440,2050,5249) -> Matrix(7,-4,16,-9) Matrix(1723,4410,706,1807) -> Matrix(3,-2,8,-5) Matrix(83,210,66,167) -> Matrix(1,-2,4,-7) Matrix(461,1134,324,797) -> Matrix(9,-2,32,-7) Matrix(377,924,-326,-799) -> Matrix(1,0,0,1) 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(13,-4,36,-11) Matrix(2141,5166,574,1385) -> Matrix(9,-2,32,-7) Matrix(715,1722,262,631) -> Matrix(13,-4,36,-11) Matrix(335,798,-212,-505) -> Matrix(1,0,-4,1) Matrix(125,294,-54,-127) -> Matrix(9,-4,16,-7) Matrix(1427,3276,-842,-1933) -> Matrix(5,-4,4,-3) Matrix(755,1722,552,1259) -> Matrix(5,-4,24,-19) Matrix(923,2100,258,587) -> Matrix(3,-2,20,-13) Matrix(1259,2856,-704,-1597) -> Matrix(23,-16,36,-25) Matrix(167,378,148,335) -> Matrix(3,-2,8,-5) Matrix(169,378,38,85) -> Matrix(1,0,0,1) Matrix(379,840,-208,-461) -> Matrix(3,-2,8,-5) Matrix(211,462,58,127) -> Matrix(3,-2,8,-5) Matrix(797,1722,330,713) -> Matrix(5,-4,4,-3) Matrix(587,1260,430,923) -> Matrix(27,-22,124,-101) Matrix(335,714,236,503) -> Matrix(23,-20,84,-73) Matrix(379,714,112,211) -> Matrix(1,0,0,1) Matrix(673,1260,180,337) -> Matrix(1,-2,4,-7) Matrix(925,1722,542,1009) -> Matrix(11,-4,36,-13) Matrix(295,546,114,211) -> Matrix(1,-2,4,-7) Matrix(965,1764,436,797) -> Matrix(5,2,12,5) Matrix(967,1764,438,799) -> Matrix(11,-2,28,-5) Matrix(209,378,162,293) -> Matrix(1,0,0,1) Matrix(211,378,24,43) -> Matrix(3,-2,8,-5) Matrix(3947,7056,1738,3107) -> Matrix(55,-36,136,-89) Matrix(3949,7056,1740,3109) -> Matrix(65,-44,164,-111) Matrix(965,1722,682,1217) -> Matrix(19,-14,72,-53) Matrix(967,1722,260,463) -> Matrix(11,-8,40,-29) Matrix(167,294,-96,-169) -> Matrix(9,-8,8,-7) Matrix(461,798,-316,-547) -> Matrix(3,-4,4,-5) Matrix(1805,3108,658,1133) -> Matrix(23,-28,60,-73) Matrix(5881,10122,2148,3697) -> Matrix(73,-92,196,-247) Matrix(2563,4410,562,967) -> Matrix(17,-22,24,-31) Matrix(587,1008,244,419) -> Matrix(3,-4,4,-5) Matrix(589,1008,246,421) -> Matrix(3,-4,4,-5) Matrix(3025,5166,2214,3781) -> Matrix(13,-18,60,-83) Matrix(1009,1722,542,925) -> Matrix(3,-4,4,-5) Matrix(419,714,98,167) -> Matrix(11,-16,20,-29) Matrix(2603,4410,1586,2687) -> Matrix(15,-26,56,-97) Matrix(1093,1848,-844,-1427) -> Matrix(1,-2,4,-7) Matrix(673,1134,200,337) -> Matrix(1,-2,4,-7) Matrix(127,210,26,43) -> Matrix(1,-2,0,1) Matrix(1049,1722,332,545) -> Matrix(3,-10,4,-13) Matrix(8191,13440,4992,8191) -> Matrix(15,-56,56,-209) Matrix(5249,8610,3200,5249) -> Matrix(1,-8,4,-31) Matrix(1051,1722,744,1219) -> Matrix(1,-8,4,-31) Matrix(335,546,154,251) -> Matrix(3,-14,8,-37) Matrix(337,546,208,337) -> Matrix(1,-14,4,-55) Matrix(209,336,130,209) -> Matrix(1,6,4,25) Matrix(211,336,-184,-293) -> Matrix(1,2,0,1) Matrix(503,798,370,587) -> Matrix(5,6,24,29) Matrix(1091,1722,638,1007) -> Matrix(5,4,16,13) Matrix(293,462,26,41) -> Matrix(1,0,4,1) Matrix(6425,10122,2692,4241) -> Matrix(1,0,8,1) Matrix(1975,3108,828,1303) -> Matrix(1,0,0,1) Matrix(295,462,242,379) -> Matrix(1,2,4,9) Matrix(377,588,134,209) -> Matrix(5,2,12,5) Matrix(379,588,136,211) -> Matrix(3,-2,8,-5) Matrix(83,126,-56,-85) -> Matrix(1,0,0,1) Matrix(1177,1722,460,673) -> Matrix(3,-2,8,-5) Matrix(1217,1764,376,545) -> Matrix(5,-4,4,-3) Matrix(1219,1764,378,547) -> Matrix(7,-8,8,-9) Matrix(379,546,-320,-461) -> Matrix(1,-2,0,1) Matrix(673,966,-526,-755) -> Matrix(3,-4,4,-5) Matrix(4955,7056,1474,2099) -> Matrix(1,-2,8,-15) Matrix(4957,7056,1476,2101) -> Matrix(1,-2,-8,17) Matrix(797,1134,324,461) -> Matrix(1,-2,0,1) Matrix(503,714,236,335) -> Matrix(7,-20,20,-57) Matrix(1007,1428,-830,-1177) -> Matrix(5,-16,-4,13) Matrix(209,294,-150,-211) -> Matrix(1,-8,0,1) Matrix(1513,2100,848,1177) -> Matrix(3,10,8,27) Matrix(1091,1512,666,923) -> Matrix(1,0,4,1) Matrix(335,462,182,251) -> Matrix(1,2,4,9) Matrix(337,462,62,85) -> Matrix(1,2,4,9) Matrix(1259,1722,552,755) -> Matrix(3,4,8,11) Matrix(3781,5166,2214,3025) -> Matrix(11,18,36,59) Matrix(923,1260,430,587) -> Matrix(13,22,36,61) Matrix(587,798,370,503) -> Matrix(5,6,24,29) Matrix(1301,1764,340,461) -> Matrix(19,20,56,59) Matrix(1303,1764,342,463) -> Matrix(17,16,52,49) Matrix(127,168,96,127) -> Matrix(1,0,8,1) 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(3,-2,8,-5) Matrix(461,588,98,125) -> Matrix(5,-4,4,-3) Matrix(463,588,100,127) -> Matrix(3,-4,4,-5) Matrix(167,210,66,83) -> Matrix(1,-2,4,-7) Matrix(169,210,136,169) -> Matrix(1,-4,4,-15) Matrix(545,672,442,545) -> Matrix(1,12,4,49) Matrix(377,462,102,125) -> Matrix(1,2,4,9) Matrix(379,462,242,295) -> Matrix(1,2,4,9) Matrix(5753,6972,4054,4913) -> Matrix(59,62,216,227) Matrix(5167,6258,3642,4411) -> Matrix(49,46,180,169) Matrix(209,252,34,41) -> Matrix(1,0,4,1) Matrix(211,252,36,43) -> Matrix(1,0,4,1) Matrix(251,294,-216,-253) -> Matrix(1,0,4,1) Matrix(335,378,148,167) -> Matrix(3,-2,8,-5) Matrix(421,462,154,169) -> Matrix(3,4,8,11) Matrix(1,0,2,1) -> Matrix(1,0,4,1) Matrix(337,-378,74,-83) -> Matrix(5,-2,8,-3) Matrix(293,-336,184,-211) -> Matrix(7,-2,32,-9) Matrix(463,-546,106,-125) -> Matrix(13,-2,20,-3) Matrix(461,-546,320,-379) -> Matrix(9,-2,32,-7) Matrix(1177,-1428,830,-1007) -> Matrix(77,-16,284,-59) Matrix(755,-966,526,-673) -> Matrix(11,-4,36,-13) Matrix(421,-546,64,-83) -> Matrix(3,-2,8,-5) Matrix(125,-168,32,-43) -> Matrix(11,-2,28,-5) Matrix(547,-756,212,-293) -> Matrix(17,-4,64,-15) Matrix(211,-294,150,-209) -> Matrix(33,-8,128,-31) Matrix(589,-840,176,-251) -> Matrix(7,-2,4,-1) Matrix(293,-420,30,-43) -> Matrix(7,-2,4,-1) Matrix(463,-672,144,-209) -> Matrix(5,-2,8,-3) Matrix(461,-672,260,-379) -> Matrix(13,-4,36,-11) Matrix(463,-714,190,-293) -> Matrix(1,0,0,1) Matrix(505,-798,212,-335) -> Matrix(1,0,-4,1) Matrix(1849,-2940,422,-671) -> Matrix(19,-4,24,-5) Matrix(463,-756,128,-209) -> Matrix(15,-4,64,-17) Matrix(547,-924,74,-125) -> Matrix(27,-8,44,-13) Matrix(421,-714,148,-251) -> Matrix(13,-4,36,-11) Matrix(463,-798,170,-293) -> Matrix(25,-8,72,-23) Matrix(169,-294,96,-167) -> Matrix(25,-8,72,-23) Matrix(1849,-3276,758,-1343) -> Matrix(11,-4,36,-13) Matrix(1597,-2856,704,-1259) -> Matrix(39,-16,100,-41) Matrix(461,-840,208,-379) -> Matrix(3,-2,8,-5) Matrix(127,-294,54,-125) -> Matrix(9,-4,16,-7) Matrix(337,-798,106,-251) -> Matrix(1,0,0,1) Matrix(755,-1848,172,-421) -> Matrix(5,-2,8,-3) Matrix(125,-336,16,-43) -> Matrix(5,-2,8,-3) Matrix(43,-126,14,-41) -> Matrix(9,-4,16,-7) Matrix(167,-546,26,-85) -> Matrix(3,-2,8,-5) Matrix(293,-966,64,-211) -> Matrix(3,-4,4,-5) 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(9,-4,16,-7) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 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. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 576 Minimal number of generators: 97 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/1 -6/1 -9/2 -7/2 -3/1 -7/3 -9/5 -7/4 -3/2 -7/5 -15/11 -7/6 0/1 1/1 7/6 21/17 21/16 15/11 7/5 3/2 21/13 7/4 9/5 2/1 42/19 7/3 5/2 105/41 21/8 63/23 3/1 7/2 11/3 19/5 42/11 4/1 21/5 13/3 9/2 5/1 21/4 11/2 17/3 63/11 6/1 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 1/4 1/3 -7/1 1/2 -13/2 3/4 1/1 -6/1 1/2 1/0 -11/2 0/1 1/0 -16/3 -1/4 0/1 -21/4 0/1 -5/1 0/1 1/4 -9/2 3/8 1/2 -22/5 2/5 1/2 -13/3 3/7 1/2 -4/1 1/2 2/3 -19/5 1/1 7/6 -15/4 3/2 1/0 -11/3 0/1 1/0 -7/2 0/1 -17/5 0/1 1/4 -10/3 0/1 1/4 -3/1 1/2 -11/4 2/3 3/4 -19/7 5/6 1/1 -27/10 1/2 1/0 -8/3 3/4 1/1 -21/8 1/1 -13/5 1/1 3/2 -18/7 1/2 1/0 -41/16 0/1 1/2 -23/9 1/2 1/1 -5/2 0/1 1/0 -22/9 0/1 1/2 -17/7 0/1 1/0 -29/12 1/5 1/4 -12/5 1/4 1/2 -7/3 1/2 -9/4 1/2 3/4 -20/9 1/2 2/3 -11/5 2/3 3/4 -2/1 1/1 1/0 -11/6 0/1 1/0 -42/23 0/1 -31/17 0/1 1/4 -20/11 0/1 1/2 -9/5 1/2 -7/4 1/1 -19/11 1/1 3/2 -31/18 6/5 5/4 -43/25 5/4 4/3 -12/7 5/4 3/2 -5/3 2/1 1/0 -8/5 -3/1 1/0 -27/17 -3/2 -19/12 -1/1 -3/4 -11/7 0/1 1/0 -3/2 1/2 1/0 -13/9 1/1 3/2 -10/7 2/1 1/0 -7/5 1/0 -11/8 -2/1 1/0 -26/19 -2/1 -7/4 -15/11 -3/2 -19/14 -9/8 -1/1 -42/31 -1/1 -23/17 -1/1 -9/10 -4/3 -1/2 0/1 -21/16 0/1 -17/13 0/1 1/8 -13/10 1/4 1/3 -22/17 0/1 1/2 -9/7 1/2 -5/4 2/1 1/0 -11/9 -2/1 1/0 -6/5 -1/2 1/0 -13/11 -1/1 -1/2 -20/17 -1/2 0/1 -7/6 0/1 -15/13 1/2 -8/7 -1/1 1/0 -1/1 0/1 1/0 0/1 0/1 1/1 0/1 1/4 9/8 1/4 1/2 8/7 1/5 1/4 7/6 0/1 13/11 1/6 1/5 6/5 1/6 1/4 11/9 2/9 1/4 16/13 6/25 1/4 21/17 1/4 5/4 1/4 2/7 19/15 3/10 1/3 14/11 1/3 9/7 1/2 22/17 0/1 1/2 13/10 1/1 1/0 17/13 -1/4 0/1 21/16 0/1 4/3 0/1 1/6 19/14 1/5 9/44 15/11 3/14 56/41 2/9 41/30 3/14 2/9 26/19 7/32 2/9 11/8 2/9 1/4 7/5 1/4 10/7 1/4 2/7 23/16 1/4 1/3 36/25 1/4 3/10 13/9 3/10 1/3 3/2 1/4 1/2 17/11 0/1 1/4 14/9 0/1 11/7 0/1 1/4 19/12 3/16 1/5 27/17 3/14 35/22 2/9 8/5 3/13 1/4 21/13 1/4 13/8 1/4 7/27 5/3 1/4 2/7 12/7 3/10 5/16 19/11 3/10 1/3 7/4 1/3 23/13 1/3 5/14 16/9 4/11 3/8 9/5 1/2 20/11 0/1 1/2 11/6 0/1 1/4 13/7 1/3 1/2 15/8 1/4 1/2 2/1 1/4 1/3 11/5 3/8 2/5 42/19 2/5 31/14 2/5 5/12 20/9 2/5 1/2 9/4 3/8 1/2 7/3 1/2 12/5 1/2 1/0 41/17 0/1 1/0 29/12 -1/1 1/0 17/7 0/1 1/4 39/16 1/4 1/2 22/9 0/1 1/2 27/11 1/2 5/2 0/1 1/4 23/9 1/3 1/2 64/25 2/5 1/2 105/41 1/2 41/16 0/1 1/2 18/7 1/4 1/2 13/5 3/10 1/3 21/8 1/3 8/3 1/3 3/8 27/10 1/4 1/2 19/7 1/3 5/14 30/11 5/14 3/8 41/15 4/11 3/8 52/19 10/27 3/8 63/23 3/8 11/4 3/8 2/5 3/1 1/2 10/3 0/1 1/0 27/8 1/2 1/0 44/13 1/1 1/0 17/5 0/1 1/0 7/2 0/1 25/7 0/1 1/4 43/12 0/1 1/6 18/5 1/6 1/4 11/3 0/1 1/4 15/4 1/4 3/10 19/5 7/22 1/3 42/11 1/3 23/6 1/3 11/32 4/1 2/5 1/2 21/5 1/2 17/4 1/2 8/15 13/3 1/2 3/5 35/8 2/3 57/13 1/2 22/5 1/2 2/3 9/2 1/2 3/4 5/1 0/1 1/0 21/4 0/1 16/3 0/1 1/8 11/2 0/1 1/4 17/3 0/1 1/4 40/7 1/5 1/4 63/11 1/4 23/4 1/4 1/3 6/1 1/4 1/2 13/2 1/3 3/8 7/1 1/2 8/1 1/1 1/0 1/0 0/1 1/2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(22,189,-17,-146) (-8/1,1/0) -> (-13/10,-22/17) Hyperbolic Matrix(20,147,-3,-22) (-8/1,-7/1) -> (-7/1,-13/2) Parabolic Matrix(62,399,-23,-148) (-13/2,-6/1) -> (-27/10,-8/3) Hyperbolic Matrix(64,357,19,106) (-6/1,-11/2) -> (10/3,27/8) 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(22,105,-13,-62) (-5/1,-9/2) -> (-12/7,-5/3) 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(64,273,15,64) (-13/3,-4/1) -> (17/4,13/3) 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(62,231,-51,-190) (-15/4,-11/3) -> (-11/9,-6/5) Hyperbolic Matrix(64,231,41,148) (-11/3,-7/2) -> (14/9,11/7) Hyperbolic Matrix(104,357,67,230) (-7/2,-17/5) -> (17/11,14/9) Hyperbolic Matrix(106,357,19,64) (-17/5,-10/3) -> (11/2,17/3) Hyperbolic Matrix(20,63,-7,-22) (-10/3,-3/1) -> (-3/1,-11/4) Parabolic 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(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(106,273,-73,-188) (-13/5,-18/7) -> (-3/2,-13/9) Hyperbolic Matrix(589,1512,164,421) (-18/7,-41/16) -> (43/12,18/5) Hyperbolic Matrix(944,2415,369,944) (-41/16,-23/9) -> (23/9,64/25) Hyperbolic Matrix(83,210,66,167) (-23/9,-5/2) -> (5/4,19/15) Hyperbolic Matrix(316,777,231,568) (-5/2,-22/9) -> (41/30,26/19) Hyperbolic Matrix(526,1281,147,358) (-22/9,-17/7) -> (25/7,43/12) Hyperbolic Matrix(295,714,226,547) (-17/7,-29/12) -> (13/10,17/13) Hyperbolic Matrix(148,357,131,316) (-29/12,-12/5) -> (9/8,8/7) Hyperbolic Matrix(62,147,-27,-64) (-12/5,-7/3) -> (-7/3,-9/4) Parabolic 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(106,231,-67,-146) (-11/5,-2/1) -> (-19/12,-11/7) Hyperbolic Matrix(148,273,103,190) (-2/1,-11/6) -> (10/7,23/16) 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(106,189,83,148) (-9/5,-7/4) -> (14/11,9/7) Hyperbolic Matrix(230,399,181,314) (-7/4,-19/11) -> (19/15,14/11) Hyperbolic Matrix(2038,3507,745,1282) (-31/18,-43/25) -> (41/15,52/19) Hyperbolic Matrix(587,1008,244,419) (-43/25,-12/7) -> (12/5,41/17) Hyperbolic Matrix(64,105,39,64) (-5/3,-8/5) -> (13/8,5/3) 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(148,231,41,64) (-11/7,-3/2) -> (18/5,11/3) Hyperbolic Matrix(190,273,103,148) (-13/9,-10/7) -> (11/6,13/7) Hyperbolic Matrix(104,147,-75,-106) (-10/7,-7/5) -> (-7/5,-11/8) Parabolic Matrix(337,462,62,85) (-11/8,-26/19) -> (16/3,11/2) Hyperbolic Matrix(568,777,231,316) (-26/19,-15/11) -> (27/11,5/2) 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(148,189,83,106) (-9/7,-5/4) -> (16/9,9/5) Hyperbolic Matrix(188,231,153,188) (-5/4,-11/9) -> (11/9,16/13) Hyperbolic Matrix(230,273,123,146) (-6/5,-13/11) -> (13/7,15/8) Hyperbolic Matrix(1198,1407,877,1030) (-20/17,-7/6) -> (56/41,41/30) Hyperbolic Matrix(818,945,599,692) (-7/6,-15/13) -> (15/11,56/41) Hyperbolic Matrix(316,357,131,148) (-8/7,-1/1) -> (41/17,29/12) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(358,-399,131,-146) (1/1,9/8) -> (30/11,41/15) 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(190,-231,51,-62) (6/5,11/9) -> (11/3,15/4) Hyperbolic Matrix(358,-441,289,-356) (16/13,21/17) -> (21/17,5/4) Parabolic Matrix(146,-189,17,-22) (22/17,13/10) -> (8/1,1/0) Hyperbolic Matrix(125,-168,32,-43) (4/3,19/14) -> (23/6,4/1) Hyperbolic Matrix(106,-147,75,-104) (11/8,7/5) -> (7/5,10/7) Parabolic Matrix(1532,-2205,453,-652) (23/16,36/25) -> (27/8,44/13) Hyperbolic Matrix(188,-273,73,-106) (13/9,3/2) -> (18/7,13/5) Hyperbolic Matrix(463,-714,190,-293) (3/2,17/11) -> (17/7,39/16) Hyperbolic Matrix(146,-231,67,-106) (11/7,19/12) -> (2/1,11/5) Hyperbolic Matrix(1849,-2940,422,-671) (27/17,35/22) -> (35/8,57/13) Hyperbolic Matrix(274,-441,169,-272) (8/5,21/13) -> (21/13,13/8) Parabolic Matrix(62,-105,13,-22) (5/3,12/7) -> (9/2,5/1) 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(272,-483,107,-190) (23/13,16/9) -> (5/2,23/9) Hyperbolic Matrix(461,-840,208,-379) (20/11,11/6) -> (31/14,20/9) Hyperbolic Matrix(190,-357,33,-62) (15/8,2/1) -> (23/4,6/1) Hyperbolic Matrix(64,-147,27,-62) (9/4,7/3) -> (7/3,12/5) Parabolic Matrix(818,-1995,319,-778) (39/16,22/9) -> (41/16,18/7) Hyperbolic Matrix(755,-1848,172,-421) (22/9,27/11) -> (57/13,22/5) Hyperbolic Matrix(4306,-11025,1681,-4304) (64/25,105/41) -> (105/41,41/16) Parabolic Matrix(148,-399,23,-62) (8/3,27/10) -> (6/1,13/2) Hyperbolic Matrix(1450,-3969,529,-1448) (52/19,63/23) -> (63/23,11/4) Parabolic Matrix(22,-63,7,-20) (11/4,3/1) -> (3/1,10/3) Parabolic 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(106,-441,25,-104) (4/1,21/5) -> (21/5,17/4) Parabolic Matrix(694,-3969,121,-692) (40/7,63/11) -> (63/11,23/4) Parabolic Matrix(22,-147,3,-20) (13/2,7/1) -> (7/1,8/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(22,189,-17,-146) -> Matrix(1,0,0,1) Matrix(20,147,-3,-22) -> Matrix(5,-2,8,-3) Matrix(62,399,-23,-148) -> Matrix(1,0,0,1) Matrix(64,357,19,106) -> Matrix(1,0,0,1) Matrix(85,462,62,337) -> Matrix(1,2,4,9) Matrix(127,672,24,127) -> Matrix(1,0,12,1) Matrix(41,210,8,41) -> Matrix(1,0,-4,1) Matrix(22,105,-13,-62) -> Matrix(7,-2,4,-1) Matrix(85,378,38,169) -> Matrix(1,0,0,1) Matrix(125,546,-106,-463) -> Matrix(5,-2,-12,5) Matrix(64,273,15,64) -> Matrix(13,-6,24,-11) Matrix(43,168,-32,-125) -> Matrix(3,-2,-4,3) Matrix(211,798,78,295) -> Matrix(1,-2,4,-7) Matrix(62,231,-51,-190) -> Matrix(1,-2,0,1) Matrix(64,231,41,148) -> Matrix(1,0,4,1) Matrix(104,357,67,230) -> Matrix(1,0,0,1) Matrix(106,357,19,64) -> Matrix(1,0,0,1) Matrix(20,63,-7,-22) -> Matrix(5,-2,8,-3) Matrix(293,798,-170,-463) -> Matrix(9,-8,8,-7) Matrix(295,798,78,211) -> Matrix(1,-2,4,-7) Matrix(127,336,48,127) -> Matrix(7,-6,20,-17) Matrix(209,546,80,209) -> Matrix(5,-6,16,-19) Matrix(106,273,-73,-188) -> Matrix(1,0,0,1) Matrix(589,1512,164,421) -> Matrix(1,0,4,1) Matrix(944,2415,369,944) -> Matrix(3,-2,8,-5) Matrix(83,210,66,167) -> Matrix(1,-2,4,-7) Matrix(316,777,231,568) -> Matrix(7,-2,32,-9) Matrix(526,1281,147,358) -> Matrix(1,0,4,1) Matrix(295,714,226,547) -> Matrix(1,0,-4,1) Matrix(148,357,131,316) -> Matrix(1,0,0,1) Matrix(62,147,-27,-64) -> Matrix(5,-2,8,-3) Matrix(169,378,38,85) -> Matrix(1,0,0,1) Matrix(379,840,-208,-461) -> Matrix(3,-2,8,-5) Matrix(106,231,-67,-146) -> Matrix(3,-2,-4,3) Matrix(148,273,103,190) -> Matrix(1,-2,4,-7) Matrix(965,1764,436,797) -> Matrix(5,2,12,5) Matrix(967,1764,438,799) -> Matrix(11,-2,28,-5) Matrix(209,378,162,293) -> Matrix(1,0,0,1) Matrix(106,189,83,148) -> Matrix(3,-2,8,-5) Matrix(230,399,181,314) -> Matrix(5,-6,16,-19) Matrix(2038,3507,745,1282) -> Matrix(25,-32,68,-87) Matrix(587,1008,244,419) -> Matrix(3,-4,4,-5) Matrix(64,105,39,64) -> Matrix(1,-4,4,-15) Matrix(211,336,-184,-293) -> Matrix(1,2,0,1) Matrix(503,798,370,587) -> Matrix(5,6,24,29) Matrix(148,231,41,64) -> Matrix(1,0,4,1) Matrix(190,273,103,148) -> Matrix(1,-2,4,-7) Matrix(104,147,-75,-106) -> Matrix(1,-4,0,1) Matrix(337,462,62,85) -> Matrix(1,2,4,9) Matrix(568,777,231,316) -> Matrix(1,2,0,1) Matrix(587,798,370,503) -> Matrix(5,6,24,29) Matrix(1301,1764,340,461) -> Matrix(19,20,56,59) Matrix(1303,1764,342,463) -> Matrix(17,16,52,49) Matrix(127,168,96,127) -> Matrix(1,0,8,1) 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(148,189,83,106) -> Matrix(3,-2,8,-5) Matrix(188,231,153,188) -> Matrix(1,4,4,17) Matrix(230,273,123,146) -> Matrix(1,0,4,1) Matrix(1198,1407,877,1030) -> Matrix(1,2,4,9) Matrix(818,945,599,692) -> Matrix(7,-2,32,-9) Matrix(316,357,131,148) -> Matrix(1,0,0,1) Matrix(1,0,2,1) -> Matrix(1,0,4,1) Matrix(358,-399,131,-146) -> Matrix(13,-4,36,-11) Matrix(293,-336,184,-211) -> Matrix(7,-2,32,-9) Matrix(463,-546,106,-125) -> Matrix(13,-2,20,-3) Matrix(461,-546,320,-379) -> Matrix(9,-2,32,-7) Matrix(190,-231,51,-62) -> Matrix(9,-2,32,-7) Matrix(358,-441,289,-356) -> Matrix(33,-8,128,-31) Matrix(146,-189,17,-22) -> Matrix(1,0,0,1) Matrix(125,-168,32,-43) -> Matrix(11,-2,28,-5) Matrix(106,-147,75,-104) -> Matrix(17,-4,64,-15) Matrix(1532,-2205,453,-652) -> Matrix(7,-2,4,-1) Matrix(188,-273,73,-106) -> Matrix(1,0,0,1) Matrix(463,-714,190,-293) -> Matrix(1,0,0,1) Matrix(146,-231,67,-106) -> Matrix(11,-2,28,-5) Matrix(1849,-2940,422,-671) -> Matrix(19,-4,24,-5) Matrix(274,-441,169,-272) -> Matrix(41,-10,160,-39) Matrix(62,-105,13,-22) -> Matrix(7,-2,4,-1) Matrix(463,-798,170,-293) -> Matrix(25,-8,72,-23) Matrix(169,-294,96,-167) -> Matrix(25,-8,72,-23) Matrix(272,-483,107,-190) -> Matrix(11,-4,36,-13) Matrix(461,-840,208,-379) -> Matrix(3,-2,8,-5) Matrix(190,-357,33,-62) -> Matrix(1,0,0,1) Matrix(64,-147,27,-62) -> Matrix(5,-2,8,-3) Matrix(818,-1995,319,-778) -> Matrix(1,0,0,1) Matrix(755,-1848,172,-421) -> Matrix(5,-2,8,-3) Matrix(4306,-11025,1681,-4304) -> Matrix(5,-2,8,-3) Matrix(148,-399,23,-62) -> Matrix(1,0,0,1) Matrix(1450,-3969,529,-1448) -> Matrix(97,-36,256,-95) Matrix(22,-63,7,-20) -> Matrix(5,-2,8,-3) Matrix(421,-1428,74,-251) -> Matrix(1,0,4,1) Matrix(85,-294,24,-83) -> Matrix(1,0,4,1) Matrix(106,-441,25,-104) -> Matrix(21,-10,40,-19) Matrix(694,-3969,121,-692) -> Matrix(9,-2,32,-7) Matrix(22,-147,3,-20) -> Matrix(5,-2,8,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 16 ----------------------------------------------------------------------- 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 (0/1,1/4) 0 21 8/7 (1/5,1/4) 0 21 7/6 0/1 2 3 13/11 (1/6,1/5) 0 21 6/5 0 7 11/9 (2/9,1/4) 0 21 21/17 1/4 8 1 5/4 (1/4,2/7) 0 21 9/7 1/2 2 7 22/17 (0/1,1/2) 0 21 13/10 (1/1,1/0) 0 21 17/13 (-1/4,0/1) 0 21 21/16 0/1 10 1 4/3 (0/1,1/6) 0 21 19/14 (1/5,9/44) 0 21 15/11 3/14 2 7 26/19 (7/32,2/9) 0 21 11/8 (2/9,1/4) 0 21 7/5 1/4 4 3 10/7 (1/4,2/7) 0 21 13/9 (3/10,1/3) 0 21 3/2 0 7 11/7 (0/1,1/4) 0 21 19/12 (3/16,1/5) 0 21 27/17 3/14 2 7 35/22 2/9 2 3 8/5 (3/13,1/4) 0 21 21/13 1/4 10 1 5/3 (1/4,2/7) 0 21 12/7 0 7 19/11 (3/10,1/3) 0 21 7/4 1/3 4 3 23/13 (1/3,5/14) 0 21 16/9 (4/11,3/8) 0 21 9/5 1/2 2 7 20/11 (0/1,1/2) 0 21 11/6 (0/1,1/4) 0 21 13/7 (1/3,1/2) 0 21 15/8 0 7 2/1 (1/4,1/3) 0 21 11/5 (3/8,2/5) 0 21 42/19 2/5 4 1 31/14 (2/5,5/12) 0 21 20/9 (2/5,1/2) 0 21 9/4 0 7 7/3 1/2 2 3 12/5 0 7 41/17 (0/1,1/0) 0 21 29/12 (-1/1,1/0) 0 21 17/7 (0/1,1/4) 0 21 22/9 (0/1,1/2) 0 21 27/11 1/2 2 7 5/2 (0/1,1/4) 0 21 23/9 (1/3,1/2) 0 21 105/41 1/2 2 1 41/16 (0/1,1/2) 0 21 18/7 0 7 13/5 (3/10,1/3) 0 21 21/8 1/3 6 1 8/3 (1/3,3/8) 0 21 27/10 0 7 19/7 (1/3,5/14) 0 21 30/11 0 7 41/15 (4/11,3/8) 0 21 63/23 3/8 4 1 11/4 (3/8,2/5) 0 21 3/1 1/2 2 7 10/3 (0/1,1/0) 0 21 17/5 (0/1,1/0) 0 21 7/2 0/1 2 3 25/7 (0/1,1/4) 0 21 43/12 (0/1,1/6) 0 21 18/5 0 7 11/3 (0/1,1/4) 0 21 15/4 0 7 19/5 (7/22,1/3) 0 21 42/11 1/3 18 1 23/6 (1/3,11/32) 0 21 4/1 (2/5,1/2) 0 21 21/5 1/2 10 1 13/3 (1/2,3/5) 0 21 35/8 2/3 2 3 57/13 1/2 2 7 22/5 (1/2,2/3) 0 21 9/2 0 7 5/1 (0/1,1/0) 0 21 21/4 0/1 8 1 16/3 (0/1,1/8) 0 21 11/2 (0/1,1/4) 0 21 17/3 (0/1,1/4) 0 21 63/11 1/4 2 1 23/4 (1/4,1/3) 0 21 6/1 0 7 13/2 (1/3,3/8) 0 21 7/1 1/2 2 3 8/1 (1/1,1/0) 0 21 1/0 (0/1,1/2) 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(316,-357,131,-148) (1/1,8/7) -> (41/17,29/12) 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(230,-273,123,-146) (13/11,6/5) -> (13/7,15/8) Glide Reflection Matrix(190,-231,51,-62) (6/5,11/9) -> (11/3,15/4) Hyperbolic Matrix(188,-231,153,-188) (11/9,21/17) -> (11/9,21/17) Reflection Matrix(169,-210,136,-169) (21/17,5/4) -> (21/17,5/4) Reflection Matrix(148,-189,83,-106) (5/4,9/7) -> (16/9,9/5) Glide Reflection Matrix(293,-378,162,-209) (9/7,22/17) -> (9/5,20/11) Glide Reflection Matrix(146,-189,17,-22) (22/17,13/10) -> (8/1,1/0) 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(568,-777,231,-316) (15/11,26/19) -> (27/11,5/2) Glide Reflection Matrix(337,-462,62,-85) (26/19,11/8) -> (16/3,11/2) Glide Reflection Matrix(106,-147,75,-104) (11/8,7/5) -> (7/5,10/7) Parabolic Matrix(190,-273,103,-148) (10/7,13/9) -> (11/6,13/7) Glide Reflection Matrix(188,-273,73,-106) (13/9,3/2) -> (18/7,13/5) Hyperbolic Matrix(148,-231,41,-64) (3/2,11/7) -> (18/5,11/3) Glide Reflection Matrix(146,-231,67,-106) (11/7,19/12) -> (2/1,11/5) 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(64,-105,39,-64) (21/13,5/3) -> (21/13,5/3) Reflection Matrix(62,-105,13,-22) (5/3,12/7) -> (9/2,5/1) 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(272,-483,107,-190) (23/13,16/9) -> (5/2,23/9) Hyperbolic Matrix(461,-840,208,-379) (20/11,11/6) -> (31/14,20/9) Hyperbolic Matrix(190,-357,33,-62) (15/8,2/1) -> (23/4,6/1) Hyperbolic 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(64,-147,27,-62) (9/4,7/3) -> (7/3,12/5) Parabolic Matrix(715,-1722,262,-631) (12/5,41/17) -> (30/11,41/15) Glide Reflection Matrix(526,-1281,147,-358) (17/7,22/9) -> (25/7,43/12) Glide Reflection Matrix(755,-1848,172,-421) (22/9,27/11) -> (57/13,22/5) Hyperbolic Matrix(944,-2415,369,-944) (23/9,105/41) -> (23/9,105/41) 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(148,-399,23,-62) (8/3,27/10) -> (6/1,13/2) Hyperbolic Matrix(295,-798,78,-211) (27/10,19/7) -> (15/4,19/5) Glide Reflection Matrix(944,-2583,345,-944) (41/15,63/23) -> (41/15,63/23) Reflection Matrix(505,-1386,184,-505) (63/23,11/4) -> (63/23,11/4) Reflection Matrix(22,-63,7,-20) (11/4,3/1) -> (3/1,10/3) Parabolic Matrix(106,-357,19,-64) (10/3,17/5) -> (11/2,17/3) Glide Reflection 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(64,-273,15,-64) (21/5,13/3) -> (21/5,13/3) 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(188,-1071,33,-188) (17/3,63/11) -> (17/3,63/11) Reflection Matrix(505,-2898,88,-505) (63/11,23/4) -> (63/11,23/4) Reflection Matrix(22,-147,3,-20) (13/2,7/1) -> (7/1,8/1) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,4,-1) (0/1,1/0) -> (0/1,1/2) Matrix(1,0,2,-1) -> Matrix(1,0,8,-1) (0/1,1/1) -> (0/1,1/4) Matrix(316,-357,131,-148) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(293,-336,184,-211) -> Matrix(7,-2,32,-9) 1/4 Matrix(463,-546,106,-125) -> Matrix(13,-2,20,-3) Matrix(230,-273,123,-146) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(190,-231,51,-62) -> Matrix(9,-2,32,-7) 1/4 Matrix(188,-231,153,-188) -> Matrix(17,-4,72,-17) (11/9,21/17) -> (2/9,1/4) Matrix(169,-210,136,-169) -> Matrix(15,-4,56,-15) (21/17,5/4) -> (1/4,2/7) Matrix(148,-189,83,-106) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(293,-378,162,-209) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(146,-189,17,-22) -> Matrix(1,0,0,1) Matrix(547,-714,226,-295) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(545,-714,416,-545) -> Matrix(-1,0,8,1) (17/13,21/16) -> (-1/4,0/1) Matrix(127,-168,96,-127) -> Matrix(1,0,12,-1) (21/16,4/3) -> (0/1,1/6) Matrix(125,-168,32,-43) -> Matrix(11,-2,28,-5) Matrix(587,-798,370,-503) -> Matrix(29,-6,140,-29) *** -> (1/5,3/14) Matrix(568,-777,231,-316) -> Matrix(9,-2,4,-1) Matrix(337,-462,62,-85) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(106,-147,75,-104) -> Matrix(17,-4,64,-15) 1/4 Matrix(190,-273,103,-148) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(188,-273,73,-106) -> Matrix(1,0,0,1) Matrix(148,-231,41,-64) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(146,-231,67,-106) -> Matrix(11,-2,28,-5) Matrix(1849,-2940,422,-671) -> Matrix(19,-4,24,-5) Matrix(209,-336,130,-209) -> Matrix(25,-6,104,-25) (8/5,21/13) -> (3/13,1/4) Matrix(64,-105,39,-64) -> Matrix(15,-4,56,-15) (21/13,5/3) -> (1/4,2/7) Matrix(62,-105,13,-22) -> Matrix(7,-2,4,-1) Matrix(463,-798,170,-293) -> Matrix(25,-8,72,-23) 1/3 Matrix(169,-294,96,-167) -> Matrix(25,-8,72,-23) 1/3 Matrix(272,-483,107,-190) -> Matrix(11,-4,36,-13) 1/3 Matrix(461,-840,208,-379) -> Matrix(3,-2,8,-5) 1/2 Matrix(190,-357,33,-62) -> Matrix(1,0,0,1) Matrix(419,-924,190,-419) -> Matrix(31,-12,80,-31) (11/5,42/19) -> (3/8,2/5) Matrix(1177,-2604,532,-1177) -> Matrix(49,-20,120,-49) (42/19,31/14) -> (2/5,5/12) Matrix(169,-378,38,-85) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(64,-147,27,-62) -> Matrix(5,-2,8,-3) 1/2 Matrix(715,-1722,262,-631) -> Matrix(3,-4,8,-11) Matrix(526,-1281,147,-358) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(755,-1848,172,-421) -> Matrix(5,-2,8,-3) 1/2 Matrix(944,-2415,369,-944) -> Matrix(5,-2,12,-5) (23/9,105/41) -> (1/3,1/2) Matrix(3361,-8610,1312,-3361) -> Matrix(1,0,4,-1) (105/41,41/16) -> (0/1,1/2) Matrix(589,-1512,164,-421) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(209,-546,80,-209) -> Matrix(19,-6,60,-19) (13/5,21/8) -> (3/10,1/3) Matrix(127,-336,48,-127) -> Matrix(17,-6,48,-17) (21/8,8/3) -> (1/3,3/8) Matrix(148,-399,23,-62) -> Matrix(1,0,0,1) Matrix(295,-798,78,-211) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(944,-2583,345,-944) -> Matrix(65,-24,176,-65) (41/15,63/23) -> (4/11,3/8) Matrix(505,-1386,184,-505) -> Matrix(31,-12,80,-31) (63/23,11/4) -> (3/8,2/5) Matrix(22,-63,7,-20) -> Matrix(5,-2,8,-3) 1/2 Matrix(106,-357,19,-64) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(85,-294,24,-83) -> Matrix(1,0,4,1) 0/1 Matrix(419,-1596,110,-419) -> Matrix(43,-14,132,-43) (19/5,42/11) -> (7/22,1/3) Matrix(505,-1932,132,-505) -> Matrix(65,-22,192,-65) (42/11,23/6) -> (1/3,11/32) Matrix(41,-168,10,-41) -> Matrix(9,-4,20,-9) (4/1,21/5) -> (2/5,1/2) Matrix(64,-273,15,-64) -> Matrix(11,-6,20,-11) (21/5,13/3) -> (1/2,3/5) Matrix(41,-210,8,-41) -> Matrix(1,0,0,-1) (5/1,21/4) -> (0/1,1/0) Matrix(127,-672,24,-127) -> Matrix(1,0,16,-1) (21/4,16/3) -> (0/1,1/8) Matrix(188,-1071,33,-188) -> Matrix(1,0,8,-1) (17/3,63/11) -> (0/1,1/4) Matrix(505,-2898,88,-505) -> Matrix(7,-2,24,-7) (63/11,23/4) -> (1/4,1/3) Matrix(22,-147,3,-20) -> Matrix(5,-2,8,-3) 1/2 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.