INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/1 -7/1 -6/1 -14/3 -9/2 -18/5 -7/2 -3/1 -14/5 -12/5 -7/3 -28/13 -15/7 -7/4 -63/40 -3/2 -7/5 -63/52 -7/6 0/1 1/1 7/6 21/17 21/16 7/5 3/2 21/13 105/64 7/4 2/1 15/7 28/13 42/19 84/37 7/3 12/5 5/2 105/41 21/8 63/23 14/5 3/1 42/13 84/25 7/2 18/5 11/3 15/4 42/11 4/1 21/5 17/4 13/3 9/2 14/3 19/4 5/1 21/4 16/3 11/2 17/3 63/11 6/1 19/3 13/2 20/3 7/1 15/2 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -1/1 -8/1 0/1 -7/1 1/0 -13/2 -1/2 -6/1 0/1 -23/4 1/2 -17/3 1/1 -11/2 1/0 -16/3 8/1 -21/4 1/0 -5/1 -3/1 -19/4 1/0 -14/3 0/1 -23/5 1/1 -9/2 1/0 -22/5 2/1 -13/3 3/1 -17/4 1/0 -21/5 1/0 -4/1 -4/1 -19/5 -9/5 -15/4 -3/2 -56/15 -4/3 -41/11 -1/1 -26/7 -6/5 -11/3 -1/1 -18/5 0/1 -7/2 1/0 -24/7 -2/1 -41/12 1/0 -17/5 -3/1 -61/18 -7/2 -105/31 -3/1 -44/13 -8/3 -27/8 -5/2 -37/11 -15/7 -10/3 -2/1 -33/10 1/0 -23/7 -1/1 -36/11 -2/1 -13/4 -5/2 -16/5 -8/5 -3/1 -1/1 -17/6 -1/2 -14/5 0/1 -25/9 1/1 -11/4 1/0 -19/7 -1/3 -27/10 1/0 -35/13 1/0 -8/3 0/1 -21/8 1/0 -13/5 -1/1 -18/7 0/1 -41/16 1/0 -105/41 1/0 -64/25 -8/1 -23/9 -1/1 -5/2 -1/2 -27/11 1/3 -22/9 2/5 -17/7 1/1 -29/12 3/2 -70/29 2/1 -41/17 1/1 -12/5 2/1 -19/8 5/2 -7/3 1/0 -23/10 -7/2 -39/17 -3/1 -16/7 0/1 -41/18 1/0 -25/11 -3/1 -34/15 -2/1 -9/4 1/0 -20/9 -4/1 -11/5 -1/1 -13/6 1/0 -28/13 0/1 -15/7 -1/1 -2/1 -2/1 -15/8 1/0 -28/15 0/1 -13/7 -1/1 -11/6 1/0 -42/23 -2/1 -31/17 -5/3 -20/11 -4/3 -9/5 -1/1 -34/19 -2/1 -59/33 -3/1 -84/47 -2/1 -25/14 -3/2 -41/23 -1/1 -16/9 0/1 -7/4 -1/1 -26/15 -6/7 -19/11 -5/7 -31/18 -1/2 -105/61 -1/1 -74/43 -2/3 -43/25 -1/1 -12/7 -2/3 -41/24 -1/2 -70/41 -2/3 -29/17 -3/5 -17/10 -1/2 -39/23 -1/3 -61/36 -5/14 -22/13 -2/7 -27/16 -1/4 -5/3 1/1 -23/14 1/0 -64/39 -8/7 -105/64 -1/1 -41/25 -1/1 -18/11 0/1 -31/19 -1/1 -13/8 1/0 -21/13 -1/1 -8/5 0/1 -27/17 -1/1 -19/12 1/2 -30/19 0/1 -41/26 1/0 -52/33 0/1 -63/40 1/0 -11/7 -1/1 -25/16 -1/2 -14/9 0/1 -17/11 1/1 -20/13 4/1 -3/2 1/0 -22/15 2/1 -19/13 -5/1 -16/11 -8/3 -29/20 -13/6 -42/29 -2/1 -13/9 -5/3 -23/16 1/0 -10/7 -2/1 -47/33 -15/7 -84/59 -2/1 -37/26 -15/8 -27/19 -5/3 -44/31 -8/5 -17/12 -3/2 -7/5 -1/1 -25/18 1/0 -43/31 -1/1 -18/13 0/1 -29/21 -1/1 -11/8 1/0 -26/19 -6/1 -41/30 1/0 -56/41 -4/1 -15/11 -3/1 -19/14 -9/4 -42/31 -2/1 -23/17 -13/7 -4/3 -4/3 -21/16 -1/1 -17/13 -1/1 -13/10 -3/4 -35/27 -1/2 -57/44 -1/2 -22/17 -2/3 -9/7 -1/1 -41/32 -1/2 -32/25 0/1 -23/18 -1/2 -14/11 0/1 -19/15 -1/1 -5/4 -3/2 -21/17 -1/1 -16/13 -8/9 -11/9 -1/1 -17/14 -1/2 -40/33 -4/7 -63/52 -1/2 -23/19 -1/3 -6/5 0/1 -19/16 -1/2 -13/11 1/1 -20/17 0/1 -7/6 -1/1 -22/19 -2/3 -15/13 -1/1 -8/7 0/1 -9/8 1/0 -10/9 -2/1 -1/1 -1/1 0/1 0/1 1/1 1/1 9/8 1/0 8/7 0/1 7/6 1/1 13/11 -1/1 6/5 0/1 23/19 1/3 17/14 1/2 11/9 1/1 16/13 8/9 21/17 1/1 5/4 3/2 19/15 1/1 14/11 0/1 23/18 1/2 9/7 1/1 22/17 2/3 13/10 3/4 17/13 1/1 21/16 1/1 4/3 4/3 19/14 9/4 15/11 3/1 56/41 4/1 41/30 1/0 26/19 6/1 11/8 1/0 18/13 0/1 7/5 1/1 24/17 2/1 41/29 1/1 17/12 3/2 61/43 7/5 105/74 3/2 44/31 8/5 27/19 5/3 37/26 15/8 10/7 2/1 33/23 1/1 23/16 1/0 36/25 2/1 13/9 5/3 16/11 8/3 3/2 1/0 17/11 -1/1 14/9 0/1 25/16 1/2 11/7 1/1 19/12 -1/2 27/17 1/1 35/22 1/1 8/5 0/1 21/13 1/1 13/8 1/0 18/11 0/1 41/25 1/1 105/64 1/1 64/39 8/7 23/14 1/0 5/3 -1/1 27/16 1/4 22/13 2/7 17/10 1/2 29/17 3/5 70/41 2/3 41/24 1/2 12/7 2/3 19/11 5/7 7/4 1/1 23/13 7/5 39/22 3/2 16/9 0/1 41/23 1/1 25/14 3/2 34/19 2/1 9/5 1/1 20/11 4/3 11/6 1/0 13/7 1/1 28/15 0/1 15/8 1/0 2/1 2/1 15/7 1/1 28/13 0/1 13/6 1/0 11/5 1/1 42/19 2/1 31/14 5/2 20/9 4/1 9/4 1/0 34/15 2/1 59/26 3/2 84/37 2/1 25/11 3/1 41/18 1/0 16/7 0/1 7/3 1/0 26/11 -6/1 19/8 -5/2 31/13 -1/1 105/44 1/0 74/31 -2/1 43/18 1/0 12/5 -2/1 41/17 -1/1 70/29 -2/1 29/12 -3/2 17/7 -1/1 39/16 -1/2 61/25 -5/9 22/9 -2/5 27/11 -1/3 5/2 1/2 23/9 1/1 64/25 8/1 105/41 1/0 41/16 1/0 18/7 0/1 31/12 1/0 13/5 1/1 21/8 1/0 8/3 0/1 27/10 1/0 19/7 1/3 30/11 0/1 41/15 1/1 52/19 0/1 63/23 1/1 11/4 1/0 25/9 -1/1 14/5 0/1 17/6 1/2 20/7 4/5 3/1 1/1 22/7 2/3 19/6 5/4 16/5 8/5 29/9 13/7 42/13 2/1 13/4 5/2 23/7 1/1 10/3 2/1 47/14 15/8 84/25 2/1 37/11 15/7 27/8 5/2 44/13 8/3 17/5 3/1 7/2 1/0 25/7 1/1 43/12 1/0 18/5 0/1 29/8 1/0 11/3 1/1 26/7 6/5 41/11 1/1 56/15 4/3 15/4 3/2 19/5 9/5 42/11 2/1 23/6 13/6 4/1 4/1 21/5 1/0 17/4 1/0 13/3 -3/1 35/8 -1/1 57/13 -1/1 22/5 -2/1 9/2 1/0 41/9 -1/1 32/7 0/1 23/5 -1/1 14/3 0/1 19/4 1/0 5/1 3/1 21/4 1/0 16/3 -8/1 11/2 1/0 17/3 -1/1 40/7 -4/3 63/11 -1/1 23/4 -1/2 6/1 0/1 19/3 -1/1 13/2 1/2 20/3 0/1 7/1 1/0 22/3 -2/1 15/2 1/0 8/1 0/1 9/1 1/1 10/1 2/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(41,378,-32,-295) (-9/1,1/0) -> (-9/7,-41/32) Hyperbolic Matrix(43,378,24,211) (-9/1,-8/1) -> (34/19,9/5) Hyperbolic Matrix(43,336,-16,-125) (-8/1,-7/1) -> (-35/13,-8/3) Hyperbolic Matrix(83,546,-64,-421) (-7/1,-13/2) -> (-13/10,-35/27) Hyperbolic Matrix(85,546,-26,-167) (-13/2,-6/1) -> (-36/11,-13/4) Hyperbolic Matrix(167,966,116,671) (-6/1,-23/4) -> (23/16,36/25) Hyperbolic Matrix(251,1428,-74,-421) (-23/4,-17/3) -> (-17/5,-61/18) Hyperbolic Matrix(83,462,30,167) (-17/3,-11/2) -> (11/4,25/9) Hyperbolic Matrix(85,462,62,337) (-11/2,-16/3) -> (26/19,11/8) Hyperbolic Matrix(127,672,24,127) (-16/3,-21/4) -> (21/4,16/3) Hyperbolic Matrix(41,210,8,41) (-21/4,-5/1) -> (5/1,21/4) Hyperbolic Matrix(43,210,26,127) (-5/1,-19/4) -> (23/14,5/3) Hyperbolic Matrix(125,588,98,461) (-19/4,-14/3) -> (14/11,23/18) Hyperbolic Matrix(127,588,100,463) (-14/3,-23/5) -> (19/15,14/11) Hyperbolic Matrix(211,966,-64,-293) (-23/5,-9/2) -> (-33/10,-23/7) Hyperbolic Matrix(85,378,38,169) (-9/2,-22/5) -> (20/9,9/4) Hyperbolic Matrix(125,546,-106,-463) (-22/5,-13/3) -> (-13/11,-20/17) Hyperbolic Matrix(167,714,98,419) (-13/3,-17/4) -> (17/10,29/17) Hyperbolic Matrix(169,714,40,169) (-17/4,-21/5) -> (21/5,17/4) Hyperbolic Matrix(41,168,10,41) (-21/5,-4/1) -> (4/1,21/5) Hyperbolic Matrix(43,168,-32,-125) (-4/1,-19/5) -> (-23/17,-4/3) Hyperbolic Matrix(211,798,78,295) (-19/5,-15/4) -> (27/10,19/7) Hyperbolic Matrix(337,1260,180,673) (-15/4,-56/15) -> (28/15,15/8) Hyperbolic Matrix(1385,5166,574,2141) (-56/15,-41/11) -> (41/17,70/29) Hyperbolic Matrix(463,1722,260,967) (-41/11,-26/7) -> (16/9,41/23) Hyperbolic Matrix(125,462,102,377) (-26/7,-11/3) -> (11/9,16/13) Hyperbolic Matrix(209,756,-128,-463) (-11/3,-18/5) -> (-18/11,-31/19) Hyperbolic Matrix(83,294,-24,-85) (-18/5,-7/2) -> (-7/2,-24/7) Parabolic Matrix(503,1722,196,671) (-24/7,-41/12) -> (41/16,18/7) Hyperbolic Matrix(505,1722,222,757) (-41/12,-17/5) -> (25/11,41/18) Hyperbolic Matrix(1847,6258,322,1091) (-61/18,-105/31) -> (63/11,23/4) Hyperbolic Matrix(2059,6972,360,1219) (-105/31,-44/13) -> (40/7,63/11) Hyperbolic Matrix(211,714,112,379) (-44/13,-27/8) -> (15/8,2/1) Hyperbolic Matrix(337,1134,200,673) (-27/8,-37/11) -> (5/3,27/16) Hyperbolic Matrix(251,840,-176,-589) (-37/11,-10/3) -> (-10/7,-47/33) Hyperbolic Matrix(127,420,-114,-377) (-10/3,-33/10) -> (-9/8,-10/9) Hyperbolic Matrix(295,966,244,799) (-23/7,-36/11) -> (6/5,23/19) Hyperbolic Matrix(209,672,-144,-463) (-13/4,-16/5) -> (-16/11,-29/20) Hyperbolic Matrix(211,672,-92,-293) (-16/5,-3/1) -> (-39/17,-16/7) Hyperbolic Matrix(251,714,-148,-421) (-3/1,-17/6) -> (-17/10,-39/23) Hyperbolic Matrix(209,588,134,377) (-17/6,-14/5) -> (14/9,25/16) Hyperbolic Matrix(211,588,136,379) (-14/5,-25/9) -> (17/11,14/9) Hyperbolic Matrix(167,462,30,83) (-25/9,-11/4) -> (11/2,17/3) Hyperbolic Matrix(293,798,-170,-463) (-11/4,-19/7) -> (-19/11,-31/18) Hyperbolic Matrix(295,798,78,211) (-19/7,-27/10) -> (15/4,19/5) Hyperbolic Matrix(1091,2940,-842,-2269) (-27/10,-35/13) -> (-35/27,-57/44) Hyperbolic Matrix(127,336,48,127) (-8/3,-21/8) -> (21/8,8/3) Hyperbolic Matrix(209,546,80,209) (-21/8,-13/5) -> (13/5,21/8) Hyperbolic Matrix(293,756,-212,-547) (-13/5,-18/7) -> (-18/13,-29/21) Hyperbolic Matrix(589,1512,164,421) (-18/7,-41/16) -> (43/12,18/5) Hyperbolic Matrix(3361,8610,1312,3361) (-41/16,-105/41) -> (105/41,41/16) Hyperbolic Matrix(5249,13440,2050,5249) (-105/41,-64/25) -> (64/25,105/41) Hyperbolic Matrix(1723,4410,706,1807) (-64/25,-23/9) -> (61/25,22/9) Hyperbolic Matrix(83,210,66,167) (-23/9,-5/2) -> (5/4,19/15) Hyperbolic Matrix(461,1134,324,797) (-5/2,-27/11) -> (27/19,37/26) Hyperbolic Matrix(377,924,-326,-799) (-27/11,-22/9) -> (-22/19,-15/13) Hyperbolic Matrix(293,714,-190,-463) (-22/9,-17/7) -> (-17/11,-20/13) Hyperbolic Matrix(295,714,226,547) (-17/7,-29/12) -> (13/10,17/13) Hyperbolic Matrix(713,1722,330,797) (-29/12,-70/29) -> (28/13,13/6) Hyperbolic Matrix(2141,5166,574,1385) (-70/29,-41/17) -> (41/11,56/15) Hyperbolic Matrix(715,1722,262,631) (-41/17,-12/5) -> (30/11,41/15) Hyperbolic Matrix(335,798,-212,-505) (-12/5,-19/8) -> (-19/12,-30/19) Hyperbolic Matrix(125,294,-54,-127) (-19/8,-7/3) -> (-7/3,-23/10) Parabolic Matrix(1427,3276,-842,-1933) (-23/10,-39/17) -> (-39/23,-61/36) Hyperbolic Matrix(755,1722,552,1259) (-16/7,-41/18) -> (41/30,26/19) Hyperbolic Matrix(923,2100,258,587) (-41/18,-25/11) -> (25/7,43/12) Hyperbolic Matrix(1259,2856,-704,-1597) (-25/11,-34/15) -> (-34/19,-59/33) Hyperbolic Matrix(167,378,148,335) (-34/15,-9/4) -> (9/8,8/7) Hyperbolic Matrix(169,378,38,85) (-9/4,-20/9) -> (22/5,9/2) Hyperbolic Matrix(379,840,-208,-461) (-20/9,-11/5) -> (-31/17,-20/11) Hyperbolic Matrix(211,462,58,127) (-11/5,-13/6) -> (29/8,11/3) Hyperbolic Matrix(797,1722,330,713) (-13/6,-28/13) -> (70/29,29/12) Hyperbolic Matrix(587,1260,430,923) (-28/13,-15/7) -> (15/11,56/41) Hyperbolic Matrix(335,714,236,503) (-15/7,-2/1) -> (44/31,27/19) Hyperbolic Matrix(379,714,112,211) (-2/1,-15/8) -> (27/8,44/13) Hyperbolic Matrix(673,1260,180,337) (-15/8,-28/15) -> (56/15,15/4) Hyperbolic Matrix(925,1722,542,1009) (-28/15,-13/7) -> (29/17,70/41) Hyperbolic Matrix(295,546,114,211) (-13/7,-11/6) -> (31/12,13/5) Hyperbolic Matrix(965,1764,436,797) (-11/6,-42/23) -> (42/19,31/14) Hyperbolic Matrix(967,1764,438,799) (-42/23,-31/17) -> (11/5,42/19) Hyperbolic Matrix(209,378,162,293) (-20/11,-9/5) -> (9/7,22/17) Hyperbolic Matrix(211,378,24,43) (-9/5,-34/19) -> (8/1,9/1) Hyperbolic Matrix(3947,7056,1738,3107) (-59/33,-84/47) -> (84/37,25/11) Hyperbolic Matrix(3949,7056,1740,3109) (-84/47,-25/14) -> (59/26,84/37) Hyperbolic Matrix(965,1722,682,1217) (-25/14,-41/23) -> (41/29,17/12) Hyperbolic Matrix(967,1722,260,463) (-41/23,-16/9) -> (26/7,41/11) Hyperbolic Matrix(167,294,-96,-169) (-16/9,-7/4) -> (-7/4,-26/15) Parabolic Matrix(461,798,-316,-547) (-26/15,-19/11) -> (-19/13,-16/11) Hyperbolic Matrix(1805,3108,658,1133) (-31/18,-105/61) -> (63/23,11/4) Hyperbolic Matrix(5881,10122,2148,3697) (-105/61,-74/43) -> (52/19,63/23) Hyperbolic Matrix(2563,4410,562,967) (-74/43,-43/25) -> (41/9,32/7) Hyperbolic Matrix(587,1008,244,419) (-43/25,-12/7) -> (12/5,41/17) Hyperbolic Matrix(589,1008,246,421) (-12/7,-41/24) -> (43/18,12/5) Hyperbolic Matrix(3025,5166,2214,3781) (-41/24,-70/41) -> (56/41,41/30) Hyperbolic Matrix(1009,1722,542,925) (-70/41,-29/17) -> (13/7,28/15) Hyperbolic Matrix(419,714,98,167) (-29/17,-17/10) -> (17/4,13/3) Hyperbolic Matrix(2603,4410,1586,2687) (-61/36,-22/13) -> (64/39,23/14) Hyperbolic Matrix(1093,1848,-844,-1427) (-22/13,-27/16) -> (-57/44,-22/17) Hyperbolic Matrix(673,1134,200,337) (-27/16,-5/3) -> (37/11,27/8) Hyperbolic Matrix(127,210,26,43) (-5/3,-23/14) -> (19/4,5/1) Hyperbolic Matrix(1049,1722,332,545) (-23/14,-64/39) -> (22/7,19/6) Hyperbolic Matrix(8191,13440,4992,8191) (-64/39,-105/64) -> (105/64,64/39) Hyperbolic Matrix(5249,8610,3200,5249) (-105/64,-41/25) -> (41/25,105/64) Hyperbolic Matrix(1051,1722,744,1219) (-41/25,-18/11) -> (24/17,41/29) Hyperbolic Matrix(335,546,154,251) (-31/19,-13/8) -> (13/6,11/5) Hyperbolic Matrix(337,546,208,337) (-13/8,-21/13) -> (21/13,13/8) Hyperbolic Matrix(209,336,130,209) (-21/13,-8/5) -> (8/5,21/13) Hyperbolic Matrix(211,336,-184,-293) (-8/5,-27/17) -> (-15/13,-8/7) Hyperbolic Matrix(503,798,370,587) (-27/17,-19/12) -> (19/14,15/11) Hyperbolic Matrix(1091,1722,638,1007) (-30/19,-41/26) -> (41/24,12/7) Hyperbolic Matrix(293,462,26,41) (-41/26,-52/33) -> (10/1,1/0) Hyperbolic Matrix(6425,10122,2692,4241) (-52/33,-63/40) -> (105/44,74/31) Hyperbolic Matrix(1975,3108,828,1303) (-63/40,-11/7) -> (31/13,105/44) Hyperbolic Matrix(295,462,242,379) (-11/7,-25/16) -> (17/14,11/9) Hyperbolic Matrix(377,588,134,209) (-25/16,-14/9) -> (14/5,17/6) Hyperbolic Matrix(379,588,136,211) (-14/9,-17/11) -> (25/9,14/5) Hyperbolic Matrix(83,126,-56,-85) (-20/13,-3/2) -> (-3/2,-22/15) Parabolic Matrix(1177,1722,460,673) (-22/15,-19/13) -> (23/9,64/25) Hyperbolic Matrix(1217,1764,376,545) (-29/20,-42/29) -> (42/13,13/4) Hyperbolic Matrix(1219,1764,378,547) (-42/29,-13/9) -> (29/9,42/13) Hyperbolic Matrix(379,546,-320,-461) (-13/9,-23/16) -> (-19/16,-13/11) Hyperbolic Matrix(673,966,-526,-755) (-23/16,-10/7) -> (-32/25,-23/18) Hyperbolic Matrix(4955,7056,1474,2099) (-47/33,-84/59) -> (84/25,37/11) Hyperbolic Matrix(4957,7056,1476,2101) (-84/59,-37/26) -> (47/14,84/25) Hyperbolic Matrix(797,1134,324,461) (-37/26,-27/19) -> (27/11,5/2) Hyperbolic Matrix(503,714,236,335) (-27/19,-44/31) -> (2/1,15/7) Hyperbolic Matrix(1007,1428,-830,-1177) (-44/31,-17/12) -> (-17/14,-40/33) Hyperbolic Matrix(209,294,-150,-211) (-17/12,-7/5) -> (-7/5,-25/18) Parabolic Matrix(1513,2100,848,1177) (-25/18,-43/31) -> (41/23,25/14) Hyperbolic Matrix(1091,1512,666,923) (-43/31,-18/13) -> (18/11,41/25) Hyperbolic Matrix(335,462,182,251) (-29/21,-11/8) -> (11/6,13/7) Hyperbolic Matrix(337,462,62,85) (-11/8,-26/19) -> (16/3,11/2) Hyperbolic Matrix(1259,1722,552,755) (-26/19,-41/30) -> (41/18,16/7) Hyperbolic Matrix(3781,5166,2214,3025) (-41/30,-56/41) -> (70/41,41/24) Hyperbolic Matrix(923,1260,430,587) (-56/41,-15/11) -> (15/7,28/13) Hyperbolic Matrix(587,798,370,503) (-15/11,-19/14) -> (19/12,27/17) Hyperbolic Matrix(1301,1764,340,461) (-19/14,-42/31) -> (42/11,23/6) Hyperbolic Matrix(1303,1764,342,463) (-42/31,-23/17) -> (19/5,42/11) Hyperbolic Matrix(127,168,96,127) (-4/3,-21/16) -> (21/16,4/3) Hyperbolic Matrix(545,714,416,545) (-21/16,-17/13) -> (17/13,21/16) Hyperbolic Matrix(547,714,226,295) (-17/13,-13/10) -> (29/12,17/7) Hyperbolic Matrix(293,378,162,209) (-22/17,-9/7) -> (9/5,20/11) Hyperbolic Matrix(3443,4410,1442,1847) (-41/32,-32/25) -> (74/31,43/18) Hyperbolic Matrix(461,588,98,125) (-23/18,-14/11) -> (14/3,19/4) Hyperbolic Matrix(463,588,100,127) (-14/11,-19/15) -> (23/5,14/3) Hyperbolic Matrix(167,210,66,83) (-19/15,-5/4) -> (5/2,23/9) Hyperbolic Matrix(169,210,136,169) (-5/4,-21/17) -> (21/17,5/4) Hyperbolic Matrix(545,672,442,545) (-21/17,-16/13) -> (16/13,21/17) Hyperbolic Matrix(377,462,102,125) (-16/13,-11/9) -> (11/3,26/7) Hyperbolic Matrix(379,462,242,295) (-11/9,-17/14) -> (25/16,11/7) Hyperbolic Matrix(5753,6972,4054,4913) (-40/33,-63/52) -> (105/74,44/31) Hyperbolic Matrix(5167,6258,3642,4411) (-63/52,-23/19) -> (61/43,105/74) Hyperbolic Matrix(209,252,34,41) (-23/19,-6/5) -> (6/1,19/3) Hyperbolic Matrix(211,252,36,43) (-6/5,-19/16) -> (23/4,6/1) Hyperbolic Matrix(251,294,-216,-253) (-20/17,-7/6) -> (-7/6,-22/19) Parabolic Matrix(335,378,148,167) (-8/7,-9/8) -> (9/4,34/15) Hyperbolic Matrix(421,462,154,169) (-10/9,-1/1) -> (41/15,52/19) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(337,-378,74,-83) (1/1,9/8) -> (9/2,41/9) Hyperbolic Matrix(293,-336,184,-211) (8/7,7/6) -> (35/22,8/5) Hyperbolic Matrix(463,-546,106,-125) (7/6,13/11) -> (13/3,35/8) Hyperbolic Matrix(461,-546,320,-379) (13/11,6/5) -> (36/25,13/9) Hyperbolic Matrix(1177,-1428,830,-1007) (23/19,17/14) -> (17/12,61/43) Hyperbolic Matrix(755,-966,526,-673) (23/18,9/7) -> (33/23,23/16) Hyperbolic Matrix(421,-546,64,-83) (22/17,13/10) -> (13/2,20/3) Hyperbolic Matrix(125,-168,32,-43) (4/3,19/14) -> (23/6,4/1) Hyperbolic Matrix(547,-756,212,-293) (11/8,18/13) -> (18/7,31/12) Hyperbolic Matrix(211,-294,150,-209) (18/13,7/5) -> (7/5,24/17) Parabolic Matrix(589,-840,176,-251) (37/26,10/7) -> (10/3,47/14) Hyperbolic Matrix(293,-420,30,-43) (10/7,33/23) -> (9/1,10/1) Hyperbolic Matrix(463,-672,144,-209) (13/9,16/11) -> (16/5,29/9) Hyperbolic Matrix(461,-672,260,-379) (16/11,3/2) -> (39/22,16/9) Hyperbolic Matrix(463,-714,190,-293) (3/2,17/11) -> (17/7,39/16) Hyperbolic Matrix(505,-798,212,-335) (11/7,19/12) -> (19/8,31/13) Hyperbolic Matrix(1849,-2940,422,-671) (27/17,35/22) -> (35/8,57/13) Hyperbolic Matrix(463,-756,128,-209) (13/8,18/11) -> (18/5,29/8) Hyperbolic Matrix(547,-924,74,-125) (27/16,22/13) -> (22/3,15/2) Hyperbolic Matrix(421,-714,148,-251) (22/13,17/10) -> (17/6,20/7) Hyperbolic Matrix(463,-798,170,-293) (12/7,19/11) -> (19/7,30/11) Hyperbolic Matrix(169,-294,96,-167) (19/11,7/4) -> (7/4,23/13) Parabolic Matrix(1849,-3276,758,-1343) (23/13,39/22) -> (39/16,61/25) Hyperbolic Matrix(1597,-2856,704,-1259) (25/14,34/19) -> (34/15,59/26) Hyperbolic Matrix(461,-840,208,-379) (20/11,11/6) -> (31/14,20/9) Hyperbolic Matrix(127,-294,54,-125) (16/7,7/3) -> (7/3,26/11) Parabolic Matrix(337,-798,106,-251) (26/11,19/8) -> (19/6,16/5) Hyperbolic Matrix(755,-1848,172,-421) (22/9,27/11) -> (57/13,22/5) Hyperbolic Matrix(125,-336,16,-43) (8/3,27/10) -> (15/2,8/1) Hyperbolic Matrix(43,-126,14,-41) (20/7,3/1) -> (3/1,22/7) Parabolic Matrix(167,-546,26,-85) (13/4,23/7) -> (19/3,13/2) Hyperbolic Matrix(293,-966,64,-211) (23/7,10/3) -> (32/7,23/5) Hyperbolic Matrix(421,-1428,74,-251) (44/13,17/5) -> (17/3,40/7) Hyperbolic Matrix(85,-294,24,-83) (17/5,7/2) -> (7/2,25/7) Parabolic Matrix(43,-294,6,-41) (20/3,7/1) -> (7/1,22/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(41,378,-32,-295) -> Matrix(1,2,-2,-3) Matrix(43,378,24,211) -> Matrix(1,2,0,1) Matrix(43,336,-16,-125) -> Matrix(1,0,0,1) Matrix(83,546,-64,-421) -> Matrix(1,2,-2,-3) Matrix(85,546,-26,-167) -> Matrix(1,-2,0,1) Matrix(167,966,116,671) -> Matrix(3,-2,2,-1) Matrix(251,1428,-74,-421) -> Matrix(1,-4,0,1) Matrix(83,462,30,167) -> Matrix(1,-2,0,1) Matrix(85,462,62,337) -> Matrix(1,-2,0,1) Matrix(127,672,24,127) -> Matrix(1,-16,0,1) Matrix(41,210,8,41) -> Matrix(1,6,0,1) Matrix(43,210,26,127) -> Matrix(1,2,0,1) Matrix(125,588,98,461) -> Matrix(1,0,2,1) Matrix(127,588,100,463) -> Matrix(1,0,0,1) Matrix(211,966,-64,-293) -> Matrix(1,-2,0,1) Matrix(85,378,38,169) -> Matrix(1,2,0,1) Matrix(125,546,-106,-463) -> Matrix(1,-2,0,1) Matrix(167,714,98,419) -> Matrix(1,-6,2,-11) Matrix(169,714,40,169) -> Matrix(1,-18,0,1) Matrix(41,168,10,41) -> Matrix(1,8,0,1) Matrix(43,168,-32,-125) -> Matrix(3,8,-2,-5) Matrix(211,798,78,295) -> Matrix(1,2,-2,-3) Matrix(337,1260,180,673) -> Matrix(3,4,2,3) Matrix(1385,5166,574,2141) -> Matrix(1,2,-2,-3) Matrix(463,1722,260,967) -> Matrix(5,6,4,5) Matrix(125,462,102,377) -> Matrix(3,2,4,3) Matrix(209,756,-128,-463) -> Matrix(1,0,0,1) Matrix(83,294,-24,-85) -> Matrix(1,-2,0,1) Matrix(503,1722,196,671) -> Matrix(1,2,0,1) Matrix(505,1722,222,757) -> Matrix(1,6,0,1) Matrix(1847,6258,322,1091) -> Matrix(3,10,-4,-13) Matrix(2059,6972,360,1219) -> Matrix(7,20,-6,-17) Matrix(211,714,112,379) -> Matrix(1,2,2,5) Matrix(337,1134,200,673) -> Matrix(1,2,6,13) Matrix(251,840,-176,-589) -> Matrix(1,0,0,1) Matrix(127,420,-114,-377) -> Matrix(1,0,0,1) Matrix(295,966,244,799) -> Matrix(1,2,2,5) Matrix(209,672,-144,-463) -> Matrix(9,16,-4,-7) Matrix(211,672,-92,-293) -> Matrix(5,8,-2,-3) Matrix(251,714,-148,-421) -> Matrix(3,2,-8,-5) Matrix(209,588,134,377) -> Matrix(1,0,4,1) Matrix(211,588,136,379) -> Matrix(1,0,-2,1) Matrix(167,462,30,83) -> Matrix(1,-2,0,1) Matrix(293,798,-170,-463) -> Matrix(1,2,-2,-3) Matrix(295,798,78,211) -> Matrix(3,-2,2,-1) Matrix(1091,2940,-842,-2269) -> Matrix(1,0,-2,1) Matrix(127,336,48,127) -> Matrix(1,0,0,1) Matrix(209,546,80,209) -> Matrix(1,2,0,1) Matrix(293,756,-212,-547) -> Matrix(1,0,0,1) Matrix(589,1512,164,421) -> Matrix(1,0,0,1) Matrix(3361,8610,1312,3361) -> Matrix(1,-6,0,1) Matrix(5249,13440,2050,5249) -> Matrix(1,16,0,1) Matrix(1723,4410,706,1807) -> Matrix(1,6,-2,-11) Matrix(83,210,66,167) -> Matrix(1,2,0,1) Matrix(461,1134,324,797) -> Matrix(11,-2,6,-1) Matrix(377,924,-326,-799) -> Matrix(1,0,-4,1) Matrix(293,714,-190,-463) -> Matrix(3,-2,2,-1) Matrix(295,714,226,547) -> Matrix(5,-6,6,-7) Matrix(713,1722,330,797) -> Matrix(1,-2,2,-3) Matrix(2141,5166,574,1385) -> Matrix(3,-2,2,-1) Matrix(715,1722,262,631) -> Matrix(1,-2,2,-3) Matrix(335,798,-212,-505) -> Matrix(1,-2,0,1) Matrix(125,294,-54,-127) -> Matrix(1,-6,0,1) Matrix(1427,3276,-842,-1933) -> Matrix(3,8,-8,-21) Matrix(755,1722,552,1259) -> Matrix(1,6,0,1) Matrix(923,2100,258,587) -> Matrix(1,4,0,1) Matrix(1259,2856,-704,-1597) -> Matrix(1,0,0,1) Matrix(167,378,148,335) -> Matrix(1,2,0,1) Matrix(169,378,38,85) -> Matrix(1,2,0,1) Matrix(379,840,-208,-461) -> Matrix(3,8,-2,-5) Matrix(211,462,58,127) -> Matrix(1,2,0,1) Matrix(797,1722,330,713) -> Matrix(3,2,-2,-1) Matrix(587,1260,430,923) -> Matrix(1,4,0,1) Matrix(335,714,236,503) -> Matrix(3,-2,2,-1) Matrix(379,714,112,211) -> Matrix(5,2,2,1) Matrix(673,1260,180,337) -> Matrix(3,4,2,3) Matrix(925,1722,542,1009) -> Matrix(1,-2,2,-3) Matrix(295,546,114,211) -> Matrix(1,2,0,1) Matrix(965,1764,436,797) -> Matrix(5,12,2,5) Matrix(967,1764,438,799) -> Matrix(7,12,4,7) Matrix(209,378,162,293) -> Matrix(1,2,0,1) Matrix(211,378,24,43) -> Matrix(1,2,0,1) Matrix(3947,7056,1738,3107) -> Matrix(5,12,2,5) Matrix(3949,7056,1740,3109) -> Matrix(7,12,4,7) Matrix(965,1722,682,1217) -> Matrix(5,6,4,5) Matrix(967,1722,260,463) -> Matrix(5,6,4,5) Matrix(167,294,-96,-169) -> Matrix(5,6,-6,-7) Matrix(461,798,-316,-547) -> Matrix(13,10,-4,-3) Matrix(1805,3108,658,1133) -> Matrix(1,0,2,1) Matrix(5881,10122,2148,3697) -> Matrix(3,2,4,3) Matrix(2563,4410,562,967) -> Matrix(3,2,-2,-1) Matrix(587,1008,244,419) -> Matrix(5,4,-4,-3) Matrix(589,1008,246,421) -> Matrix(7,4,-2,-1) Matrix(3025,5166,2214,3781) -> Matrix(5,2,2,1) Matrix(1009,1722,542,925) -> Matrix(3,2,-2,-1) Matrix(419,714,98,167) -> Matrix(11,6,-2,-1) Matrix(2603,4410,1586,2687) -> Matrix(17,6,14,5) Matrix(1093,1848,-844,-1427) -> Matrix(1,0,2,1) Matrix(673,1134,200,337) -> Matrix(13,2,6,1) Matrix(127,210,26,43) -> Matrix(1,2,0,1) Matrix(1049,1722,332,545) -> Matrix(5,6,4,5) Matrix(8191,13440,4992,8191) -> Matrix(15,16,14,15) Matrix(5249,8610,3200,5249) -> Matrix(7,6,8,7) Matrix(1051,1722,744,1219) -> Matrix(1,2,0,1) Matrix(335,546,154,251) -> Matrix(1,2,0,1) Matrix(337,546,208,337) -> Matrix(1,2,0,1) Matrix(209,336,130,209) -> Matrix(1,0,2,1) Matrix(211,336,-184,-293) -> Matrix(1,0,0,1) Matrix(503,798,370,587) -> Matrix(5,2,2,1) Matrix(1091,1722,638,1007) -> Matrix(1,-2,2,-3) Matrix(293,462,26,41) -> Matrix(1,2,0,1) Matrix(6425,10122,2692,4241) -> Matrix(1,-2,0,1) Matrix(1975,3108,828,1303) -> Matrix(1,0,0,1) Matrix(295,462,242,379) -> Matrix(3,2,4,3) Matrix(377,588,134,209) -> Matrix(1,0,4,1) Matrix(379,588,136,211) -> Matrix(1,0,-2,1) Matrix(83,126,-56,-85) -> Matrix(1,-2,0,1) Matrix(1177,1722,460,673) -> Matrix(1,6,0,1) Matrix(1217,1764,376,545) -> Matrix(17,36,8,17) Matrix(1219,1764,378,547) -> Matrix(19,36,10,19) Matrix(379,546,-320,-461) -> Matrix(1,2,-2,-3) Matrix(673,966,-526,-755) -> Matrix(1,2,-2,-3) Matrix(4955,7056,1474,2099) -> Matrix(29,60,14,29) Matrix(4957,7056,1476,2101) -> Matrix(31,60,16,31) Matrix(797,1134,324,461) -> Matrix(1,2,-6,-11) Matrix(503,714,236,335) -> Matrix(1,2,-2,-3) Matrix(1007,1428,-830,-1177) -> Matrix(3,4,-4,-5) Matrix(209,294,-150,-211) -> Matrix(1,2,-2,-3) Matrix(1513,2100,848,1177) -> Matrix(3,4,2,3) Matrix(1091,1512,666,923) -> Matrix(1,0,2,1) Matrix(335,462,182,251) -> Matrix(1,2,0,1) Matrix(337,462,62,85) -> Matrix(1,-2,0,1) Matrix(1259,1722,552,755) -> Matrix(1,6,0,1) Matrix(3781,5166,2214,3025) -> Matrix(1,2,2,5) Matrix(923,1260,430,587) -> Matrix(1,4,0,1) Matrix(587,798,370,503) -> Matrix(1,2,2,5) Matrix(1301,1764,340,461) -> Matrix(21,44,10,21) Matrix(1303,1764,342,463) -> Matrix(23,44,12,23) Matrix(127,168,96,127) -> Matrix(7,8,6,7) Matrix(545,714,416,545) -> Matrix(19,18,20,19) Matrix(547,714,226,295) -> Matrix(7,6,-6,-5) Matrix(293,378,162,209) -> Matrix(1,2,0,1) Matrix(3443,4410,1442,1847) -> Matrix(3,2,-2,-1) Matrix(461,588,98,125) -> Matrix(1,0,2,1) Matrix(463,588,100,127) -> Matrix(1,0,0,1) Matrix(167,210,66,83) -> Matrix(1,2,0,1) Matrix(169,210,136,169) -> Matrix(5,6,4,5) Matrix(545,672,442,545) -> Matrix(17,16,18,17) Matrix(377,462,102,125) -> Matrix(3,2,4,3) Matrix(379,462,242,295) -> Matrix(3,2,4,3) Matrix(5753,6972,4054,4913) -> Matrix(37,20,24,13) Matrix(5167,6258,3642,4411) -> Matrix(23,10,16,7) Matrix(209,252,34,41) -> Matrix(1,0,2,1) Matrix(211,252,36,43) -> Matrix(1,0,0,1) Matrix(251,294,-216,-253) -> Matrix(1,2,-2,-3) Matrix(335,378,148,167) -> Matrix(1,2,0,1) Matrix(421,462,154,169) -> Matrix(1,2,0,1) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(337,-378,74,-83) -> Matrix(1,-2,0,1) Matrix(293,-336,184,-211) -> Matrix(1,0,0,1) Matrix(463,-546,106,-125) -> Matrix(1,-2,0,1) Matrix(461,-546,320,-379) -> Matrix(3,-2,2,-1) Matrix(1177,-1428,830,-1007) -> Matrix(5,-4,4,-3) Matrix(755,-966,526,-673) -> Matrix(3,-2,2,-1) Matrix(421,-546,64,-83) -> Matrix(3,-2,2,-1) Matrix(125,-168,32,-43) -> Matrix(5,-8,2,-3) Matrix(547,-756,212,-293) -> Matrix(1,0,0,1) Matrix(211,-294,150,-209) -> Matrix(3,-2,2,-1) Matrix(589,-840,176,-251) -> Matrix(1,0,0,1) Matrix(293,-420,30,-43) -> Matrix(1,0,0,1) Matrix(463,-672,144,-209) -> Matrix(7,-16,4,-9) Matrix(461,-672,260,-379) -> Matrix(3,-8,2,-5) Matrix(463,-714,190,-293) -> Matrix(1,2,-2,-3) Matrix(505,-798,212,-335) -> Matrix(1,-2,0,1) Matrix(1849,-2940,422,-671) -> Matrix(1,0,-2,1) Matrix(463,-756,128,-209) -> Matrix(1,0,0,1) Matrix(547,-924,74,-125) -> Matrix(1,0,-4,1) Matrix(421,-714,148,-251) -> Matrix(5,-2,8,-3) Matrix(463,-798,170,-293) -> Matrix(3,-2,2,-1) Matrix(169,-294,96,-167) -> Matrix(7,-6,6,-5) Matrix(1849,-3276,758,-1343) -> Matrix(5,-8,-8,13) Matrix(1597,-2856,704,-1259) -> Matrix(1,0,0,1) Matrix(461,-840,208,-379) -> Matrix(5,-8,2,-3) Matrix(127,-294,54,-125) -> Matrix(1,-6,0,1) Matrix(337,-798,106,-251) -> Matrix(3,10,2,7) Matrix(755,-1848,172,-421) -> Matrix(1,0,2,1) Matrix(125,-336,16,-43) -> Matrix(1,0,0,1) Matrix(43,-126,14,-41) -> Matrix(3,-2,2,-1) Matrix(167,-546,26,-85) -> Matrix(1,-2,0,1) Matrix(293,-966,64,-211) -> Matrix(1,-2,0,1) Matrix(421,-1428,74,-251) -> Matrix(1,-4,0,1) Matrix(85,-294,24,-83) -> Matrix(1,-2,0,1) Matrix(43,-294,6,-41) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 Degree of the the map X: 64 Degree of the the map Y: 192 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- 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 0/1 7/6 6/5 14/11 7/5 3/2 14/9 12/7 7/4 28/15 2/1 28/13 42/19 84/37 7/3 12/5 105/41 18/7 21/8 63/23 14/5 3/1 42/13 84/25 7/2 18/5 15/4 42/11 4/1 21/5 9/2 14/3 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 0/1 0/1 1/1 1/1 9/8 1/0 8/7 0/1 7/6 1/1 13/11 -1/1 6/5 0/1 23/19 1/3 17/14 1/2 11/9 1/1 16/13 8/9 21/17 1/1 5/4 3/2 19/15 1/1 14/11 0/1 23/18 1/2 9/7 1/1 22/17 2/3 13/10 3/4 17/13 1/1 21/16 1/1 4/3 4/3 19/14 9/4 15/11 3/1 56/41 4/1 41/30 1/0 26/19 6/1 11/8 1/0 18/13 0/1 7/5 1/1 24/17 2/1 41/29 1/1 17/12 3/2 61/43 7/5 105/74 3/2 44/31 8/5 27/19 5/3 37/26 15/8 10/7 2/1 33/23 1/1 23/16 1/0 36/25 2/1 13/9 5/3 16/11 8/3 3/2 1/0 17/11 -1/1 14/9 0/1 25/16 1/2 11/7 1/1 19/12 -1/2 27/17 1/1 35/22 1/1 8/5 0/1 21/13 1/1 13/8 1/0 18/11 0/1 41/25 1/1 105/64 1/1 64/39 8/7 23/14 1/0 5/3 -1/1 27/16 1/4 22/13 2/7 17/10 1/2 29/17 3/5 70/41 2/3 41/24 1/2 12/7 2/3 19/11 5/7 7/4 1/1 23/13 7/5 39/22 3/2 16/9 0/1 41/23 1/1 25/14 3/2 34/19 2/1 9/5 1/1 20/11 4/3 11/6 1/0 13/7 1/1 28/15 0/1 15/8 1/0 2/1 2/1 15/7 1/1 28/13 0/1 13/6 1/0 11/5 1/1 42/19 2/1 31/14 5/2 20/9 4/1 9/4 1/0 34/15 2/1 59/26 3/2 84/37 2/1 25/11 3/1 41/18 1/0 16/7 0/1 7/3 1/0 26/11 -6/1 19/8 -5/2 31/13 -1/1 105/44 1/0 74/31 -2/1 43/18 1/0 12/5 -2/1 41/17 -1/1 70/29 -2/1 29/12 -3/2 17/7 -1/1 39/16 -1/2 61/25 -5/9 22/9 -2/5 27/11 -1/3 5/2 1/2 23/9 1/1 64/25 8/1 105/41 1/0 41/16 1/0 18/7 0/1 31/12 1/0 13/5 1/1 21/8 1/0 8/3 0/1 27/10 1/0 19/7 1/3 30/11 0/1 41/15 1/1 52/19 0/1 63/23 1/1 11/4 1/0 25/9 -1/1 14/5 0/1 17/6 1/2 20/7 4/5 3/1 1/1 22/7 2/3 19/6 5/4 16/5 8/5 29/9 13/7 42/13 2/1 13/4 5/2 23/7 1/1 10/3 2/1 47/14 15/8 84/25 2/1 37/11 15/7 27/8 5/2 44/13 8/3 17/5 3/1 7/2 1/0 25/7 1/1 43/12 1/0 18/5 0/1 29/8 1/0 11/3 1/1 26/7 6/5 41/11 1/1 56/15 4/3 15/4 3/2 19/5 9/5 42/11 2/1 23/6 13/6 4/1 4/1 21/5 1/0 17/4 1/0 13/3 -3/1 35/8 -1/1 57/13 -1/1 22/5 -2/1 9/2 1/0 41/9 -1/1 32/7 0/1 23/5 -1/1 14/3 0/1 19/4 1/0 5/1 3/1 21/4 1/0 16/3 -8/1 11/2 1/0 17/3 -1/1 40/7 -4/3 63/11 -1/1 23/4 -1/2 6/1 0/1 19/3 -1/1 13/2 1/2 20/3 0/1 7/1 1/0 22/3 -2/1 15/2 1/0 8/1 0/1 9/1 1/1 10/1 2/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(337,-378,74,-83) (1/1,9/8) -> (9/2,41/9) Hyperbolic Matrix(335,-378,187,-211) (9/8,8/7) -> (34/19,9/5) 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(799,-966,555,-671) (6/5,23/19) -> (23/16,36/25) Hyperbolic Matrix(1177,-1428,830,-1007) (23/19,17/14) -> (17/12,61/43) Hyperbolic Matrix(379,-462,137,-167) (17/14,11/9) -> (11/4,25/9) Hyperbolic Matrix(377,-462,275,-337) (11/9,16/13) -> (26/19,11/8) Hyperbolic Matrix(545,-672,103,-127) (16/13,21/17) -> (21/4,16/3) Hyperbolic Matrix(169,-210,33,-41) (21/17,5/4) -> (5/1,21/4) Hyperbolic Matrix(167,-210,101,-127) (5/4,19/15) -> (23/14,5/3) Hyperbolic Matrix(463,-588,363,-461) (19/15,14/11) -> (14/11,23/18) Parabolic Matrix(755,-966,526,-673) (23/18,9/7) -> (33/23,23/16) Hyperbolic Matrix(293,-378,131,-169) (9/7,22/17) -> (20/9,9/4) Hyperbolic Matrix(421,-546,64,-83) (22/17,13/10) -> (13/2,20/3) Hyperbolic Matrix(547,-714,321,-419) (13/10,17/13) -> (17/10,29/17) Hyperbolic Matrix(545,-714,129,-169) (17/13,21/16) -> (21/5,17/4) Hyperbolic Matrix(127,-168,31,-41) (21/16,4/3) -> (4/1,21/5) Hyperbolic Matrix(125,-168,32,-43) (4/3,19/14) -> (23/6,4/1) Hyperbolic Matrix(587,-798,217,-295) (19/14,15/11) -> (27/10,19/7) Hyperbolic Matrix(923,-1260,493,-673) (15/11,56/41) -> (28/15,15/8) Hyperbolic Matrix(3781,-5166,1567,-2141) (56/41,41/30) -> (41/17,70/29) Hyperbolic Matrix(1259,-1722,707,-967) (41/30,26/19) -> (16/9,41/23) 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(1219,-1722,475,-671) (24/17,41/29) -> (41/16,18/7) Hyperbolic Matrix(1217,-1722,535,-757) (41/29,17/12) -> (25/11,41/18) Hyperbolic Matrix(4411,-6258,769,-1091) (61/43,105/74) -> (63/11,23/4) Hyperbolic Matrix(4913,-6972,859,-1219) (105/74,44/31) -> (40/7,63/11) Hyperbolic Matrix(503,-714,267,-379) (44/31,27/19) -> (15/8,2/1) Hyperbolic Matrix(797,-1134,473,-673) (27/19,37/26) -> (5/3,27/16) Hyperbolic 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(379,-588,243,-377) (17/11,14/9) -> (14/9,25/16) Parabolic Matrix(295,-462,53,-83) (25/16,11/7) -> (11/2,17/3) Hyperbolic Matrix(505,-798,212,-335) (11/7,19/12) -> (19/8,31/13) Hyperbolic Matrix(503,-798,133,-211) (19/12,27/17) -> (15/4,19/5) Hyperbolic Matrix(1849,-2940,422,-671) (27/17,35/22) -> (35/8,57/13) Hyperbolic Matrix(209,-336,79,-127) (8/5,21/13) -> (21/8,8/3) Hyperbolic Matrix(337,-546,129,-209) (21/13,13/8) -> (13/5,21/8) Hyperbolic Matrix(463,-756,128,-209) (13/8,18/11) -> (18/5,29/8) Hyperbolic Matrix(923,-1512,257,-421) (18/11,41/25) -> (43/12,18/5) Hyperbolic Matrix(5249,-8610,2049,-3361) (41/25,105/64) -> (105/41,41/16) Hyperbolic Matrix(8191,-13440,3199,-5249) (105/64,64/39) -> (64/25,105/41) Hyperbolic Matrix(2687,-4410,1101,-1807) (64/39,23/14) -> (61/25,22/9) 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(1009,-1722,467,-797) (29/17,70/41) -> (28/13,13/6) Hyperbolic Matrix(3025,-5166,811,-1385) (70/41,41/24) -> (41/11,56/15) Hyperbolic Matrix(1007,-1722,369,-631) (41/24,12/7) -> (30/11,41/15) 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(1177,-2100,329,-587) (41/23,25/14) -> (25/7,43/12) Hyperbolic Matrix(1597,-2856,704,-1259) (25/14,34/19) -> (34/15,59/26) Hyperbolic Matrix(209,-378,47,-85) (9/5,20/11) -> (22/5,9/2) Hyperbolic Matrix(461,-840,208,-379) (20/11,11/6) -> (31/14,20/9) Hyperbolic Matrix(251,-462,69,-127) (11/6,13/7) -> (29/8,11/3) Hyperbolic Matrix(925,-1722,383,-713) (13/7,28/15) -> (70/29,29/12) Hyperbolic Matrix(335,-714,99,-211) (2/1,15/7) -> (27/8,44/13) Hyperbolic Matrix(587,-1260,157,-337) (15/7,28/13) -> (56/15,15/4) Hyperbolic Matrix(251,-546,97,-211) (13/6,11/5) -> (31/12,13/5) Hyperbolic Matrix(799,-1764,361,-797) (11/5,42/19) -> (42/19,31/14) Parabolic Matrix(167,-378,19,-43) (9/4,34/15) -> (8/1,9/1) Hyperbolic Matrix(3109,-7056,1369,-3107) (59/26,84/37) -> (84/37,25/11) Parabolic Matrix(755,-1722,203,-463) (41/18,16/7) -> (26/7,41/11) 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(1303,-3108,475,-1133) (31/13,105/44) -> (63/23,11/4) Hyperbolic Matrix(4241,-10122,1549,-3697) (105/44,74/31) -> (52/19,63/23) Hyperbolic Matrix(1847,-4410,405,-967) (74/31,43/18) -> (41/9,32/7) Hyperbolic Matrix(421,-1008,175,-419) (43/18,12/5) -> (12/5,41/17) Parabolic Matrix(295,-714,69,-167) (29/12,17/7) -> (17/4,13/3) Hyperbolic Matrix(755,-1848,172,-421) (22/9,27/11) -> (57/13,22/5) Hyperbolic Matrix(461,-1134,137,-337) (27/11,5/2) -> (37/11,27/8) Hyperbolic Matrix(83,-210,17,-43) (5/2,23/9) -> (19/4,5/1) Hyperbolic Matrix(673,-1722,213,-545) (23/9,64/25) -> (22/7,19/6) Hyperbolic Matrix(125,-336,16,-43) (8/3,27/10) -> (15/2,8/1) Hyperbolic Matrix(169,-462,15,-41) (41/15,52/19) -> (10/1,1/0) Hyperbolic Matrix(211,-588,75,-209) (25/9,14/5) -> (14/5,17/6) Parabolic Matrix(43,-126,14,-41) (20/7,3/1) -> (3/1,22/7) Parabolic Matrix(547,-1764,169,-545) (29/9,42/13) -> (42/13,13/4) 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(2101,-7056,625,-2099) (47/14,84/25) -> (84/25,37/11) 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(125,-462,23,-85) (11/3,26/7) -> (16/3,11/2) Hyperbolic Matrix(463,-1764,121,-461) (19/5,42/11) -> (42/11,23/6) Parabolic Matrix(127,-588,27,-125) (23/5,14/3) -> (14/3,19/4) Parabolic Matrix(43,-252,7,-41) (23/4,6/1) -> (6/1,19/3) Parabolic Matrix(43,-294,6,-41) (20/3,7/1) -> (7/1,22/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,1,1) Matrix(337,-378,74,-83) -> Matrix(1,-2,0,1) Matrix(335,-378,187,-211) -> Matrix(1,-2,1,-1) Matrix(293,-336,184,-211) -> Matrix(1,0,0,1) Matrix(463,-546,106,-125) -> Matrix(1,-2,0,1) Matrix(461,-546,320,-379) -> Matrix(3,-2,2,-1) Matrix(799,-966,555,-671) -> Matrix(5,-2,3,-1) Matrix(1177,-1428,830,-1007) -> Matrix(5,-4,4,-3) Matrix(379,-462,137,-167) -> Matrix(3,-2,-1,1) Matrix(377,-462,275,-337) -> Matrix(3,-2,-1,1) Matrix(545,-672,103,-127) -> Matrix(17,-16,-1,1) Matrix(169,-210,33,-41) -> Matrix(5,-6,1,-1) Matrix(167,-210,101,-127) -> Matrix(1,-2,1,-1) Matrix(463,-588,363,-461) -> Matrix(1,0,1,1) Matrix(755,-966,526,-673) -> Matrix(3,-2,2,-1) Matrix(293,-378,131,-169) -> Matrix(1,-2,1,-1) Matrix(421,-546,64,-83) -> Matrix(3,-2,2,-1) Matrix(547,-714,321,-419) -> Matrix(7,-6,13,-11) Matrix(545,-714,129,-169) -> Matrix(19,-18,-1,1) Matrix(127,-168,31,-41) -> Matrix(7,-8,1,-1) Matrix(125,-168,32,-43) -> Matrix(5,-8,2,-3) Matrix(587,-798,217,-295) -> Matrix(1,-2,-1,3) Matrix(923,-1260,493,-673) -> Matrix(1,-4,1,-3) Matrix(3781,-5166,1567,-2141) -> Matrix(1,-2,-1,3) Matrix(1259,-1722,707,-967) -> Matrix(1,-6,1,-5) Matrix(547,-756,212,-293) -> Matrix(1,0,0,1) Matrix(211,-294,150,-209) -> Matrix(3,-2,2,-1) Matrix(1219,-1722,475,-671) -> Matrix(1,-2,1,-1) Matrix(1217,-1722,535,-757) -> Matrix(5,-6,1,-1) Matrix(4411,-6258,769,-1091) -> Matrix(7,-10,-9,13) Matrix(4913,-6972,859,-1219) -> Matrix(13,-20,-11,17) Matrix(503,-714,267,-379) -> Matrix(1,-2,3,-5) Matrix(797,-1134,473,-673) -> Matrix(1,-2,7,-13) Matrix(589,-840,176,-251) -> Matrix(1,0,0,1) Matrix(293,-420,30,-43) -> Matrix(1,0,0,1) Matrix(463,-672,144,-209) -> Matrix(7,-16,4,-9) Matrix(461,-672,260,-379) -> Matrix(3,-8,2,-5) Matrix(463,-714,190,-293) -> Matrix(1,2,-2,-3) Matrix(379,-588,243,-377) -> Matrix(1,0,3,1) Matrix(295,-462,53,-83) -> Matrix(3,-2,-1,1) Matrix(505,-798,212,-335) -> Matrix(1,-2,0,1) Matrix(503,-798,133,-211) -> Matrix(5,-2,3,-1) Matrix(1849,-2940,422,-671) -> Matrix(1,0,-2,1) Matrix(209,-336,79,-127) -> Matrix(1,0,-1,1) Matrix(337,-546,129,-209) -> Matrix(1,-2,1,-1) Matrix(463,-756,128,-209) -> Matrix(1,0,0,1) Matrix(923,-1512,257,-421) -> Matrix(1,0,-1,1) Matrix(5249,-8610,2049,-3361) -> Matrix(7,-6,-1,1) Matrix(8191,-13440,3199,-5249) -> Matrix(15,-16,1,-1) Matrix(2687,-4410,1101,-1807) -> Matrix(5,-6,-9,11) Matrix(547,-924,74,-125) -> Matrix(1,0,-4,1) Matrix(421,-714,148,-251) -> Matrix(5,-2,8,-3) Matrix(1009,-1722,467,-797) -> Matrix(3,-2,5,-3) Matrix(3025,-5166,811,-1385) -> Matrix(5,-2,3,-1) Matrix(1007,-1722,369,-631) -> Matrix(3,-2,5,-3) Matrix(463,-798,170,-293) -> Matrix(3,-2,2,-1) Matrix(169,-294,96,-167) -> Matrix(7,-6,6,-5) Matrix(1849,-3276,758,-1343) -> Matrix(5,-8,-8,13) Matrix(1177,-2100,329,-587) -> Matrix(3,-4,1,-1) Matrix(1597,-2856,704,-1259) -> Matrix(1,0,0,1) Matrix(209,-378,47,-85) -> Matrix(1,-2,1,-1) Matrix(461,-840,208,-379) -> Matrix(5,-8,2,-3) Matrix(251,-462,69,-127) -> Matrix(1,-2,1,-1) Matrix(925,-1722,383,-713) -> Matrix(1,2,-1,-1) Matrix(335,-714,99,-211) -> Matrix(3,2,1,1) Matrix(587,-1260,157,-337) -> Matrix(1,-4,1,-3) Matrix(251,-546,97,-211) -> Matrix(1,-2,1,-1) Matrix(799,-1764,361,-797) -> Matrix(7,-12,3,-5) Matrix(167,-378,19,-43) -> Matrix(1,-2,1,-1) Matrix(3109,-7056,1369,-3107) -> Matrix(7,-12,3,-5) Matrix(755,-1722,203,-463) -> Matrix(1,-6,1,-5) Matrix(127,-294,54,-125) -> Matrix(1,-6,0,1) Matrix(337,-798,106,-251) -> Matrix(3,10,2,7) Matrix(1303,-3108,475,-1133) -> Matrix(1,0,1,1) Matrix(4241,-10122,1549,-3697) -> Matrix(1,2,1,3) Matrix(1847,-4410,405,-967) -> Matrix(1,2,-1,-1) Matrix(421,-1008,175,-419) -> Matrix(1,4,-1,-3) Matrix(295,-714,69,-167) -> Matrix(5,6,-1,-1) Matrix(755,-1848,172,-421) -> Matrix(1,0,2,1) Matrix(461,-1134,137,-337) -> Matrix(11,2,5,1) Matrix(83,-210,17,-43) -> Matrix(1,-2,1,-1) Matrix(673,-1722,213,-545) -> Matrix(1,-6,1,-5) Matrix(125,-336,16,-43) -> Matrix(1,0,0,1) Matrix(169,-462,15,-41) -> Matrix(1,-2,1,-1) Matrix(211,-588,75,-209) -> Matrix(1,0,3,1) Matrix(43,-126,14,-41) -> Matrix(3,-2,2,-1) Matrix(547,-1764,169,-545) -> Matrix(19,-36,9,-17) Matrix(167,-546,26,-85) -> Matrix(1,-2,0,1) Matrix(293,-966,64,-211) -> Matrix(1,-2,0,1) Matrix(2101,-7056,625,-2099) -> Matrix(31,-60,15,-29) Matrix(421,-1428,74,-251) -> Matrix(1,-4,0,1) Matrix(85,-294,24,-83) -> Matrix(1,-2,0,1) Matrix(125,-462,23,-85) -> Matrix(3,-2,-1,1) Matrix(463,-1764,121,-461) -> Matrix(23,-44,11,-21) Matrix(127,-588,27,-125) -> Matrix(1,0,1,1) Matrix(43,-252,7,-41) -> Matrix(1,0,1,1) Matrix(43,-294,6,-41) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 1 1 2/1 2/1 1 21 15/7 1/1 1 7 28/13 0/1 1 3 13/6 1/0 1 21 11/5 1/1 1 21 42/19 2/1 3 1 20/9 4/1 1 21 9/4 1/0 1 7 34/15 2/1 1 21 84/37 2/1 3 1 25/11 3/1 1 21 41/18 1/0 1 21 16/7 0/1 1 21 7/3 1/0 3 3 26/11 -6/1 1 21 19/8 -5/2 1 21 12/5 -2/1 1 7 41/17 -1/1 1 21 70/29 -2/1 1 3 29/12 -3/2 1 21 17/7 -1/1 1 21 22/9 -2/5 1 21 27/11 -1/3 1 7 5/2 1/2 1 21 23/9 1/1 1 21 64/25 8/1 1 21 105/41 1/0 11 1 41/16 1/0 1 21 18/7 0/1 1 7 13/5 1/1 1 21 21/8 1/0 1 1 8/3 0/1 1 21 27/10 1/0 1 7 19/7 1/3 1 21 30/11 0/1 1 7 41/15 1/1 1 21 52/19 0/1 1 21 63/23 1/1 1 1 11/4 1/0 1 21 25/9 -1/1 1 21 14/5 0/1 3 3 17/6 1/2 1 21 20/7 4/5 1 21 3/1 1/1 1 7 22/7 2/3 1 21 19/6 5/4 1 21 16/5 8/5 1 21 42/13 2/1 9 1 13/4 5/2 1 21 23/7 1/1 1 21 10/3 2/1 1 21 84/25 2/1 15 1 37/11 15/7 1 21 27/8 5/2 1 7 44/13 8/3 1 21 17/5 3/1 1 21 7/2 1/0 1 3 25/7 1/1 1 21 43/12 1/0 1 21 18/5 0/1 1 7 29/8 1/0 1 21 11/3 1/1 1 21 26/7 6/5 1 21 41/11 1/1 1 21 56/15 4/3 1 3 15/4 3/2 1 7 19/5 9/5 1 21 42/11 2/1 11 1 4/1 4/1 1 21 21/5 1/0 13 1 17/4 1/0 1 21 13/3 -3/1 1 21 22/5 -2/1 1 21 9/2 1/0 1 7 32/7 0/1 1 21 23/5 -1/1 1 21 14/3 0/1 1 3 19/4 1/0 1 21 5/1 3/1 1 21 21/4 1/0 11 1 16/3 -8/1 1 21 11/2 1/0 1 21 17/3 -1/1 1 21 40/7 -4/3 1 21 63/11 -1/1 5 1 23/4 -1/2 1 21 6/1 0/1 1 7 19/3 -1/1 1 21 13/2 1/2 1 21 20/3 0/1 1 21 7/1 1/0 1 3 22/3 -2/1 1 21 15/2 1/0 1 7 8/1 0/1 1 21 9/1 1/1 1 7 10/1 2/1 1 21 1/0 1/0 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(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(335,-714,99,-211) (2/1,15/7) -> (27/8,44/13) Hyperbolic Matrix(587,-1260,157,-337) (15/7,28/13) -> (56/15,15/4) Hyperbolic 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(379,-840,171,-379) (42/19,20/9) -> (42/19,20/9) Reflection Matrix(169,-378,38,-85) (20/9,9/4) -> (22/5,9/2) Glide Reflection Matrix(167,-378,19,-43) (9/4,34/15) -> (8/1,9/1) Hyperbolic Matrix(1259,-2856,555,-1259) (34/15,84/37) -> (34/15,84/37) 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(755,-1722,203,-463) (41/18,16/7) -> (26/7,41/11) 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(335,-798,123,-293) (19/8,12/5) -> (19/7,30/11) 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(295,-714,69,-167) (29/12,17/7) -> (17/4,13/3) Hyperbolic Matrix(293,-714,103,-251) (17/7,22/9) -> (17/6,20/7) Glide Reflection Matrix(377,-924,51,-125) (22/9,27/11) -> (22/3,15/2) Glide Reflection Matrix(461,-1134,137,-337) (27/11,5/2) -> (37/11,27/8) Hyperbolic Matrix(83,-210,17,-43) (5/2,23/9) -> (19/4,5/1) Hyperbolic Matrix(673,-1722,213,-545) (23/9,64/25) -> (22/7,19/6) 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(293,-756,81,-209) (18/7,13/5) -> (18/5,29/8) 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(169,-462,15,-41) (41/15,52/19) -> (10/1,1/0) Hyperbolic 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(211,-588,75,-209) (25/9,14/5) -> (14/5,17/6) Parabolic Matrix(43,-126,14,-41) (20/7,3/1) -> (3/1,22/7) Parabolic Matrix(209,-672,65,-209) (16/5,42/13) -> (16/5,42/13) 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(251,-840,75,-251) (10/3,84/25) -> (10/3,84/25) 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(125,-462,23,-85) (11/3,26/7) -> (16/3,11/2) Hyperbolic Matrix(419,-1596,110,-419) (19/5,42/11) -> (19/5,42/11) Reflection Matrix(43,-168,11,-43) (42/11,4/1) -> (42/11,4/1) 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(125,-546,19,-83) (13/3,22/5) -> (13/2,20/3) Glide Reflection Matrix(83,-378,9,-41) (9/2,32/7) -> (9/1,10/1) Glide Reflection Matrix(127,-588,27,-125) (23/5,14/3) -> (14/3,19/4) Parabolic 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,-252,7,-41) (23/4,6/1) -> (6/1,19/3) Parabolic 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(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Matrix(335,-714,99,-211) -> Matrix(3,2,1,1) Matrix(587,-1260,157,-337) -> Matrix(1,-4,1,-3) 2/1 Matrix(797,-1722,330,-713) -> Matrix(3,-2,-2,1) Matrix(211,-462,58,-127) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(419,-924,190,-419) -> Matrix(3,-4,2,-3) (11/5,42/19) -> (1/1,2/1) Matrix(379,-840,171,-379) -> Matrix(3,-8,1,-3) (42/19,20/9) -> (2/1,4/1) Matrix(169,-378,38,-85) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(167,-378,19,-43) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(1259,-2856,555,-1259) -> Matrix(1,0,1,-1) (34/15,84/37) -> (0/1,2/1) Matrix(1849,-4200,814,-1849) -> Matrix(5,-12,2,-5) (84/37,25/11) -> (2/1,3/1) Matrix(923,-2100,258,-587) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(755,-1722,203,-463) -> Matrix(1,-6,1,-5) Matrix(127,-294,54,-125) -> Matrix(1,-6,0,1) 1/0 Matrix(337,-798,106,-251) -> Matrix(3,10,2,7) Matrix(335,-798,123,-293) -> Matrix(1,2,1,1) Matrix(715,-1722,262,-631) -> Matrix(1,2,2,3) Matrix(2141,-5166,574,-1385) -> Matrix(3,2,2,1) Matrix(295,-714,69,-167) -> Matrix(5,6,-1,-1) Matrix(293,-714,103,-251) -> Matrix(3,2,5,3) Matrix(377,-924,51,-125) -> Matrix(-1,0,3,1) *** -> (-2/3,0/1) Matrix(461,-1134,137,-337) -> Matrix(11,2,5,1) Matrix(83,-210,17,-43) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(673,-1722,213,-545) -> Matrix(1,-6,1,-5) Matrix(5249,-13440,2050,-5249) -> Matrix(-1,16,0,1) (64/25,105/41) -> (8/1,1/0) Matrix(3361,-8610,1312,-3361) -> Matrix(1,6,0,-1) (105/41,41/16) -> (-3/1,1/0) Matrix(589,-1512,164,-421) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(293,-756,81,-209) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(209,-546,80,-209) -> Matrix(-1,2,0,1) (13/5,21/8) -> (1/1,1/0) Matrix(127,-336,48,-127) -> Matrix(1,0,0,-1) (21/8,8/3) -> (0/1,1/0) Matrix(125,-336,16,-43) -> Matrix(1,0,0,1) Matrix(295,-798,78,-211) -> Matrix(3,2,2,1) Matrix(169,-462,15,-41) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(2393,-6552,874,-2393) -> Matrix(1,0,2,-1) (52/19,63/23) -> (0/1,1/1) Matrix(505,-1386,184,-505) -> Matrix(-1,2,0,1) (63/23,11/4) -> (1/1,1/0) Matrix(167,-462,30,-83) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(211,-588,75,-209) -> Matrix(1,0,3,1) 0/1 Matrix(43,-126,14,-41) -> Matrix(3,-2,2,-1) 1/1 Matrix(209,-672,65,-209) -> Matrix(9,-16,5,-9) (16/5,42/13) -> (8/5,2/1) Matrix(337,-1092,104,-337) -> Matrix(9,-20,4,-9) (42/13,13/4) -> (2/1,5/2) Matrix(167,-546,26,-85) -> Matrix(1,-2,0,1) 1/0 Matrix(293,-966,64,-211) -> Matrix(1,-2,0,1) 1/0 Matrix(251,-840,75,-251) -> Matrix(1,0,1,-1) (10/3,84/25) -> (0/1,2/1) Matrix(1849,-6216,550,-1849) -> Matrix(29,-60,14,-29) (84/25,37/11) -> (2/1,15/7) Matrix(421,-1428,74,-251) -> Matrix(1,-4,0,1) 1/0 Matrix(85,-294,24,-83) -> Matrix(1,-2,0,1) 1/0 Matrix(125,-462,23,-85) -> Matrix(3,-2,-1,1) Matrix(419,-1596,110,-419) -> Matrix(19,-36,10,-19) (19/5,42/11) -> (9/5,2/1) Matrix(43,-168,11,-43) -> Matrix(3,-8,1,-3) (42/11,4/1) -> (2/1,4/1) Matrix(41,-168,10,-41) -> Matrix(-1,8,0,1) (4/1,21/5) -> (4/1,1/0) Matrix(169,-714,40,-169) -> Matrix(1,18,0,-1) (21/5,17/4) -> (-9/1,1/0) Matrix(125,-546,19,-83) -> Matrix(1,2,1,1) Matrix(83,-378,9,-41) -> Matrix(1,2,1,1) Matrix(127,-588,27,-125) -> Matrix(1,0,1,1) 0/1 Matrix(41,-210,8,-41) -> Matrix(-1,6,0,1) (5/1,21/4) -> (3/1,1/0) Matrix(127,-672,24,-127) -> Matrix(1,16,0,-1) (21/4,16/3) -> (-8/1,1/0) Matrix(881,-5040,154,-881) -> Matrix(7,8,-6,-7) (40/7,63/11) -> (-4/3,-1/1) Matrix(505,-2898,88,-505) -> Matrix(3,2,-4,-3) (63/11,23/4) -> (-1/1,-1/2) Matrix(43,-252,7,-41) -> Matrix(1,0,1,1) 0/1 Matrix(43,-294,6,-41) -> Matrix(1,-2,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.