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 -6/7 -5/7 -2/3 -4/7 -7/15 -13/28 -19/42 -37/84 -3/7 -5/12 -23/63 -5/14 -1/3 -13/42 -25/84 -2/7 -5/18 -4/15 -11/42 -2/9 -3/14 -11/63 -1/6 -3/19 -3/20 -1/7 -2/15 -1/9 -1/10 0/1 1/9 1/8 1/7 2/13 1/6 3/17 2/11 3/16 4/21 1/5 4/19 3/14 2/9 3/13 4/17 5/21 1/4 3/11 5/18 2/7 1/3 5/14 8/21 41/105 2/5 5/12 3/7 13/28 7/15 1/2 4/7 64/105 13/21 40/63 2/3 5/7 16/21 17/21 52/63 6/7 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -8/9 -3/7 -7/8 -5/13 -3/8 -6/7 -1/3 -11/13 -5/16 -5/6 -2/7 -19/23 -11/40 -14/17 -4/15 -1/4 -9/11 -1/4 -13/16 -13/51 -1/4 -17/21 -1/4 -4/5 -1/4 -4/17 -15/19 -1/4 -11/14 -2/9 -18/23 -8/37 -3/14 -7/9 -3/14 -17/22 -5/24 -1/5 -10/13 -4/19 -5/24 -13/17 -13/64 -16/21 -1/5 -3/4 -1/5 -3/16 -14/19 -2/11 -9/50 -11/15 -1/6 -41/56 -2/11 -30/41 -2/11 -5/28 -19/26 -5/28 -3/17 -8/11 -2/11 -1/6 -13/18 -4/23 -5/7 -1/6 -17/24 -6/37 -29/41 -29/180 -12/17 -4/25 -7/44 -43/61 -19/120 -74/105 -3/19 -31/44 -3/19 -11/70 -19/27 -1/6 -26/37 -5/32 -2/13 -7/10 -1/6 -3/19 -23/33 -1/6 -16/23 -1/6 0/1 -25/36 -4/25 -9/13 -5/32 -11/16 -5/33 -3/20 -2/3 -1/7 -11/17 -5/36 -9/14 -2/15 -16/25 -2/15 -1/8 -7/11 -1/8 -12/19 -3/22 -2/15 -17/27 -5/38 -22/35 -3/23 -5/8 -5/39 -1/8 -13/21 -1/8 -8/13 -1/8 -8/65 -11/18 -4/33 -25/41 -25/208 -64/105 -3/25 -39/64 -3/25 -35/292 -14/23 -8/67 -5/42 -3/5 -1/8 -16/27 -1/9 -13/22 -5/44 -1/9 -10/17 -1/8 0/1 -17/29 -1/8 -41/70 -2/17 -24/41 -1/8 -2/17 -7/12 -2/17 -11/19 -5/44 -4/7 -1/9 -13/23 -3/28 -22/39 -1/9 -9/16 -7/65 -3/28 -23/41 -23/216 -14/25 -11/104 -2/19 -19/34 -5/48 -3/29 -5/9 -1/10 -11/20 -1/9 -3/28 -6/11 -2/19 -1/10 -7/13 -3/28 -15/28 -2/19 -8/15 -3/29 -1/2 -1/10 -1/11 -7/15 -3/34 -13/28 -2/23 -6/13 -4/47 -1/12 -5/11 -1/12 -19/42 0/1 -14/31 -1/10 0/1 -9/20 -1/11 -1/12 -4/9 -1/11 -15/34 -7/80 -9/103 -26/59 -23/264 -2/23 -37/84 -2/23 -11/25 -9/104 -18/41 -2/23 -1/12 -7/16 -3/35 -1/12 -3/7 -1/12 -11/26 -1/12 -3/37 -8/19 -5/62 -2/25 -13/31 -1/12 -44/105 -3/37 -31/74 -3/37 -5/62 -18/43 -1/12 -2/25 -5/12 -2/25 -17/41 -17/216 -29/70 -4/51 -12/29 -5/64 -6/77 -7/17 -3/40 -16/39 -1/13 -25/61 -1/12 -9/22 -1/12 -1/13 -11/27 -1/14 -2/5 -1/12 0/1 -9/23 -1/12 -25/64 -1/12 -1/13 -41/105 -1/12 -16/41 -1/12 -2/25 -7/18 -2/25 -12/31 -3/38 -4/51 -5/13 -5/64 -8/21 -1/13 -3/8 -1/13 -3/40 -10/27 -1/13 -7/19 -5/68 -11/30 -4/55 -15/41 -15/208 -19/52 -17/237 -1/14 -23/63 -1/14 -4/11 -1/14 -2/29 -9/25 -3/44 -5/14 0/1 -6/17 -1/12 0/1 -7/20 -5/64 -1/13 -1/3 -1/14 -7/22 -7/104 -1/15 -6/19 -3/46 -2/31 -5/16 -1/15 -1/16 -9/29 -1/20 -13/42 0/1 -4/13 -1/12 0/1 -7/23 -3/40 -3/10 -1/14 -3/43 -14/47 -5/72 -2/29 -25/84 -2/29 -11/37 -3/44 -8/27 -1/15 -13/44 -3/41 -1/14 -5/17 -5/72 -2/7 -1/15 -7/25 -7/108 -12/43 -2/31 -1/16 -5/18 -2/31 -8/29 -1/16 -2/33 -3/11 -1/16 -7/26 -1/16 -7/113 -11/41 -11/180 -15/56 -2/33 -4/15 -1/17 -5/19 -1/20 -11/42 0/1 -6/23 -1/10 0/1 -1/4 -1/15 -1/16 -5/21 -1/16 -4/17 -1/16 -4/65 -3/13 -1/16 -8/35 -1/17 -13/57 -1/18 -5/22 -1/16 -1/17 -2/9 -1/17 -9/41 -9/160 -7/32 -1/18 -5/91 -5/23 -1/20 -3/14 0/1 -4/19 -1/14 -2/29 -1/5 -1/16 -4/21 -1/17 -3/16 -1/17 -3/52 -2/11 -2/35 -1/18 -3/17 -3/52 -7/40 -7/125 -1/18 -11/63 -1/18 -4/23 -1/18 -4/73 -1/6 0/1 -3/19 -3/52 -2/13 -1/16 0/1 -3/20 -1/16 -1/17 -1/7 -1/18 -3/22 -3/56 -1/19 -2/15 -1/19 -1/8 -1/19 -1/20 -1/9 -1/18 -1/10 -1/18 -1/19 0/1 -1/20 0/1 1/9 -1/22 1/8 -1/20 -1/21 1/7 -1/22 2/13 -1/24 0/1 1/6 0/1 4/23 -4/87 -1/22 3/17 -3/68 2/11 -1/22 -2/45 3/16 -3/68 -1/23 4/21 -1/23 1/5 -1/24 4/19 -2/51 -1/26 3/14 0/1 5/23 -1/20 2/9 -1/23 5/22 -1/23 -1/24 3/13 -1/24 4/17 -4/95 -1/24 5/21 -1/24 1/4 -1/24 -1/25 5/19 -1/20 4/15 -1/23 15/56 -2/47 11/41 -11/260 7/26 -7/167 -1/24 3/11 -1/24 5/18 -2/49 2/7 -1/25 7/24 -2/51 12/41 -3/76 -2/51 5/17 -5/128 18/61 -8/207 -1/26 31/105 -1/26 13/44 -1/26 -3/79 8/27 -1/25 11/37 -3/76 3/10 -3/77 -1/26 10/33 -3/79 7/23 -3/80 11/36 0/1 4/13 -1/28 0/1 5/16 -1/24 -1/25 1/3 -1/26 6/17 -1/28 0/1 5/14 0/1 9/25 -3/76 4/11 -2/51 -1/26 7/19 -5/132 10/27 -1/27 13/35 -1/26 3/8 -3/80 -1/27 8/21 -1/27 5/13 -5/136 7/18 -2/55 16/41 -2/55 -1/28 41/105 -1/28 25/64 -1/27 -1/28 9/23 -1/28 2/5 -1/28 0/1 11/27 -1/26 9/22 -1/27 -1/28 7/17 -3/80 12/29 -6/163 -5/136 29/70 -4/109 17/41 -17/464 5/12 -2/55 8/19 -2/55 -5/138 3/7 -1/28 10/23 -4/113 -7/198 17/39 -5/142 7/16 -1/28 -3/85 18/41 -1/28 -2/57 11/25 -9/256 15/34 -9/257 -7/200 4/9 -1/29 9/20 -1/28 -1/29 5/11 -1/28 6/13 -1/28 -4/113 13/28 -2/57 7/15 -3/86 1/2 -1/29 -1/30 8/15 -3/91 15/28 -2/61 7/13 -3/92 6/11 -1/30 -2/61 23/42 -2/61 17/31 -3/92 11/20 -3/92 -1/31 5/9 -1/30 19/34 -3/91 -5/152 33/59 -21/640 47/84 -2/61 14/25 -2/61 -11/336 23/41 -23/704 9/16 -3/92 -7/215 4/7 -1/31 15/26 -5/156 -9/281 11/19 -5/156 18/31 -16/501 -3/94 61/105 -3/94 43/74 -3/94 -41/1285 25/43 -25/784 7/12 -2/63 24/41 -2/63 -1/32 41/70 -2/63 17/29 -1/32 10/17 -1/32 0/1 23/39 -1/30 36/61 -4/123 -5/154 13/22 -1/31 -5/156 16/27 -1/31 3/5 -1/32 14/23 -5/158 -8/253 39/64 -35/1108 -3/95 64/105 -3/95 25/41 -25/792 11/18 -4/127 19/31 -1/32 8/13 -8/255 -1/32 13/21 -1/32 5/8 -1/32 -5/161 17/27 -5/162 12/19 -2/65 -3/98 19/30 -2/65 26/41 -1/32 -2/65 33/52 -3/98 -1/33 40/63 -1/33 7/11 -1/32 16/25 -1/32 -2/65 9/14 -2/65 11/17 -5/164 13/20 -1/32 -1/33 2/3 -1/33 15/22 -1/33 -3/100 13/19 -3/100 11/16 -3/100 -5/167 20/29 -11/368 -2/67 29/42 -2/67 9/13 -5/168 16/23 -1/34 0/1 7/10 -3/101 -1/34 33/47 -3/100 59/84 -2/67 26/37 -2/67 -5/168 19/27 -1/34 31/44 -11/370 -3/101 12/17 -7/236 -4/135 5/7 -1/34 18/25 -13/444 -6/205 31/43 -31/1060 13/18 -4/137 21/29 -5/172 8/11 -1/34 -2/69 19/26 -3/103 -5/172 30/41 -5/172 -2/69 41/56 -2/69 11/15 -1/34 14/19 -9/310 -2/69 31/42 -2/69 17/23 -11/380 3/4 -3/104 -1/35 16/21 -1/35 13/17 -13/456 10/13 -5/176 -4/141 27/35 -3/106 44/57 -1/35 17/22 -1/35 -5/176 7/9 -3/106 32/41 -2/71 -1/36 25/32 -1/35 -3/106 18/23 -3/106 -8/283 11/14 -2/71 15/19 -1/36 4/5 -4/143 -1/36 17/21 -1/36 13/16 -1/36 -13/469 9/11 -1/36 14/17 -1/36 -4/145 33/40 -19/690 -3/109 52/63 -3/109 19/23 -11/400 5/6 -2/73 16/19 -3/110 -10/367 11/13 -5/184 17/20 -5/184 -1/37 6/7 -1/37 19/22 -1/37 -7/260 13/15 -5/186 7/8 -3/112 -5/187 8/9 -3/113 9/10 -9/341 -1/38 1/1 -1/40 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(83,74,-378,-337) (-1/1,-8/9) -> (-2/9,-9/41) Hyperbolic Matrix(167,148,378,335) (-8/9,-7/8) -> (15/34,4/9) Hyperbolic Matrix(211,184,-336,-293) (-7/8,-6/7) -> (-22/35,-5/8) Hyperbolic Matrix(125,106,-546,-463) (-6/7,-11/13) -> (-3/13,-8/35) Hyperbolic Matrix(379,320,-546,-461) (-11/13,-5/6) -> (-25/36,-9/13) Hyperbolic Matrix(295,244,966,799) (-5/6,-19/23) -> (7/23,11/36) Hyperbolic Matrix(1007,830,-1428,-1177) (-19/23,-14/17) -> (-12/17,-43/61) Hyperbolic Matrix(295,242,462,379) (-14/17,-9/11) -> (7/11,16/25) Hyperbolic Matrix(125,102,462,377) (-9/11,-13/16) -> (7/26,3/11) Hyperbolic Matrix(545,442,672,545) (-13/16,-17/21) -> (17/21,13/16) Hyperbolic Matrix(169,136,210,169) (-17/21,-4/5) -> (4/5,17/21) Hyperbolic Matrix(83,66,210,167) (-4/5,-15/19) -> (9/23,2/5) Hyperbolic Matrix(127,100,588,463) (-15/19,-11/14) -> (3/14,5/23) Hyperbolic Matrix(125,98,588,461) (-11/14,-18/23) -> (4/19,3/14) Hyperbolic Matrix(673,526,-966,-755) (-18/23,-7/9) -> (-23/33,-16/23) Hyperbolic Matrix(209,162,378,293) (-7/9,-17/22) -> (11/20,5/9) Hyperbolic Matrix(83,64,-546,-421) (-17/22,-10/13) -> (-2/13,-3/20) Hyperbolic Matrix(295,226,714,547) (-10/13,-13/17) -> (7/17,12/29) Hyperbolic Matrix(545,416,714,545) (-13/17,-16/21) -> (16/21,13/17) Hyperbolic Matrix(127,96,168,127) (-16/21,-3/4) -> (3/4,16/21) Hyperbolic Matrix(43,32,-168,-125) (-3/4,-14/19) -> (-6/23,-1/4) Hyperbolic Matrix(503,370,798,587) (-14/19,-11/15) -> (17/27,12/19) Hyperbolic Matrix(587,430,1260,923) (-11/15,-41/56) -> (13/28,7/15) Hyperbolic Matrix(3025,2214,5166,3781) (-41/56,-30/41) -> (24/41,41/70) Hyperbolic Matrix(755,552,1722,1259) (-30/41,-19/26) -> (7/16,18/41) Hyperbolic Matrix(85,62,462,337) (-19/26,-8/11) -> (2/11,3/16) Hyperbolic Matrix(293,212,-756,-547) (-8/11,-13/18) -> (-7/18,-12/31) Hyperbolic Matrix(209,150,-294,-211) (-13/18,-5/7) -> (-5/7,-17/24) Parabolic Matrix(1051,744,1722,1219) (-17/24,-29/41) -> (25/41,11/18) Hyperbolic Matrix(965,682,1722,1217) (-29/41,-12/17) -> (14/25,23/41) Hyperbolic Matrix(5167,3642,6258,4411) (-43/61,-74/105) -> (52/63,19/23) Hyperbolic Matrix(5753,4054,6972,4913) (-74/105,-31/44) -> (33/40,52/63) Hyperbolic Matrix(335,236,714,503) (-31/44,-19/27) -> (7/15,1/2) Hyperbolic Matrix(461,324,1134,797) (-19/27,-26/37) -> (2/5,11/27) Hyperbolic Matrix(251,176,-840,-589) (-26/37,-7/10) -> (-3/10,-14/47) Hyperbolic Matrix(43,30,-420,-293) (-7/10,-23/33) -> (-1/9,-1/10) Hyperbolic Matrix(167,116,966,671) (-16/23,-25/36) -> (1/6,4/23) Hyperbolic Matrix(209,144,-672,-463) (-9/13,-11/16) -> (-5/16,-9/29) Hyperbolic Matrix(379,260,-672,-461) (-11/16,-2/3) -> (-22/39,-9/16) Hyperbolic Matrix(293,190,-714,-463) (-2/3,-11/17) -> (-7/17,-16/39) Hyperbolic Matrix(211,136,588,379) (-11/17,-9/14) -> (5/14,9/25) Hyperbolic Matrix(209,134,588,377) (-9/14,-16/25) -> (6/17,5/14) Hyperbolic Matrix(379,242,462,295) (-16/25,-7/11) -> (9/11,14/17) Hyperbolic Matrix(335,212,-798,-505) (-7/11,-12/19) -> (-8/19,-13/31) Hyperbolic Matrix(587,370,798,503) (-12/19,-17/27) -> (11/15,14/19) Hyperbolic Matrix(671,422,-2940,-1849) (-17/27,-22/35) -> (-8/35,-13/57) Hyperbolic Matrix(209,130,336,209) (-5/8,-13/21) -> (13/21,5/8) Hyperbolic Matrix(337,208,546,337) (-13/21,-8/13) -> (8/13,13/21) Hyperbolic Matrix(209,128,-756,-463) (-8/13,-11/18) -> (-5/18,-8/29) Hyperbolic Matrix(1091,666,1512,923) (-11/18,-25/41) -> (31/43,13/18) Hyperbolic Matrix(5249,3200,8610,5249) (-25/41,-64/105) -> (64/105,25/41) Hyperbolic Matrix(8191,4992,13440,8191) (-64/105,-39/64) -> (39/64,64/105) Hyperbolic Matrix(2603,1586,4410,2687) (-39/64,-14/23) -> (36/61,13/22) Hyperbolic Matrix(43,26,210,127) (-14/23,-3/5) -> (1/5,4/19) Hyperbolic Matrix(337,200,1134,673) (-3/5,-16/27) -> (8/27,11/37) Hyperbolic Matrix(125,74,-924,-547) (-16/27,-13/22) -> (-3/22,-2/15) Hyperbolic Matrix(251,148,-714,-421) (-13/22,-10/17) -> (-6/17,-7/20) Hyperbolic Matrix(167,98,714,419) (-10/17,-17/29) -> (3/13,4/17) Hyperbolic Matrix(925,542,1722,1009) (-17/29,-41/70) -> (15/28,7/13) Hyperbolic Matrix(3781,2214,5166,3025) (-41/70,-24/41) -> (30/41,41/56) Hyperbolic Matrix(1091,638,1722,1007) (-24/41,-7/12) -> (19/30,26/41) Hyperbolic Matrix(293,170,-798,-463) (-7/12,-11/19) -> (-7/19,-11/30) Hyperbolic Matrix(167,96,-294,-169) (-11/19,-4/7) -> (-4/7,-13/23) Parabolic Matrix(1343,758,-3276,-1849) (-13/23,-22/39) -> (-16/39,-25/61) Hyperbolic Matrix(463,260,1722,967) (-9/16,-23/41) -> (11/41,7/26) Hyperbolic Matrix(1513,848,2100,1177) (-23/41,-14/25) -> (18/25,31/43) Hyperbolic Matrix(1259,704,-2856,-1597) (-14/25,-19/34) -> (-15/34,-26/59) Hyperbolic Matrix(43,24,378,211) (-19/34,-5/9) -> (1/9,1/8) Hyperbolic Matrix(293,162,378,209) (-5/9,-11/20) -> (17/22,7/9) Hyperbolic Matrix(379,208,-840,-461) (-11/20,-6/11) -> (-14/31,-9/20) Hyperbolic Matrix(335,182,462,251) (-6/11,-7/13) -> (21/29,8/11) Hyperbolic Matrix(1009,542,1722,925) (-7/13,-15/28) -> (41/70,17/29) Hyperbolic Matrix(337,180,1260,673) (-15/28,-8/15) -> (4/15,15/56) Hyperbolic Matrix(211,112,714,379) (-8/15,-1/2) -> (13/44,8/27) Hyperbolic Matrix(503,236,714,335) (-1/2,-7/15) -> (19/27,31/44) Hyperbolic Matrix(923,430,1260,587) (-7/15,-13/28) -> (41/56,11/15) Hyperbolic Matrix(713,330,1722,797) (-13/28,-6/13) -> (12/29,29/70) Hyperbolic Matrix(335,154,546,251) (-6/13,-5/11) -> (19/31,8/13) Hyperbolic Matrix(967,438,1764,799) (-5/11,-19/42) -> (23/42,17/31) Hyperbolic Matrix(965,436,1764,797) (-19/42,-14/31) -> (6/11,23/42) Hyperbolic Matrix(85,38,378,169) (-9/20,-4/9) -> (2/9,5/22) Hyperbolic Matrix(335,148,378,167) (-4/9,-15/34) -> (7/8,8/9) Hyperbolic Matrix(3949,1740,7056,3109) (-26/59,-37/84) -> (47/84,14/25) Hyperbolic Matrix(3947,1738,7056,3107) (-37/84,-11/25) -> (33/59,47/84) Hyperbolic Matrix(505,222,1722,757) (-11/25,-18/41) -> (12/41,5/17) Hyperbolic Matrix(1259,552,1722,755) (-18/41,-7/16) -> (19/26,30/41) Hyperbolic Matrix(125,54,-294,-127) (-7/16,-3/7) -> (-3/7,-11/26) Parabolic Matrix(251,106,-798,-337) (-11/26,-8/19) -> (-6/19,-5/16) Hyperbolic Matrix(1975,828,3108,1303) (-13/31,-44/105) -> (40/63,7/11) Hyperbolic Matrix(6425,2692,10122,4241) (-44/105,-31/74) -> (33/52,40/63) Hyperbolic Matrix(3443,1442,4410,1847) (-31/74,-18/43) -> (32/41,25/32) Hyperbolic Matrix(589,246,1008,421) (-18/43,-5/12) -> (7/12,24/41) Hyperbolic Matrix(587,244,1008,419) (-5/12,-17/41) -> (25/43,7/12) Hyperbolic Matrix(1385,574,5166,2141) (-17/41,-29/70) -> (15/56,11/41) Hyperbolic Matrix(797,330,1722,713) (-29/70,-12/29) -> (6/13,13/28) Hyperbolic Matrix(547,226,714,295) (-12/29,-7/17) -> (13/17,10/13) Hyperbolic Matrix(1723,706,4410,1807) (-25/61,-9/22) -> (25/64,9/23) Hyperbolic Matrix(421,172,-1848,-755) (-9/22,-11/27) -> (-13/57,-5/22) Hyperbolic Matrix(797,324,1134,461) (-11/27,-2/5) -> (26/37,19/27) Hyperbolic Matrix(167,66,210,83) (-2/5,-9/23) -> (15/19,4/5) Hyperbolic Matrix(1177,460,1722,673) (-9/23,-25/64) -> (15/22,13/19) Hyperbolic Matrix(5249,2050,13440,5249) (-25/64,-41/105) -> (41/105,25/64) Hyperbolic Matrix(3361,1312,8610,3361) (-41/105,-16/41) -> (16/41,41/105) Hyperbolic Matrix(503,196,1722,671) (-16/41,-7/18) -> (7/24,12/41) Hyperbolic Matrix(295,114,546,211) (-12/31,-5/13) -> (7/13,6/11) Hyperbolic Matrix(209,80,546,209) (-5/13,-8/21) -> (8/21,5/13) Hyperbolic Matrix(127,48,336,127) (-8/21,-3/8) -> (3/8,8/21) Hyperbolic Matrix(43,16,-336,-125) (-3/8,-10/27) -> (-2/15,-1/8) Hyperbolic Matrix(211,78,798,295) (-10/27,-7/19) -> (5/19,4/15) Hyperbolic Matrix(715,262,1722,631) (-11/30,-15/41) -> (17/41,5/12) Hyperbolic Matrix(421,154,462,169) (-15/41,-19/52) -> (9/10,1/1) Hyperbolic Matrix(5881,2148,10122,3697) (-19/52,-23/63) -> (61/105,43/74) Hyperbolic Matrix(1805,658,3108,1133) (-23/63,-4/11) -> (18/31,61/105) Hyperbolic Matrix(83,30,462,167) (-4/11,-9/25) -> (3/17,2/11) Hyperbolic Matrix(379,136,588,211) (-9/25,-5/14) -> (9/14,11/17) Hyperbolic Matrix(377,134,588,209) (-5/14,-6/17) -> (16/25,9/14) Hyperbolic Matrix(41,14,-126,-43) (-7/20,-1/3) -> (-1/3,-7/22) Parabolic Matrix(1049,332,1722,545) (-7/22,-6/19) -> (14/23,39/64) Hyperbolic Matrix(1219,378,1764,547) (-9/29,-13/42) -> (29/42,9/13) Hyperbolic Matrix(1217,376,1764,545) (-13/42,-4/13) -> (20/29,29/42) Hyperbolic Matrix(85,26,-546,-167) (-4/13,-7/23) -> (-3/19,-2/13) Hyperbolic Matrix(211,64,-966,-293) (-7/23,-3/10) -> (-7/32,-5/23) Hyperbolic Matrix(4957,1476,7056,2101) (-14/47,-25/84) -> (59/84,26/37) Hyperbolic Matrix(4955,1474,7056,2099) (-25/84,-11/37) -> (33/47,59/84) Hyperbolic Matrix(673,200,1134,337) (-11/37,-8/27) -> (16/27,3/5) Hyperbolic Matrix(379,112,714,211) (-8/27,-13/44) -> (1/2,8/15) Hyperbolic Matrix(251,74,-1428,-421) (-13/44,-5/17) -> (-3/17,-7/40) Hyperbolic Matrix(83,24,-294,-85) (-5/17,-2/7) -> (-2/7,-7/25) Parabolic Matrix(923,258,2100,587) (-7/25,-12/43) -> (18/41,11/25) Hyperbolic Matrix(589,164,1512,421) (-12/43,-5/18) -> (7/18,16/41) Hyperbolic Matrix(211,58,462,127) (-8/29,-3/11) -> (5/11,6/13) Hyperbolic Matrix(377,102,462,125) (-3/11,-7/26) -> (13/16,9/11) Hyperbolic Matrix(967,260,1722,463) (-7/26,-11/41) -> (23/41,9/16) Hyperbolic Matrix(2141,574,5166,1385) (-11/41,-15/56) -> (29/70,17/41) Hyperbolic Matrix(673,180,1260,337) (-15/56,-4/15) -> (8/15,15/28) Hyperbolic Matrix(295,78,798,211) (-4/15,-5/19) -> (7/19,10/27) Hyperbolic Matrix(1303,342,1764,463) (-5/19,-11/42) -> (31/42,17/23) Hyperbolic Matrix(1301,340,1764,461) (-11/42,-6/23) -> (14/19,31/42) Hyperbolic Matrix(41,10,168,41) (-1/4,-5/21) -> (5/21,1/4) Hyperbolic Matrix(169,40,714,169) (-5/21,-4/17) -> (4/17,5/21) Hyperbolic Matrix(419,98,714,167) (-4/17,-3/13) -> (17/29,10/17) Hyperbolic Matrix(169,38,378,85) (-5/22,-2/9) -> (4/9,9/20) Hyperbolic Matrix(2563,562,4410,967) (-9/41,-7/32) -> (43/74,25/43) Hyperbolic Matrix(463,100,588,127) (-5/23,-3/14) -> (11/14,15/19) Hyperbolic Matrix(461,98,588,125) (-3/14,-4/19) -> (18/23,11/14) Hyperbolic Matrix(127,26,210,43) (-4/19,-1/5) -> (3/5,14/23) Hyperbolic Matrix(41,8,210,41) (-1/5,-4/21) -> (4/21,1/5) Hyperbolic Matrix(127,24,672,127) (-4/21,-3/16) -> (3/16,4/21) Hyperbolic Matrix(337,62,462,85) (-3/16,-2/11) -> (8/11,19/26) Hyperbolic Matrix(167,30,462,83) (-2/11,-3/17) -> (9/25,4/11) Hyperbolic Matrix(2059,360,6972,1219) (-7/40,-11/63) -> (31/105,13/44) Hyperbolic Matrix(1847,322,6258,1091) (-11/63,-4/23) -> (18/61,31/105) Hyperbolic Matrix(211,36,252,43) (-4/23,-1/6) -> (5/6,16/19) Hyperbolic Matrix(209,34,252,41) (-1/6,-3/19) -> (19/23,5/6) Hyperbolic Matrix(41,6,-294,-43) (-3/20,-1/7) -> (-1/7,-3/22) Parabolic Matrix(211,24,378,43) (-1/8,-1/9) -> (5/9,19/34) Hyperbolic Matrix(293,26,462,41) (-1/10,0/1) -> (26/41,33/52) Hyperbolic Matrix(295,-32,378,-41) (0/1,1/9) -> (7/9,32/41) Hyperbolic Matrix(125,-16,336,-43) (1/8,1/7) -> (13/35,3/8) Hyperbolic Matrix(421,-64,546,-83) (1/7,2/13) -> (10/13,27/35) Hyperbolic Matrix(167,-26,546,-85) (2/13,1/6) -> (11/36,4/13) Hyperbolic Matrix(421,-74,1428,-251) (4/23,3/17) -> (5/17,18/61) Hyperbolic Matrix(293,-64,966,-211) (5/23,2/9) -> (10/33,7/23) Hyperbolic Matrix(463,-106,546,-125) (5/22,3/13) -> (11/13,17/20) Hyperbolic Matrix(125,-32,168,-43) (1/4,5/19) -> (17/23,3/4) Hyperbolic Matrix(463,-128,756,-209) (3/11,5/18) -> (11/18,19/31) Hyperbolic Matrix(85,-24,294,-83) (5/18,2/7) -> (2/7,7/24) Parabolic Matrix(589,-176,840,-251) (11/37,3/10) -> (7/10,33/47) Hyperbolic Matrix(377,-114,420,-127) (3/10,10/33) -> (8/9,9/10) Hyperbolic Matrix(463,-144,672,-209) (4/13,5/16) -> (11/16,20/29) Hyperbolic Matrix(293,-92,672,-211) (5/16,1/3) -> (17/39,7/16) Hyperbolic Matrix(421,-148,714,-251) (1/3,6/17) -> (10/17,23/39) Hyperbolic Matrix(463,-170,798,-293) (4/11,7/19) -> (11/19,18/31) Hyperbolic Matrix(2269,-842,2940,-1091) (10/27,13/35) -> (27/35,44/57) Hyperbolic Matrix(547,-212,756,-293) (5/13,7/18) -> (13/18,21/29) Hyperbolic Matrix(799,-326,924,-377) (11/27,9/22) -> (19/22,13/15) Hyperbolic Matrix(463,-190,714,-293) (9/22,7/17) -> (11/17,13/20) Hyperbolic Matrix(505,-212,798,-335) (5/12,8/19) -> (12/19,19/30) Hyperbolic Matrix(127,-54,294,-125) (8/19,3/7) -> (3/7,10/23) Parabolic Matrix(1933,-842,3276,-1427) (10/23,17/39) -> (23/39,36/61) Hyperbolic Matrix(1597,-704,2856,-1259) (11/25,15/34) -> (19/34,33/59) Hyperbolic Matrix(461,-208,840,-379) (9/20,5/11) -> (17/31,11/20) Hyperbolic Matrix(169,-96,294,-167) (9/16,4/7) -> (4/7,15/26) Parabolic Matrix(547,-316,798,-461) (15/26,11/19) -> (13/19,11/16) Hyperbolic Matrix(1427,-844,1848,-1093) (13/22,16/27) -> (44/57,17/22) Hyperbolic Matrix(293,-184,336,-211) (5/8,17/27) -> (13/15,7/8) Hyperbolic Matrix(85,-56,126,-83) (13/20,2/3) -> (2/3,15/22) Parabolic Matrix(461,-320,546,-379) (9/13,16/23) -> (16/19,11/13) Hyperbolic Matrix(755,-526,966,-673) (16/23,7/10) -> (25/32,18/23) Hyperbolic Matrix(1177,-830,1428,-1007) (31/44,12/17) -> (14/17,33/40) Hyperbolic Matrix(211,-150,294,-209) (12/17,5/7) -> (5/7,18/25) Parabolic Matrix(253,-216,294,-251) (17/20,6/7) -> (6/7,19/22) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-40,1) Matrix(83,74,-378,-337) -> Matrix(9,4,-160,-71) Matrix(167,148,378,335) -> Matrix(19,8,-544,-229) Matrix(211,184,-336,-293) -> Matrix(27,10,-208,-77) Matrix(125,106,-546,-463) -> Matrix(19,6,-320,-101) Matrix(379,320,-546,-461) -> Matrix(33,10,-208,-63) Matrix(295,244,966,799) -> Matrix(7,2,-200,-57) Matrix(1007,830,-1428,-1177) -> Matrix(89,24,-560,-151) Matrix(295,242,462,379) -> Matrix(23,6,-740,-193) Matrix(125,102,462,377) -> Matrix(23,6,-556,-145) Matrix(545,442,672,545) -> Matrix(103,26,-3712,-937) Matrix(169,136,210,169) -> Matrix(33,8,-1184,-287) Matrix(83,66,210,167) -> Matrix(17,4,-472,-111) Matrix(127,100,588,463) -> Matrix(9,2,-176,-39) Matrix(125,98,588,461) -> Matrix(9,2,-248,-55) Matrix(673,526,-966,-755) -> Matrix(37,8,-236,-51) Matrix(209,162,378,293) -> Matrix(9,2,-284,-63) Matrix(83,64,-546,-421) -> Matrix(19,4,-328,-69) Matrix(295,226,714,547) -> Matrix(49,10,-1328,-271) Matrix(545,416,714,545) -> Matrix(129,26,-4520,-911) Matrix(127,96,168,127) -> Matrix(31,6,-1080,-209) Matrix(43,32,-168,-125) -> Matrix(11,2,-160,-29) Matrix(503,370,798,587) -> Matrix(67,12,-2172,-389) Matrix(587,430,1260,923) -> Matrix(21,4,-604,-115) Matrix(3025,2214,5166,3781) -> Matrix(45,8,-1412,-251) Matrix(755,552,1722,1259) -> Matrix(67,12,-1904,-341) Matrix(85,62,462,337) -> Matrix(23,4,-512,-89) Matrix(293,212,-756,-547) -> Matrix(57,10,-724,-127) Matrix(209,150,-294,-211) -> Matrix(59,10,-360,-61) Matrix(1051,744,1722,1219) -> Matrix(235,38,-7452,-1205) Matrix(965,682,1722,1217) -> Matrix(187,30,-5716,-917) Matrix(5167,3642,6258,4411) -> Matrix(569,90,-20680,-3271) Matrix(5753,4054,6972,4913) -> Matrix(571,90,-20740,-3269) Matrix(335,236,714,503) -> Matrix(51,8,-1460,-229) Matrix(461,324,1134,797) -> Matrix(13,2,-332,-51) Matrix(251,176,-840,-589) -> Matrix(1,0,-8,1) Matrix(43,30,-420,-293) -> Matrix(13,2,-228,-35) Matrix(167,116,966,671) -> Matrix(25,4,-544,-87) Matrix(209,144,-672,-463) -> Matrix(13,2,-228,-35) Matrix(379,260,-672,-461) -> Matrix(41,6,-376,-55) Matrix(293,190,-714,-463) -> Matrix(15,2,-188,-25) Matrix(211,136,588,379) -> Matrix(15,2,-368,-49) Matrix(209,134,588,377) -> Matrix(15,2,-428,-57) Matrix(379,242,462,295) -> Matrix(47,6,-1700,-217) Matrix(335,212,-798,-505) -> Matrix(31,4,-380,-49) Matrix(587,370,798,503) -> Matrix(91,12,-3132,-413) Matrix(671,422,-2940,-1849) -> Matrix(61,8,-1060,-139) Matrix(209,130,336,209) -> Matrix(79,10,-2536,-321) Matrix(337,208,546,337) -> Matrix(129,16,-4120,-511) Matrix(209,128,-756,-463) -> Matrix(49,6,-776,-95) Matrix(1091,666,1512,923) -> Matrix(265,32,-9068,-1095) Matrix(5249,3200,8610,5249) -> Matrix(1249,150,-39560,-4751) Matrix(8191,4992,13440,8191) -> Matrix(1751,210,-55440,-6649) Matrix(2603,1586,4410,2687) -> Matrix(167,20,-5152,-617) Matrix(43,26,210,127) -> Matrix(17,2,-400,-47) Matrix(337,200,1134,673) -> Matrix(35,4,-884,-101) Matrix(125,74,-924,-547) -> Matrix(17,2,-332,-39) Matrix(251,148,-714,-421) -> Matrix(1,0,-4,1) Matrix(167,98,714,419) -> Matrix(33,4,-784,-95) Matrix(925,542,1722,1009) -> Matrix(67,8,-2052,-245) Matrix(3781,2214,5166,3025) -> Matrix(69,8,-2372,-275) Matrix(1091,638,1722,1007) -> Matrix(1,0,-24,1) Matrix(293,170,-798,-463) -> Matrix(87,10,-1192,-137) Matrix(167,96,-294,-169) -> Matrix(71,8,-648,-73) Matrix(1343,758,-3276,-1849) -> Matrix(37,4,-472,-51) Matrix(463,260,1722,967) -> Matrix(131,14,-3116,-333) Matrix(1513,848,2100,1177) -> Matrix(377,40,-12884,-1367) Matrix(1259,704,-2856,-1597) -> Matrix(229,24,-2624,-275) Matrix(43,24,378,211) -> Matrix(19,2,-428,-45) Matrix(293,162,378,209) -> Matrix(17,2,-604,-71) Matrix(379,208,-840,-461) -> Matrix(19,2,-200,-21) Matrix(335,182,462,251) -> Matrix(39,4,-1336,-137) Matrix(1009,542,1722,925) -> Matrix(75,8,-2372,-253) Matrix(337,180,1260,673) -> Matrix(77,8,-1800,-187) Matrix(211,112,714,379) -> Matrix(19,2,-504,-53) Matrix(503,236,714,335) -> Matrix(91,8,-3060,-269) Matrix(923,430,1260,587) -> Matrix(45,4,-1564,-139) Matrix(713,330,1722,797) -> Matrix(163,14,-4436,-381) Matrix(335,154,546,251) -> Matrix(49,4,-1556,-127) Matrix(967,438,1764,799) -> Matrix(27,2,-824,-61) Matrix(965,436,1764,797) -> Matrix(19,2,-580,-61) Matrix(85,38,378,169) -> Matrix(1,0,-12,1) Matrix(335,148,378,167) -> Matrix(91,8,-3424,-301) Matrix(3949,1740,7056,3109) -> Matrix(781,68,-23832,-2075) Matrix(3947,1738,7056,3107) -> Matrix(691,60,-21064,-1829) Matrix(505,222,1722,757) -> Matrix(93,8,-2360,-203) Matrix(1259,552,1722,755) -> Matrix(139,12,-4784,-413) Matrix(125,54,-294,-127) -> Matrix(71,6,-864,-73) Matrix(251,106,-798,-337) -> Matrix(49,4,-772,-63) Matrix(1975,828,3108,1303) -> Matrix(25,2,-788,-63) Matrix(6425,2692,10122,4241) -> Matrix(173,14,-5672,-459) Matrix(3443,1442,4410,1847) -> Matrix(49,4,-1752,-143) Matrix(589,246,1008,421) -> Matrix(49,4,-1556,-127) Matrix(587,244,1008,419) -> Matrix(151,12,-4744,-377) Matrix(1385,574,5166,2141) -> Matrix(331,26,-7804,-613) Matrix(797,330,1722,713) -> Matrix(179,14,-5076,-397) Matrix(547,226,714,295) -> Matrix(129,10,-4528,-351) Matrix(1723,706,4410,1807) -> Matrix(25,2,-688,-55) Matrix(421,172,-1848,-755) -> Matrix(1,0,-4,1) Matrix(797,324,1134,461) -> Matrix(29,2,-972,-67) Matrix(167,66,210,83) -> Matrix(49,4,-1752,-143) Matrix(1177,460,1722,673) -> Matrix(51,4,-1696,-133) Matrix(5249,2050,13440,5249) -> Matrix(25,2,-688,-55) Matrix(3361,1312,8610,3361) -> Matrix(49,4,-1360,-111) Matrix(503,196,1722,671) -> Matrix(51,4,-1288,-101) Matrix(295,114,546,211) -> Matrix(25,2,-788,-63) Matrix(209,80,546,209) -> Matrix(129,10,-3496,-271) Matrix(127,48,336,127) -> Matrix(79,6,-2120,-161) Matrix(43,16,-336,-125) -> Matrix(27,2,-500,-37) Matrix(211,78,798,295) -> Matrix(27,2,-608,-45) Matrix(715,262,1722,631) -> Matrix(193,14,-5280,-383) Matrix(421,154,462,169) -> Matrix(111,8,-4232,-305) Matrix(5881,2148,10122,3697) -> Matrix(1285,92,-40268,-2883) Matrix(1805,658,3108,1133) -> Matrix(311,22,-9740,-689) Matrix(83,30,462,167) -> Matrix(1,0,-8,1) Matrix(379,136,588,211) -> Matrix(31,2,-1008,-65) Matrix(377,134,588,209) -> Matrix(23,2,-748,-65) Matrix(41,14,-126,-43) -> Matrix(27,2,-392,-29) Matrix(1049,332,1722,545) -> Matrix(213,14,-6740,-443) Matrix(1219,378,1764,547) -> Matrix(45,2,-1508,-67) Matrix(1217,376,1764,545) -> Matrix(13,2,-436,-67) Matrix(85,26,-546,-167) -> Matrix(1,0,-4,1) Matrix(211,64,-966,-293) -> Matrix(27,2,-500,-37) Matrix(4957,1476,7056,2101) -> Matrix(289,20,-9696,-671) Matrix(4955,1474,7056,2099) -> Matrix(175,12,-5848,-401) Matrix(673,200,1134,337) -> Matrix(59,4,-1844,-125) Matrix(379,112,714,211) -> Matrix(27,2,-824,-61) Matrix(251,74,-1428,-421) -> Matrix(57,4,-1012,-71) Matrix(83,24,-294,-85) -> Matrix(59,4,-900,-61) Matrix(923,258,2100,587) -> Matrix(63,4,-1780,-113) Matrix(589,164,1512,421) -> Matrix(1,0,-12,1) Matrix(211,58,462,127) -> Matrix(31,2,-884,-57) Matrix(377,102,462,125) -> Matrix(95,6,-3436,-217) Matrix(967,260,1722,463) -> Matrix(227,14,-6956,-429) Matrix(2141,574,5166,1385) -> Matrix(427,26,-11644,-709) Matrix(673,180,1260,337) -> Matrix(133,8,-4040,-243) Matrix(295,78,798,211) -> Matrix(35,2,-928,-53) Matrix(1303,342,1764,463) -> Matrix(51,2,-1760,-69) Matrix(1301,340,1764,461) -> Matrix(11,2,-380,-69) Matrix(41,10,168,41) -> Matrix(31,2,-760,-49) Matrix(169,40,714,169) -> Matrix(129,8,-3080,-191) Matrix(419,98,714,167) -> Matrix(65,4,-2064,-127) Matrix(169,38,378,85) -> Matrix(1,0,-12,1) Matrix(2563,562,4410,967) -> Matrix(465,26,-14576,-815) Matrix(463,100,588,127) -> Matrix(41,2,-1456,-71) Matrix(461,98,588,125) -> Matrix(25,2,-888,-71) Matrix(127,26,210,43) -> Matrix(33,2,-1040,-63) Matrix(41,8,210,41) -> Matrix(33,2,-776,-47) Matrix(127,24,672,127) -> Matrix(103,6,-2352,-137) Matrix(337,62,462,85) -> Matrix(71,4,-2432,-137) Matrix(167,30,462,83) -> Matrix(1,0,-8,1) Matrix(2059,360,6972,1219) -> Matrix(179,10,-4672,-261) Matrix(1847,322,6258,1091) -> Matrix(217,12,-5624,-311) Matrix(211,36,252,43) -> Matrix(39,2,-1424,-73) Matrix(209,34,252,41) -> Matrix(31,2,-1132,-73) Matrix(41,6,-294,-43) -> Matrix(35,2,-648,-37) Matrix(211,24,378,43) -> Matrix(35,2,-1068,-61) Matrix(293,26,462,41) -> Matrix(39,2,-1268,-65) Matrix(295,-32,378,-41) -> Matrix(41,2,-1456,-71) Matrix(125,-16,336,-43) -> Matrix(43,2,-1140,-53) Matrix(421,-64,546,-83) -> Matrix(91,4,-3208,-141) Matrix(167,-26,546,-85) -> Matrix(1,0,-4,1) Matrix(421,-74,1428,-251) -> Matrix(89,4,-2292,-103) Matrix(293,-64,966,-211) -> Matrix(43,2,-1140,-53) Matrix(463,-106,546,-125) -> Matrix(139,6,-5120,-221) Matrix(125,-32,168,-43) -> Matrix(51,2,-1760,-69) Matrix(463,-128,756,-209) -> Matrix(145,6,-4616,-191) Matrix(85,-24,294,-83) -> Matrix(99,4,-2500,-101) Matrix(589,-176,840,-251) -> Matrix(1,0,-8,1) Matrix(377,-114,420,-127) -> Matrix(157,6,-5940,-227) Matrix(463,-144,672,-209) -> Matrix(45,2,-1508,-67) Matrix(293,-92,672,-211) -> Matrix(47,2,-1340,-57) Matrix(421,-148,714,-251) -> Matrix(1,0,-4,1) Matrix(463,-170,798,-293) -> Matrix(263,10,-8232,-313) Matrix(2269,-842,2940,-1091) -> Matrix(107,4,-3772,-141) Matrix(547,-212,756,-293) -> Matrix(273,10,-9364,-343) Matrix(799,-326,924,-377) -> Matrix(161,6,-5984,-223) Matrix(463,-190,714,-293) -> Matrix(55,2,-1788,-65) Matrix(505,-212,798,-335) -> Matrix(111,4,-3580,-129) Matrix(127,-54,294,-125) -> Matrix(167,6,-4704,-169) Matrix(1933,-842,3276,-1427) -> Matrix(227,8,-6952,-245) Matrix(1597,-704,2856,-1259) -> Matrix(685,24,-20864,-731) Matrix(461,-208,840,-379) -> Matrix(59,2,-1800,-61) Matrix(169,-96,294,-167) -> Matrix(247,8,-7688,-249) Matrix(547,-316,798,-461) -> Matrix(63,2,-2048,-65) Matrix(1427,-844,1848,-1093) -> Matrix(1,0,-4,1) Matrix(293,-184,336,-211) -> Matrix(323,10,-12048,-373) Matrix(85,-56,126,-83) -> Matrix(131,4,-4356,-133) Matrix(461,-320,546,-379) -> Matrix(337,10,-12368,-367) Matrix(755,-526,966,-673) -> Matrix(269,8,-9516,-283) Matrix(1177,-830,1428,-1007) -> Matrix(809,24,-29360,-871) Matrix(211,-150,294,-209) -> Matrix(339,10,-11560,-341) Matrix(253,-216,294,-251) -> Matrix(443,12,-16428,-445) 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): 48 Degree of the the map X: 96 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 -6/7 -11/15 -5/7 -2/3 -4/7 -5/9 -19/42 -3/7 -1/3 -2/7 -11/42 -2/9 -1/6 -1/7 0/1 1/8 1/7 1/6 3/17 4/21 1/5 2/9 3/13 5/21 1/4 5/19 3/11 2/7 31/105 3/10 1/3 8/21 41/105 2/5 3/7 1/2 5/9 4/7 61/105 13/21 2/3 5/7 11/15 16/21 17/21 6/7 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -7/8 -5/13 -3/8 -6/7 -1/3 -11/13 -5/16 -5/6 -2/7 -9/11 -1/4 -4/5 -1/4 -4/17 -7/9 -3/14 -17/22 -5/24 -1/5 -10/13 -4/19 -5/24 -13/17 -13/64 -16/21 -1/5 -3/4 -1/5 -3/16 -14/19 -2/11 -9/50 -11/15 -1/6 -19/26 -5/28 -3/17 -8/11 -2/11 -1/6 -5/7 -1/6 -7/10 -1/6 -3/19 -9/13 -5/32 -2/3 -1/7 -7/11 -1/8 -12/19 -3/22 -2/15 -17/27 -5/38 -22/35 -3/23 -5/8 -5/39 -1/8 -3/5 -1/8 -7/12 -2/17 -11/19 -5/44 -4/7 -1/9 -5/9 -1/10 -11/20 -1/9 -3/28 -6/11 -2/19 -1/10 -1/2 -1/10 -1/11 -5/11 -1/12 -19/42 0/1 -14/31 -1/10 0/1 -9/20 -1/11 -1/12 -4/9 -1/11 -3/7 -1/12 -5/12 -2/25 -12/29 -5/64 -6/77 -7/17 -3/40 -9/22 -1/12 -1/13 -2/5 -1/12 0/1 -9/23 -1/12 -16/41 -1/12 -2/25 -7/18 -2/25 -5/13 -5/64 -8/21 -1/13 -3/8 -1/13 -3/40 -10/27 -1/13 -7/19 -5/68 -11/30 -4/55 -15/41 -15/208 -4/11 -1/14 -2/29 -1/3 -1/14 -3/10 -1/14 -3/43 -5/17 -5/72 -2/7 -1/15 -3/11 -1/16 -4/15 -1/17 -5/19 -1/20 -11/42 0/1 -6/23 -1/10 0/1 -1/4 -1/15 -1/16 -3/13 -1/16 -8/35 -1/17 -5/22 -1/16 -1/17 -2/9 -1/17 -1/5 -1/16 -4/21 -1/17 -3/16 -1/17 -3/52 -2/11 -2/35 -1/18 -1/6 0/1 -2/13 -1/16 0/1 -1/7 -1/18 -1/8 -1/19 -1/20 0/1 -1/20 0/1 1/8 -1/20 -1/21 1/7 -1/22 2/13 -1/24 0/1 1/6 0/1 4/23 -4/87 -1/22 3/17 -3/68 2/11 -1/22 -2/45 3/16 -3/68 -1/23 4/21 -1/23 1/5 -1/24 2/9 -1/23 5/22 -1/23 -1/24 3/13 -1/24 4/17 -4/95 -1/24 5/21 -1/24 1/4 -1/24 -1/25 5/19 -1/20 4/15 -1/23 3/11 -1/24 5/18 -2/49 2/7 -1/25 7/24 -2/51 12/41 -3/76 -2/51 5/17 -5/128 18/61 -8/207 -1/26 31/105 -1/26 13/44 -1/26 -3/79 8/27 -1/25 3/10 -3/77 -1/26 1/3 -1/26 4/11 -2/51 -1/26 7/19 -5/132 10/27 -1/27 3/8 -3/80 -1/27 8/21 -1/27 5/13 -5/136 7/18 -2/55 16/41 -2/55 -1/28 41/105 -1/28 25/64 -1/27 -1/28 9/23 -1/28 2/5 -1/28 0/1 11/27 -1/26 9/22 -1/27 -1/28 7/17 -3/80 12/29 -6/163 -5/136 17/41 -17/464 5/12 -2/55 3/7 -1/28 4/9 -1/29 9/20 -1/28 -1/29 5/11 -1/28 1/2 -1/29 -1/30 8/15 -3/91 7/13 -3/92 6/11 -1/30 -2/61 23/42 -2/61 17/31 -3/92 11/20 -3/92 -1/31 5/9 -1/30 9/16 -3/92 -7/215 4/7 -1/31 15/26 -5/156 -9/281 11/19 -5/156 18/31 -16/501 -3/94 61/105 -3/94 43/74 -3/94 -41/1285 25/43 -25/784 7/12 -2/63 3/5 -1/32 8/13 -8/255 -1/32 13/21 -1/32 5/8 -1/32 -5/161 17/27 -5/162 12/19 -2/65 -3/98 7/11 -1/32 9/14 -2/65 11/17 -5/164 13/20 -1/32 -1/33 2/3 -1/33 9/13 -5/168 16/23 -1/34 0/1 7/10 -3/101 -1/34 5/7 -1/34 8/11 -1/34 -2/69 19/26 -3/103 -5/172 30/41 -5/172 -2/69 41/56 -2/69 11/15 -1/34 14/19 -9/310 -2/69 31/42 -2/69 17/23 -11/380 3/4 -3/104 -1/35 16/21 -1/35 13/17 -13/456 10/13 -5/176 -4/141 17/22 -1/35 -5/176 7/9 -3/106 11/14 -2/71 15/19 -1/36 4/5 -4/143 -1/36 17/21 -1/36 13/16 -1/36 -13/469 9/11 -1/36 5/6 -2/73 16/19 -3/110 -10/367 11/13 -5/184 17/20 -5/184 -1/37 6/7 -1/37 19/22 -1/37 -7/260 13/15 -5/186 7/8 -3/112 -5/187 8/9 -3/113 1/1 -1/40 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(148,131,357,316) (-1/1,-7/8) -> (12/29,17/41) Hyperbolic Matrix(211,184,-336,-293) (-7/8,-6/7) -> (-22/35,-5/8) Hyperbolic Matrix(125,106,-546,-463) (-6/7,-11/13) -> (-3/13,-8/35) Hyperbolic Matrix(146,123,273,230) (-11/13,-5/6) -> (8/15,7/13) Hyperbolic Matrix(62,51,-231,-190) (-5/6,-9/11) -> (-3/11,-4/15) Hyperbolic Matrix(188,153,231,188) (-9/11,-4/5) -> (13/16,9/11) Hyperbolic Matrix(106,83,189,148) (-4/5,-7/9) -> (5/9,9/16) Hyperbolic Matrix(209,162,378,293) (-7/9,-17/22) -> (11/20,5/9) Hyperbolic Matrix(22,17,-189,-146) (-17/22,-10/13) -> (-1/8,0/1) Hyperbolic Matrix(295,226,714,547) (-10/13,-13/17) -> (7/17,12/29) Hyperbolic Matrix(545,416,714,545) (-13/17,-16/21) -> (16/21,13/17) Hyperbolic Matrix(127,96,168,127) (-16/21,-3/4) -> (3/4,16/21) Hyperbolic Matrix(43,32,-168,-125) (-3/4,-14/19) -> (-6/23,-1/4) Hyperbolic Matrix(503,370,798,587) (-14/19,-11/15) -> (17/27,12/19) Hyperbolic Matrix(316,231,777,568) (-11/15,-19/26) -> (2/5,11/27) Hyperbolic Matrix(85,62,462,337) (-19/26,-8/11) -> (2/11,3/16) Hyperbolic Matrix(104,75,-147,-106) (-8/11,-5/7) -> (-5/7,-7/10) Parabolic Matrix(148,103,273,190) (-7/10,-9/13) -> (7/13,6/11) Hyperbolic Matrix(106,73,-273,-188) (-9/13,-2/3) -> (-7/18,-5/13) Hyperbolic Matrix(64,41,231,148) (-2/3,-7/11) -> (3/11,5/18) Hyperbolic Matrix(106,67,-231,-146) (-7/11,-12/19) -> (-1/2,-5/11) Hyperbolic Matrix(587,370,798,503) (-12/19,-17/27) -> (11/15,14/19) Hyperbolic Matrix(1492,939,2037,1282) (-17/27,-22/35) -> (41/56,11/15) Hyperbolic Matrix(64,39,105,64) (-5/8,-3/5) -> (3/5,8/13) Hyperbolic Matrix(22,13,-105,-62) (-3/5,-7/12) -> (-2/9,-1/5) Hyperbolic Matrix(293,170,-798,-463) (-7/12,-11/19) -> (-7/19,-11/30) Hyperbolic Matrix(314,181,399,230) (-11/19,-4/7) -> (11/14,15/19) Hyperbolic Matrix(148,83,189,106) (-4/7,-5/9) -> (7/9,11/14) Hyperbolic Matrix(293,162,378,209) (-5/9,-11/20) -> (17/22,7/9) Hyperbolic Matrix(379,208,-840,-461) (-11/20,-6/11) -> (-14/31,-9/20) Hyperbolic Matrix(190,103,273,148) (-6/11,-1/2) -> (16/23,7/10) Hyperbolic Matrix(967,438,1764,799) (-5/11,-19/42) -> (23/42,17/31) Hyperbolic Matrix(965,436,1764,797) (-19/42,-14/31) -> (6/11,23/42) Hyperbolic Matrix(85,38,378,169) (-9/20,-4/9) -> (2/9,5/22) Hyperbolic Matrix(62,27,-147,-64) (-4/9,-3/7) -> (-3/7,-5/12) Parabolic Matrix(316,131,357,148) (-5/12,-12/29) -> (7/8,8/9) Hyperbolic Matrix(547,226,714,295) (-12/29,-7/17) -> (13/17,10/13) Hyperbolic Matrix(314,129,1071,440) (-7/17,-9/22) -> (12/41,5/17) Hyperbolic Matrix(568,231,777,316) (-9/22,-2/5) -> (19/26,30/41) Hyperbolic Matrix(167,66,210,83) (-2/5,-9/23) -> (15/19,4/5) Hyperbolic Matrix(944,369,2415,944) (-9/23,-16/41) -> (25/64,9/23) Hyperbolic Matrix(503,196,1722,671) (-16/41,-7/18) -> (7/24,12/41) Hyperbolic Matrix(209,80,546,209) (-5/13,-8/21) -> (8/21,5/13) Hyperbolic Matrix(127,48,336,127) (-8/21,-3/8) -> (3/8,8/21) Hyperbolic Matrix(62,23,-399,-148) (-3/8,-10/27) -> (-1/6,-2/13) Hyperbolic Matrix(211,78,798,295) (-10/27,-7/19) -> (5/19,4/15) Hyperbolic Matrix(715,262,1722,631) (-11/30,-15/41) -> (17/41,5/12) Hyperbolic Matrix(2038,745,3507,1282) (-15/41,-4/11) -> (43/74,25/43) Hyperbolic Matrix(20,7,-63,-22) (-4/11,-1/3) -> (-1/3,-3/10) Parabolic Matrix(64,19,357,106) (-3/10,-5/17) -> (3/17,2/11) Hyperbolic Matrix(230,67,357,104) (-5/17,-2/7) -> (9/14,11/17) Hyperbolic Matrix(148,41,231,64) (-2/7,-3/11) -> (7/11,9/14) Hyperbolic Matrix(295,78,798,211) (-4/15,-5/19) -> (7/19,10/27) Hyperbolic Matrix(1303,342,1764,463) (-5/19,-11/42) -> (31/42,17/23) Hyperbolic Matrix(1301,340,1764,461) (-11/42,-6/23) -> (14/19,31/42) Hyperbolic Matrix(64,15,273,64) (-1/4,-3/13) -> (3/13,4/17) Hyperbolic Matrix(1952,445,2667,608) (-8/35,-5/22) -> (30/41,41/56) Hyperbolic Matrix(169,38,378,85) (-5/22,-2/9) -> (4/9,9/20) Hyperbolic Matrix(41,8,210,41) (-1/5,-4/21) -> (4/21,1/5) Hyperbolic Matrix(127,24,672,127) (-4/21,-3/16) -> (3/16,4/21) Hyperbolic Matrix(337,62,462,85) (-3/16,-2/11) -> (8/11,19/26) Hyperbolic Matrix(106,19,357,64) (-2/11,-1/6) -> (8/27,3/10) Hyperbolic Matrix(20,3,-147,-22) (-2/13,-1/7) -> (-1/7,-1/8) Parabolic Matrix(146,-17,189,-22) (0/1,1/8) -> (10/13,17/22) Hyperbolic Matrix(22,-3,147,-20) (1/8,1/7) -> (1/7,2/13) Parabolic Matrix(148,-23,399,-62) (2/13,1/6) -> (10/27,3/8) Hyperbolic Matrix(190,-33,357,-62) (1/6,4/23) -> (1/2,8/15) Hyperbolic Matrix(421,-74,1428,-251) (4/23,3/17) -> (5/17,18/61) Hyperbolic Matrix(62,-13,105,-22) (1/5,2/9) -> (7/12,3/5) Hyperbolic Matrix(463,-106,546,-125) (5/22,3/13) -> (11/13,17/20) Hyperbolic Matrix(106,-25,441,-104) (4/17,5/21) -> (5/21,1/4) Parabolic Matrix(125,-32,168,-43) (1/4,5/19) -> (17/23,3/4) Hyperbolic Matrix(190,-51,231,-62) (4/15,3/11) -> (9/11,5/6) Hyperbolic Matrix(85,-24,294,-83) (5/18,2/7) -> (2/7,7/24) Parabolic Matrix(3256,-961,11025,-3254) (18/61,31/105) -> (31/105,13/44) Parabolic Matrix(652,-193,777,-230) (13/44,8/27) -> (5/6,16/19) Hyperbolic Matrix(22,-7,63,-20) (3/10,1/3) -> (1/3,4/11) Parabolic Matrix(463,-170,798,-293) (4/11,7/19) -> (11/19,18/31) Hyperbolic Matrix(188,-73,273,-106) (5/13,7/18) -> (2/3,9/13) Hyperbolic Matrix(316,-123,483,-188) (7/18,16/41) -> (13/20,2/3) Hyperbolic Matrix(4306,-1681,11025,-4304) (16/41,41/105) -> (41/105,25/64) Parabolic Matrix(400,-157,693,-272) (9/23,2/5) -> (15/26,11/19) Hyperbolic Matrix(799,-326,924,-377) (11/27,9/22) -> (19/22,13/15) Hyperbolic Matrix(463,-190,714,-293) (9/22,7/17) -> (11/17,13/20) Hyperbolic Matrix(64,-27,147,-62) (5/12,3/7) -> (3/7,4/9) Parabolic Matrix(461,-208,840,-379) (9/20,5/11) -> (17/31,11/20) Hyperbolic Matrix(146,-67,231,-106) (5/11,1/2) -> (12/19,7/11) Hyperbolic Matrix(169,-96,294,-167) (9/16,4/7) -> (4/7,15/26) Parabolic Matrix(6406,-3721,11025,-6404) (18/31,61/105) -> (61/105,43/74) Parabolic Matrix(356,-207,399,-232) (25/43,7/12) -> (8/9,1/1) Hyperbolic Matrix(274,-169,441,-272) (8/13,13/21) -> (13/21,5/8) Parabolic Matrix(293,-184,336,-211) (5/8,17/27) -> (13/15,7/8) Hyperbolic Matrix(461,-320,546,-379) (9/13,16/23) -> (16/19,11/13) Hyperbolic Matrix(106,-75,147,-104) (7/10,5/7) -> (5/7,8/11) Parabolic Matrix(358,-289,441,-356) (4/5,17/21) -> (17/21,13/16) Parabolic Matrix(253,-216,294,-251) (17/20,6/7) -> (6/7,19/22) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-40,1) Matrix(148,131,357,316) -> Matrix(17,7,-464,-191) Matrix(211,184,-336,-293) -> Matrix(27,10,-208,-77) Matrix(125,106,-546,-463) -> Matrix(19,6,-320,-101) Matrix(146,123,273,230) -> Matrix(23,7,-700,-213) Matrix(62,51,-231,-190) -> Matrix(11,3,-180,-49) Matrix(188,153,231,188) -> Matrix(35,9,-1264,-325) Matrix(106,83,189,148) -> Matrix(23,5,-704,-153) Matrix(209,162,378,293) -> Matrix(9,2,-284,-63) Matrix(22,17,-189,-146) -> Matrix(5,1,-76,-15) Matrix(295,226,714,547) -> Matrix(49,10,-1328,-271) Matrix(545,416,714,545) -> Matrix(129,26,-4520,-911) Matrix(127,96,168,127) -> Matrix(31,6,-1080,-209) Matrix(43,32,-168,-125) -> Matrix(11,2,-160,-29) Matrix(503,370,798,587) -> Matrix(67,12,-2172,-389) Matrix(316,231,777,568) -> Matrix(17,3,-448,-79) Matrix(85,62,462,337) -> Matrix(23,4,-512,-89) Matrix(104,75,-147,-106) -> Matrix(29,5,-180,-31) Matrix(148,103,273,190) -> Matrix(7,1,-204,-29) Matrix(106,73,-273,-188) -> Matrix(33,5,-416,-63) Matrix(64,41,231,148) -> Matrix(23,3,-560,-73) Matrix(106,67,-231,-146) -> Matrix(7,1,-92,-13) Matrix(587,370,798,503) -> Matrix(91,12,-3132,-413) Matrix(1492,939,2037,1282) -> Matrix(53,7,-1840,-243) Matrix(64,39,105,64) -> Matrix(25,3,-792,-95) Matrix(22,13,-105,-62) -> Matrix(9,1,-136,-15) Matrix(293,170,-798,-463) -> Matrix(87,10,-1192,-137) Matrix(314,181,399,230) -> Matrix(97,11,-3448,-391) Matrix(148,83,189,106) -> Matrix(47,5,-1664,-177) Matrix(293,162,378,209) -> Matrix(17,2,-604,-71) Matrix(379,208,-840,-461) -> Matrix(19,2,-200,-21) Matrix(190,103,273,148) -> Matrix(11,1,-364,-33) Matrix(967,438,1764,799) -> Matrix(27,2,-824,-61) Matrix(965,436,1764,797) -> Matrix(19,2,-580,-61) Matrix(85,38,378,169) -> Matrix(1,0,-12,1) Matrix(62,27,-147,-64) -> Matrix(35,3,-432,-37) Matrix(316,131,357,148) -> Matrix(89,7,-3344,-263) Matrix(547,226,714,295) -> Matrix(129,10,-4528,-351) Matrix(314,129,1071,440) -> Matrix(15,1,-376,-25) Matrix(568,231,777,316) -> Matrix(41,3,-1408,-103) Matrix(167,66,210,83) -> Matrix(49,4,-1752,-143) Matrix(944,369,2415,944) -> Matrix(37,3,-1024,-83) Matrix(503,196,1722,671) -> Matrix(51,4,-1288,-101) Matrix(209,80,546,209) -> Matrix(129,10,-3496,-271) Matrix(127,48,336,127) -> Matrix(79,6,-2120,-161) Matrix(62,23,-399,-148) -> Matrix(13,1,-248,-19) Matrix(211,78,798,295) -> Matrix(27,2,-608,-45) Matrix(715,262,1722,631) -> Matrix(193,14,-5280,-383) Matrix(2038,745,3507,1282) -> Matrix(487,35,-15264,-1097) Matrix(20,7,-63,-22) -> Matrix(13,1,-196,-15) Matrix(64,19,357,106) -> Matrix(15,1,-316,-21) Matrix(230,67,357,104) -> Matrix(73,5,-2380,-163) Matrix(148,41,231,64) -> Matrix(47,3,-1520,-97) Matrix(295,78,798,211) -> Matrix(35,2,-928,-53) Matrix(1303,342,1764,463) -> Matrix(51,2,-1760,-69) Matrix(1301,340,1764,461) -> Matrix(11,2,-380,-69) Matrix(64,15,273,64) -> Matrix(49,3,-1160,-71) Matrix(1952,445,2667,608) -> Matrix(53,3,-1820,-103) Matrix(169,38,378,85) -> Matrix(1,0,-12,1) Matrix(41,8,210,41) -> Matrix(33,2,-776,-47) Matrix(127,24,672,127) -> Matrix(103,6,-2352,-137) Matrix(337,62,462,85) -> Matrix(71,4,-2432,-137) Matrix(106,19,357,64) -> Matrix(19,1,-476,-25) Matrix(20,3,-147,-22) -> Matrix(17,1,-324,-19) Matrix(146,-17,189,-22) -> Matrix(25,1,-876,-35) Matrix(22,-3,147,-20) -> Matrix(21,1,-484,-23) Matrix(148,-23,399,-62) -> Matrix(21,1,-568,-27) Matrix(190,-33,357,-62) -> Matrix(65,3,-1972,-91) Matrix(421,-74,1428,-251) -> Matrix(89,4,-2292,-103) Matrix(62,-13,105,-22) -> Matrix(25,1,-776,-31) Matrix(463,-106,546,-125) -> Matrix(139,6,-5120,-221) Matrix(106,-25,441,-104) -> Matrix(119,5,-2880,-121) Matrix(125,-32,168,-43) -> Matrix(51,2,-1760,-69) Matrix(190,-51,231,-62) -> Matrix(71,3,-2580,-109) Matrix(85,-24,294,-83) -> Matrix(99,4,-2500,-101) Matrix(3256,-961,11025,-3254) -> Matrix(285,11,-7436,-287) Matrix(652,-193,777,-230) -> Matrix(23,1,-852,-37) Matrix(22,-7,63,-20) -> Matrix(25,1,-676,-27) Matrix(463,-170,798,-293) -> Matrix(263,10,-8232,-313) Matrix(188,-73,273,-106) -> Matrix(137,5,-4576,-167) Matrix(316,-123,483,-188) -> Matrix(83,3,-2684,-97) Matrix(4306,-1681,11025,-4304) -> Matrix(27,1,-784,-29) Matrix(400,-157,693,-272) -> Matrix(247,9,-7712,-281) Matrix(799,-326,924,-377) -> Matrix(161,6,-5984,-223) Matrix(463,-190,714,-293) -> Matrix(55,2,-1788,-65) Matrix(64,-27,147,-62) -> Matrix(83,3,-2352,-85) Matrix(461,-208,840,-379) -> Matrix(59,2,-1800,-61) Matrix(146,-67,231,-106) -> Matrix(27,1,-892,-33) Matrix(169,-96,294,-167) -> Matrix(247,8,-7688,-249) Matrix(6406,-3721,11025,-6404) -> Matrix(5357,171,-167884,-5359) Matrix(356,-207,399,-232) -> Matrix(345,11,-13016,-415) Matrix(274,-169,441,-272) -> Matrix(415,13,-13312,-417) Matrix(293,-184,336,-211) -> Matrix(323,10,-12048,-373) Matrix(461,-320,546,-379) -> Matrix(337,10,-12368,-367) Matrix(106,-75,147,-104) -> Matrix(169,5,-5780,-171) Matrix(358,-289,441,-356) -> Matrix(611,17,-22032,-613) Matrix(253,-216,294,-251) -> Matrix(443,12,-16428,-445) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/20,0/1) 0 21 1/8 (-1/20,-1/21) 0 21 1/7 -1/22 1 3 2/13 (-1/24,0/1) 0 21 1/6 0/1 2 7 2/11 (-1/22,-2/45) 0 21 3/16 (-3/68,-1/23) 0 21 4/21 -1/23 4 1 1/5 -1/24 1 21 2/9 -1/23 2 7 5/22 (-1/23,-1/24) 0 21 3/13 -1/24 1 21 5/21 -1/24 5 1 1/4 (-1/24,-1/25) 0 21 5/19 -1/20 1 21 4/15 -1/23 2 7 3/11 -1/24 1 21 2/7 -1/25 2 3 5/17 -5/128 1 21 31/105 -1/26 11 1 13/44 (-1/26,-3/79) 0 21 8/27 -1/25 2 7 3/10 (-3/77,-1/26) 0 21 1/3 -1/26 1 7 4/11 (-2/51,-1/26) 0 21 7/19 -5/132 1 21 10/27 -1/27 2 7 3/8 (-3/80,-1/27) 0 21 8/21 -1/27 8 1 5/13 -5/136 1 21 7/18 -2/55 2 7 16/41 (-2/55,-1/28) 0 21 41/105 -1/28 1 1 9/23 -1/28 1 21 2/5 (-1/28,0/1) 0 21 9/22 (-1/27,-1/28) 0 21 7/17 -3/80 1 21 12/29 (-6/163,-5/136) 0 21 5/12 -2/55 2 7 3/7 -1/28 3 3 4/9 -1/29 2 7 9/20 (-1/28,-1/29) 0 21 5/11 -1/28 1 21 1/2 (-1/29,-1/30) 0 21 6/11 (-1/30,-2/61) 0 21 23/42 -2/61 2 1 17/31 -3/92 1 21 11/20 (-3/92,-1/31) 0 21 5/9 -1/30 1 7 4/7 -1/31 4 3 11/19 -5/156 1 21 18/31 (-16/501,-3/94) 0 21 61/105 -3/94 19 1 25/43 -25/784 1 21 7/12 -2/63 2 7 3/5 -1/32 1 21 13/21 -1/32 13 1 5/8 (-1/32,-5/161) 0 21 17/27 -5/162 1 7 12/19 (-2/65,-3/98) 0 21 7/11 -1/32 1 21 9/14 -2/65 2 3 11/17 -5/164 1 21 13/20 (-1/32,-1/33) 0 21 2/3 -1/33 2 7 9/13 -5/168 1 21 16/23 (-1/34,0/1) 0 21 7/10 (-3/101,-1/34) 0 21 5/7 -1/34 5 3 8/11 (-1/34,-2/69) 0 21 19/26 (-3/103,-5/172) 0 21 30/41 (-5/172,-2/69) 0 21 11/15 -1/34 1 7 14/19 (-9/310,-2/69) 0 21 31/42 -2/69 10 1 17/23 -11/380 1 21 3/4 (-3/104,-1/35) 0 21 16/21 -1/35 16 1 13/17 -13/456 1 21 10/13 (-5/176,-4/141) 0 21 17/22 (-1/35,-5/176) 0 21 7/9 -3/106 1 7 11/14 -2/71 4 3 15/19 -1/36 1 21 4/5 (-4/143,-1/36) 0 21 17/21 -1/36 17 1 9/11 -1/36 1 21 5/6 -2/73 2 7 16/19 (-3/110,-10/367) 0 21 11/13 -5/184 1 21 17/20 (-5/184,-1/37) 0 21 6/7 -1/37 6 3 19/22 (-1/37,-7/260) 0 21 13/15 -5/186 1 7 7/8 (-3/112,-5/187) 0 21 8/9 -3/113 2 7 1/1 -1/40 1 21 1/0 0/1 20 1 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(146,-17,189,-22) (0/1,1/8) -> (10/13,17/22) Hyperbolic Matrix(22,-3,147,-20) (1/8,1/7) -> (1/7,2/13) Parabolic Matrix(148,-23,399,-62) (2/13,1/6) -> (10/27,3/8) Hyperbolic Matrix(106,-19,357,-64) (1/6,2/11) -> (8/27,3/10) Glide Reflection Matrix(337,-62,462,-85) (2/11,3/16) -> (8/11,19/26) Glide Reflection Matrix(127,-24,672,-127) (3/16,4/21) -> (3/16,4/21) Reflection Matrix(41,-8,210,-41) (4/21,1/5) -> (4/21,1/5) Reflection Matrix(62,-13,105,-22) (1/5,2/9) -> (7/12,3/5) Hyperbolic Matrix(169,-38,378,-85) (2/9,5/22) -> (4/9,9/20) Glide Reflection Matrix(463,-106,546,-125) (5/22,3/13) -> (11/13,17/20) Hyperbolic Matrix(64,-15,273,-64) (3/13,5/21) -> (3/13,5/21) Reflection Matrix(41,-10,168,-41) (5/21,1/4) -> (5/21,1/4) Reflection Matrix(125,-32,168,-43) (1/4,5/19) -> (17/23,3/4) Hyperbolic Matrix(295,-78,798,-211) (5/19,4/15) -> (7/19,10/27) Glide Reflection Matrix(190,-51,231,-62) (4/15,3/11) -> (9/11,5/6) Hyperbolic Matrix(148,-41,231,-64) (3/11,2/7) -> (7/11,9/14) Glide Reflection Matrix(230,-67,357,-104) (2/7,5/17) -> (9/14,11/17) Glide Reflection Matrix(526,-155,1785,-526) (5/17,31/105) -> (5/17,31/105) Reflection Matrix(2729,-806,9240,-2729) (31/105,13/44) -> (31/105,13/44) Reflection Matrix(652,-193,777,-230) (13/44,8/27) -> (5/6,16/19) Hyperbolic Matrix(22,-7,63,-20) (3/10,1/3) -> (1/3,4/11) Parabolic Matrix(463,-170,798,-293) (4/11,7/19) -> (11/19,18/31) Hyperbolic Matrix(127,-48,336,-127) (3/8,8/21) -> (3/8,8/21) Reflection Matrix(209,-80,546,-209) (8/21,5/13) -> (8/21,5/13) Reflection Matrix(188,-73,273,-106) (5/13,7/18) -> (2/3,9/13) Hyperbolic Matrix(316,-123,483,-188) (7/18,16/41) -> (13/20,2/3) Hyperbolic Matrix(3361,-1312,8610,-3361) (16/41,41/105) -> (16/41,41/105) Reflection Matrix(944,-369,2415,-944) (41/105,9/23) -> (41/105,9/23) Reflection Matrix(167,-66,210,-83) (9/23,2/5) -> (15/19,4/5) Glide Reflection Matrix(568,-231,777,-316) (2/5,9/22) -> (19/26,30/41) Glide Reflection Matrix(463,-190,714,-293) (9/22,7/17) -> (11/17,13/20) Hyperbolic Matrix(547,-226,714,-295) (7/17,12/29) -> (13/17,10/13) Glide Reflection Matrix(316,-131,357,-148) (12/29,5/12) -> (7/8,8/9) Glide Reflection Matrix(64,-27,147,-62) (5/12,3/7) -> (3/7,4/9) Parabolic Matrix(461,-208,840,-379) (9/20,5/11) -> (17/31,11/20) Hyperbolic Matrix(146,-67,231,-106) (5/11,1/2) -> (12/19,7/11) Hyperbolic Matrix(190,-103,273,-148) (1/2,6/11) -> (16/23,7/10) Glide Reflection Matrix(505,-276,924,-505) (6/11,23/42) -> (6/11,23/42) Reflection Matrix(1427,-782,2604,-1427) (23/42,17/31) -> (23/42,17/31) Reflection Matrix(293,-162,378,-209) (11/20,5/9) -> (17/22,7/9) Glide Reflection Matrix(148,-83,189,-106) (5/9,4/7) -> (7/9,11/14) Glide Reflection Matrix(314,-181,399,-230) (4/7,11/19) -> (11/14,15/19) Glide Reflection Matrix(3781,-2196,6510,-3781) (18/31,61/105) -> (18/31,61/105) Reflection Matrix(2624,-1525,4515,-2624) (61/105,25/43) -> (61/105,25/43) Reflection Matrix(356,-207,399,-232) (25/43,7/12) -> (8/9,1/1) Hyperbolic Matrix(64,-39,105,-64) (3/5,13/21) -> (3/5,13/21) Reflection Matrix(209,-130,336,-209) (13/21,5/8) -> (13/21,5/8) Reflection Matrix(293,-184,336,-211) (5/8,17/27) -> (13/15,7/8) Hyperbolic Matrix(587,-370,798,-503) (17/27,12/19) -> (11/15,14/19) Glide Reflection Matrix(461,-320,546,-379) (9/13,16/23) -> (16/19,11/13) Hyperbolic Matrix(106,-75,147,-104) (7/10,5/7) -> (5/7,8/11) Parabolic Matrix(818,-599,945,-692) (30/41,11/15) -> (19/22,13/15) Glide Reflection Matrix(1177,-868,1596,-1177) (14/19,31/42) -> (14/19,31/42) Reflection Matrix(1427,-1054,1932,-1427) (31/42,17/23) -> (31/42,17/23) Reflection Matrix(127,-96,168,-127) (3/4,16/21) -> (3/4,16/21) Reflection Matrix(545,-416,714,-545) (16/21,13/17) -> (16/21,13/17) Reflection Matrix(169,-136,210,-169) (4/5,17/21) -> (4/5,17/21) Reflection Matrix(188,-153,231,-188) (17/21,9/11) -> (17/21,9/11) Reflection Matrix(253,-216,294,-251) (17/20,6/7) -> (6/7,19/22) Parabolic Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,40,1) (0/1,1/0) -> (-1/20,0/1) Matrix(146,-17,189,-22) -> Matrix(25,1,-876,-35) Matrix(22,-3,147,-20) -> Matrix(21,1,-484,-23) -1/22 Matrix(148,-23,399,-62) -> Matrix(21,1,-568,-27) Matrix(106,-19,357,-64) -> Matrix(21,1,-524,-25) Matrix(337,-62,462,-85) -> Matrix(89,4,-3048,-137) Matrix(127,-24,672,-127) -> Matrix(137,6,-3128,-137) (3/16,4/21) -> (-3/68,-1/23) Matrix(41,-8,210,-41) -> Matrix(47,2,-1104,-47) (4/21,1/5) -> (-1/23,-1/24) Matrix(62,-13,105,-22) -> Matrix(25,1,-776,-31) Matrix(169,-38,378,-85) -> Matrix(-1,0,52,1) *** -> (-1/26,0/1) Matrix(463,-106,546,-125) -> Matrix(139,6,-5120,-221) Matrix(64,-15,273,-64) -> Matrix(71,3,-1680,-71) (3/13,5/21) -> (-3/70,-1/24) Matrix(41,-10,168,-41) -> Matrix(49,2,-1200,-49) (5/21,1/4) -> (-1/24,-1/25) Matrix(125,-32,168,-43) -> Matrix(51,2,-1760,-69) Matrix(295,-78,798,-211) -> Matrix(45,2,-1192,-53) Matrix(190,-51,231,-62) -> Matrix(71,3,-2580,-109) Matrix(148,-41,231,-64) -> Matrix(73,3,-2360,-97) Matrix(230,-67,357,-104) -> Matrix(127,5,-4140,-163) Matrix(526,-155,1785,-526) -> Matrix(129,5,-3328,-129) (5/17,31/105) -> (-5/128,-1/26) Matrix(2729,-806,9240,-2729) -> Matrix(157,6,-4108,-157) (31/105,13/44) -> (-1/26,-3/79) Matrix(652,-193,777,-230) -> Matrix(23,1,-852,-37) Matrix(22,-7,63,-20) -> Matrix(25,1,-676,-27) -1/26 Matrix(463,-170,798,-293) -> Matrix(263,10,-8232,-313) Matrix(127,-48,336,-127) -> Matrix(161,6,-4320,-161) (3/8,8/21) -> (-3/80,-1/27) Matrix(209,-80,546,-209) -> Matrix(271,10,-7344,-271) (8/21,5/13) -> (-1/27,-5/136) Matrix(188,-73,273,-106) -> Matrix(137,5,-4576,-167) Matrix(316,-123,483,-188) -> Matrix(83,3,-2684,-97) Matrix(3361,-1312,8610,-3361) -> Matrix(111,4,-3080,-111) (16/41,41/105) -> (-2/55,-1/28) Matrix(944,-369,2415,-944) -> Matrix(83,3,-2296,-83) (41/105,9/23) -> (-3/82,-1/28) Matrix(167,-66,210,-83) -> Matrix(111,4,-3968,-143) Matrix(568,-231,777,-316) -> Matrix(79,3,-2712,-103) Matrix(463,-190,714,-293) -> Matrix(55,2,-1788,-65) Matrix(547,-226,714,-295) -> Matrix(271,10,-9512,-351) Matrix(316,-131,357,-148) -> Matrix(191,7,-7176,-263) Matrix(64,-27,147,-62) -> Matrix(83,3,-2352,-85) -1/28 Matrix(461,-208,840,-379) -> Matrix(59,2,-1800,-61) -1/30 Matrix(146,-67,231,-106) -> Matrix(27,1,-892,-33) Matrix(190,-103,273,-148) -> Matrix(29,1,-956,-33) Matrix(505,-276,924,-505) -> Matrix(121,4,-3660,-121) (6/11,23/42) -> (-1/30,-2/61) Matrix(1427,-782,2604,-1427) -> Matrix(367,12,-11224,-367) (23/42,17/31) -> (-2/61,-3/92) Matrix(293,-162,378,-209) -> Matrix(63,2,-2236,-71) Matrix(148,-83,189,-106) -> Matrix(153,5,-5416,-177) Matrix(314,-181,399,-230) -> Matrix(343,11,-12192,-391) Matrix(3781,-2196,6510,-3781) -> Matrix(3007,96,-94188,-3007) (18/31,61/105) -> (-16/501,-3/94) Matrix(2624,-1525,4515,-2624) -> Matrix(2351,75,-73696,-2351) (61/105,25/43) -> (-3/94,-25/784) Matrix(356,-207,399,-232) -> Matrix(345,11,-13016,-415) Matrix(64,-39,105,-64) -> Matrix(95,3,-3008,-95) (3/5,13/21) -> (-3/94,-1/32) Matrix(209,-130,336,-209) -> Matrix(321,10,-10304,-321) (13/21,5/8) -> (-1/32,-5/161) Matrix(293,-184,336,-211) -> Matrix(323,10,-12048,-373) Matrix(587,-370,798,-503) -> Matrix(389,12,-13388,-413) Matrix(461,-320,546,-379) -> Matrix(337,10,-12368,-367) Matrix(106,-75,147,-104) -> Matrix(169,5,-5780,-171) -1/34 Matrix(818,-599,945,-692) -> Matrix(311,9,-11576,-335) Matrix(1177,-868,1596,-1177) -> Matrix(1241,36,-42780,-1241) (14/19,31/42) -> (-9/310,-2/69) Matrix(1427,-1054,1932,-1427) -> Matrix(1519,44,-52440,-1519) (31/42,17/23) -> (-2/69,-11/380) Matrix(127,-96,168,-127) -> Matrix(209,6,-7280,-209) (3/4,16/21) -> (-3/104,-1/35) Matrix(545,-416,714,-545) -> Matrix(911,26,-31920,-911) (16/21,13/17) -> (-1/35,-13/456) Matrix(169,-136,210,-169) -> Matrix(287,8,-10296,-287) (4/5,17/21) -> (-4/143,-1/36) Matrix(188,-153,231,-188) -> Matrix(325,9,-11736,-325) (17/21,9/11) -> (-1/36,-9/326) Matrix(253,-216,294,-251) -> Matrix(443,12,-16428,-445) -1/37 Matrix(-1,2,0,1) -> Matrix(-1,0,80,1) (1/1,1/0) -> (-1/40,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.