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 -1/1 -6/13 -11/25 -5/12 -9/23 -4/11 -1/3 -5/19 -2/9 -3/17 -1/7 -1/8 0/1 1/6 3/11 1/3 2/5 13/29 1/2 5/9 5/7 3/4 1/1 15/13 11/9 4/3 7/5 33/23 3/2 17/11 11/7 5/3 9/5 2/1 15/7 11/5 29/13 39/17 7/3 5/2 13/5 81/31 71/27 8/3 19/7 3/1 43/13 10/3 17/5 65/19 7/2 11/3 19/5 4/1 113/27 21/5 17/4 13/3 57/13 9/2 23/5 5/1 47/9 27/5 11/2 17/3 6/1 7/1 8/1 25/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/25 -6/13 1/22 -11/24 4/85 1/21 -5/11 1/22 -9/20 1/21 4/83 -4/9 0/1 1/21 -11/25 1/20 -18/41 6/119 5/99 -25/57 4/79 -7/16 3/59 2/39 -3/7 1/19 -8/19 0/1 1/19 -21/50 1/19 2/37 -13/31 5/92 -5/12 1/18 -17/41 4/71 -12/29 7/123 2/35 -7/17 1/18 -16/39 2/35 5/87 -9/22 0/1 1/17 -2/5 1/17 2/33 -9/23 1/16 -16/41 9/143 8/127 -7/18 4/63 3/47 -12/31 4/63 3/47 -5/13 2/31 -13/34 3/46 -8/21 4/61 1/15 -11/29 7/106 -3/8 1/15 4/59 -13/35 7/102 -10/27 2/29 11/159 -7/19 3/43 -18/49 11/157 4/57 -11/30 4/57 5/71 -4/11 1/14 -9/25 4/55 -5/14 7/95 2/27 -11/31 5/67 -6/17 7/93 4/53 -13/37 6/79 -7/20 12/157 1/13 -1/3 1/12 -7/22 14/155 1/11 -6/19 1/11 12/131 -5/16 4/43 7/75 -14/45 11/117 8/85 -9/29 5/53 -4/13 2/21 7/73 -7/23 4/41 -3/10 1/10 -8/27 5/49 4/39 -13/44 4/39 11/107 -5/17 3/29 -7/24 11/105 2/19 -16/55 2/19 25/237 -9/31 7/66 -2/7 4/37 1/9 -9/32 1/9 18/161 -7/25 7/62 -5/18 1/9 4/35 -8/29 3/26 -3/11 2/17 -7/26 3/25 4/33 -4/15 3/25 4/33 -5/19 1/8 -6/23 7/55 6/47 -7/27 3/23 -1/4 2/15 1/7 -4/17 0/1 1/7 -7/30 5/33 2/13 -10/43 2/13 7/45 -3/13 1/6 -5/22 2/13 7/45 -12/53 3/19 22/139 -7/31 4/25 -2/9 1/6 -5/23 5/28 -8/37 2/11 1/5 -3/14 0/1 1/5 -1/5 1/5 -2/11 2/9 3/13 -3/17 1/4 -4/23 4/15 3/11 -5/29 2/7 -1/6 0/1 1/3 -2/13 4/13 1/3 -3/20 1/3 6/17 -1/7 1/2 -2/15 1/3 4/11 -1/8 1/2 0/1 -1/1 0/1 1/6 -1/4 3/17 -1/5 5/28 -3/13 -2/9 2/11 -4/19 -1/5 3/16 -1/5 0/1 4/21 -1/9 0/1 1/5 -1/4 2/9 -1/5 -4/21 3/13 -2/11 4/17 -1/6 1/4 -1/5 0/1 3/11 -1/6 5/18 -6/37 -5/31 7/25 -4/25 2/7 -3/19 -2/13 5/17 -1/8 8/27 -1/6 3/10 -1/7 0/1 4/13 -2/13 -1/7 1/3 -1/7 5/14 -1/9 0/1 4/11 -1/7 -2/15 7/19 -1/8 3/8 -1/7 0/1 8/21 -1/7 -2/15 21/55 -5/37 13/34 -17/127 -2/15 5/13 -5/38 12/31 -3/23 -4/31 7/18 -4/31 -5/39 2/5 -1/8 9/22 -4/33 -3/25 16/39 -5/41 -4/33 7/17 -4/33 5/12 -7/59 -2/17 13/31 -1/9 8/19 -3/25 -2/17 3/7 -1/8 7/16 -2/17 -5/43 11/25 -1/9 15/34 -3/26 4/9 -1/9 0/1 13/29 -1/8 9/20 -2/17 -1/9 5/11 -2/17 6/13 -4/35 -9/79 1/2 -1/9 -2/19 5/9 -1/10 9/16 -9/91 -8/81 4/7 -4/41 -3/31 15/26 -3/31 -2/21 11/19 -1/10 29/50 -2/21 -1/11 18/31 -1/10 7/12 -4/41 -3/31 17/29 -5/52 10/17 -7/73 -2/21 13/22 -1/10 3/5 -2/21 8/13 -3/32 21/34 -4/43 -1/11 34/55 -10/107 -7/75 13/21 -5/54 5/8 -4/43 -1/11 12/19 -4/43 -9/97 31/49 -4/43 19/30 -5/54 7/11 -7/76 2/3 -1/11 -4/45 11/16 -5/57 -2/23 20/29 -3/34 9/13 -7/80 7/10 -2/23 -11/127 19/27 -5/58 12/17 -2/23 -7/81 29/41 -5/58 17/24 -2/23 -3/35 5/7 -3/35 13/18 -11/129 -4/47 21/29 -9/106 29/40 -24/283 -5/59 37/51 -6/71 8/11 -4/47 -5/59 19/26 -4/47 -5/59 11/15 -1/12 3/4 -1/12 13/17 -1/12 36/47 -7/85 -6/73 23/30 -6/73 -5/61 10/13 -6/73 -5/61 17/22 -5/61 -14/171 7/9 -4/49 18/23 -10/123 -3/37 11/14 -16/197 -3/37 15/19 -11/136 4/5 -7/87 -2/25 17/21 -15/188 13/16 -2/25 -9/113 9/11 -5/63 5/6 -7/89 -4/51 11/13 -6/77 6/7 -12/155 -1/13 1/1 -1/14 8/7 -14/209 -1/15 15/13 -1/15 22/19 -1/15 -38/571 7/6 -1/15 -12/181 6/5 -4/61 -7/107 17/14 -11/169 -8/123 11/9 -5/77 16/13 -9/139 -2/31 21/17 -15/232 26/21 -37/573 -2/31 5/4 -2/31 -7/109 14/11 -3/47 -16/251 23/18 -3/47 -10/157 9/7 -4/63 31/24 -4/63 -5/79 22/17 -14/221 -5/79 13/10 -5/79 -6/95 4/3 -1/16 19/14 -7/113 -6/97 53/39 -5/81 34/25 -7/113 -6/97 15/11 -1/16 11/8 -5/81 -4/65 51/37 -6/97 40/29 -5/81 -24/389 29/21 -9/146 47/34 -29/471 -4/65 65/47 -4/65 18/13 -4/65 -11/179 25/18 -4/65 -3/49 32/23 -5/81 -4/65 7/5 -3/49 31/22 -2/33 -1/17 24/17 -3/49 -2/33 41/29 -5/82 17/12 -7/115 -2/33 27/19 -5/82 10/7 -11/181 -2/33 33/23 -2/33 56/39 -2/33 -61/1007 23/16 -2/33 -25/413 13/9 -7/116 16/11 -2/33 -5/83 19/13 -2/33 3/2 -4/67 -1/17 17/11 -1/17 31/20 -1/17 -40/681 14/9 -1/17 -18/307 11/7 -7/120 30/19 -5/86 49/31 -4/69 68/43 -1/17 -4/69 19/12 -9/155 -4/69 27/17 -1/17 8/5 -1/17 -4/69 29/18 -5/87 -2/35 21/13 -5/86 55/34 -7/121 -10/173 89/55 -4/69 34/21 -1/17 -4/69 47/29 -7/121 13/8 -3/52 18/11 -2/35 -3/53 41/25 -1/18 23/14 -1/17 -4/69 5/3 -2/35 22/13 -1/18 17/10 -2/35 -7/123 12/7 -3/53 -4/71 31/18 -1/18 19/11 -1/18 7/4 -3/53 -4/71 9/5 -1/18 11/6 -7/127 -6/109 13/7 -3/55 15/8 -2/37 -1/19 17/9 -1/18 2/1 -2/37 -1/19 15/7 -7/134 13/6 -9/173 -4/77 11/5 -2/39 31/14 -1/19 -4/77 20/9 -1/19 -2/39 29/13 -1/20 38/17 -1/21 0/1 9/4 -1/19 0/1 34/15 -3/58 25/11 -1/19 41/18 -5/97 -2/39 16/7 -5/97 -2/39 39/17 -2/39 62/27 -2/39 -19/371 23/10 -2/39 -7/137 7/3 -1/20 33/14 -2/37 -1/19 59/25 -1/19 26/11 -1/19 -4/77 19/8 -2/39 -3/59 69/29 -1/20 50/21 -1/19 -2/39 31/13 -1/19 12/5 -2/39 -7/137 29/12 -3/59 -22/433 17/7 -4/79 5/2 -1/20 23/9 -4/81 64/25 -6/121 -5/101 41/16 -4/81 -3/61 141/55 -3/61 100/39 -3/61 -2/41 59/23 -1/20 18/7 -5/101 -4/81 49/19 -3/61 31/12 -4/81 -3/61 13/5 -5/102 47/18 -27/553 -2/41 81/31 -2/41 115/44 -2/41 -61/1251 34/13 -2/41 -17/349 55/21 -5/103 76/29 -3/62 21/8 -2/41 -1/21 71/27 -3/62 50/19 -4/83 -1/21 29/11 -2/41 8/3 -1/21 0/1 27/10 -1/21 0/1 19/7 -1/20 30/11 -3/61 -2/41 41/15 -2/41 11/4 -2/41 -1/21 25/9 -3/62 64/23 -12/251 -1/21 39/14 -1/21 -6/127 14/5 -1/19 0/1 3/1 -1/21 13/4 -1/21 -2/43 23/7 -1/22 33/10 -1/23 0/1 43/13 0/1 10/3 -1/21 0/1 27/8 -1/22 71/21 -1/23 44/13 -1/21 0/1 17/5 -1/20 41/12 -10/209 -1/21 65/19 -1/21 89/26 -1/21 -26/547 24/7 -1/21 -8/169 7/2 -2/43 -3/65 11/3 -1/22 15/4 -4/89 -3/67 34/9 -16/357 -3/67 19/5 -2/45 42/11 -2/45 -1/23 65/17 -1/22 23/6 -3/67 -2/45 4/1 -1/23 0/1 25/6 -1/23 0/1 46/11 -1/21 0/1 113/27 -1/21 67/16 -1/21 -2/43 21/5 -1/22 17/4 -1/22 13/3 -2/45 35/8 -1/23 0/1 57/13 -1/22 22/5 -2/45 -1/23 9/2 -4/91 -1/23 23/5 -1/23 37/8 -1/23 -16/369 14/3 -1/23 -6/139 5/1 -1/24 26/5 -1/29 0/1 47/9 0/1 21/4 -1/19 0/1 16/3 -1/23 0/1 27/5 -2/45 11/2 -1/23 -4/93 28/5 -2/47 -3/71 45/8 -2/47 -3/71 17/3 -1/23 23/4 -2/47 -3/71 6/1 -1/24 7/1 0/1 8/1 -2/49 -1/25 25/3 -1/25 17/2 -1/25 -4/101 9/1 -1/26 1/0 -1/27 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(265,124,156,73) (-1/2,-6/13) -> (22/13,17/10) Hyperbolic Matrix(933,428,412,189) (-6/13,-11/24) -> (9/4,34/15) Hyperbolic Matrix(823,376,1136,519) (-11/24,-5/11) -> (21/29,29/40) Hyperbolic Matrix(53,24,-360,-163) (-5/11,-9/20) -> (-3/20,-1/7) Hyperbolic Matrix(353,158,458,205) (-9/20,-4/9) -> (10/13,17/22) Hyperbolic Matrix(549,242,-1250,-551) (-4/9,-11/25) -> (-11/25,-18/41) Parabolic Matrix(4591,2014,1794,787) (-18/41,-25/57) -> (23/9,64/25) Hyperbolic Matrix(1443,632,1048,459) (-25/57,-7/16) -> (11/8,51/37) Hyperbolic Matrix(51,22,146,63) (-7/16,-3/7) -> (1/3,5/14) Hyperbolic Matrix(47,20,148,63) (-3/7,-8/19) -> (4/13,1/3) Hyperbolic Matrix(1689,710,1306,549) (-8/19,-21/50) -> (31/24,22/17) Hyperbolic Matrix(1253,526,1546,649) (-21/50,-13/31) -> (17/21,13/16) Hyperbolic Matrix(673,282,1062,445) (-13/31,-5/12) -> (19/30,7/11) Hyperbolic Matrix(1151,478,1818,755) (-5/12,-17/41) -> (31/49,19/30) Hyperbolic Matrix(623,258,-1770,-733) (-17/41,-12/29) -> (-6/17,-13/37) Hyperbolic Matrix(953,394,670,277) (-12/29,-7/17) -> (27/19,10/7) Hyperbolic Matrix(287,118,-1238,-509) (-7/17,-16/39) -> (-10/43,-3/13) Hyperbolic Matrix(1045,428,188,77) (-16/39,-9/22) -> (11/2,28/5) Hyperbolic Matrix(423,172,332,135) (-9/22,-2/5) -> (14/11,23/18) Hyperbolic Matrix(413,162,-1058,-415) (-2/5,-9/23) -> (-9/23,-16/41) Parabolic Matrix(457,178,-1466,-571) (-16/41,-7/18) -> (-5/16,-14/45) Hyperbolic Matrix(733,284,1004,389) (-7/18,-12/31) -> (8/11,19/26) Hyperbolic Matrix(321,124,44,17) (-12/31,-5/13) -> (7/1,8/1) Hyperbolic Matrix(271,104,456,175) (-5/13,-13/34) -> (13/22,3/5) Hyperbolic Matrix(907,346,270,103) (-13/34,-8/21) -> (10/3,27/8) Hyperbolic Matrix(453,172,1172,445) (-8/21,-11/29) -> (5/13,12/31) Hyperbolic Matrix(317,120,-1128,-427) (-11/29,-3/8) -> (-9/32,-7/25) Hyperbolic Matrix(2093,778,1294,481) (-3/8,-13/35) -> (21/13,55/34) Hyperbolic Matrix(803,298,-2762,-1025) (-13/35,-10/27) -> (-16/55,-9/31) Hyperbolic Matrix(1065,394,446,165) (-10/27,-7/19) -> (31/13,12/5) Hyperbolic Matrix(2743,1008,1064,391) (-7/19,-18/49) -> (18/7,49/19) Hyperbolic Matrix(267,98,1414,519) (-18/49,-11/30) -> (3/16,4/21) Hyperbolic Matrix(617,226,1062,389) (-11/30,-4/11) -> (18/31,7/12) Hyperbolic Matrix(133,48,568,205) (-4/11,-9/25) -> (3/13,4/17) Hyperbolic Matrix(479,172,220,79) (-9/25,-5/14) -> (13/6,11/5) Hyperbolic Matrix(697,248,1824,649) (-5/14,-11/31) -> (21/55,13/34) Hyperbolic Matrix(305,108,-1172,-415) (-11/31,-6/17) -> (-6/23,-7/27) Hyperbolic Matrix(1813,636,2500,877) (-13/37,-7/20) -> (29/40,37/51) Hyperbolic Matrix(41,14,-126,-43) (-7/20,-1/3) -> (-1/3,-7/22) Parabolic Matrix(617,196,532,169) (-7/22,-6/19) -> (22/19,7/6) Hyperbolic Matrix(287,90,-1266,-397) (-6/19,-5/16) -> (-5/22,-12/53) Hyperbolic Matrix(3371,1048,2480,771) (-14/45,-9/29) -> (53/39,34/25) Hyperbolic Matrix(1701,526,650,201) (-9/29,-4/13) -> (34/13,55/21) Hyperbolic Matrix(203,62,442,135) (-4/13,-7/23) -> (5/11,6/13) Hyperbolic Matrix(521,158,122,37) (-7/23,-3/10) -> (17/4,13/3) Hyperbolic Matrix(957,284,556,165) (-3/10,-8/27) -> (12/7,31/18) Hyperbolic Matrix(1271,376,240,71) (-8/27,-13/44) -> (21/4,16/3) Hyperbolic Matrix(835,246,594,175) (-13/44,-5/17) -> (7/5,31/22) Hyperbolic Matrix(397,116,948,277) (-5/17,-7/24) -> (5/12,13/31) Hyperbolic Matrix(2609,760,1816,529) (-7/24,-16/55) -> (56/39,23/16) Hyperbolic Matrix(1145,332,1852,537) (-9/31,-2/7) -> (34/55,13/21) Hyperbolic Matrix(665,188,428,121) (-2/7,-9/32) -> (31/20,14/9) Hyperbolic Matrix(1009,282,390,109) (-7/25,-5/18) -> (31/12,13/5) Hyperbolic Matrix(231,64,776,215) (-5/18,-8/29) -> (8/27,3/10) Hyperbolic Matrix(387,106,230,63) (-8/29,-3/11) -> (5/3,22/13) Hyperbolic Matrix(383,104,232,63) (-3/11,-7/26) -> (23/14,5/3) Hyperbolic Matrix(613,164,228,61) (-7/26,-4/15) -> (8/3,27/10) Hyperbolic Matrix(189,50,-722,-191) (-4/15,-5/19) -> (-5/19,-6/23) Parabolic Matrix(1283,332,228,59) (-7/27,-1/4) -> (45/8,17/3) Hyperbolic Matrix(259,62,330,79) (-1/4,-4/17) -> (18/23,11/14) Hyperbolic Matrix(145,34,806,189) (-4/17,-7/30) -> (5/28,2/11) Hyperbolic Matrix(2849,664,1240,289) (-7/30,-10/43) -> (62/27,23/10) Hyperbolic Matrix(509,116,724,165) (-3/13,-5/22) -> (7/10,19/27) Hyperbolic Matrix(3943,892,2860,647) (-12/53,-7/31) -> (51/37,40/29) Hyperbolic Matrix(1371,308,868,195) (-7/31,-2/9) -> (30/19,49/31) Hyperbolic Matrix(789,172,500,109) (-2/9,-5/23) -> (11/7,30/19) Hyperbolic Matrix(1145,248,928,201) (-5/23,-8/37) -> (16/13,21/17) Hyperbolic Matrix(1427,308,644,139) (-8/37,-3/14) -> (31/14,20/9) Hyperbolic Matrix(107,22,34,7) (-3/14,-1/5) -> (3/1,13/4) Hyperbolic Matrix(103,20,36,7) (-1/5,-2/11) -> (14/5,3/1) Hyperbolic Matrix(101,18,-578,-103) (-2/11,-3/17) -> (-3/17,-4/23) Parabolic Matrix(1083,188,1492,259) (-4/23,-5/29) -> (37/51,8/11) Hyperbolic Matrix(2129,364,1316,225) (-5/29,-1/6) -> (55/34,89/55) Hyperbolic Matrix(301,48,232,37) (-1/6,-2/13) -> (22/17,13/10) Hyperbolic Matrix(761,116,164,25) (-2/13,-3/20) -> (37/8,14/3) Hyperbolic Matrix(715,98,518,71) (-1/7,-2/15) -> (40/29,29/21) Hyperbolic Matrix(257,34,582,77) (-2/15,-1/8) -> (15/34,4/9) Hyperbolic Matrix(93,10,158,17) (-1/8,0/1) -> (10/17,13/22) Hyperbolic Matrix(121,-18,74,-11) (0/1,1/6) -> (13/8,18/11) Hyperbolic Matrix(503,-86,310,-53) (1/6,3/17) -> (47/29,13/8) Hyperbolic Matrix(1807,-322,1330,-237) (3/17,5/28) -> (19/14,53/39) Hyperbolic Matrix(709,-132,188,-35) (2/11,3/16) -> (15/4,34/9) Hyperbolic Matrix(235,-46,46,-9) (4/21,1/5) -> (5/1,26/5) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(365,-82,138,-31) (2/9,3/13) -> (29/11,8/3) Hyperbolic Matrix(565,-134,974,-231) (4/17,1/4) -> (29/50,18/31) Hyperbolic Matrix(67,-18,242,-65) (1/4,3/11) -> (3/11,5/18) Parabolic Matrix(417,-116,284,-79) (5/18,7/25) -> (19/13,3/2) Hyperbolic Matrix(589,-166,110,-31) (7/25,2/7) -> (16/3,27/5) Hyperbolic Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(583,-172,844,-249) (5/17,8/27) -> (20/29,9/13) Hyperbolic Matrix(235,-72,408,-125) (3/10,4/13) -> (4/7,15/26) Hyperbolic Matrix(431,-156,268,-97) (5/14,4/11) -> (8/5,29/18) Hyperbolic Matrix(779,-286,286,-105) (4/11,7/19) -> (19/7,30/11) Hyperbolic Matrix(449,-166,614,-227) (7/19,3/8) -> (19/26,11/15) Hyperbolic Matrix(365,-138,82,-31) (3/8,8/21) -> (22/5,9/2) Hyperbolic Matrix(3911,-1492,1156,-441) (8/21,21/55) -> (71/21,44/13) Hyperbolic Matrix(1053,-404,404,-155) (13/34,5/13) -> (13/5,47/18) Hyperbolic Matrix(1393,-540,988,-383) (12/31,7/18) -> (31/22,24/17) Hyperbolic Matrix(81,-32,200,-79) (7/18,2/5) -> (2/5,9/22) Parabolic Matrix(1689,-692,2204,-903) (9/22,16/39) -> (36/47,23/30) Hyperbolic Matrix(4049,-1662,2502,-1027) (16/39,7/17) -> (89/55,34/21) Hyperbolic Matrix(217,-90,258,-107) (7/17,5/12) -> (5/6,11/13) Hyperbolic Matrix(1125,-472,808,-339) (13/31,8/19) -> (32/23,7/5) Hyperbolic Matrix(393,-166,670,-283) (8/19,3/7) -> (17/29,10/17) Hyperbolic Matrix(273,-118,118,-51) (3/7,7/16) -> (23/10,7/3) Hyperbolic Matrix(583,-256,312,-137) (7/16,11/25) -> (13/7,15/8) Hyperbolic Matrix(3089,-1362,914,-403) (11/25,15/34) -> (27/8,71/21) Hyperbolic Matrix(2071,-926,870,-389) (4/9,13/29) -> (69/29,50/21) Hyperbolic Matrix(1931,-868,812,-365) (13/29,9/20) -> (19/8,69/29) Hyperbolic Matrix(521,-236,404,-183) (9/20,5/11) -> (9/7,31/24) Hyperbolic Matrix(535,-248,192,-89) (6/13,1/2) -> (39/14,14/5) Hyperbolic Matrix(91,-50,162,-89) (1/2,5/9) -> (5/9,9/16) Parabolic Matrix(215,-122,178,-101) (9/16,4/7) -> (6/5,17/14) Hyperbolic Matrix(1225,-708,372,-215) (15/26,11/19) -> (23/7,33/10) Hyperbolic Matrix(1135,-658,602,-349) (11/19,29/50) -> (15/8,17/9) Hyperbolic Matrix(1041,-610,442,-259) (7/12,17/29) -> (7/3,33/14) Hyperbolic Matrix(121,-74,18,-11) (3/5,8/13) -> (6/1,7/1) Hyperbolic Matrix(503,-310,86,-53) (8/13,21/34) -> (23/4,6/1) Hyperbolic Matrix(4431,-2738,1730,-1069) (21/34,34/55) -> (64/25,41/16) Hyperbolic Matrix(431,-268,156,-97) (13/21,5/8) -> (11/4,25/9) Hyperbolic Matrix(619,-390,446,-281) (5/8,12/19) -> (18/13,25/18) Hyperbolic Matrix(2419,-1530,634,-401) (12/19,31/49) -> (19/5,42/11) Hyperbolic Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(133,-90,34,-23) (2/3,11/16) -> (23/6,4/1) Hyperbolic Matrix(1825,-1256,696,-479) (11/16,20/29) -> (76/29,21/8) Hyperbolic Matrix(429,-298,298,-207) (9/13,7/10) -> (23/16,13/9) Hyperbolic Matrix(1183,-834,722,-509) (19/27,12/17) -> (18/11,41/25) Hyperbolic Matrix(1871,-1322,426,-301) (12/17,29/41) -> (57/13,22/5) Hyperbolic Matrix(2803,-1984,640,-453) (29/41,17/24) -> (35/8,57/13) Hyperbolic Matrix(1393,-988,540,-383) (17/24,5/7) -> (49/19,31/12) Hyperbolic Matrix(619,-446,390,-281) (5/7,13/18) -> (19/12,27/17) Hyperbolic Matrix(1885,-1364,1364,-987) (13/18,21/29) -> (29/21,47/34) Hyperbolic Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(4473,-3424,1744,-1335) (13/17,36/47) -> (100/39,59/23) Hyperbolic Matrix(1425,-1094,254,-195) (23/30,10/13) -> (28/5,45/8) Hyperbolic Matrix(521,-404,236,-183) (17/22,7/9) -> (11/5,31/14) Hyperbolic Matrix(1117,-872,424,-331) (7/9,18/23) -> (50/19,29/11) Hyperbolic Matrix(1017,-802,298,-235) (11/14,15/19) -> (17/5,41/12) Hyperbolic Matrix(651,-526,526,-425) (4/5,17/21) -> (21/17,26/21) Hyperbolic Matrix(525,-428,92,-75) (13/16,9/11) -> (17/3,23/4) Hyperbolic Matrix(199,-164,108,-89) (9/11,5/6) -> (11/6,13/7) Hyperbolic Matrix(575,-488,152,-129) (11/13,6/7) -> (34/9,19/5) Hyperbolic Matrix(15,-14,14,-13) (6/7,1/1) -> (1/1,8/7) Parabolic Matrix(391,-450,338,-389) (8/7,15/13) -> (15/13,22/19) Parabolic Matrix(217,-258,90,-107) (7/6,6/5) -> (12/5,29/12) Hyperbolic Matrix(719,-876,316,-385) (17/14,11/9) -> (25/11,41/18) Hyperbolic Matrix(917,-1126,566,-695) (11/9,16/13) -> (34/21,47/29) Hyperbolic Matrix(2551,-3160,976,-1209) (26/21,5/4) -> (115/44,34/13) Hyperbolic Matrix(173,-218,50,-63) (5/4,14/11) -> (24/7,7/2) Hyperbolic Matrix(479,-614,110,-141) (23/18,9/7) -> (13/3,35/8) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(1673,-2276,652,-887) (34/25,15/11) -> (59/23,18/7) Hyperbolic Matrix(449,-614,166,-227) (15/11,11/8) -> (27/10,19/7) Hyperbolic Matrix(2585,-3574,494,-683) (47/34,65/47) -> (47/9,21/4) Hyperbolic Matrix(1833,-2536,352,-487) (65/47,18/13) -> (26/5,47/9) Hyperbolic Matrix(891,-1238,398,-553) (25/18,32/23) -> (38/17,9/4) Hyperbolic Matrix(2657,-3754,1010,-1427) (24/17,41/29) -> (71/27,50/19) Hyperbolic Matrix(1461,-2068,556,-787) (41/29,17/12) -> (21/8,71/27) Hyperbolic Matrix(127,-180,12,-17) (17/12,27/19) -> (9/1,1/0) Hyperbolic Matrix(1519,-2178,1058,-1517) (10/7,33/23) -> (33/23,56/39) Parabolic Matrix(583,-844,172,-249) (13/9,16/11) -> (44/13,17/5) Hyperbolic Matrix(1423,-2076,900,-1313) (16/11,19/13) -> (49/31,68/43) Hyperbolic Matrix(375,-578,242,-373) (3/2,17/11) -> (17/11,31/20) Parabolic Matrix(1627,-2574,390,-617) (68/43,19/12) -> (25/6,46/11) Hyperbolic Matrix(1005,-1598,422,-671) (27/17,8/5) -> (50/21,31/13) Hyperbolic Matrix(439,-708,204,-329) (29/18,21/13) -> (15/7,13/6) Hyperbolic Matrix(551,-904,64,-105) (41/25,23/14) -> (17/2,9/1) Hyperbolic Matrix(393,-670,166,-283) (17/10,12/7) -> (26/11,19/8) Hyperbolic Matrix(565,-974,134,-231) (31/18,19/11) -> (21/5,17/4) Hyperbolic Matrix(235,-408,72,-125) (19/11,7/4) -> (13/4,23/7) Hyperbolic Matrix(91,-162,50,-89) (7/4,9/5) -> (9/5,11/6) Parabolic Matrix(443,-844,116,-221) (17/9,2/1) -> (42/11,65/17) Hyperbolic Matrix(473,-1010,170,-363) (2/1,15/7) -> (25/9,64/23) Hyperbolic Matrix(755,-1682,338,-753) (20/9,29/13) -> (29/13,38/17) Parabolic Matrix(1661,-3770,634,-1439) (34/15,25/11) -> (55/21,76/29) Hyperbolic Matrix(247,-564,60,-137) (41/18,16/7) -> (4/1,25/6) Hyperbolic Matrix(1327,-3042,578,-1325) (16/7,39/17) -> (39/17,62/27) Parabolic Matrix(775,-1828,92,-217) (33/14,59/25) -> (25/3,17/2) Hyperbolic Matrix(475,-1122,58,-137) (59/25,26/11) -> (8/1,25/3) Hyperbolic Matrix(401,-970,74,-179) (29/12,17/7) -> (27/5,11/2) Hyperbolic Matrix(81,-200,32,-79) (17/7,5/2) -> (5/2,23/9) Parabolic Matrix(5493,-14080,1312,-3363) (41/16,141/55) -> (113/27,67/16) Hyperbolic Matrix(6937,-17786,1658,-4251) (141/55,100/39) -> (46/11,113/27) Hyperbolic Matrix(5023,-13122,1922,-5021) (47/18,81/31) -> (81/31,115/44) Parabolic Matrix(623,-1700,188,-513) (30/11,41/15) -> (43/13,10/3) Hyperbolic Matrix(667,-1826,202,-553) (41/15,11/4) -> (33/10,43/13) Hyperbolic Matrix(2383,-6632,696,-1937) (64/23,39/14) -> (89/26,24/7) Hyperbolic Matrix(2471,-8450,722,-2469) (41/12,65/19) -> (65/19,89/26) Parabolic Matrix(67,-242,18,-65) (7/2,11/3) -> (11/3,15/4) Parabolic Matrix(1265,-4838,302,-1155) (65/17,23/6) -> (67/16,21/5) Hyperbolic Matrix(231,-1058,50,-229) (9/2,23/5) -> (23/5,37/8) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,52,1) Matrix(265,124,156,73) -> Matrix(43,-2,-752,35) Matrix(933,428,412,189) -> Matrix(85,-4,-1636,77) Matrix(823,376,1136,519) -> Matrix(79,-4,-928,47) Matrix(53,24,-360,-163) -> Matrix(43,-2,108,-5) Matrix(353,158,458,205) -> Matrix(121,-6,-1472,73) Matrix(549,242,-1250,-551) -> Matrix(121,-6,2400,-119) Matrix(4591,2014,1794,787) -> Matrix(1,0,-40,1) Matrix(1443,632,1048,459) -> Matrix(41,-2,-676,33) Matrix(51,22,146,63) -> Matrix(39,-2,-292,15) Matrix(47,20,148,63) -> Matrix(37,-2,-240,13) Matrix(1689,710,1306,549) -> Matrix(261,-14,-4120,221) Matrix(1253,526,1546,649) -> Matrix(371,-20,-4656,251) Matrix(673,282,1062,445) -> Matrix(293,-16,-3168,173) Matrix(1151,478,1818,755) -> Matrix(427,-24,-4608,259) Matrix(623,258,-1770,-733) -> Matrix(247,-14,3264,-185) Matrix(953,394,670,277) -> Matrix(139,-8,-2276,131) Matrix(287,118,-1238,-509) -> Matrix(71,-4,444,-25) Matrix(1045,428,188,77) -> Matrix(69,-4,-1604,93) Matrix(423,172,332,135) -> Matrix(173,-10,-2716,157) Matrix(413,162,-1058,-415) -> Matrix(161,-10,2560,-159) Matrix(457,178,-1466,-571) -> Matrix(253,-16,2704,-171) Matrix(733,284,1004,389) -> Matrix(127,-8,-1508,95) Matrix(321,124,44,17) -> Matrix(31,-2,-728,47) Matrix(271,104,456,175) -> Matrix(123,-8,-1276,83) Matrix(907,346,270,103) -> Matrix(61,-4,-1296,85) Matrix(453,172,1172,445) -> Matrix(243,-16,-1868,123) Matrix(317,120,-1128,-427) -> Matrix(211,-14,1884,-125) Matrix(2093,778,1294,481) -> Matrix(263,-18,-4544,311) Matrix(803,298,-2762,-1025) -> Matrix(407,-28,3852,-265) Matrix(1065,394,446,165) -> Matrix(115,-8,-2228,155) Matrix(2743,1008,1064,391) -> Matrix(343,-24,-6960,487) Matrix(267,98,1414,519) -> Matrix(57,-4,-356,25) Matrix(617,226,1062,389) -> Matrix(113,-8,-1144,81) Matrix(133,48,568,205) -> Matrix(83,-6,-484,35) Matrix(479,172,220,79) -> Matrix(137,-10,-2644,193) Matrix(697,248,1824,649) -> Matrix(269,-20,-2004,149) Matrix(305,108,-1172,-415) -> Matrix(187,-14,1456,-109) Matrix(1813,636,2500,877) -> Matrix(473,-36,-5584,425) Matrix(41,14,-126,-43) -> Matrix(25,-2,288,-23) Matrix(617,196,532,169) -> Matrix(287,-26,-4316,391) Matrix(287,90,-1266,-397) -> Matrix(151,-14,960,-89) Matrix(3371,1048,2480,771) -> Matrix(107,-10,-1744,163) Matrix(1701,526,650,201) -> Matrix(211,-20,-4336,411) Matrix(203,62,442,135) -> Matrix(103,-10,-896,87) Matrix(521,158,122,37) -> Matrix(61,-6,-1352,133) Matrix(957,284,556,165) -> Matrix(79,-8,-1412,143) Matrix(1271,376,240,71) -> Matrix(39,-4,-848,87) Matrix(835,246,594,175) -> Matrix(175,-18,-2868,295) Matrix(397,116,948,277) -> Matrix(77,-8,-664,69) Matrix(2609,760,1816,529) -> Matrix(685,-72,-11312,1189) Matrix(1145,332,1852,537) -> Matrix(169,-18,-1812,193) Matrix(665,188,428,121) -> Matrix(199,-22,-3392,375) Matrix(1009,282,390,109) -> Matrix(141,-16,-2864,325) Matrix(231,64,776,215) -> Matrix(35,-4,-236,27) Matrix(387,106,230,63) -> Matrix(69,-8,-1216,141) Matrix(383,104,232,63) -> Matrix(67,-8,-1164,139) Matrix(613,164,228,61) -> Matrix(33,-4,-668,81) Matrix(189,50,-722,-191) -> Matrix(81,-10,640,-79) Matrix(1283,332,228,59) -> Matrix(31,-4,-736,95) Matrix(259,62,330,79) -> Matrix(67,-10,-824,123) Matrix(145,34,806,189) -> Matrix(27,-4,-128,19) Matrix(2849,664,1240,289) -> Matrix(157,-24,-3068,469) Matrix(509,116,724,165) -> Matrix(53,-8,-616,93) Matrix(3943,892,2860,647) -> Matrix(239,-38,-3868,615) Matrix(1371,308,868,195) -> Matrix(149,-24,-2564,413) Matrix(789,172,500,109) -> Matrix(91,-16,-1564,275) Matrix(1145,248,928,201) -> Matrix(109,-20,-1684,309) Matrix(1427,308,644,139) -> Matrix(21,-4,-404,77) Matrix(107,22,34,7) -> Matrix(11,-2,-236,43) Matrix(103,20,36,7) -> Matrix(9,-2,-184,41) Matrix(101,18,-578,-103) -> Matrix(25,-6,96,-23) Matrix(1083,188,1492,259) -> Matrix(31,-8,-368,95) Matrix(2129,364,1316,225) -> Matrix(37,-10,-640,173) Matrix(301,48,232,37) -> Matrix(23,-6,-364,95) Matrix(761,116,164,25) -> Matrix(31,-10,-716,231) Matrix(715,98,518,71) -> Matrix(17,-4,-276,65) Matrix(257,34,582,77) -> Matrix(11,-4,-96,35) Matrix(93,10,158,17) -> Matrix(5,-2,-52,21) Matrix(121,-18,74,-11) -> Matrix(5,2,-88,-35) Matrix(503,-86,310,-53) -> Matrix(43,10,-744,-173) Matrix(1807,-322,1330,-237) -> Matrix(15,4,-244,-65) Matrix(709,-132,188,-35) -> Matrix(23,4,-512,-89) Matrix(235,-46,46,-9) -> Matrix(1,0,-20,1) Matrix(115,-24,24,-5) -> Matrix(9,2,-212,-47) Matrix(365,-82,138,-31) -> Matrix(21,4,-436,-83) Matrix(565,-134,974,-231) -> Matrix(11,2,-116,-21) Matrix(67,-18,242,-65) -> Matrix(35,6,-216,-37) Matrix(417,-116,284,-79) -> Matrix(87,14,-1448,-233) Matrix(589,-166,110,-31) -> Matrix(13,2,-280,-43) Matrix(173,-50,218,-63) -> Matrix(53,8,-656,-99) Matrix(583,-172,844,-249) -> Matrix(9,2,-104,-23) Matrix(235,-72,408,-125) -> Matrix(11,2,-116,-21) Matrix(431,-156,268,-97) -> Matrix(13,2,-228,-35) Matrix(779,-286,286,-105) -> Matrix(31,4,-628,-81) Matrix(449,-166,614,-227) -> Matrix(33,4,-388,-47) Matrix(365,-138,82,-31) -> Matrix(29,4,-660,-91) Matrix(3911,-1492,1156,-441) -> Matrix(15,2,-308,-41) Matrix(1053,-404,404,-155) -> Matrix(151,20,-3088,-409) Matrix(1393,-540,988,-383) -> Matrix(47,6,-760,-97) Matrix(81,-32,200,-79) -> Matrix(63,8,-512,-65) Matrix(1689,-692,2204,-903) -> Matrix(15,2,-188,-25) Matrix(4049,-1662,2502,-1027) -> Matrix(131,16,-2268,-277) Matrix(217,-90,258,-107) -> Matrix(117,14,-1496,-179) Matrix(1125,-472,808,-339) -> Matrix(15,2,-248,-33) Matrix(393,-166,670,-283) -> Matrix(69,8,-716,-83) Matrix(273,-118,118,-51) -> Matrix(33,4,-652,-79) Matrix(583,-256,312,-137) -> Matrix(69,8,-1268,-147) Matrix(3089,-1362,914,-403) -> Matrix(17,2,-400,-47) Matrix(2071,-926,870,-389) -> Matrix(17,2,-332,-39) Matrix(1931,-868,812,-365) -> Matrix(33,4,-652,-79) Matrix(521,-236,404,-183) -> Matrix(49,6,-776,-95) Matrix(535,-248,192,-89) -> Matrix(35,4,-744,-85) Matrix(91,-50,162,-89) -> Matrix(99,10,-1000,-101) Matrix(215,-122,178,-101) -> Matrix(163,16,-2496,-245) Matrix(1225,-708,372,-215) -> Matrix(21,2,-452,-43) Matrix(1135,-658,602,-349) -> Matrix(1,0,-8,1) Matrix(1041,-610,442,-259) -> Matrix(21,2,-368,-35) Matrix(121,-74,18,-11) -> Matrix(21,2,-536,-51) Matrix(503,-310,86,-53) -> Matrix(107,10,-2536,-237) Matrix(4431,-2738,1730,-1069) -> Matrix(85,8,-1732,-163) Matrix(431,-268,156,-97) -> Matrix(21,2,-452,-43) Matrix(619,-390,446,-281) -> Matrix(85,8,-1392,-131) Matrix(2419,-1530,634,-401) -> Matrix(151,14,-3376,-313) Matrix(187,-120,120,-77) -> Matrix(153,14,-2612,-239) Matrix(133,-90,34,-23) -> Matrix(45,4,-1024,-91) Matrix(1825,-1256,696,-479) -> Matrix(137,12,-2820,-247) Matrix(429,-298,298,-207) -> Matrix(321,28,-5308,-463) Matrix(1183,-834,722,-509) -> Matrix(93,8,-1616,-139) Matrix(1871,-1322,426,-301) -> Matrix(139,12,-3116,-269) Matrix(2803,-1984,640,-453) -> Matrix(23,2,-564,-49) Matrix(1393,-988,540,-383) -> Matrix(71,6,-1432,-121) Matrix(619,-446,390,-281) -> Matrix(93,8,-1616,-139) Matrix(1885,-1364,1364,-987) -> Matrix(847,72,-13752,-1169) Matrix(97,-72,128,-95) -> Matrix(143,12,-1728,-145) Matrix(4473,-3424,1744,-1335) -> Matrix(49,4,-968,-79) Matrix(1425,-1094,254,-195) -> Matrix(97,8,-2316,-191) Matrix(521,-404,236,-183) -> Matrix(73,6,-1448,-119) Matrix(1117,-872,424,-331) -> Matrix(25,2,-488,-39) Matrix(1017,-802,298,-235) -> Matrix(173,14,-3596,-291) Matrix(651,-526,526,-425) -> Matrix(751,60,-11628,-929) Matrix(525,-428,92,-75) -> Matrix(151,12,-3536,-281) Matrix(199,-164,108,-89) -> Matrix(177,14,-3224,-255) Matrix(575,-488,152,-129) -> Matrix(257,20,-5744,-447) Matrix(15,-14,14,-13) -> Matrix(27,2,-392,-29) Matrix(391,-450,338,-389) -> Matrix(779,52,-11700,-781) Matrix(217,-258,90,-107) -> Matrix(213,14,-4184,-275) Matrix(719,-876,316,-385) -> Matrix(277,18,-5340,-347) Matrix(917,-1126,566,-695) -> Matrix(525,34,-9064,-587) Matrix(2551,-3160,976,-1209) -> Matrix(1673,108,-34312,-2215) Matrix(173,-218,50,-63) -> Matrix(125,8,-2672,-171) Matrix(479,-614,110,-141) -> Matrix(157,10,-3564,-227) Matrix(97,-128,72,-95) -> Matrix(191,12,-3072,-193) Matrix(1673,-2276,652,-887) -> Matrix(33,2,-644,-39) Matrix(449,-614,166,-227) -> Matrix(65,4,-1284,-79) Matrix(2585,-3574,494,-683) -> Matrix(65,4,-764,-47) Matrix(1833,-2536,352,-487) -> Matrix(65,4,-2064,-127) Matrix(891,-1238,398,-553) -> Matrix(65,4,-1284,-79) Matrix(2657,-3754,1010,-1427) -> Matrix(229,14,-4760,-291) Matrix(1461,-2068,556,-787) -> Matrix(263,16,-5408,-329) Matrix(127,-180,12,-17) -> Matrix(33,2,-776,-47) Matrix(1519,-2178,1058,-1517) -> Matrix(2375,144,-39204,-2377) Matrix(583,-844,172,-249) -> Matrix(33,2,-776,-47) Matrix(1423,-2076,900,-1313) -> Matrix(365,22,-6288,-379) Matrix(375,-578,242,-373) -> Matrix(747,44,-12716,-749) Matrix(1627,-2574,390,-617) -> Matrix(69,4,-1432,-83) Matrix(1005,-1598,422,-671) -> Matrix(35,2,-648,-37) Matrix(439,-708,204,-329) -> Matrix(33,2,-644,-39) Matrix(551,-904,64,-105) -> Matrix(1,0,-8,1) Matrix(393,-670,166,-283) -> Matrix(141,8,-2732,-155) Matrix(565,-974,134,-231) -> Matrix(35,2,-788,-45) Matrix(235,-408,72,-125) -> Matrix(35,2,-788,-45) Matrix(91,-162,50,-89) -> Matrix(179,10,-3240,-181) Matrix(443,-844,116,-221) -> Matrix(1,0,-4,1) Matrix(473,-1010,170,-363) -> Matrix(191,10,-3992,-209) Matrix(755,-1682,338,-753) -> Matrix(39,2,-800,-41) Matrix(1661,-3770,634,-1439) -> Matrix(233,12,-4796,-247) Matrix(247,-564,60,-137) -> Matrix(39,2,-800,-41) Matrix(1327,-3042,578,-1325) -> Matrix(935,48,-18252,-937) Matrix(775,-1828,92,-217) -> Matrix(113,6,-2844,-151) Matrix(475,-1122,58,-137) -> Matrix(115,6,-2856,-149) Matrix(401,-970,74,-179) -> Matrix(197,10,-4472,-227) Matrix(81,-200,32,-79) -> Matrix(159,8,-3200,-161) Matrix(5493,-14080,1312,-3363) -> Matrix(203,10,-4324,-213) Matrix(6937,-17786,1658,-4251) -> Matrix(41,2,-800,-39) Matrix(5023,-13122,1922,-5021) -> Matrix(3607,176,-73964,-3609) Matrix(623,-1700,188,-513) -> Matrix(41,2,-800,-39) Matrix(667,-1826,202,-553) -> Matrix(41,2,-964,-47) Matrix(2383,-6632,696,-1937) -> Matrix(419,20,-8820,-421) Matrix(2471,-8450,722,-2469) -> Matrix(755,36,-15876,-757) Matrix(67,-242,18,-65) -> Matrix(131,6,-2904,-133) Matrix(1265,-4838,302,-1155) -> Matrix(89,4,-1936,-87) Matrix(231,-1058,50,-229) -> Matrix(459,20,-10580,-461) 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): 288 Minimal number of generators: 49 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: 30 Genus: 10 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 3/11 1/3 5/9 29/41 1/1 4/3 7/5 33/23 17/11 5/3 9/5 2/1 29/13 39/17 7/3 5/2 13/5 19/7 41/15 3/1 17/5 11/3 4/1 13/3 23/5 5/1 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 -1/1 0/1 1/6 -1/4 1/5 -1/4 2/9 -1/5 -4/21 1/4 -1/5 0/1 3/11 -1/6 2/7 -3/19 -2/13 5/17 -1/8 3/10 -1/7 0/1 1/3 -1/7 4/11 -1/7 -2/15 7/19 -1/8 3/8 -1/7 0/1 5/13 -5/38 2/5 -1/8 3/7 -1/8 7/16 -2/17 -5/43 4/9 -1/9 0/1 1/2 -1/9 -2/19 5/9 -1/10 4/7 -4/41 -3/31 11/19 -1/10 7/12 -4/41 -3/31 10/17 -7/73 -2/21 3/5 -2/21 8/13 -3/32 13/21 -5/54 5/8 -4/43 -1/11 7/11 -7/76 2/3 -1/11 -4/45 9/13 -7/80 7/10 -2/23 -11/127 12/17 -2/23 -7/81 29/41 -5/58 17/24 -2/23 -3/35 5/7 -3/35 8/11 -4/47 -5/59 11/15 -1/12 3/4 -1/12 1/1 -1/14 4/3 -1/16 15/11 -1/16 11/8 -5/81 -4/65 18/13 -4/65 -11/179 7/5 -3/49 10/7 -11/181 -2/33 33/23 -2/33 23/16 -2/33 -25/413 13/9 -7/116 3/2 -4/67 -1/17 17/11 -1/17 14/9 -1/17 -18/307 11/7 -7/120 19/12 -9/155 -4/69 8/5 -1/17 -4/69 21/13 -5/86 13/8 -3/52 18/11 -2/35 -3/53 5/3 -2/35 17/10 -2/35 -7/123 12/7 -3/53 -4/71 19/11 -1/18 7/4 -3/53 -4/71 9/5 -1/18 2/1 -2/37 -1/19 11/5 -2/39 20/9 -1/19 -2/39 29/13 -1/20 9/4 -1/19 0/1 16/7 -5/97 -2/39 39/17 -2/39 23/10 -2/39 -7/137 7/3 -1/20 5/2 -1/20 13/5 -5/102 21/8 -2/41 -1/21 29/11 -2/41 8/3 -1/21 0/1 19/7 -1/20 30/11 -3/61 -2/41 41/15 -2/41 11/4 -2/41 -1/21 3/1 -1/21 10/3 -1/21 0/1 17/5 -1/20 7/2 -2/43 -3/65 11/3 -1/22 4/1 -1/23 0/1 13/3 -2/45 22/5 -2/45 -1/23 9/2 -4/91 -1/23 23/5 -1/23 14/3 -1/23 -6/139 5/1 -1/24 6/1 -1/24 7/1 0/1 1/0 -1/27 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(121,-18,74,-11) (0/1,1/6) -> (13/8,18/11) Hyperbolic Matrix(60,-11,11,-2) (1/6,1/5) -> (5/1,6/1) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(171,-40,124,-29) (2/9,1/4) -> (11/8,18/13) Hyperbolic Matrix(34,-9,121,-32) (1/4,3/11) -> (3/11,2/7) Parabolic Matrix(142,-41,97,-28) (2/7,5/17) -> (13/9,3/2) Hyperbolic Matrix(346,-103,215,-64) (5/17,3/10) -> (8/5,21/13) Hyperbolic Matrix(22,-7,63,-20) (3/10,1/3) -> (1/3,4/11) Parabolic Matrix(779,-286,286,-105) (4/11,7/19) -> (19/7,30/11) Hyperbolic Matrix(164,-61,285,-106) (7/19,3/8) -> (4/7,11/19) Hyperbolic Matrix(335,-128,212,-81) (3/8,5/13) -> (11/7,19/12) Hyperbolic Matrix(130,-51,51,-20) (5/13,2/5) -> (5/2,13/5) Hyperbolic Matrix(70,-29,29,-12) (2/5,3/7) -> (7/3,5/2) Hyperbolic Matrix(273,-118,118,-51) (3/7,7/16) -> (23/10,7/3) Hyperbolic Matrix(380,-167,223,-98) (7/16,4/9) -> (17/10,12/7) Hyperbolic Matrix(87,-40,124,-57) (4/9,1/2) -> (7/10,12/17) Hyperbolic Matrix(46,-25,81,-44) (1/2,5/9) -> (5/9,4/7) Parabolic Matrix(284,-165,389,-226) (11/19,7/12) -> (8/11,11/15) Hyperbolic Matrix(380,-223,167,-98) (7/12,10/17) -> (9/4,16/7) Hyperbolic Matrix(124,-73,17,-10) (10/17,3/5) -> (7/1,1/0) Hyperbolic Matrix(121,-74,18,-11) (3/5,8/13) -> (6/1,7/1) Hyperbolic Matrix(546,-337,337,-208) (8/13,13/21) -> (21/13,13/8) Hyperbolic Matrix(346,-215,103,-64) (13/21,5/8) -> (10/3,17/5) Hyperbolic Matrix(335,-212,128,-81) (5/8,7/11) -> (13/5,21/8) Hyperbolic Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(142,-97,41,-28) (2/3,9/13) -> (17/5,7/2) Hyperbolic Matrix(429,-298,298,-207) (9/13,7/10) -> (23/16,13/9) Hyperbolic Matrix(1190,-841,1681,-1188) (12/17,29/41) -> (29/41,17/24) Parabolic Matrix(466,-331,107,-76) (17/24,5/7) -> (13/3,22/5) Hyperbolic Matrix(171,-124,40,-29) (5/7,8/11) -> (4/1,13/3) Hyperbolic Matrix(120,-89,89,-66) (11/15,3/4) -> (4/3,15/11) Hyperbolic Matrix(8,-7,7,-6) (3/4,1/1) -> (1/1,4/3) Parabolic Matrix(284,-389,165,-226) (15/11,11/8) -> (12/7,19/11) Hyperbolic Matrix(417,-578,158,-219) (18/13,7/5) -> (29/11,8/3) Hyperbolic Matrix(87,-124,40,-57) (7/5,10/7) -> (2/1,11/5) Hyperbolic Matrix(760,-1089,529,-758) (10/7,33/23) -> (33/23,23/16) Parabolic Matrix(188,-289,121,-186) (3/2,17/11) -> (17/11,14/9) Parabolic Matrix(309,-490,70,-111) (19/12,8/5) -> (22/5,9/2) Hyperbolic Matrix(106,-175,63,-104) (18/11,5/3) -> (5/3,17/10) Parabolic Matrix(164,-285,61,-106) (19/11,7/4) -> (8/3,19/7) Hyperbolic Matrix(46,-81,25,-44) (7/4,9/5) -> (9/5,2/1) Parabolic Matrix(366,-811,139,-308) (11/5,20/9) -> (21/8,29/11) Hyperbolic Matrix(378,-841,169,-376) (20/9,29/13) -> (29/13,9/4) Parabolic Matrix(664,-1521,289,-662) (16/7,39/17) -> (39/17,23/10) Parabolic Matrix(616,-1681,225,-614) (30/11,41/15) -> (41/15,11/4) Parabolic Matrix(22,-63,7,-20) (11/4,3/1) -> (3/1,10/3) Parabolic Matrix(34,-121,9,-32) (7/2,11/3) -> (11/3,4/1) Parabolic Matrix(116,-529,25,-114) (9/2,23/5) -> (23/5,14/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,26,1) Matrix(121,-18,74,-11) -> Matrix(5,2,-88,-35) Matrix(60,-11,11,-2) -> Matrix(5,1,-116,-23) Matrix(115,-24,24,-5) -> Matrix(9,2,-212,-47) Matrix(171,-40,124,-29) -> Matrix(29,5,-470,-81) Matrix(34,-9,121,-32) -> Matrix(17,3,-108,-19) Matrix(142,-41,97,-28) -> Matrix(33,5,-548,-83) Matrix(346,-103,215,-64) -> Matrix(27,4,-466,-69) Matrix(22,-7,63,-20) -> Matrix(13,2,-98,-15) Matrix(779,-286,286,-105) -> Matrix(31,4,-628,-81) Matrix(164,-61,285,-106) -> Matrix(31,4,-318,-41) Matrix(335,-128,212,-81) -> Matrix(67,9,-1154,-155) Matrix(130,-51,51,-20) -> Matrix(39,5,-788,-101) Matrix(70,-29,29,-12) -> Matrix(25,3,-492,-59) Matrix(273,-118,118,-51) -> Matrix(33,4,-652,-79) Matrix(380,-167,223,-98) -> Matrix(61,7,-1072,-123) Matrix(87,-40,124,-57) -> Matrix(61,7,-706,-81) Matrix(46,-25,81,-44) -> Matrix(49,5,-500,-51) Matrix(284,-165,389,-226) -> Matrix(81,8,-962,-95) Matrix(380,-223,167,-98) -> Matrix(73,7,-1408,-135) Matrix(124,-73,17,-10) -> Matrix(21,2,-494,-47) Matrix(121,-74,18,-11) -> Matrix(21,2,-536,-51) Matrix(546,-337,337,-208) -> Matrix(161,15,-2780,-259) Matrix(346,-215,103,-64) -> Matrix(43,4,-914,-85) Matrix(335,-212,128,-81) -> Matrix(97,9,-1994,-185) Matrix(187,-120,120,-77) -> Matrix(153,14,-2612,-239) Matrix(142,-97,41,-28) -> Matrix(57,5,-1220,-107) Matrix(429,-298,298,-207) -> Matrix(321,28,-5308,-463) Matrix(1190,-841,1681,-1188) -> Matrix(289,25,-3364,-291) Matrix(466,-331,107,-76) -> Matrix(81,7,-1840,-159) Matrix(171,-124,40,-29) -> Matrix(59,5,-1310,-111) Matrix(120,-89,89,-66) -> Matrix(131,11,-2108,-177) Matrix(8,-7,7,-6) -> Matrix(13,1,-196,-15) Matrix(284,-389,165,-226) -> Matrix(129,8,-2306,-143) Matrix(417,-578,158,-219) -> Matrix(179,11,-3694,-227) Matrix(87,-124,40,-57) -> Matrix(115,7,-2218,-135) Matrix(760,-1089,529,-758) -> Matrix(1187,72,-19602,-1189) Matrix(188,-289,121,-186) -> Matrix(373,22,-6358,-375) Matrix(309,-490,70,-111) -> Matrix(121,7,-2714,-157) Matrix(106,-175,63,-104) -> Matrix(139,8,-2450,-141) Matrix(164,-285,61,-106) -> Matrix(71,4,-1438,-81) Matrix(46,-81,25,-44) -> Matrix(89,5,-1620,-91) Matrix(366,-811,139,-308) -> Matrix(77,4,-1598,-83) Matrix(378,-841,169,-376) -> Matrix(19,1,-400,-21) Matrix(664,-1521,289,-662) -> Matrix(467,24,-9126,-469) Matrix(616,-1681,225,-614) -> Matrix(163,8,-3362,-165) Matrix(22,-63,7,-20) -> Matrix(41,2,-882,-43) Matrix(34,-121,9,-32) -> Matrix(65,3,-1452,-67) Matrix(116,-529,25,-114) -> Matrix(229,10,-5290,-231) 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): 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 -1/1 0/1 26 1 1/1 -1/14 2 14 4/3 -1/16 6 4 15/11 -1/16 2 14 11/8 (-5/81,-4/65) 0 28 7/5 -3/49 2 7 10/7 (-11/181,-2/33) 0 28 33/23 -2/33 18 1 13/9 -7/116 2 14 3/2 (-4/67,-1/17) 0 28 17/11 -1/17 22 1 11/7 -7/120 2 14 8/5 (-1/17,-4/69) 0 28 21/13 -5/86 2 14 13/8 -3/52 2 4 5/3 -2/35 2 7 17/10 (-2/35,-7/123) 0 28 12/7 (-3/53,-4/71) 0 28 19/11 -1/18 2 14 7/4 (-3/53,-4/71) 0 28 9/5 -1/18 10 2 2/1 (-2/37,-1/19) 0 28 11/5 -2/39 2 7 20/9 (-1/19,-2/39) 0 28 29/13 -1/20 2 2 9/4 (-1/19,0/1) 0 28 16/7 (-5/97,-2/39) 0 28 39/17 -2/39 6 1 7/3 -1/20 2 14 5/2 -1/20 4 4 13/5 -5/102 2 14 21/8 (-2/41,-1/21) 0 28 8/3 (-1/21,0/1) 0 28 19/7 -1/20 2 14 41/15 -2/41 2 1 11/4 (-2/41,-1/21) 0 28 3/1 -1/21 2 7 10/3 (-1/21,0/1) 0 28 17/5 -1/20 2 14 7/2 (-2/43,-3/65) 0 28 11/3 -1/22 6 2 4/1 (-1/23,0/1) 0 28 13/3 -2/45 2 7 22/5 (-2/45,-1/23) 0 28 9/2 (-4/91,-1/23) 0 28 23/5 -1/23 10 1 5/1 -1/24 2 14 6/1 -1/24 2 4 7/1 0/1 2 7 1/0 (-1/27,0/1) 0 28 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(7,-8,6,-7) (1/1,4/3) -> (1/1,4/3) Reflection Matrix(89,-120,66,-89) (4/3,15/11) -> (4/3,15/11) Reflection Matrix(284,-389,165,-226) (15/11,11/8) -> (12/7,19/11) Hyperbolic Matrix(124,-171,29,-40) (11/8,7/5) -> (4/1,13/3) Glide Reflection Matrix(87,-124,40,-57) (7/5,10/7) -> (2/1,11/5) Hyperbolic Matrix(461,-660,322,-461) (10/7,33/23) -> (10/7,33/23) Reflection Matrix(298,-429,207,-298) (33/23,13/9) -> (33/23,13/9) Reflection Matrix(97,-142,28,-41) (13/9,3/2) -> (17/5,7/2) Glide Reflection Matrix(67,-102,44,-67) (3/2,17/11) -> (3/2,17/11) Reflection Matrix(120,-187,77,-120) (17/11,11/7) -> (17/11,11/7) Reflection Matrix(212,-335,81,-128) (11/7,8/5) -> (13/5,21/8) Glide Reflection Matrix(215,-346,64,-103) (8/5,21/13) -> (10/3,17/5) Glide Reflection Matrix(337,-546,208,-337) (21/13,13/8) -> (21/13,13/8) Reflection Matrix(74,-121,11,-18) (13/8,5/3) -> (6/1,7/1) Glide Reflection Matrix(73,-124,10,-17) (5/3,17/10) -> (7/1,1/0) Glide Reflection Matrix(223,-380,98,-167) (17/10,12/7) -> (9/4,16/7) Glide Reflection Matrix(164,-285,61,-106) (19/11,7/4) -> (8/3,19/7) Hyperbolic Matrix(46,-81,25,-44) (7/4,9/5) -> (9/5,2/1) Parabolic Matrix(227,-502,52,-115) (11/5,20/9) -> (13/3,22/5) Glide Reflection Matrix(378,-841,169,-376) (20/9,29/13) -> (29/13,9/4) Parabolic Matrix(545,-1248,238,-545) (16/7,39/17) -> (16/7,39/17) Reflection Matrix(118,-273,51,-118) (39/17,7/3) -> (39/17,7/3) Reflection Matrix(29,-70,12,-29) (7/3,5/2) -> (7/3,5/2) Reflection Matrix(51,-130,20,-51) (5/2,13/5) -> (5/2,13/5) Reflection Matrix(138,-365,31,-82) (21/8,8/3) -> (22/5,9/2) Glide Reflection Matrix(286,-779,105,-286) (19/7,41/15) -> (19/7,41/15) Reflection Matrix(329,-902,120,-329) (41/15,11/4) -> (41/15,11/4) Reflection Matrix(22,-63,7,-20) (11/4,3/1) -> (3/1,10/3) Parabolic Matrix(34,-121,9,-32) (7/2,11/3) -> (11/3,4/1) Parabolic Matrix(91,-414,20,-91) (9/2,23/5) -> (9/2,23/5) Reflection Matrix(24,-115,5,-24) (23/5,5/1) -> (23/5,5/1) Reflection Matrix(11,-60,2,-11) (5/1,6/1) -> (5/1,6/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,54,1) (-1/1,1/0) -> (-1/27,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,28,1) (-1/1,1/1) -> (-1/14,0/1) Matrix(7,-8,6,-7) -> Matrix(15,1,-224,-15) (1/1,4/3) -> (-1/14,-1/16) Matrix(89,-120,66,-89) -> Matrix(177,11,-2848,-177) (4/3,15/11) -> (-1/16,-11/178) Matrix(284,-389,165,-226) -> Matrix(129,8,-2306,-143) Matrix(124,-171,29,-40) -> Matrix(81,5,-1798,-111) Matrix(87,-124,40,-57) -> Matrix(115,7,-2218,-135) Matrix(461,-660,322,-461) -> Matrix(725,44,-11946,-725) (10/7,33/23) -> (-11/181,-2/33) Matrix(298,-429,207,-298) -> Matrix(463,28,-7656,-463) (33/23,13/9) -> (-2/33,-7/116) Matrix(97,-142,28,-41) -> Matrix(83,5,-1776,-107) Matrix(67,-102,44,-67) -> Matrix(135,8,-2278,-135) (3/2,17/11) -> (-4/67,-1/17) Matrix(120,-187,77,-120) -> Matrix(239,14,-4080,-239) (17/11,11/7) -> (-1/17,-7/120) Matrix(212,-335,81,-128) -> Matrix(155,9,-3186,-185) Matrix(215,-346,64,-103) -> Matrix(69,4,-1466,-85) Matrix(337,-546,208,-337) -> Matrix(259,15,-4472,-259) (21/13,13/8) -> (-5/86,-3/52) Matrix(74,-121,11,-18) -> Matrix(35,2,-892,-51) Matrix(73,-124,10,-17) -> Matrix(35,2,-822,-47) Matrix(223,-380,98,-167) -> Matrix(123,7,-2372,-135) Matrix(164,-285,61,-106) -> Matrix(71,4,-1438,-81) Matrix(46,-81,25,-44) -> Matrix(89,5,-1620,-91) -1/18 Matrix(227,-502,52,-115) -> Matrix(-1,0,42,1) *** -> (-1/21,0/1) Matrix(378,-841,169,-376) -> Matrix(19,1,-400,-21) -1/20 Matrix(545,-1248,238,-545) -> Matrix(389,20,-7566,-389) (16/7,39/17) -> (-5/97,-2/39) Matrix(118,-273,51,-118) -> Matrix(79,4,-1560,-79) (39/17,7/3) -> (-2/39,-1/20) Matrix(29,-70,12,-29) -> Matrix(59,3,-1160,-59) (7/3,5/2) -> (-3/58,-1/20) Matrix(51,-130,20,-51) -> Matrix(101,5,-2040,-101) (5/2,13/5) -> (-1/20,-5/102) Matrix(138,-365,31,-82) -> Matrix(83,4,-1888,-91) Matrix(286,-779,105,-286) -> Matrix(81,4,-1640,-81) (19/7,41/15) -> (-1/20,-2/41) Matrix(329,-902,120,-329) -> Matrix(83,4,-1722,-83) (41/15,11/4) -> (-2/41,-1/21) Matrix(22,-63,7,-20) -> Matrix(41,2,-882,-43) -1/21 Matrix(34,-121,9,-32) -> Matrix(65,3,-1452,-67) -1/22 Matrix(91,-414,20,-91) -> Matrix(183,8,-4186,-183) (9/2,23/5) -> (-4/91,-1/23) Matrix(24,-115,5,-24) -> Matrix(47,2,-1104,-47) (23/5,5/1) -> (-1/23,-1/24) Matrix(11,-60,2,-11) -> Matrix(23,1,-528,-23) (5/1,6/1) -> (-1/22,-1/24) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.