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 -1/2 1/0 -1/2 -1/1 0/1 -6/13 -1/2 -11/24 -1/5 0/1 -5/11 -1/1 0/1 -9/20 -1/1 -4/5 -4/9 -1/1 -2/3 -11/25 -1/2 -18/41 -5/11 -4/9 -25/57 -1/2 -5/12 -7/16 -1/3 0/1 -3/7 -1/2 1/0 -8/19 -1/1 0/1 -21/50 -1/1 0/1 -13/31 -1/1 -2/3 -5/12 -1/2 -17/41 -1/2 -5/12 -12/29 -2/5 -1/3 -7/17 -1/3 0/1 -16/39 -1/3 0/1 -9/22 -1/1 0/1 -2/5 -1/1 0/1 -9/23 -1/2 -16/41 -4/9 -3/7 -7/18 -2/5 -1/3 -12/31 -4/11 -1/3 -5/13 -1/2 -1/4 -13/34 -1/4 -8/21 -1/5 0/1 -11/29 -1/7 0/1 -3/8 0/1 1/1 -13/35 -1/1 0/1 -10/27 -1/1 0/1 -7/19 -1/2 1/0 -18/49 -1/1 0/1 -11/30 -2/1 -1/1 -4/11 -1/2 -9/25 -1/2 -1/4 -5/14 -1/3 0/1 -11/31 -1/2 -1/4 -6/17 -1/5 0/1 -13/37 -1/6 -1/8 -7/20 -1/13 0/1 -1/3 -1/1 0/1 -7/22 -1/13 0/1 -6/19 0/1 1/11 -5/16 0/1 1/3 -14/45 2/3 1/1 -9/29 1/2 1/0 -4/13 0/1 1/1 -7/23 1/2 1/0 -3/10 1/0 -8/27 -1/1 -2/3 -13/44 -1/1 0/1 -5/17 -1/2 1/0 -7/24 -1/1 0/1 -16/55 -1/1 0/1 -9/31 -1/1 0/1 -2/7 -1/3 0/1 -9/32 0/1 1/13 -7/25 0/1 1/5 -5/18 0/1 1/3 -8/29 1/2 -3/11 1/2 1/0 -7/26 1/1 4/3 -4/15 1/1 2/1 -5/19 1/0 -6/23 -3/1 -2/1 -7/27 -3/2 1/0 -1/4 -1/1 0/1 -4/17 -1/1 0/1 -7/30 0/1 1/1 -10/43 0/1 1/1 -3/13 0/1 1/1 -5/22 1/1 2/1 -12/53 2/1 15/7 -7/31 5/2 1/0 -2/9 1/0 -5/23 -2/1 -1/1 -8/37 -1/1 0/1 -3/14 -1/1 0/1 -1/5 -1/2 1/0 -2/11 0/1 1/1 -3/17 1/0 -4/23 -6/1 -5/1 -5/29 -7/2 1/0 -1/6 -2/1 -1/1 -2/13 -4/3 -1/1 -3/20 -1/1 -4/5 -1/7 -1/1 0/1 -2/15 0/1 1/3 -1/8 1/0 0/1 -1/1 0/1 1/6 -1/2 3/17 -1/2 -1/4 5/28 -1/3 0/1 2/11 -1/5 0/1 3/16 -2/1 -1/1 4/21 -1/1 0/1 1/5 -1/1 0/1 2/9 -1/1 -4/5 3/13 -3/4 -1/2 4/17 -1/2 1/4 -1/1 -2/3 3/11 -1/2 5/18 -5/11 -4/9 7/25 -1/2 -5/12 2/7 -1/3 0/1 5/17 -1/1 0/1 8/27 -1/2 3/10 -1/1 0/1 4/13 -1/1 0/1 1/3 -1/2 1/0 5/14 -1/3 0/1 4/11 -1/1 0/1 7/19 -1/1 0/1 3/8 -1/1 0/1 8/21 -1/1 0/1 21/55 -3/4 -1/2 13/34 -1/1 -2/3 5/13 -1/1 -2/3 12/31 -2/3 -3/5 7/18 -2/3 -3/5 2/5 -1/2 9/22 -4/9 -3/7 16/39 -3/7 -20/47 7/17 -1/2 -5/12 5/12 -2/5 -1/3 13/31 -1/2 -3/8 8/19 -2/5 -1/3 3/7 -1/3 0/1 7/16 -1/3 0/1 11/25 -1/2 -1/4 15/34 -1/4 4/9 -1/1 0/1 13/29 -1/2 9/20 -2/5 -1/3 5/11 -1/2 -1/4 6/13 -1/3 0/1 1/2 -1/1 0/1 5/9 -1/2 9/16 -4/9 -3/7 4/7 -2/5 -1/3 15/26 -2/5 -1/3 11/19 -2/5 -1/3 29/50 -1/3 0/1 18/31 -1/2 7/12 -4/11 -1/3 17/29 -1/3 -4/13 10/17 -1/3 -2/7 13/22 -1/4 3/5 -1/2 -1/4 8/13 -1/4 21/34 -4/19 -1/5 34/55 -1/7 0/1 13/21 -1/5 0/1 5/8 -1/5 0/1 12/19 -1/5 0/1 31/49 -3/16 -1/6 19/30 -1/6 7/11 -1/7 0/1 2/3 0/1 1/1 11/16 -1/1 -4/5 20/29 -1/2 9/13 -1/1 0/1 7/10 -1/1 0/1 19/27 -2/1 -1/1 12/17 -1/1 0/1 29/41 -1/2 17/24 -1/1 0/1 5/7 -1/2 1/0 13/18 -1/1 0/1 21/29 -1/1 0/1 29/40 -1/5 0/1 37/51 1/2 1/0 8/11 -2/1 -1/1 19/26 -1/1 0/1 11/15 -1/1 0/1 3/4 -1/2 13/17 -2/5 -1/3 36/47 -1/3 -10/31 23/30 -1/3 -2/7 10/13 -1/3 0/1 17/22 -1/3 -2/7 7/9 -1/2 -1/4 18/23 -1/5 0/1 11/14 -1/5 0/1 15/19 -1/1 0/1 4/5 -1/3 0/1 17/21 -1/3 0/1 13/16 -2/5 -1/3 9/11 -1/2 -1/4 5/6 -1/5 0/1 11/13 -1/6 -1/8 6/7 -1/13 0/1 1/1 -1/1 0/1 8/7 -1/13 0/1 15/13 0/1 22/19 0/1 1/35 7/6 0/1 1/11 6/5 0/1 1/3 17/14 2/3 1/1 11/9 1/2 1/0 16/13 1/1 2/1 21/17 0/1 1/1 26/21 0/1 1/1 5/4 0/1 1/1 14/11 0/1 1/3 23/18 0/1 1/3 9/7 1/2 1/0 31/24 2/3 1/1 22/17 2/3 1/1 13/10 0/1 1/1 4/3 1/0 19/14 -2/1 -1/1 53/39 -3/2 1/0 34/25 -4/3 -1/1 15/11 -1/1 0/1 11/8 -1/1 -2/3 51/37 -1/2 -1/4 40/29 0/1 1/3 29/21 -1/1 0/1 47/34 -1/1 0/1 65/47 -1/2 1/0 18/13 -1/1 0/1 25/18 -1/1 0/1 32/23 -1/1 0/1 7/5 -1/2 1/0 31/22 -1/1 0/1 24/17 -1/1 0/1 41/29 1/0 17/12 -1/1 0/1 27/19 -1/1 -2/3 10/7 -1/1 0/1 33/23 -1/2 1/0 56/39 -1/1 0/1 23/16 -1/1 0/1 13/9 -1/1 0/1 16/11 -4/3 -1/1 19/13 -3/4 -1/2 3/2 -1/3 0/1 17/11 0/1 31/20 0/1 1/29 14/9 0/1 1/13 11/7 0/1 1/5 30/19 1/4 49/31 1/4 3/10 68/43 8/25 1/3 19/12 0/1 1/3 27/17 1/4 1/2 8/5 0/1 1/3 29/18 0/1 1/1 21/13 0/1 1/3 55/34 0/1 1/5 89/55 1/4 3/10 34/21 1/3 4/11 47/29 3/8 1/2 13/8 1/2 18/11 2/3 1/1 41/25 4/5 1/1 23/14 1/1 4/3 5/3 1/2 1/0 22/13 1/2 17/10 2/3 1/1 12/7 1/1 4/3 31/18 1/0 19/11 1/1 2/1 7/4 1/1 2/1 9/5 1/0 11/6 -3/1 -2/1 13/7 -3/2 1/0 15/8 -2/1 -1/1 17/9 -4/3 -1/1 2/1 -1/1 0/1 15/7 0/1 1/3 13/6 0/1 1/1 11/5 1/2 1/0 31/14 1/1 2/1 20/9 1/1 2/1 29/13 1/0 38/17 -1/1 0/1 9/4 -1/1 0/1 34/15 1/2 25/11 1/2 1/0 41/18 2/3 1/1 16/7 0/1 1/1 39/17 1/2 1/0 62/27 0/1 1/1 23/10 0/1 1/1 7/3 0/1 1/1 33/14 8/9 1/1 59/25 1/1 26/11 1/1 8/7 19/8 1/1 2/1 69/29 3/2 50/21 1/1 2/1 31/13 3/2 1/0 12/5 1/1 2/1 29/12 2/1 15/7 17/7 5/2 1/0 5/2 1/0 23/9 -7/2 1/0 64/25 -17/5 -10/3 41/16 -22/7 -3/1 141/55 -3/1 100/39 -3/1 -50/17 59/23 -3/1 -14/5 18/7 -3/1 -2/1 49/19 -5/2 1/0 31/12 -3/1 -2/1 13/5 -2/1 -1/1 47/18 -2/1 -1/1 81/31 -3/2 1/0 115/44 -2/1 -1/1 34/13 -2/1 -1/1 55/21 -3/2 1/0 76/29 -3/2 21/8 -1/1 0/1 71/27 1/0 50/19 -3/1 -2/1 29/11 -3/2 1/0 8/3 -1/1 0/1 27/10 -1/1 -2/3 19/7 -1/1 0/1 30/11 -1/1 0/1 41/15 -1/2 1/0 11/4 -1/1 0/1 25/9 -1/1 0/1 64/23 -1/5 0/1 39/14 0/1 1/3 14/5 0/1 1/1 3/1 -1/2 1/0 13/4 -1/1 0/1 23/7 -1/1 0/1 33/10 -1/1 0/1 43/13 -1/2 1/0 10/3 -1/1 0/1 27/8 1/0 71/21 -3/2 1/0 44/13 -4/3 -1/1 17/5 -1/1 0/1 41/12 -1/5 0/1 65/19 0/1 89/26 0/1 1/11 24/7 0/1 1/3 7/2 0/1 1/1 11/3 1/0 15/4 -6/1 -5/1 34/9 -21/5 -4/1 19/5 -7/2 1/0 42/11 -10/3 -3/1 65/17 -22/7 -3/1 23/6 -3/1 -14/5 4/1 -2/1 -1/1 25/6 -4/3 -1/1 46/11 -12/11 -1/1 113/27 -1/1 67/16 -1/1 -12/13 21/5 -1/1 0/1 17/4 1/0 13/3 -3/2 1/0 35/8 -2/1 -5/3 57/13 -3/2 22/5 -4/3 -1/1 9/2 -4/3 -1/1 23/5 -1/1 37/8 -1/1 -12/13 14/3 -1/1 -4/5 5/1 -1/1 0/1 26/5 -1/1 0/1 47/9 -1/2 1/0 21/4 -1/1 0/1 16/3 -1/1 -2/3 27/5 -1/2 -1/4 11/2 0/1 1/3 28/5 0/1 1/1 45/8 1/1 2/1 17/3 1/2 1/0 23/4 2/3 1/1 6/1 1/0 7/1 -3/2 1/0 8/1 -6/5 -1/1 25/3 -1/1 17/2 -1/1 -10/11 9/1 -1/1 -2/3 1/0 -1/1 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(1,0,0,1) Matrix(265,124,156,73) -> Matrix(3,2,4,3) Matrix(933,428,412,189) -> Matrix(1,0,4,1) Matrix(823,376,1136,519) -> Matrix(1,0,0,1) Matrix(53,24,-360,-163) -> Matrix(1,0,0,1) Matrix(353,158,458,205) -> Matrix(3,2,-8,-5) Matrix(549,242,-1250,-551) -> Matrix(11,6,-24,-13) Matrix(4591,2014,1794,787) -> Matrix(43,18,-12,-5) Matrix(1443,632,1048,459) -> Matrix(5,2,-8,-3) Matrix(51,22,146,63) -> Matrix(1,0,0,1) Matrix(47,20,148,63) -> Matrix(1,0,0,1) Matrix(1689,710,1306,549) -> Matrix(3,2,4,3) Matrix(1253,526,1546,649) -> Matrix(3,2,-8,-5) Matrix(673,282,1062,445) -> Matrix(3,2,-20,-13) Matrix(1151,478,1818,755) -> Matrix(9,4,-52,-23) Matrix(623,258,-1770,-733) -> Matrix(5,2,-28,-11) Matrix(953,394,670,277) -> Matrix(5,2,-8,-3) Matrix(287,118,-1238,-509) -> Matrix(1,0,4,1) Matrix(1045,428,188,77) -> Matrix(1,0,4,1) Matrix(423,172,332,135) -> Matrix(1,0,4,1) Matrix(413,162,-1058,-415) -> Matrix(7,4,-16,-9) Matrix(457,178,-1466,-571) -> Matrix(5,2,12,5) Matrix(733,284,1004,389) -> Matrix(5,2,-8,-3) Matrix(321,124,44,17) -> Matrix(7,2,-4,-1) Matrix(271,104,456,175) -> Matrix(1,0,0,1) Matrix(907,346,270,103) -> Matrix(1,0,4,1) Matrix(453,172,1172,445) -> Matrix(13,2,-20,-3) Matrix(317,120,-1128,-427) -> Matrix(1,0,12,1) Matrix(2093,778,1294,481) -> Matrix(1,0,4,1) Matrix(803,298,-2762,-1025) -> Matrix(1,0,0,1) Matrix(1065,394,446,165) -> Matrix(1,2,0,1) Matrix(2743,1008,1064,391) -> Matrix(1,-2,0,1) Matrix(267,98,1414,519) -> Matrix(1,0,0,1) Matrix(617,226,1062,389) -> Matrix(3,2,-8,-5) Matrix(133,48,568,205) -> Matrix(5,2,-8,-3) Matrix(479,172,220,79) -> Matrix(1,0,4,1) Matrix(697,248,1824,649) -> Matrix(5,2,-8,-3) Matrix(305,108,-1172,-415) -> Matrix(7,2,-4,-1) Matrix(1813,636,2500,877) -> Matrix(1,0,8,1) Matrix(41,14,-126,-43) -> Matrix(1,0,0,1) Matrix(617,196,532,169) -> Matrix(1,0,24,1) Matrix(287,90,-1266,-397) -> Matrix(7,-2,4,-1) Matrix(3371,1048,2480,771) -> Matrix(1,-2,0,1) Matrix(1701,526,650,201) -> Matrix(1,-2,0,1) Matrix(203,62,442,135) -> Matrix(1,0,-4,1) Matrix(521,158,122,37) -> Matrix(1,-2,0,1) Matrix(957,284,556,165) -> Matrix(1,2,0,1) Matrix(1271,376,240,71) -> Matrix(1,0,0,1) Matrix(835,246,594,175) -> Matrix(1,0,0,1) Matrix(397,116,948,277) -> Matrix(3,2,-8,-5) Matrix(2609,760,1816,529) -> Matrix(1,0,0,1) Matrix(1145,332,1852,537) -> Matrix(1,0,-4,1) Matrix(665,188,428,121) -> Matrix(1,0,16,1) Matrix(1009,282,390,109) -> Matrix(9,-2,-4,1) Matrix(231,64,776,215) -> Matrix(1,0,-4,1) Matrix(387,106,230,63) -> Matrix(1,0,0,1) Matrix(383,104,232,63) -> Matrix(1,0,0,1) Matrix(613,164,228,61) -> Matrix(1,-2,0,1) Matrix(189,50,-722,-191) -> Matrix(1,-4,0,1) Matrix(1283,332,228,59) -> Matrix(1,2,0,1) Matrix(259,62,330,79) -> Matrix(1,0,-4,1) Matrix(145,34,806,189) -> Matrix(1,0,-4,1) Matrix(2849,664,1240,289) -> Matrix(1,0,0,1) Matrix(509,116,724,165) -> Matrix(1,-2,0,1) Matrix(3943,892,2860,647) -> Matrix(1,-2,-4,9) Matrix(1371,308,868,195) -> Matrix(1,-4,4,-15) Matrix(789,172,500,109) -> Matrix(1,2,4,9) Matrix(1145,248,928,201) -> Matrix(1,2,0,1) Matrix(1427,308,644,139) -> Matrix(1,2,0,1) Matrix(107,22,34,7) -> Matrix(1,0,0,1) Matrix(103,20,36,7) -> Matrix(1,0,0,1) Matrix(101,18,-578,-103) -> Matrix(1,-6,0,1) Matrix(1083,188,1492,259) -> Matrix(1,4,0,1) Matrix(2129,364,1316,225) -> Matrix(1,2,4,9) Matrix(301,48,232,37) -> Matrix(1,2,0,1) Matrix(761,116,164,25) -> Matrix(7,8,-8,-9) Matrix(715,98,518,71) -> Matrix(1,0,0,1) Matrix(257,34,582,77) -> Matrix(1,0,-4,1) Matrix(93,10,158,17) -> Matrix(1,2,-4,-7) Matrix(121,-18,74,-11) -> Matrix(3,2,4,3) Matrix(503,-86,310,-53) -> Matrix(5,2,12,5) Matrix(1807,-322,1330,-237) -> Matrix(7,2,-4,-1) Matrix(709,-132,188,-35) -> Matrix(1,-4,0,1) Matrix(235,-46,46,-9) -> Matrix(1,0,0,1) Matrix(115,-24,24,-5) -> Matrix(1,0,0,1) Matrix(365,-82,138,-31) -> Matrix(5,4,-4,-3) Matrix(565,-134,974,-231) -> Matrix(3,2,-8,-5) Matrix(67,-18,242,-65) -> Matrix(11,6,-24,-13) Matrix(417,-116,284,-79) -> Matrix(9,4,-16,-7) Matrix(589,-166,110,-31) -> Matrix(5,2,-8,-3) Matrix(173,-50,218,-63) -> Matrix(1,0,0,1) Matrix(583,-172,844,-249) -> Matrix(1,0,0,1) Matrix(235,-72,408,-125) -> Matrix(3,2,-8,-5) Matrix(431,-156,268,-97) -> Matrix(1,0,4,1) Matrix(779,-286,286,-105) -> Matrix(1,0,0,1) Matrix(449,-166,614,-227) -> Matrix(1,0,0,1) Matrix(365,-138,82,-31) -> Matrix(5,4,-4,-3) Matrix(3911,-1492,1156,-441) -> Matrix(5,4,-4,-3) Matrix(1053,-404,404,-155) -> Matrix(5,4,-4,-3) Matrix(1393,-540,988,-383) -> Matrix(3,2,-8,-5) Matrix(81,-32,200,-79) -> Matrix(11,6,-24,-13) Matrix(1689,-692,2204,-903) -> Matrix(23,10,-76,-33) Matrix(4049,-1662,2502,-1027) -> Matrix(19,8,64,27) Matrix(217,-90,258,-107) -> Matrix(5,2,-28,-11) Matrix(1125,-472,808,-339) -> Matrix(5,2,-8,-3) Matrix(393,-166,670,-283) -> Matrix(11,4,-36,-13) Matrix(273,-118,118,-51) -> Matrix(1,0,4,1) Matrix(583,-256,312,-137) -> Matrix(7,2,-4,-1) Matrix(3089,-1362,914,-403) -> Matrix(7,2,-4,-1) Matrix(2071,-926,870,-389) -> Matrix(1,2,0,1) Matrix(1931,-868,812,-365) -> Matrix(11,4,8,3) Matrix(521,-236,404,-183) -> Matrix(1,0,4,1) Matrix(535,-248,192,-89) -> Matrix(1,0,4,1) Matrix(91,-50,162,-89) -> Matrix(7,4,-16,-9) Matrix(215,-122,178,-101) -> Matrix(5,2,12,5) Matrix(1225,-708,372,-215) -> Matrix(5,2,-8,-3) Matrix(1135,-658,602,-349) -> Matrix(7,2,-4,-1) Matrix(1041,-610,442,-259) -> Matrix(13,4,16,5) Matrix(121,-74,18,-11) -> Matrix(7,2,-4,-1) Matrix(503,-310,86,-53) -> Matrix(9,2,4,1) Matrix(4431,-2738,1730,-1069) -> Matrix(53,10,-16,-3) Matrix(431,-268,156,-97) -> Matrix(1,0,4,1) Matrix(619,-390,446,-281) -> Matrix(1,0,4,1) Matrix(2419,-1530,634,-401) -> Matrix(53,10,-16,-3) Matrix(187,-120,120,-77) -> Matrix(1,0,12,1) Matrix(133,-90,34,-23) -> Matrix(1,-2,0,1) Matrix(1825,-1256,696,-479) -> Matrix(5,4,-4,-3) Matrix(429,-298,298,-207) -> Matrix(1,0,0,1) Matrix(1183,-834,722,-509) -> Matrix(3,2,4,3) Matrix(1871,-1322,426,-301) -> Matrix(5,4,-4,-3) Matrix(2803,-1984,640,-453) -> Matrix(7,2,-4,-1) Matrix(1393,-988,540,-383) -> Matrix(1,-2,0,1) Matrix(619,-446,390,-281) -> Matrix(1,0,4,1) Matrix(1885,-1364,1364,-987) -> Matrix(1,0,0,1) Matrix(97,-72,128,-95) -> Matrix(3,2,-8,-5) Matrix(4473,-3424,1744,-1335) -> Matrix(57,20,-20,-7) Matrix(1425,-1094,254,-195) -> Matrix(1,0,4,1) Matrix(521,-404,236,-183) -> Matrix(1,0,4,1) Matrix(1117,-872,424,-331) -> Matrix(7,2,-4,-1) Matrix(1017,-802,298,-235) -> Matrix(1,0,0,1) Matrix(651,-526,526,-425) -> Matrix(1,0,4,1) Matrix(525,-428,92,-75) -> Matrix(1,0,4,1) Matrix(199,-164,108,-89) -> Matrix(7,2,-4,-1) Matrix(575,-488,152,-129) -> Matrix(31,4,-8,-1) Matrix(15,-14,14,-13) -> Matrix(1,0,0,1) Matrix(391,-450,338,-389) -> Matrix(1,0,48,1) Matrix(217,-258,90,-107) -> Matrix(7,-2,4,-1) Matrix(719,-876,316,-385) -> Matrix(1,0,0,1) Matrix(917,-1126,566,-695) -> Matrix(3,-2,8,-5) Matrix(2551,-3160,976,-1209) -> Matrix(1,-2,0,1) Matrix(173,-218,50,-63) -> Matrix(1,0,0,1) Matrix(479,-614,110,-141) -> Matrix(1,-2,0,1) Matrix(97,-128,72,-95) -> Matrix(1,-2,0,1) Matrix(1673,-2276,652,-887) -> Matrix(11,14,-4,-5) Matrix(449,-614,166,-227) -> Matrix(1,0,0,1) Matrix(2585,-3574,494,-683) -> Matrix(1,0,0,1) Matrix(1833,-2536,352,-487) -> Matrix(1,0,0,1) Matrix(891,-1238,398,-553) -> Matrix(1,0,0,1) Matrix(2657,-3754,1010,-1427) -> Matrix(1,-2,0,1) Matrix(1461,-2068,556,-787) -> Matrix(1,0,0,1) Matrix(127,-180,12,-17) -> Matrix(1,0,0,1) Matrix(1519,-2178,1058,-1517) -> Matrix(1,0,0,1) Matrix(583,-844,172,-249) -> Matrix(1,0,0,1) Matrix(1423,-2076,900,-1313) -> Matrix(5,4,16,13) Matrix(375,-578,242,-373) -> Matrix(1,0,32,1) Matrix(1627,-2574,390,-617) -> Matrix(11,-4,-8,3) Matrix(1005,-1598,422,-671) -> Matrix(7,-2,4,-1) Matrix(439,-708,204,-329) -> Matrix(1,0,0,1) Matrix(551,-904,64,-105) -> Matrix(7,-6,-8,7) Matrix(393,-670,166,-283) -> Matrix(5,-4,4,-3) Matrix(565,-974,134,-231) -> Matrix(1,-2,0,1) Matrix(235,-408,72,-125) -> Matrix(1,-2,0,1) Matrix(91,-162,50,-89) -> Matrix(1,-4,0,1) Matrix(443,-844,116,-221) -> Matrix(13,10,-4,-3) Matrix(473,-1010,170,-363) -> Matrix(1,0,-4,1) Matrix(755,-1682,338,-753) -> Matrix(1,-2,0,1) Matrix(1661,-3770,634,-1439) -> Matrix(1,-2,0,1) Matrix(247,-564,60,-137) -> Matrix(1,-2,0,1) Matrix(1327,-3042,578,-1325) -> Matrix(1,0,0,1) Matrix(775,-1828,92,-217) -> Matrix(19,-18,-20,19) Matrix(475,-1122,58,-137) -> Matrix(13,-14,-12,13) Matrix(401,-970,74,-179) -> Matrix(1,-2,-4,9) Matrix(81,-200,32,-79) -> Matrix(1,-6,0,1) Matrix(5493,-14080,1312,-3363) -> Matrix(19,58,-20,-61) Matrix(6937,-17786,1658,-4251) -> Matrix(29,86,-28,-83) Matrix(5023,-13122,1922,-5021) -> Matrix(1,0,0,1) Matrix(623,-1700,188,-513) -> Matrix(1,0,0,1) Matrix(667,-1826,202,-553) -> Matrix(1,0,0,1) Matrix(2383,-6632,696,-1937) -> Matrix(1,0,8,1) Matrix(2471,-8450,722,-2469) -> Matrix(1,0,16,1) Matrix(67,-242,18,-65) -> Matrix(1,-6,0,1) Matrix(1265,-4838,302,-1155) -> Matrix(7,22,-8,-25) Matrix(231,-1058,50,-229) -> Matrix(15,16,-16,-17) 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): 24 Degree of the the map X: 48 Degree of the the map Y: 192 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- 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: 24 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/1 15/13 4/3 7/5 33/23 17/11 5/3 9/5 2/1 29/13 39/17 7/3 5/2 3/1 11/3 19/5 4/1 13/3 23/5 5/1 17/3 6/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 0/1 -1/1 0/1 1/6 -1/2 3/17 -1/2 -1/4 2/11 -1/5 0/1 1/5 -1/1 0/1 2/9 -1/1 -4/5 1/4 -1/1 -2/3 1/3 -1/2 1/0 2/5 -1/2 7/17 -1/2 -5/12 5/12 -2/5 -1/3 3/7 -1/3 0/1 7/16 -1/3 0/1 4/9 -1/1 0/1 5/11 -1/2 -1/4 1/2 -1/1 0/1 3/5 -1/2 -1/4 8/13 -1/4 5/8 -1/5 0/1 7/11 -1/7 0/1 2/3 0/1 1/1 9/13 -1/1 0/1 7/10 -1/1 0/1 12/17 -1/1 0/1 5/7 -1/2 1/0 3/4 -1/2 7/9 -1/2 -1/4 4/5 -1/3 0/1 9/11 -1/2 -1/4 5/6 -1/5 0/1 11/13 -1/6 -1/8 6/7 -1/13 0/1 1/1 -1/1 0/1 8/7 -1/13 0/1 15/13 0/1 7/6 0/1 1/11 6/5 0/1 1/3 11/9 1/2 1/0 16/13 1/1 2/1 5/4 0/1 1/1 14/11 0/1 1/3 9/7 1/2 1/0 4/3 1/0 7/5 -1/2 1/0 24/17 -1/1 0/1 41/29 1/0 17/12 -1/1 0/1 10/7 -1/1 0/1 33/23 -1/2 1/0 23/16 -1/1 0/1 13/9 -1/1 0/1 16/11 -4/3 -1/1 3/2 -1/3 0/1 17/11 0/1 14/9 0/1 1/13 11/7 0/1 1/5 19/12 0/1 1/3 8/5 0/1 1/3 13/8 1/2 5/3 1/2 1/0 7/4 1/1 2/1 9/5 1/0 11/6 -3/1 -2/1 13/7 -3/2 1/0 2/1 -1/1 0/1 11/5 1/2 1/0 20/9 1/1 2/1 29/13 1/0 9/4 -1/1 0/1 25/11 1/2 1/0 16/7 0/1 1/1 39/17 1/2 1/0 23/10 0/1 1/1 7/3 0/1 1/1 19/8 1/1 2/1 12/5 1/1 2/1 29/12 2/1 15/7 17/7 5/2 1/0 5/2 1/0 3/1 -1/2 1/0 7/2 0/1 1/1 11/3 1/0 15/4 -6/1 -5/1 34/9 -21/5 -4/1 19/5 -7/2 1/0 4/1 -2/1 -1/1 13/3 -3/2 1/0 9/2 -4/3 -1/1 23/5 -1/1 14/3 -1/1 -4/5 5/1 -1/1 0/1 16/3 -1/1 -2/3 27/5 -1/2 -1/4 11/2 0/1 1/3 17/3 1/2 1/0 6/1 1/0 1/0 -1/1 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(38,-5,61,-8) (0/1,1/6) -> (8/13,5/8) Hyperbolic Matrix(204,-35,35,-6) (1/6,3/17) -> (17/3,6/1) Hyperbolic Matrix(428,-77,189,-34) (3/17,2/11) -> (9/4,25/11) Hyperbolic Matrix(223,-42,154,-29) (2/11,1/5) -> (13/9,16/11) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(101,-24,80,-19) (2/9,1/4) -> (5/4,14/11) Hyperbolic Matrix(33,-10,10,-3) (1/4,1/3) -> (3/1,7/2) Hyperbolic Matrix(30,-11,11,-4) (1/3,2/5) -> (5/2,3/1) Hyperbolic Matrix(170,-69,69,-28) (2/5,7/17) -> (17/7,5/2) Hyperbolic Matrix(217,-90,258,-107) (7/17,5/12) -> (5/6,11/13) Hyperbolic Matrix(265,-112,168,-71) (5/12,3/7) -> (11/7,19/12) Hyperbolic Matrix(273,-118,118,-51) (3/7,7/16) -> (23/10,7/3) Hyperbolic Matrix(301,-132,244,-107) (7/16,4/9) -> (16/13,5/4) Hyperbolic Matrix(319,-144,144,-65) (4/9,5/11) -> (11/5,20/9) Hyperbolic Matrix(172,-79,135,-62) (5/11,1/2) -> (14/11,9/7) Hyperbolic Matrix(45,-26,26,-15) (1/2,3/5) -> (5/3,7/4) Hyperbolic Matrix(130,-79,79,-48) (3/5,8/13) -> (13/8,5/3) Hyperbolic Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(223,-154,42,-29) (2/3,9/13) -> (5/1,16/3) Hyperbolic Matrix(429,-298,298,-207) (9/13,7/10) -> (23/16,13/9) Hyperbolic Matrix(394,-277,165,-116) (7/10,12/17) -> (19/8,12/5) Hyperbolic Matrix(287,-204,204,-145) (12/17,5/7) -> (7/5,24/17) Hyperbolic Matrix(56,-41,41,-30) (5/7,3/4) -> (4/3,7/5) Hyperbolic Matrix(72,-55,55,-42) (3/4,7/9) -> (9/7,4/3) Hyperbolic Matrix(101,-80,24,-19) (7/9,4/5) -> (4/1,13/3) Hyperbolic Matrix(301,-244,132,-107) (4/5,9/11) -> (25/11,16/7) 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(196,-225,169,-194) (8/7,15/13) -> (15/13,7/6) Parabolic Matrix(217,-258,90,-107) (7/6,6/5) -> (12/5,29/12) Hyperbolic Matrix(83,-100,44,-53) (6/5,11/9) -> (13/7,2/1) Hyperbolic Matrix(320,-393,57,-70) (11/9,16/13) -> (11/2,17/3) Hyperbolic Matrix(754,-1065,337,-476) (24/17,41/29) -> (29/13,9/4) Hyperbolic Matrix(928,-1313,417,-590) (41/29,17/12) -> (20/9,29/13) Hyperbolic Matrix(284,-403,179,-254) (17/12,10/7) -> (19/12,8/5) Hyperbolic Matrix(760,-1089,529,-758) (10/7,33/23) -> (33/23,23/16) Parabolic Matrix(233,-342,62,-91) (16/11,3/2) -> (15/4,34/9) Hyperbolic Matrix(188,-289,121,-186) (3/2,17/11) -> (17/11,14/9) Parabolic Matrix(38,-61,5,-8) (8/5,13/8) -> (6/1,1/0) Hyperbolic Matrix(91,-162,50,-89) (7/4,9/5) -> (9/5,11/6) Parabolic Matrix(58,-125,13,-28) (2/1,11/5) -> (13/3,9/2) Hyperbolic Matrix(664,-1521,289,-662) (16/7,39/17) -> (39/17,23/10) Parabolic Matrix(401,-970,74,-179) (29/12,17/7) -> (27/5,11/2) Hyperbolic Matrix(67,-242,18,-65) (7/2,11/3) -> (11/3,15/4) Parabolic Matrix(107,-412,20,-77) (19/5,4/1) -> (16/3,27/5) Hyperbolic 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(1,0,0,1) Matrix(38,-5,61,-8) -> Matrix(1,1,-6,-5) Matrix(204,-35,35,-6) -> Matrix(3,1,2,1) Matrix(428,-77,189,-34) -> Matrix(1,0,4,1) Matrix(223,-42,154,-29) -> Matrix(1,1,-2,-1) Matrix(115,-24,24,-5) -> Matrix(1,0,0,1) Matrix(101,-24,80,-19) -> Matrix(1,1,-2,-1) Matrix(33,-10,10,-3) -> Matrix(1,1,-2,-1) Matrix(30,-11,11,-4) -> Matrix(1,1,-2,-1) Matrix(170,-69,69,-28) -> Matrix(11,5,2,1) Matrix(217,-90,258,-107) -> Matrix(5,2,-28,-11) Matrix(265,-112,168,-71) -> Matrix(3,1,14,5) Matrix(273,-118,118,-51) -> Matrix(1,0,4,1) Matrix(301,-132,244,-107) -> Matrix(3,1,2,1) Matrix(319,-144,144,-65) -> Matrix(3,1,2,1) Matrix(172,-79,135,-62) -> Matrix(1,0,4,1) Matrix(45,-26,26,-15) -> Matrix(3,1,2,1) Matrix(130,-79,79,-48) -> Matrix(3,1,2,1) Matrix(265,-168,112,-71) -> Matrix(7,1,6,1) Matrix(187,-120,120,-77) -> Matrix(1,0,12,1) Matrix(223,-154,42,-29) -> Matrix(1,1,-2,-1) Matrix(429,-298,298,-207) -> Matrix(1,0,0,1) Matrix(394,-277,165,-116) -> Matrix(1,2,0,1) Matrix(287,-204,204,-145) -> Matrix(1,1,-2,-1) Matrix(56,-41,41,-30) -> Matrix(1,1,-2,-1) Matrix(72,-55,55,-42) -> Matrix(3,1,2,1) Matrix(101,-80,24,-19) -> Matrix(1,1,-2,-1) Matrix(301,-244,132,-107) -> Matrix(3,1,2,1) Matrix(199,-164,108,-89) -> Matrix(7,2,-4,-1) Matrix(575,-488,152,-129) -> Matrix(31,4,-8,-1) Matrix(15,-14,14,-13) -> Matrix(1,0,0,1) Matrix(196,-225,169,-194) -> Matrix(1,0,24,1) Matrix(217,-258,90,-107) -> Matrix(7,-2,4,-1) Matrix(83,-100,44,-53) -> Matrix(3,-1,-2,1) Matrix(320,-393,57,-70) -> Matrix(1,-1,2,-1) Matrix(754,-1065,337,-476) -> Matrix(1,0,0,1) Matrix(928,-1313,417,-590) -> Matrix(1,2,0,1) Matrix(284,-403,179,-254) -> Matrix(1,1,2,3) Matrix(760,-1089,529,-758) -> Matrix(1,0,0,1) Matrix(233,-342,62,-91) -> Matrix(9,5,-2,-1) Matrix(188,-289,121,-186) -> Matrix(1,0,16,1) Matrix(38,-61,5,-8) -> Matrix(3,-1,-2,1) Matrix(91,-162,50,-89) -> Matrix(1,-4,0,1) Matrix(58,-125,13,-28) -> Matrix(3,-1,-2,1) Matrix(664,-1521,289,-662) -> Matrix(1,0,0,1) Matrix(401,-970,74,-179) -> Matrix(1,-2,-4,9) Matrix(67,-242,18,-65) -> Matrix(1,-6,0,1) Matrix(107,-412,20,-77) -> Matrix(1,3,-2,-5) Matrix(116,-529,25,-114) -> Matrix(7,8,-8,-9) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 3 Number of equivalence classes of elliptic points of order 2: 2 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): 12 ----------------------------------------------------------------------- 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 (-1/1,0/1) 0 1 1/1 (-1/1,0/1) 0 14 15/13 0/1 24 1 7/6 (0/1,1/11) 0 28 6/5 (0/1,1/3) 0 28 11/9 (1/2,1/0) 0 7 5/4 (0/1,1/1) 0 28 9/7 (1/2,1/0) 0 7 4/3 1/0 1 4 7/5 (-1/2,1/0) 0 7 41/29 1/0 2 2 17/12 (-1/1,0/1) 0 28 10/7 (-1/1,0/1) 0 28 33/23 (-1/1,0/1) 0 1 13/9 (-1/1,0/1) 0 14 3/2 (-1/3,0/1) 0 28 17/11 0/1 16 1 11/7 (0/1,1/5) 0 14 8/5 (0/1,1/3) 0 28 13/8 1/2 2 4 5/3 (1/2,1/0) 0 7 9/5 1/0 4 2 13/7 (-3/2,1/0) 0 7 2/1 (-1/1,0/1) 0 28 11/5 (1/2,1/0) 0 7 29/13 1/0 2 2 9/4 (-1/1,0/1) 0 28 25/11 (1/2,1/0) 0 7 16/7 (0/1,1/1) 0 28 39/17 (0/1,1/1) 0 1 7/3 (0/1,1/1) 0 14 19/8 (1/1,2/1) 0 28 12/5 (1/1,2/1) 0 28 29/12 (2/1,15/7) 0 28 17/7 (5/2,1/0) 0 7 5/2 1/0 3 4 3/1 (-1/2,1/0) 0 7 11/3 1/0 6 2 19/5 (-7/2,1/0) 0 7 4/1 (-2/1,-1/1) 0 28 13/3 (-3/2,1/0) 0 7 9/2 (-4/3,-1/1) 0 28 23/5 -1/1 8 1 5/1 (-1/1,0/1) 0 14 16/3 (-1/1,-2/3) 0 28 27/5 (-1/2,-1/4) 0 7 11/2 (0/1,1/3) 0 28 17/3 (1/2,1/0) 0 7 6/1 1/0 2 4 1/0 (-1/1,0/1) 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(14,-15,13,-14) (1/1,15/13) -> (1/1,15/13) Reflection Matrix(181,-210,156,-181) (15/13,7/6) -> (15/13,7/6) Reflection Matrix(217,-258,90,-107) (7/6,6/5) -> (12/5,29/12) Hyperbolic Matrix(83,-100,44,-53) (6/5,11/9) -> (13/7,2/1) Hyperbolic Matrix(244,-301,107,-132) (11/9,5/4) -> (25/11,16/7) Glide Reflection Matrix(80,-101,19,-24) (5/4,9/7) -> (4/1,13/3) Glide Reflection Matrix(55,-72,42,-55) (9/7,4/3) -> (9/7,4/3) Reflection Matrix(41,-56,30,-41) (4/3,7/5) -> (4/3,7/5) Reflection Matrix(204,-287,145,-204) (7/5,41/29) -> (7/5,41/29) Reflection Matrix(609,-862,272,-385) (41/29,17/12) -> (29/13,9/4) Glide Reflection Matrix(277,-394,116,-165) (17/12,10/7) -> (19/8,12/5) Glide Reflection 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(154,-223,29,-42) (13/9,3/2) -> (5/1,16/3) 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(168,-265,71,-112) (11/7,8/5) -> (7/3,19/8) Glide Reflection Matrix(38,-61,5,-8) (8/5,13/8) -> (6/1,1/0) Hyperbolic Matrix(79,-130,48,-79) (13/8,5/3) -> (13/8,5/3) Reflection Matrix(26,-45,15,-26) (5/3,9/5) -> (5/3,9/5) Reflection Matrix(64,-117,35,-64) (9/5,13/7) -> (9/5,13/7) Reflection Matrix(58,-125,13,-28) (2/1,11/5) -> (13/3,9/2) Hyperbolic Matrix(144,-319,65,-144) (11/5,29/13) -> (11/5,29/13) Reflection Matrix(189,-428,34,-77) (9/4,25/11) -> (11/2,17/3) Glide Reflection 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(401,-970,74,-179) (29/12,17/7) -> (27/5,11/2) Hyperbolic Matrix(69,-170,28,-69) (17/7,5/2) -> (17/7,5/2) Reflection Matrix(11,-30,4,-11) (5/2,3/1) -> (5/2,3/1) Reflection Matrix(10,-33,3,-10) (3/1,11/3) -> (3/1,11/3) Reflection Matrix(56,-209,15,-56) (11/3,19/5) -> (11/3,19/5) Reflection Matrix(107,-412,20,-77) (19/5,4/1) -> (16/3,27/5) Hyperbolic 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(35,-204,6,-35) (17/3,6/1) -> (17/3,6/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,2,1) (-1/1,1/1) -> (-1/1,0/1) Matrix(14,-15,13,-14) -> Matrix(-1,0,2,1) (1/1,15/13) -> (-1/1,0/1) Matrix(181,-210,156,-181) -> Matrix(1,0,22,-1) (15/13,7/6) -> (0/1,1/11) Matrix(217,-258,90,-107) -> Matrix(7,-2,4,-1) Matrix(83,-100,44,-53) -> Matrix(3,-1,-2,1) Matrix(244,-301,107,-132) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(80,-101,19,-24) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(55,-72,42,-55) -> Matrix(-1,1,0,1) (9/7,4/3) -> (1/2,1/0) Matrix(41,-56,30,-41) -> Matrix(1,1,0,-1) (4/3,7/5) -> (-1/2,1/0) Matrix(204,-287,145,-204) -> Matrix(1,1,0,-1) (7/5,41/29) -> (-1/2,1/0) Matrix(609,-862,272,-385) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(277,-394,116,-165) -> Matrix(3,2,2,1) Matrix(461,-660,322,-461) -> Matrix(-1,0,2,1) (10/7,33/23) -> (-1/1,0/1) Matrix(298,-429,207,-298) -> Matrix(-1,0,2,1) (33/23,13/9) -> (-1/1,0/1) Matrix(154,-223,29,-42) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(67,-102,44,-67) -> Matrix(-1,0,6,1) (3/2,17/11) -> (-1/3,0/1) Matrix(120,-187,77,-120) -> Matrix(1,0,10,-1) (17/11,11/7) -> (0/1,1/5) Matrix(168,-265,71,-112) -> Matrix(5,-1,4,-1) Matrix(38,-61,5,-8) -> Matrix(3,-1,-2,1) Matrix(79,-130,48,-79) -> Matrix(-1,1,0,1) (13/8,5/3) -> (1/2,1/0) Matrix(26,-45,15,-26) -> Matrix(-1,1,0,1) (5/3,9/5) -> (1/2,1/0) Matrix(64,-117,35,-64) -> Matrix(1,3,0,-1) (9/5,13/7) -> (-3/2,1/0) Matrix(58,-125,13,-28) -> Matrix(3,-1,-2,1) Matrix(144,-319,65,-144) -> Matrix(-1,1,0,1) (11/5,29/13) -> (1/2,1/0) Matrix(189,-428,34,-77) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(545,-1248,238,-545) -> Matrix(1,0,2,-1) (16/7,39/17) -> (0/1,1/1) Matrix(118,-273,51,-118) -> Matrix(1,0,2,-1) (39/17,7/3) -> (0/1,1/1) Matrix(401,-970,74,-179) -> Matrix(1,-2,-4,9) Matrix(69,-170,28,-69) -> Matrix(-1,5,0,1) (17/7,5/2) -> (5/2,1/0) Matrix(11,-30,4,-11) -> Matrix(1,1,0,-1) (5/2,3/1) -> (-1/2,1/0) Matrix(10,-33,3,-10) -> Matrix(1,1,0,-1) (3/1,11/3) -> (-1/2,1/0) Matrix(56,-209,15,-56) -> Matrix(1,7,0,-1) (11/3,19/5) -> (-7/2,1/0) Matrix(107,-412,20,-77) -> Matrix(1,3,-2,-5) Matrix(91,-414,20,-91) -> Matrix(7,8,-6,-7) (9/2,23/5) -> (-4/3,-1/1) Matrix(24,-115,5,-24) -> Matrix(-1,0,2,1) (23/5,5/1) -> (-1/1,0/1) Matrix(35,-204,6,-35) -> Matrix(-1,1,0,1) (17/3,6/1) -> (1/2,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.