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 1/1 -6/13 0/1 -11/24 3/7 1/2 -5/11 1/2 1/1 -9/20 1/1 4/3 -4/9 1/1 2/1 -11/25 1/0 -18/41 -1/1 0/1 -25/57 1/0 -7/16 -1/1 0/1 -3/7 1/2 1/0 -8/19 0/1 1/1 -21/50 1/1 2/1 -13/31 2/1 1/0 -5/12 1/0 -17/41 1/0 -12/29 -3/1 -2/1 -7/17 -1/1 1/0 -16/39 -1/1 -4/5 -9/22 -1/2 -1/3 -2/5 0/1 1/2 -9/23 1/1 -16/41 2/1 1/0 -7/18 0/1 1/1 -12/31 0/1 1/1 -5/13 1/0 -13/34 0/1 -8/21 1/1 1/0 -11/29 0/1 1/0 -3/8 0/1 1/1 -13/35 0/1 1/0 -10/27 0/1 1/3 -7/19 1/2 1/0 -18/49 0/1 1/2 -11/30 2/3 1/1 -4/11 1/1 -9/25 3/2 -5/14 1/1 2/1 -11/31 5/2 1/0 -6/17 3/1 4/1 -13/37 1/0 -7/20 9/1 1/0 -1/3 0/1 1/0 -7/22 9/1 1/0 -6/19 -9/1 1/0 -5/16 -4/1 -3/1 -14/45 -2/1 1/0 -9/29 -5/2 1/0 -4/13 -2/1 -1/1 -7/23 -3/2 -3/10 -1/1 -8/27 -1/1 -2/3 -13/44 -1/2 0/1 -5/17 -1/2 1/0 -7/24 -1/3 0/1 -16/55 0/1 1/3 -9/31 0/1 1/0 -2/7 -1/1 0/1 -9/32 0/1 1/1 -7/25 0/1 1/0 -5/18 -1/1 1/0 -8/29 0/1 -3/11 1/0 -7/26 -1/1 0/1 -4/15 -1/1 0/1 -5/19 -1/1 -6/23 -1/1 -2/3 -7/27 -1/2 1/0 -1/4 -1/2 0/1 -4/17 1/3 1/2 -7/30 4/5 1/1 -10/43 1/1 6/5 -3/13 1/1 1/0 -5/22 2/1 3/1 -12/53 -3/1 1/0 -7/31 1/0 -2/9 1/0 -5/23 -2/1 1/0 -8/37 -2/1 -1/1 -3/14 -1/1 0/1 -1/5 -1/2 1/0 -2/11 0/1 1/1 -3/17 1/0 -4/23 -2/1 -1/1 -5/29 1/0 -1/6 -2/1 -1/1 -2/13 -4/3 -1/1 -3/20 -1/1 -6/7 -1/7 -1/1 -1/2 -2/15 -1/2 -3/7 -1/8 0/1 0/1 -1/1 0/1 1/6 0/1 3/17 1/2 1/0 5/28 2/3 1/1 2/11 3/1 1/0 3/16 -2/1 -1/1 4/21 0/1 1/0 1/5 -1/1 1/0 2/9 -1/1 -4/5 3/13 -1/2 4/17 -1/1 1/4 -1/1 -2/3 3/11 -1/2 5/18 -1/3 0/1 7/25 -1/2 2/7 -1/3 0/1 5/17 0/1 1/0 8/27 0/1 3/10 -1/1 1/0 4/13 -1/1 0/1 1/3 -1/2 1/0 5/14 -1/3 0/1 4/11 -1/1 1/0 7/19 -1/1 -1/2 3/8 -1/1 0/1 8/21 -1/1 -2/3 21/55 -3/4 -1/2 13/34 -5/7 -2/3 5/13 -2/3 -1/2 12/31 -3/5 -1/2 7/18 -2/3 -1/2 2/5 -1/2 9/22 -1/2 -2/5 16/39 -1/3 0/1 7/17 -1/2 5/12 -3/7 -2/5 13/31 -1/2 -3/8 8/19 -2/5 -1/3 3/7 -1/2 -1/3 7/16 -1/3 -4/13 11/25 -3/10 -1/4 15/34 -2/7 4/9 -1/4 -1/5 13/29 0/1 9/20 -1/3 0/1 5/11 -1/4 6/13 -1/5 0/1 1/2 0/1 1/0 5/9 -1/1 9/16 -2/3 -1/2 4/7 -1/1 0/1 15/26 -1/1 1/0 11/19 -1/1 -1/2 29/50 -1/1 -2/3 18/31 -1/1 7/12 -1/1 0/1 17/29 -1/1 -3/4 10/17 -1/1 -2/3 13/22 -2/3 3/5 -1/2 8/13 0/1 21/34 -1/1 0/1 34/55 -1/3 0/1 13/21 -1/2 0/1 5/8 -1/1 -1/2 12/19 -1/2 0/1 31/49 -1/2 19/30 -1/2 7/11 -1/2 0/1 2/3 -1/1 0/1 11/16 -1/3 0/1 20/29 0/1 9/13 -1/2 0/1 7/10 0/1 1/1 19/27 -1/1 1/0 12/17 -1/1 0/1 29/41 0/1 17/24 -1/1 1/0 5/7 -1/2 1/0 13/18 0/1 1/0 21/29 -1/1 1/0 29/40 3/1 1/0 37/51 1/0 8/11 -2/1 -1/1 19/26 -2/1 -1/1 11/15 -1/1 1/0 3/4 -1/1 13/17 -1/1 -3/4 36/47 -1/1 -4/5 23/30 -3/4 -2/3 10/13 -1/1 -4/5 17/22 -1/1 -6/7 7/9 -3/4 18/23 -1/1 -3/4 11/14 -11/16 -2/3 15/19 -2/3 -5/8 4/5 -1/1 -2/3 17/21 -2/3 -5/8 13/16 -2/3 -3/5 9/11 -5/8 -1/2 5/6 -3/5 -4/7 11/13 -1/2 6/7 -9/17 -1/2 1/1 -1/2 0/1 8/7 -9/17 -1/2 15/13 -1/2 22/19 -1/2 -27/55 7/6 -1/2 -9/19 6/5 -4/9 -3/7 17/14 -1/2 -2/5 11/9 -1/2 -5/12 16/13 -3/7 -2/5 21/17 -5/12 -2/5 26/21 -11/27 -2/5 5/4 -2/5 -1/3 14/11 -2/5 -11/28 23/18 -3/8 -1/3 9/7 -3/8 31/24 -4/11 -1/3 22/17 -6/17 -1/3 13/10 -4/11 -1/3 4/3 -1/3 19/14 -1/3 0/1 53/39 -3/10 -1/4 34/25 -2/7 -1/4 15/11 -1/3 -1/4 11/8 -1/3 -2/7 51/37 -1/4 40/29 -1/4 -3/13 29/21 -1/3 -1/4 47/34 -2/7 -1/4 65/47 -1/4 18/13 -1/4 0/1 25/18 -1/3 -1/4 32/23 -1/3 0/1 7/5 -1/2 -1/4 31/22 -1/4 0/1 24/17 -1/3 -1/4 41/29 0/1 17/12 -1/3 0/1 27/19 -1/3 -1/4 10/7 -1/5 0/1 33/23 0/1 56/39 0/1 1/7 23/16 0/1 1/1 13/9 -1/2 0/1 16/11 -1/1 0/1 19/13 -1/2 3/2 -1/3 0/1 17/11 0/1 31/20 0/1 1/1 14/9 -1/1 0/1 11/7 -1/2 0/1 30/19 -1/2 49/31 -1/2 68/43 -2/5 -1/3 19/12 -1/2 0/1 27/17 -1/2 -1/4 8/5 -1/2 -1/3 29/18 -1/5 0/1 21/13 -1/2 0/1 55/34 -1/1 0/1 89/55 -1/2 34/21 -1/3 0/1 47/29 -1/2 -1/4 13/8 0/1 18/11 -1/1 0/1 41/25 -1/1 1/0 23/14 -1/1 -2/3 5/3 -1/2 22/13 -2/5 17/10 -2/5 -1/3 12/7 -1/3 0/1 31/18 -1/3 19/11 -1/2 -1/3 7/4 -1/3 0/1 9/5 -1/3 11/6 -1/3 -2/7 13/7 -1/2 -1/4 15/8 -1/3 -2/7 17/9 -1/3 -1/4 2/1 -1/4 0/1 15/7 0/1 1/4 13/6 0/1 1/1 11/5 1/0 31/14 -1/1 -2/3 20/9 -1/1 0/1 29/13 0/1 38/17 0/1 1/1 9/4 1/1 1/0 34/15 -2/1 25/11 -3/2 1/0 41/18 -2/1 -3/2 16/7 -4/3 -1/1 39/17 -1/1 62/27 -1/1 -16/17 23/10 -1/1 -6/7 7/3 -1/1 -1/2 33/14 -2/1 -1/1 59/25 -1/1 26/11 -1/1 -4/5 19/8 -1/1 -2/3 69/29 -2/3 50/21 -1/1 -1/2 31/13 -3/4 -1/2 12/5 -2/3 -3/5 29/12 -1/2 -3/7 17/7 -1/2 5/2 -1/2 23/9 -1/2 64/25 -5/11 -4/9 41/16 -4/9 -3/7 141/55 -3/7 100/39 -3/7 -2/5 59/23 -1/2 -3/7 18/7 -1/2 -2/5 49/19 -1/2 -5/12 31/12 -1/2 -3/7 13/5 -1/2 -2/5 47/18 -7/17 -2/5 81/31 -2/5 115/44 -2/5 -17/43 34/13 -2/5 -5/13 55/21 -1/2 -3/8 76/29 -2/5 21/8 -2/5 -1/3 71/27 -2/5 50/19 -5/13 -3/8 29/11 -3/8 8/3 -1/3 0/1 27/10 -1/3 0/1 19/7 -1/2 -1/3 30/11 -3/8 -1/3 41/15 -1/3 11/4 -1/3 -1/4 25/9 -1/4 0/1 64/23 -1/12 0/1 39/14 0/1 1/4 14/5 -1/1 0/1 3/1 -1/2 -1/4 13/4 -1/3 0/1 23/7 -1/2 -1/3 33/10 -3/8 -1/3 43/13 -1/3 10/3 -1/3 -1/4 27/8 0/1 71/21 -1/2 -1/4 44/13 -1/3 0/1 17/5 -1/4 0/1 41/12 -1/12 0/1 65/19 0/1 89/26 0/1 1/20 24/7 0/1 1/4 7/2 -1/1 0/1 11/3 -1/2 15/4 -2/5 -1/3 34/9 -3/5 -1/2 19/5 -1/2 42/11 -1/2 -4/9 65/17 -1/2 -3/7 23/6 -3/7 -2/5 4/1 -2/5 -1/3 25/6 -1/2 0/1 46/11 -2/5 -1/3 113/27 -1/3 67/16 -1/3 0/1 21/5 -1/2 -1/3 17/4 -1/3 13/3 -1/2 35/8 -1/2 -3/7 57/13 -2/5 22/5 -2/5 -1/3 9/2 -4/11 -1/3 23/5 -1/3 37/8 -1/3 -16/49 14/3 -1/3 -6/19 5/1 -1/3 -1/4 26/5 -2/7 -1/4 47/9 -1/4 21/4 -1/4 0/1 16/3 -1/3 -2/7 27/5 -1/4 11/2 -1/4 -3/13 28/5 -1/5 -2/11 45/8 -1/6 0/1 17/3 -1/4 -1/6 23/4 -1/5 0/1 6/1 0/1 7/1 -1/2 8/1 -2/5 -1/3 25/3 -1/3 17/2 -1/3 -4/13 9/1 -1/3 -1/4 1/0 -1/3 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(1,0,4,1) Matrix(265,124,156,73) -> Matrix(1,-2,-2,5) Matrix(933,428,412,189) -> Matrix(5,-2,-2,1) Matrix(823,376,1136,519) -> Matrix(1,0,-2,1) Matrix(53,24,-360,-163) -> Matrix(3,-2,-4,3) Matrix(353,158,458,205) -> Matrix(3,-2,-4,3) Matrix(549,242,-1250,-551) -> Matrix(1,-2,0,1) Matrix(4591,2014,1794,787) -> Matrix(1,-4,-2,9) Matrix(1443,632,1048,459) -> Matrix(1,2,-4,-7) Matrix(51,22,146,63) -> Matrix(1,0,-2,1) Matrix(47,20,148,63) -> Matrix(1,0,-2,1) Matrix(1689,710,1306,549) -> Matrix(5,-6,-14,17) Matrix(1253,526,1546,649) -> Matrix(5,-8,-8,13) Matrix(673,282,1062,445) -> Matrix(1,-2,-2,5) Matrix(1151,478,1818,755) -> Matrix(1,2,-2,-3) Matrix(623,258,-1770,-733) -> Matrix(1,6,0,1) Matrix(953,394,670,277) -> Matrix(1,2,-4,-7) Matrix(287,118,-1238,-509) -> Matrix(1,2,0,1) Matrix(1045,428,188,77) -> Matrix(3,2,-14,-9) Matrix(423,172,332,135) -> Matrix(7,2,-18,-5) Matrix(413,162,-1058,-415) -> Matrix(3,-2,2,-1) Matrix(457,178,-1466,-571) -> Matrix(1,-4,0,1) Matrix(733,284,1004,389) -> Matrix(1,-2,0,1) Matrix(321,124,44,17) -> Matrix(1,-2,-2,5) Matrix(271,104,456,175) -> Matrix(1,2,-2,-3) Matrix(907,346,270,103) -> Matrix(1,0,-4,1) Matrix(453,172,1172,445) -> Matrix(1,2,-2,-3) Matrix(317,120,-1128,-427) -> Matrix(1,0,0,1) Matrix(2093,778,1294,481) -> Matrix(1,0,-2,1) Matrix(803,298,-2762,-1025) -> Matrix(1,0,0,1) Matrix(1065,394,446,165) -> Matrix(3,-2,-4,3) Matrix(2743,1008,1064,391) -> Matrix(5,-2,-12,5) Matrix(267,98,1414,519) -> Matrix(1,0,-2,1) Matrix(617,226,1062,389) -> Matrix(3,-2,-4,3) Matrix(133,48,568,205) -> Matrix(1,-2,0,1) Matrix(479,172,220,79) -> Matrix(1,-2,2,-3) Matrix(697,248,1824,649) -> Matrix(3,-8,-4,11) Matrix(305,108,-1172,-415) -> Matrix(1,-2,-2,5) Matrix(1813,636,2500,877) -> Matrix(1,-6,0,1) Matrix(41,14,-126,-43) -> Matrix(1,0,0,1) Matrix(617,196,532,169) -> Matrix(1,-18,-2,37) Matrix(287,90,-1266,-397) -> Matrix(1,6,0,1) Matrix(3371,1048,2480,771) -> Matrix(1,4,-4,-15) Matrix(1701,526,650,201) -> Matrix(3,8,-8,-21) Matrix(203,62,442,135) -> Matrix(1,2,-6,-11) Matrix(521,158,122,37) -> Matrix(1,2,-4,-7) Matrix(957,284,556,165) -> Matrix(3,2,-8,-5) Matrix(1271,376,240,71) -> Matrix(1,0,-2,1) Matrix(835,246,594,175) -> Matrix(1,0,-2,1) Matrix(397,116,948,277) -> Matrix(3,2,-8,-5) Matrix(2609,760,1816,529) -> Matrix(1,0,4,1) Matrix(1145,332,1852,537) -> Matrix(1,0,-2,1) Matrix(665,188,428,121) -> Matrix(1,0,0,1) Matrix(1009,282,390,109) -> Matrix(1,-2,-2,5) Matrix(231,64,776,215) -> Matrix(1,0,0,1) Matrix(387,106,230,63) -> Matrix(1,-2,-2,5) Matrix(383,104,232,63) -> Matrix(1,2,-2,-3) Matrix(613,164,228,61) -> Matrix(1,0,-2,1) Matrix(189,50,-722,-191) -> Matrix(1,2,-2,-3) Matrix(1283,332,228,59) -> Matrix(1,0,-4,1) Matrix(259,62,330,79) -> Matrix(7,-2,-10,3) Matrix(145,34,806,189) -> Matrix(3,-2,2,-1) Matrix(2849,664,1240,289) -> Matrix(11,-10,-12,11) Matrix(509,116,724,165) -> Matrix(1,-2,0,1) Matrix(3943,892,2860,647) -> Matrix(1,0,-4,1) Matrix(1371,308,868,195) -> Matrix(1,-2,-2,5) Matrix(789,172,500,109) -> Matrix(1,2,-2,-3) Matrix(1145,248,928,201) -> Matrix(5,8,-12,-19) Matrix(1427,308,644,139) -> Matrix(1,2,-2,-3) Matrix(107,22,34,7) -> Matrix(1,0,-2,1) Matrix(103,20,36,7) -> Matrix(1,0,-2,1) Matrix(101,18,-578,-103) -> Matrix(1,-2,0,1) Matrix(1083,188,1492,259) -> Matrix(1,0,0,1) Matrix(2129,364,1316,225) -> Matrix(1,2,-2,-3) Matrix(301,48,232,37) -> Matrix(3,2,-8,-5) Matrix(761,116,164,25) -> Matrix(9,10,-28,-31) Matrix(715,98,518,71) -> Matrix(1,0,-2,1) Matrix(257,34,582,77) -> Matrix(5,2,-18,-7) Matrix(93,10,158,17) -> Matrix(1,2,-2,-3) Matrix(121,-18,74,-11) -> Matrix(1,0,0,1) Matrix(503,-86,310,-53) -> Matrix(1,0,-4,1) Matrix(1807,-322,1330,-237) -> Matrix(3,-2,-10,7) Matrix(709,-132,188,-35) -> Matrix(1,0,-2,1) Matrix(235,-46,46,-9) -> Matrix(1,2,-4,-7) Matrix(115,-24,24,-5) -> Matrix(1,2,-4,-7) Matrix(365,-82,138,-31) -> Matrix(5,4,-14,-11) Matrix(565,-134,974,-231) -> Matrix(1,0,0,1) Matrix(67,-18,242,-65) -> Matrix(3,2,-8,-5) Matrix(417,-116,284,-79) -> Matrix(1,0,0,1) Matrix(589,-166,110,-31) -> Matrix(5,2,-18,-7) Matrix(173,-50,218,-63) -> Matrix(5,2,-8,-3) Matrix(583,-172,844,-249) -> Matrix(1,0,-2,1) Matrix(235,-72,408,-125) -> Matrix(1,0,0,1) Matrix(431,-156,268,-97) -> Matrix(1,0,-2,1) Matrix(779,-286,286,-105) -> Matrix(3,2,-8,-5) Matrix(449,-166,614,-227) -> Matrix(3,2,-2,-1) Matrix(365,-138,82,-31) -> Matrix(5,4,-14,-11) Matrix(3911,-1492,1156,-441) -> Matrix(3,2,-8,-5) Matrix(1053,-404,404,-155) -> Matrix(7,4,-16,-9) Matrix(1393,-540,988,-383) -> Matrix(3,2,-14,-9) Matrix(81,-32,200,-79) -> Matrix(7,4,-16,-9) Matrix(1689,-692,2204,-903) -> Matrix(11,4,-14,-5) Matrix(4049,-1662,2502,-1027) -> Matrix(1,0,0,1) Matrix(217,-90,258,-107) -> Matrix(13,6,-24,-11) Matrix(1125,-472,808,-339) -> Matrix(5,2,-18,-7) Matrix(393,-166,670,-283) -> Matrix(11,4,-14,-5) Matrix(273,-118,118,-51) -> Matrix(5,2,-8,-3) Matrix(583,-256,312,-137) -> Matrix(7,2,-18,-5) Matrix(3089,-1362,914,-403) -> Matrix(7,2,-18,-5) Matrix(2071,-926,870,-389) -> Matrix(9,2,-14,-3) Matrix(1931,-868,812,-365) -> Matrix(5,2,-8,-3) Matrix(521,-236,404,-183) -> Matrix(13,4,-36,-11) Matrix(535,-248,192,-89) -> Matrix(1,0,4,1) Matrix(91,-50,162,-89) -> Matrix(1,2,-2,-3) Matrix(215,-122,178,-101) -> Matrix(7,4,-16,-9) Matrix(1225,-708,372,-215) -> Matrix(3,2,-8,-5) Matrix(1135,-658,602,-349) -> Matrix(1,0,-2,1) Matrix(1041,-610,442,-259) -> Matrix(3,2,-2,-1) Matrix(121,-74,18,-11) -> Matrix(1,0,0,1) Matrix(503,-310,86,-53) -> Matrix(1,0,-4,1) Matrix(4431,-2738,1730,-1069) -> Matrix(7,4,-16,-9) Matrix(431,-268,156,-97) -> Matrix(1,0,-2,1) Matrix(619,-390,446,-281) -> Matrix(1,0,-2,1) Matrix(2419,-1530,634,-401) -> Matrix(7,4,-16,-9) Matrix(187,-120,120,-77) -> Matrix(1,0,0,1) Matrix(133,-90,34,-23) -> Matrix(3,2,-8,-5) Matrix(1825,-1256,696,-479) -> Matrix(7,2,-18,-5) Matrix(429,-298,298,-207) -> Matrix(1,0,0,1) Matrix(1183,-834,722,-509) -> Matrix(1,0,0,1) Matrix(1871,-1322,426,-301) -> Matrix(3,2,-8,-5) Matrix(2803,-1984,640,-453) -> Matrix(1,-2,-2,5) Matrix(1393,-988,540,-383) -> Matrix(1,-2,-2,5) Matrix(619,-446,390,-281) -> Matrix(1,0,-2,1) Matrix(1885,-1364,1364,-987) -> Matrix(1,2,-4,-7) Matrix(97,-72,128,-95) -> Matrix(3,4,-4,-5) Matrix(4473,-3424,1744,-1335) -> Matrix(13,10,-30,-23) Matrix(1425,-1094,254,-195) -> Matrix(3,2,-14,-9) Matrix(521,-404,236,-183) -> Matrix(5,4,-4,-3) Matrix(1117,-872,424,-331) -> Matrix(17,12,-44,-31) Matrix(1017,-802,298,-235) -> Matrix(3,2,-20,-13) Matrix(651,-526,526,-425) -> Matrix(31,20,-76,-49) Matrix(525,-428,92,-75) -> Matrix(3,2,-20,-13) Matrix(199,-164,108,-89) -> Matrix(3,2,-14,-9) Matrix(575,-488,152,-129) -> Matrix(11,6,-24,-13) Matrix(15,-14,14,-13) -> Matrix(1,0,0,1) Matrix(391,-450,338,-389) -> Matrix(71,36,-144,-73) Matrix(217,-258,90,-107) -> Matrix(13,6,-24,-11) Matrix(719,-876,316,-385) -> Matrix(19,8,-12,-5) Matrix(917,-1126,566,-695) -> Matrix(5,2,-8,-3) Matrix(2551,-3160,976,-1209) -> Matrix(79,32,-200,-81) Matrix(173,-218,50,-63) -> Matrix(5,2,-8,-3) Matrix(479,-614,110,-141) -> Matrix(21,8,-50,-19) Matrix(97,-128,72,-95) -> Matrix(11,4,-36,-13) Matrix(1673,-2276,652,-887) -> Matrix(15,4,-34,-9) Matrix(449,-614,166,-227) -> Matrix(7,2,-18,-5) Matrix(2585,-3574,494,-683) -> Matrix(7,2,-32,-9) Matrix(1833,-2536,352,-487) -> Matrix(9,2,-32,-7) Matrix(891,-1238,398,-553) -> Matrix(1,0,4,1) Matrix(2657,-3754,1010,-1427) -> Matrix(11,2,-28,-5) Matrix(1461,-2068,556,-787) -> Matrix(7,2,-18,-5) Matrix(127,-180,12,-17) -> Matrix(1,0,0,1) Matrix(1519,-2178,1058,-1517) -> Matrix(1,0,12,1) Matrix(583,-844,172,-249) -> Matrix(1,0,-2,1) Matrix(1423,-2076,900,-1313) -> Matrix(3,2,-8,-5) Matrix(375,-578,242,-373) -> Matrix(1,0,4,1) Matrix(1627,-2574,390,-617) -> Matrix(1,0,0,1) Matrix(1005,-1598,422,-671) -> Matrix(5,2,-8,-3) Matrix(439,-708,204,-329) -> Matrix(1,0,6,1) Matrix(551,-904,64,-105) -> Matrix(1,2,-4,-7) Matrix(393,-670,166,-283) -> Matrix(11,4,-14,-5) Matrix(565,-974,134,-231) -> Matrix(1,0,0,1) Matrix(235,-408,72,-125) -> Matrix(1,0,0,1) Matrix(91,-162,50,-89) -> Matrix(5,2,-18,-7) Matrix(443,-844,116,-221) -> Matrix(15,4,-34,-9) Matrix(473,-1010,170,-363) -> Matrix(1,0,-8,1) Matrix(755,-1682,338,-753) -> Matrix(1,0,2,1) Matrix(1661,-3770,634,-1439) -> Matrix(1,0,-2,1) Matrix(247,-564,60,-137) -> Matrix(1,2,-4,-7) Matrix(1327,-3042,578,-1325) -> Matrix(19,20,-20,-21) Matrix(775,-1828,92,-217) -> Matrix(5,6,-16,-19) Matrix(475,-1122,58,-137) -> Matrix(7,6,-20,-17) Matrix(401,-970,74,-179) -> Matrix(1,0,-2,1) Matrix(81,-200,32,-79) -> Matrix(7,4,-16,-9) Matrix(5493,-14080,1312,-3363) -> Matrix(9,4,-34,-15) Matrix(6937,-17786,1658,-4251) -> Matrix(19,8,-50,-21) Matrix(5023,-13122,1922,-5021) -> Matrix(119,48,-300,-121) Matrix(623,-1700,188,-513) -> Matrix(11,4,-36,-13) Matrix(667,-1826,202,-553) -> Matrix(13,4,-36,-11) Matrix(2383,-6632,696,-1937) -> Matrix(1,0,16,1) Matrix(2471,-8450,722,-2469) -> Matrix(1,0,32,1) Matrix(67,-242,18,-65) -> Matrix(3,2,-8,-5) Matrix(1265,-4838,302,-1155) -> Matrix(5,2,-8,-3) Matrix(231,-1058,50,-229) -> Matrix(59,20,-180,-61) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 44 Degree of the the map X: 44 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 -1/1 1/6 3/11 1/3 2/5 13/29 5/9 5/7 3/4 1/1 15/13 11/9 4/3 65/47 7/5 33/23 17/11 5/3 9/5 2/1 11/5 29/13 39/17 7/3 59/25 5/2 141/55 13/5 81/31 19/7 41/15 3/1 17/5 65/19 7/2 11/3 19/5 4/1 13/3 9/2 23/5 5/1 27/5 11/2 17/3 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 0/1 3/17 1/2 1/0 2/11 3/1 1/0 3/16 -2/1 -1/1 1/5 -1/1 1/0 2/9 -1/1 -4/5 3/13 -1/2 1/4 -1/1 -2/3 3/11 -1/2 5/18 -1/3 0/1 7/25 -1/2 2/7 -1/3 0/1 5/17 0/1 1/0 3/10 -1/1 1/0 1/3 -1/2 1/0 4/11 -1/1 1/0 7/19 -1/1 -1/2 3/8 -1/1 0/1 8/21 -1/1 -2/3 13/34 -5/7 -2/3 5/13 -2/3 -1/2 7/18 -2/3 -1/2 2/5 -1/2 9/22 -1/2 -2/5 16/39 -1/3 0/1 7/17 -1/2 5/12 -3/7 -2/5 8/19 -2/5 -1/3 3/7 -1/2 -1/3 7/16 -1/3 -4/13 11/25 -3/10 -1/4 4/9 -1/4 -1/5 13/29 0/1 9/20 -1/3 0/1 5/11 -1/4 1/2 0/1 1/0 5/9 -1/1 9/16 -2/3 -1/2 4/7 -1/1 0/1 11/19 -1/1 -1/2 7/12 -1/1 0/1 17/29 -1/1 -3/4 10/17 -1/1 -2/3 3/5 -1/2 8/13 0/1 21/34 -1/1 0/1 13/21 -1/2 0/1 5/8 -1/1 -1/2 12/19 -1/2 0/1 7/11 -1/2 0/1 2/3 -1/1 0/1 11/16 -1/3 0/1 9/13 -1/2 0/1 7/10 0/1 1/1 12/17 -1/1 0/1 29/41 0/1 17/24 -1/1 1/0 5/7 -1/2 1/0 13/18 0/1 1/0 21/29 -1/1 1/0 8/11 -2/1 -1/1 11/15 -1/1 1/0 3/4 -1/1 13/17 -1/1 -3/4 36/47 -1/1 -4/5 23/30 -3/4 -2/3 10/13 -1/1 -4/5 7/9 -3/4 11/14 -11/16 -2/3 15/19 -2/3 -5/8 4/5 -1/1 -2/3 13/16 -2/3 -3/5 9/11 -5/8 -1/2 5/6 -3/5 -4/7 11/13 -1/2 6/7 -9/17 -1/2 1/1 -1/2 0/1 8/7 -9/17 -1/2 15/13 -1/2 7/6 -1/2 -9/19 6/5 -4/9 -3/7 17/14 -1/2 -2/5 11/9 -1/2 -5/12 16/13 -3/7 -2/5 5/4 -2/5 -1/3 14/11 -2/5 -11/28 9/7 -3/8 13/10 -4/11 -1/3 4/3 -1/3 19/14 -1/3 0/1 34/25 -2/7 -1/4 15/11 -1/3 -1/4 11/8 -1/3 -2/7 29/21 -1/3 -1/4 47/34 -2/7 -1/4 65/47 -1/4 18/13 -1/4 0/1 25/18 -1/3 -1/4 7/5 -1/2 -1/4 24/17 -1/3 -1/4 41/29 0/1 17/12 -1/3 0/1 10/7 -1/5 0/1 33/23 0/1 23/16 0/1 1/1 13/9 -1/2 0/1 16/11 -1/1 0/1 19/13 -1/2 3/2 -1/3 0/1 17/11 0/1 14/9 -1/1 0/1 11/7 -1/2 0/1 19/12 -1/2 0/1 27/17 -1/2 -1/4 8/5 -1/2 -1/3 21/13 -1/2 0/1 34/21 -1/3 0/1 47/29 -1/2 -1/4 13/8 0/1 18/11 -1/1 0/1 5/3 -1/2 17/10 -2/5 -1/3 12/7 -1/3 0/1 19/11 -1/2 -1/3 7/4 -1/3 0/1 9/5 -1/3 11/6 -1/3 -2/7 13/7 -1/2 -1/4 15/8 -1/3 -2/7 2/1 -1/4 0/1 11/5 1/0 20/9 -1/1 0/1 29/13 0/1 9/4 1/1 1/0 25/11 -3/2 1/0 41/18 -2/1 -3/2 16/7 -4/3 -1/1 39/17 -1/1 23/10 -1/1 -6/7 7/3 -1/1 -1/2 33/14 -2/1 -1/1 59/25 -1/1 26/11 -1/1 -4/5 19/8 -1/1 -2/3 12/5 -2/3 -3/5 29/12 -1/2 -3/7 17/7 -1/2 5/2 -1/2 23/9 -1/2 41/16 -4/9 -3/7 141/55 -3/7 100/39 -3/7 -2/5 59/23 -1/2 -3/7 18/7 -1/2 -2/5 13/5 -1/2 -2/5 47/18 -7/17 -2/5 81/31 -2/5 34/13 -2/5 -5/13 21/8 -2/5 -1/3 29/11 -3/8 8/3 -1/3 0/1 19/7 -1/2 -1/3 30/11 -3/8 -1/3 41/15 -1/3 11/4 -1/3 -1/4 3/1 -1/2 -1/4 10/3 -1/3 -1/4 17/5 -1/4 0/1 41/12 -1/12 0/1 65/19 0/1 24/7 0/1 1/4 7/2 -1/1 0/1 11/3 -1/2 15/4 -2/5 -1/3 34/9 -3/5 -1/2 19/5 -1/2 23/6 -3/7 -2/5 4/1 -2/5 -1/3 13/3 -1/2 22/5 -2/5 -1/3 9/2 -4/11 -1/3 23/5 -1/3 14/3 -1/3 -6/19 5/1 -1/3 -1/4 16/3 -1/3 -2/7 27/5 -1/4 11/2 -1/4 -3/13 17/3 -1/4 -1/6 23/4 -1/5 0/1 6/1 0/1 7/1 -1/2 1/0 -1/3 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(503,-86,310,-53) (1/6,3/17) -> (47/29,13/8) Hyperbolic Matrix(428,-77,189,-34) (3/17,2/11) -> (9/4,25/11) Hyperbolic Matrix(709,-132,188,-35) (2/11,3/16) -> (15/4,34/9) Hyperbolic Matrix(376,-71,519,-98) (3/16,1/5) -> (21/29,8/11) 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(158,-37,205,-48) (3/13,1/4) -> (10/13,7/9) 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(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(365,-138,82,-31) (3/8,8/21) -> (22/5,9/2) Hyperbolic Matrix(526,-201,649,-248) (8/21,13/34) -> (4/5,13/16) Hyperbolic Matrix(1053,-404,404,-155) (13/34,5/13) -> (13/5,47/18) Hyperbolic Matrix(282,-109,445,-172) (5/13,7/18) -> (12/19,7/11) 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(1132,-465,297,-122) (16/39,7/17) -> (19/5,23/6) Hyperbolic Matrix(217,-90,258,-107) (7/17,5/12) -> (5/6,11/13) Hyperbolic Matrix(394,-165,277,-116) (5/12,8/19) -> (17/12,10/7) 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(428,-189,77,-34) (11/25,4/9) -> (11/2,17/3) Hyperbolic Matrix(754,-337,1065,-476) (4/9,13/29) -> (29/41,17/24) Hyperbolic Matrix(928,-417,1313,-590) (13/29,9/20) -> (12/17,29/41) Hyperbolic Matrix(502,-227,115,-52) (9/20,5/11) -> (13/3,22/5) Hyperbolic Matrix(172,-79,135,-62) (5/11,1/2) -> (14/11,9/7) 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(284,-165,389,-226) (11/19,7/12) -> (8/11,11/15) Hyperbolic Matrix(1041,-610,442,-259) (7/12,17/29) -> (7/3,33/14) 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(503,-310,86,-53) (8/13,21/34) -> (23/4,6/1) Hyperbolic Matrix(778,-481,537,-332) (21/34,13/21) -> (13/9,16/11) Hyperbolic Matrix(346,-215,103,-64) (13/21,5/8) -> (10/3,17/5) Hyperbolic Matrix(619,-390,446,-281) (5/8,12/19) -> (18/13,25/18) 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(778,-537,481,-332) (11/16,9/13) -> (21/13,34/21) 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(704,-499,443,-314) (17/24,5/7) -> (27/17,8/5) 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(476,-365,253,-194) (23/30,10/13) -> (15/8,2/1) Hyperbolic Matrix(172,-135,79,-62) (7/9,11/14) -> (2/1,11/5) Hyperbolic Matrix(1017,-802,298,-235) (11/14,15/19) -> (17/5,41/12) 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(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(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(526,-649,201,-248) (16/13,5/4) -> (34/13,21/8) Hyperbolic Matrix(173,-218,50,-63) (5/4,14/11) -> (24/7,7/2) Hyperbolic Matrix(158,-205,37,-48) (9/7,13/10) -> (4/1,13/3) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(974,-1323,427,-580) (19/14,34/25) -> (41/18,16/7) Hyperbolic Matrix(1673,-2276,652,-887) (34/25,15/11) -> (59/23,18/7) Hyperbolic Matrix(284,-389,165,-226) (15/11,11/8) -> (12/7,19/11) Hyperbolic Matrix(376,-519,71,-98) (11/8,29/21) -> (5/1,16/3) Hyperbolic Matrix(3056,-4225,2209,-3054) (47/34,65/47) -> (65/47,18/13) Parabolic Matrix(246,-343,175,-244) (25/18,7/5) -> (7/5,24/17) Parabolic 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(760,-1089,529,-758) (10/7,33/23) -> (33/23,23/16) Parabolic Matrix(786,-1147,307,-448) (16/11,19/13) -> (23/9,41/16) Hyperbolic Matrix(188,-289,121,-186) (3/2,17/11) -> (17/11,14/9) Parabolic Matrix(282,-445,109,-172) (11/7,19/12) -> (18/7,13/5) Hyperbolic Matrix(106,-175,63,-104) (18/11,5/3) -> (5/3,17/10) Parabolic Matrix(393,-670,166,-283) (17/10,12/7) -> (26/11,19/8) Hyperbolic Matrix(164,-285,61,-106) (19/11,7/4) -> (8/3,19/7) Hyperbolic Matrix(91,-162,50,-89) (7/4,9/5) -> (9/5,11/6) Parabolic Matrix(366,-811,139,-308) (11/5,20/9) -> (21/8,29/11) Hyperbolic Matrix(664,-1521,289,-662) (16/7,39/17) -> (39/17,23/10) Parabolic Matrix(1476,-3481,625,-1474) (33/14,59/25) -> (59/25,26/11) Parabolic 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(7756,-19881,3025,-7754) (41/16,141/55) -> (141/55,100/39) Parabolic Matrix(2512,-6561,961,-2510) (47/18,81/31) -> (81/31,34/13) 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(1236,-4225,361,-1234) (41/12,65/19) -> (65/19,24/7) Parabolic Matrix(67,-242,18,-65) (7/2,11/3) -> (11/3,15/4) 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(1,0,2,1) Matrix(121,-18,74,-11) -> Matrix(1,0,0,1) Matrix(503,-86,310,-53) -> Matrix(1,0,-4,1) Matrix(428,-77,189,-34) -> Matrix(1,-2,0,1) Matrix(709,-132,188,-35) -> Matrix(1,0,-2,1) Matrix(376,-71,519,-98) -> Matrix(1,0,0,1) Matrix(115,-24,24,-5) -> Matrix(1,2,-4,-7) Matrix(365,-82,138,-31) -> Matrix(5,4,-14,-11) Matrix(158,-37,205,-48) -> Matrix(1,2,-2,-3) Matrix(67,-18,242,-65) -> Matrix(3,2,-8,-5) Matrix(417,-116,284,-79) -> Matrix(1,0,0,1) Matrix(589,-166,110,-31) -> Matrix(5,2,-18,-7) Matrix(173,-50,218,-63) -> Matrix(5,2,-8,-3) Matrix(346,-103,215,-64) -> Matrix(1,0,-2,1) Matrix(22,-7,63,-20) -> Matrix(1,0,0,1) Matrix(779,-286,286,-105) -> Matrix(3,2,-8,-5) Matrix(164,-61,285,-106) -> Matrix(1,0,0,1) Matrix(365,-138,82,-31) -> Matrix(5,4,-14,-11) Matrix(526,-201,649,-248) -> Matrix(11,8,-18,-13) Matrix(1053,-404,404,-155) -> Matrix(7,4,-16,-9) Matrix(282,-109,445,-172) -> Matrix(3,2,-8,-5) Matrix(81,-32,200,-79) -> Matrix(7,4,-16,-9) Matrix(1689,-692,2204,-903) -> Matrix(11,4,-14,-5) Matrix(1132,-465,297,-122) -> Matrix(3,2,-8,-5) Matrix(217,-90,258,-107) -> Matrix(13,6,-24,-11) Matrix(394,-165,277,-116) -> Matrix(5,2,-18,-7) Matrix(393,-166,670,-283) -> Matrix(11,4,-14,-5) Matrix(273,-118,118,-51) -> Matrix(5,2,-8,-3) Matrix(583,-256,312,-137) -> Matrix(7,2,-18,-5) Matrix(428,-189,77,-34) -> Matrix(7,2,-32,-9) Matrix(754,-337,1065,-476) -> Matrix(1,0,4,1) Matrix(928,-417,1313,-590) -> Matrix(1,0,2,1) Matrix(502,-227,115,-52) -> Matrix(7,2,-18,-5) Matrix(172,-79,135,-62) -> Matrix(11,2,-28,-5) Matrix(91,-50,162,-89) -> Matrix(1,2,-2,-3) Matrix(215,-122,178,-101) -> Matrix(7,4,-16,-9) Matrix(284,-165,389,-226) -> Matrix(3,2,-2,-1) Matrix(1041,-610,442,-259) -> Matrix(3,2,-2,-1) Matrix(124,-73,17,-10) -> Matrix(3,2,-8,-5) Matrix(121,-74,18,-11) -> Matrix(1,0,0,1) Matrix(503,-310,86,-53) -> Matrix(1,0,-4,1) Matrix(778,-481,537,-332) -> Matrix(1,0,0,1) Matrix(346,-215,103,-64) -> Matrix(1,0,-2,1) Matrix(619,-390,446,-281) -> Matrix(1,0,-2,1) Matrix(187,-120,120,-77) -> Matrix(1,0,0,1) Matrix(133,-90,34,-23) -> Matrix(3,2,-8,-5) Matrix(778,-537,481,-332) -> Matrix(1,0,0,1) Matrix(429,-298,298,-207) -> Matrix(1,0,0,1) Matrix(394,-277,165,-116) -> Matrix(1,2,-2,-3) Matrix(704,-499,443,-314) -> Matrix(1,0,-2,1) Matrix(619,-446,390,-281) -> Matrix(1,0,-2,1) Matrix(1885,-1364,1364,-987) -> Matrix(1,2,-4,-7) Matrix(97,-72,128,-95) -> Matrix(3,4,-4,-5) Matrix(4473,-3424,1744,-1335) -> Matrix(13,10,-30,-23) Matrix(476,-365,253,-194) -> Matrix(3,2,-8,-5) Matrix(172,-135,79,-62) -> Matrix(3,2,4,3) Matrix(1017,-802,298,-235) -> Matrix(3,2,-20,-13) Matrix(525,-428,92,-75) -> Matrix(3,2,-20,-13) Matrix(199,-164,108,-89) -> Matrix(3,2,-14,-9) Matrix(575,-488,152,-129) -> Matrix(11,6,-24,-13) Matrix(15,-14,14,-13) -> Matrix(1,0,0,1) Matrix(196,-225,169,-194) -> Matrix(35,18,-72,-37) Matrix(217,-258,90,-107) -> Matrix(13,6,-24,-11) Matrix(719,-876,316,-385) -> Matrix(19,8,-12,-5) Matrix(917,-1126,566,-695) -> Matrix(5,2,-8,-3) Matrix(526,-649,201,-248) -> Matrix(19,8,-50,-21) Matrix(173,-218,50,-63) -> Matrix(5,2,-8,-3) Matrix(158,-205,37,-48) -> Matrix(5,2,-18,-7) Matrix(97,-128,72,-95) -> Matrix(11,4,-36,-13) Matrix(974,-1323,427,-580) -> Matrix(13,4,-10,-3) Matrix(1673,-2276,652,-887) -> Matrix(15,4,-34,-9) Matrix(284,-389,165,-226) -> Matrix(7,2,-18,-5) Matrix(376,-519,71,-98) -> Matrix(1,0,0,1) Matrix(3056,-4225,2209,-3054) -> Matrix(7,2,-32,-9) Matrix(246,-343,175,-244) -> Matrix(1,0,0,1) Matrix(754,-1065,337,-476) -> Matrix(1,0,4,1) Matrix(928,-1313,417,-590) -> Matrix(1,0,2,1) Matrix(760,-1089,529,-758) -> Matrix(1,0,6,1) Matrix(786,-1147,307,-448) -> Matrix(7,4,-16,-9) Matrix(188,-289,121,-186) -> Matrix(1,0,2,1) Matrix(282,-445,109,-172) -> Matrix(3,2,-8,-5) Matrix(106,-175,63,-104) -> Matrix(3,2,-8,-5) Matrix(393,-670,166,-283) -> Matrix(11,4,-14,-5) Matrix(164,-285,61,-106) -> Matrix(1,0,0,1) Matrix(91,-162,50,-89) -> Matrix(5,2,-18,-7) Matrix(366,-811,139,-308) -> Matrix(3,2,-8,-5) Matrix(664,-1521,289,-662) -> Matrix(9,10,-10,-11) Matrix(1476,-3481,625,-1474) -> Matrix(5,6,-6,-7) Matrix(401,-970,74,-179) -> Matrix(1,0,-2,1) Matrix(81,-200,32,-79) -> Matrix(7,4,-16,-9) Matrix(7756,-19881,3025,-7754) -> Matrix(41,18,-98,-43) Matrix(2512,-6561,961,-2510) -> Matrix(59,24,-150,-61) Matrix(616,-1681,225,-614) -> Matrix(11,4,-36,-13) Matrix(22,-63,7,-20) -> Matrix(1,0,0,1) Matrix(1236,-4225,361,-1234) -> Matrix(1,0,16,1) Matrix(67,-242,18,-65) -> Matrix(3,2,-8,-5) Matrix(116,-529,25,-114) -> Matrix(29,10,-90,-31) 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): 22 ----------------------------------------------------------------------- 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 2 1 1/1 (-1/2,0/1) 0 14 15/13 -1/2 18 1 7/6 (-1/2,-9/19) 0 28 6/5 (-4/9,-3/7) 0 28 11/9 0 7 16/13 (-3/7,-2/5) 0 28 5/4 (-2/5,-1/3) 0 28 14/11 (-2/5,-11/28) 0 28 9/7 -3/8 2 7 13/10 (-4/11,-1/3) 0 28 4/3 -1/3 2 4 19/14 (-1/3,0/1) 0 28 34/25 (-2/7,-1/4) 0 28 15/11 (-1/3,-1/4) 0 14 11/8 (-1/3,-2/7) 0 28 29/21 (-1/3,-1/4) 0 14 65/47 -1/4 2 1 18/13 (-1/4,0/1) 0 28 7/5 0 7 24/17 (-1/3,-1/4) 0 28 41/29 0/1 2 2 17/12 (-1/3,0/1) 0 28 10/7 (-1/5,0/1) 0 28 33/23 0/1 6 1 13/9 (-1/2,0/1) 0 14 16/11 (-1/1,0/1) 0 28 3/2 (-1/3,0/1) 0 28 17/11 0/1 2 1 11/7 (-1/2,0/1) 0 14 19/12 (-1/2,0/1) 0 28 27/17 0 7 8/5 (-1/2,-1/3) 0 28 21/13 (-1/2,0/1) 0 14 34/21 (-1/3,0/1) 0 28 13/8 0/1 2 4 5/3 -1/2 2 7 17/10 (-2/5,-1/3) 0 28 12/7 (-1/3,0/1) 0 28 19/11 (-1/2,-1/3) 0 14 7/4 (-1/3,0/1) 0 28 9/5 -1/3 2 2 11/6 (-1/3,-2/7) 0 28 13/7 0 7 2/1 (-1/4,0/1) 0 28 11/5 1/0 2 7 20/9 (-1/1,0/1) 0 28 29/13 0/1 2 2 9/4 (1/1,1/0) 0 28 25/11 0 7 41/18 (-2/1,-3/2) 0 28 16/7 (-4/3,-1/1) 0 28 39/17 -1/1 10 1 7/3 (-1/1,-1/2) 0 14 59/25 -1/1 6 1 26/11 (-1/1,-4/5) 0 28 19/8 (-1/1,-2/3) 0 28 12/5 (-2/3,-3/5) 0 28 29/12 (-1/2,-3/7) 0 28 17/7 -1/2 2 7 5/2 -1/2 2 4 23/9 -1/2 2 7 41/16 (-4/9,-3/7) 0 28 141/55 -3/7 2 1 59/23 (-1/2,-3/7) 0 14 18/7 (-1/2,-2/5) 0 28 13/5 (-1/2,-2/5) 0 14 81/31 -2/5 6 1 34/13 (-2/5,-5/13) 0 28 21/8 (-2/5,-1/3) 0 28 8/3 (-1/3,0/1) 0 28 19/7 (-1/2,-1/3) 0 14 41/15 -1/3 4 1 11/4 (-1/3,-1/4) 0 28 3/1 0 7 10/3 (-1/3,-1/4) 0 28 17/5 (-1/4,0/1) 0 14 65/19 0/1 16 1 24/7 (0/1,1/4) 0 28 7/2 (-1/1,0/1) 0 28 11/3 -1/2 2 2 15/4 (-2/5,-1/3) 0 28 19/5 -1/2 2 7 23/6 (-3/7,-2/5) 0 28 4/1 (-2/5,-1/3) 0 28 13/3 -1/2 2 7 22/5 (-2/5,-1/3) 0 28 9/2 (-4/11,-1/3) 0 28 23/5 -1/3 10 1 5/1 (-1/3,-1/4) 0 14 16/3 (-1/3,-2/7) 0 28 27/5 -1/4 2 7 11/2 (-1/4,-3/13) 0 28 17/3 0 7 23/4 (-1/5,0/1) 0 28 6/1 0/1 2 4 7/1 -1/2 2 7 1/0 (-1/3,0/1) 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(164,-199,89,-108) (6/5,11/9) -> (11/6,13/7) Glide Reflection Matrix(428,-525,75,-92) (11/9,16/13) -> (17/3,23/4) Glide Reflection Matrix(526,-649,201,-248) (16/13,5/4) -> (34/13,21/8) Hyperbolic Matrix(173,-218,50,-63) (5/4,14/11) -> (24/7,7/2) Hyperbolic Matrix(135,-172,62,-79) (14/11,9/7) -> (2/1,11/5) Glide Reflection Matrix(158,-205,37,-48) (9/7,13/10) -> (4/1,13/3) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(974,-1323,427,-580) (19/14,34/25) -> (41/18,16/7) Hyperbolic Matrix(1673,-2276,652,-887) (34/25,15/11) -> (59/23,18/7) Hyperbolic Matrix(284,-389,165,-226) (15/11,11/8) -> (12/7,19/11) Hyperbolic Matrix(376,-519,71,-98) (11/8,29/21) -> (5/1,16/3) Hyperbolic Matrix(1364,-1885,987,-1364) (29/21,65/47) -> (29/21,65/47) Reflection Matrix(1691,-2340,1222,-1691) (65/47,18/13) -> (65/47,18/13) Reflection Matrix(446,-619,281,-390) (18/13,7/5) -> (19/12,27/17) Glide Reflection Matrix(499,-704,314,-443) (7/5,24/17) -> (27/17,8/5) Glide Reflection 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(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(537,-778,332,-481) (13/9,16/11) -> (21/13,34/21) Glide Reflection Matrix(90,-133,23,-34) (16/11,3/2) -> (23/6,4/1) 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(282,-445,109,-172) (11/7,19/12) -> (18/7,13/5) Hyperbolic Matrix(215,-346,64,-103) (8/5,21/13) -> (10/3,17/5) Glide Reflection Matrix(310,-503,53,-86) (34/21,13/8) -> (23/4,6/1) Glide 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(393,-670,166,-283) (17/10,12/7) -> (26/11,19/8) Hyperbolic Matrix(164,-285,61,-106) (19/11,7/4) -> (8/3,19/7) Hyperbolic Matrix(91,-162,50,-89) (7/4,9/5) -> (9/5,11/6) Parabolic Matrix(312,-583,137,-256) (13/7,2/1) -> (25/11,41/18) Glide Reflection Matrix(227,-502,52,-115) (11/5,20/9) -> (13/3,22/5) Glide 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(176,-413,75,-176) (7/3,59/25) -> (7/3,59/25) Reflection Matrix(1299,-3068,550,-1299) (59/25,26/11) -> (59/25,26/11) Reflection 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(511,-1308,134,-343) (23/9,41/16) -> (19/5,23/6) Glide Reflection Matrix(4511,-11562,1760,-4511) (41/16,141/55) -> (41/16,141/55) Reflection Matrix(3244,-8319,1265,-3244) (141/55,59/23) -> (141/55,59/23) Reflection Matrix(404,-1053,155,-404) (13/5,81/31) -> (13/5,81/31) Reflection Matrix(2107,-5508,806,-2107) (81/31,34/13) -> (81/31,34/13) 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(324,-1105,95,-324) (17/5,65/19) -> (17/5,65/19) Reflection Matrix(911,-3120,266,-911) (65/19,24/7) -> (65/19,24/7) Reflection Matrix(67,-242,18,-65) (7/2,11/3) -> (11/3,15/4) Parabolic Matrix(188,-709,35,-132) (15/4,19/5) -> (16/3,27/5) Glide Reflection 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 IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,6,1) (-1/1,1/0) -> (-1/3,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,4,1) (-1/1,1/1) -> (-1/2,0/1) Matrix(14,-15,13,-14) -> Matrix(-1,0,4,1) (1/1,15/13) -> (-1/2,0/1) Matrix(181,-210,156,-181) -> Matrix(37,18,-76,-37) (15/13,7/6) -> (-1/2,-9/19) Matrix(217,-258,90,-107) -> Matrix(13,6,-24,-11) -1/2 Matrix(164,-199,89,-108) -> Matrix(5,2,-22,-9) Matrix(428,-525,75,-92) -> Matrix(5,2,-32,-13) Matrix(526,-649,201,-248) -> Matrix(19,8,-50,-21) -2/5 Matrix(173,-218,50,-63) -> Matrix(5,2,-8,-3) -1/2 Matrix(135,-172,62,-79) -> Matrix(5,2,8,3) Matrix(158,-205,37,-48) -> Matrix(5,2,-18,-7) -1/3 Matrix(97,-128,72,-95) -> Matrix(11,4,-36,-13) -1/3 Matrix(974,-1323,427,-580) -> Matrix(13,4,-10,-3) Matrix(1673,-2276,652,-887) -> Matrix(15,4,-34,-9) Matrix(284,-389,165,-226) -> Matrix(7,2,-18,-5) -1/3 Matrix(376,-519,71,-98) -> Matrix(1,0,0,1) Matrix(1364,-1885,987,-1364) -> Matrix(7,2,-24,-7) (29/21,65/47) -> (-1/3,-1/4) Matrix(1691,-2340,1222,-1691) -> Matrix(-1,0,8,1) (65/47,18/13) -> (-1/4,0/1) Matrix(446,-619,281,-390) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(499,-704,314,-443) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(754,-1065,337,-476) -> Matrix(1,0,4,1) 0/1 Matrix(928,-1313,417,-590) -> Matrix(1,0,2,1) 0/1 Matrix(277,-394,116,-165) -> Matrix(7,2,-10,-3) Matrix(461,-660,322,-461) -> Matrix(-1,0,10,1) (10/7,33/23) -> (-1/5,0/1) Matrix(298,-429,207,-298) -> Matrix(-1,0,4,1) (33/23,13/9) -> (-1/2,0/1) Matrix(537,-778,332,-481) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(90,-133,23,-34) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(67,-102,44,-67) -> Matrix(-1,0,6,1) (3/2,17/11) -> (-1/3,0/1) Matrix(120,-187,77,-120) -> Matrix(-1,0,4,1) (17/11,11/7) -> (-1/2,0/1) Matrix(282,-445,109,-172) -> Matrix(3,2,-8,-5) -1/2 Matrix(215,-346,64,-103) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(310,-503,53,-86) -> Matrix(-1,0,8,1) *** -> (-1/4,0/1) Matrix(74,-121,11,-18) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(73,-124,10,-17) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(393,-670,166,-283) -> Matrix(11,4,-14,-5) Matrix(164,-285,61,-106) -> Matrix(1,0,0,1) Matrix(91,-162,50,-89) -> Matrix(5,2,-18,-7) -1/3 Matrix(312,-583,137,-256) -> Matrix(5,2,-2,-1) Matrix(227,-502,52,-115) -> Matrix(1,2,-2,-5) Matrix(189,-428,34,-77) -> Matrix(1,2,-4,-9) Matrix(545,-1248,238,-545) -> Matrix(7,8,-6,-7) (16/7,39/17) -> (-4/3,-1/1) Matrix(118,-273,51,-118) -> Matrix(3,2,-4,-3) (39/17,7/3) -> (-1/1,-1/2) Matrix(176,-413,75,-176) -> Matrix(3,2,-4,-3) (7/3,59/25) -> (-1/1,-1/2) Matrix(1299,-3068,550,-1299) -> Matrix(9,8,-10,-9) (59/25,26/11) -> (-1/1,-4/5) Matrix(401,-970,74,-179) -> Matrix(1,0,-2,1) 0/1 Matrix(81,-200,32,-79) -> Matrix(7,4,-16,-9) -1/2 Matrix(511,-1308,134,-343) -> Matrix(13,6,-28,-13) *** -> (-1/2,-3/7) Matrix(4511,-11562,1760,-4511) -> Matrix(55,24,-126,-55) (41/16,141/55) -> (-4/9,-3/7) Matrix(3244,-8319,1265,-3244) -> Matrix(13,6,-28,-13) (141/55,59/23) -> (-1/2,-3/7) Matrix(404,-1053,155,-404) -> Matrix(9,4,-20,-9) (13/5,81/31) -> (-1/2,-2/5) Matrix(2107,-5508,806,-2107) -> Matrix(51,20,-130,-51) (81/31,34/13) -> (-2/5,-5/13) Matrix(138,-365,31,-82) -> Matrix(11,4,-30,-11) *** -> (-2/5,-1/3) Matrix(286,-779,105,-286) -> Matrix(5,2,-12,-5) (19/7,41/15) -> (-1/2,-1/3) Matrix(329,-902,120,-329) -> Matrix(7,2,-24,-7) (41/15,11/4) -> (-1/3,-1/4) Matrix(22,-63,7,-20) -> Matrix(1,0,0,1) Matrix(324,-1105,95,-324) -> Matrix(-1,0,8,1) (17/5,65/19) -> (-1/4,0/1) Matrix(911,-3120,266,-911) -> Matrix(1,0,8,-1) (65/19,24/7) -> (0/1,1/4) Matrix(67,-242,18,-65) -> Matrix(3,2,-8,-5) -1/2 Matrix(188,-709,35,-132) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(91,-414,20,-91) -> Matrix(23,8,-66,-23) (9/2,23/5) -> (-4/11,-1/3) Matrix(24,-115,5,-24) -> Matrix(7,2,-24,-7) (23/5,5/1) -> (-1/3,-1/4) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.