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): 1440 Minimal number of generators: 241 Number of equivalence classes of cusps: 80 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -9/20 -8/19 -7/18 -1/3 -5/16 -3/14 -2/13 -1/7 0/1 2/9 5/17 1/3 3/8 1/2 4/7 9/13 5/7 23/32 5/6 1/1 6/5 37/29 7/5 13/9 3/2 11/7 27/17 34/21 41/25 5/3 7/4 9/5 2/1 15/7 11/5 23/10 7/3 31/13 17/7 5/2 111/43 8/3 3/1 67/21 16/5 135/41 10/3 17/5 7/2 69/19 11/3 26/7 15/4 87/23 35/9 4/1 17/4 13/3 9/2 14/3 24/5 73/15 5/1 37/7 16/3 11/2 28/5 17/3 6/1 19/3 13/2 7/1 15/2 23/3 39/5 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/1 -7/15 0/1 -6/13 5/4 -11/24 1/1 -5/11 0/1 2/1 -14/31 1/2 -9/20 1/1 -22/49 5/4 -13/29 4/3 -4/9 3/2 -11/25 4/3 2/1 -18/41 7/2 -25/57 0/1 -7/16 1/1 -10/23 3/2 -13/30 1/1 -3/7 2/1 -14/33 5/2 -11/26 3/1 -8/19 1/0 -21/50 1/1 -13/31 0/1 2/1 -5/12 3/1 -17/41 0/1 -12/29 3/2 -7/17 2/1 4/1 -9/22 3/1 -11/27 4/1 -2/5 1/0 -11/28 1/1 -20/51 1/0 -9/23 0/1 2/1 -7/18 1/0 -12/31 1/0 -17/44 -1/1 -5/13 0/1 -18/47 1/0 -13/34 -5/3 -8/21 -1/2 -11/29 0/1 2/3 -14/37 5/4 -3/8 1/1 -10/27 1/0 -17/46 -1/1 -7/19 -2/1 -25/68 -1/1 -43/117 -2/3 0/1 -18/49 -1/2 -11/30 1/1 -4/11 -1/2 -13/36 3/7 -9/25 0/1 -14/39 3/2 -5/14 1/1 -16/45 1/0 -11/31 2/1 -6/17 1/0 -7/20 -1/1 -1/3 0/1 2/1 -6/19 1/2 -5/16 1/1 -9/29 2/1 -13/42 1/1 -4/13 1/0 -11/36 3/1 -18/59 1/0 -7/23 0/1 -10/33 -3/4 -13/43 -2/7 0/1 -3/10 1/3 -11/37 0/1 2/3 -19/64 1/1 -8/27 1/0 -21/71 0/1 2/7 -13/44 1/3 -18/61 1/2 -5/17 2/3 -12/41 1/2 -7/24 1/1 -2/7 1/0 -11/39 2/1 -9/32 5/1 -7/25 -2/1 0/1 -12/43 -1/4 -5/18 1/3 -13/47 0/1 2/5 -21/76 1/2 -8/29 5/8 -11/40 1/1 -14/51 5/4 -3/11 0/1 -10/37 1/2 -7/26 1/1 -4/15 1/1 -5/19 0/1 2/1 -6/23 1/0 -7/27 2/3 -1/4 1/1 -6/25 7/6 -5/21 4/3 -4/17 3/2 -7/30 1/3 -10/43 1/1 -3/13 4/3 2/1 -8/35 7/4 -5/22 3/1 -12/53 1/0 -7/31 0/1 -2/9 3/2 -7/32 3/1 -12/55 1/0 -5/23 0/1 2/1 -3/14 1/1 -7/33 4/3 2/1 -4/19 3/2 -5/24 5/3 -1/5 2/1 -4/21 1/0 -7/37 2/1 4/1 -10/53 1/0 -3/16 3/1 -2/11 1/0 -7/39 0/1 -5/28 7/5 -8/45 11/6 -11/62 15/7 -3/17 2/1 4/1 -1/6 3/1 -4/25 13/4 -3/19 4/1 -2/13 1/0 -5/33 -2/1 -3/20 -1/1 -1/7 0/1 2/1 -4/29 7/4 -3/22 7/3 -2/15 1/0 -1/8 5/1 -2/17 1/0 -1/9 0/1 0/1 1/0 1/8 -3/1 2/15 1/0 1/7 0/1 1/6 -5/1 2/11 1/0 1/5 -2/1 0/1 6/29 1/0 5/24 -1/1 4/19 -1/4 3/14 1/1 2/9 1/0 5/22 -5/1 8/35 1/0 3/13 -4/1 1/4 -3/1 5/19 -4/3 4/15 1/0 7/26 1/0 3/11 -4/1 -2/1 5/18 -7/5 7/25 0/1 2/7 1/0 5/17 1/0 8/27 1/0 3/10 -3/1 4/13 1/0 5/16 -11/5 6/19 -3/2 1/3 -2/1 7/20 -1/1 6/17 -9/4 5/14 -5/3 14/39 -3/2 9/25 -2/1 0/1 13/36 -9/5 4/11 -3/2 3/8 -1/1 8/21 1/0 21/55 -2/1 34/89 1/0 47/123 -2/1 0/1 13/34 -1/1 31/81 -4/3 18/47 -5/6 5/13 -2/1 0/1 2/5 -3/2 7/17 0/1 5/12 -3/1 3/7 -2/1 -4/3 4/9 -3/2 9/20 -1/1 14/31 -3/2 5/11 -4/3 1/2 -1/1 6/11 1/0 11/20 -1/1 5/9 -2/1 0/1 4/7 -1/1 11/19 -6/7 -4/5 18/31 -5/6 25/43 -10/13 32/55 -3/4 7/12 -1/1 24/41 -15/22 17/29 -2/3 -8/13 10/17 -1/2 23/39 -4/5 -2/3 13/22 -3/5 16/27 -1/2 3/5 0/1 11/18 -1/1 19/31 -4/5 -2/3 8/13 -5/8 5/8 -1/3 7/11 0/1 2/1 16/25 1/0 9/14 -5/1 2/3 1/0 9/13 -1/1 16/23 -7/8 7/10 -1/1 26/37 -3/4 45/64 -17/25 19/27 -2/3 -4/7 12/17 -1/2 17/24 -1/1 22/31 -1/2 5/7 -2/3 28/39 -11/20 23/32 -1/2 18/25 -1/2 49/68 -3/7 31/43 -2/5 0/1 13/18 -1/3 8/11 1/0 3/4 -1/3 10/13 3/4 7/9 0/1 11/14 -3/1 26/33 1/0 15/19 -2/1 -4/3 4/5 1/0 21/26 -1/1 17/21 -2/1 0/1 13/16 -1/1 9/11 -2/1 5/6 -1/1 11/13 0/1 17/20 -3/5 6/7 -1/2 13/15 -2/3 20/23 -1/2 27/31 -2/5 0/1 7/8 -1/1 8/9 -1/2 1/1 -2/1 0/1 8/7 1/0 15/13 2/1 7/6 1/1 6/5 1/0 17/14 -1/1 28/23 -1/2 11/9 -2/1 27/22 -1/3 43/35 0/1 2/3 16/13 1/0 5/4 -1/1 24/19 1/0 43/34 1/0 19/15 -4/1 -2/1 33/26 -1/1 14/11 -3/2 37/29 -1/1 60/47 -9/10 23/18 -1/1 9/7 0/1 13/10 -3/7 17/13 -2/9 0/1 4/3 1/2 15/11 0/1 2/1 41/30 3/1 67/49 2/1 26/19 1/0 11/8 -1/1 29/21 0/1 2/5 18/13 1/2 25/18 1/1 32/23 1/1 39/28 11/9 7/5 2/1 24/17 1/0 41/29 0/1 2/1 17/12 1/1 44/31 1/0 27/19 4/3 2/1 37/26 3/1 10/7 1/0 13/9 1/0 16/11 1/0 3/2 -1/1 17/11 -2/1 14/9 -5/4 25/16 -1/1 36/23 -1/2 11/7 -2/3 0/1 19/12 -1/5 27/17 0/1 35/22 1/9 8/5 1/2 21/13 0/1 2/3 55/34 1/1 34/21 1/1 81/50 1/1 47/29 6/5 13/8 5/3 44/27 5/2 31/19 2/1 4/1 49/30 3/1 18/11 1/0 41/25 1/0 64/39 1/0 23/14 -5/1 5/3 0/1 27/16 1/1 49/29 6/5 4/3 22/13 3/2 83/49 2/1 61/36 7/3 39/23 2/1 4/1 56/33 1/0 17/10 1/1 46/27 3/2 29/17 8/5 2/1 12/7 1/0 7/4 1/0 16/9 1/0 57/32 -3/1 98/55 -35/12 41/23 -8/3 66/37 -5/2 25/14 -1/1 9/5 -2/1 0/1 11/6 -1/1 13/7 2/1 15/8 -7/1 2/1 1/0 15/7 1/0 28/13 1/0 13/6 -7/1 11/5 -4/1 31/14 -3/1 20/9 1/0 29/13 -2/1 0/1 9/4 -3/1 16/7 1/2 23/10 1/0 30/13 1/0 7/3 -4/1 -2/1 19/8 -7/3 31/13 -2/1 43/18 -13/7 12/5 -3/2 29/12 -1/1 46/19 -9/8 17/7 0/1 39/16 -1/1 22/9 1/0 5/2 -3/1 18/7 -3/2 49/19 -6/5 80/31 -15/14 111/43 -1/1 142/55 -21/22 31/12 -1/1 75/29 0/1 44/17 -1/2 57/22 -1/3 13/5 -2/1 0/1 8/3 1/0 19/7 -4/1 -2/1 49/18 3/1 128/47 1/0 79/29 -6/1 30/11 1/0 71/26 -3/1 41/15 -4/1 11/4 -3/1 47/17 -8/3 36/13 -9/4 97/35 -2/1 61/22 -9/5 25/9 -2/1 0/1 64/23 1/0 39/14 -3/1 14/5 -5/2 31/11 -20/9 -2/1 48/17 -29/14 65/23 -2/1 17/6 -9/5 3/1 -2/1 19/6 -3/1 35/11 -16/7 -2/1 51/16 -27/13 67/21 -2/1 16/5 -11/6 29/9 -2/1 -8/5 13/4 -1/1 23/7 -2/1 -4/3 79/24 -7/5 135/41 -4/3 56/17 -5/4 33/10 -1/1 10/3 -3/2 17/5 -1/1 24/7 -1/2 7/2 -1/1 39/11 -2/1 0/1 71/20 -1/1 103/29 0/1 32/9 1/0 25/7 0/1 68/19 1/0 43/12 1/0 18/5 -7/2 29/8 -11/5 69/19 -2/1 109/30 -41/21 40/11 -15/8 11/3 -2/1 -4/3 26/7 -1/1 15/4 -1/1 34/9 1/0 87/23 1/0 140/37 1/0 53/14 -13/1 19/5 -4/1 23/6 -3/1 27/7 -12/5 -2/1 31/8 -15/7 35/9 -2/1 4/1 -3/2 17/4 -13/9 13/3 -4/3 9/2 -1/1 23/5 -2/3 60/13 -1/2 217/47 0/1 157/34 1/1 97/21 -2/1 0/1 37/8 -1/1 51/11 -4/5 -2/3 14/3 -1/2 33/7 0/1 19/4 1/3 24/5 1/0 29/6 -1/1 34/7 1/0 73/15 -2/1 39/8 -1/1 5/1 -2/1 0/1 21/4 -7/3 37/7 -2/1 53/10 -21/11 16/3 -7/4 11/2 -1/1 28/5 -3/2 17/3 -2/1 6/1 -5/4 19/3 -1/1 32/5 -15/16 13/2 -1/1 7/1 0/1 15/2 -1/1 23/3 -4/1 -2/1 31/4 -7/3 39/5 -2/1 8/1 -3/2 9/1 -4/3 -6/5 10/1 -1/1 1/0 -1/1 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(415,194,246,115) (-1/2,-7/15) -> (5/3,27/16) Hyperbolic Matrix(249,116,-908,-423) (-7/15,-6/13) -> (-14/51,-3/11) Hyperbolic Matrix(893,410,734,337) (-6/13,-11/24) -> (17/14,28/23) Hyperbolic Matrix(647,296,-2188,-1001) (-11/24,-5/11) -> (-21/71,-13/44) Hyperbolic Matrix(1445,654,886,401) (-5/11,-14/31) -> (44/27,31/19) Hyperbolic Matrix(719,324,-1600,-721) (-14/31,-9/20) -> (-9/20,-22/49) Parabolic Matrix(4951,2222,1914,859) (-22/49,-13/29) -> (75/29,44/17) Hyperbolic Matrix(157,70,-554,-247) (-13/29,-4/9) -> (-2/7,-11/39) Hyperbolic Matrix(549,242,946,417) (-4/9,-11/25) -> (11/19,18/31) Hyperbolic Matrix(783,344,-2588,-1137) (-11/25,-18/41) -> (-10/33,-13/43) Hyperbolic Matrix(1801,790,2510,1101) (-18/41,-25/57) -> (5/7,28/39) Hyperbolic Matrix(4703,2062,1722,755) (-25/57,-7/16) -> (71/26,41/15) Hyperbolic Matrix(545,238,158,69) (-7/16,-10/23) -> (24/7,7/2) Hyperbolic Matrix(853,370,-2174,-943) (-10/23,-13/30) -> (-11/28,-20/51) Hyperbolic Matrix(79,34,230,99) (-13/30,-3/7) -> (1/3,7/20) Hyperbolic Matrix(75,32,232,99) (-3/7,-14/33) -> (6/19,1/3) Hyperbolic Matrix(1453,616,1144,485) (-14/33,-11/26) -> (33/26,14/11) Hyperbolic Matrix(607,256,-1444,-609) (-11/26,-8/19) -> (-8/19,-21/50) Parabolic Matrix(2577,1082,1822,765) (-21/50,-13/31) -> (41/29,17/12) Hyperbolic Matrix(225,94,-754,-315) (-13/31,-5/12) -> (-3/10,-11/37) Hyperbolic Matrix(829,344,976,405) (-5/12,-17/41) -> (11/13,17/20) Hyperbolic Matrix(449,186,-1726,-715) (-17/41,-12/29) -> (-6/23,-7/27) Hyperbolic Matrix(223,92,-972,-401) (-12/29,-7/17) -> (-3/13,-8/35) Hyperbolic Matrix(371,152,-1340,-549) (-7/17,-9/22) -> (-5/18,-13/47) Hyperbolic Matrix(519,212,448,183) (-9/22,-11/27) -> (15/13,7/6) Hyperbolic Matrix(521,212,-1708,-695) (-11/27,-2/5) -> (-18/59,-7/23) Hyperbolic Matrix(361,142,-1594,-627) (-2/5,-11/28) -> (-5/22,-12/53) Hyperbolic Matrix(2607,1022,-7094,-2781) (-20/51,-9/23) -> (-43/117,-18/49) Hyperbolic Matrix(215,84,796,311) (-9/23,-7/18) -> (7/26,3/11) Hyperbolic Matrix(289,112,1076,417) (-7/18,-12/31) -> (4/15,7/26) Hyperbolic Matrix(1361,526,1938,749) (-12/31,-17/44) -> (7/10,26/37) Hyperbolic Matrix(503,194,70,27) (-17/44,-5/13) -> (7/1,15/2) Hyperbolic Matrix(73,28,-644,-247) (-5/13,-18/47) -> (-2/17,-1/9) Hyperbolic Matrix(1709,654,358,137) (-18/47,-13/34) -> (19/4,24/5) Hyperbolic Matrix(283,108,-1208,-461) (-13/34,-8/21) -> (-4/17,-7/30) Hyperbolic Matrix(495,188,-1772,-673) (-8/21,-11/29) -> (-7/25,-12/43) Hyperbolic Matrix(707,268,1844,699) (-11/29,-14/37) -> (18/47,5/13) Hyperbolic Matrix(69,26,-422,-159) (-14/37,-3/8) -> (-1/6,-4/25) Hyperbolic Matrix(209,78,142,53) (-3/8,-10/27) -> (16/11,3/2) Hyperbolic Matrix(557,206,630,233) (-10/27,-17/46) -> (7/8,8/9) Hyperbolic Matrix(2095,774,766,283) (-17/46,-7/19) -> (41/15,11/4) Hyperbolic Matrix(4735,1742,2922,1075) (-7/19,-25/68) -> (81/50,47/29) Hyperbolic Matrix(10925,4016,2364,869) (-25/68,-43/117) -> (97/21,37/8) Hyperbolic Matrix(207,76,-1528,-561) (-18/49,-11/30) -> (-3/22,-2/15) Hyperbolic Matrix(137,50,-622,-227) (-11/30,-4/11) -> (-2/9,-7/32) Hyperbolic Matrix(343,124,-1928,-697) (-4/11,-13/36) -> (-5/28,-8/45) Hyperbolic Matrix(621,224,-2204,-795) (-13/36,-9/25) -> (-11/39,-9/32) Hyperbolic Matrix(345,124,-1444,-519) (-9/25,-14/39) -> (-6/25,-5/21) Hyperbolic Matrix(1717,616,616,221) (-14/39,-5/14) -> (39/14,14/5) Hyperbolic Matrix(1641,584,340,121) (-5/14,-16/45) -> (24/5,29/6) Hyperbolic Matrix(3891,1382,2182,775) (-16/45,-11/31) -> (41/23,66/37) Hyperbolic Matrix(1157,410,206,73) (-11/31,-6/17) -> (28/5,17/3) Hyperbolic Matrix(747,262,134,47) (-6/17,-7/20) -> (11/2,28/5) Hyperbolic Matrix(607,212,272,95) (-7/20,-1/3) -> (29/13,9/4) Hyperbolic Matrix(645,206,454,145) (-1/3,-6/19) -> (44/31,27/19) Hyperbolic Matrix(1093,344,448,141) (-6/19,-5/16) -> (39/16,22/9) Hyperbolic Matrix(1403,436,576,179) (-5/16,-9/29) -> (17/7,39/16) Hyperbolic Matrix(2293,710,830,257) (-9/29,-13/42) -> (11/4,47/17) Hyperbolic Matrix(317,98,1530,473) (-13/42,-4/13) -> (6/29,5/24) Hyperbolic Matrix(569,174,1586,485) (-4/13,-11/36) -> (5/14,14/39) Hyperbolic Matrix(1775,542,822,251) (-11/36,-18/59) -> (28/13,13/6) Hyperbolic Matrix(191,58,-1202,-365) (-7/23,-10/33) -> (-4/25,-3/19) Hyperbolic Matrix(503,152,-2836,-857) (-13/43,-3/10) -> (-11/62,-3/17) Hyperbolic Matrix(4633,1376,1000,297) (-11/37,-19/64) -> (37/8,51/11) Hyperbolic Matrix(2563,760,1440,427) (-19/64,-8/27) -> (16/9,57/32) Hyperbolic Matrix(311,92,-2248,-665) (-8/27,-21/71) -> (-1/7,-4/29) Hyperbolic Matrix(623,184,-3308,-977) (-13/44,-18/61) -> (-10/53,-3/16) Hyperbolic Matrix(2681,790,750,221) (-18/61,-5/17) -> (25/7,68/19) Hyperbolic Matrix(997,292,2612,765) (-5/17,-12/41) -> (8/21,21/55) Hyperbolic Matrix(1801,526,1058,309) (-12/41,-7/24) -> (17/10,46/27) Hyperbolic Matrix(433,126,622,181) (-7/24,-2/7) -> (16/23,7/10) Hyperbolic Matrix(1833,514,674,189) (-9/32,-7/25) -> (19/7,49/18) Hyperbolic Matrix(1649,460,1036,289) (-12/43,-5/18) -> (35/22,8/5) Hyperbolic Matrix(3465,958,2738,757) (-13/47,-21/76) -> (43/34,19/15) Hyperbolic Matrix(2795,772,3892,1075) (-21/76,-8/29) -> (28/39,23/32) Hyperbolic Matrix(305,84,1456,401) (-8/29,-11/40) -> (5/24,4/19) Hyperbolic Matrix(1943,534,302,83) (-11/40,-14/51) -> (32/5,13/2) Hyperbolic Matrix(59,16,424,115) (-3/11,-10/37) -> (2/15,1/7) Hyperbolic Matrix(1629,440,1144,309) (-10/37,-7/26) -> (37/26,10/7) Hyperbolic Matrix(901,242,242,65) (-7/26,-4/15) -> (26/7,15/4) Hyperbolic Matrix(659,174,178,47) (-4/15,-5/19) -> (11/3,26/7) Hyperbolic Matrix(237,62,-1250,-327) (-5/19,-6/23) -> (-4/21,-7/37) Hyperbolic Matrix(475,122,1242,319) (-7/27,-1/4) -> (13/34,31/81) Hyperbolic Matrix(815,198,638,155) (-1/4,-6/25) -> (60/47,23/18) Hyperbolic Matrix(347,82,402,95) (-5/21,-4/17) -> (6/7,13/15) Hyperbolic Matrix(2637,614,1894,441) (-7/30,-10/43) -> (32/23,39/28) Hyperbolic Matrix(517,120,56,13) (-10/43,-3/13) -> (9/1,10/1) Hyperbolic Matrix(1769,404,740,169) (-8/35,-5/22) -> (43/18,12/5) Hyperbolic Matrix(5117,1158,1878,425) (-12/53,-7/31) -> (79/29,30/11) Hyperbolic Matrix(967,218,794,179) (-7/31,-2/9) -> (28/23,11/9) Hyperbolic Matrix(1409,308,2420,529) (-7/32,-12/55) -> (32/55,7/12) Hyperbolic Matrix(3433,748,2024,441) (-12/55,-5/23) -> (39/23,56/33) Hyperbolic Matrix(167,36,-784,-169) (-5/23,-3/14) -> (-3/14,-7/33) Parabolic Matrix(1397,296,892,189) (-7/33,-4/19) -> (36/23,11/7) Hyperbolic Matrix(833,174,1058,221) (-4/19,-5/24) -> (11/14,26/33) Hyperbolic Matrix(167,34,54,11) (-5/24,-1/5) -> (3/1,19/6) Hyperbolic Matrix(763,146,162,31) (-1/5,-4/21) -> (14/3,33/7) Hyperbolic Matrix(2171,410,2494,471) (-7/37,-10/53) -> (20/23,27/31) Hyperbolic Matrix(161,30,542,101) (-3/16,-2/11) -> (8/27,3/10) Hyperbolic Matrix(1557,280,4076,733) (-2/11,-7/39) -> (21/55,34/89) Hyperbolic Matrix(1717,308,1232,221) (-7/39,-5/28) -> (39/28,7/5) Hyperbolic Matrix(7385,1312,2032,361) (-8/45,-11/62) -> (109/30,40/11) Hyperbolic Matrix(479,84,268,47) (-3/17,-1/6) -> (25/14,9/5) Hyperbolic Matrix(103,16,-676,-105) (-3/19,-2/13) -> (-2/13,-5/33) Parabolic Matrix(2693,406,1970,297) (-5/33,-3/20) -> (41/30,67/49) Hyperbolic Matrix(671,100,208,31) (-3/20,-1/7) -> (29/9,13/4) Hyperbolic Matrix(1889,260,356,49) (-4/29,-3/22) -> (53/10,16/3) Hyperbolic Matrix(303,40,356,47) (-2/15,-1/8) -> (17/20,6/7) Hyperbolic Matrix(903,110,550,67) (-1/8,-2/17) -> (64/39,23/14) Hyperbolic Matrix(147,16,248,27) (-1/9,0/1) -> (16/27,3/5) Hyperbolic Matrix(197,-24,156,-19) (0/1,1/8) -> (5/4,24/19) Hyperbolic Matrix(1207,-158,466,-61) (1/8,2/15) -> (44/17,57/22) Hyperbolic Matrix(191,-28,116,-17) (1/7,1/6) -> (23/14,5/3) Hyperbolic Matrix(187,-32,76,-13) (1/6,2/11) -> (22/9,5/2) Hyperbolic Matrix(409,-76,296,-55) (2/11,1/5) -> (29/21,18/13) Hyperbolic Matrix(1533,-316,4012,-827) (1/5,6/29) -> (34/89,47/123) Hyperbolic Matrix(217,-46,618,-131) (4/19,3/14) -> (7/20,6/17) Hyperbolic Matrix(73,-16,324,-71) (3/14,2/9) -> (2/9,5/22) Parabolic Matrix(1827,-416,1076,-245) (5/22,8/35) -> (56/33,17/10) Hyperbolic Matrix(715,-164,824,-189) (8/35,3/13) -> (13/15,20/23) Hyperbolic Matrix(107,-26,70,-17) (3/13,1/4) -> (3/2,17/11) Hyperbolic Matrix(557,-146,454,-119) (1/4,5/19) -> (11/9,27/22) Hyperbolic Matrix(1077,-286,418,-111) (5/19,4/15) -> (18/7,49/19) Hyperbolic Matrix(449,-124,344,-95) (3/11,5/18) -> (13/10,17/13) Hyperbolic Matrix(1171,-326,722,-201) (5/18,7/25) -> (47/29,13/8) Hyperbolic Matrix(585,-164,824,-231) (7/25,2/7) -> (22/31,5/7) Hyperbolic Matrix(171,-50,578,-169) (2/7,5/17) -> (5/17,8/27) Parabolic Matrix(203,-62,370,-113) (3/10,4/13) -> (6/11,11/20) Hyperbolic Matrix(873,-272,536,-167) (4/13,5/16) -> (13/8,44/27) Hyperbolic Matrix(1271,-400,1808,-569) (5/16,6/19) -> (26/37,45/64) Hyperbolic Matrix(455,-162,778,-277) (6/17,5/14) -> (7/12,24/41) Hyperbolic Matrix(2461,-884,1456,-523) (14/39,9/25) -> (49/29,22/13) Hyperbolic Matrix(2425,-874,874,-315) (9/25,13/36) -> (61/22,25/9) Hyperbolic Matrix(2651,-958,1486,-537) (13/36,4/11) -> (66/37,25/14) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(4967,-1898,1018,-389) (47/123,13/34) -> (39/8,5/1) Hyperbolic Matrix(9865,-3776,5536,-2119) (31/81,18/47) -> (98/55,41/23) Hyperbolic Matrix(127,-50,94,-37) (5/13,2/5) -> (4/3,15/11) Hyperbolic Matrix(187,-76,32,-13) (2/5,7/17) -> (17/3,6/1) Hyperbolic Matrix(343,-142,186,-77) (7/17,5/12) -> (11/6,13/7) Hyperbolic Matrix(217,-92,92,-39) (5/12,3/7) -> (7/3,19/8) Hyperbolic Matrix(245,-108,152,-67) (3/7,4/9) -> (8/5,21/13) Hyperbolic Matrix(1033,-464,728,-327) (4/9,9/20) -> (17/12,44/31) Hyperbolic Matrix(1879,-848,2608,-1177) (9/20,14/31) -> (18/25,49/68) Hyperbolic Matrix(2363,-1068,1728,-781) (14/31,5/11) -> (67/49,26/19) Hyperbolic Matrix(271,-124,212,-97) (5/11,1/2) -> (23/18,9/7) Hyperbolic Matrix(343,-186,142,-77) (1/2,6/11) -> (12/5,29/12) Hyperbolic Matrix(737,-406,1022,-563) (11/20,5/9) -> (31/43,13/18) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(3005,-1746,1086,-631) (18/31,25/43) -> (47/17,36/13) Hyperbolic Matrix(9849,-5728,3616,-2103) (25/43,32/55) -> (128/47,79/29) Hyperbolic Matrix(2663,-1560,944,-553) (24/41,17/29) -> (31/11,48/17) Hyperbolic Matrix(249,-146,278,-163) (17/29,10/17) -> (8/9,1/1) Hyperbolic Matrix(1413,-832,304,-179) (10/17,23/39) -> (51/11,14/3) Hyperbolic Matrix(3237,-1910,1910,-1127) (23/39,13/22) -> (61/36,39/23) Hyperbolic Matrix(2461,-1456,884,-523) (13/22,16/27) -> (64/23,39/14) Hyperbolic Matrix(191,-116,28,-17) (3/5,11/18) -> (13/2,7/1) Hyperbolic Matrix(709,-434,874,-535) (11/18,19/31) -> (17/21,13/16) Hyperbolic Matrix(873,-536,272,-167) (19/31,8/13) -> (16/5,29/9) Hyperbolic Matrix(245,-152,108,-67) (8/13,5/8) -> (9/4,16/7) Hyperbolic Matrix(297,-188,188,-119) (5/8,7/11) -> (11/7,19/12) Hyperbolic Matrix(1289,-824,912,-583) (7/11,16/25) -> (24/17,41/29) Hyperbolic Matrix(403,-258,214,-137) (16/25,9/14) -> (15/8,2/1) Hyperbolic Matrix(107,-70,26,-17) (9/14,2/3) -> (4/1,17/4) Hyperbolic Matrix(235,-162,338,-233) (2/3,9/13) -> (9/13,16/23) Parabolic Matrix(3617,-2544,1136,-799) (45/64,19/27) -> (35/11,51/16) Hyperbolic Matrix(1033,-728,464,-327) (19/27,12/17) -> (20/9,29/13) Hyperbolic Matrix(1289,-912,824,-583) (12/17,17/24) -> (25/16,36/23) Hyperbolic Matrix(747,-530,926,-657) (17/24,22/31) -> (4/5,21/26) Hyperbolic Matrix(1843,-1326,1458,-1049) (23/32,18/25) -> (24/19,43/34) Hyperbolic Matrix(4961,-3576,1508,-1087) (49/68,31/43) -> (23/7,79/24) Hyperbolic Matrix(409,-296,76,-55) (13/18,8/11) -> (16/3,11/2) Hyperbolic Matrix(127,-94,50,-37) (8/11,3/4) -> (5/2,18/7) Hyperbolic Matrix(449,-344,124,-95) (3/4,10/13) -> (18/5,29/8) Hyperbolic Matrix(347,-268,224,-173) (10/13,7/9) -> (17/11,14/9) Hyperbolic Matrix(271,-212,124,-97) (7/9,11/14) -> (13/6,11/5) Hyperbolic Matrix(1723,-1358,1402,-1105) (26/33,15/19) -> (43/35,16/13) Hyperbolic Matrix(197,-156,24,-19) (15/19,4/5) -> (8/1,9/1) Hyperbolic Matrix(2505,-2026,706,-571) (21/26,17/21) -> (39/11,71/20) Hyperbolic Matrix(557,-454,146,-119) (13/16,9/11) -> (19/5,23/6) Hyperbolic Matrix(121,-100,144,-119) (9/11,5/6) -> (5/6,11/13) Parabolic Matrix(5643,-4918,1222,-1065) (27/31,7/8) -> (157/34,97/21) Hyperbolic Matrix(249,-278,146,-163) (1/1,8/7) -> (46/27,29/17) Hyperbolic Matrix(941,-1084,204,-235) (8/7,15/13) -> (23/5,60/13) Hyperbolic Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(1679,-2062,434,-533) (27/22,43/35) -> (27/7,31/8) Hyperbolic Matrix(709,-874,434,-535) (16/13,5/4) -> (49/30,18/11) Hyperbolic Matrix(1047,-1328,272,-345) (19/15,33/26) -> (23/6,27/7) Hyperbolic Matrix(2147,-2738,1682,-2145) (14/11,37/29) -> (37/29,60/47) Parabolic Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(553,-724,152,-199) (17/13,4/3) -> (40/11,11/3) Hyperbolic Matrix(855,-1168,112,-153) (15/11,41/30) -> (15/2,23/3) Hyperbolic Matrix(557,-764,148,-203) (26/19,11/8) -> (15/4,34/9) Hyperbolic Matrix(481,-664,92,-127) (11/8,29/21) -> (5/1,21/4) Hyperbolic Matrix(609,-844,184,-255) (18/13,25/18) -> (33/10,10/3) Hyperbolic Matrix(203,-282,18,-25) (25/18,32/23) -> (10/1,1/0) Hyperbolic Matrix(585,-824,164,-231) (7/5,24/17) -> (32/9,25/7) Hyperbolic Matrix(1271,-1808,400,-569) (27/19,37/26) -> (19/6,35/11) Hyperbolic Matrix(235,-338,162,-233) (10/7,13/9) -> (13/9,16/11) Parabolic Matrix(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(919,-1458,578,-917) (19/12,27/17) -> (27/17,35/22) Parabolic Matrix(2017,-3262,1194,-1931) (21/13,55/34) -> (27/16,49/29) Hyperbolic Matrix(2857,-4624,1764,-2855) (55/34,34/21) -> (34/21,81/50) Parabolic Matrix(1303,-2128,368,-601) (31/19,49/30) -> (7/2,39/11) Hyperbolic Matrix(2051,-3362,1250,-2049) (18/11,41/25) -> (41/25,64/39) Parabolic Matrix(899,-1522,114,-193) (22/13,83/49) -> (39/5,8/1) Hyperbolic Matrix(2923,-4952,376,-637) (83/49,61/36) -> (31/4,39/5) Hyperbolic Matrix(455,-778,162,-277) (29/17,12/7) -> (14/5,31/11) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(6249,-11132,2420,-4311) (57/32,98/55) -> (142/55,31/12) Hyperbolic Matrix(203,-370,62,-113) (9/5,11/6) -> (13/4,23/7) Hyperbolic Matrix(523,-974,138,-257) (13/7,15/8) -> (53/14,19/5) Hyperbolic Matrix(211,-450,98,-209) (2/1,15/7) -> (15/7,28/13) Parabolic Matrix(1205,-2666,466,-1031) (11/5,31/14) -> (31/12,75/29) Hyperbolic Matrix(1081,-2396,328,-727) (31/14,20/9) -> (56/17,33/10) Hyperbolic Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(1239,-2854,346,-797) (23/10,30/13) -> (68/19,43/12) Hyperbolic Matrix(517,-1198,186,-431) (30/13,7/3) -> (25/9,64/23) Hyperbolic Matrix(807,-1922,338,-805) (19/8,31/13) -> (31/13,43/18) Parabolic Matrix(1491,-3614,578,-1401) (46/19,17/7) -> (49/19,80/31) Hyperbolic Matrix(9547,-24642,3698,-9545) (80/31,111/43) -> (111/43,142/55) Parabolic Matrix(661,-1714,86,-223) (57/22,13/5) -> (23/3,31/4) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(5011,-13644,1324,-3605) (49/18,128/47) -> (140/37,53/14) Hyperbolic Matrix(1203,-3284,248,-677) (30/11,71/26) -> (29/6,34/7) Hyperbolic Matrix(595,-1648,152,-421) (36/13,97/35) -> (35/9,4/1) Hyperbolic Matrix(1855,-5142,478,-1325) (97/35,61/22) -> (31/8,35/9) Hyperbolic Matrix(1507,-4256,472,-1333) (48/17,65/23) -> (67/21,16/5) Hyperbolic Matrix(1575,-4454,494,-1397) (65/23,17/6) -> (51/16,67/21) Hyperbolic Matrix(217,-618,46,-131) (17/6,3/1) -> (33/7,19/4) Hyperbolic Matrix(11645,-38338,2522,-8303) (79/24,135/41) -> (217/47,157/34) Hyperbolic Matrix(6149,-20252,1332,-4387) (135/41,56/17) -> (60/13,217/47) Hyperbolic Matrix(171,-578,50,-169) (10/3,17/5) -> (17/5,24/7) Parabolic Matrix(2591,-9200,532,-1889) (71/20,103/29) -> (73/15,39/8) Hyperbolic Matrix(1643,-5838,338,-1201) (103/29,32/9) -> (34/7,73/15) Hyperbolic Matrix(2623,-9522,722,-2621) (29/8,69/19) -> (69/19,109/30) Parabolic Matrix(4003,-15138,1058,-4001) (34/9,87/23) -> (87/23,140/37) Parabolic Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(519,-2738,98,-517) (21/4,37/7) -> (37/7,53/10) Parabolic Matrix(115,-722,18,-113) (6/1,19/3) -> (19/3,32/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(415,194,246,115) -> Matrix(1,0,0,1) Matrix(249,116,-908,-423) -> Matrix(1,0,0,1) Matrix(893,410,734,337) -> Matrix(3,-4,-2,3) Matrix(647,296,-2188,-1001) -> Matrix(1,-2,4,-7) Matrix(1445,654,886,401) -> Matrix(1,2,0,1) Matrix(719,324,-1600,-721) -> Matrix(7,-6,6,-5) Matrix(4951,2222,1914,859) -> Matrix(3,-4,-2,3) Matrix(157,70,-554,-247) -> Matrix(1,-2,2,-3) Matrix(549,242,946,417) -> Matrix(3,-2,-4,3) Matrix(783,344,-2588,-1137) -> Matrix(1,-2,-2,5) Matrix(1801,790,2510,1101) -> Matrix(1,2,-2,-3) Matrix(4703,2062,1722,755) -> Matrix(1,-4,0,1) Matrix(545,238,158,69) -> Matrix(1,-2,0,1) Matrix(853,370,-2174,-943) -> Matrix(1,-2,2,-3) Matrix(79,34,230,99) -> Matrix(3,-4,-2,3) Matrix(75,32,232,99) -> Matrix(1,-4,0,1) Matrix(1453,616,1144,485) -> Matrix(1,-4,0,1) Matrix(607,256,-1444,-609) -> Matrix(1,-2,0,1) Matrix(2577,1082,1822,765) -> Matrix(1,0,0,1) Matrix(225,94,-754,-315) -> Matrix(1,-2,2,-3) Matrix(829,344,976,405) -> Matrix(1,0,-2,1) Matrix(449,186,-1726,-715) -> Matrix(1,-2,2,-3) Matrix(223,92,-972,-401) -> Matrix(3,-8,2,-5) Matrix(371,152,-1340,-549) -> Matrix(1,-2,2,-3) Matrix(519,212,448,183) -> Matrix(1,-2,0,1) Matrix(521,212,-1708,-695) -> Matrix(1,-4,0,1) Matrix(361,142,-1594,-627) -> Matrix(1,2,0,1) Matrix(2607,1022,-7094,-2781) -> Matrix(1,0,-2,1) Matrix(215,84,796,311) -> Matrix(1,-4,0,1) Matrix(289,112,1076,417) -> Matrix(1,2,0,1) Matrix(1361,526,1938,749) -> Matrix(3,4,-4,-5) Matrix(503,194,70,27) -> Matrix(1,0,0,1) Matrix(73,28,-644,-247) -> Matrix(1,0,0,1) Matrix(1709,654,358,137) -> Matrix(1,2,0,1) Matrix(283,108,-1208,-461) -> Matrix(1,2,0,1) Matrix(495,188,-1772,-673) -> Matrix(1,0,-2,1) Matrix(707,268,1844,699) -> Matrix(1,0,-2,1) Matrix(69,26,-422,-159) -> Matrix(1,2,0,1) Matrix(209,78,142,53) -> Matrix(1,-2,0,1) Matrix(557,206,630,233) -> Matrix(1,2,-2,-3) Matrix(2095,774,766,283) -> Matrix(1,-2,0,1) Matrix(4735,1742,2922,1075) -> Matrix(7,8,6,7) Matrix(10925,4016,2364,869) -> Matrix(3,2,-2,-1) Matrix(207,76,-1528,-561) -> Matrix(5,2,2,1) Matrix(137,50,-622,-227) -> Matrix(1,2,0,1) Matrix(343,124,-1928,-697) -> Matrix(7,-2,4,-1) Matrix(621,224,-2204,-795) -> Matrix(3,-2,2,-1) Matrix(345,124,-1444,-519) -> Matrix(5,-4,4,-3) Matrix(1717,616,616,221) -> Matrix(1,-4,0,1) Matrix(1641,584,340,121) -> Matrix(1,-2,0,1) Matrix(3891,1382,2182,775) -> Matrix(5,-2,-2,1) Matrix(1157,410,206,73) -> Matrix(3,-4,-2,3) Matrix(747,262,134,47) -> Matrix(3,2,-2,-1) Matrix(607,212,272,95) -> Matrix(1,-2,0,1) Matrix(645,206,454,145) -> Matrix(3,-2,2,-1) Matrix(1093,344,448,141) -> Matrix(1,0,-2,1) Matrix(1403,436,576,179) -> Matrix(1,-2,0,1) Matrix(2293,710,830,257) -> Matrix(5,-2,-2,1) Matrix(317,98,1530,473) -> Matrix(1,-2,0,1) Matrix(569,174,1586,485) -> Matrix(3,-4,-2,3) Matrix(1775,542,822,251) -> Matrix(1,-10,0,1) Matrix(191,58,-1202,-365) -> Matrix(1,4,0,1) Matrix(503,152,-2836,-857) -> Matrix(9,2,4,1) Matrix(4633,1376,1000,297) -> Matrix(5,-4,-6,5) Matrix(2563,760,1440,427) -> Matrix(1,-4,0,1) Matrix(311,92,-2248,-665) -> Matrix(7,-2,4,-1) Matrix(623,184,-3308,-977) -> Matrix(3,-2,2,-1) Matrix(2681,790,750,221) -> Matrix(3,-2,2,-1) Matrix(997,292,2612,765) -> Matrix(1,0,-2,1) Matrix(1801,526,1058,309) -> Matrix(5,-4,4,-3) Matrix(433,126,622,181) -> Matrix(7,-6,-8,7) Matrix(1833,514,674,189) -> Matrix(1,-2,0,1) Matrix(1649,460,1036,289) -> Matrix(1,0,6,1) Matrix(3465,958,2738,757) -> Matrix(9,-4,-2,1) Matrix(2795,772,3892,1075) -> Matrix(15,-8,-28,15) Matrix(305,84,1456,401) -> Matrix(3,-2,-4,3) Matrix(1943,534,302,83) -> Matrix(11,-10,-12,11) Matrix(59,16,424,115) -> Matrix(1,0,-2,1) Matrix(1629,440,1144,309) -> Matrix(7,-4,2,-1) Matrix(901,242,242,65) -> Matrix(3,-2,-4,3) Matrix(659,174,178,47) -> Matrix(3,-4,-2,3) Matrix(237,62,-1250,-327) -> Matrix(1,2,0,1) Matrix(475,122,1242,319) -> Matrix(1,-2,0,1) Matrix(815,198,638,155) -> Matrix(3,-2,-4,3) Matrix(347,82,402,95) -> Matrix(1,-2,0,1) Matrix(2637,614,1894,441) -> Matrix(7,-6,6,-5) Matrix(517,120,56,13) -> Matrix(7,-8,-6,7) Matrix(1769,404,740,169) -> Matrix(11,-20,-6,11) Matrix(5117,1158,1878,425) -> Matrix(1,-6,0,1) Matrix(967,218,794,179) -> Matrix(1,-2,0,1) Matrix(1409,308,2420,529) -> Matrix(3,-8,-4,11) Matrix(3433,748,2024,441) -> Matrix(1,2,0,1) Matrix(167,36,-784,-169) -> Matrix(3,-2,2,-1) Matrix(1397,296,892,189) -> Matrix(1,-2,0,1) Matrix(833,174,1058,221) -> Matrix(3,-4,-2,3) Matrix(167,34,54,11) -> Matrix(3,-4,-2,3) Matrix(763,146,162,31) -> Matrix(1,-2,-2,5) Matrix(2171,410,2494,471) -> Matrix(1,-4,-2,9) Matrix(161,30,542,101) -> Matrix(1,-6,0,1) Matrix(1557,280,4076,733) -> Matrix(1,-2,0,1) Matrix(1717,308,1232,221) -> Matrix(3,-2,2,-1) Matrix(7385,1312,2032,361) -> Matrix(27,-52,-14,27) Matrix(479,84,268,47) -> Matrix(1,-4,0,1) Matrix(103,16,-676,-105) -> Matrix(1,-6,0,1) Matrix(2693,406,1970,297) -> Matrix(1,4,0,1) Matrix(671,100,208,31) -> Matrix(3,2,-2,-1) Matrix(1889,260,356,49) -> Matrix(15,-28,-8,15) Matrix(303,40,356,47) -> Matrix(1,-2,-2,5) Matrix(903,110,550,67) -> Matrix(1,-10,0,1) Matrix(147,16,248,27) -> Matrix(1,0,-2,1) Matrix(197,-24,156,-19) -> Matrix(1,2,0,1) Matrix(1207,-158,466,-61) -> Matrix(1,2,-2,-3) Matrix(191,-28,116,-17) -> Matrix(1,0,0,1) Matrix(187,-32,76,-13) -> Matrix(1,2,0,1) Matrix(409,-76,296,-55) -> Matrix(1,2,2,5) Matrix(1533,-316,4012,-827) -> Matrix(1,0,0,1) Matrix(217,-46,618,-131) -> Matrix(1,-2,0,1) Matrix(73,-16,324,-71) -> Matrix(1,-6,0,1) Matrix(1827,-416,1076,-245) -> Matrix(1,6,0,1) Matrix(715,-164,824,-189) -> Matrix(1,6,-2,-11) Matrix(107,-26,70,-17) -> Matrix(1,2,0,1) Matrix(557,-146,454,-119) -> Matrix(1,2,-2,-3) Matrix(1077,-286,418,-111) -> Matrix(3,2,-2,-1) Matrix(449,-124,344,-95) -> Matrix(1,2,-4,-7) Matrix(1171,-326,722,-201) -> Matrix(5,6,4,5) Matrix(585,-164,824,-231) -> Matrix(1,2,-2,-3) Matrix(171,-50,578,-169) -> Matrix(1,-4,0,1) Matrix(203,-62,370,-113) -> Matrix(1,2,0,1) Matrix(873,-272,536,-167) -> Matrix(5,12,2,5) Matrix(1271,-400,1808,-569) -> Matrix(7,12,-10,-17) Matrix(455,-162,778,-277) -> Matrix(7,12,-10,-17) Matrix(2461,-884,1456,-523) -> Matrix(5,6,4,5) Matrix(2425,-874,874,-315) -> Matrix(1,0,0,1) Matrix(2651,-958,1486,-537) -> Matrix(9,16,-4,-7) Matrix(97,-36,256,-95) -> Matrix(1,2,-2,-3) Matrix(4967,-1898,1018,-389) -> Matrix(1,0,0,1) Matrix(9865,-3776,5536,-2119) -> Matrix(17,20,-6,-7) Matrix(127,-50,94,-37) -> Matrix(1,2,0,1) Matrix(187,-76,32,-13) -> Matrix(3,2,-2,-1) Matrix(343,-142,186,-77) -> Matrix(1,2,0,1) Matrix(217,-92,92,-39) -> Matrix(5,8,-2,-3) Matrix(245,-108,152,-67) -> Matrix(1,2,0,1) Matrix(1033,-464,728,-327) -> Matrix(3,4,2,3) Matrix(1879,-848,2608,-1177) -> Matrix(5,8,-12,-19) Matrix(2363,-1068,1728,-781) -> Matrix(7,10,2,3) Matrix(271,-124,212,-97) -> Matrix(3,4,-4,-5) Matrix(343,-186,142,-77) -> Matrix(3,2,-2,-1) Matrix(737,-406,1022,-563) -> Matrix(1,0,-2,1) Matrix(113,-64,196,-111) -> Matrix(5,6,-6,-7) Matrix(3005,-1746,1086,-631) -> Matrix(33,26,-14,-11) Matrix(9849,-5728,3616,-2103) -> Matrix(37,28,-4,-3) Matrix(2663,-1560,944,-553) -> Matrix(43,28,-20,-13) Matrix(249,-146,278,-163) -> Matrix(3,2,-8,-5) Matrix(1413,-832,304,-179) -> Matrix(1,0,0,1) Matrix(3237,-1910,1910,-1127) -> Matrix(11,8,4,3) Matrix(2461,-1456,884,-523) -> Matrix(11,6,-2,-1) Matrix(191,-116,28,-17) -> Matrix(1,0,0,1) Matrix(709,-434,874,-535) -> Matrix(5,4,-4,-3) Matrix(873,-536,272,-167) -> Matrix(17,12,-10,-7) Matrix(245,-152,108,-67) -> Matrix(3,2,-2,-1) Matrix(297,-188,188,-119) -> Matrix(1,0,-2,1) Matrix(1289,-824,912,-583) -> Matrix(1,0,0,1) Matrix(403,-258,214,-137) -> Matrix(1,-2,0,1) Matrix(107,-70,26,-17) -> Matrix(3,2,-2,-1) Matrix(235,-162,338,-233) -> Matrix(7,8,-8,-9) Matrix(3617,-2544,1136,-799) -> Matrix(31,20,-14,-9) Matrix(1033,-728,464,-327) -> Matrix(7,4,-2,-1) Matrix(1289,-912,824,-583) -> Matrix(1,0,0,1) Matrix(747,-530,926,-657) -> Matrix(3,2,-2,-1) Matrix(1843,-1326,1458,-1049) -> Matrix(5,2,2,1) Matrix(4961,-3576,1508,-1087) -> Matrix(7,2,-4,-1) Matrix(409,-296,76,-55) -> Matrix(7,2,-4,-1) Matrix(127,-94,50,-37) -> Matrix(3,2,-2,-1) Matrix(449,-344,124,-95) -> Matrix(5,-2,-2,1) Matrix(347,-268,224,-173) -> Matrix(1,-2,0,1) Matrix(271,-212,124,-97) -> Matrix(1,-4,0,1) Matrix(1723,-1358,1402,-1105) -> Matrix(1,2,0,1) Matrix(197,-156,24,-19) -> Matrix(3,2,-2,-1) Matrix(2505,-2026,706,-571) -> Matrix(1,0,0,1) Matrix(557,-454,146,-119) -> Matrix(1,-2,0,1) Matrix(121,-100,144,-119) -> Matrix(1,2,-2,-3) Matrix(5643,-4918,1222,-1065) -> Matrix(1,0,2,1) Matrix(249,-278,146,-163) -> Matrix(3,-2,2,-1) Matrix(941,-1084,204,-235) -> Matrix(1,0,-2,1) Matrix(121,-144,100,-119) -> Matrix(1,-2,0,1) Matrix(1679,-2062,434,-533) -> Matrix(9,-2,-4,1) Matrix(709,-874,434,-535) -> Matrix(1,4,0,1) Matrix(1047,-1328,272,-345) -> Matrix(5,8,-2,-3) Matrix(2147,-2738,1682,-2145) -> Matrix(11,12,-12,-13) Matrix(249,-322,58,-75) -> Matrix(5,4,-4,-3) Matrix(553,-724,152,-199) -> Matrix(11,2,-6,-1) Matrix(855,-1168,112,-153) -> Matrix(1,-4,0,1) Matrix(557,-764,148,-203) -> Matrix(1,0,0,1) Matrix(481,-664,92,-127) -> Matrix(5,-2,-2,1) Matrix(609,-844,184,-255) -> Matrix(1,-2,0,1) Matrix(203,-282,18,-25) -> Matrix(1,0,-2,1) Matrix(585,-824,164,-231) -> Matrix(1,-2,0,1) Matrix(1271,-1808,400,-569) -> Matrix(5,-12,-2,5) Matrix(235,-338,162,-233) -> Matrix(1,-8,0,1) Matrix(997,-1556,412,-643) -> Matrix(5,4,-4,-3) Matrix(919,-1458,578,-917) -> Matrix(1,0,14,1) Matrix(2017,-3262,1194,-1931) -> Matrix(7,-6,6,-5) Matrix(2857,-4624,1764,-2855) -> Matrix(15,-14,14,-13) Matrix(1303,-2128,368,-601) -> Matrix(1,-4,0,1) Matrix(2051,-3362,1250,-2049) -> Matrix(1,-20,0,1) Matrix(899,-1522,114,-193) -> Matrix(7,-12,-4,7) Matrix(2923,-4952,376,-637) -> Matrix(13,-28,-6,13) Matrix(455,-778,162,-277) -> Matrix(5,-12,-2,5) Matrix(113,-196,64,-111) -> Matrix(1,-6,0,1) Matrix(6249,-11132,2420,-4311) -> Matrix(9,28,-10,-31) Matrix(203,-370,62,-113) -> Matrix(3,2,-2,-1) Matrix(523,-974,138,-257) -> Matrix(1,-6,0,1) Matrix(211,-450,98,-209) -> Matrix(1,-12,0,1) Matrix(1205,-2666,466,-1031) -> Matrix(1,4,-2,-7) Matrix(1081,-2396,328,-727) -> Matrix(5,14,-4,-11) Matrix(481,-1102,134,-307) -> Matrix(1,-4,0,1) Matrix(1239,-2854,346,-797) -> Matrix(1,10,0,1) Matrix(517,-1198,186,-431) -> Matrix(1,2,0,1) Matrix(807,-1922,338,-805) -> Matrix(19,40,-10,-21) Matrix(1491,-3614,578,-1401) -> Matrix(7,6,-6,-5) Matrix(9547,-24642,3698,-9545) -> Matrix(35,36,-36,-37) Matrix(661,-1714,86,-223) -> Matrix(1,-2,0,1) Matrix(97,-256,36,-95) -> Matrix(1,-2,0,1) Matrix(5011,-13644,1324,-3605) -> Matrix(1,-16,0,1) Matrix(1203,-3284,248,-677) -> Matrix(1,2,0,1) Matrix(595,-1648,152,-421) -> Matrix(11,24,-6,-13) Matrix(1855,-5142,478,-1325) -> Matrix(25,48,-12,-23) Matrix(1507,-4256,472,-1333) -> Matrix(39,80,-20,-41) Matrix(1575,-4454,494,-1397) -> Matrix(37,72,-18,-35) Matrix(217,-618,46,-131) -> Matrix(1,2,-2,-3) Matrix(11645,-38338,2522,-8303) -> Matrix(3,4,8,11) Matrix(6149,-20252,1332,-4387) -> Matrix(3,4,-10,-13) Matrix(171,-578,50,-169) -> Matrix(3,4,-4,-5) Matrix(2591,-9200,532,-1889) -> Matrix(3,2,-2,-1) Matrix(1643,-5838,338,-1201) -> Matrix(1,-2,0,1) Matrix(2623,-9522,722,-2621) -> Matrix(51,104,-26,-53) Matrix(4003,-15138,1058,-4001) -> Matrix(1,-36,0,1) Matrix(73,-324,16,-71) -> Matrix(5,6,-6,-7) Matrix(519,-2738,98,-517) -> Matrix(27,56,-14,-29) Matrix(115,-722,18,-113) -> Matrix(19,20,-20,-21) 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): 80 Degree of the the map X: 80 Degree of the the map Y: 240 ----------------------------------------------------------------------- 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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): 720 Minimal number of generators: 121 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: 50 Genus: 36 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 2/9 1/3 3/8 4/7 5/7 5/6 1/1 6/5 7/5 13/9 27/17 34/21 5/3 83/49 7/4 2/1 15/7 11/5 23/10 31/13 17/7 13/5 8/3 97/35 65/23 3/1 135/41 17/5 103/29 69/19 11/3 87/23 4/1 17/4 13/3 9/2 14/3 5/1 37/7 16/3 11/2 17/3 6/1 19/3 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 1/0 1/8 -3/1 1/7 0/1 1/6 -5/1 2/11 1/0 1/5 -2/1 0/1 4/19 -1/4 3/14 1/1 2/9 1/0 5/22 -5/1 8/35 1/0 3/13 -4/1 1/4 -3/1 5/19 -4/3 4/15 1/0 3/11 -4/1 -2/1 5/18 -7/5 7/25 0/1 2/7 1/0 5/17 1/0 3/10 -3/1 4/13 1/0 5/16 -11/5 1/3 -2/1 6/17 -9/4 5/14 -5/3 9/25 -2/1 0/1 13/36 -9/5 4/11 -3/2 3/8 -1/1 8/21 1/0 13/34 -1/1 5/13 -2/1 0/1 2/5 -3/2 7/17 0/1 5/12 -3/1 3/7 -2/1 -4/3 4/9 -3/2 9/20 -1/1 14/31 -3/2 5/11 -4/3 1/2 -1/1 6/11 1/0 11/20 -1/1 5/9 -2/1 0/1 4/7 -1/1 11/19 -6/7 -4/5 7/12 -1/1 24/41 -15/22 17/29 -2/3 -8/13 10/17 -1/2 23/39 -4/5 -2/3 13/22 -3/5 3/5 0/1 11/18 -1/1 19/31 -4/5 -2/3 8/13 -5/8 5/8 -1/3 7/11 0/1 2/1 16/25 1/0 9/14 -5/1 2/3 1/0 9/13 -1/1 7/10 -1/1 19/27 -2/3 -4/7 12/17 -1/2 17/24 -1/1 22/31 -1/2 5/7 -2/3 23/32 -1/2 18/25 -1/2 49/68 -3/7 31/43 -2/5 0/1 13/18 -1/3 8/11 1/0 3/4 -1/3 10/13 3/4 7/9 0/1 11/14 -3/1 15/19 -2/1 -4/3 4/5 1/0 21/26 -1/1 17/21 -2/1 0/1 13/16 -1/1 9/11 -2/1 5/6 -1/1 11/13 0/1 6/7 -1/2 7/8 -1/1 1/1 -2/1 0/1 8/7 1/0 7/6 1/1 6/5 1/0 17/14 -1/1 11/9 -2/1 27/22 -1/3 16/13 1/0 5/4 -1/1 24/19 1/0 19/15 -4/1 -2/1 14/11 -3/2 37/29 -1/1 23/18 -1/1 9/7 0/1 13/10 -3/7 17/13 -2/9 0/1 4/3 1/2 15/11 0/1 2/1 41/30 3/1 26/19 1/0 11/8 -1/1 29/21 0/1 2/5 18/13 1/2 25/18 1/1 32/23 1/1 7/5 2/1 24/17 1/0 17/12 1/1 27/19 4/3 2/1 10/7 1/0 13/9 1/0 3/2 -1/1 17/11 -2/1 14/9 -5/4 25/16 -1/1 11/7 -2/3 0/1 19/12 -1/5 27/17 0/1 8/5 1/2 21/13 0/1 2/3 55/34 1/1 34/21 1/1 47/29 6/5 13/8 5/3 31/19 2/1 4/1 49/30 3/1 18/11 1/0 41/25 1/0 23/14 -5/1 5/3 0/1 22/13 3/2 83/49 2/1 61/36 7/3 39/23 2/1 4/1 17/10 1/1 29/17 8/5 2/1 12/7 1/0 7/4 1/0 16/9 1/0 9/5 -2/1 0/1 11/6 -1/1 13/7 2/1 15/8 -7/1 2/1 1/0 15/7 1/0 13/6 -7/1 11/5 -4/1 31/14 -3/1 20/9 1/0 9/4 -3/1 16/7 1/2 23/10 1/0 30/13 1/0 7/3 -4/1 -2/1 19/8 -7/3 31/13 -2/1 12/5 -3/2 29/12 -1/1 46/19 -9/8 17/7 0/1 22/9 1/0 5/2 -3/1 18/7 -3/2 49/19 -6/5 80/31 -15/14 111/43 -1/1 31/12 -1/1 44/17 -1/2 13/5 -2/1 0/1 8/3 1/0 19/7 -4/1 -2/1 30/11 1/0 11/4 -3/1 36/13 -9/4 97/35 -2/1 61/22 -9/5 25/9 -2/1 0/1 14/5 -5/2 31/11 -20/9 -2/1 48/17 -29/14 65/23 -2/1 17/6 -9/5 3/1 -2/1 16/5 -11/6 13/4 -1/1 23/7 -2/1 -4/3 79/24 -7/5 135/41 -4/3 56/17 -5/4 33/10 -1/1 10/3 -3/2 17/5 -1/1 7/2 -1/1 39/11 -2/1 0/1 71/20 -1/1 103/29 0/1 32/9 1/0 25/7 0/1 43/12 1/0 18/5 -7/2 29/8 -11/5 69/19 -2/1 40/11 -15/8 11/3 -2/1 -4/3 15/4 -1/1 34/9 1/0 87/23 1/0 53/14 -13/1 19/5 -4/1 23/6 -3/1 4/1 -3/2 17/4 -13/9 13/3 -4/3 9/2 -1/1 23/5 -2/3 37/8 -1/1 14/3 -1/2 19/4 1/3 5/1 -2/1 0/1 21/4 -7/3 37/7 -2/1 16/3 -7/4 11/2 -1/1 17/3 -2/1 6/1 -5/4 19/3 -1/1 13/2 -1/1 7/1 0/1 8/1 -3/2 9/1 -4/3 -6/5 1/0 -1/1 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(197,-24,156,-19) (0/1,1/8) -> (5/4,24/19) Hyperbolic Matrix(194,-27,115,-16) (1/8,1/7) -> (5/3,22/13) Hyperbolic Matrix(191,-28,116,-17) (1/7,1/6) -> (23/14,5/3) Hyperbolic Matrix(187,-32,76,-13) (1/6,2/11) -> (22/9,5/2) Hyperbolic Matrix(409,-76,296,-55) (2/11,1/5) -> (29/21,18/13) Hyperbolic Matrix(654,-137,401,-84) (1/5,4/19) -> (13/8,31/19) Hyperbolic Matrix(146,-31,471,-100) (4/19,3/14) -> (4/13,5/16) Hyperbolic Matrix(73,-16,324,-71) (3/14,2/9) -> (2/9,5/22) Parabolic Matrix(2222,-507,859,-196) (5/22,8/35) -> (31/12,44/17) Hyperbolic Matrix(788,-181,357,-82) (8/35,3/13) -> (11/5,31/14) Hyperbolic Matrix(107,-26,70,-17) (3/13,1/4) -> (3/2,17/11) Hyperbolic Matrix(557,-146,454,-119) (1/4,5/19) -> (11/9,27/22) Hyperbolic Matrix(1077,-286,418,-111) (5/19,4/15) -> (18/7,49/19) Hyperbolic Matrix(242,-65,417,-112) (4/15,3/11) -> (11/19,7/12) Hyperbolic Matrix(449,-124,344,-95) (3/11,5/18) -> (13/10,17/13) Hyperbolic Matrix(1171,-326,722,-201) (5/18,7/25) -> (47/29,13/8) Hyperbolic Matrix(585,-164,824,-231) (7/25,2/7) -> (22/31,5/7) Hyperbolic Matrix(238,-69,69,-20) (2/7,5/17) -> (17/5,7/2) Hyperbolic Matrix(340,-101,101,-30) (5/17,3/10) -> (10/3,17/5) Hyperbolic Matrix(203,-62,370,-113) (3/10,4/13) -> (6/11,11/20) Hyperbolic Matrix(34,-11,99,-32) (5/16,1/3) -> (1/3,6/17) Parabolic Matrix(455,-162,778,-277) (6/17,5/14) -> (7/12,24/41) Hyperbolic Matrix(616,-221,485,-174) (5/14,9/25) -> (19/15,14/11) Hyperbolic Matrix(2425,-874,874,-315) (9/25,13/36) -> (61/22,25/9) Hyperbolic Matrix(872,-315,227,-82) (13/36,4/11) -> (23/6,4/1) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(1082,-413,765,-292) (8/21,13/34) -> (24/17,17/12) Hyperbolic Matrix(446,-171,699,-268) (13/34,5/13) -> (7/11,16/25) Hyperbolic Matrix(127,-50,94,-37) (5/13,2/5) -> (4/3,15/11) Hyperbolic Matrix(187,-76,32,-13) (2/5,7/17) -> (17/3,6/1) Hyperbolic Matrix(343,-142,186,-77) (7/17,5/12) -> (11/6,13/7) Hyperbolic Matrix(217,-92,92,-39) (5/12,3/7) -> (7/3,19/8) Hyperbolic Matrix(245,-108,152,-67) (3/7,4/9) -> (8/5,21/13) Hyperbolic Matrix(212,-95,183,-82) (4/9,9/20) -> (8/7,7/6) Hyperbolic Matrix(1879,-848,2608,-1177) (9/20,14/31) -> (18/25,49/68) Hyperbolic Matrix(1120,-507,243,-110) (14/31,5/11) -> (23/5,37/8) Hyperbolic Matrix(271,-124,212,-97) (5/11,1/2) -> (23/18,9/7) Hyperbolic Matrix(343,-186,142,-77) (1/2,6/11) -> (12/5,29/12) Hyperbolic Matrix(737,-406,1022,-563) (11/20,5/9) -> (31/43,13/18) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(2663,-1560,944,-553) (24/41,17/29) -> (31/11,48/17) Hyperbolic Matrix(526,-309,749,-440) (17/29,10/17) -> (7/10,19/27) Hyperbolic Matrix(1854,-1093,1357,-800) (10/17,23/39) -> (15/11,41/30) Hyperbolic Matrix(3237,-1910,1910,-1127) (23/39,13/22) -> (61/36,39/23) Hyperbolic Matrix(194,-115,27,-16) (13/22,3/5) -> (7/1,8/1) Hyperbolic Matrix(191,-116,28,-17) (3/5,11/18) -> (13/2,7/1) Hyperbolic Matrix(709,-434,874,-535) (11/18,19/31) -> (17/21,13/16) Hyperbolic Matrix(654,-401,137,-84) (19/31,8/13) -> (19/4,5/1) Hyperbolic Matrix(245,-152,108,-67) (8/13,5/8) -> (9/4,16/7) Hyperbolic Matrix(297,-188,188,-119) (5/8,7/11) -> (11/7,19/12) Hyperbolic Matrix(403,-258,214,-137) (16/25,9/14) -> (15/8,2/1) Hyperbolic Matrix(107,-70,26,-17) (9/14,2/3) -> (4/1,17/4) Hyperbolic Matrix(78,-53,53,-36) (2/3,9/13) -> (13/9,3/2) Hyperbolic Matrix(260,-181,181,-126) (9/13,7/10) -> (10/7,13/9) Hyperbolic Matrix(206,-145,233,-164) (19/27,12/17) -> (7/8,1/1) Hyperbolic Matrix(774,-547,283,-200) (12/17,17/24) -> (30/11,11/4) Hyperbolic Matrix(747,-530,926,-657) (17/24,22/31) -> (4/5,21/26) Hyperbolic Matrix(1742,-1251,1075,-772) (5/7,23/32) -> (34/21,47/29) Hyperbolic Matrix(2610,-1877,1613,-1160) (23/32,18/25) -> (55/34,34/21) Hyperbolic Matrix(4961,-3576,1508,-1087) (49/68,31/43) -> (23/7,79/24) Hyperbolic Matrix(409,-296,76,-55) (13/18,8/11) -> (16/3,11/2) Hyperbolic Matrix(127,-94,50,-37) (8/11,3/4) -> (5/2,18/7) Hyperbolic Matrix(449,-344,124,-95) (3/4,10/13) -> (18/5,29/8) Hyperbolic Matrix(347,-268,224,-173) (10/13,7/9) -> (17/11,14/9) Hyperbolic Matrix(271,-212,124,-97) (7/9,11/14) -> (13/6,11/5) Hyperbolic Matrix(616,-485,221,-174) (11/14,15/19) -> (25/9,14/5) Hyperbolic Matrix(197,-156,24,-19) (15/19,4/5) -> (8/1,9/1) Hyperbolic Matrix(2505,-2026,706,-571) (21/26,17/21) -> (39/11,71/20) Hyperbolic Matrix(557,-454,146,-119) (13/16,9/11) -> (19/5,23/6) Hyperbolic Matrix(121,-100,144,-119) (9/11,5/6) -> (5/6,11/13) Parabolic Matrix(262,-223,47,-40) (11/13,6/7) -> (11/2,17/3) Hyperbolic Matrix(212,-183,95,-82) (6/7,7/8) -> (20/9,9/4) Hyperbolic Matrix(206,-233,145,-164) (1/1,8/7) -> (17/12,27/19) Hyperbolic Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(436,-531,179,-218) (17/14,11/9) -> (17/7,22/9) Hyperbolic Matrix(710,-873,257,-316) (27/22,16/13) -> (11/4,36/13) Hyperbolic Matrix(709,-874,434,-535) (16/13,5/4) -> (49/30,18/11) Hyperbolic Matrix(1224,-1549,757,-958) (24/19,19/15) -> (21/13,55/34) Hyperbolic Matrix(542,-691,251,-320) (14/11,37/29) -> (15/7,13/6) Hyperbolic Matrix(328,-419,155,-198) (37/29,23/18) -> (2/1,15/7) Hyperbolic Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(553,-724,152,-199) (17/13,4/3) -> (40/11,11/3) Hyperbolic Matrix(1376,-1881,297,-406) (41/30,26/19) -> (37/8,14/3) Hyperbolic Matrix(557,-764,148,-203) (26/19,11/8) -> (15/4,34/9) Hyperbolic Matrix(481,-664,92,-127) (11/8,29/21) -> (5/1,21/4) Hyperbolic Matrix(609,-844,184,-255) (18/13,25/18) -> (33/10,10/3) Hyperbolic Matrix(1104,-1535,479,-666) (25/18,32/23) -> (23/10,30/13) Hyperbolic Matrix(790,-1101,221,-308) (32/23,7/5) -> (25/7,43/12) Hyperbolic Matrix(585,-824,164,-231) (7/5,24/17) -> (32/9,25/7) Hyperbolic Matrix(526,-749,309,-440) (27/19,10/7) -> (17/10,29/17) Hyperbolic Matrix(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(514,-805,189,-296) (25/16,11/7) -> (19/7,30/11) Hyperbolic Matrix(460,-729,289,-458) (19/12,27/17) -> (27/17,8/5) Parabolic Matrix(1303,-2128,368,-601) (31/19,49/30) -> (7/2,39/11) Hyperbolic Matrix(534,-875,83,-136) (18/11,41/25) -> (19/3,13/2) Hyperbolic Matrix(416,-683,67,-110) (41/25,23/14) -> (6/1,19/3) Hyperbolic Matrix(4068,-6889,2401,-4066) (22/13,83/49) -> (83/49,61/36) Parabolic Matrix(1142,-1937,441,-748) (39/23,17/10) -> (44/17,13/5) Hyperbolic Matrix(455,-778,162,-277) (29/17,12/7) -> (14/5,31/11) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(174,-311,47,-84) (16/9,9/5) -> (11/3,15/4) Hyperbolic Matrix(203,-370,62,-113) (9/5,11/6) -> (13/4,23/7) Hyperbolic Matrix(523,-974,138,-257) (13/7,15/8) -> (53/14,19/5) Hyperbolic Matrix(1081,-2396,328,-727) (31/14,20/9) -> (56/17,33/10) Hyperbolic Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(120,-277,13,-30) (30/13,7/3) -> (9/1,1/0) Hyperbolic Matrix(404,-961,169,-402) (19/8,31/13) -> (31/13,12/5) Parabolic Matrix(1491,-3614,578,-1401) (46/19,17/7) -> (49/19,80/31) Hyperbolic Matrix(4976,-12843,1315,-3394) (80/31,111/43) -> (87/23,53/14) Hyperbolic Matrix(2506,-6471,663,-1712) (111/43,31/12) -> (34/9,87/23) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(3396,-9409,1225,-3394) (36/13,97/35) -> (97/35,61/22) Parabolic Matrix(1496,-4225,529,-1494) (48/17,65/23) -> (65/23,17/6) Parabolic Matrix(34,-99,11,-32) (17/6,3/1) -> (3/1,16/5) Parabolic Matrix(146,-471,31,-100) (16/5,13/4) -> (14/3,19/4) Hyperbolic Matrix(5536,-18225,1681,-5534) (79/24,135/41) -> (135/41,56/17) Parabolic Matrix(2988,-10609,841,-2986) (71/20,103/29) -> (103/29,32/9) Parabolic Matrix(1312,-4761,361,-1310) (29/8,69/19) -> (69/19,40/11) Parabolic Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(260,-1369,49,-258) (21/4,37/7) -> (37/7,16/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,1,1) Matrix(197,-24,156,-19) -> Matrix(1,2,0,1) Matrix(194,-27,115,-16) -> Matrix(1,0,1,1) Matrix(191,-28,116,-17) -> Matrix(1,0,0,1) Matrix(187,-32,76,-13) -> Matrix(1,2,0,1) Matrix(409,-76,296,-55) -> Matrix(1,2,2,5) Matrix(654,-137,401,-84) -> Matrix(3,2,1,1) Matrix(146,-31,471,-100) -> Matrix(3,-2,-1,1) Matrix(73,-16,324,-71) -> Matrix(1,-6,0,1) Matrix(2222,-507,859,-196) -> Matrix(1,4,-1,-3) Matrix(788,-181,357,-82) -> Matrix(3,16,-1,-5) Matrix(107,-26,70,-17) -> Matrix(1,2,0,1) Matrix(557,-146,454,-119) -> Matrix(1,2,-2,-3) Matrix(1077,-286,418,-111) -> Matrix(3,2,-2,-1) Matrix(242,-65,417,-112) -> Matrix(1,-2,-1,3) Matrix(449,-124,344,-95) -> Matrix(1,2,-4,-7) Matrix(1171,-326,722,-201) -> Matrix(5,6,4,5) Matrix(585,-164,824,-231) -> Matrix(1,2,-2,-3) Matrix(238,-69,69,-20) -> Matrix(1,2,-1,-1) Matrix(340,-101,101,-30) -> Matrix(1,6,-1,-5) Matrix(203,-62,370,-113) -> Matrix(1,2,0,1) Matrix(34,-11,99,-32) -> Matrix(1,4,-1,-3) Matrix(455,-162,778,-277) -> Matrix(7,12,-10,-17) Matrix(616,-221,485,-174) -> Matrix(3,4,-1,-1) Matrix(2425,-874,874,-315) -> Matrix(1,0,0,1) Matrix(872,-315,227,-82) -> Matrix(7,12,-3,-5) Matrix(97,-36,256,-95) -> Matrix(1,2,-2,-3) Matrix(1082,-413,765,-292) -> Matrix(1,0,1,1) Matrix(446,-171,699,-268) -> Matrix(1,0,1,1) Matrix(127,-50,94,-37) -> Matrix(1,2,0,1) Matrix(187,-76,32,-13) -> Matrix(3,2,-2,-1) Matrix(343,-142,186,-77) -> Matrix(1,2,0,1) Matrix(217,-92,92,-39) -> Matrix(5,8,-2,-3) Matrix(245,-108,152,-67) -> Matrix(1,2,0,1) Matrix(212,-95,183,-82) -> Matrix(1,2,-1,-1) Matrix(1879,-848,2608,-1177) -> Matrix(5,8,-12,-19) Matrix(1120,-507,243,-110) -> Matrix(1,2,-3,-5) Matrix(271,-124,212,-97) -> Matrix(3,4,-4,-5) Matrix(343,-186,142,-77) -> Matrix(3,2,-2,-1) Matrix(737,-406,1022,-563) -> Matrix(1,0,-2,1) Matrix(113,-64,196,-111) -> Matrix(5,6,-6,-7) Matrix(2663,-1560,944,-553) -> Matrix(43,28,-20,-13) Matrix(526,-309,749,-440) -> Matrix(7,4,-9,-5) Matrix(1854,-1093,1357,-800) -> Matrix(5,4,1,1) Matrix(3237,-1910,1910,-1127) -> Matrix(11,8,4,3) Matrix(194,-115,27,-16) -> Matrix(1,0,1,1) Matrix(191,-116,28,-17) -> Matrix(1,0,0,1) Matrix(709,-434,874,-535) -> Matrix(5,4,-4,-3) Matrix(654,-401,137,-84) -> Matrix(3,2,1,1) Matrix(245,-152,108,-67) -> Matrix(3,2,-2,-1) Matrix(297,-188,188,-119) -> Matrix(1,0,-2,1) Matrix(403,-258,214,-137) -> Matrix(1,-2,0,1) Matrix(107,-70,26,-17) -> Matrix(3,2,-2,-1) Matrix(78,-53,53,-36) -> Matrix(1,2,-1,-1) Matrix(260,-181,181,-126) -> Matrix(7,6,1,1) Matrix(206,-145,233,-164) -> Matrix(3,2,-5,-3) Matrix(774,-547,283,-200) -> Matrix(1,2,-1,-1) Matrix(747,-530,926,-657) -> Matrix(3,2,-2,-1) Matrix(1742,-1251,1075,-772) -> Matrix(15,8,13,7) Matrix(2610,-1877,1613,-1160) -> Matrix(13,6,15,7) Matrix(4961,-3576,1508,-1087) -> Matrix(7,2,-4,-1) Matrix(409,-296,76,-55) -> Matrix(7,2,-4,-1) Matrix(127,-94,50,-37) -> Matrix(3,2,-2,-1) Matrix(449,-344,124,-95) -> Matrix(5,-2,-2,1) Matrix(347,-268,224,-173) -> Matrix(1,-2,0,1) Matrix(271,-212,124,-97) -> Matrix(1,-4,0,1) Matrix(616,-485,221,-174) -> Matrix(3,4,-1,-1) Matrix(197,-156,24,-19) -> Matrix(3,2,-2,-1) Matrix(2505,-2026,706,-571) -> Matrix(1,0,0,1) Matrix(557,-454,146,-119) -> Matrix(1,-2,0,1) Matrix(121,-100,144,-119) -> Matrix(1,2,-2,-3) Matrix(262,-223,47,-40) -> Matrix(5,2,-3,-1) Matrix(212,-183,95,-82) -> Matrix(1,2,-1,-1) Matrix(206,-233,145,-164) -> Matrix(1,-2,1,-1) Matrix(121,-144,100,-119) -> Matrix(1,-2,0,1) Matrix(436,-531,179,-218) -> Matrix(1,2,-1,-1) Matrix(710,-873,257,-316) -> Matrix(3,-2,-1,1) Matrix(709,-874,434,-535) -> Matrix(1,4,0,1) Matrix(1224,-1549,757,-958) -> Matrix(1,4,1,5) Matrix(542,-691,251,-320) -> Matrix(9,10,-1,-1) Matrix(328,-419,155,-198) -> Matrix(3,2,1,1) Matrix(249,-322,58,-75) -> Matrix(5,4,-4,-3) Matrix(553,-724,152,-199) -> Matrix(11,2,-6,-1) Matrix(1376,-1881,297,-406) -> Matrix(1,-4,-1,5) Matrix(557,-764,148,-203) -> Matrix(1,0,0,1) Matrix(481,-664,92,-127) -> Matrix(5,-2,-2,1) Matrix(609,-844,184,-255) -> Matrix(1,-2,0,1) Matrix(1104,-1535,479,-666) -> Matrix(9,-8,-1,1) Matrix(790,-1101,221,-308) -> Matrix(1,-2,1,-1) Matrix(585,-824,164,-231) -> Matrix(1,-2,0,1) Matrix(526,-749,309,-440) -> Matrix(1,-4,1,-3) Matrix(997,-1556,412,-643) -> Matrix(5,4,-4,-3) Matrix(514,-805,189,-296) -> Matrix(1,2,-1,-1) Matrix(460,-729,289,-458) -> Matrix(1,0,7,1) Matrix(1303,-2128,368,-601) -> Matrix(1,-4,0,1) Matrix(534,-875,83,-136) -> Matrix(1,-10,-1,11) Matrix(416,-683,67,-110) -> Matrix(1,10,-1,-9) Matrix(4068,-6889,2401,-4066) -> Matrix(11,-20,5,-9) Matrix(1142,-1937,441,-748) -> Matrix(1,-2,-1,3) Matrix(455,-778,162,-277) -> Matrix(5,-12,-2,5) Matrix(113,-196,64,-111) -> Matrix(1,-6,0,1) Matrix(174,-311,47,-84) -> Matrix(1,4,-1,-3) Matrix(203,-370,62,-113) -> Matrix(3,2,-2,-1) Matrix(523,-974,138,-257) -> Matrix(1,-6,0,1) Matrix(1081,-2396,328,-727) -> Matrix(5,14,-4,-11) Matrix(481,-1102,134,-307) -> Matrix(1,-4,0,1) Matrix(120,-277,13,-30) -> Matrix(1,8,-1,-7) Matrix(404,-961,169,-402) -> Matrix(9,20,-5,-11) Matrix(1491,-3614,578,-1401) -> Matrix(7,6,-6,-5) Matrix(4976,-12843,1315,-3394) -> Matrix(27,28,-1,-1) Matrix(2506,-6471,663,-1712) -> Matrix(9,8,1,1) Matrix(97,-256,36,-95) -> Matrix(1,-2,0,1) Matrix(3396,-9409,1225,-3394) -> Matrix(17,36,-9,-19) Matrix(1496,-4225,529,-1494) -> Matrix(37,76,-19,-39) Matrix(34,-99,11,-32) -> Matrix(1,4,-1,-3) Matrix(146,-471,31,-100) -> Matrix(1,2,-3,-5) Matrix(5536,-18225,1681,-5534) -> Matrix(35,48,-27,-37) Matrix(2988,-10609,841,-2986) -> Matrix(1,0,1,1) Matrix(1312,-4761,361,-1310) -> Matrix(25,52,-13,-27) Matrix(73,-324,16,-71) -> Matrix(5,6,-6,-7) Matrix(260,-1369,49,-258) -> Matrix(13,28,-7,-15) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 80 ----------------------------------------------------------------------- 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 1 1 1/1 (-2/1,0/1) 0 11 8/7 1/0 1 22 7/6 1/1 1 22 6/5 1/0 1 2 17/14 -1/1 1 22 11/9 -2/1 1 11 16/13 1/0 1 22 5/4 -1/1 1 22 19/15 (-4/1,-2/1) 0 11 14/11 -3/2 1 22 9/7 0/1 1 11 13/10 -3/7 1 22 4/3 1/2 1 22 11/8 -1/1 1 22 18/13 1/2 1 22 25/18 1/1 1 22 32/23 1/1 7 2 7/5 2/1 1 11 24/17 1/0 1 22 17/12 1/1 1 22 27/19 (4/3,2/1) 0 11 10/7 1/0 1 22 13/9 1/0 4 1 3/2 -1/1 1 22 14/9 -5/4 1 22 25/16 -1/1 1 22 11/7 (-2/3,0/1) 0 11 27/17 0/1 7 1 8/5 1/2 1 22 13/8 5/3 1 22 31/19 (2/1,4/1) 0 11 49/30 3/1 1 22 18/11 1/0 1 22 5/3 0/1 1 11 22/13 3/2 1 22 83/49 2/1 5 1 39/23 (2/1,4/1) 0 11 17/10 1/1 1 22 29/17 (8/5,2/1) 0 11 12/7 1/0 1 22 7/4 1/0 3 2 16/9 1/0 1 22 9/5 (-2/1,0/1) 0 11 11/6 -1/1 1 22 2/1 1/0 1 22 15/7 1/0 6 1 13/6 -7/1 1 22 11/5 -4/1 1 11 31/14 -3/1 1 22 20/9 1/0 1 22 9/4 -3/1 1 22 16/7 1/2 1 22 23/10 1/0 7 2 30/13 1/0 1 22 7/3 (-4/1,-2/1) 0 11 31/13 -2/1 5 1 12/5 -3/2 1 22 29/12 -1/1 1 22 46/19 -9/8 1 22 17/7 0/1 1 11 5/2 -3/1 1 22 18/7 -3/2 1 22 31/12 -1/1 1 22 44/17 -1/2 1 22 13/5 (-2/1,0/1) 0 11 8/3 1/0 1 2 19/7 (-4/1,-2/1) 0 11 30/11 1/0 1 22 11/4 -3/1 1 22 36/13 -9/4 1 22 97/35 -2/1 9 1 25/9 (-2/1,0/1) 0 11 14/5 -5/2 1 22 31/11 (-20/9,-2/1) 0 11 65/23 -2/1 19 1 17/6 -9/5 1 22 3/1 -2/1 1 11 16/5 -11/6 1 22 13/4 -1/1 1 22 23/7 (-2/1,-4/3) 0 11 135/41 -4/3 3 1 56/17 -5/4 1 22 33/10 -1/1 1 22 10/3 -3/2 1 22 17/5 -1/1 2 1 7/2 -1/1 1 22 39/11 (-2/1,0/1) 0 11 103/29 0/1 1 1 32/9 1/0 1 22 25/7 0/1 1 11 43/12 1/0 7 2 18/5 -7/2 1 22 29/8 -11/5 1 22 69/19 -2/1 13 1 11/3 (-2/1,-4/3) 0 11 15/4 -1/1 1 22 34/9 1/0 1 22 87/23 1/0 18 1 53/14 -13/1 1 22 19/5 -4/1 1 11 23/6 -3/1 1 22 4/1 -3/2 1 22 17/4 -13/9 1 22 13/3 -4/3 1 11 9/2 -1/1 3 2 23/5 -2/3 1 11 37/8 -1/1 1 22 14/3 -1/2 1 22 19/4 1/3 1 22 5/1 (-2/1,0/1) 0 11 37/7 -2/1 7 1 16/3 -7/4 1 22 11/2 -1/1 1 22 17/3 -2/1 1 11 6/1 -5/4 1 22 19/3 -1/1 10 1 13/2 -1/1 1 22 7/1 0/1 1 11 8/1 -3/2 1 22 9/1 (-4/3,-6/5) 0 11 1/0 -1/1 1 22 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(206,-233,145,-164) (1/1,8/7) -> (17/12,27/19) Hyperbolic Matrix(183,-212,82,-95) (8/7,7/6) -> (20/9,9/4) Glide Reflection Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(337,-410,60,-73) (17/14,11/9) -> (11/2,17/3) Glide Reflection Matrix(454,-557,119,-146) (11/9,16/13) -> (19/5,23/6) Glide Reflection Matrix(709,-874,434,-535) (16/13,5/4) -> (49/30,18/11) Hyperbolic Matrix(156,-197,19,-24) (5/4,19/15) -> (8/1,9/1) Glide Reflection Matrix(485,-616,174,-221) (19/15,14/11) -> (25/9,14/5) Glide Reflection Matrix(212,-271,97,-124) (14/11,9/7) -> (13/6,11/5) Glide Reflection Matrix(249,-322,58,-75) (9/7,13/10) -> (17/4,13/3) Hyperbolic Matrix(344,-449,95,-124) (13/10,4/3) -> (18/5,29/8) Glide Reflection Matrix(94,-127,37,-50) (4/3,11/8) -> (5/2,18/7) Glide Reflection Matrix(296,-409,55,-76) (11/8,18/13) -> (16/3,11/2) Glide Reflection Matrix(609,-844,184,-255) (18/13,25/18) -> (33/10,10/3) Hyperbolic Matrix(1104,-1535,479,-666) (25/18,32/23) -> (23/10,30/13) Hyperbolic Matrix(790,-1101,221,-308) (32/23,7/5) -> (25/7,43/12) Hyperbolic Matrix(585,-824,164,-231) (7/5,24/17) -> (32/9,25/7) Hyperbolic Matrix(547,-774,200,-283) (24/17,17/12) -> (30/11,11/4) Glide Reflection Matrix(526,-749,309,-440) (27/19,10/7) -> (17/10,29/17) Hyperbolic Matrix(181,-260,126,-181) (10/7,13/9) -> (10/7,13/9) Reflection Matrix(53,-78,36,-53) (13/9,3/2) -> (13/9,3/2) Reflection Matrix(70,-107,17,-26) (3/2,14/9) -> (4/1,17/4) Glide Reflection Matrix(997,-1556,412,-643) (14/9,25/16) -> (29/12,46/19) Hyperbolic Matrix(514,-805,189,-296) (25/16,11/7) -> (19/7,30/11) Hyperbolic Matrix(188,-297,119,-188) (11/7,27/17) -> (11/7,27/17) Reflection Matrix(271,-432,170,-271) (27/17,8/5) -> (27/17,8/5) Reflection Matrix(152,-245,67,-108) (8/5,13/8) -> (9/4,16/7) Glide Reflection Matrix(401,-654,84,-137) (13/8,31/19) -> (19/4,5/1) Glide Reflection Matrix(1303,-2128,368,-601) (31/19,49/30) -> (7/2,39/11) Hyperbolic Matrix(116,-191,17,-28) (18/11,5/3) -> (13/2,7/1) Glide Reflection Matrix(115,-194,16,-27) (5/3,22/13) -> (7/1,8/1) Glide Reflection Matrix(2157,-3652,1274,-2157) (22/13,83/49) -> (22/13,83/49) Reflection Matrix(1910,-3237,1127,-1910) (83/49,39/23) -> (83/49,39/23) Reflection Matrix(1142,-1937,441,-748) (39/23,17/10) -> (44/17,13/5) Hyperbolic Matrix(455,-778,162,-277) (29/17,12/7) -> (14/5,31/11) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(174,-311,47,-84) (16/9,9/5) -> (11/3,15/4) Hyperbolic Matrix(203,-370,62,-113) (9/5,11/6) -> (13/4,23/7) Hyperbolic Matrix(186,-343,77,-142) (11/6,2/1) -> (12/5,29/12) Glide Reflection Matrix(29,-60,14,-29) (2/1,15/7) -> (2/1,15/7) Reflection Matrix(181,-390,84,-181) (15/7,13/6) -> (15/7,13/6) Reflection Matrix(507,-1120,110,-243) (11/5,31/14) -> (23/5,37/8) Glide Reflection Matrix(1081,-2396,328,-727) (31/14,20/9) -> (56/17,33/10) Hyperbolic Matrix(481,-1102,134,-307) (16/7,23/10) -> (43/12,18/5) Hyperbolic Matrix(120,-277,13,-30) (30/13,7/3) -> (9/1,1/0) Hyperbolic Matrix(92,-217,39,-92) (7/3,31/13) -> (7/3,31/13) Reflection Matrix(311,-744,130,-311) (31/13,12/5) -> (31/13,12/5) Reflection Matrix(732,-1775,193,-468) (46/19,17/7) -> (53/14,19/5) Glide Reflection Matrix(76,-187,13,-32) (17/7,5/2) -> (17/3,6/1) Glide Reflection Matrix(418,-1077,111,-286) (18/7,31/12) -> (15/4,34/9) Glide Reflection Matrix(797,-2062,172,-445) (31/12,44/17) -> (37/8,14/3) Glide Reflection Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(315,-872,82,-227) (11/4,36/13) -> (23/6,4/1) Glide Reflection Matrix(2521,-6984,910,-2521) (36/13,97/35) -> (36/13,97/35) Reflection Matrix(874,-2425,315,-874) (97/35,25/9) -> (97/35,25/9) Reflection Matrix(714,-2015,253,-714) (31/11,65/23) -> (31/11,65/23) Reflection Matrix(781,-2210,276,-781) (65/23,17/6) -> (65/23,17/6) Reflection Matrix(34,-99,11,-32) (17/6,3/1) -> (3/1,16/5) Parabolic Matrix(146,-471,31,-100) (16/5,13/4) -> (14/3,19/4) Hyperbolic Matrix(944,-3105,287,-944) (23/7,135/41) -> (23/7,135/41) Reflection Matrix(4591,-15120,1394,-4591) (135/41,56/17) -> (135/41,56/17) Reflection Matrix(101,-340,30,-101) (10/3,17/5) -> (10/3,17/5) Reflection Matrix(69,-238,20,-69) (17/5,7/2) -> (17/5,7/2) Reflection Matrix(1132,-4017,319,-1132) (39/11,103/29) -> (39/11,103/29) Reflection Matrix(1855,-6592,522,-1855) (103/29,32/9) -> (103/29,32/9) Reflection Matrix(1103,-4002,304,-1103) (29/8,69/19) -> (29/8,69/19) Reflection Matrix(208,-759,57,-208) (69/19,11/3) -> (69/19,11/3) Reflection Matrix(1565,-5916,414,-1565) (34/9,87/23) -> (34/9,87/23) Reflection Matrix(2437,-9222,644,-2437) (87/23,53/14) -> (87/23,53/14) Reflection Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(36,-185,7,-36) (5/1,37/7) -> (5/1,37/7) Reflection Matrix(223,-1184,42,-223) (37/7,16/3) -> (37/7,16/3) Reflection Matrix(37,-228,6,-37) (6/1,19/3) -> (6/1,19/3) Reflection Matrix(77,-494,12,-77) (19/3,13/2) -> (19/3,13/2) 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(-1,0,1,1) (-1/1,1/1) -> (-2/1,0/1) Matrix(206,-233,145,-164) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(183,-212,82,-95) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(121,-144,100,-119) -> Matrix(1,-2,0,1) 1/0 Matrix(337,-410,60,-73) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(454,-557,119,-146) -> Matrix(3,2,-1,-1) Matrix(709,-874,434,-535) -> Matrix(1,4,0,1) 1/0 Matrix(156,-197,19,-24) -> Matrix(1,-2,-1,1) Matrix(485,-616,174,-221) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(212,-271,97,-124) -> Matrix(5,4,-1,-1) Matrix(249,-322,58,-75) -> Matrix(5,4,-4,-3) -1/1 Matrix(344,-449,95,-124) -> Matrix(7,2,-3,-1) Matrix(94,-127,37,-50) -> Matrix(1,-2,-1,1) Matrix(296,-409,55,-76) -> Matrix(5,-2,-3,1) Matrix(609,-844,184,-255) -> Matrix(1,-2,0,1) 1/0 Matrix(1104,-1535,479,-666) -> Matrix(9,-8,-1,1) Matrix(790,-1101,221,-308) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(585,-824,164,-231) -> Matrix(1,-2,0,1) 1/0 Matrix(547,-774,200,-283) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(526,-749,309,-440) -> Matrix(1,-4,1,-3) 2/1 Matrix(181,-260,126,-181) -> Matrix(-1,6,0,1) (10/7,13/9) -> (3/1,1/0) Matrix(53,-78,36,-53) -> Matrix(1,2,0,-1) (13/9,3/2) -> (-1/1,1/0) Matrix(70,-107,17,-26) -> Matrix(1,-2,-1,1) Matrix(997,-1556,412,-643) -> Matrix(5,4,-4,-3) -1/1 Matrix(514,-805,189,-296) -> Matrix(1,2,-1,-1) (-2/1,0/1).(-1/1,1/0) Matrix(188,-297,119,-188) -> Matrix(-1,0,3,1) (11/7,27/17) -> (-2/3,0/1) Matrix(271,-432,170,-271) -> Matrix(1,0,4,-1) (27/17,8/5) -> (0/1,1/2) Matrix(152,-245,67,-108) -> Matrix(1,-2,-1,1) Matrix(401,-654,84,-137) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1303,-2128,368,-601) -> Matrix(1,-4,0,1) 1/0 Matrix(116,-191,17,-28) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(115,-194,16,-27) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2157,-3652,1274,-2157) -> Matrix(7,-12,4,-7) (22/13,83/49) -> (3/2,2/1) Matrix(1910,-3237,1127,-1910) -> Matrix(3,-8,1,-3) (83/49,39/23) -> (2/1,4/1) Matrix(1142,-1937,441,-748) -> Matrix(1,-2,-1,3) Matrix(455,-778,162,-277) -> Matrix(5,-12,-2,5) Matrix(113,-196,64,-111) -> Matrix(1,-6,0,1) 1/0 Matrix(174,-311,47,-84) -> Matrix(1,4,-1,-3) -2/1 Matrix(203,-370,62,-113) -> Matrix(3,2,-2,-1) -1/1 Matrix(186,-343,77,-142) -> Matrix(1,-2,-1,1) Matrix(29,-60,14,-29) -> Matrix(1,2,0,-1) (2/1,15/7) -> (-1/1,1/0) Matrix(181,-390,84,-181) -> Matrix(1,14,0,-1) (15/7,13/6) -> (-7/1,1/0) Matrix(507,-1120,110,-243) -> Matrix(1,2,-2,-5) Matrix(1081,-2396,328,-727) -> Matrix(5,14,-4,-11) Matrix(481,-1102,134,-307) -> Matrix(1,-4,0,1) 1/0 Matrix(120,-277,13,-30) -> Matrix(1,8,-1,-7) Matrix(92,-217,39,-92) -> Matrix(3,8,-1,-3) (7/3,31/13) -> (-4/1,-2/1) Matrix(311,-744,130,-311) -> Matrix(7,12,-4,-7) (31/13,12/5) -> (-2/1,-3/2) Matrix(732,-1775,193,-468) -> Matrix(5,4,-1,-1) Matrix(76,-187,13,-32) -> Matrix(1,-2,-1,1) Matrix(418,-1077,111,-286) -> Matrix(1,2,1,1) Matrix(797,-2062,172,-445) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(97,-256,36,-95) -> Matrix(1,-2,0,1) 1/0 Matrix(315,-872,82,-227) -> Matrix(5,12,-2,-5) *** -> (-3/1,-2/1) Matrix(2521,-6984,910,-2521) -> Matrix(17,36,-8,-17) (36/13,97/35) -> (-9/4,-2/1) Matrix(874,-2425,315,-874) -> Matrix(-1,0,1,1) (97/35,25/9) -> (-2/1,0/1) Matrix(714,-2015,253,-714) -> Matrix(19,40,-9,-19) (31/11,65/23) -> (-20/9,-2/1) Matrix(781,-2210,276,-781) -> Matrix(19,36,-10,-19) (65/23,17/6) -> (-2/1,-9/5) Matrix(34,-99,11,-32) -> Matrix(1,4,-1,-3) -2/1 Matrix(146,-471,31,-100) -> Matrix(1,2,-3,-5) Matrix(944,-3105,287,-944) -> Matrix(5,8,-3,-5) (23/7,135/41) -> (-2/1,-4/3) Matrix(4591,-15120,1394,-4591) -> Matrix(31,40,-24,-31) (135/41,56/17) -> (-4/3,-5/4) Matrix(101,-340,30,-101) -> Matrix(5,6,-4,-5) (10/3,17/5) -> (-3/2,-1/1) Matrix(69,-238,20,-69) -> Matrix(1,2,0,-1) (17/5,7/2) -> (-1/1,1/0) Matrix(1132,-4017,319,-1132) -> Matrix(-1,0,1,1) (39/11,103/29) -> (-2/1,0/1) Matrix(1855,-6592,522,-1855) -> Matrix(1,0,0,-1) (103/29,32/9) -> (0/1,1/0) Matrix(1103,-4002,304,-1103) -> Matrix(21,44,-10,-21) (29/8,69/19) -> (-11/5,-2/1) Matrix(208,-759,57,-208) -> Matrix(5,8,-3,-5) (69/19,11/3) -> (-2/1,-4/3) Matrix(1565,-5916,414,-1565) -> Matrix(-1,10,0,1) (34/9,87/23) -> (5/1,1/0) Matrix(2437,-9222,644,-2437) -> Matrix(1,26,0,-1) (87/23,53/14) -> (-13/1,1/0) Matrix(73,-324,16,-71) -> Matrix(5,6,-6,-7) -1/1 Matrix(36,-185,7,-36) -> Matrix(-1,0,1,1) (5/1,37/7) -> (-2/1,0/1) Matrix(223,-1184,42,-223) -> Matrix(15,28,-8,-15) (37/7,16/3) -> (-2/1,-7/4) Matrix(37,-228,6,-37) -> Matrix(9,10,-8,-9) (6/1,19/3) -> (-5/4,-1/1) Matrix(77,-494,12,-77) -> Matrix(11,10,-12,-11) (19/3,13/2) -> (-1/1,-5/6) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.