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): 1536 Minimal number of generators: 257 Number of equivalence classes of cusps: 72 Genus: 93 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -7/15 -3/7 -5/13 -1/3 -1/5 0/1 1/7 3/13 7/25 1/3 9/23 5/11 1/2 7/13 3/5 5/7 7/9 1/1 9/7 37/27 19/13 3/2 49/31 5/3 9/5 31/17 2/1 11/5 7/3 45/19 17/7 5/2 23/9 117/43 47/17 3/1 49/15 10/3 99/29 7/2 25/7 11/3 19/5 127/33 4/1 21/5 13/3 9/2 14/3 19/4 53/11 5/1 21/4 27/5 11/2 17/3 23/4 6/1 25/4 13/2 27/4 7/1 15/2 8/1 17/2 9/1 19/2 29/3 10/1 11/1 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 1/4 -7/15 1/4 -13/28 1/3 1/2 -6/13 1/6 -11/24 0/1 1/0 -16/35 1/10 -21/46 1/8 1/7 -5/11 1/4 -9/20 1/5 1/4 -4/9 1/2 -11/25 1/0 -18/41 -1/6 -7/16 0/1 1/8 -17/39 1/4 -10/23 1/6 -13/30 0/1 1/6 -3/7 1/4 -14/33 1/2 -11/26 1/3 1/2 -30/71 1/2 -19/45 3/8 -8/19 1/2 -13/31 1/0 -18/43 -1/10 -5/12 0/1 1/8 -12/29 1/6 -19/46 5/26 1/5 -7/17 1/4 -9/22 2/9 1/4 -2/5 1/2 -7/18 1/5 1/4 -12/31 3/14 -17/44 5/22 3/13 -5/13 1/4 -23/60 7/26 3/11 -18/47 7/26 -13/34 1/4 2/7 -21/55 1/4 -29/76 2/7 3/10 -8/21 3/10 -3/8 0/1 1/2 -16/43 1/14 -13/35 1/8 -23/62 1/7 3/20 -10/27 1/6 -17/46 0/1 1/2 -7/19 1/6 -25/68 0/1 1/4 -18/49 1/6 -11/30 3/16 1/5 -15/41 1/4 -4/11 3/14 -5/14 1/4 2/7 -21/59 5/16 -16/45 5/14 -11/31 1/4 -6/17 1/2 -1/3 1/4 -7/22 1/3 1/2 -6/19 1/2 -5/16 1/4 1/3 -9/29 1/2 -13/42 -1/2 0/1 -4/13 1/6 -3/10 1/4 2/7 -8/27 1/2 -5/17 1/4 -7/24 3/10 4/13 -2/7 1/2 -7/25 3/8 -19/68 5/11 1/2 -12/43 1/2 -5/18 0/1 1/4 -13/47 1/4 -8/29 1/2 -3/11 1/4 -7/26 1/4 1/3 -11/41 1/4 -4/15 3/10 -5/19 1/4 -6/23 3/10 -1/4 1/3 1/2 -4/17 1/2 -7/30 1/3 3/8 -10/43 1/2 -13/56 0/1 1/0 -3/13 1/4 -11/48 7/22 1/3 -8/35 5/14 -5/22 0/1 1/2 -7/31 1/4 -2/9 3/10 -3/14 1/3 3/8 -7/33 3/8 -4/19 1/2 -13/62 1/3 5/14 -9/43 3/8 -5/24 1/3 3/8 -6/29 7/18 -1/5 1/2 -5/26 0/1 1/4 -4/21 1/2 -11/58 0/1 1/6 -7/37 1/4 -3/16 0/1 1/4 -5/27 1/4 -7/38 1/4 1/3 -2/11 3/10 -1/6 2/5 1/2 -2/13 1/2 -3/20 0/1 1/2 -1/7 1/4 -3/22 5/16 1/3 -2/15 5/14 -1/8 3/8 2/5 0/1 1/2 1/9 1/0 1/8 0/1 1/4 2/15 1/2 3/22 3/7 7/16 1/7 1/2 2/13 1/2 1/6 2/3 3/4 1/5 1/0 4/19 1/2 3/14 0/1 1/2 2/9 1/2 7/31 7/16 12/53 1/2 5/22 5/11 1/2 3/13 1/2 4/17 1/2 1/4 1/2 2/3 4/15 5/6 3/11 3/4 8/29 5/6 5/18 11/12 1/1 7/25 1/1 2/7 3/2 3/10 0/1 1/0 4/13 1/2 9/29 1/0 5/16 0/1 1/0 1/3 1/2 6/17 7/10 11/31 3/4 5/14 3/4 1/1 4/11 1/2 3/8 3/4 1/1 8/21 11/14 5/13 7/8 12/31 9/10 7/18 15/16 1/1 9/23 1/1 2/5 3/2 11/27 1/0 9/22 1/1 1/0 7/17 1/0 19/46 0/1 1/0 31/75 1/0 12/29 1/2 29/70 -1/6 0/1 17/41 1/4 5/12 0/1 1/2 3/7 1/0 10/23 1/2 7/16 3/4 1/1 4/9 1/2 13/29 1/0 9/20 0/1 1/2 5/11 1/2 6/13 1/2 1/2 1/2 1/1 10/19 19/18 9/17 9/8 8/15 7/6 7/13 3/2 13/24 1/2 1/1 6/11 3/2 5/9 1/0 9/16 1/1 9/8 22/39 3/2 13/23 5/4 17/30 4/3 3/2 4/7 3/2 15/26 3/1 1/0 11/19 1/0 18/31 3/2 7/12 1/1 1/0 17/29 7/4 10/17 3/2 3/5 1/0 14/23 -1/2 25/41 1/0 36/59 -1/2 11/18 -1/2 0/1 30/49 1/2 19/31 1/0 8/13 1/2 5/8 0/1 1/0 22/35 1/6 17/27 1/2 29/46 1/4 1/3 41/65 3/8 12/19 1/2 31/49 1/2 19/30 1/2 5/9 7/11 3/4 9/14 1/1 5/4 20/31 3/2 11/17 1/0 24/37 1/2 13/20 1/1 1/0 2/3 1/2 9/13 5/4 7/10 4/3 3/2 19/27 13/8 12/17 11/6 17/24 3/1 1/0 22/31 3/2 27/38 2/1 1/0 5/7 1/0 13/18 1/1 1/0 34/47 1/2 21/29 1/0 8/11 1/2 11/15 5/4 3/4 2/1 1/0 10/13 9/2 7/9 1/0 18/23 -11/2 11/14 -3/1 1/0 37/47 1/0 26/33 -3/2 15/19 1/0 19/24 -2/1 1/0 23/29 -3/2 4/5 -1/2 9/11 1/2 14/17 1/2 5/6 1/1 1/0 1/1 1/0 8/7 1/2 7/6 0/1 1/0 6/5 1/2 17/14 1/1 1/0 11/9 1/0 27/22 1/3 1/2 16/13 5/6 21/17 5/4 26/21 3/2 5/4 2/1 1/0 14/11 11/2 9/7 1/0 22/17 -17/2 35/27 1/0 13/10 -5/1 1/0 30/23 -7/2 17/13 1/0 55/42 -3/1 1/0 38/29 -7/2 21/16 -7/2 -3/1 25/19 -5/2 4/3 -3/2 23/17 1/0 19/14 -1/1 1/0 34/25 -1/2 15/11 1/0 26/19 -7/6 37/27 -1/1 48/35 -13/14 11/8 -1/1 -3/4 18/13 -1/2 43/31 -1/4 111/80 -1/4 0/1 68/49 -1/6 93/67 0/1 25/18 0/1 1/0 7/5 -1/2 24/17 -1/6 41/29 -1/8 17/12 0/1 1/2 10/7 -1/2 33/23 -1/2 23/16 -3/8 -1/3 36/25 -3/10 13/9 -1/4 29/20 -1/5 -1/6 45/31 -1/8 16/11 -1/10 19/13 0/1 22/15 1/14 3/2 0/1 1/2 14/9 5/6 39/25 1/1 25/16 1/1 9/8 11/7 1/0 30/19 3/2 49/31 1/0 68/43 1/2 19/12 1/1 1/0 65/41 1/0 111/70 3/4 1/1 46/29 3/2 27/17 1/0 8/5 3/2 21/13 1/0 76/47 3/2 55/34 3/1 1/0 34/21 1/2 47/29 3/2 13/8 2/1 1/0 57/35 3/2 44/27 11/6 31/19 9/4 49/30 5/2 13/5 67/41 11/4 18/11 7/2 5/3 1/0 22/13 -5/2 61/36 -3/1 1/0 161/95 -3/1 100/59 -5/2 39/23 1/0 17/10 -3/1 -5/2 80/47 -5/2 63/37 -5/2 46/27 -13/6 29/17 1/0 70/41 -3/2 41/24 -2/1 1/0 53/31 1/0 65/38 -3/1 1/0 12/7 -3/2 19/11 1/0 7/4 -1/1 1/0 16/9 -7/6 41/23 -1/1 25/14 -1/1 -11/12 9/5 -3/4 29/16 -5/8 -3/5 20/11 -1/2 51/28 -11/21 -1/2 31/17 -1/2 11/6 -1/2 -2/5 13/7 -1/4 28/15 -1/2 15/8 -1/4 -1/5 2/1 1/2 17/8 1/1 5/4 15/7 1/0 13/6 3/1 1/0 11/5 1/0 31/14 -7/1 1/0 51/23 1/0 20/9 -9/2 9/4 -2/1 1/0 16/7 -1/2 55/24 -1/1 -1/2 39/17 1/0 23/10 -1/1 1/0 30/13 -3/2 7/3 1/0 26/11 -7/6 45/19 -1/1 64/27 -17/18 19/8 -1/1 -5/6 31/13 -1/2 43/18 -1/1 -5/6 12/5 -1/2 41/17 -3/4 111/46 -23/34 -2/3 70/29 -17/26 29/12 -5/8 -3/5 46/19 -1/2 109/45 -7/12 63/26 -9/16 -5/9 17/7 -1/2 22/9 -1/2 5/2 -1/4 0/1 23/9 0/1 41/16 0/1 1/32 18/7 1/14 49/19 1/10 31/12 0/1 1/8 44/17 3/22 57/22 3/19 1/6 13/5 1/4 47/18 0/1 1/4 128/49 1/6 81/31 1/4 34/13 1/2 21/8 0/1 1/6 29/11 1/4 8/3 1/2 35/13 1/2 27/10 1/2 3/5 46/17 1/2 19/7 3/4 68/25 13/14 117/43 1/1 166/61 27/26 49/18 1/1 7/6 79/29 3/2 30/11 1/2 11/4 1/2 1/1 47/17 1/1 83/30 1/1 7/6 36/13 3/2 25/9 1/0 14/5 1/2 17/6 3/4 1/1 20/7 3/2 23/8 1/1 1/0 3/1 1/0 25/8 -1/1 1/0 22/7 -1/2 19/6 -5/4 -1/1 16/5 -1/2 13/4 -1/2 0/1 49/15 0/1 85/26 0/1 1/6 36/11 1/2 23/7 1/0 10/3 -1/2 37/11 -1/2 27/8 -1/2 0/1 71/21 -1/2 44/13 1/2 61/18 -1/1 -1/2 17/5 1/0 58/17 -3/2 99/29 -1/1 140/41 -9/10 41/12 -1/1 -3/4 24/7 -1/2 31/9 -1/2 38/11 -1/2 7/2 -1/4 0/1 25/7 0/1 43/12 0/1 1/24 18/5 1/10 47/13 1/6 123/34 0/1 1/6 76/21 1/6 29/8 1/6 1/5 40/11 1/2 51/14 0/1 1/4 11/3 1/4 37/10 4/9 1/2 63/17 1/2 26/7 1/2 15/4 1/1 1/0 19/5 1/0 23/6 0/1 1/2 50/13 1/2 127/33 1/1 77/20 1/1 1/0 27/7 1/0 4/1 1/2 25/6 1/1 1/0 21/5 1/0 59/14 5/4 4/3 38/9 3/2 17/4 2/1 1/0 13/3 1/0 35/8 -4/1 1/0 57/13 1/0 22/5 -5/2 9/2 -1/1 1/0 14/3 -1/2 33/7 -1/2 52/11 -1/2 19/4 -1/3 -1/4 24/5 -1/10 53/11 0/1 82/17 1/30 29/6 0/1 1/10 5/1 1/0 26/5 -1/2 47/9 -1/2 21/4 -1/3 -1/4 58/11 -1/6 37/7 -1/4 53/10 -1/4 0/1 16/3 -1/6 27/5 0/1 38/7 1/14 11/2 0/1 1/4 28/5 1/2 17/3 1/2 23/4 1/1 3/2 29/5 1/0 6/1 -1/2 31/5 1/2 56/9 1/2 25/4 0/1 1/2 19/3 1/0 32/5 1/6 45/7 1/4 13/2 1/2 1/1 20/3 1/2 27/4 1/1 1/0 7/1 1/0 15/2 -1/2 0/1 8/1 -1/2 17/2 1/1 1/0 9/1 1/0 19/2 -1/4 0/1 29/3 0/1 10/1 1/2 11/1 1/0 1/0 0/1 1/0 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(299,140,724,339) (-1/2,-7/15) -> (7/17,19/46) Hyperbolic Matrix(1917,892,836,389) (-7/15,-13/28) -> (55/24,39/17) Hyperbolic Matrix(2025,938,598,277) (-13/28,-6/13) -> (44/13,61/18) Hyperbolic Matrix(593,272,944,433) (-6/13,-11/24) -> (5/8,22/35) Hyperbolic Matrix(1297,594,238,109) (-11/24,-16/35) -> (38/7,11/2) Hyperbolic Matrix(2827,1292,1652,755) (-16/35,-21/46) -> (65/38,12/7) Hyperbolic Matrix(5707,2604,2356,1075) (-21/46,-5/11) -> (109/45,63/26) Hyperbolic Matrix(173,78,-814,-367) (-5/11,-9/20) -> (-3/14,-7/33) Hyperbolic Matrix(521,234,118,53) (-9/20,-4/9) -> (22/5,9/2) Hyperbolic Matrix(403,178,686,303) (-4/9,-11/25) -> (17/29,10/17) Hyperbolic Matrix(2339,1028,1372,603) (-11/25,-18/41) -> (46/27,29/17) Hyperbolic Matrix(2051,900,572,251) (-18/41,-7/16) -> (43/12,18/5) Hyperbolic Matrix(55,24,456,199) (-7/16,-17/39) -> (1/9,1/8) Hyperbolic Matrix(455,198,1018,443) (-17/39,-10/23) -> (4/9,13/29) Hyperbolic Matrix(907,394,-2378,-1033) (-10/23,-13/30) -> (-29/76,-8/21) Hyperbolic Matrix(509,220,900,389) (-13/30,-3/7) -> (13/23,17/30) Hyperbolic Matrix(503,214,778,331) (-3/7,-14/33) -> (20/31,11/17) Hyperbolic Matrix(387,164,-1220,-517) (-14/33,-11/26) -> (-7/22,-6/19) Hyperbolic Matrix(4321,1826,1886,797) (-11/26,-30/71) -> (16/7,55/24) Hyperbolic Matrix(999,422,1882,795) (-30/71,-19/45) -> (9/17,8/15) Hyperbolic Matrix(223,94,994,419) (-19/45,-8/19) -> (2/9,7/31) Hyperbolic Matrix(609,256,992,417) (-8/19,-13/31) -> (19/31,8/13) Hyperbolic Matrix(2697,1130,1654,693) (-13/31,-18/43) -> (44/27,31/19) Hyperbolic Matrix(1979,828,772,323) (-18/43,-5/12) -> (41/16,18/7) Hyperbolic Matrix(53,22,330,137) (-5/12,-12/29) -> (2/13,1/6) Hyperbolic Matrix(653,270,1202,497) (-12/29,-19/46) -> (13/24,6/11) Hyperbolic Matrix(325,134,-1414,-583) (-19/46,-7/17) -> (-3/13,-11/48) Hyperbolic Matrix(161,66,-866,-355) (-7/17,-9/22) -> (-3/16,-5/27) Hyperbolic Matrix(485,198,218,89) (-9/22,-2/5) -> (20/9,9/4) Hyperbolic Matrix(159,62,418,163) (-2/5,-7/18) -> (3/8,8/21) Hyperbolic Matrix(263,102,-838,-325) (-7/18,-12/31) -> (-6/19,-5/16) Hyperbolic Matrix(2659,1028,732,283) (-12/31,-17/44) -> (29/8,40/11) Hyperbolic Matrix(519,200,-1352,-521) (-17/44,-5/13) -> (-5/13,-23/60) Parabolic Matrix(3267,1252,2492,955) (-23/60,-18/47) -> (38/29,21/16) Hyperbolic Matrix(2953,1130,1142,437) (-18/47,-13/34) -> (31/12,44/17) Hyperbolic Matrix(1555,594,1966,751) (-13/34,-21/55) -> (15/19,19/24) Hyperbolic Matrix(1137,434,-6002,-2291) (-21/55,-29/76) -> (-11/58,-7/37) Hyperbolic Matrix(53,20,204,77) (-8/21,-3/8) -> (1/4,4/15) Hyperbolic Matrix(305,114,206,77) (-3/8,-16/43) -> (22/15,3/2) Hyperbolic Matrix(1937,720,304,113) (-16/43,-13/35) -> (19/3,32/5) Hyperbolic Matrix(1525,566,714,265) (-13/35,-23/62) -> (17/8,15/7) Hyperbolic Matrix(205,76,1524,565) (-23/62,-10/27) -> (2/15,3/22) Hyperbolic Matrix(1677,620,2740,1013) (-10/27,-17/46) -> (11/18,30/49) Hyperbolic Matrix(661,244,-2132,-787) (-17/46,-7/19) -> (-9/29,-13/42) Hyperbolic Matrix(1925,708,2428,893) (-7/19,-25/68) -> (19/24,23/29) Hyperbolic Matrix(1317,484,-5668,-2083) (-25/68,-18/49) -> (-10/43,-13/56) Hyperbolic Matrix(2021,742,1114,409) (-18/49,-11/30) -> (29/16,20/11) Hyperbolic Matrix(153,56,-1112,-407) (-11/30,-15/41) -> (-1/7,-3/22) Hyperbolic Matrix(203,74,502,183) (-15/41,-4/11) -> (2/5,11/27) Hyperbolic Matrix(251,90,198,71) (-4/11,-5/14) -> (5/4,14/11) Hyperbolic Matrix(3775,1344,896,319) (-5/14,-21/59) -> (21/5,59/14) Hyperbolic Matrix(995,354,1886,671) (-21/59,-16/45) -> (10/19,9/17) Hyperbolic Matrix(3573,1270,2186,777) (-16/45,-11/31) -> (67/41,18/11) Hyperbolic Matrix(1885,668,1188,421) (-11/31,-6/17) -> (46/29,27/17) Hyperbolic Matrix(245,86,-886,-311) (-6/17,-1/3) -> (-13/47,-8/29) Hyperbolic Matrix(237,76,-1132,-363) (-1/3,-7/22) -> (-13/62,-9/43) Hyperbolic Matrix(1113,346,1766,549) (-5/16,-9/29) -> (17/27,29/46) Hyperbolic Matrix(881,272,2128,657) (-13/42,-4/13) -> (12/29,29/70) Hyperbolic Matrix(139,42,182,55) (-4/13,-3/10) -> (3/4,10/13) Hyperbolic Matrix(47,14,-366,-109) (-3/10,-8/27) -> (-2/15,-1/8) Hyperbolic Matrix(865,256,544,161) (-8/27,-5/17) -> (27/17,8/5) Hyperbolic Matrix(499,146,270,79) (-5/17,-7/24) -> (11/6,13/7) Hyperbolic Matrix(227,66,-994,-289) (-7/24,-2/7) -> (-8/35,-5/22) Hyperbolic Matrix(221,62,802,225) (-2/7,-7/25) -> (3/11,8/29) Hyperbolic Matrix(2309,646,890,249) (-7/25,-19/68) -> (57/22,13/5) Hyperbolic Matrix(3553,992,1952,545) (-19/68,-12/43) -> (20/11,51/28) Hyperbolic Matrix(977,272,176,49) (-12/43,-5/18) -> (11/2,28/5) Hyperbolic Matrix(267,74,-1418,-393) (-5/18,-13/47) -> (-7/37,-3/16) Hyperbolic Matrix(929,256,352,97) (-8/29,-3/11) -> (29/11,8/3) Hyperbolic Matrix(659,178,174,47) (-3/11,-7/26) -> (15/4,19/5) Hyperbolic Matrix(439,118,-2102,-565) (-7/26,-11/41) -> (-9/43,-5/24) Hyperbolic Matrix(1485,398,1138,305) (-11/41,-4/15) -> (30/23,17/13) Hyperbolic Matrix(303,80,784,207) (-4/15,-5/19) -> (5/13,12/31) Hyperbolic Matrix(1129,296,1560,409) (-5/19,-6/23) -> (34/47,21/29) Hyperbolic Matrix(1037,270,434,113) (-6/23,-1/4) -> (43/18,12/5) Hyperbolic Matrix(41,10,86,21) (-1/4,-4/17) -> (6/13,1/2) Hyperbolic Matrix(753,176,1168,273) (-4/17,-7/30) -> (9/14,20/31) Hyperbolic Matrix(2377,554,502,117) (-7/30,-10/43) -> (52/11,19/4) Hyperbolic Matrix(751,174,82,19) (-13/56,-3/13) -> (9/1,19/2) Hyperbolic Matrix(3737,856,1576,361) (-11/48,-8/35) -> (64/27,19/8) Hyperbolic Matrix(619,140,84,19) (-5/22,-7/31) -> (7/1,15/2) Hyperbolic Matrix(331,74,246,55) (-7/31,-2/9) -> (4/3,23/17) Hyperbolic Matrix(287,62,162,35) (-2/9,-3/14) -> (7/4,16/9) Hyperbolic Matrix(1175,248,488,103) (-7/33,-4/19) -> (12/5,41/17) Hyperbolic Matrix(3809,800,1376,289) (-4/19,-13/62) -> (83/30,36/13) Hyperbolic Matrix(685,142,82,17) (-5/24,-6/29) -> (8/1,17/2) Hyperbolic Matrix(2057,424,1208,249) (-6/29,-1/5) -> (63/37,46/27) Hyperbolic Matrix(1547,298,950,183) (-1/5,-5/26) -> (13/8,57/35) Hyperbolic Matrix(1345,258,318,61) (-5/26,-4/21) -> (38/9,17/4) Hyperbolic Matrix(3873,736,1184,225) (-4/21,-11/58) -> (85/26,36/11) Hyperbolic Matrix(2983,550,1882,347) (-5/27,-7/38) -> (19/12,65/41) Hyperbolic Matrix(1057,194,158,29) (-7/38,-2/11) -> (20/3,27/4) Hyperbolic Matrix(117,20,76,13) (-2/11,-1/6) -> (3/2,14/9) Hyperbolic Matrix(37,6,154,25) (-1/6,-2/13) -> (4/17,1/4) Hyperbolic Matrix(301,46,530,81) (-2/13,-3/20) -> (17/30,4/7) Hyperbolic Matrix(375,56,904,135) (-3/20,-1/7) -> (17/41,5/12) Hyperbolic Matrix(1221,166,890,121) (-3/22,-2/15) -> (48/35,11/8) Hyperbolic Matrix(181,22,74,9) (-1/8,0/1) -> (22/9,5/2) Hyperbolic Matrix(149,-12,236,-19) (0/1,1/9) -> (41/65,12/19) Hyperbolic Matrix(283,-36,228,-29) (1/8,2/15) -> (26/21,5/4) Hyperbolic Matrix(1181,-162,226,-31) (3/22,1/7) -> (47/9,21/4) Hyperbolic Matrix(527,-80,112,-17) (1/7,2/13) -> (14/3,33/7) Hyperbolic Matrix(81,-14,110,-19) (1/6,1/5) -> (11/15,3/4) Hyperbolic Matrix(899,-188,636,-133) (1/5,4/19) -> (24/17,41/29) Hyperbolic Matrix(397,-84,52,-11) (4/19,3/14) -> (15/2,8/1) Hyperbolic Matrix(341,-74,106,-23) (3/14,2/9) -> (16/5,13/4) Hyperbolic Matrix(7203,-1630,2974,-673) (7/31,12/53) -> (46/19,109/45) Hyperbolic Matrix(2661,-604,1564,-355) (12/53,5/22) -> (17/10,80/47) Hyperbolic Matrix(1121,-256,416,-95) (5/22,3/13) -> (35/13,27/10) Hyperbolic Matrix(699,-164,260,-61) (3/13,4/17) -> (8/3,35/13) Hyperbolic Matrix(403,-108,556,-149) (4/15,3/11) -> (21/29,8/11) Hyperbolic Matrix(853,-236,300,-83) (8/29,5/18) -> (17/6,20/7) Hyperbolic Matrix(1327,-370,850,-237) (5/18,7/25) -> (39/25,25/16) Hyperbolic Matrix(623,-176,400,-113) (7/25,2/7) -> (14/9,39/25) Hyperbolic Matrix(223,-66,98,-29) (2/7,3/10) -> (9/4,16/7) Hyperbolic Matrix(171,-52,148,-45) (3/10,4/13) -> (8/7,7/6) Hyperbolic Matrix(1027,-318,830,-257) (4/13,9/29) -> (21/17,26/21) Hyperbolic Matrix(1927,-600,440,-137) (9/29,5/16) -> (35/8,57/13) Hyperbolic Matrix(877,-276,340,-107) (5/16,1/3) -> (49/19,31/12) Hyperbolic Matrix(853,-300,236,-83) (1/3,6/17) -> (18/5,47/13) Hyperbolic Matrix(899,-318,2174,-769) (6/17,11/31) -> (31/75,12/29) Hyperbolic Matrix(1675,-596,756,-269) (11/31,5/14) -> (31/14,51/23) Hyperbolic Matrix(329,-118,566,-203) (5/14,4/11) -> (18/31,7/12) Hyperbolic Matrix(211,-78,46,-17) (4/11,3/8) -> (9/2,14/3) Hyperbolic Matrix(555,-212,788,-301) (8/21,5/13) -> (19/27,12/17) Hyperbolic Matrix(877,-340,276,-107) (12/31,7/18) -> (19/6,16/5) Hyperbolic Matrix(1313,-512,736,-287) (7/18,9/23) -> (41/23,25/14) Hyperbolic Matrix(573,-226,322,-127) (9/23,2/5) -> (16/9,41/23) Hyperbolic Matrix(1137,-464,272,-111) (11/27,9/22) -> (25/6,21/5) Hyperbolic Matrix(1249,-512,544,-223) (9/22,7/17) -> (39/17,23/10) Hyperbolic Matrix(10303,-4258,7426,-3069) (19/46,31/75) -> (43/31,111/80) Hyperbolic Matrix(7421,-3076,3076,-1275) (29/70,17/41) -> (41/17,111/46) Hyperbolic Matrix(157,-66,226,-95) (5/12,3/7) -> (9/13,7/10) Hyperbolic Matrix(1115,-484,804,-349) (3/7,10/23) -> (18/13,43/31) Hyperbolic Matrix(1403,-612,580,-253) (10/23,7/16) -> (29/12,46/19) Hyperbolic Matrix(377,-166,134,-59) (7/16,4/9) -> (14/5,17/6) Hyperbolic Matrix(1105,-496,176,-79) (13/29,9/20) -> (25/4,19/3) Hyperbolic Matrix(1037,-468,308,-139) (9/20,5/11) -> (37/11,27/8) Hyperbolic Matrix(591,-272,176,-81) (5/11,6/13) -> (10/3,37/11) Hyperbolic Matrix(1263,-656,464,-241) (1/2,10/19) -> (166/61,49/18) Hyperbolic Matrix(397,-212,500,-267) (8/15,7/13) -> (23/29,4/5) Hyperbolic Matrix(873,-472,664,-359) (7/13,13/24) -> (21/16,25/19) Hyperbolic Matrix(391,-216,248,-137) (6/11,5/9) -> (11/7,30/19) Hyperbolic Matrix(369,-206,206,-115) (5/9,9/16) -> (25/14,9/5) Hyperbolic Matrix(695,-392,328,-185) (9/16,22/39) -> (2/1,17/8) Hyperbolic Matrix(981,-554,1514,-855) (22/39,13/23) -> (11/17,24/37) Hyperbolic Matrix(691,-398,974,-561) (4/7,15/26) -> (17/24,22/31) Hyperbolic Matrix(1157,-668,892,-515) (15/26,11/19) -> (35/27,13/10) Hyperbolic Matrix(1459,-846,526,-305) (11/19,18/31) -> (36/13,25/9) Hyperbolic Matrix(949,-556,524,-307) (7/12,17/29) -> (9/5,29/16) Hyperbolic Matrix(121,-72,200,-119) (10/17,3/5) -> (3/5,14/23) Parabolic Matrix(3599,-2194,2226,-1357) (14/23,25/41) -> (21/13,76/47) Hyperbolic Matrix(6401,-3904,3776,-2303) (25/41,36/59) -> (100/59,39/23) Hyperbolic Matrix(8625,-5264,2384,-1455) (36/59,11/18) -> (123/34,76/21) Hyperbolic Matrix(3591,-2200,2104,-1289) (30/49,19/31) -> (29/17,70/41) Hyperbolic Matrix(139,-86,118,-73) (8/13,5/8) -> (7/6,6/5) Hyperbolic Matrix(983,-618,746,-469) (22/35,17/27) -> (25/19,4/3) Hyperbolic Matrix(10205,-6436,6436,-4059) (29/46,41/65) -> (65/41,111/70) Hyperbolic Matrix(2471,-1562,666,-421) (12/19,31/49) -> (63/17,26/7) Hyperbolic Matrix(3429,-2170,1882,-1191) (31/49,19/30) -> (51/28,31/17) Hyperbolic Matrix(1469,-932,900,-571) (19/30,7/11) -> (31/19,49/30) Hyperbolic Matrix(429,-274,274,-175) (7/11,9/14) -> (25/16,11/7) Hyperbolic Matrix(2795,-1814,2134,-1385) (24/37,13/20) -> (55/42,38/29) Hyperbolic Matrix(155,-102,38,-25) (13/20,2/3) -> (4/1,25/6) Hyperbolic Matrix(359,-248,152,-105) (2/3,9/13) -> (7/3,26/11) Hyperbolic Matrix(1109,-780,300,-211) (7/10,19/27) -> (11/3,37/10) Hyperbolic Matrix(899,-636,188,-133) (12/17,17/24) -> (19/4,24/5) Hyperbolic Matrix(6025,-4278,4342,-3083) (22/31,27/38) -> (111/80,68/49) Hyperbolic Matrix(1777,-1264,336,-239) (27/38,5/7) -> (37/7,53/10) Hyperbolic Matrix(317,-228,260,-187) (5/7,13/18) -> (17/14,11/9) Hyperbolic Matrix(2117,-1530,1338,-967) (13/18,34/47) -> (68/43,19/12) Hyperbolic Matrix(555,-406,406,-297) (8/11,11/15) -> (15/11,26/19) Hyperbolic Matrix(253,-196,324,-251) (10/13,7/9) -> (7/9,18/23) Parabolic Matrix(1741,-1364,1076,-843) (18/23,11/14) -> (55/34,34/21) Hyperbolic Matrix(3797,-2988,2220,-1747) (11/14,37/47) -> (53/31,65/38) Hyperbolic Matrix(2989,-2354,466,-367) (37/47,26/33) -> (32/5,45/7) Hyperbolic Matrix(967,-762,250,-197) (26/33,15/19) -> (27/7,4/1) Hyperbolic Matrix(299,-244,212,-173) (4/5,9/11) -> (7/5,24/17) Hyperbolic Matrix(597,-490,106,-87) (9/11,14/17) -> (28/5,17/3) Hyperbolic Matrix(841,-694,246,-203) (14/17,5/6) -> (41/12,24/7) Hyperbolic Matrix(121,-102,70,-59) (5/6,1/1) -> (19/11,7/4) Hyperbolic Matrix(197,-220,60,-67) (1/1,8/7) -> (36/11,23/7) Hyperbolic Matrix(535,-648,232,-281) (6/5,17/14) -> (23/10,30/13) Hyperbolic Matrix(1251,-1534,862,-1057) (11/9,27/22) -> (29/20,45/31) Hyperbolic Matrix(1709,-2100,660,-811) (27/22,16/13) -> (44/17,57/22) Hyperbolic Matrix(1403,-1732,516,-637) (16/13,21/17) -> (19/7,68/25) Hyperbolic Matrix(253,-324,196,-251) (14/11,9/7) -> (9/7,22/17) Parabolic Matrix(655,-848,112,-145) (22/17,35/27) -> (29/5,6/1) Hyperbolic Matrix(625,-814,334,-435) (13/10,30/23) -> (28/15,15/8) Hyperbolic Matrix(2135,-2794,554,-725) (17/13,55/42) -> (77/20,27/7) Hyperbolic Matrix(557,-754,82,-111) (23/17,19/14) -> (27/4,7/1) Hyperbolic Matrix(855,-1162,298,-405) (19/14,34/25) -> (20/7,23/8) Hyperbolic Matrix(1667,-2268,380,-517) (34/25,15/11) -> (57/13,22/5) Hyperbolic Matrix(1999,-2738,1458,-1997) (26/19,37/27) -> (37/27,48/35) Parabolic Matrix(403,-556,108,-149) (11/8,18/13) -> (26/7,15/4) Hyperbolic Matrix(2091,-2902,214,-297) (68/49,93/67) -> (29/3,10/1) Hyperbolic Matrix(1795,-2492,188,-261) (93/67,25/18) -> (19/2,29/3) Hyperbolic Matrix(911,-1266,562,-781) (25/18,7/5) -> (47/29,13/8) Hyperbolic Matrix(901,-1274,186,-263) (41/29,17/12) -> (29/6,5/1) Hyperbolic Matrix(555,-788,212,-301) (17/12,10/7) -> (34/13,21/8) Hyperbolic Matrix(1091,-1564,316,-453) (10/7,33/23) -> (31/9,38/11) Hyperbolic Matrix(1721,-2470,710,-1019) (33/23,23/16) -> (63/26,17/7) Hyperbolic Matrix(827,-1190,262,-377) (23/16,36/25) -> (22/7,19/6) Hyperbolic Matrix(1455,-2096,656,-945) (36/25,13/9) -> (51/23,20/9) Hyperbolic Matrix(889,-1286,262,-379) (13/9,29/20) -> (61/18,17/5) Hyperbolic Matrix(2205,-3202,418,-607) (45/31,16/11) -> (58/11,37/7) Hyperbolic Matrix(495,-722,338,-493) (16/11,19/13) -> (19/13,22/15) Parabolic Matrix(2593,-4096,992,-1567) (30/19,49/31) -> (81/31,34/13) Hyperbolic Matrix(7451,-11780,2852,-4509) (49/31,68/43) -> (128/49,81/31) Hyperbolic Matrix(10989,-17426,3218,-5103) (111/70,46/29) -> (140/41,41/12) Hyperbolic Matrix(245,-394,74,-119) (8/5,21/13) -> (23/7,10/3) Hyperbolic Matrix(2959,-4786,562,-909) (76/47,55/34) -> (21/4,58/11) Hyperbolic Matrix(2529,-4096,928,-1503) (34/21,47/29) -> (79/29,30/11) Hyperbolic Matrix(1047,-1706,170,-277) (57/35,44/27) -> (6/1,31/5) Hyperbolic Matrix(1883,-3076,292,-477) (49/30,67/41) -> (45/7,13/2) Hyperbolic Matrix(121,-200,72,-119) (18/11,5/3) -> (5/3,22/13) Parabolic Matrix(1117,-1892,356,-603) (22/13,61/36) -> (25/8,22/7) Hyperbolic Matrix(11887,-20144,3088,-5233) (61/36,161/95) -> (127/33,77/20) Hyperbolic Matrix(12243,-20750,3182,-5393) (161/95,100/59) -> (50/13,127/33) Hyperbolic Matrix(819,-1390,142,-241) (39/23,17/10) -> (23/4,29/5) Hyperbolic Matrix(3529,-6008,568,-967) (80/47,63/37) -> (31/5,56/9) Hyperbolic Matrix(4999,-8538,1914,-3269) (70/41,41/24) -> (47/18,128/49) Hyperbolic Matrix(295,-504,24,-41) (41/24,53/31) -> (11/1,1/0) Hyperbolic Matrix(329,-566,118,-203) (12/7,19/11) -> (25/9,14/5) Hyperbolic Matrix(1007,-1840,272,-497) (31/17,11/6) -> (37/10,63/17) Hyperbolic Matrix(235,-438,22,-41) (13/7,28/15) -> (10/1,11/1) Hyperbolic Matrix(589,-1108,244,-459) (15/8,2/1) -> (70/29,29/12) Hyperbolic Matrix(173,-372,20,-43) (15/7,13/6) -> (17/2,9/1) Hyperbolic Matrix(221,-484,100,-219) (13/6,11/5) -> (11/5,31/14) Parabolic Matrix(395,-916,116,-269) (30/13,7/3) -> (17/5,58/17) Hyperbolic Matrix(1711,-4050,722,-1709) (26/11,45/19) -> (45/19,64/27) Parabolic Matrix(435,-1036,76,-181) (19/8,31/13) -> (17/3,23/4) Hyperbolic Matrix(2059,-4916,756,-1805) (31/13,43/18) -> (49/18,79/29) Hyperbolic Matrix(4613,-11132,956,-2307) (111/46,70/29) -> (82/17,29/6) Hyperbolic Matrix(447,-1090,130,-317) (17/7,22/9) -> (24/7,31/9) Hyperbolic Matrix(415,-1058,162,-413) (5/2,23/9) -> (23/9,41/16) Parabolic Matrix(1333,-3434,394,-1015) (18/7,49/19) -> (71/21,44/13) Hyperbolic Matrix(453,-1180,124,-323) (13/5,47/18) -> (51/14,11/3) Hyperbolic Matrix(405,-1066,106,-279) (21/8,29/11) -> (19/5,23/6) Hyperbolic Matrix(1253,-3386,346,-935) (27/10,46/17) -> (76/21,29/8) Hyperbolic Matrix(267,-724,52,-141) (46/17,19/7) -> (5/1,26/5) Hyperbolic Matrix(10063,-27378,3698,-10061) (68/25,117/43) -> (117/43,166/61) Parabolic Matrix(223,-610,34,-93) (30/11,11/4) -> (13/2,20/3) Hyperbolic Matrix(1599,-4418,578,-1597) (11/4,47/17) -> (47/17,83/30) Parabolic Matrix(49,-144,16,-47) (23/8,3/1) -> (3/1,25/8) Parabolic Matrix(1471,-4802,450,-1469) (13/4,49/15) -> (49/15,85/26) Parabolic Matrix(2959,-10002,818,-2765) (27/8,71/21) -> (47/13,123/34) Hyperbolic Matrix(5743,-19602,1682,-5741) (58/17,99/29) -> (99/29,140/41) Parabolic Matrix(725,-2508,172,-595) (38/11,7/2) -> (59/14,38/9) Hyperbolic Matrix(351,-1250,98,-349) (7/2,25/7) -> (25/7,43/12) Parabolic Matrix(807,-2936,152,-553) (40/11,51/14) -> (53/10,16/3) Hyperbolic Matrix(661,-2538,106,-407) (23/6,50/13) -> (56/9,25/4) Hyperbolic Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) Parabolic Matrix(699,-3302,134,-633) (33/7,52/11) -> (26/5,47/9) Hyperbolic Matrix(1167,-5618,242,-1165) (24/5,53/11) -> (53/11,82/17) Parabolic Matrix(271,-1458,50,-269) (16/3,27/5) -> (27/5,38/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(299,140,724,339) -> Matrix(1,0,-4,1) Matrix(1917,892,836,389) -> Matrix(1,0,-4,1) Matrix(2025,938,598,277) -> Matrix(1,0,-4,1) Matrix(593,272,944,433) -> Matrix(1,0,0,1) Matrix(1297,594,238,109) -> Matrix(1,0,4,1) Matrix(2827,1292,1652,755) -> Matrix(17,-2,-8,1) Matrix(5707,2604,2356,1075) -> Matrix(23,-4,-40,7) Matrix(173,78,-814,-367) -> Matrix(11,-2,28,-5) Matrix(521,234,118,53) -> Matrix(9,-2,-4,1) Matrix(403,178,686,303) -> Matrix(7,-2,4,-1) Matrix(2339,1028,1372,603) -> Matrix(1,-2,0,1) Matrix(2051,900,572,251) -> Matrix(1,0,16,1) Matrix(55,24,456,199) -> Matrix(1,0,-4,1) Matrix(455,198,1018,443) -> Matrix(1,0,-4,1) Matrix(907,394,-2378,-1033) -> Matrix(9,-2,32,-7) Matrix(509,220,900,389) -> Matrix(21,-4,16,-3) Matrix(503,214,778,331) -> Matrix(7,-2,4,-1) Matrix(387,164,-1220,-517) -> Matrix(1,0,0,1) Matrix(4321,1826,1886,797) -> Matrix(1,0,-4,1) Matrix(999,422,1882,795) -> Matrix(19,-6,16,-5) Matrix(223,94,994,419) -> Matrix(3,-2,8,-5) Matrix(609,256,992,417) -> Matrix(1,0,0,1) Matrix(2697,1130,1654,693) -> Matrix(9,2,4,1) Matrix(1979,828,772,323) -> Matrix(1,0,24,1) Matrix(53,22,330,137) -> Matrix(13,-2,20,-3) Matrix(653,270,1202,497) -> Matrix(21,-4,16,-3) Matrix(325,134,-1414,-583) -> Matrix(9,-2,32,-7) Matrix(161,66,-866,-355) -> Matrix(9,-2,32,-7) Matrix(485,198,218,89) -> Matrix(17,-4,-4,1) Matrix(159,62,418,163) -> Matrix(19,-4,24,-5) Matrix(263,102,-838,-325) -> Matrix(9,-2,32,-7) Matrix(2659,1028,732,283) -> Matrix(9,-2,32,-7) Matrix(519,200,-1352,-521) -> Matrix(25,-6,96,-23) Matrix(3267,1252,2492,955) -> Matrix(1,0,-4,1) Matrix(2953,1130,1142,437) -> Matrix(7,-2,60,-17) Matrix(1555,594,1966,751) -> Matrix(1,0,-4,1) Matrix(1137,434,-6002,-2291) -> Matrix(7,-2,32,-9) Matrix(53,20,204,77) -> Matrix(5,-2,8,-3) Matrix(305,114,206,77) -> Matrix(1,0,0,1) Matrix(1937,720,304,113) -> Matrix(1,0,-8,1) Matrix(1525,566,714,265) -> Matrix(15,-2,8,-1) Matrix(205,76,1524,565) -> Matrix(11,-2,28,-5) Matrix(1677,620,2740,1013) -> Matrix(1,0,-4,1) Matrix(661,244,-2132,-787) -> Matrix(1,0,-4,1) Matrix(1925,708,2428,893) -> Matrix(9,-2,-4,1) Matrix(1317,484,-5668,-2083) -> Matrix(1,0,-4,1) Matrix(2021,742,1114,409) -> Matrix(23,-4,-40,7) Matrix(153,56,-1112,-407) -> Matrix(9,-2,32,-7) Matrix(203,74,502,183) -> Matrix(1,0,-4,1) Matrix(251,90,198,71) -> Matrix(15,-4,4,-1) Matrix(3775,1344,896,319) -> Matrix(19,-6,16,-5) Matrix(995,354,1886,671) -> Matrix(43,-14,40,-13) Matrix(3573,1270,2186,777) -> Matrix(21,-8,8,-3) Matrix(1885,668,1188,421) -> Matrix(7,-2,4,-1) Matrix(245,86,-886,-311) -> Matrix(1,0,0,1) Matrix(237,76,-1132,-363) -> Matrix(13,-4,36,-11) Matrix(1113,346,1766,549) -> Matrix(1,0,0,1) Matrix(881,272,2128,657) -> Matrix(1,0,-4,1) Matrix(139,42,182,55) -> Matrix(15,-4,4,-1) Matrix(47,14,-366,-109) -> Matrix(13,-4,36,-11) Matrix(865,256,544,161) -> Matrix(7,-2,4,-1) Matrix(499,146,270,79) -> Matrix(7,-2,-24,7) Matrix(227,66,-994,-289) -> Matrix(13,-4,36,-11) Matrix(221,62,802,225) -> Matrix(17,-6,20,-7) Matrix(2309,646,890,249) -> Matrix(5,-2,28,-11) Matrix(3553,992,1952,545) -> Matrix(11,-6,-20,11) Matrix(977,272,176,49) -> Matrix(1,0,0,1) Matrix(267,74,-1418,-393) -> Matrix(1,0,0,1) Matrix(929,256,352,97) -> Matrix(1,0,0,1) Matrix(659,178,174,47) -> Matrix(7,-2,4,-1) Matrix(439,118,-2102,-565) -> Matrix(13,-4,36,-11) Matrix(1485,398,1138,305) -> Matrix(9,-2,-4,1) Matrix(303,80,784,207) -> Matrix(17,-6,20,-7) Matrix(1129,296,1560,409) -> Matrix(7,-2,4,-1) Matrix(1037,270,434,113) -> Matrix(13,-4,-16,5) Matrix(41,10,86,21) -> Matrix(5,-2,8,-3) Matrix(753,176,1168,273) -> Matrix(7,-2,4,-1) Matrix(2377,554,502,117) -> Matrix(5,-2,-12,5) Matrix(751,174,82,19) -> Matrix(1,0,-4,1) Matrix(3737,856,1576,361) -> Matrix(37,-12,-40,13) Matrix(619,140,84,19) -> Matrix(1,0,-4,1) Matrix(331,74,246,55) -> Matrix(1,0,-4,1) Matrix(287,62,162,35) -> Matrix(11,-4,-8,3) Matrix(1175,248,488,103) -> Matrix(1,0,-4,1) Matrix(3809,800,1376,289) -> Matrix(7,-2,4,-1) Matrix(685,142,82,17) -> Matrix(5,-2,8,-3) Matrix(2057,424,1208,249) -> Matrix(29,-12,-12,5) Matrix(1547,298,950,183) -> Matrix(7,-2,4,-1) Matrix(1345,258,318,61) -> Matrix(7,-2,4,-1) Matrix(3873,736,1184,225) -> Matrix(1,0,0,1) Matrix(2983,550,1882,347) -> Matrix(7,-2,4,-1) Matrix(1057,194,158,29) -> Matrix(7,-2,4,-1) Matrix(117,20,76,13) -> Matrix(5,-2,8,-3) Matrix(37,6,154,25) -> Matrix(9,-4,16,-7) Matrix(301,46,530,81) -> Matrix(5,-4,4,-3) Matrix(375,56,904,135) -> Matrix(1,0,0,1) Matrix(1221,166,890,121) -> Matrix(25,-8,-28,9) Matrix(181,22,74,9) -> Matrix(5,-2,-12,5) Matrix(149,-12,236,-19) -> Matrix(3,-2,8,-5) Matrix(283,-36,228,-29) -> Matrix(7,-2,4,-1) Matrix(1181,-162,226,-31) -> Matrix(9,-4,-20,9) Matrix(527,-80,112,-17) -> Matrix(7,-4,-12,7) Matrix(81,-14,110,-19) -> Matrix(5,-4,4,-3) Matrix(899,-188,636,-133) -> Matrix(1,0,-8,1) Matrix(397,-84,52,-11) -> Matrix(1,0,-4,1) Matrix(341,-74,106,-23) -> Matrix(1,0,-4,1) Matrix(7203,-1630,2974,-673) -> Matrix(1,0,-4,1) Matrix(2661,-604,1564,-355) -> Matrix(49,-22,-20,9) Matrix(1121,-256,416,-95) -> Matrix(17,-8,32,-15) Matrix(699,-164,260,-61) -> Matrix(11,-6,24,-13) Matrix(403,-108,556,-149) -> Matrix(5,-4,4,-3) Matrix(853,-236,300,-83) -> Matrix(9,-8,8,-7) Matrix(1327,-370,850,-237) -> Matrix(21,-20,20,-19) Matrix(623,-176,400,-113) -> Matrix(7,-8,8,-9) Matrix(223,-66,98,-29) -> Matrix(1,-2,0,1) Matrix(171,-52,148,-45) -> Matrix(1,0,0,1) Matrix(1027,-318,830,-257) -> Matrix(5,-4,4,-3) Matrix(1927,-600,440,-137) -> Matrix(1,-4,0,1) Matrix(877,-276,340,-107) -> Matrix(1,0,8,1) Matrix(853,-300,236,-83) -> Matrix(3,-2,20,-13) Matrix(899,-318,2174,-769) -> Matrix(3,-2,-4,3) Matrix(1675,-596,756,-269) -> Matrix(27,-20,-4,3) Matrix(329,-118,566,-203) -> Matrix(5,-4,4,-3) Matrix(211,-78,46,-17) -> Matrix(3,-2,-4,3) Matrix(555,-212,788,-301) -> Matrix(27,-22,16,-13) Matrix(877,-340,276,-107) -> Matrix(11,-10,-12,11) Matrix(1313,-512,736,-287) -> Matrix(27,-26,-28,27) Matrix(573,-226,322,-127) -> Matrix(9,-10,-8,9) Matrix(1137,-464,272,-111) -> Matrix(1,0,0,1) Matrix(1249,-512,544,-223) -> Matrix(1,-2,0,1) Matrix(10303,-4258,7426,-3069) -> Matrix(1,0,-4,1) Matrix(7421,-3076,3076,-1275) -> Matrix(11,-2,-16,3) Matrix(157,-66,226,-95) -> Matrix(5,-4,4,-3) Matrix(1115,-484,804,-349) -> Matrix(1,0,-4,1) Matrix(1403,-612,580,-253) -> Matrix(7,-4,-12,7) Matrix(377,-166,134,-59) -> Matrix(1,0,0,1) Matrix(1105,-496,176,-79) -> Matrix(1,0,0,1) Matrix(1037,-468,308,-139) -> Matrix(1,0,-4,1) Matrix(591,-272,176,-81) -> Matrix(3,-2,-4,3) Matrix(1263,-656,464,-241) -> Matrix(9,-8,8,-7) Matrix(397,-212,500,-267) -> Matrix(5,-6,-4,5) Matrix(873,-472,664,-359) -> Matrix(1,-4,0,1) Matrix(391,-216,248,-137) -> Matrix(1,0,0,1) Matrix(369,-206,206,-115) -> Matrix(3,-2,-4,3) Matrix(695,-392,328,-185) -> Matrix(3,-4,4,-5) Matrix(981,-554,1514,-855) -> Matrix(3,-4,4,-5) Matrix(691,-398,974,-561) -> Matrix(1,0,0,1) Matrix(1157,-668,892,-515) -> Matrix(1,-8,0,1) Matrix(1459,-846,526,-305) -> Matrix(1,0,0,1) Matrix(949,-556,524,-307) -> Matrix(5,-8,-8,13) Matrix(121,-72,200,-119) -> Matrix(1,-2,0,1) Matrix(3599,-2194,2226,-1357) -> Matrix(1,2,0,1) Matrix(6401,-3904,3776,-2303) -> Matrix(1,-2,0,1) Matrix(8625,-5264,2384,-1455) -> Matrix(1,0,8,1) Matrix(3591,-2200,2104,-1289) -> Matrix(1,-2,0,1) Matrix(139,-86,118,-73) -> Matrix(1,0,0,1) Matrix(983,-618,746,-469) -> Matrix(9,-2,-4,1) Matrix(10205,-6436,6436,-4059) -> Matrix(5,-2,8,-3) Matrix(2471,-1562,666,-421) -> Matrix(9,-4,16,-7) Matrix(3429,-2170,1882,-1191) -> Matrix(31,-16,-60,31) Matrix(1469,-932,900,-571) -> Matrix(19,-12,8,-5) Matrix(429,-274,274,-175) -> Matrix(5,-4,4,-3) Matrix(2795,-1814,2134,-1385) -> Matrix(1,-4,0,1) Matrix(155,-102,38,-25) -> Matrix(1,0,0,1) Matrix(359,-248,152,-105) -> Matrix(5,-6,-4,5) Matrix(1109,-780,300,-211) -> Matrix(5,-8,12,-19) Matrix(899,-636,188,-133) -> Matrix(1,-2,-4,9) Matrix(6025,-4278,4342,-3083) -> Matrix(1,-2,-4,9) Matrix(1777,-1264,336,-239) -> Matrix(1,-2,-4,9) Matrix(317,-228,260,-187) -> Matrix(1,0,0,1) Matrix(2117,-1530,1338,-967) -> Matrix(1,0,0,1) Matrix(555,-406,406,-297) -> Matrix(5,-6,-4,5) Matrix(253,-196,324,-251) -> Matrix(1,-10,0,1) Matrix(1741,-1364,1076,-843) -> Matrix(1,6,0,1) Matrix(3797,-2988,2220,-1747) -> Matrix(1,0,0,1) Matrix(2989,-2354,466,-367) -> Matrix(1,2,4,9) Matrix(967,-762,250,-197) -> Matrix(1,2,0,1) Matrix(299,-244,212,-173) -> Matrix(1,0,-4,1) Matrix(597,-490,106,-87) -> Matrix(1,0,0,1) Matrix(841,-694,246,-203) -> Matrix(3,-2,-4,3) Matrix(121,-102,70,-59) -> Matrix(1,-2,0,1) Matrix(197,-220,60,-67) -> Matrix(1,0,0,1) Matrix(535,-648,232,-281) -> Matrix(1,-2,0,1) Matrix(1251,-1534,862,-1057) -> Matrix(1,0,-8,1) Matrix(1709,-2100,660,-811) -> Matrix(3,-2,20,-13) Matrix(1403,-1732,516,-637) -> Matrix(7,-8,8,-9) Matrix(253,-324,196,-251) -> Matrix(1,-14,0,1) Matrix(655,-848,112,-145) -> Matrix(1,8,0,1) Matrix(625,-814,334,-435) -> Matrix(1,4,-4,-15) Matrix(2135,-2794,554,-725) -> Matrix(1,4,0,1) Matrix(557,-754,82,-111) -> Matrix(1,2,0,1) Matrix(855,-1162,298,-405) -> Matrix(1,2,0,1) Matrix(1667,-2268,380,-517) -> Matrix(1,-2,0,1) Matrix(1999,-2738,1458,-1997) -> Matrix(19,20,-20,-21) Matrix(403,-556,108,-149) -> Matrix(3,2,4,3) Matrix(2091,-2902,214,-297) -> Matrix(1,0,8,1) Matrix(1795,-2492,188,-261) -> Matrix(1,0,-4,1) Matrix(911,-1266,562,-781) -> Matrix(1,2,0,1) Matrix(901,-1274,186,-263) -> Matrix(1,0,8,1) Matrix(555,-788,212,-301) -> Matrix(1,0,4,1) Matrix(1091,-1564,316,-453) -> Matrix(3,2,-8,-5) Matrix(1721,-2470,710,-1019) -> Matrix(13,6,-24,-11) Matrix(827,-1190,262,-377) -> Matrix(7,2,-4,-1) Matrix(1455,-2096,656,-945) -> Matrix(23,6,-4,-1) Matrix(889,-1286,262,-379) -> Matrix(1,0,4,1) Matrix(2205,-3202,418,-607) -> Matrix(1,0,4,1) Matrix(495,-722,338,-493) -> Matrix(1,0,24,1) Matrix(2593,-4096,992,-1567) -> Matrix(1,-2,4,-7) Matrix(7451,-11780,2852,-4509) -> Matrix(1,0,4,1) Matrix(10989,-17426,3218,-5103) -> Matrix(7,-6,-8,7) Matrix(245,-394,74,-119) -> Matrix(1,-2,0,1) Matrix(2959,-4786,562,-909) -> Matrix(1,-2,-4,9) Matrix(2529,-4096,928,-1503) -> Matrix(1,0,0,1) Matrix(1047,-1706,170,-277) -> Matrix(1,-2,4,-7) Matrix(1883,-3076,292,-477) -> Matrix(3,-8,8,-21) Matrix(121,-200,72,-119) -> Matrix(1,-6,0,1) Matrix(1117,-1892,356,-603) -> Matrix(1,2,0,1) Matrix(11887,-20144,3088,-5233) -> Matrix(1,4,0,1) Matrix(12243,-20750,3182,-5393) -> Matrix(3,8,4,11) Matrix(819,-1390,142,-241) -> Matrix(1,4,0,1) Matrix(3529,-6008,568,-967) -> Matrix(1,2,4,9) Matrix(4999,-8538,1914,-3269) -> Matrix(1,2,4,9) Matrix(295,-504,24,-41) -> Matrix(1,2,0,1) Matrix(329,-566,118,-203) -> Matrix(1,2,0,1) Matrix(1007,-1840,272,-497) -> Matrix(13,6,28,13) Matrix(235,-438,22,-41) -> Matrix(1,0,4,1) Matrix(589,-1108,244,-459) -> Matrix(13,2,-20,-3) Matrix(173,-372,20,-43) -> Matrix(1,-2,0,1) Matrix(221,-484,100,-219) -> Matrix(1,-10,0,1) Matrix(395,-916,116,-269) -> Matrix(1,0,0,1) Matrix(1711,-4050,722,-1709) -> Matrix(23,24,-24,-25) Matrix(435,-1036,76,-181) -> Matrix(3,2,4,3) Matrix(2059,-4916,756,-1805) -> Matrix(1,2,0,1) Matrix(4613,-11132,956,-2307) -> Matrix(3,2,64,43) Matrix(447,-1090,130,-317) -> Matrix(5,2,-8,-3) Matrix(415,-1058,162,-413) -> Matrix(1,0,36,1) Matrix(1333,-3434,394,-1015) -> Matrix(1,0,-12,1) Matrix(453,-1180,124,-323) -> Matrix(1,0,0,1) Matrix(405,-1066,106,-279) -> Matrix(1,0,-4,1) Matrix(1253,-3386,346,-935) -> Matrix(3,-2,20,-13) Matrix(267,-724,52,-141) -> Matrix(3,-2,-4,3) Matrix(10063,-27378,3698,-10061) -> Matrix(41,-40,40,-39) Matrix(223,-610,34,-93) -> Matrix(1,0,0,1) Matrix(1599,-4418,578,-1597) -> Matrix(9,-8,8,-7) Matrix(49,-144,16,-47) -> Matrix(1,-2,0,1) Matrix(1471,-4802,450,-1469) -> Matrix(1,0,8,1) Matrix(2959,-10002,818,-2765) -> Matrix(1,0,8,1) Matrix(5743,-19602,1682,-5741) -> Matrix(11,12,-12,-13) Matrix(725,-2508,172,-595) -> Matrix(11,4,8,3) Matrix(351,-1250,98,-349) -> Matrix(1,0,28,1) Matrix(807,-2936,152,-553) -> Matrix(1,0,-8,1) Matrix(661,-2538,106,-407) -> Matrix(1,0,0,1) Matrix(157,-676,36,-155) -> Matrix(1,-6,0,1) Matrix(699,-3302,134,-633) -> Matrix(5,2,-8,-3) Matrix(1167,-5618,242,-1165) -> Matrix(1,0,40,1) Matrix(271,-1458,50,-269) -> Matrix(1,0,20,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 43 Degree of the the map X: 86 Degree of the the map Y: 256 ----------------------------------------------------------------------- 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): 768 Minimal number of generators: 129 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: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -3/7 -5/13 -1/3 -3/11 -1/5 -1/7 0/1 1/7 3/13 1/3 7/17 5/11 1/2 7/13 3/5 5/7 7/9 1/1 9/7 7/5 3/2 49/31 5/3 9/5 31/17 13/7 2/1 11/5 7/3 45/19 17/7 5/2 23/9 3/1 49/15 10/3 7/2 25/7 11/3 4/1 13/3 9/2 14/3 53/11 5/1 27/5 11/2 6/1 13/2 7/1 8/1 9/1 29/3 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 0/1 1/4 -6/13 1/6 -5/11 1/4 -9/20 1/5 1/4 -4/9 1/2 -7/16 0/1 1/8 -10/23 1/6 -3/7 1/4 -14/33 1/2 -11/26 1/3 1/2 -8/19 1/2 -5/12 0/1 1/8 -12/29 1/6 -7/17 1/4 -9/22 2/9 1/4 -2/5 1/2 -7/18 1/5 1/4 -5/13 1/4 -13/34 1/4 2/7 -8/21 3/10 -3/8 0/1 1/2 -13/35 1/8 -10/27 1/6 -7/19 1/6 -11/30 3/16 1/5 -15/41 1/4 -4/11 3/14 -5/14 1/4 2/7 -11/31 1/4 -6/17 1/2 -1/3 1/4 -7/22 1/3 1/2 -6/19 1/2 -5/16 1/4 1/3 -9/29 1/2 -4/13 1/6 -3/10 1/4 2/7 -8/27 1/2 -5/17 1/4 -7/24 3/10 4/13 -2/7 1/2 -5/18 0/1 1/4 -3/11 1/4 -7/26 1/4 1/3 -11/41 1/4 -4/15 3/10 -1/4 1/3 1/2 -4/17 1/2 -7/30 1/3 3/8 -3/13 1/4 -11/48 7/22 1/3 -8/35 5/14 -5/22 0/1 1/2 -2/9 3/10 -3/14 1/3 3/8 -7/33 3/8 -4/19 1/2 -1/5 1/2 -4/21 1/2 -11/58 0/1 1/6 -7/37 1/4 -3/16 0/1 1/4 -5/27 1/4 -2/11 3/10 -1/6 2/5 1/2 -2/13 1/2 -3/20 0/1 1/2 -1/7 1/4 -3/22 5/16 1/3 -2/15 5/14 -1/8 3/8 2/5 0/1 1/2 1/9 1/0 1/8 0/1 1/4 1/7 1/2 2/13 1/2 1/6 2/3 3/4 1/5 1/0 2/9 1/2 3/13 1/2 4/17 1/2 1/4 1/2 2/3 4/15 5/6 3/11 3/4 2/7 3/2 3/10 0/1 1/0 1/3 1/2 5/14 3/4 1/1 4/11 1/2 3/8 3/4 1/1 8/21 11/14 5/13 7/8 2/5 3/2 9/22 1/1 1/0 7/17 1/0 12/29 1/2 17/41 1/4 5/12 0/1 1/2 3/7 1/0 4/9 1/2 5/11 1/2 6/13 1/2 1/2 1/2 1/1 9/17 9/8 8/15 7/6 7/13 3/2 6/11 3/2 5/9 1/0 9/16 1/1 9/8 4/7 3/2 3/5 1/0 8/13 1/2 5/8 0/1 1/0 17/27 1/2 29/46 1/4 1/3 41/65 3/8 12/19 1/2 7/11 3/4 9/14 1/1 5/4 2/3 1/2 9/13 5/4 7/10 4/3 3/2 19/27 13/8 12/17 11/6 5/7 1/0 13/18 1/1 1/0 21/29 1/0 8/11 1/2 11/15 5/4 3/4 2/1 1/0 7/9 1/0 11/14 -3/1 1/0 4/5 -1/2 9/11 1/2 5/6 1/1 1/0 1/1 1/0 8/7 1/2 7/6 0/1 1/0 6/5 1/2 17/14 1/1 1/0 11/9 1/0 16/13 5/6 5/4 2/1 1/0 9/7 1/0 13/10 -5/1 1/0 4/3 -3/2 11/8 -1/1 -3/4 18/13 -1/2 25/18 0/1 1/0 7/5 -1/2 24/17 -1/6 17/12 0/1 1/2 10/7 -1/2 3/2 0/1 1/2 14/9 5/6 25/16 1/1 9/8 11/7 1/0 30/19 3/2 49/31 1/0 19/12 1/1 1/0 46/29 3/2 27/17 1/0 8/5 3/2 5/3 1/0 12/7 -3/2 19/11 1/0 7/4 -1/1 1/0 16/9 -7/6 25/14 -1/1 -11/12 9/5 -3/4 20/11 -1/2 31/17 -1/2 11/6 -1/2 -2/5 13/7 -1/4 15/8 -1/4 -1/5 2/1 1/2 11/5 1/0 20/9 -9/2 9/4 -2/1 1/0 16/7 -1/2 39/17 1/0 23/10 -1/1 1/0 30/13 -3/2 7/3 1/0 26/11 -7/6 45/19 -1/1 64/27 -17/18 19/8 -1/1 -5/6 12/5 -1/2 41/17 -3/4 111/46 -23/34 -2/3 70/29 -17/26 29/12 -5/8 -3/5 17/7 -1/2 22/9 -1/2 5/2 -1/4 0/1 23/9 0/1 41/16 0/1 1/32 18/7 1/14 13/5 1/4 47/18 0/1 1/4 81/31 1/4 34/13 1/2 21/8 0/1 1/6 8/3 1/2 19/7 3/4 49/18 1/1 7/6 30/11 1/2 11/4 1/2 1/1 3/1 1/0 13/4 -1/2 0/1 49/15 0/1 85/26 0/1 1/6 36/11 1/2 23/7 1/0 10/3 -1/2 17/5 1/0 58/17 -3/2 99/29 -1/1 41/12 -1/1 -3/4 24/7 -1/2 31/9 -1/2 7/2 -1/4 0/1 25/7 0/1 43/12 0/1 1/24 18/5 1/10 11/3 1/4 37/10 4/9 1/2 63/17 1/2 26/7 1/2 15/4 1/1 1/0 4/1 1/2 13/3 1/0 22/5 -5/2 9/2 -1/1 1/0 14/3 -1/2 33/7 -1/2 19/4 -1/3 -1/4 24/5 -1/10 53/11 0/1 82/17 1/30 29/6 0/1 1/10 5/1 1/0 16/3 -1/6 27/5 0/1 38/7 1/14 11/2 0/1 1/4 6/1 -1/2 13/2 1/2 1/1 7/1 1/0 15/2 -1/2 0/1 8/1 -1/2 9/1 1/0 19/2 -1/4 0/1 29/3 0/1 10/1 1/2 1/0 0/1 1/0 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(121,56,296,137) (-1/2,-6/13) -> (2/5,9/22) Hyperbolic Matrix(239,110,-654,-301) (-6/13,-5/11) -> (-15/41,-4/11) Hyperbolic Matrix(173,78,-814,-367) (-5/11,-9/20) -> (-3/14,-7/33) Hyperbolic Matrix(521,234,118,53) (-9/20,-4/9) -> (22/5,9/2) Hyperbolic Matrix(113,50,174,77) (-4/9,-7/16) -> (9/14,2/3) Hyperbolic Matrix(225,98,-962,-419) (-7/16,-10/23) -> (-4/17,-7/30) Hyperbolic Matrix(167,72,-392,-169) (-10/23,-3/7) -> (-3/7,-14/33) Parabolic Matrix(387,164,-1220,-517) (-14/33,-11/26) -> (-7/22,-6/19) Hyperbolic Matrix(109,46,-718,-303) (-11/26,-8/19) -> (-2/13,-3/20) Hyperbolic Matrix(219,92,388,163) (-8/19,-5/12) -> (9/16,4/7) Hyperbolic Matrix(53,22,330,137) (-5/12,-12/29) -> (2/13,1/6) Hyperbolic Matrix(547,226,-1474,-609) (-12/29,-7/17) -> (-13/35,-10/27) Hyperbolic Matrix(161,66,-866,-355) (-7/17,-9/22) -> (-3/16,-5/27) Hyperbolic Matrix(485,198,218,89) (-9/22,-2/5) -> (20/9,9/4) Hyperbolic Matrix(159,62,418,163) (-2/5,-7/18) -> (3/8,8/21) Hyperbolic Matrix(259,100,-676,-261) (-7/18,-5/13) -> (-5/13,-13/34) Parabolic Matrix(309,118,-982,-375) (-13/34,-8/21) -> (-6/19,-5/16) Hyperbolic Matrix(53,20,204,77) (-8/21,-3/8) -> (1/4,4/15) Hyperbolic Matrix(409,152,-1784,-663) (-3/8,-13/35) -> (-3/13,-11/48) Hyperbolic Matrix(303,112,560,207) (-10/27,-7/19) -> (7/13,6/11) Hyperbolic Matrix(605,222,962,353) (-7/19,-11/30) -> (5/8,17/27) Hyperbolic Matrix(153,56,-1112,-407) (-11/30,-15/41) -> (-1/7,-3/22) Hyperbolic Matrix(199,72,152,55) (-4/11,-5/14) -> (13/10,4/3) Hyperbolic Matrix(647,230,346,123) (-5/14,-11/31) -> (13/7,15/8) Hyperbolic Matrix(1885,668,1188,421) (-11/31,-6/17) -> (46/29,27/17) Hyperbolic Matrix(199,70,-742,-261) (-6/17,-1/3) -> (-11/41,-4/15) Hyperbolic Matrix(187,60,-988,-317) (-1/3,-7/22) -> (-11/58,-7/37) Hyperbolic Matrix(1113,346,1766,549) (-5/16,-9/29) -> (17/27,29/46) Hyperbolic Matrix(323,100,604,187) (-9/29,-4/13) -> (8/15,7/13) Hyperbolic Matrix(183,56,232,71) (-4/13,-3/10) -> (11/14,4/5) Hyperbolic Matrix(47,14,-366,-109) (-3/10,-8/27) -> (-2/15,-1/8) Hyperbolic Matrix(865,256,544,161) (-8/27,-5/17) -> (27/17,8/5) Hyperbolic Matrix(499,146,270,79) (-5/17,-7/24) -> (11/6,13/7) Hyperbolic Matrix(227,66,-994,-289) (-7/24,-2/7) -> (-8/35,-5/22) Hyperbolic Matrix(177,50,46,13) (-2/7,-5/18) -> (15/4,4/1) Hyperbolic Matrix(131,36,-484,-133) (-5/18,-3/11) -> (-3/11,-7/26) Parabolic Matrix(305,82,-1618,-435) (-7/26,-11/41) -> (-7/37,-3/16) Hyperbolic Matrix(347,92,132,35) (-4/15,-1/4) -> (21/8,8/3) Hyperbolic Matrix(41,10,86,21) (-1/4,-4/17) -> (6/13,1/2) Hyperbolic Matrix(43,10,374,87) (-7/30,-3/13) -> (1/9,1/8) Hyperbolic Matrix(3737,856,1576,361) (-11/48,-8/35) -> (64/27,19/8) Hyperbolic Matrix(249,56,40,9) (-5/22,-2/9) -> (6/1,13/2) Hyperbolic Matrix(287,62,162,35) (-2/9,-3/14) -> (7/4,16/9) Hyperbolic Matrix(1175,248,488,103) (-7/33,-4/19) -> (12/5,41/17) Hyperbolic Matrix(39,8,-200,-41) (-4/19,-1/5) -> (-1/5,-4/21) Parabolic Matrix(3873,736,1184,225) (-4/21,-11/58) -> (85/26,36/11) Hyperbolic Matrix(315,58,38,7) (-5/27,-2/11) -> (8/1,9/1) Hyperbolic Matrix(117,20,76,13) (-2/11,-1/6) -> (3/2,14/9) Hyperbolic Matrix(37,6,154,25) (-1/6,-2/13) -> (4/17,1/4) Hyperbolic Matrix(375,56,904,135) (-3/20,-1/7) -> (17/41,5/12) Hyperbolic Matrix(1001,136,184,25) (-3/22,-2/15) -> (38/7,11/2) Hyperbolic Matrix(181,22,74,9) (-1/8,0/1) -> (22/9,5/2) Hyperbolic Matrix(149,-12,236,-19) (0/1,1/9) -> (41/65,12/19) Hyperbolic Matrix(397,-52,84,-11) (1/8,1/7) -> (33/7,19/4) Hyperbolic Matrix(527,-80,112,-17) (1/7,2/13) -> (14/3,33/7) Hyperbolic Matrix(81,-14,110,-19) (1/6,1/5) -> (11/15,3/4) Hyperbolic Matrix(211,-46,78,-17) (1/5,2/9) -> (8/3,19/7) Hyperbolic Matrix(79,-18,338,-77) (2/9,3/13) -> (3/13,4/17) Parabolic Matrix(403,-108,556,-149) (4/15,3/11) -> (21/29,8/11) Hyperbolic Matrix(275,-76,76,-21) (3/11,2/7) -> (18/5,11/3) Hyperbolic Matrix(223,-66,98,-29) (2/7,3/10) -> (9/4,16/7) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(189,-68,164,-59) (5/14,4/11) -> (8/7,7/6) Hyperbolic Matrix(211,-78,46,-17) (4/11,3/8) -> (9/2,14/3) Hyperbolic Matrix(555,-212,788,-301) (8/21,5/13) -> (19/27,12/17) Hyperbolic Matrix(299,-116,116,-45) (5/13,2/5) -> (18/7,13/5) Hyperbolic Matrix(1249,-512,544,-223) (9/22,7/17) -> (39/17,23/10) Hyperbolic Matrix(1403,-580,612,-253) (7/17,12/29) -> (16/7,39/17) Hyperbolic Matrix(589,-244,1108,-459) (12/29,17/41) -> (9/17,8/15) Hyperbolic Matrix(157,-66,226,-95) (5/12,3/7) -> (9/13,7/10) Hyperbolic Matrix(223,-98,66,-29) (3/7,4/9) -> (10/3,17/5) Hyperbolic Matrix(111,-50,242,-109) (4/9,5/11) -> (5/11,6/13) Parabolic Matrix(1969,-1040,816,-431) (1/2,9/17) -> (41/17,111/46) Hyperbolic Matrix(391,-216,248,-137) (6/11,5/9) -> (11/7,30/19) Hyperbolic Matrix(369,-206,206,-115) (5/9,9/16) -> (25/14,9/5) Hyperbolic Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(139,-86,118,-73) (8/13,5/8) -> (7/6,6/5) Hyperbolic Matrix(1649,-1040,176,-111) (29/46,41/65) -> (9/1,19/2) Hyperbolic Matrix(391,-248,216,-137) (12/19,7/11) -> (9/5,20/11) Hyperbolic Matrix(429,-274,274,-175) (7/11,9/14) -> (25/16,11/7) Hyperbolic Matrix(359,-248,152,-105) (2/3,9/13) -> (7/3,26/11) Hyperbolic Matrix(1109,-780,300,-211) (7/10,19/27) -> (11/3,37/10) Hyperbolic Matrix(299,-212,244,-173) (12/17,5/7) -> (11/9,16/13) Hyperbolic Matrix(317,-228,260,-187) (5/7,13/18) -> (17/14,11/9) Hyperbolic Matrix(1597,-1156,612,-443) (13/18,21/29) -> (13/5,47/18) Hyperbolic Matrix(295,-216,56,-41) (8/11,11/15) -> (5/1,16/3) Hyperbolic Matrix(127,-98,162,-125) (3/4,7/9) -> (7/9,11/14) Parabolic Matrix(299,-244,212,-173) (4/5,9/11) -> (7/5,24/17) Hyperbolic Matrix(317,-260,228,-187) (9/11,5/6) -> (25/18,7/5) Hyperbolic Matrix(121,-102,70,-59) (5/6,1/1) -> (19/11,7/4) Hyperbolic Matrix(197,-220,60,-67) (1/1,8/7) -> (36/11,23/7) Hyperbolic Matrix(535,-648,232,-281) (6/5,17/14) -> (23/10,30/13) Hyperbolic Matrix(343,-424,72,-89) (16/13,5/4) -> (19/4,24/5) Hyperbolic Matrix(127,-162,98,-125) (5/4,9/7) -> (9/7,13/10) Parabolic Matrix(81,-110,14,-19) (4/3,11/8) -> (11/2,6/1) Hyperbolic Matrix(403,-556,108,-149) (11/8,18/13) -> (26/7,15/4) Hyperbolic Matrix(965,-1338,282,-391) (18/13,25/18) -> (41/12,24/7) Hyperbolic Matrix(1193,-1686,438,-619) (24/17,17/12) -> (49/18,30/11) Hyperbolic Matrix(555,-788,212,-301) (17/12,10/7) -> (34/13,21/8) Hyperbolic Matrix(157,-226,66,-95) (10/7,3/2) -> (19/8,12/5) Hyperbolic Matrix(675,-1052,188,-293) (14/9,25/16) -> (43/12,18/5) Hyperbolic Matrix(2593,-4096,992,-1567) (30/19,49/31) -> (81/31,34/13) Hyperbolic Matrix(2429,-3842,930,-1471) (49/31,19/12) -> (47/18,81/31) Hyperbolic Matrix(149,-236,12,-19) (19/12,46/29) -> (10/1,1/0) Hyperbolic Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(271,-466,82,-141) (12/7,19/11) -> (23/7,10/3) Hyperbolic Matrix(621,-1106,242,-431) (16/9,25/14) -> (41/16,18/7) Hyperbolic Matrix(1135,-2066,306,-557) (20/11,31/17) -> (63/17,26/7) Hyperbolic Matrix(1007,-1840,272,-497) (31/17,11/6) -> (37/10,63/17) Hyperbolic Matrix(589,-1108,244,-459) (15/8,2/1) -> (70/29,29/12) Hyperbolic Matrix(111,-242,50,-109) (2/1,11/5) -> (11/5,20/9) Parabolic Matrix(395,-916,116,-269) (30/13,7/3) -> (17/5,58/17) Hyperbolic Matrix(1711,-4050,722,-1709) (26/11,45/19) -> (45/19,64/27) Parabolic Matrix(4613,-11132,956,-2307) (111/46,70/29) -> (82/17,29/6) Hyperbolic Matrix(421,-1018,122,-295) (29/12,17/7) -> (31/9,7/2) Hyperbolic Matrix(447,-1090,130,-317) (17/7,22/9) -> (24/7,31/9) Hyperbolic Matrix(415,-1058,162,-413) (5/2,23/9) -> (23/9,41/16) Parabolic Matrix(293,-796,60,-163) (19/7,49/18) -> (29/6,5/1) Hyperbolic Matrix(197,-538,26,-71) (30/11,11/4) -> (15/2,8/1) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(1471,-4802,450,-1469) (13/4,49/15) -> (49/15,85/26) Parabolic Matrix(783,-2672,80,-273) (58/17,99/29) -> (29/3,10/1) Hyperbolic Matrix(899,-3070,94,-321) (99/29,41/12) -> (19/2,29/3) Hyperbolic Matrix(351,-1250,98,-349) (7/2,25/7) -> (25/7,43/12) Parabolic Matrix(79,-338,18,-77) (4/1,13/3) -> (13/3,22/5) Parabolic Matrix(1167,-5618,242,-1165) (24/5,53/11) -> (53/11,82/17) Parabolic Matrix(271,-1458,50,-269) (16/3,27/5) -> (27/5,38/7) Parabolic Matrix(29,-196,4,-27) (13/2,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(121,56,296,137) -> Matrix(3,-1,4,-1) Matrix(239,110,-654,-301) -> Matrix(3,-1,16,-5) Matrix(173,78,-814,-367) -> Matrix(11,-2,28,-5) Matrix(521,234,118,53) -> Matrix(9,-2,-4,1) Matrix(113,50,174,77) -> Matrix(3,-1,4,-1) Matrix(225,98,-962,-419) -> Matrix(5,-1,16,-3) Matrix(167,72,-392,-169) -> Matrix(5,-1,16,-3) Matrix(387,164,-1220,-517) -> Matrix(1,0,0,1) Matrix(109,46,-718,-303) -> Matrix(3,-1,4,-1) Matrix(219,92,388,163) -> Matrix(1,1,0,1) Matrix(53,22,330,137) -> Matrix(13,-2,20,-3) Matrix(547,226,-1474,-609) -> Matrix(5,-1,36,-7) Matrix(161,66,-866,-355) -> Matrix(9,-2,32,-7) Matrix(485,198,218,89) -> Matrix(17,-4,-4,1) Matrix(159,62,418,163) -> Matrix(19,-4,24,-5) Matrix(259,100,-676,-261) -> Matrix(13,-3,48,-11) Matrix(309,118,-982,-375) -> Matrix(3,-1,16,-5) Matrix(53,20,204,77) -> Matrix(5,-2,8,-3) Matrix(409,152,-1784,-663) -> Matrix(9,-1,28,-3) Matrix(303,112,560,207) -> Matrix(3,-1,4,-1) Matrix(605,222,962,353) -> Matrix(5,-1,16,-3) Matrix(153,56,-1112,-407) -> Matrix(9,-2,32,-7) Matrix(199,72,152,55) -> Matrix(13,-3,-4,1) Matrix(647,230,346,123) -> Matrix(3,-1,-8,3) Matrix(1885,668,1188,421) -> Matrix(7,-2,4,-1) Matrix(199,70,-742,-261) -> Matrix(5,-1,16,-3) Matrix(187,60,-988,-317) -> Matrix(3,-1,16,-5) Matrix(1113,346,1766,549) -> Matrix(1,0,0,1) Matrix(323,100,604,187) -> Matrix(1,1,0,1) Matrix(183,56,232,71) -> Matrix(5,-1,-4,1) Matrix(47,14,-366,-109) -> Matrix(13,-4,36,-11) Matrix(865,256,544,161) -> Matrix(7,-2,4,-1) Matrix(499,146,270,79) -> Matrix(7,-2,-24,7) Matrix(227,66,-994,-289) -> Matrix(13,-4,36,-11) Matrix(177,50,46,13) -> Matrix(3,-1,4,-1) Matrix(131,36,-484,-133) -> Matrix(5,-1,16,-3) Matrix(305,82,-1618,-435) -> Matrix(3,-1,16,-5) Matrix(347,92,132,35) -> Matrix(3,-1,16,-5) Matrix(41,10,86,21) -> Matrix(5,-2,8,-3) Matrix(43,10,374,87) -> Matrix(3,-1,4,-1) Matrix(3737,856,1576,361) -> Matrix(37,-12,-40,13) Matrix(249,56,40,9) -> Matrix(3,-1,4,-1) Matrix(287,62,162,35) -> Matrix(11,-4,-8,3) Matrix(1175,248,488,103) -> Matrix(1,0,-4,1) Matrix(39,8,-200,-41) -> Matrix(3,-1,4,-1) Matrix(3873,736,1184,225) -> Matrix(1,0,0,1) Matrix(315,58,38,7) -> Matrix(3,-1,4,-1) Matrix(117,20,76,13) -> Matrix(5,-2,8,-3) Matrix(37,6,154,25) -> Matrix(9,-4,16,-7) Matrix(375,56,904,135) -> Matrix(1,0,0,1) Matrix(1001,136,184,25) -> Matrix(3,-1,28,-9) Matrix(181,22,74,9) -> Matrix(5,-2,-12,5) Matrix(149,-12,236,-19) -> Matrix(3,-2,8,-5) Matrix(397,-52,84,-11) -> Matrix(3,-1,-8,3) Matrix(527,-80,112,-17) -> Matrix(7,-4,-12,7) Matrix(81,-14,110,-19) -> Matrix(5,-4,4,-3) Matrix(211,-46,78,-17) -> Matrix(3,-1,4,-1) Matrix(79,-18,338,-77) -> Matrix(15,-7,28,-13) Matrix(403,-108,556,-149) -> Matrix(5,-4,4,-3) Matrix(275,-76,76,-21) -> Matrix(1,-1,8,-7) Matrix(223,-66,98,-29) -> Matrix(1,-2,0,1) Matrix(25,-8,72,-23) -> Matrix(3,-1,4,-1) Matrix(189,-68,164,-59) -> Matrix(1,-1,4,-3) Matrix(211,-78,46,-17) -> Matrix(3,-2,-4,3) Matrix(555,-212,788,-301) -> Matrix(27,-22,16,-13) Matrix(299,-116,116,-45) -> Matrix(1,-1,12,-11) Matrix(1249,-512,544,-223) -> Matrix(1,-2,0,1) Matrix(1403,-580,612,-253) -> Matrix(1,-1,0,1) Matrix(589,-244,1108,-459) -> Matrix(5,1,4,1) Matrix(157,-66,226,-95) -> Matrix(5,-4,4,-3) Matrix(223,-98,66,-29) -> Matrix(1,-1,0,1) Matrix(111,-50,242,-109) -> Matrix(3,-1,4,-1) Matrix(1969,-1040,816,-431) -> Matrix(19,-21,-28,31) Matrix(391,-216,248,-137) -> Matrix(1,0,0,1) Matrix(369,-206,206,-115) -> Matrix(3,-2,-4,3) Matrix(61,-36,100,-59) -> Matrix(1,-1,0,1) Matrix(139,-86,118,-73) -> Matrix(1,0,0,1) Matrix(1649,-1040,176,-111) -> Matrix(3,-1,-8,3) Matrix(391,-248,216,-137) -> Matrix(5,-3,-8,5) Matrix(429,-274,274,-175) -> Matrix(5,-4,4,-3) Matrix(359,-248,152,-105) -> Matrix(5,-6,-4,5) Matrix(1109,-780,300,-211) -> Matrix(5,-8,12,-19) Matrix(299,-212,244,-173) -> Matrix(1,-1,0,1) Matrix(317,-228,260,-187) -> Matrix(1,0,0,1) Matrix(1597,-1156,612,-443) -> Matrix(1,-1,4,-3) Matrix(295,-216,56,-41) -> Matrix(1,-1,-4,5) Matrix(127,-98,162,-125) -> Matrix(1,-5,0,1) Matrix(299,-244,212,-173) -> Matrix(1,0,-4,1) Matrix(317,-260,228,-187) -> Matrix(1,-1,0,1) Matrix(121,-102,70,-59) -> Matrix(1,-2,0,1) Matrix(197,-220,60,-67) -> Matrix(1,0,0,1) Matrix(535,-648,232,-281) -> Matrix(1,-2,0,1) Matrix(343,-424,72,-89) -> Matrix(1,-1,-4,5) Matrix(127,-162,98,-125) -> Matrix(1,-7,0,1) Matrix(81,-110,14,-19) -> Matrix(1,1,0,1) Matrix(403,-556,108,-149) -> Matrix(3,2,4,3) Matrix(965,-1338,282,-391) -> Matrix(3,1,-4,-1) Matrix(1193,-1686,438,-619) -> Matrix(5,1,4,1) Matrix(555,-788,212,-301) -> Matrix(1,0,4,1) Matrix(157,-226,66,-95) -> Matrix(3,1,-4,-1) Matrix(675,-1052,188,-293) -> Matrix(1,-1,16,-15) Matrix(2593,-4096,992,-1567) -> Matrix(1,-2,4,-7) Matrix(2429,-3842,930,-1471) -> Matrix(1,-1,4,-3) Matrix(149,-236,12,-19) -> Matrix(1,-1,0,1) Matrix(61,-100,36,-59) -> Matrix(1,-3,0,1) Matrix(271,-466,82,-141) -> Matrix(1,1,0,1) Matrix(621,-1106,242,-431) -> Matrix(1,1,20,21) Matrix(1135,-2066,306,-557) -> Matrix(13,7,24,13) Matrix(1007,-1840,272,-497) -> Matrix(13,6,28,13) Matrix(589,-1108,244,-459) -> Matrix(13,2,-20,-3) Matrix(111,-242,50,-109) -> Matrix(1,-5,0,1) Matrix(395,-916,116,-269) -> Matrix(1,0,0,1) Matrix(1711,-4050,722,-1709) -> Matrix(23,24,-24,-25) Matrix(4613,-11132,956,-2307) -> Matrix(3,2,64,43) Matrix(421,-1018,122,-295) -> Matrix(5,3,-12,-7) Matrix(447,-1090,130,-317) -> Matrix(5,2,-8,-3) Matrix(415,-1058,162,-413) -> Matrix(1,0,36,1) Matrix(293,-796,60,-163) -> Matrix(1,-1,4,-3) Matrix(197,-538,26,-71) -> Matrix(1,-1,0,1) Matrix(25,-72,8,-23) -> Matrix(1,-1,0,1) Matrix(1471,-4802,450,-1469) -> Matrix(1,0,8,1) Matrix(783,-2672,80,-273) -> Matrix(1,1,4,5) Matrix(899,-3070,94,-321) -> Matrix(1,1,-8,-7) Matrix(351,-1250,98,-349) -> Matrix(1,0,28,1) Matrix(79,-338,18,-77) -> Matrix(1,-3,0,1) Matrix(1167,-5618,242,-1165) -> Matrix(1,0,40,1) Matrix(271,-1458,50,-269) -> Matrix(1,0,20,1) Matrix(29,-196,4,-27) -> Matrix(1,-1,0,1) 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): 43 ----------------------------------------------------------------------- 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 0/1 1/2 1 32 1/8 (0/1,1/4) 0 32 1/7 1/2 5 4 1/6 (2/3,3/4) 0 32 1/5 1/0 1 16 2/9 1/2 1 32 3/13 1/2 7 2 1/4 (1/2,2/3) 0 32 3/11 3/4 1 16 2/7 3/2 1 32 3/10 (0/1,1/0) 0 32 1/3 1/2 1 8 5/14 (3/4,1/1) 0 32 4/11 1/2 1 32 3/8 (3/4,1/1) 0 32 5/13 7/8 1 16 2/5 3/2 1 32 7/17 1/0 1 4 12/29 1/2 1 32 5/12 (0/1,1/2) 0 32 3/7 1/0 1 16 4/9 1/2 1 32 5/11 1/2 1 2 1/2 (1/2,1/1) 0 32 6/11 3/2 1 32 5/9 1/0 1 16 4/7 3/2 1 32 3/5 1/0 1 4 8/13 1/2 1 32 5/8 (0/1,1/0) 0 32 12/19 1/2 1 32 7/11 3/4 1 16 2/3 1/2 1 32 9/13 5/4 1 16 7/10 (4/3,3/2) 0 32 12/17 11/6 1 32 5/7 1/0 1 8 13/18 (1/1,1/0) 0 32 8/11 1/2 1 32 11/15 5/4 1 16 3/4 (2/1,1/0) 0 32 7/9 1/0 5 2 4/5 -1/2 1 32 9/11 1/2 1 8 5/6 (1/1,1/0) 0 32 1/1 1/0 1 16 8/7 1/2 1 32 7/6 (0/1,1/0) 0 32 6/5 1/2 1 32 17/14 (1/1,1/0) 0 32 11/9 1/0 1 8 16/13 5/6 1 32 5/4 (2/1,1/0) 0 32 9/7 1/0 7 2 4/3 -3/2 1 32 11/8 (-1/1,-3/4) 0 32 18/13 -1/2 1 32 25/18 (0/1,1/0) 0 32 7/5 -1/2 1 8 24/17 -1/6 1 32 17/12 (0/1,1/2) 0 32 10/7 -1/2 1 32 3/2 (0/1,1/2) 0 32 11/7 1/0 1 16 30/19 3/2 1 32 49/31 1/0 1 2 19/12 (1/1,1/0) 0 32 8/5 3/2 1 32 5/3 1/0 3 4 12/7 -3/2 1 32 19/11 1/0 1 16 7/4 (-1/1,1/0) 0 32 9/5 -3/4 1 16 20/11 -1/2 1 32 31/17 -1/2 13 2 11/6 (-1/2,-2/5) 0 32 2/1 1/2 1 32 11/5 1/0 5 2 9/4 (-2/1,1/0) 0 32 16/7 -1/2 1 32 23/10 (-1/1,1/0) 0 32 30/13 -3/2 1 32 7/3 1/0 1 16 26/11 -7/6 1 32 45/19 -1/1 12 1 19/8 (-1/1,-5/6) 0 32 12/5 -1/2 1 32 29/12 (-5/8,-3/5) 0 32 17/7 -1/2 5 4 5/2 (-1/4,0/1) 0 32 23/9 0/1 18 1 18/7 1/14 1 32 13/5 1/4 1 16 8/3 1/2 1 32 19/7 3/4 1 16 49/18 (1/1,7/6) 0 32 30/11 1/2 1 32 11/4 (1/2,1/1) 0 32 3/1 1/0 1 8 13/4 (-1/2,0/1) 0 32 49/15 0/1 4 1 36/11 1/2 1 32 23/7 1/0 1 16 10/3 -1/2 1 32 17/5 1/0 1 16 58/17 -3/2 1 32 99/29 -1/1 6 1 41/12 (-1/1,-3/4) 0 32 24/7 -1/2 1 32 7/2 (-1/4,0/1) 0 32 25/7 0/1 14 1 18/5 1/10 1 32 11/3 1/4 1 16 4/1 1/2 1 32 13/3 1/0 3 2 9/2 (-1/1,1/0) 0 32 14/3 -1/2 1 32 19/4 (-1/3,-1/4) 0 32 24/5 -1/10 1 32 53/11 0/1 20 1 29/6 (0/1,1/10) 0 32 5/1 1/0 1 16 16/3 -1/6 1 32 27/5 0/1 10 1 11/2 (0/1,1/4) 0 32 6/1 -1/2 1 32 7/1 1/0 1 4 8/1 -1/2 1 32 1/0 (0/1,1/0) 0 32 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(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(199,-24,58,-7) (0/1,1/8) -> (24/7,7/2) Glide Reflection Matrix(339,-46,140,-19) (1/8,1/7) -> (29/12,17/7) Glide Reflection Matrix(137,-22,56,-9) (1/7,1/6) -> (17/7,5/2) Glide Reflection Matrix(81,-14,110,-19) (1/6,1/5) -> (11/15,3/4) Hyperbolic Matrix(211,-46,78,-17) (1/5,2/9) -> (8/3,19/7) Hyperbolic Matrix(53,-12,234,-53) (2/9,3/13) -> (2/9,3/13) Reflection Matrix(25,-6,104,-25) (3/13,1/4) -> (3/13,1/4) Reflection Matrix(77,-20,50,-13) (1/4,3/11) -> (3/2,11/7) Glide Reflection Matrix(275,-76,76,-21) (3/11,2/7) -> (18/5,11/3) Hyperbolic Matrix(223,-66,98,-29) (2/7,3/10) -> (9/4,16/7) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(189,-68,164,-59) (5/14,4/11) -> (8/7,7/6) Hyperbolic Matrix(211,-78,46,-17) (4/11,3/8) -> (9/2,14/3) Hyperbolic Matrix(163,-62,92,-35) (3/8,5/13) -> (7/4,9/5) Glide Reflection Matrix(299,-116,116,-45) (5/13,2/5) -> (18/7,13/5) Hyperbolic Matrix(137,-56,22,-9) (2/5,7/17) -> (6/1,7/1) Glide Reflection Matrix(339,-140,46,-19) (7/17,12/29) -> (7/1,8/1) Glide Reflection Matrix(679,-282,248,-103) (12/29,5/12) -> (30/11,11/4) Glide Reflection Matrix(157,-66,226,-95) (5/12,3/7) -> (9/13,7/10) Hyperbolic Matrix(223,-98,66,-29) (3/7,4/9) -> (10/3,17/5) Hyperbolic Matrix(89,-40,198,-89) (4/9,5/11) -> (4/9,5/11) Reflection Matrix(21,-10,44,-21) (5/11,1/2) -> (5/11,1/2) Reflection Matrix(207,-112,146,-79) (1/2,6/11) -> (17/12,10/7) Glide Reflection Matrix(391,-216,248,-137) (6/11,5/9) -> (11/7,30/19) Hyperbolic Matrix(163,-92,62,-35) (5/9,4/7) -> (13/5,8/3) Glide Reflection Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(139,-86,118,-73) (8/13,5/8) -> (7/6,6/5) Hyperbolic Matrix(353,-222,256,-161) (5/8,12/19) -> (11/8,18/13) Glide Reflection Matrix(391,-248,216,-137) (12/19,7/11) -> (9/5,20/11) Hyperbolic Matrix(77,-50,20,-13) (7/11,2/3) -> (11/3,4/1) Glide Reflection Matrix(359,-248,152,-105) (2/3,9/13) -> (7/3,26/11) Hyperbolic Matrix(207,-146,112,-79) (7/10,12/17) -> (11/6,2/1) Glide Reflection Matrix(299,-212,244,-173) (12/17,5/7) -> (11/9,16/13) Hyperbolic Matrix(317,-228,260,-187) (5/7,13/18) -> (17/14,11/9) Hyperbolic Matrix(353,-256,222,-161) (13/18,8/11) -> (19/12,8/5) Glide Reflection Matrix(295,-216,56,-41) (8/11,11/15) -> (5/1,16/3) Hyperbolic Matrix(55,-42,72,-55) (3/4,7/9) -> (3/4,7/9) Reflection Matrix(71,-56,90,-71) (7/9,4/5) -> (7/9,4/5) Reflection Matrix(299,-244,212,-173) (4/5,9/11) -> (7/5,24/17) Hyperbolic Matrix(317,-260,228,-187) (9/11,5/6) -> (25/18,7/5) Hyperbolic Matrix(121,-102,70,-59) (5/6,1/1) -> (19/11,7/4) Hyperbolic Matrix(197,-220,60,-67) (1/1,8/7) -> (36/11,23/7) Hyperbolic Matrix(535,-648,232,-281) (6/5,17/14) -> (23/10,30/13) Hyperbolic Matrix(343,-424,72,-89) (16/13,5/4) -> (19/4,24/5) Hyperbolic Matrix(71,-90,56,-71) (5/4,9/7) -> (5/4,9/7) Reflection Matrix(55,-72,42,-55) (9/7,4/3) -> (9/7,4/3) Reflection Matrix(81,-110,14,-19) (4/3,11/8) -> (11/2,6/1) Hyperbolic Matrix(965,-1338,282,-391) (18/13,25/18) -> (41/12,24/7) Hyperbolic Matrix(1193,-1686,438,-619) (24/17,17/12) -> (49/18,30/11) Hyperbolic Matrix(157,-226,66,-95) (10/7,3/2) -> (19/8,12/5) Hyperbolic Matrix(1861,-2940,1178,-1861) (30/19,49/31) -> (30/19,49/31) Reflection Matrix(1177,-1862,744,-1177) (49/31,19/12) -> (49/31,19/12) Reflection Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(271,-466,82,-141) (12/7,19/11) -> (23/7,10/3) Hyperbolic Matrix(681,-1240,374,-681) (20/11,31/17) -> (20/11,31/17) Reflection Matrix(373,-682,204,-373) (31/17,11/6) -> (31/17,11/6) Reflection Matrix(21,-44,10,-21) (2/1,11/5) -> (2/1,11/5) Reflection Matrix(89,-198,40,-89) (11/5,9/4) -> (11/5,9/4) Reflection Matrix(87,-200,10,-23) (16/7,23/10) -> (8/1,1/0) Glide Reflection Matrix(395,-916,116,-269) (30/13,7/3) -> (17/5,58/17) Hyperbolic Matrix(989,-2340,418,-989) (26/11,45/19) -> (26/11,45/19) Reflection Matrix(721,-1710,304,-721) (45/19,19/8) -> (45/19,19/8) Reflection Matrix(263,-634,56,-135) (12/5,29/12) -> (14/3,19/4) Glide Reflection Matrix(91,-230,36,-91) (5/2,23/9) -> (5/2,23/9) Reflection Matrix(323,-828,126,-323) (23/9,18/7) -> (23/9,18/7) Reflection Matrix(293,-796,60,-163) (19/7,49/18) -> (29/6,5/1) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(391,-1274,120,-391) (13/4,49/15) -> (13/4,49/15) Reflection Matrix(1079,-3528,330,-1079) (49/15,36/11) -> (49/15,36/11) Reflection Matrix(3365,-11484,986,-3365) (58/17,99/29) -> (58/17,99/29) Reflection Matrix(2377,-8118,696,-2377) (99/29,41/12) -> (99/29,41/12) Reflection Matrix(99,-350,28,-99) (7/2,25/7) -> (7/2,25/7) Reflection Matrix(251,-900,70,-251) (25/7,18/5) -> (25/7,18/5) Reflection Matrix(25,-104,6,-25) (4/1,13/3) -> (4/1,13/3) Reflection Matrix(53,-234,12,-53) (13/3,9/2) -> (13/3,9/2) Reflection Matrix(529,-2544,110,-529) (24/5,53/11) -> (24/5,53/11) Reflection Matrix(637,-3074,132,-637) (53/11,29/6) -> (53/11,29/6) Reflection Matrix(161,-864,30,-161) (16/3,27/5) -> (16/3,27/5) Reflection Matrix(109,-594,20,-109) (27/5,11/2) -> (27/5,11/2) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,4,-1) (-1/1,0/1) -> (0/1,1/2) Matrix(199,-24,58,-7) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(339,-46,140,-19) -> Matrix(7,-3,-12,5) Matrix(137,-22,56,-9) -> Matrix(3,-2,-8,5) Matrix(81,-14,110,-19) -> Matrix(5,-4,4,-3) 1/1 Matrix(211,-46,78,-17) -> Matrix(3,-1,4,-1) 1/2 Matrix(53,-12,234,-53) -> Matrix(7,-3,16,-7) (2/9,3/13) -> (3/8,1/2) Matrix(25,-6,104,-25) -> Matrix(7,-4,12,-7) (3/13,1/4) -> (1/2,2/3) Matrix(77,-20,50,-13) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(275,-76,76,-21) -> Matrix(1,-1,8,-7) Matrix(223,-66,98,-29) -> Matrix(1,-2,0,1) 1/0 Matrix(25,-8,72,-23) -> Matrix(3,-1,4,-1) 1/2 Matrix(189,-68,164,-59) -> Matrix(1,-1,4,-3) 1/2 Matrix(211,-78,46,-17) -> Matrix(3,-2,-4,3) Matrix(163,-62,92,-35) -> Matrix(5,-4,-4,3) Matrix(299,-116,116,-45) -> Matrix(1,-1,12,-11) Matrix(137,-56,22,-9) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(339,-140,46,-19) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(679,-282,248,-103) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(157,-66,226,-95) -> Matrix(5,-4,4,-3) 1/1 Matrix(223,-98,66,-29) -> Matrix(1,-1,0,1) 1/0 Matrix(89,-40,198,-89) -> Matrix(-1,1,0,1) (4/9,5/11) -> (1/2,1/0) Matrix(21,-10,44,-21) -> Matrix(3,-2,4,-3) (5/11,1/2) -> (1/2,1/1) Matrix(207,-112,146,-79) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(391,-216,248,-137) -> Matrix(1,0,0,1) Matrix(163,-92,62,-35) -> Matrix(1,-1,4,-5) Matrix(61,-36,100,-59) -> Matrix(1,-1,0,1) 1/0 Matrix(139,-86,118,-73) -> Matrix(1,0,0,1) Matrix(353,-222,256,-161) -> Matrix(3,-1,-4,1) Matrix(391,-248,216,-137) -> Matrix(5,-3,-8,5) Matrix(77,-50,20,-13) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(359,-248,152,-105) -> Matrix(5,-6,-4,5) Matrix(207,-146,112,-79) -> Matrix(1,-2,-4,7) Matrix(299,-212,244,-173) -> Matrix(1,-1,0,1) 1/0 Matrix(317,-228,260,-187) -> Matrix(1,0,0,1) Matrix(353,-256,222,-161) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(295,-216,56,-41) -> Matrix(1,-1,-4,5) Matrix(55,-42,72,-55) -> Matrix(-1,4,0,1) (3/4,7/9) -> (2/1,1/0) Matrix(71,-56,90,-71) -> Matrix(1,1,0,-1) (7/9,4/5) -> (-1/2,1/0) Matrix(299,-244,212,-173) -> Matrix(1,0,-4,1) 0/1 Matrix(317,-260,228,-187) -> Matrix(1,-1,0,1) 1/0 Matrix(121,-102,70,-59) -> Matrix(1,-2,0,1) 1/0 Matrix(197,-220,60,-67) -> Matrix(1,0,0,1) Matrix(535,-648,232,-281) -> Matrix(1,-2,0,1) 1/0 Matrix(343,-424,72,-89) -> Matrix(1,-1,-4,5) Matrix(71,-90,56,-71) -> Matrix(-1,4,0,1) (5/4,9/7) -> (2/1,1/0) Matrix(55,-72,42,-55) -> Matrix(1,3,0,-1) (9/7,4/3) -> (-3/2,1/0) Matrix(81,-110,14,-19) -> Matrix(1,1,0,1) 1/0 Matrix(965,-1338,282,-391) -> Matrix(3,1,-4,-1) -1/2 Matrix(1193,-1686,438,-619) -> Matrix(5,1,4,1) Matrix(157,-226,66,-95) -> Matrix(3,1,-4,-1) -1/2 Matrix(1861,-2940,1178,-1861) -> Matrix(-1,3,0,1) (30/19,49/31) -> (3/2,1/0) Matrix(1177,-1862,744,-1177) -> Matrix(-1,2,0,1) (49/31,19/12) -> (1/1,1/0) Matrix(61,-100,36,-59) -> Matrix(1,-3,0,1) 1/0 Matrix(271,-466,82,-141) -> Matrix(1,1,0,1) 1/0 Matrix(681,-1240,374,-681) -> Matrix(17,9,-32,-17) (20/11,31/17) -> (-9/16,-1/2) Matrix(373,-682,204,-373) -> Matrix(9,4,-20,-9) (31/17,11/6) -> (-1/2,-2/5) Matrix(21,-44,10,-21) -> Matrix(-1,1,0,1) (2/1,11/5) -> (1/2,1/0) Matrix(89,-198,40,-89) -> Matrix(1,4,0,-1) (11/5,9/4) -> (-2/1,1/0) Matrix(87,-200,10,-23) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(395,-916,116,-269) -> Matrix(1,0,0,1) Matrix(989,-2340,418,-989) -> Matrix(13,14,-12,-13) (26/11,45/19) -> (-7/6,-1/1) Matrix(721,-1710,304,-721) -> Matrix(11,10,-12,-11) (45/19,19/8) -> (-1/1,-5/6) Matrix(263,-634,56,-135) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(91,-230,36,-91) -> Matrix(-1,0,8,1) (5/2,23/9) -> (-1/4,0/1) Matrix(323,-828,126,-323) -> Matrix(1,0,28,-1) (23/9,18/7) -> (0/1,1/14) Matrix(293,-796,60,-163) -> Matrix(1,-1,4,-3) 1/2 Matrix(25,-72,8,-23) -> Matrix(1,-1,0,1) 1/0 Matrix(391,-1274,120,-391) -> Matrix(-1,0,4,1) (13/4,49/15) -> (-1/2,0/1) Matrix(1079,-3528,330,-1079) -> Matrix(1,0,4,-1) (49/15,36/11) -> (0/1,1/2) Matrix(3365,-11484,986,-3365) -> Matrix(5,6,-4,-5) (58/17,99/29) -> (-3/2,-1/1) Matrix(2377,-8118,696,-2377) -> Matrix(7,6,-8,-7) (99/29,41/12) -> (-1/1,-3/4) Matrix(99,-350,28,-99) -> Matrix(-1,0,8,1) (7/2,25/7) -> (-1/4,0/1) Matrix(251,-900,70,-251) -> Matrix(1,0,20,-1) (25/7,18/5) -> (0/1,1/10) Matrix(25,-104,6,-25) -> Matrix(-1,1,0,1) (4/1,13/3) -> (1/2,1/0) Matrix(53,-234,12,-53) -> Matrix(1,2,0,-1) (13/3,9/2) -> (-1/1,1/0) Matrix(529,-2544,110,-529) -> Matrix(-1,0,20,1) (24/5,53/11) -> (-1/10,0/1) Matrix(637,-3074,132,-637) -> Matrix(1,0,20,-1) (53/11,29/6) -> (0/1,1/10) Matrix(161,-864,30,-161) -> Matrix(-1,0,12,1) (16/3,27/5) -> (-1/6,0/1) Matrix(109,-594,20,-109) -> Matrix(1,0,8,-1) (27/5,11/2) -> (0/1,1/4) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.