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 -3/7 -5/13 -1/3 -3/11 -1/5 -1/7 0/1 1/7 5/27 3/13 7/25 1/3 9/23 7/17 5/11 1/2 7/13 17/31 3/5 13/19 5/7 7/9 1/1 8/7 9/7 7/5 3/2 5/3 161/95 9/5 31/17 13/7 21/11 2/1 11/5 67/29 7/3 45/19 17/7 5/2 23/9 47/17 3/1 16/5 49/15 10/3 24/7 7/2 25/7 11/3 4/1 13/3 22/5 9/2 14/3 24/5 53/11 5/1 16/3 27/5 11/2 6/1 13/2 20/3 7/1 22/3 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 1/4 -6/13 2/7 3/10 -5/11 1/2 -14/31 0/1 1/4 -9/20 1/4 -4/9 1/4 2/7 -7/16 3/8 -10/23 0/1 1/2 -13/30 1/4 -16/37 0/1 1/2 -3/7 1/4 -17/40 7/24 -14/33 3/10 1/3 -11/26 1/4 -8/19 3/10 1/3 -5/12 3/8 -17/41 1/2 -12/29 0/1 1/4 -7/17 1/2 -23/56 1/4 -16/39 3/10 1/3 -9/22 1/4 -2/5 1/4 1/3 -11/28 3/8 -9/23 1/2 -7/18 3/8 -19/49 1/2 -31/80 3/8 -12/31 1/3 1/2 -5/13 1/2 -13/34 1/4 -8/21 0/1 1/2 -19/50 1/4 -30/79 1/4 5/19 -11/29 3/10 -3/8 1/4 -13/35 5/14 -10/27 4/11 3/8 -7/19 1/2 -11/30 1/4 -15/41 5/14 -4/11 2/5 1/2 -5/14 1/0 -11/31 1/4 -6/17 1/3 1/2 -1/3 1/2 -7/22 1/4 -6/19 0/1 1/2 -5/16 1/4 -9/29 1/2 -13/42 5/16 -17/55 5/14 -4/13 2/5 1/2 -3/10 3/4 -11/37 1/2 -19/64 7/8 -8/27 1/1 3/2 -13/44 1/0 -31/105 -1/2 -18/61 0/1 1/2 -5/17 1/0 -17/58 -1/4 -12/41 0/1 1/4 -7/24 1/0 -16/55 -3/2 -1/1 -9/31 -1/2 -11/38 -1/8 -2/7 0/1 1/4 -5/18 3/8 -13/47 1/2 -8/29 2/5 1/2 -11/40 7/16 -3/11 1/2 -13/48 5/8 -10/37 3/5 5/8 -7/26 3/4 -11/41 1/2 -4/15 1/2 1/1 -1/4 1/4 -4/17 1/2 2/3 -7/30 1/0 -10/43 1/2 1/1 -3/13 1/2 -11/48 7/8 -8/35 1/1 5/4 -5/22 1/0 -2/9 -1/2 0/1 -7/32 1/16 -5/23 1/6 -3/14 1/4 -7/33 3/10 -11/52 1/4 -4/19 1/4 1/3 -13/62 3/8 -9/43 1/2 -5/24 1/4 -1/5 1/2 -4/21 0/1 1/0 -11/58 1/4 -7/37 1/2 -3/16 1/0 -5/27 1/2 -2/11 -1/2 0/1 -5/28 1/12 -3/17 1/6 -1/6 1/4 -2/13 1/2 1/1 -3/20 1/0 -1/7 1/2 -4/29 -1/1 -1/2 -3/22 -1/4 -2/15 0/1 1/6 -1/8 1/0 -2/17 1/4 1/3 -1/9 1/2 0/1 0/1 1/2 1/10 1/0 2/19 0/1 1/6 1/9 1/2 1/8 1/4 1/7 1/2 2/13 1/1 1/0 5/32 -1/4 3/19 1/2 1/6 1/4 3/17 1/0 2/11 -1/2 0/1 5/27 0/1 8/43 0/1 1/18 3/16 1/8 7/37 1/6 4/21 1/6 1/5 1/5 1/2 2/9 1/3 1/2 5/22 5/12 3/13 1/2 7/30 7/12 4/17 1/2 2/3 9/38 3/4 5/21 1/2 1/4 1/0 5/19 1/2 4/15 1/2 1/1 3/11 -1/2 11/40 1/0 8/29 -1/3 -1/4 5/18 -1/8 7/25 0/1 9/32 1/20 2/7 0/1 1/6 7/24 1/4 5/17 1/2 13/44 1/0 8/27 0/1 1/4 3/10 1/4 4/13 0/1 1/4 1/3 1/2 5/14 1/0 4/11 1/1 1/0 15/41 1/2 11/30 1/0 18/49 7/8 1/1 7/19 3/2 24/65 5/2 3/1 17/46 1/0 10/27 3/1 1/0 3/8 1/0 11/29 -1/2 19/50 -1/4 8/21 -1/4 0/1 5/13 -1/2 17/44 -3/16 12/31 -1/6 0/1 7/18 -1/12 9/23 0/1 11/28 1/24 2/5 0/1 1/6 9/22 1/4 16/39 2/9 5/22 7/17 1/4 12/29 3/11 5/18 17/41 3/10 5/12 1/4 18/43 5/16 1/3 13/31 1/4 21/50 7/24 8/19 5/16 1/3 3/7 1/2 4/9 2/5 1/2 9/20 9/20 5/11 1/2 11/24 11/20 6/13 1/2 3/5 13/28 3/4 7/15 1/2 1/2 1/0 9/17 1/10 8/15 1/7 1/6 7/13 1/6 6/11 2/9 1/4 17/31 1/4 11/20 1/4 5/9 3/10 9/16 7/20 4/7 1/3 1/2 7/12 3/8 31/53 1/2 24/41 2/5 1/2 17/29 1/2 27/46 13/32 37/63 5/12 10/17 5/12 3/7 3/5 1/2 14/23 7/12 3/5 25/41 1/2 36/59 1/2 3/5 11/18 7/12 19/31 9/14 27/44 11/16 35/57 3/4 8/13 1/2 2/3 21/34 1/0 13/21 1/2 18/29 2/3 3/4 5/8 3/4 17/27 1/2 29/46 3/4 41/65 1/2 12/19 1/2 1/1 7/11 1/2 9/14 5/4 2/3 0/1 1/0 13/19 0/1 24/35 0/1 1/24 11/16 1/12 20/29 1/8 1/7 29/42 1/4 9/13 1/6 25/36 3/16 16/23 1/5 3/14 23/33 1/4 30/43 2/7 3/10 37/53 1/2 7/10 1/4 26/37 0/1 1/2 45/64 1/4 19/27 1/2 12/17 0/1 1/0 5/7 1/4 28/39 5/16 1/3 23/32 3/8 18/25 0/1 1/2 13/18 1/4 21/29 5/18 8/11 3/10 1/3 11/15 1/2 25/34 1/4 14/19 1/3 1/2 31/42 3/8 17/23 1/2 3/4 3/8 16/21 3/7 7/16 29/38 7/16 13/17 1/2 23/30 7/16 56/73 4/9 1/2 33/43 1/2 10/13 5/11 1/2 7/9 1/2 18/23 1/2 9/17 11/14 11/20 4/5 1/2 2/3 17/21 5/6 30/37 15/16 1/1 43/53 1/1 13/16 5/4 35/43 5/2 22/27 -1/1 1/0 31/38 1/4 9/11 1/2 5/6 1/0 1/1 1/2 8/7 1/1 1/0 7/6 1/0 6/5 1/2 1/1 23/19 3/2 17/14 1/0 28/23 -1/2 0/1 11/9 1/0 16/13 -1/4 0/1 5/4 1/4 24/19 2/5 1/2 19/15 1/2 71/56 3/8 52/41 3/8 2/5 33/26 3/8 47/37 1/2 61/48 3/8 14/11 3/7 1/2 9/7 1/2 22/17 1/2 7/13 35/27 1/2 13/10 9/16 4/3 1/2 2/3 11/8 1/0 18/13 1/2 1/1 25/18 1/0 7/5 1/2 24/17 1/2 3/5 17/12 11/16 10/7 3/4 4/5 3/2 1/0 20/13 1/2 1/1 17/11 1/2 31/20 3/4 14/9 5/6 1/1 25/16 9/8 11/7 3/2 41/26 11/4 71/45 7/2 101/64 15/4 30/19 5/1 1/0 79/50 1/0 49/31 1/0 19/12 1/0 46/29 -1/1 -1/2 27/17 1/0 35/22 -1/4 8/5 0/1 1/2 21/13 1/2 13/8 1/0 31/19 1/2 80/49 0/1 1/2 49/30 1/0 18/11 0/1 1/4 5/3 1/2 22/13 2/3 3/4 61/36 3/4 161/95 1/1 100/59 1/2 1/1 39/23 1/2 56/33 1/2 3/5 73/43 1/2 17/10 3/4 29/17 7/10 41/24 3/4 12/7 1/2 1/1 19/11 1/2 64/37 3/4 1/1 45/26 1/4 26/15 1/2 3/5 33/19 1/2 73/42 3/4 40/23 1/2 2/3 7/4 3/4 30/17 3/4 4/5 23/13 5/6 62/35 5/6 1/1 225/127 1/1 163/92 3/4 101/57 5/6 39/22 3/4 55/31 5/6 16/9 9/10 1/1 25/14 9/8 9/5 1/2 20/11 1/2 1/1 31/17 1/2 42/23 1/2 2/3 11/6 3/4 24/13 1/1 1/0 37/20 5/8 13/7 3/4 28/15 4/5 5/6 15/8 7/8 17/9 9/10 19/10 19/20 21/11 1/1 2/1 1/1 1/0 13/6 1/0 11/5 1/0 31/14 1/0 20/9 0/1 1/0 69/31 1/0 49/22 1/4 29/13 1/2 9/4 1/0 25/11 1/2 16/7 1/1 3/2 39/17 1/0 62/27 -1/1 -1/2 23/10 1/0 30/13 -1/2 0/1 67/29 0/1 104/45 0/1 1/10 37/16 1/4 7/3 1/2 26/11 7/8 1/1 45/19 1/1 64/27 1/1 17/16 19/8 5/4 12/5 0/1 1/0 41/17 -1/2 111/46 -1/12 70/29 0/1 1/8 29/12 1/0 46/19 0/1 1/2 17/7 1/2 22/9 1/2 1/1 49/20 1/0 27/11 1/2 5/2 3/4 23/9 1/1 41/16 33/32 18/7 1/1 15/14 31/12 9/8 13/5 7/6 47/18 5/4 81/31 5/4 34/13 5/4 14/11 21/8 11/8 8/3 1/1 3/2 19/7 3/2 49/18 17/8 30/11 5/2 3/1 11/4 1/0 47/17 1/1 83/30 9/8 36/13 1/1 5/4 25/9 3/2 14/5 1/1 3/2 45/16 13/8 31/11 3/2 79/28 1/0 48/17 3/2 2/1 17/6 7/4 20/7 3/1 1/0 23/8 1/0 3/1 1/0 25/8 1/0 22/7 0/1 1/0 19/6 -1/4 16/5 0/1 1/2 45/14 3/4 29/9 1/2 13/4 1/0 49/15 0/1 85/26 1/8 36/11 0/1 1/4 23/7 1/2 10/3 0/1 1/2 17/5 1/2 58/17 5/6 1/1 99/29 1/1 41/12 1/0 24/7 1/2 1/1 31/9 1/2 38/11 3/4 1/1 7/2 3/4 25/7 1/1 43/12 25/24 18/5 1/1 11/10 47/13 7/6 76/21 1/1 7/6 29/8 5/4 11/3 3/2 37/10 5/4 100/27 4/3 3/2 63/17 3/2 26/7 1/1 3/2 15/4 5/4 4/1 2/1 1/0 17/4 1/0 13/3 1/0 35/8 1/0 22/5 -5/1 1/0 75/17 1/0 128/29 -4/1 1/0 53/12 1/0 84/19 -5/1 -9/2 31/7 -7/2 9/2 1/0 32/7 -1/1 -5/6 55/12 1/0 78/17 -1/1 -1/2 23/5 -1/2 14/3 0/1 1/0 33/7 -1/2 19/4 1/0 24/5 -1/8 0/1 53/11 0/1 82/17 0/1 1/32 29/6 1/12 5/1 1/2 16/3 5/6 1/1 27/5 1/1 38/7 1/1 15/14 11/2 5/4 6/1 3/2 2/1 13/2 1/0 20/3 9/2 5/1 27/4 1/0 7/1 1/0 29/4 1/0 22/3 -7/2 -3/1 15/2 1/0 23/3 -3/2 8/1 -1/2 0/1 9/1 1/2 19/2 3/4 29/3 1/1 10/1 1/1 3/2 1/0 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(1403,634,582,263) (-5/11,-14/31) -> (12/5,41/17) Hyperbolic Matrix(817,368,464,209) (-14/31,-9/20) -> (7/4,30/17) Hyperbolic Matrix(233,104,56,25) (-9/20,-4/9) -> (4/1,17/4) 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(341,148,-1076,-467) (-10/23,-13/30) -> (-7/22,-6/19) Hyperbolic Matrix(453,196,1916,829) (-13/30,-16/37) -> (4/17,9/38) Hyperbolic Matrix(1351,584,2200,951) (-16/37,-3/7) -> (35/57,8/13) Hyperbolic Matrix(1669,710,2842,1209) (-3/7,-17/40) -> (27/46,37/63) Hyperbolic Matrix(669,284,1444,613) (-17/40,-14/33) -> (6/13,13/28) Hyperbolic Matrix(1335,566,-3446,-1461) (-14/33,-11/26) -> (-31/80,-12/31) 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(327,136,440,183) (-5/12,-17/41) -> (17/23,3/4) Hyperbolic Matrix(1531,634,326,135) (-17/41,-12/29) -> (14/3,33/7) Hyperbolic Matrix(547,226,-1474,-609) (-12/29,-7/17) -> (-13/35,-10/27) Hyperbolic Matrix(1957,804,-6628,-2723) (-7/17,-23/56) -> (-13/44,-31/105) Hyperbolic Matrix(2173,892,324,133) (-23/56,-16/39) -> (20/3,27/4) Hyperbolic Matrix(1517,622,978,401) (-16/39,-9/22) -> (31/20,14/9) Hyperbolic Matrix(109,44,52,21) (-9/22,-2/5) -> (2/1,13/6) Hyperbolic Matrix(529,208,1264,497) (-2/5,-11/28) -> (5/12,18/43) Hyperbolic Matrix(1159,454,314,123) (-11/28,-9/23) -> (11/3,37/10) Hyperbolic Matrix(947,370,366,143) (-9/23,-7/18) -> (31/12,13/5) Hyperbolic Matrix(1361,528,1776,689) (-7/18,-19/49) -> (13/17,23/30) Hyperbolic Matrix(1357,526,-6478,-2511) (-19/49,-31/80) -> (-13/62,-9/43) Hyperbolic Matrix(207,80,784,303) (-12/31,-5/13) -> (5/19,4/15) Hyperbolic Matrix(413,158,1090,417) (-5/13,-13/34) -> (3/8,11/29) Hyperbolic Matrix(309,118,-982,-375) (-13/34,-8/21) -> (-6/19,-5/16) Hyperbolic Matrix(1757,668,1444,549) (-8/21,-19/50) -> (17/14,28/23) Hyperbolic Matrix(7741,2940,4900,1861) (-19/50,-30/79) -> (30/19,79/50) Hyperbolic Matrix(3403,1292,4180,1587) (-30/79,-11/29) -> (35/43,22/27) Hyperbolic Matrix(929,352,256,97) (-11/29,-3/8) -> (29/8,11/3) 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(1109,406,-3734,-1367) (-11/30,-15/41) -> (-11/37,-19/64) Hyperbolic Matrix(199,72,152,55) (-4/11,-5/14) -> (13/10,4/3) Hyperbolic Matrix(597,212,-2036,-723) (-5/14,-11/31) -> (-5/17,-17/58) 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(4171,1292,2644,819) (-9/29,-13/42) -> (41/26,71/45) Hyperbolic Matrix(1759,544,928,287) (-13/42,-17/55) -> (17/9,19/10) Hyperbolic Matrix(2131,658,3054,943) (-17/55,-4/13) -> (30/43,37/53) Hyperbolic Matrix(183,56,232,71) (-4/13,-3/10) -> (11/14,4/5) Hyperbolic Matrix(455,136,184,55) (-3/10,-11/37) -> (27/11,5/2) Hyperbolic Matrix(2729,810,502,149) (-19/64,-8/27) -> (38/7,11/2) Hyperbolic Matrix(1635,484,956,283) (-8/27,-13/44) -> (41/24,12/7) Hyperbolic Matrix(271,80,2544,751) (-31/105,-18/61) -> (2/19,1/9) Hyperbolic Matrix(1269,374,682,201) (-18/61,-5/17) -> (13/7,28/15) Hyperbolic Matrix(5249,1538,2174,637) (-17/58,-12/41) -> (70/29,29/12) Hyperbolic Matrix(2441,714,1494,437) (-12/41,-7/24) -> (49/30,18/11) Hyperbolic Matrix(1353,394,182,53) (-7/24,-16/55) -> (22/3,15/2) Hyperbolic Matrix(3521,1024,1984,577) (-16/55,-9/31) -> (55/31,16/9) Hyperbolic Matrix(269,78,1714,497) (-9/31,-11/38) -> (5/32,3/19) Hyperbolic Matrix(989,286,1442,417) (-11/38,-2/7) -> (24/35,11/16) Hyperbolic Matrix(177,50,46,13) (-2/7,-5/18) -> (15/4,4/1) Hyperbolic Matrix(267,74,-1418,-393) (-5/18,-13/47) -> (-7/37,-3/16) Hyperbolic Matrix(1679,464,1328,367) (-13/47,-8/29) -> (24/19,19/15) Hyperbolic Matrix(973,268,2516,693) (-8/29,-11/40) -> (17/44,12/31) Hyperbolic Matrix(263,72,-968,-265) (-11/40,-3/11) -> (-3/11,-13/48) Parabolic Matrix(1841,498,2414,653) (-13/48,-10/37) -> (16/21,29/38) Hyperbolic Matrix(615,166,2234,603) (-10/37,-7/26) -> (11/40,8/29) Hyperbolic Matrix(439,118,-2102,-565) (-7/26,-11/41) -> (-9/43,-5/24) Hyperbolic Matrix(347,92,132,35) (-4/15,-1/4) -> (21/8,8/3) Hyperbolic Matrix(169,40,376,89) (-1/4,-4/17) -> (4/9,9/20) Hyperbolic Matrix(1753,408,2376,553) (-7/30,-10/43) -> (14/19,31/42) Hyperbolic Matrix(1919,446,3042,707) (-10/43,-3/13) -> (41/65,12/19) Hyperbolic Matrix(3737,856,1576,361) (-11/48,-8/35) -> (64/27,19/8) Hyperbolic Matrix(913,208,496,113) (-8/35,-5/22) -> (11/6,24/13) Hyperbolic Matrix(249,56,40,9) (-5/22,-2/9) -> (6/1,13/2) Hyperbolic Matrix(163,36,412,91) (-2/9,-7/32) -> (11/28,2/5) Hyperbolic Matrix(1229,268,2004,437) (-7/32,-5/23) -> (19/31,27/44) Hyperbolic Matrix(733,158,450,97) (-5/23,-3/14) -> (13/8,31/19) Hyperbolic Matrix(731,156,164,35) (-3/14,-7/33) -> (31/7,9/2) Hyperbolic Matrix(1379,292,732,155) (-7/33,-11/52) -> (15/8,17/9) Hyperbolic Matrix(2109,446,610,129) (-11/52,-4/19) -> (38/11,7/2) Hyperbolic Matrix(3809,800,1376,289) (-4/19,-13/62) -> (83/30,36/13) Hyperbolic Matrix(563,116,364,75) (-5/24,-1/5) -> (17/11,31/20) Hyperbolic Matrix(633,122,358,69) (-1/5,-4/21) -> (30/17,23/13) Hyperbolic Matrix(3873,736,1184,225) (-4/21,-11/58) -> (85/26,36/11) Hyperbolic Matrix(707,132,316,59) (-3/16,-5/27) -> (29/13,9/4) Hyperbolic Matrix(315,58,38,7) (-5/27,-2/11) -> (8/1,9/1) Hyperbolic Matrix(155,28,548,99) (-2/11,-5/28) -> (9/32,2/7) Hyperbolic Matrix(935,166,1594,283) (-5/28,-3/17) -> (17/29,27/46) Hyperbolic Matrix(463,80,272,47) (-3/17,-1/6) -> (17/10,29/17) Hyperbolic Matrix(77,12,340,53) (-1/6,-2/13) -> (2/9,5/22) Hyperbolic Matrix(375,56,904,135) (-3/20,-1/7) -> (17/41,5/12) Hyperbolic Matrix(1487,208,336,47) (-1/7,-4/29) -> (84/19,31/7) Hyperbolic Matrix(2077,286,1634,225) (-4/29,-3/22) -> (61/48,14/11) Hyperbolic Matrix(221,30,1186,161) (-3/22,-2/15) -> (8/43,3/16) Hyperbolic Matrix(589,78,370,49) (-2/15,-1/8) -> (35/22,8/5) Hyperbolic Matrix(653,78,946,113) (-1/8,-2/17) -> (20/29,29/42) Hyperbolic Matrix(869,100,252,29) (-2/17,-1/9) -> (31/9,38/11) Hyperbolic Matrix(431,46,178,19) (-1/9,0/1) -> (46/19,17/7) Hyperbolic Matrix(583,-56,760,-73) (0/1,1/10) -> (23/30,56/73) Hyperbolic Matrix(1743,-178,754,-77) (1/10,2/19) -> (104/45,37/16) Hyperbolic Matrix(173,-20,372,-43) (1/9,1/8) -> (13/28,7/15) Hyperbolic Matrix(397,-52,84,-11) (1/8,1/7) -> (33/7,19/4) Hyperbolic Matrix(223,-34,610,-93) (1/7,2/13) -> (4/11,15/41) Hyperbolic Matrix(2273,-352,1440,-223) (2/13,5/32) -> (101/64,30/19) Hyperbolic Matrix(1105,-176,496,-79) (3/19,1/6) -> (49/22,29/13) Hyperbolic Matrix(435,-76,1036,-181) (1/6,3/17) -> (13/31,21/50) Hyperbolic Matrix(597,-106,490,-87) (3/17,2/11) -> (28/23,11/9) Hyperbolic Matrix(271,-50,1458,-269) (2/11,5/27) -> (5/27,8/43) Parabolic Matrix(3229,-610,1858,-351) (3/16,7/37) -> (33/19,73/42) Hyperbolic Matrix(3605,-684,2124,-403) (7/37,4/21) -> (56/33,73/43) Hyperbolic Matrix(267,-52,724,-141) (4/21,1/5) -> (7/19,24/65) Hyperbolic Matrix(211,-46,78,-17) (1/5,2/9) -> (8/3,19/7) Hyperbolic Matrix(157,-36,676,-155) (5/22,3/13) -> (3/13,7/30) Parabolic Matrix(1245,-292,388,-91) (7/30,4/17) -> (16/5,45/14) Hyperbolic Matrix(1553,-368,2224,-527) (9/38,5/21) -> (37/53,7/10) Hyperbolic Matrix(1137,-272,464,-111) (5/21,1/4) -> (49/20,27/11) Hyperbolic Matrix(405,-106,1066,-279) (1/4,5/19) -> (11/29,19/50) Hyperbolic Matrix(403,-108,556,-149) (4/15,3/11) -> (21/29,8/11) Hyperbolic Matrix(1255,-344,1784,-489) (3/11,11/40) -> (45/64,19/27) Hyperbolic Matrix(853,-236,300,-83) (8/29,5/18) -> (17/6,20/7) Hyperbolic Matrix(351,-98,1250,-349) (5/18,7/25) -> (7/25,9/32) Parabolic Matrix(447,-130,1090,-317) (2/7,7/24) -> (9/22,16/39) Hyperbolic Matrix(841,-246,694,-203) (7/24,5/17) -> (23/19,17/14) Hyperbolic Matrix(889,-262,1286,-379) (5/17,13/44) -> (29/42,9/13) Hyperbolic Matrix(1481,-438,470,-139) (13/44,8/27) -> (22/7,19/6) Hyperbolic Matrix(1037,-308,468,-139) (8/27,3/10) -> (31/14,20/9) Hyperbolic Matrix(245,-74,394,-119) (3/10,4/13) -> (18/29,5/8) Hyperbolic Matrix(341,-106,74,-23) (4/13,1/3) -> (23/5,14/3) Hyperbolic Matrix(377,-134,166,-59) (1/3,5/14) -> (9/4,25/11) Hyperbolic Matrix(189,-68,164,-59) (5/14,4/11) -> (8/7,7/6) Hyperbolic Matrix(1781,-652,2412,-883) (15/41,11/30) -> (31/42,17/23) Hyperbolic Matrix(1967,-722,2738,-1005) (11/30,18/49) -> (28/39,23/32) Hyperbolic Matrix(1403,-516,1732,-637) (18/49,7/19) -> (17/21,30/37) Hyperbolic Matrix(2897,-1070,398,-147) (24/65,17/46) -> (29/4,22/3) Hyperbolic Matrix(1541,-570,538,-199) (17/46,10/27) -> (20/7,23/8) Hyperbolic Matrix(1121,-416,256,-95) (10/27,3/8) -> (35/8,22/5) Hyperbolic Matrix(3293,-1252,2596,-987) (19/50,8/21) -> (52/41,33/26) Hyperbolic Matrix(555,-212,788,-301) (8/21,5/13) -> (19/27,12/17) Hyperbolic Matrix(1709,-660,2100,-811) (5/13,17/44) -> (13/16,35/43) Hyperbolic Matrix(877,-340,276,-107) (12/31,7/18) -> (19/6,16/5) Hyperbolic Matrix(415,-162,1058,-413) (7/18,9/23) -> (9/23,11/28) Parabolic Matrix(1407,-578,2018,-829) (16/39,7/17) -> (23/33,30/43) 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(1083,-454,1510,-633) (18/43,13/31) -> (5/7,28/39) Hyperbolic Matrix(4055,-1704,2344,-985) (21/50,8/19) -> (64/37,45/26) Hyperbolic Matrix(315,-134,134,-57) (8/19,3/7) -> (7/3,26/11) Hyperbolic Matrix(223,-98,66,-29) (3/7,4/9) -> (10/3,17/5) Hyperbolic Matrix(221,-100,484,-219) (9/20,5/11) -> (5/11,11/24) Parabolic Matrix(921,-424,328,-151) (11/24,6/13) -> (14/5,45/16) Hyperbolic Matrix(695,-328,392,-185) (7/15,1/2) -> (39/22,55/31) Hyperbolic Matrix(1969,-1040,816,-431) (1/2,9/17) -> (41/17,111/46) Hyperbolic Matrix(625,-334,814,-435) (8/15,7/13) -> (33/43,10/13) Hyperbolic Matrix(1945,-1064,744,-407) (6/11,17/31) -> (81/31,34/13) Hyperbolic Matrix(3429,-1882,2170,-1191) (17/31,11/20) -> (79/50,49/31) Hyperbolic Matrix(949,-524,556,-307) (11/20,5/9) -> (29/17,41/24) Hyperbolic Matrix(369,-206,206,-115) (5/9,9/16) -> (25/14,9/5) Hyperbolic Matrix(121,-70,102,-59) (4/7,7/12) -> (7/6,6/5) Hyperbolic Matrix(3797,-2220,2988,-1747) (7/12,31/53) -> (47/37,61/48) Hyperbolic Matrix(4321,-2528,5632,-3295) (31/53,24/41) -> (56/73,33/43) Hyperbolic Matrix(3591,-2104,2200,-1289) (24/41,17/29) -> (31/19,80/49) Hyperbolic Matrix(2661,-1564,604,-355) (37/63,10/17) -> (22/5,75/17) Hyperbolic Matrix(121,-72,200,-119) (10/17,3/5) -> (3/5,14/23) Parabolic Matrix(3061,-1866,1770,-1079) (14/23,25/41) -> (19/11,64/37) Hyperbolic Matrix(6401,-3904,3776,-2303) (25/41,36/59) -> (100/59,39/23) Hyperbolic Matrix(4649,-2838,1014,-619) (36/59,11/18) -> (55/12,78/17) Hyperbolic Matrix(1469,-900,932,-571) (11/18,19/31) -> (11/7,41/26) Hyperbolic Matrix(5829,-3578,2618,-1607) (27/44,35/57) -> (69/31,49/22) Hyperbolic Matrix(911,-562,1266,-781) (8/13,21/34) -> (23/32,18/25) Hyperbolic Matrix(1463,-904,1128,-697) (21/34,13/21) -> (35/27,13/10) Hyperbolic Matrix(1423,-882,434,-269) (13/21,18/29) -> (36/11,23/7) 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(495,-338,722,-493) (2/3,13/19) -> (13/19,24/35) Parabolic Matrix(1251,-862,1534,-1057) (11/16,20/29) -> (22/27,31/38) Hyperbolic Matrix(1701,-1180,604,-419) (9/13,25/36) -> (45/16,31/11) Hyperbolic Matrix(2417,-1680,528,-367) (25/36,16/23) -> (32/7,55/12) Hyperbolic Matrix(2943,-2050,1282,-893) (16/23,23/33) -> (39/17,62/27) Hyperbolic Matrix(827,-580,452,-317) (7/10,26/37) -> (42/23,11/6) Hyperbolic Matrix(5261,-3698,3026,-2127) (26/37,45/64) -> (73/42,40/23) Hyperbolic Matrix(299,-212,244,-173) (12/17,5/7) -> (11/9,16/13) Hyperbolic Matrix(1115,-804,484,-349) (18/25,13/18) -> (23/10,30/13) 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(1661,-1220,516,-379) (11/15,25/34) -> (45/14,29/9) Hyperbolic Matrix(3135,-2306,866,-637) (25/34,14/19) -> (76/21,29/8) Hyperbolic Matrix(873,-664,472,-359) (3/4,16/21) -> (24/13,37/20) Hyperbolic Matrix(4501,-3436,2540,-1939) (29/38,13/17) -> (101/57,39/22) Hyperbolic Matrix(253,-196,324,-251) (10/13,7/9) -> (7/9,18/23) Parabolic Matrix(1399,-1096,808,-633) (18/23,11/14) -> (45/26,26/15) Hyperbolic Matrix(283,-228,36,-29) (4/5,17/21) -> (23/3,8/1) Hyperbolic Matrix(883,-716,460,-373) (30/37,43/53) -> (21/11,2/1) Hyperbolic Matrix(1343,-1090,706,-573) (43/53,13/16) -> (19/10,21/11) Hyperbolic Matrix(2961,-2416,1744,-1423) (31/38,9/11) -> (73/43,17/10) Hyperbolic Matrix(317,-260,228,-187) (9/11,5/6) -> (25/18,7/5) Hyperbolic Matrix(139,-118,86,-73) (5/6,1/1) -> (21/13,13/8) Hyperbolic Matrix(211,-236,76,-85) (1/1,8/7) -> (36/13,25/9) Hyperbolic Matrix(1187,-1436,348,-421) (6/5,23/19) -> (17/5,58/17) Hyperbolic Matrix(343,-424,72,-89) (16/13,5/4) -> (19/4,24/5) Hyperbolic Matrix(397,-500,212,-267) (5/4,24/19) -> (28/15,15/8) Hyperbolic Matrix(8101,-10268,4572,-5795) (19/15,71/56) -> (163/92,101/57) Hyperbolic Matrix(9341,-11844,2116,-2683) (71/56,52/41) -> (128/29,53/12) Hyperbolic Matrix(5583,-7090,3538,-4493) (33/26,47/37) -> (71/45,101/64) Hyperbolic Matrix(253,-324,196,-251) (14/11,9/7) -> (9/7,22/17) Parabolic Matrix(2175,-2818,1282,-1661) (22/17,35/27) -> (39/23,56/33) Hyperbolic 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(691,-974,398,-561) (7/5,24/17) -> (26/15,33/19) 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(681,-1046,278,-427) (3/2,20/13) -> (22/9,49/20) Hyperbolic Matrix(981,-1514,554,-855) (20/13,17/11) -> (23/13,62/35) Hyperbolic Matrix(675,-1052,188,-293) (14/9,25/16) -> (43/12,18/5) 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(915,-1454,494,-785) (27/17,35/22) -> (37/20,13/7) Hyperbolic Matrix(245,-394,74,-119) (8/5,21/13) -> (23/7,10/3) Hyperbolic Matrix(4813,-7860,1300,-2123) (80/49,49/30) -> (37/10,100/27) 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(23585,-39968,13312,-22559) (61/36,161/95) -> (225/127,163/92) Hyperbolic Matrix(19165,-32482,10818,-18335) (161/95,100/59) -> (62/35,225/127) Hyperbolic Matrix(329,-566,118,-203) (12/7,19/11) -> (25/9,14/5) Hyperbolic Matrix(2009,-3496,712,-1239) (40/23,7/4) -> (79/28,48/17) 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(3149,-5746,850,-1551) (31/17,42/23) -> (100/27,63/17) Hyperbolic Matrix(221,-484,100,-219) (13/6,11/5) -> (11/5,31/14) Parabolic Matrix(4643,-10332,1052,-2341) (20/9,69/31) -> (75/17,128/29) Hyperbolic Matrix(527,-1202,146,-333) (25/11,16/7) -> (18/5,47/13) Hyperbolic Matrix(2271,-5218,514,-1181) (62/27,23/10) -> (53/12,84/19) Hyperbolic Matrix(3887,-8978,1682,-3885) (30/13,67/29) -> (67/29,104/45) Parabolic Matrix(733,-1700,260,-603) (37/16,7/3) -> (31/11,79/28) 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(899,-2174,318,-769) (29/12,46/19) -> (48/17,17/6) 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(447,-1154,98,-253) (18/7,31/12) -> (9/2,32/7) Hyperbolic Matrix(293,-796,60,-163) (19/7,49/18) -> (29/6,5/1) Hyperbolic 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(227,-734,30,-97) (29/9,13/4) -> (15/2,23/3) Hyperbolic 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(1497,-5414,326,-1179) (47/13,76/21) -> (78/17,23/5) Hyperbolic Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) 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(57,-392,8,-55) (27/4,7/1) -> (7/1,29/4) 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(7,-2,32,-9) Matrix(239,110,-654,-301) -> Matrix(13,-4,36,-11) Matrix(1403,634,582,263) -> Matrix(1,0,-4,1) Matrix(817,368,464,209) -> Matrix(19,-4,24,-5) Matrix(233,104,56,25) -> Matrix(15,-4,4,-1) Matrix(113,50,174,77) -> Matrix(7,-2,4,-1) Matrix(225,98,-962,-419) -> Matrix(5,-2,8,-3) Matrix(341,148,-1076,-467) -> Matrix(1,0,0,1) Matrix(453,196,1916,829) -> Matrix(5,-2,8,-3) Matrix(1351,584,2200,951) -> Matrix(5,-2,8,-3) Matrix(1669,710,2842,1209) -> Matrix(43,-12,104,-29) Matrix(669,284,1444,613) -> Matrix(27,-8,44,-13) Matrix(1335,566,-3446,-1461) -> Matrix(13,-4,36,-11) Matrix(109,46,-718,-303) -> Matrix(7,-2,4,-1) Matrix(219,92,388,163) -> Matrix(13,-4,36,-11) Matrix(327,136,440,183) -> Matrix(1,0,0,1) Matrix(1531,634,326,135) -> Matrix(1,0,-4,1) Matrix(547,226,-1474,-609) -> Matrix(13,-4,36,-11) Matrix(1957,804,-6628,-2723) -> Matrix(1,0,-4,1) Matrix(2173,892,324,133) -> Matrix(23,-6,4,-1) Matrix(1517,622,978,401) -> Matrix(5,-2,8,-3) Matrix(109,44,52,21) -> Matrix(7,-2,4,-1) Matrix(529,208,1264,497) -> Matrix(11,-4,36,-13) Matrix(1159,454,314,123) -> Matrix(7,-2,4,-1) Matrix(947,370,366,143) -> Matrix(19,-6,16,-5) Matrix(1361,528,1776,689) -> Matrix(3,-2,8,-5) Matrix(1357,526,-6478,-2511) -> Matrix(1,0,0,1) Matrix(207,80,784,303) -> Matrix(5,-2,8,-3) Matrix(413,158,1090,417) -> Matrix(1,0,-4,1) Matrix(309,118,-982,-375) -> Matrix(1,0,0,1) Matrix(1757,668,1444,549) -> Matrix(1,0,-4,1) Matrix(7741,2940,4900,1861) -> Matrix(39,-10,4,-1) Matrix(3403,1292,4180,1587) -> Matrix(15,-4,4,-1) Matrix(929,352,256,97) -> Matrix(19,-6,16,-5) Matrix(409,152,-1784,-663) -> Matrix(17,-6,20,-7) Matrix(303,112,560,207) -> Matrix(5,-2,28,-11) Matrix(605,222,962,353) -> Matrix(5,-2,8,-3) Matrix(1109,406,-3734,-1367) -> Matrix(17,-6,20,-7) Matrix(199,72,152,55) -> Matrix(9,-4,16,-7) Matrix(597,212,-2036,-723) -> Matrix(1,0,-4,1) Matrix(1885,668,1188,421) -> Matrix(1,0,-4,1) Matrix(199,70,-742,-261) -> Matrix(5,-2,8,-3) Matrix(187,60,-988,-317) -> Matrix(1,0,0,1) Matrix(1113,346,1766,549) -> Matrix(5,-2,8,-3) Matrix(4171,1292,2644,819) -> Matrix(15,-4,4,-1) Matrix(1759,544,928,287) -> Matrix(41,-14,44,-15) Matrix(2131,658,3054,943) -> Matrix(11,-4,36,-13) Matrix(183,56,232,71) -> Matrix(9,-4,16,-7) Matrix(455,136,184,55) -> Matrix(1,0,0,1) Matrix(2729,810,502,149) -> Matrix(13,-12,12,-11) Matrix(1635,484,956,283) -> Matrix(3,-4,4,-5) Matrix(271,80,2544,751) -> Matrix(1,0,4,1) Matrix(1269,374,682,201) -> Matrix(3,-4,4,-5) Matrix(5249,1538,2174,637) -> Matrix(1,0,4,1) Matrix(2441,714,1494,437) -> Matrix(1,0,0,1) Matrix(1353,394,182,53) -> Matrix(1,-2,0,1) Matrix(3521,1024,1984,577) -> Matrix(7,6,8,7) Matrix(269,78,1714,497) -> Matrix(1,0,4,1) Matrix(989,286,1442,417) -> Matrix(1,0,20,1) Matrix(177,50,46,13) -> Matrix(7,-2,4,-1) Matrix(267,74,-1418,-393) -> Matrix(5,-2,8,-3) Matrix(1679,464,1328,367) -> Matrix(1,0,0,1) Matrix(973,268,2516,693) -> Matrix(5,-2,-32,13) Matrix(263,72,-968,-265) -> Matrix(13,-6,24,-11) Matrix(1841,498,2414,653) -> Matrix(11,-6,24,-13) Matrix(615,166,2234,603) -> Matrix(3,-2,-4,3) Matrix(439,118,-2102,-565) -> Matrix(3,-2,8,-5) Matrix(347,92,132,35) -> Matrix(5,-4,4,-3) Matrix(169,40,376,89) -> Matrix(7,-4,16,-9) Matrix(1753,408,2376,553) -> Matrix(3,-2,8,-5) Matrix(1919,446,3042,707) -> Matrix(1,0,0,1) Matrix(3737,856,1576,361) -> Matrix(13,-12,12,-11) Matrix(913,208,496,113) -> Matrix(3,-4,4,-5) Matrix(249,56,40,9) -> Matrix(1,2,0,1) Matrix(163,36,412,91) -> Matrix(1,0,8,1) Matrix(1229,268,2004,437) -> Matrix(21,-2,32,-3) Matrix(733,158,450,97) -> Matrix(1,0,-4,1) Matrix(731,156,164,35) -> Matrix(9,-2,-4,1) Matrix(1379,292,732,155) -> Matrix(17,-6,20,-7) Matrix(2109,446,610,129) -> Matrix(5,-2,8,-3) Matrix(3809,800,1376,289) -> Matrix(19,-6,16,-5) Matrix(563,116,364,75) -> Matrix(5,-2,8,-3) Matrix(633,122,358,69) -> Matrix(3,-4,4,-5) Matrix(3873,736,1184,225) -> Matrix(1,0,4,1) Matrix(707,132,316,59) -> Matrix(1,0,0,1) Matrix(315,58,38,7) -> Matrix(1,0,0,1) Matrix(155,28,548,99) -> Matrix(1,0,8,1) Matrix(935,166,1594,283) -> Matrix(11,-2,28,-5) Matrix(463,80,272,47) -> Matrix(5,-2,8,-3) Matrix(77,12,340,53) -> Matrix(3,-2,8,-5) Matrix(375,56,904,135) -> Matrix(1,-2,4,-7) Matrix(1487,208,336,47) -> Matrix(1,-4,0,1) Matrix(2077,286,1634,225) -> Matrix(5,2,12,5) Matrix(221,30,1186,161) -> Matrix(1,0,12,1) Matrix(589,78,370,49) -> Matrix(1,0,-4,1) Matrix(653,78,946,113) -> Matrix(1,0,4,1) Matrix(869,100,252,29) -> Matrix(5,-2,8,-3) Matrix(431,46,178,19) -> Matrix(1,0,0,1) Matrix(583,-56,760,-73) -> Matrix(7,-4,16,-9) Matrix(1743,-178,754,-77) -> Matrix(1,0,4,1) Matrix(173,-20,372,-43) -> Matrix(5,-2,8,-3) Matrix(397,-52,84,-11) -> Matrix(1,0,-4,1) Matrix(223,-34,610,-93) -> Matrix(1,0,0,1) Matrix(2273,-352,1440,-223) -> Matrix(1,4,0,1) Matrix(1105,-176,496,-79) -> Matrix(1,0,0,1) Matrix(435,-76,1036,-181) -> Matrix(1,-2,4,-7) Matrix(597,-106,490,-87) -> Matrix(1,0,0,1) Matrix(271,-50,1458,-269) -> Matrix(1,0,20,1) Matrix(3229,-610,1858,-351) -> Matrix(13,-2,20,-3) Matrix(3605,-684,2124,-403) -> Matrix(13,-2,20,-3) Matrix(267,-52,724,-141) -> Matrix(7,-2,4,-1) Matrix(211,-46,78,-17) -> Matrix(7,-2,4,-1) Matrix(157,-36,676,-155) -> Matrix(13,-6,24,-11) Matrix(1245,-292,388,-91) -> Matrix(3,-2,8,-5) Matrix(1553,-368,2224,-527) -> Matrix(3,-2,8,-5) Matrix(1137,-272,464,-111) -> Matrix(1,0,0,1) Matrix(405,-106,1066,-279) -> Matrix(1,0,-4,1) Matrix(403,-108,556,-149) -> Matrix(1,-2,4,-7) Matrix(1255,-344,1784,-489) -> Matrix(1,0,4,1) Matrix(853,-236,300,-83) -> Matrix(9,2,4,1) Matrix(351,-98,1250,-349) -> Matrix(1,0,28,1) Matrix(447,-130,1090,-317) -> Matrix(7,-2,32,-9) Matrix(841,-246,694,-203) -> Matrix(7,-2,4,-1) Matrix(889,-262,1286,-379) -> Matrix(1,0,4,1) Matrix(1481,-438,470,-139) -> Matrix(1,0,-4,1) Matrix(1037,-308,468,-139) -> Matrix(1,0,-4,1) Matrix(245,-74,394,-119) -> Matrix(5,-2,8,-3) Matrix(341,-106,74,-23) -> Matrix(1,0,-4,1) Matrix(377,-134,166,-59) -> Matrix(1,0,0,1) Matrix(189,-68,164,-59) -> Matrix(1,0,0,1) Matrix(1781,-652,2412,-883) -> Matrix(3,-2,8,-5) Matrix(1967,-722,2738,-1005) -> Matrix(3,-2,8,-5) Matrix(1403,-516,1732,-637) -> Matrix(7,-8,8,-9) Matrix(2897,-1070,398,-147) -> Matrix(1,-6,0,1) Matrix(1541,-570,538,-199) -> Matrix(1,0,0,1) Matrix(1121,-416,256,-95) -> Matrix(1,-8,0,1) Matrix(3293,-1252,2596,-987) -> Matrix(5,2,12,5) Matrix(555,-212,788,-301) -> Matrix(1,0,4,1) Matrix(1709,-660,2100,-811) -> Matrix(9,2,4,1) Matrix(877,-340,276,-107) -> Matrix(1,0,8,1) Matrix(415,-162,1058,-413) -> Matrix(1,0,36,1) Matrix(1407,-578,2018,-829) -> Matrix(17,-4,64,-15) Matrix(1403,-580,612,-253) -> Matrix(15,-4,4,-1) Matrix(589,-244,1108,-459) -> Matrix(7,-2,60,-17) Matrix(1083,-454,1510,-633) -> Matrix(1,0,0,1) Matrix(4055,-1704,2344,-985) -> Matrix(7,-2,4,-1) Matrix(315,-134,134,-57) -> Matrix(5,-2,8,-3) Matrix(223,-98,66,-29) -> Matrix(5,-2,8,-3) Matrix(221,-100,484,-219) -> Matrix(21,-10,40,-19) Matrix(921,-424,328,-151) -> Matrix(17,-10,12,-7) Matrix(695,-328,392,-185) -> Matrix(3,-4,4,-5) Matrix(1969,-1040,816,-431) -> Matrix(1,0,-12,1) Matrix(625,-334,814,-435) -> Matrix(23,-4,52,-9) Matrix(1945,-1064,744,-407) -> Matrix(101,-24,80,-19) Matrix(3429,-1882,2170,-1191) -> Matrix(63,-16,4,-1) Matrix(949,-524,556,-307) -> Matrix(29,-8,40,-11) Matrix(369,-206,206,-115) -> Matrix(7,-2,4,-1) Matrix(121,-70,102,-59) -> Matrix(5,-2,8,-3) Matrix(3797,-2220,2988,-1747) -> Matrix(1,0,0,1) Matrix(4321,-2528,5632,-3295) -> Matrix(3,-2,8,-5) Matrix(3591,-2104,2200,-1289) -> Matrix(5,-2,8,-3) Matrix(2661,-1564,604,-355) -> Matrix(53,-22,-12,5) Matrix(121,-72,200,-119) -> Matrix(13,-6,24,-11) Matrix(3061,-1866,1770,-1079) -> Matrix(3,-2,8,-5) Matrix(6401,-3904,3776,-2303) -> Matrix(3,-2,8,-5) Matrix(4649,-2838,1014,-619) -> Matrix(7,-4,-12,7) Matrix(1469,-900,932,-571) -> Matrix(19,-12,8,-5) Matrix(5829,-3578,2618,-1607) -> Matrix(3,-2,-4,3) Matrix(911,-562,1266,-781) -> Matrix(3,-2,8,-5) Matrix(1463,-904,1128,-697) -> Matrix(9,-4,16,-7) Matrix(1423,-882,434,-269) -> Matrix(3,-2,8,-5) Matrix(1649,-1040,176,-111) -> Matrix(1,0,0,1) Matrix(391,-248,216,-137) -> Matrix(1,0,0,1) Matrix(429,-274,274,-175) -> Matrix(5,-4,4,-3) Matrix(495,-338,722,-493) -> Matrix(1,0,24,1) Matrix(1251,-862,1534,-1057) -> Matrix(1,0,-8,1) Matrix(1701,-1180,604,-419) -> Matrix(15,-2,8,-1) Matrix(2417,-1680,528,-367) -> Matrix(11,-2,-16,3) Matrix(2943,-2050,1282,-893) -> Matrix(9,-2,-4,1) Matrix(827,-580,452,-317) -> Matrix(5,-2,8,-3) Matrix(5261,-3698,3026,-2127) -> Matrix(5,-2,8,-3) Matrix(299,-212,244,-173) -> Matrix(1,0,-4,1) Matrix(1115,-804,484,-349) -> Matrix(1,0,-4,1) Matrix(1597,-1156,612,-443) -> Matrix(59,-16,48,-13) Matrix(295,-216,56,-41) -> Matrix(5,-2,8,-3) Matrix(1661,-1220,516,-379) -> Matrix(5,-2,8,-3) Matrix(3135,-2306,866,-637) -> Matrix(19,-6,16,-5) Matrix(873,-664,472,-359) -> Matrix(9,-4,16,-7) Matrix(4501,-3436,2540,-1939) -> Matrix(37,-16,44,-19) Matrix(253,-196,324,-251) -> Matrix(29,-14,56,-27) Matrix(1399,-1096,808,-633) -> Matrix(11,-6,24,-13) Matrix(283,-228,36,-29) -> Matrix(3,-2,-4,3) Matrix(883,-716,460,-373) -> Matrix(17,-16,16,-15) Matrix(1343,-1090,706,-573) -> Matrix(23,-24,24,-25) Matrix(2961,-2416,1744,-1423) -> Matrix(5,-2,8,-3) Matrix(317,-260,228,-187) -> Matrix(1,0,0,1) Matrix(139,-118,86,-73) -> Matrix(1,0,0,1) Matrix(211,-236,76,-85) -> Matrix(5,-4,4,-3) Matrix(1187,-1436,348,-421) -> Matrix(3,-4,4,-5) Matrix(343,-424,72,-89) -> Matrix(1,0,-4,1) Matrix(397,-500,212,-267) -> Matrix(17,-6,20,-7) Matrix(8101,-10268,4572,-5795) -> Matrix(17,-6,20,-7) Matrix(9341,-11844,2116,-2683) -> Matrix(27,-10,-8,3) Matrix(5583,-7090,3538,-4493) -> Matrix(43,-18,12,-5) Matrix(253,-324,196,-251) -> Matrix(21,-10,40,-19) Matrix(2175,-2818,1282,-1661) -> Matrix(7,-4,16,-9) Matrix(81,-110,14,-19) -> Matrix(5,-4,4,-3) Matrix(403,-556,108,-149) -> Matrix(5,-4,4,-3) Matrix(965,-1338,282,-391) -> Matrix(1,0,0,1) Matrix(691,-974,398,-561) -> Matrix(1,0,0,1) Matrix(1193,-1686,438,-619) -> Matrix(19,-12,8,-5) Matrix(555,-788,212,-301) -> Matrix(31,-22,24,-17) Matrix(157,-226,66,-95) -> Matrix(5,-4,4,-3) Matrix(681,-1046,278,-427) -> Matrix(1,0,0,1) Matrix(981,-1514,554,-855) -> Matrix(3,-4,4,-5) Matrix(675,-1052,188,-293) -> Matrix(17,-16,16,-15) Matrix(2429,-3842,930,-1471) -> Matrix(5,26,4,21) Matrix(149,-236,12,-19) -> Matrix(1,2,0,1) Matrix(915,-1454,494,-785) -> Matrix(3,2,4,3) Matrix(245,-394,74,-119) -> Matrix(1,0,0,1) Matrix(4813,-7860,1300,-2123) -> Matrix(5,-4,4,-3) Matrix(121,-200,72,-119) -> Matrix(5,-2,8,-3) Matrix(1117,-1892,356,-603) -> Matrix(3,-2,-4,3) Matrix(23585,-39968,13312,-22559) -> Matrix(1,0,0,1) Matrix(19165,-32482,10818,-18335) -> Matrix(3,-4,4,-5) Matrix(329,-566,118,-203) -> Matrix(5,-4,4,-3) Matrix(2009,-3496,712,-1239) -> Matrix(5,-4,4,-3) Matrix(621,-1106,242,-431) -> Matrix(25,-24,24,-23) Matrix(1135,-2066,306,-557) -> Matrix(5,-4,4,-3) Matrix(3149,-5746,850,-1551) -> Matrix(17,-10,12,-7) Matrix(221,-484,100,-219) -> Matrix(1,-2,0,1) Matrix(4643,-10332,1052,-2341) -> Matrix(1,-4,0,1) Matrix(527,-1202,146,-333) -> Matrix(9,-8,8,-7) Matrix(2271,-5218,514,-1181) -> Matrix(1,-4,0,1) Matrix(3887,-8978,1682,-3885) -> Matrix(1,0,12,1) Matrix(733,-1700,260,-603) -> Matrix(7,-2,4,-1) Matrix(1711,-4050,722,-1709) -> Matrix(25,-24,24,-23) Matrix(4613,-11132,956,-2307) -> Matrix(1,0,24,1) Matrix(899,-2174,318,-769) -> Matrix(7,-2,4,-1) Matrix(447,-1090,130,-317) -> Matrix(1,0,0,1) Matrix(415,-1058,162,-413) -> Matrix(37,-36,36,-35) Matrix(447,-1154,98,-253) -> Matrix(9,-10,-8,9) Matrix(293,-796,60,-163) -> Matrix(1,-2,4,-7) Matrix(223,-610,34,-93) -> Matrix(1,2,0,1) Matrix(1599,-4418,578,-1597) -> Matrix(9,-8,8,-7) Matrix(49,-144,16,-47) -> Matrix(1,-2,0,1) Matrix(227,-734,30,-97) -> Matrix(1,-2,0,1) Matrix(1471,-4802,450,-1469) -> Matrix(1,0,8,1) Matrix(783,-2672,80,-273) -> Matrix(9,-8,8,-7) Matrix(899,-3070,94,-321) -> Matrix(3,-4,4,-5) Matrix(351,-1250,98,-349) -> Matrix(29,-28,28,-27) Matrix(1497,-5414,326,-1179) -> Matrix(5,-6,-4,5) Matrix(157,-676,36,-155) -> Matrix(1,-14,0,1) Matrix(1167,-5618,242,-1165) -> Matrix(1,0,40,1) Matrix(271,-1458,50,-269) -> Matrix(21,-20,20,-19) Matrix(57,-392,8,-55) -> Matrix(1,-10,0,1) 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 1/4 -6/13 2/7 3/10 -5/11 1/2 -9/20 1/4 -4/9 1/4 2/7 -7/16 3/8 -10/23 0/1 1/2 -3/7 1/4 -14/33 3/10 1/3 -11/26 1/4 -8/19 3/10 1/3 -5/12 3/8 -12/29 0/1 1/4 -7/17 1/2 -9/22 1/4 -2/5 1/4 1/3 -7/18 3/8 -5/13 1/2 -13/34 1/4 -8/21 0/1 1/2 -3/8 1/4 -13/35 5/14 -10/27 4/11 3/8 -7/19 1/2 -11/30 1/4 -15/41 5/14 -4/11 2/5 1/2 -5/14 1/0 -11/31 1/4 -6/17 1/3 1/2 -1/3 1/2 -7/22 1/4 -6/19 0/1 1/2 -5/16 1/4 -9/29 1/2 -4/13 2/5 1/2 -3/10 3/4 -8/27 1/1 3/2 -5/17 1/0 -7/24 1/0 -2/7 0/1 1/4 -5/18 3/8 -3/11 1/2 -7/26 3/4 -11/41 1/2 -4/15 1/2 1/1 -1/4 1/4 -4/17 1/2 2/3 -7/30 1/0 -3/13 1/2 -11/48 7/8 -8/35 1/1 5/4 -5/22 1/0 -2/9 -1/2 0/1 -3/14 1/4 -7/33 3/10 -4/19 1/4 1/3 -1/5 1/2 -4/21 0/1 1/0 -11/58 1/4 -7/37 1/2 -3/16 1/0 -5/27 1/2 -2/11 -1/2 0/1 -1/6 1/4 -2/13 1/2 1/1 -3/20 1/0 -1/7 1/2 -3/22 -1/4 -2/15 0/1 1/6 -1/8 1/0 0/1 0/1 1/2 1/9 1/2 1/8 1/4 1/7 1/2 2/13 1/1 1/0 1/6 1/4 1/5 1/2 2/9 1/3 1/2 3/13 1/2 4/17 1/2 2/3 1/4 1/0 4/15 1/2 1/1 3/11 -1/2 2/7 0/1 1/6 3/10 1/4 1/3 1/2 5/14 1/0 4/11 1/1 1/0 3/8 1/0 8/21 -1/4 0/1 5/13 -1/2 2/5 0/1 1/6 9/22 1/4 7/17 1/4 12/29 3/11 5/18 17/41 3/10 5/12 1/4 3/7 1/2 4/9 2/5 1/2 5/11 1/2 6/13 1/2 3/5 1/2 1/0 9/17 1/10 8/15 1/7 1/6 7/13 1/6 6/11 2/9 1/4 5/9 3/10 9/16 7/20 4/7 1/3 1/2 3/5 1/2 8/13 1/2 2/3 5/8 3/4 17/27 1/2 29/46 3/4 41/65 1/2 12/19 1/2 1/1 7/11 1/2 9/14 5/4 2/3 0/1 1/0 9/13 1/6 7/10 1/4 19/27 1/2 12/17 0/1 1/0 5/7 1/4 13/18 1/4 21/29 5/18 8/11 3/10 1/3 11/15 1/2 3/4 3/8 7/9 1/2 11/14 11/20 4/5 1/2 2/3 9/11 1/2 5/6 1/0 1/1 1/2 8/7 1/1 1/0 7/6 1/0 6/5 1/2 1/1 17/14 1/0 11/9 1/0 16/13 -1/4 0/1 5/4 1/4 9/7 1/2 13/10 9/16 4/3 1/2 2/3 11/8 1/0 18/13 1/2 1/1 25/18 1/0 7/5 1/2 24/17 1/2 3/5 17/12 11/16 10/7 3/4 4/5 3/2 1/0 14/9 5/6 1/1 25/16 9/8 11/7 3/2 30/19 5/1 1/0 49/31 1/0 19/12 1/0 46/29 -1/1 -1/2 27/17 1/0 8/5 0/1 1/2 5/3 1/2 12/7 1/2 1/1 19/11 1/2 7/4 3/4 16/9 9/10 1/1 25/14 9/8 9/5 1/2 20/11 1/2 1/1 31/17 1/2 11/6 3/4 13/7 3/4 15/8 7/8 2/1 1/1 1/0 11/5 1/0 20/9 0/1 1/0 9/4 1/0 16/7 1/1 3/2 39/17 1/0 23/10 1/0 30/13 -1/2 0/1 7/3 1/2 26/11 7/8 1/1 45/19 1/1 64/27 1/1 17/16 19/8 5/4 12/5 0/1 1/0 41/17 -1/2 111/46 -1/12 70/29 0/1 1/8 29/12 1/0 17/7 1/2 22/9 1/2 1/1 5/2 3/4 23/9 1/1 41/16 33/32 18/7 1/1 15/14 13/5 7/6 47/18 5/4 81/31 5/4 34/13 5/4 14/11 21/8 11/8 8/3 1/1 3/2 19/7 3/2 49/18 17/8 30/11 5/2 3/1 11/4 1/0 3/1 1/0 13/4 1/0 49/15 0/1 85/26 1/8 36/11 0/1 1/4 23/7 1/2 10/3 0/1 1/2 17/5 1/2 58/17 5/6 1/1 99/29 1/1 41/12 1/0 24/7 1/2 1/1 31/9 1/2 7/2 3/4 25/7 1/1 43/12 25/24 18/5 1/1 11/10 11/3 3/2 37/10 5/4 63/17 3/2 26/7 1/1 3/2 15/4 5/4 4/1 2/1 1/0 13/3 1/0 22/5 -5/1 1/0 9/2 1/0 14/3 0/1 1/0 33/7 -1/2 19/4 1/0 24/5 -1/8 0/1 53/11 0/1 82/17 0/1 1/32 29/6 1/12 5/1 1/2 16/3 5/6 1/1 27/5 1/1 38/7 1/1 15/14 11/2 5/4 6/1 3/2 2/1 13/2 1/0 7/1 1/0 15/2 1/0 8/1 -1/2 0/1 9/1 1/2 19/2 3/4 29/3 1/1 10/1 1/1 3/2 1/0 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(7,-2,32,-9) Matrix(239,110,-654,-301) -> Matrix(13,-4,36,-11) Matrix(173,78,-814,-367) -> Matrix(5,-1,16,-3) Matrix(521,234,118,53) -> Matrix(13,-3,-4,1) Matrix(113,50,174,77) -> Matrix(7,-2,4,-1) Matrix(225,98,-962,-419) -> Matrix(5,-2,8,-3) Matrix(167,72,-392,-169) -> Matrix(5,-1,16,-3) Matrix(387,164,-1220,-517) -> Matrix(3,-1,16,-5) Matrix(109,46,-718,-303) -> Matrix(7,-2,4,-1) Matrix(219,92,388,163) -> Matrix(13,-4,36,-11) Matrix(53,22,330,137) -> Matrix(3,-1,4,-1) Matrix(547,226,-1474,-609) -> Matrix(13,-4,36,-11) Matrix(161,66,-866,-355) -> Matrix(3,-1,4,-1) Matrix(485,198,218,89) -> Matrix(3,-1,4,-1) Matrix(159,62,418,163) -> Matrix(3,-1,-8,3) Matrix(259,100,-676,-261) -> Matrix(3,-1,4,-1) Matrix(309,118,-982,-375) -> Matrix(1,0,0,1) Matrix(53,20,204,77) -> Matrix(3,-1,4,-1) Matrix(409,152,-1784,-663) -> Matrix(17,-6,20,-7) Matrix(303,112,560,207) -> Matrix(5,-2,28,-11) Matrix(605,222,962,353) -> Matrix(5,-2,8,-3) Matrix(153,56,-1112,-407) -> Matrix(3,-1,-8,3) Matrix(199,72,152,55) -> Matrix(9,-4,16,-7) Matrix(647,230,346,123) -> Matrix(7,-1,8,-1) Matrix(1885,668,1188,421) -> Matrix(1,0,-4,1) Matrix(199,70,-742,-261) -> Matrix(5,-2,8,-3) Matrix(187,60,-988,-317) -> Matrix(1,0,0,1) Matrix(1113,346,1766,549) -> Matrix(5,-2,8,-3) Matrix(323,100,604,187) -> Matrix(3,-1,16,-5) Matrix(183,56,232,71) -> Matrix(9,-4,16,-7) Matrix(47,14,-366,-109) -> Matrix(1,-1,4,-3) Matrix(865,256,544,161) -> Matrix(1,-1,0,1) Matrix(499,146,270,79) -> Matrix(3,-1,4,-1) Matrix(227,66,-994,-289) -> Matrix(1,1,0,1) Matrix(177,50,46,13) -> Matrix(7,-2,4,-1) Matrix(131,36,-484,-133) -> Matrix(7,-3,12,-5) Matrix(305,82,-1618,-435) -> Matrix(1,-1,4,-3) Matrix(347,92,132,35) -> Matrix(5,-4,4,-3) Matrix(41,10,86,21) -> Matrix(3,-1,4,-1) Matrix(43,10,374,87) -> Matrix(1,-1,4,-3) Matrix(3737,856,1576,361) -> Matrix(13,-12,12,-11) Matrix(249,56,40,9) -> Matrix(1,2,0,1) Matrix(287,62,162,35) -> Matrix(7,-1,8,-1) Matrix(1175,248,488,103) -> Matrix(3,-1,4,-1) Matrix(39,8,-200,-41) -> Matrix(3,-1,4,-1) Matrix(3873,736,1184,225) -> Matrix(1,0,4,1) Matrix(315,58,38,7) -> Matrix(1,0,0,1) Matrix(117,20,76,13) -> Matrix(3,-1,4,-1) Matrix(37,6,154,25) -> Matrix(3,-1,4,-1) Matrix(375,56,904,135) -> Matrix(1,-2,4,-7) Matrix(1001,136,184,25) -> Matrix(9,1,8,1) Matrix(181,22,74,9) -> Matrix(3,-1,4,-1) Matrix(149,-12,236,-19) -> Matrix(3,-1,4,-1) Matrix(397,-52,84,-11) -> Matrix(1,0,-4,1) Matrix(527,-80,112,-17) -> Matrix(1,-1,0,1) Matrix(81,-14,110,-19) -> Matrix(1,-1,4,-3) Matrix(211,-46,78,-17) -> Matrix(7,-2,4,-1) Matrix(79,-18,338,-77) -> Matrix(7,-3,12,-5) Matrix(403,-108,556,-149) -> Matrix(1,-2,4,-7) Matrix(275,-76,76,-21) -> Matrix(5,1,4,1) Matrix(223,-66,98,-29) -> Matrix(3,-1,4,-1) Matrix(25,-8,72,-23) -> Matrix(3,-1,4,-1) Matrix(189,-68,164,-59) -> Matrix(1,0,0,1) Matrix(211,-78,46,-17) -> Matrix(1,-1,0,1) Matrix(555,-212,788,-301) -> Matrix(1,0,4,1) Matrix(299,-116,116,-45) -> Matrix(9,1,8,1) Matrix(1249,-512,544,-223) -> Matrix(5,-1,-4,1) Matrix(1403,-580,612,-253) -> Matrix(15,-4,4,-1) Matrix(589,-244,1108,-459) -> Matrix(7,-2,60,-17) Matrix(157,-66,226,-95) -> Matrix(3,-1,16,-5) Matrix(223,-98,66,-29) -> Matrix(5,-2,8,-3) Matrix(111,-50,242,-109) -> Matrix(11,-5,20,-9) Matrix(1969,-1040,816,-431) -> Matrix(1,0,-12,1) Matrix(391,-216,248,-137) -> Matrix(11,-3,4,-1) Matrix(369,-206,206,-115) -> Matrix(7,-2,4,-1) Matrix(61,-36,100,-59) -> Matrix(7,-3,12,-5) Matrix(139,-86,118,-73) -> Matrix(1,-1,4,-3) Matrix(1649,-1040,176,-111) -> Matrix(1,0,0,1) Matrix(391,-248,216,-137) -> Matrix(1,0,0,1) Matrix(429,-274,274,-175) -> Matrix(5,-4,4,-3) Matrix(359,-248,152,-105) -> Matrix(7,-1,8,-1) Matrix(1109,-780,300,-211) -> Matrix(1,1,0,1) Matrix(299,-212,244,-173) -> Matrix(1,0,-4,1) Matrix(317,-228,260,-187) -> Matrix(3,-1,4,-1) Matrix(1597,-1156,612,-443) -> Matrix(59,-16,48,-13) Matrix(295,-216,56,-41) -> Matrix(5,-2,8,-3) Matrix(127,-98,162,-125) -> Matrix(15,-7,28,-13) Matrix(299,-244,212,-173) -> Matrix(3,-1,4,-1) Matrix(317,-260,228,-187) -> Matrix(1,0,0,1) Matrix(121,-102,70,-59) -> Matrix(3,-1,4,-1) Matrix(197,-220,60,-67) -> Matrix(1,-1,4,-3) Matrix(535,-648,232,-281) -> Matrix(1,-1,0,1) Matrix(343,-424,72,-89) -> Matrix(1,0,-4,1) Matrix(127,-162,98,-125) -> Matrix(11,-5,20,-9) Matrix(81,-110,14,-19) -> Matrix(5,-4,4,-3) Matrix(403,-556,108,-149) -> Matrix(5,-4,4,-3) Matrix(965,-1338,282,-391) -> Matrix(1,0,0,1) Matrix(1193,-1686,438,-619) -> Matrix(19,-12,8,-5) Matrix(555,-788,212,-301) -> Matrix(31,-22,24,-17) Matrix(157,-226,66,-95) -> Matrix(5,-4,4,-3) Matrix(675,-1052,188,-293) -> Matrix(17,-16,16,-15) Matrix(2593,-4096,992,-1567) -> Matrix(5,-39,4,-31) Matrix(2429,-3842,930,-1471) -> Matrix(5,26,4,21) Matrix(149,-236,12,-19) -> Matrix(1,2,0,1) Matrix(61,-100,36,-59) -> Matrix(3,-1,4,-1) Matrix(271,-466,82,-141) -> Matrix(1,-1,4,-3) Matrix(621,-1106,242,-431) -> Matrix(25,-24,24,-23) Matrix(1135,-2066,306,-557) -> Matrix(5,-4,4,-3) Matrix(1007,-1840,272,-497) -> Matrix(11,-7,8,-5) Matrix(589,-1108,244,-459) -> Matrix(1,-1,8,-7) Matrix(111,-242,50,-109) -> Matrix(1,-1,0,1) Matrix(395,-916,116,-269) -> Matrix(3,-1,4,-1) Matrix(1711,-4050,722,-1709) -> Matrix(25,-24,24,-23) Matrix(4613,-11132,956,-2307) -> Matrix(1,0,24,1) Matrix(421,-1018,122,-295) -> Matrix(3,-1,4,-1) Matrix(447,-1090,130,-317) -> Matrix(1,0,0,1) Matrix(415,-1058,162,-413) -> Matrix(37,-36,36,-35) Matrix(293,-796,60,-163) -> Matrix(1,-2,4,-7) Matrix(197,-538,26,-71) -> Matrix(1,-3,0,1) 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(9,-8,8,-7) Matrix(899,-3070,94,-321) -> Matrix(3,-4,4,-5) Matrix(351,-1250,98,-349) -> Matrix(29,-28,28,-27) Matrix(79,-338,18,-77) -> Matrix(1,-7,0,1) Matrix(1167,-5618,242,-1165) -> Matrix(1,0,40,1) Matrix(271,-1458,50,-269) -> Matrix(21,-20,20,-19) Matrix(29,-196,4,-27) -> Matrix(1,-5,0,1) 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 (0/1,1/2) 0 32 1/8 1/4 1 32 1/7 1/2 1 4 1/6 1/4 1 32 1/5 1/2 1 16 2/9 (1/3,1/2) 0 32 3/13 1/2 3 2 1/4 1/0 1 32 3/11 -1/2 1 16 2/7 (0/1,1/6) 0 32 3/10 1/4 1 32 1/3 1/2 1 8 5/14 1/0 1 32 4/11 (1/1,1/0) 0 32 3/8 1/0 1 32 5/13 -1/2 1 16 2/5 (0/1,1/6) 0 32 7/17 1/4 5 4 12/29 (3/11,5/18) 0 32 5/12 1/4 1 32 3/7 1/2 1 16 4/9 (2/5,1/2) 0 32 5/11 1/2 5 2 1/2 1/0 1 32 6/11 (2/9,1/4) 0 32 5/9 3/10 1 16 4/7 (1/3,1/2) 0 32 3/5 1/2 3 4 8/13 (1/2,2/3) 0 32 5/8 3/4 1 32 12/19 (1/2,1/1) 0 32 7/11 1/2 1 16 2/3 (0/1,1/0) 0 32 9/13 1/6 1 16 7/10 1/4 1 32 12/17 (0/1,1/0) 0 32 5/7 1/4 1 8 13/18 1/4 1 32 8/11 (3/10,1/3) 0 32 11/15 1/2 1 16 3/4 3/8 1 32 7/9 1/2 7 2 4/5 (1/2,2/3) 0 32 9/11 1/2 1 8 5/6 1/0 1 32 1/1 1/2 1 16 8/7 (1/1,1/0) 0 32 7/6 1/0 1 32 6/5 (1/2,1/1) 0 32 17/14 1/0 1 32 11/9 1/0 1 8 16/13 (-1/4,0/1) 0 32 5/4 1/4 1 32 9/7 1/2 5 2 4/3 (1/2,2/3) 0 32 11/8 1/0 1 32 18/13 (1/2,1/1) 0 32 25/18 1/0 1 32 7/5 1/2 1 8 24/17 (1/2,3/5) 0 32 17/12 11/16 1 32 10/7 (3/4,4/5) 0 32 3/2 1/0 1 32 11/7 3/2 1 16 30/19 (5/1,1/0) 0 32 49/31 1/0 13 2 19/12 1/0 1 32 8/5 (0/1,1/2) 0 32 5/3 1/2 1 4 12/7 (1/2,1/1) 0 32 19/11 1/2 1 16 7/4 3/4 1 32 9/5 1/2 1 16 20/11 (1/2,1/1) 0 32 31/17 1/2 1 2 11/6 3/4 1 32 2/1 (1/1,1/0) 0 32 11/5 1/0 1 2 9/4 1/0 1 32 16/7 (1/1,3/2) 0 32 23/10 1/0 1 32 30/13 (-1/2,0/1) 0 32 7/3 1/2 1 16 26/11 (7/8,1/1) 0 32 45/19 1/1 12 1 19/8 5/4 1 32 12/5 (0/1,1/0) 0 32 29/12 1/0 1 32 17/7 1/2 1 4 5/2 3/4 1 32 23/9 1/1 18 1 18/7 (1/1,15/14) 0 32 13/5 7/6 1 16 8/3 (1/1,3/2) 0 32 19/7 3/2 1 16 49/18 17/8 1 32 30/11 (5/2,3/1) 0 32 11/4 1/0 1 32 3/1 1/0 1 8 13/4 1/0 1 32 49/15 0/1 4 1 36/11 (0/1,1/4) 0 32 23/7 1/2 1 16 10/3 (0/1,1/2) 0 32 17/5 1/2 1 16 58/17 (5/6,1/1) 0 32 99/29 1/1 6 1 41/12 1/0 1 32 24/7 (1/2,1/1) 0 32 7/2 3/4 1 32 25/7 1/1 14 1 18/5 (1/1,11/10) 0 32 11/3 3/2 1 16 4/1 (2/1,1/0) 0 32 13/3 1/0 7 2 9/2 1/0 1 32 14/3 (0/1,1/0) 0 32 19/4 1/0 1 32 24/5 (-1/8,0/1) 0 32 53/11 0/1 20 1 29/6 1/12 1 32 5/1 1/2 1 16 16/3 (5/6,1/1) 0 32 27/5 1/1 10 1 11/2 5/4 1 32 6/1 (3/2,2/1) 0 32 7/1 1/0 5 4 8/1 (-1/2,0/1) 0 32 1/0 1/0 1 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(-1,1,0,1) *** -> (1/2,1/0) Matrix(339,-46,140,-19) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(137,-22,56,-9) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(81,-14,110,-19) -> Matrix(1,-1,4,-3) 1/2 Matrix(211,-46,78,-17) -> Matrix(7,-2,4,-1) Matrix(53,-12,234,-53) -> Matrix(5,-2,12,-5) (2/9,3/13) -> (1/3,1/2) Matrix(25,-6,104,-25) -> Matrix(-1,1,0,1) (3/13,1/4) -> (1/2,1/0) Matrix(77,-20,50,-13) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(275,-76,76,-21) -> Matrix(5,1,4,1) Matrix(223,-66,98,-29) -> Matrix(3,-1,4,-1) 1/2 Matrix(25,-8,72,-23) -> Matrix(3,-1,4,-1) 1/2 Matrix(189,-68,164,-59) -> Matrix(1,0,0,1) Matrix(211,-78,46,-17) -> Matrix(1,-1,0,1) 1/0 Matrix(163,-62,92,-35) -> Matrix(3,1,4,1) Matrix(299,-116,116,-45) -> Matrix(9,1,8,1) Matrix(137,-56,22,-9) -> Matrix(9,-2,4,-1) Matrix(339,-140,46,-19) -> Matrix(11,-3,-4,1) Matrix(679,-282,248,-103) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(157,-66,226,-95) -> Matrix(3,-1,16,-5) 1/4 Matrix(223,-98,66,-29) -> Matrix(5,-2,8,-3) 1/2 Matrix(89,-40,198,-89) -> Matrix(9,-4,20,-9) (4/9,5/11) -> (2/5,1/2) Matrix(21,-10,44,-21) -> Matrix(-1,1,0,1) (5/11,1/2) -> (1/2,1/0) Matrix(207,-112,146,-79) -> Matrix(11,-2,16,-3) Matrix(391,-216,248,-137) -> Matrix(11,-3,4,-1) Matrix(163,-92,62,-35) -> Matrix(11,-4,8,-3) Matrix(61,-36,100,-59) -> Matrix(7,-3,12,-5) 1/2 Matrix(139,-86,118,-73) -> Matrix(1,-1,4,-3) 1/2 Matrix(353,-222,256,-161) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(391,-248,216,-137) -> Matrix(1,0,0,1) Matrix(77,-50,20,-13) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(359,-248,152,-105) -> Matrix(7,-1,8,-1) Matrix(207,-146,112,-79) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(299,-212,244,-173) -> Matrix(1,0,-4,1) 0/1 Matrix(317,-228,260,-187) -> Matrix(3,-1,4,-1) 1/2 Matrix(353,-256,222,-161) -> Matrix(3,-1,-4,1) Matrix(295,-216,56,-41) -> Matrix(5,-2,8,-3) 1/2 Matrix(55,-42,72,-55) -> Matrix(7,-3,16,-7) (3/4,7/9) -> (3/8,1/2) Matrix(71,-56,90,-71) -> Matrix(7,-4,12,-7) (7/9,4/5) -> (1/2,2/3) Matrix(299,-244,212,-173) -> Matrix(3,-1,4,-1) 1/2 Matrix(317,-260,228,-187) -> Matrix(1,0,0,1) Matrix(121,-102,70,-59) -> Matrix(3,-1,4,-1) 1/2 Matrix(197,-220,60,-67) -> Matrix(1,-1,4,-3) 1/2 Matrix(535,-648,232,-281) -> Matrix(1,-1,0,1) 1/0 Matrix(343,-424,72,-89) -> Matrix(1,0,-4,1) 0/1 Matrix(71,-90,56,-71) -> Matrix(3,-1,8,-3) (5/4,9/7) -> (1/4,1/2) Matrix(55,-72,42,-55) -> Matrix(7,-4,12,-7) (9/7,4/3) -> (1/2,2/3) Matrix(81,-110,14,-19) -> Matrix(5,-4,4,-3) 1/1 Matrix(965,-1338,282,-391) -> Matrix(1,0,0,1) Matrix(1193,-1686,438,-619) -> Matrix(19,-12,8,-5) Matrix(157,-226,66,-95) -> Matrix(5,-4,4,-3) 1/1 Matrix(1861,-2940,1178,-1861) -> Matrix(-1,10,0,1) (30/19,49/31) -> (5/1,1/0) Matrix(1177,-1862,744,-1177) -> Matrix(1,3,0,-1) (49/31,19/12) -> (-3/2,1/0) Matrix(61,-100,36,-59) -> Matrix(3,-1,4,-1) 1/2 Matrix(271,-466,82,-141) -> Matrix(1,-1,4,-3) 1/2 Matrix(681,-1240,374,-681) -> Matrix(3,-2,4,-3) (20/11,31/17) -> (1/2,1/1) Matrix(373,-682,204,-373) -> Matrix(5,-3,8,-5) (31/17,11/6) -> (1/2,3/4) Matrix(21,-44,10,-21) -> Matrix(-1,2,0,1) (2/1,11/5) -> (1/1,1/0) Matrix(89,-198,40,-89) -> Matrix(-1,1,0,1) (11/5,9/4) -> (1/2,1/0) Matrix(87,-200,10,-23) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(395,-916,116,-269) -> Matrix(3,-1,4,-1) 1/2 Matrix(989,-2340,418,-989) -> Matrix(15,-14,16,-15) (26/11,45/19) -> (7/8,1/1) Matrix(721,-1710,304,-721) -> Matrix(9,-10,8,-9) (45/19,19/8) -> (1/1,5/4) Matrix(263,-634,56,-135) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(91,-230,36,-91) -> Matrix(7,-6,8,-7) (5/2,23/9) -> (3/4,1/1) Matrix(323,-828,126,-323) -> Matrix(29,-30,28,-29) (23/9,18/7) -> (1/1,15/14) Matrix(293,-796,60,-163) -> Matrix(1,-2,4,-7) Matrix(25,-72,8,-23) -> Matrix(1,-1,0,1) 1/0 Matrix(391,-1274,120,-391) -> Matrix(1,0,0,-1) (13/4,49/15) -> (0/1,1/0) Matrix(1079,-3528,330,-1079) -> Matrix(1,0,8,-1) (49/15,36/11) -> (0/1,1/4) Matrix(3365,-11484,986,-3365) -> Matrix(11,-10,12,-11) (58/17,99/29) -> (5/6,1/1) Matrix(2377,-8118,696,-2377) -> Matrix(-1,2,0,1) (99/29,41/12) -> (1/1,1/0) Matrix(99,-350,28,-99) -> Matrix(7,-6,8,-7) (7/2,25/7) -> (3/4,1/1) Matrix(251,-900,70,-251) -> Matrix(21,-22,20,-21) (25/7,18/5) -> (1/1,11/10) Matrix(25,-104,6,-25) -> Matrix(-1,4,0,1) (4/1,13/3) -> (2/1,1/0) Matrix(53,-234,12,-53) -> Matrix(1,3,0,-1) (13/3,9/2) -> (-3/2,1/0) Matrix(529,-2544,110,-529) -> Matrix(-1,0,16,1) (24/5,53/11) -> (-1/8,0/1) Matrix(637,-3074,132,-637) -> Matrix(1,0,24,-1) (53/11,29/6) -> (0/1,1/12) Matrix(161,-864,30,-161) -> Matrix(11,-10,12,-11) (16/3,27/5) -> (5/6,1/1) Matrix(109,-594,20,-109) -> Matrix(9,-10,8,-9) (27/5,11/2) -> (1/1,5/4) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.