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: 96 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/1 -8/1 -7/1 -6/1 -5/1 -13/3 -4/1 -11/3 -25/7 -17/5 -3/1 -14/5 -13/5 -7/3 -11/5 -2/1 -1/1 -3/5 -5/9 -1/2 -3/7 -5/13 -1/3 -5/17 -3/11 -1/4 -1/5 -1/9 0/1 1/7 3/17 1/5 3/13 1/4 1/3 7/17 3/7 5/11 1/2 7/13 3/5 5/7 17/23 3/4 7/9 11/13 1/1 13/11 5/4 9/7 7/5 19/13 3/2 11/7 49/31 5/3 7/4 9/5 31/17 13/7 2/1 11/5 9/4 7/3 12/5 17/7 5/2 23/9 8/3 41/15 11/4 3/1 49/15 10/3 7/2 25/7 11/3 4/1 13/3 9/2 23/5 14/3 53/11 5/1 16/3 27/5 11/2 17/3 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 -9/1 1/0 -8/1 -4/1 -7/1 -3/1 -1/1 -13/2 1/2 1/0 -6/1 -4/1 -2/1 -11/2 -3/2 1/0 -16/3 -2/1 -5/1 1/0 -24/5 -4/1 -19/4 -5/2 -14/3 -2/1 0/1 -23/5 -3/1 -9/2 -5/2 1/0 -22/5 -2/1 -8/5 -13/3 -3/1 -1/1 -17/4 1/0 -4/1 -2/1 -15/4 -3/2 -11/3 -1/1 -29/8 1/0 -18/5 -2/1 0/1 -43/12 1/0 -25/7 -3/1 -1/1 -7/2 -3/2 1/0 -24/7 0/1 -41/12 1/0 -17/5 -2/1 -27/8 -3/2 -10/3 -2/1 -4/3 -13/4 1/0 -29/9 -1/1 -16/5 -2/1 -3/1 -1/1 -17/6 -1/2 1/0 -31/11 0/1 -45/16 1/0 -14/5 -2/1 0/1 -11/4 -1/2 -30/11 -2/1 0/1 -49/18 -5/2 1/0 -68/25 -2/1 -19/7 -1/1 -27/10 1/2 1/0 -8/3 0/1 -21/8 -3/2 -13/5 -1/1 -31/12 -3/4 -18/7 -4/5 -2/3 -23/9 -1/1 -3/5 -51/20 -1/2 -28/11 -2/5 -5/2 -1/2 1/0 -22/9 -2/1 0/1 -17/7 -1/1 1/1 -29/12 1/0 -41/17 0/1 -12/5 0/1 -19/8 1/0 -26/11 -2/1 -4/3 -7/3 -1/1 -30/13 -2/1 0/1 -23/10 -3/4 -1/2 -16/7 0/1 -25/11 -1/1 -9/4 -1/2 -20/9 0/1 -11/5 -1/1 1/1 -13/6 -1/2 1/0 -2/1 -2/1 0/1 -1/1 -1/1 1/1 -2/3 -2/1 0/1 -11/17 -1/1 -9/14 1/2 1/0 -25/39 -1/1 1/1 -16/25 0/1 -7/11 1/0 -19/30 -3/2 1/0 -12/19 0/1 -17/27 -1/1 -5/8 1/0 -28/45 2/1 -23/37 -1/1 -18/29 0/1 2/1 -13/21 1/0 -21/34 -5/2 1/0 -8/13 -2/1 -19/31 1/0 -11/18 -3/2 1/0 -14/23 -2/3 0/1 -3/5 -1/1 1/1 -13/22 -3/2 1/0 -10/17 -2/3 0/1 -17/29 0/1 -7/12 -1/2 -25/43 -1/1 -68/117 -4/7 -43/74 -1/2 -5/12 -18/31 -2/5 0/1 -11/19 0/1 -15/26 1/2 1/0 -4/7 0/1 -13/23 -1/1 -9/16 1/0 -23/41 -1/1 1/1 -14/25 -2/3 0/1 -5/9 0/1 -11/20 1/0 -6/11 0/1 2/1 -7/13 -1/1 -1/2 -1/2 1/0 -6/13 -2/1 0/1 -11/24 1/0 -5/11 -1/1 1/1 -19/42 -1/2 1/0 -14/31 0/1 2/3 -9/20 1/0 -4/9 -2/1 -15/34 -5/2 1/0 -11/25 -1/1 -7/16 1/0 -17/39 -5/3 -1/1 -10/23 -2/1 -4/3 -3/7 -1/1 -14/33 -2/1 0/1 -11/26 -3/4 -1/2 -30/71 -2/5 0/1 -49/116 -1/2 -19/45 -1/1 -1/3 -8/19 0/1 -5/12 1/0 -17/41 1/0 -12/29 0/1 -19/46 -3/2 1/0 -7/17 -1/1 1/1 -16/39 -2/1 -9/22 -1/2 1/0 -2/5 -2/1 0/1 -11/28 -5/2 -9/23 -5/3 -1/1 -25/64 -3/2 -16/41 -2/1 -7/18 -3/2 -5/4 -5/13 -1/1 -13/34 -3/4 -1/2 -21/55 -1/1 -29/76 -5/6 -8/21 -2/3 -3/8 1/0 -13/35 -1/1 -1/3 -10/27 0/1 2/1 -7/19 -1/1 -18/49 -2/5 0/1 -29/79 1/1 -11/30 -1/2 1/0 -15/41 -1/1 1/1 -4/11 -2/1 -5/14 -1/2 1/0 -11/31 1/0 -6/17 -2/1 0/1 -7/20 1/0 -1/3 -1/1 -7/22 -5/6 -3/4 -6/19 -2/3 0/1 -5/16 -1/2 -14/45 -2/5 0/1 -9/29 -1/1 -4/13 0/1 -3/10 -3/4 -1/2 -11/37 -1/1 -3/5 -19/64 -1/2 -8/27 -2/3 -5/17 -1/2 -17/58 -1/2 -1/4 -29/99 -1/1 -1/3 -41/140 -1/2 -12/41 0/1 -7/24 1/0 -9/31 -1/1 1/1 -11/38 -3/2 1/0 -2/7 -2/3 0/1 -9/32 -1/2 -16/57 0/1 -7/25 -1/1 -1/3 -19/68 -1/6 -12/43 0/1 -5/18 -1/2 1/0 -3/11 -1/1 -7/26 -3/4 -1/2 -18/67 -2/1 0/1 -29/108 -5/6 -11/41 -1/1 -4/15 -2/3 -1/4 -1/2 -4/17 0/1 -7/30 -1/2 1/0 -10/43 -2/5 0/1 -13/56 -1/2 -3/13 -1/1 -1/3 -11/48 1/0 -8/35 -2/3 -5/22 -5/8 -1/2 -2/9 -2/5 0/1 -5/23 -1/3 -18/83 -2/13 0/1 -13/60 1/0 -8/37 0/1 -3/14 -1/2 1/0 -7/33 -3/7 -1/3 -4/19 -2/5 -1/5 0/1 -4/21 -2/1 -11/58 -5/6 -3/4 -7/37 -1/1 -3/16 -1/2 -5/27 -1/1 -1/3 -17/92 -1/2 -12/65 0/1 -7/38 -1/2 -1/4 -2/11 -2/3 0/1 -1/6 -1/2 -1/4 -2/13 0/1 2/1 -3/20 -1/2 -1/7 -1/1 -1/3 -3/22 -1/2 -1/4 -2/15 -2/5 0/1 -1/8 -1/4 -1/9 0/1 0/1 0/1 1/9 -1/1 1/1 1/8 -1/2 1/7 0/1 2/13 0/1 2/13 1/6 1/4 1/2 3/17 1/2 5/28 1/2 2/11 0/1 2/3 1/5 1/1 4/19 2/1 3/14 -3/2 1/0 5/23 0/1 2/9 -2/3 0/1 5/22 -1/4 -1/6 3/13 0/1 4/17 0/1 1/4 1/2 4/15 2/1 3/11 -1/1 1/1 2/7 0/1 2/1 9/31 1/0 7/24 1/0 12/41 -2/1 5/17 -1/1 8/27 0/1 3/10 -1/2 1/0 1/3 0/1 5/14 1/4 1/2 4/11 2/5 15/41 1/2 11/30 1/4 1/2 18/49 0/1 2/5 7/19 1/3 10/27 2/5 4/9 3/8 1/2 8/21 0/1 5/13 1/3 1/1 2/5 0/1 2/3 9/22 1/2 1/0 7/17 1/1 12/29 0/1 17/41 -1/1 1/1 5/12 1/0 18/43 0/1 2/5 13/31 1/2 8/19 2/3 3/7 1/1 10/23 0/1 2/3 7/16 1/0 11/25 0/1 4/9 0/1 9/20 1/0 5/11 0/1 6/13 0/1 2/3 1/2 1/2 1/0 9/17 -1/1 1/1 8/15 0/1 7/13 1/1 6/11 2/1 4/1 5/9 -1/1 14/25 -2/1 0/1 9/16 1/0 4/7 0/1 3/5 0/1 8/13 0/1 37/60 1/4 29/47 1/4 50/81 0/1 2/7 21/34 1/4 3/10 13/21 1/5 1/3 18/29 4/11 2/5 5/8 1/2 17/27 0/1 29/46 1/2 1/0 41/65 -1/1 1/1 12/19 0/1 7/11 1/3 16/25 0/1 9/14 1/4 1/2 2/3 0/1 2/3 9/13 1/1 16/23 2/1 23/33 1/0 30/43 -4/1 -2/1 7/10 -1/2 1/0 19/27 1/3 1/1 12/17 0/1 5/7 0/1 13/18 3/8 1/2 21/29 3/5 1/1 8/11 0/1 11/15 1/1 14/19 0/1 2/3 31/42 1/4 1/2 17/23 1/2 3/4 1/2 10/13 2/3 4/5 7/9 1/1 18/23 8/7 6/5 11/14 5/4 3/2 4/5 2/1 9/11 1/0 5/6 1/2 1/0 11/13 0/1 6/7 0/1 2/3 1/1 -1/1 1/1 8/7 4/3 7/6 3/2 1/0 13/11 1/0 6/5 0/1 2/1 17/14 3/2 1/0 11/9 0/1 16/13 0/1 5/4 1/2 14/11 2/3 4/5 9/7 1/1 22/17 8/7 6/5 13/10 5/4 3/2 4/3 2/1 23/17 2/1 19/14 3/2 1/0 15/11 1/1 26/19 0/1 2/1 37/27 1/1 3/1 11/8 1/0 18/13 2/1 8/3 43/31 3/1 68/49 2/1 93/67 1/1 3/1 25/18 5/2 1/0 7/5 1/0 24/17 2/1 41/29 1/1 58/41 0/1 2/1 75/53 1/1 17/12 1/0 10/7 -2/1 0/1 33/23 0/1 23/16 1/2 13/9 1/1 16/11 2/3 19/13 1/1 3/2 3/2 1/0 14/9 2/1 4/1 25/16 1/0 11/7 3/1 30/19 6/1 8/1 49/31 1/0 68/43 -6/1 19/12 1/0 46/29 0/1 2/1 27/17 1/0 8/5 2/1 5/3 1/0 12/7 -2/1 43/25 -2/1 31/18 -3/2 -5/4 81/47 -1/1 50/29 -4/5 -2/3 19/11 -1/1 1/1 26/15 -2/3 0/1 33/19 0/1 7/4 1/0 16/9 0/1 25/14 -1/2 1/0 9/5 -1/1 20/11 0/1 51/28 -1/10 31/17 0/1 11/6 1/4 1/2 13/7 1/1 15/8 1/0 2/1 0/1 2/1 13/6 3/2 1/0 11/5 1/0 31/14 -1/2 1/0 20/9 0/1 9/4 1/0 25/11 1/0 16/7 0/1 39/17 1/1 23/10 3/2 1/0 30/13 0/1 2/1 7/3 1/1 26/11 0/1 2/3 71/30 3/4 5/6 45/19 1/1 64/27 6/5 19/8 3/2 31/13 2/1 43/18 5/2 1/0 12/5 0/1 41/17 -1/1 1/1 111/46 1/2 1/0 70/29 0/1 2/1 29/12 1/0 17/7 1/1 39/16 3/2 22/9 0/1 2/1 5/2 3/2 1/0 28/11 2/1 23/9 1/1 3/1 64/25 2/1 41/16 1/0 18/7 0/1 2/1 13/5 1/1 3/1 47/18 11/2 1/0 128/49 12/1 81/31 1/0 34/13 -2/1 0/1 21/8 1/0 8/3 2/1 35/13 2/1 27/10 9/4 5/2 19/7 3/1 49/18 5/2 1/0 79/29 2/1 30/11 2/1 4/1 71/26 3/2 1/0 41/15 2/1 11/4 5/2 3/1 1/0 13/4 -3/2 62/19 -8/7 -10/9 49/15 -1/1 85/26 -11/12 -9/10 36/11 -4/5 23/7 -1/1 -1/3 10/3 -2/1 0/1 37/11 0/1 27/8 1/0 17/5 -1/1 58/17 -2/3 0/1 99/29 -1/1 -1/3 140/41 0/1 41/12 -1/2 24/7 0/1 31/9 0/1 38/11 0/1 2/7 7/2 1/2 1/0 32/9 0/1 25/7 -1/1 1/1 68/19 0/1 43/12 1/0 18/5 0/1 2/1 11/3 -1/1 1/1 37/10 -1/2 -1/4 63/17 0/1 89/24 1/10 26/7 0/1 2/7 15/4 1/2 4/1 2/1 17/4 1/0 13/3 1/0 35/8 1/0 22/5 -6/1 -4/1 9/2 -3/2 1/0 23/5 1/0 37/8 1/0 14/3 -2/3 0/1 33/7 0/1 19/4 1/2 24/5 0/1 77/16 1/2 53/11 1/1 82/17 0/1 2/1 29/6 1/2 1/0 5/1 1/1 16/3 2/1 43/8 1/0 27/5 1/1 3/1 38/7 0/1 2/1 11/2 3/2 1/0 28/5 2/1 45/8 1/0 17/3 2/1 6/1 2/1 4/1 13/2 13/2 1/0 7/1 1/0 15/2 -11/2 1/0 8/1 -2/1 9/1 -1/1 1/1 19/2 1/2 1/0 29/3 -1/1 1/1 10/1 0/1 2/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(7,72,24,247) (-9/1,1/0) -> (9/31,7/24) Hyperbolic Matrix(39,328,56,471) (-9/1,-8/1) -> (16/23,23/33) Hyperbolic Matrix(19,148,-52,-405) (-8/1,-7/1) -> (-15/41,-4/11) Hyperbolic Matrix(17,112,-80,-527) (-7/1,-13/2) -> (-3/14,-7/33) Hyperbolic Matrix(53,340,12,77) (-13/2,-6/1) -> (22/5,9/2) Hyperbolic Matrix(13,76,20,117) (-6/1,-11/2) -> (9/14,2/3) Hyperbolic Matrix(29,156,-124,-667) (-11/2,-16/3) -> (-4/17,-7/30) Hyperbolic Matrix(39,200,-8,-41) (-16/3,-5/1) -> (-5/1,-24/5) Parabolic Matrix(177,848,-464,-2223) (-24/5,-19/4) -> (-29/76,-8/21) Hyperbolic Matrix(17,80,-112,-527) (-19/4,-14/3) -> (-2/13,-3/20) Hyperbolic Matrix(159,736,-256,-1185) (-14/3,-23/5) -> (-23/37,-18/29) Hyperbolic Matrix(143,656,80,367) (-23/5,-9/2) -> (25/14,9/5) Hyperbolic Matrix(9,40,56,249) (-9/2,-22/5) -> (2/13,1/6) Hyperbolic Matrix(95,416,-256,-1121) (-22/5,-13/3) -> (-13/35,-10/27) Hyperbolic Matrix(29,124,-156,-667) (-13/3,-17/4) -> (-3/16,-5/27) Hyperbolic Matrix(89,376,40,169) (-17/4,-4/1) -> (20/9,9/4) Hyperbolic Matrix(35,132,92,347) (-4/1,-15/4) -> (3/8,8/21) Hyperbolic Matrix(131,484,-36,-133) (-15/4,-11/3) -> (-11/3,-29/8) Parabolic Matrix(73,264,-232,-839) (-29/8,-18/5) -> (-6/19,-5/16) Hyperbolic Matrix(49,176,272,977) (-18/5,-43/12) -> (5/28,2/11) Hyperbolic Matrix(633,2264,-248,-887) (-43/12,-25/7) -> (-23/9,-51/20) Hyperbolic Matrix(113,400,-176,-623) (-25/7,-7/2) -> (-9/14,-25/39) Hyperbolic Matrix(157,540,-380,-1307) (-7/2,-24/7) -> (-12/29,-19/46) Hyperbolic Matrix(371,1268,-596,-2037) (-24/7,-41/12) -> (-5/8,-28/45) Hyperbolic Matrix(597,2036,-212,-723) (-41/12,-17/5) -> (-31/11,-45/16) Hyperbolic Matrix(161,544,256,865) (-17/5,-27/8) -> (5/8,17/27) Hyperbolic Matrix(81,272,-176,-591) (-27/8,-10/3) -> (-6/13,-11/24) Hyperbolic Matrix(71,232,56,183) (-10/3,-13/4) -> (5/4,14/11) Hyperbolic Matrix(187,604,100,323) (-13/4,-29/9) -> (13/7,15/8) Hyperbolic Matrix(707,2276,-260,-837) (-29/9,-16/5) -> (-68/25,-19/7) Hyperbolic Matrix(59,188,-220,-701) (-16/5,-3/1) -> (-11/41,-4/15) Hyperbolic Matrix(139,396,-364,-1037) (-3/1,-17/6) -> (-13/34,-21/55) Hyperbolic Matrix(421,1188,668,1885) (-17/6,-31/11) -> (17/27,29/46) Hyperbolic Matrix(725,2036,-1716,-4819) (-45/16,-14/5) -> (-30/71,-49/116) Hyperbolic Matrix(55,152,72,199) (-14/5,-11/4) -> (3/4,10/13) Hyperbolic Matrix(19,52,-148,-405) (-11/4,-30/11) -> (-2/15,-1/8) Hyperbolic Matrix(797,2172,-1372,-3739) (-30/11,-49/18) -> (-43/74,-18/31) Hyperbolic Matrix(391,1064,-2120,-5769) (-49/18,-68/25) -> (-12/65,-7/38) Hyperbolic Matrix(207,560,112,303) (-19/7,-27/10) -> (11/6,13/7) Hyperbolic Matrix(95,256,-416,-1121) (-27/10,-8/3) -> (-8/35,-5/22) Hyperbolic Matrix(77,204,20,53) (-8/3,-21/8) -> (15/4,4/1) Hyperbolic Matrix(259,676,-100,-261) (-21/8,-13/5) -> (-13/5,-31/12) Parabolic Matrix(121,312,-344,-887) (-31/12,-18/7) -> (-6/17,-7/20) Hyperbolic Matrix(287,736,-512,-1313) (-18/7,-23/9) -> (-23/41,-14/25) Hyperbolic Matrix(1569,4000,992,2529) (-51/20,-28/11) -> (68/43,19/12) Hyperbolic Matrix(497,1264,208,529) (-28/11,-5/2) -> (43/18,12/5) Hyperbolic Matrix(21,52,44,109) (-5/2,-22/9) -> (6/13,1/2) Hyperbolic Matrix(223,544,-512,-1249) (-22/9,-17/7) -> (-17/39,-10/23) Hyperbolic Matrix(157,380,-540,-1307) (-17/7,-29/12) -> (-7/24,-9/31) Hyperbolic Matrix(679,1640,248,599) (-29/12,-41/17) -> (41/15,11/4) Hyperbolic Matrix(183,440,136,327) (-41/17,-12/5) -> (4/3,23/17) Hyperbolic Matrix(163,388,92,219) (-12/5,-19/8) -> (7/4,16/9) Hyperbolic Matrix(211,500,-468,-1109) (-19/8,-26/11) -> (-14/31,-9/20) Hyperbolic Matrix(167,392,-72,-169) (-26/11,-7/3) -> (-7/3,-30/13) Parabolic Matrix(271,624,-1008,-2321) (-30/13,-23/10) -> (-7/26,-18/67) Hyperbolic Matrix(223,512,-544,-1249) (-23/10,-16/7) -> (-16/39,-9/22) Hyperbolic Matrix(225,512,352,801) (-16/7,-25/11) -> (7/11,16/25) Hyperbolic Matrix(177,400,-304,-687) (-25/11,-9/4) -> (-7/12,-25/43) Hyperbolic Matrix(25,56,104,233) (-9/4,-20/9) -> (4/17,1/4) Hyperbolic Matrix(211,468,-500,-1109) (-20/9,-11/5) -> (-19/45,-8/19) Hyperbolic Matrix(81,176,-272,-591) (-11/5,-13/6) -> (-3/10,-11/37) Hyperbolic Matrix(137,296,56,121) (-13/6,-2/1) -> (22/9,5/2) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(271,176,368,239) (-2/3,-11/17) -> (11/15,14/19) Hyperbolic Matrix(725,468,268,173) (-11/17,-9/14) -> (27/10,19/7) Hyperbolic Matrix(799,512,-2848,-1825) (-25/39,-16/25) -> (-16/57,-7/25) Hyperbolic Matrix(801,512,352,225) (-16/25,-7/11) -> (25/11,16/7) Hyperbolic Matrix(789,500,172,109) (-7/11,-19/30) -> (9/2,23/5) Hyperbolic Matrix(613,388,-1572,-995) (-19/30,-12/19) -> (-16/41,-7/18) Hyperbolic Matrix(603,380,868,547) (-12/19,-17/27) -> (9/13,16/23) Hyperbolic Matrix(865,544,256,161) (-17/27,-5/8) -> (27/8,17/5) Hyperbolic Matrix(3641,2264,-6264,-3895) (-28/45,-23/37) -> (-25/43,-68/117) Hyperbolic Matrix(503,312,424,263) (-18/29,-13/21) -> (13/11,6/5) Hyperbolic Matrix(589,364,500,309) (-13/21,-21/34) -> (7/6,13/11) Hyperbolic Matrix(331,204,-748,-461) (-21/34,-8/13) -> (-4/9,-15/34) Hyperbolic Matrix(417,256,992,609) (-8/13,-19/31) -> (13/31,8/19) Hyperbolic Matrix(85,52,492,301) (-19/31,-11/18) -> (1/6,3/17) Hyperbolic Matrix(577,352,736,449) (-11/18,-14/23) -> (18/23,11/14) Hyperbolic Matrix(567,344,328,199) (-14/23,-3/5) -> (19/11,26/15) Hyperbolic Matrix(391,232,632,375) (-3/5,-13/22) -> (21/34,13/21) Hyperbolic Matrix(705,416,544,321) (-13/22,-10/17) -> (22/17,13/10) Hyperbolic Matrix(463,272,80,47) (-10/17,-17/29) -> (17/3,6/1) Hyperbolic Matrix(923,540,388,227) (-17/29,-7/12) -> (19/8,31/13) Hyperbolic Matrix(14971,8700,5732,3331) (-68/117,-43/74) -> (47/18,128/49) Hyperbolic Matrix(455,264,536,311) (-18/31,-11/19) -> (11/13,6/7) Hyperbolic Matrix(381,220,452,261) (-11/19,-15/26) -> (5/6,11/13) Hyperbolic Matrix(229,132,-1060,-611) (-15/26,-4/7) -> (-8/37,-3/14) Hyperbolic Matrix(219,124,740,419) (-4/7,-13/23) -> (5/17,8/27) Hyperbolic Matrix(737,416,512,289) (-13/23,-9/16) -> (23/16,13/9) Hyperbolic Matrix(1169,656,-2992,-1679) (-9/16,-23/41) -> (-9/23,-25/64) Hyperbolic Matrix(143,80,656,367) (-14/25,-5/9) -> (5/23,2/9) Hyperbolic Matrix(283,156,644,355) (-5/9,-11/20) -> (7/16,11/25) Hyperbolic Matrix(139,76,-492,-269) (-11/20,-6/11) -> (-2/7,-9/32) Hyperbolic Matrix(207,112,560,303) (-6/11,-7/13) -> (7/19,10/27) Hyperbolic Matrix(277,148,204,109) (-7/13,-1/2) -> (19/14,15/11) Hyperbolic Matrix(121,56,296,137) (-1/2,-6/13) -> (2/5,9/22) Hyperbolic Matrix(473,216,-1592,-727) (-11/24,-5/11) -> (-11/37,-19/64) Hyperbolic Matrix(1405,636,-4796,-2171) (-5/11,-19/42) -> (-17/58,-29/99) Hyperbolic Matrix(1813,820,524,237) (-19/42,-14/31) -> (38/11,7/2) Hyperbolic Matrix(233,104,56,25) (-9/20,-4/9) -> (4/1,17/4) Hyperbolic Matrix(1261,556,-3436,-1515) (-15/34,-11/25) -> (-29/79,-11/30) Hyperbolic Matrix(801,352,512,225) (-11/25,-7/16) -> (25/16,11/7) Hyperbolic Matrix(55,24,456,199) (-7/16,-17/39) -> (1/9,1/8) 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(1277,540,1828,773) (-11/26,-30/71) -> (30/43,7/10) Hyperbolic Matrix(5209,2200,-17784,-7511) (-49/116,-19/45) -> (-29/99,-41/140) 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(599,248,1640,679) (-17/41,-12/29) -> (4/11,15/41) Hyperbolic Matrix(601,248,-2072,-855) (-19/46,-7/17) -> (-9/31,-11/38) Hyperbolic Matrix(487,200,56,23) (-7/17,-16/39) -> (8/1,9/1) 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(633,248,-2264,-887) (-11/28,-9/23) -> (-7/25,-19/68) Hyperbolic Matrix(5777,2256,2256,881) (-25/64,-16/41) -> (64/25,41/16) Hyperbolic Matrix(259,100,-676,-261) (-7/18,-5/13) -> (-5/13,-13/34) Parabolic Matrix(2431,928,-9056,-3457) (-21/55,-29/76) -> (-29/108,-11/41) 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(707,260,-2276,-837) (-7/19,-18/49) -> (-14/45,-9/29) Hyperbolic Matrix(1667,612,-7684,-2821) (-18/49,-29/79) -> (-5/23,-18/83) 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(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(149,52,-788,-275) (-7/20,-1/3) -> (-7/37,-3/16) Hyperbolic Matrix(187,60,-988,-317) (-1/3,-7/22) -> (-11/58,-7/37) Hyperbolic Matrix(745,232,-3208,-999) (-5/16,-14/45) -> (-10/43,-13/56) 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(2185,648,408,121) (-19/64,-8/27) -> (16/3,43/8) Hyperbolic Matrix(865,256,544,161) (-8/27,-5/17) -> (27/17,8/5) Hyperbolic Matrix(6517,1908,1356,397) (-41/140,-12/41) -> (24/5,77/16) Hyperbolic Matrix(725,212,-3348,-979) (-12/41,-7/24) -> (-13/60,-8/37) Hyperbolic Matrix(1485,428,628,181) (-11/38,-2/7) -> (26/11,71/30) Hyperbolic Matrix(4627,1300,1292,363) (-9/32,-16/57) -> (68/19,43/12) 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(131,36,-484,-133) (-5/18,-3/11) -> (-3/11,-7/26) Parabolic Matrix(7567,2032,2320,623) (-18/67,-29/108) -> (13/4,62/19) 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(501,116,-2708,-627) (-13/56,-3/13) -> (-5/27,-17/92) 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(367,80,656,143) (-2/9,-5/23) -> (5/9,14/25) Hyperbolic Matrix(8947,1940,2412,523) (-18/83,-13/60) -> (89/24,26/7) 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(15545,2872,4552,841) (-17/92,-12/65) -> (140/41,41/12) Hyperbolic Matrix(1921,352,704,129) (-7/38,-2/11) -> (30/11,71/26) Hyperbolic Matrix(117,20,76,13) (-2/11,-1/6) -> (3/2,14/9) 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(1001,136,184,25) (-3/22,-2/15) -> (38/7,11/2) Hyperbolic Matrix(471,56,328,39) (-1/8,-1/9) -> (33/23,23/16) Hyperbolic Matrix(247,24,72,7) (-1/9,0/1) -> (24/7,31/9) 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(1441,-256,2336,-415) (3/17,5/28) -> (37/60,29/47) Hyperbolic Matrix(295,-56,216,-41) (2/11,1/5) -> (15/11,26/19) 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(1315,-284,764,-165) (3/14,5/23) -> (43/25,31/18) 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(275,-76,76,-21) (3/11,2/7) -> (18/5,11/3) Hyperbolic Matrix(1091,-316,1564,-453) (2/7,9/31) -> (23/33,30/43) Hyperbolic Matrix(1709,-500,2772,-811) (7/24,12/41) -> (8/13,37/60) Hyperbolic Matrix(2919,-856,2104,-617) (12/41,5/17) -> (43/31,68/49) Hyperbolic Matrix(1037,-308,468,-139) (8/27,3/10) -> (31/14,20/9) 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(1781,-652,2412,-883) (15/41,11/30) -> (31/42,17/23) Hyperbolic Matrix(2529,-928,4096,-1503) (11/30,18/49) -> (50/81,21/34) Hyperbolic Matrix(3111,-1144,2200,-809) (18/49,7/19) -> (41/29,58/41) Hyperbolic Matrix(1121,-416,256,-95) (10/27,3/8) -> (35/8,22/5) 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(2797,-1172,4532,-1899) (18/43,13/31) -> (29/47,50/81) Hyperbolic Matrix(359,-152,248,-105) (8/19,3/7) -> (13/9,16/11) Hyperbolic Matrix(1115,-484,804,-349) (3/7,10/23) -> (18/13,43/31) Hyperbolic Matrix(1249,-544,512,-223) (10/23,7/16) -> (39/16,22/9) Hyperbolic Matrix(687,-304,400,-177) (11/25,4/9) -> (12/7,43/25) 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(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(1313,-736,512,-287) (14/25,9/16) -> (41/16,18/7) Hyperbolic Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(1601,-992,928,-575) (13/21,18/29) -> (50/29,19/11) Hyperbolic Matrix(1185,-736,256,-159) (18/29,5/8) -> (37/8,14/3) 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(623,-400,176,-113) (16/25,9/14) -> (7/2,32/9) 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(253,-196,324,-251) (10/13,7/9) -> (7/9,18/23) 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(171,-148,52,-45) (6/7,1/1) -> (23/7,10/3) 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(253,-324,196,-251) (14/11,9/7) -> (9/7,22/17) Parabolic Matrix(1781,-2412,652,-883) (23/17,19/14) -> (71/26,41/15) Hyperbolic Matrix(1539,-2108,284,-389) (26/19,37/27) -> (27/5,38/7) Hyperbolic Matrix(1377,-1888,256,-351) (37/27,11/8) -> (43/8,27/5) Hyperbolic Matrix(403,-556,108,-149) (11/8,18/13) -> (26/7,15/4) Hyperbolic Matrix(14231,-19752,4168,-5785) (68/49,93/67) -> (99/29,140/41) Hyperbolic Matrix(1795,-2492,188,-261) (93/67,25/18) -> (19/2,29/3) Hyperbolic Matrix(6519,-9224,1352,-1913) (58/41,75/53) -> (53/11,82/17) Hyperbolic Matrix(4717,-6676,980,-1387) (75/53,17/12) -> (77/16,53/11) 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(1327,-1936,560,-817) (16/11,19/13) -> (45/19,64/27) Hyperbolic Matrix(1013,-1484,428,-627) (19/13,3/2) -> (71/30,45/19) 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(7451,-11780,2852,-4509) (49/31,68/43) -> (128/49,81/31) 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(4877,-8404,1492,-2571) (31/18,81/47) -> (49/15,85/26) Hyperbolic Matrix(4335,-7472,1328,-2289) (81/47,50/29) -> (62/19,49/15) Hyperbolic Matrix(1755,-3044,644,-1117) (26/15,33/19) -> (79/29,30/11) Hyperbolic Matrix(923,-1604,164,-285) (33/19,7/4) -> (45/8,17/3) Hyperbolic Matrix(437,-780,172,-307) (16/9,25/14) -> (5/2,28/11) Hyperbolic Matrix(3277,-5972,884,-1611) (51/28,31/17) -> (63/17,89/24) 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(221,-484,100,-219) (13/6,11/5) -> (11/5,31/14) Parabolic Matrix(499,-1132,108,-245) (9/4,25/11) -> (23/5,37/8) Hyperbolic Matrix(395,-916,116,-269) (30/13,7/3) -> (17/5,58/17) 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(477,-1156,196,-475) (29/12,17/7) -> (17/7,39/16) Parabolic Matrix(829,-2116,324,-827) (28/11,23/9) -> (23/9,64/25) Parabolic 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(783,-2672,80,-273) (58/17,99/29) -> (29/3,10/1) Hyperbolic Matrix(651,-2228,116,-397) (41/12,24/7) -> (28/5,45/8) Hyperbolic Matrix(701,-2500,196,-699) (32/9,25/7) -> (25/7,68/19) Parabolic Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) Parabolic Matrix(29,-196,4,-27) (13/2,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(7,72,24,247) -> Matrix(1,0,0,1) Matrix(39,328,56,471) -> Matrix(1,6,0,1) Matrix(19,148,-52,-405) -> Matrix(1,2,0,1) Matrix(17,112,-80,-527) -> Matrix(1,0,-2,1) Matrix(53,340,12,77) -> Matrix(1,-2,0,1) Matrix(13,76,20,117) -> Matrix(1,2,2,5) Matrix(29,156,-124,-667) -> Matrix(1,2,-2,-3) Matrix(39,200,-8,-41) -> Matrix(1,-2,0,1) Matrix(177,848,-464,-2223) -> Matrix(3,10,-4,-13) Matrix(17,80,-112,-527) -> Matrix(1,2,0,1) Matrix(159,736,-256,-1185) -> Matrix(1,2,0,1) Matrix(143,656,80,367) -> Matrix(1,2,0,1) Matrix(9,40,56,249) -> Matrix(1,2,4,9) Matrix(95,416,-256,-1121) -> Matrix(1,2,-2,-3) Matrix(29,124,-156,-667) -> Matrix(1,2,-2,-3) Matrix(89,376,40,169) -> Matrix(1,2,0,1) Matrix(35,132,92,347) -> Matrix(1,2,0,1) Matrix(131,484,-36,-133) -> Matrix(1,2,-2,-3) Matrix(73,264,-232,-839) -> Matrix(1,2,-2,-3) Matrix(49,176,272,977) -> Matrix(1,0,2,1) Matrix(633,2264,-248,-887) -> Matrix(1,4,-2,-7) Matrix(113,400,-176,-623) -> Matrix(1,2,0,1) Matrix(157,540,-380,-1307) -> Matrix(1,0,0,1) Matrix(371,1268,-596,-2037) -> Matrix(1,2,0,1) Matrix(597,2036,-212,-723) -> Matrix(1,2,0,1) Matrix(161,544,256,865) -> Matrix(1,2,0,1) Matrix(81,272,-176,-591) -> Matrix(1,2,-2,-3) Matrix(71,232,56,183) -> Matrix(1,0,2,1) Matrix(187,604,100,323) -> Matrix(1,2,0,1) Matrix(707,2276,-260,-837) -> Matrix(1,0,0,1) Matrix(59,188,-220,-701) -> Matrix(3,4,-4,-5) Matrix(139,396,-364,-1037) -> Matrix(1,2,-2,-3) Matrix(421,1188,668,1885) -> Matrix(1,0,2,1) Matrix(725,2036,-1716,-4819) -> Matrix(1,0,-2,1) Matrix(55,152,72,199) -> Matrix(3,2,4,3) Matrix(19,52,-148,-405) -> Matrix(1,0,-2,1) Matrix(797,2172,-1372,-3739) -> Matrix(1,0,-2,1) Matrix(391,1064,-2120,-5769) -> Matrix(1,2,-2,-3) Matrix(207,560,112,303) -> Matrix(1,0,2,1) Matrix(95,256,-416,-1121) -> Matrix(1,2,-2,-3) Matrix(77,204,20,53) -> Matrix(1,2,0,1) Matrix(259,676,-100,-261) -> Matrix(5,6,-6,-7) Matrix(121,312,-344,-887) -> Matrix(5,4,-4,-3) Matrix(287,736,-512,-1313) -> Matrix(3,2,-2,-1) Matrix(1569,4000,992,2529) -> Matrix(7,4,-2,-1) Matrix(497,1264,208,529) -> Matrix(5,2,2,1) Matrix(21,52,44,109) -> Matrix(1,0,2,1) Matrix(223,544,-512,-1249) -> Matrix(3,2,-2,-1) Matrix(157,380,-540,-1307) -> Matrix(1,0,0,1) Matrix(679,1640,248,599) -> Matrix(5,2,2,1) Matrix(183,440,136,327) -> Matrix(1,2,0,1) Matrix(163,388,92,219) -> Matrix(1,0,0,1) Matrix(211,500,-468,-1109) -> Matrix(1,2,0,1) Matrix(167,392,-72,-169) -> Matrix(1,2,-2,-3) Matrix(271,624,-1008,-2321) -> Matrix(1,0,0,1) Matrix(223,512,-544,-1249) -> Matrix(3,2,-2,-1) Matrix(225,512,352,801) -> Matrix(1,0,4,1) Matrix(177,400,-304,-687) -> Matrix(1,0,0,1) Matrix(25,56,104,233) -> Matrix(1,0,4,1) Matrix(211,468,-500,-1109) -> Matrix(1,0,-2,1) Matrix(81,176,-272,-591) -> Matrix(1,2,-2,-3) Matrix(137,296,56,121) -> Matrix(1,2,0,1) Matrix(3,4,-4,-5) -> Matrix(1,0,0,1) Matrix(271,176,368,239) -> Matrix(1,0,2,1) Matrix(725,468,268,173) -> Matrix(5,2,2,1) Matrix(799,512,-2848,-1825) -> Matrix(1,0,-2,1) Matrix(801,512,352,225) -> Matrix(1,0,0,1) Matrix(789,500,172,109) -> Matrix(1,0,0,1) Matrix(613,388,-1572,-995) -> Matrix(3,2,-2,-1) Matrix(603,380,868,547) -> Matrix(1,2,0,1) Matrix(865,544,256,161) -> Matrix(1,0,0,1) Matrix(3641,2264,-6264,-3895) -> Matrix(1,2,-2,-3) Matrix(503,312,424,263) -> Matrix(1,0,0,1) Matrix(589,364,500,309) -> Matrix(1,4,0,1) Matrix(331,204,-748,-461) -> Matrix(1,0,0,1) Matrix(417,256,992,609) -> Matrix(1,0,2,1) Matrix(85,52,492,301) -> Matrix(1,2,2,5) Matrix(577,352,736,449) -> Matrix(5,6,4,5) Matrix(567,344,328,199) -> Matrix(1,0,0,1) Matrix(391,232,632,375) -> Matrix(1,0,4,1) Matrix(705,416,544,321) -> Matrix(5,6,4,5) Matrix(463,272,80,47) -> Matrix(5,2,2,1) Matrix(923,540,388,227) -> Matrix(1,2,0,1) Matrix(14971,8700,5732,3331) -> Matrix(17,8,2,1) Matrix(455,264,536,311) -> Matrix(1,0,4,1) Matrix(381,220,452,261) -> Matrix(1,0,0,1) Matrix(229,132,-1060,-611) -> Matrix(1,0,-2,1) Matrix(219,124,740,419) -> Matrix(1,0,0,1) Matrix(737,416,512,289) -> Matrix(1,0,2,1) Matrix(1169,656,-2992,-1679) -> Matrix(3,2,-2,-1) Matrix(143,80,656,367) -> Matrix(1,0,0,1) Matrix(283,156,644,355) -> Matrix(1,0,0,1) Matrix(139,76,-492,-269) -> Matrix(1,0,-2,1) Matrix(207,112,560,303) -> Matrix(1,2,2,5) Matrix(277,148,204,109) -> Matrix(1,2,0,1) Matrix(121,56,296,137) -> Matrix(1,0,2,1) Matrix(473,216,-1592,-727) -> Matrix(1,2,-2,-3) Matrix(1405,636,-4796,-2171) -> Matrix(1,0,-2,1) Matrix(1813,820,524,237) -> Matrix(1,0,2,1) Matrix(233,104,56,25) -> Matrix(1,4,0,1) Matrix(1261,556,-3436,-1515) -> Matrix(1,2,0,1) Matrix(801,352,512,225) -> Matrix(1,4,0,1) Matrix(55,24,456,199) -> Matrix(1,2,-2,-3) Matrix(167,72,-392,-169) -> Matrix(1,2,-2,-3) Matrix(387,164,-1220,-517) -> Matrix(1,2,-2,-3) Matrix(1277,540,1828,773) -> Matrix(3,2,-2,-1) Matrix(5209,2200,-17784,-7511) -> Matrix(1,0,0,1) Matrix(219,92,388,163) -> Matrix(1,0,0,1) Matrix(327,136,440,183) -> Matrix(1,0,2,1) Matrix(599,248,1640,679) -> Matrix(1,2,2,5) Matrix(601,248,-2072,-855) -> Matrix(1,0,0,1) Matrix(487,200,56,23) -> Matrix(1,0,0,1) Matrix(109,44,52,21) -> Matrix(1,2,0,1) Matrix(529,208,1264,497) -> Matrix(1,2,2,5) Matrix(633,248,-2264,-887) -> Matrix(1,2,-4,-7) Matrix(5777,2256,2256,881) -> Matrix(3,4,2,3) Matrix(259,100,-676,-261) -> Matrix(5,6,-6,-7) Matrix(2431,928,-9056,-3457) -> Matrix(1,0,0,1) Matrix(53,20,204,77) -> Matrix(1,0,2,1) Matrix(409,152,-1784,-663) -> Matrix(1,0,0,1) Matrix(303,112,560,207) -> Matrix(1,2,0,1) Matrix(707,260,-2276,-837) -> Matrix(1,0,0,1) Matrix(1667,612,-7684,-2821) -> Matrix(1,0,-4,1) Matrix(153,56,-1112,-407) -> Matrix(1,0,-2,1) Matrix(199,72,152,55) -> Matrix(3,4,2,3) Matrix(597,212,-2036,-723) -> Matrix(1,0,-2,1) Matrix(1885,668,1188,421) -> Matrix(1,2,0,1) Matrix(149,52,-788,-275) -> Matrix(1,2,-2,-3) Matrix(187,60,-988,-317) -> Matrix(1,0,0,1) Matrix(745,232,-3208,-999) -> Matrix(1,0,0,1) Matrix(323,100,604,187) -> Matrix(1,0,2,1) Matrix(183,56,232,71) -> Matrix(1,2,0,1) Matrix(2185,648,408,121) -> Matrix(1,0,2,1) Matrix(865,256,544,161) -> Matrix(1,0,2,1) Matrix(6517,1908,1356,397) -> Matrix(1,0,4,1) Matrix(725,212,-3348,-979) -> Matrix(1,0,0,1) Matrix(1485,428,628,181) -> Matrix(3,2,4,3) Matrix(4627,1300,1292,363) -> Matrix(1,0,2,1) Matrix(3553,992,1952,545) -> Matrix(1,0,-4,1) Matrix(977,272,176,49) -> Matrix(1,2,0,1) Matrix(131,36,-484,-133) -> Matrix(1,2,-2,-3) Matrix(7567,2032,2320,623) -> Matrix(9,8,-8,-7) Matrix(347,92,132,35) -> Matrix(1,0,2,1) Matrix(169,40,376,89) -> Matrix(1,0,2,1) Matrix(1753,408,2376,553) -> Matrix(1,0,4,1) Matrix(501,116,-2708,-627) -> Matrix(1,0,0,1) Matrix(3737,856,1576,361) -> Matrix(3,4,2,3) Matrix(249,56,40,9) -> Matrix(9,4,2,1) Matrix(367,80,656,143) -> Matrix(1,0,2,1) Matrix(8947,1940,2412,523) -> Matrix(1,0,10,1) Matrix(1175,248,488,103) -> Matrix(5,2,2,1) Matrix(39,8,-200,-41) -> Matrix(1,0,2,1) Matrix(3873,736,1184,225) -> Matrix(5,6,-6,-7) Matrix(15545,2872,4552,841) -> Matrix(1,0,0,1) Matrix(1921,352,704,129) -> Matrix(5,2,2,1) Matrix(117,20,76,13) -> Matrix(5,2,2,1) Matrix(77,12,340,53) -> Matrix(1,0,-2,1) Matrix(375,56,904,135) -> Matrix(1,0,2,1) Matrix(1001,136,184,25) -> Matrix(5,2,2,1) Matrix(471,56,328,39) -> Matrix(1,0,6,1) Matrix(247,24,72,7) -> Matrix(1,0,0,1) Matrix(149,-12,236,-19) -> Matrix(1,0,0,1) Matrix(397,-52,84,-11) -> Matrix(1,0,4,1) Matrix(527,-80,112,-17) -> Matrix(1,0,-8,1) Matrix(1441,-256,2336,-415) -> Matrix(1,0,2,1) Matrix(295,-56,216,-41) -> Matrix(3,-2,2,-1) Matrix(899,-188,636,-133) -> Matrix(1,0,0,1) Matrix(397,-84,52,-11) -> Matrix(1,-4,0,1) Matrix(1315,-284,764,-165) -> Matrix(3,2,-2,-1) Matrix(1121,-256,416,-95) -> Matrix(17,2,8,1) Matrix(699,-164,260,-61) -> Matrix(11,-2,6,-1) Matrix(403,-108,556,-149) -> Matrix(1,-2,2,-3) Matrix(275,-76,76,-21) -> Matrix(1,0,0,1) Matrix(1091,-316,1564,-453) -> Matrix(1,-4,0,1) Matrix(1709,-500,2772,-811) -> Matrix(1,2,4,9) Matrix(2919,-856,2104,-617) -> Matrix(1,4,0,1) Matrix(1037,-308,468,-139) -> Matrix(1,0,0,1) Matrix(25,-8,72,-23) -> Matrix(1,0,4,1) Matrix(189,-68,164,-59) -> Matrix(7,-2,4,-1) Matrix(1781,-652,2412,-883) -> Matrix(1,0,0,1) Matrix(2529,-928,4096,-1503) -> Matrix(5,-2,18,-7) Matrix(3111,-1144,2200,-809) -> Matrix(1,0,-2,1) Matrix(1121,-416,256,-95) -> Matrix(17,-8,-2,1) Matrix(555,-212,788,-301) -> Matrix(1,0,0,1) Matrix(299,-116,116,-45) -> Matrix(3,-2,2,-1) Matrix(1249,-512,544,-223) -> Matrix(3,-2,2,-1) Matrix(1403,-580,612,-253) -> Matrix(1,0,0,1) Matrix(589,-244,1108,-459) -> Matrix(1,0,0,1) Matrix(2797,-1172,4532,-1899) -> Matrix(5,-2,18,-7) Matrix(359,-152,248,-105) -> Matrix(1,0,0,1) Matrix(1115,-484,804,-349) -> Matrix(1,2,0,1) Matrix(1249,-544,512,-223) -> Matrix(3,-2,2,-1) Matrix(687,-304,400,-177) -> Matrix(1,-2,0,1) Matrix(1037,-468,308,-139) -> Matrix(1,0,0,1) Matrix(591,-272,176,-81) -> Matrix(1,0,-2,1) Matrix(1969,-1040,816,-431) -> Matrix(1,0,0,1) Matrix(391,-216,248,-137) -> Matrix(1,4,0,1) Matrix(1313,-736,512,-287) -> Matrix(1,2,0,1) Matrix(61,-36,100,-59) -> Matrix(1,0,4,1) Matrix(1601,-992,928,-575) -> Matrix(1,0,-4,1) Matrix(1185,-736,256,-159) -> Matrix(5,-2,-2,1) Matrix(1649,-1040,176,-111) -> Matrix(1,0,0,1) Matrix(391,-248,216,-137) -> Matrix(1,0,-4,1) Matrix(623,-400,176,-113) -> Matrix(1,0,-2,1) Matrix(359,-248,152,-105) -> Matrix(1,0,0,1) Matrix(1109,-780,300,-211) -> Matrix(1,0,-2,1) Matrix(299,-212,244,-173) -> Matrix(1,0,0,1) Matrix(317,-228,260,-187) -> Matrix(1,0,-2,1) Matrix(1597,-1156,612,-443) -> Matrix(7,-4,2,-1) Matrix(295,-216,56,-41) -> Matrix(3,-2,2,-1) Matrix(253,-196,324,-251) -> Matrix(11,-10,10,-9) Matrix(299,-244,212,-173) -> Matrix(1,0,0,1) Matrix(317,-260,228,-187) -> Matrix(1,2,0,1) Matrix(171,-148,52,-45) -> Matrix(1,0,-2,1) Matrix(197,-220,60,-67) -> Matrix(1,0,-2,1) Matrix(535,-648,232,-281) -> Matrix(1,0,0,1) Matrix(343,-424,72,-89) -> Matrix(1,0,0,1) Matrix(253,-324,196,-251) -> Matrix(11,-10,10,-9) Matrix(1781,-2412,652,-883) -> Matrix(1,0,0,1) Matrix(1539,-2108,284,-389) -> Matrix(1,0,0,1) Matrix(1377,-1888,256,-351) -> Matrix(1,0,0,1) Matrix(403,-556,108,-149) -> Matrix(1,-2,2,-3) Matrix(14231,-19752,4168,-5785) -> Matrix(1,-2,-2,5) Matrix(1795,-2492,188,-261) -> Matrix(1,-2,0,1) Matrix(6519,-9224,1352,-1913) -> Matrix(1,0,0,1) Matrix(4717,-6676,980,-1387) -> Matrix(1,-2,2,-3) Matrix(555,-788,212,-301) -> Matrix(1,0,0,1) Matrix(1091,-1564,316,-453) -> Matrix(1,0,4,1) Matrix(1327,-1936,560,-817) -> Matrix(9,-8,8,-7) Matrix(1013,-1484,428,-627) -> Matrix(5,-6,6,-7) Matrix(675,-1052,188,-293) -> Matrix(1,-2,0,1) Matrix(2593,-4096,992,-1567) -> Matrix(1,-8,0,1) Matrix(7451,-11780,2852,-4509) -> Matrix(1,18,0,1) Matrix(149,-236,12,-19) -> Matrix(1,0,0,1) Matrix(61,-100,36,-59) -> Matrix(1,-4,0,1) Matrix(4877,-8404,1492,-2571) -> Matrix(13,14,-14,-15) Matrix(4335,-7472,1328,-2289) -> Matrix(13,12,-12,-11) Matrix(1755,-3044,644,-1117) -> Matrix(5,2,2,1) Matrix(923,-1604,164,-285) -> Matrix(1,2,0,1) Matrix(437,-780,172,-307) -> Matrix(1,2,0,1) Matrix(3277,-5972,884,-1611) -> Matrix(1,0,20,1) Matrix(1007,-1840,272,-497) -> Matrix(1,0,-6,1) Matrix(589,-1108,244,-459) -> Matrix(1,0,0,1) Matrix(221,-484,100,-219) -> Matrix(1,-2,0,1) Matrix(499,-1132,108,-245) -> Matrix(1,-2,0,1) Matrix(395,-916,116,-269) -> Matrix(1,0,-2,1) Matrix(2059,-4916,756,-1805) -> Matrix(1,0,0,1) Matrix(4613,-11132,956,-2307) -> Matrix(1,0,0,1) Matrix(477,-1156,196,-475) -> Matrix(3,-2,2,-1) Matrix(829,-2116,324,-827) -> Matrix(1,0,0,1) Matrix(293,-796,60,-163) -> Matrix(1,-2,0,1) Matrix(25,-72,8,-23) -> Matrix(1,-4,0,1) Matrix(783,-2672,80,-273) -> Matrix(1,0,2,1) Matrix(651,-2228,116,-397) -> Matrix(5,2,2,1) Matrix(701,-2500,196,-699) -> Matrix(1,0,0,1) Matrix(157,-676,36,-155) -> Matrix(1,-14,0,1) Matrix(29,-196,4,-27) -> Matrix(1,-12,0,1) 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 cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 53 Degree of the the map X: 53 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- 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 -9/1 1/0 5 2 -8/1 -4/1 1 16 -7/1 (-3/1,-1/1) 0 8 -13/2 0 16 -6/1 0 16 -11/2 0 16 -16/3 -2/1 1 16 -5/1 1/0 1 4 -24/5 -4/1 1 16 -19/4 -5/2 1 16 -33/7 (-3/1,-7/3) 0 8 -14/3 0 16 -23/5 -3/1 1 8 -9/2 0 16 -22/5 0 16 -13/3 (-3/1,-1/1) 0 8 -43/10 0 16 -30/7 0 16 -17/4 1/0 1 16 -4/1 -2/1 1 16 -15/4 -3/2 1 16 -11/3 -1/1 1 2 -29/8 1/0 1 16 -18/5 0 16 -43/12 1/0 1 16 -25/7 (-3/1,-1/1) 0 8 -7/2 0 16 -24/7 0/1 1 16 -41/12 1/0 1 16 -17/5 -2/1 1 4 -27/8 -3/2 1 16 -10/3 0 16 -13/4 1/0 1 16 -29/9 -1/1 1 4 -16/5 -2/1 1 16 -19/6 0 16 -3/1 -1/1 1 8 -17/6 0 16 -31/11 0/1 1 4 -45/16 1/0 1 16 -14/5 0 16 -11/4 -1/2 1 16 -41/15 (-1/1,1/1) 0 8 -30/11 0 16 -49/18 0 16 -117/43 (-3/1,-1/1) 0 8 -68/25 -2/1 1 16 -19/7 -1/1 1 4 -27/10 0 16 -35/13 (-3/1,-1/1) 0 8 -8/3 0/1 1 16 -21/8 -3/2 1 16 -13/5 -1/1 3 2 -31/12 -3/4 1 16 -80/31 0/1 1 16 -49/19 -1/1 1 8 -18/7 0 16 -23/9 (-1/1,-3/5) 0 8 -51/20 -1/2 1 16 -28/11 -2/5 1 16 -5/2 0 16 -22/9 0 16 -17/7 (-1/1,1/1) 0 8 -46/19 0 16 -29/12 1/0 1 16 -41/17 0/1 1 2 -12/5 0/1 1 16 -19/8 1/0 1 16 -26/11 0 16 -7/3 -1/1 1 4 -30/13 0 16 -83/36 -5/6 1 16 -53/23 -1/1 1 8 -23/10 0 16 -39/17 (-1/1,-3/5) 0 8 -16/7 0/1 1 16 -25/11 -1/1 1 8 -9/4 -1/2 1 16 -20/9 0/1 1 16 -31/14 0 16 -42/19 0 16 -53/24 1/0 1 16 -11/5 (-1/1,1/1) 0 8 -24/11 0/1 1 16 -13/6 0 16 -2/1 0 16 -13/7 -1/1 1 8 -11/6 0 16 -31/17 (-1/1,1/1) 0 8 -20/11 0/1 1 16 -9/5 1/0 1 4 -25/14 0 16 -41/23 (-1/1,1/1) 0 8 -16/9 0/1 1 16 -23/13 -1/1 1 8 -7/4 1/0 1 16 -40/23 2/1 1 16 -33/19 -1/1 1 8 -26/15 0 16 -19/11 1/0 2 2 -31/18 0 16 -74/43 0 16 -117/68 -7/4 1 16 -43/25 -1/1 1 8 -12/7 -2/1 1 16 -29/17 1/0 2 4 -17/10 0 16 -22/13 0 16 -5/3 (-1/1,1/1) 0 8 -1/1 (-1/1,1/1) 0 2 1/1 (-1/1,1/1) 0 8 7/6 0 16 13/11 1/0 2 2 6/5 0 16 11/9 0/1 1 4 5/4 1/2 1 16 14/11 0 16 9/7 1/1 5 2 22/17 0 16 13/10 0 16 4/3 2/1 1 16 23/17 2/1 1 2 19/14 0 16 15/11 1/1 1 8 11/8 1/0 1 16 18/13 0 16 25/18 0 16 7/5 1/0 1 4 24/17 2/1 1 16 17/12 1/0 1 16 10/7 0 16 33/23 0/1 5 2 23/16 1/2 1 16 13/9 1/1 1 8 3/2 0 16 14/9 0 16 25/16 1/0 1 16 11/7 3/1 1 8 19/12 1/0 1 16 46/29 0 16 27/17 1/0 1 4 8/5 2/1 1 16 5/3 1/0 2 2 12/7 -2/1 1 16 31/18 0 16 81/47 -1/1 13 2 19/11 (-1/1,1/1) 0 8 26/15 0 16 33/19 0/1 2 4 7/4 1/0 1 16 16/9 0/1 1 16 25/14 0 16 9/5 -1/1 1 8 20/11 0/1 1 16 51/28 -1/10 1 16 31/17 0/1 13 2 11/6 0 16 13/7 1/1 1 4 15/8 1/0 1 16 2/1 0 16 13/6 0 16 11/5 1/0 1 2 20/9 0/1 1 16 9/4 1/0 1 16 25/11 1/0 1 4 16/7 0/1 1 16 23/10 0 16 30/13 0 16 7/3 1/1 1 8 26/11 0 16 45/19 1/1 7 2 19/8 3/2 1 16 31/13 2/1 2 4 43/18 0 16 12/5 0/1 1 16 41/17 (-1/1,1/1) 0 8 70/29 0 16 29/12 1/0 1 16 17/7 1/1 1 2 39/16 3/2 1 16 22/9 0 16 5/2 0 16 28/11 2/1 1 16 23/9 (1/1,3/1) 0 2 13/5 (1/1,3/1) 0 8 34/13 0 16 21/8 1/0 1 16 8/3 2/1 1 16 27/10 0 16 19/7 3/1 1 8 49/18 0 16 79/29 2/1 2 4 30/11 0 16 71/26 0 16 41/15 2/1 1 2 11/4 5/2 1 16 3/1 1/0 2 4 13/4 -3/2 1 16 62/19 0 16 49/15 -1/1 13 2 23/7 (-1/1,-1/3) 0 8 10/3 0 16 37/11 0/1 1 2 27/8 1/0 1 16 17/5 -1/1 1 8 58/17 0 16 99/29 (-1/1,-1/3) 0 2 41/12 -1/2 1 16 24/7 0/1 1 16 31/9 0/1 5 2 38/11 0 16 7/2 0 16 32/9 0/1 1 16 25/7 (-1/1,1/1) 0 2 11/3 (-1/1,1/1) 0 8 37/10 0 16 63/17 0/1 13 2 89/24 1/10 1 16 26/7 0 16 15/4 1/2 1 16 4/1 2/1 1 16 17/4 1/0 1 16 13/3 1/0 7 2 35/8 1/0 1 16 22/5 0 16 9/2 0 16 23/5 1/0 1 4 37/8 1/0 1 16 14/3 0 16 19/4 1/2 1 16 24/5 0/1 1 16 53/11 1/1 1 2 29/6 0 16 5/1 1/1 1 8 16/3 2/1 1 16 27/5 (1/1,3/1) 0 2 11/2 0 16 28/5 2/1 1 16 45/8 1/0 1 16 17/3 2/1 2 4 6/1 0 16 13/2 0 16 7/1 1/0 6 2 15/2 0 16 8/1 -2/1 1 16 9/1 (-1/1,1/1) 0 8 29/3 (-1/1,1/1) 0 2 10/1 0 16 1/0 1/0 1 16 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(24,247,7,72) (-9/1,1/0) -> (24/7,31/9) Glide Reflection Matrix(56,471,39,328) (-9/1,-8/1) -> (33/23,23/16) Glide Reflection Matrix(52,405,-19,-148) (-8/1,-7/1) -> (-11/4,-41/15) Glide Reflection Matrix(80,527,-17,-112) (-7/1,-13/2) -> (-33/7,-14/3) Glide Reflection Matrix(53,340,12,77) (-13/2,-6/1) -> (22/5,9/2) Hyperbolic Matrix(20,117,13,76) (-6/1,-11/2) -> (3/2,14/9) Glide Reflection Matrix(124,667,-29,-156) (-11/2,-16/3) -> (-30/7,-17/4) Glide Reflection Matrix(39,200,-8,-41) (-16/3,-5/1) -> (-5/1,-24/5) Parabolic Matrix(524,2509,-203,-972) (-24/5,-19/4) -> (-31/12,-80/31) Glide Reflection Matrix(248,1175,103,488) (-19/4,-33/7) -> (12/5,41/17) Glide Reflection Matrix(229,1060,-132,-611) (-14/3,-23/5) -> (-33/19,-26/15) Hyperbolic Matrix(143,656,80,367) (-23/5,-9/2) -> (25/14,9/5) Hyperbolic Matrix(56,249,9,40) (-9/2,-22/5) -> (6/1,13/2) Glide Reflection Matrix(256,1121,-95,-416) (-22/5,-13/3) -> (-27/10,-35/13) Glide Reflection Matrix(1317,5668,-484,-2083) (-13/3,-43/10) -> (-49/18,-117/43) Hyperbolic Matrix(797,3420,292,1253) (-43/10,-30/7) -> (30/11,71/26) Hyperbolic Matrix(89,376,40,169) (-17/4,-4/1) -> (20/9,9/4) Hyperbolic Matrix(92,347,35,132) (-4/1,-15/4) -> (21/8,8/3) Glide Reflection Matrix(131,484,-36,-133) (-15/4,-11/3) -> (-11/3,-29/8) Parabolic Matrix(232,839,-73,-264) (-29/8,-18/5) -> (-16/5,-19/6) Glide Reflection Matrix(272,977,49,176) (-18/5,-43/12) -> (11/2,28/5) Glide Reflection Matrix(633,2264,-248,-887) (-43/12,-25/7) -> (-23/9,-51/20) Hyperbolic Matrix(139,492,-76,-269) (-25/7,-7/2) -> (-11/6,-31/17) Hyperbolic Matrix(380,1307,-157,-540) (-7/2,-24/7) -> (-46/19,-29/12) Glide Reflection Matrix(529,1808,-304,-1039) (-24/7,-41/12) -> (-7/4,-40/23) Hyperbolic Matrix(597,2036,-212,-723) (-41/12,-17/5) -> (-31/11,-45/16) Hyperbolic Matrix(256,865,161,544) (-17/5,-27/8) -> (27/17,8/5) Glide Reflection Matrix(176,591,-81,-272) (-27/8,-10/3) -> (-24/11,-13/6) Glide Reflection Matrix(71,232,56,183) (-10/3,-13/4) -> (5/4,14/11) Hyperbolic Matrix(187,604,100,323) (-13/4,-29/9) -> (13/7,15/8) Hyperbolic Matrix(707,2276,-260,-837) (-29/9,-16/5) -> (-68/25,-19/7) Hyperbolic Matrix(341,1076,-148,-467) (-19/6,-3/1) -> (-53/23,-23/10) Hyperbolic Matrix(312,887,-121,-344) (-3/1,-17/6) -> (-49/19,-18/7) Glide Reflection Matrix(668,1885,421,1188) (-17/6,-31/11) -> (46/29,27/17) Glide Reflection Matrix(937,2632,-424,-1191) (-45/16,-14/5) -> (-42/19,-53/24) Hyperbolic Matrix(72,199,55,152) (-14/5,-11/4) -> (13/10,4/3) Glide Reflection Matrix(1516,4141,-555,-1516) (-41/15,-101/37) -> (-41/15,-101/37) Reflection Matrix(704,1921,129,352) (-71/26,-30/11) -> (38/7,11/2) Glide Reflection Matrix(1372,3739,-797,-2172) (-30/11,-49/18) -> (-31/18,-74/43) Glide Reflection Matrix(10880,29601,-3999,-10880) (-117/43,-253/93) -> (-117/43,-253/93) Reflection Matrix(6288,17105,1841,5008) (-185/68,-68/25) -> (140/41,41/12) Glide Reflection Matrix(207,560,112,303) (-19/7,-27/10) -> (11/6,13/7) Hyperbolic Matrix(664,1785,-247,-664) (-35/13,-51/19) -> (-35/13,-51/19) Reflection Matrix(496,1329,209,560) (-43/16,-8/3) -> (64/27,19/8) Glide Reflection Matrix(77,204,20,53) (-8/3,-21/8) -> (15/4,4/1) Hyperbolic Matrix(259,676,-100,-261) (-21/8,-13/5) -> (-13/5,-31/12) Parabolic Matrix(3220,8307,-1397,-3604) (-80/31,-49/19) -> (-83/36,-53/23) Glide Reflection Matrix(512,1313,-287,-736) (-18/7,-23/9) -> (-25/14,-41/23) Glide Reflection Matrix(1240,3161,681,1736) (-51/20,-28/11) -> (20/11,51/28) Glide Reflection Matrix(497,1264,208,529) (-28/11,-5/2) -> (43/18,12/5) Hyperbolic Matrix(44,109,21,52) (-5/2,-22/9) -> (2/1,13/6) Glide Reflection Matrix(512,1249,-223,-544) (-22/9,-17/7) -> (-23/10,-39/17) Glide Reflection Matrix(764,1853,-315,-764) (-17/7,-109/45) -> (-17/7,-109/45) Reflection Matrix(2025,4904,856,2073) (-63/26,-46/19) -> (26/11,71/30) Hyperbolic Matrix(679,1640,248,599) (-29/12,-41/17) -> (41/15,11/4) Hyperbolic Matrix(183,440,136,327) (-41/17,-12/5) -> (4/3,23/17) Hyperbolic Matrix(163,388,92,219) (-12/5,-19/8) -> (7/4,16/9) Hyperbolic Matrix(468,1109,-211,-500) (-19/8,-26/11) -> (-20/9,-31/14) Glide Reflection Matrix(167,392,-72,-169) (-26/11,-7/3) -> (-7/3,-30/13) Parabolic Matrix(2401,5536,736,1697) (-30/13,-83/36) -> (13/4,62/19) Hyperbolic Matrix(199,456,24,55) (-39/17,-16/7) -> (8/1,9/1) Hyperbolic Matrix(352,801,225,512) (-16/7,-25/11) -> (25/16,11/7) Glide Reflection Matrix(304,687,-177,-400) (-25/11,-9/4) -> (-43/25,-12/7) Glide Reflection Matrix(104,233,25,56) (-9/4,-20/9) -> (4/1,17/4) Glide Reflection Matrix(820,1813,237,524) (-31/14,-42/19) -> (38/11,7/2) Glide Reflection Matrix(2544,5617,529,1168) (-53/24,-64/29) -> (24/5,77/16) Glide Reflection Matrix(584,1287,-265,-584) (-117/53,-11/5) -> (-117/53,-11/5) Reflection Matrix(296,649,-135,-296) (-11/5,-59/27) -> (-11/5,-59/27) Reflection Matrix(729,1592,136,297) (-35/16,-24/11) -> (16/3,43/8) Hyperbolic Matrix(137,296,56,121) (-13/6,-2/1) -> (22/9,5/2) Hyperbolic Matrix(148,277,109,204) (-2/1,-13/7) -> (19/14,15/11) Glide Reflection Matrix(303,560,112,207) (-13/7,-11/6) -> (27/10,19/7) Hyperbolic Matrix(1208,2201,-663,-1208) (-31/17,-71/39) -> (-31/17,-71/39) Reflection Matrix(1523,2772,428,779) (-51/28,-20/11) -> (32/9,57/16) Hyperbolic Matrix(355,644,156,283) (-20/11,-9/5) -> (25/11,16/7) Hyperbolic Matrix(367,656,80,143) (-9/5,-25/14) -> (9/2,23/5) Hyperbolic Matrix(1680,2993,-943,-1680) (-41/23,-73/41) -> (-41/23,-73/41) Reflection Matrix(1355,2412,532,947) (-57/32,-16/9) -> (28/11,51/20) Hyperbolic Matrix(416,737,289,512) (-16/9,-23/13) -> (23/16,13/9) Glide Reflection Matrix(419,740,124,219) (-23/13,-7/4) -> (27/8,17/5) Hyperbolic Matrix(3212,5581,-1867,-3244) (-40/23,-33/19) -> (-117/68,-43/25) Glide Reflection Matrix(261,452,220,381) (-26/15,-19/11) -> (13/11,6/5) Hyperbolic Matrix(311,536,264,455) (-19/11,-31/18) -> (7/6,13/11) Hyperbolic Matrix(5595,9628,1508,2595) (-74/43,-117/68) -> (89/24,26/7) Hyperbolic Matrix(540,923,227,388) (-12/7,-29/17) -> (19/8,31/13) Glide Reflection Matrix(272,463,47,80) (-29/17,-17/10) -> (17/3,6/1) Glide Reflection Matrix(416,705,321,544) (-17/10,-22/13) -> (22/17,13/10) Glide Reflection Matrix(325,548,188,317) (-22/13,-5/3) -> (19/11,26/15) Hyperbolic Matrix(4,5,-3,-4) (-5/3,-1/1) -> (-5/3,-1/1) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(148,-171,45,-52) (1/1,7/6) -> (23/7,10/3) Glide Reflection Matrix(260,-317,187,-228) (6/5,11/9) -> (25/18,7/5) Glide Reflection Matrix(244,-299,173,-212) (11/9,5/4) -> (7/5,24/17) Glide Reflection Matrix(253,-324,196,-251) (14/11,9/7) -> (9/7,22/17) Parabolic Matrix(1781,-2412,652,-883) (23/17,19/14) -> (71/26,41/15) Hyperbolic Matrix(216,-295,41,-56) (15/11,11/8) -> (5/1,16/3) Glide Reflection Matrix(403,-556,108,-149) (11/8,18/13) -> (26/7,15/4) Hyperbolic Matrix(804,-1115,349,-484) (18/13,25/18) -> (23/10,30/13) Glide Reflection Matrix(636,-899,133,-188) (24/17,17/12) -> (19/4,24/5) Glide Reflection 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(248,-359,105,-152) (13/9,3/2) -> (7/3,26/11) Glide Reflection Matrix(400,-623,113,-176) (14/9,25/16) -> (7/2,32/9) Glide Reflection Matrix(248,-391,137,-216) (11/7,19/12) -> (9/5,20/11) Glide Reflection 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(764,-1315,165,-284) (12/7,31/18) -> (37/8,14/3) Glide Reflection Matrix(3796,-6541,1163,-2004) (31/18,81/47) -> (62/19,49/15) Glide Reflection Matrix(892,-1539,517,-892) (81/47,19/11) -> (81/47,19/11) Reflection Matrix(1755,-3044,644,-1117) (26/15,33/19) -> (79/29,30/11) Hyperbolic Matrix(923,-1604,164,-285) (33/19,7/4) -> (45/8,17/3) Hyperbolic Matrix(437,-780,172,-307) (16/9,25/14) -> (5/2,28/11) Hyperbolic Matrix(3277,-5972,884,-1611) (51/28,31/17) -> (63/17,89/24) 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(272,-591,81,-176) (13/6,11/5) -> (10/3,37/11) Glide Reflection Matrix(468,-1037,139,-308) (11/5,20/9) -> (37/11,27/8) Glide Reflection Matrix(499,-1132,108,-245) (9/4,25/11) -> (23/5,37/8) Hyperbolic Matrix(544,-1249,223,-512) (16/7,23/10) -> (39/16,22/9) Glide Reflection Matrix(395,-916,116,-269) (30/13,7/3) -> (17/5,58/17) Hyperbolic Matrix(1844,-4365,779,-1844) (97/41,45/19) -> (97/41,45/19) Reflection Matrix(1576,-3735,665,-1576) (45/19,83/35) -> (45/19,83/35) Reflection Matrix(2059,-4916,756,-1805) (31/13,43/18) -> (49/18,79/29) Hyperbolic Matrix(3076,-7421,1275,-3076) (41/17,181/75) -> (41/17,181/75) Reflection Matrix(3712,-8959,769,-1856) (111/46,70/29) -> (82/17,29/6) Glide Reflection Matrix(477,-1156,196,-475) (29/12,17/7) -> (17/7,39/16) Parabolic Matrix(712,-1817,279,-712) (79/31,23/9) -> (79/31,23/9) Reflection Matrix(116,-299,45,-116) (23/9,13/5) -> (23/9,13/5) Reflection Matrix(328,-855,89,-232) (13/5,34/13) -> (11/3,37/10) Glide Reflection Matrix(416,-1121,95,-256) (8/3,27/10) -> (35/8,22/5) Glide 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(344,-1127,105,-344) (49/15,23/7) -> (49/15,23/7) Reflection Matrix(783,-2672,80,-273) (58/17,99/29) -> (29/3,10/1) Hyperbolic Matrix(5248,-17919,1537,-5248) (99/29,181/53) -> (99/29,181/53) Reflection Matrix(651,-2228,116,-397) (41/12,24/7) -> (28/5,45/8) Hyperbolic Matrix(624,-2225,175,-624) (89/25,25/7) -> (89/25,25/7) Reflection Matrix(76,-275,21,-76) (25/7,11/3) -> (25/7,11/3) Reflection Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) Parabolic Matrix(84,-397,11,-52) (14/3,19/4) -> (15/2,8/1) Glide Reflection Matrix(1112,-5353,231,-1112) (101/21,53/11) -> (101/21,53/11) Reflection Matrix(1220,-5883,253,-1220) (53/11,111/23) -> (53/11,111/23) Reflection Matrix(296,-1593,55,-296) (59/11,27/5) -> (59/11,27/5) Reflection Matrix(244,-1323,45,-244) (27/5,49/9) -> (27/5,49/9) Reflection Matrix(29,-196,4,-27) (13/2,7/1) -> (7/1,15/2) Parabolic Matrix(28,-261,3,-28) (9/1,29/3) -> (9/1,29/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(24,247,7,72) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(56,471,39,328) -> Matrix(0,1,1,6) Matrix(52,405,-19,-148) -> Matrix(0,1,1,2) Matrix(80,527,-17,-112) -> Matrix(-2,1,1,0) Matrix(53,340,12,77) -> Matrix(1,-2,0,1) 1/0 Matrix(20,117,13,76) -> Matrix(2,5,1,2) Matrix(124,667,-29,-156) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(39,200,-8,-41) -> Matrix(1,-2,0,1) 1/0 Matrix(524,2509,-203,-972) -> Matrix(2,5,-3,-8) Matrix(248,1175,103,488) -> Matrix(2,5,1,2) Matrix(229,1060,-132,-611) -> Matrix(1,2,0,1) 1/0 Matrix(143,656,80,367) -> Matrix(1,2,0,1) 1/0 Matrix(56,249,9,40) -> Matrix(4,9,1,2) Matrix(256,1121,-95,-416) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(1317,5668,-484,-2083) -> Matrix(1,0,0,1) Matrix(797,3420,292,1253) -> Matrix(1,4,0,1) 1/0 Matrix(89,376,40,169) -> Matrix(1,2,0,1) 1/0 Matrix(92,347,35,132) -> Matrix(0,1,1,2) Matrix(131,484,-36,-133) -> Matrix(1,2,-2,-3) -1/1 Matrix(232,839,-73,-264) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(272,977,49,176) -> Matrix(2,1,1,0) Matrix(633,2264,-248,-887) -> Matrix(1,4,-2,-7) Matrix(139,492,-76,-269) -> Matrix(1,2,0,1) 1/0 Matrix(380,1307,-157,-540) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(529,1808,-304,-1039) -> Matrix(1,2,0,1) 1/0 Matrix(597,2036,-212,-723) -> Matrix(1,2,0,1) 1/0 Matrix(256,865,161,544) -> Matrix(0,1,1,2) Matrix(176,591,-81,-272) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(71,232,56,183) -> Matrix(1,0,2,1) 0/1 Matrix(187,604,100,323) -> Matrix(1,2,0,1) 1/0 Matrix(707,2276,-260,-837) -> Matrix(1,0,0,1) Matrix(341,1076,-148,-467) -> Matrix(3,4,-4,-5) -1/1 Matrix(312,887,-121,-344) -> Matrix(4,3,-5,-4) *** -> (-1/1,-3/5) Matrix(668,1885,421,1188) -> Matrix(2,1,1,0) Matrix(937,2632,-424,-1191) -> Matrix(1,0,0,1) Matrix(72,199,55,152) -> Matrix(4,3,3,2) Matrix(1516,4141,-555,-1516) -> Matrix(0,1,1,0) (-41/15,-101/37) -> (-1/1,1/1) Matrix(704,1921,129,352) -> Matrix(2,1,1,0) Matrix(1372,3739,-797,-2172) -> Matrix(-2,1,1,0) Matrix(10880,29601,-3999,-10880) -> Matrix(2,3,-1,-2) (-117/43,-253/93) -> (-3/1,-1/1) Matrix(6288,17105,1841,5008) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(207,560,112,303) -> Matrix(1,0,2,1) 0/1 Matrix(664,1785,-247,-664) -> Matrix(2,3,-1,-2) (-35/13,-51/19) -> (-3/1,-1/1) Matrix(496,1329,209,560) -> Matrix(4,3,3,2) Matrix(77,204,20,53) -> Matrix(1,2,0,1) 1/0 Matrix(259,676,-100,-261) -> Matrix(5,6,-6,-7) -1/1 Matrix(3220,8307,-1397,-3604) -> Matrix(6,5,-7,-6) *** -> (-1/1,-5/7) Matrix(512,1313,-287,-736) -> Matrix(2,1,-3,-2) *** -> (-1/1,-1/3) Matrix(1240,3161,681,1736) -> Matrix(2,1,-15,-8) Matrix(497,1264,208,529) -> Matrix(5,2,2,1) Matrix(44,109,21,52) -> Matrix(2,1,1,0) Matrix(512,1249,-223,-544) -> Matrix(2,1,-3,-2) *** -> (-1/1,-1/3) Matrix(764,1853,-315,-764) -> Matrix(0,1,1,0) (-17/7,-109/45) -> (-1/1,1/1) Matrix(2025,4904,856,2073) -> Matrix(3,2,4,3) Matrix(679,1640,248,599) -> Matrix(5,2,2,1) Matrix(183,440,136,327) -> Matrix(1,2,0,1) 1/0 Matrix(163,388,92,219) -> Matrix(1,0,0,1) Matrix(468,1109,-211,-500) -> Matrix(0,1,1,2) Matrix(167,392,-72,-169) -> Matrix(1,2,-2,-3) -1/1 Matrix(2401,5536,736,1697) -> Matrix(9,8,-8,-7) -1/1 Matrix(199,456,24,55) -> Matrix(3,2,-2,-1) -1/1 Matrix(352,801,225,512) -> Matrix(4,1,1,0) Matrix(304,687,-177,-400) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(104,233,25,56) -> Matrix(4,1,1,0) Matrix(820,1813,237,524) -> Matrix(0,1,1,2) Matrix(2544,5617,529,1168) -> Matrix(0,1,1,2) Matrix(584,1287,-265,-584) -> Matrix(0,1,1,0) (-117/53,-11/5) -> (-1/1,1/1) Matrix(296,649,-135,-296) -> Matrix(0,1,1,0) (-11/5,-59/27) -> (-1/1,1/1) Matrix(729,1592,136,297) -> Matrix(1,2,0,1) 1/0 Matrix(137,296,56,121) -> Matrix(1,2,0,1) 1/0 Matrix(148,277,109,204) -> Matrix(2,1,1,0) Matrix(303,560,112,207) -> Matrix(5,2,2,1) Matrix(1208,2201,-663,-1208) -> Matrix(0,1,1,0) (-31/17,-71/39) -> (-1/1,1/1) Matrix(1523,2772,428,779) -> Matrix(1,0,0,1) Matrix(355,644,156,283) -> Matrix(1,0,0,1) Matrix(367,656,80,143) -> Matrix(1,0,0,1) Matrix(1680,2993,-943,-1680) -> Matrix(0,1,1,0) (-41/23,-73/41) -> (-1/1,1/1) Matrix(1355,2412,532,947) -> Matrix(1,2,0,1) 1/0 Matrix(416,737,289,512) -> Matrix(0,1,1,2) Matrix(419,740,124,219) -> Matrix(1,0,0,1) Matrix(3212,5581,-1867,-3244) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(261,452,220,381) -> Matrix(1,0,0,1) Matrix(311,536,264,455) -> Matrix(1,4,0,1) 1/0 Matrix(5595,9628,1508,2595) -> Matrix(1,2,6,13) Matrix(540,923,227,388) -> Matrix(2,1,1,0) Matrix(272,463,47,80) -> Matrix(2,5,1,2) Matrix(416,705,321,544) -> Matrix(6,5,5,4) Matrix(325,548,188,317) -> Matrix(1,0,0,1) Matrix(4,5,-3,-4) -> Matrix(0,1,1,0) (-5/3,-1/1) -> (-1/1,1/1) Matrix(0,1,1,0) -> Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Matrix(148,-171,45,-52) -> Matrix(0,1,1,-2) Matrix(260,-317,187,-228) -> Matrix(2,1,1,0) Matrix(244,-299,173,-212) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(253,-324,196,-251) -> Matrix(11,-10,10,-9) 1/1 Matrix(1781,-2412,652,-883) -> Matrix(1,0,0,1) Matrix(216,-295,41,-56) -> Matrix(2,-3,1,-2) *** -> (1/1,3/1) Matrix(403,-556,108,-149) -> Matrix(1,-2,2,-3) 1/1 Matrix(804,-1115,349,-484) -> Matrix(0,1,1,-2) Matrix(636,-899,133,-188) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(555,-788,212,-301) -> Matrix(1,0,0,1) Matrix(1091,-1564,316,-453) -> Matrix(1,0,4,1) 0/1 Matrix(248,-359,105,-152) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(400,-623,113,-176) -> Matrix(0,1,1,-2) Matrix(248,-391,137,-216) -> Matrix(0,1,1,-4) Matrix(149,-236,12,-19) -> Matrix(1,0,0,1) Matrix(61,-100,36,-59) -> Matrix(1,-4,0,1) 1/0 Matrix(764,-1315,165,-284) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(3796,-6541,1163,-2004) -> Matrix(12,13,-11,-12) *** -> (-13/11,-1/1) Matrix(892,-1539,517,-892) -> Matrix(0,1,1,0) (81/47,19/11) -> (-1/1,1/1) Matrix(1755,-3044,644,-1117) -> Matrix(5,2,2,1) Matrix(923,-1604,164,-285) -> Matrix(1,2,0,1) 1/0 Matrix(437,-780,172,-307) -> Matrix(1,2,0,1) 1/0 Matrix(3277,-5972,884,-1611) -> Matrix(1,0,20,1) 0/1 Matrix(1007,-1840,272,-497) -> Matrix(1,0,-6,1) 0/1 Matrix(589,-1108,244,-459) -> Matrix(1,0,0,1) Matrix(272,-591,81,-176) -> Matrix(0,1,1,-2) Matrix(468,-1037,139,-308) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(499,-1132,108,-245) -> Matrix(1,-2,0,1) 1/0 Matrix(544,-1249,223,-512) -> Matrix(2,-3,1,-2) *** -> (1/1,3/1) Matrix(395,-916,116,-269) -> Matrix(1,0,-2,1) 0/1 Matrix(1844,-4365,779,-1844) -> Matrix(6,-5,7,-6) (97/41,45/19) -> (5/7,1/1) Matrix(1576,-3735,665,-1576) -> Matrix(8,-9,7,-8) (45/19,83/35) -> (1/1,9/7) Matrix(2059,-4916,756,-1805) -> Matrix(1,0,0,1) Matrix(3076,-7421,1275,-3076) -> Matrix(0,1,1,0) (41/17,181/75) -> (-1/1,1/1) Matrix(3712,-8959,769,-1856) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(477,-1156,196,-475) -> Matrix(3,-2,2,-1) 1/1 Matrix(712,-1817,279,-712) -> Matrix(2,-3,1,-2) (79/31,23/9) -> (1/1,3/1) Matrix(116,-299,45,-116) -> Matrix(2,-3,1,-2) (23/9,13/5) -> (1/1,3/1) Matrix(328,-855,89,-232) -> Matrix(0,1,1,-2) Matrix(416,-1121,95,-256) -> Matrix(8,-17,-1,2) Matrix(293,-796,60,-163) -> Matrix(1,-2,0,1) 1/0 Matrix(25,-72,8,-23) -> Matrix(1,-4,0,1) 1/0 Matrix(344,-1127,105,-344) -> Matrix(2,1,-3,-2) (49/15,23/7) -> (-1/1,-1/3) Matrix(783,-2672,80,-273) -> Matrix(1,0,2,1) 0/1 Matrix(5248,-17919,1537,-5248) -> Matrix(2,1,-3,-2) (99/29,181/53) -> (-1/1,-1/3) Matrix(651,-2228,116,-397) -> Matrix(5,2,2,1) Matrix(624,-2225,175,-624) -> Matrix(0,1,1,0) (89/25,25/7) -> (-1/1,1/1) Matrix(76,-275,21,-76) -> Matrix(0,1,1,0) (25/7,11/3) -> (-1/1,1/1) Matrix(157,-676,36,-155) -> Matrix(1,-14,0,1) 1/0 Matrix(84,-397,11,-52) -> Matrix(-4,1,1,0) Matrix(1112,-5353,231,-1112) -> Matrix(2,-1,3,-2) (101/21,53/11) -> (1/3,1/1) Matrix(1220,-5883,253,-1220) -> Matrix(0,1,1,0) (53/11,111/23) -> (-1/1,1/1) Matrix(296,-1593,55,-296) -> Matrix(2,-3,1,-2) (59/11,27/5) -> (1/1,3/1) Matrix(244,-1323,45,-244) -> Matrix(2,-3,1,-2) (27/5,49/9) -> (1/1,3/1) Matrix(29,-196,4,-27) -> Matrix(1,-12,0,1) 1/0 Matrix(28,-261,3,-28) -> Matrix(0,1,1,0) (9/1,29/3) -> (-1/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.