INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -7/1 -6/1 -5/1 -9/2 -4/1 -10/3 -3/1 -11/4 -12/5 -13/6 -2/1 -1/1 -12/19 -11/18 -10/17 -9/16 -1/2 -6/13 -5/12 -4/11 -3/10 -1/4 -2/9 -1/8 0/1 1/6 1/4 3/11 2/5 1/2 5/9 8/13 3/4 1/1 15/13 5/4 4/3 3/2 17/11 43/27 8/5 13/8 5/3 7/4 9/5 2/1 11/5 29/13 9/4 7/3 5/2 8/3 14/5 3/1 10/3 7/2 11/3 4/1 13/3 9/2 23/5 14/3 5/1 47/9 11/2 6/1 7/1 8/1 25/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 1/0 -7/1 -4/1 1/0 -6/1 -3/1 -1/1 -11/2 -2/1 -5/1 -1/1 -19/4 1/0 -14/3 -1/1 1/1 -9/2 1/0 -22/5 -7/1 -5/1 -13/3 -4/1 1/0 -4/1 -3/1 -1/1 -15/4 1/0 -26/7 -3/1 -1/1 -11/3 -1/1 -29/8 1/0 -18/5 -3/1 -1/1 -25/7 -2/1 1/0 -7/2 -2/1 -24/7 -1/1 1/1 -17/5 -1/1 -10/3 1/0 -23/7 -3/1 -36/11 -3/1 -1/1 -13/4 1/0 -3/1 -2/1 1/0 -17/6 -2/1 -14/5 -3/1 -1/1 -11/4 -2/1 -30/11 -5/3 -1/1 -19/7 -1/1 -8/3 -3/1 -1/1 -21/8 -5/2 -34/13 -2/1 -13/5 -1/1 -18/7 -3/1 -1/1 -5/2 -2/1 -22/9 -3/1 -1/1 -17/7 -2/1 1/0 -12/5 -2/1 -31/13 -2/1 -7/4 -50/21 -19/11 -5/3 -19/8 -3/2 -7/3 -1/1 -23/10 -2/1 -16/7 -7/5 -1/1 -9/4 1/0 -20/9 -5/3 -1/1 -11/5 -2/1 1/0 -13/6 -2/1 -2/1 -3/1 -1/1 -1/1 -1/1 -2/3 -1/1 -1/3 -11/17 -1/2 0/1 -20/31 -1/1 -3/5 -9/14 0/1 -16/25 -1/1 -5/7 -23/36 -1/2 -7/11 -1/1 -19/30 -2/3 -12/19 -1/2 -29/46 -2/5 -17/27 -1/2 0/1 -22/35 -1/1 -1/3 -5/8 -1/2 -18/29 -1/1 -1/3 -13/21 -1/1 -21/34 -2/5 -8/13 -1/1 -1/3 -19/31 -1/1 -11/18 -1/2 -25/41 -1/3 -14/23 -1/1 -1/3 -3/5 -1/2 0/1 -13/22 0/1 -10/17 0/1 -27/46 0/1 -17/29 -1/1 -24/41 -1/1 1/1 -7/12 -1/2 -25/43 -1/2 0/1 -18/31 -1/1 -1/3 -11/19 -1/1 -26/45 -1/1 -1/3 -15/26 0/1 -4/7 -1/1 -1/3 -13/23 -1/4 0/1 -9/16 0/1 -23/41 0/1 1/2 -14/25 -1/1 1/1 -5/9 -1/1 -11/20 -1/2 -6/11 -1/1 -1/3 -7/13 -1/4 0/1 -1/2 0/1 -6/13 0/1 -11/24 1/4 -5/11 0/1 1/2 -9/20 1/0 -22/49 3/5 1/1 -13/29 1/1 -4/9 -1/1 1/1 -7/16 1/0 -10/23 -1/1 1/1 -3/7 -1/1 -8/19 -1/1 -1/3 -5/12 0/1 -12/29 1/5 1/3 -31/75 1/3 -19/46 0/1 -7/17 0/1 1/2 -23/56 1/2 -16/39 1/3 1/1 -9/22 2/3 -2/5 -1/1 1/1 -7/18 0/1 -5/13 -1/1 -13/34 0/1 -21/55 0/1 1/0 -8/21 -1/1 1/1 -3/8 1/0 -7/19 -1/1 -4/11 0/1 -9/25 1/1 -5/14 0/1 -11/31 1/1 -6/17 -1/1 1/1 -7/20 1/0 -1/3 0/1 1/0 -4/13 -1/1 1/1 -3/10 1/0 -8/27 -3/1 -1/1 -13/44 1/0 -18/61 -3/1 -1/1 -23/78 -2/1 -5/17 -1/1 -7/24 1/0 -16/55 -1/1 -3/5 -9/31 -1/2 0/1 -2/7 -1/1 1/1 -7/25 0/1 1/0 -12/43 1/3 1/1 -17/61 1/1 -22/79 7/9 1/1 -5/18 2/1 -8/29 1/0 -11/40 1/0 -3/11 -1/1 -7/26 0/1 -4/15 -1/1 1/1 -1/4 1/0 -3/13 0/1 1/0 -2/9 1/0 -5/23 -4/1 1/0 -3/14 -2/1 -7/33 -2/1 1/0 -11/52 1/0 -4/19 -3/1 -1/1 -5/24 1/0 -1/5 -1/1 -2/11 -5/3 -1/1 -1/6 0/1 -1/7 0/1 1/0 -1/8 1/0 -1/9 -1/1 0/1 -1/1 1/1 1/7 -1/1 1/6 0/1 3/17 1/1 2/11 -1/1 1/1 3/16 1/0 4/21 -1/1 1/1 1/5 0/1 1/0 2/9 -1/1 -1/3 5/22 0/1 3/13 -1/1 1/4 1/0 4/15 -7/5 -1/1 3/11 -1/1 8/29 -1/1 -13/15 5/18 -4/5 2/7 -1/1 -3/5 7/24 -1/2 5/17 -2/3 -1/2 8/27 -1/2 3/10 0/1 4/13 -1/1 -1/3 1/3 -1/1 5/14 0/1 4/11 -1/1 -1/3 7/19 -1/2 0/1 10/27 -1/1 -1/3 3/8 -1/2 2/5 0/1 5/12 1/2 13/31 1/1 8/19 1/1 3/1 19/45 1/1 11/26 0/1 3/7 0/1 1/0 10/23 -1/1 1/1 7/16 1/0 4/9 -1/1 1/1 5/11 -1/1 6/13 -1/1 1/1 1/2 0/1 6/11 -1/1 1/1 5/9 -1/1 1/1 14/25 -1/1 1/1 9/16 1/0 4/7 -1/1 1/1 15/26 0/1 11/19 0/1 1/0 7/12 1/0 17/29 0/1 1/0 10/17 -1/1 -1/3 13/22 0/1 3/5 -1/1 14/23 -1/1 -1/3 25/41 -1/4 0/1 11/18 0/1 8/13 0/1 21/34 0/1 13/21 0/1 1/4 5/8 1/2 17/27 1/1 12/19 1/1 3/1 7/11 0/1 1/0 2/3 -1/1 1/1 9/13 -2/1 1/0 16/23 -5/3 -1/1 7/10 0/1 19/27 -2/1 1/0 12/17 -5/3 -1/1 5/7 -1/1 3/4 0/1 7/9 1/1 18/23 -1/1 1/1 11/14 0/1 15/19 0/1 1/0 19/24 1/2 4/5 -1/1 1/1 9/11 -1/1 5/6 0/1 11/13 -1/1 6/7 -1/1 1/1 1/1 0/1 1/0 8/7 -1/1 1/1 15/13 -1/1 1/1 7/6 0/1 13/11 -1/1 6/5 -1/1 1/1 11/9 1/1 16/13 1/3 1/1 21/17 0/1 1/0 26/21 1/3 1/1 5/4 1/0 4/3 1/0 11/8 1/0 40/29 -3/1 -1/1 29/21 -2/1 1/0 47/34 -2/1 65/47 -1/1 18/13 -3/1 -1/1 25/18 -4/3 32/23 -1/1 -3/5 7/5 -1/1 24/17 -1/1 1/1 41/29 -1/1 1/1 17/12 1/0 27/19 0/1 1/0 10/7 -3/1 -1/1 23/16 -1/2 13/9 0/1 1/0 3/2 0/1 17/11 -1/1 1/1 31/20 1/0 14/9 -1/1 1/1 11/7 0/1 1/0 19/12 1/0 46/29 -1/1 1/1 27/17 -1/1 35/22 0/1 43/27 -1/1 1/1 8/5 -1/1 1/1 29/18 0/1 21/13 0/1 1/0 13/8 1/0 31/19 -2/1 1/0 18/11 -3/1 -1/1 41/25 0/1 1/0 23/14 0/1 5/3 -1/1 22/13 0/1 17/10 0/1 46/27 -1/1 1/1 29/17 0/1 1/2 41/24 1/2 53/31 1/1 12/7 -1/1 1/1 19/11 0/1 1/0 7/4 1/0 16/9 -1/1 1/1 9/5 -1/1 1/1 20/11 -1/1 1/1 11/6 0/1 2/1 -1/1 1/1 15/7 0/1 1/0 13/6 0/1 11/5 1/1 20/9 5/7 1/1 49/22 8/9 29/13 1/1 9/4 3/2 16/7 1/1 3/1 55/24 1/0 39/17 1/1 3/1 23/10 2/1 7/3 2/1 1/0 5/2 1/0 13/5 -4/1 1/0 47/18 -4/1 81/31 -3/1 115/44 -5/2 34/13 -3/1 -1/1 55/21 -1/1 21/8 1/0 71/27 -5/1 -3/1 121/46 -4/1 50/19 -5/1 -3/1 29/11 -3/1 8/3 -3/1 -1/1 27/10 -2/1 19/7 -2/1 1/0 30/11 -3/1 -1/1 41/15 -3/1 -1/1 52/19 -3/1 -1/1 11/4 1/0 25/9 -2/1 -3/2 64/23 -5/3 -1/1 39/14 -2/1 14/5 -5/3 -1/1 3/1 -1/1 13/4 1/0 23/7 0/1 1/0 33/10 0/1 43/13 -1/1 1/1 10/3 -1/1 1/1 27/8 1/0 17/5 0/1 1/0 41/12 1/0 65/19 -1/1 89/26 0/1 24/7 -1/1 1/1 31/9 -1/1 7/2 0/1 18/5 -1/1 1/1 11/3 -1/1 1/1 26/7 -1/1 1/1 15/4 1/0 4/1 -1/1 1/1 13/3 1/1 35/8 3/4 57/13 1/1 79/18 8/7 22/5 1/1 5/3 31/7 2/1 1/0 9/2 0/1 32/7 5/7 1/1 23/5 1/1 60/13 1/1 15/13 37/8 5/4 14/3 1/1 5/3 5/1 2/1 1/0 26/5 1/1 3/1 47/9 3/1 21/4 1/0 16/3 1/1 3/1 11/2 4/1 6/1 1/0 13/2 -6/1 7/1 -3/1 8/1 -3/1 -1/1 25/3 -1/1 17/2 0/1 9/1 0/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,96,-40,-349) (-8/1,1/0) -> (-8/29,-11/40) Hyperbolic Matrix(13,96,44,325) (-8/1,-7/1) -> (5/17,8/27) Hyperbolic Matrix(11,68,16,99) (-7/1,-6/1) -> (2/3,9/13) Hyperbolic Matrix(43,240,12,67) (-6/1,-11/2) -> (7/2,18/5) Hyperbolic Matrix(7,36,20,103) (-11/2,-5/1) -> (1/3,5/14) Hyperbolic Matrix(51,248,-80,-389) (-5/1,-19/4) -> (-23/36,-7/11) Hyperbolic Matrix(45,212,-128,-603) (-19/4,-14/3) -> (-6/17,-7/20) Hyperbolic Matrix(71,324,-16,-73) (-14/3,-9/2) -> (-9/2,-22/5) Parabolic Matrix(165,724,116,509) (-22/5,-13/3) -> (27/19,10/7) Hyperbolic Matrix(43,184,68,291) (-13/3,-4/1) -> (12/19,7/11) Hyperbolic Matrix(71,268,40,151) (-4/1,-15/4) -> (7/4,16/9) Hyperbolic Matrix(61,228,164,613) (-15/4,-26/7) -> (10/27,3/8) Hyperbolic Matrix(63,232,104,383) (-26/7,-11/3) -> (3/5,14/23) Hyperbolic Matrix(11,40,-96,-349) (-11/3,-29/8) -> (-1/8,-1/9) Hyperbolic Matrix(215,776,64,231) (-29/8,-18/5) -> (10/3,27/8) Hyperbolic Matrix(239,856,-380,-1361) (-18/5,-25/7) -> (-17/27,-22/35) Hyperbolic Matrix(175,624,76,271) (-25/7,-7/2) -> (23/10,7/3) Hyperbolic Matrix(103,356,-160,-553) (-7/2,-24/7) -> (-20/31,-9/14) Hyperbolic Matrix(243,832,92,315) (-24/7,-17/5) -> (29/11,8/3) Hyperbolic Matrix(119,400,-36,-121) (-17/5,-10/3) -> (-10/3,-23/7) Parabolic Matrix(271,888,-972,-3185) (-23/7,-36/11) -> (-12/43,-17/61) Hyperbolic Matrix(49,160,260,849) (-36/11,-13/4) -> (3/16,4/21) Hyperbolic Matrix(51,164,88,283) (-13/4,-3/1) -> (11/19,7/12) Hyperbolic Matrix(45,128,-212,-603) (-3/1,-17/6) -> (-3/14,-7/33) Hyperbolic Matrix(231,652,-400,-1129) (-17/6,-14/5) -> (-26/45,-15/26) Hyperbolic Matrix(175,484,-64,-177) (-14/5,-11/4) -> (-11/4,-30/11) Parabolic Matrix(97,264,212,577) (-30/11,-19/7) -> (5/11,6/13) Hyperbolic Matrix(67,180,16,43) (-19/7,-8/3) -> (4/1,13/3) Hyperbolic Matrix(155,408,68,179) (-8/3,-21/8) -> (9/4,16/7) Hyperbolic Matrix(191,500,-416,-1089) (-21/8,-34/13) -> (-6/13,-11/24) Hyperbolic Matrix(175,456,104,271) (-34/13,-13/5) -> (5/3,22/13) Hyperbolic Matrix(107,276,88,227) (-13/5,-18/7) -> (6/5,11/9) Hyperbolic Matrix(19,48,36,91) (-18/7,-5/2) -> (1/2,6/11) Hyperbolic Matrix(135,332,172,423) (-5/2,-22/9) -> (18/23,11/14) Hyperbolic Matrix(351,856,-604,-1473) (-22/9,-17/7) -> (-25/43,-18/31) Hyperbolic Matrix(239,576,-100,-241) (-17/7,-12/5) -> (-12/5,-31/13) Parabolic Matrix(1095,2608,668,1591) (-31/13,-50/21) -> (18/11,41/25) Hyperbolic Matrix(365,868,-812,-1931) (-50/21,-19/8) -> (-9/20,-22/49) Hyperbolic Matrix(63,148,20,47) (-19/8,-7/3) -> (3/1,13/4) Hyperbolic Matrix(151,348,128,295) (-7/3,-23/10) -> (7/6,13/11) Hyperbolic Matrix(237,544,44,101) (-23/10,-16/7) -> (16/3,11/2) Hyperbolic Matrix(23,52,88,199) (-16/7,-9/4) -> (1/4,4/15) Hyperbolic Matrix(159,356,-272,-609) (-9/4,-20/9) -> (-24/41,-7/12) Hyperbolic Matrix(161,356,232,513) (-20/9,-11/5) -> (9/13,16/23) Hyperbolic Matrix(191,416,-500,-1089) (-11/5,-13/6) -> (-13/34,-21/55) Hyperbolic Matrix(73,156,124,265) (-13/6,-2/1) -> (10/17,13/22) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(399,260,244,159) (-2/3,-11/17) -> (31/19,18/11) Hyperbolic Matrix(551,356,-1896,-1225) (-11/17,-20/31) -> (-16/55,-9/31) Hyperbolic Matrix(237,152,856,549) (-9/14,-16/25) -> (8/29,5/18) Hyperbolic Matrix(619,396,780,499) (-16/25,-23/36) -> (19/24,4/5) Hyperbolic Matrix(385,244,456,289) (-7/11,-19/30) -> (5/6,11/13) Hyperbolic Matrix(911,576,-1444,-913) (-19/30,-12/19) -> (-12/19,-29/46) Parabolic Matrix(1669,1052,376,237) (-29/46,-17/27) -> (31/7,9/2) Hyperbolic Matrix(599,376,-2028,-1273) (-22/35,-5/8) -> (-13/44,-18/61) Hyperbolic Matrix(373,232,664,413) (-5/8,-18/29) -> (14/25,9/16) Hyperbolic Matrix(445,276,-1256,-779) (-18/29,-13/21) -> (-11/31,-6/17) Hyperbolic Matrix(511,316,76,47) (-13/21,-21/34) -> (13/2,7/1) Hyperbolic Matrix(661,408,-1612,-995) (-21/34,-8/13) -> (-16/39,-9/22) Hyperbolic Matrix(293,180,-656,-403) (-8/13,-19/31) -> (-13/29,-4/9) Hyperbolic Matrix(791,484,-1296,-793) (-19/31,-11/18) -> (-11/18,-25/41) Parabolic Matrix(2507,1528,1580,963) (-25/41,-14/23) -> (46/29,27/17) Hyperbolic Matrix(211,128,572,347) (-14/23,-3/5) -> (7/19,10/27) Hyperbolic Matrix(553,328,204,121) (-3/5,-13/22) -> (27/10,19/7) Hyperbolic Matrix(679,400,-1156,-681) (-13/22,-10/17) -> (-10/17,-27/46) Parabolic Matrix(1629,956,472,277) (-27/46,-17/29) -> (31/9,7/2) Hyperbolic Matrix(1619,948,-3916,-2293) (-17/29,-24/41) -> (-12/29,-31/75) Hyperbolic Matrix(1073,624,-2612,-1519) (-7/12,-25/43) -> (-7/17,-23/56) Hyperbolic Matrix(131,76,736,427) (-18/31,-11/19) -> (3/17,2/11) Hyperbolic Matrix(3121,1804,1192,689) (-11/19,-26/45) -> (34/13,55/21) Hyperbolic Matrix(597,344,328,189) (-15/26,-4/7) -> (20/11,11/6) Hyperbolic Matrix(325,184,-1164,-659) (-4/7,-13/23) -> (-7/25,-12/43) Hyperbolic Matrix(575,324,-1024,-577) (-13/23,-9/16) -> (-9/16,-23/41) Parabolic Matrix(2611,1464,1532,859) (-23/41,-14/25) -> (46/27,29/17) Hyperbolic Matrix(379,212,320,179) (-14/25,-5/9) -> (13/11,6/5) Hyperbolic Matrix(65,36,-316,-175) (-5/9,-11/20) -> (-5/24,-1/5) Hyperbolic Matrix(685,376,184,101) (-11/20,-6/11) -> (26/7,15/4) Hyperbolic Matrix(125,68,-432,-235) (-6/11,-7/13) -> (-9/31,-2/7) Hyperbolic Matrix(299,160,484,259) (-7/13,-1/2) -> (21/34,13/21) Hyperbolic Matrix(265,124,156,73) (-1/2,-6/13) -> (22/13,17/10) Hyperbolic Matrix(569,260,720,329) (-11/24,-5/11) -> (15/19,19/24) Hyperbolic Matrix(513,232,356,161) (-5/11,-9/20) -> (23/16,13/9) Hyperbolic Matrix(1471,660,-5280,-2369) (-22/49,-13/29) -> (-17/61,-22/79) Hyperbolic Matrix(199,88,52,23) (-4/9,-7/16) -> (15/4,4/1) Hyperbolic Matrix(101,44,544,237) (-7/16,-10/23) -> (2/11,3/16) Hyperbolic Matrix(295,128,348,151) (-10/23,-3/7) -> (11/13,6/7) Hyperbolic Matrix(47,20,148,63) (-3/7,-8/19) -> (4/13,1/3) Hyperbolic Matrix(239,100,-576,-241) (-8/19,-5/12) -> (-5/12,-12/29) Parabolic Matrix(1955,808,-6632,-2741) (-31/75,-19/46) -> (-23/78,-5/17) Hyperbolic Matrix(1337,552,2192,905) (-19/46,-7/17) -> (25/41,11/18) Hyperbolic Matrix(3041,1248,1328,545) (-23/56,-16/39) -> (16/7,55/24) Hyperbolic Matrix(521,212,376,153) (-9/22,-2/5) -> (18/13,25/18) Hyperbolic Matrix(91,36,48,19) (-2/5,-7/18) -> (11/6,2/1) Hyperbolic Matrix(227,88,276,107) (-7/18,-5/13) -> (9/11,5/6) Hyperbolic Matrix(271,104,456,175) (-5/13,-13/34) -> (13/22,3/5) Hyperbolic Matrix(2809,1072,2036,777) (-21/55,-8/21) -> (40/29,29/21) Hyperbolic Matrix(179,68,408,155) (-8/21,-3/8) -> (7/16,4/9) Hyperbolic Matrix(43,16,180,67) (-3/8,-7/19) -> (3/13,1/4) Hyperbolic Matrix(175,64,-484,-177) (-7/19,-4/11) -> (-4/11,-9/25) Parabolic Matrix(479,172,220,79) (-9/25,-5/14) -> (13/6,11/5) Hyperbolic Matrix(607,216,1436,511) (-5/14,-11/31) -> (19/45,11/26) Hyperbolic Matrix(173,60,-816,-283) (-7/20,-1/3) -> (-7/33,-11/52) Hyperbolic Matrix(283,88,164,51) (-1/3,-4/13) -> (12/7,19/11) Hyperbolic Matrix(119,36,-400,-121) (-4/13,-3/10) -> (-3/10,-8/27) Parabolic Matrix(1271,376,240,71) (-8/27,-13/44) -> (21/4,16/3) Hyperbolic Matrix(11281,3328,4288,1265) (-18/61,-23/78) -> (121/46,50/19) Hyperbolic Matrix(397,116,948,277) (-5/17,-7/24) -> (5/12,13/31) Hyperbolic Matrix(3475,1012,752,219) (-7/24,-16/55) -> (60/13,37/8) Hyperbolic Matrix(271,76,624,175) (-2/7,-7/25) -> (3/7,10/23) Hyperbolic Matrix(6637,1848,1512,421) (-22/79,-5/18) -> (79/18,22/5) Hyperbolic Matrix(231,64,776,215) (-5/18,-8/29) -> (8/27,3/10) Hyperbolic Matrix(2431,668,928,255) (-11/40,-3/11) -> (55/21,21/8) Hyperbolic Matrix(383,104,232,63) (-3/11,-7/26) -> (23/14,5/3) Hyperbolic Matrix(613,164,228,61) (-7/26,-4/15) -> (8/3,27/10) Hyperbolic Matrix(151,40,268,71) (-4/15,-1/4) -> (9/16,4/7) Hyperbolic Matrix(291,68,184,43) (-1/4,-3/13) -> (11/7,19/12) Hyperbolic Matrix(71,16,-324,-73) (-3/13,-2/9) -> (-2/9,-5/23) Parabolic Matrix(427,92,608,131) (-5/23,-3/14) -> (7/10,19/27) Hyperbolic Matrix(2913,616,1064,225) (-11/52,-4/19) -> (52/19,11/4) Hyperbolic Matrix(1169,244,848,177) (-4/19,-5/24) -> (11/8,40/29) Hyperbolic Matrix(103,20,36,7) (-1/5,-2/11) -> (14/5,3/1) Hyperbolic Matrix(67,12,240,43) (-2/11,-1/6) -> (5/18,2/7) Hyperbolic Matrix(99,16,68,11) (-1/6,-1/7) -> (13/9,3/2) Hyperbolic Matrix(325,44,96,13) (-1/7,-1/8) -> (27/8,17/5) Hyperbolic Matrix(91,8,216,19) (-1/9,0/1) -> (8/19,19/45) Hyperbolic Matrix(123,-16,100,-13) (0/1,1/7) -> (11/9,16/13) Hyperbolic Matrix(25,-4,144,-23) (1/7,1/6) -> (1/6,3/17) Parabolic Matrix(845,-164,304,-59) (4/21,1/5) -> (25/9,64/23) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(1165,-264,684,-155) (2/9,5/22) -> (17/10,46/27) Hyperbolic Matrix(1049,-240,660,-151) (5/22,3/13) -> (27/17,35/22) Hyperbolic Matrix(133,-36,484,-131) (4/15,3/11) -> (3/11,8/29) Parabolic Matrix(1237,-360,780,-227) (2/7,7/24) -> (19/12,46/29) Hyperbolic Matrix(1105,-324,324,-95) (7/24,5/17) -> (17/5,41/12) Hyperbolic Matrix(235,-72,408,-125) (3/10,4/13) -> (4/7,15/26) Hyperbolic Matrix(431,-156,268,-97) (5/14,4/11) -> (8/5,29/18) Hyperbolic Matrix(163,-60,144,-53) (4/11,7/19) -> (1/1,8/7) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(1125,-472,808,-339) (13/31,8/19) -> (32/23,7/5) Hyperbolic Matrix(667,-284,256,-109) (11/26,3/7) -> (13/5,47/18) Hyperbolic Matrix(937,-408,604,-263) (10/23,7/16) -> (31/20,14/9) Hyperbolic Matrix(327,-148,232,-105) (4/9,5/11) -> (7/5,24/17) Hyperbolic Matrix(535,-248,192,-89) (6/13,1/2) -> (39/14,14/5) Hyperbolic Matrix(181,-100,324,-179) (6/11,5/9) -> (5/9,14/25) Parabolic Matrix(1225,-708,372,-215) (15/26,11/19) -> (23/7,33/10) Hyperbolic Matrix(1537,-900,900,-527) (7/12,17/29) -> (29/17,41/24) Hyperbolic Matrix(1165,-684,264,-155) (17/29,10/17) -> (22/5,31/7) Hyperbolic Matrix(1549,-944,1252,-763) (14/23,25/41) -> (21/17,26/21) Hyperbolic Matrix(417,-256,676,-415) (11/18,8/13) -> (8/13,21/34) Parabolic Matrix(431,-268,156,-97) (13/21,5/8) -> (11/4,25/9) Hyperbolic Matrix(1049,-660,240,-151) (5/8,17/27) -> (13/3,35/8) Hyperbolic Matrix(1237,-780,360,-227) (17/27,12/19) -> (24/7,31/9) Hyperbolic Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(527,-368,116,-81) (16/23,7/10) -> (9/2,32/7) Hyperbolic Matrix(789,-556,640,-451) (19/27,12/17) -> (16/13,21/17) Hyperbolic Matrix(327,-232,148,-105) (12/17,5/7) -> (11/5,20/9) Hyperbolic Matrix(49,-36,64,-47) (5/7,3/4) -> (3/4,7/9) Parabolic Matrix(1117,-872,424,-331) (7/9,18/23) -> (50/19,29/11) Hyperbolic Matrix(1299,-1024,940,-741) (11/14,15/19) -> (29/21,47/34) Hyperbolic Matrix(123,-100,16,-13) (4/5,9/11) -> (7/1,8/1) Hyperbolic Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(963,-1108,352,-405) (8/7,15/13) -> (41/15,52/19) Hyperbolic Matrix(687,-796,208,-241) (15/13,7/6) -> (33/10,43/13) Hyperbolic Matrix(2551,-3160,976,-1209) (26/21,5/4) -> (115/44,34/13) Hyperbolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(6393,-8840,1868,-2583) (47/34,65/47) -> (65/19,89/26) Hyperbolic Matrix(1833,-2536,352,-487) (65/47,18/13) -> (26/5,47/9) Hyperbolic Matrix(1487,-2068,668,-929) (25/18,32/23) -> (20/9,49/22) Hyperbolic Matrix(963,-1360,604,-853) (24/17,41/29) -> (43/27,8/5) Hyperbolic Matrix(1461,-2068,556,-787) (41/29,17/12) -> (21/8,71/27) Hyperbolic Matrix(127,-180,12,-17) (17/12,27/19) -> (9/1,1/0) Hyperbolic Matrix(483,-692,104,-149) (10/7,23/16) -> (37/8,14/3) Hyperbolic Matrix(331,-508,144,-221) (3/2,17/11) -> (39/17,23/10) Hyperbolic Matrix(1385,-2144,604,-935) (17/11,31/20) -> (55/24,39/17) Hyperbolic Matrix(4829,-7688,1836,-2923) (35/22,43/27) -> (71/27,121/46) Hyperbolic Matrix(439,-708,204,-329) (29/18,21/13) -> (15/7,13/6) Hyperbolic Matrix(417,-676,256,-415) (21/13,13/8) -> (13/8,31/19) Parabolic Matrix(551,-904,64,-105) (41/25,23/14) -> (17/2,9/1) Hyperbolic Matrix(5509,-9416,2108,-3603) (41/24,53/31) -> (81/31,115/44) Hyperbolic Matrix(423,-724,52,-89) (53/31,12/7) -> (8/1,25/3) Hyperbolic Matrix(235,-408,72,-125) (19/11,7/4) -> (13/4,23/7) Hyperbolic Matrix(181,-324,100,-179) (16/9,9/5) -> (9/5,20/11) Parabolic Matrix(187,-400,36,-77) (2/1,15/7) -> (5/1,26/5) Hyperbolic Matrix(2281,-5084,520,-1159) (49/22,29/13) -> (57/13,79/18) Hyperbolic Matrix(683,-1528,156,-349) (29/13,9/4) -> (35/8,57/13) Hyperbolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(977,-2552,116,-303) (47/18,81/31) -> (25/3,17/2) Hyperbolic Matrix(623,-1700,188,-513) (30/11,41/15) -> (43/13,10/3) Hyperbolic Matrix(2383,-6632,696,-1937) (64/23,39/14) -> (89/26,24/7) Hyperbolic Matrix(963,-3292,184,-629) (41/12,65/19) -> (47/9,21/4) Hyperbolic Matrix(133,-484,36,-131) (18/5,11/3) -> (11/3,26/7) Parabolic Matrix(461,-2116,100,-459) (32/7,23/5) -> (23/5,60/13) Parabolic Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(11,96,-40,-349) -> Matrix(1,-2,0,1) Matrix(13,96,44,325) -> Matrix(1,6,-2,-11) Matrix(11,68,16,99) -> Matrix(1,2,0,1) Matrix(43,240,12,67) -> Matrix(1,2,0,1) Matrix(7,36,20,103) -> Matrix(1,2,-2,-3) Matrix(51,248,-80,-389) -> Matrix(1,2,-2,-3) Matrix(45,212,-128,-603) -> Matrix(1,0,0,1) Matrix(71,324,-16,-73) -> Matrix(1,-6,0,1) Matrix(165,724,116,509) -> Matrix(1,4,0,1) Matrix(43,184,68,291) -> Matrix(1,4,0,1) Matrix(71,268,40,151) -> Matrix(1,2,0,1) Matrix(61,228,164,613) -> Matrix(1,2,-2,-3) Matrix(63,232,104,383) -> Matrix(1,2,-2,-3) Matrix(11,40,-96,-349) -> Matrix(1,0,0,1) Matrix(215,776,64,231) -> Matrix(1,2,0,1) Matrix(239,856,-380,-1361) -> Matrix(1,2,-2,-3) Matrix(175,624,76,271) -> Matrix(1,4,0,1) Matrix(103,356,-160,-553) -> Matrix(1,2,-2,-3) Matrix(243,832,92,315) -> Matrix(1,-2,0,1) Matrix(119,400,-36,-121) -> Matrix(1,-2,0,1) Matrix(271,888,-972,-3185) -> Matrix(1,2,2,5) Matrix(49,160,260,849) -> Matrix(1,2,0,1) Matrix(51,164,88,283) -> Matrix(1,2,0,1) Matrix(45,128,-212,-603) -> Matrix(1,0,0,1) Matrix(231,652,-400,-1129) -> Matrix(1,2,-2,-3) Matrix(175,484,-64,-177) -> Matrix(3,8,-2,-5) Matrix(97,264,212,577) -> Matrix(1,2,-2,-3) Matrix(67,180,16,43) -> Matrix(1,2,0,1) Matrix(155,408,68,179) -> Matrix(1,4,0,1) Matrix(191,500,-416,-1089) -> Matrix(1,2,6,13) Matrix(175,456,104,271) -> Matrix(1,2,-2,-3) Matrix(107,276,88,227) -> Matrix(1,2,0,1) Matrix(19,48,36,91) -> Matrix(1,2,0,1) Matrix(135,332,172,423) -> Matrix(1,2,0,1) Matrix(351,856,-604,-1473) -> Matrix(1,2,-2,-3) Matrix(239,576,-100,-241) -> Matrix(7,16,-4,-9) Matrix(1095,2608,668,1591) -> Matrix(1,2,-4,-7) Matrix(365,868,-812,-1931) -> Matrix(1,2,-2,-3) Matrix(63,148,20,47) -> Matrix(1,2,-2,-3) Matrix(151,348,128,295) -> Matrix(1,2,-2,-3) Matrix(237,544,44,101) -> Matrix(7,10,2,3) Matrix(23,52,88,199) -> Matrix(1,0,0,1) Matrix(159,356,-272,-609) -> Matrix(1,2,-2,-3) Matrix(161,356,232,513) -> Matrix(1,0,0,1) Matrix(191,416,-500,-1089) -> Matrix(1,2,0,1) Matrix(73,156,124,265) -> Matrix(1,2,-2,-3) Matrix(3,4,-4,-5) -> Matrix(1,2,-2,-3) Matrix(399,260,244,159) -> Matrix(3,2,-2,-1) Matrix(551,356,-1896,-1225) -> Matrix(1,0,0,1) Matrix(237,152,856,549) -> Matrix(3,4,-4,-5) Matrix(619,396,780,499) -> Matrix(3,2,4,3) Matrix(385,244,456,289) -> Matrix(3,2,-2,-1) Matrix(911,576,-1444,-913) -> Matrix(7,4,-16,-9) Matrix(1669,1052,376,237) -> Matrix(5,2,2,1) Matrix(599,376,-2028,-1273) -> Matrix(3,2,-2,-1) Matrix(373,232,664,413) -> Matrix(1,0,2,1) Matrix(445,276,-1256,-779) -> Matrix(1,0,2,1) Matrix(511,316,76,47) -> Matrix(7,4,-2,-1) Matrix(661,408,-1612,-995) -> Matrix(1,0,4,1) Matrix(293,180,-656,-403) -> Matrix(1,0,2,1) Matrix(791,484,-1296,-793) -> Matrix(3,2,-8,-5) Matrix(2507,1528,1580,963) -> Matrix(1,0,2,1) Matrix(211,128,572,347) -> Matrix(1,0,0,1) Matrix(553,328,204,121) -> Matrix(3,2,-2,-1) Matrix(679,400,-1156,-681) -> Matrix(1,0,2,1) Matrix(1629,956,472,277) -> Matrix(1,0,0,1) Matrix(1619,948,-3916,-2293) -> Matrix(1,0,4,1) Matrix(1073,624,-2612,-1519) -> Matrix(1,0,4,1) Matrix(131,76,736,427) -> Matrix(1,0,2,1) Matrix(3121,1804,1192,689) -> Matrix(3,2,-2,-1) Matrix(597,344,328,189) -> Matrix(1,0,2,1) Matrix(325,184,-1164,-659) -> Matrix(1,0,4,1) Matrix(575,324,-1024,-577) -> Matrix(1,0,6,1) Matrix(2611,1464,1532,859) -> Matrix(1,0,0,1) Matrix(379,212,320,179) -> Matrix(1,0,0,1) Matrix(65,36,-316,-175) -> Matrix(3,2,-2,-1) Matrix(685,376,184,101) -> Matrix(1,0,2,1) Matrix(125,68,-432,-235) -> Matrix(1,0,2,1) Matrix(299,160,484,259) -> Matrix(1,0,8,1) Matrix(265,124,156,73) -> Matrix(1,0,2,1) Matrix(569,260,720,329) -> Matrix(1,0,-2,1) Matrix(513,232,356,161) -> Matrix(1,0,-2,1) Matrix(1471,660,-5280,-2369) -> Matrix(1,-2,2,-3) Matrix(199,88,52,23) -> Matrix(1,0,0,1) Matrix(101,44,544,237) -> Matrix(1,0,0,1) Matrix(295,128,348,151) -> Matrix(1,0,0,1) Matrix(47,20,148,63) -> Matrix(1,0,0,1) Matrix(239,100,-576,-241) -> Matrix(1,0,6,1) Matrix(1955,808,-6632,-2741) -> Matrix(5,-2,-2,1) Matrix(1337,552,2192,905) -> Matrix(1,0,-6,1) Matrix(3041,1248,1328,545) -> Matrix(3,-2,2,-1) Matrix(521,212,376,153) -> Matrix(1,-2,0,1) Matrix(91,36,48,19) -> Matrix(1,0,0,1) Matrix(227,88,276,107) -> Matrix(1,0,0,1) Matrix(271,104,456,175) -> Matrix(1,0,0,1) Matrix(2809,1072,2036,777) -> Matrix(1,-2,0,1) Matrix(179,68,408,155) -> Matrix(1,0,0,1) Matrix(43,16,180,67) -> Matrix(1,0,0,1) Matrix(175,64,-484,-177) -> Matrix(1,0,2,1) Matrix(479,172,220,79) -> Matrix(1,0,0,1) Matrix(607,216,1436,511) -> Matrix(1,0,0,1) Matrix(173,60,-816,-283) -> Matrix(1,-2,0,1) Matrix(283,88,164,51) -> Matrix(1,0,0,1) Matrix(119,36,-400,-121) -> Matrix(1,-2,0,1) Matrix(1271,376,240,71) -> Matrix(1,4,0,1) Matrix(11281,3328,4288,1265) -> Matrix(1,-2,0,1) Matrix(397,116,948,277) -> Matrix(1,0,2,1) Matrix(3475,1012,752,219) -> Matrix(5,6,4,5) Matrix(271,76,624,175) -> Matrix(1,0,0,1) Matrix(6637,1848,1512,421) -> Matrix(7,-6,6,-5) Matrix(231,64,776,215) -> Matrix(1,-2,-2,5) Matrix(2431,668,928,255) -> Matrix(1,0,0,1) Matrix(383,104,232,63) -> Matrix(1,0,0,1) Matrix(613,164,228,61) -> Matrix(1,-2,0,1) Matrix(151,40,268,71) -> Matrix(1,0,0,1) Matrix(291,68,184,43) -> Matrix(1,0,0,1) Matrix(71,16,-324,-73) -> Matrix(1,-4,0,1) Matrix(427,92,608,131) -> Matrix(1,2,0,1) Matrix(2913,616,1064,225) -> Matrix(1,0,0,1) Matrix(1169,244,848,177) -> Matrix(1,0,0,1) Matrix(103,20,36,7) -> Matrix(1,0,0,1) Matrix(67,12,240,43) -> Matrix(3,4,-4,-5) Matrix(99,16,68,11) -> Matrix(1,0,0,1) Matrix(325,44,96,13) -> Matrix(1,0,0,1) Matrix(91,8,216,19) -> Matrix(1,2,0,1) Matrix(123,-16,100,-13) -> Matrix(1,0,2,1) Matrix(25,-4,144,-23) -> Matrix(1,0,2,1) Matrix(845,-164,304,-59) -> Matrix(3,2,-2,-1) Matrix(115,-24,24,-5) -> Matrix(1,2,0,1) Matrix(1165,-264,684,-155) -> Matrix(1,0,2,1) Matrix(1049,-240,660,-151) -> Matrix(1,0,0,1) Matrix(133,-36,484,-131) -> Matrix(9,10,-10,-11) Matrix(1237,-360,780,-227) -> Matrix(3,2,-2,-1) Matrix(1105,-324,324,-95) -> Matrix(3,2,-2,-1) Matrix(235,-72,408,-125) -> Matrix(1,0,2,1) Matrix(431,-156,268,-97) -> Matrix(1,0,2,1) Matrix(163,-60,144,-53) -> Matrix(1,0,2,1) Matrix(41,-16,100,-39) -> Matrix(1,0,4,1) Matrix(1125,-472,808,-339) -> Matrix(1,0,-2,1) Matrix(667,-284,256,-109) -> Matrix(1,-4,0,1) Matrix(937,-408,604,-263) -> Matrix(1,0,0,1) Matrix(327,-148,232,-105) -> Matrix(1,0,0,1) Matrix(535,-248,192,-89) -> Matrix(3,2,-2,-1) Matrix(181,-100,324,-179) -> Matrix(1,0,0,1) Matrix(1225,-708,372,-215) -> Matrix(1,0,0,1) Matrix(1537,-900,900,-527) -> Matrix(1,0,2,1) Matrix(1165,-684,264,-155) -> Matrix(1,2,0,1) Matrix(1549,-944,1252,-763) -> Matrix(1,0,4,1) Matrix(417,-256,676,-415) -> Matrix(1,0,10,1) Matrix(431,-268,156,-97) -> Matrix(5,-2,-2,1) Matrix(1049,-660,240,-151) -> Matrix(1,-2,2,-3) Matrix(1237,-780,360,-227) -> Matrix(1,-2,0,1) Matrix(187,-120,120,-77) -> Matrix(1,0,0,1) Matrix(527,-368,116,-81) -> Matrix(1,0,2,1) Matrix(789,-556,640,-451) -> Matrix(1,2,0,1) Matrix(327,-232,148,-105) -> Matrix(1,0,2,1) Matrix(49,-36,64,-47) -> Matrix(1,0,2,1) Matrix(1117,-872,424,-331) -> Matrix(1,-4,0,1) Matrix(1299,-1024,940,-741) -> Matrix(1,-2,0,1) Matrix(123,-100,16,-13) -> Matrix(1,-2,0,1) Matrix(163,-144,60,-53) -> Matrix(1,-2,0,1) Matrix(963,-1108,352,-405) -> Matrix(1,-2,0,1) Matrix(687,-796,208,-241) -> Matrix(1,0,0,1) Matrix(2551,-3160,976,-1209) -> Matrix(5,-2,-2,1) Matrix(49,-64,36,-47) -> Matrix(1,-2,0,1) Matrix(6393,-8840,1868,-2583) -> Matrix(1,2,-2,-3) Matrix(1833,-2536,352,-487) -> Matrix(1,4,0,1) Matrix(1487,-2068,668,-929) -> Matrix(5,4,6,5) Matrix(963,-1360,604,-853) -> Matrix(1,0,0,1) Matrix(1461,-2068,556,-787) -> Matrix(1,-4,0,1) Matrix(127,-180,12,-17) -> Matrix(1,0,0,1) Matrix(483,-692,104,-149) -> Matrix(3,4,2,3) Matrix(331,-508,144,-221) -> Matrix(1,2,0,1) Matrix(1385,-2144,604,-935) -> Matrix(1,2,0,1) Matrix(4829,-7688,1836,-2923) -> Matrix(1,-4,0,1) Matrix(439,-708,204,-329) -> Matrix(1,0,0,1) Matrix(417,-676,256,-415) -> Matrix(1,-2,0,1) Matrix(551,-904,64,-105) -> Matrix(1,0,0,1) Matrix(5509,-9416,2108,-3603) -> Matrix(11,-8,-4,3) Matrix(423,-724,52,-89) -> Matrix(1,-2,0,1) Matrix(235,-408,72,-125) -> Matrix(1,0,0,1) Matrix(181,-324,100,-179) -> Matrix(1,0,0,1) Matrix(187,-400,36,-77) -> Matrix(1,2,0,1) Matrix(2281,-5084,520,-1159) -> Matrix(17,-16,16,-15) Matrix(683,-1528,156,-349) -> Matrix(5,-6,6,-7) Matrix(41,-100,16,-39) -> Matrix(1,-6,0,1) Matrix(977,-2552,116,-303) -> Matrix(1,4,-2,-7) Matrix(623,-1700,188,-513) -> Matrix(1,2,0,1) Matrix(2383,-6632,696,-1937) -> Matrix(1,2,-2,-3) Matrix(963,-3292,184,-629) -> Matrix(1,4,0,1) Matrix(133,-484,36,-131) -> Matrix(1,0,0,1) Matrix(461,-2116,100,-459) -> Matrix(11,-10,10,-9) Matrix(25,-144,4,-23) -> Matrix(1,-10,0,1) 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): 32 Degree of the the map X: 32 Degree of the the map Y: 192 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 576 Minimal number of generators: 97 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -6/13 -5/12 -4/11 -1/3 -3/10 -2/9 -1/8 0/1 1/6 3/11 1/3 2/5 1/2 5/9 3/4 1/1 4/3 3/2 17/11 5/3 9/5 2/1 11/5 29/13 7/3 5/2 71/27 8/3 3/1 43/13 10/3 17/5 7/2 11/3 4/1 13/3 9/2 23/5 5/1 47/9 11/2 6/1 7/1 8/1 25/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/1 -1/2 0/1 -6/13 0/1 -5/11 0/1 1/2 -4/9 -1/1 1/1 -7/16 1/0 -3/7 -1/1 -8/19 -1/1 -1/3 -5/12 0/1 -12/29 1/5 1/3 -7/17 0/1 1/2 -2/5 -1/1 1/1 -7/18 0/1 -5/13 -1/1 -13/34 0/1 -8/21 -1/1 1/1 -3/8 1/0 -7/19 -1/1 -4/11 0/1 -9/25 1/1 -5/14 0/1 -1/3 0/1 1/0 -4/13 -1/1 1/1 -3/10 1/0 -8/27 -3/1 -1/1 -5/17 -1/1 -2/7 -1/1 1/1 -5/18 2/1 -8/29 1/0 -3/11 -1/1 -4/15 -1/1 1/1 -1/4 1/0 -3/13 0/1 1/0 -2/9 1/0 -5/23 -4/1 1/0 -3/14 -2/1 -1/5 -1/1 -2/11 -5/3 -1/1 -1/6 0/1 -1/7 0/1 1/0 -1/8 1/0 0/1 -1/1 1/1 1/6 0/1 1/5 0/1 1/0 2/9 -1/1 -1/3 3/13 -1/1 1/4 1/0 3/11 -1/1 5/18 -4/5 2/7 -1/1 -3/5 5/17 -2/3 -1/2 8/27 -1/2 3/10 0/1 4/13 -1/1 -1/3 1/3 -1/1 5/14 0/1 4/11 -1/1 -1/3 3/8 -1/2 2/5 0/1 5/12 1/2 8/19 1/1 3/1 3/7 0/1 1/0 7/16 1/0 4/9 -1/1 1/1 5/11 -1/1 6/13 -1/1 1/1 1/2 0/1 5/9 -1/1 1/1 9/16 1/0 4/7 -1/1 1/1 15/26 0/1 11/19 0/1 1/0 7/12 1/0 17/29 0/1 1/0 10/17 -1/1 -1/3 13/22 0/1 3/5 -1/1 8/13 0/1 5/8 1/2 12/19 1/1 3/1 7/11 0/1 1/0 2/3 -1/1 1/1 9/13 -2/1 1/0 7/10 0/1 19/27 -2/1 1/0 12/17 -5/3 -1/1 5/7 -1/1 3/4 0/1 7/9 1/1 11/14 0/1 15/19 0/1 1/0 4/5 -1/1 1/1 9/11 -1/1 5/6 0/1 6/7 -1/1 1/1 1/1 0/1 1/0 6/5 -1/1 1/1 11/9 1/1 5/4 1/0 4/3 1/0 11/8 1/0 18/13 -3/1 -1/1 25/18 -4/3 7/5 -1/1 24/17 -1/1 1/1 41/29 -1/1 1/1 17/12 1/0 27/19 0/1 1/0 10/7 -3/1 -1/1 23/16 -1/2 13/9 0/1 1/0 3/2 0/1 17/11 -1/1 1/1 14/9 -1/1 1/1 11/7 0/1 1/0 19/12 1/0 27/17 -1/1 8/5 -1/1 1/1 29/18 0/1 21/13 0/1 1/0 13/8 1/0 18/11 -3/1 -1/1 41/25 0/1 1/0 23/14 0/1 5/3 -1/1 22/13 0/1 17/10 0/1 12/7 -1/1 1/1 19/11 0/1 1/0 7/4 1/0 9/5 -1/1 1/1 11/6 0/1 2/1 -1/1 1/1 15/7 0/1 1/0 13/6 0/1 11/5 1/1 20/9 5/7 1/1 29/13 1/1 9/4 3/2 16/7 1/1 3/1 39/17 1/1 3/1 23/10 2/1 7/3 2/1 1/0 5/2 1/0 13/5 -4/1 1/0 47/18 -4/1 81/31 -3/1 34/13 -3/1 -1/1 21/8 1/0 71/27 -5/1 -3/1 50/19 -5/1 -3/1 29/11 -3/1 8/3 -3/1 -1/1 19/7 -2/1 1/0 30/11 -3/1 -1/1 41/15 -3/1 -1/1 11/4 1/0 14/5 -5/3 -1/1 3/1 -1/1 13/4 1/0 23/7 0/1 1/0 33/10 0/1 43/13 -1/1 1/1 10/3 -1/1 1/1 27/8 1/0 17/5 0/1 1/0 41/12 1/0 65/19 -1/1 24/7 -1/1 1/1 7/2 0/1 11/3 -1/1 1/1 15/4 1/0 4/1 -1/1 1/1 13/3 1/1 35/8 3/4 57/13 1/1 22/5 1/1 5/3 9/2 0/1 23/5 1/1 37/8 5/4 14/3 1/1 5/3 5/1 2/1 1/0 26/5 1/1 3/1 47/9 3/1 21/4 1/0 16/3 1/1 3/1 11/2 4/1 6/1 1/0 7/1 -3/1 8/1 -3/1 -1/1 25/3 -1/1 17/2 0/1 9/1 0/1 1/0 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(265,124,156,73) (-1/2,-6/13) -> (22/13,17/10) Hyperbolic Matrix(153,70,518,237) (-6/13,-5/11) -> (5/17,8/27) Hyperbolic Matrix(103,46,150,67) (-5/11,-4/9) -> (2/3,9/13) Hyperbolic Matrix(199,88,52,23) (-4/9,-7/16) -> (15/4,4/1) Hyperbolic Matrix(51,22,146,63) (-7/16,-3/7) -> (1/3,5/14) Hyperbolic Matrix(47,20,148,63) (-3/7,-8/19) -> (4/13,1/3) Hyperbolic Matrix(239,100,-576,-241) (-8/19,-5/12) -> (-5/12,-12/29) Parabolic Matrix(953,394,670,277) (-12/29,-7/17) -> (27/19,10/7) Hyperbolic Matrix(239,98,378,155) (-7/17,-2/5) -> (12/19,7/11) Hyperbolic Matrix(91,36,48,19) (-2/5,-7/18) -> (11/6,2/1) Hyperbolic Matrix(227,88,276,107) (-7/18,-5/13) -> (9/11,5/6) Hyperbolic Matrix(271,104,456,175) (-5/13,-13/34) -> (13/22,3/5) Hyperbolic Matrix(907,346,270,103) (-13/34,-8/21) -> (10/3,27/8) Hyperbolic Matrix(179,68,408,155) (-8/21,-3/8) -> (7/16,4/9) Hyperbolic Matrix(43,16,180,67) (-3/8,-7/19) -> (3/13,1/4) Hyperbolic Matrix(175,64,-484,-177) (-7/19,-4/11) -> (-4/11,-9/25) Parabolic Matrix(479,172,220,79) (-9/25,-5/14) -> (13/6,11/5) Hyperbolic Matrix(175,62,302,107) (-5/14,-1/3) -> (11/19,7/12) Hyperbolic Matrix(283,88,164,51) (-1/3,-4/13) -> (12/7,19/11) Hyperbolic Matrix(119,36,-400,-121) (-4/13,-3/10) -> (-3/10,-8/27) Parabolic Matrix(237,70,518,153) (-8/27,-5/17) -> (5/11,6/13) Hyperbolic Matrix(159,46,38,11) (-5/17,-2/7) -> (4/1,13/3) Hyperbolic Matrix(351,98,154,43) (-2/7,-5/18) -> (9/4,16/7) Hyperbolic Matrix(231,64,776,215) (-5/18,-8/29) -> (8/27,3/10) Hyperbolic Matrix(387,106,230,63) (-8/29,-3/11) -> (5/3,22/13) Hyperbolic Matrix(231,62,190,51) (-3/11,-4/15) -> (6/5,11/9) Hyperbolic Matrix(151,40,268,71) (-4/15,-1/4) -> (9/16,4/7) Hyperbolic Matrix(291,68,184,43) (-1/4,-3/13) -> (11/7,19/12) Hyperbolic Matrix(71,16,-324,-73) (-3/13,-2/9) -> (-2/9,-5/23) Parabolic Matrix(427,92,608,131) (-5/23,-3/14) -> (7/10,19/27) Hyperbolic Matrix(107,22,34,7) (-3/14,-1/5) -> (3/1,13/4) Hyperbolic Matrix(103,20,36,7) (-1/5,-2/11) -> (14/5,3/1) Hyperbolic Matrix(67,12,240,43) (-2/11,-1/6) -> (5/18,2/7) Hyperbolic Matrix(99,16,68,11) (-1/6,-1/7) -> (13/9,3/2) Hyperbolic Matrix(325,44,96,13) (-1/7,-1/8) -> (27/8,17/5) Hyperbolic Matrix(93,10,158,17) (-1/8,0/1) -> (10/17,13/22) Hyperbolic Matrix(121,-18,74,-11) (0/1,1/6) -> (13/8,18/11) Hyperbolic Matrix(191,-34,118,-21) (1/6,1/5) -> (21/13,13/8) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(365,-82,138,-31) (2/9,3/13) -> (29/11,8/3) Hyperbolic Matrix(67,-18,242,-65) (1/4,3/11) -> (3/11,5/18) Parabolic Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(235,-72,408,-125) (3/10,4/13) -> (4/7,15/26) Hyperbolic Matrix(431,-156,268,-97) (5/14,4/11) -> (8/5,29/18) Hyperbolic Matrix(103,-38,122,-45) (4/11,3/8) -> (5/6,6/7) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(435,-182,98,-41) (5/12,8/19) -> (22/5,9/2) Hyperbolic Matrix(393,-166,670,-283) (8/19,3/7) -> (17/29,10/17) Hyperbolic Matrix(273,-118,118,-51) (3/7,7/16) -> (23/10,7/3) Hyperbolic Matrix(327,-148,232,-105) (4/9,5/11) -> (7/5,24/17) Hyperbolic Matrix(305,-142,58,-27) (6/13,1/2) -> (21/4,16/3) Hyperbolic Matrix(91,-50,162,-89) (1/2,5/9) -> (5/9,9/16) Parabolic Matrix(1225,-708,372,-215) (15/26,11/19) -> (23/7,33/10) Hyperbolic Matrix(1519,-890,582,-341) (7/12,17/29) -> (13/5,47/18) Hyperbolic Matrix(121,-74,18,-11) (3/5,8/13) -> (6/1,7/1) Hyperbolic Matrix(191,-118,34,-21) (8/13,5/8) -> (11/2,6/1) Hyperbolic Matrix(619,-390,446,-281) (5/8,12/19) -> (18/13,25/18) Hyperbolic Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(429,-298,298,-207) (9/13,7/10) -> (23/16,13/9) Hyperbolic Matrix(1183,-834,722,-509) (19/27,12/17) -> (18/11,41/25) Hyperbolic Matrix(327,-232,148,-105) (12/17,5/7) -> (11/5,20/9) Hyperbolic Matrix(49,-36,64,-47) (5/7,3/4) -> (3/4,7/9) Parabolic Matrix(549,-430,346,-271) (7/9,11/14) -> (19/12,27/17) Hyperbolic Matrix(1017,-802,298,-235) (11/14,15/19) -> (17/5,41/12) Hyperbolic Matrix(123,-100,16,-13) (4/5,9/11) -> (7/1,8/1) Hyperbolic Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(103,-122,38,-45) (1/1,6/5) -> (8/3,19/7) Hyperbolic Matrix(227,-278,138,-169) (11/9,5/4) -> (23/14,5/3) Hyperbolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(283,-390,82,-113) (11/8,18/13) -> (24/7,7/2) Hyperbolic Matrix(409,-570,94,-131) (25/18,7/5) -> (13/3,35/8) Hyperbolic Matrix(2657,-3754,1010,-1427) (24/17,41/29) -> (71/27,50/19) Hyperbolic Matrix(1461,-2068,556,-787) (41/29,17/12) -> (21/8,71/27) Hyperbolic Matrix(127,-180,12,-17) (17/12,27/19) -> (9/1,1/0) Hyperbolic Matrix(483,-692,104,-149) (10/7,23/16) -> (37/8,14/3) Hyperbolic Matrix(331,-508,144,-221) (3/2,17/11) -> (39/17,23/10) Hyperbolic Matrix(527,-818,230,-357) (17/11,14/9) -> (16/7,39/17) Hyperbolic Matrix(995,-1582,378,-601) (27/17,8/5) -> (50/19,29/11) Hyperbolic Matrix(439,-708,204,-329) (29/18,21/13) -> (15/7,13/6) Hyperbolic Matrix(551,-904,64,-105) (41/25,23/14) -> (17/2,9/1) Hyperbolic Matrix(487,-830,186,-317) (17/10,12/7) -> (34/13,21/8) Hyperbolic Matrix(235,-408,72,-125) (19/11,7/4) -> (13/4,23/7) Hyperbolic Matrix(91,-162,50,-89) (7/4,9/5) -> (9/5,11/6) Parabolic Matrix(187,-400,36,-77) (2/1,15/7) -> (5/1,26/5) Hyperbolic Matrix(799,-1778,182,-405) (20/9,29/13) -> (57/13,22/5) Hyperbolic Matrix(683,-1528,156,-349) (29/13,9/4) -> (35/8,57/13) Hyperbolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(977,-2552,116,-303) (47/18,81/31) -> (25/3,17/2) Hyperbolic Matrix(573,-1498,70,-183) (81/31,34/13) -> (8/1,25/3) Hyperbolic Matrix(623,-1700,188,-513) (30/11,41/15) -> (43/13,10/3) Hyperbolic Matrix(667,-1826,202,-553) (41/15,11/4) -> (33/10,43/13) Hyperbolic Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(963,-3292,184,-629) (41/12,65/19) -> (47/9,21/4) Hyperbolic Matrix(823,-2818,158,-541) (65/19,24/7) -> (26/5,47/9) Hyperbolic Matrix(67,-242,18,-65) (7/2,11/3) -> (11/3,15/4) Parabolic Matrix(231,-1058,50,-229) (9/2,23/5) -> (23/5,37/8) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(0,-1,1,2) Matrix(265,124,156,73) -> Matrix(1,0,2,1) Matrix(153,70,518,237) -> Matrix(4,-1,-7,2) Matrix(103,46,150,67) -> Matrix(0,-1,1,0) Matrix(199,88,52,23) -> Matrix(1,0,0,1) Matrix(51,22,146,63) -> Matrix(0,-1,1,2) Matrix(47,20,148,63) -> Matrix(1,0,0,1) Matrix(239,100,-576,-241) -> Matrix(1,0,6,1) Matrix(953,394,670,277) -> Matrix(2,-1,1,0) Matrix(239,98,378,155) -> Matrix(2,-1,1,0) Matrix(91,36,48,19) -> Matrix(1,0,0,1) Matrix(227,88,276,107) -> Matrix(1,0,0,1) Matrix(271,104,456,175) -> Matrix(1,0,0,1) Matrix(907,346,270,103) -> Matrix(0,-1,1,0) Matrix(179,68,408,155) -> Matrix(1,0,0,1) Matrix(43,16,180,67) -> Matrix(1,0,0,1) Matrix(175,64,-484,-177) -> Matrix(1,0,2,1) Matrix(479,172,220,79) -> Matrix(1,0,0,1) Matrix(175,62,302,107) -> Matrix(0,-1,1,0) Matrix(283,88,164,51) -> Matrix(1,0,0,1) Matrix(119,36,-400,-121) -> Matrix(1,-2,0,1) Matrix(237,70,518,153) -> Matrix(0,-1,1,2) Matrix(159,46,38,11) -> Matrix(0,-1,1,0) Matrix(351,98,154,43) -> Matrix(2,-1,1,0) Matrix(231,64,776,215) -> Matrix(1,-2,-2,5) Matrix(387,106,230,63) -> Matrix(0,-1,1,2) Matrix(231,62,190,51) -> Matrix(0,-1,1,0) Matrix(151,40,268,71) -> Matrix(1,0,0,1) Matrix(291,68,184,43) -> Matrix(1,0,0,1) Matrix(71,16,-324,-73) -> Matrix(1,-4,0,1) Matrix(427,92,608,131) -> Matrix(1,2,0,1) Matrix(107,22,34,7) -> Matrix(0,-1,1,2) Matrix(103,20,36,7) -> Matrix(1,0,0,1) Matrix(67,12,240,43) -> Matrix(3,4,-4,-5) Matrix(99,16,68,11) -> Matrix(1,0,0,1) Matrix(325,44,96,13) -> Matrix(1,0,0,1) Matrix(93,10,158,17) -> Matrix(0,-1,1,2) Matrix(121,-18,74,-11) -> Matrix(2,1,-1,0) Matrix(191,-34,118,-21) -> Matrix(0,-1,1,0) Matrix(115,-24,24,-5) -> Matrix(1,2,0,1) Matrix(365,-82,138,-31) -> Matrix(4,1,-1,0) Matrix(67,-18,242,-65) -> Matrix(4,5,-5,-6) Matrix(173,-50,218,-63) -> Matrix(2,1,3,2) Matrix(235,-72,408,-125) -> Matrix(1,0,2,1) Matrix(431,-156,268,-97) -> Matrix(1,0,2,1) Matrix(103,-38,122,-45) -> Matrix(2,1,-1,0) Matrix(41,-16,100,-39) -> Matrix(1,0,4,1) Matrix(435,-182,98,-41) -> Matrix(2,-1,1,0) Matrix(393,-166,670,-283) -> Matrix(0,-1,1,0) Matrix(273,-118,118,-51) -> Matrix(2,-1,1,0) Matrix(327,-148,232,-105) -> Matrix(1,0,0,1) Matrix(305,-142,58,-27) -> Matrix(2,-1,1,0) Matrix(91,-50,162,-89) -> Matrix(0,-1,1,0) Matrix(1225,-708,372,-215) -> Matrix(1,0,0,1) Matrix(1519,-890,582,-341) -> Matrix(4,1,-1,0) Matrix(121,-74,18,-11) -> Matrix(4,1,-1,0) Matrix(191,-118,34,-21) -> Matrix(6,-1,1,0) Matrix(619,-390,446,-281) -> Matrix(2,-3,-1,2) Matrix(187,-120,120,-77) -> Matrix(1,0,0,1) Matrix(429,-298,298,-207) -> Matrix(0,-1,1,2) Matrix(1183,-834,722,-509) -> Matrix(0,-1,1,2) Matrix(327,-232,148,-105) -> Matrix(1,0,2,1) Matrix(49,-36,64,-47) -> Matrix(1,0,2,1) Matrix(549,-430,346,-271) -> Matrix(0,-1,1,0) Matrix(1017,-802,298,-235) -> Matrix(0,-1,1,0) Matrix(123,-100,16,-13) -> Matrix(1,-2,0,1) Matrix(163,-144,60,-53) -> Matrix(1,-2,0,1) Matrix(103,-122,38,-45) -> Matrix(2,1,-1,0) Matrix(227,-278,138,-169) -> Matrix(0,-1,1,0) Matrix(49,-64,36,-47) -> Matrix(1,-2,0,1) Matrix(283,-390,82,-113) -> Matrix(0,-1,1,2) Matrix(409,-570,94,-131) -> Matrix(0,-1,1,0) Matrix(2657,-3754,1010,-1427) -> Matrix(4,1,-1,0) Matrix(1461,-2068,556,-787) -> Matrix(1,-4,0,1) Matrix(127,-180,12,-17) -> Matrix(1,0,0,1) Matrix(483,-692,104,-149) -> Matrix(3,4,2,3) Matrix(331,-508,144,-221) -> Matrix(1,2,0,1) Matrix(527,-818,230,-357) -> Matrix(2,-1,1,0) Matrix(995,-1582,378,-601) -> Matrix(4,1,-1,0) Matrix(439,-708,204,-329) -> Matrix(1,0,0,1) Matrix(551,-904,64,-105) -> Matrix(1,0,0,1) Matrix(487,-830,186,-317) -> Matrix(2,1,-1,0) Matrix(235,-408,72,-125) -> Matrix(1,0,0,1) Matrix(91,-162,50,-89) -> Matrix(0,-1,1,0) Matrix(187,-400,36,-77) -> Matrix(1,2,0,1) Matrix(799,-1778,182,-405) -> Matrix(6,-5,5,-4) Matrix(683,-1528,156,-349) -> Matrix(5,-6,6,-7) Matrix(41,-100,16,-39) -> Matrix(1,-6,0,1) Matrix(977,-2552,116,-303) -> Matrix(1,4,-2,-7) Matrix(573,-1498,70,-183) -> Matrix(2,5,-1,-2) Matrix(623,-1700,188,-513) -> Matrix(1,2,0,1) Matrix(667,-1826,202,-553) -> Matrix(0,-1,1,2) Matrix(119,-330,22,-61) -> Matrix(4,7,1,2) Matrix(963,-3292,184,-629) -> Matrix(1,4,0,1) Matrix(823,-2818,158,-541) -> Matrix(2,-1,1,0) Matrix(67,-242,18,-65) -> Matrix(0,-1,1,0) Matrix(231,-1058,50,-229) -> Matrix(6,-5,5,-4) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 ----------------------------------------------------------------------- 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 -1/1 1 2 0/1 (-1/1,1/1) 0 14 1/6 0/1 1 2 1/5 (-1/1,1/1).(0/1,1/0) 0 14 2/9 (-1/1,-1/3) 0 14 1/4 1/0 1 14 3/11 -1/1 5 2 2/7 (-1/1,-3/5) 0 14 5/17 (-1/1,-3/5).(-2/3,-1/2) 0 14 3/10 0/1 1 14 1/3 -1/1 1 14 4/11 (-1/1,-1/3) 0 14 3/8 -1/2 1 14 2/5 0/1 2 2 5/12 1/2 1 14 8/19 (1/1,3/1) 0 14 3/7 (-1/1,1/1).(0/1,1/0) 0 14 4/9 (-1/1,1/1) 0 14 5/11 -1/1 1 14 1/2 0/1 1 14 5/9 (-1/1,1/1).(0/1,1/0) 0 2 4/7 (-1/1,1/1) 0 14 7/12 1/0 1 14 17/29 (-1/1,1/1).(0/1,1/0) 0 14 10/17 (-1/1,-1/3) 0 14 3/5 -1/1 1 14 8/13 0/1 5 2 5/8 1/2 1 14 7/11 (-1/1,1/1).(0/1,1/0) 0 14 2/3 (-1/1,1/1) 0 14 7/10 0/1 1 14 12/17 (-5/3,-1/1) 0 14 5/7 -1/1 1 14 3/4 0/1 1 2 7/9 1/1 1 14 11/14 0/1 1 14 15/19 (-1/1,1/1).(0/1,1/0) 0 14 4/5 (-1/1,1/1) 0 14 5/6 0/1 1 14 6/7 (-1/1,1/1) 0 14 1/1 (-1/1,1/1).(0/1,1/0) 0 14 6/5 (-1/1,1/1) 0 14 5/4 1/0 1 14 4/3 1/0 1 2 11/8 1/0 1 14 18/13 (-3/1,-1/1) 0 14 7/5 -1/1 1 14 24/17 (-1/1,1/1) 0 14 41/29 (-1/1,1/1).(0/1,1/0) 0 2 17/12 1/0 1 14 10/7 (-3/1,-1/1) 0 14 3/2 0/1 1 14 17/11 (-1/1,1/1).(0/1,1/0) 0 2 14/9 (-1/1,1/1) 0 14 11/7 (-1/1,1/1).(0/1,1/0) 0 14 8/5 (-1/1,1/1) 0 14 21/13 (-1/1,1/1).(0/1,1/0) 0 14 13/8 1/0 1 2 18/11 (-3/1,-1/1) 0 14 5/3 -1/1 1 14 17/10 0/1 1 14 12/7 (-1/1,1/1) 0 14 7/4 1/0 1 14 9/5 (-1/1,1/1).(0/1,1/0) 0 2 2/1 (-1/1,1/1) 0 14 11/5 1/1 1 14 20/9 (5/7,1/1) 0 14 29/13 1/1 11 2 9/4 3/2 1 14 7/3 (1/1,3/1).(2/1,1/0) 0 14 5/2 1/0 3 2 13/5 (-5/1,-3/1).(-4/1,1/0) 0 14 47/18 -4/1 1 14 81/31 -3/1 3 2 34/13 (-3/1,-1/1) 0 14 21/8 1/0 1 14 8/3 (-3/1,-1/1) 0 14 19/7 (-3/1,-1/1).(-2/1,1/0) 0 14 30/11 (-3/1,-1/1) 0 14 41/15 (-3/1,-1/1).(-2/1,1/0) 0 2 11/4 1/0 1 14 3/1 -1/1 1 14 10/3 (-1/1,1/1) 0 14 17/5 (-1/1,1/1).(0/1,1/0) 0 14 41/12 1/0 1 14 65/19 -1/1 1 2 24/7 (-1/1,1/1) 0 14 7/2 0/1 1 14 11/3 (-1/1,1/1).(0/1,1/0) 0 2 4/1 (-1/1,1/1) 0 14 9/2 0/1 1 14 23/5 1/1 5 2 14/3 (1/1,5/3) 0 14 5/1 (1/1,3/1).(2/1,1/0) 0 14 11/2 4/1 1 14 6/1 1/0 5 2 7/1 -3/1 1 14 1/0 1/0 1 14 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(121,-18,74,-11) (0/1,1/6) -> (13/8,18/11) Hyperbolic Matrix(191,-34,118,-21) (1/6,1/5) -> (21/13,13/8) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(67,-16,46,-11) (2/9,1/4) -> (10/7,3/2) Glide Reflection Matrix(23,-6,88,-23) (1/4,3/11) -> (1/4,3/11) Reflection Matrix(43,-12,154,-43) (3/11,2/7) -> (3/11,2/7) Reflection Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(237,-70,44,-13) (5/17,3/10) -> (5/1,11/2) Glide Reflection Matrix(63,-20,22,-7) (3/10,1/3) -> (11/4,3/1) Glide Reflection Matrix(63,-22,20,-7) (1/3,4/11) -> (3/1,10/3) Glide Reflection Matrix(103,-38,122,-45) (4/11,3/8) -> (5/6,6/7) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(277,-116,394,-165) (5/12,8/19) -> (7/10,12/17) Glide Reflection Matrix(393,-166,670,-283) (8/19,3/7) -> (17/29,10/17) Hyperbolic Matrix(155,-68,98,-43) (3/7,4/9) -> (11/7,8/5) Glide Reflection Matrix(327,-148,232,-105) (4/9,5/11) -> (7/5,24/17) Hyperbolic Matrix(135,-62,172,-79) (5/11,1/2) -> (7/9,11/14) Glide Reflection Matrix(19,-10,36,-19) (1/2,5/9) -> (1/2,5/9) Reflection Matrix(71,-40,126,-71) (5/9,4/7) -> (5/9,4/7) Reflection Matrix(107,-62,88,-51) (4/7,7/12) -> (6/5,5/4) Glide Reflection Matrix(1519,-890,582,-341) (7/12,17/29) -> (13/5,47/18) Hyperbolic Matrix(175,-104,106,-63) (10/17,3/5) -> (18/11,5/3) Glide Reflection Matrix(121,-74,18,-11) (3/5,8/13) -> (6/1,7/1) Hyperbolic Matrix(191,-118,34,-21) (8/13,5/8) -> (11/2,6/1) Hyperbolic Matrix(155,-98,68,-43) (5/8,7/11) -> (9/4,7/3) Glide Reflection Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(67,-46,16,-11) (2/3,7/10) -> (4/1,9/2) Glide Reflection Matrix(327,-232,148,-105) (12/17,5/7) -> (11/5,20/9) Hyperbolic Matrix(49,-36,64,-47) (5/7,3/4) -> (3/4,7/9) Parabolic Matrix(1017,-802,298,-235) (11/14,15/19) -> (17/5,41/12) Hyperbolic Matrix(107,-88,62,-51) (4/5,5/6) -> (12/7,7/4) Glide Reflection Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(103,-122,38,-45) (1/1,6/5) -> (8/3,19/7) Hyperbolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(283,-390,82,-113) (11/8,18/13) -> (24/7,7/2) Hyperbolic Matrix(153,-212,70,-97) (18/13,7/5) -> (2/1,11/5) Glide Reflection Matrix(1393,-1968,986,-1393) (24/17,41/29) -> (24/17,41/29) Reflection Matrix(985,-1394,696,-985) (41/29,17/12) -> (41/29,17/12) Reflection Matrix(243,-346,92,-131) (17/12,10/7) -> (21/8,8/3) Glide Reflection Matrix(67,-102,44,-67) (3/2,17/11) -> (3/2,17/11) Reflection Matrix(307,-476,198,-307) (17/11,14/9) -> (17/11,14/9) Reflection Matrix(215,-346,64,-103) (8/5,21/13) -> (10/3,17/5) Glide Reflection Matrix(73,-124,10,-17) (5/3,17/10) -> (7/1,1/0) Glide Reflection Matrix(487,-830,186,-317) (17/10,12/7) -> (34/13,21/8) Hyperbolic Matrix(71,-126,40,-71) (7/4,9/5) -> (7/4,9/5) Reflection Matrix(19,-36,10,-19) (9/5,2/1) -> (9/5,2/1) Reflection Matrix(521,-1160,234,-521) (20/9,29/13) -> (20/9,29/13) Reflection Matrix(233,-522,104,-233) (29/13,9/4) -> (29/13,9/4) Reflection Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(2915,-7614,1116,-2915) (47/18,81/31) -> (47/18,81/31) Reflection Matrix(2107,-5508,806,-2107) (81/31,34/13) -> (81/31,34/13) Reflection Matrix(901,-2460,330,-901) (30/11,41/15) -> (30/11,41/15) Reflection Matrix(329,-902,120,-329) (41/15,11/4) -> (41/15,11/4) Reflection Matrix(1559,-5330,456,-1559) (41/12,65/19) -> (41/12,65/19) Reflection Matrix(911,-3120,266,-911) (65/19,24/7) -> (65/19,24/7) Reflection Matrix(43,-154,12,-43) (7/2,11/3) -> (7/2,11/3) Reflection Matrix(23,-88,6,-23) (11/3,4/1) -> (11/3,4/1) Reflection Matrix(91,-414,20,-91) (9/2,23/5) -> (9/2,23/5) Reflection Matrix(139,-644,30,-139) (23/5,14/3) -> (23/5,14/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Matrix(-1,0,2,1) -> Matrix(0,1,1,0) (-1/1,0/1) -> (-1/1,1/1) Matrix(121,-18,74,-11) -> Matrix(2,1,-1,0) -1/1 Matrix(191,-34,118,-21) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(115,-24,24,-5) -> Matrix(1,2,0,1) 1/0 Matrix(67,-16,46,-11) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(23,-6,88,-23) -> Matrix(1,2,0,-1) (1/4,3/11) -> (-1/1,1/0) Matrix(43,-12,154,-43) -> Matrix(4,3,-5,-4) (3/11,2/7) -> (-1/1,-3/5) Matrix(173,-50,218,-63) -> Matrix(2,1,3,2) Matrix(237,-70,44,-13) -> Matrix(7,4,2,1) Matrix(63,-20,22,-7) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(63,-22,20,-7) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(103,-38,122,-45) -> Matrix(2,1,-1,0) -1/1 Matrix(41,-16,100,-39) -> Matrix(1,0,4,1) 0/1 Matrix(277,-116,394,-165) -> Matrix(-2,1,1,0) Matrix(393,-166,670,-283) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(155,-68,98,-43) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(327,-148,232,-105) -> Matrix(1,0,0,1) Matrix(135,-62,172,-79) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(19,-10,36,-19) -> Matrix(1,0,0,-1) (1/2,5/9) -> (0/1,1/0) Matrix(71,-40,126,-71) -> Matrix(0,1,1,0) (5/9,4/7) -> (-1/1,1/1) Matrix(107,-62,88,-51) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1519,-890,582,-341) -> Matrix(4,1,-1,0) Matrix(175,-104,106,-63) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(121,-74,18,-11) -> Matrix(4,1,-1,0) Matrix(191,-118,34,-21) -> Matrix(6,-1,1,0) Matrix(155,-98,68,-43) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(187,-120,120,-77) -> Matrix(1,0,0,1) Matrix(67,-46,16,-11) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(327,-232,148,-105) -> Matrix(1,0,2,1) 0/1 Matrix(49,-36,64,-47) -> Matrix(1,0,2,1) 0/1 Matrix(1017,-802,298,-235) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(107,-88,62,-51) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(163,-144,60,-53) -> Matrix(1,-2,0,1) 1/0 Matrix(103,-122,38,-45) -> Matrix(2,1,-1,0) -1/1 Matrix(49,-64,36,-47) -> Matrix(1,-2,0,1) 1/0 Matrix(283,-390,82,-113) -> Matrix(0,-1,1,2) -1/1 Matrix(153,-212,70,-97) -> Matrix(0,1,1,2) Matrix(1393,-1968,986,-1393) -> Matrix(0,1,1,0) (24/17,41/29) -> (-1/1,1/1) Matrix(985,-1394,696,-985) -> Matrix(1,0,0,-1) (41/29,17/12) -> (0/1,1/0) Matrix(243,-346,92,-131) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(67,-102,44,-67) -> Matrix(1,0,0,-1) (3/2,17/11) -> (0/1,1/0) Matrix(307,-476,198,-307) -> Matrix(0,1,1,0) (17/11,14/9) -> (-1/1,1/1) Matrix(215,-346,64,-103) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(73,-124,10,-17) -> Matrix(-2,1,1,0) Matrix(487,-830,186,-317) -> Matrix(2,1,-1,0) -1/1 Matrix(71,-126,40,-71) -> Matrix(1,0,0,-1) (7/4,9/5) -> (0/1,1/0) Matrix(19,-36,10,-19) -> Matrix(0,1,1,0) (9/5,2/1) -> (-1/1,1/1) Matrix(521,-1160,234,-521) -> Matrix(6,-5,7,-6) (20/9,29/13) -> (5/7,1/1) Matrix(233,-522,104,-233) -> Matrix(5,-6,4,-5) (29/13,9/4) -> (1/1,3/2) Matrix(41,-100,16,-39) -> Matrix(1,-6,0,1) 1/0 Matrix(2915,-7614,1116,-2915) -> Matrix(7,24,-2,-7) (47/18,81/31) -> (-4/1,-3/1) Matrix(2107,-5508,806,-2107) -> Matrix(2,3,-1,-2) (81/31,34/13) -> (-3/1,-1/1) Matrix(901,-2460,330,-901) -> Matrix(2,3,-1,-2) (30/11,41/15) -> (-3/1,-1/1) Matrix(329,-902,120,-329) -> Matrix(1,4,0,-1) (41/15,11/4) -> (-2/1,1/0) Matrix(1559,-5330,456,-1559) -> Matrix(1,2,0,-1) (41/12,65/19) -> (-1/1,1/0) Matrix(911,-3120,266,-911) -> Matrix(0,1,1,0) (65/19,24/7) -> (-1/1,1/1) Matrix(43,-154,12,-43) -> Matrix(1,0,0,-1) (7/2,11/3) -> (0/1,1/0) Matrix(23,-88,6,-23) -> Matrix(0,1,1,0) (11/3,4/1) -> (-1/1,1/1) Matrix(91,-414,20,-91) -> Matrix(1,0,2,-1) (9/2,23/5) -> (0/1,1/1) Matrix(139,-644,30,-139) -> Matrix(4,-5,3,-4) (23/5,14/3) -> (1/1,5/3) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.