INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1440 Minimal number of generators: 241 Number of equivalence classes of cusps: 80 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -6/1 -11/2 -16/3 -24/5 -14/3 -4/1 -11/3 -18/5 -11/4 -12/5 -11/5 -2/1 -11/6 -11/7 -22/15 -33/23 -11/8 -11/9 -22/19 0/1 1/1 11/9 22/17 11/8 3/2 11/7 22/13 55/32 11/6 2/1 15/7 11/5 12/5 22/9 5/2 44/17 55/21 132/49 11/4 3/1 22/7 33/10 10/3 44/13 7/2 154/43 18/5 11/3 132/35 88/23 4/1 21/5 17/4 176/41 13/3 22/5 9/2 132/29 88/19 14/3 19/4 110/23 5/1 21/4 16/3 11/2 17/3 6/1 44/7 19/3 13/2 20/3 7/1 22/3 15/2 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -1/1 0/1 -8/1 -3/2 1/0 -7/1 -1/1 -6/7 -13/2 -5/7 -2/3 -6/1 -3/4 -1/2 -23/4 -2/3 -3/5 -17/3 -2/3 -3/5 -11/2 -1/2 -27/5 -2/5 -1/3 -43/8 -1/3 -2/7 -16/3 -1/2 -1/4 -5/1 -1/1 0/1 -24/5 -1/2 -1/4 -19/4 0/1 1/1 -14/3 -3/2 1/0 -23/5 -1/1 0/1 -32/7 -3/2 1/0 -9/2 -4/3 -1/1 -22/5 -1/1 -13/3 -1/1 -8/9 -17/4 -1/1 -4/5 -21/5 -1/1 -4/5 -4/1 -3/4 -1/2 -23/6 -2/3 -3/5 -19/5 -1/1 -2/3 -34/9 -5/8 -1/2 -49/13 -2/3 -3/5 -15/4 -3/5 -4/7 -11/3 -1/2 -29/8 -3/7 -2/5 -47/13 -3/7 -2/5 -18/5 -1/2 -3/8 -7/2 -1/3 0/1 -24/7 -3/2 1/0 -17/5 -1/1 0/1 -10/3 -1/2 1/0 -13/4 -1/1 0/1 -29/9 -2/1 -1/1 -45/14 -4/3 -1/1 -16/5 -3/2 1/0 -3/1 -1/1 -2/3 -17/6 -2/3 -3/5 -31/11 -3/5 -10/17 -14/5 -7/12 -1/2 -11/4 -1/2 -30/11 -1/2 -9/20 -19/7 -3/7 -2/5 -65/24 -2/5 -1/3 -46/17 -1/2 -3/8 -27/10 -2/5 -1/3 -62/23 -1/2 -3/8 -35/13 -2/5 -1/3 -8/3 -1/2 -1/4 -29/11 0/1 1/5 -50/19 1/2 1/0 -21/8 -1/1 0/1 -13/5 -1/1 0/1 -18/7 -1/2 1/0 -41/16 -2/1 -1/1 -23/9 -1/1 -4/5 -5/2 -1/1 0/1 -22/9 -1/1 -17/7 -1/1 -4/5 -46/19 -5/6 -3/4 -29/12 -1/1 -2/3 -41/17 -1/1 -2/3 -53/22 -1/1 0/1 -12/5 -3/4 -1/2 -55/23 -1/2 -43/18 -1/1 0/1 -117/49 -1/1 -2/3 -74/31 -3/4 -1/2 -31/13 -1/1 -4/5 -19/8 -1/1 -2/3 -7/3 -1/1 -2/3 -23/10 -5/7 -2/3 -16/7 -3/4 -1/2 -25/11 -2/3 -7/11 -34/15 -5/8 -1/2 -9/4 -2/3 -3/5 -47/21 -3/5 -4/7 -38/17 -7/12 -1/2 -29/13 -4/7 -13/23 -20/9 -11/20 -1/2 -11/5 -1/2 -24/11 -1/2 -9/20 -13/6 -2/5 -1/3 -15/7 -1/3 0/1 -2/1 -1/2 1/0 -15/8 -1/1 -2/3 -13/7 -2/3 -3/5 -11/6 -1/2 -31/17 -8/17 -7/15 -20/11 -1/2 -9/20 -49/27 -4/9 -3/7 -29/16 -10/23 -3/7 -9/5 -2/5 -1/3 -43/24 -2/5 -1/3 -34/19 -1/2 -3/8 -25/14 -4/11 -1/3 -66/37 -1/3 -41/23 -1/3 -4/13 -16/9 -1/2 -1/4 -23/13 -1/3 -2/7 -30/17 -1/2 -1/4 -7/4 -1/3 0/1 -26/15 -1/2 -3/8 -71/41 -2/5 -1/3 -45/26 -6/17 -1/3 -19/11 -1/3 0/1 -50/29 -1/2 -1/4 -31/18 -1/5 0/1 -43/25 -1/1 0/1 -55/32 -1/2 -12/7 -1/2 -1/4 -41/24 -1/3 0/1 -29/17 -1/3 0/1 -46/27 -1/4 -1/6 -17/10 -1/5 0/1 -22/13 0/1 -5/3 -1/1 0/1 -28/17 -1/2 -1/4 -23/14 -1/5 0/1 -41/25 0/1 1/1 -18/11 -1/2 1/0 -31/19 -1/1 0/1 -44/27 -1/2 1/0 -13/8 -1/1 0/1 -34/21 -1/2 1/0 -89/55 -1/1 0/1 -55/34 1/0 -76/47 -3/2 1/0 -21/13 -1/1 0/1 -50/31 -3/2 1/0 -79/49 -2/1 -5/3 -29/18 -6/5 -1/1 -66/41 -1/1 -37/23 -1/1 -10/11 -8/5 -3/4 -1/2 -35/22 -2/3 -3/5 -132/83 -5/8 -1/2 -97/61 -2/3 -3/5 -62/39 -5/8 -1/2 -27/17 -2/3 -3/5 -46/29 -5/8 -1/2 -19/12 -3/5 -4/7 -11/7 -1/2 -25/16 -5/11 -4/9 -14/9 -1/2 -5/12 -17/11 -2/5 -1/3 -20/13 -3/8 -5/14 -23/15 -1/3 -6/19 -3/2 -1/3 0/1 -22/15 0/1 -19/13 0/1 1/5 -16/11 1/2 1/0 -45/31 0/1 1/3 -29/20 0/1 1/1 -13/9 -1/1 0/1 -23/16 -1/1 0/1 -33/23 1/0 -43/30 -1/1 0/1 -10/7 -1/2 1/0 -27/19 -1/1 0/1 -44/31 -1/2 1/0 -17/12 -1/1 0/1 -41/29 -1/3 0/1 -65/46 -1/9 0/1 -24/17 1/2 1/0 -31/22 -3/1 -2/1 -7/5 -1/1 -2/3 -25/18 -1/1 -2/3 -68/49 -7/10 -11/16 -111/80 -29/43 -2/3 -154/111 -2/3 -43/31 -2/3 -11/17 -61/44 -2/3 -3/5 -18/13 -5/8 -1/2 -11/8 -1/2 -26/19 -1/2 -7/16 -41/30 -3/7 -2/5 -15/11 -3/7 -2/5 -49/36 -2/5 -1/3 -132/97 -1/2 -3/8 -83/61 -2/5 -1/3 -34/25 -1/2 -3/8 -19/14 -1/3 0/1 -42/31 -1/2 -3/8 -65/48 -2/5 -1/3 -88/65 -1/2 -3/8 -23/17 -2/5 -1/3 -4/3 -1/2 -1/4 -21/16 -1/5 0/1 -17/13 -1/5 0/1 -30/23 -1/6 -1/8 -103/79 -1/7 0/1 -176/135 -1/6 -1/8 -73/56 -1/7 0/1 -43/33 -1/5 0/1 -13/10 -1/9 0/1 -22/17 0/1 -9/7 0/1 1/3 -50/39 1/2 1/0 -91/71 0/1 1/1 -132/103 1/2 1/0 -41/32 0/1 1/1 -32/25 1/2 1/0 -55/43 1/0 -23/18 -1/1 0/1 -37/29 0/1 1/1 -88/69 1/2 1/0 -51/40 0/1 1/1 -14/11 1/2 1/0 -19/15 -2/1 -1/1 -43/34 -8/7 -1/1 -110/87 -1/1 -67/53 -1/1 -12/13 -24/19 -3/4 -1/2 -29/23 0/1 1/1 -5/4 -1/1 0/1 -21/17 -1/1 -4/5 -16/13 -3/4 -1/2 -11/9 -1/2 -28/23 -1/2 -5/12 -45/37 -7/17 -2/5 -17/14 -2/5 -1/3 -23/19 -2/5 -1/3 -6/5 -1/2 -1/4 -25/21 -1/3 0/1 -44/37 -1/2 -1/4 -19/16 -1/3 0/1 -13/11 -1/3 -2/7 -20/17 -1/4 -3/14 -7/6 -1/7 0/1 -22/19 0/1 -15/13 0/1 1/9 -8/7 1/2 1/0 -9/8 -1/1 0/1 -10/9 -1/2 1/0 -1/1 -1/1 0/1 0/1 -1/2 1/0 1/1 -1/1 0/1 9/8 -1/1 0/1 8/7 -1/2 -1/4 7/6 0/1 1/5 13/11 2/3 1/1 6/5 1/2 1/0 23/19 1/1 2/1 17/14 1/1 2/1 11/9 1/0 27/22 -3/1 -2/1 43/35 -2/1 -5/3 16/13 -3/2 1/0 5/4 -1/1 0/1 24/19 -3/2 1/0 19/15 -1/1 -2/3 14/11 -1/2 -1/4 23/18 -1/1 0/1 32/25 -1/2 -1/4 9/7 -1/5 0/1 22/17 0/1 13/10 0/1 1/7 17/13 0/1 1/3 21/16 0/1 1/3 4/3 1/2 1/0 23/17 1/1 2/1 19/14 0/1 1/1 34/25 3/2 1/0 49/36 1/1 2/1 15/11 2/1 3/1 11/8 1/0 29/21 -4/1 -3/1 47/34 -4/1 -3/1 18/13 -5/2 1/0 7/5 -2/1 -1/1 24/17 -1/2 -1/4 17/12 -1/1 0/1 10/7 -1/2 1/0 13/9 -1/1 0/1 29/20 -1/3 0/1 45/31 -1/5 0/1 16/11 -1/2 -1/4 3/2 0/1 1/1 17/11 1/1 2/1 31/20 2/1 7/3 14/9 5/2 1/0 11/7 1/0 30/19 -11/2 1/0 19/12 -4/1 -3/1 65/41 -3/1 -2/1 46/29 -5/2 1/0 27/17 -3/1 -2/1 62/39 -5/2 1/0 35/22 -3/1 -2/1 8/5 -3/2 1/0 29/18 -1/1 -6/7 50/31 -3/4 -1/2 21/13 -1/1 0/1 13/8 -1/1 0/1 18/11 -1/2 1/0 41/25 -1/3 0/1 23/14 0/1 1/3 5/3 -1/1 0/1 22/13 0/1 17/10 0/1 1/3 46/27 1/4 1/2 29/17 0/1 1/1 41/24 0/1 1/1 53/31 -1/1 0/1 12/7 1/2 1/0 55/32 1/0 43/25 -1/1 0/1 117/68 0/1 1/1 74/43 1/2 1/0 31/18 0/1 1/3 19/11 0/1 1/1 7/4 0/1 1/1 23/13 2/3 1/1 16/9 1/2 1/0 25/14 1/1 4/3 34/19 3/2 1/0 9/5 1/1 2/1 47/26 2/1 3/1 38/21 5/2 1/0 29/16 3/1 10/3 20/11 9/2 1/0 11/6 1/0 24/13 -11/2 1/0 13/7 -3/1 -2/1 15/8 -2/1 -1/1 2/1 -1/2 1/0 15/7 0/1 1/1 13/6 1/1 2/1 11/5 1/0 31/14 -9/1 -8/1 20/9 -11/2 1/0 49/22 -5/1 -4/1 29/13 -13/3 -4/1 9/4 -3/1 -2/1 43/19 -3/1 -2/1 34/15 -5/2 1/0 25/11 -7/3 -2/1 66/29 -2/1 41/18 -2/1 -9/5 16/7 -3/2 1/0 23/10 -2/1 -5/3 30/13 -3/2 1/0 7/3 -2/1 -1/1 26/11 -5/2 1/0 71/30 -3/1 -2/1 45/19 -11/5 -2/1 19/8 -2/1 -1/1 50/21 -3/2 1/0 31/13 -4/3 -1/1 43/18 -1/1 0/1 55/23 1/0 12/5 -3/2 1/0 41/17 -2/1 -1/1 29/12 -2/1 -1/1 46/19 -3/2 -5/4 17/7 -4/3 -1/1 22/9 -1/1 5/2 -1/1 0/1 28/11 -3/2 1/0 23/9 -4/3 -1/1 41/16 -1/1 -2/3 18/7 -1/2 1/0 31/12 -1/1 0/1 44/17 -1/2 1/0 13/5 -1/1 0/1 34/13 -1/2 1/0 89/34 -1/1 0/1 55/21 -1/2 76/29 -1/2 -1/4 21/8 -1/1 0/1 50/19 -1/2 -1/4 79/30 -1/3 -2/7 29/11 -1/7 0/1 66/25 0/1 37/14 0/1 1/9 8/3 1/2 1/0 35/13 1/1 2/1 132/49 3/2 1/0 97/36 1/1 2/1 62/23 3/2 1/0 27/10 1/1 2/1 46/17 3/2 1/0 19/7 2/1 3/1 11/4 1/0 25/9 -6/1 -5/1 14/5 -7/2 1/0 17/6 -3/1 -2/1 20/7 -5/2 -9/4 23/8 -2/1 -13/7 3/1 -2/1 -1/1 22/7 -1/1 19/6 -1/1 -6/7 16/5 -3/4 -1/2 45/14 -1/1 -4/5 29/9 -1/1 -2/3 13/4 -1/1 0/1 23/7 -1/1 0/1 33/10 -1/2 43/13 -1/1 0/1 10/3 -1/2 1/0 27/8 -1/1 0/1 44/13 -1/2 1/0 17/5 -1/1 0/1 41/12 -2/1 -1/1 65/19 -8/7 -1/1 24/7 -3/4 -1/2 31/9 -2/5 -1/3 7/2 0/1 1/1 25/7 0/1 1/1 68/19 3/4 5/6 111/31 14/15 1/1 154/43 1/1 43/12 1/1 6/5 61/17 1/1 2/1 18/5 3/2 1/0 11/3 1/0 26/7 -9/2 1/0 41/11 -4/1 -3/1 15/4 -4/1 -3/1 49/13 -3/1 -2/1 132/35 -5/2 1/0 83/22 -3/1 -2/1 34/9 -5/2 1/0 19/5 -2/1 -1/1 42/11 -5/2 1/0 65/17 -3/1 -2/1 88/23 -5/2 1/0 23/6 -3/1 -2/1 4/1 -3/2 1/0 21/5 -4/3 -1/1 17/4 -4/3 -1/1 30/7 -5/4 -7/6 103/24 -6/5 -1/1 176/41 -5/4 -7/6 73/17 -6/5 -1/1 43/10 -4/3 -1/1 13/3 -8/7 -1/1 22/5 -1/1 9/2 -1/1 -4/5 50/11 -3/4 -1/2 91/20 -1/1 -2/3 132/29 -3/4 -1/2 41/9 -1/1 -2/3 32/7 -3/4 -1/2 55/12 -1/2 23/5 -1/1 0/1 37/8 -1/1 -2/3 88/19 -3/4 -1/2 51/11 -1/1 -2/3 14/3 -3/4 -1/2 19/4 -1/3 0/1 43/9 -1/9 0/1 110/23 0/1 67/14 0/1 1/11 24/5 1/2 1/0 29/6 -1/1 -2/3 5/1 -1/1 0/1 21/4 0/1 1/3 16/3 1/2 1/0 11/2 1/0 28/5 -7/2 1/0 45/8 -10/3 -3/1 17/3 -3/1 -2/1 23/4 -3/1 -2/1 6/1 -3/2 1/0 25/4 -2/1 -1/1 44/7 -3/2 1/0 19/3 -2/1 -1/1 13/2 -2/1 -5/3 20/3 -3/2 -11/8 7/1 -6/5 -1/1 22/3 -1/1 15/2 -1/1 -10/11 8/1 -3/4 -1/2 9/1 -1/1 0/1 10/1 -1/2 1/0 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(43,396,-24,-221) (-9/1,1/0) -> (-9/5,-43/24) Hyperbolic Matrix(43,352,16,131) (-9/1,-8/1) -> (8/3,35/13) Hyperbolic Matrix(45,352,-28,-219) (-8/1,-7/1) -> (-37/23,-8/5) Hyperbolic Matrix(45,308,-32,-219) (-7/1,-13/2) -> (-31/22,-7/5) Hyperbolic Matrix(131,836,-76,-485) (-13/2,-6/1) -> (-50/29,-31/18) Hyperbolic Matrix(221,1276,84,485) (-6/1,-23/4) -> (21/8,50/19) Hyperbolic Matrix(131,748,100,571) (-23/4,-17/3) -> (17/13,21/16) Hyperbolic Matrix(87,484,-16,-89) (-17/3,-11/2) -> (-11/2,-27/5) Parabolic Matrix(703,3784,196,1055) (-27/5,-43/8) -> (43/12,61/17) Hyperbolic Matrix(263,1408,82,439) (-43/8,-16/3) -> (16/5,45/14) Hyperbolic Matrix(43,220,-26,-133) (-16/3,-5/1) -> (-5/3,-28/17) Hyperbolic Matrix(265,1276,-146,-703) (-5/1,-24/5) -> (-20/11,-49/27) Hyperbolic Matrix(397,1892,-286,-1363) (-24/5,-19/4) -> (-25/18,-68/49) Hyperbolic Matrix(177,836,112,529) (-19/4,-14/3) -> (30/19,19/12) Hyperbolic Matrix(219,1012,-124,-573) (-14/3,-23/5) -> (-23/13,-30/17) Hyperbolic Matrix(527,2420,-326,-1497) (-23/5,-32/7) -> (-76/47,-21/13) Hyperbolic Matrix(395,1804,-164,-749) (-32/7,-9/2) -> (-53/22,-12/5) Hyperbolic Matrix(89,396,20,89) (-9/2,-22/5) -> (22/5,9/2) Hyperbolic Matrix(131,572,30,131) (-22/5,-13/3) -> (13/3,22/5) Hyperbolic Matrix(175,748,-62,-265) (-13/3,-17/4) -> (-17/6,-31/11) Hyperbolic Matrix(177,748,146,617) (-17/4,-21/5) -> (23/19,17/14) Hyperbolic Matrix(43,176,32,131) (-21/5,-4/1) -> (4/3,23/17) Hyperbolic Matrix(45,176,34,133) (-4/1,-23/6) -> (21/16,4/3) Hyperbolic Matrix(439,1672,-162,-617) (-23/6,-19/5) -> (-19/7,-65/24) Hyperbolic Matrix(395,1496,174,659) (-19/5,-34/9) -> (34/15,25/11) Hyperbolic Matrix(1189,4488,-874,-3299) (-34/9,-49/13) -> (-83/61,-34/25) Hyperbolic Matrix(397,1496,82,309) (-49/13,-15/4) -> (29/6,5/1) Hyperbolic Matrix(131,484,-36,-133) (-15/4,-11/3) -> (-11/3,-29/8) Parabolic Matrix(705,2552,292,1057) (-29/8,-47/13) -> (41/17,29/12) Hyperbolic Matrix(439,1584,268,967) (-47/13,-18/5) -> (18/11,41/25) Hyperbolic Matrix(87,308,-50,-177) (-18/5,-7/2) -> (-7/4,-26/15) Hyperbolic Matrix(89,308,-76,-263) (-7/2,-24/7) -> (-20/17,-7/6) Hyperbolic Matrix(219,748,-142,-485) (-24/7,-17/5) -> (-17/11,-20/13) Hyperbolic Matrix(131,440,-92,-309) (-17/5,-10/3) -> (-10/7,-27/19) Hyperbolic Matrix(175,572,-108,-353) (-10/3,-13/4) -> (-13/8,-34/21) Hyperbolic Matrix(177,572,82,265) (-13/4,-29/9) -> (15/7,13/6) Hyperbolic Matrix(2025,6512,-848,-2727) (-29/9,-45/14) -> (-43/18,-117/49) Hyperbolic Matrix(617,1980,110,353) (-45/14,-16/5) -> (28/5,45/8) Hyperbolic Matrix(221,704,-124,-395) (-16/5,-3/1) -> (-41/23,-16/9) Hyperbolic Matrix(263,748,-186,-529) (-3/1,-17/6) -> (-17/12,-41/29) Hyperbolic Matrix(969,2728,-406,-1143) (-31/11,-14/5) -> (-74/31,-31/13) Hyperbolic Matrix(175,484,-64,-177) (-14/5,-11/4) -> (-11/4,-30/11) Parabolic Matrix(307,836,242,659) (-30/11,-19/7) -> (19/15,14/11) Hyperbolic Matrix(2113,5720,-1560,-4223) (-65/24,-46/17) -> (-42/31,-65/48) Hyperbolic Matrix(749,2024,440,1189) (-46/17,-27/10) -> (17/10,46/27) Hyperbolic Matrix(1893,5104,800,2157) (-27/10,-62/23) -> (26/11,71/30) Hyperbolic Matrix(3037,8184,-1910,-5147) (-62/23,-35/13) -> (-97/61,-62/39) Hyperbolic Matrix(131,352,16,43) (-35/13,-8/3) -> (8/1,9/1) Hyperbolic Matrix(133,352,-116,-307) (-8/3,-29/11) -> (-15/13,-8/7) Hyperbolic Matrix(969,2552,-434,-1143) (-29/11,-50/19) -> (-38/17,-29/13) Hyperbolic Matrix(485,1276,84,221) (-50/19,-21/8) -> (23/4,6/1) Hyperbolic Matrix(219,572,-152,-397) (-21/8,-13/5) -> (-13/9,-23/16) Hyperbolic Matrix(307,792,-188,-485) (-13/5,-18/7) -> (-18/11,-31/19) Hyperbolic Matrix(617,1584,446,1145) (-18/7,-41/16) -> (47/34,18/13) Hyperbolic Matrix(395,1012,-258,-661) (-41/16,-23/9) -> (-23/15,-3/2) Hyperbolic Matrix(87,220,-70,-177) (-23/9,-5/2) -> (-5/4,-21/17) Hyperbolic Matrix(89,220,36,89) (-5/2,-22/9) -> (22/9,5/2) Hyperbolic Matrix(307,748,126,307) (-22/9,-17/7) -> (17/7,22/9) Hyperbolic Matrix(835,2024,526,1275) (-17/7,-46/19) -> (46/29,27/17) Hyperbolic Matrix(309,748,164,397) (-46/19,-29/12) -> (15/8,2/1) Hyperbolic Matrix(747,1804,200,483) (-29/12,-41/17) -> (41/11,15/4) Hyperbolic Matrix(1187,2860,-530,-1277) (-41/17,-53/22) -> (-9/4,-47/21) Hyperbolic Matrix(2023,4840,772,1847) (-12/5,-55/23) -> (55/21,76/29) Hyperbolic Matrix(3037,7260,1160,2773) (-55/23,-43/18) -> (89/34,55/21) Hyperbolic Matrix(4663,11132,-3576,-8537) (-117/49,-74/31) -> (-30/23,-103/79) Hyperbolic Matrix(351,836,-296,-705) (-31/13,-19/8) -> (-19/16,-13/11) Hyperbolic Matrix(131,308,-94,-221) (-19/8,-7/3) -> (-7/5,-25/18) Hyperbolic Matrix(439,1012,-344,-793) (-7/3,-23/10) -> (-23/18,-37/29) Hyperbolic Matrix(441,1012,-268,-615) (-23/10,-16/7) -> (-28/17,-23/14) Hyperbolic Matrix(309,704,-212,-483) (-16/7,-25/11) -> (-19/13,-16/11) Hyperbolic Matrix(659,1496,174,395) (-25/11,-34/15) -> (34/9,19/5) Hyperbolic Matrix(175,396,-156,-353) (-34/15,-9/4) -> (-9/8,-10/9) Hyperbolic Matrix(2597,5808,-2026,-4531) (-47/21,-38/17) -> (-50/39,-91/71) Hyperbolic Matrix(573,1276,-454,-1011) (-29/13,-20/9) -> (-24/19,-29/23) Hyperbolic Matrix(219,484,-100,-221) (-20/9,-11/5) -> (-11/5,-24/11) Parabolic Matrix(263,572,40,87) (-24/11,-13/6) -> (13/2,20/3) Hyperbolic Matrix(265,572,82,177) (-13/6,-15/7) -> (29/9,13/4) Hyperbolic Matrix(351,748,206,439) (-15/7,-2/1) -> (46/27,29/17) Hyperbolic Matrix(397,748,164,309) (-2/1,-15/8) -> (29/12,46/19) Hyperbolic Matrix(307,572,212,395) (-15/8,-13/7) -> (13/9,29/20) Hyperbolic Matrix(263,484,-144,-265) (-13/7,-11/6) -> (-11/6,-31/17) Parabolic Matrix(749,1364,218,397) (-31/17,-20/11) -> (24/7,31/9) Hyperbolic Matrix(1189,2156,316,573) (-49/27,-29/16) -> (15/4,49/13) Hyperbolic Matrix(1409,2552,-874,-1583) (-29/16,-9/5) -> (-79/49,-29/18) Hyperbolic Matrix(2507,4488,958,1715) (-43/24,-34/19) -> (34/13,89/34) Hyperbolic Matrix(837,1496,616,1101) (-34/19,-25/14) -> (19/14,34/25) Hyperbolic Matrix(1011,1804,320,571) (-25/14,-66/37) -> (22/7,19/6) Hyperbolic Matrix(617,1100,198,353) (-66/37,-41/23) -> (3/1,22/7) Hyperbolic Matrix(397,704,-322,-571) (-16/9,-23/13) -> (-21/17,-16/13) Hyperbolic Matrix(923,1628,-724,-1277) (-30/17,-7/4) -> (-51/40,-14/11) Hyperbolic Matrix(2947,5104,1854,3211) (-26/15,-71/41) -> (27/17,62/39) Hyperbolic Matrix(2287,3960,406,703) (-71/41,-45/26) -> (45/8,17/3) Hyperbolic Matrix(967,1672,-764,-1321) (-45/26,-19/11) -> (-19/15,-43/34) Hyperbolic Matrix(791,1364,-664,-1145) (-19/11,-50/29) -> (-6/5,-25/21) Hyperbolic Matrix(1099,1892,-844,-1453) (-31/18,-43/25) -> (-43/33,-13/10) Hyperbolic Matrix(2201,3784,666,1145) (-43/25,-55/32) -> (33/10,43/13) Hyperbolic Matrix(1409,2420,308,529) (-55/32,-12/7) -> (32/7,55/12) Hyperbolic Matrix(1055,1804,-824,-1409) (-12/7,-41/24) -> (-41/32,-32/25) Hyperbolic Matrix(1495,2552,1082,1847) (-41/24,-29/17) -> (29/21,47/34) Hyperbolic Matrix(439,748,206,351) (-29/17,-46/27) -> (2/1,15/7) Hyperbolic Matrix(1189,2024,440,749) (-46/27,-17/10) -> (27/10,46/17) Hyperbolic Matrix(441,748,260,441) (-17/10,-22/13) -> (22/13,17/10) Hyperbolic Matrix(131,220,78,131) (-22/13,-5/3) -> (5/3,22/13) Hyperbolic Matrix(2199,3608,-1556,-2553) (-23/14,-41/25) -> (-41/29,-65/46) Hyperbolic Matrix(1101,1804,296,485) (-41/25,-18/11) -> (26/7,41/11) Hyperbolic Matrix(1187,1936,458,747) (-31/19,-44/27) -> (44/17,13/5) Hyperbolic Matrix(1189,1936,460,749) (-44/27,-13/8) -> (31/12,44/17) Hyperbolic Matrix(2773,4488,1224,1981) (-34/21,-89/55) -> (43/19,34/15) Hyperbolic Matrix(4487,7260,2610,4223) (-89/55,-55/34) -> (55/32,43/25) Hyperbolic Matrix(2993,4840,1742,2817) (-55/34,-76/47) -> (12/7,55/32) Hyperbolic Matrix(791,1276,654,1055) (-21/13,-50/31) -> (6/5,23/19) Hyperbolic Matrix(2729,4400,-2128,-3431) (-50/31,-79/49) -> (-9/7,-50/39) Hyperbolic Matrix(1011,1628,136,219) (-29/18,-66/41) -> (22/3,15/2) Hyperbolic Matrix(793,1276,110,177) (-66/41,-37/23) -> (7/1,22/3) Hyperbolic Matrix(221,352,194,309) (-8/5,-35/22) -> (9/8,8/7) Hyperbolic Matrix(10955,17424,4066,6467) (-35/22,-132/83) -> (132/49,97/36) Hyperbolic Matrix(10957,17424,4068,6469) (-132/83,-97/61) -> (35/13,132/49) Hyperbolic Matrix(2685,4268,748,1189) (-62/39,-27/17) -> (61/17,18/5) Hyperbolic Matrix(1275,2024,526,835) (-27/17,-46/29) -> (46/19,17/7) Hyperbolic Matrix(1055,1672,-778,-1233) (-46/29,-19/12) -> (-19/14,-42/31) Hyperbolic Matrix(307,484,-196,-309) (-19/12,-11/7) -> (-11/7,-25/16) Parabolic Matrix(395,616,84,131) (-25/16,-14/9) -> (14/3,19/4) Hyperbolic Matrix(483,748,-370,-573) (-14/9,-17/11) -> (-17/13,-30/23) Hyperbolic Matrix(1231,1892,-974,-1497) (-20/13,-23/15) -> (-67/53,-24/19) Hyperbolic Matrix(747,1100,328,483) (-3/2,-22/15) -> (66/29,41/18) Hyperbolic Matrix(1233,1804,542,793) (-22/15,-19/13) -> (25/11,66/29) Hyperbolic Matrix(969,1408,788,1145) (-16/11,-45/31) -> (43/35,16/13) Hyperbolic Matrix(3123,4532,-2396,-3477) (-45/31,-29/20) -> (-73/56,-43/33) Hyperbolic Matrix(395,572,212,307) (-29/20,-13/9) -> (13/7,15/8) Hyperbolic Matrix(1409,2024,-1102,-1583) (-23/16,-33/23) -> (-55/43,-23/18) Hyperbolic Matrix(2639,3784,1104,1583) (-33/23,-43/30) -> (43/18,55/23) Hyperbolic Matrix(307,440,30,43) (-43/30,-10/7) -> (10/1,1/0) Hyperbolic Matrix(1363,1936,402,571) (-27/19,-44/31) -> (44/13,17/5) Hyperbolic Matrix(1365,1936,404,573) (-44/31,-17/12) -> (27/8,44/13) Hyperbolic Matrix(5015,7084,-3614,-5105) (-65/46,-24/17) -> (-68/49,-111/80) Hyperbolic Matrix(967,1364,436,615) (-24/17,-31/22) -> (31/14,20/9) Hyperbolic Matrix(16237,22528,3394,4709) (-111/80,-154/111) -> (110/23,67/14) Hyperbolic Matrix(8183,11352,1712,2375) (-154/111,-43/31) -> (43/9,110/23) Hyperbolic Matrix(2729,3784,2222,3081) (-43/31,-61/44) -> (27/22,43/35) Hyperbolic Matrix(3079,4268,1142,1583) (-61/44,-18/13) -> (62/23,27/10) Hyperbolic Matrix(351,484,-256,-353) (-18/13,-11/8) -> (-11/8,-26/19) Parabolic Matrix(1319,1804,514,703) (-26/19,-41/30) -> (41/16,18/7) Hyperbolic Matrix(1321,1804,774,1057) (-41/30,-15/11) -> (29/17,41/24) Hyperbolic Matrix(1583,2156,710,967) (-15/11,-49/36) -> (49/22,29/13) Hyperbolic Matrix(12803,17424,3394,4619) (-49/36,-132/97) -> (132/35,83/22) Hyperbolic Matrix(12805,17424,3396,4621) (-132/97,-83/61) -> (49/13,132/35) Hyperbolic Matrix(1101,1496,616,837) (-34/25,-19/14) -> (25/14,34/19) Hyperbolic Matrix(5719,7744,1494,2023) (-65/48,-88/65) -> (88/23,23/6) Hyperbolic Matrix(5721,7744,1496,2025) (-88/65,-23/17) -> (65/17,88/23) Hyperbolic Matrix(131,176,32,43) (-23/17,-4/3) -> (4/1,21/5) Hyperbolic Matrix(133,176,34,45) (-4/3,-21/16) -> (23/6,4/1) Hyperbolic Matrix(571,748,100,131) (-21/16,-17/13) -> (17/3,23/4) Hyperbolic Matrix(23759,30976,5534,7215) (-103/79,-176/135) -> (176/41,73/17) Hyperbolic Matrix(23761,30976,5536,7217) (-176/135,-73/56) -> (103/24,176/41) Hyperbolic Matrix(441,572,340,441) (-13/10,-22/17) -> (22/17,13/10) Hyperbolic Matrix(307,396,238,307) (-22/17,-9/7) -> (9/7,22/17) Hyperbolic Matrix(13595,17424,2986,3827) (-91/71,-132/103) -> (132/29,41/9) Hyperbolic Matrix(13597,17424,2988,3829) (-132/103,-41/32) -> (91/20,132/29) Hyperbolic Matrix(1891,2420,790,1011) (-32/25,-55/43) -> (55/23,12/5) Hyperbolic Matrix(6071,7744,1310,1671) (-37/29,-88/69) -> (88/19,51/11) Hyperbolic Matrix(6073,7744,1312,1673) (-88/69,-51/40) -> (37/8,88/19) Hyperbolic Matrix(485,616,174,221) (-14/11,-19/15) -> (25/9,14/5) Hyperbolic Matrix(8977,11352,2506,3169) (-43/34,-110/87) -> (154/43,43/12) Hyperbolic Matrix(17819,22528,4976,6291) (-110/87,-67/53) -> (111/31,154/43) Hyperbolic Matrix(1187,1496,872,1099) (-29/23,-5/4) -> (49/36,15/11) Hyperbolic Matrix(395,484,-324,-397) (-16/13,-11/9) -> (-11/9,-28/23) Parabolic Matrix(1627,1980,1120,1363) (-28/23,-45/37) -> (45/31,16/11) Hyperbolic Matrix(3257,3960,1376,1673) (-45/37,-17/14) -> (71/30,45/19) Hyperbolic Matrix(617,748,146,177) (-17/14,-23/19) -> (21/5,17/4) Hyperbolic Matrix(1055,1276,654,791) (-23/19,-6/5) -> (50/31,21/13) Hyperbolic Matrix(1627,1936,258,307) (-25/21,-44/37) -> (44/7,19/3) Hyperbolic Matrix(1629,1936,260,309) (-44/37,-19/16) -> (25/4,44/7) Hyperbolic Matrix(485,572,262,309) (-13/11,-20/17) -> (24/13,13/7) Hyperbolic Matrix(1099,1276,416,483) (-7/6,-22/19) -> (66/25,37/14) Hyperbolic Matrix(1409,1628,534,617) (-22/19,-15/13) -> (29/11,66/25) Hyperbolic Matrix(309,352,194,221) (-8/7,-9/8) -> (35/22,8/5) Hyperbolic Matrix(397,440,120,133) (-10/9,-1/1) -> (43/13,10/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(353,-396,156,-175) (1/1,9/8) -> (9/4,43/19) Hyperbolic Matrix(307,-352,116,-133) (8/7,7/6) -> (37/14,8/3) Hyperbolic Matrix(263,-308,76,-89) (7/6,13/11) -> (31/9,7/2) Hyperbolic Matrix(705,-836,296,-351) (13/11,6/5) -> (50/21,31/13) Hyperbolic Matrix(397,-484,324,-395) (17/14,11/9) -> (11/9,27/22) Parabolic Matrix(177,-220,70,-87) (16/13,5/4) -> (5/2,28/11) Hyperbolic Matrix(1011,-1276,454,-573) (5/4,24/19) -> (20/9,49/22) Hyperbolic Matrix(1495,-1892,418,-529) (24/19,19/15) -> (25/7,68/19) Hyperbolic Matrix(793,-1012,344,-439) (14/11,23/18) -> (23/10,30/13) Hyperbolic Matrix(1893,-2420,722,-923) (23/18,32/25) -> (76/29,21/8) Hyperbolic Matrix(1409,-1804,824,-1055) (32/25,9/7) -> (53/31,12/7) Hyperbolic Matrix(573,-748,370,-483) (13/10,17/13) -> (17/11,31/20) Hyperbolic Matrix(1233,-1672,778,-1055) (23/17,19/14) -> (19/12,65/41) Hyperbolic Matrix(3299,-4488,874,-1189) (34/25,49/36) -> (83/22,34/9) Hyperbolic Matrix(353,-484,256,-351) (15/11,11/8) -> (11/8,29/21) Parabolic Matrix(221,-308,94,-131) (18/13,7/5) -> (7/3,26/11) Hyperbolic Matrix(219,-308,32,-45) (7/5,24/17) -> (20/3,7/1) Hyperbolic Matrix(529,-748,186,-263) (24/17,17/12) -> (17/6,20/7) Hyperbolic Matrix(309,-440,92,-131) (17/12,10/7) -> (10/3,27/8) Hyperbolic Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(4487,-6512,2608,-3785) (29/20,45/31) -> (43/25,117/68) Hyperbolic Matrix(483,-704,212,-309) (16/11,3/2) -> (41/18,16/7) Hyperbolic Matrix(485,-748,142,-219) (3/2,17/11) -> (17/5,41/12) Hyperbolic Matrix(1759,-2728,1022,-1585) (31/20,14/9) -> (74/43,31/18) Hyperbolic Matrix(309,-484,196,-307) (14/9,11/7) -> (11/7,30/19) Parabolic Matrix(3607,-5720,944,-1497) (65/41,46/29) -> (42/11,65/17) Hyperbolic Matrix(5147,-8184,1910,-3037) (62/39,35/22) -> (97/36,62/23) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(1583,-2552,874,-1409) (29/18,50/31) -> (38/21,29/16) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(485,-792,188,-307) (13/8,18/11) -> (18/7,31/12) Hyperbolic Matrix(617,-1012,214,-351) (41/25,23/14) -> (23/8,3/1) Hyperbolic Matrix(133,-220,26,-43) (23/14,5/3) -> (5/1,21/4) Hyperbolic Matrix(1673,-2860,926,-1583) (41/24,53/31) -> (9/5,47/26) Hyperbolic Matrix(6469,-11132,1508,-2595) (117/68,74/43) -> (30/7,103/24) Hyperbolic Matrix(485,-836,76,-131) (31/18,19/11) -> (19/3,13/2) Hyperbolic Matrix(177,-308,50,-87) (19/11,7/4) -> (7/2,25/7) Hyperbolic Matrix(573,-1012,124,-219) (7/4,23/13) -> (23/5,37/8) Hyperbolic Matrix(571,-1012,224,-397) (23/13,16/9) -> (28/11,23/9) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(221,-396,24,-43) (34/19,9/5) -> (9/1,10/1) Hyperbolic Matrix(3211,-5808,706,-1277) (47/26,38/21) -> (50/11,91/20) Hyperbolic Matrix(703,-1276,146,-265) (29/16,20/11) -> (24/5,29/6) Hyperbolic Matrix(265,-484,144,-263) (20/11,11/6) -> (11/6,24/13) Parabolic Matrix(221,-484,100,-219) (13/6,11/5) -> (11/5,31/14) Parabolic Matrix(1143,-2552,434,-969) (29/13,9/4) -> (79/30,29/11) Hyperbolic Matrix(307,-704,58,-133) (16/7,23/10) -> (21/4,16/3) Hyperbolic Matrix(705,-1628,152,-351) (30/13,7/3) -> (51/11,14/3) Hyperbolic Matrix(705,-1672,148,-351) (45/19,19/8) -> (19/4,43/9) Hyperbolic Matrix(573,-1364,92,-219) (19/8,50/21) -> (6/1,25/4) Hyperbolic Matrix(793,-1892,184,-439) (31/13,43/18) -> (43/10,13/3) Hyperbolic Matrix(749,-1804,164,-395) (12/5,41/17) -> (41/9,32/7) Hyperbolic Matrix(1409,-3608,412,-1055) (23/9,41/16) -> (41/12,65/19) Hyperbolic Matrix(1671,-4400,368,-969) (50/19,79/30) -> (9/2,50/11) Hyperbolic Matrix(617,-1672,162,-439) (46/17,19/7) -> (19/5,42/11) Hyperbolic Matrix(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(265,-748,62,-175) (14/5,17/6) -> (17/4,30/7) Hyperbolic Matrix(661,-1892,138,-395) (20/7,23/8) -> (67/14,24/5) Hyperbolic Matrix(1409,-4532,328,-1055) (45/14,29/9) -> (73/17,43/10) Hyperbolic Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(2069,-7084,578,-1979) (65/19,24/7) -> (68/19,111/31) Hyperbolic Matrix(133,-484,36,-131) (18/5,11/3) -> (11/3,26/7) Parabolic Matrix(89,-484,16,-87) (16/3,11/2) -> (11/2,28/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(43,396,-24,-221) -> Matrix(3,2,-8,-5) Matrix(43,352,16,131) -> Matrix(1,2,0,1) Matrix(45,352,-28,-219) -> Matrix(3,4,-4,-5) Matrix(45,308,-32,-219) -> Matrix(5,4,-4,-3) Matrix(131,836,-76,-485) -> Matrix(3,2,-8,-5) Matrix(221,1276,84,485) -> Matrix(3,2,-8,-5) Matrix(131,748,100,571) -> Matrix(3,2,4,3) Matrix(87,484,-16,-89) -> Matrix(7,4,-16,-9) Matrix(703,3784,196,1055) -> Matrix(11,4,8,3) Matrix(263,1408,82,439) -> Matrix(5,2,-8,-3) Matrix(43,220,-26,-133) -> Matrix(1,0,0,1) Matrix(265,1276,-146,-703) -> Matrix(7,4,-16,-9) Matrix(397,1892,-286,-1363) -> Matrix(3,-2,-4,3) Matrix(177,836,112,529) -> Matrix(1,-4,0,1) Matrix(219,1012,-124,-573) -> Matrix(1,2,-4,-7) Matrix(527,2420,-326,-1497) -> Matrix(1,0,0,1) Matrix(395,1804,-164,-749) -> Matrix(3,4,-4,-5) Matrix(89,396,20,89) -> Matrix(7,8,-8,-9) Matrix(131,572,30,131) -> Matrix(17,16,-16,-15) Matrix(175,748,-62,-265) -> Matrix(17,14,-28,-23) Matrix(177,748,146,617) -> Matrix(3,2,4,3) Matrix(43,176,32,131) -> Matrix(3,2,4,3) Matrix(45,176,34,133) -> Matrix(3,2,4,3) Matrix(439,1672,-162,-617) -> Matrix(7,4,-16,-9) Matrix(395,1496,174,659) -> Matrix(19,12,-8,-5) Matrix(1189,4488,-874,-3299) -> Matrix(7,4,-16,-9) Matrix(397,1496,82,309) -> Matrix(3,2,-8,-5) Matrix(131,484,-36,-133) -> Matrix(11,6,-24,-13) Matrix(705,2552,292,1057) -> Matrix(19,8,-12,-5) Matrix(439,1584,268,967) -> Matrix(5,2,-8,-3) Matrix(87,308,-50,-177) -> Matrix(1,0,0,1) Matrix(89,308,-76,-263) -> Matrix(1,0,-4,1) Matrix(219,748,-142,-485) -> Matrix(3,2,-8,-5) Matrix(131,440,-92,-309) -> Matrix(1,0,0,1) Matrix(175,572,-108,-353) -> Matrix(1,0,0,1) Matrix(177,572,82,265) -> Matrix(1,2,0,1) Matrix(2025,6512,-848,-2727) -> Matrix(3,4,-4,-5) Matrix(617,1980,110,353) -> Matrix(1,-2,0,1) Matrix(221,704,-124,-395) -> Matrix(1,2,-4,-7) Matrix(263,748,-186,-529) -> Matrix(3,2,-8,-5) Matrix(969,2728,-406,-1143) -> Matrix(3,2,-8,-5) Matrix(175,484,-64,-177) -> Matrix(15,8,-32,-17) Matrix(307,836,242,659) -> Matrix(9,4,-16,-7) Matrix(2113,5720,-1560,-4223) -> Matrix(1,0,0,1) Matrix(749,2024,440,1189) -> Matrix(5,2,12,5) Matrix(1893,5104,800,2157) -> Matrix(21,8,-8,-3) Matrix(3037,8184,-1910,-5147) -> Matrix(9,4,-16,-7) Matrix(131,352,16,43) -> Matrix(5,2,-8,-3) Matrix(133,352,-116,-307) -> Matrix(1,0,4,1) Matrix(969,2552,-434,-1143) -> Matrix(7,-4,-12,7) Matrix(485,1276,84,221) -> Matrix(1,-2,0,1) Matrix(219,572,-152,-397) -> Matrix(1,0,0,1) Matrix(307,792,-188,-485) -> Matrix(1,0,0,1) Matrix(617,1584,446,1145) -> Matrix(1,-2,0,1) Matrix(395,1012,-258,-661) -> Matrix(1,2,-4,-7) Matrix(87,220,-70,-177) -> Matrix(1,0,0,1) Matrix(89,220,36,89) -> Matrix(1,0,0,1) Matrix(307,748,126,307) -> Matrix(9,8,-8,-7) Matrix(835,2024,526,1275) -> Matrix(13,10,-4,-3) Matrix(309,748,164,397) -> Matrix(5,4,-4,-3) Matrix(747,1804,200,483) -> Matrix(13,10,-4,-3) Matrix(1187,2860,-530,-1277) -> Matrix(5,2,-8,-3) Matrix(2023,4840,772,1847) -> Matrix(3,2,-8,-5) Matrix(3037,7260,1160,2773) -> Matrix(1,0,0,1) Matrix(4663,11132,-3576,-8537) -> Matrix(3,2,-20,-13) Matrix(351,836,-296,-705) -> Matrix(3,2,-8,-5) Matrix(131,308,-94,-221) -> Matrix(1,0,0,1) Matrix(439,1012,-344,-793) -> Matrix(3,2,4,3) Matrix(441,1012,-268,-615) -> Matrix(3,2,-8,-5) Matrix(309,704,-212,-483) -> Matrix(3,2,4,3) Matrix(659,1496,174,395) -> Matrix(19,12,-8,-5) Matrix(175,396,-156,-353) -> Matrix(3,2,-8,-5) Matrix(2597,5808,-2026,-4531) -> Matrix(7,4,12,7) Matrix(573,1276,-454,-1011) -> Matrix(7,4,-16,-9) Matrix(219,484,-100,-221) -> Matrix(19,10,-40,-21) Matrix(263,572,40,87) -> Matrix(19,8,-12,-5) Matrix(265,572,82,177) -> Matrix(5,2,-8,-3) Matrix(351,748,206,439) -> Matrix(1,0,4,1) Matrix(397,748,164,309) -> Matrix(5,4,-4,-3) Matrix(307,572,212,395) -> Matrix(3,2,-8,-5) Matrix(263,484,-144,-265) -> Matrix(19,10,-40,-21) Matrix(749,1364,218,397) -> Matrix(13,6,-24,-11) Matrix(1189,2156,316,573) -> Matrix(41,18,-16,-7) Matrix(1409,2552,-874,-1583) -> Matrix(19,8,-12,-5) Matrix(2507,4488,958,1715) -> Matrix(5,2,-8,-3) Matrix(837,1496,616,1101) -> Matrix(11,4,8,3) Matrix(1011,1804,320,571) -> Matrix(29,10,-32,-11) Matrix(617,1100,198,353) -> Matrix(19,6,-16,-5) Matrix(397,704,-322,-571) -> Matrix(5,2,-8,-3) Matrix(923,1628,-724,-1277) -> Matrix(1,0,4,1) Matrix(2947,5104,1854,3211) -> Matrix(21,8,-8,-3) Matrix(2287,3960,406,703) -> Matrix(21,8,-8,-3) Matrix(967,1672,-764,-1321) -> Matrix(7,2,-4,-1) Matrix(791,1364,-664,-1145) -> Matrix(1,0,0,1) Matrix(1099,1892,-844,-1453) -> Matrix(1,0,-4,1) Matrix(2201,3784,666,1145) -> Matrix(1,0,0,1) Matrix(1409,2420,308,529) -> Matrix(5,2,-8,-3) Matrix(1055,1804,-824,-1409) -> Matrix(1,0,4,1) Matrix(1495,2552,1082,1847) -> Matrix(15,4,-4,-1) Matrix(439,748,206,351) -> Matrix(1,0,4,1) Matrix(1189,2024,440,749) -> Matrix(9,2,4,1) Matrix(441,748,260,441) -> Matrix(1,0,8,1) Matrix(131,220,78,131) -> Matrix(1,0,0,1) Matrix(2199,3608,-1556,-2553) -> Matrix(1,0,-4,1) Matrix(1101,1804,296,485) -> Matrix(1,-4,0,1) Matrix(1187,1936,458,747) -> Matrix(1,0,0,1) Matrix(1189,1936,460,749) -> Matrix(1,0,0,1) Matrix(2773,4488,1224,1981) -> Matrix(1,-2,0,1) Matrix(4487,7260,2610,4223) -> Matrix(1,0,0,1) Matrix(2993,4840,1742,2817) -> Matrix(1,2,0,1) Matrix(791,1276,654,1055) -> Matrix(1,2,0,1) Matrix(2729,4400,-2128,-3431) -> Matrix(1,2,0,1) Matrix(1011,1628,136,219) -> Matrix(15,16,-16,-17) Matrix(793,1276,110,177) -> Matrix(17,16,-16,-15) Matrix(221,352,194,309) -> Matrix(3,2,-8,-5) Matrix(10955,17424,4066,6467) -> Matrix(13,8,8,5) Matrix(10957,17424,4068,6469) -> Matrix(13,8,8,5) Matrix(2685,4268,748,1189) -> Matrix(13,8,8,5) Matrix(1275,2024,526,835) -> Matrix(17,10,-12,-7) Matrix(1055,1672,-778,-1233) -> Matrix(7,4,-16,-9) Matrix(307,484,-196,-309) -> Matrix(15,8,-32,-17) Matrix(395,616,84,131) -> Matrix(9,4,-16,-7) Matrix(483,748,-370,-573) -> Matrix(5,2,-28,-11) Matrix(1231,1892,-974,-1497) -> Matrix(17,6,-20,-7) Matrix(747,1100,328,483) -> Matrix(15,2,-8,-1) Matrix(1233,1804,542,793) -> Matrix(17,-2,-8,1) Matrix(969,1408,788,1145) -> Matrix(1,-2,0,1) Matrix(3123,4532,-2396,-3477) -> Matrix(1,0,-8,1) Matrix(395,572,212,307) -> Matrix(1,-2,0,1) Matrix(1409,2024,-1102,-1583) -> Matrix(1,0,0,1) Matrix(2639,3784,1104,1583) -> Matrix(1,0,0,1) Matrix(307,440,30,43) -> Matrix(1,0,0,1) Matrix(1363,1936,402,571) -> Matrix(1,0,0,1) Matrix(1365,1936,404,573) -> Matrix(1,0,0,1) Matrix(5015,7084,-3614,-5105) -> Matrix(11,-2,-16,3) Matrix(967,1364,436,615) -> Matrix(1,-6,0,1) Matrix(16237,22528,3394,4709) -> Matrix(3,2,76,51) Matrix(8183,11352,1712,2375) -> Matrix(3,2,-44,-29) Matrix(2729,3784,2222,3081) -> Matrix(19,12,-8,-5) Matrix(3079,4268,1142,1583) -> Matrix(13,8,8,5) Matrix(351,484,-256,-353) -> Matrix(11,6,-24,-13) Matrix(1319,1804,514,703) -> Matrix(9,4,-16,-7) Matrix(1321,1804,774,1057) -> Matrix(5,2,12,5) Matrix(1583,2156,710,967) -> Matrix(37,14,-8,-3) Matrix(12803,17424,3394,4619) -> Matrix(21,8,-8,-3) Matrix(12805,17424,3396,4621) -> Matrix(21,8,-8,-3) Matrix(1101,1496,616,837) -> Matrix(11,4,8,3) Matrix(5719,7744,1494,2023) -> Matrix(21,8,-8,-3) Matrix(5721,7744,1496,2025) -> Matrix(21,8,-8,-3) Matrix(131,176,32,43) -> Matrix(7,2,-4,-1) Matrix(133,176,34,45) -> Matrix(7,2,-4,-1) Matrix(571,748,100,131) -> Matrix(7,2,-4,-1) Matrix(23759,30976,5534,7215) -> Matrix(43,6,-36,-5) Matrix(23761,30976,5536,7217) -> Matrix(43,6,-36,-5) Matrix(441,572,340,441) -> Matrix(1,0,16,1) Matrix(307,396,238,307) -> Matrix(1,0,-8,1) Matrix(13595,17424,2986,3827) -> Matrix(3,-2,-4,3) Matrix(13597,17424,2988,3829) -> Matrix(3,-2,-4,3) Matrix(1891,2420,790,1011) -> Matrix(1,-2,0,1) Matrix(6071,7744,1310,1671) -> Matrix(3,-2,-4,3) Matrix(6073,7744,1312,1673) -> Matrix(3,-2,-4,3) Matrix(485,616,174,221) -> Matrix(1,-4,0,1) Matrix(8977,11352,2506,3169) -> Matrix(13,14,12,13) Matrix(17819,22528,4976,6291) -> Matrix(27,26,28,27) Matrix(1187,1496,872,1099) -> Matrix(1,2,0,1) Matrix(395,484,-324,-397) -> Matrix(7,4,-16,-9) Matrix(1627,1980,1120,1363) -> Matrix(5,2,-8,-3) Matrix(3257,3960,1376,1673) -> Matrix(21,8,-8,-3) Matrix(617,748,146,177) -> Matrix(7,2,-4,-1) Matrix(1055,1276,654,791) -> Matrix(5,2,-8,-3) Matrix(1627,1936,258,307) -> Matrix(7,2,-4,-1) Matrix(1629,1936,260,309) -> Matrix(7,2,-4,-1) Matrix(485,572,262,309) -> Matrix(15,4,-4,-1) Matrix(1099,1276,416,483) -> Matrix(1,0,16,1) Matrix(1409,1628,534,617) -> Matrix(1,0,-16,1) Matrix(309,352,194,221) -> Matrix(1,-2,0,1) Matrix(397,440,120,133) -> Matrix(1,0,0,1) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(353,-396,156,-175) -> Matrix(1,-2,0,1) Matrix(307,-352,116,-133) -> Matrix(1,0,4,1) Matrix(263,-308,76,-89) -> Matrix(1,0,-4,1) Matrix(705,-836,296,-351) -> Matrix(1,-2,0,1) Matrix(397,-484,324,-395) -> Matrix(1,-4,0,1) Matrix(177,-220,70,-87) -> Matrix(1,0,0,1) Matrix(1011,-1276,454,-573) -> Matrix(1,-4,0,1) Matrix(1495,-1892,418,-529) -> Matrix(3,2,4,3) Matrix(793,-1012,344,-439) -> Matrix(7,2,-4,-1) Matrix(1893,-2420,722,-923) -> Matrix(1,0,0,1) Matrix(1409,-1804,824,-1055) -> Matrix(1,0,4,1) Matrix(573,-748,370,-483) -> Matrix(7,-2,4,-1) Matrix(1233,-1672,778,-1055) -> Matrix(1,-4,0,1) Matrix(3299,-4488,874,-1189) -> Matrix(1,-4,0,1) Matrix(353,-484,256,-351) -> Matrix(1,-6,0,1) Matrix(221,-308,94,-131) -> Matrix(1,0,0,1) Matrix(219,-308,32,-45) -> Matrix(5,4,-4,-3) Matrix(529,-748,186,-263) -> Matrix(1,-2,0,1) Matrix(309,-440,92,-131) -> Matrix(1,0,0,1) Matrix(397,-572,152,-219) -> Matrix(1,0,0,1) Matrix(4487,-6512,2608,-3785) -> Matrix(1,0,4,1) Matrix(483,-704,212,-309) -> Matrix(7,2,-4,-1) Matrix(485,-748,142,-219) -> Matrix(1,-2,0,1) Matrix(1759,-2728,1022,-1585) -> Matrix(1,-2,0,1) Matrix(309,-484,196,-307) -> Matrix(1,-8,0,1) Matrix(3607,-5720,944,-1497) -> Matrix(1,0,0,1) Matrix(5147,-8184,1910,-3037) -> Matrix(1,4,0,1) Matrix(219,-352,28,-45) -> Matrix(3,4,-4,-5) Matrix(1583,-2552,874,-1409) -> Matrix(11,8,4,3) Matrix(353,-572,108,-175) -> Matrix(1,0,0,1) Matrix(485,-792,188,-307) -> Matrix(1,0,0,1) Matrix(617,-1012,214,-351) -> Matrix(7,2,-4,-1) Matrix(133,-220,26,-43) -> Matrix(1,0,0,1) Matrix(1673,-2860,926,-1583) -> Matrix(1,2,0,1) Matrix(6469,-11132,1508,-2595) -> Matrix(5,-6,-4,5) Matrix(485,-836,76,-131) -> Matrix(1,-2,0,1) Matrix(177,-308,50,-87) -> Matrix(1,0,0,1) Matrix(573,-1012,124,-219) -> Matrix(3,-2,-4,3) Matrix(571,-1012,224,-397) -> Matrix(1,-2,0,1) Matrix(395,-704,124,-221) -> Matrix(3,-2,-4,3) Matrix(221,-396,24,-43) -> Matrix(1,-2,0,1) Matrix(3211,-5808,706,-1277) -> Matrix(3,-8,-4,11) Matrix(703,-1276,146,-265) -> Matrix(1,-4,0,1) Matrix(265,-484,144,-263) -> Matrix(1,-10,0,1) Matrix(221,-484,100,-219) -> Matrix(1,-10,0,1) Matrix(1143,-2552,434,-969) -> Matrix(1,4,-4,-15) Matrix(307,-704,58,-133) -> Matrix(1,2,0,1) Matrix(705,-1628,152,-351) -> Matrix(3,4,-4,-5) Matrix(705,-1672,148,-351) -> Matrix(1,2,-4,-7) Matrix(573,-1364,92,-219) -> Matrix(1,0,0,1) Matrix(793,-1892,184,-439) -> Matrix(5,4,-4,-3) Matrix(749,-1804,164,-395) -> Matrix(3,4,-4,-5) Matrix(1409,-3608,412,-1055) -> Matrix(5,4,-4,-3) Matrix(1671,-4400,368,-969) -> Matrix(5,2,-8,-3) Matrix(617,-1672,162,-439) -> Matrix(1,-4,0,1) Matrix(177,-484,64,-175) -> Matrix(1,-8,0,1) Matrix(265,-748,62,-175) -> Matrix(5,14,-4,-11) Matrix(661,-1892,138,-395) -> Matrix(1,2,4,9) Matrix(1409,-4532,328,-1055) -> Matrix(9,8,-8,-7) Matrix(615,-2024,134,-441) -> Matrix(1,0,0,1) Matrix(2069,-7084,578,-1979) -> Matrix(7,6,8,7) Matrix(133,-484,36,-131) -> Matrix(1,-6,0,1) Matrix(89,-484,16,-87) -> Matrix(1,-4,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 30 Degree of the the map X: 60 Degree of the the map Y: 240 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 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): 360 Minimal number of generators: 61 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: 30 Genus: 16 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 11/5 12/5 22/9 44/17 11/4 3/1 22/7 33/10 10/3 44/13 18/5 11/3 4/1 22/5 9/2 88/19 14/3 110/23 5/1 16/3 11/2 6/1 44/7 20/3 7/1 22/3 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/2 1/0 1/1 -1/1 0/1 7/6 0/1 1/5 13/11 2/3 1/1 6/5 1/2 1/0 11/9 1/0 16/13 -3/2 1/0 5/4 -1/1 0/1 14/11 -1/2 -1/4 23/18 -1/1 0/1 9/7 -1/5 0/1 4/3 1/2 1/0 11/8 1/0 18/13 -5/2 1/0 7/5 -2/1 -1/1 24/17 -1/2 -1/4 17/12 -1/1 0/1 10/7 -1/2 1/0 13/9 -1/1 0/1 3/2 0/1 1/1 14/9 5/2 1/0 11/7 1/0 8/5 -3/2 1/0 29/18 -1/1 -6/7 21/13 -1/1 0/1 13/8 -1/1 0/1 18/11 -1/2 1/0 23/14 0/1 1/3 5/3 -1/1 0/1 12/7 1/2 1/0 31/18 0/1 1/3 19/11 0/1 1/1 7/4 0/1 1/1 23/13 2/3 1/1 16/9 1/2 1/0 25/14 1/1 4/3 9/5 1/1 2/1 20/11 9/2 1/0 11/6 1/0 2/1 -1/2 1/0 11/5 1/0 20/9 -11/2 1/0 9/4 -3/1 -2/1 16/7 -3/2 1/0 23/10 -2/1 -5/3 30/13 -3/2 1/0 7/3 -2/1 -1/1 26/11 -5/2 1/0 19/8 -2/1 -1/1 50/21 -3/2 1/0 31/13 -4/3 -1/1 43/18 -1/1 0/1 12/5 -3/2 1/0 17/7 -4/3 -1/1 22/9 -1/1 5/2 -1/1 0/1 28/11 -3/2 1/0 23/9 -4/3 -1/1 41/16 -1/1 -2/3 18/7 -1/2 1/0 31/12 -1/1 0/1 44/17 -1/2 1/0 13/5 -1/1 0/1 34/13 -1/2 1/0 55/21 -1/2 76/29 -1/2 -1/4 21/8 -1/1 0/1 8/3 1/2 1/0 11/4 1/0 14/5 -7/2 1/0 17/6 -3/1 -2/1 20/7 -5/2 -9/4 3/1 -2/1 -1/1 22/7 -1/1 19/6 -1/1 -6/7 16/5 -3/4 -1/2 13/4 -1/1 0/1 23/7 -1/1 0/1 33/10 -1/2 10/3 -1/2 1/0 27/8 -1/1 0/1 44/13 -1/2 1/0 17/5 -1/1 0/1 24/7 -3/4 -1/2 31/9 -2/5 -1/3 7/2 0/1 1/1 25/7 0/1 1/1 68/19 3/4 5/6 43/12 1/1 6/5 18/5 3/2 1/0 11/3 1/0 4/1 -3/2 1/0 13/3 -8/7 -1/1 22/5 -1/1 9/2 -1/1 -4/5 32/7 -3/4 -1/2 55/12 -1/2 23/5 -1/1 0/1 37/8 -1/1 -2/3 88/19 -3/4 -1/2 51/11 -1/1 -2/3 14/3 -3/4 -1/2 19/4 -1/3 0/1 43/9 -1/9 0/1 110/23 0/1 67/14 0/1 1/11 24/5 1/2 1/0 5/1 -1/1 0/1 21/4 0/1 1/3 16/3 1/2 1/0 11/2 1/0 6/1 -3/2 1/0 25/4 -2/1 -1/1 44/7 -3/2 1/0 19/3 -2/1 -1/1 13/2 -2/1 -5/3 20/3 -3/2 -11/8 7/1 -6/5 -1/1 22/3 -1/1 15/2 -1/1 -10/11 8/1 -3/4 -1/2 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(155,-176,96,-109) (1/1,7/6) -> (29/18,21/13) Hyperbolic Matrix(263,-308,76,-89) (7/6,13/11) -> (31/9,7/2) Hyperbolic Matrix(705,-836,296,-351) (13/11,6/5) -> (50/21,31/13) Hyperbolic Matrix(109,-132,19,-23) (6/5,11/9) -> (11/2,6/1) Hyperbolic Matrix(287,-352,53,-65) (11/9,16/13) -> (16/3,11/2) Hyperbolic Matrix(177,-220,70,-87) (16/13,5/4) -> (5/2,28/11) Hyperbolic Matrix(243,-308,86,-109) (5/4,14/11) -> (14/5,17/6) Hyperbolic Matrix(793,-1012,344,-439) (14/11,23/18) -> (23/10,30/13) Hyperbolic Matrix(859,-1100,360,-461) (23/18,9/7) -> (31/13,43/18) Hyperbolic Matrix(67,-88,16,-21) (9/7,4/3) -> (4/1,13/3) Hyperbolic Matrix(65,-88,17,-23) (4/3,11/8) -> (11/3,4/1) Hyperbolic Matrix(287,-396,79,-109) (11/8,18/13) -> (18/5,11/3) Hyperbolic Matrix(221,-308,94,-131) (18/13,7/5) -> (7/3,26/11) Hyperbolic Matrix(219,-308,32,-45) (7/5,24/17) -> (20/3,7/1) Hyperbolic Matrix(529,-748,186,-263) (24/17,17/12) -> (17/6,20/7) Hyperbolic Matrix(309,-440,92,-131) (17/12,10/7) -> (10/3,27/8) Hyperbolic Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(243,-352,136,-197) (13/9,3/2) -> (25/14,9/5) Hyperbolic Matrix(199,-308,42,-65) (3/2,14/9) -> (14/3,19/4) Hyperbolic Matrix(197,-308,71,-111) (14/9,11/7) -> (11/4,14/5) Hyperbolic Matrix(111,-176,41,-65) (11/7,8/5) -> (8/3,11/4) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(485,-792,188,-307) (13/8,18/11) -> (18/7,31/12) Hyperbolic Matrix(725,-1188,202,-331) (18/11,23/14) -> (43/12,18/5) Hyperbolic Matrix(133,-220,26,-43) (23/14,5/3) -> (5/1,21/4) Hyperbolic Matrix(155,-264,64,-109) (5/3,12/7) -> (12/5,17/7) Hyperbolic Matrix(639,-1100,140,-241) (12/7,31/18) -> (9/2,32/7) Hyperbolic Matrix(485,-836,76,-131) (31/18,19/11) -> (19/3,13/2) Hyperbolic Matrix(177,-308,50,-87) (19/11,7/4) -> (7/2,25/7) Hyperbolic Matrix(573,-1012,124,-219) (7/4,23/13) -> (23/5,37/8) Hyperbolic Matrix(571,-1012,224,-397) (23/13,16/9) -> (28/11,23/9) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(461,-836,134,-243) (9/5,20/11) -> (24/7,31/9) Hyperbolic Matrix(241,-440,109,-199) (20/11,11/6) -> (11/5,20/9) Hyperbolic Matrix(23,-44,11,-21) (11/6,2/1) -> (2/1,11/5) Parabolic Matrix(197,-440,30,-67) (20/9,9/4) -> (13/2,20/3) Hyperbolic Matrix(155,-352,48,-109) (9/4,16/7) -> (16/5,13/4) Hyperbolic Matrix(307,-704,58,-133) (16/7,23/10) -> (21/4,16/3) Hyperbolic Matrix(705,-1628,152,-351) (30/13,7/3) -> (51/11,14/3) Hyperbolic Matrix(595,-1408,232,-549) (26/11,19/8) -> (41/16,18/7) Hyperbolic Matrix(573,-1364,92,-219) (19/8,50/21) -> (6/1,25/4) Hyperbolic Matrix(1473,-3520,562,-1343) (43/18,12/5) -> (76/29,21/8) Hyperbolic Matrix(199,-484,81,-197) (17/7,22/9) -> (22/9,5/2) Parabolic Matrix(859,-2200,180,-461) (23/9,41/16) -> (19/4,43/9) Hyperbolic Matrix(749,-1936,289,-747) (31/12,44/17) -> (44/17,13/5) Parabolic Matrix(639,-1672,193,-505) (34/13,55/21) -> (33/10,10/3) Hyperbolic Matrix(2267,-5940,495,-1297) (55/21,76/29) -> (32/7,55/12) Hyperbolic Matrix(67,-176,8,-21) (21/8,8/3) -> (8/1,1/0) Hyperbolic Matrix(243,-704,68,-197) (20/7,3/1) -> (25/7,68/19) Hyperbolic Matrix(155,-484,49,-153) (3/1,22/7) -> (22/7,19/6) Parabolic Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(573,-1936,169,-571) (27/8,44/13) -> (44/13,17/5) Parabolic Matrix(155,-528,32,-109) (17/5,24/7) -> (24/5,5/1) Hyperbolic Matrix(1561,-5588,326,-1167) (68/19,43/12) -> (67/14,24/5) Hyperbolic Matrix(111,-484,25,-109) (13/3,22/5) -> (22/5,9/2) Parabolic Matrix(1673,-7744,361,-1671) (37/8,88/19) -> (88/19,51/11) Parabolic Matrix(2531,-12100,529,-2529) (43/9,110/23) -> (110/23,67/14) Parabolic Matrix(309,-1936,49,-307) (25/4,44/7) -> (44/7,19/3) Parabolic Matrix(67,-484,9,-65) (7/1,22/3) -> (22/3,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,1,-2,-1) Matrix(155,-176,96,-109) -> Matrix(1,1,-2,-1) Matrix(263,-308,76,-89) -> Matrix(1,0,-4,1) Matrix(705,-836,296,-351) -> Matrix(1,-2,0,1) Matrix(109,-132,19,-23) -> Matrix(1,-2,0,1) Matrix(287,-352,53,-65) -> Matrix(1,2,0,1) Matrix(177,-220,70,-87) -> Matrix(1,0,0,1) Matrix(243,-308,86,-109) -> Matrix(5,3,-2,-1) Matrix(793,-1012,344,-439) -> Matrix(7,2,-4,-1) Matrix(859,-1100,360,-461) -> Matrix(1,1,-2,-1) Matrix(67,-88,16,-21) -> Matrix(3,-1,-2,1) Matrix(65,-88,17,-23) -> Matrix(1,-2,0,1) Matrix(287,-396,79,-109) -> Matrix(1,4,0,1) Matrix(221,-308,94,-131) -> Matrix(1,0,0,1) Matrix(219,-308,32,-45) -> Matrix(5,4,-4,-3) Matrix(529,-748,186,-263) -> Matrix(1,-2,0,1) Matrix(309,-440,92,-131) -> Matrix(1,0,0,1) Matrix(397,-572,152,-219) -> Matrix(1,0,0,1) Matrix(243,-352,136,-197) -> Matrix(3,1,2,1) Matrix(199,-308,42,-65) -> Matrix(1,-1,-2,3) Matrix(197,-308,71,-111) -> Matrix(1,-6,0,1) Matrix(111,-176,41,-65) -> Matrix(1,2,0,1) Matrix(219,-352,28,-45) -> Matrix(3,4,-4,-5) Matrix(353,-572,108,-175) -> Matrix(1,0,0,1) Matrix(485,-792,188,-307) -> Matrix(1,0,0,1) Matrix(725,-1188,202,-331) -> Matrix(3,1,2,1) Matrix(133,-220,26,-43) -> Matrix(1,0,0,1) Matrix(155,-264,64,-109) -> Matrix(3,-1,-2,1) Matrix(639,-1100,140,-241) -> Matrix(1,1,-2,-1) Matrix(485,-836,76,-131) -> Matrix(1,-2,0,1) Matrix(177,-308,50,-87) -> Matrix(1,0,0,1) Matrix(573,-1012,124,-219) -> Matrix(3,-2,-4,3) Matrix(571,-1012,224,-397) -> Matrix(1,-2,0,1) Matrix(395,-704,124,-221) -> Matrix(3,-2,-4,3) Matrix(461,-836,134,-243) -> Matrix(1,-3,-2,7) Matrix(241,-440,109,-199) -> Matrix(1,-10,0,1) Matrix(23,-44,11,-21) -> Matrix(1,0,0,1) Matrix(197,-440,30,-67) -> Matrix(3,11,-2,-7) Matrix(155,-352,48,-109) -> Matrix(1,3,-2,-5) Matrix(307,-704,58,-133) -> Matrix(1,2,0,1) Matrix(705,-1628,152,-351) -> Matrix(3,4,-4,-5) Matrix(595,-1408,232,-549) -> Matrix(1,3,-2,-5) Matrix(573,-1364,92,-219) -> Matrix(1,0,0,1) Matrix(1473,-3520,562,-1343) -> Matrix(1,1,-2,-1) Matrix(199,-484,81,-197) -> Matrix(3,4,-4,-5) Matrix(859,-2200,180,-461) -> Matrix(1,1,-6,-5) Matrix(749,-1936,289,-747) -> Matrix(1,1,-2,-1) Matrix(639,-1672,193,-505) -> Matrix(1,0,0,1) Matrix(2267,-5940,495,-1297) -> Matrix(5,2,-8,-3) Matrix(67,-176,8,-21) -> Matrix(1,1,-2,-1) Matrix(243,-704,68,-197) -> Matrix(1,1,2,3) Matrix(155,-484,49,-153) -> Matrix(7,8,-8,-9) Matrix(615,-2024,134,-441) -> Matrix(1,0,0,1) Matrix(573,-1936,169,-571) -> Matrix(1,1,-2,-1) Matrix(155,-528,32,-109) -> Matrix(1,1,-2,-1) Matrix(1561,-5588,326,-1167) -> Matrix(1,-1,6,-5) Matrix(111,-484,25,-109) -> Matrix(11,12,-12,-13) Matrix(1673,-7744,361,-1671) -> Matrix(7,5,-10,-7) Matrix(2531,-12100,529,-2529) -> Matrix(1,0,20,1) Matrix(309,-1936,49,-307) -> Matrix(3,5,-2,-3) Matrix(67,-484,9,-65) -> Matrix(15,16,-16,-17) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 3 Number of equivalence classes of elliptic points of order 2: 2 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): 15 ----------------------------------------------------------------------- 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 0/1 (-1/1,0/1).(-1/2,1/0) 0 1 2/1 (-1/2,1/0) 0 11 11/5 1/0 5 2 20/9 (-6/1,-5/1).(-11/2,1/0) 0 11 9/4 (-3/1,-2/1) 0 22 16/7 (-2/1,-1/1).(-3/2,1/0) 0 11 23/10 (-2/1,-5/3) 0 22 7/3 (-2/1,-1/1) 0 22 19/8 (-2/1,-1/1) 0 22 31/13 (-4/3,-1/1) 0 22 12/5 (-2/1,-1/1).(-3/2,1/0) 0 11 22/9 -1/1 4 1 5/2 (-1/1,0/1) 0 22 23/9 (-4/3,-1/1) 0 22 18/7 (-1/2,1/0) 0 11 44/17 (-1/1,0/1).(-1/2,1/0) 0 1 13/5 (-1/1,0/1) 0 22 21/8 (-1/1,0/1) 0 22 8/3 (0/1,1/1).(1/2,1/0) 0 11 11/4 1/0 4 2 14/5 (-7/2,1/0) 0 11 3/1 (-2/1,-1/1) 0 22 22/7 -1/1 8 1 16/5 (-1/1,-2/3).(-3/4,-1/2) 0 11 13/4 (-1/1,0/1) 0 22 23/7 (-1/1,0/1) 0 22 33/10 -1/2 1 2 10/3 (-1/2,1/0) 0 11 44/13 (-1/1,0/1).(-1/2,1/0) 0 1 17/5 (-1/1,0/1) 0 22 24/7 (-1/1,-2/3).(-3/4,-1/2) 0 11 7/2 (0/1,1/1) 0 22 25/7 (0/1,1/1) 0 22 43/12 (1/1,6/5) 0 22 18/5 (3/2,1/0) 0 11 11/3 1/0 3 2 4/1 (-2/1,-1/1).(-3/2,1/0) 0 11 22/5 -1/1 12 1 9/2 (-1/1,-4/5) 0 22 32/7 (-1/1,-2/3).(-3/4,-1/2) 0 11 55/12 -1/2 1 2 23/5 (-1/1,0/1) 0 22 37/8 (-1/1,-2/3) 0 22 88/19 (-1/1,-2/3).(-3/4,-1/2) 0 1 14/3 (-3/4,-1/2) 0 11 19/4 (-1/3,0/1) 0 22 43/9 (-1/9,0/1) 0 22 110/23 0/1 20 1 24/5 (0/1,1/1).(1/2,1/0) 0 11 5/1 (-1/1,0/1) 0 22 21/4 (0/1,1/3) 0 22 16/3 (0/1,1/1).(1/2,1/0) 0 11 11/2 1/0 2 2 6/1 (-3/2,1/0) 0 11 44/7 (-2/1,-1/1).(-3/2,1/0) 0 1 19/3 (-2/1,-1/1) 0 22 13/2 (-2/1,-5/3) 0 22 20/3 (-3/2,-11/8).(-7/5,-4/3) 0 11 7/1 (-6/5,-1/1) 0 22 22/3 -1/1 16 1 8/1 (-1/1,-2/3).(-3/4,-1/2) 0 11 1/0 (-1/1,0/1) 0 22 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(21,-44,10,-21) (2/1,11/5) -> (2/1,11/5) Reflection Matrix(199,-440,90,-199) (11/5,20/9) -> (11/5,20/9) Reflection Matrix(197,-440,30,-67) (20/9,9/4) -> (13/2,20/3) Hyperbolic Matrix(155,-352,48,-109) (9/4,16/7) -> (16/5,13/4) Hyperbolic Matrix(307,-704,58,-133) (16/7,23/10) -> (21/4,16/3) Hyperbolic Matrix(439,-1012,95,-219) (23/10,7/3) -> (23/5,37/8) Glide Reflection Matrix(131,-308,37,-87) (7/3,19/8) -> (7/2,25/7) Glide Reflection Matrix(351,-836,55,-131) (19/8,31/13) -> (19/3,13/2) Glide Reflection Matrix(461,-1100,101,-241) (31/13,12/5) -> (9/2,32/7) Glide Reflection Matrix(109,-264,45,-109) (12/5,22/9) -> (12/5,22/9) Reflection Matrix(89,-220,36,-89) (22/9,5/2) -> (22/9,5/2) Reflection Matrix(87,-220,17,-43) (5/2,23/9) -> (5/1,21/4) Glide Reflection Matrix(463,-1188,129,-331) (23/9,18/7) -> (43/12,18/5) Glide Reflection Matrix(307,-792,119,-307) (18/7,44/17) -> (18/7,44/17) Reflection Matrix(441,-1144,170,-441) (44/17,13/5) -> (44/17,13/5) Reflection Matrix(219,-572,67,-175) (13/5,21/8) -> (13/4,23/7) Glide Reflection Matrix(67,-176,8,-21) (21/8,8/3) -> (8/1,1/0) Hyperbolic Matrix(65,-176,24,-65) (8/3,11/4) -> (8/3,11/4) Reflection Matrix(111,-308,40,-111) (11/4,14/5) -> (11/4,14/5) Reflection Matrix(109,-308,23,-65) (14/5,3/1) -> (14/3,19/4) Glide Reflection Matrix(43,-132,14,-43) (3/1,22/7) -> (3/1,22/7) Reflection Matrix(111,-352,35,-111) (22/7,16/5) -> (22/7,16/5) Reflection Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(199,-660,60,-199) (33/10,10/3) -> (33/10,10/3) Reflection Matrix(131,-440,39,-131) (10/3,44/13) -> (10/3,44/13) Reflection Matrix(441,-1496,130,-441) (44/13,17/5) -> (44/13,17/5) Reflection Matrix(155,-528,32,-109) (17/5,24/7) -> (24/5,5/1) Hyperbolic Matrix(89,-308,13,-45) (24/7,7/2) -> (20/3,7/1) Glide Reflection Matrix(529,-1892,111,-397) (25/7,43/12) -> (19/4,43/9) Glide Reflection Matrix(109,-396,30,-109) (18/5,11/3) -> (18/5,11/3) Reflection Matrix(23,-88,6,-23) (11/3,4/1) -> (11/3,4/1) Reflection Matrix(21,-88,5,-21) (4/1,22/5) -> (4/1,22/5) Reflection Matrix(89,-396,20,-89) (22/5,9/2) -> (22/5,9/2) Reflection Matrix(769,-3520,168,-769) (32/7,55/12) -> (32/7,55/12) Reflection Matrix(1407,-6512,304,-1407) (37/8,88/19) -> (37/8,88/19) Reflection Matrix(265,-1232,57,-265) (88/19,14/3) -> (88/19,14/3) Reflection Matrix(1979,-9460,414,-1979) (43/9,110/23) -> (43/9,110/23) Reflection Matrix(551,-2640,115,-551) (110/23,24/5) -> (110/23,24/5) Reflection Matrix(65,-352,12,-65) (16/3,11/2) -> (16/3,11/2) Reflection Matrix(23,-132,4,-23) (11/2,6/1) -> (11/2,6/1) Reflection Matrix(43,-264,7,-43) (6/1,44/7) -> (6/1,44/7) Reflection Matrix(265,-1672,42,-265) (44/7,19/3) -> (44/7,19/3) Reflection Matrix(43,-308,6,-43) (7/1,22/3) -> (7/1,22/3) Reflection Matrix(23,-176,3,-23) (22/3,8/1) -> (22/3,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,1,-1) -> Matrix(1,1,0,-1) (0/1,2/1) -> (-1/2,1/0) Matrix(21,-44,10,-21) -> Matrix(1,1,0,-1) (2/1,11/5) -> (-1/2,1/0) Matrix(199,-440,90,-199) -> Matrix(1,11,0,-1) (11/5,20/9) -> (-11/2,1/0) Matrix(197,-440,30,-67) -> Matrix(3,11,-2,-7) Matrix(155,-352,48,-109) -> Matrix(1,3,-2,-5) Matrix(307,-704,58,-133) -> Matrix(1,2,0,1) 1/0 Matrix(439,-1012,95,-219) -> Matrix(3,5,-4,-7) Matrix(131,-308,37,-87) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(351,-836,55,-131) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(461,-1100,101,-241) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(109,-264,45,-109) -> Matrix(3,4,-2,-3) (12/5,22/9) -> (-2/1,-1/1) Matrix(89,-220,36,-89) -> Matrix(-1,0,2,1) (22/9,5/2) -> (-1/1,0/1) Matrix(87,-220,17,-43) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(463,-1188,129,-331) -> Matrix(3,2,2,1) Matrix(307,-792,119,-307) -> Matrix(1,1,0,-1) (18/7,44/17) -> (-1/2,1/0) Matrix(441,-1144,170,-441) -> Matrix(-1,0,2,1) (44/17,13/5) -> (-1/1,0/1) Matrix(219,-572,67,-175) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(67,-176,8,-21) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(65,-176,24,-65) -> Matrix(-1,1,0,1) (8/3,11/4) -> (1/2,1/0) Matrix(111,-308,40,-111) -> Matrix(1,7,0,-1) (11/4,14/5) -> (-7/2,1/0) Matrix(109,-308,23,-65) -> Matrix(1,2,-2,-5) Matrix(43,-132,14,-43) -> Matrix(3,4,-2,-3) (3/1,22/7) -> (-2/1,-1/1) Matrix(111,-352,35,-111) -> Matrix(5,4,-6,-5) (22/7,16/5) -> (-1/1,-2/3) Matrix(615,-2024,134,-441) -> Matrix(1,0,0,1) Matrix(199,-660,60,-199) -> Matrix(1,1,0,-1) (33/10,10/3) -> (-1/2,1/0) Matrix(131,-440,39,-131) -> Matrix(1,1,0,-1) (10/3,44/13) -> (-1/2,1/0) Matrix(441,-1496,130,-441) -> Matrix(-1,0,2,1) (44/13,17/5) -> (-1/1,0/1) Matrix(155,-528,32,-109) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(89,-308,13,-45) -> Matrix(5,1,-4,-1) Matrix(529,-1892,111,-397) -> Matrix(1,-1,-4,3) Matrix(109,-396,30,-109) -> Matrix(-1,3,0,1) (18/5,11/3) -> (3/2,1/0) Matrix(23,-88,6,-23) -> Matrix(1,3,0,-1) (11/3,4/1) -> (-3/2,1/0) Matrix(21,-88,5,-21) -> Matrix(3,4,-2,-3) (4/1,22/5) -> (-2/1,-1/1) Matrix(89,-396,20,-89) -> Matrix(9,8,-10,-9) (22/5,9/2) -> (-1/1,-4/5) Matrix(769,-3520,168,-769) -> Matrix(5,3,-8,-5) (32/7,55/12) -> (-3/4,-1/2) Matrix(1407,-6512,304,-1407) -> Matrix(5,4,-6,-5) (37/8,88/19) -> (-1/1,-2/3) Matrix(265,-1232,57,-265) -> Matrix(5,3,-8,-5) (88/19,14/3) -> (-3/4,-1/2) Matrix(1979,-9460,414,-1979) -> Matrix(-1,0,18,1) (43/9,110/23) -> (-1/9,0/1) Matrix(551,-2640,115,-551) -> Matrix(1,0,2,-1) (110/23,24/5) -> (0/1,1/1) Matrix(65,-352,12,-65) -> Matrix(-1,1,0,1) (16/3,11/2) -> (1/2,1/0) Matrix(23,-132,4,-23) -> Matrix(1,3,0,-1) (11/2,6/1) -> (-3/2,1/0) Matrix(43,-264,7,-43) -> Matrix(1,3,0,-1) (6/1,44/7) -> (-3/2,1/0) Matrix(265,-1672,42,-265) -> Matrix(3,4,-2,-3) (44/7,19/3) -> (-2/1,-1/1) Matrix(43,-308,6,-43) -> Matrix(11,12,-10,-11) (7/1,22/3) -> (-6/5,-1/1) Matrix(23,-176,3,-23) -> Matrix(5,4,-6,-5) (22/3,8/1) -> (-1/1,-2/3) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.