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): 1800 Minimal number of generators: 301 Number of equivalence classes of cusps: 84 Genus: 109 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -4/9 -3/8 -2/7 -1/6 0/1 1/9 2/13 1/4 4/11 7/18 3/7 11/24 1/2 9/16 2/3 51/74 11/14 9/11 7/8 1/1 8/7 11/9 14/11 29/21 44/31 3/2 76/49 46/29 31/19 16/9 13/7 2/1 17/8 7/3 53/22 5/2 18/7 13/5 163/62 127/48 73/27 183/67 11/4 147/53 37/13 3/1 19/6 16/5 10/3 58/17 7/2 39/11 11/3 19/5 4/1 17/4 13/3 102/23 9/2 41/9 14/3 19/4 62/13 5/1 21/4 16/3 11/2 17/3 6/1 43/7 56/9 19/3 13/2 20/3 7/1 22/3 15/2 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/4 -8/17 0/1 1/3 -7/15 0/1 1/6 -6/13 1/5 1/4 -11/24 2/9 1/4 -5/11 1/4 2/7 -14/31 2/7 3/10 -9/20 1/3 2/5 -13/29 1/3 2/5 -4/9 0/1 -15/34 1/6 2/11 -11/25 1/5 2/9 -18/41 0/1 1/5 -7/16 1/5 2/9 -24/55 2/9 1/4 -17/39 1/5 1/4 -10/23 2/9 1/4 -13/30 4/17 1/4 -3/7 1/4 2/7 -14/33 1/4 2/7 -11/26 2/7 -19/45 2/7 3/10 -8/19 2/7 1/3 -29/69 2/7 -21/50 2/7 3/10 -34/81 3/10 1/3 -47/112 4/13 -13/31 5/16 1/3 -5/12 1/3 1/2 -12/29 0/1 1/4 -7/17 0/1 -9/22 0/1 1/4 -2/5 1/4 1/3 -11/28 3/10 4/13 -9/23 8/25 1/3 -7/18 1/3 6/17 -12/31 3/8 2/5 -29/75 3/8 2/5 -17/44 1/3 2/5 -5/13 2/5 1/2 -13/34 1/2 4/7 -8/21 0/1 1/2 -19/50 1/2 4/7 -11/29 1/2 1/1 -25/66 1/1 2/1 -14/37 0/1 1/1 -3/8 0/1 -16/43 0/1 1/5 -29/78 0/1 1/6 -13/35 1/6 1/5 -23/62 1/5 6/29 -10/27 2/9 1/4 -17/46 1/4 4/15 -7/19 0/1 1/4 -11/30 1/4 4/15 -4/11 1/4 1/3 -13/36 2/7 1/3 -9/25 4/13 1/3 -5/14 1/3 2/5 -6/17 1/3 2/5 -13/37 2/5 1/2 -7/20 0/1 1/2 -1/3 0/1 1/3 -6/19 0/1 1/4 -5/16 2/7 1/3 -4/13 2/7 1/3 -7/23 1/3 4/11 -17/56 1/3 4/11 -10/33 1/3 2/5 -3/10 1/3 1/2 -8/27 4/9 1/2 -13/44 1/2 4/7 -5/17 0/1 1/2 -12/41 4/9 1/2 -19/65 1/2 8/15 -7/24 1/2 2/3 -9/31 1/1 1/0 -2/7 0/1 -11/39 1/5 1/4 -20/71 0/1 1/4 -9/32 0/1 1/5 -7/25 1/5 1/4 -12/43 4/17 1/4 -17/61 1/4 4/15 -5/18 0/1 1/4 -8/29 4/17 1/4 -11/40 1/4 8/31 -3/11 1/4 2/7 -10/37 2/7 1/3 -7/26 2/7 3/10 -4/15 6/19 1/3 -5/19 1/3 8/23 -11/42 5/14 4/11 -6/23 4/11 3/8 -1/4 1/3 1/2 -4/17 0/1 1/2 -3/13 0/1 -5/22 0/1 1/2 -2/9 1/4 1/3 -5/23 1/3 5/14 -18/83 4/11 -13/60 1/3 3/8 -8/37 3/8 2/5 -11/51 2/5 -3/14 1/3 2/5 -10/47 4/11 3/8 -17/80 3/8 8/21 -7/33 3/8 2/5 -4/19 2/5 -5/24 2/5 1/2 -6/29 1/3 2/5 -7/34 2/5 3/7 -1/5 2/5 1/2 -5/26 1/2 10/19 -4/21 1/2 4/7 -3/16 1/2 2/3 -5/27 1/2 1/1 -7/38 1/2 2/3 -2/11 2/3 1/1 -9/50 1/1 4/3 -7/39 1/1 1/0 -5/28 0/1 1/1 -3/17 2/3 1/1 -7/40 3/2 2/1 -4/23 2/1 1/0 -1/6 0/1 -3/19 2/7 1/3 -5/32 0/1 1/3 -2/13 2/7 1/3 -7/46 1/3 12/35 -5/33 1/3 5/14 -3/20 3/8 2/5 -1/7 2/5 1/2 -3/22 1/2 6/11 -2/15 1/2 2/3 -1/8 1/2 1/1 -1/9 0/1 1/0 -1/10 0/1 1/3 0/1 0/1 1/2 1/10 0/1 1/1 1/9 0/1 1/8 0/1 1/1 1/7 0/1 1/4 3/20 0/1 1/3 2/13 0/1 1/6 1/3 1/2 4/23 1/3 2/5 3/17 2/5 2/11 2/5 1/2 1/5 1/2 2/3 3/14 2/3 3/4 2/9 1/1 2/1 3/13 1/1 2/1 1/4 0/1 4/15 1/4 2/7 3/11 1/3 2/5 5/18 0/1 1/3 2/7 1/3 2/5 9/31 2/5 16/55 2/5 1/2 7/24 2/5 1/2 5/17 1/3 1/2 18/61 0/1 1/2 31/105 0/1 1/3 13/44 1/3 3/8 8/27 2/5 11/37 2/5 3/7 3/10 2/5 1/2 7/23 2/5 18/59 2/5 3/7 11/36 5/12 3/7 4/13 4/9 1/2 1/3 1/2 2/3 5/14 1/2 2/3 9/25 3/5 2/3 13/36 1/2 2/3 4/11 2/3 15/41 2/3 3/4 11/30 2/3 1/1 7/19 2/3 3/4 3/8 2/3 1/1 14/37 1/2 2/3 11/29 2/3 19/50 2/3 3/4 8/21 2/3 3/4 21/55 3/4 4/5 13/34 3/4 1/1 18/47 4/5 5/13 5/6 1/1 7/18 1/1 9/23 1/1 7/6 2/5 1/1 1/0 9/22 -2/1 1/0 16/39 0/1 7/17 0/1 1/0 19/46 0/1 31/75 0/1 1/0 12/29 -1/1 0/1 5/12 0/1 1/2 13/31 0/1 1/0 34/81 0/1 21/50 0/1 1/0 29/69 -1/1 0/1 37/88 0/1 8/19 0/1 1/1 19/45 1/1 2/1 30/71 2/1 1/0 11/26 0/1 1/0 3/7 0/1 10/23 0/1 1/4 17/39 0/1 1/2 41/94 0/1 24/55 0/1 1/2 7/16 0/1 1/3 11/25 1/3 2/5 37/84 3/8 2/5 26/59 2/5 15/34 2/5 1/2 19/43 4/9 1/2 23/52 1/2 4/9 0/1 1/2 9/20 1/2 4/7 14/31 2/3 5/11 0/1 1/1 16/35 0/1 1/2 27/59 0/1 1/1 38/83 0/1 1/0 11/24 0/1 6/13 0/1 1/2 1/2 1/2 1/1 7/13 2/3 6/11 3/4 4/5 5/9 8/9 1/1 9/16 1/1 13/23 1/1 20/19 4/7 1/1 6/5 15/26 1/1 6/5 11/19 4/3 18/31 4/3 3/2 61/105 1/1 4/3 43/74 4/3 11/8 25/43 7/5 3/2 7/12 3/2 2/1 17/29 3/2 2/1 10/17 1/1 2/1 33/56 1/1 4/3 23/39 3/2 2/1 13/22 2/1 16/27 1/1 3/2 3/5 2/1 1/0 8/13 -4/1 1/0 21/34 -2/1 13/21 -1/1 0/1 31/50 0/1 1/0 49/79 1/1 1/0 18/29 -1/1 1/0 5/8 0/1 1/0 12/19 -4/1 1/0 19/30 -2/1 1/0 45/71 -3/1 -2/1 26/41 -2/1 -3/2 7/11 -1/1 1/0 16/25 -1/1 -2/3 9/14 -1/1 0/1 2/3 0/1 11/16 0/1 1/3 31/45 0/1 1/2 51/74 0/1 20/29 0/1 1/4 9/13 1/4 1/3 16/23 1/3 6/17 7/10 2/5 1/2 12/17 1/2 4/7 29/41 2/3 17/24 0/1 1/1 39/55 0/1 1/2 22/31 1/2 1/1 5/7 0/1 1/2 8/11 1/2 4/7 19/26 2/3 30/41 1/2 4/7 41/56 1/2 3/5 11/15 1/2 2/3 25/34 3/5 2/3 39/53 9/14 2/3 14/19 2/3 3/4 3/4 1/2 1/1 13/17 2/3 23/30 1/2 1/1 33/43 1/2 2/3 43/56 2/3 3/4 10/13 2/3 1/1 7/9 4/5 1/1 11/14 1/1 15/19 1/1 8/7 4/5 1/1 2/1 25/31 2/1 1/0 21/26 1/1 1/0 17/21 2/1 1/0 13/16 -2/1 1/0 35/43 -1/1 1/0 22/27 0/1 1/0 9/11 0/1 32/39 1/2 2/3 55/67 1/2 1/1 23/28 0/1 1/2 14/17 1/2 2/3 5/6 1/1 2/1 11/13 2/1 1/0 6/7 0/1 1/0 13/15 -1/1 1/0 33/38 -2/1 1/0 53/61 -2/1 -1/1 20/23 -1/1 -1/2 7/8 0/1 8/9 0/1 1/2 9/10 0/1 1/0 1/1 0/1 1/1 10/9 0/1 1/2 9/8 0/1 1/0 8/7 0/1 15/13 1/3 1/2 7/6 0/1 1/2 6/5 2/3 1/1 17/14 2/1 1/0 11/9 0/1 16/13 2/5 1/2 21/17 1/2 2/3 26/21 1/2 1/1 5/4 2/3 1/1 14/11 1/1 23/18 1/1 10/9 9/7 1/1 4/3 22/17 1/1 4/3 35/27 3/2 2/1 83/64 3/2 5/3 48/37 2/1 13/10 1/1 2/1 17/13 2/1 21/16 2/1 1/0 4/3 1/1 1/0 19/14 3/2 2/1 15/11 2/1 1/0 11/8 4/1 1/0 29/21 1/0 47/34 -12/1 1/0 18/13 -4/1 1/0 7/5 0/1 1/0 31/22 1/1 1/0 24/17 0/1 1/1 17/12 4/1 1/0 44/31 1/0 71/50 -20/1 1/0 27/19 -8/1 1/0 10/7 -2/1 1/0 13/9 -1/1 -1/2 3/2 0/1 17/11 1/3 1/2 31/20 0/1 1/2 76/49 0/1 121/78 0/1 1/6 45/29 0/1 1/4 59/38 1/4 1/3 14/9 0/1 1/3 11/7 1/3 1/2 52/33 2/5 41/26 3/8 2/5 30/19 2/5 1/2 49/31 2/5 19/12 4/9 1/2 46/29 1/2 73/46 1/2 12/23 27/17 1/2 4/7 8/5 0/1 1/2 29/18 1/3 1/2 21/13 0/1 1/3 13/8 4/9 1/2 31/19 1/2 49/30 1/2 20/39 18/11 1/2 8/15 5/3 1/2 2/3 27/16 3/4 1/1 49/29 1/2 1/1 22/13 2/3 61/36 5/7 3/4 39/23 2/3 3/4 56/33 4/5 1/1 17/10 2/3 1/1 12/7 2/3 3/4 43/25 3/4 7/9 74/43 11/14 4/5 31/18 3/4 4/5 81/47 3/4 1/1 131/76 5/6 1/1 50/29 2/3 3/4 19/11 4/5 64/37 4/5 5/6 45/26 14/17 5/6 26/15 6/7 1/1 7/4 6/7 1/1 16/9 1/1 25/14 1/1 22/21 9/5 1/1 8/7 20/11 5/4 4/3 31/17 1/1 4/3 42/23 4/3 53/29 1/1 5/4 11/6 4/3 3/2 24/13 3/2 2/1 13/7 2/1 15/8 1/1 2/1 2/1 1/1 1/0 17/8 1/0 32/15 -3/1 1/0 15/7 -1/1 1/0 13/6 0/1 1/0 24/11 0/1 35/16 0/1 1/0 46/21 -1/2 0/1 57/26 0/1 1/4 11/5 0/1 1/1 31/14 2/1 20/9 4/1 1/0 9/4 0/1 1/0 16/7 -1/1 0/1 55/24 0/1 1/0 39/17 0/1 1/0 23/10 -1/2 0/1 7/3 0/1 26/11 0/1 1/2 71/30 1/2 2/3 116/49 2/3 45/19 2/3 1/1 19/8 0/1 1/1 12/5 0/1 1/0 53/22 0/1 94/39 0/1 1/12 41/17 0/1 1/6 29/12 0/1 1/3 104/43 1/3 1/2 179/74 1/2 1/1 75/31 0/1 1/2 121/50 0/1 1/2 46/19 0/1 17/7 0/1 1/2 56/23 2/5 1/2 39/16 0/1 22/9 2/5 1/2 5/2 1/2 1/1 18/7 1/1 31/12 1/1 11/10 13/5 1/1 5/4 60/23 4/3 3/2 47/18 4/3 81/31 4/3 3/2 34/13 1/1 3/2 89/34 1/1 4/3 144/55 5/4 4/3 199/76 4/3 55/21 4/3 3/2 76/29 4/3 21/8 3/2 2/1 92/35 5/3 2/1 163/62 2/1 71/27 1/1 2/1 50/19 3/2 2/1 79/30 5/3 2/1 29/11 2/1 66/25 1/1 2/1 37/14 2/1 1/0 82/31 4/1 1/0 127/48 1/0 45/17 0/1 1/0 8/3 1/1 2/1 27/10 4/3 3/2 73/27 3/2 119/44 3/2 20/13 46/17 3/2 8/5 19/7 3/2 2/1 49/18 7/4 2/1 79/29 2/1 5/2 30/11 1/1 2/1 71/26 1/1 3/2 183/67 3/2 295/108 3/2 11/7 112/41 3/2 5/3 41/15 3/2 2/1 11/4 2/1 36/13 2/1 1/0 61/22 3/2 2/1 147/53 2/1 233/84 2/1 21/10 86/31 2/1 9/4 25/9 2/1 3/1 39/14 3/1 1/0 53/19 1/1 1/0 14/5 2/1 1/0 17/6 1/1 2/1 37/13 2/1 57/20 2/1 7/3 20/7 2/1 3/1 3/1 2/1 1/0 19/6 1/0 35/11 -22/1 1/0 16/5 -10/1 1/0 13/4 -4/1 1/0 36/11 -3/1 -5/2 23/7 -2/1 33/10 -1/1 1/0 10/3 -2/1 1/0 37/11 -3/1 -2/1 27/8 -2/1 17/5 -1/1 1/0 58/17 1/0 99/29 -5/1 1/0 41/12 -3/1 1/0 24/7 -2/1 1/0 79/23 -3/1 -2/1 55/16 -2/1 1/0 31/9 -2/1 38/11 -2/1 1/0 7/2 -2/1 -1/1 39/11 -1/1 71/20 -1/1 -10/11 32/9 -1/1 -4/5 25/7 -1/1 -1/2 18/5 -1/1 0/1 29/8 0/1 1/0 98/27 1/0 69/19 -4/1 1/0 109/30 -3/1 -2/1 40/11 -2/1 1/0 51/14 -2/1 11/3 -2/1 -1/1 26/7 -3/4 -2/3 93/25 -1/1 -1/2 67/18 -2/3 41/11 -1/1 -2/3 97/26 -2/3 -3/5 56/15 -2/3 -1/2 15/4 -2/3 -1/2 19/5 -1/2 0/1 4/1 0/1 21/5 0/1 1/2 38/9 1/3 1/2 17/4 2/5 1/2 13/3 2/3 1/1 22/5 0/1 1/1 31/7 0/1 1/2 102/23 1/2 71/16 1/2 4/7 40/9 1/2 2/3 9/2 2/3 1/1 41/9 1/1 73/16 1/1 26/25 32/7 1/1 12/11 23/5 1/1 5/4 14/3 3/2 2/1 19/4 1/1 2/1 62/13 2/1 105/22 2/1 7/3 43/9 2/1 3/1 67/14 2/1 1/0 24/5 2/1 1/0 77/16 1/2 1/1 130/27 1/1 5/4 53/11 1/1 2/1 29/6 2/1 5/1 2/1 1/0 21/4 1/0 37/7 -14/1 1/0 16/3 -6/1 1/0 11/2 -2/1 1/0 28/5 -4/1 1/0 17/3 -2/1 40/7 -1/1 1/0 63/11 -2/1 1/0 23/4 -2/1 -1/1 6/1 -1/1 1/0 43/7 -1/1 80/13 -1/1 -11/12 37/6 -1/1 -5/6 31/5 -1/1 -2/3 56/9 -2/3 25/4 -2/3 -1/2 44/7 -1/2 0/1 19/3 -1/1 -1/2 13/2 0/1 46/7 1/1 1/0 33/5 0/1 1/0 20/3 -1/1 0/1 7/1 -1/2 0/1 22/3 0/1 37/5 0/1 1/10 15/2 0/1 1/4 8/1 0/1 1/1 17/2 0/1 1/0 9/1 0/1 10/1 0/1 1/1 11/1 2/1 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(761,362,288,137) (-1/2,-8/17) -> (66/25,37/14) Hyperbolic Matrix(1793,842,658,309) (-8/17,-7/15) -> (79/29,30/11) Hyperbolic Matrix(279,130,470,219) (-7/15,-6/13) -> (16/27,3/5) Hyperbolic Matrix(369,170,280,129) (-6/13,-11/24) -> (21/16,4/3) Hyperbolic Matrix(463,212,-1662,-761) (-11/24,-5/11) -> (-17/61,-5/18) Hyperbolic Matrix(637,288,1462,661) (-5/11,-14/31) -> (10/23,17/39) Hyperbolic Matrix(913,412,-2462,-1111) (-14/31,-9/20) -> (-23/62,-10/27) Hyperbolic Matrix(633,284,-2084,-935) (-9/20,-13/29) -> (-7/23,-17/56) Hyperbolic Matrix(451,202,998,447) (-13/29,-4/9) -> (14/31,5/11) Hyperbolic Matrix(625,276,1524,673) (-4/9,-15/34) -> (9/22,16/39) Hyperbolic Matrix(445,196,-1696,-747) (-15/34,-11/25) -> (-5/19,-11/42) Hyperbolic Matrix(979,430,2320,1019) (-11/25,-18/41) -> (8/19,19/45) Hyperbolic Matrix(1249,548,-3298,-1447) (-18/41,-7/16) -> (-25/66,-14/37) Hyperbolic Matrix(5145,2246,1954,853) (-7/16,-24/55) -> (50/19,79/30) Hyperbolic Matrix(3461,1510,1240,541) (-24/55,-17/39) -> (53/19,14/5) Hyperbolic Matrix(533,232,618,269) (-17/39,-10/23) -> (6/7,13/15) Hyperbolic Matrix(973,422,528,229) (-10/23,-13/30) -> (11/6,24/13) Hyperbolic Matrix(619,268,-2118,-917) (-13/30,-3/7) -> (-19/65,-7/24) Hyperbolic Matrix(1041,442,-2692,-1143) (-3/7,-14/33) -> (-12/31,-29/75) Hyperbolic Matrix(519,220,1130,479) (-14/33,-11/26) -> (11/24,6/13) Hyperbolic Matrix(1037,438,2512,1061) (-11/26,-19/45) -> (7/17,19/46) Hyperbolic Matrix(517,218,-1468,-619) (-19/45,-8/19) -> (-6/17,-13/37) Hyperbolic Matrix(861,362,88,37) (-8/19,-29/69) -> (9/1,10/1) Hyperbolic Matrix(5345,2246,1554,653) (-29/69,-21/50) -> (55/16,31/9) Hyperbolic Matrix(3277,1376,774,325) (-21/50,-34/81) -> (38/9,17/4) Hyperbolic Matrix(6205,2604,946,397) (-34/81,-47/112) -> (13/2,46/7) Hyperbolic Matrix(12493,5242,3358,1409) (-47/112,-13/31) -> (93/25,67/18) Hyperbolic Matrix(1117,468,432,181) (-13/31,-5/12) -> (31/12,13/5) Hyperbolic Matrix(255,106,344,143) (-5/12,-12/29) -> (14/19,3/4) Hyperbolic Matrix(257,106,594,245) (-12/29,-7/17) -> (3/7,10/23) Hyperbolic Matrix(253,104,596,245) (-7/17,-9/22) -> (11/26,3/7) Hyperbolic Matrix(421,172,678,277) (-9/22,-2/5) -> (18/29,5/8) Hyperbolic Matrix(1073,422,328,129) (-2/5,-11/28) -> (13/4,36/11) Hyperbolic Matrix(245,96,-1396,-547) (-11/28,-9/23) -> (-3/17,-7/40) Hyperbolic Matrix(737,288,412,161) (-9/23,-7/18) -> (25/14,9/5) Hyperbolic Matrix(407,158,492,191) (-7/18,-12/31) -> (14/17,5/6) Hyperbolic Matrix(569,220,-2770,-1071) (-29/75,-17/44) -> (-7/34,-1/5) Hyperbolic Matrix(83,32,568,219) (-17/44,-5/13) -> (1/7,3/20) Hyperbolic Matrix(245,94,-894,-343) (-5/13,-13/34) -> (-11/40,-3/11) Hyperbolic Matrix(325,124,726,277) (-13/34,-8/21) -> (4/9,9/20) Hyperbolic Matrix(163,62,-1212,-461) (-8/21,-19/50) -> (-3/22,-2/15) Hyperbolic Matrix(1453,552,2498,949) (-19/50,-11/29) -> (25/43,7/12) Hyperbolic Matrix(723,274,-4024,-1525) (-11/29,-25/66) -> (-9/50,-7/39) Hyperbolic Matrix(239,90,-640,-241) (-14/37,-3/8) -> (-3/8,-16/43) Parabolic Matrix(2629,978,3422,1273) (-16/43,-29/78) -> (43/56,10/13) Hyperbolic Matrix(5095,1894,6206,2307) (-29/78,-13/35) -> (55/67,23/28) Hyperbolic Matrix(555,206,-3656,-1357) (-13/35,-23/62) -> (-7/46,-5/33) Hyperbolic Matrix(319,118,-1668,-617) (-10/27,-17/46) -> (-5/26,-4/21) Hyperbolic Matrix(1029,380,1270,469) (-17/46,-7/19) -> (17/21,13/16) Hyperbolic Matrix(397,146,-1346,-495) (-7/19,-11/30) -> (-13/44,-5/17) Hyperbolic Matrix(159,58,392,143) (-11/30,-4/11) -> (2/5,9/22) Hyperbolic Matrix(469,170,80,29) (-4/11,-13/36) -> (23/4,6/1) Hyperbolic Matrix(233,84,-1484,-535) (-13/36,-9/25) -> (-3/19,-5/32) Hyperbolic Matrix(701,252,548,197) (-9/25,-5/14) -> (23/18,9/7) Hyperbolic Matrix(311,110,540,191) (-5/14,-6/17) -> (4/7,15/26) Hyperbolic Matrix(769,270,-3620,-1271) (-13/37,-7/20) -> (-17/80,-7/33) Hyperbolic Matrix(229,80,770,269) (-7/20,-1/3) -> (11/37,3/10) Hyperbolic Matrix(733,232,218,69) (-1/3,-6/19) -> (10/3,37/11) Hyperbolic Matrix(217,68,-1018,-319) (-6/19,-5/16) -> (-3/14,-10/47) Hyperbolic Matrix(507,158,292,91) (-5/16,-4/13) -> (26/15,7/4) Hyperbolic Matrix(287,88,362,111) (-4/13,-7/23) -> (15/19,4/5) Hyperbolic Matrix(1649,500,2800,849) (-17/56,-10/33) -> (10/17,33/56) Hyperbolic Matrix(73,22,428,129) (-10/33,-3/10) -> (1/6,4/23) Hyperbolic Matrix(355,106,144,43) (-3/10,-8/27) -> (22/9,5/2) Hyperbolic Matrix(2061,610,1490,441) (-8/27,-13/44) -> (47/34,18/13) Hyperbolic Matrix(1133,332,918,269) (-5/17,-12/41) -> (16/13,21/17) Hyperbolic Matrix(2475,724,776,227) (-12/41,-19/65) -> (35/11,16/5) Hyperbolic Matrix(213,62,-1412,-411) (-7/24,-9/31) -> (-5/33,-3/20) Hyperbolic Matrix(139,40,-490,-141) (-9/31,-2/7) -> (-2/7,-11/39) Parabolic Matrix(3065,864,486,137) (-11/39,-20/71) -> (44/7,19/3) Hyperbolic Matrix(10927,3076,4174,1175) (-20/71,-9/32) -> (89/34,144/55) Hyperbolic Matrix(349,98,-1948,-547) (-9/32,-7/25) -> (-7/39,-5/28) Hyperbolic Matrix(2149,600,1250,349) (-7/25,-12/43) -> (12/7,43/25) Hyperbolic Matrix(2567,716,484,135) (-12/43,-17/61) -> (37/7,16/3) Hyperbolic Matrix(621,172,278,77) (-5/18,-8/29) -> (20/9,9/4) Hyperbolic Matrix(2141,590,1310,361) (-8/29,-11/40) -> (49/30,18/11) Hyperbolic Matrix(479,130,70,19) (-3/11,-10/37) -> (20/3,7/1) Hyperbolic Matrix(341,92,-1642,-443) (-10/37,-7/26) -> (-5/24,-6/29) Hyperbolic Matrix(411,110,340,91) (-7/26,-4/15) -> (6/5,17/14) Hyperbolic Matrix(271,72,478,127) (-4/15,-5/19) -> (13/23,4/7) Hyperbolic Matrix(543,142,608,159) (-11/42,-6/23) -> (8/9,9/10) Hyperbolic Matrix(269,70,880,229) (-6/23,-1/4) -> (11/36,4/13) Hyperbolic Matrix(525,124,326,77) (-1/4,-4/17) -> (8/5,29/18) Hyperbolic Matrix(457,106,194,45) (-4/17,-3/13) -> (7/3,26/11) Hyperbolic Matrix(453,104,196,45) (-3/13,-5/22) -> (23/10,7/3) Hyperbolic Matrix(259,58,192,43) (-5/22,-2/9) -> (4/3,19/14) Hyperbolic Matrix(127,28,322,71) (-2/9,-5/23) -> (9/23,2/5) Hyperbolic Matrix(5365,1164,2936,637) (-5/23,-18/83) -> (42/23,53/29) Hyperbolic Matrix(9769,2118,7532,1633) (-18/83,-13/60) -> (83/64,48/37) Hyperbolic Matrix(3317,718,4532,981) (-13/60,-8/37) -> (30/41,41/56) Hyperbolic Matrix(1149,248,3952,853) (-8/37,-11/51) -> (9/31,16/55) Hyperbolic Matrix(65,14,636,137) (-11/51,-3/14) -> (1/10,1/9) Hyperbolic Matrix(9273,1972,3428,729) (-10/47,-17/80) -> (119/44,46/17) Hyperbolic Matrix(1841,390,760,161) (-7/33,-4/19) -> (46/19,17/7) Hyperbolic Matrix(823,172,378,79) (-4/19,-5/24) -> (13/6,24/11) Hyperbolic Matrix(2333,482,818,169) (-6/29,-7/34) -> (57/20,20/7) Hyperbolic Matrix(1057,206,744,145) (-1/5,-5/26) -> (71/50,27/19) Hyperbolic Matrix(679,128,122,23) (-4/21,-3/16) -> (11/2,28/5) Hyperbolic Matrix(429,80,370,69) (-3/16,-5/27) -> (15/13,7/6) Hyperbolic Matrix(2699,498,4352,803) (-5/27,-7/38) -> (31/50,49/79) Hyperbolic Matrix(491,90,60,11) (-7/38,-2/11) -> (8/1,17/2) Hyperbolic Matrix(2381,430,670,121) (-2/11,-9/50) -> (71/20,32/9) Hyperbolic Matrix(1583,282,668,119) (-5/28,-3/17) -> (45/19,19/8) Hyperbolic Matrix(607,106,544,95) (-7/40,-4/23) -> (10/9,9/8) Hyperbolic Matrix(1029,178,422,73) (-4/23,-1/6) -> (39/16,22/9) Hyperbolic Matrix(655,104,296,47) (-1/6,-3/19) -> (11/5,31/14) Hyperbolic Matrix(2013,314,1186,185) (-5/32,-2/13) -> (56/33,17/10) Hyperbolic Matrix(2421,370,530,81) (-2/13,-7/46) -> (73/16,32/7) Hyperbolic Matrix(941,140,410,61) (-3/20,-1/7) -> (39/17,23/10) Hyperbolic Matrix(1105,154,696,97) (-1/7,-3/22) -> (73/46,27/17) Hyperbolic Matrix(575,76,174,23) (-2/15,-1/8) -> (33/10,10/3) Hyperbolic Matrix(283,32,168,19) (-1/8,-1/9) -> (5/3,27/16) Hyperbolic Matrix(615,64,836,87) (-1/9,-1/10) -> (25/34,39/53) Hyperbolic Matrix(387,38,112,11) (-1/10,0/1) -> (38/11,7/2) Hyperbolic Matrix(509,-40,140,-11) (0/1,1/10) -> (109/30,40/11) Hyperbolic Matrix(943,-108,358,-41) (1/9,1/8) -> (79/30,29/11) Hyperbolic Matrix(531,-70,220,-29) (1/8,1/7) -> (41/17,29/12) Hyperbolic Matrix(1129,-170,870,-131) (3/20,2/13) -> (48/37,13/10) Hyperbolic Matrix(217,-34,734,-115) (2/13,1/6) -> (13/44,8/27) Hyperbolic Matrix(467,-82,1532,-269) (4/23,3/17) -> (7/23,18/59) Hyperbolic Matrix(551,-98,298,-53) (3/17,2/11) -> (24/13,13/7) Hyperbolic Matrix(337,-62,212,-39) (2/11,1/5) -> (27/17,8/5) Hyperbolic Matrix(207,-44,494,-105) (1/5,3/14) -> (5/12,13/31) Hyperbolic Matrix(287,-62,412,-89) (3/14,2/9) -> (16/23,7/10) Hyperbolic Matrix(367,-84,284,-65) (2/9,3/13) -> (9/7,22/17) Hyperbolic Matrix(325,-76,526,-123) (3/13,1/4) -> (21/34,13/21) Hyperbolic Matrix(317,-84,434,-115) (1/4,4/15) -> (8/11,19/26) Hyperbolic Matrix(355,-96,196,-53) (4/15,3/11) -> (9/5,20/11) Hyperbolic Matrix(275,-76,626,-173) (3/11,5/18) -> (7/16,11/25) Hyperbolic Matrix(351,-98,548,-153) (5/18,2/7) -> (16/25,9/14) Hyperbolic Matrix(2249,-652,852,-247) (2/7,9/31) -> (29/11,66/25) Hyperbolic Matrix(4261,-1240,890,-259) (16/55,7/24) -> (67/14,24/5) Hyperbolic Matrix(581,-170,270,-79) (7/24,5/17) -> (15/7,13/6) Hyperbolic Matrix(3899,-1150,4750,-1401) (5/17,18/61) -> (32/39,55/67) Hyperbolic Matrix(5637,-1664,12314,-3635) (18/61,31/105) -> (27/59,38/83) Hyperbolic Matrix(5249,-1550,850,-251) (31/105,13/44) -> (37/6,31/5) Hyperbolic Matrix(2391,-710,1310,-389) (8/27,11/37) -> (31/17,42/23) Hyperbolic Matrix(653,-198,498,-151) (3/10,7/23) -> (17/13,21/16) Hyperbolic Matrix(3985,-1216,2566,-783) (18/59,11/36) -> (59/38,14/9) Hyperbolic Matrix(381,-118,268,-83) (4/13,1/3) -> (27/19,10/7) Hyperbolic Matrix(259,-92,442,-157) (1/3,5/14) -> (7/12,17/29) Hyperbolic Matrix(957,-344,1544,-555) (5/14,9/25) -> (13/21,31/50) Hyperbolic Matrix(2095,-756,3306,-1193) (9/25,13/36) -> (19/30,45/71) Hyperbolic Matrix(1101,-398,2498,-903) (13/36,4/11) -> (26/59,15/34) Hyperbolic Matrix(1537,-562,3662,-1339) (4/11,15/41) -> (13/31,34/81) Hyperbolic Matrix(1867,-684,2634,-965) (15/41,11/30) -> (17/24,39/55) Hyperbolic Matrix(805,-296,1096,-403) (11/30,7/19) -> (11/15,25/34) Hyperbolic Matrix(183,-68,218,-81) (7/19,3/8) -> (5/6,11/13) Hyperbolic Matrix(653,-246,146,-55) (3/8,14/37) -> (40/9,9/2) Hyperbolic Matrix(2249,-852,652,-247) (14/37,11/29) -> (31/9,38/11) Hyperbolic Matrix(943,-358,108,-41) (11/29,19/50) -> (17/2,9/1) Hyperbolic Matrix(3115,-1184,834,-317) (19/50,8/21) -> (56/15,15/4) Hyperbolic Matrix(3437,-1312,1412,-539) (8/21,21/55) -> (17/7,56/23) Hyperbolic Matrix(2387,-912,3112,-1189) (21/55,13/34) -> (23/30,33/43) Hyperbolic Matrix(3615,-1384,2134,-817) (13/34,18/47) -> (22/13,61/36) Hyperbolic Matrix(1193,-458,758,-291) (18/47,5/13) -> (11/7,52/33) Hyperbolic Matrix(253,-98,648,-251) (5/13,7/18) -> (7/18,9/23) Parabolic Matrix(3437,-1412,1312,-539) (16/39,7/17) -> (55/21,76/29) Hyperbolic Matrix(3857,-1594,8844,-3655) (19/46,31/75) -> (17/39,41/94) Hyperbolic Matrix(1025,-424,1274,-527) (31/75,12/29) -> (4/5,25/31) Hyperbolic Matrix(531,-220,70,-29) (12/29,5/12) -> (15/2,8/1) Hyperbolic Matrix(4297,-1804,9754,-4095) (34/81,21/50) -> (37/84,26/59) Hyperbolic Matrix(7745,-3254,2254,-947) (21/50,29/69) -> (79/23,55/16) Hyperbolic Matrix(17495,-7354,6654,-2797) (29/69,37/88) -> (163/62,71/27) Hyperbolic Matrix(11193,-4708,4258,-1791) (37/88,8/19) -> (92/35,163/62) Hyperbolic Matrix(2637,-1114,5764,-2435) (19/45,30/71) -> (16/35,27/59) Hyperbolic Matrix(6081,-2570,1370,-579) (30/71,11/26) -> (71/16,40/9) Hyperbolic Matrix(4177,-1822,9122,-3979) (41/94,24/55) -> (38/83,11/24) Hyperbolic Matrix(6231,-2720,1670,-729) (24/55,7/16) -> (97/26,56/15) Hyperbolic Matrix(5277,-2324,6074,-2675) (11/25,37/84) -> (33/38,53/61) Hyperbolic Matrix(417,-184,34,-15) (15/34,19/43) -> (11/1,1/0) Hyperbolic Matrix(7801,-3448,2948,-1303) (19/43,23/52) -> (127/48,45/17) Hyperbolic Matrix(5407,-2394,2044,-905) (23/52,4/9) -> (82/31,127/48) Hyperbolic Matrix(2171,-978,828,-373) (9/20,14/31) -> (76/29,21/8) Hyperbolic Matrix(2333,-1066,4016,-1835) (5/11,16/35) -> (18/31,61/105) Hyperbolic Matrix(581,-270,170,-79) (6/13,1/2) -> (41/12,24/7) Hyperbolic Matrix(325,-174,424,-227) (1/2,7/13) -> (13/17,23/30) Hyperbolic Matrix(551,-298,98,-53) (7/13,6/11) -> (28/5,17/3) Hyperbolic Matrix(355,-196,96,-53) (6/11,5/9) -> (11/3,26/7) Hyperbolic Matrix(289,-162,512,-287) (5/9,9/16) -> (9/16,13/23) Parabolic Matrix(1077,-622,1522,-879) (15/26,11/19) -> (29/41,17/24) Hyperbolic Matrix(697,-404,854,-495) (11/19,18/31) -> (22/27,9/11) Hyperbolic Matrix(6799,-3950,3100,-1801) (61/105,43/74) -> (57/26,11/5) Hyperbolic Matrix(4395,-2554,2404,-1397) (43/74,25/43) -> (53/29,11/6) Hyperbolic Matrix(631,-370,220,-129) (17/29,10/17) -> (20/7,3/1) Hyperbolic Matrix(8115,-4784,2234,-1317) (33/56,23/39) -> (69/19,109/30) Hyperbolic Matrix(3615,-2134,1384,-817) (23/39,13/22) -> (47/18,81/31) Hyperbolic Matrix(629,-372,722,-427) (13/22,16/27) -> (20/23,7/8) Hyperbolic Matrix(155,-94,94,-57) (3/5,8/13) -> (18/11,5/3) Hyperbolic Matrix(1267,-782,1732,-1069) (8/13,21/34) -> (19/26,30/41) Hyperbolic Matrix(2963,-1838,1388,-861) (49/79,18/29) -> (32/15,15/7) Hyperbolic Matrix(337,-212,62,-39) (5/8,12/19) -> (16/3,11/2) Hyperbolic Matrix(857,-542,1042,-659) (12/19,19/30) -> (23/28,14/17) Hyperbolic Matrix(7131,-4520,2570,-1629) (45/71,26/41) -> (86/31,25/9) Hyperbolic Matrix(1193,-758,458,-291) (26/41,7/11) -> (13/5,60/23) Hyperbolic Matrix(977,-624,274,-175) (7/11,16/25) -> (32/9,25/7) Hyperbolic Matrix(61,-40,90,-59) (9/14,2/3) -> (2/3,11/16) Parabolic Matrix(2043,-1406,356,-245) (11/16,31/45) -> (63/11,23/4) Hyperbolic Matrix(13025,-8974,4974,-3427) (31/45,51/74) -> (199/76,55/21) Hyperbolic Matrix(16427,-11324,6274,-4325) (51/74,20/29) -> (144/55,199/76) Hyperbolic Matrix(1301,-898,1598,-1103) (20/29,9/13) -> (35/43,22/27) Hyperbolic Matrix(945,-656,206,-143) (9/13,16/23) -> (32/7,23/5) Hyperbolic Matrix(381,-268,118,-83) (7/10,12/17) -> (16/5,13/4) Hyperbolic Matrix(1465,-1036,1786,-1263) (12/17,29/41) -> (9/11,32/39) Hyperbolic Matrix(7431,-5270,2720,-1929) (39/55,22/31) -> (112/41,41/15) Hyperbolic Matrix(2749,-1952,1052,-747) (22/31,5/7) -> (81/31,34/13) Hyperbolic Matrix(203,-146,146,-105) (5/7,8/11) -> (18/13,7/5) Hyperbolic Matrix(3405,-2494,2194,-1607) (41/56,11/15) -> (45/29,59/38) Hyperbolic Matrix(5761,-4240,2390,-1759) (39/53,14/19) -> (94/39,41/17) Hyperbolic Matrix(653,-498,198,-151) (3/4,13/17) -> (23/7,33/10) Hyperbolic Matrix(7723,-5928,4978,-3821) (33/43,43/56) -> (121/78,45/29) Hyperbolic Matrix(367,-284,84,-65) (10/13,7/9) -> (13/3,22/5) Hyperbolic Matrix(309,-242,392,-307) (7/9,11/14) -> (11/14,15/19) Parabolic Matrix(7499,-6050,3100,-2501) (25/31,21/26) -> (179/74,75/31) Hyperbolic Matrix(2653,-2146,2046,-1655) (21/26,17/21) -> (35/27,83/64) Hyperbolic Matrix(1627,-1324,1874,-1525) (13/16,35/43) -> (13/15,33/38) Hyperbolic Matrix(731,-620,270,-229) (11/13,6/7) -> (46/17,19/7) Hyperbolic Matrix(9149,-7950,1900,-1651) (53/61,20/23) -> (130/27,53/11) Hyperbolic Matrix(903,-796,346,-305) (7/8,8/9) -> (60/23,47/18) Hyperbolic Matrix(497,-454,104,-95) (9/10,1/1) -> (43/9,67/14) Hyperbolic Matrix(735,-814,214,-237) (1/1,10/9) -> (24/7,79/23) Hyperbolic Matrix(703,-796,446,-505) (9/8,8/7) -> (52/33,41/26) Hyperbolic Matrix(629,-722,372,-427) (8/7,15/13) -> (49/29,22/13) Hyperbolic Matrix(183,-218,68,-81) (7/6,6/5) -> (8/3,27/10) Hyperbolic Matrix(857,-1042,542,-659) (17/14,11/9) -> (49/31,19/12) Hyperbolic Matrix(697,-854,404,-495) (11/9,16/13) -> (50/29,19/11) Hyperbolic Matrix(1475,-1824,224,-277) (21/17,26/21) -> (46/7,33/5) Hyperbolic Matrix(1025,-1274,424,-527) (26/21,5/4) -> (29/12,104/43) Hyperbolic Matrix(309,-392,242,-307) (5/4,14/11) -> (14/11,23/18) Parabolic Matrix(981,-1270,370,-479) (22/17,35/27) -> (45/17,8/3) Hyperbolic Matrix(325,-424,174,-227) (13/10,17/13) -> (13/7,15/8) Hyperbolic Matrix(805,-1096,296,-403) (19/14,15/11) -> (19/7,49/18) Hyperbolic Matrix(317,-434,84,-115) (15/11,11/8) -> (15/4,19/5) Hyperbolic Matrix(1219,-1682,882,-1217) (11/8,29/21) -> (29/21,47/34) Parabolic Matrix(1163,-1636,686,-965) (7/5,31/22) -> (61/36,39/23) Hyperbolic Matrix(1867,-2634,684,-965) (31/22,24/17) -> (30/11,71/26) Hyperbolic Matrix(1077,-1522,622,-879) (24/17,17/12) -> (45/26,26/15) Hyperbolic Matrix(2729,-3872,1922,-2727) (17/12,44/31) -> (44/31,71/50) Parabolic Matrix(287,-412,62,-89) (10/7,13/9) -> (23/5,14/3) Hyperbolic Matrix(61,-90,40,-59) (13/9,3/2) -> (3/2,17/11) Parabolic Matrix(1961,-3038,1138,-1763) (17/11,31/20) -> (31/18,81/47) Hyperbolic Matrix(7449,-11552,4802,-7447) (31/20,76/49) -> (76/49,121/78) Parabolic Matrix(351,-548,98,-153) (14/9,11/7) -> (25/7,18/5) Hyperbolic Matrix(2095,-3306,756,-1193) (41/26,30/19) -> (36/13,61/22) Hyperbolic Matrix(2345,-3706,1356,-2143) (30/19,49/31) -> (19/11,64/37) Hyperbolic Matrix(2669,-4232,1682,-2667) (19/12,46/29) -> (46/29,73/46) Parabolic Matrix(957,-1544,344,-555) (29/18,21/13) -> (25/9,39/14) Hyperbolic Matrix(325,-526,76,-123) (21/13,13/8) -> (17/4,13/3) Hyperbolic Matrix(1179,-1922,722,-1177) (13/8,31/19) -> (31/19,49/30) Parabolic Matrix(5095,-8606,2956,-4993) (27/16,49/29) -> (81/47,131/76) Hyperbolic Matrix(593,-1006,56,-95) (39/23,56/33) -> (10/1,11/1) Hyperbolic Matrix(259,-442,92,-157) (17/10,12/7) -> (14/5,17/6) Hyperbolic Matrix(4649,-8000,1250,-2151) (43/25,74/43) -> (26/7,93/25) Hyperbolic Matrix(2333,-4016,1066,-1835) (74/43,31/18) -> (35/16,46/21) Hyperbolic Matrix(4057,-6994,844,-1455) (131/76,50/29) -> (24/5,77/16) Hyperbolic Matrix(2069,-3580,330,-571) (64/37,45/26) -> (25/4,44/7) Hyperbolic Matrix(289,-512,162,-287) (7/4,16/9) -> (16/9,25/14) Parabolic Matrix(1631,-2970,620,-1129) (20/11,31/17) -> (71/27,50/19) Hyperbolic Matrix(361,-688,138,-263) (15/8,2/1) -> (34/13,89/34) Hyperbolic Matrix(273,-578,128,-271) (2/1,17/8) -> (17/8,32/15) Parabolic Matrix(2637,-5764,1114,-2435) (24/11,35/16) -> (71/30,116/49) Hyperbolic Matrix(7129,-15620,2570,-5631) (46/21,57/26) -> (233/84,86/31) Hyperbolic Matrix(1135,-2516,466,-1033) (31/14,20/9) -> (56/23,39/16) Hyperbolic Matrix(275,-626,76,-173) (9/4,16/7) -> (18/5,29/8) Hyperbolic Matrix(2355,-5396,896,-2053) (16/7,55/24) -> (21/8,92/35) Hyperbolic Matrix(3857,-8844,1594,-3655) (55/24,39/17) -> (75/31,121/50) Hyperbolic Matrix(2867,-6784,1084,-2565) (26/11,71/30) -> (37/14,82/31) Hyperbolic Matrix(2583,-6116,416,-985) (116/49,45/19) -> (31/5,56/9) Hyperbolic Matrix(207,-494,44,-105) (19/8,12/5) -> (14/3,19/4) Hyperbolic Matrix(2333,-5618,968,-2331) (12/5,53/22) -> (53/22,94/39) Parabolic Matrix(20973,-50728,7678,-18571) (104/43,179/74) -> (295/108,112/41) Hyperbolic Matrix(3275,-7926,526,-1273) (121/50,46/19) -> (56/9,25/4) Hyperbolic Matrix(253,-648,98,-251) (5/2,18/7) -> (18/7,31/12) Parabolic Matrix(3943,-10658,1458,-3941) (27/10,73/27) -> (73/27,119/44) Parabolic Matrix(1101,-2998,148,-403) (49/18,79/29) -> (37/5,15/2) Hyperbolic Matrix(24523,-66978,8978,-24521) (71/26,183/67) -> (183/67,295/108) Parabolic Matrix(455,-1244,94,-257) (41/15,11/4) -> (29/6,5/1) Hyperbolic Matrix(823,-2276,226,-625) (11/4,36/13) -> (40/11,51/14) Hyperbolic Matrix(15583,-43218,5618,-15581) (61/22,147/53) -> (147/53,233/84) Parabolic Matrix(2165,-6034,634,-1767) (39/14,53/19) -> (99/29,41/12) Hyperbolic Matrix(963,-2738,338,-961) (17/6,37/13) -> (37/13,57/20) Parabolic Matrix(229,-722,72,-227) (3/1,19/6) -> (19/6,35/11) Parabolic Matrix(467,-1532,82,-269) (36/11,23/7) -> (17/3,40/7) Hyperbolic Matrix(1065,-3586,286,-963) (37/11,27/8) -> (67/18,41/11) Hyperbolic Matrix(217,-734,34,-115) (27/8,17/5) -> (19/3,13/2) Hyperbolic Matrix(1973,-6728,578,-1971) (17/5,58/17) -> (58/17,99/29) Parabolic Matrix(859,-3042,242,-857) (7/2,39/11) -> (39/11,71/20) Parabolic Matrix(2733,-9916,616,-2235) (29/8,98/27) -> (102/23,71/16) Hyperbolic Matrix(2775,-10076,626,-2273) (98/27,69/19) -> (31/7,102/23) Hyperbolic Matrix(829,-3022,172,-627) (51/14,11/3) -> (53/11,29/6) Hyperbolic Matrix(2273,-8476,476,-1775) (41/11,97/26) -> (105/22,43/9) Hyperbolic Matrix(41,-160,10,-39) (19/5,4/1) -> (4/1,21/5) Parabolic Matrix(767,-3234,134,-565) (21/5,38/9) -> (40/7,63/11) Hyperbolic Matrix(305,-1346,46,-203) (22/5,31/7) -> (33/5,20/3) Hyperbolic Matrix(739,-3362,162,-737) (9/2,41/9) -> (41/9,73/16) Parabolic Matrix(1613,-7688,338,-1611) (19/4,62/13) -> (62/13,105/22) Parabolic Matrix(2279,-10970,370,-1781) (77/16,130/27) -> (80/13,37/6) Hyperbolic Matrix(169,-882,32,-167) (5/1,21/4) -> (21/4,37/7) Parabolic Matrix(603,-3698,98,-601) (6/1,43/7) -> (43/7,80/13) Parabolic Matrix(133,-968,18,-131) (7/1,22/3) -> (22/3,37/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(761,362,288,137) -> Matrix(7,-2,4,-1) Matrix(1793,842,658,309) -> Matrix(7,-2,4,-1) Matrix(279,130,470,219) -> Matrix(11,-2,6,-1) Matrix(369,170,280,129) -> Matrix(1,0,-4,1) Matrix(463,212,-1662,-761) -> Matrix(9,-2,32,-7) Matrix(637,288,1462,661) -> Matrix(7,-2,18,-5) Matrix(913,412,-2462,-1111) -> Matrix(13,-4,62,-19) Matrix(633,284,-2084,-935) -> Matrix(7,-2,18,-5) Matrix(451,202,998,447) -> Matrix(5,-2,8,-3) Matrix(625,276,1524,673) -> Matrix(1,0,-6,1) Matrix(445,196,-1696,-747) -> Matrix(31,-6,88,-17) Matrix(979,430,2320,1019) -> Matrix(1,0,-4,1) Matrix(1249,548,-3298,-1447) -> Matrix(1,0,-4,1) Matrix(5145,2246,1954,853) -> Matrix(35,-8,22,-5) Matrix(3461,1510,1240,541) -> Matrix(1,0,-4,1) Matrix(533,232,618,269) -> Matrix(9,-2,-4,1) Matrix(973,422,528,229) -> Matrix(35,-8,22,-5) Matrix(619,268,-2118,-917) -> Matrix(25,-6,46,-11) Matrix(1041,442,-2692,-1143) -> Matrix(13,-4,36,-11) Matrix(519,220,1130,479) -> Matrix(7,-2,18,-5) Matrix(1037,438,2512,1061) -> Matrix(7,-2,-10,3) Matrix(517,218,-1468,-619) -> Matrix(13,-4,36,-11) Matrix(861,362,88,37) -> Matrix(7,-2,4,-1) Matrix(5345,2246,1554,653) -> Matrix(27,-8,-10,3) Matrix(3277,1376,774,325) -> Matrix(13,-4,36,-11) Matrix(6205,2604,946,397) -> Matrix(13,-4,10,-3) Matrix(12493,5242,3358,1409) -> Matrix(19,-6,-22,7) Matrix(1117,468,432,181) -> Matrix(31,-10,28,-9) Matrix(255,106,344,143) -> Matrix(5,-2,8,-3) Matrix(257,106,594,245) -> Matrix(1,0,0,1) Matrix(253,104,596,245) -> Matrix(1,0,-4,1) Matrix(421,172,678,277) -> Matrix(1,0,-4,1) Matrix(1073,422,328,129) -> Matrix(27,-8,-10,3) Matrix(245,96,-1396,-547) -> Matrix(19,-6,16,-5) Matrix(737,288,412,161) -> Matrix(49,-16,46,-15) Matrix(407,158,492,191) -> Matrix(11,-4,14,-5) Matrix(569,220,-2770,-1071) -> Matrix(21,-8,50,-19) Matrix(83,32,568,219) -> Matrix(5,-2,18,-7) Matrix(245,94,-894,-343) -> Matrix(9,-4,34,-15) Matrix(325,124,726,277) -> Matrix(1,0,0,1) Matrix(163,62,-1212,-461) -> Matrix(5,-2,8,-3) Matrix(1453,552,2498,949) -> Matrix(17,-10,12,-7) Matrix(723,274,-4024,-1525) -> Matrix(3,-2,2,-1) Matrix(239,90,-640,-241) -> Matrix(1,0,4,1) Matrix(2629,978,3422,1273) -> Matrix(9,-2,14,-3) Matrix(5095,1894,6206,2307) -> Matrix(1,0,-4,1) Matrix(555,206,-3656,-1357) -> Matrix(31,-6,88,-17) Matrix(319,118,-1668,-617) -> Matrix(25,-6,46,-11) Matrix(1029,380,1270,469) -> Matrix(7,-2,4,-1) Matrix(397,146,-1346,-495) -> Matrix(1,0,-2,1) Matrix(159,58,392,143) -> Matrix(7,-2,4,-1) Matrix(469,170,80,29) -> Matrix(1,0,-4,1) Matrix(233,84,-1484,-535) -> Matrix(7,-2,18,-5) Matrix(701,252,548,197) -> Matrix(25,-8,22,-7) Matrix(311,110,540,191) -> Matrix(13,-4,10,-3) Matrix(769,270,-3620,-1271) -> Matrix(19,-8,50,-21) Matrix(229,80,770,269) -> Matrix(3,-2,8,-5) Matrix(733,232,218,69) -> Matrix(9,-2,-4,1) Matrix(217,68,-1018,-319) -> Matrix(13,-4,36,-11) Matrix(507,158,292,91) -> Matrix(11,-4,14,-5) Matrix(287,88,362,111) -> Matrix(13,-4,10,-3) Matrix(1649,500,2800,849) -> Matrix(1,0,-2,1) Matrix(73,22,428,129) -> Matrix(1,0,0,1) Matrix(355,106,144,43) -> Matrix(5,-2,8,-3) Matrix(2061,610,1490,441) -> Matrix(17,-8,-2,1) Matrix(1133,332,918,269) -> Matrix(5,-2,8,-3) Matrix(2475,724,776,227) -> Matrix(29,-14,-2,1) Matrix(213,62,-1412,-411) -> Matrix(5,-4,14,-11) Matrix(139,40,-490,-141) -> Matrix(1,0,4,1) Matrix(3065,864,486,137) -> Matrix(1,0,-6,1) Matrix(10927,3076,4174,1175) -> Matrix(21,-4,16,-3) Matrix(349,98,-1948,-547) -> Matrix(1,0,-4,1) Matrix(2149,600,1250,349) -> Matrix(43,-10,56,-13) Matrix(2567,716,484,135) -> Matrix(41,-10,-4,1) Matrix(621,172,278,77) -> Matrix(1,0,-4,1) Matrix(2141,590,1310,361) -> Matrix(49,-12,94,-23) Matrix(479,130,70,19) -> Matrix(7,-2,-10,3) Matrix(341,92,-1642,-443) -> Matrix(13,-4,36,-11) Matrix(411,110,340,91) -> Matrix(13,-4,10,-3) Matrix(271,72,478,127) -> Matrix(37,-12,34,-11) Matrix(543,142,608,159) -> Matrix(11,-4,14,-5) Matrix(269,70,880,229) -> Matrix(21,-8,50,-19) Matrix(525,124,326,77) -> Matrix(1,0,0,1) Matrix(457,106,194,45) -> Matrix(1,0,0,1) Matrix(453,104,196,45) -> Matrix(1,0,-4,1) Matrix(259,58,192,43) -> Matrix(7,-2,4,-1) Matrix(127,28,322,71) -> Matrix(7,-2,4,-1) Matrix(5365,1164,2936,637) -> Matrix(1,0,-2,1) Matrix(9769,2118,7532,1633) -> Matrix(49,-18,30,-11) Matrix(3317,718,4532,981) -> Matrix(27,-10,46,-17) Matrix(1149,248,3952,853) -> Matrix(21,-8,50,-19) Matrix(65,14,636,137) -> Matrix(5,-2,8,-3) Matrix(9273,1972,3428,729) -> Matrix(97,-36,62,-23) Matrix(1841,390,760,161) -> Matrix(5,-2,18,-7) Matrix(823,172,378,79) -> Matrix(5,-2,-2,1) Matrix(2333,482,818,169) -> Matrix(21,-8,8,-3) Matrix(1057,206,744,145) -> Matrix(21,-10,-2,1) Matrix(679,128,122,23) -> Matrix(1,0,-2,1) Matrix(429,80,370,69) -> Matrix(3,-2,8,-5) Matrix(2699,498,4352,803) -> Matrix(3,-2,2,-1) Matrix(491,90,60,11) -> Matrix(3,-2,2,-1) Matrix(2381,430,670,121) -> Matrix(7,-6,-8,7) Matrix(1583,282,668,119) -> Matrix(1,0,0,1) Matrix(607,106,544,95) -> Matrix(1,-2,2,-3) Matrix(1029,178,422,73) -> Matrix(1,0,2,1) Matrix(655,104,296,47) -> Matrix(7,-2,4,-1) Matrix(2013,314,1186,185) -> Matrix(5,-2,8,-3) Matrix(2421,370,530,81) -> Matrix(43,-14,40,-13) Matrix(941,140,410,61) -> Matrix(5,-2,-2,1) Matrix(1105,154,696,97) -> Matrix(13,-6,24,-11) Matrix(575,76,174,23) -> Matrix(1,0,-2,1) Matrix(283,32,168,19) -> Matrix(1,-2,2,-3) Matrix(615,64,836,87) -> Matrix(9,-2,14,-3) Matrix(387,38,112,11) -> Matrix(5,-2,-2,1) Matrix(509,-40,140,-11) -> Matrix(5,-2,-2,1) Matrix(943,-108,358,-41) -> Matrix(7,-2,4,-1) Matrix(531,-70,220,-29) -> Matrix(1,0,2,1) Matrix(1129,-170,870,-131) -> Matrix(7,-2,4,-1) Matrix(217,-34,734,-115) -> Matrix(7,-2,18,-5) Matrix(467,-82,1532,-269) -> Matrix(21,-8,50,-19) Matrix(551,-98,298,-53) -> Matrix(19,-8,12,-5) Matrix(337,-62,212,-39) -> Matrix(5,-2,8,-3) Matrix(207,-44,494,-105) -> Matrix(3,-2,2,-1) Matrix(287,-62,412,-89) -> Matrix(5,-4,14,-11) Matrix(367,-84,284,-65) -> Matrix(3,-2,2,-1) Matrix(325,-76,526,-123) -> Matrix(1,-2,0,1) Matrix(317,-84,434,-115) -> Matrix(9,-2,14,-3) Matrix(355,-96,196,-53) -> Matrix(19,-6,16,-5) Matrix(275,-76,626,-173) -> Matrix(1,0,0,1) Matrix(351,-98,548,-153) -> Matrix(1,0,-4,1) Matrix(2249,-652,852,-247) -> Matrix(1,0,-2,1) Matrix(4261,-1240,890,-259) -> Matrix(1,0,-2,1) Matrix(581,-170,270,-79) -> Matrix(5,-2,-2,1) Matrix(3899,-1150,4750,-1401) -> Matrix(5,-2,8,-3) Matrix(5637,-1664,12314,-3635) -> Matrix(1,0,-2,1) Matrix(5249,-1550,850,-251) -> Matrix(7,-2,-10,3) Matrix(2391,-710,1310,-389) -> Matrix(33,-14,26,-11) Matrix(653,-198,498,-151) -> Matrix(1,0,-2,1) Matrix(3985,-1216,2566,-783) -> Matrix(5,-2,8,-3) Matrix(381,-118,268,-83) -> Matrix(13,-6,-2,1) Matrix(259,-92,442,-157) -> Matrix(5,-4,4,-3) Matrix(957,-344,1544,-555) -> Matrix(3,-2,2,-1) Matrix(2095,-756,3306,-1193) -> Matrix(1,0,-2,1) Matrix(1101,-398,2498,-903) -> Matrix(7,-4,16,-9) Matrix(1537,-562,3662,-1339) -> Matrix(3,-2,-4,3) Matrix(1867,-684,2634,-965) -> Matrix(3,-2,2,-1) Matrix(805,-296,1096,-403) -> Matrix(11,-8,18,-13) Matrix(183,-68,218,-81) -> Matrix(5,-4,4,-3) Matrix(653,-246,146,-55) -> Matrix(1,0,0,1) Matrix(2249,-852,652,-247) -> Matrix(1,0,-2,1) Matrix(943,-358,108,-41) -> Matrix(3,-2,-4,3) Matrix(3115,-1184,834,-317) -> Matrix(5,-4,-6,5) Matrix(3437,-1312,1412,-539) -> Matrix(5,-4,14,-11) Matrix(2387,-912,3112,-1189) -> Matrix(3,-2,2,-1) Matrix(3615,-1384,2134,-817) -> Matrix(23,-18,32,-25) Matrix(1193,-458,758,-291) -> Matrix(7,-6,20,-17) Matrix(253,-98,648,-251) -> Matrix(13,-12,12,-11) Matrix(3437,-1412,1312,-539) -> Matrix(3,4,2,3) Matrix(3857,-1594,8844,-3655) -> Matrix(1,0,2,1) Matrix(1025,-424,1274,-527) -> Matrix(1,2,0,1) Matrix(531,-220,70,-29) -> Matrix(1,0,2,1) Matrix(4297,-1804,9754,-4095) -> Matrix(3,-2,8,-5) Matrix(7745,-3254,2254,-947) -> Matrix(1,-2,0,1) Matrix(17495,-7354,6654,-2797) -> Matrix(1,2,0,1) Matrix(11193,-4708,4258,-1791) -> Matrix(7,-2,4,-1) Matrix(2637,-1114,5764,-2435) -> Matrix(1,-2,2,-3) Matrix(6081,-2570,1370,-579) -> Matrix(1,-4,2,-7) Matrix(4177,-1822,9122,-3979) -> Matrix(1,0,-2,1) Matrix(6231,-2720,1670,-729) -> Matrix(3,-2,-4,3) Matrix(5277,-2324,6074,-2675) -> Matrix(11,-4,-8,3) Matrix(417,-184,34,-15) -> Matrix(5,-2,-2,1) Matrix(7801,-3448,2948,-1303) -> Matrix(9,-4,-2,1) Matrix(5407,-2394,2044,-905) -> Matrix(7,-4,2,-1) Matrix(2171,-978,828,-373) -> Matrix(17,-10,12,-7) Matrix(2333,-1066,4016,-1835) -> Matrix(5,-4,4,-3) Matrix(581,-270,170,-79) -> Matrix(5,-2,-2,1) Matrix(325,-174,424,-227) -> Matrix(1,0,0,1) Matrix(551,-298,98,-53) -> Matrix(11,-8,-4,3) Matrix(355,-196,96,-53) -> Matrix(7,-6,-8,7) Matrix(289,-162,512,-287) -> Matrix(29,-28,28,-27) Matrix(1077,-622,1522,-879) -> Matrix(5,-6,6,-7) Matrix(697,-404,854,-495) -> Matrix(3,-4,-2,3) Matrix(6799,-3950,3100,-1801) -> Matrix(3,-4,4,-5) Matrix(4395,-2554,2404,-1397) -> Matrix(23,-32,18,-25) Matrix(631,-370,220,-129) -> Matrix(5,-8,2,-3) Matrix(8115,-4784,2234,-1317) -> Matrix(7,-10,-2,3) Matrix(3615,-2134,1384,-817) -> Matrix(11,-18,8,-13) Matrix(629,-372,722,-427) -> Matrix(1,-2,0,1) Matrix(155,-94,94,-57) -> Matrix(1,-4,2,-7) Matrix(1267,-782,1732,-1069) -> Matrix(1,0,2,1) Matrix(2963,-1838,1388,-861) -> Matrix(1,-2,0,1) Matrix(337,-212,62,-39) -> Matrix(1,-2,0,1) Matrix(857,-542,1042,-659) -> Matrix(1,2,2,5) Matrix(7131,-4520,2570,-1629) -> Matrix(5,12,2,5) Matrix(1193,-758,458,-291) -> Matrix(5,6,4,5) Matrix(977,-624,274,-175) -> Matrix(1,2,-2,-3) Matrix(61,-40,90,-59) -> Matrix(1,0,4,1) Matrix(2043,-1406,356,-245) -> Matrix(5,-2,-2,1) Matrix(13025,-8974,4974,-3427) -> Matrix(5,-4,4,-3) Matrix(16427,-11324,6274,-4325) -> Matrix(21,-4,16,-3) Matrix(1301,-898,1598,-1103) -> Matrix(1,0,-4,1) Matrix(945,-656,206,-143) -> Matrix(19,-6,16,-5) Matrix(381,-268,118,-83) -> Matrix(13,-6,-2,1) Matrix(1465,-1036,1786,-1263) -> Matrix(3,-2,8,-5) Matrix(7431,-5270,2720,-1929) -> Matrix(7,-2,4,-1) Matrix(2749,-1952,1052,-747) -> Matrix(5,-4,4,-3) Matrix(203,-146,146,-105) -> Matrix(1,0,-2,1) Matrix(3405,-2494,2194,-1607) -> Matrix(3,-2,14,-9) Matrix(5761,-4240,2390,-1759) -> Matrix(3,-2,32,-21) Matrix(653,-498,198,-151) -> Matrix(1,0,-2,1) Matrix(7723,-5928,4978,-3821) -> Matrix(3,-2,14,-9) Matrix(367,-284,84,-65) -> Matrix(3,-2,2,-1) Matrix(309,-242,392,-307) -> Matrix(13,-12,12,-11) Matrix(7499,-6050,3100,-2501) -> Matrix(1,-2,2,-3) Matrix(2653,-2146,2046,-1655) -> Matrix(3,-8,2,-5) Matrix(1627,-1324,1874,-1525) -> Matrix(1,0,0,1) Matrix(731,-620,270,-229) -> Matrix(3,-8,2,-5) Matrix(9149,-7950,1900,-1651) -> Matrix(3,4,2,3) Matrix(903,-796,346,-305) -> Matrix(5,-4,4,-3) Matrix(497,-454,104,-95) -> Matrix(1,2,0,1) Matrix(735,-814,214,-237) -> Matrix(5,-2,-2,1) Matrix(703,-796,446,-505) -> Matrix(3,-2,8,-5) Matrix(629,-722,372,-427) -> Matrix(5,-2,8,-3) Matrix(183,-218,68,-81) -> Matrix(5,-4,4,-3) Matrix(857,-1042,542,-659) -> Matrix(1,2,2,5) Matrix(697,-854,404,-495) -> Matrix(11,-4,14,-5) Matrix(1475,-1824,224,-277) -> Matrix(3,-2,2,-1) Matrix(1025,-1274,424,-527) -> Matrix(3,-2,8,-5) Matrix(309,-392,242,-307) -> Matrix(13,-12,12,-11) Matrix(981,-1270,370,-479) -> Matrix(1,-2,2,-3) Matrix(325,-424,174,-227) -> Matrix(1,0,0,1) Matrix(805,-1096,296,-403) -> Matrix(3,-8,2,-5) Matrix(317,-434,84,-115) -> Matrix(1,-2,-2,5) Matrix(1219,-1682,882,-1217) -> Matrix(1,-16,0,1) Matrix(1163,-1636,686,-965) -> Matrix(3,2,4,3) Matrix(1867,-2634,684,-965) -> Matrix(3,-2,2,-1) Matrix(1077,-1522,622,-879) -> Matrix(5,-6,6,-7) Matrix(2729,-3872,1922,-2727) -> Matrix(1,-24,0,1) Matrix(287,-412,62,-89) -> Matrix(3,4,2,3) Matrix(61,-90,40,-59) -> Matrix(1,0,4,1) Matrix(1961,-3038,1138,-1763) -> Matrix(11,-4,14,-5) Matrix(7449,-11552,4802,-7447) -> Matrix(1,0,4,1) Matrix(351,-548,98,-153) -> Matrix(1,0,-4,1) Matrix(2095,-3306,756,-1193) -> Matrix(1,0,-2,1) Matrix(2345,-3706,1356,-2143) -> Matrix(17,-6,20,-7) Matrix(2669,-4232,1682,-2667) -> Matrix(33,-16,64,-31) Matrix(957,-1544,344,-555) -> Matrix(3,-2,2,-1) Matrix(325,-526,76,-123) -> Matrix(5,-2,8,-3) Matrix(1179,-1922,722,-1177) -> Matrix(49,-24,96,-47) Matrix(5095,-8606,2956,-4993) -> Matrix(1,-2,2,-3) Matrix(593,-1006,56,-95) -> Matrix(5,-4,4,-3) Matrix(259,-442,92,-157) -> Matrix(5,-4,4,-3) Matrix(4649,-8000,1250,-2151) -> Matrix(13,-10,-22,17) Matrix(2333,-4016,1066,-1835) -> Matrix(5,-4,4,-3) Matrix(4057,-6994,844,-1455) -> Matrix(5,-4,4,-3) Matrix(2069,-3580,330,-571) -> Matrix(5,-4,-16,13) Matrix(289,-512,162,-287) -> Matrix(29,-28,28,-27) Matrix(1631,-2970,620,-1129) -> Matrix(1,-2,2,-3) Matrix(361,-688,138,-263) -> Matrix(3,-2,2,-1) Matrix(273,-578,128,-271) -> Matrix(1,-4,0,1) Matrix(2637,-5764,1114,-2435) -> Matrix(1,-2,2,-3) Matrix(7129,-15620,2570,-5631) -> Matrix(13,2,6,1) Matrix(1135,-2516,466,-1033) -> Matrix(1,-2,2,-3) Matrix(275,-626,76,-173) -> Matrix(1,0,0,1) Matrix(2355,-5396,896,-2053) -> Matrix(3,-2,2,-1) Matrix(3857,-8844,1594,-3655) -> Matrix(1,0,2,1) Matrix(2867,-6784,1084,-2565) -> Matrix(7,-4,2,-1) Matrix(2583,-6116,416,-985) -> Matrix(5,-4,-6,5) Matrix(207,-494,44,-105) -> Matrix(3,-2,2,-1) Matrix(2333,-5618,968,-2331) -> Matrix(1,0,12,1) Matrix(20973,-50728,7678,-18571) -> Matrix(19,-8,12,-5) Matrix(3275,-7926,526,-1273) -> Matrix(3,-2,-4,3) Matrix(253,-648,98,-251) -> Matrix(13,-12,12,-11) Matrix(3943,-10658,1458,-3941) -> Matrix(49,-72,32,-47) Matrix(1101,-2998,148,-403) -> Matrix(1,-2,8,-15) Matrix(24523,-66978,8978,-24521) -> Matrix(25,-36,16,-23) Matrix(455,-1244,94,-257) -> Matrix(5,-8,2,-3) Matrix(823,-2276,226,-625) -> Matrix(1,-4,0,1) Matrix(15583,-43218,5618,-15581) -> Matrix(25,-48,12,-23) Matrix(2165,-6034,634,-1767) -> Matrix(1,-6,0,1) Matrix(963,-2738,338,-961) -> Matrix(9,-16,4,-7) Matrix(229,-722,72,-227) -> Matrix(1,-24,0,1) Matrix(467,-1532,82,-269) -> Matrix(3,8,-2,-5) Matrix(1065,-3586,286,-963) -> Matrix(1,4,-2,-7) Matrix(217,-734,34,-115) -> Matrix(1,2,-2,-3) Matrix(1973,-6728,578,-1971) -> Matrix(1,-4,0,1) Matrix(859,-3042,242,-857) -> Matrix(11,12,-12,-13) Matrix(2733,-9916,616,-2235) -> Matrix(1,-4,2,-7) Matrix(2775,-10076,626,-2273) -> Matrix(1,4,2,9) Matrix(829,-3022,172,-627) -> Matrix(3,4,2,3) Matrix(2273,-8476,476,-1775) -> Matrix(11,8,4,3) Matrix(41,-160,10,-39) -> Matrix(1,0,4,1) Matrix(767,-3234,134,-565) -> Matrix(5,-2,-2,1) Matrix(305,-1346,46,-203) -> Matrix(1,0,-2,1) Matrix(739,-3362,162,-737) -> Matrix(29,-28,28,-27) Matrix(1613,-7688,338,-1611) -> Matrix(9,-16,4,-7) Matrix(2279,-10970,370,-1781) -> Matrix(7,-6,-8,7) Matrix(169,-882,32,-167) -> Matrix(1,-16,0,1) Matrix(603,-3698,98,-601) -> Matrix(11,12,-12,-13) Matrix(133,-968,18,-131) -> Matrix(1,0,12,1) 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): 78 Degree of the the map X: 78 Degree of the the map Y: 300 ----------------------------------------------------------------------- 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): 300 Minimal number of generators: 51 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: 28 Genus: 12 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/4 4/11 3/7 2/3 1/1 14/11 29/21 3/2 31/19 16/9 2/1 7/3 18/7 73/27 11/4 37/13 3/1 10/3 58/17 4/1 9/2 5/1 6/1 7/1 22/3 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 0/1 1/2 1/6 1/3 1/2 1/5 1/2 2/3 2/9 1/1 2/1 1/4 0/1 3/11 1/3 2/5 2/7 1/3 2/5 3/10 2/5 1/2 1/3 1/2 2/3 5/14 1/2 2/3 9/25 3/5 2/3 4/11 2/3 11/30 2/3 1/1 7/19 2/3 3/4 3/8 2/3 1/1 2/5 1/1 1/0 7/17 0/1 1/0 12/29 -1/1 0/1 5/12 0/1 1/2 8/19 0/1 1/1 3/7 0/1 7/16 0/1 1/3 4/9 0/1 1/2 5/11 0/1 1/1 6/13 0/1 1/2 1/2 1/2 1/1 4/7 1/1 6/5 7/12 3/2 2/1 17/29 3/2 2/1 10/17 1/1 2/1 3/5 2/1 1/0 8/13 -4/1 1/0 5/8 0/1 1/0 2/3 0/1 5/7 0/1 1/2 8/11 1/2 4/7 3/4 1/2 1/1 4/5 1/1 2/1 5/6 1/1 2/1 11/13 2/1 1/0 6/7 0/1 1/0 1/1 0/1 1/1 7/6 0/1 1/2 6/5 2/3 1/1 5/4 2/3 1/1 14/11 1/1 9/7 1/1 4/3 4/3 1/1 1/0 11/8 4/1 1/0 29/21 1/0 18/13 -4/1 1/0 7/5 0/1 1/0 3/2 0/1 8/5 0/1 1/2 13/8 4/9 1/2 31/19 1/2 18/11 1/2 8/15 5/3 1/2 2/3 17/10 2/3 1/1 12/7 2/3 3/4 7/4 6/7 1/1 16/9 1/1 9/5 1/1 8/7 2/1 1/1 1/0 9/4 0/1 1/0 16/7 -1/1 0/1 7/3 0/1 19/8 0/1 1/1 12/5 0/1 1/0 5/2 1/2 1/1 18/7 1/1 13/5 1/1 5/4 8/3 1/1 2/1 27/10 4/3 3/2 73/27 3/2 46/17 3/2 8/5 19/7 3/2 2/1 30/11 1/1 2/1 11/4 2/1 25/9 2/1 3/1 14/5 2/1 1/0 17/6 1/1 2/1 37/13 2/1 20/7 2/1 3/1 3/1 2/1 1/0 10/3 -2/1 1/0 17/5 -1/1 1/0 58/17 1/0 41/12 -3/1 1/0 24/7 -2/1 1/0 7/2 -2/1 -1/1 11/3 -2/1 -1/1 4/1 0/1 9/2 2/3 1/1 5/1 2/1 1/0 6/1 -1/1 1/0 7/1 -1/2 0/1 22/3 0/1 15/2 0/1 1/4 8/1 0/1 1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(44,-7,107,-17) (0/1,1/6) -> (2/5,7/17) Hyperbolic Matrix(63,-11,86,-15) (1/6,1/5) -> (8/11,3/4) Hyperbolic Matrix(83,-18,143,-31) (1/5,2/9) -> (4/7,7/12) Hyperbolic Matrix(21,-5,80,-19) (2/9,1/4) -> (1/4,3/11) Parabolic Matrix(79,-22,97,-27) (3/11,2/7) -> (4/5,5/6) Hyperbolic Matrix(78,-23,173,-51) (2/7,3/10) -> (4/9,5/11) Hyperbolic Matrix(95,-29,154,-47) (3/10,1/3) -> (8/13,5/8) Hyperbolic Matrix(259,-92,442,-157) (1/3,5/14) -> (7/12,17/29) Hyperbolic Matrix(220,-79,479,-172) (5/14,9/25) -> (5/11,6/13) Hyperbolic Matrix(221,-80,605,-219) (9/25,4/11) -> (4/11,11/30) Parabolic Matrix(438,-161,1061,-390) (11/30,7/19) -> (7/17,12/29) Hyperbolic Matrix(183,-68,218,-81) (7/19,3/8) -> (5/6,11/13) Hyperbolic Matrix(144,-55,55,-21) (3/8,2/5) -> (13/5,8/3) Hyperbolic Matrix(531,-220,70,-29) (12/29,5/12) -> (15/2,8/1) Hyperbolic Matrix(177,-74,299,-125) (5/12,8/19) -> (10/17,3/5) Hyperbolic Matrix(106,-45,245,-104) (8/19,3/7) -> (3/7,7/16) Parabolic Matrix(105,-46,121,-53) (7/16,4/9) -> (6/7,1/1) Hyperbolic Matrix(581,-270,170,-79) (6/13,1/2) -> (41/12,24/7) Hyperbolic Matrix(32,-17,17,-9) (1/2,4/7) -> (9/5,2/1) Hyperbolic Matrix(631,-370,220,-129) (17/29,10/17) -> (20/7,3/1) Hyperbolic Matrix(155,-94,94,-57) (3/5,8/13) -> (18/11,5/3) Hyperbolic Matrix(31,-20,45,-29) (5/8,2/3) -> (2/3,5/7) Parabolic Matrix(203,-146,146,-105) (5/7,8/11) -> (18/13,7/5) Hyperbolic Matrix(56,-43,43,-33) (3/4,4/5) -> (9/7,4/3) Hyperbolic Matrix(731,-620,270,-229) (11/13,6/7) -> (46/17,19/7) Hyperbolic Matrix(105,-121,46,-53) (1/1,7/6) -> (9/4,16/7) Hyperbolic Matrix(183,-218,68,-81) (7/6,6/5) -> (8/3,27/10) Hyperbolic Matrix(79,-97,22,-27) (6/5,5/4) -> (7/2,11/3) Hyperbolic Matrix(155,-196,121,-153) (5/4,14/11) -> (14/11,9/7) Parabolic Matrix(63,-86,11,-15) (4/3,11/8) -> (5/1,6/1) Hyperbolic Matrix(610,-841,441,-608) (11/8,29/21) -> (29/21,18/13) Parabolic Matrix(31,-45,20,-29) (7/5,3/2) -> (3/2,8/5) Parabolic Matrix(95,-154,29,-47) (8/5,13/8) -> (3/1,10/3) Hyperbolic Matrix(590,-961,361,-588) (13/8,31/19) -> (31/19,18/11) Parabolic Matrix(177,-299,74,-125) (5/3,17/10) -> (19/8,12/5) Hyperbolic Matrix(259,-442,92,-157) (17/10,12/7) -> (14/5,17/6) Hyperbolic Matrix(83,-143,18,-31) (12/7,7/4) -> (9/2,5/1) Hyperbolic Matrix(145,-256,81,-143) (7/4,16/9) -> (16/9,9/5) Parabolic Matrix(78,-173,23,-51) (2/1,9/4) -> (10/3,17/5) Hyperbolic Matrix(106,-245,45,-104) (16/7,7/3) -> (7/3,19/8) Parabolic Matrix(44,-107,7,-17) (12/5,5/2) -> (6/1,7/1) Hyperbolic Matrix(127,-324,49,-125) (5/2,18/7) -> (18/7,13/5) Parabolic Matrix(1972,-5329,729,-1970) (27/10,73/27) -> (73/27,46/17) Parabolic Matrix(67,-182,7,-19) (19/7,30/11) -> (8/1,1/0) Hyperbolic Matrix(221,-605,80,-219) (30/11,11/4) -> (11/4,25/9) Parabolic Matrix(251,-698,73,-203) (25/9,14/5) -> (24/7,7/2) Hyperbolic Matrix(482,-1369,169,-480) (17/6,37/13) -> (37/13,20/7) Parabolic Matrix(987,-3364,289,-985) (17/5,58/17) -> (58/17,41/12) Parabolic Matrix(21,-80,5,-19) (11/3,4/1) -> (4/1,9/2) Parabolic Matrix(67,-484,9,-65) (7/1,22/3) -> (22/3,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,2,1) Matrix(44,-7,107,-17) -> Matrix(1,0,-2,1) Matrix(63,-11,86,-15) -> Matrix(5,-2,8,-3) Matrix(83,-18,143,-31) -> Matrix(5,-4,4,-3) Matrix(21,-5,80,-19) -> Matrix(1,0,2,1) Matrix(79,-22,97,-27) -> Matrix(1,0,-2,1) Matrix(78,-23,173,-51) -> Matrix(5,-2,8,-3) Matrix(95,-29,154,-47) -> Matrix(5,-2,-2,1) Matrix(259,-92,442,-157) -> Matrix(5,-4,4,-3) Matrix(220,-79,479,-172) -> Matrix(3,-2,8,-5) Matrix(221,-80,605,-219) -> Matrix(13,-8,18,-11) Matrix(438,-161,1061,-390) -> Matrix(3,-2,-4,3) Matrix(183,-68,218,-81) -> Matrix(5,-4,4,-3) Matrix(144,-55,55,-21) -> Matrix(5,-4,4,-3) Matrix(531,-220,70,-29) -> Matrix(1,0,2,1) Matrix(177,-74,299,-125) -> Matrix(3,-2,2,-1) Matrix(106,-45,245,-104) -> Matrix(1,0,2,1) Matrix(105,-46,121,-53) -> Matrix(1,0,-2,1) Matrix(581,-270,170,-79) -> Matrix(5,-2,-2,1) Matrix(32,-17,17,-9) -> Matrix(3,-2,2,-1) Matrix(631,-370,220,-129) -> Matrix(5,-8,2,-3) Matrix(155,-94,94,-57) -> Matrix(1,-4,2,-7) Matrix(31,-20,45,-29) -> Matrix(1,0,2,1) Matrix(203,-146,146,-105) -> Matrix(1,0,-2,1) Matrix(56,-43,43,-33) -> Matrix(3,-2,2,-1) Matrix(731,-620,270,-229) -> Matrix(3,-8,2,-5) Matrix(105,-121,46,-53) -> Matrix(1,0,-2,1) Matrix(183,-218,68,-81) -> Matrix(5,-4,4,-3) Matrix(79,-97,22,-27) -> Matrix(1,0,-2,1) Matrix(155,-196,121,-153) -> Matrix(7,-6,6,-5) Matrix(63,-86,11,-15) -> Matrix(1,-2,0,1) Matrix(610,-841,441,-608) -> Matrix(1,-8,0,1) Matrix(31,-45,20,-29) -> Matrix(1,0,2,1) Matrix(95,-154,29,-47) -> Matrix(5,-2,-2,1) Matrix(590,-961,361,-588) -> Matrix(25,-12,48,-23) Matrix(177,-299,74,-125) -> Matrix(3,-2,2,-1) Matrix(259,-442,92,-157) -> Matrix(5,-4,4,-3) Matrix(83,-143,18,-31) -> Matrix(5,-4,4,-3) Matrix(145,-256,81,-143) -> Matrix(15,-14,14,-13) Matrix(78,-173,23,-51) -> Matrix(1,-2,0,1) Matrix(106,-245,45,-104) -> Matrix(1,0,2,1) Matrix(44,-107,7,-17) -> Matrix(1,0,-2,1) Matrix(127,-324,49,-125) -> Matrix(7,-6,6,-5) Matrix(1972,-5329,729,-1970) -> Matrix(25,-36,16,-23) Matrix(67,-182,7,-19) -> Matrix(1,-2,2,-3) Matrix(221,-605,80,-219) -> Matrix(5,-8,2,-3) Matrix(251,-698,73,-203) -> Matrix(1,-4,0,1) Matrix(482,-1369,169,-480) -> Matrix(5,-8,2,-3) Matrix(987,-3364,289,-985) -> Matrix(1,-2,0,1) Matrix(21,-80,5,-19) -> Matrix(1,0,2,1) Matrix(67,-484,9,-65) -> Matrix(1,0,6,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 13 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 2 1 1/1 (0/1,1/1) 0 25 7/6 (0/1,1/2) 0 25 6/5 (2/3,1/1) 0 25 5/4 (2/3,1/1) 0 25 14/11 1/1 6 1 4/3 (1/1,1/0) 0 25 11/8 (4/1,1/0) 0 25 29/21 1/0 8 1 7/5 (0/1,1/0) 0 25 3/2 0/1 2 5 8/5 (0/1,1/2) 0 25 13/8 (4/9,1/2) 0 25 31/19 1/2 12 1 5/3 (1/2,2/3) 0 25 17/10 (2/3,1/1) 0 25 12/7 (2/3,3/4) 0 25 7/4 (6/7,1/1) 0 25 16/9 1/1 14 1 2/1 (1/1,1/0) 0 25 9/4 (0/1,1/0) 0 25 16/7 (-1/1,0/1) 0 25 7/3 0/1 2 5 19/8 (0/1,1/1) 0 25 12/5 (0/1,1/0) 0 25 5/2 (1/2,1/1) 0 25 18/7 1/1 6 1 8/3 (1/1,2/1) 0 25 27/10 (4/3,3/2) 0 25 73/27 3/2 4 1 19/7 (3/2,2/1) 0 25 30/11 (1/1,2/1) 0 25 11/4 2/1 2 5 25/9 (2/1,3/1) 0 25 14/5 (2/1,1/0) 0 25 17/6 (1/1,2/1) 0 25 37/13 2/1 2 1 3/1 (2/1,1/0) 0 25 10/3 (-2/1,1/0) 0 25 17/5 (-1/1,1/0) 0 25 58/17 1/0 2 1 24/7 (-2/1,1/0) 0 25 7/2 (-2/1,-1/1) 0 25 11/3 (-2/1,-1/1) 0 25 4/1 0/1 2 5 9/2 (2/3,1/1) 0 25 5/1 (2/1,1/0) 0 25 6/1 (-1/1,1/0) 0 25 7/1 (-1/2,0/1) 0 25 22/3 0/1 6 1 8/1 (0/1,1/1) 0 25 1/0 (0/1,1/0) 0 25 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(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(105,-121,46,-53) (1/1,7/6) -> (9/4,16/7) Hyperbolic Matrix(183,-218,68,-81) (7/6,6/5) -> (8/3,27/10) Hyperbolic Matrix(79,-97,22,-27) (6/5,5/4) -> (7/2,11/3) Hyperbolic Matrix(111,-140,88,-111) (5/4,14/11) -> (5/4,14/11) Reflection Matrix(43,-56,33,-43) (14/11,4/3) -> (14/11,4/3) Reflection Matrix(63,-86,11,-15) (4/3,11/8) -> (5/1,6/1) Hyperbolic Matrix(463,-638,336,-463) (11/8,29/21) -> (11/8,29/21) Reflection Matrix(146,-203,105,-146) (29/21,7/5) -> (29/21,7/5) Reflection Matrix(31,-45,20,-29) (7/5,3/2) -> (3/2,8/5) Parabolic Matrix(95,-154,29,-47) (8/5,13/8) -> (3/1,10/3) Hyperbolic Matrix(495,-806,304,-495) (13/8,31/19) -> (13/8,31/19) Reflection Matrix(94,-155,57,-94) (31/19,5/3) -> (31/19,5/3) Reflection Matrix(177,-299,74,-125) (5/3,17/10) -> (19/8,12/5) Hyperbolic Matrix(259,-442,92,-157) (17/10,12/7) -> (14/5,17/6) Hyperbolic Matrix(83,-143,18,-31) (12/7,7/4) -> (9/2,5/1) Hyperbolic Matrix(127,-224,72,-127) (7/4,16/9) -> (7/4,16/9) Reflection Matrix(17,-32,9,-17) (16/9,2/1) -> (16/9,2/1) Reflection Matrix(78,-173,23,-51) (2/1,9/4) -> (10/3,17/5) Hyperbolic Matrix(106,-245,45,-104) (16/7,7/3) -> (7/3,19/8) Parabolic Matrix(44,-107,7,-17) (12/5,5/2) -> (6/1,7/1) Hyperbolic Matrix(71,-180,28,-71) (5/2,18/7) -> (5/2,18/7) Reflection Matrix(55,-144,21,-55) (18/7,8/3) -> (18/7,8/3) Reflection Matrix(1459,-3942,540,-1459) (27/10,73/27) -> (27/10,73/27) Reflection Matrix(512,-1387,189,-512) (73/27,19/7) -> (73/27,19/7) Reflection Matrix(67,-182,7,-19) (19/7,30/11) -> (8/1,1/0) Hyperbolic Matrix(221,-605,80,-219) (30/11,11/4) -> (11/4,25/9) Parabolic Matrix(251,-698,73,-203) (25/9,14/5) -> (24/7,7/2) Hyperbolic Matrix(443,-1258,156,-443) (17/6,37/13) -> (17/6,37/13) Reflection Matrix(38,-111,13,-38) (37/13,3/1) -> (37/13,3/1) Reflection Matrix(579,-1972,170,-579) (17/5,58/17) -> (17/5,58/17) Reflection Matrix(407,-1392,119,-407) (58/17,24/7) -> (58/17,24/7) Reflection Matrix(21,-80,5,-19) (11/3,4/1) -> (4/1,9/2) Parabolic 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(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(0,1,1,0) -> Matrix(1,0,2,-1) (-1/1,1/1) -> (0/1,1/1) Matrix(105,-121,46,-53) -> Matrix(1,0,-2,1) 0/1 Matrix(183,-218,68,-81) -> Matrix(5,-4,4,-3) 1/1 Matrix(79,-97,22,-27) -> Matrix(1,0,-2,1) 0/1 Matrix(111,-140,88,-111) -> Matrix(5,-4,6,-5) (5/4,14/11) -> (2/3,1/1) Matrix(43,-56,33,-43) -> Matrix(-1,2,0,1) (14/11,4/3) -> (1/1,1/0) Matrix(63,-86,11,-15) -> Matrix(1,-2,0,1) 1/0 Matrix(463,-638,336,-463) -> Matrix(-1,8,0,1) (11/8,29/21) -> (4/1,1/0) Matrix(146,-203,105,-146) -> Matrix(1,0,0,-1) (29/21,7/5) -> (0/1,1/0) Matrix(31,-45,20,-29) -> Matrix(1,0,2,1) 0/1 Matrix(95,-154,29,-47) -> Matrix(5,-2,-2,1) Matrix(495,-806,304,-495) -> Matrix(17,-8,36,-17) (13/8,31/19) -> (4/9,1/2) Matrix(94,-155,57,-94) -> Matrix(7,-4,12,-7) (31/19,5/3) -> (1/2,2/3) Matrix(177,-299,74,-125) -> Matrix(3,-2,2,-1) 1/1 Matrix(259,-442,92,-157) -> Matrix(5,-4,4,-3) 1/1 Matrix(83,-143,18,-31) -> Matrix(5,-4,4,-3) 1/1 Matrix(127,-224,72,-127) -> Matrix(13,-12,14,-13) (7/4,16/9) -> (6/7,1/1) Matrix(17,-32,9,-17) -> Matrix(-1,2,0,1) (16/9,2/1) -> (1/1,1/0) Matrix(78,-173,23,-51) -> Matrix(1,-2,0,1) 1/0 Matrix(106,-245,45,-104) -> Matrix(1,0,2,1) 0/1 Matrix(44,-107,7,-17) -> Matrix(1,0,-2,1) 0/1 Matrix(71,-180,28,-71) -> Matrix(3,-2,4,-3) (5/2,18/7) -> (1/2,1/1) Matrix(55,-144,21,-55) -> Matrix(3,-4,2,-3) (18/7,8/3) -> (1/1,2/1) Matrix(1459,-3942,540,-1459) -> Matrix(17,-24,12,-17) (27/10,73/27) -> (4/3,3/2) Matrix(512,-1387,189,-512) -> Matrix(7,-12,4,-7) (73/27,19/7) -> (3/2,2/1) Matrix(67,-182,7,-19) -> Matrix(1,-2,2,-3) 1/1 Matrix(221,-605,80,-219) -> Matrix(5,-8,2,-3) 2/1 Matrix(251,-698,73,-203) -> Matrix(1,-4,0,1) 1/0 Matrix(443,-1258,156,-443) -> Matrix(3,-4,2,-3) (17/6,37/13) -> (1/1,2/1) Matrix(38,-111,13,-38) -> Matrix(-1,4,0,1) (37/13,3/1) -> (2/1,1/0) Matrix(579,-1972,170,-579) -> Matrix(1,2,0,-1) (17/5,58/17) -> (-1/1,1/0) Matrix(407,-1392,119,-407) -> Matrix(1,4,0,-1) (58/17,24/7) -> (-2/1,1/0) Matrix(21,-80,5,-19) -> Matrix(1,0,2,1) 0/1 Matrix(43,-308,6,-43) -> Matrix(-1,0,4,1) (7/1,22/3) -> (-1/2,0/1) Matrix(23,-176,3,-23) -> Matrix(1,0,2,-1) (22/3,8/1) -> (0/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.