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): 1728 Minimal number of generators: 289 Number of equivalence classes of cusps: 80 Genus: 105 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -15/17 -13/17 -11/17 -9/17 -1/2 -5/12 -7/17 -33/85 -103/272 -5/16 -9/29 -5/17 -1/4 -31/136 -7/31 -23/102 -3/14 -3/16 -5/27 -3/17 -1/6 -5/33 -1/8 -3/25 -1/10 0/1 1/10 1/9 2/17 1/8 1/7 5/34 2/13 3/19 1/6 3/17 2/11 1/5 7/34 3/14 5/23 2/9 3/13 4/17 5/21 1/4 9/34 4/15 3/11 2/7 5/17 31/102 16/51 1/3 6/17 13/34 2/5 7/17 5/12 15/34 7/15 8/17 1/2 9/17 19/34 10/17 21/34 11/17 2/3 12/17 25/34 13/17 79/102 67/85 27/34 14/17 29/34 15/17 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/0 -10/11 1/1 -9/10 -1/1 1/1 -8/9 1/1 -15/17 0/1 -7/8 -1/1 1/1 -6/7 -1/1 -29/34 0/1 -23/27 0/1 1/4 -40/47 1/3 -17/20 1/3 1/1 -11/13 1/1 1/0 -16/19 1/1 -21/25 -1/1 -1/2 -5/6 -1/1 1/1 -19/23 -1/2 0/1 -14/17 0/1 -9/11 0/1 1/1 -4/5 -1/1 -27/34 0/1 -23/29 0/1 1/6 -19/24 1/3 1/1 -34/43 1/1 -15/19 0/1 1/2 -26/33 1/1 -37/47 0/1 1/0 -11/14 1/1 3/1 -7/9 0/1 1/1 -38/49 3/1 -31/40 3/1 5/1 -55/71 14/1 1/0 -79/102 1/0 -24/31 -7/1 -41/53 -5/2 -2/1 -17/22 -5/3 -1/1 -27/35 -1/1 -2/3 -10/13 -1/3 -13/17 0/1 -16/21 1/1 -19/25 1/3 1/2 -3/4 -1/1 1/1 -17/23 -1/2 0/1 -14/19 -1/5 -25/34 0/1 -11/15 0/1 1/4 -30/41 1/1 -19/26 1/3 1/1 -27/37 2/5 1/2 -8/11 1/1 -29/40 1/1 3/1 -50/69 1/1 -21/29 2/1 1/0 -13/18 -1/1 1/1 -5/7 -1/1 0/1 -12/17 0/1 -19/27 0/1 1/4 -26/37 3/7 -33/47 0/1 1/4 -7/10 1/3 1/1 -37/53 0/1 1/2 -30/43 3/5 -23/33 0/1 1/1 -39/56 9/11 1/1 -16/23 1/1 -9/13 3/1 1/0 -2/3 1/1 -11/17 0/1 -20/31 1/7 -9/14 1/3 1/1 -7/11 1/1 2/1 -12/19 -3/1 -29/46 -3/1 -1/1 -17/27 -2/1 1/0 -39/62 -7/5 -1/1 -22/35 -1/1 -27/43 -3/2 -1/1 -5/8 -1/1 -1/3 -23/37 -1/2 -2/5 -64/103 -1/3 -41/66 -1/3 -7/23 -18/29 -1/5 -13/21 -1/8 0/1 -21/34 0/1 -8/13 1/5 -27/44 1/3 3/7 -19/31 0/1 1/0 -11/18 1/3 1/1 -3/5 0/1 1/0 -10/17 0/1 -17/29 0/1 1/6 -24/41 1/3 -31/53 0/1 1/6 -7/12 1/3 1/1 -39/67 0/1 1/2 -32/55 1/3 -25/43 1/2 1/1 -43/74 -1/1 1/1 -18/31 1/5 -11/19 2/5 1/2 -4/7 1/1 -17/30 -1/1 -1/3 -13/23 0/1 1/0 -9/16 -1/1 -1/3 -23/41 -1/2 0/1 -14/25 -1/5 -19/34 0/1 -5/9 0/1 1/3 -11/20 1/3 3/7 -17/31 1/2 4/7 -6/11 1/1 -7/13 -1/1 1/0 -8/15 -1/1 -9/17 0/1 -10/19 1/1 -1/2 -1/1 1/1 -8/17 1/0 -7/15 0/1 1/0 -20/43 3/1 -13/28 -3/1 -1/1 -19/41 -1/2 0/1 -6/13 -1/1 -11/24 3/5 1/1 -16/35 1/1 -5/11 1/1 4/3 -9/20 1/1 3/1 -22/49 3/1 -35/78 1/1 5/3 -13/29 2/1 5/2 -30/67 3/1 -17/38 3/1 5/1 -4/9 3/1 -15/34 1/0 -11/25 -5/1 1/0 -7/16 -1/1 1/1 -3/7 0/1 1/1 -11/26 1/1 7/5 -19/45 3/2 2/1 -8/19 3/1 -37/88 1/1 3/1 -66/157 3/1 -29/69 2/1 1/0 -50/119 2/1 -21/50 1/1 3/1 -13/31 3/2 2/1 -5/12 3/1 5/1 -7/17 1/0 -9/22 -3/1 -1/1 -11/27 -2/1 1/0 -13/32 -7/5 -1/1 -2/5 1/1 -13/33 1/1 6/5 -11/28 1/1 5/3 -9/23 2/1 1/0 -7/18 7/3 3/1 -33/85 3/1 -59/152 3/1 65/21 -26/67 3/1 -19/49 10/3 7/2 -12/31 5/1 -5/13 7/1 1/0 -13/34 1/0 -8/21 -9/1 -11/29 -4/1 1/0 -25/66 -23/7 -3/1 -64/169 -3/1 -103/272 -3/1 -39/103 -3/1 -32/11 -14/37 -7/3 -3/8 -1/1 1/1 -19/51 0/1 -16/43 1/3 -13/35 2/3 1/1 -23/62 1/1 3/1 -33/89 0/1 1/2 -10/27 1/1 -7/19 4/1 1/0 -11/30 -3/1 -1/1 -37/101 -8/7 -1/1 -26/71 -3/5 -15/41 0/1 1/0 -4/11 1/1 -21/58 1/1 3/1 -17/47 2/1 5/2 -47/130 3/1 5/1 -30/83 3/1 -13/36 7/3 3/1 -9/25 1/1 1/0 -23/64 7/3 3/1 -37/103 3/1 16/5 -14/39 3/1 -19/53 2/1 1/0 -5/14 3/1 5/1 -11/31 10/1 1/0 -6/17 1/0 -1/3 0/1 1/0 -9/28 -11/1 -9/1 -8/25 -5/1 -7/22 -5/1 -3/1 -6/19 -5/1 -5/16 -3/1 -1/1 -9/29 0/1 1/0 -4/13 -5/1 -11/36 -5/1 -3/1 -7/23 -2/1 1/0 -31/102 -2/1 -24/79 -5/3 -41/135 -2/1 -3/2 -17/56 -5/3 -1/1 -27/89 -3/2 -4/3 -10/33 -1/1 -13/43 -1/1 -1/2 -3/10 -1/1 1/1 -5/17 1/0 -7/24 -9/1 -7/1 -9/31 -6/1 -11/2 -20/69 -5/1 -11/38 -5/1 -13/3 -2/7 -3/1 -11/39 -2/1 -3/2 -9/32 -1/1 -1/3 -7/25 1/1 1/0 -5/18 -5/1 -3/1 -23/83 -11/4 -8/3 -18/65 -17/7 -13/47 -9/4 -2/1 -8/29 -3/1 -3/11 -2/1 -1/1 -4/15 3/1 -9/34 1/0 -5/19 -8/1 1/0 -1/4 -3/1 -1/1 -6/25 -1/1 -11/46 -3/1 -1/1 -5/21 0/1 1/0 -4/17 1/0 -3/13 -3/1 1/0 -11/48 -11/3 -3/1 -19/83 -7/2 -10/3 -27/118 -41/13 -3/1 -8/35 -3/1 -13/57 -22/7 -3/1 -31/136 -3/1 -18/79 -3/1 -5/22 -3/1 -13/5 -7/31 -9/4 -2/1 -23/102 -2/1 -16/71 -13/7 -9/40 -5/3 -1/1 -2/9 -3/1 -9/41 -2/1 -3/2 -7/32 -1/1 1/1 -5/23 -2/1 1/0 -13/60 -1/1 1/1 -8/37 -7/3 -3/14 -5/3 -1/1 -7/33 -1/1 0/1 -18/85 0/1 -11/52 -1/1 1/1 -4/19 -3/1 -9/43 -3/2 -1/1 -5/24 -3/1 -1/1 -11/53 -2/1 1/0 -6/29 -1/1 -7/34 1/0 -1/5 -2/1 1/0 -3/16 -5/3 -1/1 -5/27 -2/1 -3/2 -2/11 -1/1 -3/17 -1/1 -4/23 -1/1 -1/6 -3/1 -1/1 -4/25 -5/3 -3/19 -2/1 -3/2 -8/51 -3/2 -5/32 -7/5 -1/1 -2/13 -7/5 -5/33 -2/1 -1/1 -3/20 -9/7 -1/1 -7/47 -5/4 -6/5 -4/27 -1/1 -5/34 -1/1 -1/7 -1/1 0/1 -1/8 -7/5 -1/1 -3/25 -7/6 -1/1 -2/17 -1/1 -1/9 -1/1 0/1 -2/19 -3/1 -1/10 -5/3 -1/1 0/1 -1/1 1/10 -1/1 -5/7 2/19 -3/5 1/9 -1/1 0/1 2/17 -1/1 1/8 -1/1 -7/9 1/7 -1/1 0/1 5/34 -1/1 4/27 -1/1 3/20 -1/1 -9/11 2/13 -7/9 3/19 -3/4 -2/3 4/25 -5/7 1/6 -1/1 -3/5 3/17 -1/1 5/28 -1/1 -7/9 2/11 -1/1 1/5 -2/3 -1/2 7/34 -1/2 6/29 -1/1 5/24 -1/1 -3/5 9/43 -1/1 -3/4 4/19 -3/5 7/33 -1/1 0/1 3/14 -1/1 -5/7 8/37 -7/11 5/23 -2/3 -1/2 7/32 -1/1 -1/3 2/9 -3/5 5/22 -13/21 -3/5 13/57 -3/5 -22/37 8/35 -3/5 3/13 -3/5 -1/2 4/17 -1/2 5/21 -1/2 0/1 11/46 -1/1 -3/5 6/25 -1/1 1/4 -1/1 -3/5 5/19 -8/15 -1/2 9/34 -1/2 4/15 -3/7 3/11 -1/1 -2/3 5/18 -3/5 -5/9 7/25 -1/2 -1/3 9/32 -1/1 1/1 2/7 -3/5 5/17 -1/2 8/27 -5/11 11/37 -5/12 -2/5 3/10 -1/1 -1/3 13/43 -1/1 1/0 10/33 -1/1 17/56 -1/1 -5/7 24/79 -5/7 31/102 -2/3 7/23 -2/3 -1/2 11/36 -3/5 -5/9 15/49 -2/3 -1/2 4/13 -5/9 5/16 -1/1 -3/5 16/51 -2/3 11/35 -2/3 -3/5 6/19 -5/9 1/3 -1/2 0/1 6/17 -1/2 11/31 -1/2 -10/21 5/14 -5/11 -3/7 19/53 -1/2 -2/5 33/92 -3/7 -1/3 14/39 -3/7 23/64 -3/7 -7/17 9/25 -1/2 -1/3 13/36 -3/7 -7/17 30/83 -3/7 17/47 -5/12 -2/5 4/11 -1/3 15/41 -1/2 0/1 11/30 -1/1 -3/5 7/19 -1/2 -4/9 3/8 -1/1 -1/3 14/37 -7/11 39/103 -32/53 -3/5 25/66 -3/5 -23/39 11/29 -4/7 -1/2 8/21 -9/17 13/34 -1/2 5/13 -1/2 -7/15 7/18 -3/7 -7/17 9/23 -1/2 -2/5 11/28 -5/13 -1/3 13/33 -6/17 -1/3 15/38 -1/3 -1/5 2/5 -1/3 7/17 -1/2 12/29 -7/15 29/70 -5/11 -23/51 17/41 -1/2 -4/9 5/12 -5/11 -3/7 18/43 -3/7 31/74 -7/17 -11/27 13/31 -2/5 -3/8 8/19 -3/7 19/45 -2/5 -3/8 30/71 -9/23 11/26 -7/19 -1/3 3/7 -1/3 0/1 7/16 -1/1 -1/3 11/25 -5/9 -1/2 15/34 -1/2 4/9 -3/7 5/11 -4/11 -1/3 16/35 -1/3 11/24 -1/3 -3/11 6/13 -1/1 13/28 -1/1 -3/5 20/43 -3/7 7/15 -1/2 0/1 8/17 -1/2 9/19 -1/2 -2/5 1/2 -1/1 -1/3 9/17 0/1 17/32 -1/1 1/1 8/15 -1/1 7/13 -1/1 -1/2 6/11 -1/3 5/9 -1/5 0/1 19/34 0/1 14/25 1/3 37/66 3/5 1/1 23/41 0/1 1/0 9/16 -1/1 1/1 13/23 -1/2 0/1 17/30 -1/1 1/1 38/67 -1/1 21/37 -3/4 -2/3 4/7 -1/3 27/47 -3/10 -2/7 23/40 -1/3 -1/5 19/33 -1/3 -4/13 34/59 -5/17 15/26 -1/3 -3/11 11/19 -1/4 -2/9 18/31 -1/7 79/136 0/1 61/105 0/1 1/4 43/74 -1/1 -1/3 25/43 -1/3 -1/4 32/55 -1/5 39/67 -1/4 0/1 7/12 -1/3 -1/5 24/41 -1/5 41/70 -5/33 -1/7 17/29 -1/8 0/1 10/17 0/1 3/5 -1/2 0/1 14/23 -1/3 25/41 -1/4 0/1 11/18 -1/3 -1/5 52/85 0/1 41/67 -1/4 0/1 30/49 -1/5 19/31 -1/2 0/1 27/44 -3/13 -1/5 8/13 -1/7 21/34 0/1 13/21 0/1 1/6 18/29 1/3 41/66 7/9 1/1 105/169 18/19 1/1 169/272 1/1 64/103 1/1 23/37 2/1 1/0 5/8 -1/1 1/1 32/51 -1/1 27/43 -1/1 -3/4 22/35 -1/1 39/62 -1/1 -7/9 56/89 -1/1 17/27 -2/3 -1/2 29/46 -1/1 -3/5 70/111 -3/5 41/65 -1/2 -2/5 12/19 -3/5 7/11 -2/5 -1/3 16/25 -1/5 41/64 -3/13 -1/5 25/39 -1/6 0/1 34/53 -1/5 43/67 -1/4 0/1 9/14 -1/3 -1/5 11/17 0/1 13/20 1/3 1/1 2/3 -1/3 13/19 -2/1 1/0 11/16 -1/1 -5/7 9/13 -1/2 -3/7 16/23 -1/3 23/33 -1/3 0/1 30/43 -3/11 37/53 -1/4 0/1 7/10 -1/3 -1/5 40/57 -1/3 33/47 -1/6 0/1 26/37 -3/13 71/101 -1/5 -8/41 45/64 -1/5 -3/17 19/27 -1/6 0/1 12/17 0/1 5/7 -1/1 0/1 13/18 -1/1 -1/3 34/47 -3/5 21/29 -1/2 -2/5 71/98 -7/19 -1/3 50/69 -1/3 29/40 -3/7 -1/3 8/11 -1/3 27/37 -1/4 -2/9 19/26 -1/3 -1/5 11/15 -1/6 0/1 25/34 0/1 14/19 1/3 17/23 0/1 1/0 3/4 -1/1 -1/3 13/17 0/1 23/30 1/3 1/1 33/43 -1/1 1/0 10/13 1/1 37/48 -1/1 -1/3 27/35 -2/1 -1/1 44/57 -1/1 105/136 -1/1 61/79 -1/1 -12/13 17/22 -1/1 -5/7 41/53 -2/3 -5/8 24/31 -7/13 79/102 -1/2 55/71 -1/2 -14/29 86/111 -9/19 31/40 -5/11 -3/7 69/89 -5/12 -2/5 38/49 -3/7 7/9 -1/3 0/1 18/23 -1/1 29/37 -4/7 -1/2 11/14 -3/7 -1/3 48/61 -1/3 37/47 -1/2 0/1 63/80 -3/7 -1/3 26/33 -1/3 67/85 -1/3 108/137 -1/3 41/52 -1/3 -9/29 15/19 -1/4 0/1 34/43 -1/3 19/24 -1/3 -1/5 42/53 -1/7 23/29 -1/8 0/1 27/34 0/1 4/5 -1/1 17/21 0/1 1/2 30/37 3/1 43/53 -2/1 -3/2 13/16 -1/1 -3/5 9/11 -1/3 0/1 14/17 0/1 19/23 0/1 1/0 5/6 -1/1 -1/3 21/25 -1/1 1/0 16/19 -1/3 11/13 -1/2 -1/3 28/33 -1/3 73/86 -1/3 -11/35 45/53 -2/7 -1/4 17/20 -1/3 -1/5 57/67 -1/4 0/1 40/47 -1/5 23/27 -1/6 0/1 29/34 0/1 6/7 -1/1 19/22 -1/1 1/1 13/15 -1/4 0/1 7/8 -1/1 -1/3 15/17 0/1 23/26 -1/1 1/1 8/9 -1/3 9/10 -1/1 -1/3 10/11 -1/3 11/12 -1/1 -1/3 1/1 -1/2 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(475,434,-1564,-1429) (-1/1,-10/11) -> (-24/79,-41/135) Hyperbolic Matrix(477,430,680,613) (-10/11,-9/10) -> (7/10,40/57) Hyperbolic Matrix(511,458,646,579) (-9/10,-8/9) -> (34/43,19/24) Hyperbolic Matrix(443,392,-1190,-1053) (-8/9,-15/17) -> (-19/51,-16/43) Hyperbolic Matrix(203,178,-544,-477) (-15/17,-7/8) -> (-3/8,-19/51) Hyperbolic Matrix(373,324,-510,-443) (-7/8,-6/7) -> (-30/41,-19/26) Hyperbolic Matrix(407,348,476,407) (-6/7,-29/34) -> (29/34,6/7) Hyperbolic Matrix(1565,1334,1836,1565) (-29/34,-23/27) -> (23/27,29/34) Hyperbolic Matrix(2311,1968,3672,3127) (-23/27,-40/47) -> (56/89,17/27) Hyperbolic Matrix(3059,2602,-7276,-6189) (-40/47,-17/20) -> (-37/88,-66/157) Hyperbolic Matrix(203,172,-884,-749) (-17/20,-11/13) -> (-3/13,-11/48) Hyperbolic Matrix(237,200,442,373) (-11/13,-16/19) -> (8/15,7/13) Hyperbolic Matrix(271,228,1292,1087) (-16/19,-21/25) -> (9/43,4/19) Hyperbolic Matrix(1225,1028,2108,1769) (-21/25,-5/6) -> (43/74,25/43) Hyperbolic Matrix(307,254,782,647) (-5/6,-19/23) -> (9/23,11/28) Hyperbolic Matrix(645,532,782,645) (-19/23,-14/17) -> (14/17,19/23) Hyperbolic Matrix(307,252,374,307) (-14/17,-9/11) -> (9/11,14/17) Hyperbolic Matrix(103,84,-374,-305) (-9/11,-4/5) -> (-8/29,-3/11) Hyperbolic Matrix(271,216,340,271) (-4/5,-27/34) -> (27/34,4/5) Hyperbolic Matrix(1565,1242,1972,1565) (-27/34,-23/29) -> (23/29,27/34) Hyperbolic Matrix(1327,1052,-2958,-2345) (-23/29,-19/24) -> (-35/78,-13/29) Hyperbolic Matrix(579,458,646,511) (-19/24,-34/43) -> (8/9,9/10) Hyperbolic Matrix(205,162,1292,1021) (-34/43,-15/19) -> (3/19,4/25) Hyperbolic Matrix(1121,884,-2890,-2279) (-15/19,-26/33) -> (-26/67,-19/49) Hyperbolic Matrix(1361,1072,-4488,-3535) (-26/33,-37/47) -> (-27/89,-10/33) Hyperbolic Matrix(239,188,-1598,-1257) (-37/47,-11/14) -> (-3/20,-7/47) Hyperbolic Matrix(169,132,-306,-239) (-11/14,-7/9) -> (-5/9,-11/20) Hyperbolic Matrix(67,52,612,475) (-7/9,-38/49) -> (2/19,1/9) Hyperbolic Matrix(3503,2716,-9690,-7513) (-38/49,-31/40) -> (-47/130,-30/83) Hyperbolic Matrix(679,526,-2108,-1633) (-31/40,-55/71) -> (-1/3,-9/28) Hyperbolic Matrix(11219,8690,14484,11219) (-55/71,-79/102) -> (79/102,55/71) Hyperbolic Matrix(4897,3792,6324,4897) (-79/102,-24/31) -> (24/31,79/102) Hyperbolic Matrix(1667,1290,-6018,-4657) (-24/31,-41/53) -> (-23/83,-18/65) Hyperbolic Matrix(1293,1000,1496,1157) (-41/53,-17/22) -> (19/22,13/15) Hyperbolic Matrix(1871,1444,-2686,-2073) (-17/22,-27/35) -> (-23/33,-39/56) Hyperbolic Matrix(135,104,-884,-681) (-27/35,-10/13) -> (-2/13,-5/33) Hyperbolic Matrix(441,338,-578,-443) (-10/13,-13/17) -> (-13/17,-16/21) Parabolic Matrix(1325,1008,2278,1733) (-16/21,-19/25) -> (25/43,32/55) Hyperbolic Matrix(611,464,1700,1291) (-19/25,-3/4) -> (23/64,9/25) Hyperbolic Matrix(443,328,782,579) (-3/4,-17/23) -> (13/23,17/30) Hyperbolic Matrix(545,402,1292,953) (-17/23,-14/19) -> (8/19,19/45) Hyperbolic Matrix(951,700,1292,951) (-14/19,-25/34) -> (25/34,14/19) Hyperbolic Matrix(749,550,1020,749) (-25/34,-11/15) -> (11/15,25/34) Hyperbolic Matrix(1631,1194,-2788,-2041) (-11/15,-30/41) -> (-24/41,-31/53) Hyperbolic Matrix(783,572,1258,919) (-19/26,-27/37) -> (23/37,5/8) Hyperbolic Matrix(985,718,1258,917) (-27/37,-8/11) -> (18/23,29/37) Hyperbolic Matrix(135,98,748,543) (-8/11,-29/40) -> (5/28,2/11) Hyperbolic Matrix(3571,2588,5678,4115) (-29/40,-50/69) -> (22/35,39/62) Hyperbolic Matrix(1767,1280,-3944,-2857) (-50/69,-21/29) -> (-13/29,-30/67) Hyperbolic Matrix(307,222,-986,-713) (-21/29,-13/18) -> (-5/16,-9/29) Hyperbolic Matrix(103,74,238,171) (-13/18,-5/7) -> (3/7,7/16) Hyperbolic Matrix(169,120,238,169) (-5/7,-12/17) -> (12/17,5/7) Hyperbolic Matrix(647,456,918,647) (-12/17,-19/27) -> (19/27,12/17) Hyperbolic Matrix(1257,884,-3434,-2415) (-19/27,-26/37) -> (-26/71,-15/41) Hyperbolic Matrix(2039,1432,2516,1767) (-26/37,-33/47) -> (17/21,30/37) Hyperbolic Matrix(1157,812,-3196,-2243) (-33/47,-7/10) -> (-21/58,-17/47) Hyperbolic Matrix(1939,1354,5406,3775) (-7/10,-37/53) -> (19/53,33/92) Hyperbolic Matrix(1361,950,2924,2041) (-37/53,-30/43) -> (20/43,7/15) Hyperbolic Matrix(1939,1352,3366,2347) (-30/43,-23/33) -> (19/33,34/59) Hyperbolic Matrix(1123,782,-4930,-3433) (-39/56,-16/23) -> (-18/79,-5/22) Hyperbolic Matrix(239,166,442,307) (-16/23,-9/13) -> (7/13,6/11) Hyperbolic Matrix(171,118,-442,-305) (-9/13,-2/3) -> (-12/31,-5/13) Hyperbolic Matrix(373,242,-578,-375) (-2/3,-11/17) -> (-11/17,-20/31) Parabolic Matrix(205,132,952,613) (-20/31,-9/14) -> (3/14,8/37) Hyperbolic Matrix(169,108,-374,-239) (-9/14,-7/11) -> (-5/11,-9/20) Hyperbolic Matrix(101,64,374,237) (-7/11,-12/19) -> (4/15,3/11) Hyperbolic Matrix(409,258,-1292,-815) (-12/19,-29/46) -> (-7/22,-6/19) Hyperbolic Matrix(917,578,2210,1393) (-29/46,-17/27) -> (17/41,5/12) Hyperbolic Matrix(1529,962,-3298,-2075) (-17/27,-39/62) -> (-13/28,-19/41) Hyperbolic Matrix(4115,2588,5678,3571) (-39/62,-22/35) -> (50/69,29/40) Hyperbolic Matrix(885,556,2924,1837) (-22/35,-27/43) -> (13/43,10/33) Hyperbolic Matrix(67,42,-544,-341) (-27/43,-5/8) -> (-1/8,-3/25) Hyperbolic Matrix(919,572,1258,783) (-5/8,-23/37) -> (27/37,19/26) Hyperbolic Matrix(3569,2218,6290,3909) (-23/37,-64/103) -> (38/67,21/37) Hyperbolic Matrix(6799,4224,-17952,-11153) (-64/103,-41/66) -> (-25/66,-64/169) Hyperbolic Matrix(1633,1014,3944,2449) (-41/66,-18/29) -> (12/29,29/70) Hyperbolic Matrix(545,338,-1972,-1223) (-18/29,-13/21) -> (-13/47,-8/29) Hyperbolic Matrix(883,546,1428,883) (-13/21,-21/34) -> (21/34,13/21) Hyperbolic Matrix(545,336,884,545) (-21/34,-8/13) -> (8/13,21/34) Hyperbolic Matrix(407,250,884,543) (-8/13,-27/44) -> (11/24,6/13) Hyperbolic Matrix(577,354,1938,1189) (-27/44,-19/31) -> (11/37,3/10) Hyperbolic Matrix(885,542,-2108,-1291) (-19/31,-11/18) -> (-21/50,-13/31) Hyperbolic Matrix(33,20,-170,-103) (-11/18,-3/5) -> (-1/5,-3/16) Hyperbolic Matrix(101,60,170,101) (-3/5,-10/17) -> (10/17,3/5) Hyperbolic Matrix(579,340,986,579) (-10/17,-17/29) -> (17/29,10/17) Hyperbolic Matrix(509,298,-1802,-1055) (-17/29,-24/41) -> (-2/7,-11/39) Hyperbolic Matrix(1393,814,1802,1053) (-31/53,-7/12) -> (17/22,41/53) Hyperbolic Matrix(1631,950,-5372,-3129) (-7/12,-39/67) -> (-41/135,-17/56) Hyperbolic Matrix(6017,3502,-14314,-8331) (-39/67,-32/55) -> (-66/157,-29/69) Hyperbolic Matrix(2245,1306,2924,1701) (-32/55,-25/43) -> (33/43,10/13) Hyperbolic Matrix(1769,1028,2108,1225) (-25/43,-43/74) -> (5/6,21/25) Hyperbolic Matrix(1463,850,-6494,-3773) (-43/74,-18/31) -> (-16/71,-9/40) Hyperbolic Matrix(817,474,-2108,-1223) (-18/31,-11/19) -> (-19/49,-12/31) Hyperbolic Matrix(239,138,-646,-373) (-11/19,-4/7) -> (-10/27,-7/19) Hyperbolic Matrix(137,78,-476,-271) (-4/7,-17/30) -> (-11/38,-2/7) Hyperbolic Matrix(579,328,782,443) (-17/30,-13/23) -> (17/23,3/4) Hyperbolic Matrix(305,172,782,441) (-13/23,-9/16) -> (7/18,9/23) Hyperbolic Matrix(851,478,1394,783) (-9/16,-23/41) -> (25/41,11/18) Hyperbolic Matrix(307,172,-1394,-781) (-23/41,-14/25) -> (-2/9,-9/41) Hyperbolic Matrix(951,532,1700,951) (-14/25,-19/34) -> (19/34,14/25) Hyperbolic Matrix(341,190,612,341) (-19/34,-5/9) -> (5/9,19/34) Hyperbolic Matrix(375,206,1054,579) (-11/20,-17/31) -> (11/31,5/14) Hyperbolic Matrix(545,298,748,409) (-17/31,-6/11) -> (8/11,27/37) Hyperbolic Matrix(307,166,442,239) (-6/11,-7/13) -> (9/13,16/23) Hyperbolic Matrix(373,200,442,237) (-7/13,-8/15) -> (16/19,11/13) Hyperbolic Matrix(305,162,-578,-307) (-8/15,-9/17) -> (-9/17,-10/19) Parabolic Matrix(307,160,850,443) (-10/19,-1/2) -> (13/36,30/83) Hyperbolic Matrix(101,48,-646,-307) (-1/2,-8/17) -> (-8/51,-5/32) Hyperbolic Matrix(239,112,510,239) (-8/17,-7/15) -> (7/15,8/17) Hyperbolic Matrix(2041,950,2924,1361) (-7/15,-20/43) -> (30/43,37/53) Hyperbolic Matrix(611,284,-1904,-885) (-20/43,-13/28) -> (-9/28,-8/25) Hyperbolic Matrix(1939,898,2278,1055) (-19/41,-6/13) -> (40/47,23/27) Hyperbolic Matrix(543,250,884,407) (-6/13,-11/24) -> (27/44,8/13) Hyperbolic Matrix(35,16,374,171) (-11/24,-16/35) -> (0/1,1/10) Hyperbolic Matrix(543,248,2380,1087) (-16/35,-5/11) -> (13/57,8/35) Hyperbolic Matrix(1973,886,-4692,-2107) (-9/20,-22/49) -> (-8/19,-37/88) Hyperbolic Matrix(205,92,1972,885) (-22/49,-35/78) -> (1/10,2/19) Hyperbolic Matrix(2583,1156,4556,2039) (-30/67,-17/38) -> (17/30,38/67) Hyperbolic Matrix(237,106,986,441) (-17/38,-4/9) -> (6/25,1/4) Hyperbolic Matrix(271,120,612,271) (-4/9,-15/34) -> (15/34,4/9) Hyperbolic Matrix(749,330,1700,749) (-15/34,-11/25) -> (11/25,15/34) Hyperbolic Matrix(237,104,850,373) (-11/25,-7/16) -> (5/18,7/25) Hyperbolic Matrix(171,74,238,103) (-7/16,-3/7) -> (5/7,13/18) Hyperbolic Matrix(33,14,238,101) (-3/7,-11/26) -> (1/8,1/7) Hyperbolic Matrix(715,302,-3298,-1393) (-11/26,-19/45) -> (-5/23,-13/60) Hyperbolic Matrix(953,402,1292,545) (-19/45,-8/19) -> (14/19,17/23) Hyperbolic Matrix(8467,3558,13838,5815) (-29/69,-50/119) -> (52/85,41/67) Hyperbolic Matrix(1395,586,4454,1871) (-50/119,-21/50) -> (5/16,16/51) Hyperbolic Matrix(239,100,-1054,-441) (-13/31,-5/12) -> (-5/22,-7/31) Hyperbolic Matrix(237,98,-578,-239) (-5/12,-7/17) -> (-7/17,-9/22) Parabolic Matrix(1157,472,1836,749) (-9/22,-11/27) -> (17/27,29/46) Hyperbolic Matrix(1735,706,3094,1259) (-11/27,-13/32) -> (37/66,23/41) Hyperbolic Matrix(781,316,1258,509) (-13/32,-2/5) -> (18/29,41/66) Hyperbolic Matrix(647,256,-1802,-713) (-2/5,-13/33) -> (-37/103,-14/39) Hyperbolic Matrix(1291,508,2244,883) (-13/33,-11/28) -> (23/40,19/33) Hyperbolic Matrix(647,254,782,307) (-11/28,-9/23) -> (19/23,5/6) Hyperbolic Matrix(441,172,782,305) (-9/23,-7/18) -> (9/16,13/23) Hyperbolic Matrix(5609,2178,-14450,-5611) (-7/18,-33/85) -> (-33/85,-59/152) Parabolic Matrix(9147,3550,10778,4183) (-59/152,-26/67) -> (28/33,73/86) Hyperbolic Matrix(339,130,884,339) (-5/13,-13/34) -> (13/34,5/13) Hyperbolic Matrix(545,208,1428,545) (-13/34,-8/21) -> (8/21,13/34) Hyperbolic Matrix(305,116,-986,-375) (-8/21,-11/29) -> (-9/29,-4/13) Hyperbolic Matrix(2311,876,3944,1495) (-11/29,-25/66) -> (41/70,17/29) Hyperbolic Matrix(45969,17408,73984,28017) (-64/169,-103/272) -> (169/272,64/103) Hyperbolic Matrix(45967,17406,73984,28015) (-103/272,-39/103) -> (105/169,169/272) Hyperbolic Matrix(5305,2008,7548,2857) (-39/103,-14/37) -> (26/37,71/101) Hyperbolic Matrix(545,206,-2516,-951) (-14/37,-3/8) -> (-13/60,-8/37) Hyperbolic Matrix(2039,758,2924,1087) (-16/43,-13/35) -> (23/33,30/43) Hyperbolic Matrix(1191,442,3026,1123) (-13/35,-23/62) -> (11/28,13/33) Hyperbolic Matrix(5237,1942,-14484,-5371) (-23/62,-33/89) -> (-17/47,-47/130) Hyperbolic Matrix(5271,1954,6698,2483) (-33/89,-10/27) -> (48/61,37/47) Hyperbolic Matrix(169,62,646,237) (-7/19,-11/30) -> (1/4,5/19) Hyperbolic Matrix(1905,698,4828,1769) (-11/30,-37/101) -> (13/33,15/38) Hyperbolic Matrix(4183,1532,11050,4047) (-37/101,-26/71) -> (14/37,39/103) Hyperbolic Matrix(849,310,1394,509) (-15/41,-4/11) -> (14/23,25/41) Hyperbolic Matrix(679,246,748,271) (-4/11,-21/58) -> (9/10,10/11) Hyperbolic Matrix(1699,614,3196,1155) (-30/83,-13/36) -> (17/32,8/15) Hyperbolic Matrix(477,172,1700,613) (-13/36,-9/25) -> (7/25,9/32) Hyperbolic Matrix(2687,966,3502,1259) (-9/25,-23/64) -> (23/30,33/43) Hyperbolic Matrix(9179,3298,13056,4691) (-23/64,-37/103) -> (71/101,45/64) Hyperbolic Matrix(747,268,-3604,-1293) (-14/39,-19/53) -> (-11/53,-6/29) Hyperbolic Matrix(849,304,-3706,-1327) (-19/53,-5/14) -> (-11/48,-19/83) Hyperbolic Matrix(747,266,952,339) (-5/14,-11/31) -> (29/37,11/14) Hyperbolic Matrix(373,132,1054,373) (-11/31,-6/17) -> (6/17,11/31) Hyperbolic Matrix(35,12,102,35) (-6/17,-1/3) -> (1/3,6/17) Hyperbolic Matrix(407,130,1700,543) (-8/25,-7/22) -> (11/46,6/25) Hyperbolic Matrix(273,86,-1292,-407) (-6/19,-5/16) -> (-11/52,-4/19) Hyperbolic Matrix(137,42,-884,-271) (-4/13,-11/36) -> (-5/32,-2/13) Hyperbolic Matrix(341,104,1564,477) (-11/36,-7/23) -> (5/23,7/32) Hyperbolic Matrix(1427,434,4692,1427) (-7/23,-31/102) -> (31/102,7/23) Hyperbolic Matrix(4897,1488,16116,4897) (-31/102,-24/79) -> (24/79,31/102) Hyperbolic Matrix(1259,382,5270,1599) (-17/56,-27/89) -> (5/21,11/46) Hyperbolic Matrix(1837,556,2924,885) (-10/33,-13/43) -> (27/43,22/35) Hyperbolic Matrix(305,92,1462,441) (-13/43,-3/10) -> (5/24,9/43) Hyperbolic Matrix(169,50,-578,-171) (-3/10,-5/17) -> (-5/17,-7/24) Parabolic Matrix(1293,376,2108,613) (-7/24,-9/31) -> (19/31,27/44) Hyperbolic Matrix(3571,1036,5746,1667) (-9/31,-20/69) -> (64/103,23/37) Hyperbolic Matrix(6799,1970,9384,2719) (-20/69,-11/38) -> (71/98,50/69) Hyperbolic Matrix(1327,374,3502,987) (-11/39,-9/32) -> (25/66,11/29) Hyperbolic Matrix(613,172,1700,477) (-9/32,-7/25) -> (9/25,13/36) Hyperbolic Matrix(373,104,850,237) (-7/25,-5/18) -> (7/16,11/25) Hyperbolic Matrix(2583,716,-11288,-3129) (-5/18,-23/83) -> (-19/83,-27/118) Hyperbolic Matrix(3367,932,4794,1327) (-18/65,-13/47) -> (33/47,26/37) Hyperbolic Matrix(237,64,374,101) (-3/11,-4/15) -> (12/19,7/11) Hyperbolic Matrix(271,72,1020,271) (-4/15,-9/34) -> (9/34,4/15) Hyperbolic Matrix(341,90,1292,341) (-9/34,-5/19) -> (5/19,9/34) Hyperbolic Matrix(237,62,646,169) (-5/19,-1/4) -> (11/30,7/19) Hyperbolic Matrix(1089,262,1700,409) (-1/4,-6/25) -> (16/25,41/64) Hyperbolic Matrix(3945,944,6256,1497) (-6/25,-11/46) -> (29/46,70/111) Hyperbolic Matrix(3025,722,3842,917) (-11/46,-5/21) -> (37/47,63/80) Hyperbolic Matrix(169,40,714,169) (-5/21,-4/17) -> (4/17,5/21) Hyperbolic Matrix(103,24,442,103) (-4/17,-3/13) -> (3/13,4/17) Hyperbolic Matrix(14179,3244,17986,4115) (-27/118,-8/35) -> (108/137,41/52) Hyperbolic Matrix(1087,248,2380,543) (-8/35,-13/57) -> (5/11,16/35) Hyperbolic Matrix(14281,3256,18496,4217) (-13/57,-31/136) -> (105/136,61/79) Hyperbolic Matrix(14279,3254,18496,4215) (-31/136,-18/79) -> (44/57,105/136) Hyperbolic Matrix(8671,1956,14926,3367) (-7/31,-23/102) -> (79/136,61/105) Hyperbolic Matrix(7445,1678,12818,2889) (-23/102,-16/71) -> (18/31,79/136) Hyperbolic Matrix(169,38,1054,237) (-9/40,-2/9) -> (4/25,1/6) Hyperbolic Matrix(1733,380,4182,917) (-9/41,-7/32) -> (29/70,17/41) Hyperbolic Matrix(477,104,1564,341) (-7/32,-5/23) -> (7/23,11/36) Hyperbolic Matrix(509,110,782,169) (-8/37,-3/14) -> (13/20,2/3) Hyperbolic Matrix(169,36,-1122,-239) (-3/14,-7/33) -> (-5/33,-3/20) Hyperbolic Matrix(1463,310,4658,987) (-7/33,-18/85) -> (16/51,11/35) Hyperbolic Matrix(3639,770,5950,1259) (-18/85,-11/52) -> (11/18,52/85) Hyperbolic Matrix(1087,228,1292,271) (-4/19,-9/43) -> (21/25,16/19) Hyperbolic Matrix(441,92,1462,305) (-9/43,-5/24) -> (3/10,13/43) Hyperbolic Matrix(1259,262,1802,375) (-5/24,-11/53) -> (37/53,7/10) Hyperbolic Matrix(407,84,1972,407) (-6/29,-7/34) -> (7/34,6/29) Hyperbolic Matrix(69,14,340,69) (-7/34,-1/5) -> (1/5,7/34) Hyperbolic Matrix(611,114,1088,203) (-3/16,-5/27) -> (23/41,9/16) Hyperbolic Matrix(273,50,748,137) (-5/27,-2/11) -> (4/11,15/41) Hyperbolic Matrix(101,18,-578,-103) (-2/11,-3/17) -> (-3/17,-4/23) Parabolic Matrix(715,124,986,171) (-4/23,-1/6) -> (29/40,8/11) Hyperbolic Matrix(883,142,2108,339) (-1/6,-4/25) -> (18/43,31/74) Hyperbolic Matrix(1021,162,1292,205) (-4/25,-3/19) -> (15/19,34/43) Hyperbolic Matrix(611,96,1292,203) (-3/19,-8/51) -> (8/17,9/19) Hyperbolic Matrix(917,136,1598,237) (-7/47,-4/27) -> (4/7,27/47) Hyperbolic Matrix(271,40,1836,271) (-4/27,-5/34) -> (5/34,4/27) Hyperbolic Matrix(69,10,476,69) (-5/34,-1/7) -> (1/7,5/34) Hyperbolic Matrix(101,14,238,33) (-1/7,-1/8) -> (11/26,3/7) Hyperbolic Matrix(1259,150,2006,239) (-3/25,-2/17) -> (32/51,27/43) Hyperbolic Matrix(35,4,306,35) (-2/17,-1/9) -> (1/9,2/17) Hyperbolic Matrix(475,52,612,67) (-1/9,-2/19) -> (38/49,7/9) Hyperbolic Matrix(781,80,986,101) (-2/19,-1/10) -> (19/24,42/53) Hyperbolic Matrix(171,16,374,35) (-1/10,0/1) -> (16/35,11/24) Hyperbolic Matrix(341,-42,544,-67) (2/17,1/8) -> (5/8,32/51) Hyperbolic Matrix(1257,-188,1598,-239) (4/27,3/20) -> (11/14,48/61) Hyperbolic Matrix(681,-104,884,-135) (3/20,2/13) -> (10/13,37/48) Hyperbolic Matrix(271,-42,884,-137) (2/13,3/19) -> (15/49,4/13) Hyperbolic Matrix(103,-18,578,-101) (1/6,3/17) -> (3/17,5/28) Parabolic Matrix(103,-20,170,-33) (2/11,1/5) -> (3/5,14/23) Hyperbolic Matrix(1293,-268,3604,-747) (6/29,5/24) -> (33/92,14/39) Hyperbolic Matrix(407,-86,1292,-273) (4/19,7/33) -> (11/35,6/19) Hyperbolic Matrix(1599,-340,2074,-441) (7/33,3/14) -> (37/48,27/35) Hyperbolic Matrix(1393,-302,3298,-715) (8/37,5/23) -> (19/45,30/71) Hyperbolic Matrix(781,-172,1394,-307) (7/32,2/9) -> (14/25,37/66) Hyperbolic Matrix(441,-100,1054,-239) (2/9,5/22) -> (5/12,18/43) Hyperbolic Matrix(2311,-526,2992,-681) (5/22,13/57) -> (61/79,17/22) Hyperbolic Matrix(749,-172,884,-203) (8/35,3/13) -> (11/13,28/33) Hyperbolic Matrix(305,-84,374,-103) (3/11,5/18) -> (13/16,9/11) Hyperbolic Matrix(1055,-298,1802,-509) (9/32,2/7) -> (24/41,41/70) Hyperbolic Matrix(171,-50,578,-169) (2/7,5/17) -> (5/17,8/27) Parabolic Matrix(715,-212,1258,-373) (8/27,11/37) -> (21/37,4/7) Hyperbolic Matrix(3535,-1072,4488,-1361) (10/33,17/56) -> (63/80,26/33) Hyperbolic Matrix(1429,-434,1564,-475) (17/56,24/79) -> (10/11,11/12) Hyperbolic Matrix(373,-114,782,-239) (11/36,15/49) -> (9/19,1/2) Hyperbolic Matrix(713,-222,986,-307) (4/13,5/16) -> (13/18,34/47) Hyperbolic Matrix(815,-258,1292,-409) (6/19,1/3) -> (41/65,12/19) Hyperbolic Matrix(1531,-548,1802,-645) (5/14,19/53) -> (45/53,17/20) Hyperbolic Matrix(713,-256,1802,-647) (14/39,23/64) -> (15/38,2/5) Hyperbolic Matrix(7513,-2716,9690,-3503) (30/83,17/47) -> (69/89,38/49) Hyperbolic Matrix(2243,-812,3196,-1157) (17/47,4/11) -> (40/57,33/47) Hyperbolic Matrix(2415,-884,3434,-1257) (15/41,11/30) -> (45/64,19/27) Hyperbolic Matrix(373,-138,646,-239) (7/19,3/8) -> (15/26,11/19) Hyperbolic Matrix(647,-244,1530,-577) (3/8,14/37) -> (30/71,11/26) Hyperbolic Matrix(11153,-4224,17952,-6799) (39/103,25/66) -> (41/66,105/169) Hyperbolic Matrix(1427,-542,1972,-749) (11/29,8/21) -> (34/47,21/29) Hyperbolic Matrix(305,-118,442,-171) (5/13,7/18) -> (11/16,9/13) Hyperbolic Matrix(239,-98,578,-237) (2/5,7/17) -> (7/17,12/29) Parabolic Matrix(5847,-2450,10064,-4217) (31/74,13/31) -> (61/105,43/74) Hyperbolic Matrix(1291,-542,2108,-885) (13/31,8/19) -> (30/49,19/31) Hyperbolic Matrix(239,-108,374,-169) (4/9,5/11) -> (7/11,16/25) Hyperbolic Matrix(2075,-962,3298,-1529) (6/13,13/28) -> (39/62,56/89) Hyperbolic Matrix(3741,-1738,4828,-2243) (13/28,20/43) -> (86/111,31/40) Hyperbolic Matrix(307,-162,578,-305) (1/2,9/17) -> (9/17,17/32) Parabolic Matrix(239,-132,306,-169) (6/11,5/9) -> (7/9,18/23) Hyperbolic Matrix(4217,-2424,5440,-3127) (27/47,23/40) -> (31/40,69/89) Hyperbolic Matrix(1565,-902,1768,-1019) (34/59,15/26) -> (23/26,8/9) Hyperbolic Matrix(441,-256,646,-375) (11/19,18/31) -> (2/3,13/19) Hyperbolic Matrix(5815,-3384,6834,-3977) (32/55,39/67) -> (57/67,40/47) Hyperbolic Matrix(749,-436,816,-475) (39/67,7/12) -> (11/12,1/1) Hyperbolic Matrix(851,-498,986,-577) (7/12,24/41) -> (6/7,19/22) Hyperbolic Matrix(4385,-2684,6834,-4183) (41/67,30/49) -> (34/53,43/67) Hyperbolic Matrix(577,-358,714,-443) (13/21,18/29) -> (4/5,17/21) Hyperbolic Matrix(11695,-7376,15096,-9521) (70/111,41/65) -> (55/71,86/111) Hyperbolic Matrix(4113,-2636,5678,-3639) (41/64,25/39) -> (21/29,71/98) Hyperbolic Matrix(2857,-1832,3604,-2311) (25/39,34/53) -> (42/53,23/29) Hyperbolic Matrix(1937,-1244,2278,-1463) (43/67,9/14) -> (17/20,57/67) Hyperbolic Matrix(375,-242,578,-373) (9/14,11/17) -> (11/17,13/20) Parabolic Matrix(1019,-698,1292,-885) (13/19,11/16) -> (41/52,15/19) Hyperbolic Matrix(2073,-1444,2686,-1871) (16/23,23/33) -> (27/35,44/57) Hyperbolic Matrix(443,-324,510,-373) (19/26,11/15) -> (13/15,7/8) Hyperbolic Matrix(443,-338,578,-441) (3/4,13/17) -> (13/17,23/30) Parabolic Matrix(2923,-2262,3604,-2789) (41/53,24/31) -> (30/37,43/53) Hyperbolic Matrix(11391,-8978,14450,-11389) (26/33,67/85) -> (67/85,108/137) Parabolic Matrix(4589,-3724,5406,-4387) (43/53,13/16) -> (73/86,45/53) Hyperbolic Matrix(511,-450,578,-509) (7/8,15/17) -> (15/17,23/26) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(475,434,-1564,-1429) -> Matrix(3,2,-2,-1) Matrix(477,430,680,613) -> Matrix(1,0,-4,1) Matrix(511,458,646,579) -> Matrix(1,0,-4,1) Matrix(443,392,-1190,-1053) -> Matrix(1,0,2,1) Matrix(203,178,-544,-477) -> Matrix(1,0,0,1) Matrix(373,324,-510,-443) -> Matrix(1,0,2,1) Matrix(407,348,476,407) -> Matrix(1,0,0,1) Matrix(1565,1334,1836,1565) -> Matrix(1,0,-10,1) Matrix(2311,1968,3672,3127) -> Matrix(7,-2,-10,3) Matrix(3059,2602,-7276,-6189) -> Matrix(3,-2,2,-1) Matrix(203,172,-884,-749) -> Matrix(1,-4,0,1) Matrix(237,200,442,373) -> Matrix(1,0,-2,1) Matrix(271,228,1292,1087) -> Matrix(1,2,-2,-3) Matrix(1225,1028,2108,1769) -> Matrix(1,0,-2,1) Matrix(307,254,782,647) -> Matrix(3,2,-8,-5) Matrix(645,532,782,645) -> Matrix(1,0,2,1) Matrix(307,252,374,307) -> Matrix(1,0,-4,1) Matrix(103,84,-374,-305) -> Matrix(1,-2,0,1) Matrix(271,216,340,271) -> Matrix(1,0,0,1) Matrix(1565,1242,1972,1565) -> Matrix(1,0,-14,1) Matrix(1327,1052,-2958,-2345) -> Matrix(7,-2,4,-1) Matrix(579,458,646,511) -> Matrix(1,0,-4,1) Matrix(205,162,1292,1021) -> Matrix(7,-2,-10,3) Matrix(1121,884,-2890,-2279) -> Matrix(13,-10,4,-3) Matrix(1361,1072,-4488,-3535) -> Matrix(3,-4,-2,3) Matrix(239,188,-1598,-1257) -> Matrix(5,-6,-4,5) Matrix(169,132,-306,-239) -> Matrix(1,0,2,1) Matrix(67,52,612,475) -> Matrix(1,0,-2,1) Matrix(3503,2716,-9690,-7513) -> Matrix(1,0,0,1) Matrix(679,526,-2108,-1633) -> Matrix(1,-14,0,1) Matrix(11219,8690,14484,11219) -> Matrix(1,-28,-2,57) Matrix(4897,3792,6324,4897) -> Matrix(1,14,-2,-27) Matrix(1667,1290,-6018,-4657) -> Matrix(5,18,-2,-7) Matrix(1293,1000,1496,1157) -> Matrix(1,2,-2,-3) Matrix(1871,1444,-2686,-2073) -> Matrix(3,2,4,3) Matrix(135,104,-884,-681) -> Matrix(5,4,-4,-3) Matrix(441,338,-578,-443) -> Matrix(1,0,4,1) Matrix(1325,1008,2278,1733) -> Matrix(1,0,-6,1) Matrix(611,464,1700,1291) -> Matrix(5,-2,-12,5) Matrix(443,328,782,579) -> Matrix(1,0,0,1) Matrix(545,402,1292,953) -> Matrix(7,2,-18,-5) Matrix(951,700,1292,951) -> Matrix(1,0,8,1) Matrix(749,550,1020,749) -> Matrix(1,0,-10,1) Matrix(1631,1194,-2788,-2041) -> Matrix(1,0,2,1) Matrix(783,572,1258,919) -> Matrix(1,0,-2,1) Matrix(985,718,1258,917) -> Matrix(3,-2,-4,3) Matrix(135,98,748,543) -> Matrix(3,-2,-4,3) Matrix(3571,2588,5678,4115) -> Matrix(3,-2,-4,3) Matrix(1767,1280,-3944,-2857) -> Matrix(5,-8,2,-3) Matrix(307,222,-986,-713) -> Matrix(1,-2,0,1) Matrix(103,74,238,171) -> Matrix(1,0,-2,1) Matrix(169,120,238,169) -> Matrix(1,0,0,1) Matrix(647,456,918,647) -> Matrix(1,0,-10,1) Matrix(1257,884,-3434,-2415) -> Matrix(1,0,-4,1) Matrix(2039,1432,2516,1767) -> Matrix(1,0,-2,1) Matrix(1157,812,-3196,-2243) -> Matrix(3,-2,2,-1) Matrix(1939,1354,5406,3775) -> Matrix(5,-2,-12,5) Matrix(1361,950,2924,2041) -> Matrix(1,0,-4,1) Matrix(1939,1352,3366,2347) -> Matrix(5,-4,-16,13) Matrix(1123,782,-4930,-3433) -> Matrix(23,-20,-8,7) Matrix(239,166,442,307) -> Matrix(1,-2,-2,5) Matrix(171,118,-442,-305) -> Matrix(1,4,0,1) Matrix(373,242,-578,-375) -> Matrix(1,0,6,1) Matrix(205,132,952,613) -> Matrix(7,-2,-10,3) Matrix(169,108,-374,-239) -> Matrix(3,-2,2,-1) Matrix(101,64,374,237) -> Matrix(1,0,-2,1) Matrix(409,258,-1292,-815) -> Matrix(1,-2,0,1) Matrix(917,578,2210,1393) -> Matrix(1,-2,-2,5) Matrix(1529,962,-3298,-2075) -> Matrix(1,2,-2,-3) Matrix(4115,2588,5678,3571) -> Matrix(1,2,-4,-7) Matrix(885,556,2924,1837) -> Matrix(1,2,-2,-3) Matrix(67,42,-544,-341) -> Matrix(5,4,-4,-3) Matrix(919,572,1258,783) -> Matrix(1,0,-2,1) Matrix(3569,2218,6290,3909) -> Matrix(11,4,-14,-5) Matrix(6799,4224,-17952,-11153) -> Matrix(69,22,-22,-7) Matrix(1633,1014,3944,2449) -> Matrix(23,6,-50,-13) Matrix(545,338,-1972,-1223) -> Matrix(7,2,-4,-1) Matrix(883,546,1428,883) -> Matrix(1,0,14,1) Matrix(545,336,884,545) -> Matrix(1,0,-12,1) Matrix(407,250,884,543) -> Matrix(1,0,-6,1) Matrix(577,354,1938,1189) -> Matrix(5,-2,-12,5) Matrix(885,542,-2108,-1291) -> Matrix(3,-2,2,-1) Matrix(33,20,-170,-103) -> Matrix(1,-2,0,1) Matrix(101,60,170,101) -> Matrix(1,0,-2,1) Matrix(579,340,986,579) -> Matrix(1,0,-14,1) Matrix(509,298,-1802,-1055) -> Matrix(9,-2,-4,1) Matrix(1393,814,1802,1053) -> Matrix(7,-2,-10,3) Matrix(1631,950,-5372,-3129) -> Matrix(1,-2,0,1) Matrix(6017,3502,-14314,-8331) -> Matrix(3,-2,2,-1) Matrix(2245,1306,2924,1701) -> Matrix(1,0,-2,1) Matrix(1769,1028,2108,1225) -> Matrix(1,0,-2,1) Matrix(1463,850,-6494,-3773) -> Matrix(3,2,-2,-1) Matrix(817,474,-2108,-1223) -> Matrix(15,-4,4,-1) Matrix(239,138,-646,-373) -> Matrix(3,-2,2,-1) Matrix(137,78,-476,-271) -> Matrix(1,-4,0,1) Matrix(579,328,782,443) -> Matrix(1,0,0,1) Matrix(305,172,782,441) -> Matrix(1,-2,-2,5) Matrix(851,478,1394,783) -> Matrix(1,0,-2,1) Matrix(307,172,-1394,-781) -> Matrix(7,2,-4,-1) Matrix(951,532,1700,951) -> Matrix(1,0,8,1) Matrix(341,190,612,341) -> Matrix(1,0,-8,1) Matrix(375,206,1054,579) -> Matrix(13,-6,-28,13) Matrix(545,298,748,409) -> Matrix(3,-2,-10,7) Matrix(307,166,442,239) -> Matrix(1,-2,-2,5) Matrix(373,200,442,237) -> Matrix(1,0,-2,1) Matrix(305,162,-578,-307) -> Matrix(1,0,2,1) Matrix(307,160,850,443) -> Matrix(5,-2,-12,5) Matrix(101,48,-646,-307) -> Matrix(3,-4,-2,3) Matrix(239,112,510,239) -> Matrix(1,0,-2,1) Matrix(2041,950,2924,1361) -> Matrix(1,0,-4,1) Matrix(611,284,-1904,-885) -> Matrix(1,-8,0,1) Matrix(1939,898,2278,1055) -> Matrix(1,0,-4,1) Matrix(543,250,884,407) -> Matrix(1,0,-6,1) Matrix(35,16,374,171) -> Matrix(5,-4,-6,5) Matrix(543,248,2380,1087) -> Matrix(13,-10,-22,17) Matrix(1973,886,-4692,-2107) -> Matrix(1,0,0,1) Matrix(205,92,1972,885) -> Matrix(1,0,-2,1) Matrix(2583,1156,4556,2039) -> Matrix(1,-4,0,1) Matrix(237,106,986,441) -> Matrix(1,-2,-2,5) Matrix(271,120,612,271) -> Matrix(1,-6,-2,13) Matrix(749,330,1700,749) -> Matrix(1,10,-2,-19) Matrix(237,104,850,373) -> Matrix(1,4,-2,-7) Matrix(171,74,238,103) -> Matrix(1,0,-2,1) Matrix(33,14,238,101) -> Matrix(1,0,-2,1) Matrix(715,302,-3298,-1393) -> Matrix(3,-4,-2,3) Matrix(953,402,1292,545) -> Matrix(1,-2,2,-3) Matrix(8467,3558,13838,5815) -> Matrix(1,-2,-4,9) Matrix(1395,586,4454,1871) -> Matrix(1,0,-2,1) Matrix(239,100,-1054,-441) -> Matrix(5,-12,-2,5) Matrix(237,98,-578,-239) -> Matrix(1,-6,0,1) Matrix(1157,472,1836,749) -> Matrix(1,4,-2,-7) Matrix(1735,706,3094,1259) -> Matrix(1,2,0,1) Matrix(781,316,1258,509) -> Matrix(1,0,2,1) Matrix(647,256,-1802,-713) -> Matrix(1,2,0,1) Matrix(1291,508,2244,883) -> Matrix(1,-2,-2,5) Matrix(647,254,782,307) -> Matrix(1,-2,0,1) Matrix(441,172,782,305) -> Matrix(1,-2,-2,5) Matrix(5609,2178,-14450,-5611) -> Matrix(37,-108,12,-35) Matrix(9147,3550,10778,4183) -> Matrix(5,-16,-14,45) Matrix(339,130,884,339) -> Matrix(1,-14,-2,29) Matrix(545,208,1428,545) -> Matrix(1,18,-2,-35) Matrix(305,116,-986,-375) -> Matrix(1,4,0,1) Matrix(2311,876,3944,1495) -> Matrix(1,4,-8,-31) Matrix(45969,17408,73984,28017) -> Matrix(29,88,28,85) Matrix(45967,17406,73984,28015) -> Matrix(29,86,30,89) Matrix(5305,2008,7548,2857) -> Matrix(3,8,-14,-37) Matrix(545,206,-2516,-951) -> Matrix(1,0,0,1) Matrix(2039,758,2924,1087) -> Matrix(3,-2,-10,7) Matrix(1191,442,3026,1123) -> Matrix(3,-4,-8,11) Matrix(5237,1942,-14484,-5371) -> Matrix(1,2,0,1) Matrix(5271,1954,6698,2483) -> Matrix(1,0,-4,1) Matrix(169,62,646,237) -> Matrix(1,4,-2,-7) Matrix(1905,698,4828,1769) -> Matrix(1,2,-4,-7) Matrix(4183,1532,11050,4047) -> Matrix(11,8,-18,-13) Matrix(849,310,1394,509) -> Matrix(1,0,-4,1) Matrix(679,246,748,271) -> Matrix(1,-2,-2,5) Matrix(1699,614,3196,1155) -> Matrix(1,-2,-2,5) Matrix(477,172,1700,613) -> Matrix(1,-2,-2,5) Matrix(2687,966,3502,1259) -> Matrix(1,-2,0,1) Matrix(9179,3298,13056,4691) -> Matrix(3,-8,-16,43) Matrix(747,268,-3604,-1293) -> Matrix(1,-4,0,1) Matrix(849,304,-3706,-1327) -> Matrix(7,-24,-2,7) Matrix(747,266,952,339) -> Matrix(1,-6,-2,13) Matrix(373,132,1054,373) -> Matrix(1,-20,-2,41) Matrix(35,12,102,35) -> Matrix(1,0,-2,1) Matrix(407,130,1700,543) -> Matrix(1,6,-2,-11) Matrix(273,86,-1292,-407) -> Matrix(1,2,0,1) Matrix(137,42,-884,-271) -> Matrix(3,8,-2,-5) Matrix(341,104,1564,477) -> Matrix(1,4,-2,-7) Matrix(1427,434,4692,1427) -> Matrix(1,4,-2,-7) Matrix(4897,1488,16116,4897) -> Matrix(11,20,-16,-29) Matrix(1259,382,5270,1599) -> Matrix(3,4,-4,-5) Matrix(1837,556,2924,885) -> Matrix(1,2,-2,-3) Matrix(305,92,1462,441) -> Matrix(1,2,-2,-3) Matrix(169,50,-578,-171) -> Matrix(1,-8,0,1) Matrix(1293,376,2108,613) -> Matrix(1,6,-4,-23) Matrix(3571,1036,5746,1667) -> Matrix(3,16,2,11) Matrix(6799,1970,9384,2719) -> Matrix(5,24,-14,-67) Matrix(1327,374,3502,987) -> Matrix(7,10,-12,-17) Matrix(613,172,1700,477) -> Matrix(1,-2,-2,5) Matrix(373,104,850,237) -> Matrix(1,4,-2,-7) Matrix(2583,716,-11288,-3129) -> Matrix(19,54,-6,-17) Matrix(3367,932,4794,1327) -> Matrix(1,2,-2,-3) Matrix(237,64,374,101) -> Matrix(1,0,-2,1) Matrix(271,72,1020,271) -> Matrix(1,-6,-2,13) Matrix(341,90,1292,341) -> Matrix(1,16,-2,-31) Matrix(237,62,646,169) -> Matrix(1,4,-2,-7) Matrix(1089,262,1700,409) -> Matrix(1,0,-4,1) Matrix(3945,944,6256,1497) -> Matrix(1,4,-2,-7) Matrix(3025,722,3842,917) -> Matrix(1,0,-2,1) Matrix(169,40,714,169) -> Matrix(1,0,-2,1) Matrix(103,24,442,103) -> Matrix(1,6,-2,-11) Matrix(14179,3244,17986,4115) -> Matrix(11,34,-34,-105) Matrix(1087,248,2380,543) -> Matrix(3,10,-10,-33) Matrix(14281,3256,18496,4217) -> Matrix(19,58,-20,-61) Matrix(14279,3254,18496,4215) -> Matrix(19,56,-18,-53) Matrix(8671,1956,14926,3367) -> Matrix(1,2,8,17) Matrix(7445,1678,12818,2889) -> Matrix(1,2,-14,-27) Matrix(169,38,1054,237) -> Matrix(3,4,-4,-5) Matrix(1733,380,4182,917) -> Matrix(9,14,-20,-31) Matrix(477,104,1564,341) -> Matrix(1,4,-2,-7) Matrix(509,110,782,169) -> Matrix(1,2,0,1) Matrix(169,36,-1122,-239) -> Matrix(3,2,-2,-1) Matrix(1463,310,4658,987) -> Matrix(5,2,-8,-3) Matrix(3639,770,5950,1259) -> Matrix(1,0,-4,1) Matrix(1087,228,1292,271) -> Matrix(1,2,-2,-3) Matrix(441,92,1462,305) -> Matrix(1,2,-2,-3) Matrix(1259,262,1802,375) -> Matrix(1,2,-4,-7) Matrix(407,84,1972,407) -> Matrix(1,2,-2,-3) Matrix(69,14,340,69) -> Matrix(1,4,-2,-7) Matrix(611,114,1088,203) -> Matrix(1,2,-2,-3) Matrix(273,50,748,137) -> Matrix(1,2,-4,-7) Matrix(101,18,-578,-103) -> Matrix(1,2,-2,-3) Matrix(715,124,986,171) -> Matrix(1,0,-2,1) Matrix(883,142,2108,339) -> Matrix(9,16,-22,-39) Matrix(1021,162,1292,205) -> Matrix(1,2,-6,-11) Matrix(611,96,1292,203) -> Matrix(5,8,-12,-19) Matrix(917,136,1598,237) -> Matrix(7,8,-22,-25) Matrix(271,40,1836,271) -> Matrix(17,18,-18,-19) Matrix(69,10,476,69) -> Matrix(1,0,0,1) Matrix(101,14,238,33) -> Matrix(1,0,-2,1) Matrix(1259,150,2006,239) -> Matrix(9,10,-10,-11) Matrix(35,4,306,35) -> Matrix(1,0,0,1) Matrix(475,52,612,67) -> Matrix(1,0,-2,1) Matrix(781,80,986,101) -> Matrix(1,2,-6,-11) Matrix(171,16,374,35) -> Matrix(3,4,-10,-13) Matrix(341,-42,544,-67) -> Matrix(5,4,-4,-3) Matrix(1257,-188,1598,-239) -> Matrix(7,6,-20,-17) Matrix(681,-104,884,-135) -> Matrix(5,4,-4,-3) Matrix(271,-42,884,-137) -> Matrix(11,8,-18,-13) Matrix(103,-18,578,-101) -> Matrix(1,2,-2,-3) Matrix(103,-20,170,-33) -> Matrix(3,2,-8,-5) Matrix(1293,-268,3604,-747) -> Matrix(7,4,-16,-9) Matrix(407,-86,1292,-273) -> Matrix(5,2,-8,-3) Matrix(1599,-340,2074,-441) -> Matrix(3,2,-2,-1) Matrix(1393,-302,3298,-715) -> Matrix(5,4,-14,-11) Matrix(781,-172,1394,-307) -> Matrix(3,2,4,3) Matrix(441,-100,1054,-239) -> Matrix(19,12,-46,-29) Matrix(2311,-526,2992,-681) -> Matrix(23,14,-28,-17) Matrix(749,-172,884,-203) -> Matrix(7,4,-16,-9) Matrix(305,-84,374,-103) -> Matrix(3,2,-8,-5) Matrix(1055,-298,1802,-509) -> Matrix(3,2,-20,-13) Matrix(171,-50,578,-169) -> Matrix(15,8,-32,-17) Matrix(715,-212,1258,-373) -> Matrix(9,4,-16,-7) Matrix(3535,-1072,4488,-1361) -> Matrix(5,4,-14,-11) Matrix(1429,-434,1564,-475) -> Matrix(3,2,-2,-1) Matrix(373,-114,782,-239) -> Matrix(7,4,-16,-9) Matrix(713,-222,986,-307) -> Matrix(3,2,-8,-5) Matrix(815,-258,1292,-409) -> Matrix(3,2,-8,-5) Matrix(1531,-548,1802,-645) -> Matrix(9,4,-34,-15) Matrix(713,-256,1802,-647) -> Matrix(5,2,-8,-3) Matrix(7513,-2716,9690,-3503) -> Matrix(1,0,0,1) Matrix(2243,-812,3196,-1157) -> Matrix(5,2,-18,-7) Matrix(2415,-884,3434,-1257) -> Matrix(1,0,-4,1) Matrix(373,-138,646,-239) -> Matrix(5,2,-18,-7) Matrix(647,-244,1530,-577) -> Matrix(5,4,-14,-11) Matrix(11153,-4224,17952,-6799) -> Matrix(37,22,42,25) Matrix(1427,-542,1972,-749) -> Matrix(11,6,-24,-13) Matrix(305,-118,442,-171) -> Matrix(9,4,-16,-7) Matrix(239,-98,578,-237) -> Matrix(11,6,-24,-13) Matrix(5847,-2450,10064,-4217) -> Matrix(5,2,12,5) Matrix(1291,-542,2108,-885) -> Matrix(5,2,-18,-7) Matrix(239,-108,374,-169) -> Matrix(5,2,-18,-7) Matrix(2075,-962,3298,-1529) -> Matrix(1,2,-2,-3) Matrix(3741,-1738,4828,-2243) -> Matrix(11,6,-24,-13) Matrix(307,-162,578,-305) -> Matrix(1,0,2,1) Matrix(239,-132,306,-169) -> Matrix(1,0,2,1) Matrix(4217,-2424,5440,-3127) -> Matrix(15,4,-34,-9) Matrix(1565,-902,1768,-1019) -> Matrix(7,2,-4,-1) Matrix(441,-256,646,-375) -> Matrix(1,0,4,1) Matrix(5815,-3384,6834,-3977) -> Matrix(1,0,0,1) Matrix(749,-436,816,-475) -> Matrix(1,0,2,1) Matrix(851,-498,986,-577) -> Matrix(1,0,4,1) Matrix(4385,-2684,6834,-4183) -> Matrix(1,0,0,1) Matrix(577,-358,714,-443) -> Matrix(1,0,-4,1) Matrix(11695,-7376,15096,-9521) -> Matrix(23,12,-48,-25) Matrix(4113,-2636,5678,-3639) -> Matrix(11,2,-28,-5) Matrix(2857,-1832,3604,-2311) -> Matrix(1,0,-2,1) Matrix(1937,-1244,2278,-1463) -> Matrix(1,0,0,1) Matrix(375,-242,578,-373) -> Matrix(1,0,6,1) Matrix(1019,-698,1292,-885) -> Matrix(1,2,-4,-7) Matrix(2073,-1444,2686,-1871) -> Matrix(7,2,-4,-1) Matrix(443,-324,510,-373) -> Matrix(1,0,2,1) Matrix(443,-338,578,-441) -> Matrix(1,0,4,1) Matrix(2923,-2262,3604,-2789) -> Matrix(7,4,-2,-1) Matrix(11391,-8978,14450,-11389) -> Matrix(35,12,-108,-37) Matrix(4589,-3724,5406,-4387) -> Matrix(3,4,-10,-13) Matrix(511,-450,578,-509) -> Matrix(1,0,2,1) 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): 86 Degree of the the map X: 86 Degree of the the map Y: 288 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. Imminent integer overflow caused the modular group computation to abort.