INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1536 Minimal number of generators: 257 Number of equivalence classes of cusps: 72 Genus: 93 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/8 -3/4 -5/8 -7/12 -1/2 -7/15 -5/12 -3/8 -95/256 -19/64 -17/64 -1/4 -15/64 -29/128 -3/14 -4/23 -11/64 -1/6 -4/27 -1/8 -1/10 0/1 1/11 1/10 1/9 1/8 2/15 1/7 2/13 5/32 4/25 1/6 2/11 3/16 4/21 1/5 4/19 3/14 7/32 2/9 3/13 4/17 1/4 8/29 9/32 2/7 5/16 1/3 17/48 3/8 12/31 2/5 13/32 5/12 7/16 43/96 1/2 9/16 7/12 5/8 31/48 2/3 11/16 67/96 23/32 3/4 25/32 13/16 27/32 7/8 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/1 -8/9 2/1 1/0 -15/17 1/1 -7/8 1/1 -6/7 2/1 1/0 -5/6 1/1 3/1 -19/23 1/1 -14/17 3/1 1/0 -9/11 3/1 -22/27 6/1 1/0 -13/16 1/0 -4/5 1/1 1/0 -11/14 1/1 3/1 -18/23 8/1 1/0 -25/32 1/0 -7/9 -3/1 -10/13 0/1 1/0 -13/17 -1/1 -29/38 -1/1 1/1 -16/21 0/1 1/0 -3/4 1/0 -17/23 1/1 -31/42 -1/1 1/1 -14/19 0/1 1/0 -11/15 1/1 -8/11 0/1 1/1 -13/18 1/1 3/1 -18/25 4/1 1/0 -23/32 1/0 -5/7 -1/1 -22/31 -1/1 -2/3 -17/24 0/1 -29/41 1/1 -12/17 -1/1 1/0 -7/10 -1/1 1/1 -23/33 1/1 -16/23 2/1 1/0 -9/13 1/1 -20/29 1/1 1/0 -11/16 1/0 -2/3 0/1 1/0 -15/23 -1/1 -13/20 1/0 -11/17 1/1 -9/14 -1/1 1/1 -16/25 -2/1 1/0 -39/61 -1/1 -23/36 0/1 -7/11 -1/1 -26/41 0/1 1/0 -19/30 -1/1 -1/3 -31/49 1/1 -12/19 0/1 1/0 -17/27 1/1 -5/8 0/1 -23/37 1/3 -41/66 7/9 1/1 -59/95 1/1 -18/29 1/1 1/0 -13/21 1/1 -8/13 0/1 1/0 -27/44 1/2 -19/31 1/1 -49/80 1/1 -30/49 1/1 4/3 -11/18 1/1 3/1 -14/23 -4/1 1/0 -17/28 -2/1 -37/61 -1/1 -20/33 -1/1 -4/5 -3/5 -1/1 -13/22 1/3 1/1 -10/17 1/2 1/1 -17/29 1/1 -24/41 0/1 1/0 -31/53 -1/1 -38/65 0/1 1/0 -7/12 0/1 -18/31 1/1 2/1 -11/19 1/1 -15/26 -1/1 1/1 -4/7 0/1 1/0 -9/16 0/1 -14/25 0/1 1/4 -47/84 0/1 -33/59 3/11 -19/34 1/3 3/7 -5/9 1/1 -11/20 1/2 -17/31 1/1 -6/11 1/1 2/1 -1/2 -1/1 1/1 -7/15 -1/1 -6/13 0/1 1/0 -5/11 1/1 -14/31 1/1 4/3 -9/20 2/1 -22/49 0/1 1/1 -13/29 1/1 -17/38 1/1 3/1 -21/47 1/1 -4/9 2/1 1/0 -7/16 1/0 -10/23 -2/1 1/0 -13/30 -5/3 -1/1 -16/37 -1/2 0/1 -3/7 1/1 -14/33 2/3 1/1 -25/59 1/1 -11/26 1/1 3/1 -19/45 3/1 -27/64 1/0 -8/19 0/1 1/0 -13/31 1/1 -31/74 1/1 5/3 -49/117 5/3 -67/160 2/1 -18/43 2/1 1/0 -5/12 1/0 -17/41 1/1 -29/70 1/1 3/1 -12/29 1/1 1/0 -7/17 3/1 -23/56 3/1 -16/39 4/1 1/0 -25/61 3/1 -9/22 3/1 5/1 -20/49 6/1 7/1 -31/76 8/1 -11/27 11/1 -13/32 1/0 -2/5 -1/1 1/0 -7/18 -3/1 -1/1 -19/49 -1/1 -31/80 -2/1 -12/31 -2/1 -1/1 -5/13 -1/1 -13/34 -3/1 -1/1 -21/55 1/1 -29/76 1/0 -8/21 0/1 1/0 -19/50 1/3 1/1 -30/79 1/1 2/1 -11/29 1/1 -3/8 1/0 -13/35 -3/1 -36/97 -28/9 -3/1 -95/256 -3/1 -59/159 -3/1 -23/62 -3/1 -19/7 -10/27 -2/1 1/0 -17/46 -3/1 -1/1 -24/65 -2/1 1/0 -31/84 -2/1 -7/19 -1/1 -11/30 -3/1 -1/1 -4/11 -1/1 0/1 -5/14 -3/1 -1/1 -11/31 -1/1 -17/48 -1/1 -6/17 -1/1 -1/2 -1/3 -1/1 -7/22 -1/1 -1/3 -6/19 -1/2 0/1 -5/16 0/1 -4/13 0/1 1/0 -7/23 -3/1 -17/56 -2/1 -10/33 -1/1 0/1 -13/43 -1/1 -3/10 -1/1 -1/3 -11/37 -1/5 -19/64 0/1 -8/27 0/1 1/2 -13/44 1/0 -5/17 -1/1 -12/41 0/1 1/0 -19/65 -1/1 -26/89 0/1 1/0 -7/24 -1/1 -2/7 -1/2 0/1 -9/32 0/1 -7/25 1/7 -19/68 1/4 -12/43 0/1 1/4 -5/18 1/3 1/1 -18/65 0/1 1/2 -31/112 0/1 -13/47 1/3 -8/29 1/2 1/1 -3/11 1/1 -10/37 -2/1 1/0 -17/63 -1/1 -7/26 -1/1 1/1 -25/93 -1/1 -43/160 0/1 -18/67 0/1 1/0 -11/41 1/1 -4/15 -1/1 0/1 -17/64 0/1 -13/49 1/3 -9/34 -1/1 1/1 -5/19 1/1 -6/23 2/1 1/0 -1/4 0/1 -5/21 1/1 -4/17 1/1 1/0 -15/64 1/0 -11/47 -3/1 -7/30 -3/1 -1/1 -3/13 -1/1 -8/35 -1/1 1/0 -21/92 -1/2 -13/57 1/1 -5/22 -3/1 -1/1 -17/75 -1/1 -29/128 -1/1 -12/53 -1/1 -4/5 -7/31 -1/1 -2/9 -1/2 0/1 -7/32 0/1 -5/23 1/5 -13/60 1/4 -34/157 3/10 1/3 -21/97 1/3 -8/37 0/1 1/2 -3/14 1/3 1/1 -7/33 1/1 -4/19 0/1 1/0 -1/5 -1/1 -5/26 -1/1 -1/3 -4/21 -1/2 0/1 -3/16 0/1 -2/11 0/1 1/1 -3/17 1/1 -4/23 0/1 1/0 -5/29 1/1 -11/64 1/0 -6/35 -1/1 1/0 -1/6 -1/1 1/1 -5/31 -1/1 -4/25 -1/2 0/1 -7/44 0/1 -3/19 -1/3 -5/32 0/1 -2/13 0/1 1/2 -3/20 1/0 -4/27 0/1 1/2 -1/7 -1/1 -3/22 1/1 3/1 -2/15 -1/1 0/1 -3/23 1/1 -1/8 0/1 -1/9 -1/1 -1/10 -1/1 1/1 -1/11 1/1 0/1 0/1 1/0 1/11 -1/1 1/10 -1/1 1/1 1/9 1/1 1/8 0/1 2/15 0/1 1/1 3/22 -3/1 -1/1 1/7 1/1 3/20 1/0 2/13 -1/2 0/1 5/32 0/1 3/19 1/3 7/44 0/1 4/25 0/1 1/2 1/6 -1/1 1/1 2/11 -1/1 0/1 3/16 0/1 4/21 0/1 1/2 5/26 1/3 1/1 1/5 1/1 4/19 0/1 1/0 3/14 -1/1 -1/3 8/37 -1/2 0/1 5/23 -1/5 7/32 0/1 2/9 0/1 1/2 7/31 1/1 5/22 1/1 3/1 13/57 -1/1 8/35 1/1 1/0 3/13 1/1 4/17 -1/1 1/0 1/4 0/1 5/19 -1/1 4/15 0/1 1/1 15/56 0/1 11/41 -1/1 18/67 0/1 1/0 7/26 -1/1 1/1 24/89 0/1 1/2 17/63 1/1 10/37 2/1 1/0 3/11 -1/1 8/29 -1/1 -1/2 5/18 -1/1 -1/3 12/43 -1/4 0/1 7/25 -1/7 9/32 0/1 2/7 0/1 1/2 7/24 1/1 12/41 0/1 1/0 5/17 1/1 13/44 1/0 21/71 1/1 8/27 -1/2 0/1 3/10 1/3 1/1 4/13 0/1 1/0 5/16 0/1 6/19 0/1 1/2 7/22 1/3 1/1 1/3 1/1 6/17 1/2 1/1 17/48 1/1 11/31 1/1 5/14 1/1 3/1 4/11 0/1 1/1 7/19 1/1 31/84 2/1 24/65 2/1 1/0 17/46 1/1 3/1 10/27 2/1 1/0 3/8 1/0 14/37 -2/1 1/0 25/66 -9/7 -1/1 36/95 -1/1 -8/9 11/29 -1/1 19/50 -1/1 -1/3 8/21 0/1 1/0 21/55 -1/1 13/34 1/1 3/1 18/47 -1/1 1/0 5/13 1/1 12/31 1/1 2/1 7/18 1/1 3/1 2/5 1/1 1/0 13/32 1/0 11/27 -11/1 20/49 -7/1 -6/1 9/22 -5/1 -3/1 25/61 -3/1 16/39 -4/1 1/0 23/56 -3/1 7/17 -3/1 26/63 -2/1 1/0 19/46 -3/1 -1/1 12/29 -1/1 1/0 5/12 1/0 23/55 -3/1 18/43 -2/1 1/0 13/31 -1/1 21/50 -1/1 -1/3 8/19 0/1 1/0 11/26 -3/1 -1/1 25/59 -1/1 14/33 -1/1 -2/3 3/7 -1/1 16/37 0/1 1/2 13/30 1/1 5/3 10/23 2/1 1/0 7/16 1/0 4/9 -2/1 1/0 17/38 -3/1 -1/1 30/67 -2/1 1/0 43/96 -2/1 13/29 -1/1 22/49 -1/1 0/1 31/69 -5/1 9/20 -2/1 5/11 -1/1 1/2 -1/1 1/1 8/15 0/1 1/1 7/13 -1/1 6/11 -2/1 -1/1 23/42 -1/1 -7/9 17/31 -1/1 11/20 -1/2 16/29 -1/1 -1/2 5/9 -1/1 19/34 -3/7 -1/3 33/59 -3/11 47/84 0/1 14/25 -1/4 0/1 9/16 0/1 4/7 0/1 1/0 11/19 -1/1 18/31 -2/1 -1/1 25/43 -1/1 7/12 0/1 24/41 0/1 1/0 17/29 -1/1 10/17 -1/1 -1/2 3/5 1/1 20/33 4/5 1/1 17/28 2/1 14/23 4/1 1/0 11/18 -3/1 -1/1 41/67 -1/1 30/49 -4/3 -1/1 49/80 -1/1 19/31 -1/1 27/44 -1/2 8/13 0/1 1/0 21/34 -1/1 1/1 13/21 -1/1 18/29 -1/1 1/0 5/8 0/1 22/35 1/2 1/1 61/97 1/1 161/256 1/1 100/159 1/1 16/15 39/62 1/1 7/5 17/27 -1/1 12/19 0/1 1/0 19/30 1/3 1/1 26/41 0/1 1/0 33/52 0/1 40/63 0/1 1/0 7/11 1/1 23/36 0/1 62/97 6/7 1/1 39/61 1/1 16/25 2/1 1/0 9/14 -1/1 1/1 20/31 -1/1 0/1 31/48 0/1 42/65 0/1 1/0 11/17 -1/1 13/20 1/0 15/23 1/1 2/3 0/1 1/0 11/16 1/0 20/29 -1/1 1/0 9/13 -1/1 25/36 0/1 16/23 -2/1 1/0 39/56 -1/1 62/89 -2/1 1/0 23/33 -1/1 30/43 -1/2 0/1 67/96 0/1 37/53 1/1 7/10 -1/1 1/1 26/37 -1/4 0/1 45/64 0/1 19/27 1/3 12/17 1/1 1/0 29/41 -1/1 17/24 0/1 22/31 2/3 1/1 5/7 1/1 23/32 1/0 18/25 -4/1 1/0 13/18 -3/1 -1/1 8/11 -1/1 0/1 19/26 -1/1 1/1 49/67 -1/1 30/41 0/1 1/0 11/15 -1/1 47/64 0/1 36/49 0/1 1/3 25/34 1/3 1/1 14/19 0/1 1/0 31/42 -1/1 1/1 17/23 -1/1 20/27 0/1 1/2 23/31 1/1 3/4 1/0 25/33 -1/1 22/29 -1/1 -1/2 19/25 -1/3 16/21 0/1 1/0 29/38 -1/1 1/1 13/17 1/1 49/64 1/0 36/47 -3/1 1/0 23/30 -1/1 1/1 10/13 0/1 1/0 17/22 1/3 1/1 58/75 6/7 1/1 99/128 1/1 41/53 1/1 24/31 0/1 1/1 31/40 2/1 7/9 3/1 25/32 1/0 18/23 -8/1 1/0 11/14 -3/1 -1/1 4/5 -1/1 1/0 13/16 1/0 22/27 -6/1 1/0 9/11 -3/1 23/28 -2/1 14/17 -3/1 1/0 19/23 -1/1 24/29 -1/1 1/0 53/64 1/0 29/35 -3/1 5/6 -3/1 -1/1 16/19 0/1 1/0 27/32 1/0 11/13 -3/1 6/7 -2/1 1/0 7/8 -1/1 15/17 -1/1 23/26 -3/1 -1/1 8/9 -2/1 1/0 1/1 -1/1 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(65,58,288,257) (-1/1,-8/9) -> (2/9,7/31) Hyperbolic Matrix(257,228,-576,-511) (-8/9,-15/17) -> (-21/47,-4/9) Hyperbolic Matrix(447,394,1088,959) (-15/17,-7/8) -> (23/56,7/17) Hyperbolic Matrix(65,56,224,193) (-7/8,-6/7) -> (2/7,7/24) Hyperbolic Matrix(129,110,-224,-191) (-6/7,-5/6) -> (-15/26,-4/7) Hyperbolic Matrix(769,636,-1856,-1535) (-5/6,-19/23) -> (-17/41,-29/70) Hyperbolic Matrix(769,634,1088,897) (-19/23,-14/17) -> (12/17,29/41) Hyperbolic Matrix(129,106,-544,-447) (-14/17,-9/11) -> (-5/21,-4/17) Hyperbolic Matrix(191,156,704,575) (-9/11,-22/27) -> (10/37,3/11) Hyperbolic Matrix(703,572,864,703) (-22/27,-13/16) -> (13/16,22/27) Hyperbolic Matrix(129,104,160,129) (-13/16,-4/5) -> (4/5,13/16) Hyperbolic Matrix(63,50,160,127) (-4/5,-11/14) -> (7/18,2/5) Hyperbolic Matrix(449,352,736,577) (-11/14,-18/23) -> (14/23,11/18) Hyperbolic Matrix(1151,900,1472,1151) (-18/23,-25/32) -> (25/32,18/23) Hyperbolic Matrix(449,350,576,449) (-25/32,-7/9) -> (7/9,25/32) Hyperbolic Matrix(127,98,-416,-321) (-7/9,-10/13) -> (-4/13,-7/23) Hyperbolic Matrix(193,148,-416,-319) (-10/13,-13/17) -> (-7/15,-6/13) Hyperbolic Matrix(1087,830,-2432,-1857) (-13/17,-29/38) -> (-17/38,-21/47) Hyperbolic Matrix(257,196,1344,1025) (-29/38,-16/21) -> (4/21,5/26) Hyperbolic Matrix(447,340,-1600,-1217) (-16/21,-3/4) -> (-19/68,-12/43) Hyperbolic Matrix(319,236,-1472,-1089) (-3/4,-17/23) -> (-5/23,-13/60) Hyperbolic Matrix(65,48,608,449) (-17/23,-31/42) -> (1/10,1/9) Hyperbolic Matrix(385,284,1216,897) (-31/42,-14/19) -> (6/19,7/22) Hyperbolic Matrix(769,566,-1216,-895) (-14/19,-11/15) -> (-31/49,-12/19) Hyperbolic Matrix(63,46,-352,-257) (-11/15,-8/11) -> (-2/11,-3/17) Hyperbolic Matrix(127,92,352,255) (-8/11,-13/18) -> (5/14,4/11) Hyperbolic Matrix(513,370,800,577) (-13/18,-18/25) -> (16/25,9/14) Hyperbolic Matrix(1151,828,1600,1151) (-18/25,-23/32) -> (23/32,18/25) Hyperbolic Matrix(321,230,448,321) (-23/32,-5/7) -> (5/7,23/32) Hyperbolic Matrix(191,136,448,319) (-5/7,-22/31) -> (14/33,3/7) Hyperbolic Matrix(767,544,-2528,-1793) (-22/31,-17/24) -> (-17/56,-10/33) Hyperbolic Matrix(65,46,544,385) (-17/24,-29/41) -> (1/9,1/8) Hyperbolic Matrix(897,634,1088,769) (-29/41,-12/17) -> (14/17,19/23) Hyperbolic Matrix(321,226,-544,-383) (-12/17,-7/10) -> (-13/22,-10/17) Hyperbolic Matrix(1153,804,-2752,-1919) (-7/10,-23/33) -> (-13/31,-31/74) Hyperbolic Matrix(833,580,-2848,-1983) (-23/33,-16/23) -> (-12/41,-19/65) Hyperbolic Matrix(193,134,-736,-511) (-16/23,-9/13) -> (-5/19,-6/23) Hyperbolic Matrix(191,132,832,575) (-9/13,-20/29) -> (8/35,3/13) Hyperbolic Matrix(639,440,928,639) (-20/29,-11/16) -> (11/16,20/29) Hyperbolic Matrix(65,44,96,65) (-11/16,-2/3) -> (2/3,11/16) Hyperbolic Matrix(447,292,1664,1087) (-2/3,-15/23) -> (11/41,18/67) Hyperbolic Matrix(575,374,1376,895) (-15/23,-13/20) -> (5/12,23/55) Hyperbolic Matrix(321,208,1088,705) (-13/20,-11/17) -> (5/17,13/44) Hyperbolic Matrix(385,248,-992,-639) (-11/17,-9/14) -> (-7/18,-19/49) Hyperbolic Matrix(577,370,800,513) (-9/14,-16/25) -> (18/25,13/18) Hyperbolic Matrix(1601,1024,3904,2497) (-16/25,-39/61) -> (25/61,16/39) Hyperbolic Matrix(2369,1514,-3904,-2495) (-39/61,-23/36) -> (-17/28,-37/61) Hyperbolic Matrix(577,368,704,449) (-23/36,-7/11) -> (9/11,23/28) Hyperbolic Matrix(1535,974,-2624,-1665) (-7/11,-26/41) -> (-24/41,-31/53) Hyperbolic Matrix(833,528,1920,1217) (-26/41,-19/30) -> (13/30,10/23) Hyperbolic Matrix(831,526,-3136,-1985) (-19/30,-31/49) -> (-13/49,-9/34) Hyperbolic Matrix(127,80,608,383) (-12/19,-17/27) -> (1/5,4/19) Hyperbolic Matrix(319,200,-512,-321) (-17/27,-5/8) -> (-5/8,-23/37) Parabolic Matrix(2881,1790,5152,3201) (-23/37,-41/66) -> (19/34,33/59) Hyperbolic Matrix(6079,3776,-16384,-10177) (-41/66,-59/95) -> (-59/159,-23/62) Hyperbolic Matrix(3839,2384,-17728,-11009) (-59/95,-18/29) -> (-34/157,-21/97) Hyperbolic Matrix(255,158,928,575) (-18/29,-13/21) -> (3/11,8/29) Hyperbolic Matrix(191,118,-416,-257) (-13/21,-8/13) -> (-6/13,-5/11) Hyperbolic Matrix(127,78,832,511) (-8/13,-27/44) -> (3/20,2/13) Hyperbolic Matrix(1089,668,1984,1217) (-27/44,-19/31) -> (17/31,11/20) Hyperbolic Matrix(1407,862,3968,2431) (-19/31,-49/80) -> (17/48,11/31) Hyperbolic Matrix(4801,2940,7840,4801) (-49/80,-30/49) -> (30/49,49/80) Hyperbolic Matrix(1471,900,-3872,-2369) (-30/49,-11/18) -> (-19/50,-30/79) Hyperbolic Matrix(577,352,736,449) (-11/18,-14/23) -> (18/23,11/14) Hyperbolic Matrix(1023,622,1472,895) (-14/23,-17/28) -> (25/36,16/23) Hyperbolic Matrix(2559,1552,6752,4095) (-37/61,-20/33) -> (36/95,11/29) Hyperbolic Matrix(895,542,2112,1279) (-20/33,-3/5) -> (25/59,14/33) Hyperbolic Matrix(257,152,-864,-511) (-3/5,-13/22) -> (-3/10,-11/37) Hyperbolic Matrix(191,112,544,319) (-10/17,-17/29) -> (1/3,6/17) Hyperbolic Matrix(321,188,-1856,-1087) (-17/29,-24/41) -> (-4/23,-5/29) Hyperbolic Matrix(65,38,768,449) (-31/53,-38/65) -> (0/1,1/11) Hyperbolic Matrix(2303,1346,6240,3647) (-38/65,-7/12) -> (31/84,24/65) Hyperbolic Matrix(447,260,-992,-577) (-7/12,-18/31) -> (-14/31,-9/20) Hyperbolic Matrix(383,222,992,575) (-18/31,-11/19) -> (5/13,12/31) Hyperbolic Matrix(703,406,-1664,-961) (-11/19,-15/26) -> (-11/26,-19/45) Hyperbolic Matrix(127,72,224,127) (-4/7,-9/16) -> (9/16,4/7) Hyperbolic Matrix(449,252,800,449) (-9/16,-14/25) -> (14/25,9/16) Hyperbolic Matrix(511,286,3200,1791) (-14/25,-47/84) -> (7/44,4/25) Hyperbolic Matrix(3135,1754,6976,3903) (-47/84,-33/59) -> (31/69,9/20) Hyperbolic Matrix(2879,1610,4576,2559) (-33/59,-19/34) -> (39/62,17/27) Hyperbolic Matrix(831,464,2176,1215) (-19/34,-5/9) -> (21/55,13/34) Hyperbolic Matrix(385,212,-928,-511) (-5/9,-11/20) -> (-5/12,-17/41) Hyperbolic Matrix(1217,668,1984,1089) (-11/20,-17/31) -> (19/31,27/44) Hyperbolic Matrix(449,246,-1984,-1087) (-17/31,-6/11) -> (-12/53,-7/31) Hyperbolic Matrix(129,70,-352,-191) (-6/11,-1/2) -> (-11/30,-4/11) Hyperbolic Matrix(127,60,-544,-257) (-1/2,-7/15) -> (-11/47,-7/30) Hyperbolic Matrix(513,232,-1696,-767) (-5/11,-14/31) -> (-10/33,-13/43) Hyperbolic Matrix(1919,862,-4704,-2113) (-9/20,-22/49) -> (-20/49,-31/76) Hyperbolic Matrix(2879,1292,4704,2111) (-22/49,-13/29) -> (41/67,30/49) Hyperbolic Matrix(1153,516,-4288,-1919) (-13/29,-17/38) -> (-7/26,-25/93) Hyperbolic Matrix(127,56,288,127) (-4/9,-7/16) -> (7/16,4/9) Hyperbolic Matrix(321,140,736,321) (-7/16,-10/23) -> (10/23,7/16) Hyperbolic Matrix(1217,528,1920,833) (-10/23,-13/30) -> (19/30,26/41) Hyperbolic Matrix(1345,582,3552,1537) (-13/30,-16/37) -> (14/37,25/66) Hyperbolic Matrix(833,360,2816,1217) (-16/37,-3/7) -> (21/71,8/27) Hyperbolic Matrix(319,136,448,191) (-3/7,-14/33) -> (22/31,5/7) Hyperbolic Matrix(1279,542,2112,895) (-14/33,-25/59) -> (3/5,20/33) Hyperbolic Matrix(321,136,1664,705) (-25/59,-11/26) -> (5/26,1/5) Hyperbolic Matrix(1919,810,2272,959) (-19/45,-27/64) -> (27/32,11/13) Hyperbolic Matrix(1537,648,1824,769) (-27/64,-8/19) -> (16/19,27/32) Hyperbolic Matrix(257,108,-1216,-511) (-8/19,-13/31) -> (-7/33,-4/19) Hyperbolic Matrix(191,80,1984,831) (-31/74,-49/117) -> (1/11,1/10) Hyperbolic Matrix(13759,5762,19712,8255) (-49/117,-67/160) -> (67/96,37/53) Hyperbolic Matrix(7681,3216,11008,4609) (-67/160,-18/43) -> (30/43,67/96) Hyperbolic Matrix(1343,562,-3520,-1473) (-18/43,-5/12) -> (-29/76,-8/21) Hyperbolic Matrix(449,186,-2624,-1087) (-29/70,-12/29) -> (-6/35,-1/6) Hyperbolic Matrix(513,212,-1856,-767) (-12/29,-7/17) -> (-13/47,-8/29) Hyperbolic Matrix(959,394,1088,447) (-7/17,-23/56) -> (7/8,15/17) Hyperbolic Matrix(1729,710,-5920,-2431) (-23/56,-16/39) -> (-26/89,-7/24) Hyperbolic Matrix(2497,1024,3904,1601) (-16/39,-25/61) -> (39/61,16/25) Hyperbolic Matrix(449,184,1408,577) (-25/61,-9/22) -> (7/22,1/3) Hyperbolic Matrix(191,78,1408,575) (-9/22,-20/49) -> (2/15,3/22) Hyperbolic Matrix(3777,1540,6752,2753) (-31/76,-11/27) -> (33/59,47/84) Hyperbolic Matrix(703,286,1728,703) (-11/27,-13/32) -> (13/32,11/27) Hyperbolic Matrix(129,52,320,129) (-13/32,-2/5) -> (2/5,13/32) Hyperbolic Matrix(127,50,160,63) (-2/5,-7/18) -> (11/14,4/5) Hyperbolic Matrix(2559,992,-9248,-3585) (-19/49,-31/80) -> (-31/112,-13/47) Hyperbolic Matrix(2561,992,3968,1537) (-31/80,-12/31) -> (20/31,31/48) Hyperbolic Matrix(575,222,992,383) (-12/31,-5/13) -> (11/19,18/31) Hyperbolic Matrix(193,74,-832,-319) (-5/13,-13/34) -> (-7/30,-3/13) Hyperbolic Matrix(1215,464,2176,831) (-13/34,-21/55) -> (5/9,19/34) Hyperbolic Matrix(1855,708,2848,1087) (-21/55,-29/76) -> (13/20,15/23) Hyperbolic Matrix(705,268,2528,961) (-8/21,-19/50) -> (5/18,12/43) Hyperbolic Matrix(1665,632,3712,1409) (-30/79,-11/29) -> (13/29,22/49) Hyperbolic Matrix(191,72,-512,-193) (-11/29,-3/8) -> (-3/8,-13/35) Parabolic Matrix(5953,2210,9312,3457) (-13/35,-36/97) -> (62/97,39/61) Hyperbolic Matrix(41217,15296,65536,24321) (-36/97,-95/256) -> (161/256,100/159) Hyperbolic Matrix(41215,15294,65536,24319) (-95/256,-59/159) -> (61/97,161/256) Hyperbolic Matrix(1343,498,3104,1151) (-23/62,-10/27) -> (16/37,13/30) Hyperbolic Matrix(449,166,2080,769) (-10/27,-17/46) -> (3/14,8/37) Hyperbolic Matrix(2431,898,5888,2175) (-17/46,-24/65) -> (26/63,19/46) Hyperbolic Matrix(5505,2032,8672,3201) (-24/65,-31/84) -> (33/52,40/63) Hyperbolic Matrix(385,142,2432,897) (-31/84,-7/19) -> (3/19,7/44) Hyperbolic Matrix(321,118,-1216,-447) (-7/19,-11/30) -> (-9/34,-5/19) Hyperbolic Matrix(255,92,352,127) (-4/11,-5/14) -> (13/18,8/11) Hyperbolic Matrix(833,296,1984,705) (-5/14,-11/31) -> (13/31,21/50) Hyperbolic Matrix(2431,862,3968,1407) (-11/31,-17/48) -> (49/80,19/31) Hyperbolic Matrix(577,204,1632,577) (-17/48,-6/17) -> (6/17,17/48) Hyperbolic Matrix(319,112,544,191) (-6/17,-1/3) -> (17/29,10/17) Hyperbolic Matrix(577,184,1408,449) (-1/3,-7/22) -> (9/22,25/61) Hyperbolic Matrix(897,284,1216,385) (-7/22,-6/19) -> (14/19,31/42) Hyperbolic Matrix(191,60,608,191) (-6/19,-5/16) -> (5/16,6/19) Hyperbolic Matrix(129,40,416,129) (-5/16,-4/13) -> (4/13,5/16) Hyperbolic Matrix(961,292,3584,1089) (-7/23,-17/56) -> (15/56,11/41) Hyperbolic Matrix(385,116,-1696,-511) (-13/43,-3/10) -> (-5/22,-17/75) Hyperbolic Matrix(2881,856,4096,1217) (-11/37,-19/64) -> (45/64,19/27) Hyperbolic Matrix(2879,854,4096,1215) (-19/64,-8/27) -> (26/37,45/64) Hyperbolic Matrix(257,76,-1728,-511) (-8/27,-13/44) -> (-3/20,-4/27) Hyperbolic Matrix(705,208,1088,321) (-13/44,-5/17) -> (11/17,13/20) Hyperbolic Matrix(961,282,1312,385) (-5/17,-12/41) -> (30/41,11/15) Hyperbolic Matrix(3073,898,11392,3329) (-19/65,-26/89) -> (24/89,17/63) Hyperbolic Matrix(193,56,224,65) (-7/24,-2/7) -> (6/7,7/8) Hyperbolic Matrix(127,36,448,127) (-2/7,-9/32) -> (9/32,2/7) Hyperbolic Matrix(449,126,1600,449) (-9/32,-7/25) -> (7/25,9/32) Hyperbolic Matrix(1409,394,-6176,-1727) (-7/25,-19/68) -> (-21/92,-13/57) Hyperbolic Matrix(961,268,2528,705) (-12/43,-5/18) -> (19/50,8/21) Hyperbolic Matrix(1537,426,4160,1153) (-5/18,-18/65) -> (24/65,17/46) Hyperbolic Matrix(6719,1860,10400,2879) (-18/65,-31/112) -> (31/48,42/65) Hyperbolic Matrix(575,158,928,255) (-8/29,-3/11) -> (13/21,18/29) Hyperbolic Matrix(575,156,704,191) (-3/11,-10/37) -> (22/27,9/11) Hyperbolic Matrix(1281,346,-5920,-1599) (-10/37,-17/63) -> (-21/97,-8/37) Hyperbolic Matrix(193,52,-1184,-319) (-17/63,-7/26) -> (-1/6,-5/31) Hyperbolic Matrix(6079,1634,13568,3647) (-25/93,-43/160) -> (43/96,13/29) Hyperbolic Matrix(7681,2064,17152,4609) (-43/160,-18/67) -> (30/67,43/96) Hyperbolic Matrix(1087,292,1664,447) (-18/67,-11/41) -> (15/23,2/3) Hyperbolic Matrix(127,34,-960,-257) (-11/41,-4/15) -> (-2/15,-3/23) Hyperbolic Matrix(3009,800,4096,1089) (-4/15,-17/64) -> (47/64,36/49) Hyperbolic Matrix(3007,798,4096,1087) (-17/64,-13/49) -> (11/15,47/64) Hyperbolic Matrix(447,116,736,191) (-6/23,-1/4) -> (17/28,14/23) Hyperbolic Matrix(511,122,800,191) (-1/4,-5/21) -> (7/11,23/36) Hyperbolic Matrix(3137,736,4096,961) (-4/17,-15/64) -> (49/64,36/47) Hyperbolic Matrix(3135,734,4096,959) (-15/64,-11/47) -> (13/17,49/64) Hyperbolic Matrix(575,132,832,191) (-3/13,-8/35) -> (20/29,9/13) Hyperbolic Matrix(3583,818,-16544,-3777) (-8/35,-21/92) -> (-13/60,-34/157) Hyperbolic Matrix(193,44,1408,321) (-13/57,-5/22) -> (3/22,1/7) Hyperbolic Matrix(12673,2872,16384,3713) (-17/75,-29/128) -> (99/128,41/53) Hyperbolic Matrix(12671,2870,16384,3711) (-29/128,-12/53) -> (58/75,99/128) Hyperbolic Matrix(257,58,288,65) (-7/31,-2/9) -> (8/9,1/1) Hyperbolic Matrix(127,28,576,127) (-2/9,-7/32) -> (7/32,2/9) Hyperbolic Matrix(321,70,1472,321) (-7/32,-5/23) -> (5/23,7/32) Hyperbolic Matrix(769,166,2080,449) (-8/37,-3/14) -> (17/46,10/27) Hyperbolic Matrix(319,68,896,191) (-3/14,-7/33) -> (11/31,5/14) Hyperbolic Matrix(383,80,608,127) (-4/19,-1/5) -> (17/27,12/19) Hyperbolic Matrix(705,136,1664,321) (-1/5,-5/26) -> (11/26,25/59) Hyperbolic Matrix(1025,196,1344,257) (-5/26,-4/21) -> (16/21,29/38) Hyperbolic Matrix(127,24,672,127) (-4/21,-3/16) -> (3/16,4/21) Hyperbolic Matrix(65,12,352,65) (-3/16,-2/11) -> (2/11,3/16) Hyperbolic Matrix(319,56,1088,191) (-3/17,-4/23) -> (12/41,5/17) Hyperbolic Matrix(3393,584,4096,705) (-5/29,-11/64) -> (53/64,29/35) Hyperbolic Matrix(3391,582,4096,703) (-11/64,-6/35) -> (24/29,53/64) Hyperbolic Matrix(2497,402,3584,577) (-5/31,-4/25) -> (62/89,23/33) Hyperbolic Matrix(1791,286,3200,511) (-4/25,-7/44) -> (47/84,14/25) Hyperbolic Matrix(897,142,2432,385) (-7/44,-3/19) -> (7/19,31/84) Hyperbolic Matrix(191,30,1216,191) (-3/19,-5/32) -> (5/32,3/19) Hyperbolic Matrix(129,20,832,129) (-5/32,-2/13) -> (2/13,5/32) Hyperbolic Matrix(511,78,832,127) (-2/13,-3/20) -> (27/44,8/13) Hyperbolic Matrix(193,28,448,65) (-4/27,-1/7) -> (3/7,16/37) Hyperbolic Matrix(321,44,1408,193) (-1/7,-3/22) -> (5/22,13/57) Hyperbolic Matrix(575,78,1408,191) (-3/22,-2/15) -> (20/49,9/22) Hyperbolic Matrix(769,100,992,129) (-3/23,-1/8) -> (31/40,7/9) Hyperbolic Matrix(385,46,544,65) (-1/8,-1/9) -> (29/41,17/24) Hyperbolic Matrix(449,48,608,65) (-1/9,-1/10) -> (31/42,17/23) Hyperbolic Matrix(447,44,640,63) (-1/10,-1/11) -> (37/53,7/10) Hyperbolic Matrix(447,40,704,63) (-1/11,0/1) -> (40/63,7/11) Hyperbolic Matrix(257,-34,960,-127) (1/8,2/15) -> (4/15,15/56) Hyperbolic Matrix(511,-76,1728,-257) (1/7,3/20) -> (13/44,21/71) Hyperbolic Matrix(319,-52,1184,-193) (4/25,1/6) -> (7/26,24/89) Hyperbolic Matrix(257,-46,352,-63) (1/6,2/11) -> (8/11,19/26) Hyperbolic Matrix(511,-108,1216,-257) (4/19,3/14) -> (21/50,8/19) Hyperbolic Matrix(1089,-236,1472,-319) (8/37,5/23) -> (17/23,20/27) Hyperbolic Matrix(1087,-246,1984,-449) (7/31,5/22) -> (23/42,17/31) Hyperbolic Matrix(1919,-438,2528,-577) (13/57,8/35) -> (22/29,19/25) Hyperbolic Matrix(319,-74,832,-193) (3/13,4/17) -> (18/47,5/13) Hyperbolic Matrix(447,-106,544,-129) (4/17,1/4) -> (23/28,14/17) Hyperbolic Matrix(511,-134,736,-193) (1/4,5/19) -> (9/13,25/36) Hyperbolic Matrix(257,-68,480,-127) (5/19,4/15) -> (8/15,7/13) Hyperbolic Matrix(1919,-516,4288,-1153) (18/67,7/26) -> (17/38,30/67) Hyperbolic Matrix(2111,-570,2848,-769) (17/63,10/37) -> (20/27,23/31) Hyperbolic Matrix(767,-212,1856,-513) (8/29,5/18) -> (19/46,12/29) Hyperbolic Matrix(1217,-340,1600,-447) (12/43,7/25) -> (19/25,16/21) Hyperbolic Matrix(1983,-580,2848,-833) (7/24,12/41) -> (16/23,39/56) Hyperbolic Matrix(449,-134,640,-191) (8/27,3/10) -> (7/10,26/37) Hyperbolic Matrix(321,-98,416,-127) (3/10,4/13) -> (10/13,17/22) Hyperbolic Matrix(191,-70,352,-129) (4/11,7/19) -> (7/13,6/11) Hyperbolic Matrix(193,-72,512,-191) (10/27,3/8) -> (3/8,14/37) Parabolic Matrix(10305,-3904,16384,-6207) (25/66,36/95) -> (100/159,39/62) Hyperbolic Matrix(2369,-900,3872,-1471) (11/29,19/50) -> (11/18,41/67) Hyperbolic Matrix(1473,-562,3520,-1343) (8/21,21/55) -> (23/55,18/43) Hyperbolic Matrix(2305,-882,3008,-1151) (13/34,18/47) -> (36/47,23/30) Hyperbolic Matrix(639,-248,992,-385) (12/31,7/18) -> (9/14,20/31) Hyperbolic Matrix(2113,-862,4704,-1919) (11/27,20/49) -> (22/49,31/69) Hyperbolic Matrix(4993,-2050,7168,-2943) (16/39,23/56) -> (39/56,62/89) Hyperbolic Matrix(1407,-580,2176,-897) (7/17,26/63) -> (42/65,11/17) Hyperbolic Matrix(511,-212,928,-385) (12/29,5/12) -> (11/20,16/29) Hyperbolic Matrix(1919,-804,2752,-1153) (18/43,13/31) -> (23/33,30/43) Hyperbolic Matrix(511,-216,608,-257) (8/19,11/26) -> (5/6,16/19) Hyperbolic Matrix(511,-228,576,-257) (4/9,17/38) -> (23/26,8/9) Hyperbolic Matrix(577,-260,992,-447) (9/20,5/11) -> (25/43,7/12) Hyperbolic Matrix(257,-118,416,-191) (5/11,1/2) -> (21/34,13/21) Hyperbolic Matrix(447,-236,608,-321) (1/2,8/15) -> (36/49,25/34) Hyperbolic Matrix(2623,-1436,3392,-1857) (6/11,23/42) -> (17/22,58/75) Hyperbolic Matrix(767,-424,928,-513) (16/29,5/9) -> (19/23,24/29) Hyperbolic Matrix(191,-110,224,-129) (4/7,11/19) -> (11/13,6/7) Hyperbolic Matrix(2303,-1338,2976,-1729) (18/31,25/43) -> (41/53,24/31) Hyperbolic Matrix(1665,-974,2624,-1535) (7/12,24/41) -> (26/41,33/52) Hyperbolic Matrix(2879,-1686,3936,-2305) (24/41,17/29) -> (49/67,30/41) Hyperbolic Matrix(383,-226,544,-321) (10/17,3/5) -> (19/27,12/17) Hyperbolic Matrix(2495,-1514,3904,-2369) (20/33,17/28) -> (23/36,62/97) Hyperbolic Matrix(639,-394,832,-513) (8/13,21/34) -> (23/30,10/13) Hyperbolic Matrix(321,-200,512,-319) (18/29,5/8) -> (5/8,22/35) Parabolic Matrix(3009,-1892,3968,-2495) (22/35,61/97) -> (25/33,22/29) Hyperbolic Matrix(895,-566,1216,-769) (12/19,19/30) -> (25/34,14/19) Hyperbolic Matrix(1537,-1090,1984,-1407) (17/24,22/31) -> (24/31,31/40) Hyperbolic Matrix(1089,-796,1312,-959) (19/26,49/67) -> (29/35,5/6) Hyperbolic Matrix(193,-144,256,-191) (23/31,3/4) -> (3/4,25/33) Parabolic Matrix(961,-734,1088,-831) (29/38,13/17) -> (15/17,23/26) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(65,58,288,257) -> Matrix(1,-2,2,-3) Matrix(257,228,-576,-511) -> Matrix(1,0,0,1) Matrix(447,394,1088,959) -> Matrix(1,-4,0,1) Matrix(65,56,224,193) -> Matrix(1,-2,2,-3) Matrix(129,110,-224,-191) -> Matrix(1,-2,0,1) Matrix(769,636,-1856,-1535) -> Matrix(1,0,0,1) Matrix(769,634,1088,897) -> Matrix(1,-2,0,1) Matrix(129,106,-544,-447) -> Matrix(1,-2,0,1) Matrix(191,156,704,575) -> Matrix(1,-4,0,1) Matrix(703,572,864,703) -> Matrix(1,-12,0,1) Matrix(129,104,160,129) -> Matrix(1,-2,0,1) Matrix(63,50,160,127) -> Matrix(1,0,0,1) Matrix(449,352,736,577) -> Matrix(1,-4,0,1) Matrix(1151,900,1472,1151) -> Matrix(1,-16,0,1) Matrix(449,350,576,449) -> Matrix(1,6,0,1) Matrix(127,98,-416,-321) -> Matrix(1,0,0,1) Matrix(193,148,-416,-319) -> Matrix(1,0,0,1) Matrix(1087,830,-2432,-1857) -> Matrix(1,2,0,1) Matrix(257,196,1344,1025) -> Matrix(1,0,2,1) Matrix(447,340,-1600,-1217) -> Matrix(1,0,4,1) Matrix(319,236,-1472,-1089) -> Matrix(1,0,4,1) Matrix(65,48,608,449) -> Matrix(1,0,0,1) Matrix(385,284,1216,897) -> Matrix(1,0,2,1) Matrix(769,566,-1216,-895) -> Matrix(1,0,0,1) Matrix(63,46,-352,-257) -> Matrix(1,0,0,1) Matrix(127,92,352,255) -> Matrix(1,0,0,1) Matrix(513,370,800,577) -> Matrix(1,-2,0,1) Matrix(1151,828,1600,1151) -> Matrix(1,-8,0,1) Matrix(321,230,448,321) -> Matrix(1,2,0,1) Matrix(191,136,448,319) -> Matrix(1,0,0,1) Matrix(767,544,-2528,-1793) -> Matrix(3,2,-2,-1) Matrix(65,46,544,385) -> Matrix(1,0,0,1) Matrix(897,634,1088,769) -> Matrix(1,-2,0,1) Matrix(321,226,-544,-383) -> Matrix(1,0,2,1) Matrix(1153,804,-2752,-1919) -> Matrix(3,-2,2,-1) Matrix(833,580,-2848,-1983) -> Matrix(1,-2,0,1) Matrix(193,134,-736,-511) -> Matrix(1,0,0,1) Matrix(191,132,832,575) -> Matrix(1,0,0,1) Matrix(639,440,928,639) -> Matrix(1,-2,0,1) Matrix(65,44,96,65) -> Matrix(1,0,0,1) Matrix(447,292,1664,1087) -> Matrix(1,0,0,1) Matrix(575,374,1376,895) -> Matrix(1,-2,0,1) Matrix(321,208,1088,705) -> Matrix(1,0,0,1) Matrix(385,248,-992,-639) -> Matrix(1,-2,0,1) Matrix(577,370,800,513) -> Matrix(1,-2,0,1) Matrix(1601,1024,3904,2497) -> Matrix(1,-2,0,1) Matrix(2369,1514,-3904,-2495) -> Matrix(3,2,-2,-1) Matrix(577,368,704,449) -> Matrix(1,-2,0,1) Matrix(1535,974,-2624,-1665) -> Matrix(1,0,0,1) Matrix(833,528,1920,1217) -> Matrix(1,2,0,1) Matrix(831,526,-3136,-1985) -> Matrix(1,0,2,1) Matrix(127,80,608,383) -> Matrix(1,0,0,1) Matrix(319,200,-512,-321) -> Matrix(1,0,2,1) Matrix(2881,1790,5152,3201) -> Matrix(3,-2,-10,7) Matrix(6079,3776,-16384,-10177) -> Matrix(23,-20,-8,7) Matrix(3839,2384,-17728,-11009) -> Matrix(3,-4,10,-13) Matrix(255,158,928,575) -> Matrix(1,0,-2,1) Matrix(191,118,-416,-257) -> Matrix(1,0,0,1) Matrix(127,78,832,511) -> Matrix(1,0,-2,1) Matrix(1089,668,1984,1217) -> Matrix(3,-2,-4,3) Matrix(1407,862,3968,2431) -> Matrix(5,-4,4,-3) Matrix(4801,2940,7840,4801) -> Matrix(7,-8,-6,7) Matrix(1471,900,-3872,-2369) -> Matrix(1,-2,2,-3) Matrix(577,352,736,449) -> Matrix(1,-4,0,1) Matrix(1023,622,1472,895) -> Matrix(1,2,0,1) Matrix(2559,1552,6752,4095) -> Matrix(3,4,-4,-5) Matrix(895,542,2112,1279) -> Matrix(3,2,-2,-1) Matrix(257,152,-864,-511) -> Matrix(1,0,-4,1) Matrix(191,112,544,319) -> Matrix(1,0,0,1) Matrix(321,188,-1856,-1087) -> Matrix(1,0,0,1) Matrix(65,38,768,449) -> Matrix(1,0,0,1) Matrix(2303,1346,6240,3647) -> Matrix(1,2,0,1) Matrix(447,260,-992,-577) -> Matrix(3,-2,2,-1) Matrix(383,222,992,575) -> Matrix(1,0,0,1) Matrix(703,406,-1664,-961) -> Matrix(1,2,0,1) Matrix(127,72,224,127) -> Matrix(1,0,0,1) Matrix(449,252,800,449) -> Matrix(1,0,-8,1) Matrix(511,286,3200,1791) -> Matrix(1,0,-2,1) Matrix(3135,1754,6976,3903) -> Matrix(9,-2,-4,1) Matrix(2879,1610,4576,2559) -> Matrix(7,-2,4,-1) Matrix(831,464,2176,1215) -> Matrix(1,0,-2,1) Matrix(385,212,-928,-511) -> Matrix(3,-2,2,-1) Matrix(1217,668,1984,1089) -> Matrix(3,-2,-4,3) Matrix(449,246,-1984,-1087) -> Matrix(3,-2,-4,3) Matrix(129,70,-352,-191) -> Matrix(1,-2,0,1) Matrix(127,60,-544,-257) -> Matrix(1,-2,0,1) Matrix(513,232,-1696,-767) -> Matrix(3,-4,-2,3) Matrix(1919,862,-4704,-2113) -> Matrix(1,6,0,1) Matrix(2879,1292,4704,2111) -> Matrix(3,-4,-2,3) Matrix(1153,516,-4288,-1919) -> Matrix(1,-2,0,1) Matrix(127,56,288,127) -> Matrix(1,-4,0,1) Matrix(321,140,736,321) -> Matrix(1,4,0,1) Matrix(1217,528,1920,833) -> Matrix(1,2,0,1) Matrix(1345,582,3552,1537) -> Matrix(3,2,-2,-1) Matrix(833,360,2816,1217) -> Matrix(1,0,0,1) Matrix(319,136,448,191) -> Matrix(1,0,0,1) Matrix(1279,542,2112,895) -> Matrix(1,-2,2,-3) Matrix(321,136,1664,705) -> Matrix(1,-2,2,-3) Matrix(1919,810,2272,959) -> Matrix(1,-6,0,1) Matrix(1537,648,1824,769) -> Matrix(1,0,0,1) Matrix(257,108,-1216,-511) -> Matrix(1,0,0,1) Matrix(191,80,1984,831) -> Matrix(1,-2,2,-3) Matrix(13759,5762,19712,8255) -> Matrix(1,-2,4,-7) Matrix(7681,3216,11008,4609) -> Matrix(1,-2,-2,5) Matrix(1343,562,-3520,-1473) -> Matrix(1,-2,0,1) Matrix(449,186,-2624,-1087) -> Matrix(1,-2,0,1) Matrix(513,212,-1856,-767) -> Matrix(1,-2,2,-3) Matrix(959,394,1088,447) -> Matrix(1,-4,0,1) Matrix(1729,710,-5920,-2431) -> Matrix(1,-4,0,1) Matrix(2497,1024,3904,1601) -> Matrix(1,-2,0,1) Matrix(449,184,1408,577) -> Matrix(1,-4,2,-7) Matrix(191,78,1408,575) -> Matrix(1,-6,0,1) Matrix(3777,1540,6752,2753) -> Matrix(1,-8,-4,33) Matrix(703,286,1728,703) -> Matrix(1,-22,0,1) Matrix(129,52,320,129) -> Matrix(1,2,0,1) Matrix(127,50,160,63) -> Matrix(1,0,0,1) Matrix(2559,992,-9248,-3585) -> Matrix(1,2,2,5) Matrix(2561,992,3968,1537) -> Matrix(1,2,-2,-3) Matrix(575,222,992,383) -> Matrix(1,0,0,1) Matrix(193,74,-832,-319) -> Matrix(1,0,0,1) Matrix(1215,464,2176,831) -> Matrix(1,0,-2,1) Matrix(1855,708,2848,1087) -> Matrix(1,0,0,1) Matrix(705,268,2528,961) -> Matrix(1,0,-4,1) Matrix(1665,632,3712,1409) -> Matrix(1,-2,0,1) Matrix(191,72,-512,-193) -> Matrix(1,-4,0,1) Matrix(5953,2210,9312,3457) -> Matrix(3,10,2,7) Matrix(41217,15296,65536,24321) -> Matrix(25,76,24,73) Matrix(41215,15294,65536,24319) -> Matrix(25,74,26,77) Matrix(1343,498,3104,1151) -> Matrix(1,2,2,5) Matrix(449,166,2080,769) -> Matrix(1,2,-2,-3) Matrix(2431,898,5888,2175) -> Matrix(1,0,0,1) Matrix(5505,2032,8672,3201) -> Matrix(1,2,0,1) Matrix(385,142,2432,897) -> Matrix(1,2,2,5) Matrix(321,118,-1216,-447) -> Matrix(1,2,0,1) Matrix(255,92,352,127) -> Matrix(1,0,0,1) Matrix(833,296,1984,705) -> Matrix(1,2,-2,-3) Matrix(2431,862,3968,1407) -> Matrix(3,4,-4,-5) Matrix(577,204,1632,577) -> Matrix(3,2,4,3) Matrix(319,112,544,191) -> Matrix(1,0,0,1) Matrix(577,184,1408,449) -> Matrix(7,4,-2,-1) Matrix(897,284,1216,385) -> Matrix(1,0,2,1) Matrix(191,60,608,191) -> Matrix(1,0,4,1) Matrix(129,40,416,129) -> Matrix(1,0,0,1) Matrix(961,292,3584,1089) -> Matrix(1,2,0,1) Matrix(385,116,-1696,-511) -> Matrix(3,2,-2,-1) Matrix(2881,856,4096,1217) -> Matrix(1,0,8,1) Matrix(2879,854,4096,1215) -> Matrix(1,0,-6,1) Matrix(257,76,-1728,-511) -> Matrix(1,0,0,1) Matrix(705,208,1088,321) -> Matrix(1,0,0,1) Matrix(961,282,1312,385) -> Matrix(1,0,0,1) Matrix(3073,898,11392,3329) -> Matrix(1,0,2,1) Matrix(193,56,224,65) -> Matrix(3,2,-2,-1) Matrix(127,36,448,127) -> Matrix(1,0,4,1) Matrix(449,126,1600,449) -> Matrix(1,0,-14,1) Matrix(1409,394,-6176,-1727) -> Matrix(1,0,-6,1) Matrix(961,268,2528,705) -> Matrix(1,0,-4,1) Matrix(1537,426,4160,1153) -> Matrix(3,-2,2,-1) Matrix(6719,1860,10400,2879) -> Matrix(1,0,-2,1) Matrix(575,158,928,255) -> Matrix(1,0,-2,1) Matrix(575,156,704,191) -> Matrix(1,-4,0,1) Matrix(1281,346,-5920,-1599) -> Matrix(1,2,2,5) Matrix(193,52,-1184,-319) -> Matrix(1,0,0,1) Matrix(6079,1634,13568,3647) -> Matrix(3,2,-2,-1) Matrix(7681,2064,17152,4609) -> Matrix(1,-2,0,1) Matrix(1087,292,1664,447) -> Matrix(1,0,0,1) Matrix(127,34,-960,-257) -> Matrix(1,0,0,1) Matrix(3009,800,4096,1089) -> Matrix(1,0,4,1) Matrix(3007,798,4096,1087) -> Matrix(1,0,-4,1) Matrix(447,116,736,191) -> Matrix(1,2,0,1) Matrix(511,122,800,191) -> Matrix(1,0,0,1) Matrix(3137,736,4096,961) -> Matrix(1,-4,0,1) Matrix(3135,734,4096,959) -> Matrix(1,4,0,1) Matrix(575,132,832,191) -> Matrix(1,0,0,1) Matrix(3583,818,-16544,-3777) -> Matrix(3,2,10,7) Matrix(193,44,1408,321) -> Matrix(1,0,0,1) Matrix(12673,2872,16384,3713) -> Matrix(11,12,10,11) Matrix(12671,2870,16384,3711) -> Matrix(11,10,12,11) Matrix(257,58,288,65) -> Matrix(3,2,-2,-1) Matrix(127,28,576,127) -> Matrix(1,0,4,1) Matrix(321,70,1472,321) -> Matrix(1,0,-10,1) Matrix(769,166,2080,449) -> Matrix(3,-2,2,-1) Matrix(319,68,896,191) -> Matrix(3,-2,2,-1) Matrix(383,80,608,127) -> Matrix(1,0,0,1) Matrix(705,136,1664,321) -> Matrix(3,2,-2,-1) Matrix(1025,196,1344,257) -> Matrix(1,0,2,1) Matrix(127,24,672,127) -> Matrix(1,0,4,1) Matrix(65,12,352,65) -> Matrix(1,0,-2,1) Matrix(319,56,1088,191) -> Matrix(1,0,0,1) Matrix(3393,584,4096,705) -> Matrix(1,-4,0,1) Matrix(3391,582,4096,703) -> Matrix(1,0,0,1) Matrix(2497,402,3584,577) -> Matrix(3,2,-2,-1) Matrix(1791,286,3200,511) -> Matrix(1,0,-2,1) Matrix(897,142,2432,385) -> Matrix(5,2,2,1) Matrix(191,30,1216,191) -> Matrix(1,0,6,1) Matrix(129,20,832,129) -> Matrix(1,0,-4,1) Matrix(511,78,832,127) -> Matrix(1,0,-2,1) Matrix(193,28,448,65) -> Matrix(1,0,0,1) Matrix(321,44,1408,193) -> Matrix(1,0,0,1) Matrix(575,78,1408,191) -> Matrix(1,-6,0,1) Matrix(769,100,992,129) -> Matrix(1,2,0,1) Matrix(385,46,544,65) -> Matrix(1,0,0,1) Matrix(449,48,608,65) -> Matrix(1,0,0,1) Matrix(447,44,640,63) -> Matrix(1,0,0,1) Matrix(447,40,704,63) -> Matrix(1,0,0,1) Matrix(257,-34,960,-127) -> Matrix(1,0,0,1) Matrix(511,-76,1728,-257) -> Matrix(1,0,0,1) Matrix(319,-52,1184,-193) -> Matrix(1,0,0,1) Matrix(257,-46,352,-63) -> Matrix(1,0,0,1) Matrix(511,-108,1216,-257) -> Matrix(1,0,0,1) Matrix(1089,-236,1472,-319) -> Matrix(1,0,4,1) Matrix(1087,-246,1984,-449) -> Matrix(3,-2,-4,3) Matrix(1919,-438,2528,-577) -> Matrix(1,0,-2,1) Matrix(319,-74,832,-193) -> Matrix(1,0,0,1) Matrix(447,-106,544,-129) -> Matrix(1,-2,0,1) Matrix(511,-134,736,-193) -> Matrix(1,0,0,1) Matrix(257,-68,480,-127) -> Matrix(1,0,0,1) Matrix(1919,-516,4288,-1153) -> Matrix(1,-2,0,1) Matrix(2111,-570,2848,-769) -> Matrix(1,-2,2,-3) Matrix(767,-212,1856,-513) -> Matrix(3,2,-2,-1) Matrix(1217,-340,1600,-447) -> Matrix(1,0,4,1) Matrix(1983,-580,2848,-833) -> Matrix(1,-2,0,1) Matrix(449,-134,640,-191) -> Matrix(1,0,-2,1) Matrix(321,-98,416,-127) -> Matrix(1,0,0,1) Matrix(191,-70,352,-129) -> Matrix(1,-2,0,1) Matrix(193,-72,512,-191) -> Matrix(1,-4,0,1) Matrix(10305,-3904,16384,-6207) -> Matrix(7,8,6,7) Matrix(2369,-900,3872,-1471) -> Matrix(3,2,-2,-1) Matrix(1473,-562,3520,-1343) -> Matrix(1,-2,0,1) Matrix(2305,-882,3008,-1151) -> Matrix(1,-2,0,1) Matrix(639,-248,992,-385) -> Matrix(1,-2,0,1) Matrix(2113,-862,4704,-1919) -> Matrix(1,6,0,1) Matrix(4993,-2050,7168,-2943) -> Matrix(1,2,0,1) Matrix(1407,-580,2176,-897) -> Matrix(1,2,0,1) Matrix(511,-212,928,-385) -> Matrix(1,2,-2,-3) Matrix(1919,-804,2752,-1153) -> Matrix(1,2,-2,-3) Matrix(511,-216,608,-257) -> Matrix(1,0,0,1) Matrix(511,-228,576,-257) -> Matrix(1,0,0,1) Matrix(577,-260,992,-447) -> Matrix(1,2,-2,-3) Matrix(257,-118,416,-191) -> Matrix(1,0,0,1) Matrix(447,-236,608,-321) -> Matrix(1,0,2,1) Matrix(2623,-1436,3392,-1857) -> Matrix(5,4,6,5) Matrix(767,-424,928,-513) -> Matrix(3,2,-2,-1) Matrix(191,-110,224,-129) -> Matrix(1,-2,0,1) Matrix(2303,-1338,2976,-1729) -> Matrix(1,2,0,1) Matrix(1665,-974,2624,-1535) -> Matrix(1,0,0,1) Matrix(2879,-1686,3936,-2305) -> Matrix(1,0,0,1) Matrix(383,-226,544,-321) -> Matrix(1,0,2,1) Matrix(2495,-1514,3904,-2369) -> Matrix(1,-2,2,-3) Matrix(639,-394,832,-513) -> Matrix(1,0,0,1) Matrix(321,-200,512,-319) -> Matrix(1,0,2,1) Matrix(3009,-1892,3968,-2495) -> Matrix(3,-2,-4,3) Matrix(895,-566,1216,-769) -> Matrix(1,0,0,1) Matrix(1537,-1090,1984,-1407) -> Matrix(3,-2,2,-1) Matrix(1089,-796,1312,-959) -> Matrix(1,-2,0,1) Matrix(193,-144,256,-191) -> Matrix(1,-2,0,1) Matrix(961,-734,1088,-831) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 55 Degree of the the map X: 55 Degree of the the map Y: 256 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. Imminent integer overflow caused the modular group computation to abort.