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: 96 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/4 -13/8 -19/12 -3/2 -17/12 -11/8 -5/4 -9/8 -1/1 -7/8 -5/6 -3/4 -17/24 -7/10 -9/14 -5/8 -7/12 -1/2 -7/15 -5/12 -13/32 -3/8 -17/48 -1/3 -3/10 -9/32 -3/11 -1/4 -15/64 -3/13 -29/128 -7/32 -3/14 -1/5 -11/64 -1/6 -5/32 -1/7 -2/15 -1/8 -1/9 0/1 1/9 1/8 1/7 2/13 1/6 2/11 3/16 1/5 3/14 2/9 3/13 1/4 4/15 3/11 2/7 3/10 4/13 5/16 1/3 4/11 3/8 2/5 5/12 7/16 4/9 1/2 9/16 4/7 7/12 5/8 9/14 31/48 2/3 11/16 7/10 11/15 3/4 4/5 13/16 5/6 7/8 1/1 9/8 5/4 4/3 11/8 17/12 3/2 19/12 13/8 7/4 15/8 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 0/1 -13/7 1/4 1/2 -11/6 1/1 -20/11 -2/3 0/1 -9/5 1/2 -25/14 -1/1 1/1 -16/9 0/1 2/1 -23/13 -1/2 1/0 -7/4 0/1 -33/19 1/4 1/2 -26/15 2/5 -19/11 1/2 -12/7 0/1 2/3 -41/24 1/1 -29/17 1/0 -17/10 1/1 -22/13 0/1 -5/3 1/2 1/0 -28/17 2/1 4/1 -23/14 -1/1 -18/11 0/1 -13/8 0/1 -34/21 0/1 -21/13 1/2 -8/5 0/1 2/3 -27/17 -1/2 1/0 -19/12 0/1 -49/31 3/8 1/2 -30/19 0/1 -11/7 1/2 -14/9 2/1 -31/20 1/0 -17/11 1/2 1/0 -3/2 -1/1 1/1 -16/11 0/1 2/1 -45/31 3/2 1/0 -29/20 0/1 -13/9 1/2 -10/7 2/1 -27/19 1/0 -17/12 1/0 -58/41 2/1 -41/29 1/0 -24/17 -2/1 0/1 -7/5 3/2 1/0 -25/18 3/1 -68/49 6/1 8/1 -43/31 1/0 -18/13 2/1 -11/8 1/0 -26/19 -2/1 -15/11 1/0 -4/3 0/1 2/1 -17/13 1/0 -13/10 1/1 -22/17 0/1 -9/7 3/2 1/0 -23/18 1/1 3/1 -14/11 2/1 -19/15 5/2 -5/4 1/0 -21/17 -3/2 -16/13 -2/1 0/1 -11/9 1/2 1/0 -6/5 2/1 -13/11 -3/2 1/0 -7/6 1/1 -8/7 2/1 4/1 -9/8 1/0 -1/1 1/0 -8/9 0/1 2/1 -7/8 1/0 -6/7 -4/1 -11/13 -5/2 1/0 -5/6 -3/1 -1/1 -19/23 1/0 -14/17 -2/1 -9/11 1/2 1/0 -22/27 4/1 -13/16 1/0 -4/5 -4/1 -2/1 -15/19 1/0 -11/14 -1/1 -7/9 -3/2 1/0 -24/31 -4/1 -2/1 -41/53 1/0 -17/22 -3/1 -1/1 -10/13 -2/1 -3/4 1/0 -14/19 -4/1 -11/15 -5/2 -41/56 -3/1 -30/41 -2/1 -49/67 -5/2 1/0 -19/26 -3/1 -7/3 -8/11 -2/1 0/1 -13/18 -3/1 -5/7 -5/2 1/0 -22/31 -2/1 -17/24 -2/1 -29/41 -11/6 -12/17 -2/1 -8/5 -19/27 -3/2 -7/10 -3/1 -1/1 -23/33 -5/2 1/0 -16/23 -2/1 0/1 -9/13 1/0 -20/29 -2/1 0/1 -11/16 1/0 -2/3 -2/1 -15/23 -3/2 -13/20 -2/1 -11/17 -5/2 1/0 -9/14 -5/3 -1/1 -25/39 -3/2 1/0 -16/25 -2/1 -4/3 -7/11 -3/2 -5/8 -1/1 -13/21 1/0 -21/34 -1/1 -29/47 -3/4 -1/2 -8/13 -2/1 0/1 -19/31 1/0 -11/18 -3/1 -1/1 -3/5 -3/2 1/0 -13/22 -1/1 1/1 -10/17 0/1 -17/29 1/0 -7/12 -2/1 -18/31 -2/1 -29/50 -5/3 -11/19 -3/2 -15/26 -5/3 -1/1 -4/7 -2/1 -4/3 -9/16 -1/1 -14/25 -2/3 -5/9 1/0 -11/20 -1/1 -6/11 -2/1 -7/13 -3/2 1/0 -1/2 -1/1 -7/15 -3/4 -6/13 0/1 -5/11 -1/2 1/0 -14/31 0/1 -9/20 0/1 -13/29 1/0 -4/9 -2/1 0/1 -7/16 -1/1 -10/23 -4/5 -3/7 -1/2 -11/26 -1/1 1/1 -19/45 -1/2 1/0 -27/64 -1/1 1/1 -8/19 -2/1 0/1 -13/31 -5/2 1/0 -31/74 -3/1 -1/1 -49/117 1/0 -67/160 -3/1 -1/1 -18/43 -2/1 -5/12 -1/1 -17/41 -1/2 -29/70 -1/1 -1/3 -41/99 -1/2 1/0 -53/128 -1/1 -12/29 -2/3 0/1 -7/17 1/2 1/0 -9/22 -3/1 -1/1 -11/27 -3/2 -13/32 -1/1 -2/5 0/1 -9/23 -3/2 1/0 -16/41 -2/1 0/1 -7/18 -3/1 -1/1 -19/49 -5/2 -9/4 -31/80 -2/1 -12/31 -2/1 -12/7 -29/75 -7/4 -3/2 -17/44 -3/2 -5/13 -3/2 -3/8 -1/1 -7/19 -3/4 -18/49 0/1 -47/128 -1/1 -29/79 -7/8 -5/6 -11/30 -1/1 -4/11 -4/5 -2/3 -5/14 -1/1 -3/5 -11/31 -1/2 -28/79 -10/19 -12/23 -17/48 -1/2 -6/17 -2/5 -1/3 -1/2 1/0 -6/19 0/1 -5/16 0/1 -4/13 -2/1 0/1 -7/23 -1/2 -17/56 0/1 -10/33 0/1 -13/43 1/2 1/0 -3/10 -1/1 1/1 -11/37 -3/2 1/0 -19/64 -1/1 -8/27 -2/3 0/1 -5/17 1/0 -12/41 -2/3 0/1 -7/24 0/1 -2/7 0/1 -9/32 -1/1 1/1 -16/57 -2/1 0/1 -7/25 -1/2 1/0 -5/18 -1/1 -18/65 0/1 -31/112 0/1 -13/47 1/4 1/2 -8/29 0/1 2/1 -3/11 1/0 -7/26 -3/1 -1/1 -18/67 -2/1 -11/41 -5/2 1/0 -4/15 -2/1 -4/3 -1/4 -1/1 -4/17 -2/1 0/1 -15/64 -1/1 -11/47 -5/6 -7/30 -1/1 -3/13 -3/4 -1/2 -5/22 -1/1 -3/5 -17/75 -5/8 -1/2 -29/128 -1/1 -3/5 -12/53 -2/3 -4/7 -7/31 -1/2 -9/40 -1/2 -2/9 0/1 -7/32 -1/1 -1/3 -12/55 -2/3 0/1 -5/23 -1/2 1/0 -3/14 -1/1 -1/5 -1/2 -4/21 -2/11 0/1 -3/16 0/1 -2/11 0/1 -3/17 3/2 1/0 -4/23 -2/1 0/1 -5/29 1/0 -11/64 -1/1 -6/35 0/1 -1/6 -1/1 1/1 -3/19 1/0 -5/32 -1/1 1/1 -2/13 0/1 -1/7 -1/2 1/0 -2/15 -2/1 -1/8 -1/1 -2/17 0/1 -1/9 -1/2 0/1 -2/1 0/1 1/9 1/2 1/0 1/8 1/0 1/7 1/0 2/13 0/1 1/6 -1/1 4/23 -2/3 0/1 3/17 1/0 2/11 0/1 3/16 0/1 1/5 1/2 1/0 3/14 -1/1 1/1 2/9 0/1 7/31 3/2 1/0 12/53 0/1 2/1 5/22 1/1 3/13 1/0 1/4 1/0 5/19 1/0 4/15 -2/3 0/1 11/41 1/2 18/67 0/1 7/26 1/1 3/11 -3/2 1/0 5/18 -1/1 1/1 2/7 0/1 7/24 1/0 12/41 -6/1 -4/1 5/17 -5/2 1/0 8/27 -2/1 -4/3 3/10 -1/1 10/33 0/1 7/23 1/2 1/0 4/13 -2/1 0/1 5/16 0/1 1/3 1/0 6/17 2/1 5/14 -1/1 4/11 0/1 2/1 3/8 1/0 8/21 -4/1 -2/1 13/34 -5/1 -3/1 18/47 -8/3 5/13 -5/2 1/0 12/31 -12/5 -2/1 7/18 -1/1 2/5 -2/1 9/22 -1/1 7/17 -1/2 12/29 0/1 2/1 5/12 1/0 13/31 1/0 8/19 -4/1 -2/1 11/26 -3/1 3/7 -3/2 1/0 7/16 -1/1 4/9 -2/3 0/1 9/20 0/1 5/11 1/0 6/13 -2/1 1/2 -1/1 1/1 8/15 -4/5 -2/3 7/13 -1/2 6/11 0/1 17/31 1/0 11/20 1/0 16/29 -2/1 0/1 5/9 -3/2 1/0 9/16 -1/1 4/7 -2/3 0/1 15/26 -1/3 26/45 0/1 37/64 -1/1 -1/3 11/19 -1/2 -1/4 18/31 0/1 43/74 -1/1 68/117 -2/3 0/1 93/160 -1/1 -1/3 25/43 -1/2 7/12 0/1 24/41 0/1 2/1 41/70 1/1 58/99 0/1 75/128 1/1 17/29 1/2 1/0 10/17 -2/1 13/22 -1/1 16/27 -2/1 -4/3 19/32 -1/1 3/5 -1/2 11/18 -1/1 30/49 -4/7 49/80 -1/2 19/31 -1/2 -5/12 8/13 -2/5 0/1 5/8 0/1 12/19 0/1 2/3 31/49 3/4 81/128 1/1 50/79 4/3 19/30 -1/1 1/1 7/11 1/2 1/0 9/14 -1/1 20/31 -2/9 0/1 31/48 0/1 11/17 1/2 2/3 0/1 11/16 1/0 9/13 -1/2 1/0 16/23 0/1 2/1 23/33 1/0 30/43 -2/1 7/10 -1/1 26/37 -2/1 45/64 -1/1 19/27 -3/4 -1/2 12/17 -2/5 0/1 29/41 -1/4 -1/6 17/24 0/1 5/7 1/0 23/32 -1/1 1/1 18/25 0/1 13/18 -1/1 1/1 8/11 -2/3 0/1 19/26 1/1 49/67 1/0 30/41 2/1 11/15 -3/2 1/0 3/4 0/1 13/17 1/2 3/4 49/64 1/1 36/47 6/5 4/3 23/30 1/1 3/1 10/13 0/1 17/22 1/1 58/75 0/1 99/128 -1/1 1/1 41/53 1/2 1/0 24/31 0/1 2/3 7/9 1/0 25/32 -1/1 1/1 18/23 0/1 11/14 -1/1 1/1 4/5 0/1 2/1 13/16 1/0 9/11 1/0 14/17 0/1 19/23 -3/2 1/0 24/29 -2/1 0/1 53/64 -1/1 29/35 1/0 5/6 -1/1 16/19 -2/1 0/1 27/32 -1/1 1/1 11/13 1/0 6/7 0/1 7/8 0/1 8/9 0/1 2/1 1/1 -1/2 1/0 10/9 -2/1 9/8 -1/1 8/7 -2/1 0/1 7/6 -1/1 1/1 13/11 1/0 19/16 1/0 6/5 -2/1 17/14 -1/1 11/9 1/0 16/13 -2/1 -4/3 5/4 -1/1 24/19 -2/1 0/1 19/15 -3/4 -1/2 14/11 0/1 23/18 -1/1 9/7 1/0 31/24 1/0 53/41 -3/2 1/0 22/17 0/1 13/10 -1/1 1/1 17/13 -1/2 1/0 21/16 1/0 4/3 -2/1 0/1 23/17 -5/2 19/14 -5/3 -1/1 15/11 -3/2 -5/4 11/8 -1/1 29/21 -3/4 -1/2 18/13 -2/3 43/31 -7/12 -1/2 25/18 -1/1 -1/3 7/5 1/0 24/17 0/1 2/1 41/29 -3/2 1/0 17/12 -1/1 44/31 -2/5 0/1 27/19 -1/2 1/0 10/7 -2/1 23/16 -1/1 13/9 -1/2 1/0 29/20 1/0 16/11 -2/1 0/1 3/2 -1/1 17/11 -1/2 48/31 -2/5 0/1 31/20 -1/1 45/29 -1/2 1/0 14/9 0/1 25/16 -1/1 11/7 -3/4 -1/2 30/19 -2/3 49/31 -1/2 68/43 -2/3 0/1 19/12 -1/2 65/41 -1/2 -1/4 46/29 0/1 27/17 1/0 8/5 -2/3 0/1 29/18 -1/1 -1/3 79/49 -1/6 129/80 0/1 50/31 0/1 21/13 -1/2 1/0 13/8 -1/1 31/19 -3/4 -1/2 18/11 -2/3 23/14 -1/1 -3/5 51/31 -11/20 -1/2 79/48 -1/2 28/17 -2/5 0/1 5/3 -1/2 27/16 0/1 22/13 0/1 17/10 -1/1 -1/3 29/17 -5/8 -1/2 70/41 -6/11 41/24 -1/2 12/7 -2/5 0/1 55/32 -1/1 -1/3 43/25 -1/2 31/18 -1/3 19/11 -1/2 1/0 26/15 -2/5 7/4 0/1 30/17 -2/1 23/13 -1/2 16/9 -2/3 0/1 57/32 -1/1 -1/3 41/23 -1/2 25/14 -1/1 9/5 -1/2 -1/4 29/16 0/1 20/11 0/1 2/1 11/6 -1/1 -1/3 13/7 -1/4 15/8 0/1 17/9 1/2 1/0 2/1 0/1 1/0 -1/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(159,296,-224,-417) (-2/1,-13/7) -> (-5/7,-22/31) Hyperbolic Matrix(95,176,224,415) (-13/7,-11/6) -> (11/26,3/7) Hyperbolic Matrix(257,468,352,641) (-11/6,-20/11) -> (8/11,19/26) Hyperbolic Matrix(31,56,-160,-289) (-20/11,-9/5) -> (-1/5,-4/21) Hyperbolic Matrix(223,400,160,287) (-9/5,-25/14) -> (25/18,7/5) Hyperbolic Matrix(287,512,-736,-1313) (-25/14,-16/9) -> (-16/41,-7/18) Hyperbolic Matrix(289,512,416,737) (-16/9,-23/13) -> (9/13,16/23) Hyperbolic Matrix(223,392,-128,-225) (-23/13,-7/4) -> (-7/4,-33/19) Parabolic Matrix(417,724,1088,1889) (-33/19,-26/15) -> (18/47,5/13) Hyperbolic Matrix(289,500,352,609) (-26/15,-19/11) -> (9/11,14/17) Hyperbolic Matrix(225,388,-352,-607) (-19/11,-12/7) -> (-16/25,-7/11) Hyperbolic Matrix(255,436,224,383) (-12/7,-41/24) -> (9/8,8/7) Hyperbolic Matrix(961,1640,-1312,-2239) (-41/24,-29/17) -> (-11/15,-41/56) Hyperbolic Matrix(223,380,544,927) (-29/17,-17/10) -> (9/22,7/17) Hyperbolic Matrix(321,544,416,705) (-17/10,-22/13) -> (10/13,17/22) Hyperbolic Matrix(31,52,-96,-161) (-22/13,-5/3) -> (-1/3,-6/19) Hyperbolic Matrix(769,1268,544,897) (-5/3,-28/17) -> (24/17,41/29) Hyperbolic Matrix(1377,2264,-992,-1631) (-28/17,-23/14) -> (-25/18,-68/49) Hyperbolic Matrix(449,736,352,577) (-23/14,-18/11) -> (14/11,23/18) Hyperbolic Matrix(415,676,-256,-417) (-18/11,-13/8) -> (-13/8,-34/21) Parabolic Matrix(225,364,416,673) (-34/21,-21/13) -> (7/13,6/11) Hyperbolic Matrix(127,204,-160,-257) (-21/13,-8/5) -> (-4/5,-15/19) Hyperbolic Matrix(161,256,544,865) (-8/5,-27/17) -> (5/17,8/27) Hyperbolic Matrix(353,560,-544,-863) (-27/17,-19/12) -> (-13/20,-11/17) Hyperbolic Matrix(1439,2276,-992,-1569) (-19/12,-49/31) -> (-45/31,-29/20) Hyperbolic Matrix(1375,2172,992,1567) (-49/31,-30/19) -> (18/13,43/31) Hyperbolic Matrix(33,52,224,353) (-30/19,-11/7) -> (1/7,2/13) Hyperbolic Matrix(97,152,-224,-351) (-11/7,-14/9) -> (-10/23,-3/7) Hyperbolic Matrix(1313,2036,-928,-1439) (-14/9,-31/20) -> (-17/12,-58/41) Hyperbolic Matrix(767,1188,-1984,-3073) (-31/20,-17/11) -> (-29/75,-17/44) Hyperbolic Matrix(223,344,352,543) (-17/11,-3/2) -> (19/30,7/11) Hyperbolic Matrix(159,232,416,607) (-3/2,-16/11) -> (8/21,13/34) Hyperbolic Matrix(449,652,1984,2881) (-16/11,-45/31) -> (7/31,12/53) Hyperbolic Matrix(417,604,-640,-927) (-29/20,-13/9) -> (-15/23,-13/20) Hyperbolic Matrix(161,232,-288,-415) (-13/9,-10/7) -> (-14/25,-5/9) Hyperbolic Matrix(191,272,224,319) (-10/7,-27/19) -> (11/13,6/7) Hyperbolic Matrix(383,544,-992,-1409) (-27/19,-17/12) -> (-17/44,-5/13) Hyperbolic Matrix(2879,4072,3936,5567) (-58/41,-41/29) -> (49/67,30/41) Hyperbolic Matrix(897,1268,544,769) (-41/29,-24/17) -> (28/17,5/3) Hyperbolic Matrix(383,540,544,767) (-24/17,-7/5) -> (19/27,12/17) Hyperbolic Matrix(287,400,160,223) (-7/5,-25/18) -> (25/14,9/5) Hyperbolic Matrix(1407,1952,-3968,-5505) (-68/49,-43/31) -> (-11/31,-28/79) Hyperbolic Matrix(1567,2172,992,1375) (-43/31,-18/13) -> (30/19,49/31) Hyperbolic Matrix(351,484,-256,-353) (-18/13,-11/8) -> (-11/8,-26/19) Parabolic Matrix(161,220,352,481) (-26/19,-15/11) -> (5/11,6/13) Hyperbolic Matrix(97,132,-352,-479) (-15/11,-4/3) -> (-8/29,-3/11) Hyperbolic Matrix(287,376,-416,-545) (-4/3,-17/13) -> (-9/13,-20/29) Hyperbolic Matrix(95,124,416,543) (-17/13,-13/10) -> (5/22,3/13) Hyperbolic Matrix(321,416,544,705) (-13/10,-22/17) -> (10/17,13/22) Hyperbolic Matrix(31,40,-224,-289) (-22/17,-9/7) -> (-1/7,-2/15) Hyperbolic Matrix(513,656,-800,-1023) (-9/7,-23/18) -> (-9/14,-25/39) Hyperbolic Matrix(577,736,352,449) (-23/18,-14/11) -> (18/11,23/14) Hyperbolic Matrix(63,80,352,447) (-14/11,-19/15) -> (3/17,2/11) Hyperbolic Matrix(159,200,-128,-161) (-19/15,-5/4) -> (-5/4,-21/17) Parabolic Matrix(607,748,960,1183) (-21/17,-16/13) -> (12/19,31/49) Hyperbolic Matrix(127,156,416,511) (-16/13,-11/9) -> (7/23,4/13) Hyperbolic Matrix(63,76,-160,-193) (-11/9,-6/5) -> (-2/5,-9/23) Hyperbolic Matrix(287,340,-352,-417) (-6/5,-13/11) -> (-9/11,-22/27) Hyperbolic Matrix(95,112,352,415) (-13/11,-7/6) -> (7/26,3/11) Hyperbolic Matrix(129,148,224,257) (-7/6,-8/7) -> (4/7,15/26) Hyperbolic Matrix(383,436,224,255) (-8/7,-9/8) -> (41/24,12/7) Hyperbolic Matrix(65,72,-288,-319) (-9/8,-1/1) -> (-7/31,-9/40) Hyperbolic Matrix(223,200,320,287) (-1/1,-8/9) -> (16/23,23/33) Hyperbolic Matrix(159,140,544,479) (-8/9,-7/8) -> (7/24,12/41) Hyperbolic Matrix(65,56,224,193) (-7/8,-6/7) -> (2/7,7/24) Hyperbolic Matrix(319,272,224,191) (-6/7,-11/13) -> (27/19,10/7) Hyperbolic Matrix(257,216,-608,-511) (-11/13,-5/6) -> (-11/26,-19/45) Hyperbolic Matrix(769,636,-1856,-1535) (-5/6,-19/23) -> (-17/41,-29/70) Hyperbolic Matrix(63,52,-544,-449) (-19/23,-14/17) -> (-2/17,-1/9) Hyperbolic Matrix(609,500,352,289) (-14/17,-9/11) -> (19/11,26/15) Hyperbolic Matrix(609,496,512,417) (-22/27,-13/16) -> (19/16,6/5) Hyperbolic Matrix(129,104,160,129) (-13/16,-4/5) -> (4/5,13/16) Hyperbolic Matrix(705,556,-1216,-959) (-15/19,-11/14) -> (-29/50,-11/19) Hyperbolic Matrix(97,76,-448,-351) (-11/14,-7/9) -> (-5/23,-3/14) Hyperbolic Matrix(31,24,288,223) (-7/9,-24/31) -> (0/1,1/9) Hyperbolic Matrix(3071,2376,1984,1535) (-24/31,-41/53) -> (17/11,48/31) Hyperbolic Matrix(2721,2104,-6496,-5023) (-41/53,-17/22) -> (-31/74,-49/117) Hyperbolic Matrix(705,544,416,321) (-17/22,-10/13) -> (22/13,17/10) Hyperbolic Matrix(95,72,-128,-97) (-10/13,-3/4) -> (-3/4,-14/19) Parabolic Matrix(223,164,-480,-353) (-14/19,-11/15) -> (-7/15,-6/13) Hyperbolic Matrix(929,680,832,609) (-41/56,-30/41) -> (10/9,9/8) Hyperbolic Matrix(2783,2036,1792,1311) (-30/41,-49/67) -> (45/29,14/9) Hyperbolic Matrix(3009,2200,-7264,-5311) (-49/67,-19/26) -> (-29/70,-41/99) Hyperbolic Matrix(641,468,352,257) (-19/26,-8/11) -> (20/11,11/6) Hyperbolic Matrix(127,92,352,255) (-8/11,-13/18) -> (5/14,4/11) Hyperbolic Matrix(161,116,-576,-415) (-13/18,-5/7) -> (-7/25,-5/18) Hyperbolic Matrix(767,544,-2528,-1793) (-22/31,-17/24) -> (-17/56,-10/33) Hyperbolic Matrix(865,612,-2848,-2015) (-17/24,-29/41) -> (-7/23,-17/56) Hyperbolic Matrix(351,248,1312,927) (-29/41,-12/17) -> (4/15,11/41) Hyperbolic Matrix(767,540,544,383) (-12/17,-19/27) -> (7/5,24/17) Hyperbolic Matrix(353,248,-864,-607) (-19/27,-7/10) -> (-9/22,-11/27) Hyperbolic Matrix(1153,804,-2752,-1919) (-7/10,-23/33) -> (-13/31,-31/74) Hyperbolic Matrix(287,200,320,223) (-23/33,-16/23) -> (8/9,1/1) Hyperbolic Matrix(737,512,416,289) (-16/23,-9/13) -> (23/13,16/9) Hyperbolic Matrix(673,464,512,353) (-20/29,-11/16) -> (21/16,4/3) 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(385,248,-992,-639) (-11/17,-9/14) -> (-7/18,-19/49) Hyperbolic Matrix(799,512,-2848,-1825) (-25/39,-16/25) -> (-16/57,-7/25) Hyperbolic Matrix(159,100,-256,-161) (-7/11,-5/8) -> (-5/8,-13/21) Parabolic Matrix(641,396,416,257) (-13/21,-21/34) -> (3/2,17/11) Hyperbolic Matrix(1503,928,-4096,-2529) (-21/34,-29/47) -> (-29/79,-11/30) Hyperbolic Matrix(1375,848,1088,671) (-29/47,-8/13) -> (24/19,19/15) Hyperbolic Matrix(417,256,992,609) (-8/13,-19/31) -> (13/31,8/19) Hyperbolic Matrix(353,216,-992,-607) (-19/31,-11/18) -> (-5/14,-11/31) Hyperbolic Matrix(33,20,160,97) (-11/18,-3/5) -> (1/5,3/14) Hyperbolic Matrix(257,152,-864,-511) (-3/5,-13/22) -> (-3/10,-11/37) Hyperbolic Matrix(705,416,544,321) (-13/22,-10/17) -> (22/17,13/10) Hyperbolic Matrix(191,112,544,319) (-10/17,-17/29) -> (1/3,6/17) Hyperbolic Matrix(417,244,-928,-543) (-17/29,-7/12) -> (-9/20,-13/29) Hyperbolic Matrix(447,260,-992,-577) (-7/12,-18/31) -> (-14/31,-9/20) Hyperbolic Matrix(1055,612,-3808,-2209) (-18/31,-29/50) -> (-5/18,-18/65) Hyperbolic Matrix(97,56,-608,-351) (-11/19,-15/26) -> (-1/6,-3/19) Hyperbolic Matrix(257,148,224,129) (-15/26,-4/7) -> (8/7,7/6) Hyperbolic Matrix(127,72,224,127) (-4/7,-9/16) -> (9/16,4/7) Hyperbolic Matrix(735,412,512,287) (-9/16,-14/25) -> (10/7,23/16) Hyperbolic Matrix(385,212,-928,-511) (-5/9,-11/20) -> (-5/12,-17/41) Hyperbolic Matrix(415,228,-992,-545) (-11/20,-6/11) -> (-18/43,-5/12) Hyperbolic Matrix(575,312,352,191) (-6/11,-7/13) -> (31/19,18/11) Hyperbolic Matrix(97,52,-416,-223) (-7/13,-1/2) -> (-7/30,-3/13) Hyperbolic Matrix(127,60,-544,-257) (-1/2,-7/15) -> (-11/47,-7/30) Hyperbolic Matrix(575,264,416,191) (-6/13,-5/11) -> (29/21,18/13) Hyperbolic Matrix(513,232,-1696,-767) (-5/11,-14/31) -> (-10/33,-13/43) Hyperbolic Matrix(161,72,-928,-415) (-13/29,-4/9) -> (-4/23,-5/29) Hyperbolic Matrix(127,56,288,127) (-4/9,-7/16) -> (7/16,4/9) Hyperbolic Matrix(799,348,512,223) (-7/16,-10/23) -> (14/9,25/16) Hyperbolic Matrix(415,176,224,95) (-3/7,-11/26) -> (11/6,13/7) Hyperbolic Matrix(2369,1000,4096,1729) (-19/45,-27/64) -> (37/64,11/19) Hyperbolic Matrix(1537,648,1824,769) (-27/64,-8/19) -> (16/19,27/32) Hyperbolic Matrix(609,256,992,417) (-8/19,-13/31) -> (19/31,8/13) Hyperbolic Matrix(14881,6232,25600,10721) (-49/117,-67/160) -> (93/160,25/43) Hyperbolic Matrix(13537,5668,17504,7329) (-67/160,-18/43) -> (58/75,99/128) Hyperbolic Matrix(9601,3976,16384,6785) (-41/99,-53/128) -> (75/128,17/29) Hyperbolic Matrix(4609,1908,5568,2305) (-53/128,-12/29) -> (24/29,53/64) Hyperbolic Matrix(513,212,-1856,-767) (-12/29,-7/17) -> (-13/47,-8/29) Hyperbolic Matrix(927,380,544,223) (-7/17,-9/22) -> (17/10,29/17) Hyperbolic Matrix(609,248,1024,417) (-11/27,-13/32) -> (19/32,3/5) Hyperbolic Matrix(1057,428,1504,609) (-13/32,-2/5) -> (26/37,45/64) Hyperbolic Matrix(481,188,-2208,-863) (-9/23,-16/41) -> (-12/55,-5/23) 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(3071,1188,3968,1535) (-12/31,-29/75) -> (41/53,24/31) Hyperbolic Matrix(95,36,-256,-97) (-5/13,-3/8) -> (-3/8,-7/19) Parabolic Matrix(1697,624,960,353) (-7/19,-18/49) -> (30/17,23/13) Hyperbolic Matrix(10369,3808,16384,6017) (-18/49,-47/128) -> (81/128,50/79) Hyperbolic Matrix(5535,2032,7232,2655) (-47/128,-29/79) -> (13/17,49/64) Hyperbolic Matrix(513,188,352,129) (-11/30,-4/11) -> (16/11,3/2) Hyperbolic Matrix(255,92,352,127) (-4/11,-5/14) -> (13/18,8/11) Hyperbolic Matrix(7585,2688,4608,1633) (-28/79,-17/48) -> (79/48,28/17) Hyperbolic Matrix(2273,804,3712,1313) (-17/48,-6/17) -> (30/49,49/80) Hyperbolic Matrix(319,112,544,191) (-6/17,-1/3) -> (17/29,10/17) Hyperbolic Matrix(865,272,512,161) (-6/19,-5/16) -> (27/16,22/13) Hyperbolic Matrix(129,40,416,129) (-5/16,-4/13) -> (4/13,5/16) Hyperbolic Matrix(511,156,416,127) (-4/13,-7/23) -> (11/9,16/13) 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(1537,456,2592,769) (-19/64,-8/27) -> (16/27,19/32) Hyperbolic Matrix(865,256,544,161) (-8/27,-5/17) -> (27/17,8/5) Hyperbolic Matrix(191,56,1088,319) (-5/17,-12/41) -> (4/23,3/17) Hyperbolic Matrix(479,140,544,159) (-12/41,-7/24) -> (7/8,8/9) Hyperbolic Matrix(193,56,224,65) (-7/24,-2/7) -> (6/7,7/8) Hyperbolic Matrix(737,208,1024,289) (-2/7,-9/32) -> (23/32,18/25) Hyperbolic Matrix(3519,988,2048,575) (-9/32,-16/57) -> (12/7,55/32) Hyperbolic Matrix(13985,3872,8672,2401) (-18/65,-31/112) -> (129/80,50/31) Hyperbolic Matrix(415,112,352,95) (-3/11,-7/26) -> (7/6,13/11) Hyperbolic Matrix(223,60,-1312,-353) (-7/26,-18/67) -> (-6/35,-1/6) Hyperbolic Matrix(6241,1676,3936,1057) (-18/67,-11/41) -> (65/41,46/29) Hyperbolic Matrix(927,248,1312,351) (-11/41,-4/15) -> (12/17,29/41) Hyperbolic Matrix(31,8,-128,-33) (-4/15,-1/4) -> (-1/4,-4/17) Parabolic Matrix(3137,736,4096,961) (-4/17,-15/64) -> (49/64,36/47) Hyperbolic Matrix(5791,1356,9152,2143) (-15/64,-11/47) -> (31/49,81/128) Hyperbolic Matrix(543,124,416,95) (-3/13,-5/22) -> (13/10,17/13) Hyperbolic Matrix(12673,2872,16384,3713) (-17/75,-29/128) -> (99/128,41/53) Hyperbolic Matrix(13633,3088,23456,5313) (-29/128,-12/53) -> (68/117,93/160) Hyperbolic Matrix(4705,1064,2976,673) (-12/53,-7/31) -> (49/31,68/43) Hyperbolic Matrix(3169,712,1856,417) (-9/40,-2/9) -> (70/41,41/24) Hyperbolic Matrix(801,176,1024,225) (-2/9,-7/32) -> (25/32,18/23) Hyperbolic Matrix(3647,796,2048,447) (-7/32,-12/55) -> (16/9,57/32) Hyperbolic Matrix(97,20,160,33) (-3/14,-1/5) -> (3/5,11/18) Hyperbolic Matrix(929,176,512,97) (-4/21,-3/16) -> (29/16,20/11) Hyperbolic Matrix(65,12,352,65) (-3/16,-2/11) -> (2/11,3/16) Hyperbolic Matrix(447,80,352,63) (-2/11,-3/17) -> (19/15,14/11) 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(6337,1088,10816,1857) (-11/64,-6/35) -> (58/99,75/128) Hyperbolic Matrix(865,136,1024,161) (-3/19,-5/32) -> (27/32,11/13) Hyperbolic Matrix(1313,204,2272,353) (-5/32,-2/13) -> (26/45,37/64) Hyperbolic Matrix(353,52,224,33) (-2/13,-1/7) -> (11/7,30/19) Hyperbolic Matrix(31,4,-256,-33) (-2/15,-1/8) -> (-1/8,-2/17) Parabolic Matrix(223,24,288,31) (-1/9,0/1) -> (24/31,7/9) Hyperbolic Matrix(703,-84,544,-65) (1/9,1/8) -> (31/24,53/41) Hyperbolic Matrix(289,-40,224,-31) (1/8,1/7) -> (9/7,31/24) Hyperbolic Matrix(351,-56,608,-97) (2/13,1/6) -> (15/26,26/45) Hyperbolic Matrix(1087,-188,1856,-321) (1/6,4/23) -> (24/41,41/70) Hyperbolic Matrix(289,-56,160,-31) (3/16,1/5) -> (9/5,29/16) Hyperbolic Matrix(351,-76,448,-97) (3/14,2/9) -> (18/23,11/14) Hyperbolic Matrix(319,-72,288,-65) (2/9,7/31) -> (1/1,10/9) Hyperbolic Matrix(3775,-856,6496,-1473) (12/53,5/22) -> (43/74,68/117) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(257,-68,480,-127) (5/19,4/15) -> (8/15,7/13) Hyperbolic Matrix(4255,-1144,7264,-1953) (18/67,7/26) -> (41/70,58/99) Hyperbolic Matrix(479,-132,352,-97) (3/11,5/18) -> (19/14,15/11) Hyperbolic Matrix(415,-116,576,-161) (5/18,2/7) -> (18/25,13/18) Hyperbolic Matrix(511,-152,864,-257) (8/27,3/10) -> (13/22,16/27) Hyperbolic Matrix(1599,-484,2752,-833) (3/10,10/33) -> (18/31,43/74) Hyperbolic Matrix(607,-184,320,-97) (10/33,7/23) -> (17/9,2/1) Hyperbolic Matrix(161,-52,96,-31) (5/16,1/3) -> (5/3,27/16) Hyperbolic Matrix(607,-216,992,-353) (6/17,5/14) -> (11/18,30/49) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(2593,-992,4096,-1567) (13/34,18/47) -> (50/79,19/30) Hyperbolic Matrix(1409,-544,992,-383) (5/13,12/31) -> (44/31,27/19) Hyperbolic Matrix(639,-248,992,-385) (12/31,7/18) -> (9/14,20/31) Hyperbolic Matrix(193,-76,160,-63) (7/18,2/5) -> (6/5,17/14) Hyperbolic Matrix(607,-248,864,-353) (2/5,9/22) -> (7/10,26/37) Hyperbolic Matrix(735,-304,544,-225) (7/17,12/29) -> (4/3,23/17) Hyperbolic Matrix(511,-212,928,-385) (12/29,5/12) -> (11/20,16/29) Hyperbolic Matrix(545,-228,992,-415) (5/12,13/31) -> (17/31,11/20) Hyperbolic Matrix(511,-216,608,-257) (8/19,11/26) -> (5/6,16/19) Hyperbolic Matrix(351,-152,224,-97) (3/7,7/16) -> (25/16,11/7) Hyperbolic Matrix(543,-244,928,-417) (4/9,9/20) -> (7/12,24/41) Hyperbolic Matrix(577,-260,992,-447) (9/20,5/11) -> (25/43,7/12) Hyperbolic Matrix(319,-148,416,-193) (6/13,1/2) -> (23/30,10/13) Hyperbolic Matrix(417,-220,544,-287) (1/2,8/15) -> (36/47,23/30) Hyperbolic Matrix(1183,-648,1696,-929) (6/11,17/31) -> (23/33,30/43) Hyperbolic Matrix(767,-424,928,-513) (16/29,5/9) -> (19/23,24/29) Hyperbolic Matrix(415,-232,288,-161) (5/9,9/16) -> (23/16,13/9) Hyperbolic Matrix(1601,-928,992,-575) (11/19,18/31) -> (50/31,21/13) Hyperbolic Matrix(6529,-4000,3968,-2431) (49/80,19/31) -> (51/31,79/48) Hyperbolic Matrix(161,-100,256,-159) (8/13,5/8) -> (5/8,12/19) Parabolic Matrix(607,-388,352,-225) (7/11,9/14) -> (31/18,19/11) Hyperbolic Matrix(5985,-3868,3712,-2399) (31/48,11/17) -> (79/49,129/80) Hyperbolic Matrix(863,-560,544,-353) (11/17,2/3) -> (46/29,27/17) Hyperbolic Matrix(545,-376,416,-287) (11/16,9/13) -> (17/13,21/16) Hyperbolic Matrix(1311,-916,1696,-1185) (30/43,7/10) -> (17/22,58/75) Hyperbolic Matrix(1023,-724,544,-385) (29/41,17/24) -> (15/8,17/9) Hyperbolic Matrix(417,-296,224,-159) (17/24,5/7) -> (13/7,15/8) Hyperbolic Matrix(1761,-1264,1024,-735) (5/7,23/32) -> (55/32,43/25) Hyperbolic Matrix(1089,-796,1312,-959) (19/26,49/67) -> (29/35,5/6) Hyperbolic Matrix(2239,-1640,1312,-961) (30/41,11/15) -> (29/17,70/41) Hyperbolic Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(1825,-1424,1024,-799) (7/9,25/32) -> (57/32,41/23) Hyperbolic Matrix(257,-204,160,-127) (11/14,4/5) -> (8/5,29/18) Hyperbolic Matrix(417,-340,352,-287) (13/16,9/11) -> (13/11,19/16) Hyperbolic Matrix(1407,-1160,1088,-897) (14/17,19/23) -> (53/41,22/17) Hyperbolic Matrix(799,-972,448,-545) (17/14,11/9) -> (41/23,25/14) Hyperbolic Matrix(161,-200,128,-159) (16/13,5/4) -> (5/4,24/19) Parabolic Matrix(991,-1268,576,-737) (23/18,9/7) -> (43/25,31/18) Hyperbolic Matrix(1599,-2168,992,-1345) (23/17,19/14) -> (29/18,79/49) Hyperbolic Matrix(353,-484,256,-351) (15/11,11/8) -> (11/8,29/21) Parabolic Matrix(1631,-2264,992,-1377) (43/31,25/18) -> (23/14,51/31) Hyperbolic Matrix(1439,-2036,928,-1313) (41/29,17/12) -> (31/20,45/29) Hyperbolic Matrix(1537,-2180,992,-1407) (17/12,44/31) -> (48/31,31/20) Hyperbolic Matrix(1471,-2132,928,-1345) (13/9,29/20) -> (19/12,65/41) Hyperbolic Matrix(1569,-2276,992,-1439) (29/20,16/11) -> (68/43,19/12) Hyperbolic Matrix(417,-676,256,-415) (21/13,13/8) -> (13/8,31/19) Parabolic Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,0,0,1) Matrix(159,296,-224,-417) -> Matrix(9,-2,-4,1) Matrix(95,176,224,415) -> Matrix(5,-2,-2,1) Matrix(257,468,352,641) -> Matrix(1,0,0,1) Matrix(31,56,-160,-289) -> Matrix(1,0,-4,1) Matrix(223,400,160,287) -> Matrix(1,0,-2,1) Matrix(287,512,-736,-1313) -> Matrix(1,-2,0,1) Matrix(289,512,416,737) -> Matrix(1,0,0,1) Matrix(223,392,-128,-225) -> Matrix(1,0,4,1) Matrix(417,724,1088,1889) -> Matrix(9,-2,-4,1) Matrix(289,500,352,609) -> Matrix(5,-2,-2,1) Matrix(225,388,-352,-607) -> Matrix(1,-2,0,1) Matrix(255,436,224,383) -> Matrix(1,0,-2,1) Matrix(961,1640,-1312,-2239) -> Matrix(5,-2,-2,1) Matrix(223,380,544,927) -> Matrix(1,0,-2,1) Matrix(321,544,416,705) -> Matrix(1,0,0,1) Matrix(31,52,-96,-161) -> Matrix(1,0,-2,1) Matrix(769,1268,544,897) -> Matrix(1,-2,0,1) Matrix(1377,2264,-992,-1631) -> Matrix(1,4,0,1) Matrix(449,736,352,577) -> Matrix(1,0,0,1) Matrix(415,676,-256,-417) -> Matrix(1,0,4,1) Matrix(225,364,416,673) -> Matrix(1,0,-4,1) Matrix(127,204,-160,-257) -> Matrix(5,-2,-2,1) Matrix(161,256,544,865) -> Matrix(1,-2,0,1) Matrix(353,560,-544,-863) -> Matrix(1,-2,0,1) Matrix(1439,2276,-992,-1569) -> Matrix(1,0,-2,1) Matrix(1375,2172,992,1567) -> Matrix(3,-2,-4,3) Matrix(33,52,224,353) -> Matrix(1,0,-2,1) Matrix(97,152,-224,-351) -> Matrix(3,-2,-4,3) Matrix(1313,2036,-928,-1439) -> Matrix(1,0,0,1) Matrix(767,1188,-1984,-3073) -> Matrix(3,2,-2,-1) Matrix(223,344,352,543) -> Matrix(1,0,0,1) Matrix(159,232,416,607) -> Matrix(1,-4,0,1) Matrix(449,652,1984,2881) -> Matrix(1,0,0,1) Matrix(417,604,-640,-927) -> Matrix(1,-2,0,1) Matrix(161,232,-288,-415) -> Matrix(1,0,-2,1) Matrix(191,272,224,319) -> Matrix(1,-2,0,1) Matrix(383,544,-992,-1409) -> Matrix(3,-4,-2,3) Matrix(2879,4072,3936,5567) -> Matrix(1,0,0,1) Matrix(897,1268,544,769) -> Matrix(1,0,-2,1) Matrix(383,540,544,767) -> Matrix(1,0,-2,1) Matrix(287,400,160,223) -> Matrix(1,-2,-2,5) Matrix(1407,1952,-3968,-5505) -> Matrix(1,4,-2,-7) Matrix(1567,2172,992,1375) -> Matrix(1,0,-2,1) Matrix(351,484,-256,-353) -> Matrix(1,-4,0,1) Matrix(161,220,352,481) -> Matrix(1,0,0,1) Matrix(97,132,-352,-479) -> Matrix(1,0,0,1) Matrix(287,376,-416,-545) -> Matrix(1,-2,0,1) Matrix(95,124,416,543) -> Matrix(1,0,0,1) Matrix(321,416,544,705) -> Matrix(1,-2,0,1) Matrix(31,40,-224,-289) -> Matrix(1,-2,0,1) Matrix(513,656,-800,-1023) -> Matrix(3,-4,-2,3) Matrix(577,736,352,449) -> Matrix(1,0,-2,1) Matrix(63,80,352,447) -> Matrix(1,-2,-2,5) Matrix(159,200,-128,-161) -> Matrix(1,-4,0,1) Matrix(607,748,960,1183) -> Matrix(1,0,2,1) Matrix(127,156,416,511) -> Matrix(1,0,0,1) Matrix(63,76,-160,-193) -> Matrix(1,-2,0,1) Matrix(287,340,-352,-417) -> Matrix(1,2,0,1) Matrix(95,112,352,415) -> Matrix(1,0,0,1) Matrix(129,148,224,257) -> Matrix(1,-2,-2,5) Matrix(383,436,224,255) -> Matrix(1,-4,-2,9) Matrix(65,72,-288,-319) -> Matrix(1,2,-2,-3) Matrix(223,200,320,287) -> Matrix(1,0,0,1) Matrix(159,140,544,479) -> Matrix(1,-6,0,1) Matrix(65,56,224,193) -> Matrix(1,4,0,1) Matrix(319,272,224,191) -> Matrix(1,2,0,1) Matrix(257,216,-608,-511) -> Matrix(1,2,0,1) Matrix(769,636,-1856,-1535) -> Matrix(1,2,-2,-3) Matrix(63,52,-544,-449) -> Matrix(1,2,-2,-3) Matrix(609,500,352,289) -> Matrix(1,0,-2,1) Matrix(609,496,512,417) -> Matrix(1,-6,0,1) Matrix(129,104,160,129) -> Matrix(1,4,0,1) Matrix(705,556,-1216,-959) -> Matrix(3,8,-2,-5) Matrix(97,76,-448,-351) -> Matrix(1,2,-2,-3) Matrix(31,24,288,223) -> Matrix(1,2,0,1) Matrix(3071,2376,1984,1535) -> Matrix(1,2,-2,-3) Matrix(2721,2104,-6496,-5023) -> Matrix(1,0,0,1) Matrix(705,544,416,321) -> Matrix(1,2,-2,-3) Matrix(95,72,-128,-97) -> Matrix(1,-2,0,1) Matrix(223,164,-480,-353) -> Matrix(1,4,-2,-7) Matrix(929,680,832,609) -> Matrix(3,8,-2,-5) Matrix(2783,2036,1792,1311) -> Matrix(1,2,0,1) Matrix(3009,2200,-7264,-5311) -> Matrix(1,2,0,1) Matrix(641,468,352,257) -> Matrix(1,2,0,1) Matrix(127,92,352,255) -> Matrix(1,2,0,1) Matrix(161,116,-576,-415) -> Matrix(1,2,0,1) Matrix(767,544,-2528,-1793) -> Matrix(1,2,4,9) Matrix(865,612,-2848,-2015) -> Matrix(1,2,-8,-15) Matrix(351,248,1312,927) -> Matrix(1,2,-4,-7) Matrix(767,540,544,383) -> Matrix(1,2,-2,-3) Matrix(353,248,-864,-607) -> Matrix(1,0,0,1) Matrix(1153,804,-2752,-1919) -> Matrix(1,0,0,1) Matrix(287,200,320,223) -> Matrix(1,2,0,1) Matrix(737,512,416,289) -> Matrix(1,2,-2,-3) Matrix(673,464,512,353) -> Matrix(1,0,0,1) Matrix(65,44,96,65) -> Matrix(1,2,0,1) Matrix(447,292,1664,1087) -> Matrix(1,2,0,1) Matrix(385,248,-992,-639) -> Matrix(5,8,-2,-3) Matrix(799,512,-2848,-1825) -> Matrix(1,2,-2,-3) Matrix(159,100,-256,-161) -> Matrix(1,2,-2,-3) Matrix(641,396,416,257) -> Matrix(1,2,-2,-3) Matrix(1503,928,-4096,-2529) -> Matrix(3,4,-4,-5) Matrix(1375,848,1088,671) -> Matrix(1,0,0,1) Matrix(417,256,992,609) -> Matrix(1,-2,0,1) Matrix(353,216,-992,-607) -> Matrix(1,4,-2,-7) Matrix(33,20,160,97) -> Matrix(1,2,0,1) Matrix(257,152,-864,-511) -> Matrix(1,0,0,1) Matrix(705,416,544,321) -> Matrix(1,0,0,1) Matrix(191,112,544,319) -> Matrix(1,2,0,1) Matrix(417,244,-928,-543) -> Matrix(1,2,0,1) Matrix(447,260,-992,-577) -> Matrix(1,2,-2,-3) Matrix(1055,612,-3808,-2209) -> Matrix(1,2,-4,-7) Matrix(97,56,-608,-351) -> Matrix(1,2,-2,-3) Matrix(257,148,224,129) -> Matrix(1,2,-2,-3) Matrix(127,72,224,127) -> Matrix(3,4,-4,-5) Matrix(735,412,512,287) -> Matrix(5,4,-4,-3) Matrix(385,212,-928,-511) -> Matrix(1,2,-2,-3) Matrix(415,228,-992,-545) -> Matrix(1,0,0,1) Matrix(575,312,352,191) -> Matrix(3,4,-4,-5) Matrix(97,52,-416,-223) -> Matrix(3,4,-4,-5) Matrix(127,60,-544,-257) -> Matrix(1,2,-2,-3) Matrix(575,264,416,191) -> Matrix(1,2,-2,-3) Matrix(513,232,-1696,-767) -> Matrix(1,0,2,1) Matrix(161,72,-928,-415) -> Matrix(1,0,0,1) Matrix(127,56,288,127) -> Matrix(1,2,-2,-3) Matrix(799,348,512,223) -> Matrix(5,4,-4,-3) Matrix(415,176,224,95) -> Matrix(1,0,-2,1) Matrix(2369,1000,4096,1729) -> Matrix(1,0,-2,1) Matrix(1537,648,1824,769) -> Matrix(1,0,0,1) Matrix(609,256,992,417) -> Matrix(1,0,-2,1) Matrix(14881,6232,25600,10721) -> Matrix(1,2,-2,-3) Matrix(13537,5668,17504,7329) -> Matrix(1,2,0,1) Matrix(9601,3976,16384,6785) -> Matrix(1,0,2,1) Matrix(4609,1908,5568,2305) -> Matrix(3,2,-2,-1) Matrix(513,212,-1856,-767) -> Matrix(1,0,2,1) Matrix(927,380,544,223) -> Matrix(1,2,-2,-3) Matrix(609,248,1024,417) -> Matrix(3,4,-4,-5) Matrix(1057,428,1504,609) -> Matrix(3,2,-2,-1) Matrix(481,188,-2208,-863) -> Matrix(1,2,-2,-3) Matrix(2559,992,-9248,-3585) -> Matrix(1,2,6,13) Matrix(2561,992,3968,1537) -> Matrix(1,2,-8,-15) Matrix(3071,1188,3968,1535) -> Matrix(1,2,-2,-3) Matrix(95,36,-256,-97) -> Matrix(5,6,-6,-7) Matrix(1697,624,960,353) -> Matrix(3,2,-2,-1) Matrix(10369,3808,16384,6017) -> Matrix(3,4,2,3) Matrix(5535,2032,7232,2655) -> Matrix(9,8,10,9) Matrix(513,188,352,129) -> Matrix(5,4,-4,-3) Matrix(255,92,352,127) -> Matrix(3,2,-2,-1) Matrix(7585,2688,4608,1633) -> Matrix(23,12,-48,-25) Matrix(2273,804,3712,1313) -> Matrix(13,6,-24,-11) Matrix(319,112,544,191) -> Matrix(1,0,2,1) Matrix(865,272,512,161) -> Matrix(1,0,0,1) Matrix(129,40,416,129) -> Matrix(1,0,0,1) Matrix(511,156,416,127) -> Matrix(3,2,-2,-1) Matrix(385,116,-1696,-511) -> Matrix(1,2,-2,-3) Matrix(2881,856,4096,1217) -> Matrix(3,4,-4,-5) Matrix(1537,456,2592,769) -> Matrix(5,4,-4,-3) Matrix(865,256,544,161) -> Matrix(1,0,0,1) Matrix(191,56,1088,319) -> Matrix(1,0,0,1) Matrix(479,140,544,159) -> Matrix(1,0,2,1) Matrix(193,56,224,65) -> Matrix(1,0,0,1) Matrix(737,208,1024,289) -> Matrix(1,0,0,1) Matrix(3519,988,2048,575) -> Matrix(1,0,-2,1) Matrix(13985,3872,8672,2401) -> Matrix(1,0,4,1) Matrix(415,112,352,95) -> Matrix(1,2,0,1) Matrix(223,60,-1312,-353) -> Matrix(1,2,0,1) Matrix(6241,1676,3936,1057) -> Matrix(1,2,-2,-3) Matrix(927,248,1312,351) -> Matrix(1,2,-4,-7) Matrix(31,8,-128,-33) -> Matrix(1,2,-2,-3) Matrix(3137,736,4096,961) -> Matrix(5,6,4,5) Matrix(5791,1356,9152,2143) -> Matrix(9,8,10,9) Matrix(543,124,416,95) -> Matrix(3,2,-2,-1) Matrix(12673,2872,16384,3713) -> Matrix(3,2,-2,-1) Matrix(13633,3088,23456,5313) -> Matrix(3,2,-8,-5) Matrix(4705,1064,2976,673) -> Matrix(3,2,-8,-5) Matrix(3169,712,1856,417) -> Matrix(13,6,-24,-11) Matrix(801,176,1024,225) -> Matrix(1,0,2,1) Matrix(3647,796,2048,447) -> Matrix(1,0,0,1) Matrix(97,20,160,33) -> Matrix(1,0,0,1) Matrix(929,176,512,97) -> Matrix(1,0,6,1) Matrix(65,12,352,65) -> Matrix(1,0,-4,1) Matrix(447,80,352,63) -> Matrix(1,0,-2,1) Matrix(319,56,1088,191) -> Matrix(1,-4,0,1) Matrix(3393,584,4096,705) -> Matrix(1,0,0,1) Matrix(6337,1088,10816,1857) -> Matrix(1,0,2,1) Matrix(865,136,1024,161) -> Matrix(1,0,0,1) Matrix(1313,204,2272,353) -> Matrix(1,0,-2,1) Matrix(353,52,224,33) -> Matrix(1,2,-2,-3) Matrix(31,4,-256,-33) -> Matrix(1,2,-2,-3) Matrix(223,24,288,31) -> Matrix(1,0,2,1) Matrix(703,-84,544,-65) -> Matrix(1,-2,0,1) Matrix(289,-40,224,-31) -> Matrix(1,0,0,1) Matrix(351,-56,608,-97) -> Matrix(1,0,-2,1) Matrix(1087,-188,1856,-321) -> Matrix(1,0,2,1) Matrix(289,-56,160,-31) -> Matrix(1,0,-4,1) Matrix(351,-76,448,-97) -> Matrix(1,0,0,1) Matrix(319,-72,288,-65) -> Matrix(1,-2,0,1) Matrix(3775,-856,6496,-1473) -> Matrix(1,0,-2,1) Matrix(33,-8,128,-31) -> Matrix(1,-2,0,1) Matrix(257,-68,480,-127) -> Matrix(1,2,-2,-3) Matrix(4255,-1144,7264,-1953) -> Matrix(1,0,0,1) Matrix(479,-132,352,-97) -> Matrix(3,2,-2,-1) Matrix(415,-116,576,-161) -> Matrix(1,0,0,1) Matrix(511,-152,864,-257) -> Matrix(1,0,0,1) Matrix(1599,-484,2752,-833) -> Matrix(1,0,0,1) Matrix(607,-184,320,-97) -> Matrix(1,0,0,1) Matrix(161,-52,96,-31) -> Matrix(1,0,-2,1) Matrix(607,-216,992,-353) -> Matrix(1,2,-2,-3) Matrix(97,-36,256,-95) -> Matrix(1,-4,0,1) Matrix(2593,-992,4096,-1567) -> Matrix(1,4,0,1) Matrix(1409,-544,992,-383) -> Matrix(1,2,0,1) Matrix(639,-248,992,-385) -> Matrix(1,2,-2,-3) Matrix(193,-76,160,-63) -> Matrix(1,0,0,1) Matrix(607,-248,864,-353) -> Matrix(1,0,0,1) Matrix(735,-304,544,-225) -> Matrix(1,-2,0,1) Matrix(511,-212,928,-385) -> Matrix(1,-2,0,1) Matrix(545,-228,992,-415) -> Matrix(1,2,0,1) Matrix(511,-216,608,-257) -> Matrix(1,2,0,1) Matrix(351,-152,224,-97) -> Matrix(3,4,-4,-5) Matrix(543,-244,928,-417) -> Matrix(1,0,2,1) Matrix(577,-260,992,-447) -> Matrix(1,0,-2,1) Matrix(319,-148,416,-193) -> Matrix(1,2,0,1) Matrix(417,-220,544,-287) -> Matrix(1,2,0,1) Matrix(1183,-648,1696,-929) -> Matrix(1,-2,0,1) Matrix(767,-424,928,-513) -> Matrix(1,0,0,1) Matrix(415,-232,288,-161) -> Matrix(1,2,-2,-3) Matrix(1601,-928,992,-575) -> Matrix(1,0,2,1) Matrix(6529,-4000,3968,-2431) -> Matrix(17,8,-32,-15) Matrix(161,-100,256,-159) -> Matrix(1,0,4,1) Matrix(607,-388,352,-225) -> Matrix(1,0,-2,1) Matrix(5985,-3868,3712,-2399) -> Matrix(1,0,-8,1) Matrix(863,-560,544,-353) -> Matrix(1,0,-2,1) Matrix(545,-376,416,-287) -> Matrix(1,0,0,1) Matrix(1311,-916,1696,-1185) -> Matrix(1,2,0,1) Matrix(1023,-724,544,-385) -> Matrix(1,0,6,1) Matrix(417,-296,224,-159) -> Matrix(1,0,-4,1) Matrix(1761,-1264,1024,-735) -> Matrix(1,0,-2,1) Matrix(1089,-796,1312,-959) -> Matrix(1,-2,0,1) Matrix(2239,-1640,1312,-961) -> Matrix(1,4,-2,-7) Matrix(97,-72,128,-95) -> Matrix(1,0,2,1) Matrix(1825,-1424,1024,-799) -> Matrix(1,0,-2,1) Matrix(257,-204,160,-127) -> Matrix(1,0,-2,1) Matrix(417,-340,352,-287) -> Matrix(1,4,0,1) Matrix(1407,-1160,1088,-897) -> Matrix(1,0,0,1) Matrix(799,-972,448,-545) -> Matrix(1,2,-2,-3) Matrix(161,-200,128,-159) -> Matrix(1,2,-2,-3) Matrix(991,-1268,576,-737) -> Matrix(1,0,-2,1) Matrix(1599,-2168,992,-1345) -> Matrix(1,2,-4,-7) Matrix(353,-484,256,-351) -> Matrix(5,6,-6,-7) Matrix(1631,-2264,992,-1377) -> Matrix(5,2,-8,-3) Matrix(1439,-2036,928,-1313) -> Matrix(1,2,-2,-3) Matrix(1537,-2180,992,-1407) -> Matrix(1,0,0,1) Matrix(1471,-2132,928,-1345) -> Matrix(1,0,-2,1) Matrix(1569,-2276,992,-1439) -> Matrix(1,2,-2,-3) Matrix(417,-676,256,-415) -> Matrix(1,2,-2,-3) Matrix(225,-392,128,-223) -> 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): 53 Degree of the the map X: 53 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. ----------------------------------------------------------------------- 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 -3/2 (-1/1,1/1) 0 8 -16/11 0 16 -29/20 0/1 1 4 -13/9 1/2 1 16 -10/7 2/1 1 16 -27/19 1/0 1 16 -17/12 1/0 1 4 -24/17 0 16 -7/5 0 16 -18/13 2/1 1 16 -11/8 1/0 2 2 -26/19 -2/1 1 16 -15/11 1/0 1 16 -4/3 0 16 -17/13 1/0 1 16 -13/10 1/1 1 8 -22/17 0/1 1 16 -9/7 0 16 -14/11 2/1 1 16 -19/15 5/2 1 16 -5/4 1/0 2 4 -21/17 -3/2 1 16 -16/13 0 16 -11/9 0 16 -6/5 2/1 1 16 -13/11 0 16 -7/6 1/1 1 8 -8/7 0 16 -1/1 1/0 1 16 -8/9 0 16 -7/8 1/0 5 2 -6/7 -4/1 1 16 -5/6 (-3/1,-1/1) 0 8 -9/11 0 16 -13/16 1/0 7 2 -4/5 0 16 -15/19 1/0 1 16 -11/14 -1/1 1 8 -7/9 0 16 -10/13 -2/1 1 16 -3/4 1/0 1 4 -14/19 -4/1 1 16 -11/15 -5/2 1 16 -30/41 -2/1 1 16 -19/26 (-3/1,-7/3) 0 8 -8/11 0 16 -13/18 -3/1 1 8 -5/7 0 16 -22/31 -2/1 1 16 -17/24 -2/1 6 2 -29/41 -11/6 1 16 -12/17 0 16 -7/10 (-3/1,-1/1) 0 8 -23/33 0 16 -16/23 0 16 -9/13 1/0 1 16 -11/16 1/0 1 2 -2/3 -2/1 1 16 -15/23 -3/2 1 16 -13/20 -2/1 1 4 -11/17 0 16 -9/14 (-5/3,-1/1) 0 8 -16/25 0 16 -7/11 -3/2 1 16 -5/8 -1/1 1 2 -13/21 1/0 1 16 -8/13 0 16 -19/31 1/0 1 16 -11/18 (-3/1,-1/1) 0 8 -3/5 0 16 -10/17 0/1 1 16 -17/29 1/0 1 16 -7/12 -2/1 1 4 -18/31 -2/1 1 16 -29/50 -5/3 1 8 -11/19 -3/2 1 16 -4/7 0 16 -9/16 -1/1 5 2 -5/9 1/0 1 16 -11/20 -1/1 1 4 -6/11 -2/1 1 16 -7/13 0 16 -1/2 -1/1 1 8 -5/11 0 16 -14/31 0/1 1 16 -9/20 0/1 1 4 -13/29 1/0 1 16 -4/9 0 16 -7/16 -1/1 5 2 -10/23 -4/5 1 16 -3/7 -1/2 1 16 -11/26 (-1/1,1/1) 0 8 -27/64 (-1/1,1/1) 0 2 -8/19 0 16 -13/31 0 16 -31/74 (-3/1,-1/1) 0 8 -67/160 (-3/1,-1/1) 0 2 -18/43 -2/1 1 16 -5/12 -1/1 1 4 -17/41 -1/2 1 16 -29/70 (-1/1,-1/3) 0 8 -53/128 -1/1 1 2 -12/29 0 16 -7/17 0 16 -9/22 (-3/1,-1/1) 0 8 -13/32 -1/1 7 2 -2/5 0/1 1 16 -9/23 0 16 -7/18 (-3/1,-1/1) 0 8 -19/49 0 16 -31/80 -2/1 13 2 -12/31 0 16 -29/75 0 16 -17/44 -3/2 1 4 -5/13 -3/2 1 16 -3/8 -1/1 3 2 -7/19 -3/4 1 16 -18/49 0/1 1 16 -11/30 -1/1 1 8 -4/11 0 16 -5/14 (-1/1,-3/5) 0 8 -11/31 -1/2 1 16 -17/48 -1/2 13 2 -6/17 -2/5 1 16 -1/3 0 16 -6/19 0/1 1 16 -5/16 0/1 1 2 -4/13 0 16 -3/10 (-1/1,1/1) 0 8 -19/64 -1/1 7 2 -8/27 0 16 -5/17 1/0 1 16 -12/41 0 16 -7/24 0/1 1 2 -2/7 0/1 1 16 -9/32 (-1/1,1/1) 0 2 -7/25 0 16 -5/18 -1/1 1 8 -18/65 0/1 1 16 -31/112 0/1 13 2 -13/47 0 16 -8/29 0 16 -3/11 1/0 1 16 -4/15 0 16 -1/4 -1/1 1 4 -4/17 0 16 -15/64 -1/1 13 2 -11/47 -5/6 1 16 -7/30 -1/1 1 8 -3/13 0 16 -5/22 (-1/1,-3/5) 0 8 -29/128 (-1/1,-3/5) 0 2 -12/53 0 16 -7/31 -1/2 1 16 -9/40 -1/2 6 2 -2/9 0/1 1 16 -7/32 (-1/1,-1/3) 0 2 -5/23 0 16 -3/14 -1/1 1 8 -1/5 -1/2 1 16 -4/21 0 16 -3/16 0/1 7 2 -2/11 0/1 1 16 -3/17 0 16 -4/23 0 16 -5/29 1/0 1 16 -11/64 -1/1 1 2 -1/6 (-1/1,1/1) 0 8 -5/32 (-1/1,1/1) 0 2 -2/13 0/1 1 16 -1/7 0 16 -2/15 -2/1 1 16 -1/8 -1/1 1 2 -2/17 0/1 1 16 -1/9 -1/2 1 16 0/1 0 16 1/9 0 16 1/8 1/0 1 2 1/7 1/0 1 16 2/13 0/1 1 16 1/6 -1/1 1 8 4/23 0 16 3/17 1/0 1 16 2/11 0/1 1 16 3/16 0/1 7 2 1/5 0 16 3/14 (-1/1,1/1) 0 8 7/32 (-1/1,1/1) 0 2 2/9 0/1 1 16 7/31 0 16 12/53 0 16 5/22 1/1 1 8 3/13 1/0 1 16 1/4 1/0 1 4 5/19 1/0 1 16 4/15 0 16 11/41 1/2 1 16 18/67 0/1 1 16 7/26 1/1 1 8 3/11 0 16 5/18 (-1/1,1/1) 0 8 9/32 (-1/1,1/1) 0 2 2/7 0/1 1 16 7/24 1/0 5 2 12/41 0 16 5/17 0 16 8/27 0 16 3/10 -1/1 1 8 10/33 0/1 1 16 7/23 0 16 4/13 0 16 5/16 0/1 1 2 1/3 1/0 1 16 6/17 2/1 1 16 5/14 -1/1 1 8 4/11 0 16 3/8 1/0 2 2 8/21 0 16 13/34 (-5/1,-3/1) 0 8 49/128 -3/1 13 2 18/47 -8/3 1 16 5/13 0 16 12/31 0 16 31/80 -2/1 13 2 19/49 -7/4 1 16 7/18 -1/1 1 8 2/5 -2/1 1 16 13/32 -1/1 7 2 11/27 0 16 9/22 -1/1 1 8 7/17 -1/2 1 16 12/29 0 16 5/12 1/0 2 4 13/31 1/0 1 16 8/19 0 16 27/64 (-3/1,-1/1) 0 2 19/45 1/0 1 16 11/26 -3/1 1 8 3/7 0 16 7/16 -1/1 5 2 4/9 0 16 17/38 -1/1 1 8 30/67 0/1 1 16 43/96 -1/1 1 2 13/29 0 16 9/20 0/1 2 4 14/31 0/1 1 16 19/42 1/1 1 8 24/53 0 16 29/64 (-1/1,1/1) 0 2 5/11 1/0 1 16 6/13 -2/1 1 16 7/15 0 16 15/32 -1/1 13 2 1/2 (-1/1,1/1) 0 8 1/0 (-1/1,1/1) 0 2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,3,0,-1) (-3/2,1/0) -> (-3/2,1/0) Reflection Matrix(159,232,416,607) (-3/2,-16/11) -> (8/21,13/34) Hyperbolic Matrix(767,1113,-1984,-2879) (-16/11,-29/20) -> (-29/75,-17/44) Glide Reflection Matrix(417,604,-640,-927) (-29/20,-13/9) -> (-15/23,-13/20) Hyperbolic Matrix(97,139,-224,-321) (-13/9,-10/7) -> (-10/23,-3/7) Glide Reflection Matrix(33,47,224,319) (-10/7,-27/19) -> (1/7,2/13) Glide Reflection Matrix(383,544,-992,-1409) (-27/19,-17/12) -> (-17/44,-5/13) Hyperbolic Matrix(353,499,-544,-769) (-17/12,-24/17) -> (-13/20,-11/17) Glide Reflection Matrix(161,227,544,767) (-24/17,-7/5) -> (5/17,8/27) Glide Reflection Matrix(127,177,-160,-223) (-7/5,-18/13) -> (-4/5,-15/19) Glide Reflection Matrix(351,484,-256,-353) (-18/13,-11/8) -> (-11/8,-26/19) Parabolic Matrix(161,220,352,481) (-26/19,-15/11) -> (5/11,6/13) Hyperbolic Matrix(97,132,-352,-479) (-15/11,-4/3) -> (-8/29,-3/11) Hyperbolic Matrix(31,41,-96,-127) (-4/3,-17/13) -> (-1/3,-6/19) Glide Reflection Matrix(95,124,416,543) (-17/13,-13/10) -> (5/22,3/13) Hyperbolic Matrix(223,289,544,705) (-13/10,-22/17) -> (9/22,7/17) Glide Reflection Matrix(31,40,-224,-289) (-22/17,-9/7) -> (-1/7,-2/15) Hyperbolic Matrix(225,287,-352,-449) (-9/7,-14/11) -> (-16/25,-7/11) Glide Reflection Matrix(63,80,352,447) (-14/11,-19/15) -> (3/17,2/11) Hyperbolic Matrix(159,200,-128,-161) (-19/15,-5/4) -> (-5/4,-21/17) Parabolic Matrix(319,393,832,1025) (-21/17,-16/13) -> (18/47,5/13) Glide Reflection Matrix(127,156,416,511) (-16/13,-11/9) -> (7/23,4/13) Hyperbolic Matrix(63,76,-160,-193) (-11/9,-6/5) -> (-2/5,-9/23) Hyperbolic Matrix(31,37,-160,-191) (-6/5,-13/11) -> (-1/5,-4/21) Glide Reflection Matrix(95,112,352,415) (-13/11,-7/6) -> (7/26,3/11) Hyperbolic Matrix(95,109,224,257) (-7/6,-8/7) -> (11/26,3/7) Glide Reflection Matrix(159,181,-224,-255) (-8/7,-1/1) -> (-5/7,-22/31) Glide Reflection Matrix(97,87,320,287) (-1/1,-8/9) -> (10/33,7/23) Glide Reflection Matrix(159,140,544,479) (-8/9,-7/8) -> (7/24,12/41) Hyperbolic Matrix(65,56,224,193) (-7/8,-6/7) -> (2/7,7/24) Hyperbolic Matrix(95,81,-224,-191) (-6/7,-5/6) -> (-3/7,-11/26) Glide Reflection Matrix(257,211,-352,-289) (-5/6,-9/11) -> (-19/26,-8/11) Glide Reflection Matrix(97,79,-512,-417) (-9/11,-13/16) -> (-4/21,-3/16) Glide Reflection Matrix(31,25,160,129) (-13/16,-4/5) -> (3/16,1/5) Glide Reflection Matrix(705,556,-1216,-959) (-15/19,-11/14) -> (-29/50,-11/19) Hyperbolic Matrix(97,76,-448,-351) (-11/14,-7/9) -> (-5/23,-3/14) Hyperbolic Matrix(289,223,-416,-321) (-7/9,-10/13) -> (-16/23,-9/13) Glide Reflection Matrix(95,72,-128,-97) (-10/13,-3/4) -> (-3/4,-14/19) Parabolic Matrix(447,329,-1216,-895) (-14/19,-11/15) -> (-7/19,-18/49) Glide Reflection Matrix(97,71,-832,-609) (-11/15,-30/41) -> (-2/17,-1/9) Glide Reflection Matrix(1631,1193,-3936,-2879) (-30/41,-19/26) -> (-17/41,-29/70) Glide Reflection Matrix(127,92,352,255) (-8/11,-13/18) -> (5/14,4/11) Hyperbolic Matrix(161,116,-576,-415) (-13/18,-5/7) -> (-7/25,-5/18) Hyperbolic Matrix(447,317,-1984,-1407) (-22/31,-17/24) -> (-7/31,-9/40) Glide Reflection Matrix(417,295,-1856,-1313) (-17/24,-29/41) -> (-9/40,-2/9) Glide Reflection Matrix(351,248,1312,927) (-29/41,-12/17) -> (4/15,11/41) Hyperbolic Matrix(223,157,-544,-383) (-12/17,-7/10) -> (-7/17,-9/22) Glide Reflection Matrix(1153,804,-2752,-1919) (-7/10,-23/33) -> (-13/31,-31/74) Hyperbolic Matrix(33,23,320,223) (-23/33,-16/23) -> (0/1,1/9) Glide Reflection Matrix(161,111,-512,-353) (-9/13,-11/16) -> (-6/19,-5/16) Glide Reflection Matrix(31,21,96,65) (-11/16,-2/3) -> (5/16,1/3) Glide Reflection Matrix(447,292,1664,1087) (-2/3,-15/23) -> (11/41,18/67) Hyperbolic Matrix(385,248,-992,-639) (-11/17,-9/14) -> (-7/18,-19/49) Hyperbolic Matrix(575,369,-896,-575) (-9/14,-41/64) -> (-9/14,-41/64) Reflection Matrix(673,431,-2400,-1537) (-25/39,-16/25) -> (-16/57,-7/25) Glide Reflection Matrix(159,100,-256,-161) (-7/11,-5/8) -> (-5/8,-13/21) Parabolic Matrix(225,139,-416,-257) (-13/21,-8/13) -> (-6/11,-7/13) Glide Reflection Matrix(417,256,992,609) (-8/13,-19/31) -> (13/31,8/19) Hyperbolic Matrix(353,216,-992,-607) (-19/31,-11/18) -> (-5/14,-11/31) Hyperbolic Matrix(33,20,160,97) (-11/18,-3/5) -> (1/5,3/14) Hyperbolic Matrix(161,95,-544,-321) (-3/5,-10/17) -> (-8/27,-5/17) Glide Reflection Matrix(191,112,544,319) (-10/17,-17/29) -> (1/3,6/17) Hyperbolic Matrix(417,244,-928,-543) (-17/29,-7/12) -> (-9/20,-13/29) Hyperbolic Matrix(447,260,-992,-577) (-7/12,-18/31) -> (-14/31,-9/20) Hyperbolic Matrix(1055,612,-3808,-2209) (-18/31,-29/50) -> (-5/18,-18/65) Hyperbolic Matrix(33,19,-224,-129) (-11/19,-4/7) -> (-2/13,-1/7) Glide Reflection Matrix(97,55,224,127) (-4/7,-9/16) -> (3/7,7/16) Glide Reflection Matrix(223,125,-512,-287) (-9/16,-5/9) -> (-7/16,-10/23) Glide Reflection Matrix(385,212,-928,-511) (-5/9,-11/20) -> (-5/12,-17/41) Hyperbolic Matrix(415,228,-992,-545) (-11/20,-6/11) -> (-18/43,-5/12) Hyperbolic Matrix(97,52,-416,-223) (-7/13,-1/2) -> (-7/30,-3/13) Hyperbolic Matrix(129,59,-352,-161) (-1/2,-5/11) -> (-11/30,-4/11) Glide Reflection Matrix(449,203,-1984,-897) (-5/11,-14/31) -> (-12/53,-7/31) Glide Reflection Matrix(161,72,-928,-415) (-13/29,-4/9) -> (-4/23,-5/29) Hyperbolic Matrix(127,56,288,127) (-4/9,-7/16) -> (7/16,4/9) Hyperbolic Matrix(703,297,-1664,-703) (-11/26,-27/64) -> (-11/26,-27/64) Reflection Matrix(1025,432,2432,1025) (-27/64,-8/19) -> (8/19,27/64) Hyperbolic Matrix(383,161,992,417) (-8/19,-13/31) -> (5/13,12/31) Glide Reflection Matrix(4959,2077,-11840,-4959) (-31/74,-67/160) -> (-31/74,-67/160) Reflection Matrix(2047,857,4512,1889) (-67/160,-18/43) -> (29/64,5/11) Glide Reflection Matrix(3711,1537,-8960,-3711) (-29/70,-53/128) -> (-29/70,-53/128) Reflection Matrix(2911,1205,6496,2689) (-53/128,-12/29) -> (43/96,13/29) Glide Reflection Matrix(513,212,-1856,-767) (-12/29,-7/17) -> (-13/47,-8/29) Hyperbolic Matrix(287,117,-704,-287) (-9/22,-13/32) -> (-9/22,-13/32) Reflection Matrix(129,52,320,129) (-13/32,-2/5) -> (2/5,13/32) Hyperbolic Matrix(481,188,-2208,-863) (-9/23,-16/41) -> (-12/55,-5/23) Hyperbolic Matrix(449,175,-1152,-449) (-25/64,-7/18) -> (-25/64,-7/18) Reflection Matrix(2559,992,-9248,-3585) (-19/49,-31/80) -> (-31/112,-13/47) Hyperbolic Matrix(1921,744,4960,1921) (-31/80,-12/31) -> (12/31,31/80) Hyperbolic Matrix(897,347,3968,1535) (-12/31,-29/75) -> (7/31,12/53) Glide Reflection Matrix(95,36,-256,-97) (-5/13,-3/8) -> (-3/8,-7/19) Parabolic Matrix(673,247,-2880,-1057) (-18/49,-11/30) -> (-11/47,-7/30) Glide Reflection Matrix(97,35,352,127) (-4/11,-5/14) -> (3/11,5/18) Glide Reflection Matrix(1825,647,-6592,-2337) (-11/31,-17/48) -> (-18/65,-31/112) Glide Reflection Matrix(1439,509,3712,1313) (-17/48,-6/17) -> (31/80,19/49) Glide Reflection Matrix(225,79,544,191) (-6/17,-1/3) -> (7/17,12/29) Glide Reflection Matrix(129,40,416,129) (-5/16,-4/13) -> (4/13,5/16) Hyperbolic Matrix(95,29,-416,-127) (-4/13,-3/10) -> (-3/13,-5/22) Glide Reflection Matrix(191,57,-640,-191) (-3/10,-19/64) -> (-3/10,-19/64) Reflection Matrix(1055,313,2592,769) (-19/64,-8/27) -> (13/32,11/27) Glide Reflection Matrix(191,56,1088,319) (-5/17,-12/41) -> (4/23,3/17) Hyperbolic Matrix(65,19,544,159) (-12/41,-7/24) -> (1/9,1/8) Glide Reflection Matrix(31,9,224,65) (-7/24,-2/7) -> (1/8,1/7) Glide Reflection Matrix(127,36,448,127) (-2/7,-9/32) -> (9/32,2/7) Hyperbolic Matrix(737,207,-2624,-737) (-9/32,-23/82) -> (-9/32,-23/82) Reflection Matrix(63,17,-352,-95) (-3/11,-4/15) -> (-2/11,-3/17) Glide Reflection Matrix(31,8,-128,-33) (-4/15,-1/4) -> (-1/4,-4/17) Parabolic Matrix(703,165,1504,353) (-4/17,-15/64) -> (7/15,15/32) Glide Reflection Matrix(3455,809,9024,2113) (-15/64,-11/47) -> (49/128,18/47) Glide Reflection Matrix(639,145,-2816,-639) (-5/22,-29/128) -> (-5/22,-29/128) Reflection Matrix(4609,1044,10176,2305) (-29/128,-12/53) -> (24/53,29/64) Hyperbolic Matrix(127,28,576,127) (-2/9,-7/32) -> (7/32,2/9) Hyperbolic Matrix(545,119,-2496,-545) (-7/32,-17/78) -> (-7/32,-17/78) Reflection Matrix(63,13,160,33) (-3/14,-1/5) -> (7/18,2/5) Glide Reflection 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(3167,545,7072,1217) (-5/29,-11/64) -> (30/67,43/96) Glide Reflection Matrix(65,11,-384,-65) (-11/64,-1/6) -> (-11/64,-1/6) Reflection Matrix(31,5,-192,-31) (-1/6,-5/32) -> (-1/6,-5/32) Reflection Matrix(959,149,2272,353) (-5/32,-2/13) -> (27/64,19/45) Glide Reflection Matrix(31,4,-256,-33) (-2/15,-1/8) -> (-1/8,-2/17) Parabolic Matrix(65,7,288,31) (-1/9,0/1) -> (2/9,7/31) Glide Reflection Matrix(257,-41,608,-97) (2/13,1/6) -> (19/45,11/26) Glide Reflection Matrix(415,-72,928,-161) (1/6,4/23) -> (4/9,17/38) Hyperbolic Matrix(97,-21,448,-97) (3/14,7/32) -> (3/14,7/32) Reflection Matrix(1535,-348,3392,-769) (12/53,5/22) -> (19/42,24/53) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(223,-59,480,-127) (5/19,4/15) -> (6/13,7/15) Glide Reflection Matrix(1919,-516,4288,-1153) (18/67,7/26) -> (17/38,30/67) Hyperbolic Matrix(161,-45,576,-161) (5/18,9/32) -> (5/18,9/32) Reflection Matrix(353,-105,864,-257) (8/27,3/10) -> (11/27,9/22) Glide Reflection Matrix(767,-232,1696,-513) (3/10,10/33) -> (14/31,19/42) Hyperbolic Matrix(385,-137,992,-353) (6/17,5/14) -> (19/49,7/18) Glide Reflection Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(1665,-637,4352,-1665) (13/34,49/128) -> (13/34,49/128) Reflection Matrix(417,-173,928,-385) (12/29,5/12) -> (13/29,9/20) Glide Reflection Matrix(447,-187,992,-415) (5/12,13/31) -> (9/20,14/31) Glide Reflection Matrix(31,-15,64,-31) (15/32,1/2) -> (15/32,1/2) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,3,0,-1) -> Matrix(0,1,1,0) (-3/2,1/0) -> (-1/1,1/1) Matrix(159,232,416,607) -> Matrix(1,-4,0,1) 1/0 Matrix(767,1113,-1984,-2879) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(417,604,-640,-927) -> Matrix(1,-2,0,1) 1/0 Matrix(97,139,-224,-321) -> Matrix(2,-3,-3,4) Matrix(33,47,224,319) -> Matrix(0,1,1,-2) Matrix(383,544,-992,-1409) -> Matrix(3,-4,-2,3) Matrix(353,499,-544,-769) -> Matrix(-2,1,1,0) Matrix(161,227,544,767) -> Matrix(-2,1,1,0) Matrix(127,177,-160,-223) -> Matrix(2,-5,-1,2) Matrix(351,484,-256,-353) -> Matrix(1,-4,0,1) 1/0 Matrix(161,220,352,481) -> Matrix(1,0,0,1) Matrix(97,132,-352,-479) -> Matrix(1,0,0,1) Matrix(31,41,-96,-127) -> Matrix(0,1,1,-2) Matrix(95,124,416,543) -> Matrix(1,0,0,1) Matrix(223,289,544,705) -> Matrix(0,1,1,-2) Matrix(31,40,-224,-289) -> Matrix(1,-2,0,1) 1/0 Matrix(225,287,-352,-449) -> Matrix(-2,1,1,0) Matrix(63,80,352,447) -> Matrix(1,-2,-2,5) Matrix(159,200,-128,-161) -> Matrix(1,-4,0,1) 1/0 Matrix(319,393,832,1025) -> Matrix(-2,1,1,0) Matrix(127,156,416,511) -> Matrix(1,0,0,1) Matrix(63,76,-160,-193) -> Matrix(1,-2,0,1) 1/0 Matrix(31,37,-160,-191) -> Matrix(0,1,1,-4) Matrix(95,112,352,415) -> Matrix(1,0,0,1) Matrix(95,109,224,257) -> Matrix(2,-5,-1,2) Matrix(159,181,-224,-255) -> Matrix(2,-9,-1,4) Matrix(97,87,320,287) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(159,140,544,479) -> Matrix(1,-6,0,1) 1/0 Matrix(65,56,224,193) -> Matrix(1,4,0,1) 1/0 Matrix(95,81,-224,-191) -> Matrix(0,1,1,2) Matrix(257,211,-352,-289) -> Matrix(-2,1,1,0) Matrix(97,79,-512,-417) -> Matrix(0,1,1,-6) Matrix(31,25,160,129) -> Matrix(0,1,1,4) Matrix(705,556,-1216,-959) -> Matrix(3,8,-2,-5) -2/1 Matrix(97,76,-448,-351) -> Matrix(1,2,-2,-3) -1/1 Matrix(289,223,-416,-321) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(95,72,-128,-97) -> Matrix(1,-2,0,1) 1/0 Matrix(447,329,-1216,-895) -> Matrix(2,5,-3,-8) Matrix(97,71,-832,-609) -> Matrix(2,5,-3,-8) Matrix(1631,1193,-3936,-2879) -> Matrix(2,5,-3,-8) Matrix(127,92,352,255) -> Matrix(1,2,0,1) 1/0 Matrix(161,116,-576,-415) -> Matrix(1,2,0,1) 1/0 Matrix(447,317,-1984,-1407) -> Matrix(6,13,-11,-24) Matrix(417,295,-1856,-1313) -> Matrix(6,11,-13,-24) Matrix(351,248,1312,927) -> Matrix(1,2,-4,-7) Matrix(223,157,-544,-383) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(1153,804,-2752,-1919) -> Matrix(1,0,0,1) Matrix(33,23,320,223) -> Matrix(0,1,1,2) Matrix(161,111,-512,-353) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(31,21,96,65) -> Matrix(0,1,1,2) Matrix(447,292,1664,1087) -> Matrix(1,2,0,1) 1/0 Matrix(385,248,-992,-639) -> Matrix(5,8,-2,-3) -2/1 Matrix(575,369,-896,-575) -> Matrix(4,5,-3,-4) (-9/14,-41/64) -> (-5/3,-1/1) Matrix(673,431,-2400,-1537) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(159,100,-256,-161) -> Matrix(1,2,-2,-3) -1/1 Matrix(225,139,-416,-257) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(417,256,992,609) -> Matrix(1,-2,0,1) 1/0 Matrix(353,216,-992,-607) -> Matrix(1,4,-2,-7) Matrix(33,20,160,97) -> Matrix(1,2,0,1) 1/0 Matrix(161,95,-544,-321) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(191,112,544,319) -> Matrix(1,2,0,1) 1/0 Matrix(417,244,-928,-543) -> Matrix(1,2,0,1) 1/0 Matrix(447,260,-992,-577) -> Matrix(1,2,-2,-3) -1/1 Matrix(1055,612,-3808,-2209) -> Matrix(1,2,-4,-7) Matrix(33,19,-224,-129) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(97,55,224,127) -> Matrix(4,5,-3,-4) *** -> (-5/3,-1/1) Matrix(223,125,-512,-287) -> Matrix(4,3,-5,-4) *** -> (-1/1,-3/5) Matrix(385,212,-928,-511) -> Matrix(1,2,-2,-3) -1/1 Matrix(415,228,-992,-545) -> Matrix(1,0,0,1) Matrix(97,52,-416,-223) -> Matrix(3,4,-4,-5) -1/1 Matrix(129,59,-352,-161) -> Matrix(4,3,-5,-4) *** -> (-1/1,-3/5) Matrix(449,203,-1984,-897) -> Matrix(4,1,-7,-2) Matrix(161,72,-928,-415) -> Matrix(1,0,0,1) Matrix(127,56,288,127) -> Matrix(1,2,-2,-3) -1/1 Matrix(703,297,-1664,-703) -> Matrix(0,1,1,0) (-11/26,-27/64) -> (-1/1,1/1) Matrix(1025,432,2432,1025) -> Matrix(1,-2,0,1) 1/0 Matrix(383,161,992,417) -> Matrix(-2,1,1,0) Matrix(4959,2077,-11840,-4959) -> Matrix(2,3,-1,-2) (-31/74,-67/160) -> (-3/1,-1/1) Matrix(2047,857,4512,1889) -> Matrix(0,1,1,2) Matrix(3711,1537,-8960,-3711) -> Matrix(2,1,-3,-2) (-29/70,-53/128) -> (-1/1,-1/3) Matrix(2911,1205,6496,2689) -> Matrix(2,1,-3,-2) *** -> (-1/1,-1/3) Matrix(513,212,-1856,-767) -> Matrix(1,0,2,1) 0/1 Matrix(287,117,-704,-287) -> Matrix(2,3,-1,-2) (-9/22,-13/32) -> (-3/1,-1/1) Matrix(129,52,320,129) -> Matrix(3,2,-2,-1) -1/1 Matrix(481,188,-2208,-863) -> Matrix(1,2,-2,-3) -1/1 Matrix(449,175,-1152,-449) -> Matrix(2,3,-1,-2) (-25/64,-7/18) -> (-3/1,-1/1) Matrix(2559,992,-9248,-3585) -> Matrix(1,2,6,13) Matrix(1921,744,4960,1921) -> Matrix(13,24,-6,-11) -2/1 Matrix(897,347,3968,1535) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(95,36,-256,-97) -> Matrix(5,6,-6,-7) -1/1 Matrix(673,247,-2880,-1057) -> Matrix(6,5,-7,-6) *** -> (-1/1,-5/7) Matrix(97,35,352,127) -> Matrix(2,1,-3,-2) *** -> (-1/1,-1/3) Matrix(1825,647,-6592,-2337) -> Matrix(2,1,-15,-8) Matrix(1439,509,3712,1313) -> Matrix(24,11,-13,-6) Matrix(225,79,544,191) -> Matrix(2,1,1,0) Matrix(129,40,416,129) -> Matrix(1,0,0,1) Matrix(95,29,-416,-127) -> Matrix(2,1,-3,-2) *** -> (-1/1,-1/3) Matrix(191,57,-640,-191) -> Matrix(0,1,1,0) (-3/10,-19/64) -> (-1/1,1/1) Matrix(1055,313,2592,769) -> Matrix(4,3,-5,-4) *** -> (-1/1,-3/5) Matrix(191,56,1088,319) -> Matrix(1,0,0,1) Matrix(65,19,544,159) -> Matrix(2,1,1,0) Matrix(31,9,224,65) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(127,36,448,127) -> Matrix(1,0,0,1) Matrix(737,207,-2624,-737) -> Matrix(0,1,1,0) (-9/32,-23/82) -> (-1/1,1/1) Matrix(63,17,-352,-95) -> Matrix(0,1,1,2) Matrix(31,8,-128,-33) -> Matrix(1,2,-2,-3) -1/1 Matrix(703,165,1504,353) -> Matrix(4,5,-3,-4) *** -> (-5/3,-1/1) Matrix(3455,809,9024,2113) -> Matrix(26,23,-9,-8) Matrix(639,145,-2816,-639) -> Matrix(4,3,-5,-4) (-5/22,-29/128) -> (-1/1,-3/5) Matrix(4609,1044,10176,2305) -> Matrix(3,2,-2,-1) -1/1 Matrix(127,28,576,127) -> Matrix(1,0,2,1) 0/1 Matrix(545,119,-2496,-545) -> Matrix(2,1,-3,-2) (-7/32,-17/78) -> (-1/1,-1/3) Matrix(63,13,160,33) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(65,12,352,65) -> Matrix(1,0,-4,1) 0/1 Matrix(319,56,1088,191) -> Matrix(1,-4,0,1) 1/0 Matrix(3167,545,7072,1217) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(65,11,-384,-65) -> Matrix(0,1,1,0) (-11/64,-1/6) -> (-1/1,1/1) Matrix(31,5,-192,-31) -> Matrix(0,1,1,0) (-1/6,-5/32) -> (-1/1,1/1) Matrix(959,149,2272,353) -> Matrix(-2,1,1,0) Matrix(31,4,-256,-33) -> Matrix(1,2,-2,-3) -1/1 Matrix(65,7,288,31) -> Matrix(2,1,1,0) Matrix(257,-41,608,-97) -> Matrix(-2,1,1,0) Matrix(415,-72,928,-161) -> Matrix(1,0,0,1) Matrix(97,-21,448,-97) -> Matrix(0,1,1,0) (3/14,7/32) -> (-1/1,1/1) Matrix(1535,-348,3392,-769) -> Matrix(1,0,0,1) Matrix(33,-8,128,-31) -> Matrix(1,-2,0,1) 1/0 Matrix(223,-59,480,-127) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(1919,-516,4288,-1153) -> Matrix(1,0,-2,1) 0/1 Matrix(161,-45,576,-161) -> Matrix(0,1,1,0) (5/18,9/32) -> (-1/1,1/1) Matrix(353,-105,864,-257) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(767,-232,1696,-513) -> Matrix(1,0,2,1) 0/1 Matrix(385,-137,992,-353) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(97,-36,256,-95) -> Matrix(1,-4,0,1) 1/0 Matrix(1665,-637,4352,-1665) -> Matrix(4,15,-1,-4) (13/34,49/128) -> (-5/1,-3/1) Matrix(417,-173,928,-385) -> Matrix(0,1,1,-2) Matrix(447,-187,992,-415) -> Matrix(0,1,1,2) Matrix(31,-15,64,-31) -> Matrix(0,1,1,0) (15/32,1/2) -> (-1/1,1/1) Matrix(-1,1,0,1) -> Matrix(0,1,1,0) (1/2,1/0) -> (-1/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.